LMFDB - Embedded newform 112.12.i.c.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,12,Mod(65,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("112.65");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	112.i (of order $3$, 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:	$86.0544362227$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 1846 x^{10} + 9475 x^{9} + 2735534 x^{8} + 11305015 x^{7} + 1247863105 x^{6} + \cdots + 4089842896896 $ x^12 - x^11 + 1846x^10 + 9475x^9 + 2735534x^8 + 11305015x^7 + 1247863105x^6 + 8299724444x^5 + 456730004116x^4 + 1967575859568x^3 + 7281700309008x^2 + 5939576563968x + 4089842896896
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{3}\cdot 7^{6} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			65.2
Root			$11.5012 - 19.9207i$ of defining polynomial
Character	$\chi$	$=$	112.65
Dual form			112.12.i.c.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-205.214 - 355.441i) q^{3} +(-41.2685 + 71.4792i) q^{5} +(43319.9 - 10035.5i) q^{7} +(4347.82 - 7530.65i) q^{9} +O(q^{10})$	\(q+(-205.214 - 355.441i) q^{3} +(-41.2685 + 71.4792i) q^{5} +(43319.9 - 10035.5i) q^{7} +(4347.82 - 7530.65i) q^{9} +(-160761. - 278447. i) q^{11} +811765. q^{13} +33875.5 q^{15} +(2.13175e6 + 3.69230e6i) q^{17} +(7.49974e6 - 1.29899e7i) q^{19} +(-1.24569e7 - 1.33383e7i) q^{21} +(-3.29099e6 + 5.70016e6i) q^{23} +(2.44107e7 + 4.22805e7i) q^{25} -7.62751e7 q^{27} +1.83362e8 q^{29} +(7.42525e7 + 1.28609e8i) q^{31} +(-6.59810e7 + 1.14282e8i) q^{33} +(-1.07042e6 + 3.51062e6i) q^{35} +(-2.93087e8 + 5.07642e8i) q^{37} +(-1.66586e8 - 2.88535e8i) q^{39} +7.84360e8 q^{41} +1.21250e9 q^{43} +(358857. + 621558. i) q^{45} +(-7.11093e8 + 1.23165e9i) q^{47} +(1.77591e9 - 8.69471e8i) q^{49} +(8.74930e8 - 1.51542e9i) q^{51} +(-1.68739e8 - 2.92264e8i) q^{53} +2.65375e7 q^{55} -6.15621e9 q^{57} +(5.07967e9 + 8.79825e9i) q^{59} +(1.96271e9 - 3.39951e9i) q^{61} +(1.12774e8 - 3.69860e8i) q^{63} +(-3.35003e7 + 5.80243e7i) q^{65} +(-8.62231e9 - 1.49343e10i) q^{67} +2.70143e9 q^{69} -1.18078e10 q^{71} +(-7.04324e9 - 1.21993e10i) q^{73} +(1.00188e10 - 1.73531e10i) q^{75} +(-9.75851e9 - 1.04490e10i) q^{77} +(3.25346e9 - 5.63515e9i) q^{79} +(1.48825e10 + 2.57773e10i) q^{81} +1.57783e9 q^{83} -3.51897e8 q^{85} +(-3.76285e10 - 6.51744e10i) q^{87} +(4.14844e10 - 7.18531e10i) q^{89} +(3.51656e10 - 8.14644e9i) q^{91} +(3.04753e10 - 5.27848e10i) q^{93} +(6.19006e8 + 1.07215e9i) q^{95} -6.77303e10 q^{97} -2.79585e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 244 q^{3} - 8782 q^{5} + 504 q^{7} - 172348 q^{9}+O(q^{10}) $ 12 * q + 244 * q^3 - 8782 * q^5 + 504 * q^7 - 172348 * q^9	$ 12 q + 244 q^{3} - 8782 q^{5} + 504 q^{7} - 172348 q^{9} + 1001572 q^{11} + 3864504 q^{13} + 1286512 q^{15} - 6704802 q^{17} - 4192212 q^{19} + 44745358 q^{21} + 33871872 q^{23} + 13695456 q^{25} - 73859384 q^{27} - 255125224 q^{29} + 331783920 q^{31} - 80899438 q^{33} - 1407354844 q^{35} - 833082774 q^{37} - 737605904 q^{39} + 3104076808 q^{41} + 1722177552 q^{43} - 7406493484 q^{45} + 1327587552 q^{47} + 11976558636 q^{49} + 13921261140 q^{51} + 6725755626 q^{53} - 26323921200 q^{55} - 16884487756 q^{57} + 26237179548 q^{59} - 14411013726 q^{61} - 45955779184 q^{63} - 16224702172 q^{65} + 4241860068 q^{67} + 46750854252 q^{69} + 37335334656 q^{71} + 6005568990 q^{73} - 17116276792 q^{75} - 51928077698 q^{77} - 11712395640 q^{79} - 12455008366 q^{81} + 100821781200 q^{83} + 138884613396 q^{85} - 119455310144 q^{87} - 48633519778 q^{89} + 160908361488 q^{91} + 266530114134 q^{93} + 72161225128 q^{95} - 401308415928 q^{97} - 367357472240 q^{99}+O(q^{100}) $ 12 * q + 244 * q^3 - 8782 * q^5 + 504 * q^7 - 172348 * q^9 + 1001572 * q^11 + 3864504 * q^13 + 1286512 * q^15 - 6704802 * q^17 - 4192212 * q^19 + 44745358 * q^21 + 33871872 * q^23 + 13695456 * q^25 - 73859384 * q^27 - 255125224 * q^29 + 331783920 * q^31 - 80899438 * q^33 - 1407354844 * q^35 - 833082774 * q^37 - 737605904 * q^39 + 3104076808 * q^41 + 1722177552 * q^43 - 7406493484 * q^45 + 1327587552 * q^47 + 11976558636 * q^49 + 13921261140 * q^51 + 6725755626 * q^53 - 26323921200 * q^55 - 16884487756 * q^57 + 26237179548 * q^59 - 14411013726 * q^61 - 45955779184 * q^63 - 16224702172 * q^65 + 4241860068 * q^67 + 46750854252 * q^69 + 37335334656 * q^71 + 6005568990 * q^73 - 17116276792 * q^75 - 51928077698 * q^77 - 11712395640 * q^79 - 12455008366 * q^81 + 100821781200 * q^83 + 138884613396 * q^85 - 119455310144 * q^87 - 48633519778 * q^89 + 160908361488 * q^91 + 266530114134 * q^93 + 72161225128 * q^95 - 401308415928 * q^97 - 367357472240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−205.214	−	355.441i	−0.487574	−	0.844503i	0.512324	−	0.858792i	$-0.328785\pi$
$3$	−205.214	−	355.441i	−0.487574	−	0.844503i	−0.999898	+	0.0142896i	$0.995451\pi$
$4$		0			0
$5$	−41.2685	+	71.4792i	−0.00590587	+	0.0102293i	−0.868963	−	0.494877i	$-0.835213\pi$
$5$	−41.2685	+	71.4792i	−0.00590587	+	0.0102293i	0.863057	+	0.505106i	$0.168547\pi$
$6$		0			0
$7$	43319.9	−	10035.5i	0.974201	−	0.225683i
$7$	43319.9	−	10035.5i	0.974201	−	0.225683i
$8$		0			0
$9$	4347.82	−	7530.65i	0.0245436	−	0.0425108i
$10$		0			0
$11$	−160761.	−	278447.i	−0.300969	−	0.521294i	0.675387	−	0.737464i	$-0.263977\pi$
$11$	−160761.	−	278447.i	−0.300969	−	0.521294i	−0.976356	+	0.216170i	$0.930643\pi$
$12$		0			0
$13$	811765.			0.606376			0.303188	−	0.952931i	$-0.401949\pi$
$13$	811765.			0.606376			0.303188	+	0.952931i	$0.401949\pi$
$14$		0			0
$15$	33875.5			0.0115182
$16$		0			0
$17$	2.13175e6	+	3.69230e6i	0.364139	+	0.630707i	0.988638	−	0.150319i	$-0.0480300\pi$
$17$	2.13175e6	+	3.69230e6i	0.364139	+	0.630707i	−0.624499	+	0.781026i	$0.714697\pi$
$18$		0			0
$19$	7.49974e6	−	1.29899e7i	0.694866	−	1.20354i	−0.275360	−	0.961341i	$-0.588797\pi$
$19$	7.49974e6	−	1.29899e7i	0.694866	−	1.20354i	0.970226	−	0.242202i	$-0.0778697\pi$
$20$		0			0
$21$	−1.24569e7	−	1.33383e7i	−0.665584	−	0.712678i
$22$		0			0
$23$	−3.29099e6	+	5.70016e6i	−0.106616	+	0.184665i	−0.914397	−	0.404818i	$-0.867335\pi$
$23$	−3.29099e6	+	5.70016e6i	−0.106616	+	0.184665i	0.807781	+	0.589482i	$0.200668\pi$
$24$		0			0
$25$	2.44107e7	+	4.22805e7i	0.499930	+	0.865905i
$26$		0			0
$27$	−7.62751e7			−1.02301
$28$		0			0
$29$	1.83362e8			1.66005			0.830024	−	0.557728i	$-0.188327\pi$
$29$	1.83362e8			1.66005			0.830024	+	0.557728i	$0.188327\pi$
$30$		0			0
$31$	7.42525e7	+	1.28609e8i	0.465824	+	0.806831i	0.999238	−	0.0390231i	$-0.0124246\pi$
$31$	7.42525e7	+	1.28609e8i	0.465824	+	0.806831i	−0.533414	+	0.845854i	$0.679091\pi$
$32$		0			0
$33$	−6.59810e7	+	1.14282e8i	−0.293489	+	0.508338i
$34$		0			0
$35$	−1.07042e6	+	3.51062e6i	−0.00344494	+	0.0112982i
$36$		0			0
$37$	−2.93087e8	+	5.07642e8i	−0.694844	+	1.20350i	0.275390	+	0.961333i	$0.411193\pi$
$37$	−2.93087e8	+	5.07642e8i	−0.694844	+	1.20350i	−0.970233	+	0.242172i	$0.922140\pi$
$38$		0			0
$39$	−1.66586e8	−	2.88535e8i	−0.295653	−	0.512086i
$40$		0			0
$41$	7.84360e8			1.05731			0.528657	−	0.848835i	$-0.322696\pi$
$41$	7.84360e8			1.05731			0.528657	+	0.848835i	$0.322696\pi$
$42$		0			0
$43$	1.21250e9			1.25778			0.628891	−	0.777493i	$-0.283509\pi$
$43$	1.21250e9			1.25778			0.628891	+	0.777493i	$0.283509\pi$
$44$		0			0
$45$	358857.	+	621558.i	0.000289903	+	0.000502126i
$46$		0			0
$47$	−7.11093e8	+	1.23165e9i	−0.452260	+	0.783338i	−0.998526	−	0.0542743i	$-0.982715\pi$
$47$	−7.11093e8	+	1.23165e9i	−0.452260	+	0.783338i	0.546266	+	0.837612i	$0.316049\pi$
$48$		0			0
$49$	1.77591e9	−	8.69471e8i	0.898135	−	0.439720i
$50$		0			0
$51$	8.74930e8	−	1.51542e9i	0.355089	−	0.615032i
$52$		0			0
$53$	−1.68739e8	−	2.92264e8i	−0.0554239	−	0.0959970i	0.836982	−	0.547230i	$-0.184318\pi$
$53$	−1.68739e8	−	2.92264e8i	−0.0554239	−	0.0959970i	−0.892406	+	0.451233i	$0.850984\pi$
$54$		0			0
$55$	2.65375e7			0.00710994
$56$		0			0
$57$	−6.15621e9			−1.35519
$58$		0			0
$59$	5.07967e9	+	8.79825e9i	0.925017	+	1.60218i	0.791534	+	0.611125i	$0.209283\pi$
$59$	5.07967e9	+	8.79825e9i	0.925017	+	1.60218i	0.133483	+	0.991051i	$0.457384\pi$
$60$		0			0
$61$	1.96271e9	−	3.39951e9i	0.297538	−	0.515350i	−0.678034	−	0.735030i	$-0.737168\pi$
$61$	1.96271e9	−	3.39951e9i	0.297538	−	0.515350i	0.975572	+	0.219680i	$0.0705013\pi$
$62$		0			0
$63$	1.12774e8	−	3.69860e8i	0.0143165	−	0.0469531i
$64$		0			0
$65$	−3.35003e7	+	5.80243e7i	−0.00358118	+	0.00620278i
$66$		0			0
$67$	−8.62231e9	−	1.49343e10i	−0.780212	−	1.35137i	−0.931818	−	0.362925i	$-0.881778\pi$
$67$	−8.62231e9	−	1.49343e10i	−0.780212	−	1.35137i	0.151607	−	0.988441i	$-0.451555\pi$
$68$		0			0
$69$	2.70143e9			0.207933
$70$		0			0
$71$	−1.18078e10			−0.776694			−0.388347	−	0.921513i	$-0.626954\pi$
$71$	−1.18078e10			−0.776694			−0.388347	+	0.921513i	$0.626954\pi$
$72$		0			0
$73$	−7.04324e9	−	1.21993e10i	−0.397646	−	0.688743i	0.595789	−	0.803141i	$-0.296840\pi$
$73$	−7.04324e9	−	1.21993e10i	−0.397646	−	0.688743i	−0.993435	+	0.114398i	$0.963506\pi$
$74$		0			0
$75$	1.00188e10	−	1.73531e10i	0.487506	−	0.844385i
$76$		0			0
$77$	−9.75851e9	−	1.04490e10i	−0.410851	−	0.439921i
$78$		0			0
$79$	3.25346e9	−	5.63515e9i	0.118959	−	0.206042i	−0.800397	−	0.599471i	$-0.795378\pi$
$79$	3.25346e9	−	5.63515e9i	0.118959	−	0.206042i	0.919355	+	0.393428i	$0.128711\pi$
$80$		0			0
$81$	1.48825e10	+	2.57773e10i	0.474252	+	0.821428i
$82$		0			0
$83$	1.57783e9			0.0439673			0.0219837	−	0.999758i	$-0.493002\pi$
$83$	1.57783e9			0.0439673			0.0219837	+	0.999758i	$0.493002\pi$
$84$		0			0
$85$	−3.51897e8			−0.00860223
$86$		0			0
$87$	−3.76285e10	−	6.51744e10i	−0.809395	−	1.40191i
$88$		0			0
$89$	4.14844e10	−	7.18531e10i	0.787480	−	1.36396i	−0.140026	−	0.990148i	$-0.544718\pi$
$89$	4.14844e10	−	7.18531e10i	0.787480	−	1.36396i	0.927506	−	0.373808i	$-0.121948\pi$
$90$		0			0
$91$	3.51656e10	−	8.14644e9i	0.590732	−	0.136848i
$92$		0			0
$93$	3.04753e10	−	5.27848e10i	0.454247	−	0.786779i
$94$		0			0
$95$	6.19006e8	+	1.07215e9i	0.00820758	+	0.0142159i
$96$		0			0
$97$	−6.77303e10			−0.800826			−0.400413	−	0.916335i	$-0.631133\pi$
$97$	−6.77303e10			−0.800826			−0.400413	+	0.916335i	$0.631133\pi$
$98$		0			0
$99$	−2.79585e9			−0.0295475
$100$		0			0
$101$	3.47903e10	+	6.02586e10i	0.329375	+	0.570494i	0.982388	−	0.186853i	$-0.0598287\pi$
$101$	3.47903e10	+	6.02586e10i	0.329375	+	0.570494i	−0.653013	+	0.757347i	$0.726495\pi$
$102$		0			0
$103$	−3.22736e10	+	5.58995e10i	−0.274311	+	0.475120i	−0.969961	−	0.243260i	$-0.921783\pi$
$103$	−3.22736e10	+	5.58995e10i	−0.274311	+	0.475120i	0.695650	+	0.718381i	$0.255116\pi$
$104$		0			0
$105$	1.46749e9	−	3.39957e8i	0.0112210	−	0.00259946i
$106$		0			0
$107$	6.79920e10	−	1.17766e11i	0.468648	−	0.811722i	−0.530710	−	0.847554i	$-0.678075\pi$
$107$	6.79920e10	−	1.17766e11i	0.468648	−	0.811722i	0.999358	+	0.0358314i	$0.0114079\pi$
$108$		0			0
$109$	−6.73541e10	−	1.16661e11i	−0.419294	−	0.726238i	0.576575	−	0.817044i	$-0.304389\pi$
$109$	−6.73541e10	−	1.16661e11i	−0.419294	−	0.726238i	−0.995869	+	0.0908063i	$0.971056\pi$
$110$		0			0
$111$	2.40582e11			1.35515
$112$		0			0
$113$	1.89413e11			0.967114			0.483557	−	0.875313i	$-0.339345\pi$
$113$	1.89413e11			0.967114			0.483557	+	0.875313i	$0.339345\pi$
$114$		0			0
$115$	−2.71628e8	−	4.70474e8i	−0.00125932	−	0.00218121i
$116$		0			0
$117$	3.52941e9	−	6.11312e9i	0.0148826	−	0.0257775i
$118$		0			0
$119$	1.29401e11	+	1.38557e11i	0.497084	+	0.532255i
$120$		0			0
$121$	9.09674e10	−	1.57560e11i	0.318835	−	0.552239i
$122$		0			0
$123$	−1.60962e11	−	2.78794e11i	−0.515519	−	0.892905i
$124$		0			0
$125$	−8.05970e9			−0.0236218
$126$		0			0
$127$	2.77933e9			0.00746482			0.00373241	−	0.999993i	$-0.498812\pi$
$127$	2.77933e9			0.00746482			0.00373241	+	0.999993i	$0.498812\pi$
$128$		0			0
$129$	−2.48822e11	−	4.30973e11i	−0.613262	−	1.06220i
$130$		0			0
$131$	4.00355e11	−	6.93435e11i	0.906678	−	1.57041i	0.0880289	−	0.996118i	$-0.471943\pi$
$131$	4.00355e11	−	6.93435e11i	0.906678	−	1.57041i	0.818649	−	0.574294i	$-0.194723\pi$
$132$		0			0
$133$	1.94528e11	−	6.37986e11i	0.405320	−	1.32931i
$134$		0			0
$135$	3.14776e9	−	5.45208e9i	0.00604179	−	0.0104647i
$136$		0			0
$137$	4.04399e10	+	7.00440e10i	0.0715892	+	0.123996i	0.899598	−	0.436719i	$-0.143860\pi$
$137$	4.04399e10	+	7.00440e10i	0.0715892	+	0.123996i	−0.828009	+	0.560715i	$0.810526\pi$
$138$		0			0
$139$	−2.27218e11			−0.371416			−0.185708	−	0.982605i	$-0.559458\pi$
$139$	−2.27218e11			−0.371416			−0.185708	+	0.982605i	$0.559458\pi$
$140$		0			0
$141$	5.83705e11			0.882041
$142$		0			0
$143$	−1.30500e11	−	2.26033e11i	−0.182500	−	0.316100i
$144$		0			0
$145$	−7.56708e9	+	1.31066e10i	−0.00980402	+	0.0169811i
$146$		0			0
$147$	−6.73487e11	−	4.52802e11i	−0.809252	−	0.544081i
$148$		0			0
$149$	−1.90994e11	+	3.30812e11i	−0.213057	+	0.369026i	−0.952670	−	0.304007i	$-0.901675\pi$
$149$	−1.90994e11	+	3.30812e11i	−0.213057	+	0.369026i	0.739613	+	0.673033i	$0.235009\pi$
$150$		0			0
$151$	−2.18087e11	−	3.77738e11i	−0.226077	−	0.391577i	0.730565	−	0.682843i	$-0.239257\pi$
$151$	−2.18087e11	−	3.77738e11i	−0.226077	−	0.391577i	−0.956642	+	0.291266i	$0.905923\pi$
$152$		0			0
$153$	3.70739e10			0.0357491
$154$		0			0
$155$	−1.22572e10			−0.0110044
$156$		0			0
$157$	−5.61440e11	−	9.72443e11i	−0.469738	−	0.813610i	0.529664	−	0.848208i	$-0.322318\pi$
$157$	−5.61440e11	−	9.72443e11i	−0.469738	−	0.813610i	−0.999401	+	0.0345981i	$0.988985\pi$
$158$		0			0
$159$	−6.92551e10	+	1.19953e11i	−0.0540465	+	0.0936112i
$160$		0			0
$161$	−8.53617e10	+	2.79957e11i	−0.0621900	+	0.203962i
$162$		0			0
$163$	1.25076e12	−	2.16638e12i	0.851416	−	1.47470i	−0.0285142	−	0.999593i	$-0.509078\pi$
$163$	1.25076e12	−	2.16638e12i	0.851416	−	1.47470i	0.879930	−	0.475103i	$-0.157589\pi$
$164$		0			0
$165$	−5.44588e9	−	9.43254e9i	−0.00346662	−	0.00600436i
$166$		0			0
$167$	−8.93153e11			−0.532090			−0.266045	−	0.963961i	$-0.585717\pi$
$167$	−8.93153e11			−0.532090			−0.266045	+	0.963961i	$0.585717\pi$
$168$		0			0
$169$	−1.13320e12			−0.632309
$170$		0			0
$171$	−6.52151e10	−	1.12956e11i	−0.0341090	−	0.0590786i
$172$		0			0
$173$	−3.48448e11	+	6.03530e11i	−0.170956	+	0.296105i	−0.938754	−	0.344587i	$-0.888019\pi$
$173$	−3.48448e11	+	6.03530e11i	−0.170956	+	0.296105i	0.767798	+	0.640692i	$0.221352\pi$
$174$		0			0
$175$	1.48177e12	+	1.58662e12i	0.682452	+	0.730739i
$176$		0			0
$177$	2.08484e12	−	3.61105e12i	0.902028	−	1.56236i
$178$		0			0
$179$	1.12918e12	+	1.95579e12i	0.459272	+	0.795482i	0.998923	−	0.0464068i	$-0.0147771\pi$
$179$	1.12918e12	+	1.95579e12i	0.459272	+	0.795482i	−0.539651	+	0.841889i	$0.681444\pi$
$180$		0			0
$181$	1.68291e12			0.643916			0.321958	−	0.946754i	$-0.395659\pi$
$181$	1.68291e12			0.643916			0.321958	+	0.946754i	$0.395659\pi$
$182$		0			0
$183$	−1.61110e12			−0.580286
$184$		0			0
$185$	−2.41905e10	−	4.18992e10i	−0.00820731	−	0.0142155i
$186$		0			0
$187$	6.85406e11	−	1.18716e12i	0.219189	−	0.379647i
$188$		0			0
$189$	−3.30423e12	+	7.65456e11i	−0.996622	+	0.230877i
$190$		0			0
$191$	−2.49846e12	+	4.32746e12i	−0.711196	+	1.23183i	0.253212	+	0.967411i	$0.418513\pi$
$191$	−2.49846e12	+	4.32746e12i	−0.711196	+	1.23183i	−0.964408	+	0.264417i	$0.914820\pi$
$192$		0			0
$193$	1.76236e12	+	3.05249e12i	0.473727	+	0.820520i	0.999548	−	0.0300760i	$-0.00957492\pi$
$193$	1.76236e12	+	3.05249e12i	0.473727	+	0.820520i	−0.525820	+	0.850596i	$0.676242\pi$
$194$		0			0
$195$	2.74990e10			0.00698435
$196$		0			0
$197$	2.05794e12			0.494162			0.247081	−	0.968995i	$-0.420529\pi$
$197$	2.05794e12			0.494162			0.247081	+	0.968995i	$0.420529\pi$
$198$		0			0
$199$	2.75717e12	+	4.77556e12i	0.626285	+	1.08476i	0.988291	+	0.152581i	$0.0487585\pi$
$199$	2.75717e12	+	4.77556e12i	0.626285	+	1.08476i	−0.362006	+	0.932176i	$0.617908\pi$
$200$		0			0
$201$	−3.53884e12	+	6.12945e12i	−0.760822	+	1.31778i
$202$		0			0
$203$	7.94323e12	−	1.84012e12i	1.61722	−	0.374644i
$204$		0			0
$205$	−3.23694e10	+	5.60654e10i	−0.00624436	+	0.0108156i
$206$		0			0
$207$	2.86173e10	+	4.95666e10i	0.00523349	+	0.00906467i
$208$		0			0
$209$	−4.82267e12			−0.836533
$210$		0			0
$211$	−6.44132e12			−1.06028			−0.530141	−	0.847909i	$-0.677861\pi$
$211$	−6.44132e12			−1.06028			−0.530141	+	0.847909i	$0.677861\pi$
$212$		0			0
$213$	2.42314e12	+	4.19700e12i	0.378696	+	0.655920i
$214$		0			0
$215$	−5.00381e10	+	8.66685e10i	−0.00742830	+	0.0128662i
$216$		0			0
$217$	4.50727e12	+	4.82618e12i	0.635894	+	0.680887i
$218$		0			0
$219$	−2.89075e12	+	5.00692e12i	−0.387764	+	0.671626i
$220$		0			0
$221$	1.73048e12	+	2.99728e12i	0.220805	+	0.382445i
$222$		0			0
$223$	−1.39124e13			−1.68937			−0.844687	−	0.535260i	$-0.820214\pi$
$223$	−1.39124e13			−1.68937			−0.844687	+	0.535260i	$0.820214\pi$
$224$		0			0
$225$	4.24533e11			0.0490803
$226$		0			0
$227$	−6.20084e11	−	1.07402e12i	−0.0682823	−	0.118268i	0.829863	−	0.557967i	$-0.188419\pi$
$227$	−6.20084e11	−	1.07402e12i	−0.0682823	−	0.118268i	−0.898145	+	0.439699i	$0.855085\pi$
$228$		0			0
$229$	−1.12150e12	+	1.94250e12i	−0.117680	+	0.203828i	−0.918848	−	0.394612i	$-0.870879\pi$
$229$	−1.12150e12	+	1.94250e12i	−0.117680	+	0.203828i	0.801168	+	0.598440i	$0.204213\pi$
$230$		0			0
$231$	−1.71142e12	+	5.61286e12i	−0.171194	+	0.561459i
$232$		0			0
$233$	−9.96014e11	+	1.72515e12i	−0.0950185	+	0.164577i	−0.909616	−	0.415449i	$-0.863624\pi$
$233$	−9.96014e11	+	1.72515e12i	−0.0950185	+	0.164577i	0.814598	+	0.580026i	$0.196958\pi$
$234$		0			0
$235$	−5.86915e10	−	1.01657e11i	−0.00534198	−	0.00925258i
$236$		0			0
$237$	−2.67062e12			−0.232005
$238$		0			0
$239$	8.92226e12			0.740093			0.370047	−	0.929013i	$-0.379342\pi$
$239$	8.92226e12			0.740093			0.370047	+	0.929013i	$0.379342\pi$
$240$		0			0
$241$	−6.72045e12	−	1.16402e13i	−0.532482	−	0.922286i	−0.999281	−	0.0379222i	$-0.987926\pi$
$241$	−6.72045e12	−	1.16402e13i	−0.532482	−	0.922286i	0.466799	−	0.884364i	$-0.345407\pi$
$242$		0			0
$243$	−6.47744e11	+	1.12193e12i	−0.0490421	+	0.0849434i
$244$		0			0
$245$	−1.11399e10	+	1.62822e11i	−0.000806249	+	0.0117842i
$246$		0			0
$247$	6.08802e12	−	1.05448e13i	0.421350	−	0.729800i
$248$		0			0
$249$	−3.23792e11	−	5.60825e11i	−0.0214373	−	0.0371305i
$250$		0			0
$251$	−1.62750e12			−0.103114			−0.0515568	−	0.998670i	$-0.516418\pi$
$251$	−1.62750e12			−0.103114			−0.0515568	+	0.998670i	$0.516418\pi$
$252$		0			0
$253$	2.11626e12			0.128353
$254$		0			0
$255$	7.22141e10	+	1.25079e11i	0.00419422	+	0.00726460i
$256$		0			0
$257$	−1.34604e13	+	2.33142e13i	−0.748906	+	1.29714i	0.199442	+	0.979910i	$0.436087\pi$
$257$	−1.34604e13	+	2.33142e13i	−0.748906	+	1.29714i	−0.948348	+	0.317233i	$0.897246\pi$
$258$		0			0
$259$	−7.60209e12	+	2.49323e13i	−0.405307	+	1.32927i
$260$		0			0
$261$	7.97226e11	−	1.38084e12i	0.0407435	−	0.0705698i
$262$		0			0
$263$	6.19104e12	+	1.07232e13i	0.303394	+	0.525494i	0.976902	−	0.213686i	$-0.0685468\pi$
$263$	6.19104e12	+	1.07232e13i	0.303394	+	0.525494i	−0.673508	+	0.739180i	$0.735213\pi$
$264$		0			0
$265$	2.78544e10			0.00130931
$266$		0			0
$267$	−3.40527e13			−1.53582
$268$		0			0
$269$	−1.33116e13	−	2.30564e13i	−0.576226	−	0.998053i	−0.995907	−	0.0903811i	$-0.971192\pi$
$269$	−1.33116e13	−	2.30564e13i	−0.576226	−	0.998053i	0.419681	−	0.907672i	$-0.362142\pi$
$270$		0			0
$271$	4.80734e12	−	8.32655e12i	0.199790	−	0.346046i	−0.748670	−	0.662943i	$-0.769307\pi$
$271$	4.80734e12	−	8.32655e12i	0.199790	−	0.346046i	0.948460	+	0.316896i	$0.102641\pi$
$272$		0			0
$273$	−1.01121e13	−	1.08275e13i	−0.403594	−	0.432151i
$274$		0			0
$275$	7.84858e12	−	1.35941e13i	0.300927	−	0.521221i
$276$		0			0
$277$	2.12538e13	+	3.68127e13i	0.783066	+	1.35631i	0.930147	+	0.367186i	$0.119679\pi$
$277$	2.12538e13	+	3.68127e13i	0.783066	+	1.35631i	−0.147081	+	0.989124i	$0.546988\pi$
$278$		0			0
$279$	1.29135e12			0.0457320
$280$		0			0
$281$	4.37974e12			0.149130			0.0745648	−	0.997216i	$-0.476243\pi$
$281$	4.37974e12			0.149130			0.0745648	+	0.997216i	$0.476243\pi$
$282$		0			0
$283$	1.13026e13	+	1.95767e13i	0.370129	+	0.641082i	0.989585	−	0.143949i	$-0.0459801\pi$
$283$	1.13026e13	+	1.95767e13i	0.370129	+	0.641082i	−0.619456	+	0.785031i	$0.712647\pi$
$284$		0			0
$285$	2.54058e11	−	4.40041e11i	0.00800360	−	0.0138626i
$286$		0			0
$287$	3.39784e13	−	7.87142e12i	1.03004	−	0.238618i
$288$		0			0
$289$	8.04724e12	−	1.39382e13i	0.234806	−	0.406696i
$290$		0			0
$291$	1.38992e13	+	2.40741e13i	0.390462	+	0.676300i
$292$		0			0
$293$	−3.30451e13			−0.893996			−0.446998	−	0.894535i	$-0.647507\pi$
$293$	−3.30451e13			−0.893996			−0.446998	+	0.894535i	$0.647507\pi$
$294$		0			0
$295$	−8.38522e11			−0.0218521
$296$		0			0
$297$	1.22621e13	+	2.12386e13i	0.307896	+	0.533291i
$298$		0			0
$299$	−2.67151e12	+	4.62719e12i	−0.0646495	+	0.111976i
$300$		0			0
$301$	5.25254e13	−	1.21680e13i	1.22533	−	0.283860i
$302$		0			0
$303$	1.42789e13	−	2.47318e13i	0.321189	−	0.556316i
$304$		0			0
$305$	1.61996e11	+	2.80586e11i	0.00351444	+	0.00608718i
$306$		0			0
$307$	−7.44512e12			−0.155815			−0.0779077	−	0.996961i	$-0.524824\pi$
$307$	−7.44512e12			−0.155815			−0.0779077	+	0.996961i	$0.524824\pi$
$308$		0			0
$309$	2.64920e13			0.534987
$310$		0			0
$311$	−4.02873e13	−	6.97797e13i	−0.785211	−	1.36002i	−0.928873	−	0.370398i	$-0.879221\pi$
$311$	−4.02873e13	−	6.97797e13i	−0.785211	−	1.36002i	0.143663	−	0.989627i	$-0.454112\pi$
$312$		0			0
$313$	1.89603e13	−	3.28402e13i	0.356740	−	0.617892i	−0.630674	−	0.776048i	$-0.717222\pi$
$313$	1.89603e13	−	3.28402e13i	0.356740	−	0.617892i	0.987414	+	0.158156i	$0.0505549\pi$
$314$		0			0
$315$	2.17833e10	+	2.33245e10i	0.000395744	+	0.000423746i
$316$		0			0
$317$	5.22997e13	−	9.05858e13i	0.917642	−	1.58940i	0.114656	−	0.993405i	$-0.463423\pi$
$317$	5.22997e13	−	9.05858e13i	0.917642	−	1.58940i	0.802986	−	0.595998i	$-0.203243\pi$
$318$		0			0
$319$	−2.94775e13	−	5.10566e13i	−0.499623	−	0.865372i
$320$		0			0
$321$	−5.58116e13			−0.914002
$322$		0			0
$323$	6.39502e13			1.01211
$324$		0			0
$325$	1.98157e13	+	3.43218e13i	0.303146	+	0.525063i
$326$		0			0
$327$	−2.76440e13	+	4.78809e13i	−0.408873	+	0.708189i
$328$		0			0
$329$	−1.84443e13	+	6.04911e13i	−0.263807	+	0.865195i
$330$		0			0
$331$	2.32829e13	−	4.03272e13i	0.322094	−	0.557884i	−0.658826	−	0.752296i	$-0.728946\pi$
$331$	2.32829e13	−	4.03272e13i	0.322094	−	0.557884i	0.980920	+	0.194412i	$0.0622798\pi$
$332$		0			0
$333$	2.54858e12	+	4.41427e12i	0.0341079	+	0.0590766i
$334$		0			0
$335$	1.42332e12			0.0184313
$336$		0			0
$337$	−4.28829e13			−0.537427			−0.268713	−	0.963220i	$-0.586598\pi$
$337$	−4.28829e13			−0.537427			−0.268713	+	0.963220i	$0.586598\pi$
$338$		0			0
$339$	−3.88702e13	−	6.73251e13i	−0.471539	−	0.816730i
$340$		0			0
$341$	2.38739e13	−	4.13508e13i	0.280397	−	0.485662i
$342$		0			0
$343$	6.82066e13	−	5.54875e13i	0.775726	−	0.631069i
$344$		0			0
$345$	−1.11484e11	+	1.93096e11i	−0.00122803	+	0.00212700i
$346$		0			0
$347$	1.22347e13	+	2.11912e13i	0.130552	+	0.226122i	0.923889	−	0.382660i	$-0.124992\pi$
$347$	1.22347e13	+	2.11912e13i	0.130552	+	0.226122i	−0.793338	+	0.608782i	$0.791658\pi$
$348$		0			0
$349$	−1.72281e13			−0.178114			−0.0890570	−	0.996027i	$-0.528385\pi$
$349$	−1.72281e13			−0.178114			−0.0890570	+	0.996027i	$0.528385\pi$
$350$		0			0
$351$	−6.19174e13			−0.620331
$352$		0			0
$353$	−7.88870e13	−	1.36636e14i	−0.766028	−	1.32680i	−0.939702	−	0.341996i	$-0.888897\pi$
$353$	−7.88870e13	−	1.36636e14i	−0.766028	−	1.32680i	0.173674	−	0.984803i	$-0.444436\pi$
$354$		0			0
$355$	4.87292e11	−	8.44015e11i	0.00458705	−	0.00794501i
$356$		0			0
$357$	2.26939e13	−	7.44283e13i	0.207126	−	0.679302i
$358$		0			0
$359$	3.45620e13	−	5.98631e13i	0.305900	−	0.529834i	−0.671562	−	0.740949i	$-0.734376\pi$
$359$	3.45620e13	−	5.98631e13i	0.305900	−	0.529834i	0.977461	+	0.211115i	$0.0677094\pi$
$360$		0			0
$361$	−5.42469e13	−	9.39585e13i	−0.465678	−	0.806578i
$362$		0			0
$363$	−7.46712e13			−0.621823
$364$		0			0
$365$	1.16266e12			0.00939379
$366$		0			0
$367$	4.35628e13	+	7.54531e13i	0.341549	+	0.591580i	0.984721	−	0.174142i	$-0.0557152\pi$
$367$	4.35628e13	+	7.54531e13i	0.341549	+	0.591580i	−0.643172	+	0.765722i	$0.722382\pi$
$368$		0			0
$369$	3.41026e12	−	5.90674e12i	0.0259503	−	0.0449472i
$370$		0			0
$371$	−1.02427e13	−	1.09675e13i	−0.0756589	−	0.0810122i
$372$		0			0
$373$	2.60882e13	−	4.51861e13i	0.187088	−	0.324046i	−0.757190	−	0.653194i	$-0.773428\pi$
$373$	2.60882e13	−	4.51861e13i	0.187088	−	0.324046i	0.944278	+	0.329149i	$0.106762\pi$
$374$		0			0
$375$	1.65396e12	+	2.86475e12i	0.0115174	+	0.0199487i
$376$		0			0
$377$	1.48847e14			1.00661
$378$		0			0
$379$	9.15118e13			0.601121			0.300560	−	0.953763i	$-0.402826\pi$
$379$	9.15118e13			0.601121			0.300560	+	0.953763i	$0.402826\pi$
$380$		0			0
$381$	−5.70357e11	−	9.87888e11i	−0.00363965	−	0.00630406i
$382$		0			0
$383$	6.61057e13	−	1.14498e14i	0.409869	−	0.709915i	−0.585005	−	0.811029i	$-0.698908\pi$
$383$	6.61057e13	−	1.14498e14i	0.409869	−	0.709915i	0.994875	+	0.101115i	$0.0322410\pi$
$384$		0			0
$385$	1.14960e12	−	2.66316e11i	0.00692651	−	0.00160459i
$386$		0			0
$387$	5.27174e12	−	9.13092e12i	0.0308705	−	0.0534693i
$388$		0			0
$389$	2.32466e13	+	4.02642e13i	0.132323	+	0.229190i	0.924572	−	0.381008i	$-0.124423\pi$
$389$	2.32466e13	+	4.02642e13i	0.132323	+	0.229190i	−0.792249	+	0.610199i	$0.791090\pi$
$390$		0			0
$391$	−2.80622e13			−0.155292
$392$		0			0
$393$	−3.28634e14			−1.76829
$394$		0			0
$395$	2.68531e11	+	4.65109e11i	0.00140511	+	0.00243372i
$396$		0			0
$397$	1.27473e14	−	2.20790e14i	0.648739	−	1.12365i	−0.334685	−	0.942330i	$-0.608630\pi$
$397$	1.27473e14	−	2.20790e14i	0.648739	−	1.12365i	0.983424	−	0.181319i	$-0.0580368\pi$
$398$		0			0
$399$	−2.66686e14	+	6.17804e13i	−1.32023	+	0.305844i
$400$		0			0
$401$	−1.22750e14	+	2.12609e14i	−0.591189	+	1.02397i	0.402883	+	0.915251i	$0.368008\pi$
$401$	−1.22750e14	+	2.12609e14i	−0.591189	+	1.02397i	−0.994073	+	0.108718i	$0.965325\pi$
$402$		0			0
$403$	6.02756e13	+	1.04400e14i	0.282464	+	0.489243i
$404$		0			0
$405$	−2.45672e12			−0.0112035
$406$		0			0
$407$	1.88468e14			0.836506
$408$		0			0
$409$	1.32933e14	+	2.30246e14i	0.574319	+	0.994750i	0.996115	+	0.0880595i	$0.0280666\pi$
$409$	1.32933e14	+	2.30246e14i	0.574319	+	0.994750i	−0.421796	+	0.906691i	$0.638600\pi$
$410$		0			0
$411$	1.65977e13	−	2.87480e13i	0.0698100	−	0.120914i
$412$		0			0
$413$	3.08346e14	+	3.30163e14i	1.26274	+	1.35208i
$414$		0			0
$415$	−6.51146e10	+	1.12782e11i	−0.000259665	+	0.000449753i
$416$		0			0
$417$	4.66283e13	+	8.07626e13i	0.181093	+	0.313662i
$418$		0			0
$419$	−2.37343e14			−0.897842			−0.448921	−	0.893571i	$-0.648192\pi$
$419$	−2.37343e14			−0.897842			−0.448921	+	0.893571i	$0.648192\pi$
$420$		0			0
$421$	3.23863e14			1.19346			0.596732	−	0.802440i	$-0.296465\pi$
$421$	3.23863e14			1.19346			0.596732	+	0.802440i	$0.296465\pi$
$422$		0			0
$423$	6.18342e12	+	1.07100e13i	0.0222002	+	0.0384518i
$424$		0			0
$425$	−1.04075e14	+	1.80263e14i	−0.364088	+	0.630619i
$426$		0			0
$427$	5.09088e13	−	1.66963e14i	0.173556	−	0.569204i
$428$		0			0
$429$	−5.35611e13	+	9.27705e13i	−0.177965	+	0.308244i
$430$		0			0
$431$	2.90007e14	+	5.02307e14i	0.939256	+	1.62684i	0.766863	+	0.641811i	$0.221817\pi$
$431$	2.90007e14	+	5.02307e14i	0.939256	+	1.62684i	0.172393	+	0.985028i	$0.444850\pi$
$432$		0			0
$433$	−5.57641e14			−1.76064			−0.880322	−	0.474377i	$-0.842673\pi$
$433$	−5.57641e14			−1.76064			−0.880322	+	0.474377i	$0.842673\pi$
$434$		0			0
$435$	6.21149e12			0.0191207
$436$		0			0
$437$	4.93631e13	+	8.54994e13i	0.148168	+	0.256635i
$438$		0			0
$439$	−2.69234e14	+	4.66326e14i	−0.788087	+	1.36501i	0.139050	+	0.990285i	$0.455595\pi$
$439$	−2.69234e14	+	4.66326e14i	−0.788087	+	1.36501i	−0.927137	+	0.374722i	$0.877738\pi$
$440$		0			0
$441$	1.17364e12	−	1.71540e13i	0.00335060	−	0.0489727i
$442$		0			0
$443$	−1.69914e14	+	2.94299e14i	−0.473160	+	0.819537i	−0.999528	−	0.0307199i	$-0.990220\pi$
$443$	−1.69914e14	+	2.94299e14i	−0.473160	+	0.819537i	0.526368	+	0.850257i	$0.323553\pi$
$444$		0			0
$445$	3.42400e12	+	5.93054e12i	0.00930151	+	0.0161107i
$446$		0			0
$447$	1.56779e14			0.415524
$448$		0			0
$449$	−5.79723e13			−0.149922			−0.0749611	−	0.997186i	$-0.523883\pi$
$449$	−5.79723e13			−0.149922			−0.0749611	+	0.997186i	$0.523883\pi$
$450$		0			0
$451$	−1.26095e14	−	2.18403e14i	−0.318219	−	0.551172i
$452$		0			0
$453$	−8.95090e13	+	1.55034e14i	−0.220458	+	0.381845i
$454$		0			0
$455$	−8.68932e11	+	2.84980e12i	−0.00208893	+	0.00685096i
$456$		0			0
$457$	−2.41252e13	+	4.17861e13i	−0.0566150	+	0.0980601i	−0.892944	−	0.450168i	$-0.851364\pi$
$457$	−2.41252e13	+	4.17861e13i	−0.0566150	+	0.0980601i	0.836329	+	0.548228i	$0.184697\pi$
$458$		0			0
$459$	−1.62599e14	−	2.81630e14i	−0.372519	−	0.645223i
$460$		0			0
$461$	7.60461e14			1.70107			0.850535	−	0.525919i	$-0.176278\pi$
$461$	7.60461e14			1.70107			0.850535	+	0.525919i	$0.176278\pi$
$462$		0			0
$463$	−1.75084e14			−0.382430			−0.191215	−	0.981548i	$-0.561243\pi$
$463$	−1.75084e14			−0.382430			−0.191215	+	0.981548i	$0.561243\pi$
$464$		0			0
$465$	2.51534e12	+	4.35670e12i	0.00536545	+	0.00929323i
$466$		0			0
$467$	6.90586e12	−	1.19613e13i	0.0143872	−	0.0249193i	−0.858742	−	0.512408i	$-0.828754\pi$
$467$	6.90586e12	−	1.19613e13i	0.0143872	−	0.0249193i	0.873129	+	0.487489i	$0.162087\pi$
$468$		0			0
$469$	−5.23391e14	−	5.60423e14i	−1.06506	−	1.14042i
$470$		0			0
$471$	−2.30431e14	+	3.99118e14i	−0.458064	+	0.793390i
$472$		0			0
$473$	−1.94923e14	−	3.37617e14i	−0.378554	−	0.655674i
$474$		0			0
$475$	7.32294e14			1.38954
$476$		0			0
$477$	−2.93458e12			−0.00544121
$478$		0			0
$479$	1.43306e14	+	2.48213e14i	0.259668	+	0.449758i	0.966153	−	0.257970i	$-0.0830536\pi$
$479$	1.43306e14	+	2.48213e14i	0.259668	+	0.449758i	−0.706485	+	0.707728i	$0.749720\pi$
$480$		0			0
$481$	−2.37918e14	+	4.12086e14i	−0.421336	+	0.729776i
$482$		0			0
$483$	1.17026e14	−	2.71101e13i	0.202569	−	0.0469269i
$484$		0			0
$485$	2.79513e12	−	4.84130e12i	0.00472958	−	0.00819186i
$486$		0			0
$487$	−8.99929e13	−	1.55872e14i	−0.148867	−	0.257845i	0.781942	−	0.623351i	$-0.214229\pi$
$487$	−8.99929e13	−	1.55872e14i	−0.148867	−	0.257845i	−0.930809	+	0.365506i	$0.880896\pi$
$488$		0			0
$489$	−1.02669e15			−1.66051
$490$		0			0
$491$	−1.03614e14			−0.163858			−0.0819292	−	0.996638i	$-0.526108\pi$
$491$	−1.03614e14			−0.163858			−0.0819292	+	0.996638i	$0.526108\pi$
$492$		0			0
$493$	3.90882e14	+	6.77027e14i	0.604488	+	1.04700i
$494$		0			0
$495$	1.15381e11	−	1.99845e11i	0.000174503	−	0.000302249i
$496$		0			0
$497$	−5.11515e14	+	1.18497e14i	−0.756656	+	0.175286i
$498$		0			0
$499$	4.96533e13	−	8.60021e13i	0.0718448	−	0.124439i	−0.827865	−	0.560927i	$-0.810445\pi$
$499$	4.96533e13	−	8.60021e13i	0.0718448	−	0.124439i	0.899710	+	0.436488i	$0.143778\pi$
$500$		0			0
$501$	1.83288e14	+	3.17464e14i	0.259433	+	0.449352i
$502$		0			0
$503$	−8.49895e14			−1.17690			−0.588452	−	0.808532i	$-0.700262\pi$
$503$	−8.49895e14			−1.17690			−0.588452	+	0.808532i	$0.700262\pi$
$504$		0			0
$505$	−5.74298e12			−0.00778098
$506$		0			0
$507$	2.32548e14	+	4.02785e14i	0.308297	+	0.533986i
$508$		0			0
$509$	6.74309e14	−	1.16794e15i	0.874805	−	1.51521i	0.0178344	−	0.999841i	$-0.494323\pi$
$509$	6.74309e14	−	1.16794e15i	0.874805	−	1.51521i	0.856970	−	0.515366i	$-0.172344\pi$
$510$		0			0
$511$	−4.27538e14	−	4.57789e14i	−0.542825	−	0.581233i
$512$		0			0
$513$	−5.72043e14	+	9.90807e14i	−0.710858	+	1.23124i
$514$		0			0
$515$	−2.66377e12	−	4.61378e12i	−0.00324009	−	0.00561200i
$516$		0			0
$517$	4.57265e14			0.544465
$518$		0			0
$519$	2.86026e14			0.333415
$520$		0			0
$521$	−1.82835e14	−	3.16680e14i	−0.208666	−	0.361421i	0.742628	−	0.669704i	$-0.233579\pi$
$521$	−1.82835e14	−	3.16680e14i	−0.208666	−	0.361421i	−0.951295	+	0.308283i	$0.900246\pi$
$522$		0			0
$523$	−1.47198e14	+	2.54955e14i	−0.164491	+	0.284908i	−0.936475	−	0.350735i	$-0.885932\pi$
$523$	−1.47198e14	+	2.54955e14i	−0.164491	+	0.284908i	0.771983	+	0.635643i	$0.219265\pi$
$524$		0			0
$525$	2.59868e14	−	8.52279e14i	0.284366	−	0.932622i
$526$		0			0
$527$	−3.16576e14	+	5.48325e14i	−0.339249	+	0.587597i
$528$		0			0
$529$	4.54744e14	+	7.87639e14i	0.477266	+	0.826649i
$530$		0			0
$531$	8.83421e13			0.0908130
$532$		0			0
$533$	6.36716e14			0.641130
$534$		0			0
$535$	5.61186e12	+	9.72002e12i	0.00553555	+	0.00958785i
$536$		0			0
$537$	4.63446e14	−	8.02711e14i	0.447858	−	0.775713i
$538$		0			0
$539$	−5.27599e14	−	3.54718e14i	−0.499534	−	0.335850i
$540$		0			0
$541$	−2.75848e14	+	4.77783e14i	−0.255909	+	0.443247i	−0.965142	−	0.261727i	$-0.915708\pi$
$541$	−2.75848e14	+	4.77783e14i	−0.255909	+	0.443247i	0.709233	+	0.704974i	$0.249041\pi$
$542$		0			0
$543$	−3.45357e14	−	5.98176e14i	−0.313956	−	0.543788i
$544$		0			0
$545$	1.11184e13			0.00990518
$546$		0			0
$547$	3.58362e14			0.312890			0.156445	−	0.987687i	$-0.449997\pi$
$547$	3.58362e14			0.312890			0.156445	+	0.987687i	$0.449997\pi$
$548$		0			0
$549$	−1.70670e13	−	2.95610e13i	−0.0146053	−	0.0252971i
$550$		0			0
$551$	1.37517e15	−	2.38186e15i	1.15351	−	1.99794i
$552$		0			0
$553$	8.43882e13	−	2.76764e14i	0.0693894	−	0.227574i
$554$		0			0
$555$	−9.92848e12	+	1.71966e13i	−0.00800334	+	0.0138622i
$556$		0			0
$557$	2.87913e14	+	4.98681e14i	0.227540	+	0.394111i	0.957079	−	0.289829i	$-0.0935983\pi$
$557$	2.87913e14	+	4.98681e14i	0.227540	+	0.394111i	−0.729538	+	0.683940i	$0.760265\pi$
$558$		0			0
$559$	9.84265e14			0.762689
$560$		0			0
$561$	−5.62620e14			−0.427483
$562$		0			0
$563$	7.45446e14	+	1.29115e15i	0.555418	+	0.962013i	0.997871	+	0.0652209i	$0.0207752\pi$
$563$	7.45446e14	+	1.29115e15i	0.555418	+	0.962013i	−0.442452	+	0.896792i	$0.645891\pi$
$564$		0			0
$565$	−7.81678e12	+	1.35391e13i	−0.00571165	+	0.00989287i
$566$		0			0
$567$	9.03397e14	+	9.67317e14i	0.647398	+	0.693205i
$568$		0			0
$569$	−4.36171e13	+	7.55470e13i	−0.0306577	+	0.0531006i	−0.880947	−	0.473215i	$-0.843093\pi$
$569$	−4.36171e13	+	7.55470e13i	−0.0306577	+	0.0531006i	0.850289	+	0.526315i	$0.176427\pi$
$570$		0			0
$571$	−5.66496e14	−	9.81199e14i	−0.390569	−	0.676486i	0.601955	−	0.798530i	$-0.294388\pi$
$571$	−5.66496e14	−	9.81199e14i	−0.390569	−	0.676486i	−0.992525	+	0.122044i	$0.961055\pi$
$572$		0			0
$573$	2.05088e15			1.38704
$574$		0			0
$575$	−3.21341e14			−0.213203
$576$		0			0
$577$	−1.08768e15	−	1.88391e15i	−0.707999	−	1.22629i	−0.965598	−	0.260038i	$-0.916265\pi$
$577$	−1.08768e15	−	1.88391e15i	−0.707999	−	1.22629i	0.257599	−	0.966252i	$-0.417068\pi$
$578$		0			0
$579$	7.23321e14	−	1.25283e15i	0.461954	−	0.800128i
$580$		0			0
$581$	6.83514e13	−	1.58342e13i	0.0428330	−	0.00992266i
$582$		0			0
$583$	−5.42533e13	+	9.39694e13i	−0.0333618	+	0.0577843i
$584$		0			0
$585$	2.91307e11	+	5.04559e11i	0.000175790	+	0.000304477i
$586$		0			0
$587$	−1.36225e15			−0.806767			−0.403384	−	0.915031i	$-0.632166\pi$
$587$	−1.36225e15			−0.806767			−0.403384	+	0.915031i	$0.632166\pi$
$588$		0			0
$589$	2.22750e15			1.29474
$590$		0			0
$591$	−4.22319e14	−	7.31478e14i	−0.240940	−	0.417321i
$592$		0			0
$593$	−7.26854e14	+	1.25895e15i	−0.407049	+	0.705029i	−0.994558	−	0.104189i	$-0.966775\pi$
$593$	−7.26854e14	+	1.25895e15i	−0.407049	+	0.705029i	0.587509	+	0.809218i	$0.300109\pi$
$594$		0			0
$595$	−1.52441e13	+	3.53144e12i	−0.00838030	+	0.00194137i
$596$		0			0
$597$	1.13162e15	−	1.96002e15i	0.610720	−	1.05780i
$598$		0			0
$599$	3.18610e14	+	5.51849e14i	0.168816	+	0.292397i	0.938004	−	0.346625i	$-0.112672\pi$
$599$	3.18610e14	+	5.51849e14i	0.168816	+	0.292397i	−0.769188	+	0.639022i	$0.779339\pi$
$600$		0			0
$601$	−2.19039e15			−1.13949			−0.569746	−	0.821821i	$-0.692958\pi$
$601$	−2.19039e15			−1.13949			−0.569746	+	0.821821i	$0.692958\pi$
$602$		0			0
$603$	−1.49953e14			−0.0765968
$604$		0			0
$605$	7.50818e12	+	1.30046e13i	0.00376600	+	0.00652290i
$606$		0			0
$607$	6.75725e14	−	1.17039e15i	0.332838	−	0.576492i	−0.650229	−	0.759738i	$-0.725327\pi$
$607$	6.75725e14	−	1.17039e15i	0.332838	−	0.576492i	0.983067	+	0.183246i	$0.0586606\pi$
$608$		0			0
$609$	−2.28412e15	−	2.44573e15i	−1.10490	−	1.18308i
$610$		0			0
$611$	−5.77240e14	+	9.99810e14i	−0.274240	+	0.474997i
$612$		0			0
$613$	−1.77906e15	−	3.08143e15i	−0.830154	−	1.43787i	−0.897916	−	0.440168i	$-0.854919\pi$
$613$	−1.77906e15	−	3.08143e15i	−0.830154	−	1.43787i	0.0677616	−	0.997702i	$-0.478414\pi$
$614$		0			0
$615$	2.65706e13			0.0121784
$616$		0			0
$617$	2.06841e15			0.931256			0.465628	−	0.884980i	$-0.345828\pi$
$617$	2.06841e15			0.931256			0.465628	+	0.884980i	$0.345828\pi$
$618$		0			0
$619$	4.84119e14	+	8.38518e14i	0.214118	+	0.370863i	0.952999	−	0.302972i	$-0.0979790\pi$
$619$	4.84119e14	+	8.38518e14i	0.214118	+	0.370863i	−0.738881	+	0.673836i	$0.764646\pi$
$620$		0			0
$621$	2.51020e14	−	4.34780e14i	0.109070	−	0.188915i
$622$		0			0
$623$	1.07602e15	−	3.52899e15i	0.459343	−	1.50649i
$624$		0			0
$625$	−1.19159e15	+	2.06390e15i	−0.499791	+	0.865663i
$626$		0			0
$627$	9.89680e14	+	1.71418e15i	0.407872	+	0.706454i
$628$		0			0
$629$	−2.49915e15			−1.01208
$630$		0			0
$631$	6.10412e14			0.242919			0.121460	−	0.992596i	$-0.461243\pi$
$631$	6.10412e14			0.242919			0.121460	+	0.992596i	$0.461243\pi$
$632$		0			0
$633$	1.32185e15	+	2.28951e15i	0.516966	+	0.895412i
$634$		0			0
$635$	−1.14699e11	+	1.98664e11i	−4.40862e−5	+	7.63596e-5i
$636$		0			0
$637$	1.44162e15	−	7.05806e14i	0.544607	−	0.266636i
$638$		0			0
$639$	−5.13384e13	+	8.89208e13i	−0.0190629	+	0.0330178i
$640$		0			0
$641$	−3.88797e14	−	6.73416e14i	−0.141907	−	0.245790i	0.786308	−	0.617835i	$-0.211990\pi$
$641$	−3.88797e14	−	6.73416e14i	−0.141907	−	0.245790i	−0.928215	+	0.372045i	$0.878657\pi$
$642$		0			0
$643$	−3.64279e15			−1.30699			−0.653497	−	0.756929i	$-0.726699\pi$
$643$	−3.64279e15			−1.30699			−0.653497	+	0.756929i	$0.726699\pi$
$644$		0			0
$645$	4.10741e13			0.0144874
$646$		0			0
$647$	−9.72162e14	−	1.68383e15i	−0.337105	−	0.583883i	0.646782	−	0.762675i	$-0.276114\pi$
$647$	−9.72162e14	−	1.68383e15i	−0.337105	−	0.583883i	−0.983887	+	0.178792i	$0.942781\pi$
$648$		0			0
$649$	1.63323e15	−	2.82884e15i	0.556803	−	0.964411i
$650$		0			0
$651$	7.90469e14	−	2.59247e15i	0.264966	−	0.868997i
$652$		0			0
$653$	1.44193e15	−	2.49750e15i	0.475250	−	0.823157i	−0.524348	−	0.851504i	$-0.675691\pi$
$653$	1.44193e15	−	2.49750e15i	0.475250	−	0.823157i	0.999598	+	0.0283472i	$0.00902440\pi$
$654$		0			0
$655$	3.30441e13	+	5.72341e13i	0.0107094	+	0.0185493i
$656$		0			0
$657$	−1.22491e14			−0.0390387
$658$		0			0
$659$	−1.18466e15			−0.371299			−0.185649	−	0.982616i	$-0.559439\pi$
$659$	−1.18466e15			−0.371299			−0.185649	+	0.982616i	$0.559439\pi$
$660$		0			0
$661$	4.64870e14	+	8.05179e14i	0.143293	+	0.248190i	0.928735	−	0.370745i	$-0.120898\pi$
$661$	4.64870e14	+	8.05179e14i	0.143293	+	0.248190i	−0.785442	+	0.618935i	$0.787564\pi$
$662$		0			0
$663$	7.10237e14	−	1.23017e15i	0.215317	−	0.372941i
$664$		0			0
$665$	3.75748e13	+	4.02334e13i	0.0112041	+	0.0119969i
$666$		0			0
$667$	−6.03442e14	+	1.04519e15i	−0.176988	+	0.306552i
$668$		0			0
$669$	2.85503e15	+	4.94505e15i	0.823695	+	1.42668i
$670$		0			0
$671$	−1.26211e15			−0.358199
$672$		0			0
$673$	−2.31418e15			−0.646123			−0.323061	−	0.946378i	$-0.604712\pi$
$673$	−2.31418e15			−0.646123			−0.323061	+	0.946378i	$0.604712\pi$
$674$		0			0
$675$	−1.86192e15	−	3.22495e15i	−0.511436	−	0.885833i
$676$		0			0
$677$	−2.01319e15	+	3.48694e15i	−0.544059	+	0.942338i	0.454606	+	0.890693i	$0.349780\pi$
$677$	−2.01319e15	+	3.48694e15i	−0.544059	+	0.942338i	−0.998665	+	0.0516458i	$0.983553\pi$
$678$		0			0
$679$	−2.93407e15	+	6.79705e14i	−0.780166	+	0.180733i
$680$		0			0
$681$	−2.54500e14	+	4.40807e14i	−0.0665853	+	0.115329i
$682$		0			0
$683$	2.89159e15	+	5.00838e15i	0.744428	+	1.28939i	0.950461	+	0.310843i	$0.100611\pi$
$683$	2.89159e15	+	5.00838e15i	0.744428	+	1.28939i	−0.206033	+	0.978545i	$0.566055\pi$
$684$		0			0
$685$	−6.67558e12			−0.00169119
$686$		0			0
$687$	9.20591e14			0.229512
$688$		0			0
$689$	−1.36976e14	−	2.37249e14i	−0.0336077	−	0.0582102i
$690$		0			0
$691$	1.92557e15	−	3.33518e15i	0.464974	−	0.805359i	−0.534226	−	0.845342i	$-0.679397\pi$
$691$	1.92557e15	−	3.33518e15i	0.464974	−	0.805359i	0.999200	+	0.0399823i	$0.0127302\pi$
$692$		0			0
$693$	−1.21116e14	+	2.80576e13i	−0.0287852	+	0.00666835i
$694$		0			0
$695$	9.37694e12	−	1.62413e13i	0.00219354	−	0.00379932i
$696$		0			0
$697$	1.67206e15	+	2.89609e15i	0.385009	+	0.666856i
$698$		0			0
$699$	8.17585e14			0.185314
$700$		0			0
$701$	−8.22432e14			−0.183506			−0.0917531	−	0.995782i	$-0.529247\pi$
$701$	−8.22432e14			−0.183506			−0.0917531	+	0.995782i	$0.529247\pi$
$702$		0			0
$703$	4.39615e15	+	7.61435e15i	0.965647	+	1.67255i
$704$		0			0
$705$	−2.40887e13	+	4.17228e13i	−0.00520922	+	0.00902263i
$706$		0			0
$707$	2.11184e15	+	2.26126e15i	0.449628	+	0.481442i
$708$		0			0
$709$	−1.91175e15	+	3.31124e15i	−0.400752	+	0.694123i	−0.993817	−	0.111032i	$-0.964585\pi$
$709$	−1.91175e15	+	3.31124e15i	−0.400752	+	0.694123i	0.593065	+	0.805155i	$0.297918\pi$
$710$		0			0
$711$	−2.82909e13	−	4.90013e13i	−0.00583935	−	0.0101140i
$712$		0			0
$713$	−9.77457e14			−0.198658
$714$		0			0
$715$	2.15422e13			0.00431129
$716$		0			0
$717$	−1.83097e15	−	3.17134e15i	−0.360850	−	0.625010i
$718$		0			0
$719$	−3.93270e15	+	6.81163e15i	−0.763276	+	1.32203i	0.177877	+	0.984053i	$0.443077\pi$
$719$	−3.93270e15	+	6.81163e15i	−0.763276	+	1.32203i	−0.941153	+	0.337980i	$0.890256\pi$
$720$		0			0
$721$	−8.37113e14	+	2.74544e15i	−0.160007	+	0.524770i
$722$		0			0
$723$	−2.75826e15	+	4.77745e15i	−0.519248	+	0.899365i
$724$		0			0
$725$	4.47599e15	+	7.75264e15i	0.829908	+	1.43744i
$726$		0			0
$727$	−7.89509e15			−1.44184			−0.720922	−	0.693017i	$-0.756281\pi$
$727$	−7.89509e15			−1.44184			−0.720922	+	0.693017i	$0.756281\pi$
$728$		0			0
$729$	5.80449e15			1.04415
$730$		0			0
$731$	2.58475e15	+	4.47691e15i	0.458007	+	0.793292i
$732$		0			0
$733$	2.30159e15	−	3.98647e15i	0.401751	−	0.695852i	−0.592187	−	0.805801i	$-0.701735\pi$
$733$	2.30159e15	−	3.98647e15i	0.401751	−	0.695852i	0.993937	+	0.109948i	$0.0350686\pi$
$734$		0			0
$735$	6.01598e13	−	2.94538e13i	0.0103449	−	0.00506478i
$736$		0			0
$737$	−2.77227e15	+	4.80171e15i	−0.469639	+	0.813439i
$738$		0			0
$739$	1.83995e15	+	3.18689e15i	0.307088	+	0.531892i	0.977724	−	0.209895i	$-0.0673122\pi$
$739$	1.83995e15	+	3.18689e15i	0.307088	+	0.531892i	−0.670636	+	0.741786i	$0.733979\pi$
$740$		0			0
$741$	−4.99739e15			−0.821757
$742$		0			0
$743$	4.11841e15			0.667255			0.333627	−	0.942705i	$-0.391727\pi$
$743$	4.11841e15			0.667255			0.333627	+	0.942705i	$0.391727\pi$
$744$		0			0
$745$	−1.57641e13	−	2.73042e13i	−0.00251658	−	0.00435884i
$746$		0			0
$747$	6.86012e12	−	1.18821e13i	0.00107912	−	0.00186908i
$748$		0			0
$749$	1.76358e15	−	5.78393e15i	0.273366	−	0.896546i
$750$		0			0
$751$	2.13637e15	−	3.70031e15i	0.326331	−	0.565221i	−0.655450	−	0.755238i	$-0.727521\pi$
$751$	2.13637e15	−	3.70031e15i	0.326331	−	0.565221i	0.981781	+	0.190017i	$0.0608544\pi$
$752$		0			0
$753$	3.33986e14	+	5.78481e14i	0.0502755	+	0.0870797i
$754$		0			0
$755$	3.60005e13			0.00534073
$756$		0			0
$757$	−9.31509e15			−1.36195			−0.680973	−	0.732309i	$-0.738443\pi$
$757$	−9.31509e15			−1.36195			−0.680973	+	0.732309i	$0.738443\pi$
$758$		0			0
$759$	−4.34285e14	−	7.52205e14i	−0.0625814	−	0.108394i
$760$		0			0
$761$	1.16069e13	−	2.01037e13i	0.00164854	−	0.00285535i	−0.865200	−	0.501427i	$-0.832809\pi$
$761$	1.16069e13	−	2.01037e13i	0.00164854	−	0.00285535i	0.866848	+	0.498572i	$0.166142\pi$
$762$		0			0
$763$	−4.08852e15	−	4.37780e15i	−0.572376	−	0.612874i
$764$		0			0
$765$	−1.52998e12	+	2.65001e12i	−0.000211130	+	0.000365687i
$766$		0			0
$767$	4.12350e15	+	7.14211e15i	0.560908	+	0.971521i
$768$		0			0
$769$	−1.13137e16			−1.51709			−0.758545	−	0.651621i	$-0.774089\pi$
$769$	−1.13137e16			−1.51709			−0.758545	+	0.651621i	$0.774089\pi$
$770$		0			0
$771$	1.10491e16			1.46059
$772$		0			0
$773$	4.41869e15	+	7.65339e15i	0.575846	+	0.997394i	0.995949	+	0.0899177i	$0.0286604\pi$
$773$	4.41869e15	+	7.65339e15i	0.575846	+	0.997394i	−0.420104	+	0.907476i	$0.638006\pi$
$774$		0			0
$775$	−3.62511e15	+	6.27887e15i	−0.465759	+	0.806719i
$776$		0			0
$777$	1.04220e16	−	2.41436e15i	1.32019	−	0.305834i
$778$		0			0
$779$	5.88249e15	−	1.01888e16i	0.734692	−	1.27252i
$780$		0			0
$781$	1.89825e15	+	3.28786e15i	0.233761	+	0.404886i
$782$		0			0
$783$	−1.39860e16			−1.69825
$784$		0			0
$785$	9.26792e13			0.0110968
$786$		0			0
$787$	−7.96581e15	−	1.37972e16i	−0.940522	−	1.62903i	−0.764478	−	0.644650i	$-0.777003\pi$
$787$	−7.96581e15	−	1.37972e16i	−0.940522	−	1.62903i	−0.176044	−	0.984382i	$-0.556330\pi$
$788$		0			0
$789$	2.54098e15	−	4.40110e15i	0.295854	−	0.512434i
$790$		0			0
$791$	8.20534e15	−	1.90084e15i	0.942163	−	0.218261i
$792$		0			0
$793$	1.59326e15	−	2.75960e15i	0.180420	−	0.312496i
$794$		0			0
$795$	−5.71611e12	−	9.90059e12i	−0.000638383	−	0.00110571i
$796$		0			0
$797$	−1.59688e16			−1.75894			−0.879472	−	0.475951i	$-0.842104\pi$
$797$	−1.59688e16			−1.75894			−0.879472	+	0.475951i	$0.842104\pi$
$798$		0			0
$799$	−6.06349e15			−0.658742
$800$		0			0
$801$	−3.60734e14	−	6.24809e14i	−0.0386552	−	0.0669528i
$802$		0			0
$803$	−2.26456e15	+	3.92234e15i	−0.239358	+	0.414581i
$804$		0			0
$805$	−1.64884e13	−	1.76550e13i	−0.00171910	−	0.00184073i
$806$		0			0
$807$	−5.46346e15	+	9.46299e15i	−0.561905	+	0.973249i
$808$		0			0
$809$	4.73536e15	+	8.20188e15i	0.480437	+	0.832141i	0.999748	−	0.0224445i	$-0.00714489\pi$
$809$	4.73536e15	+	8.20188e15i	0.480437	+	0.832141i	−0.519312	+	0.854585i	$0.673812\pi$
$810$		0			0
$811$	−1.11952e16			−1.12051			−0.560257	−	0.828319i	$-0.689298\pi$
$811$	−1.11952e16			−1.12051			−0.560257	+	0.828319i	$0.689298\pi$
$812$		0			0
$813$	−3.94613e15			−0.389649
$814$		0			0
$815$	1.03234e14	+	1.78806e14i	0.0100567	+	0.0174187i
$816$		0			0
$817$	9.09343e15	−	1.57503e16i	0.873990	−	1.51380i
$818$		0			0
$819$	9.15458e13	−	3.00239e14i	0.00868115	−	0.0284712i
$820$		0			0
$821$	−4.64980e15	+	8.05369e15i	−0.435057	+	0.753542i	−0.997300	−	0.0734305i	$-0.976605\pi$
$821$	−4.64980e15	+	8.05369e15i	−0.435057	+	0.753542i	0.562243	+	0.826972i	$0.309939\pi$
$822$		0			0
$823$	5.33016e15	+	9.23211e15i	0.492086	+	0.852319i	0.999958	−	0.00911381i	$-0.00290106\pi$
$823$	5.33016e15	+	9.23211e15i	0.492086	+	0.852319i	−0.507872	+	0.861433i	$0.669568\pi$
$824$		0			0
$825$	−6.44256e15			−0.586897
$826$		0			0
$827$	−9.03988e15			−0.812611			−0.406305	−	0.913737i	$-0.633183\pi$
$827$	−9.03988e15			−0.812611			−0.406305	+	0.913737i	$0.633183\pi$
$828$		0			0
$829$	5.50791e15	+	9.53997e15i	0.488581	+	0.846247i	0.999914	−	0.0131356i	$-0.00418132\pi$
$829$	5.50791e15	+	9.53997e15i	0.488581	+	0.846247i	−0.511333	+	0.859383i	$0.670848\pi$
$830$		0			0
$831$	8.72317e15	−	1.51090e16i	0.763605	−	1.32260i
$832$		0			0
$833$	6.99613e15	+	4.70368e15i	0.604380	+	0.406340i
$834$		0			0
$835$	3.68591e13	−	6.38419e13i	0.00314246	−	0.00544289i
$836$		0			0
$837$	−5.66362e15	−	9.80967e15i	−0.476545	−	0.825400i
$838$		0			0
$839$	1.18970e16			0.987980			0.493990	−	0.869468i	$-0.335538\pi$
$839$	1.18970e16			0.987980			0.493990	+	0.869468i	$0.335538\pi$
$840$		0			0
$841$	2.14211e16			1.75576
$842$		0			0
$843$	−8.98785e14	−	1.55674e15i	−0.0727117	−	0.125940i
$844$		0			0
$845$	4.67654e13	−	8.10001e13i	0.00373433	−	0.00646805i
$846$		0			0
$847$	2.35951e15	−	7.73839e15i	0.185979	−	0.609947i
$848$		0			0
$849$	4.63891e15	−	8.03483e15i	0.360930	−	0.625150i
$850$		0			0
$851$	−1.92909e15	−	3.34128e15i	−0.148163	−	0.256626i
$852$		0			0
$853$	−1.47382e16			−1.11744			−0.558722	−	0.829355i	$-0.688708\pi$
$853$	−1.47382e16			−1.11744			−0.558722	+	0.829355i	$0.688708\pi$
$854$		0			0
$855$	1.07653e13			0.000805774
$856$		0			0
$857$	−4.46011e15	−	7.72514e15i	−0.329573	−	0.570837i	0.652854	−	0.757483i	$-0.273571\pi$
$857$	−4.46011e15	−	7.72514e15i	−0.329573	−	0.570837i	−0.982427	+	0.186647i	$0.940238\pi$
$858$		0			0
$859$	5.09225e15	−	8.82004e15i	0.371490	−	0.643440i	−0.618305	−	0.785939i	$-0.712180\pi$
$859$	5.09225e15	−	8.82004e15i	0.371490	−	0.643440i	0.989795	+	0.142498i	$0.0455135\pi$
$860$		0			0
$861$	−9.77068e15	−	1.04620e16i	−0.703732	−	0.753525i
$862$		0			0
$863$	−1.60360e15	+	2.77752e15i	−0.114035	+	0.197514i	−0.917393	−	0.397981i	$-0.869711\pi$
$863$	−1.60360e15	+	2.77752e15i	−0.114035	+	0.197514i	0.803359	+	0.595495i	$0.203044\pi$
$864$		0			0
$865$	−2.87599e13	−	4.98136e13i	−0.00201929	−	0.00349751i
$866$		0			0
$867$	−6.60563e15			−0.457941
$868$		0			0
$869$	−2.09212e15			−0.143212
$870$		0			0
$871$	−6.99929e15	−	1.21231e16i	−0.473101	−	0.819436i
$872$		0			0
$873$	−2.94479e14	+	5.10053e14i	−0.0196552	+	0.0340437i
$874$		0			0
$875$	−3.49145e14	+	8.08828e13i	−0.0230124	+	0.00533104i
$876$		0			0
$877$	8.01432e15	−	1.38812e16i	0.521638	−	0.903503i	−0.478046	−	0.878335i	$-0.658655\pi$
$877$	8.01432e15	−	1.38812e16i	0.521638	−	0.903503i	0.999683	−	0.0251680i	$-0.00801206\pi$
$878$		0			0
$879$	6.78132e15	+	1.17456e16i	0.435889	+	0.754982i
$880$		0			0
$881$	1.00255e16			0.636413			0.318206	−	0.948021i	$-0.396920\pi$
$881$	1.00255e16			0.636413			0.318206	+	0.948021i	$0.396920\pi$
$882$		0			0
$883$	2.12241e16			1.33059			0.665297	−	0.746579i	$-0.268305\pi$
$883$	2.12241e16			1.33059			0.665297	+	0.746579i	$0.268305\pi$
$884$		0			0
$885$	1.72077e14	+	2.98046e14i	0.0106545	+	0.0184542i
$886$		0			0
$887$	6.35864e15	−	1.10135e16i	0.388852	−	0.673512i	−0.603443	−	0.797406i	$-0.706205\pi$
$887$	6.35864e15	−	1.10135e16i	0.388852	−	0.673512i	0.992295	+	0.123894i	$0.0395384\pi$
$888$		0			0
$889$	1.20400e14	−	2.78918e13i	0.00727223	−	0.00168468i
$890$		0			0
$891$	4.78507e15	−	8.28798e15i	0.285470	−	0.494449i
$892$		0			0
$893$	1.06660e16	+	1.84741e16i	0.628521	+	1.08863i
$894$		0			0
$895$	−1.86398e14			−0.0108496
$896$		0			0
$897$	2.19293e15			0.126086
$898$		0			0
$899$	1.36151e16	+	2.35820e16i	0.773290	+	1.33938i
$900$		0			0
$901$	7.19416e14	−	1.24607e15i	0.0403640	−	0.0699125i
$902$		0			0
$903$	−1.51040e16	−	1.61727e16i	−0.837160	−	0.896394i
$904$		0			0
$905$	−6.94512e13	+	1.20293e14i	−0.00380288	+	0.00658678i
$906$		0			0
$907$	1.23956e16	+	2.14698e16i	0.670544	+	1.16142i	0.977750	+	0.209774i	$0.0672727\pi$
$907$	1.23956e16	+	2.14698e16i	0.670544	+	1.16142i	−0.307206	+	0.951643i	$0.599394\pi$
$908$		0			0
$909$	6.05048e14			0.0323362
$910$		0			0
$911$	1.73889e16			0.918167			0.459083	−	0.888393i	$-0.348178\pi$
$911$	1.73889e16			0.918167			0.459083	+	0.888393i	$0.348178\pi$
$912$		0			0
$913$	−2.53654e14	−	4.39341e14i	−0.0132328	−	0.0229199i
$914$		0			0
$915$	6.64878e13	−	1.15160e14i	0.00342710	−	0.00593590i
$916$		0			0
$917$	1.03844e16	−	3.40573e16i	0.528872	−	1.73452i
$918$		0			0
$919$	3.45031e15	−	5.97611e15i	0.173629	−	0.300735i	−0.766057	−	0.642773i	$-0.777784\pi$
$919$	3.45031e15	−	5.97611e15i	0.173629	−	0.300735i	0.939686	+	0.342038i	$0.111117\pi$
$920$		0			0
$921$	1.52784e15	+	2.64630e15i	0.0759715	+	0.131587i
$922$		0			0
$923$	−9.58520e15			−0.470968
$924$		0			0
$925$	−2.86178e16			−1.38949
$926$		0			0
$927$	2.80640e14	+	4.86083e14i	0.0134651	+	0.0233223i
$928$		0			0
$929$	1.78581e16	−	3.09311e16i	0.846735	−	1.46659i	−0.0373705	−	0.999301i	$-0.511898\pi$
$929$	1.78581e16	−	3.09311e16i	0.846735	−	1.46659i	0.884106	−	0.467287i	$-0.154768\pi$
$930$		0			0
$931$	2.02446e15	−	2.95897e16i	0.0948607	−	1.38649i
$932$		0			0
$933$	−1.65351e16	+	2.86395e16i	−0.765696	+	1.32622i
$934$		0			0
$935$	5.65714e13	+	9.79845e13i	0.00258900	+	0.00448429i
$936$		0			0
$937$	5.48163e15			0.247937			0.123969	−	0.992286i	$-0.460438\pi$
$937$	5.48163e15			0.247937			0.123969	+	0.992286i	$0.460438\pi$
$938$		0			0
$939$	−1.55637e16			−0.695748
$940$		0			0
$941$	−3.02542e15	−	5.24018e15i	−0.133673	−	0.231528i	0.791417	−	0.611277i	$-0.209344\pi$
$941$	−3.02542e15	−	5.24018e15i	−0.133673	−	0.231528i	−0.925090	+	0.379749i	$0.876010\pi$
$942$		0			0
$943$	−2.58132e15	+	4.47098e15i	−0.112727	+	0.195249i
$944$		0			0
$945$	8.16466e13	−	2.67773e14i	0.00352422	−	0.0115582i
$946$		0			0
$947$	−7.98445e15	+	1.38295e16i	−0.340659	+	0.590039i	−0.984555	−	0.175074i	$-0.943984\pi$
$947$	−7.98445e15	+	1.38295e16i	−0.340659	+	0.590039i	0.643896	+	0.765113i	$0.277317\pi$
$948$		0			0
$949$	−5.71745e15	−	9.90292e15i	−0.241123	−	0.417637i
$950$		0			0
$951$	−4.29306e16			−1.78967
$952$		0			0
$953$	3.45602e16			1.42418			0.712091	−	0.702087i	$-0.247748\pi$
$953$	3.45602e16			1.42418			0.712091	+	0.702087i	$0.247748\pi$
$954$		0			0
$955$	−2.06216e14	−	3.57176e14i	−0.00840046	−	0.0145500i
$956$		0			0
$957$	−1.20984e16	+	2.09551e16i	−0.487206	+	0.843866i
$958$		0			0
$959$	2.45478e15	+	2.62847e15i	0.0977260	+	0.104641i
$960$		0			0
$961$	1.67736e15	−	2.90527e15i	0.0660157	−	0.114343i
$962$		0			0
$963$	−5.91234e14	−	1.02405e15i	−0.0230046	−	0.0398452i
$964$		0			0
$965$	−2.90919e14			−0.0111911
$966$		0			0
$967$	1.58618e16			0.603263			0.301631	−	0.953425i	$-0.402469\pi$
$967$	1.58618e16			0.603263			0.301631	+	0.953425i	$0.402469\pi$
$968$		0			0
$969$	−1.31235e16	−	2.27305e16i	−0.493479	−	0.854730i
$970$		0			0
$971$	1.13669e16	−	1.96881e16i	0.422608	−	0.731978i	−0.573586	−	0.819145i	$-0.694448\pi$
$971$	1.13669e16	−	1.96881e16i	0.422608	−	0.731978i	0.996194	+	0.0871673i	$0.0277815\pi$
$972$		0			0
$973$	−9.84306e15	+	2.28024e15i	−0.361834	+	0.0838222i
$974$		0			0
$975$	8.13293e15	−	1.40866e16i	0.295612	−	0.512014i
$976$		0			0
$977$	1.92064e16	+	3.32664e16i	0.690281	+	1.19560i	0.971746	+	0.236030i	$0.0758463\pi$
$977$	1.92064e16	+	3.32664e16i	0.690281	+	1.19560i	−0.281465	+	0.959571i	$0.590820\pi$
$978$		0			0
$979$	−2.66764e16			−0.948029
$980$		0			0
$981$	−1.17138e15			−0.0411639
$982$		0			0
$983$	1.84544e15	+	3.19640e15i	0.0641292	+	0.111075i	0.896307	−	0.443433i	$-0.146240\pi$
$983$	1.84544e15	+	3.19640e15i	0.0641292	+	0.111075i	−0.832178	+	0.554508i	$0.812906\pi$
$984$		0			0
$985$	−8.49283e13	+	1.47100e14i	−0.00291845	+	0.00505491i
$986$		0			0
$987$	2.52861e16	−	5.85775e15i	0.859285	−	0.199061i
$988$		0			0
$989$	−3.99033e15	+	6.91145e15i	−0.134100	+	0.232268i
$990$		0			0
$991$	−1.72541e16	−	2.98850e16i	−0.573439	−	0.993225i	−0.996209	−	0.0869886i	$-0.972276\pi$
$991$	−1.72541e16	−	2.98850e16i	−0.573439	−	0.993225i	0.422770	−	0.906237i	$-0.361058\pi$
$992$		0			0
$993$	−1.91119e16			−0.628179
$994$		0			0
$995$	−4.55137e14			−0.0147950
$996$		0			0
$997$	5.81831e14	+	1.00776e15i	0.0187057	+	0.0323992i	0.875227	−	0.483713i	$-0.160712\pi$
$997$	5.81831e14	+	1.00776e15i	0.0187057	+	0.0323992i	−0.856521	+	0.516112i	$0.827379\pi$
$998$		0			0
$999$	2.23552e16	−	3.87204e16i	0.710835	−	1.23120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.12.i.c.65.2		12
4.3	odd	2		7.12.c.a.2.2	✓	12
7.4	even	3	inner	112.12.i.c.81.2		12
12.11	even	2		63.12.e.b.37.5		12
28.3	even	6		49.12.c.i.18.2		12
28.11	odd	6		7.12.c.a.4.2	yes	12
28.19	even	6		49.12.a.f.1.5		6
28.23	odd	6		49.12.a.g.1.5		6
28.27	even	2		49.12.c.i.30.2		12
84.11	even	6		63.12.e.b.46.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.12.c.a.2.2	✓	12	4.3	odd	2
7.12.c.a.4.2	yes	12	28.11	odd	6
49.12.a.f.1.5		6	28.19	even	6
49.12.a.g.1.5		6	28.23	odd	6
49.12.c.i.18.2		12	28.3	even	6
49.12.c.i.30.2		12	28.27	even	2
63.12.e.b.37.5		12	12.11	even	2
63.12.e.b.46.5		12	84.11	even	6
112.12.i.c.65.2		12	1.1	even	1	trivial
112.12.i.c.81.2		12	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-205.214 - 355.441i) q^{3} +(-41.2685 + 71.4792i) q^{5} +(43319.9 - 10035.5i) q^{7} +(4347.82 - 7530.65i) q^{9} +O(q^{10})\)	\(q+(-205.214 - 355.441i) q^{3} +(-41.2685 + 71.4792i) q^{5} +(43319.9 - 10035.5i) q^{7} +(4347.82 - 7530.65i) q^{9} +(-160761. - 278447. i) q^{11} +811765. q^{13} +33875.5 q^{15} +(2.13175e6 + 3.69230e6i) q^{17} +(7.49974e6 - 1.29899e7i) q^{19} +(-1.24569e7 - 1.33383e7i) q^{21} +(-3.29099e6 + 5.70016e6i) q^{23} +(2.44107e7 + 4.22805e7i) q^{25} -7.62751e7 q^{27} +1.83362e8 q^{29} +(7.42525e7 + 1.28609e8i) q^{31} +(-6.59810e7 + 1.14282e8i) q^{33} +(-1.07042e6 + 3.51062e6i) q^{35} +(-2.93087e8 + 5.07642e8i) q^{37} +(-1.66586e8 - 2.88535e8i) q^{39} +7.84360e8 q^{41} +1.21250e9 q^{43} +(358857. + 621558. i) q^{45} +(-7.11093e8 + 1.23165e9i) q^{47} +(1.77591e9 - 8.69471e8i) q^{49} +(8.74930e8 - 1.51542e9i) q^{51} +(-1.68739e8 - 2.92264e8i) q^{53} +2.65375e7 q^{55} -6.15621e9 q^{57} +(5.07967e9 + 8.79825e9i) q^{59} +(1.96271e9 - 3.39951e9i) q^{61} +(1.12774e8 - 3.69860e8i) q^{63} +(-3.35003e7 + 5.80243e7i) q^{65} +(-8.62231e9 - 1.49343e10i) q^{67} +2.70143e9 q^{69} -1.18078e10 q^{71} +(-7.04324e9 - 1.21993e10i) q^{73} +(1.00188e10 - 1.73531e10i) q^{75} +(-9.75851e9 - 1.04490e10i) q^{77} +(3.25346e9 - 5.63515e9i) q^{79} +(1.48825e10 + 2.57773e10i) q^{81} +1.57783e9 q^{83} -3.51897e8 q^{85} +(-3.76285e10 - 6.51744e10i) q^{87} +(4.14844e10 - 7.18531e10i) q^{89} +(3.51656e10 - 8.14644e9i) q^{91} +(3.04753e10 - 5.27848e10i) q^{93} +(6.19006e8 + 1.07215e9i) q^{95} -6.77303e10 q^{97} -2.79585e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 244 q^{3} - 8782 q^{5} + 504 q^{7} - 172348 q^{9}+O(q^{10}) \) 12 * q + 244 * q^3 - 8782 * q^5 + 504 * q^7 - 172348 * q^9	\( 12 q + 244 q^{3} - 8782 q^{5} + 504 q^{7} - 172348 q^{9} + 1001572 q^{11} + 3864504 q^{13} + 1286512 q^{15} - 6704802 q^{17} - 4192212 q^{19} + 44745358 q^{21} + 33871872 q^{23} + 13695456 q^{25} - 73859384 q^{27} - 255125224 q^{29} + 331783920 q^{31} - 80899438 q^{33} - 1407354844 q^{35} - 833082774 q^{37} - 737605904 q^{39} + 3104076808 q^{41} + 1722177552 q^{43} - 7406493484 q^{45} + 1327587552 q^{47} + 11976558636 q^{49} + 13921261140 q^{51} + 6725755626 q^{53} - 26323921200 q^{55} - 16884487756 q^{57} + 26237179548 q^{59} - 14411013726 q^{61} - 45955779184 q^{63} - 16224702172 q^{65} + 4241860068 q^{67} + 46750854252 q^{69} + 37335334656 q^{71} + 6005568990 q^{73} - 17116276792 q^{75} - 51928077698 q^{77} - 11712395640 q^{79} - 12455008366 q^{81} + 100821781200 q^{83} + 138884613396 q^{85} - 119455310144 q^{87} - 48633519778 q^{89} + 160908361488 q^{91} + 266530114134 q^{93} + 72161225128 q^{95} - 401308415928 q^{97} - 367357472240 q^{99}+O(q^{100}) \) 12 * q + 244 * q^3 - 8782 * q^5 + 504 * q^7 - 172348 * q^9 + 1001572 * q^11 + 3864504 * q^13 + 1286512 * q^15 - 6704802 * q^17 - 4192212 * q^19 + 44745358 * q^21 + 33871872 * q^23 + 13695456 * q^25 - 73859384 * q^27 - 255125224 * q^29 + 331783920 * q^31 - 80899438 * q^33 - 1407354844 * q^35 - 833082774 * q^37 - 737605904 * q^39 + 3104076808 * q^41 + 1722177552 * q^43 - 7406493484 * q^45 + 1327587552 * q^47 + 11976558636 * q^49 + 13921261140 * q^51 + 6725755626 * q^53 - 26323921200 * q^55 - 16884487756 * q^57 + 26237179548 * q^59 - 14411013726 * q^61 - 45955779184 * q^63 - 16224702172 * q^65 + 4241860068 * q^67 + 46750854252 * q^69 + 37335334656 * q^71 + 6005568990 * q^73 - 17116276792 * q^75 - 51928077698 * q^77 - 11712395640 * q^79 - 12455008366 * q^81 + 100821781200 * q^83 + 138884613396 * q^85 - 119455310144 * q^87 - 48633519778 * q^89 + 160908361488 * q^91 + 266530114134 * q^93 + 72161225128 * q^95 - 401308415928 * q^97 - 367357472240 * q^99

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