LMFDB - Embedded newform 80.13.p.c.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,13,Mod(17,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("80.17");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	80.p (of order $4$, degree $2$, not 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:	$73.1195053821$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 7950x^{8} + 16939113x^{6} + 4574579500x^{4} + 337520899536x^{2} + 6615595526400 $ x^10 + 7950x^8 + 16939113x^6 + 4574579500x^4 + 337520899536x^2 + 6615595526400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{29}\cdot 3^{2}\cdot 5^{9} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.2
Root			$-5.61354i$ of defining polynomial
Character	$\chi$	$=$	80.33
Dual form			80.13.p.c.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-539.020 - 539.020i) q^{3} +(12911.0 - 8800.45i) q^{5} +(-25919.1 + 25919.1i) q^{7} +49644.2i q^{9} +O(q^{10})$	\(q+(-539.020 - 539.020i) q^{3} +(12911.0 - 8800.45i) q^{5} +(-25919.1 + 25919.1i) q^{7} +49644.2i q^{9} +3.09771e6 q^{11} +(218406. + 218406. i) q^{13} +(-1.17029e7 - 2.21564e6i) q^{15} +(-5.19743e6 + 5.19743e6i) q^{17} +4.05319e7i q^{19} +2.79419e7 q^{21} +(1.59332e8 + 1.59332e8i) q^{23} +(8.92447e7 - 2.27244e8i) q^{25} +(-2.59698e8 + 2.59698e8i) q^{27} +8.83295e8i q^{29} -8.39705e8 q^{31} +(-1.66973e9 - 1.66973e9i) q^{33} +(-1.06541e8 + 5.62741e8i) q^{35} +(-2.38160e9 + 2.38160e9i) q^{37} -2.35451e8i q^{39} +3.94637e9 q^{41} +(-2.54090e9 - 2.54090e9i) q^{43} +(4.36891e8 + 6.40954e8i) q^{45} +(-2.54897e9 + 2.54897e9i) q^{47} +1.24977e10i q^{49} +5.60303e9 q^{51} +(-8.59160e8 - 8.59160e8i) q^{53} +(3.99944e10 - 2.72613e10i) q^{55} +(2.18475e10 - 2.18475e10i) q^{57} +3.93789e10i q^{59} +4.84317e10 q^{61} +(-1.28674e9 - 1.28674e9i) q^{63} +(4.74191e9 + 8.97758e8i) q^{65} +(4.84002e10 - 4.84002e10i) q^{67} -1.71766e11i q^{69} +7.15971e10 q^{71} +(3.85852e10 + 3.85852e10i) q^{73} +(-1.70594e11 + 7.43846e10i) q^{75} +(-8.02901e10 + 8.02901e10i) q^{77} -5.14852e10i q^{79} +3.06348e11 q^{81} +(3.03062e11 + 3.03062e11i) q^{83} +(-2.13640e10 + 1.12843e11i) q^{85} +(4.76114e11 - 4.76114e11i) q^{87} +5.82860e11i q^{89} -1.13218e10 q^{91} +(4.52618e11 + 4.52618e11i) q^{93} +(3.56699e11 + 5.23306e11i) q^{95} +(3.48911e11 - 3.48911e11i) q^{97} +1.53784e11i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 318 q^{3} - 4250 q^{5} - 279598 q^{7}+O(q^{10}) $ 10 * q - 318 * q^3 - 4250 * q^5 - 279598 * q^7	$ 10 q - 318 q^{3} - 4250 q^{5} - 279598 q^{7} - 312620 q^{11} + 5290738 q^{13} + 5821650 q^{15} - 41269502 q^{17} + 107493420 q^{21} + 510099842 q^{23} + 942201250 q^{25} + 1993958640 q^{27} - 3077089820 q^{31} - 7503698004 q^{33} - 9330787150 q^{35} - 2599618502 q^{37} + 7412079020 q^{41} + 5784410402 q^{43} - 10510145100 q^{45} - 16053249598 q^{47} + 33139878180 q^{51} + 101763514618 q^{53} + 84180068500 q^{55} + 27733489920 q^{57} + 7731718220 q^{61} - 207465112158 q^{63} - 338075024150 q^{65} + 80010636002 q^{67} + 46557252580 q^{71} - 448527032342 q^{73} - 719724648750 q^{75} - 425580405844 q^{77} + 1107831051810 q^{81} + 91118376722 q^{83} + 543768569650 q^{85} + 2078422804320 q^{87} - 2737742572220 q^{91} - 91295366484 q^{93} + 1044695070000 q^{95} - 1409507601302 q^{97}+O(q^{100}) $ 10 * q - 318 * q^3 - 4250 * q^5 - 279598 * q^7 - 312620 * q^11 + 5290738 * q^13 + 5821650 * q^15 - 41269502 * q^17 + 107493420 * q^21 + 510099842 * q^23 + 942201250 * q^25 + 1993958640 * q^27 - 3077089820 * q^31 - 7503698004 * q^33 - 9330787150 * q^35 - 2599618502 * q^37 + 7412079020 * q^41 + 5784410402 * q^43 - 10510145100 * q^45 - 16053249598 * q^47 + 33139878180 * q^51 + 101763514618 * q^53 + 84180068500 * q^55 + 27733489920 * q^57 + 7731718220 * q^61 - 207465112158 * q^63 - 338075024150 * q^65 + 80010636002 * q^67 + 46557252580 * q^71 - 448527032342 * q^73 - 719724648750 * q^75 - 425580405844 * q^77 + 1107831051810 * q^81 + 91118376722 * q^83 + 543768569650 * q^85 + 2078422804320 * q^87 - 2737742572220 * q^91 - 91295366484 * q^93 + 1044695070000 * q^95 - 1409507601302 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	−539.020	−	539.020i	−0.739396	−	0.739396i	0.233065	−	0.972461i	$-0.425125\pi$
$3$	−539.020	−	539.020i	−0.739396	−	0.739396i	−0.972461	+	0.233065i	$0.925125\pi$
$4$		0			0
$5$	12911.0	−	8800.45i	0.826301	−	0.563229i
$5$	12911.0	−	8800.45i	0.826301	−	0.563229i
$6$		0			0
$7$	−25919.1	+	25919.1i	−0.220309	+	0.220309i	−0.808629	−	0.588319i	$-0.799790\pi$
$7$	−25919.1	+	25919.1i	−0.220309	+	0.220309i	0.588319	+	0.808629i	$0.299790\pi$
$8$		0			0
$9$			49644.2i			0.0934143i
$10$		0			0
$11$	3.09771e6			1.74858			0.874289	−	0.485405i	$-0.161328\pi$
$11$	3.09771e6			1.74858			0.874289	+	0.485405i	$0.161328\pi$
$12$		0			0
$13$	218406.	+	218406.i	0.0452486	+	0.0452486i	0.729369	−	0.684120i	$-0.239814\pi$
$13$	218406.	+	218406.i	0.0452486	+	0.0452486i	−0.684120	+	0.729369i	$0.739814\pi$
$14$		0			0
$15$	−1.17029e7	−	2.21564e6i	−1.02741	−	0.194514i
$16$		0			0
$17$	−5.19743e6	+	5.19743e6i	−0.215325	+	0.215325i	−0.806525	−	0.591200i	$-0.798654\pi$
$17$	−5.19743e6	+	5.19743e6i	−0.215325	+	0.215325i	0.591200	+	0.806525i	$0.298654\pi$
$18$		0			0
$19$			4.05319e7i			0.861540i	0.902462	+	0.430770i	$0.141758\pi$
$19$			4.05319e7i			0.861540i	−0.902462	+	0.430770i	$0.858242\pi$
$20$		0			0
$21$	2.79419e7			0.325792
$22$		0			0
$23$	1.59332e8	+	1.59332e8i	1.07631	+	1.07631i	0.996837	+	0.0794684i	$0.0253223\pi$
$23$	1.59332e8	+	1.59332e8i	1.07631	+	1.07631i	0.0794684	+	0.996837i	$0.474678\pi$
$24$		0			0
$25$	8.92447e7	−	2.27244e8i	0.365546	−	0.930793i
$26$		0			0
$27$	−2.59698e8	+	2.59698e8i	−0.670326	+	0.670326i
$28$		0			0
$29$			8.83295e8i			1.48497i	0.669862	+	0.742485i	$0.266353\pi$
$29$			8.83295e8i			1.48497i	−0.669862	+	0.742485i	$0.733647\pi$
$30$		0			0
$31$	−8.39705e8			−0.946143			−0.473071	−	0.881024i	$-0.656855\pi$
$31$	−8.39705e8			−0.946143			−0.473071	+	0.881024i	$0.656855\pi$
$32$		0			0
$33$	−1.66973e9	−	1.66973e9i	−1.29289	−	1.29289i
$34$		0			0
$35$	−1.06541e8	+	5.62741e8i	−0.0579571	+	0.306126i
$36$		0			0
$37$	−2.38160e9	+	2.38160e9i	−0.928238	+	0.928238i	−0.997592	−	0.0693543i	$-0.977906\pi$
$37$	−2.38160e9	+	2.38160e9i	−0.928238	+	0.928238i	0.0693543	+	0.997592i	$0.477906\pi$
$38$		0			0
$39$		−	2.35451e8i		−	0.0669133i
$40$		0			0
$41$	3.94637e9			0.830796			0.415398	−	0.909640i	$-0.363642\pi$
$41$	3.94637e9			0.830796			0.415398	+	0.909640i	$0.363642\pi$
$42$		0			0
$43$	−2.54090e9	−	2.54090e9i	−0.401954	−	0.401954i	0.476967	−	0.878921i	$-0.341736\pi$
$43$	−2.54090e9	−	2.54090e9i	−0.401954	−	0.401954i	−0.878921	+	0.476967i	$0.841736\pi$
$44$		0			0
$45$	4.36891e8	+	6.40954e8i	0.0526136	+	0.0771883i
$46$		0			0
$47$	−2.54897e9	+	2.54897e9i	−0.236471	+	0.236471i	−0.815387	−	0.578916i	$-0.803476\pi$
$47$	−2.54897e9	+	2.54897e9i	−0.236471	+	0.236471i	0.578916	+	0.815387i	$0.303476\pi$
$48$		0			0
$49$			1.24977e10i			0.902928i
$50$		0			0
$51$	5.60303e9			0.318421
$52$		0			0
$53$	−8.59160e8	−	8.59160e8i	−0.0387631	−	0.0387631i	0.687460	−	0.726223i	$-0.258726\pi$
$53$	−8.59160e8	−	8.59160e8i	−0.0387631	−	0.0387631i	−0.726223	+	0.687460i	$0.758726\pi$
$54$		0			0
$55$	3.99944e10	−	2.72613e10i	1.44485	−	0.984850i
$56$		0			0
$57$	2.18475e10	−	2.18475e10i	0.637020	−	0.637020i
$58$		0			0
$59$			3.93789e10i			0.933581i	0.884368	+	0.466791i	$0.154590\pi$
$59$			3.93789e10i			0.933581i	−0.884368	+	0.466791i	$0.845410\pi$
$60$		0			0
$61$	4.84317e10			0.940050			0.470025	−	0.882653i	$-0.344245\pi$
$61$	4.84317e10			0.940050			0.470025	+	0.882653i	$0.344245\pi$
$62$		0			0
$63$	−1.28674e9	−	1.28674e9i	−0.0205800	−	0.0205800i
$64$		0			0
$65$	4.74191e9	+	8.97758e8i	0.0628743	+	0.0119036i
$66$		0			0
$67$	4.84002e10	−	4.84002e10i	0.535055	−	0.535055i	−0.387017	−	0.922072i	$-0.626495\pi$
$67$	4.84002e10	−	4.84002e10i	0.535055	−	0.535055i	0.922072	+	0.387017i	$0.126495\pi$
$68$		0			0
$69$		−	1.71766e11i		−	1.59163i
$70$		0			0
$71$	7.15971e10			0.558914			0.279457	−	0.960158i	$-0.409846\pi$
$71$	7.15971e10			0.558914			0.279457	+	0.960158i	$0.409846\pi$
$72$		0			0
$73$	3.85852e10	+	3.85852e10i	0.254967	+	0.254967i	0.823003	−	0.568036i	$-0.192297\pi$
$73$	3.85852e10	+	3.85852e10i	0.254967	+	0.254967i	−0.568036	+	0.823003i	$0.692297\pi$
$74$		0			0
$75$	−1.70594e11	+	7.43846e10i	−0.958509	+	0.417942i
$76$		0			0
$77$	−8.02901e10	+	8.02901e10i	−0.385228	+	0.385228i
$78$		0			0
$79$		−	5.14852e10i		−	0.211797i	−0.994377	−	0.105899i	$-0.966228\pi$
$79$		−	5.14852e10i		−	0.211797i	0.994377	−	0.105899i	$-0.0337719\pi$
$80$		0			0
$81$	3.06348e11			1.08469
$82$		0			0
$83$	3.03062e11	+	3.03062e11i	0.926964	+	0.926964i	0.997509	−	0.0705448i	$-0.0224738\pi$
$83$	3.03062e11	+	3.03062e11i	0.926964	+	0.926964i	−0.0705448	+	0.997509i	$0.522474\pi$
$84$		0			0
$85$	−2.13640e10	+	1.12843e11i	−0.0566460	+	0.299201i
$86$		0			0
$87$	4.76114e11	−	4.76114e11i	1.09798	−	1.09798i
$88$		0			0
$89$			5.82860e11i			1.17280i	0.810021	+	0.586400i	$0.199455\pi$
$89$			5.82860e11i			1.17280i	−0.810021	+	0.586400i	$0.800545\pi$
$90$		0			0
$91$	−1.13218e10			−0.0199373
$92$		0			0
$93$	4.52618e11	+	4.52618e11i	0.699575	+	0.699575i
$94$		0			0
$95$	3.56699e11	+	5.23306e11i	0.485245	+	0.711892i
$96$		0			0
$97$	3.48911e11	−	3.48911e11i	0.418874	−	0.418874i	−0.465941	−	0.884816i	$-0.654284\pi$
$97$	3.48911e11	−	3.48911e11i	0.418874	−	0.418874i	0.884816	+	0.465941i	$0.154284\pi$
$98$		0			0
$99$			1.53784e11i			0.163342i
$100$		0			0
$101$	5.06940e11			0.477560			0.238780	−	0.971074i	$-0.423253\pi$
$101$	5.06940e11			0.477560			0.238780	+	0.971074i	$0.423253\pi$
$102$		0			0
$103$	−3.60580e11	−	3.60580e11i	−0.301980	−	0.301980i	0.539808	−	0.841788i	$-0.318497\pi$
$103$	−3.60580e11	−	3.60580e11i	−0.301980	−	0.301980i	−0.841788	+	0.539808i	$0.818497\pi$
$104$		0			0
$105$	3.60756e11	−	2.45901e11i	0.269202	−	0.183495i
$106$		0			0
$107$	−9.00792e10	+	9.00792e10i	−0.0600236	+	0.0600236i	−0.736481	−	0.676458i	$-0.763514\pi$
$107$	−9.00792e10	+	9.00792e10i	−0.0600236	+	0.0600236i	0.676458	+	0.736481i	$0.263514\pi$
$108$		0			0
$109$		−	2.27009e12i		−	1.35358i	−0.736175	−	0.676791i	$-0.763370\pi$
$109$		−	2.27009e12i		−	1.35358i	0.736175	−	0.676791i	$-0.236630\pi$
$110$		0			0
$111$	2.56746e12			1.37267
$112$		0			0
$113$	8.92132e11	+	8.92132e11i	0.428507	+	0.428507i	0.888120	−	0.459612i	$-0.152012\pi$
$113$	8.92132e11	+	8.92132e11i	0.428507	+	0.428507i	−0.459612	+	0.888120i	$0.652012\pi$
$114$		0			0
$115$	3.45932e12	+	6.54933e11i	1.49556	+	0.283146i
$116$		0			0
$117$	−1.08426e10	+	1.08426e10i	−0.00422687	+	0.00422687i
$118$		0			0
$119$		−	2.69426e11i		−	0.0948762i
$120$		0			0
$121$	6.45740e12			2.05753
$122$		0			0
$123$	−2.12717e12	−	2.12717e12i	−0.614287	−	0.614287i
$124$		0			0
$125$	−8.47620e11	−	3.71934e12i	−0.222199	−	0.975001i
$126$		0			0
$127$	9.96091e11	−	9.96091e11i	0.237398	−	0.237398i	−0.578374	−	0.815772i	$-0.696313\pi$
$127$	9.96091e11	−	9.96091e11i	0.237398	−	0.237398i	0.815772	+	0.578374i	$0.196313\pi$
$128$		0			0
$129$			2.73919e12i			0.594407i
$130$		0			0
$131$	4.14351e12			0.819861			0.409930	−	0.912117i	$-0.365553\pi$
$131$	4.14351e12			0.819861			0.409930	+	0.912117i	$0.365553\pi$
$132$		0			0
$133$	−1.05055e12	−	1.05055e12i	−0.189805	−	0.189805i
$134$		0			0
$135$	−1.06749e12	+	5.63841e12i	−0.176344	+	0.931438i
$136$		0			0
$137$	−4.00874e12	+	4.00874e12i	−0.606296	+	0.606296i	−0.941976	−	0.335680i	$-0.891034\pi$
$137$	−4.00874e12	+	4.00874e12i	−0.606296	+	0.606296i	0.335680	+	0.941976i	$0.391034\pi$
$138$		0			0
$139$		−	1.89953e12i		−	0.263364i	−0.991292	−	0.131682i	$-0.957962\pi$
$139$		−	1.89953e12i		−	0.263364i	0.991292	−	0.131682i	$-0.0420378\pi$
$140$		0			0
$141$	2.74789e12			0.349691
$142$		0			0
$143$	6.76560e11	+	6.76560e11i	0.0791207	+	0.0791207i
$144$		0			0
$145$	7.77340e12	+	1.14042e13i	0.836378	+	1.22703i
$146$		0			0
$147$	6.73650e12	−	6.73650e12i	0.667622	−	0.667622i
$148$		0			0
$149$		−	9.62747e12i		−	0.879822i	−0.898041	−	0.439911i	$-0.855010\pi$
$149$		−	9.62747e12i		−	0.879822i	0.898041	−	0.439911i	$-0.144990\pi$
$150$		0			0
$151$	−1.22511e13			−1.03351			−0.516756	−	0.856133i	$-0.672860\pi$
$151$	−1.22511e13			−1.03351			−0.516756	+	0.856133i	$0.672860\pi$
$152$		0			0
$153$	−2.58022e11	−	2.58022e11i	−0.0201145	−	0.0201145i
$154$		0			0
$155$	−1.08414e13	+	7.38979e12i	−0.781799	+	0.532895i
$156$		0			0
$157$	−1.69702e13	+	1.69702e13i	−1.13316	+	1.13316i	−0.143508	+	0.989649i	$0.545838\pi$
$157$	−1.69702e13	+	1.69702e13i	−1.13316	+	1.13316i	−0.989649	+	0.143508i	$0.954162\pi$
$158$		0			0
$159$			9.26209e11i			0.0573227i
$160$		0			0
$161$	−8.25949e12			−0.474240
$162$		0			0
$163$	−7.79515e12	−	7.79515e12i	−0.415622	−	0.415622i	0.468070	−	0.883692i	$-0.344950\pi$
$163$	−7.79515e12	−	7.79515e12i	−0.415622	−	0.415622i	−0.883692	+	0.468070i	$0.844950\pi$
$164$		0			0
$165$	−3.62522e13	−	6.86342e12i	−1.79651	−	0.340124i
$166$		0			0
$167$	−1.66021e13	+	1.66021e13i	−0.765359	+	0.765359i	−0.977286	−	0.211927i	$-0.932026\pi$
$167$	−1.66021e13	+	1.66021e13i	−0.765359	+	0.765359i	0.211927	+	0.977286i	$0.432026\pi$
$168$		0			0
$169$		−	2.32027e13i		−	0.995905i
$170$		0			0
$171$	−2.01218e12			−0.0804802
$172$		0			0
$173$	−1.00359e13	−	1.00359e13i	−0.374353	−	0.374353i	0.494707	−	0.869060i	$-0.335276\pi$
$173$	−1.00359e13	−	1.00359e13i	−0.374353	−	0.374353i	−0.869060	+	0.494707i	$0.835276\pi$
$174$		0			0
$175$	3.57684e12	+	8.20313e12i	0.124529	+	0.285595i
$176$		0			0
$177$	2.12260e13	−	2.12260e13i	0.690287	−	0.690287i
$178$		0			0
$179$		−	8.18577e12i		−	0.248852i	−0.992229	−	0.124426i	$-0.960291\pi$
$179$		−	8.18577e12i		−	0.248852i	0.992229	−	0.124426i	$-0.0397090\pi$
$180$		0			0
$181$	4.39825e13			1.25086			0.625430	−	0.780280i	$-0.284924\pi$
$181$	4.39825e13			1.25086			0.625430	+	0.780280i	$0.284924\pi$
$182$		0			0
$183$	−2.61057e13	−	2.61057e13i	−0.695070	−	0.695070i
$184$		0			0
$185$	−9.78958e12	+	5.17080e13i	−0.244193	+	1.28981i
$186$		0			0
$187$	−1.61001e13	+	1.61001e13i	−0.376513	+	0.376513i
$188$		0			0
$189$		−	1.34623e13i		−	0.295358i
$190$		0			0
$191$	4.06524e13			0.837309			0.418655	−	0.908146i	$-0.362502\pi$
$191$	4.06524e13			0.837309			0.418655	+	0.908146i	$0.362502\pi$
$192$		0			0
$193$	−4.23509e13	−	4.23509e13i	−0.819443	−	0.819443i	0.166584	−	0.986027i	$-0.446726\pi$
$193$	−4.23509e13	−	4.23509e13i	−0.819443	−	0.819443i	−0.986027	+	0.166584i	$0.946726\pi$
$194$		0			0
$195$	−2.07207e12	−	3.03989e12i	−0.0376875	−	0.0552905i
$196$		0			0
$197$	−4.07555e13	+	4.07555e13i	−0.697250	+	0.697250i	−0.963817	−	0.266566i	$-0.914111\pi$
$197$	−4.07555e13	+	4.07555e13i	−0.697250	+	0.697250i	0.266566	+	0.963817i	$0.414111\pi$
$198$		0			0
$199$		−	3.02911e13i		−	0.487750i	−0.969807	−	0.243875i	$-0.921581\pi$
$199$		−	3.02911e13i		−	0.487750i	0.969807	−	0.243875i	$-0.0784186\pi$
$200$		0			0
$201$	−5.21774e13			−0.791236
$202$		0			0
$203$	−2.28943e13	−	2.28943e13i	−0.327153	−	0.327153i
$204$		0			0
$205$	5.09513e13	−	3.47298e13i	0.686487	−	0.467928i
$206$		0			0
$207$	−7.90990e12	+	7.90990e12i	−0.100542	+	0.100542i
$208$		0			0
$209$			1.25556e14i			1.50647i
$210$		0			0
$211$	−2.20402e13			−0.249758			−0.124879	−	0.992172i	$-0.539854\pi$
$211$	−2.20402e13			−0.249758			−0.124879	+	0.992172i	$0.539854\pi$
$212$		0			0
$213$	−3.85923e13	−	3.85923e13i	−0.413259	−	0.413259i
$214$		0			0
$215$	−5.51664e13	−	1.04443e13i	−0.558527	−	0.105743i
$216$		0			0
$217$	2.17644e13	−	2.17644e13i	0.208444	−	0.208444i
$218$		0			0
$219$		−	4.15964e13i		−	0.377043i
$220$		0			0
$221$	−2.27030e12			−0.0194863
$222$		0			0
$223$	5.90143e12	+	5.90143e12i	0.0479875	+	0.0479875i	0.730693	−	0.682706i	$-0.239197\pi$
$223$	5.90143e12	+	5.90143e12i	0.0479875	+	0.0479875i	−0.682706	+	0.730693i	$0.739197\pi$
$224$		0			0
$225$	1.12814e13	+	4.43048e12i	0.0869494	+	0.0341472i
$226$		0			0
$227$	−1.11295e14	+	1.11295e14i	−0.813427	+	0.813427i	−0.985146	−	0.171719i	$-0.945068\pi$
$227$	−1.11295e14	+	1.11295e14i	−0.813427	+	0.813427i	0.171719	+	0.985146i	$0.445068\pi$
$228$		0			0
$229$			8.37007e12i			0.0580385i	0.999579	+	0.0290193i	$0.00923842\pi$
$229$			8.37007e12i			0.0580385i	−0.999579	+	0.0290193i	$0.990762\pi$
$230$		0			0
$231$	8.65559e13			0.569672
$232$		0			0
$233$	−1.31058e14	−	1.31058e14i	−0.819081	−	0.819081i	0.166894	−	0.985975i	$-0.446626\pi$
$233$	−1.31058e14	−	1.31058e14i	−0.819081	−	0.819081i	−0.985975	+	0.166894i	$0.946626\pi$
$234$		0			0
$235$	−1.04775e13	+	5.53417e13i	−0.0622088	+	0.328583i
$236$		0			0
$237$	−2.77516e13	+	2.77516e13i	−0.156602	+	0.156602i
$238$		0			0
$239$			1.32912e14i			0.713142i	0.934268	+	0.356571i	$0.116054\pi$
$239$			1.32912e14i			0.713142i	−0.934268	+	0.356571i	$0.883946\pi$
$240$		0			0
$241$	−2.84388e13			−0.145147			−0.0725737	−	0.997363i	$-0.523121\pi$
$241$	−2.84388e13			−0.145147			−0.0725737	+	0.997363i	$0.523121\pi$
$242$		0			0
$243$	−2.71134e13	−	2.71134e13i	−0.131688	−	0.131688i
$244$		0			0
$245$	1.09985e14	+	1.61357e14i	0.508555	+	0.746090i
$246$		0			0
$247$	−8.85243e12	+	8.85243e12i	−0.0389835	+	0.0389835i
$248$		0			0
$249$		−	3.26713e14i		−	1.37079i
$250$		0			0
$251$	3.80658e14			1.52227			0.761136	−	0.648592i	$-0.224642\pi$
$251$	3.80658e14			1.52227			0.761136	+	0.648592i	$0.224642\pi$
$252$		0			0
$253$	4.93565e14	+	4.93565e14i	1.88201	+	1.88201i
$254$		0			0
$255$	7.23405e13	−	4.93092e13i	0.263112	−	0.179344i
$256$		0			0
$257$	2.52586e14	−	2.52586e14i	0.876617	−	0.876617i	−0.116566	−	0.993183i	$-0.537189\pi$
$257$	2.52586e14	−	2.52586e14i	0.876617	−	0.876617i	0.993183	+	0.116566i	$0.0371887\pi$
$258$		0			0
$259$		−	1.23458e14i		−	0.408998i
$260$		0			0
$261$	−4.38505e13			−0.138717
$262$		0			0
$263$	4.19253e14	+	4.19253e14i	1.26690	+	1.26690i	0.947681	+	0.319218i	$0.103420\pi$
$263$	4.19253e14	+	4.19253e14i	1.26690	+	1.26690i	0.319218	+	0.947681i	$0.396580\pi$
$264$		0			0
$265$	−1.86536e13	−	3.53158e12i	−0.0538625	−	0.0101975i
$266$		0			0
$267$	3.14173e14	−	3.14173e14i	0.867165	−	0.867165i
$268$		0			0
$269$			2.74435e14i			0.724311i	0.932118	+	0.362156i	$0.117959\pi$
$269$			2.74435e14i			0.724311i	−0.932118	+	0.362156i	$0.882041\pi$
$270$		0			0
$271$	−3.12952e14			−0.790062			−0.395031	−	0.918668i	$-0.629266\pi$
$271$	−3.12952e14			−0.790062			−0.395031	+	0.918668i	$0.629266\pi$
$272$		0			0
$273$	6.10268e12	+	6.10268e12i	0.0147416	+	0.0147416i
$274$		0			0
$275$	2.76454e14	−	7.03938e14i	0.639186	−	1.62757i
$276$		0			0
$277$	3.81668e14	−	3.81668e14i	0.844904	−	0.844904i	−0.144588	−	0.989492i	$-0.546186\pi$
$277$	3.81668e14	−	3.81668e14i	0.844904	−	0.844904i	0.989492	+	0.144588i	$0.0461857\pi$
$278$		0			0
$279$		−	4.16865e13i		−	0.0883833i
$280$		0			0
$281$	4.23479e14			0.860190			0.430095	−	0.902784i	$-0.358480\pi$
$281$	4.23479e14			0.860190			0.430095	+	0.902784i	$0.358480\pi$
$282$		0			0
$283$	1.02770e13	+	1.02770e13i	0.0200055	+	0.0200055i	0.717039	−	0.697033i	$-0.245497\pi$
$283$	1.02770e13	+	1.02770e13i	0.0200055	+	0.0200055i	−0.697033	+	0.717039i	$0.745497\pi$
$284$		0			0
$285$	8.98042e13	−	4.74340e14i	0.167582	−	0.885158i
$286$		0			0
$287$	−1.02286e14	+	1.02286e14i	−0.183032	+	0.183032i
$288$		0			0
$289$			5.28596e14i			0.907270i
$290$		0			0
$291$	−3.76140e14			−0.619428
$292$		0			0
$293$	−5.38974e14	−	5.38974e14i	−0.851848	−	0.851848i	0.138512	−	0.990361i	$-0.455768\pi$
$293$	−5.38974e14	−	5.38974e14i	−0.851848	−	0.851848i	−0.990361	+	0.138512i	$0.955768\pi$
$294$		0			0
$295$	3.46553e14	+	5.08420e14i	0.525820	+	0.771419i
$296$		0			0
$297$	−8.04471e14	+	8.04471e14i	−1.17212	+	1.17212i
$298$		0			0
$299$			6.95982e13i			0.0974026i
$300$		0			0
$301$	1.31716e14			0.177108
$302$		0			0
$303$	−2.73251e14	−	2.73251e14i	−0.353106	−	0.353106i
$304$		0			0
$305$	6.25300e14	−	4.26221e14i	0.776764	−	0.529464i
$306$		0			0
$307$	6.74366e14	−	6.74366e14i	0.805500	−	0.805500i	−0.178449	−	0.983949i	$-0.557108\pi$
$307$	6.74366e14	−	6.74366e14i	0.805500	−	0.805500i	0.983949	+	0.178449i	$0.0571079\pi$
$308$		0			0
$309$			3.88720e14i			0.446566i
$310$		0			0
$311$	1.38259e14			0.152803			0.0764014	−	0.997077i	$-0.475657\pi$
$311$	1.38259e14			0.152803			0.0764014	+	0.997077i	$0.475657\pi$
$312$		0			0
$313$	1.82418e13	+	1.82418e13i	0.0194000	+	0.0194000i	0.716740	−	0.697340i	$-0.245633\pi$
$313$	1.82418e13	+	1.82418e13i	0.0194000	+	0.0194000i	−0.697340	+	0.716740i	$0.745633\pi$
$314$		0			0
$315$	−2.79368e13	−	5.28912e12i	−0.0285966	−	0.00541402i
$316$		0			0
$317$	−3.07817e13	+	3.07817e13i	−0.0303345	+	0.0303345i	−0.722111	−	0.691777i	$-0.756828\pi$
$317$	−3.07817e13	+	3.07817e13i	−0.0303345	+	0.0303345i	0.691777	+	0.722111i	$0.256828\pi$
$318$		0			0
$319$			2.73620e15i			2.59659i
$320$		0			0
$321$	9.71090e13			0.0887625
$322$		0			0
$323$	−2.10662e14	−	2.10662e14i	−0.185511	−	0.185511i
$324$		0			0
$325$	6.91232e13	−	3.01400e13i	0.0586575	−	0.0255766i
$326$		0			0
$327$	−1.22362e15	+	1.22362e15i	−1.00083	+	1.00083i
$328$		0			0
$329$		−	1.32134e14i		−	0.104193i
$330$		0			0
$331$	−1.29706e15			−0.986264			−0.493132	−	0.869955i	$-0.664148\pi$
$331$	−1.29706e15			−0.986264			−0.493132	+	0.869955i	$0.664148\pi$
$332$		0			0
$333$	−1.18233e14	−	1.18233e14i	−0.0867107	−	0.0867107i
$334$		0			0
$335$	1.98949e14	−	1.05084e15i	0.140758	−	0.743475i
$336$		0			0
$337$	−8.59122e14	+	8.59122e14i	−0.586510	+	0.586510i	−0.936684	−	0.350174i	$-0.886122\pi$
$337$	−8.59122e14	+	8.59122e14i	−0.586510	+	0.586510i	0.350174	+	0.936684i	$0.386122\pi$
$338$		0			0
$339$		−	9.61754e14i		−	0.633674i
$340$		0			0
$341$	−2.60117e15			−1.65441
$342$		0			0
$343$	−6.82684e14	−	6.82684e14i	−0.419232	−	0.419232i
$344$		0			0
$345$	−1.51162e15	−	2.21766e15i	−0.896454	−	1.31517i
$346$		0			0
$347$	−1.71021e14	+	1.71021e14i	−0.0979652	+	0.0979652i	−0.754391	−	0.656426i	$-0.772068\pi$
$347$	−1.71021e14	+	1.71021e14i	−0.0979652	+	0.0979652i	0.656426	+	0.754391i	$0.272068\pi$
$348$		0			0
$349$			2.75961e14i			0.152720i	0.997080	+	0.0763598i	$0.0243298\pi$
$349$			2.75961e14i			0.152720i	−0.997080	+	0.0763598i	$0.975670\pi$
$350$		0			0
$351$	−1.13439e14			−0.0606626
$352$		0			0
$353$	2.02181e15	+	2.02181e15i	1.04494	+	1.04494i	0.998941	+	0.0460028i	$0.0146483\pi$
$353$	2.02181e15	+	2.02181e15i	1.04494	+	1.04494i	0.0460028	+	0.998941i	$0.485352\pi$
$354$		0			0
$355$	9.24386e14	−	6.30087e14i	0.461831	−	0.314797i
$356$		0			0
$357$	−1.45226e14	+	1.45226e14i	−0.0701511	+	0.0701511i
$358$		0			0
$359$			3.46771e14i			0.161986i	0.996715	+	0.0809928i	$0.0258091\pi$
$359$			3.46771e14i			0.161986i	−0.996715	+	0.0809928i	$0.974191\pi$
$360$		0			0
$361$	5.70478e14			0.257748
$362$		0			0
$363$	−3.48067e15	−	3.48067e15i	−1.52133	−	1.52133i
$364$		0			0
$365$	8.37740e14	+	1.58605e14i	0.354284	+	0.0670747i
$366$		0			0
$367$	1.67313e15	−	1.67313e15i	0.684752	−	0.684752i	−0.276315	−	0.961067i	$-0.589113\pi$
$367$	1.67313e15	−	1.67313e15i	0.684752	−	0.684752i	0.961067	+	0.276315i	$0.0891133\pi$
$368$		0			0
$369$			1.95914e14i			0.0776082i
$370$		0			0
$371$	4.45374e13			0.0170797
$372$		0			0
$373$	−3.24133e15	−	3.24133e15i	−1.20357	−	1.20357i	−0.973074	−	0.230494i	$-0.925966\pi$
$373$	−3.24133e15	−	3.24133e15i	−1.20357	−	1.20357i	−0.230494	−	0.973074i	$-0.574034\pi$
$374$		0			0
$375$	−1.54791e15	+	2.46168e15i	−0.556620	+	0.885205i
$376$		0			0
$377$	−1.92917e14	+	1.92917e14i	−0.0671928	+	0.0671928i
$378$		0			0
$379$		−	8.72549e14i		−	0.294411i	−0.989106	−	0.147206i	$-0.952972\pi$
$379$		−	8.72549e14i		−	0.294411i	0.989106	−	0.147206i	$-0.0470279\pi$
$380$		0			0
$381$	−1.07383e15			−0.351062
$382$		0			0
$383$	2.34046e15	+	2.34046e15i	0.741496	+	0.741496i	0.972866	−	0.231370i	$-0.0743207\pi$
$383$	2.34046e15	+	2.34046e15i	0.741496	+	0.741496i	−0.231370	+	0.972866i	$0.574321\pi$
$384$		0			0
$385$	−3.30032e14	+	1.74321e15i	−0.101343	+	0.535286i
$386$		0			0
$387$	1.26141e14	−	1.26141e14i	0.0375482	−	0.0375482i
$388$		0			0
$389$		−	1.14159e15i		−	0.329468i	−0.986338	−	0.164734i	$-0.947323\pi$
$389$		−	1.14159e15i		−	0.329468i	0.986338	−	0.164734i	$-0.0526765\pi$
$390$		0			0
$391$	−1.65623e15			−0.463511
$392$		0			0
$393$	−2.23343e15	−	2.23343e15i	−0.606202	−	0.606202i
$394$		0			0
$395$	−4.53093e14	−	6.64723e14i	−0.119290	−	0.175008i
$396$		0			0
$397$	−1.02085e15	+	1.02085e15i	−0.260746	+	0.260746i	−0.825357	−	0.564611i	$-0.809026\pi$
$397$	−1.02085e15	+	1.02085e15i	−0.260746	+	0.260746i	0.564611	+	0.825357i	$0.309026\pi$
$398$		0			0
$399$			1.13254e15i			0.280683i
$400$		0			0
$401$	5.91775e15			1.42328			0.711640	−	0.702544i	$-0.247953\pi$
$401$	5.91775e15			1.42328			0.711640	+	0.702544i	$0.247953\pi$
$402$		0			0
$403$	−1.83397e14	−	1.83397e14i	−0.0428116	−	0.0428116i
$404$		0			0
$405$	3.95524e15	−	2.69600e15i	0.896279	−	0.610928i
$406$		0			0
$407$	−7.37753e15	+	7.37753e15i	−1.62310	+	1.62310i
$408$		0			0
$409$			6.24641e15i			1.33441i	0.744872	+	0.667207i	$0.232510\pi$
$409$			6.24641e15i			1.33441i	−0.744872	+	0.667207i	$0.767490\pi$
$410$		0			0
$411$	4.32159e15			0.896587
$412$		0			0
$413$	−1.02067e15	−	1.02067e15i	−0.205676	−	0.205676i
$414$		0			0
$415$	6.57990e15	+	1.24574e15i	1.28804	+	0.243858i
$416$		0			0
$417$	−1.02388e15	+	1.02388e15i	−0.194730	+	0.194730i
$418$		0			0
$419$		−	4.06984e15i		−	0.752130i	−0.926593	−	0.376065i	$-0.877277\pi$
$419$		−	4.06984e15i		−	0.752130i	0.926593	−	0.376065i	$-0.122723\pi$
$420$		0			0
$421$	2.00557e15			0.360201			0.180101	−	0.983648i	$-0.442358\pi$
$421$	2.00557e15			0.360201			0.180101	+	0.983648i	$0.442358\pi$
$422$		0			0
$423$	−1.26541e14	−	1.26541e14i	−0.0220897	−	0.0220897i
$424$		0			0
$425$	7.17244e14	+	1.64493e15i	0.121712	+	0.279135i
$426$		0			0
$427$	−1.25531e15	+	1.25531e15i	−0.207102	+	0.207102i
$428$		0			0
$429$		−	7.29359e14i		−	0.117003i
$430$		0			0
$431$	4.02256e15			0.627536			0.313768	−	0.949500i	$-0.398409\pi$
$431$	4.02256e15			0.627536			0.313768	+	0.949500i	$0.398409\pi$
$432$		0			0
$433$	−9.03132e15	−	9.03132e15i	−1.37033	−	1.37033i	−0.859954	−	0.510372i	$-0.829508\pi$
$433$	−9.03132e15	−	9.03132e15i	−1.37033	−	1.37033i	−0.510372	−	0.859954i	$-0.670492\pi$
$434$		0			0
$435$	1.95706e15	−	1.03371e16i	0.288848	−	1.52568i
$436$		0			0
$437$	−6.45803e15	+	6.45803e15i	−0.927281	+	0.927281i
$438$		0			0
$439$			1.27889e16i			1.78668i	0.449384	+	0.893339i	$0.351644\pi$
$439$			1.27889e16i			1.78668i	−0.449384	+	0.893339i	$0.648356\pi$
$440$		0			0
$441$	−6.20437e14			−0.0843464
$442$		0			0
$443$	−9.71435e15	−	9.71435e15i	−1.28526	−	1.28526i	−0.937632	−	0.347629i	$-0.886987\pi$
$443$	−9.71435e15	−	9.71435e15i	−1.28526	−	1.28526i	−0.347629	−	0.937632i	$-0.613013\pi$
$444$		0			0
$445$	5.12943e15	+	7.52528e15i	0.660555	+	0.969086i
$446$		0			0
$447$	−5.18940e15	+	5.18940e15i	−0.650537	+	0.650537i
$448$		0			0
$449$		−	1.02086e15i		−	0.124591i	−0.998058	−	0.0622956i	$-0.980158\pi$
$449$		−	1.02086e15i		−	0.124591i	0.998058	−	0.0622956i	$-0.0198422\pi$
$450$		0			0
$451$	1.22247e16			1.45271
$452$		0			0
$453$	6.60361e15	+	6.60361e15i	0.764174	+	0.764174i
$454$		0			0
$455$	−1.46175e14	+	9.96370e13i	−0.0164742	+	0.0112293i
$456$		0			0
$457$	9.89481e15	−	9.89481e15i	1.08620	−	1.08620i	0.0902858	−	0.995916i	$-0.471222\pi$
$457$	9.89481e15	−	9.89481e15i	1.08620	−	1.08620i	0.995916	−	0.0902858i	$-0.0287780\pi$
$458$		0			0
$459$		−	2.69952e15i		−	0.288676i
$460$		0			0
$461$	1.56885e16			1.63446			0.817232	−	0.576309i	$-0.195507\pi$
$461$	1.56885e16			1.63446			0.817232	+	0.576309i	$0.195507\pi$
$462$		0			0
$463$	−4.93326e15	−	4.93326e15i	−0.500781	−	0.500781i	0.410900	−	0.911681i	$-0.365215\pi$
$463$	−4.93326e15	−	4.93326e15i	−0.500781	−	0.500781i	−0.911681	+	0.410900i	$0.865215\pi$
$464$		0			0
$465$	9.82697e15	+	1.86048e15i	0.972080	+	0.184038i
$466$		0			0
$467$	1.26329e16	−	1.26329e16i	1.21787	−	1.21787i	0.249491	−	0.968377i	$-0.419737\pi$
$467$	1.26329e16	−	1.26329e16i	1.21787	−	1.21787i	0.968377	−	0.249491i	$-0.0802634\pi$
$468$		0			0
$469$			2.50898e15i			0.235755i
$470$		0			0
$471$	1.82946e16			1.67571
$472$		0			0
$473$	−7.87097e15	−	7.87097e15i	−0.702848	−	0.702848i
$474$		0			0
$475$	9.21066e15	+	3.61726e15i	0.801916	+	0.314933i
$476$		0			0
$477$	4.26523e13	−	4.26523e13i	0.00362103	−	0.00362103i
$478$		0			0
$479$			1.01746e16i			0.842373i	0.906974	+	0.421186i	$0.138386\pi$
$479$			1.01746e16i			0.842373i	−0.906974	+	0.421186i	$0.861614\pi$
$480$		0			0
$481$	−1.04031e15			−0.0840029
$482$		0			0
$483$	4.45203e15	+	4.45203e15i	0.350651	+	0.350651i
$484$		0			0
$485$	1.43420e15	−	7.57534e15i	0.110194	−	0.582038i
$486$		0			0
$487$	−8.05083e15	+	8.05083e15i	−0.603486	+	0.603486i	−0.941236	−	0.337750i	$-0.890334\pi$
$487$	−8.05083e15	+	8.05083e15i	−0.603486	+	0.603486i	0.337750	+	0.941236i	$0.390334\pi$
$488$		0			0
$489$			8.40348e15i			0.614619i
$490$		0			0
$491$	−6.93230e14			−0.0494753			−0.0247377	−	0.999694i	$-0.507875\pi$
$491$	−6.93230e14			−0.0494753			−0.0247377	+	0.999694i	$0.507875\pi$
$492$		0			0
$493$	−4.59086e15	−	4.59086e15i	−0.319752	−	0.319752i
$494$		0			0
$495$	1.35336e15	+	1.98549e15i	0.0919991	+	0.134970i
$496$		0			0
$497$	−1.85573e15	+	1.85573e15i	−0.123134	+	0.123134i
$498$		0			0
$499$		−	2.56966e16i		−	1.66446i	−0.554433	−	0.832228i	$-0.687065\pi$
$499$		−	2.56966e16i		−	1.66446i	0.554433	−	0.832228i	$-0.312935\pi$
$500$		0			0
$501$	1.78978e16			1.13181
$502$		0			0
$503$	8.81939e15	+	8.81939e15i	0.544541	+	0.544541i	0.924857	−	0.380316i	$-0.124185\pi$
$503$	8.81939e15	+	8.81939e15i	0.544541	+	0.544541i	−0.380316	+	0.924857i	$0.624185\pi$
$504$		0			0
$505$	6.54507e15	−	4.46130e15i	0.394608	−	0.268976i
$506$		0			0
$507$	−1.25067e16	+	1.25067e16i	−0.736369	+	0.736369i
$508$		0			0
$509$		−	3.89530e15i		−	0.223993i	−0.993709	−	0.111996i	$-0.964276\pi$
$509$		−	3.89530e15i		−	0.223993i	0.993709	−	0.111996i	$-0.0357245\pi$
$510$		0			0
$511$	−2.00019e15			−0.112343
$512$		0			0
$513$	−1.05261e16	−	1.05261e16i	−0.577513	−	0.577513i
$514$		0			0
$515$	−7.82870e15	−	1.48216e15i	−0.419610	−	0.0794424i
$516$		0			0
$517$	−7.89598e15	+	7.89598e15i	−0.413488	+	0.413488i
$518$		0			0
$519$			1.08192e16i			0.553591i
$520$		0			0
$521$	−1.26859e16			−0.634300			−0.317150	−	0.948375i	$-0.602726\pi$
$521$	−1.26859e16			−0.634300			−0.317150	+	0.948375i	$0.602726\pi$
$522$		0			0
$523$	−1.45509e16	−	1.45509e16i	−0.711018	−	0.711018i	0.255730	−	0.966748i	$-0.417684\pi$
$523$	−1.45509e16	−	1.45509e16i	−0.711018	−	0.711018i	−0.966748	+	0.255730i	$0.917684\pi$
$524$		0			0
$525$	2.49366e15	−	6.34964e15i	0.119092	−	0.303245i
$526$		0			0
$527$	4.36431e15	−	4.36431e15i	0.203728	−	0.203728i
$528$		0			0
$529$			2.88587e16i			1.31687i
$530$		0			0
$531$	−1.95494e15			−0.0872098
$532$		0			0
$533$	8.61911e14	+	8.61911e14i	0.0375923	+	0.0375923i
$534$		0			0
$535$	−3.70270e14	+	1.95575e15i	−0.0157905	+	0.0834046i
$536$		0			0
$537$	−4.41229e15	+	4.41229e15i	−0.184000	+	0.184000i
$538$		0			0
$539$			3.87142e16i			1.57884i
$540$		0			0
$541$	−2.92043e16			−1.16483			−0.582416	−	0.812891i	$-0.697892\pi$
$541$	−2.92043e16			−1.16483			−0.582416	+	0.812891i	$0.697892\pi$
$542$		0			0
$543$	−2.37075e16	−	2.37075e16i	−0.924881	−	0.924881i
$544$		0			0
$545$	−1.99778e16	−	2.93090e16i	−0.762376	−	1.11847i
$546$		0			0
$547$	−1.10726e16	+	1.10726e16i	−0.413359	+	0.413359i	−0.882907	−	0.469548i	$-0.844417\pi$
$547$	−1.10726e16	+	1.10726e16i	−0.413359	+	0.413359i	0.469548	+	0.882907i	$0.344417\pi$
$548$		0			0
$549$			2.40435e15i			0.0878141i
$550$		0			0
$551$	−3.58017e16			−1.27936
$552$		0			0
$553$	1.33445e15	+	1.33445e15i	0.0466608	+	0.0466608i
$554$		0			0
$555$	3.31484e16	−	2.25949e16i	1.13424	−	0.773128i
$556$		0			0
$557$	−3.92342e16	+	3.92342e16i	−1.31381	+	1.31381i	−0.395235	+	0.918580i	$0.629337\pi$
$557$	−3.92342e16	+	3.92342e16i	−1.31381	+	1.31381i	−0.918580	+	0.395235i	$0.870663\pi$
$558$		0			0
$559$		−	1.10990e15i		−	0.0363757i
$560$		0			0
$561$	1.73566e16			0.556785
$562$		0			0
$563$	−3.76537e16	−	3.76537e16i	−1.18238	−	1.18238i	−0.979126	−	0.203253i	$-0.934848\pi$
$563$	−3.76537e16	−	3.76537e16i	−1.18238	−	1.18238i	−0.203253	−	0.979126i	$-0.565152\pi$
$564$		0			0
$565$	1.93694e16	+	3.66710e15i	0.595424	+	0.112728i
$566$		0			0
$567$	−7.94028e15	+	7.94028e15i	−0.238967	+	0.238967i
$568$		0			0
$569$			2.60414e16i			0.767344i	0.923469	+	0.383672i	$0.125341\pi$
$569$			2.60414e16i			0.767344i	−0.923469	+	0.383672i	$0.874659\pi$
$570$		0			0
$571$	−3.06137e16			−0.883281			−0.441640	−	0.897192i	$-0.645603\pi$
$571$	−3.06137e16			−0.883281			−0.441640	+	0.897192i	$0.645603\pi$
$572$		0			0
$573$	−2.19125e16	−	2.19125e16i	−0.619104	−	0.619104i
$574$		0			0
$575$	5.04268e16	−	2.19878e16i	1.39526	−	0.608379i
$576$		0			0
$577$	−7.25066e14	+	7.25066e14i	−0.0196482	+	0.0196482i	−0.716863	−	0.697214i	$-0.754423\pi$
$577$	−7.25066e14	+	7.25066e14i	−0.0196482	+	0.0196482i	0.697214	+	0.716863i	$0.254423\pi$
$578$		0			0
$579$			4.56560e16i			1.21179i
$580$		0			0
$581$	−1.57102e16			−0.408437
$582$		0			0
$583$	−2.66143e15	−	2.66143e15i	−0.0677804	−	0.0677804i
$584$		0			0
$585$	−4.45685e13	+	2.35408e14i	−0.00111197	+	0.00587336i
$586$		0			0
$587$	−6.56817e15	+	6.56817e15i	−0.160552	+	0.160552i	−0.782811	−	0.622259i	$-0.786215\pi$
$587$	−6.56817e15	+	6.56817e15i	−0.160552	+	0.160552i	0.622259	+	0.782811i	$0.286215\pi$
$588$		0			0
$589$		−	3.40349e16i		−	0.815140i
$590$		0			0
$591$	4.39360e16			1.03109
$592$		0			0
$593$	−1.61896e16	−	1.61896e16i	−0.372313	−	0.372313i	0.496006	−	0.868319i	$-0.334799\pi$
$593$	−1.61896e16	−	1.61896e16i	−0.372313	−	0.372313i	−0.868319	+	0.496006i	$0.834799\pi$
$594$		0			0
$595$	−2.37107e15	−	3.47854e15i	−0.0534370	−	0.0783963i
$596$		0			0
$597$	−1.63275e16	+	1.63275e16i	−0.360640	+	0.360640i
$598$		0			0
$599$			9.31837e15i			0.201734i	0.994900	+	0.100867i	$0.0321617\pi$
$599$			9.31837e15i			0.201734i	−0.994900	+	0.100867i	$0.967838\pi$
$600$		0			0
$601$	6.53301e16			1.38633			0.693165	−	0.720779i	$-0.256216\pi$
$601$	6.53301e16			1.38633			0.693165	+	0.720779i	$0.256216\pi$
$602$		0			0
$603$	2.40279e15	+	2.40279e15i	0.0499818	+	0.0499818i
$604$		0			0
$605$	8.33712e16	−	5.68281e16i	1.70014	−	1.15886i
$606$		0			0
$607$	−6.16138e15	+	6.16138e15i	−0.123182	+	0.123182i	−0.766010	−	0.642829i	$-0.777761\pi$
$607$	−6.16138e15	+	6.16138e15i	−0.123182	+	0.123182i	0.642829	+	0.766010i	$0.277761\pi$
$608$		0			0
$609$			2.46809e16i			0.483791i
$610$		0			0
$611$	−1.11342e15			−0.0213999
$612$		0			0
$613$	−1.93532e16	−	1.93532e16i	−0.364746	−	0.364746i	0.500811	−	0.865557i	$-0.333035\pi$
$613$	−1.93532e16	−	1.93532e16i	−0.364746	−	0.364746i	−0.865557	+	0.500811i	$0.833035\pi$
$614$		0			0
$615$	−4.61838e16	−	8.74373e15i	−0.853571	−	0.161602i
$616$		0			0
$617$	5.97005e15	−	5.97005e15i	0.108210	−	0.108210i	−0.650929	−	0.759139i	$-0.725620\pi$
$617$	5.97005e15	−	5.97005e15i	0.108210	−	0.108210i	0.759139	+	0.650929i	$0.225620\pi$
$618$		0			0
$619$			5.29012e16i			0.940420i	0.882555	+	0.470210i	$0.155822\pi$
$619$			5.29012e16i			0.940420i	−0.882555	+	0.470210i	$0.844178\pi$
$620$		0			0
$621$	−8.27564e16			−1.44295
$622$		0			0
$623$	−1.51072e16	−	1.51072e16i	−0.258379	−	0.258379i
$624$		0			0
$625$	−4.36754e16	−	4.05607e16i	−0.732752	−	0.680496i
$626$		0			0
$627$	6.76774e16	−	6.76774e16i	1.11388	−	1.11388i
$628$		0			0
$629$		−	2.47564e16i		−	0.399746i
$630$		0			0
$631$	−1.05279e17			−1.66788			−0.833938	−	0.551858i	$-0.813919\pi$
$631$	−1.05279e17			−1.66788			−0.833938	+	0.551858i	$0.813919\pi$
$632$		0			0
$633$	1.18801e16	+	1.18801e16i	0.184670	+	0.184670i
$634$		0			0
$635$	4.09443e15	−	2.16265e16i	0.0624527	−	0.329871i
$636$		0			0
$637$	−2.72957e15	+	2.72957e15i	−0.0408562	+	0.0408562i
$638$		0			0
$639$			3.55438e15i			0.0522106i
$640$		0			0
$641$	1.87110e15			0.0269742			0.0134871	−	0.999909i	$-0.495707\pi$
$641$	1.87110e15			0.0269742			0.0134871	+	0.999909i	$0.495707\pi$
$642$		0			0
$643$	7.81577e16	+	7.81577e16i	1.10587	+	1.10587i	0.993687	+	0.112188i	$0.0357859\pi$
$643$	7.81577e16	+	7.81577e16i	1.10587	+	1.10587i	0.112188	+	0.993687i	$0.464214\pi$
$644$		0			0
$645$	2.41061e16	+	3.53655e16i	0.334787	+	0.491159i
$646$		0			0
$647$	2.90069e16	−	2.90069e16i	0.395436	−	0.395436i	−0.481184	−	0.876620i	$-0.659793\pi$
$647$	2.90069e16	−	2.90069e16i	0.395436	−	0.395436i	0.876620	+	0.481184i	$0.159793\pi$
$648$		0			0
$649$			1.21985e17i			1.63244i
$650$		0			0
$651$	−2.34629e16			−0.308245
$652$		0			0
$653$	5.85946e15	+	5.85946e15i	0.0755751	+	0.0755751i	0.743884	−	0.668309i	$-0.232982\pi$
$653$	5.85946e15	+	5.85946e15i	0.0755751	+	0.0755751i	−0.668309	+	0.743884i	$0.732982\pi$
$654$		0			0
$655$	5.34966e16	−	3.64647e16i	0.677452	−	0.461769i
$656$		0			0
$657$	−1.91553e15	+	1.91553e15i	−0.0238176	+	0.0238176i
$658$		0			0
$659$		−	1.33700e17i		−	1.63237i	−0.577792	−	0.816184i	$-0.696086\pi$
$659$		−	1.33700e17i		−	1.63237i	0.577792	−	0.816184i	$-0.303914\pi$
$660$		0			0
$661$	1.59727e16			0.191501			0.0957503	−	0.995405i	$-0.469475\pi$
$661$	1.59727e16			0.191501			0.0957503	+	0.995405i	$0.469475\pi$
$662$		0			0
$663$	1.22374e15	+	1.22374e15i	0.0144081	+	0.0144081i
$664$		0			0
$665$	−2.28090e16	−	4.31830e15i	−0.263740	−	0.0499324i
$666$		0			0
$667$	−1.40737e17	+	1.40737e17i	−1.59828	+	1.59828i
$668$		0			0
$669$		−	6.36198e15i		−	0.0709636i
$670$		0			0
$671$	1.50028e17			1.64375
$672$		0			0
$673$	7.93028e16	+	7.93028e16i	0.853489	+	0.853489i	0.990561	−	0.137072i	$-0.0437692\pi$
$673$	7.93028e16	+	7.93028e16i	0.853489	+	0.853489i	−0.137072	+	0.990561i	$0.543769\pi$
$674$		0			0
$675$	3.58383e16	+	8.21916e16i	0.378900	+	0.868970i
$676$		0			0
$677$	8.12517e16	−	8.12517e16i	0.843918	−	0.843918i	−0.145448	−	0.989366i	$-0.546462\pi$
$677$	8.12517e16	−	8.12517e16i	0.843918	−	0.843918i	0.989366	+	0.145448i	$0.0464622\pi$
$678$		0			0
$679$			1.80869e16i			0.184564i
$680$		0			0
$681$	1.19980e17			1.20289
$682$		0			0
$683$	−1.70461e16	−	1.70461e16i	−0.167919	−	0.167919i	0.618145	−	0.786064i	$-0.287884\pi$
$683$	−1.70461e16	−	1.70461e16i	−0.167919	−	0.167919i	−0.786064	+	0.618145i	$0.787884\pi$
$684$		0			0
$685$	−1.64779e16	+	8.70355e16i	−0.159500	+	0.842467i
$686$		0			0
$687$	4.51164e15	−	4.51164e15i	0.0429135	−	0.0429135i
$688$		0			0
$689$		−	3.75292e14i		−	0.00350795i
$690$		0			0
$691$	2.15124e17			1.97615			0.988077	−	0.153963i	$-0.0492036\pi$
$691$	2.15124e17			1.97615			0.988077	+	0.153963i	$0.0492036\pi$
$692$		0			0
$693$	−3.98594e15	−	3.98594e15i	−0.0359858	−	0.0359858i
$694$		0			0
$695$	−1.67167e16	−	2.45247e16i	−0.148334	−	0.217618i
$696$		0			0
$697$	−2.05109e16	+	2.05109e16i	−0.178891	+	0.178891i
$698$		0			0
$699$			1.41285e17i			1.21125i
$700$		0			0
$701$	−4.88232e16			−0.411451			−0.205726	−	0.978610i	$-0.565955\pi$
$701$	−4.88232e16			−0.411451			−0.205726	+	0.978610i	$0.565955\pi$
$702$		0			0
$703$	−9.65310e16	−	9.65310e16i	−0.799714	−	0.799714i
$704$		0			0
$705$	3.54779e16	−	2.41827e16i	0.288950	−	0.196956i
$706$		0			0
$707$	−1.31394e16	+	1.31394e16i	−0.105211	+	0.105211i
$708$		0			0
$709$			4.80538e16i			0.378312i	0.981947	+	0.189156i	$0.0605752\pi$
$709$			4.80538e16i			0.378312i	−0.981947	+	0.189156i	$0.939425\pi$
$710$		0			0
$711$	2.55594e15			0.0197849
$712$		0			0
$713$	−1.33792e17	−	1.33792e17i	−1.01834	−	1.01834i
$714$		0			0
$715$	1.46891e16	+	2.78100e15i	0.109941	+	0.0208144i
$716$		0			0
$717$	7.16421e16	−	7.16421e16i	0.527295	−	0.527295i
$718$		0			0
$719$		−	7.85015e16i		−	0.568205i	−0.958794	−	0.284102i	$-0.908304\pi$
$719$		−	7.85015e16i		−	0.568205i	0.958794	−	0.284102i	$-0.0916956\pi$
$720$		0			0
$721$	1.86918e16			0.133058
$722$		0			0
$723$	1.53291e16	+	1.53291e16i	0.107322	+	0.107322i
$724$		0			0
$725$	2.00724e17	+	7.88294e16i	1.38220	+	0.542825i
$726$		0			0
$727$	6.05514e16	−	6.05514e16i	0.410126	−	0.410126i	−0.471656	−	0.881782i	$-0.656344\pi$
$727$	6.05514e16	−	6.05514e16i	0.410126	−	0.410126i	0.881782	+	0.471656i	$0.156344\pi$
$728$		0			0
$729$		−	1.33576e17i		−	0.889948i
$730$		0			0
$731$	2.64122e16			0.173102
$732$		0			0
$733$	6.96866e16	+	6.96866e16i	0.449289	+	0.449289i	0.895118	−	0.445829i	$-0.147091\pi$
$733$	6.96866e16	+	6.96866e16i	0.449289	+	0.449289i	−0.445829	+	0.895118i	$0.647091\pi$
$734$		0			0
$735$	2.76904e16	−	1.46259e17i	0.175632	−	0.927680i
$736$		0			0
$737$	1.49930e17	−	1.49930e17i	0.935586	−	0.935586i
$738$		0			0
$739$			1.56451e17i			0.960534i	0.877122	+	0.480267i	$0.159460\pi$
$739$			1.56451e17i			0.960534i	−0.877122	+	0.480267i	$0.840540\pi$
$740$		0			0
$741$	9.54327e15			0.0576485
$742$		0			0
$743$	1.10089e17	+	1.10089e17i	0.654353	+	0.654353i	0.954038	−	0.299685i	$-0.0968817\pi$
$743$	1.10089e17	+	1.10089e17i	0.654353	+	0.654353i	−0.299685	+	0.954038i	$0.596882\pi$
$744$		0			0
$745$	−8.47261e16	−	1.24300e17i	−0.495541	−	0.726997i
$746$		0			0
$747$	−1.50453e16	+	1.50453e16i	−0.0865917	+	0.0865917i
$748$		0			0
$749$		−	4.66955e15i		−	0.0264475i
$750$		0			0
$751$	1.54289e17			0.859996			0.429998	−	0.902830i	$-0.358514\pi$
$751$	1.54289e17			0.859996			0.429998	+	0.902830i	$0.358514\pi$
$752$		0			0
$753$	−2.05182e17	−	2.05182e17i	−1.12556	−	1.12556i
$754$		0			0
$755$	−1.58174e17	+	1.07816e17i	−0.853991	+	0.582103i
$756$		0			0
$757$	−2.46753e17	+	2.46753e17i	−1.31125	+	1.31125i	−0.390762	+	0.920492i	$0.627789\pi$
$757$	−2.46753e17	+	2.46753e17i	−1.31125	+	1.31125i	−0.920492	+	0.390762i	$0.872211\pi$
$758$		0			0
$759$		−	5.32082e17i		−	2.78310i
$760$		0			0
$761$	2.72843e16			0.140477			0.0702385	−	0.997530i	$-0.477624\pi$
$761$	2.72843e16			0.140477			0.0702385	+	0.997530i	$0.477624\pi$
$762$		0			0
$763$	5.88388e16	+	5.88388e16i	0.298206	+	0.298206i
$764$		0			0
$765$	−5.60202e15	−	1.06060e15i	−0.0279496	−	0.00529155i
$766$		0			0
$767$	−8.60061e15	+	8.60061e15i	−0.0422432	+	0.0422432i
$768$		0			0
$769$			1.45838e17i			0.705201i	0.935774	+	0.352601i	$0.114703\pi$
$769$			1.45838e17i			0.705201i	−0.935774	+	0.352601i	$0.885297\pi$
$770$		0			0
$771$	−2.72297e17			−1.29633
$772$		0			0
$773$	7.64565e16	+	7.64565e16i	0.358375	+	0.358375i	0.863214	−	0.504839i	$-0.168448\pi$
$773$	7.64565e16	+	7.64565e16i	0.358375	+	0.358375i	−0.504839	+	0.863214i	$0.668448\pi$
$774$		0			0
$775$	−7.49392e16	+	1.90818e17i	−0.345859	+	0.880663i
$776$		0			0
$777$	−6.65465e16	+	6.65465e16i	−0.302412	+	0.302412i
$778$		0			0
$779$			1.59954e17i			0.715764i
$780$		0			0
$781$	2.21787e17			0.977306
$782$		0			0
$783$	−2.29390e17	−	2.29390e17i	−0.995415	−	0.995415i
$784$		0			0
$785$	−6.97562e16	+	3.68448e17i	−0.298102	+	1.57456i
$786$		0			0
$787$	−1.29592e17	+	1.29592e17i	−0.545417	+	0.545417i	−0.925112	−	0.379695i	$-0.876029\pi$
$787$	−1.29592e17	+	1.29592e17i	−0.545417	+	0.545417i	0.379695	+	0.925112i	$0.376029\pi$
$788$		0			0
$789$		−	4.51972e17i		−	1.87348i
$790$		0			0
$791$	−4.62466e16			−0.188808
$792$		0			0
$793$	1.05778e16	+	1.05778e16i	0.0425359	+	0.0425359i
$794$		0			0
$795$	8.15106e15	+	1.19582e16i	0.0322858	+	0.0473658i
$796$		0			0
$797$	−2.20257e17	+	2.20257e17i	−0.859370	+	0.859370i	−0.991264	−	0.131894i	$-0.957894\pi$
$797$	−2.20257e17	+	2.20257e17i	−0.859370	+	0.859370i	0.131894	+	0.991264i	$0.457894\pi$
$798$		0			0
$799$		−	2.64962e16i		−	0.101836i
$800$		0			0
$801$	−2.89356e16			−0.109556
$802$		0			0
$803$	1.19526e17	+	1.19526e17i	0.445830	+	0.445830i
$804$		0			0
$805$	−1.06638e17	+	7.26873e16i	−0.391865	+	0.267106i
$806$		0			0
$807$	1.47926e17	−	1.47926e17i	0.535553	−	0.535553i
$808$		0			0
$809$			7.87560e16i			0.280926i	0.990086	+	0.140463i	$0.0448592\pi$
$809$			7.87560e16i			0.280926i	−0.990086	+	0.140463i	$0.955141\pi$
$810$		0			0
$811$	7.27861e16			0.255813			0.127907	−	0.991786i	$-0.459174\pi$
$811$	7.27861e16			0.255813			0.127907	+	0.991786i	$0.459174\pi$
$812$		0			0
$813$	1.68687e17	+	1.68687e17i	0.584169	+	0.584169i
$814$		0			0
$815$	−1.69244e17	−	3.20419e16i	−0.577519	−	0.109338i
$816$		0			0
$817$	1.02987e17	−	1.02987e17i	0.346300	−	0.346300i
$818$		0			0
$819$		−	5.62062e14i		−	0.00186243i
$820$		0			0
$821$	−5.22455e17			−1.70604			−0.853022	−	0.521875i	$-0.825233\pi$
$821$	−5.22455e17			−1.70604			−0.853022	+	0.521875i	$0.825233\pi$
$822$		0			0
$823$	1.20238e17	+	1.20238e17i	0.386940	+	0.386940i	0.873594	−	0.486655i	$-0.161783\pi$
$823$	1.20238e17	+	1.20238e17i	0.386940	+	0.386940i	−0.486655	+	0.873594i	$0.661783\pi$
$824$		0			0
$825$	−5.28451e17	+	2.30422e17i	−1.67603	+	0.730804i
$826$		0			0
$827$	−2.64978e15	+	2.64978e15i	−0.00828279	+	0.00828279i	−0.711236	−	0.702953i	$-0.751864\pi$
$827$	−2.64978e15	+	2.64978e15i	−0.00828279	+	0.00828279i	0.702953	+	0.711236i	$0.251864\pi$
$828$		0			0
$829$		−	2.74209e17i		−	0.844800i	−0.906409	−	0.422400i	$-0.861188\pi$
$829$		−	2.74209e17i		−	0.844800i	0.906409	−	0.422400i	$-0.138812\pi$
$830$		0			0
$831$	−4.11454e17			−1.24944
$832$		0			0
$833$	−6.49558e16	−	6.49558e16i	−0.194423	−	0.194423i
$834$		0			0
$835$	−6.82430e16	+	3.60456e17i	−0.201344	+	1.06349i
$836$		0			0
$837$	2.18070e17	−	2.18070e17i	0.634224	−	0.634224i
$838$		0			0
$839$		−	1.46168e17i		−	0.419065i	−0.977802	−	0.209532i	$-0.932806\pi$
$839$		−	1.46168e17i		−	0.419065i	0.977802	−	0.209532i	$-0.0671941\pi$
$840$		0			0
$841$	−4.26395e17			−1.20514
$842$		0			0
$843$	−2.28264e17	−	2.28264e17i	−0.636021	−	0.636021i
$844$		0			0
$845$	−2.04194e17	−	2.99569e17i	−0.560923	−	0.822917i
$846$		0			0
$847$	−1.67370e17	+	1.67370e17i	−0.453292	+	0.453292i
$848$		0			0
$849$		−	1.10791e16i		−	0.0295840i
$850$		0			0
$851$	−7.58931e17			−1.99814
$852$		0			0
$853$	2.89032e17	+	2.89032e17i	0.750329	+	0.750329i	0.974541	−	0.224211i	$-0.0719805\pi$
$853$	2.89032e17	+	2.89032e17i	0.750329	+	0.750329i	−0.224211	+	0.974541i	$0.571981\pi$
$854$		0			0
$855$	−2.59791e16	+	1.77081e16i	−0.0665009	+	0.0453288i
$856$		0			0
$857$	4.45141e17	−	4.45141e17i	1.12360	−	1.12360i	0.132408	−	0.991195i	$-0.457729\pi$
$857$	4.45141e17	−	4.45141e17i	1.12360	−	1.12360i	0.991195	−	0.132408i	$-0.0422710\pi$
$858$		0			0
$859$		−	2.36186e17i		−	0.587888i	−0.955823	−	0.293944i	$-0.905032\pi$
$859$		−	2.36186e17i		−	0.587888i	0.955823	−	0.293944i	$-0.0949679\pi$
$860$		0			0
$861$	1.10269e17			0.270666
$862$		0			0
$863$	−1.64474e16	−	1.64474e16i	−0.0398137	−	0.0398137i	0.686920	−	0.726733i	$-0.258962\pi$
$863$	−1.64474e16	−	1.64474e16i	−0.0398137	−	0.0398137i	−0.726733	+	0.686920i	$0.758962\pi$
$864$		0			0
$865$	−2.17895e17	−	4.12527e16i	−0.520175	−	0.0984818i
$866$		0			0
$867$	2.84924e17	−	2.84924e17i	0.670832	−	0.670832i
$868$		0			0
$869$		−	1.59486e17i		−	0.370344i
$870$		0			0
$871$	2.11418e16			0.0484210
$872$		0			0
$873$	1.73214e16	+	1.73214e16i	0.0391289	+	0.0391289i
$874$		0			0
$875$	1.18372e17	+	7.44324e16i	0.263754	+	0.165849i
$876$		0			0
$877$	−5.51826e17	+	5.51826e17i	−1.21284	+	1.21284i	−0.242755	+	0.970088i	$0.578051\pi$
$877$	−5.51826e17	+	5.51826e17i	−1.21284	+	1.21284i	−0.970088	+	0.242755i	$0.921949\pi$
$878$		0			0
$879$			5.81036e17i			1.25971i
$880$		0			0
$881$	8.50701e17			1.81937			0.909686	−	0.415296i	$-0.136322\pi$
$881$	8.50701e17			1.81937			0.909686	+	0.415296i	$0.136322\pi$
$882$		0			0
$883$	5.82619e17	+	5.82619e17i	1.22919	+	1.22919i	0.964269	+	0.264925i	$0.0853472\pi$
$883$	5.82619e17	+	5.82619e17i	1.22919	+	1.22919i	0.264925	+	0.964269i	$0.414653\pi$
$884$		0			0
$885$	8.72496e16	−	4.60847e17i	0.181595	−	0.959174i
$886$		0			0
$887$	4.27211e17	−	4.27211e17i	0.877204	−	0.877204i	−0.116040	−	0.993245i	$-0.537020\pi$
$887$	4.27211e17	−	4.27211e17i	0.877204	−	0.877204i	0.993245	+	0.116040i	$0.0370202\pi$
$888$		0			0
$889$			5.16357e16i			0.104602i
$890$		0			0
$891$	9.48978e17			1.89666
$892$		0			0
$893$	−1.03315e17	−	1.03315e17i	−0.203729	−	0.203729i
$894$		0			0
$895$	−7.20385e16	−	1.05686e17i	−0.140161	−	0.205627i
$896$		0			0
$897$	3.75148e16	−	3.75148e16i	0.0720192	−	0.0720192i
$898$		0			0
$899$		−	7.41707e17i		−	1.40499i
$900$		0			0
$901$	8.93084e15			0.0166934
$902$		0			0
$903$	−7.09974e16	−	7.09974e16i	−0.130953	−	0.130953i
$904$		0			0
$905$	5.67856e17	−	3.87066e17i	1.03359	−	0.704521i
$906$		0			0
$907$	1.64933e17	−	1.64933e17i	0.296254	−	0.296254i	−0.543291	−	0.839545i	$-0.682822\pi$
$907$	1.64933e17	−	1.64933e17i	0.296254	−	0.296254i	0.839545	+	0.543291i	$0.182822\pi$
$908$		0			0
$909$			2.51666e16i			0.0446109i
$910$		0			0
$911$	8.63395e16			0.151043			0.0755213	−	0.997144i	$-0.475938\pi$
$911$	8.63395e16			0.151043			0.0755213	+	0.997144i	$0.475938\pi$
$912$		0			0
$913$	9.38799e17	+	9.38799e17i	1.62087	+	1.62087i
$914$		0			0
$915$	−5.66791e17	−	1.07307e17i	−0.965820	−	0.182853i
$916$		0			0
$917$	−1.07396e17	+	1.07396e17i	−0.180623	+	0.180623i
$918$		0			0
$919$			1.07561e17i			0.178551i	0.996007	+	0.0892754i	$0.0284551\pi$
$919$			1.07561e17i			0.178551i	−0.996007	+	0.0892754i	$0.971545\pi$
$920$		0			0
$921$	−7.26994e17			−1.19117
$922$		0			0
$923$	1.56372e16	+	1.56372e16i	0.0252901	+	0.0252901i
$924$		0			0
$925$	3.28661e17	+	7.53752e17i	0.524684	+	1.20331i
$926$		0			0
$927$	1.79007e16	−	1.79007e16i	0.0282093	−	0.0282093i
$928$		0			0
$929$			1.95773e17i			0.304550i	0.988338	+	0.152275i	$0.0486599\pi$
$929$			1.95773e17i			0.304550i	−0.988338	+	0.152275i	$0.951340\pi$
$930$		0			0
$931$	−5.06555e17			−0.777909
$932$		0			0
$933$	−7.45244e16	−	7.45244e16i	−0.112982	−	0.112982i
$934$		0			0
$935$	−6.61796e16	+	3.49557e17i	−0.0990500	+	0.523176i
$936$		0			0
$937$	3.81428e16	−	3.81428e16i	0.0563606	−	0.0563606i	−0.678365	−	0.734725i	$-0.737311\pi$
$937$	3.81428e16	−	3.81428e16i	0.0563606	−	0.0563606i	0.734725	+	0.678365i	$0.237311\pi$
$938$		0			0
$939$		−	1.96654e16i		−	0.0286885i
$940$		0			0
$941$	−4.15167e17			−0.597977			−0.298989	−	0.954257i	$-0.596649\pi$
$941$	−4.15167e17			−0.597977			−0.298989	+	0.954257i	$0.596649\pi$
$942$		0			0
$943$	6.28782e17	+	6.28782e17i	0.894190	+	0.894190i
$944$		0			0
$945$	−1.18474e17	−	1.73811e17i	−0.166354	−	0.244055i
$946$		0			0
$947$	6.57038e17	−	6.57038e17i	0.910942	−	0.910942i	−0.0854044	−	0.996346i	$-0.527218\pi$
$947$	6.57038e17	−	6.57038e17i	0.910942	−	0.910942i	0.996346	+	0.0854044i	$0.0272182\pi$
$948$		0			0
$949$			1.68545e16i			0.0230738i
$950$		0			0
$951$	3.31839e16			0.0448584
$952$		0			0
$953$	3.03136e17	+	3.03136e17i	0.404651	+	0.404651i	0.879868	−	0.475218i	$-0.157631\pi$
$953$	3.03136e17	+	3.03136e17i	0.404651	+	0.404651i	−0.475218	+	0.879868i	$0.657631\pi$
$954$		0			0
$955$	5.24861e17	−	3.57760e17i	0.691869	−	0.471597i
$956$		0			0
$957$	1.47486e18	−	1.47486e18i	1.91991	−	1.91991i
$958$		0			0
$959$		−	2.07806e17i		−	0.267145i
$960$		0			0
$961$	−8.25581e16			−0.104814
$962$		0			0
$963$	−4.47191e15	−	4.47191e15i	−0.00560706	−	0.00560706i
$964$		0			0
$965$	−9.19497e17	−	1.74083e17i	−1.13864	−	0.215572i
$966$		0			0
$967$	−3.68569e17	+	3.68569e17i	−0.450775	+	0.450775i	−0.895612	−	0.444837i	$-0.853262\pi$
$967$	−3.68569e17	+	3.68569e17i	−0.450775	+	0.450775i	0.444837	+	0.895612i	$0.353262\pi$
$968$		0			0
$969$			2.27102e17i			0.274333i
$970$		0			0
$971$	−6.06451e17			−0.723569			−0.361785	−	0.932262i	$-0.617832\pi$
$971$	−6.06451e17			−0.723569			−0.361785	+	0.932262i	$0.617832\pi$
$972$		0			0
$973$	4.92341e16	+	4.92341e16i	0.0580215	+	0.0580215i
$974$		0			0
$975$	−5.35049e16	−	2.10127e16i	−0.0622824	−	0.0244599i
$976$		0			0
$977$	−1.52077e17	+	1.52077e17i	−0.174862	+	0.174862i	−0.789112	−	0.614250i	$-0.789459\pi$
$977$	−1.52077e17	+	1.52077e17i	−0.174862	+	0.174862i	0.614250	+	0.789112i	$0.289459\pi$
$978$		0			0
$979$			1.80553e18i			2.05073i
$980$		0			0
$981$	1.12697e17			0.126444
$982$		0			0
$983$	1.10745e18	+	1.10745e18i	1.22745	+	1.22745i	0.964926	+	0.262524i	$0.0845548\pi$
$983$	1.10745e18	+	1.10745e18i	1.22745	+	1.22745i	0.262524	+	0.964926i	$0.415445\pi$
$984$		0			0
$985$	−1.67525e17	+	8.84859e17i	−0.183427	+	0.968850i
$986$		0			0
$987$	−7.12230e16	+	7.12230e16i	−0.0770402	+	0.0770402i
$988$		0			0
$989$		−	8.09692e17i		−	0.865251i
$990$		0			0
$991$	−7.10456e17			−0.750059			−0.375029	−	0.927013i	$-0.622367\pi$
$991$	−7.10456e17			−0.750059			−0.375029	+	0.927013i	$0.622367\pi$
$992$		0			0
$993$	6.99143e17	+	6.99143e17i	0.729240	+	0.729240i
$994$		0			0
$995$	−2.66576e17	−	3.91087e17i	−0.274715	−	0.403028i
$996$		0			0
$997$	8.39748e17	−	8.39748e17i	0.855023	−	0.855023i	−0.135724	−	0.990747i	$-0.543336\pi$
$997$	8.39748e17	−	8.39748e17i	0.855023	−	0.855023i	0.990747	+	0.135724i	$0.0433359\pi$
$998$		0			0
$999$		−	1.23700e18i		−	1.24444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.13.p.c.33.2		10
4.3	odd	2		5.13.c.a.3.4	yes	10
5.2	odd	4	inner	80.13.p.c.17.2		10
12.11	even	2		45.13.g.a.28.2		10
20.3	even	4		25.13.c.b.7.2		10
20.7	even	4		5.13.c.a.2.4	✓	10
20.19	odd	2		25.13.c.b.18.2		10
60.47	odd	4		45.13.g.a.37.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.13.c.a.2.4	✓	10	20.7	even	4
5.13.c.a.3.4	yes	10	4.3	odd	2
25.13.c.b.7.2		10	20.3	even	4
25.13.c.b.18.2		10	20.19	odd	2
45.13.g.a.28.2		10	12.11	even	2
45.13.g.a.37.2		10	60.47	odd	4
80.13.p.c.17.2		10	5.2	odd	4	inner
80.13.p.c.33.2		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-539.020 - 539.020i) q^{3} +(12911.0 - 8800.45i) q^{5} +(-25919.1 + 25919.1i) q^{7} +49644.2i q^{9} +O(q^{10})\)	\(q+(-539.020 - 539.020i) q^{3} +(12911.0 - 8800.45i) q^{5} +(-25919.1 + 25919.1i) q^{7} +49644.2i q^{9} +3.09771e6 q^{11} +(218406. + 218406. i) q^{13} +(-1.17029e7 - 2.21564e6i) q^{15} +(-5.19743e6 + 5.19743e6i) q^{17} +4.05319e7i q^{19} +2.79419e7 q^{21} +(1.59332e8 + 1.59332e8i) q^{23} +(8.92447e7 - 2.27244e8i) q^{25} +(-2.59698e8 + 2.59698e8i) q^{27} +8.83295e8i q^{29} -8.39705e8 q^{31} +(-1.66973e9 - 1.66973e9i) q^{33} +(-1.06541e8 + 5.62741e8i) q^{35} +(-2.38160e9 + 2.38160e9i) q^{37} -2.35451e8i q^{39} +3.94637e9 q^{41} +(-2.54090e9 - 2.54090e9i) q^{43} +(4.36891e8 + 6.40954e8i) q^{45} +(-2.54897e9 + 2.54897e9i) q^{47} +1.24977e10i q^{49} +5.60303e9 q^{51} +(-8.59160e8 - 8.59160e8i) q^{53} +(3.99944e10 - 2.72613e10i) q^{55} +(2.18475e10 - 2.18475e10i) q^{57} +3.93789e10i q^{59} +4.84317e10 q^{61} +(-1.28674e9 - 1.28674e9i) q^{63} +(4.74191e9 + 8.97758e8i) q^{65} +(4.84002e10 - 4.84002e10i) q^{67} -1.71766e11i q^{69} +7.15971e10 q^{71} +(3.85852e10 + 3.85852e10i) q^{73} +(-1.70594e11 + 7.43846e10i) q^{75} +(-8.02901e10 + 8.02901e10i) q^{77} -5.14852e10i q^{79} +3.06348e11 q^{81} +(3.03062e11 + 3.03062e11i) q^{83} +(-2.13640e10 + 1.12843e11i) q^{85} +(4.76114e11 - 4.76114e11i) q^{87} +5.82860e11i q^{89} -1.13218e10 q^{91} +(4.52618e11 + 4.52618e11i) q^{93} +(3.56699e11 + 5.23306e11i) q^{95} +(3.48911e11 - 3.48911e11i) q^{97} +1.53784e11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 318 q^{3} - 4250 q^{5} - 279598 q^{7}+O(q^{10}) \) 10 * q - 318 * q^3 - 4250 * q^5 - 279598 * q^7	\( 10 q - 318 q^{3} - 4250 q^{5} - 279598 q^{7} - 312620 q^{11} + 5290738 q^{13} + 5821650 q^{15} - 41269502 q^{17} + 107493420 q^{21} + 510099842 q^{23} + 942201250 q^{25} + 1993958640 q^{27} - 3077089820 q^{31} - 7503698004 q^{33} - 9330787150 q^{35} - 2599618502 q^{37} + 7412079020 q^{41} + 5784410402 q^{43} - 10510145100 q^{45} - 16053249598 q^{47} + 33139878180 q^{51} + 101763514618 q^{53} + 84180068500 q^{55} + 27733489920 q^{57} + 7731718220 q^{61} - 207465112158 q^{63} - 338075024150 q^{65} + 80010636002 q^{67} + 46557252580 q^{71} - 448527032342 q^{73} - 719724648750 q^{75} - 425580405844 q^{77} + 1107831051810 q^{81} + 91118376722 q^{83} + 543768569650 q^{85} + 2078422804320 q^{87} - 2737742572220 q^{91} - 91295366484 q^{93} + 1044695070000 q^{95} - 1409507601302 q^{97}+O(q^{100}) \) 10 * q - 318 * q^3 - 4250 * q^5 - 279598 * q^7 - 312620 * q^11 + 5290738 * q^13 + 5821650 * q^15 - 41269502 * q^17 + 107493420 * q^21 + 510099842 * q^23 + 942201250 * q^25 + 1993958640 * q^27 - 3077089820 * q^31 - 7503698004 * q^33 - 9330787150 * q^35 - 2599618502 * q^37 + 7412079020 * q^41 + 5784410402 * q^43 - 10510145100 * q^45 - 16053249598 * q^47 + 33139878180 * q^51 + 101763514618 * q^53 + 84180068500 * q^55 + 27733489920 * q^57 + 7731718220 * q^61 - 207465112158 * q^63 - 338075024150 * q^65 + 80010636002 * q^67 + 46557252580 * q^71 - 448527032342 * q^73 - 719724648750 * q^75 - 425580405844 * q^77 + 1107831051810 * q^81 + 91118376722 * q^83 + 543768569650 * q^85 + 2078422804320 * q^87 - 2737742572220 * q^91 - 91295366484 * q^93 + 1044695070000 * q^95 - 1409507601302 * q^97

Introduction

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