LMFDB - Embedded newform 84.12.i.a.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(25,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("84.25");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} + 198245134 x^{12} + 414863096508 x^{11} + \cdots + 37\!\cdots\!56 $ x^14 - 6x^13 + 198245134x^12 + 414863096508x^11 + 26949056203541719x^10 + 65398284799267941978x^9 + 2028387875108119977261582x^8 + 6445062169106156227737324792x^7 + 111668469386916870576107083796769x^6 + 325583881393416391390922284227512022x^5 + 3320063138939962847561145196113433362264x^4 + 9575836750537552288866777850271834960214456x^3 + 68507643214686757134474644335292207644539438816x^2 + 142358467144947535218510754697116911147938126144352*x + 378103215519089647001740821506658140294236360807649856
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{12}\cdot 7^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.7
Root			$-4471.65 - 7745.12i$ of defining polynomial
Character	$\chi$	$=$	84.37
Dual form			84.12.i.a.25.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(121.500 + 210.444i) q^{3} +(4987.65 - 8638.86i) q^{5} +(6340.58 - 44012.8i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})$	\(q+(121.500 + 210.444i) q^{3} +(4987.65 - 8638.86i) q^{5} +(6340.58 - 44012.8i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(423689. + 733850. i) q^{11} -779580. q^{13} +2.42400e6 q^{15} +(5.75336e6 + 9.96512e6i) q^{17} +(-7.03792e6 + 1.21900e7i) q^{19} +(1.00326e7 - 4.01321e6i) q^{21} +(2.60274e7 - 4.50808e7i) q^{23} +(-2.53392e7 - 4.38889e7i) q^{25} -1.43489e7 q^{27} +1.03239e8 q^{29} +(-2.99588e7 - 5.18902e7i) q^{31} +(-1.02956e8 + 1.78326e8i) q^{33} +(-3.48596e8 - 2.74296e8i) q^{35} +(2.06198e8 - 3.57145e8i) q^{37} +(-9.47190e7 - 1.64058e8i) q^{39} +8.38305e8 q^{41} +7.99033e8 q^{43} +(2.94516e8 + 5.10116e8i) q^{45} +(-2.61262e8 + 4.52519e8i) q^{47} +(-1.89692e9 - 5.58133e8i) q^{49} +(-1.39807e9 + 2.42152e9i) q^{51} +(7.45239e8 + 1.29079e9i) q^{53} +8.45284e9 q^{55} -3.42043e9 q^{57} +(1.94643e9 + 3.37131e9i) q^{59} +(4.09952e9 - 7.10058e9i) q^{61} +(2.06352e9 + 1.62370e9i) q^{63} +(-3.88827e9 + 6.73468e9i) q^{65} +(-2.66112e9 - 4.60919e9i) q^{67} +1.26493e10 q^{69} -5.14461e9 q^{71} +(-7.07831e9 - 1.22600e10i) q^{73} +(6.15744e9 - 1.06650e10i) q^{75} +(3.49852e10 - 1.39947e10i) q^{77} +(-3.09437e9 + 5.35961e9i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} +8.06164e9 q^{83} +1.14783e11 q^{85} +(1.25435e10 + 2.17260e10i) q^{87} +(3.41668e10 - 5.91787e10i) q^{89} +(-4.94299e9 + 3.43115e10i) q^{91} +(7.28000e9 - 1.26093e10i) q^{93} +(7.02054e10 + 1.21599e11i) q^{95} +1.16999e11 q^{97} -5.00368e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 1701 q^{3} + 7218 q^{5} + 35001 q^{7} - 413343 q^{9}+O(q^{10}) $ 14 * q + 1701 * q^3 + 7218 * q^5 + 35001 * q^7 - 413343 * q^9	$ 14 q + 1701 q^{3} + 7218 q^{5} + 35001 q^{7} - 413343 q^{9} + 54450 q^{11} + 1534982 q^{13} + 3507948 q^{15} + 1478880 q^{17} - 22875935 q^{19} + 3394224 q^{21} + 62540568 q^{23} - 62136141 q^{25} - 200884698 q^{27} + 102097728 q^{29} + 188600405 q^{31} - 13231350 q^{33} - 253840734 q^{35} + 199685599 q^{37} + 186500313 q^{39} - 693868716 q^{41} - 620701754 q^{43} + 426215682 q^{45} + 2771987346 q^{47} - 5209147075 q^{49} - 359367840 q^{51} + 6487034184 q^{53} + 10046238656 q^{55} - 11117704410 q^{57} - 8183838888 q^{59} + 4069556330 q^{61} - 1241977617 q^{63} - 1520229906 q^{65} + 15766443531 q^{67} + 30394716048 q^{69} - 33183285444 q^{71} - 31685143839 q^{73} + 15099082263 q^{75} + 3261253500 q^{77} + 21999509987 q^{79} - 24407490807 q^{81} - 63053885988 q^{83} + 35204204624 q^{85} + 12404873952 q^{87} + 67041904680 q^{89} - 190876959523 q^{91} - 45829898415 q^{93} + 133488871470 q^{95} + 284083418100 q^{97} - 6430436100 q^{99}+O(q^{100}) $ 14 * q + 1701 * q^3 + 7218 * q^5 + 35001 * q^7 - 413343 * q^9 + 54450 * q^11 + 1534982 * q^13 + 3507948 * q^15 + 1478880 * q^17 - 22875935 * q^19 + 3394224 * q^21 + 62540568 * q^23 - 62136141 * q^25 - 200884698 * q^27 + 102097728 * q^29 + 188600405 * q^31 - 13231350 * q^33 - 253840734 * q^35 + 199685599 * q^37 + 186500313 * q^39 - 693868716 * q^41 - 620701754 * q^43 + 426215682 * q^45 + 2771987346 * q^47 - 5209147075 * q^49 - 359367840 * q^51 + 6487034184 * q^53 + 10046238656 * q^55 - 11117704410 * q^57 - 8183838888 * q^59 + 4069556330 * q^61 - 1241977617 * q^63 - 1520229906 * q^65 + 15766443531 * q^67 + 30394716048 * q^69 - 33183285444 * q^71 - 31685143839 * q^73 + 15099082263 * q^75 + 3261253500 * q^77 + 21999509987 * q^79 - 24407490807 * q^81 - 63053885988 * q^83 + 35204204624 * q^85 + 12404873952 * q^87 + 67041904680 * q^89 - 190876959523 * q^91 - 45829898415 * q^93 + 133488871470 * q^95 + 284083418100 * q^97 - 6430436100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	121.500	+	210.444i	0.288675	+	0.500000i
$3$	121.500	+	210.444i	0.288675	+	0.500000i
$4$		0			0
$5$	4987.65	−	8638.86i	0.713774	−	1.23629i	−0.249656	−	0.968335i	$-0.580318\pi$
$5$	4987.65	−	8638.86i	0.713774	−	1.23629i	0.963430	−	0.267959i	$-0.0863491\pi$
$6$		0			0
$7$	6340.58	−	44012.8i	0.142590	−	0.989782i
$7$	6340.58	−	44012.8i	0.142590	−	0.989782i
$8$		0			0
$9$	−29524.5	+	51137.9i	−0.166667	+	0.288675i
$10$		0			0
$11$	423689.	+	733850.i	0.793208	+	1.37388i	0.923971	+	0.382463i	$0.124924\pi$
$11$	423689.	+	733850.i	0.793208	+	1.37388i	−0.130763	+	0.991414i	$0.541743\pi$
$12$		0			0
$13$	−779580.			−0.582334			−0.291167	−	0.956672i	$-0.594044\pi$
$13$	−779580.			−0.582334			−0.291167	+	0.956672i	$0.594044\pi$
$14$		0			0
$15$	2.42400e6			0.824196
$16$		0			0
$17$	5.75336e6	+	9.96512e6i	0.982772	+	1.70221i	0.651447	+	0.758694i	$0.274162\pi$
$17$	5.75336e6	+	9.96512e6i	0.982772	+	1.70221i	0.331325	+	0.943517i	$0.392504\pi$
$18$		0			0
$19$	−7.03792e6	+	1.21900e7i	−0.652078	+	1.12943i	0.330540	+	0.943792i	$0.392769\pi$
$19$	−7.03792e6	+	1.21900e7i	−0.652078	+	1.12943i	−0.982618	+	0.185640i	$0.940564\pi$
$20$		0			0
$21$	1.00326e7	−	4.01321e6i	0.536053	−	0.214430i
$22$		0			0
$23$	2.60274e7	−	4.50808e7i	0.843195	−	1.46046i	−0.0439839	−	0.999032i	$-0.514005\pi$
$23$	2.60274e7	−	4.50808e7i	0.843195	−	1.46046i	0.887179	−	0.461425i	$-0.152662\pi$
$24$		0			0
$25$	−2.53392e7	−	4.38889e7i	−0.518948	−	0.898844i
$26$		0			0
$27$	−1.43489e7			−0.192450
$28$		0			0
$29$	1.03239e8			0.934659			0.467329	−	0.884083i	$-0.345216\pi$
$29$	1.03239e8			0.934659			0.467329	+	0.884083i	$0.345216\pi$
$30$		0			0
$31$	−2.99588e7	−	5.18902e7i	−0.187947	−	0.325534i	0.756619	−	0.653857i	$-0.226850\pi$
$31$	−2.99588e7	−	5.18902e7i	−0.187947	−	0.325534i	−0.944566	+	0.328323i	$0.893517\pi$
$32$		0			0
$33$	−1.02956e8	+	1.78326e8i	−0.457959	+	0.793208i
$34$		0			0
$35$	−3.48596e8	−	2.74296e8i	−1.12188	−	0.882764i
$36$		0			0
$37$	2.06198e8	−	3.57145e8i	0.488849	−	0.846711i	−0.511069	−	0.859540i	$-0.670750\pi$
$37$	2.06198e8	−	3.57145e8i	0.488849	−	0.846711i	0.999918	+	0.0128290i	$0.00408371\pi$
$38$		0			0
$39$	−9.47190e7	−	1.64058e8i	−0.168105	−	0.291167i
$40$		0			0
$41$	8.38305e8			1.13003			0.565016	−	0.825080i	$-0.308870\pi$
$41$	8.38305e8			1.13003			0.565016	+	0.825080i	$0.308870\pi$
$42$		0			0
$43$	7.99033e8			0.828873			0.414437	−	0.910078i	$-0.363979\pi$
$43$	7.99033e8			0.828873			0.414437	+	0.910078i	$0.363979\pi$
$44$		0			0
$45$	2.94516e8	+	5.10116e8i	0.237925	+	0.412098i
$46$		0			0
$47$	−2.61262e8	+	4.52519e8i	−0.166164	+	0.287805i	−0.937068	−	0.349147i	$-0.886472\pi$
$47$	−2.61262e8	+	4.52519e8i	−0.166164	+	0.287805i	0.770904	+	0.636952i	$0.219805\pi$
$48$		0			0
$49$	−1.89692e9	−	5.58133e8i	−0.959336	−	0.282266i
$50$		0			0
$51$	−1.39807e9	+	2.42152e9i	−0.567404	+	0.982772i
$52$		0			0
$53$	7.45239e8	+	1.29079e9i	0.244781	+	0.423974i	0.962070	−	0.272802i	$-0.0879505\pi$
$53$	7.45239e8	+	1.29079e9i	0.244781	+	0.423974i	−0.717289	+	0.696776i	$0.754617\pi$
$54$		0			0
$55$	8.45284e9			2.26469
$56$		0			0
$57$	−3.42043e9			−0.752955
$58$		0			0
$59$	1.94643e9	+	3.37131e9i	0.354448	+	0.613922i	0.987023	−	0.160577i	$-0.0513355\pi$
$59$	1.94643e9	+	3.37131e9i	0.354448	+	0.613922i	−0.632575	+	0.774499i	$0.718002\pi$
$60$		0			0
$61$	4.09952e9	−	7.10058e9i	0.621469	−	1.07642i	−0.367744	−	0.929927i	$-0.619870\pi$
$61$	4.09952e9	−	7.10058e9i	0.621469	−	1.07642i	0.989212	−	0.146488i	$-0.0467970\pi$
$62$		0			0
$63$	2.06352e9	+	1.62370e9i	0.261960	+	0.206126i
$64$		0			0
$65$	−3.88827e9	+	6.73468e9i	−0.415655	+	0.719936i
$66$		0			0
$67$	−2.66112e9	−	4.60919e9i	−0.240798	−	0.417074i	0.720144	−	0.693825i	$-0.244076\pi$
$67$	−2.66112e9	−	4.60919e9i	−0.240798	−	0.417074i	−0.960942	+	0.276750i	$0.910742\pi$
$68$		0			0
$69$	1.26493e10			0.973638
$70$		0			0
$71$	−5.14461e9			−0.338401			−0.169201	−	0.985582i	$-0.554119\pi$
$71$	−5.14461e9			−0.338401			−0.169201	+	0.985582i	$0.554119\pi$
$72$		0			0
$73$	−7.07831e9	−	1.22600e10i	−0.399626	−	0.692172i	0.594054	−	0.804425i	$-0.297527\pi$
$73$	−7.07831e9	−	1.22600e10i	−0.399626	−	0.692172i	−0.993680	+	0.112253i	$0.964193\pi$
$74$		0			0
$75$	6.15744e9	−	1.06650e10i	0.299615	−	0.518948i
$76$		0			0
$77$	3.49852e10	−	1.39947e10i	1.47294	−	0.589201i
$78$		0			0
$79$	−3.09437e9	+	5.35961e9i	−0.113142	+	0.195968i	−0.917036	−	0.398806i	$-0.869425\pi$
$79$	−3.09437e9	+	5.35961e9i	−0.113142	+	0.195968i	0.803894	+	0.594773i	$0.202758\pi$
$80$		0			0
$81$	−1.74339e9	−	3.01964e9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	8.06164e9			0.224644			0.112322	−	0.993672i	$-0.464171\pi$
$83$	8.06164e9			0.224644			0.112322	+	0.993672i	$0.464171\pi$
$84$		0			0
$85$	1.14783e11			2.80591
$86$		0			0
$87$	1.25435e10	+	2.17260e10i	0.269813	+	0.467329i
$88$		0			0
$89$	3.41668e10	−	5.91787e10i	0.648574	−	1.12336i	−0.334890	−	0.942257i	$-0.608699\pi$
$89$	3.41668e10	−	5.91787e10i	0.648574	−	1.12336i	0.983464	−	0.181106i	$-0.0579677\pi$
$90$		0			0
$91$	−4.94299e9	+	3.43115e10i	−0.0830351	+	0.576384i
$92$		0			0
$93$	7.28000e9	−	1.26093e10i	0.108511	−	0.187947i
$94$		0			0
$95$	7.02054e10	+	1.21599e11i	0.930873	+	1.61232i
$96$		0			0
$97$	1.16999e11			1.38336			0.691681	−	0.722203i	$-0.256870\pi$
$97$	1.16999e11			1.38336			0.691681	+	0.722203i	$0.256870\pi$
$98$		0			0
$99$	−5.00368e10			−0.528805
$100$		0			0
$101$	−2.89293e10	−	5.01070e10i	−0.273886	−	0.474385i	0.695967	−	0.718074i	$-0.254976\pi$
$101$	−2.89293e10	−	5.01070e10i	−0.273886	−	0.474385i	−0.969854	+	0.243689i	$0.921643\pi$
$102$		0			0
$103$	−8.15013e10	+	1.41164e11i	−0.692723	+	1.19983i	0.278219	+	0.960518i	$0.410256\pi$
$103$	−8.15013e10	+	1.41164e11i	−0.692723	+	1.19983i	−0.970942	+	0.239314i	$0.923077\pi$
$104$		0			0
$105$	1.53695e10	−	1.06687e11i	0.117522	−	0.815774i
$106$		0			0
$107$	1.31019e11	−	2.26932e11i	0.903077	−	1.56418i	0.0795995	−	0.996827i	$-0.474636\pi$
$107$	1.31019e11	−	2.26932e11i	0.903077	−	1.56418i	0.823478	−	0.567349i	$-0.192031\pi$
$108$		0			0
$109$	9.58220e10	+	1.65968e11i	0.596512	+	1.03319i	0.993332	+	0.115293i	$0.0367806\pi$
$109$	9.58220e10	+	1.65968e11i	0.596512	+	1.03319i	−0.396819	+	0.917897i	$0.629886\pi$
$110$		0			0
$111$	1.00212e11			0.564474
$112$		0			0
$113$	−2.37853e10			−0.121444			−0.0607221	−	0.998155i	$-0.519340\pi$
$113$	−2.37853e10			−0.121444			−0.0607221	+	0.998155i	$0.519340\pi$
$114$		0			0
$115$	−2.59631e11	−	4.49695e11i	−1.20370	−	2.08487i
$116$		0			0
$117$	2.30167e10	−	3.98661e10i	0.0970557	−	0.168105i
$118$		0			0
$119$	4.75072e11	−	1.90037e11i	1.82495	−	0.730011i
$120$		0			0
$121$	−2.16368e11	+	3.74761e11i	−0.758357	+	1.31351i
$122$		0			0
$123$	1.01854e11	+	1.76416e11i	0.326212	+	0.565016i
$124$		0			0
$125$	−1.84579e10			−0.0540975
$126$		0			0
$127$	−1.16687e11			−0.313403			−0.156702	−	0.987646i	$-0.550086\pi$
$127$	−1.16687e11			−0.313403			−0.156702	+	0.987646i	$0.550086\pi$
$128$		0			0
$129$	9.70825e10	+	1.68152e11i	0.239275	+	0.414437i
$130$		0			0
$131$	−4.25827e11	+	7.37554e11i	−0.964364	+	1.67033i	−0.253050	+	0.967453i	$0.581434\pi$
$131$	−4.25827e11	+	7.37554e11i	−0.964364	+	1.67033i	−0.711314	+	0.702874i	$0.751900\pi$
$132$		0			0
$133$	4.91893e11	+	3.87050e11i	1.02491	+	0.806461i
$134$		0			0
$135$	−7.15673e10	+	1.23958e11i	−0.137366	+	0.237925i
$136$		0			0
$137$	−1.66436e11	−	2.88276e11i	−0.294635	−	0.510323i	0.680265	−	0.732967i	$-0.261865\pi$
$137$	−1.66436e11	−	2.88276e11i	−0.294635	−	0.510323i	−0.974900	+	0.222643i	$0.928532\pi$
$138$		0			0
$139$	1.05305e12			1.72134			0.860669	−	0.509165i	$-0.170046\pi$
$139$	1.05305e12			1.72134			0.860669	+	0.509165i	$0.170046\pi$
$140$		0			0
$141$	−1.26973e11			−0.191870
$142$		0			0
$143$	−3.30299e11	−	5.72095e11i	−0.461912	−	0.800055i
$144$		0			0
$145$	5.14918e11	−	8.91864e11i	0.667136	−	1.15551i
$146$		0			0
$147$	−1.13020e11	−	4.67009e11i	−0.135803	−	0.561151i
$148$		0			0
$149$	−7.66823e11	+	1.32818e12i	−0.855403	+	1.48160i	0.0208673	+	0.999782i	$0.493357\pi$
$149$	−7.66823e11	+	1.32818e12i	−0.855403	+	1.48160i	−0.876270	+	0.481820i	$0.839976\pi$
$150$		0			0
$151$	−8.52666e11	−	1.47686e12i	−0.883905	−	1.53097i	−0.846964	−	0.531651i	$-0.821572\pi$
$151$	−8.52666e11	−	1.47686e12i	−0.883905	−	1.53097i	−0.0369413	−	0.999317i	$-0.511761\pi$
$152$		0			0
$153$	−6.79461e11			−0.655181
$154$		0			0
$155$	−5.97697e11			−0.536607
$156$		0			0
$157$	−3.87092e11	−	6.70462e11i	−0.323866	−	0.560953i	0.657416	−	0.753528i	$-0.271649\pi$
$157$	−3.87092e11	−	6.70462e11i	−0.323866	−	0.560953i	−0.981282	+	0.192575i	$0.938316\pi$
$158$		0			0
$159$	−1.81093e11	+	3.13662e11i	−0.141325	+	0.244781i
$160$		0			0
$161$	−1.81910e12	−	1.43138e12i	−1.32530	−	1.04283i
$162$		0			0
$163$	−3.40772e11	+	5.90234e11i	−0.231970	+	0.401784i	−0.958388	−	0.285470i	$-0.907850\pi$
$163$	−3.40772e11	+	5.90234e11i	−0.231970	+	0.401784i	0.726418	+	0.687253i	$0.241184\pi$
$164$		0			0
$165$	1.02702e12	+	1.77885e12i	0.653758	+	1.13234i
$166$		0			0
$167$	−2.36222e11			−0.140728			−0.0703640	−	0.997521i	$-0.522416\pi$
$167$	−2.36222e11			−0.140728			−0.0703640	+	0.997521i	$0.522416\pi$
$168$		0			0
$169$	−1.18442e12			−0.660887
$170$		0			0
$171$	−4.15582e11	−	7.19810e11i	−0.217359	−	0.376478i
$172$		0			0
$173$	−3.70958e10	+	6.42519e10i	−0.0182000	+	0.0315233i	−0.874982	−	0.484156i	$-0.839127\pi$
$173$	−3.70958e10	+	6.42519e10i	−0.0182000	+	0.0315233i	0.856782	+	0.515679i	$0.172460\pi$
$174$		0			0
$175$	−2.09234e12	+	8.36969e11i	−0.963656	+	0.385479i
$176$		0			0
$177$	−4.72982e11	+	8.19229e11i	−0.204641	+	0.354448i
$178$		0			0
$179$	1.09770e11	+	1.90128e11i	0.0446471	+	0.0773310i	0.887485	−	0.460836i	$-0.152450\pi$
$179$	1.09770e11	+	1.90128e11i	0.0446471	+	0.0773310i	−0.842838	+	0.538167i	$0.819117\pi$
$180$		0			0
$181$	6.70619e11			0.256592			0.128296	−	0.991736i	$-0.459049\pi$
$181$	6.70619e11			0.256592			0.128296	+	0.991736i	$0.459049\pi$
$182$		0			0
$183$	1.99237e12			0.717610
$184$		0			0
$185$	−2.05688e12	−	3.56263e12i	−0.697855	−	1.20872i
$186$		0			0
$187$	−4.87527e12	+	8.44421e12i	−1.55908	+	2.70041i
$188$		0			0
$189$	−9.09804e10	+	6.31535e11i	−0.0274415	+	0.190484i
$190$		0			0
$191$	−3.60876e11	+	6.25056e11i	−0.102725	+	0.177924i	−0.912806	−	0.408393i	$-0.866089\pi$
$191$	−3.60876e11	+	6.25056e11i	−0.102725	+	0.177924i	0.810082	+	0.586317i	$0.199423\pi$
$192$		0			0
$193$	1.07189e12	+	1.85657e12i	0.288129	+	0.499053i	0.973363	−	0.229269i	$-0.0736336\pi$
$193$	1.07189e12	+	1.85657e12i	0.288129	+	0.499053i	−0.685234	+	0.728323i	$0.740300\pi$
$194$		0			0
$195$	−1.88970e12			−0.479957
$196$		0			0
$197$	2.80167e12			0.672748			0.336374	−	0.941728i	$-0.390799\pi$
$197$	2.80167e12			0.672748			0.336374	+	0.941728i	$0.390799\pi$
$198$		0			0
$199$	2.13480e12	+	3.69758e12i	0.484914	+	0.839896i	0.999850	−	0.0173326i	$-0.00551741\pi$
$199$	2.13480e12	+	3.69758e12i	0.484914	+	0.839896i	−0.514935	+	0.857229i	$0.672184\pi$
$200$		0			0
$201$	6.46652e11	−	1.12003e12i	0.139025	−	0.240798i
$202$		0			0
$203$	6.54592e11	−	4.54382e12i	0.133273	−	0.925108i
$204$		0			0
$205$	4.18117e12	−	7.24200e12i	0.806588	−	1.39705i
$206$		0			0
$207$	1.53689e12	+	2.66198e12i	0.281065	+	0.486819i
$208$		0			0
$209$	−1.19275e13			−2.06893
$210$		0			0
$211$	−5.91778e12			−0.974104			−0.487052	−	0.873373i	$-0.661928\pi$
$211$	−5.91778e12			−0.974104			−0.487052	+	0.873373i	$0.661928\pi$
$212$		0			0
$213$	−6.25070e11	−	1.08265e12i	−0.0976880	−	0.169201i
$214$		0			0
$215$	3.98530e12	−	6.90274e12i	0.591629	−	1.02473i
$216$		0			0
$217$	−2.47379e12	+	9.89557e11i	−0.349007	+	0.139609i
$218$		0			0
$219$	1.72003e12	−	2.97918e12i	0.230724	−	0.399626i
$220$		0			0
$221$	−4.48521e12	−	7.76861e12i	−0.572302	−	0.991255i
$222$		0			0
$223$	1.47610e13			1.79242			0.896210	−	0.443631i	$-0.146310\pi$
$223$	1.47610e13			1.79242			0.896210	+	0.443631i	$0.146310\pi$
$224$		0			0
$225$	2.99251e12			0.345965
$226$		0			0
$227$	1.68201e12	+	2.91333e12i	0.185220	+	0.320810i	0.943651	−	0.330943i	$-0.107367\pi$
$227$	1.68201e12	+	2.91333e12i	0.185220	+	0.320810i	−0.758431	+	0.651754i	$0.774034\pi$
$228$		0			0
$229$	−1.71199e12	+	2.96526e12i	−0.179641	+	0.311148i	−0.941758	−	0.336292i	$-0.890827\pi$
$229$	−1.71199e12	+	2.96526e12i	−0.179641	+	0.311148i	0.762116	+	0.647440i	$0.224160\pi$
$230$		0			0
$231$	7.19580e12	+	5.66208e12i	0.719802	+	0.566383i
$232$		0			0
$233$	9.21643e12	−	1.59633e13i	0.879236	−	1.52288i	0.0270548	−	0.999634i	$-0.491387\pi$
$233$	9.21643e12	−	1.59633e13i	0.879236	−	1.52288i	0.852181	−	0.523247i	$-0.175280\pi$
$234$		0			0
$235$	2.60616e12	+	4.51401e12i	0.237208	+	0.410856i
$236$		0			0
$237$	−1.50387e12			−0.130645
$238$		0			0
$239$	5.30045e12			0.439668			0.219834	−	0.975537i	$-0.429448\pi$
$239$	5.30045e12			0.439668			0.219834	+	0.975537i	$0.429448\pi$
$240$		0			0
$241$	7.17556e12	+	1.24284e13i	0.568541	+	0.984742i	0.996711	+	0.0810435i	$0.0258253\pi$
$241$	7.17556e12	+	1.24284e13i	0.568541	+	0.984742i	−0.428170	+	0.903698i	$0.640841\pi$
$242$		0			0
$243$	4.23644e11	−	7.33773e11i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−1.42828e13	+	1.36035e13i	−1.03371	+	0.984546i
$246$		0			0
$247$	5.48662e12	−	9.50311e12i	0.379727	−	0.657707i
$248$		0			0
$249$	9.79490e11	+	1.69653e12i	0.0648490	+	0.112322i
$250$		0			0
$251$	−6.53478e12			−0.414024			−0.207012	−	0.978338i	$-0.566374\pi$
$251$	−6.53478e12			−0.414024			−0.207012	+	0.978338i	$0.566374\pi$
$252$		0			0
$253$	4.41101e13			2.67532
$254$		0			0
$255$	1.39461e13	+	2.41554e13i	0.809996	+	1.40295i
$256$		0			0
$257$	4.68344e11	−	8.11196e11i	0.0260575	−	0.0451329i	−0.852703	−	0.522397i	$-0.825038\pi$
$257$	4.68344e11	−	8.11196e11i	0.0260575	−	0.0451329i	0.878760	+	0.477264i	$0.158371\pi$
$258$		0			0
$259$	−1.44115e13	−	1.13398e13i	−0.768354	−	0.604586i
$260$		0			0
$261$	−3.04807e12	+	5.27941e12i	−0.155776	+	0.269813i
$262$		0			0
$263$	7.69445e12	+	1.33272e13i	0.377069	+	0.653103i	0.990634	−	0.136541i	$-0.0435985\pi$
$263$	7.69445e12	+	1.33272e13i	0.377069	+	0.653103i	−0.613565	+	0.789644i	$0.710265\pi$
$264$		0			0
$265$	1.48680e13			0.698874
$266$		0			0
$267$	1.66051e13			0.748909
$268$		0			0
$269$	−1.73751e13	−	3.00946e13i	−0.752126	−	1.30272i	−0.946790	−	0.321851i	$-0.895695\pi$
$269$	−1.73751e13	−	3.00946e13i	−0.752126	−	1.30272i	0.194664	−	0.980870i	$-0.437638\pi$
$270$		0			0
$271$	2.50486e12	−	4.33855e12i	0.104101	−	0.180308i	−0.809270	−	0.587437i	$-0.800137\pi$
$271$	2.50486e12	−	4.33855e12i	0.104101	−	0.180308i	0.913370	+	0.407130i	$0.133470\pi$
$272$		0			0
$273$	−7.82122e12	+	3.12862e12i	−0.312162	+	0.124870i
$274$		0			0
$275$	2.14719e13	−	3.71904e13i	0.823267	−	1.42594i
$276$		0			0
$277$	−1.56172e13	−	2.70498e13i	−0.575393	−	0.996611i	−0.995999	−	0.0893669i	$-0.971516\pi$
$277$	−1.56172e13	−	2.70498e13i	−0.575393	−	0.996611i	0.420605	−	0.907244i	$-0.361818\pi$
$278$		0			0
$279$	3.53808e12			0.125298
$280$		0			0
$281$	−1.69604e13			−0.577498			−0.288749	−	0.957405i	$-0.593239\pi$
$281$	−1.69604e13			−0.577498			−0.288749	+	0.957405i	$0.593239\pi$
$282$		0			0
$283$	1.56823e13	+	2.71626e13i	0.513553	+	0.889500i	0.999876	+	0.0157208i	$0.00500430\pi$
$283$	1.56823e13	+	2.71626e13i	0.513553	+	0.889500i	−0.486324	+	0.873779i	$0.661662\pi$
$284$		0			0
$285$	−1.70599e13	+	2.95486e13i	−0.537440	+	0.930873i
$286$		0			0
$287$	5.31534e12	−	3.68961e13i	0.161131	−	1.11849i
$288$		0			0
$289$	−4.90664e13	+	8.49856e13i	−1.43168	+	2.47975i
$290$		0			0
$291$	1.42153e13	+	2.46217e13i	0.399342	+	0.691681i
$292$		0			0
$293$	1.14960e13			0.311010			0.155505	−	0.987835i	$-0.450300\pi$
$293$	1.14960e13			0.311010			0.155505	+	0.987835i	$0.450300\pi$
$294$		0			0
$295$	3.88324e13			1.01198
$296$		0			0
$297$	−6.07947e12	−	1.05299e13i	−0.152653	−	0.264403i
$298$		0			0
$299$	−2.02905e13	+	3.51441e13i	−0.491021	+	0.850474i
$300$		0			0
$301$	5.06633e12	−	3.51677e13i	0.118189	−	0.820404i
$302$		0			0
$303$	7.02982e12	−	1.21760e13i	0.158128	−	0.273886i
$304$		0			0
$305$	−4.08940e13	−	7.08304e13i	−0.887177	−	1.53664i
$306$		0			0
$307$	−5.80705e12			−0.121533			−0.0607666	−	0.998152i	$-0.519355\pi$
$307$	−5.80705e12			−0.121533			−0.0607666	+	0.998152i	$0.519355\pi$
$308$		0			0
$309$	−3.96096e13			−0.799888
$310$		0			0
$311$	−1.60195e13	−	2.77466e13i	−0.312224	−	0.540789i	0.666619	−	0.745399i	$-0.267741\pi$
$311$	−1.60195e13	−	2.77466e13i	−0.312224	−	0.540789i	−0.978844	+	0.204610i	$0.934407\pi$
$312$		0			0
$313$	4.73164e13	−	8.19544e13i	0.890262	−	1.54198i	0.0507009	−	0.998714i	$-0.483854\pi$
$313$	4.73164e13	−	8.19544e13i	0.890262	−	1.54198i	0.839561	−	0.543265i	$-0.182812\pi$
$314$		0			0
$315$	2.43190e13	−	9.72802e12i	0.441813	−	0.176733i
$316$		0			0
$317$	2.64621e13	−	4.58337e13i	0.464299	−	0.804190i	−0.534870	−	0.844934i	$-0.679640\pi$
$317$	2.64621e13	−	4.58337e13i	0.464299	−	0.804190i	0.999170	+	0.0407442i	$0.0129729\pi$
$318$		0			0
$319$	4.37410e13	+	7.57617e13i	0.741379	+	1.28411i
$320$		0			0
$321$	6.36754e13			1.04278
$322$		0			0
$323$	−1.61967e14			−2.56338
$324$		0			0
$325$	1.97540e13	+	3.42149e13i	0.302201	+	0.523427i
$326$		0			0
$327$	−2.32847e13	+	4.03303e13i	−0.344396	+	0.596512i
$328$		0			0
$329$	1.82601e13	+	1.43681e13i	0.261171	+	0.205505i
$330$		0			0
$331$	−6.99210e13	+	1.21107e14i	−0.967283	+	1.67538i	−0.263932	+	0.964541i	$0.585019\pi$
$331$	−6.99210e13	+	1.21107e14i	−0.967283	+	1.67538i	−0.703351	+	0.710842i	$0.748314\pi$
$332$		0			0
$333$	1.21758e13	+	2.10891e13i	0.162950	+	0.282237i
$334$		0			0
$335$	−5.30909e13			−0.687502
$336$		0			0
$337$	−1.30785e14			−1.63906			−0.819530	−	0.573037i	$-0.805765\pi$
$337$	−1.30785e14			−1.63906			−0.819530	+	0.573037i	$0.805765\pi$
$338$		0			0
$339$	−2.88991e12	−	5.00548e12i	−0.0350579	−	0.0607221i
$340$		0			0
$341$	2.53864e13	−	4.39706e13i	0.298162	−	0.516432i
$342$		0			0
$343$	−3.65925e13	+	7.99499e13i	−0.416174	+	0.909285i
$344$		0			0
$345$	6.30904e13	−	1.09276e14i	0.694958	−	1.20370i
$346$		0			0
$347$	3.07469e13	+	5.32552e13i	0.328087	+	0.568264i	0.982132	−	0.188192i	$-0.0602627\pi$
$347$	3.07469e13	+	5.32552e13i	0.328087	+	0.568264i	−0.654045	+	0.756456i	$0.726929\pi$
$348$		0			0
$349$	−1.06491e14			−1.10096			−0.550480	−	0.834848i	$-0.685555\pi$
$349$	−1.06491e14			−1.10096			−0.550480	+	0.834848i	$0.685555\pi$
$350$		0			0
$351$	1.11861e13			0.112070
$352$		0			0
$353$	−7.70363e13	−	1.33431e14i	−0.748056	−	1.29567i	−0.948753	−	0.316018i	$-0.897654\pi$
$353$	−7.70363e13	−	1.33431e14i	−0.748056	−	1.29567i	0.200697	−	0.979653i	$-0.435679\pi$
$354$		0			0
$355$	−2.56595e13	+	4.44436e13i	−0.241542	+	0.418363i
$356$		0			0
$357$	9.77134e13	+	7.68867e13i	0.891824	+	0.701739i
$358$		0			0
$359$	9.33953e10	−	1.61765e11i	0.000826620	−	0.00143175i	−0.865612	−	0.500716i	$-0.833070\pi$
$359$	9.33953e10	−	1.61765e11i	0.000826620	−	0.00143175i	0.866438	+	0.499284i	$0.166404\pi$
$360$		0			0
$361$	−4.08196e13	−	7.07016e13i	−0.350412	−	0.606931i
$362$		0			0
$363$	−1.05155e14			−0.875676
$364$		0			0
$365$	−1.41216e14			−1.14097
$366$		0			0
$367$	−3.13726e13	−	5.43389e13i	−0.245973	−	0.426037i	0.716432	−	0.697657i	$-0.245774\pi$
$367$	−3.13726e13	−	5.43389e13i	−0.245973	−	0.426037i	−0.962405	+	0.271620i	$0.912441\pi$
$368$		0			0
$369$	−2.47505e13	+	4.28692e13i	−0.188339	+	0.326212i
$370$		0			0
$371$	6.15366e13	−	2.46157e13i	0.454545	−	0.181826i
$372$		0			0
$373$	−4.79538e13	+	8.30585e13i	−0.343894	+	0.595642i	−0.985152	−	0.171683i	$-0.945079\pi$
$373$	−4.79538e13	+	8.30585e13i	−0.343894	+	0.595642i	0.641258	+	0.767325i	$0.278413\pi$
$374$		0			0
$375$	−2.24263e12	−	3.88435e12i	−0.0156166	−	0.0270487i
$376$		0			0
$377$	−8.04827e13			−0.544284
$378$		0			0
$379$	5.34853e13			0.351333			0.175667	−	0.984450i	$-0.443792\pi$
$379$	5.34853e13			0.351333			0.175667	+	0.984450i	$0.443792\pi$
$380$		0			0
$381$	−1.41775e13	−	2.45562e13i	−0.0904717	−	0.156702i
$382$		0			0
$383$	−1.15332e14	+	1.99762e14i	−0.715086	+	1.23857i	0.247840	+	0.968801i	$0.420279\pi$
$383$	−1.15332e14	+	1.99762e14i	−0.715086	+	1.23857i	−0.962926	+	0.269765i	$0.913054\pi$
$384$		0			0
$385$	5.35959e13	−	3.72033e14i	0.322922	−	2.24154i
$386$		0			0
$387$	−2.35911e13	+	4.08609e13i	−0.138146	+	0.239275i
$388$		0			0
$389$	−3.96021e13	−	6.85928e13i	−0.225421	−	0.390441i	0.731024	−	0.682351i	$-0.239043\pi$
$389$	−3.96021e13	−	6.85928e13i	−0.225421	−	0.390441i	−0.956446	+	0.291910i	$0.905709\pi$
$390$		0			0
$391$	5.98981e14			3.31468
$392$		0			0
$393$	−2.06952e14			−1.11355
$394$		0			0
$395$	3.08673e13	+	5.34638e13i	0.161516	+	0.279753i
$396$		0			0
$397$	−1.68428e13	+	2.91727e13i	−0.0857171	+	0.148466i	−0.905697	−	0.423927i	$-0.860651\pi$
$397$	−1.68428e13	+	2.91727e13i	−0.0857171	+	0.148466i	0.819979	+	0.572393i	$0.193985\pi$
$398$		0			0
$399$	−2.16875e13	+	1.50543e14i	−0.107364	+	0.745261i
$400$		0			0
$401$	−7.99473e13	+	1.38473e14i	−0.385043	+	0.666914i	−0.991775	−	0.127992i	$-0.959147\pi$
$401$	−7.99473e13	+	1.38473e14i	−0.385043	+	0.666914i	0.606732	+	0.794907i	$0.292480\pi$
$402$		0			0
$403$	2.33553e13	+	4.04526e13i	0.109448	+	0.189569i
$404$		0			0
$405$	−3.47817e13			−0.158617
$406$		0			0
$407$	3.49454e14			1.55103
$408$		0			0
$409$	1.43148e14	+	2.47940e14i	0.618455	+	1.07119i	0.989768	+	0.142687i	$0.0455743\pi$
$409$	1.43148e14	+	2.47940e14i	0.618455	+	1.07119i	−0.371313	+	0.928508i	$0.621092\pi$
$410$		0			0
$411$	4.04440e13	−	7.00511e13i	0.170108	−	0.294635i
$412$		0			0
$413$	1.60722e14	−	6.42916e13i	0.658189	−	0.263287i
$414$		0			0
$415$	4.02087e13	−	6.96434e13i	0.160345	−	0.277725i
$416$		0			0
$417$	1.27945e14	+	2.21607e14i	0.496907	+	0.860669i
$418$		0			0
$419$	1.92895e14			0.729697			0.364849	−	0.931067i	$-0.381121\pi$
$419$	1.92895e14			0.729697			0.364849	+	0.931067i	$0.381121\pi$
$420$		0			0
$421$	−3.42122e14			−1.26075			−0.630375	−	0.776291i	$-0.717099\pi$
$421$	−3.42122e14			−1.26075			−0.630375	+	0.776291i	$0.717099\pi$
$422$		0			0
$423$	−1.54272e13	−	2.67208e13i	−0.0553881	−	0.0959350i
$424$		0			0
$425$	2.91572e14	−	5.05017e14i	1.02001	−	1.76672i
$426$		0			0
$427$	−2.86523e14	−	2.25453e14i	−0.976801	−	0.768605i
$428$		0			0
$429$	8.02627e13	−	1.39019e14i	0.266685	−	0.461912i
$430$		0			0
$431$	2.28717e13	+	3.96150e13i	0.0740754	+	0.128302i	0.900684	−	0.434475i	$-0.143066\pi$
$431$	2.28717e13	+	3.96150e13i	0.0740754	+	0.128302i	−0.826608	+	0.562778i	$0.809733\pi$
$432$		0			0
$433$	1.26665e14			0.399921			0.199961	−	0.979804i	$-0.435919\pi$
$433$	1.26665e14			0.399921			0.199961	+	0.979804i	$0.435919\pi$
$434$		0			0
$435$	2.50250e14			0.770342
$436$		0			0
$437$	3.66358e14	+	6.34551e14i	1.09966	+	1.90466i
$438$		0			0
$439$	1.71750e14	−	2.97480e14i	0.502739	−	0.870770i	−0.497256	−	0.867604i	$-0.665659\pi$
$439$	1.71750e14	−	2.97480e14i	0.502739	−	0.870770i	0.999995	−	0.00316608i	$-0.00100780\pi$
$440$		0			0
$441$	8.45474e13	−	8.05260e13i	0.241373	−	0.229892i
$442$		0			0
$443$	1.89338e14	−	3.27943e14i	0.527251	−	0.913226i	−0.472244	−	0.881468i	$-0.656556\pi$
$443$	1.89338e14	−	3.27943e14i	0.527251	−	0.913226i	0.999496	−	0.0317582i	$-0.0101107\pi$
$444$		0			0
$445$	−3.40824e14	−	5.90325e14i	−0.925871	−	1.60366i
$446$		0			0
$447$	−3.72676e14			−0.987735
$448$		0			0
$449$	−5.17450e14			−1.33818			−0.669089	−	0.743182i	$-0.733315\pi$
$449$	−5.17450e14			−1.33818			−0.669089	+	0.743182i	$0.733315\pi$
$450$		0			0
$451$	3.55180e14	+	6.15190e14i	0.896350	+	1.55252i
$452$		0			0
$453$	2.07198e14	−	3.58877e14i	0.510323	−	0.883905i
$454$		0			0
$455$	2.71758e14	+	2.13835e14i	0.653311	+	0.514064i
$456$		0			0
$457$	1.24660e14	−	2.15918e14i	0.292543	−	0.506699i	−0.681867	−	0.731476i	$-0.738832\pi$
$457$	1.24660e14	−	2.15918e14i	0.292543	−	0.506699i	0.974410	+	0.224777i	$0.0721652\pi$
$458$		0			0
$459$	−8.25545e13	−	1.42989e14i	−0.189135	−	0.327591i
$460$		0			0
$461$	−1.92178e14			−0.429882			−0.214941	−	0.976627i	$-0.568956\pi$
$461$	−1.92178e14			−0.429882			−0.214941	+	0.976627i	$0.568956\pi$
$462$		0			0
$463$	−1.03491e14			−0.226052			−0.113026	−	0.993592i	$-0.536054\pi$
$463$	−1.03491e14			−0.226052			−0.113026	+	0.993592i	$0.536054\pi$
$464$		0			0
$465$	−7.26201e13	−	1.25782e14i	−0.154905	−	0.268304i
$466$		0			0
$467$	−3.27918e14	+	5.67970e14i	−0.683159	+	1.18327i	0.290852	+	0.956768i	$0.406061\pi$
$467$	−3.27918e14	+	5.67970e14i	−0.683159	+	1.18327i	−0.974012	+	0.226498i	$0.927272\pi$
$468$		0			0
$469$	−2.19736e14	+	8.78983e13i	−0.447148	+	0.178867i
$470$		0			0
$471$	9.40633e13	−	1.62922e14i	0.186984	−	0.323866i
$472$		0			0
$473$	3.38541e14	+	5.86371e14i	0.657469	+	1.13877i
$474$		0			0
$475$	7.13342e14			1.35358
$476$		0			0
$477$	−8.80112e13			−0.163188
$478$		0			0
$479$	4.81820e14	+	8.34537e14i	0.873051	+	1.51217i	0.858825	+	0.512270i	$0.171195\pi$
$479$	4.81820e14	+	8.34537e14i	0.873051	+	1.51217i	0.0142262	+	0.999899i	$0.495472\pi$
$480$		0			0
$481$	−1.60748e14	+	2.78423e14i	−0.284673	+	0.493068i
$482$		0			0
$483$	8.02041e13	−	5.56732e14i	0.138831	−	0.963689i
$484$		0			0
$485$	5.83548e14	−	1.01073e15i	0.987409	−	1.71024i
$486$		0			0
$487$	−1.11887e14	−	1.93793e14i	−0.185084	−	0.320575i	0.758521	−	0.651649i	$-0.225922\pi$
$487$	−1.11887e14	−	1.93793e14i	−0.185084	−	0.320575i	−0.943605	+	0.331074i	$0.892589\pi$
$488$		0			0
$489$	−1.65615e14			−0.267856
$490$		0			0
$491$	5.56691e14			0.880372			0.440186	−	0.897907i	$-0.354913\pi$
$491$	5.56691e14			0.880372			0.440186	+	0.897907i	$0.354913\pi$
$492$		0			0
$493$	5.93969e14	+	1.02879e15i	0.918557	+	1.59099i
$494$		0			0
$495$	−2.49566e14	+	4.32261e14i	−0.377448	+	0.653758i
$496$		0			0
$497$	−3.26198e13	+	2.26429e14i	−0.0482527	+	0.334943i
$498$		0			0
$499$	−8.95193e13	+	1.55052e14i	−0.129528	+	0.224349i	−0.923494	−	0.383613i	$-0.874680\pi$
$499$	−8.95193e13	+	1.55052e14i	−0.129528	+	0.224349i	0.793966	+	0.607962i	$0.208013\pi$
$500$		0			0
$501$	−2.87010e13	−	4.97116e13i	−0.0406247	−	0.0703640i
$502$		0			0
$503$	−7.92183e14			−1.09699			−0.548494	−	0.836155i	$-0.684799\pi$
$503$	−7.92183e14			−1.09699			−0.548494	+	0.836155i	$0.684799\pi$
$504$		0			0
$505$	−5.77157e14			−0.781972
$506$		0			0
$507$	−1.43906e14	−	2.49253e14i	−0.190782	−	0.330444i
$508$		0			0
$509$	−3.60691e14	+	6.24735e14i	−0.467937	+	0.810491i	−0.999329	−	0.0366356i	$-0.988336\pi$
$509$	−3.60691e14	+	6.24735e14i	−0.467937	+	0.810491i	0.531392	+	0.847126i	$0.321669\pi$
$510$		0			0
$511$	−5.84476e14	+	2.33800e14i	−0.742082	+	0.296845i
$512$		0			0
$513$	1.00986e14	−	1.74914e14i	0.125493	−	0.217359i
$514$		0			0
$515$	8.13000e14	+	1.40816e15i	0.988897	+	1.71282i
$516$		0			0
$517$	−4.42775e14			−0.527211
$518$		0			0
$519$	−1.80286e13			−0.0210156
$520$		0			0
$521$	−5.08053e14	−	8.79973e14i	−0.579831	−	1.00430i	−0.995498	−	0.0947796i	$-0.969785\pi$
$521$	−5.08053e14	−	8.79973e14i	−0.579831	−	1.00430i	0.415668	−	0.909517i	$-0.363548\pi$
$522$		0			0
$523$	−8.62100e13	+	1.49320e14i	−0.0963382	+	0.166863i	−0.910166	−	0.414243i	$-0.864046\pi$
$523$	−8.62100e13	+	1.49320e14i	−0.0963382	+	0.166863i	0.813828	+	0.581106i	$0.197380\pi$
$524$		0			0
$525$	−4.30354e14	−	3.38628e14i	−0.470923	−	0.370550i
$526$		0			0
$527$	3.44728e14	−	5.97087e14i	0.369418	−	0.639851i
$528$		0			0
$529$	−8.78450e14	−	1.52152e15i	−0.921957	−	1.59688i
$530$		0			0
$531$	−2.29869e14			−0.236299
$532$		0			0
$533$	−6.53526e14			−0.658056
$534$		0			0
$535$	−1.30696e15	−	2.26372e15i	−1.28919	−	2.23294i
$536$		0			0
$537$	−2.66742e13	+	4.62010e13i	−0.0257770	+	0.0446471i
$538$		0			0
$539$	−3.94118e14	−	1.62853e15i	−0.373154	−	1.54190i
$540$		0			0
$541$	6.93188e14	−	1.20064e15i	0.643082	−	1.11385i	−0.341659	−	0.939824i	$-0.610989\pi$
$541$	6.93188e14	−	1.20064e15i	0.643082	−	1.11385i	0.984741	−	0.174026i	$-0.0556778\pi$
$542$		0			0
$543$	8.14802e13	+	1.41128e14i	0.0740718	+	0.128296i
$544$		0			0
$545$	1.91171e15			1.70310
$546$		0			0
$547$	−1.44994e15			−1.26596			−0.632980	−	0.774168i	$-0.718168\pi$
$547$	−1.44994e15			−1.26596			−0.632980	+	0.774168i	$0.718168\pi$
$548$		0			0
$549$	2.42073e14	+	4.19282e14i	0.207156	+	0.358805i
$550$		0			0
$551$	−7.26585e14	+	1.25848e15i	−0.609471	+	1.05563i
$552$		0			0
$553$	2.16271e14	+	1.70175e14i	0.177832	+	0.139929i
$554$		0			0
$555$	4.99823e14	−	8.65719e14i	0.402907	−	0.697855i
$556$		0			0
$557$	4.75569e14	+	8.23710e14i	0.375846	+	0.650985i	0.990453	−	0.137849i	$-0.0440188\pi$
$557$	4.75569e14	+	8.23710e14i	0.375846	+	0.650985i	−0.614607	+	0.788833i	$0.710685\pi$
$558$		0			0
$559$	−6.22910e14			−0.482681
$560$		0			0
$561$	−2.36938e15			−1.80028
$562$		0			0
$563$	1.30049e15	+	2.25252e15i	0.968974	+	1.67831i	0.698536	+	0.715575i	$0.253835\pi$
$563$	1.30049e15	+	2.25252e15i	0.968974	+	1.67831i	0.270438	+	0.962737i	$0.412832\pi$
$564$		0			0
$565$	−1.18633e14	+	2.05478e14i	−0.0866838	+	0.150141i
$566$		0			0
$567$	−1.43957e14	+	5.75852e13i	−0.103163	+	0.0412671i
$568$		0			0
$569$	−1.06839e15	+	1.85051e15i	−0.750955	+	1.30069i	0.196405	+	0.980523i	$0.437073\pi$
$569$	−1.06839e15	+	1.85051e15i	−0.750955	+	1.30069i	−0.947360	+	0.320170i	$0.896260\pi$
$570$		0			0
$571$	7.97369e14	+	1.38108e15i	0.549744	+	0.952185i	0.998292	+	0.0584258i	$0.0186081\pi$
$571$	7.97369e14	+	1.38108e15i	0.549744	+	0.952185i	−0.448548	+	0.893759i	$0.648059\pi$
$572$		0			0
$573$	−1.75386e14			−0.118616
$574$		0			0
$575$	−2.63806e15			−1.75030
$576$		0			0
$577$	3.79258e14	+	6.56893e14i	0.246869	+	0.427590i	0.962656	−	0.270729i	$-0.0872648\pi$
$577$	3.79258e14	+	6.56893e14i	0.246869	+	0.427590i	−0.715786	+	0.698320i	$0.753931\pi$
$578$		0			0
$579$	−2.60470e14	+	4.51147e14i	−0.166351	+	0.288129i
$580$		0			0
$581$	5.11155e13	−	3.54815e14i	0.0320320	−	0.222348i
$582$		0			0
$583$	−6.31498e14	+	1.09379e15i	−0.388325	+	0.672598i
$584$		0			0
$585$	−2.29599e14	−	3.97676e14i	−0.138552	−	0.239979i
$586$		0			0
$587$	−4.11354e14			−0.243616			−0.121808	−	0.992554i	$-0.538869\pi$
$587$	−4.11354e14			−0.243616			−0.121808	+	0.992554i	$0.538869\pi$
$588$		0			0
$589$	8.43392e14			0.490225
$590$		0			0
$591$	3.40403e14	+	5.89595e14i	0.194206	+	0.336374i
$592$		0			0
$593$	3.57881e14	−	6.19868e14i	0.200418	−	0.347135i	−0.748245	−	0.663423i	$-0.769103\pi$
$593$	3.57881e14	−	6.19868e14i	0.200418	−	0.347135i	0.948663	+	0.316288i	$0.102437\pi$
$594$		0			0
$595$	7.27791e14	−	5.05192e15i	0.400095	−	2.77724i
$596$		0			0
$597$	−5.18756e14	+	8.98512e14i	−0.279965	+	0.484914i
$598$		0			0
$599$	−2.84205e14	−	4.92257e14i	−0.150586	−	0.260822i	0.780857	−	0.624710i	$-0.214783\pi$
$599$	−2.84205e14	−	4.92257e14i	−0.150586	−	0.260822i	−0.931443	+	0.363887i	$0.881449\pi$
$600$		0			0
$601$	1.10895e15			0.576905			0.288452	−	0.957494i	$-0.406859\pi$
$601$	1.10895e15			0.576905			0.288452	+	0.957494i	$0.406859\pi$
$602$		0			0
$603$	3.14273e14			0.160532
$604$		0			0
$605$	2.15834e15	+	3.73835e15i	1.08259	+	1.87510i
$606$		0			0
$607$	−1.29176e15	+	2.23739e15i	−0.636272	+	1.10205i	0.349972	+	0.936760i	$0.386191\pi$
$607$	−1.29176e15	+	2.23739e15i	−0.636272	+	1.10205i	−0.986244	+	0.165295i	$0.947142\pi$
$608$		0			0
$609$	1.03575e15	−	4.14319e14i	0.501027	−	0.200419i
$610$		0			0
$611$	2.03674e14	−	3.52774e14i	0.0967631	−	0.167599i
$612$		0			0
$613$	3.93710e14	+	6.81926e14i	0.183715	+	0.318203i	0.943143	−	0.332388i	$-0.107854\pi$
$613$	3.93710e14	+	6.81926e14i	0.183715	+	0.318203i	−0.759428	+	0.650591i	$0.774521\pi$
$614$		0			0
$615$	2.03205e15			0.931367
$616$		0			0
$617$	−2.31786e15			−1.04356			−0.521781	−	0.853080i	$-0.674732\pi$
$617$	−2.31786e15			−1.04356			−0.521781	+	0.853080i	$0.674732\pi$
$618$		0			0
$619$	−5.96403e14	−	1.03300e15i	−0.263780	−	0.456880i	0.703463	−	0.710731i	$-0.251636\pi$
$619$	−5.96403e14	−	1.03300e15i	−0.263780	−	0.456880i	−0.967243	+	0.253852i	$0.918303\pi$
$620$		0			0
$621$	−3.73465e14	+	6.46861e14i	−0.162273	+	0.281065i
$622$		0			0
$623$	−2.38798e15	−	1.87900e15i	−1.01940	−	0.802127i
$624$		0			0
$625$	1.14521e15	−	1.98356e15i	0.480334	−	0.831963i
$626$		0			0
$627$	−1.44920e15	−	2.51008e15i	−0.597250	−	1.03447i
$628$		0			0
$629$	4.74532e15			1.92171
$630$		0			0
$631$	−2.26884e15			−0.902905			−0.451452	−	0.892295i	$-0.649094\pi$
$631$	−2.26884e15			−0.902905			−0.451452	+	0.892295i	$0.649094\pi$
$632$		0			0
$633$	−7.19010e14	−	1.24536e15i	−0.281200	−	0.487052i
$634$		0			0
$635$	−5.81996e14	+	1.00805e15i	−0.223699	+	0.387458i
$636$		0			0
$637$	1.47880e15	+	4.35109e14i	0.558654	+	0.164373i
$638$		0			0
$639$	1.51892e14	−	2.63085e14i	0.0564002	−	0.0976880i
$640$		0			0
$641$	−1.31661e15	−	2.28044e15i	−0.480549	−	0.832336i	0.519202	−	0.854652i	$-0.326229\pi$
$641$	−1.31661e15	−	2.28044e15i	−0.480549	−	0.832336i	−0.999751	+	0.0223160i	$0.992896\pi$
$642$		0			0
$643$	3.87700e13			0.0139103			0.00695513	−	0.999976i	$-0.497786\pi$
$643$	3.87700e13			0.0139103			0.00695513	+	0.999976i	$0.497786\pi$
$644$		0			0
$645$	1.93685e15			0.683154
$646$		0			0
$647$	−2.79096e15	−	4.83409e15i	−0.967788	−	1.67626i	−0.701930	−	0.712246i	$-0.747678\pi$
$647$	−2.79096e15	−	4.83409e15i	−0.967788	−	1.67626i	−0.265858	−	0.964012i	$-0.585655\pi$
$648$		0			0
$649$	−1.64936e15	+	2.85677e15i	−0.562302	+	0.973935i
$650$		0			0
$651$	−5.08812e14	−	4.00363e14i	−0.170554	−	0.134202i
$652$		0			0
$653$	−7.29281e14	+	1.26315e15i	−0.240366	+	0.416326i	−0.960818	−	0.277178i	$-0.910601\pi$
$653$	−7.29281e14	+	1.26315e15i	−0.240366	+	0.416326i	0.720453	+	0.693504i	$0.243934\pi$
$654$		0			0
$655$	4.24775e15	+	7.35732e15i	1.37668	+	2.38447i
$656$		0			0
$657$	8.35934e14			0.266417
$658$		0			0
$659$	2.66992e15			0.836812			0.418406	−	0.908260i	$-0.362589\pi$
$659$	2.66992e15			0.836812			0.418406	+	0.908260i	$0.362589\pi$
$660$		0			0
$661$	1.59358e15	+	2.76015e15i	0.491207	+	0.850796i	0.999949	−	0.0101235i	$-0.00322246\pi$
$661$	1.59358e15	+	2.76015e15i	0.491207	+	0.850796i	−0.508742	+	0.860919i	$0.669889\pi$
$662$		0			0
$663$	1.08991e15	−	1.88777e15i	0.330418	−	0.572302i
$664$		0			0
$665$	5.79706e15	−	2.31892e15i	1.72858	−	0.691461i
$666$		0			0
$667$	2.68704e15	−	4.65408e15i	0.788100	−	1.36503i
$668$		0			0
$669$	1.79346e15	+	3.10637e15i	0.517427	+	0.896210i
$670$		0			0
$671$	6.94769e15			1.97182
$672$		0			0
$673$	−3.46267e15			−0.966782			−0.483391	−	0.875405i	$-0.660595\pi$
$673$	−3.46267e15			−0.966782			−0.483391	+	0.875405i	$0.660595\pi$
$674$		0			0
$675$	3.63590e14	+	6.29757e14i	0.0998715	+	0.172983i
$676$		0			0
$677$	−7.01365e14	+	1.21480e15i	−0.189543	+	0.328297i	−0.945098	−	0.326788i	$-0.894034\pi$
$677$	−7.01365e14	+	1.21480e15i	−0.189543	+	0.328297i	0.755555	+	0.655085i	$0.227367\pi$
$678$		0			0
$679$	7.41839e14	−	5.14943e15i	0.197254	−	1.36923i
$680$		0			0
$681$	−4.08730e14	+	7.07940e14i	−0.106937	+	0.185220i
$682$		0			0
$683$	−4.72063e14	−	8.17638e14i	−0.121531	−	0.210498i	0.798841	−	0.601543i	$-0.205447\pi$
$683$	−4.72063e14	−	8.17638e14i	−0.121531	−	0.210498i	−0.920372	+	0.391045i	$0.872114\pi$
$684$		0			0
$685$	−3.32050e15			−0.841213
$686$		0			0
$687$	−8.32028e14			−0.207432
$688$		0			0
$689$	−5.80973e14	−	1.00628e15i	−0.142544	−	0.246894i
$690$		0			0
$691$	4.25557e13	−	7.37087e13i	0.0102761	−	0.0177988i	−0.860842	−	0.508873i	$-0.830062\pi$
$691$	4.25557e13	−	7.37087e13i	0.0102761	−	0.0177988i	0.871118	+	0.491074i	$0.163396\pi$
$692$		0			0
$693$	−3.17262e14	+	2.20226e15i	−0.0754024	+	0.523402i
$694$		0			0
$695$	5.25223e15	−	9.09712e15i	1.22865	−	2.12808i
$696$		0			0
$697$	4.82307e15	+	8.35381e15i	1.11056	+	1.92355i
$698$		0			0
$699$	4.47919e15			1.01525
$700$		0			0
$701$	−1.88852e15			−0.421380			−0.210690	−	0.977553i	$-0.567571\pi$
$701$	−1.88852e15			−0.421380			−0.210690	+	0.977553i	$0.567571\pi$
$702$		0			0
$703$	2.90241e15	+	5.02712e15i	0.637535	+	1.10424i
$704$		0			0
$705$	−6.33298e14	+	1.09690e15i	−0.136952	+	0.237208i
$706$		0			0
$707$	−2.38878e15	+	9.55551e14i	−0.508591	+	0.203445i
$708$		0			0
$709$	3.31898e15	−	5.74865e15i	0.695746	−	1.20507i	−0.274182	−	0.961678i	$-0.588407\pi$
$709$	3.31898e15	−	5.74865e15i	0.695746	−	1.20507i	0.969928	−	0.243390i	$-0.0782596\pi$
$710$		0			0
$711$	−1.82720e14	−	3.16480e14i	−0.0377140	−	0.0653226i
$712$		0			0
$713$	−3.11901e15			−0.633904
$714$		0			0
$715$	−6.58967e15			−1.31880
$716$		0			0
$717$	6.44005e14	+	1.11545e15i	0.126921	+	0.219834i
$718$		0			0
$719$	−1.38384e15	+	2.39689e15i	−0.268583	+	0.465199i	−0.968496	−	0.249029i	$-0.919889\pi$
$719$	−1.38384e15	+	2.39689e15i	−0.268583	+	0.465199i	0.699913	+	0.714228i	$0.253222\pi$
$720$		0			0
$721$	5.69627e15	+	4.48216e15i	1.08880	+	0.856729i
$722$		0			0
$723$	−1.74366e15	+	3.02011e15i	−0.328247	+	0.568541i
$724$		0			0
$725$	−2.61599e15	−	4.53102e15i	−0.485039	−	0.840112i
$726$		0			0
$727$	−3.14769e15			−0.574847			−0.287424	−	0.957804i	$-0.592799\pi$
$727$	−3.14769e15			−0.574847			−0.287424	+	0.957804i	$0.592799\pi$
$728$		0			0
$729$	2.05891e14			0.0370370
$730$		0			0
$731$	4.59713e15	+	7.96246e15i	0.814594	+	1.41092i
$732$		0			0
$733$	2.74382e15	−	4.75244e15i	0.478943	−	0.829554i	−0.520765	−	0.853700i	$-0.674353\pi$
$733$	2.74382e15	−	4.75244e15i	0.478943	−	0.829554i	0.999708	+	0.0241459i	$0.00768663\pi$
$734$		0			0
$735$	−4.59813e15	−	1.35291e15i	−0.790681	−	0.232643i
$736$		0			0
$737$	2.25497e15	−	3.90573e15i	0.382006	−	0.661654i
$738$		0			0
$739$	−5.07891e15	−	8.79693e15i	−0.847669	−	1.46820i	−0.883283	−	0.468839i	$-0.844672\pi$
$739$	−5.07891e15	−	8.79693e15i	−0.847669	−	1.46820i	0.0356150	−	0.999366i	$-0.488661\pi$
$740$		0			0
$741$	2.66650e15			0.438471
$742$		0			0
$743$	−1.02606e16			−1.66240			−0.831198	−	0.555977i	$-0.812344\pi$
$743$	−1.02606e16			−1.66240			−0.831198	+	0.555977i	$0.812344\pi$
$744$		0			0
$745$	7.64929e15	+	1.32490e16i	1.22113	+	2.11506i
$746$		0			0
$747$	−2.38016e14	+	4.12256e14i	−0.0374406	+	0.0648490i
$748$		0			0
$749$	−9.15718e15	−	7.20541e15i	−1.41942	−	1.11689i
$750$		0			0
$751$	4.70947e15	−	8.15703e15i	0.719369	−	1.24598i	−0.241881	−	0.970306i	$-0.577764\pi$
$751$	4.70947e15	−	8.15703e15i	0.719369	−	1.24598i	0.961250	−	0.275678i	$-0.0889024\pi$
$752$		0			0
$753$	−7.93976e14	−	1.37521e15i	−0.119518	−	0.207012i
$754$		0			0
$755$	−1.70112e16			−2.52363
$756$		0			0
$757$	−3.83576e15			−0.560820			−0.280410	−	0.959880i	$-0.590470\pi$
$757$	−3.83576e15			−0.560820			−0.280410	+	0.959880i	$0.590470\pi$
$758$		0			0
$759$	5.35938e15	+	9.28271e15i	0.772297	+	1.33766i
$760$		0			0
$761$	2.03651e15	−	3.52733e15i	0.289248	−	0.500992i	−0.684383	−	0.729123i	$-0.739928\pi$
$761$	2.03651e15	−	3.52733e15i	0.289248	−	0.500992i	0.973630	+	0.228131i	$0.0732615\pi$
$762$		0			0
$763$	7.91230e15	−	3.16505e15i	1.10769	−	0.443094i
$764$		0			0
$765$	−3.38891e15	+	5.86977e15i	−0.467652	+	0.809996i
$766$		0			0
$767$	−1.51740e15	−	2.62821e15i	−0.206407	−	0.357507i
$768$		0			0
$769$	2.76454e15			0.370704			0.185352	−	0.982672i	$-0.440657\pi$
$769$	2.76454e15			0.370704			0.185352	+	0.982672i	$0.440657\pi$
$770$		0			0
$771$	2.27615e14			0.0300886
$772$		0			0
$773$	1.95356e15	+	3.38366e15i	0.254588	+	0.440960i	0.964784	−	0.263045i	$-0.0847267\pi$
$773$	1.95356e15	+	3.38366e15i	0.254588	+	0.440960i	−0.710195	+	0.704005i	$0.751393\pi$
$774$		0			0
$775$	−1.51827e15	+	2.62972e15i	−0.195069	+	0.337870i
$776$		0			0
$777$	6.35403e14	−	4.41061e15i	0.0804884	−	0.558706i
$778$		0			0
$779$	−5.89992e15	+	1.02190e16i	−0.736869	+	1.27629i
$780$		0			0
$781$	−2.17971e15	−	3.77537e15i	−0.268422	−	0.464921i
$782$		0			0
$783$	−1.48136e15			−0.179875
$784$		0			0
$785$	−7.72271e15			−0.924670
$786$		0			0
$787$	−2.35960e15	−	4.08695e15i	−0.278598	−	0.482546i	0.692439	−	0.721477i	$-0.256536\pi$
$787$	−2.35960e15	−	4.08695e15i	−0.278598	−	0.482546i	−0.971037	+	0.238931i	$0.923203\pi$
$788$		0			0
$789$	−1.86975e15	+	3.23851e15i	−0.217701	+	0.377069i
$790$		0			0
$791$	−1.50813e14	+	1.04686e15i	−0.0173168	+	0.120203i
$792$		0			0
$793$	−3.19591e15	+	5.53547e15i	−0.361902	+	0.626833i
$794$		0			0
$795$	1.80646e15	+	3.12888e15i	0.201748	+	0.349437i
$796$		0			0
$797$	3.65817e15			0.402942			0.201471	−	0.979494i	$-0.435428\pi$
$797$	3.65817e15			0.402942			0.201471	+	0.979494i	$0.435428\pi$
$798$		0			0
$799$	−6.01254e15			−0.653206
$800$		0			0
$801$	2.01752e15	+	3.49444e15i	0.216191	+	0.374454i
$802$		0			0
$803$	5.99800e15	−	1.03888e16i	0.633973	−	1.09807i
$804$		0			0
$805$	−2.14385e16	+	8.57577e15i	−2.23521	+	0.894120i
$806$		0			0
$807$	4.22216e15	−	7.31299e15i	0.434240	−	0.752126i
$808$		0			0
$809$	1.03881e15	+	1.79927e15i	0.105395	+	0.182549i	0.913899	−	0.405941i	$-0.133056\pi$
$809$	1.03881e15	+	1.79927e15i	0.105395	+	0.182549i	−0.808505	+	0.588490i	$0.799723\pi$
$810$		0			0
$811$	4.10667e15			0.411032			0.205516	−	0.978654i	$-0.434113\pi$
$811$	4.10667e15			0.411032			0.205516	+	0.978654i	$0.434113\pi$
$812$		0			0
$813$	1.21736e15			0.120205
$814$		0			0
$815$	3.39930e15	+	5.88776e15i	0.331148	+	0.573566i
$816$		0			0
$817$	−5.62353e15	+	9.74024e15i	−0.540490	+	0.936157i
$818$		0			0
$819$	−1.60868e15	−	1.26580e15i	−0.152548	−	0.120034i
$820$		0			0
$821$	9.58321e15	−	1.65986e16i	0.896651	−	1.55305i	0.0649036	−	0.997892i	$-0.479326\pi$
$821$	9.58321e15	−	1.65986e16i	0.896651	−	1.55305i	0.831748	−	0.555154i	$-0.187341\pi$
$822$		0			0
$823$	4.84606e15	+	8.39363e15i	0.447394	+	0.774909i	0.998216	−	0.0597140i	$-0.0190189\pi$
$823$	4.84606e15	+	8.39363e15i	0.447394	+	0.774909i	−0.550822	+	0.834623i	$0.685686\pi$
$824$		0			0
$825$	1.04353e16			0.950627
$826$		0			0
$827$	−6.38672e15			−0.574113			−0.287057	−	0.957914i	$-0.592677\pi$
$827$	−6.38672e15			−0.574113			−0.287057	+	0.957914i	$0.592677\pi$
$828$		0			0
$829$	−9.07328e15	−	1.57154e16i	−0.804849	−	1.39404i	−0.916393	−	0.400280i	$-0.868913\pi$
$829$	−9.07328e15	−	1.57154e16i	−0.804849	−	1.39404i	0.111544	−	0.993760i	$-0.464421\pi$
$830$		0			0
$831$	3.79498e15	−	6.57310e15i	0.332204	−	0.575393i
$832$		0			0
$833$	−5.35182e15	−	2.21142e16i	−0.462332	−	1.91040i
$834$		0			0
$835$	−1.17819e15	+	2.04069e15i	−0.100448	+	0.173981i
$836$		0			0
$837$	4.29876e14	+	7.44568e14i	0.0361704	+	0.0626490i
$838$		0			0
$839$	−1.06308e16			−0.882823			−0.441412	−	0.897305i	$-0.645522\pi$
$839$	−1.06308e16			−0.882823			−0.441412	+	0.897305i	$0.645522\pi$
$840$		0			0
$841$	−1.54230e15			−0.126413
$842$		0			0
$843$	−2.06068e15	−	3.56921e15i	−0.166709	−	0.288749i
$844$		0			0
$845$	−5.90745e15	+	1.02320e16i	−0.471724	+	0.817050i
$846$		0			0
$847$	1.51224e16	+	1.18992e16i	1.19196	+	0.937902i
$848$		0			0
$849$	−3.81081e15	+	6.60051e15i	−0.296500	+	0.513553i
$850$		0			0
$851$	−1.07336e16	−	1.85911e16i	−0.824390	−	1.42788i
$852$		0			0
$853$	−1.28925e15			−0.0977500			−0.0488750	−	0.998805i	$-0.515564\pi$
$853$	−1.28925e15			−0.0977500			−0.0488750	+	0.998805i	$0.515564\pi$
$854$		0			0
$855$	−8.29112e15			−0.620582
$856$		0			0
$857$	5.00063e15	+	8.66134e15i	0.369513	+	0.640015i	0.989489	−	0.144605i	$-0.0461912\pi$
$857$	5.00063e15	+	8.66134e15i	0.369513	+	0.640015i	−0.619976	+	0.784620i	$0.712858\pi$
$858$		0			0
$859$	−7.21775e15	+	1.25015e16i	−0.526550	+	0.912011i	0.472972	+	0.881078i	$0.343181\pi$
$859$	−7.21775e15	+	1.25015e16i	−0.526550	+	0.912011i	−0.999521	+	0.0309334i	$0.990152\pi$
$860$		0			0
$861$	8.41039e15	−	3.36430e15i	0.605757	−	0.242313i
$862$		0			0
$863$	−7.20775e15	+	1.24842e16i	−0.512555	+	0.887771i	0.487339	+	0.873213i	$0.337968\pi$
$863$	−7.20775e15	+	1.24842e16i	−0.512555	+	0.887771i	−0.999894	+	0.0145582i	$0.995366\pi$
$864$		0			0
$865$	3.70042e14	+	6.40932e14i	0.0259814	+	0.0450011i
$866$		0			0
$867$	−2.38463e16			−1.65316
$868$		0			0
$869$	−5.24420e15			−0.358980
$870$		0			0
$871$	2.07456e15	+	3.59324e15i	0.140225	+	0.242877i
$872$		0			0
$873$	−3.45432e15	+	5.98307e15i	−0.230560	+	0.399342i
$874$		0			0
$875$	−1.17034e14	+	8.12383e14i	−0.00771377	+	0.0535447i
$876$		0			0
$877$	6.96716e15	−	1.20675e16i	0.453480	−	0.785451i	−0.545119	−	0.838359i	$-0.683516\pi$
$877$	6.96716e15	−	1.20675e16i	0.453480	−	0.785451i	0.998599	+	0.0529078i	$0.0168489\pi$
$878$		0			0
$879$	1.39676e15	+	2.41926e15i	0.0897809	+	0.155505i
$880$		0			0
$881$	2.49324e16			1.58269			0.791345	−	0.611370i	$-0.209381\pi$
$881$	2.49324e16			1.58269			0.791345	+	0.611370i	$0.209381\pi$
$882$		0			0
$883$	2.20922e16			1.38502			0.692509	−	0.721409i	$-0.256505\pi$
$883$	2.20922e16			1.38502			0.692509	+	0.721409i	$0.256505\pi$
$884$		0			0
$885$	4.71814e15	+	8.17205e15i	0.292134	+	0.505992i
$886$		0			0
$887$	1.21177e16	−	2.09885e16i	0.741040	−	1.28352i	−0.210982	−	0.977490i	$-0.567666\pi$
$887$	1.21177e16	−	2.09885e16i	0.741040	−	1.28352i	0.952022	−	0.306029i	$-0.0990005\pi$
$888$		0			0
$889$	−7.39866e14	+	5.13574e15i	−0.0446882	+	0.310201i
$890$		0			0
$891$	1.47731e15	−	2.55878e15i	0.0881342	−	0.152653i
$892$		0			0
$893$	−3.67748e15	−	6.36958e15i	−0.216704	−	0.375343i
$894$		0			0
$895$	2.18998e15			0.127472
$896$		0			0
$897$	−9.86116e15			−0.566983
$898$		0			0
$899$	−3.09291e15	−	5.35707e15i	−0.175666	−	0.304263i
$900$		0			0
$901$	−8.57526e15	+	1.48528e16i	−0.481128	+	0.833339i
$902$		0			0
$903$	8.01639e15	−	3.20669e15i	0.444320	−	0.177736i
$904$		0			0
$905$	3.34481e15	−	5.79338e15i	0.183149	−	0.317223i
$906$		0			0
$907$	−9.72286e15	−	1.68405e16i	−0.525961	−	0.910992i	−0.999543	−	0.0302417i	$-0.990372\pi$
$907$	−9.72286e15	−	1.68405e16i	−0.525961	−	0.910992i	0.473581	−	0.880750i	$-0.342961\pi$
$908$		0			0
$909$	3.41649e15			0.182591
$910$		0			0
$911$	−9.41580e14			−0.0497171			−0.0248586	−	0.999691i	$-0.507914\pi$
$911$	−9.41580e14			−0.0497171			−0.0248586	+	0.999691i	$0.507914\pi$
$912$		0			0
$913$	3.41563e15	+	5.91604e15i	0.178189	+	0.308633i
$914$		0			0
$915$	9.93724e15	−	1.72118e16i	0.512212	−	0.887177i
$916$		0			0
$917$	2.97618e16	+	2.34183e16i	1.51575	+	1.19268i
$918$		0			0
$919$	−6.75195e15	+	1.16947e16i	−0.339777	+	0.588511i	−0.984391	−	0.175997i	$-0.943685\pi$
$919$	−6.75195e15	+	1.16947e16i	−0.339777	+	0.588511i	0.644613	+	0.764509i	$0.277018\pi$
$920$		0			0
$921$	−7.05557e14	−	1.22206e15i	−0.0350836	−	0.0607666i
$922$		0			0
$923$	4.01064e15			0.197062
$924$		0			0
$925$	−2.08996e16			−1.01475
$926$		0			0
$927$	−4.81257e15	−	8.33562e15i	−0.230908	−	0.399944i
$928$		0			0
$929$	−4.99096e15	+	8.64459e15i	−0.236645	+	0.409881i	−0.959749	−	0.280857i	$-0.909381\pi$
$929$	−4.99096e15	+	8.64459e15i	−0.236645	+	0.409881i	0.723104	+	0.690739i	$0.242715\pi$
$930$		0			0
$931$	2.01540e16	−	1.91954e16i	0.944363	−	0.899446i
$932$		0			0
$933$	3.89274e15	−	6.74242e15i	0.180263	−	0.312224i
$934$		0			0
$935$	4.86323e16	+	8.42336e16i	2.22567	+	3.85497i
$936$		0			0
$937$	1.92762e15			0.0871876			0.0435938	−	0.999049i	$-0.486119\pi$
$937$	1.92762e15			0.0871876			0.0435938	+	0.999049i	$0.486119\pi$
$938$		0			0
$939$	2.29958e16			1.02799
$940$		0			0
$941$	−8.24781e15	−	1.42856e16i	−0.364415	−	0.631184i	0.624267	−	0.781211i	$-0.285398\pi$
$941$	−8.24781e15	−	1.42856e16i	−0.364415	−	0.631184i	−0.988682	+	0.150026i	$0.952064\pi$
$942$		0			0
$943$	2.18189e16	−	3.77915e16i	0.952838	−	1.65036i
$944$		0			0
$945$	5.00197e15	+	3.93584e15i	0.215907	+	0.169888i
$946$		0			0
$947$	−7.62198e15	+	1.32016e16i	−0.325194	+	0.563253i	−0.981552	−	0.191197i	$-0.938763\pi$
$947$	−7.62198e15	+	1.32016e16i	−0.325194	+	0.563253i	0.656358	+	0.754450i	$0.272096\pi$
$948$		0			0
$949$	5.51811e15	+	9.55764e15i	0.232716	+	0.403076i
$950$		0			0
$951$	1.28606e16			0.536127
$952$		0			0
$953$	1.39190e16			0.573583			0.286792	−	0.957993i	$-0.407411\pi$
$953$	1.39190e16			0.573583			0.286792	+	0.957993i	$0.407411\pi$
$954$		0			0
$955$	3.59985e15	+	6.23512e15i	0.146644	+	0.253996i
$956$		0			0
$957$	−1.06291e16	+	1.84101e16i	−0.428035	+	0.741379i
$958$		0			0
$959$	−1.37431e16	+	5.49748e15i	−0.547121	+	0.218858i
$960$		0			0
$961$	1.09092e16	−	1.88952e16i	0.429352	−	0.743659i
$962$		0			0
$963$	7.73657e15	+	1.34001e16i	0.301026	+	0.521392i
$964$		0			0
$965$	2.13849e16			0.822635
$966$		0			0
$967$	−2.80305e16			−1.06607			−0.533035	−	0.846093i	$-0.678949\pi$
$967$	−2.80305e16			−1.06607			−0.533035	+	0.846093i	$0.678949\pi$
$968$		0			0
$969$	−1.96790e16	−	3.40850e16i	−0.739983	−	1.28169i
$970$		0			0
$971$	−1.68124e16	+	2.91199e16i	−0.625062	+	1.08264i	0.363467	+	0.931607i	$0.381593\pi$
$971$	−1.68124e16	+	2.91199e16i	−0.625062	+	1.08264i	−0.988529	+	0.151032i	$0.951740\pi$
$972$		0			0
$973$	6.67692e15	−	4.63475e16i	0.245446	−	1.70375i
$974$		0			0
$975$	−4.80021e15	+	8.31421e15i	−0.174476	+	0.302201i
$976$		0			0
$977$	−1.46583e16	−	2.53888e16i	−0.526820	−	0.912479i	−0.999512	−	0.0312507i	$-0.990051\pi$
$977$	−1.46583e16	−	2.53888e16i	−0.526820	−	0.912479i	0.472692	−	0.881228i	$-0.343282\pi$
$978$		0			0
$979$	5.79044e16			2.05782
$980$		0			0
$981$	−1.13164e16			−0.397675
$982$		0			0
$983$	6.95012e15	+	1.20380e16i	0.241517	+	0.418320i	0.961147	−	0.276038i	$-0.0890217\pi$
$983$	6.95012e15	+	1.20380e16i	0.241517	+	0.418320i	−0.719630	+	0.694358i	$0.755688\pi$
$984$		0			0
$985$	1.39737e16	−	2.42032e16i	0.480190	−	0.831714i
$986$		0			0
$987$	−8.05084e14	+	5.58844e15i	−0.0273588	+	0.189909i
$988$		0			0
$989$	2.07968e16	−	3.60211e16i	0.698902	−	1.21053i
$990$		0			0
$991$	−3.03031e15	−	5.24865e15i	−0.100712	−	0.174439i	0.811266	−	0.584677i	$-0.198779\pi$
$991$	−3.03031e15	−	5.24865e15i	−0.100712	−	0.174439i	−0.911978	+	0.410239i	$0.865445\pi$
$992$		0			0
$993$	−3.39816e16			−1.11692
$994$		0			0
$995$	4.25905e16			1.38448
$996$		0			0
$997$	−2.66158e16	−	4.60998e16i	−0.855688	−	1.48210i	−0.876005	−	0.482302i	$-0.839801\pi$
$997$	−2.66158e16	−	4.60998e16i	−0.855688	−	1.48210i	0.0203170	−	0.999794i	$-0.493532\pi$
$998$		0			0
$999$	−2.95871e15	+	5.12464e15i	−0.0940790	+	0.162950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.i.a.37.7	yes	14
3.2	odd	2		252.12.k.b.37.1		14
7.4	even	3	inner	84.12.i.a.25.7	✓	14
21.11	odd	6		252.12.k.b.109.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.a.25.7	✓	14	7.4	even	3	inner
84.12.i.a.37.7	yes	14	1.1	even	1	trivial
252.12.k.b.37.1		14	3.2	odd	2
252.12.k.b.109.1		14	21.11	odd	6

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(121.500 + 210.444i) q^{3} +(4987.65 - 8638.86i) q^{5} +(6340.58 - 44012.8i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})\)	\(q+(121.500 + 210.444i) q^{3} +(4987.65 - 8638.86i) q^{5} +(6340.58 - 44012.8i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(423689. + 733850. i) q^{11} -779580. q^{13} +2.42400e6 q^{15} +(5.75336e6 + 9.96512e6i) q^{17} +(-7.03792e6 + 1.21900e7i) q^{19} +(1.00326e7 - 4.01321e6i) q^{21} +(2.60274e7 - 4.50808e7i) q^{23} +(-2.53392e7 - 4.38889e7i) q^{25} -1.43489e7 q^{27} +1.03239e8 q^{29} +(-2.99588e7 - 5.18902e7i) q^{31} +(-1.02956e8 + 1.78326e8i) q^{33} +(-3.48596e8 - 2.74296e8i) q^{35} +(2.06198e8 - 3.57145e8i) q^{37} +(-9.47190e7 - 1.64058e8i) q^{39} +8.38305e8 q^{41} +7.99033e8 q^{43} +(2.94516e8 + 5.10116e8i) q^{45} +(-2.61262e8 + 4.52519e8i) q^{47} +(-1.89692e9 - 5.58133e8i) q^{49} +(-1.39807e9 + 2.42152e9i) q^{51} +(7.45239e8 + 1.29079e9i) q^{53} +8.45284e9 q^{55} -3.42043e9 q^{57} +(1.94643e9 + 3.37131e9i) q^{59} +(4.09952e9 - 7.10058e9i) q^{61} +(2.06352e9 + 1.62370e9i) q^{63} +(-3.88827e9 + 6.73468e9i) q^{65} +(-2.66112e9 - 4.60919e9i) q^{67} +1.26493e10 q^{69} -5.14461e9 q^{71} +(-7.07831e9 - 1.22600e10i) q^{73} +(6.15744e9 - 1.06650e10i) q^{75} +(3.49852e10 - 1.39947e10i) q^{77} +(-3.09437e9 + 5.35961e9i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} +8.06164e9 q^{83} +1.14783e11 q^{85} +(1.25435e10 + 2.17260e10i) q^{87} +(3.41668e10 - 5.91787e10i) q^{89} +(-4.94299e9 + 3.43115e10i) q^{91} +(7.28000e9 - 1.26093e10i) q^{93} +(7.02054e10 + 1.21599e11i) q^{95} +1.16999e11 q^{97} -5.00368e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 1701 q^{3} + 7218 q^{5} + 35001 q^{7} - 413343 q^{9}+O(q^{10}) \) 14 * q + 1701 * q^3 + 7218 * q^5 + 35001 * q^7 - 413343 * q^9	\( 14 q + 1701 q^{3} + 7218 q^{5} + 35001 q^{7} - 413343 q^{9} + 54450 q^{11} + 1534982 q^{13} + 3507948 q^{15} + 1478880 q^{17} - 22875935 q^{19} + 3394224 q^{21} + 62540568 q^{23} - 62136141 q^{25} - 200884698 q^{27} + 102097728 q^{29} + 188600405 q^{31} - 13231350 q^{33} - 253840734 q^{35} + 199685599 q^{37} + 186500313 q^{39} - 693868716 q^{41} - 620701754 q^{43} + 426215682 q^{45} + 2771987346 q^{47} - 5209147075 q^{49} - 359367840 q^{51} + 6487034184 q^{53} + 10046238656 q^{55} - 11117704410 q^{57} - 8183838888 q^{59} + 4069556330 q^{61} - 1241977617 q^{63} - 1520229906 q^{65} + 15766443531 q^{67} + 30394716048 q^{69} - 33183285444 q^{71} - 31685143839 q^{73} + 15099082263 q^{75} + 3261253500 q^{77} + 21999509987 q^{79} - 24407490807 q^{81} - 63053885988 q^{83} + 35204204624 q^{85} + 12404873952 q^{87} + 67041904680 q^{89} - 190876959523 q^{91} - 45829898415 q^{93} + 133488871470 q^{95} + 284083418100 q^{97} - 6430436100 q^{99}+O(q^{100}) \) 14 * q + 1701 * q^3 + 7218 * q^5 + 35001 * q^7 - 413343 * q^9 + 54450 * q^11 + 1534982 * q^13 + 3507948 * q^15 + 1478880 * q^17 - 22875935 * q^19 + 3394224 * q^21 + 62540568 * q^23 - 62136141 * q^25 - 200884698 * q^27 + 102097728 * q^29 + 188600405 * q^31 - 13231350 * q^33 - 253840734 * q^35 + 199685599 * q^37 + 186500313 * q^39 - 693868716 * q^41 - 620701754 * q^43 + 426215682 * q^45 + 2771987346 * q^47 - 5209147075 * q^49 - 359367840 * q^51 + 6487034184 * q^53 + 10046238656 * q^55 - 11117704410 * q^57 - 8183838888 * q^59 + 4069556330 * q^61 - 1241977617 * q^63 - 1520229906 * q^65 + 15766443531 * q^67 + 30394716048 * q^69 - 33183285444 * q^71 - 31685143839 * q^73 + 15099082263 * q^75 + 3261253500 * q^77 + 21999509987 * q^79 - 24407490807 * q^81 - 63053885988 * q^83 + 35204204624 * q^85 + 12404873952 * q^87 + 67041904680 * q^89 - 190876959523 * q^91 - 45829898415 * q^93 + 133488871470 * q^95 + 284083418100 * q^97 - 6430436100 * q^99

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