LMFDB - Embedded newform 126.9.n.d.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, 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:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 26382 x^{18} + 177344 x^{17} + 298653216 x^{16} - 1823810808 x^{15} + \cdots + 42\!\cdots\!32 $ x^20 - 8x^19 - 26382x^18 + 177344x^17 + 298653216x^16 - 1823810808x^15 - 1891249463672x^14 + 11806020599312x^13 + 7316478649605270x^12 - 52687155135219848x^11 - 17677778016929268548x^10 + 159557587043375632176x^9 + 25942214297922759947412x^8 - 305008424965479773875688x^7 - 20749002299789629192234200x^6 + 325395581603349554951740400x^5 + 6083917772973420120813872017x^4 - 144252792084909643404755532432x^3 + 1061914206438596097569355774114x^2 - 3448453709078208081753932409840*x + 4271031984253419377206782621732
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{40}\cdot 3^{18}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.2
Root			$-49.5297 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.9.n.d.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-268.774 + 155.177i) q^{5} +(-1576.44 - 1810.98i) q^{7} +1448.15 q^{8} +O(q^{10})$	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-268.774 + 155.177i) q^{5} +(-1576.44 - 1810.98i) q^{7} +1448.15 q^{8} +(3040.83 + 1755.63i) q^{10} +(-3661.80 + 6342.42i) q^{11} +10650.9i q^{13} +(-8826.18 + 25690.3i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-24538.6 - 14167.4i) q^{17} +(-106850. + 61689.9i) q^{19} -39725.3i q^{20} +82857.0 q^{22} +(-161854. - 280339. i) q^{23} +(-147153. + 254876. i) q^{25} +(104357. - 60250.8i) q^{26} +(301641. - 58847.9i) q^{28} +69364.9 q^{29} +(586773. + 338774. i) q^{31} +(-92681.9 + 160530. i) q^{32} +320571. i q^{34} +(704729. + 242117. i) q^{35} +(669316. + 1.15929e6i) q^{37} +(1.20887e6 + 697942. i) q^{38} +(-389227. + 224720. i) q^{40} +100893. i q^{41} +1.01821e6 q^{43} +(-468710. - 811829. i) q^{44} +(-1.83117e6 + 3.17167e6i) q^{46} +(3.43073e6 - 1.98073e6i) q^{47} +(-794472. + 5.70979e6i) q^{49} +3.32969e6 q^{50} +(-1.18067e6 - 681659. i) q^{52} +(6.75277e6 - 1.16961e7i) q^{53} -2.27290e6i q^{55} +(-2.28293e6 - 2.62257e6i) q^{56} +(-392387. - 679634. i) q^{58} +(-69929.9 - 40374.0i) q^{59} +(3.34359e6 - 1.93042e6i) q^{61} -7.66558e6i q^{62} +2.09715e6 q^{64} +(-1.65278e6 - 2.86270e6i) q^{65} +(-654528. + 1.13368e6i) q^{67} +(3.14094e6 - 1.81342e6i) q^{68} +(-1.61430e6 - 8.27452e6i) q^{70} +3.90189e7 q^{71} +(1.19130e7 + 6.87798e6i) q^{73} +(7.57245e6 - 1.31159e7i) q^{74} -1.57926e7i q^{76} +(1.72586e7 - 3.36701e6i) q^{77} +(-2.54875e7 - 4.41457e7i) q^{79} +(4.40360e6 + 2.54242e6i) q^{80} +(988549. - 570739. i) q^{82} -6.90089e7i q^{83} +8.79380e6 q^{85} +(-5.75984e6 - 9.97634e6i) q^{86} +(-5.30285e6 + 9.18480e6i) q^{88} +(9.62567e7 - 5.55738e7i) q^{89} +(1.92886e7 - 1.67906e7i) q^{91} +4.14346e7 q^{92} +(-3.88142e7 - 2.24094e7i) q^{94} +(1.91457e7 - 3.31613e7i) q^{95} +3.18635e7i q^{97} +(6.04385e7 - 2.45153e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) $ 20 * q - 1280 * q^4 + 4186 * q^7	$ 20 q - 1280 q^{4} + 4186 q^{7} - 17664 q^{10} - 163840 q^{16} - 250890 q^{19} + 420864 q^{22} + 258962 q^{25} - 1189888 q^{28} + 342762 q^{31} - 4806598 q^{37} + 2260992 q^{40} + 6968252 q^{43} - 4357632 q^{46} - 26046538 q^{49} + 2075904 q^{52} + 2455296 q^{58} - 15410424 q^{61} + 41943040 q^{64} - 70041074 q^{67} - 25804800 q^{70} + 220264098 q^{73} + 12860578 q^{79} + 12085248 q^{82} + 29161632 q^{85} - 26935296 q^{88} - 311022894 q^{91} + 332230656 q^{94}+O(q^{100}) $ 20 * q - 1280 * q^4 + 4186 * q^7 - 17664 * q^10 - 163840 * q^16 - 250890 * q^19 + 420864 * q^22 + 258962 * q^25 - 1189888 * q^28 + 342762 * q^31 - 4806598 * q^37 + 2260992 * q^40 + 6968252 * q^43 - 4357632 * q^46 - 26046538 * q^49 + 2075904 * q^52 + 2455296 * q^58 - 15410424 * q^61 + 41943040 * q^64 - 70041074 * q^67 - 25804800 * q^70 + 220264098 * q^73 + 12860578 * q^79 + 12085248 * q^82 + 29161632 * q^85 - 26935296 * q^88 - 311022894 * q^91 + 332230656 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	−268.774	+	155.177i	−0.430039	+	0.248283i	−0.699363	−	0.714766i	$-0.746533\pi$
$5$	−268.774	+	155.177i	−0.430039	+	0.248283i	0.269324	+	0.963050i	$0.413200\pi$
$6$		0			0
$7$	−1576.44	−	1810.98i	−0.656577	−	0.754259i
$7$	−1576.44	−	1810.98i	−0.656577	−	0.754259i
$8$	1448.15			0.353553
$9$		0			0
$10$	3040.83	+	1755.63i	0.304083	+	0.175563i
$11$	−3661.80	+	6342.42i	−0.250106	+	0.433196i	−0.963555	−	0.267512i	$-0.913799\pi$
$11$	−3661.80	+	6342.42i	−0.250106	+	0.433196i	0.713449	+	0.700707i	$0.247132\pi$
$12$		0			0
$13$			10650.9i			0.372919i	0.982463	+	0.186459i	$0.0597013\pi$
$13$			10650.9i			0.372919i	−0.982463	+	0.186459i	$0.940299\pi$
$14$	−8826.18	+	25690.3i	−0.229753	+	0.668740i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	−24538.6	−	14167.4i	−0.293802	−	0.169626i	0.345853	−	0.938289i	$-0.387589\pi$
$17$	−24538.6	−	14167.4i	−0.293802	−	0.169626i	−0.639655	+	0.768662i	$0.720923\pi$
$18$		0			0
$19$	−106850.	+	61689.9i	−0.819899	+	0.473369i	−0.850382	−	0.526166i	$-0.823629\pi$
$19$	−106850.	+	61689.9i	−0.819899	+	0.473369i	0.0304823	+	0.999535i	$0.490296\pi$
$20$		−	39725.3i		−	0.248283i
$21$		0			0
$22$	82857.0			0.353703
$23$	−161854.	−	280339.i	−0.578378	−	1.00178i	−0.995666	−	0.0930051i	$-0.970353\pi$
$23$	−161854.	−	280339.i	−0.578378	−	1.00178i	0.417288	−	0.908774i	$-0.362981\pi$
$24$		0			0
$25$	−147153.	+	254876.i	−0.376711	+	0.652483i
$26$	104357.	−	60250.8i	0.228365	−	0.131847i
$27$		0			0
$28$	301641.	−	58847.9i	0.490748	−	0.0957412i
$29$	69364.9			0.0980726			0.0490363	−	0.998797i	$-0.484385\pi$
$29$	69364.9			0.0980726			0.0490363	+	0.998797i	$0.484385\pi$
$30$		0			0
$31$	586773.	+	338774.i	0.635366	+	0.366829i	0.782827	−	0.622239i	$-0.213777\pi$
$31$	586773.	+	338774.i	0.635366	+	0.366829i	−0.147461	+	0.989068i	$0.547110\pi$
$32$	−92681.9	+	160530.i	−0.0883883	+	0.153093i
$33$		0			0
$34$			320571.i			0.239888i
$35$	704729.	+	242117.i	0.469623	+	0.161344i
$36$		0			0
$37$	669316.	+	1.15929e6i	0.357129	+	0.618565i	0.987480	−	0.157745i	$-0.0504225\pi$
$37$	669316.	+	1.15929e6i	0.357129	+	0.618565i	−0.630351	+	0.776310i	$0.717089\pi$
$38$	1.20887e6	+	697942.i	0.579756	+	0.334723i
$39$		0			0
$40$	−389227.	+	224720.i	−0.152042	+	0.0877813i
$41$			100893.i			0.0357048i	0.999841	+	0.0178524i	$0.00568291\pi$
$41$			100893.i			0.0357048i	−0.999841	+	0.0178524i	$0.994317\pi$
$42$		0			0
$43$	1.01821e6			0.297826			0.148913	−	0.988850i	$-0.452423\pi$
$43$	1.01821e6			0.297826			0.148913	+	0.988850i	$0.452423\pi$
$44$	−468710.	−	811829.i	−0.125053	−	0.216598i
$45$		0			0
$46$	−1.83117e6	+	3.17167e6i	−0.408975	+	0.708365i
$47$	3.43073e6	−	1.98073e6i	0.703064	−	0.405914i	−0.105424	−	0.994427i	$-0.533620\pi$
$47$	3.43073e6	−	1.98073e6i	0.703064	−	0.405914i	0.808487	+	0.588513i	$0.200287\pi$
$48$		0			0
$49$	−794472.	+	5.70979e6i	−0.137814	+	0.990458i
$50$	3.32969e6			0.532750
$51$		0			0
$52$	−1.18067e6	−	681659.i	−0.161479	−	0.0932297i
$53$	6.75277e6	−	1.16961e7i	0.855812	−	1.48231i	−0.0200782	−	0.999798i	$-0.506392\pi$
$53$	6.75277e6	−	1.16961e7i	0.855812	−	1.48231i	0.875890	−	0.482511i	$-0.160275\pi$
$54$		0			0
$55$		−	2.27290e6i		−	0.248388i
$56$	−2.28293e6	−	2.62257e6i	−0.232135	−	0.266671i
$57$		0			0
$58$	−392387.	−	679634.i	−0.0346739	−	0.0600570i
$59$	−69929.9	−	40374.0i	−0.00577105	−	0.00333192i	0.497112	−	0.867687i	$-0.334394\pi$
$59$	−69929.9	−	40374.0i	−0.00577105	−	0.00333192i	−0.502883	+	0.864355i	$0.667727\pi$
$60$		0			0
$61$	3.34359e6	−	1.93042e6i	0.241487	−	0.139422i	−0.374373	−	0.927278i	$-0.622142\pi$
$61$	3.34359e6	−	1.93042e6i	0.241487	−	0.139422i	0.615860	+	0.787856i	$0.288809\pi$
$62$		−	7.66558e6i		−	0.518774i
$63$		0			0
$64$	2.09715e6			0.125000
$65$	−1.65278e6	−	2.86270e6i	−0.0925894	−	0.160370i
$66$		0			0
$67$	−654528.	+	1.13368e6i	−0.0324810	+	0.0562587i	−0.881809	−	0.471607i	$-0.843674\pi$
$67$	−654528.	+	1.13368e6i	−0.0324810	+	0.0562587i	0.849328	+	0.527866i	$0.177008\pi$
$68$	3.14094e6	−	1.81342e6i	0.146901	−	0.0848132i
$69$		0			0
$70$	−1.61430e6	−	8.27452e6i	−0.0672343	−	0.344628i
$71$	3.90189e7			1.53547			0.767735	−	0.640767i	$-0.221384\pi$
$71$	3.90189e7			1.53547			0.767735	+	0.640767i	$0.221384\pi$
$72$		0			0
$73$	1.19130e7	+	6.87798e6i	0.419498	+	0.242197i	0.694862	−	0.719143i	$-0.255465\pi$
$73$	1.19130e7	+	6.87798e6i	0.419498	+	0.242197i	−0.275365	+	0.961340i	$0.588799\pi$
$74$	7.57245e6	−	1.31159e7i	0.252528	−	0.437391i
$75$		0			0
$76$		−	1.57926e7i		−	0.473369i
$77$	1.72586e7	−	3.36701e6i	0.490955	−	0.0957816i
$78$		0			0
$79$	−2.54875e7	−	4.41457e7i	−0.654364	−	1.13339i	−0.982053	−	0.188606i	$-0.939603\pi$
$79$	−2.54875e7	−	4.41457e7i	−0.654364	−	1.13339i	0.327689	−	0.944786i	$-0.393730\pi$
$80$	4.40360e6	+	2.54242e6i	0.107510	+	0.0620708i
$81$		0			0
$82$	988549.	−	570739.i	0.0218647	−	0.0126236i
$83$		−	6.90089e7i		−	1.45410i	−0.686587	−	0.727048i	$-0.740892\pi$
$83$		−	6.90089e7i		−	1.45410i	0.686587	−	0.727048i	$-0.259108\pi$
$84$		0			0
$85$	8.79380e6			0.168462
$86$	−5.75984e6	−	9.97634e6i	−0.105297	−	0.182380i
$87$		0			0
$88$	−5.30285e6	+	9.18480e6i	−0.0884257	+	0.153158i
$89$	9.62567e7	−	5.55738e7i	1.53416	−	0.885748i	0.534997	−	0.844854i	$-0.320313\pi$
$89$	9.62567e7	−	5.55738e7i	1.53416	−	0.885748i	0.999163	−	0.0408946i	$-0.0130208\pi$
$90$		0			0
$91$	1.92886e7	−	1.67906e7i	0.281277	−	0.244850i
$92$	4.14346e7			0.578378
$93$		0			0
$94$	−3.88142e7	−	2.24094e7i	−0.497141	−	0.287025i
$95$	1.91457e7	−	3.31613e7i	0.235059	−	0.407134i
$96$		0			0
$97$			3.18635e7i			0.359921i	0.983674	+	0.179960i	$0.0575970\pi$
$97$			3.18635e7i			0.359921i	−0.983674	+	0.179960i	$0.942403\pi$
$98$	6.04385e7	−	2.45153e7i	0.655254	−	0.265786i
$99$		0			0
$100$	−1.88356e7	−	3.26241e7i	−0.188356	−	0.326241i
$101$	1.65849e7	+	9.57532e6i	0.159378	+	0.0920170i	0.577568	−	0.816343i	$-0.304002\pi$
$101$	1.65849e7	+	9.57532e6i	0.159378	+	0.0920170i	−0.418190	+	0.908360i	$0.637335\pi$
$102$		0			0
$103$	1.10127e8	−	6.35820e7i	0.978467	−	0.564918i	0.0766597	−	0.997057i	$-0.475574\pi$
$103$	1.10127e8	−	6.35820e7i	0.978467	−	0.564918i	0.901807	+	0.432139i	$0.142241\pi$
$104$			1.54242e7i			0.131847i
$105$		0			0
$106$	−1.52798e8			−1.21030
$107$	−1.48164e7	−	2.56628e7i	−0.113034	−	0.195781i	0.803958	−	0.594686i	$-0.202724\pi$
$107$	−1.48164e7	−	2.56628e7i	−0.113034	−	0.195781i	−0.916992	+	0.398905i	$0.869390\pi$
$108$		0			0
$109$	−3.17985e7	+	5.50767e7i	−0.225269	+	0.390177i	−0.956400	−	0.292060i	$-0.905659\pi$
$109$	−3.17985e7	+	5.50767e7i	−0.225269	+	0.390177i	0.731131	+	0.682237i	$0.238993\pi$
$110$	−2.22698e7	+	1.28575e7i	−0.152106	+	0.0878184i
$111$		0			0
$112$	−1.27817e7	+	3.72036e7i	−0.0812299	+	0.236435i
$113$	6.26869e7			0.384470			0.192235	−	0.981349i	$-0.438426\pi$
$113$	6.26869e7			0.384470			0.192235	+	0.981349i	$0.438426\pi$
$114$		0			0
$115$	8.70043e7	+	5.02319e7i	0.497450	+	0.287203i
$116$	−4.43935e6	+	7.68918e6i	−0.0245182	+	0.0424667i
$117$		0			0
$118$			913560.i			0.00471204i
$119$	1.30269e7	+	6.67729e7i	0.0649610	+	0.332975i
$120$		0			0
$121$	8.03619e7	+	1.39191e8i	0.374894	+	0.649336i
$122$	−3.78284e7	−	2.18402e7i	−0.170757	−	0.0985866i
$123$		0			0
$124$	−7.51070e7	+	4.33631e7i	−0.317683	+	0.183414i
$125$		−	2.12571e8i		−	0.870690i
$126$		0			0
$127$	1.76344e8			0.677870			0.338935	−	0.940810i	$-0.389933\pi$
$127$	1.76344e8			0.677870			0.338935	+	0.940810i	$0.389933\pi$
$128$	−1.18633e7	−	2.05478e7i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.86991e7	+	3.23877e7i	−0.0654706	+	0.113398i
$131$	−3.77244e8	+	2.17802e8i	−1.28096	+	0.739565i	−0.977025	−	0.213126i	$-0.931635\pi$
$131$	−3.77244e8	+	2.17802e8i	−1.28096	+	0.739565i	−0.303940	+	0.952691i	$0.598302\pi$
$132$		0			0
$133$	2.80162e8	+	9.62526e7i	0.895370	+	0.307614i
$134$	1.48103e7			0.0459351
$135$		0			0
$136$	−3.55357e7	−	2.05165e7i	−0.103875	−	0.0599720i
$137$	−4.69296e7	+	8.12844e7i	−0.133218	+	0.230741i	−0.924915	−	0.380173i	$-0.875865\pi$
$137$	−4.69296e7	+	8.12844e7i	−0.133218	+	0.230741i	0.791697	+	0.610914i	$0.209198\pi$
$138$		0			0
$139$			4.71582e8i			1.26327i	0.775264	+	0.631637i	$0.217617\pi$
$139$			4.71582e8i			1.26327i	−0.775264	+	0.631637i	$0.782383\pi$
$140$	−7.19416e7	+	6.26246e7i	−0.187270	+	0.163017i
$141$		0			0
$142$	−2.20724e8	−	3.82306e8i	−0.542871	−	0.940280i
$143$	−6.75526e7	−	3.90015e7i	−0.161547	−	0.0932690i
$144$		0			0
$145$	−1.86435e7	+	1.07638e7i	−0.0421750	+	0.0243498i
$146$		−	1.55631e8i		−	0.342519i
$147$		0			0
$148$	−1.71345e8			−0.357129
$149$	1.57471e8	+	2.72748e8i	0.319488	+	0.553370i	0.980381	−	0.197110i	$-0.0631556\pi$
$149$	1.57471e8	+	2.72748e8i	0.319488	+	0.553370i	−0.660893	+	0.750480i	$0.729822\pi$
$150$		0			0
$151$	−2.86581e7	+	4.96373e7i	−0.0551238	+	0.0954773i	−0.892271	−	0.451501i	$-0.850889\pi$
$151$	−2.86581e7	+	4.96373e7i	−0.0551238	+	0.0954773i	0.837147	+	0.546978i	$0.184222\pi$
$152$	−1.54736e8	+	8.93366e7i	−0.289878	+	0.167361i
$153$		0			0
$154$	−1.30619e8	−	1.50052e8i	−0.232233	−	0.266784i
$155$	−2.10280e8			−0.364309
$156$		0			0
$157$	3.39259e8	+	1.95871e8i	0.558383	+	0.322383i	0.752496	−	0.658596i	$-0.228850\pi$
$157$	3.39259e8	+	1.95871e8i	0.558383	+	0.322383i	−0.194113	+	0.980979i	$0.562183\pi$
$158$	−2.88358e8	+	4.99451e8i	−0.462705	+	0.801429i
$159$		0			0
$160$		−	5.75284e7i		−	0.0877813i
$161$	−2.52534e8	+	7.35051e8i	−0.375852	+	1.09399i
$162$		0			0
$163$	−1.47340e8	−	2.55200e8i	−0.208723	−	0.361518i	0.742590	−	0.669747i	$-0.233597\pi$
$163$	−1.47340e8	−	2.55200e8i	−0.208723	−	0.361518i	−0.951312	+	0.308228i	$0.900264\pi$
$164$	−1.11842e7	−	6.45718e6i	−0.0154607	−	0.00892621i
$165$		0			0
$166$	−6.76147e8	+	3.90373e8i	−0.890448	+	0.514100i
$167$			6.60799e8i			0.849578i	0.905292	+	0.424789i	$0.139652\pi$
$167$			6.60799e8i			0.849578i	−0.905292	+	0.424789i	$0.860348\pi$
$168$		0			0
$169$	7.02288e8			0.860932
$170$	−4.97452e7	−	8.61613e7i	−0.0595602	−	0.103161i
$171$		0			0
$172$	−6.51652e7	+	1.12869e8i	−0.0744564	+	0.128962i
$173$	−6.64676e8	+	3.83751e8i	−0.742037	+	0.428415i	−0.822810	−	0.568317i	$-0.807595\pi$
$173$	−6.64676e8	+	3.83751e8i	−0.742037	+	0.428415i	0.0807723	+	0.996733i	$0.474261\pi$
$174$		0			0
$175$	6.93552e8	−	1.35307e8i	0.739481	−	0.144267i
$176$	1.19990e8			0.125053
$177$		0			0
$178$	−1.08902e9	−	6.28746e8i	−1.08482	−	0.626319i
$179$	−4.75953e8	+	8.24374e8i	−0.463609	+	0.802994i	−0.999138	−	0.0415230i	$-0.986779\pi$
$179$	−4.75953e8	+	8.24374e8i	−0.463609	+	0.802994i	0.535529	+	0.844517i	$0.320112\pi$
$180$		0			0
$181$		−	9.01212e8i		−	0.839678i	−0.907599	−	0.419839i	$-0.862087\pi$
$181$		−	9.01212e8i		−	0.839678i	0.907599	−	0.419839i	$-0.137913\pi$
$182$	−2.73626e8	−	9.40070e7i	−0.249386	−	0.0856791i
$183$		0			0
$184$	−2.34389e8	−	4.05974e8i	−0.204487	−	0.354182i
$185$	−3.59790e8	−	2.07725e8i	−0.307158	−	0.177338i
$186$		0			0
$187$	1.79711e8	−	1.03756e8i	0.146963	−	0.0848491i
$188$			5.07067e8i			0.405914i
$189$		0			0
$190$	−4.33218e8			−0.332424
$191$	−7.42001e8	−	1.28518e9i	−0.557533	−	0.965676i	−0.997702	−	0.0677608i	$-0.978415\pi$
$191$	−7.42001e8	−	1.28518e9i	−0.557533	−	0.965676i	0.440168	−	0.897915i	$-0.354919\pi$
$192$		0			0
$193$	4.48723e8	−	7.77211e8i	0.323407	−	0.560157i	−0.657782	−	0.753208i	$-0.728505\pi$
$193$	4.48723e8	−	7.77211e8i	0.323407	−	0.560157i	0.981189	+	0.193052i	$0.0618385\pi$
$194$	3.12198e8	−	1.80247e8i	0.220406	−	0.127251i
$195$		0			0
$196$	−5.82092e8	−	4.53495e8i	−0.394427	−	0.307290i
$197$	−4.96873e8			−0.329898			−0.164949	−	0.986302i	$-0.552746\pi$
$197$	−4.96873e8			−0.329898			−0.164949	+	0.986302i	$0.552746\pi$
$198$		0			0
$199$	1.81303e9	+	1.04675e9i	1.15609	+	0.667469i	0.950364	−	0.311141i	$-0.100711\pi$
$199$	1.81303e9	+	1.04675e9i	1.15609	+	0.667469i	0.205726	+	0.978610i	$0.434044\pi$
$200$	−2.13100e8	+	3.69100e8i	−0.133187	+	0.230687i
$201$		0			0
$202$		−	2.16665e8i		−	0.130132i
$203$	−1.09350e8	−	1.25618e8i	−0.0643922	−	0.0739722i
$204$		0			0
$205$	−1.56563e7	−	2.71175e7i	−0.00886491	−	0.0153545i
$206$	−1.24595e9	−	7.19348e8i	−0.691880	−	0.399457i
$207$		0			0
$208$	1.51126e8	−	8.72524e7i	0.0807393	−	0.0466148i
$209$		−	9.03584e8i		−	0.473569i
$210$		0			0
$211$	3.78210e8			0.190811			0.0954055	−	0.995438i	$-0.469585\pi$
$211$	3.78210e8			0.190811			0.0954055	+	0.995438i	$0.469585\pi$
$212$	8.64354e8	+	1.49711e9i	0.427906	+	0.741155i
$213$		0			0
$214$	−1.67629e8	+	2.90342e8i	−0.0799271	+	0.138438i
$215$	−2.73668e8	+	1.58002e8i	−0.128077	+	0.0739450i
$216$		0			0
$217$	−3.11502e8	−	1.59669e9i	−0.140482	−	0.720081i
$218$	7.19518e8			0.318578
$219$		0			0
$220$	2.51954e8	+	1.45466e8i	0.107555	+	0.0620970i
$221$	1.50896e8	−	2.61359e8i	0.0632569	−	0.109564i
$222$		0			0
$223$			2.00508e9i			0.810799i	0.914140	+	0.405399i	$0.132868\pi$
$223$			2.00508e9i			0.810799i	−0.914140	+	0.405399i	$0.867132\pi$
$224$	4.36823e8	−	8.52208e7i	0.173506	−	0.0338496i
$225$		0			0
$226$	−3.54610e8	−	6.14203e8i	−0.135931	−	0.235439i
$227$	3.28618e9	+	1.89728e9i	1.23762	+	0.714541i	0.968608	−	0.248595i	$-0.0799687\pi$
$227$	3.28618e9	+	1.89728e9i	1.23762	+	0.714541i	0.269015	+	0.963136i	$0.413302\pi$
$228$		0			0
$229$	−4.40451e9	+	2.54295e9i	−1.60161	+	0.924688i	−0.610441	+	0.792062i	$0.709008\pi$
$229$	−4.40451e9	+	2.54295e9i	−1.60161	+	0.924688i	−0.991166	+	0.132627i	$0.957659\pi$
$230$		−	1.13662e9i		−	0.406166i
$231$		0			0
$232$	1.00451e8			0.0346739
$233$	2.76575e8	+	4.79042e8i	0.0938403	+	0.162536i	0.909124	−	0.416526i	$-0.136752\pi$
$233$	2.76575e8	+	4.79042e8i	0.0938403	+	0.162536i	−0.815284	+	0.579062i	$0.803419\pi$
$234$		0			0
$235$	−6.14727e8	+	1.06474e9i	−0.201563	+	0.349118i
$236$	8.95103e6	−	5.16788e6i	0.00288553	−	0.00166596i
$237$		0			0
$238$	5.80547e8	−	5.05361e8i	0.180938	−	0.157505i
$239$	2.56851e9			0.787208			0.393604	−	0.919280i	$-0.371228\pi$
$239$	2.56851e9			0.787208			0.393604	+	0.919280i	$0.371228\pi$
$240$		0			0
$241$	3.64458e9	+	2.10420e9i	1.08039	+	0.623762i	0.931001	−	0.365017i	$-0.118937\pi$
$241$	3.64458e9	+	2.10420e9i	1.08039	+	0.623762i	0.149386	+	0.988779i	$0.452270\pi$
$242$	9.09192e8	−	1.57477e9i	0.265090	−	0.459150i
$243$		0			0
$244$			4.94188e8i			0.139422i
$245$	−6.72495e8	−	1.65793e9i	−0.186648	−	0.460153i
$246$		0			0
$247$	−6.57055e8	−	1.13805e9i	−0.176528	−	0.305756i
$248$	8.49739e8	+	4.90597e8i	0.224636	+	0.129693i
$249$		0			0
$250$	−2.08276e9	+	1.20248e9i	−0.533187	+	0.307835i
$251$		−	3.46167e9i		−	0.872149i	−0.899910	−	0.436075i	$-0.856368\pi$
$251$		−	3.46167e9i		−	0.872149i	0.899910	−	0.436075i	$-0.143632\pi$
$252$		0			0
$253$	2.37070e9			0.578622
$254$	−9.97554e8	−	1.72781e9i	−0.239663	−	0.415109i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	6.47296e9	−	3.73717e9i	1.48378	−	0.856663i	0.483954	−	0.875094i	$-0.339200\pi$
$257$	6.47296e9	−	3.73717e9i	1.48378	−	0.856663i	0.999830	+	0.0184307i	$0.00586702\pi$
$258$		0			0
$259$	1.04431e9	−	3.03967e9i	0.232076	−	0.675503i
$260$	4.23111e8			0.0925894
$261$		0			0
$262$	4.26803e9	+	2.46415e9i	0.905779	+	0.522952i
$263$	2.44409e9	−	4.23328e9i	0.510850	−	0.884819i	−0.489071	−	0.872244i	$-0.662664\pi$
$263$	2.44409e9	−	4.23328e9i	0.510850	−	0.884819i	0.999921	−	0.0125746i	$-0.00400273\pi$
$264$		0			0
$265$			4.19149e9i			0.849934i
$266$	−6.41757e8	−	3.28950e9i	−0.128187	−	0.657058i
$267$		0			0
$268$	−8.37796e7	−	1.45111e8i	−0.0162405	−	0.0281294i
$269$	4.83878e9	+	2.79367e9i	0.924116	+	0.533539i	0.884946	−	0.465694i	$-0.154195\pi$
$269$	4.83878e9	+	2.79367e9i	0.924116	+	0.533539i	0.0391702	+	0.999233i	$0.487529\pi$
$270$		0			0
$271$	7.15012e8	−	4.12812e8i	0.132567	−	0.0765377i	−0.432250	−	0.901754i	$-0.642280\pi$
$271$	7.15012e8	−	4.12812e8i	0.132567	−	0.0765377i	0.564817	+	0.825216i	$0.308947\pi$
$272$			4.64237e8i			0.0848132i
$273$		0			0
$274$	1.06189e9			0.188399
$275$	−1.07769e9	−	1.86661e9i	−0.188435	−	0.326379i
$276$		0			0
$277$	−6.19157e8	+	1.07241e9i	−0.105168	+	0.182156i	−0.913807	−	0.406149i	$-0.866871\pi$
$277$	−6.19157e8	+	1.07241e9i	−0.105168	+	0.182156i	0.808639	+	0.588305i	$0.200205\pi$
$278$	4.62054e9	−	2.66767e9i	0.773595	−	0.446635i
$279$		0			0
$280$	1.02056e9	+	3.50623e8i	0.166037	+	0.0570437i
$281$	−6.05362e9			−0.970934			−0.485467	−	0.874255i	$-0.661350\pi$
$281$	−6.05362e9			−0.970934			−0.485467	+	0.874255i	$0.661350\pi$
$282$		0			0
$283$	−4.30770e9	−	2.48705e9i	−0.671583	−	0.387738i	0.125093	−	0.992145i	$-0.460077\pi$
$283$	−4.30770e9	−	2.48705e9i	−0.671583	−	0.387738i	−0.796676	+	0.604407i	$0.793410\pi$
$284$	−2.49721e9	+	4.32529e9i	−0.383868	+	0.664878i
$285$		0			0
$286$			8.82504e8i			0.131902i
$287$	1.82716e8	−	1.59052e8i	0.0269307	−	0.0234430i
$288$		0			0
$289$	−3.08645e9	−	5.34589e9i	−0.442454	−	0.766352i
$290$	2.10927e8	+	1.21779e8i	0.0298223	+	0.0172179i
$291$		0			0
$292$	−1.52486e9	+	8.80381e8i	−0.209749	+	0.121099i
$293$		−	3.27714e8i		−	0.0444656i	−0.999753	−	0.0222328i	$-0.992922\pi$
$293$		−	3.27714e8i		−	0.0444656i	0.999753	−	0.0222328i	$-0.00707751\pi$
$294$		0			0
$295$	2.50605e7			0.00330904
$296$	9.69274e8	+	1.67883e9i	0.126264	+	0.218696i
$297$		0			0
$298$	1.78158e9	−	3.08579e9i	0.225912	−	0.391292i
$299$	2.98587e9	−	1.72389e9i	0.373582	−	0.215688i
$300$		0			0
$301$	−1.60514e9	−	1.84395e9i	−0.195545	−	0.224638i
$302$	6.48459e8			0.0779569
$303$		0			0
$304$	1.75063e9	+	1.01073e9i	0.204975	+	0.118342i
$305$	−5.99114e8	+	1.03770e9i	−0.0692325	+	0.119914i
$306$		0			0
$307$		−	8.10763e9i		−	0.912726i	−0.889794	−	0.456363i	$-0.849152\pi$
$307$		−	8.10763e9i		−	0.912726i	0.889794	−	0.456363i	$-0.150848\pi$
$308$	−7.31311e8	+	2.12862e9i	−0.0812642	+	0.236535i
$309$		0			0
$310$	1.18952e9	+	2.06031e9i	0.128803	+	0.223093i
$311$	−1.56453e8	−	9.03280e7i	−0.0167240	−	0.00965563i	0.491615	−	0.870813i	$-0.336407\pi$
$311$	−1.56453e8	−	9.03280e7i	−0.0167240	−	0.00965563i	−0.508339	+	0.861157i	$0.669740\pi$
$312$		0			0
$313$	−1.22575e10	+	7.07687e9i	−1.27710	+	0.737333i	−0.976314	−	0.216359i	$-0.930582\pi$
$313$	−1.22575e10	+	7.07687e9i	−1.27710	+	0.737333i	−0.300785	+	0.953692i	$0.597249\pi$
$314$		−	4.43206e9i		−	0.455918i
$315$		0			0
$316$	6.52481e9			0.654364
$317$	−5.00979e8	−	8.67721e8i	−0.0496115	−	0.0859296i	0.840153	−	0.542349i	$-0.182465\pi$
$317$	−5.00979e8	−	8.67721e8i	−0.0496115	−	0.0859296i	−0.889765	+	0.456419i	$0.849132\pi$
$318$		0			0
$319$	−2.54000e8	+	4.39941e8i	−0.0245285	+	0.0424846i
$320$	−5.63661e8	+	3.25430e8i	−0.0537549	+	0.0310354i
$321$		0			0
$322$	8.63055e9	−	1.68375e9i	0.802814	−	0.156623i
$323$	3.49594e9			0.321184
$324$		0			0
$325$	−2.71467e9	−	1.56731e9i	−0.243323	−	0.140483i
$326$	−1.66696e9	+	2.88726e9i	−0.147589	+	0.255632i
$327$		0			0
$328$			1.46109e8i			0.0126236i
$329$	−8.99539e9	−	3.09046e9i	−0.767780	−	0.263779i
$330$		0			0
$331$	−1.17799e10	−	2.04034e10i	−0.981363	−	1.69977i	−0.657101	−	0.753803i	$-0.728217\pi$
$331$	−1.17799e10	−	2.04034e10i	−0.981363	−	1.69977i	−0.324262	−	0.945967i	$-0.605116\pi$
$332$	7.64973e9	+	4.41657e9i	0.629642	+	0.363524i
$333$		0			0
$334$	6.47448e9	−	3.73804e9i	0.520258	−	0.300371i
$335$		−	4.06271e8i		−	0.0322579i
$336$		0			0
$337$	−1.43143e10			−1.10982			−0.554909	−	0.831911i	$-0.687247\pi$
$337$	−1.43143e10			−1.10982			−0.554909	+	0.831911i	$0.687247\pi$
$338$	−3.97274e9	−	6.88099e9i	−0.304385	−	0.527211i
$339$		0			0
$340$	−5.62803e8	+	9.74804e8i	−0.0421154	+	0.0729460i
$341$	−4.29729e9	+	2.48104e9i	−0.317817	+	0.183492i
$342$		0			0
$343$	1.15927e10	−	7.56238e9i	0.837548	−	0.546364i
$344$	1.47452e9			0.105297
$345$		0			0
$346$	7.51995e9	+	4.34165e9i	0.524700	+	0.302935i
$347$	−1.10906e10	+	1.92095e10i	−0.764957	+	1.32494i	0.175312	+	0.984513i	$0.443906\pi$
$347$	−1.10906e10	+	1.92095e10i	−0.764957	+	1.32494i	−0.940269	+	0.340431i	$0.889427\pi$
$348$		0			0
$349$			1.18526e10i			0.798939i	0.916747	+	0.399469i	$0.130806\pi$
$349$			1.18526e10i			0.798939i	−0.916747	+	0.399469i	$0.869194\pi$
$350$	−5.24905e9	−	6.02998e9i	−0.349791	−	0.401832i
$351$		0			0
$352$	−6.78764e8	−	1.17565e9i	−0.0442128	−	0.0765789i
$353$	7.82017e9	+	4.51498e9i	0.503636	+	0.290775i	0.730214	−	0.683218i	$-0.239420\pi$
$353$	7.82017e9	+	4.51498e9i	0.503636	+	0.290775i	−0.226578	+	0.973993i	$0.572754\pi$
$354$		0			0
$355$	−1.04873e10	+	6.05483e9i	−0.660312	+	0.381231i
$356$			1.42269e10i			0.885748i
$357$		0			0
$358$	1.07696e10			0.655642
$359$	4.52198e9	+	7.83230e9i	0.272239	+	0.471532i	0.969435	−	0.245349i	$-0.0789024\pi$
$359$	4.52198e9	+	7.83230e9i	0.272239	+	0.471532i	−0.697196	+	0.716881i	$0.745569\pi$
$360$		0			0
$361$	−8.80483e8	+	1.52504e9i	−0.0518432	+	0.0897951i
$362$	−8.83004e9	+	5.09803e9i	−0.514196	+	0.296871i
$363$		0			0
$364$	6.26785e8	+	3.21276e9i	0.0357037	+	0.183009i
$365$	−4.26921e9			−0.240534
$366$		0			0
$367$	1.00786e10	+	5.81889e9i	0.555567	+	0.320757i	0.751364	−	0.659888i	$-0.229396\pi$
$367$	1.00786e10	+	5.81889e9i	0.555567	+	0.320757i	−0.195798	+	0.980644i	$0.562730\pi$
$368$	−2.65181e9	+	4.59307e9i	−0.144594	+	0.250445i
$369$		0			0
$370$			4.70028e9i			0.250794i
$371$	−3.18268e10	+	6.20916e9i	−1.67995	+	0.327746i
$372$		0			0
$373$	−5.13001e9	−	8.88545e9i	−0.265023	−	0.459033i	0.702547	−	0.711638i	$-0.252046\pi$
$373$	−5.13001e9	−	8.88545e9i	−0.265023	−	0.459033i	−0.967570	+	0.252605i	$0.918713\pi$
$374$	−2.03320e9	−	1.17387e9i	−0.103918	−	0.0599973i
$375$		0			0
$376$	4.96822e9	−	2.86840e9i	0.248571	−	0.143512i
$377$			7.38800e8i			0.0365731i
$378$		0			0
$379$	4.77524e9			0.231440			0.115720	−	0.993282i	$-0.463082\pi$
$379$	4.77524e9			0.231440			0.115720	+	0.993282i	$0.463082\pi$
$380$	2.45065e9	+	4.24465e9i	0.117530	+	0.203567i
$381$		0			0
$382$	−8.39478e9	+	1.45402e10i	−0.394236	+	0.682836i
$383$	−6.79135e8	+	3.92099e8i	−0.0315617	+	0.0182222i	−0.515698	−	0.856771i	$-0.672467\pi$
$383$	−6.79135e8	+	3.92099e8i	−0.0315617	+	0.0182222i	0.484136	+	0.874993i	$0.339134\pi$
$384$		0			0
$385$	−4.11618e9	+	3.58310e9i	−0.187349	+	0.163086i
$386$	−1.01534e10			−0.457366
$387$		0			0
$388$	−3.53211e9	−	2.03927e9i	−0.155850	−	0.0899802i
$389$	−2.19787e10	+	3.80682e10i	−0.959849	+	1.66251i	−0.236989	+	0.971512i	$0.576161\pi$
$389$	−2.19787e10	+	3.80682e10i	−0.959849	+	1.66251i	−0.722860	+	0.690995i	$0.757173\pi$
$390$		0			0
$391$			9.17217e9i			0.392433i
$392$	−1.15052e9	+	8.26866e9i	−0.0487247	+	0.350180i
$393$		0			0
$394$	2.81074e9	+	4.86834e9i	0.116637	+	0.202021i
$395$	1.37008e10	+	7.91015e9i	0.562804	+	0.324935i
$396$		0			0
$397$	1.07480e10	−	6.20534e9i	0.432677	−	0.249806i	−0.267809	−	0.963472i	$-0.586300\pi$
$397$	1.07480e10	−	6.20534e9i	0.432677	−	0.249806i	0.700487	+	0.713666i	$0.252966\pi$
$398$		−	2.36853e10i		−	0.943943i
$399$		0			0
$400$	4.82190e9			0.188356
$401$	−1.07369e10	−	1.85968e10i	−0.415240	−	0.719218i	0.580213	−	0.814465i	$-0.302969\pi$
$401$	−1.07369e10	−	1.85968e10i	−0.415240	−	0.719218i	−0.995454	+	0.0952470i	$0.969636\pi$
$402$		0			0
$403$	−3.60826e9	+	6.24968e9i	−0.136797	+	0.236940i
$404$	−2.12287e9	+	1.22564e9i	−0.0796890	+	0.0460085i
$405$		0			0
$406$	−6.12227e8	+	1.78201e9i	−0.0225324	+	0.0655851i
$407$	−9.80360e9			−0.357279
$408$		0			0
$409$	2.54644e9	+	1.47019e9i	0.0909998	+	0.0525388i	0.544809	−	0.838560i	$-0.316602\pi$
$409$	2.54644e9	+	1.47019e9i	0.0909998	+	0.0525388i	−0.453810	+	0.891099i	$0.649935\pi$
$410$	−1.77131e8	+	3.06800e8i	−0.00626844	+	0.0108573i
$411$		0			0
$412$			1.62770e10i			0.564918i
$413$	3.71239e7	+	1.90289e8i	0.00127601	+	0.00654053i
$414$		0			0
$415$	1.07086e10	+	1.85478e10i	0.361027	+	0.625318i
$416$	−1.70979e9	−	9.87148e8i	−0.0570913	−	0.0329617i
$417$		0			0
$418$	−8.85328e9	+	5.11144e9i	−0.290001	+	0.167432i
$419$		−	4.30557e10i		−	1.39693i	−0.715644	−	0.698465i	$-0.753867\pi$
$419$		−	4.30557e10i		−	1.39693i	0.715644	−	0.698465i	$-0.246133\pi$
$420$		0			0
$421$	−3.61456e10			−1.15061			−0.575303	−	0.817940i	$-0.695116\pi$
$421$	−3.61456e10			−1.15061			−0.575303	+	0.817940i	$0.695116\pi$
$422$	−2.13948e9	−	3.70569e9i	−0.0674619	−	0.116847i
$423$		0			0
$424$	9.77905e9	−	1.69378e10i	0.302575	−	0.524075i
$425$	7.22185e9	−	4.16954e9i	0.221357	−	0.127800i
$426$		0			0
$427$	−8.76691e9	−	3.01197e9i	−0.263715	−	0.0906021i
$428$	3.79301e9			0.113034
$429$		0			0
$430$	3.09620e9	+	1.78759e9i	0.0905638	+	0.0522870i
$431$	−2.01395e10	+	3.48827e10i	−0.583634	+	1.01088i	0.411411	+	0.911450i	$0.365036\pi$
$431$	−2.01395e10	+	3.48827e10i	−0.583634	+	1.01088i	−0.995044	+	0.0994331i	$0.968297\pi$
$432$		0			0
$433$			1.73001e8i			0.00492151i	0.999997	+	0.00246075i	$0.000783283\pi$
$433$			1.73001e8i			0.00492151i	−0.999997	+	0.00246075i	$0.999217\pi$
$434$	−1.38822e10	+	1.20843e10i	−0.391290	+	0.340615i
$435$		0			0
$436$	−4.07021e9	−	7.04981e9i	−0.112634	−	0.195088i
$437$	3.45882e10	+	1.99695e10i	0.948423	+	0.547572i
$438$		0			0
$439$	2.74094e10	−	1.58248e10i	0.737974	−	0.426070i	−0.0833580	−	0.996520i	$-0.526565\pi$
$439$	2.74094e10	−	1.58248e10i	0.737974	−	0.426070i	0.821332	+	0.570450i	$0.193231\pi$
$440$		−	3.29152e9i		−	0.0878184i
$441$		0			0
$442$	−3.41438e9			−0.0894587
$443$	−8.41169e9	−	1.45695e10i	−0.218408	−	0.378294i	0.735914	−	0.677076i	$-0.236753\pi$
$443$	−8.41169e9	−	1.45695e10i	−0.218408	−	0.378294i	−0.954321	+	0.298782i	$0.903420\pi$
$444$		0			0
$445$	−1.72476e10	+	2.98736e10i	−0.439833	+	0.761812i
$446$	1.96457e10	−	1.13425e10i	0.496511	−	0.286661i
$447$		0			0
$448$	−3.30604e9	−	3.79789e9i	−0.0820721	−	0.0942824i
$449$	5.40760e10			1.33051			0.665257	−	0.746614i	$-0.268322\pi$
$449$	5.40760e10			1.33051			0.665257	+	0.746614i	$0.268322\pi$
$450$		0			0
$451$	−6.39908e8	−	3.69451e8i	−0.0154672	−	0.00892998i
$452$	−4.01196e9	+	6.94892e9i	−0.0961176	+	0.166481i
$453$		0			0
$454$		−	4.29305e10i		−	1.01051i
$455$	−2.57877e9	+	7.50601e9i	−0.0601682	+	0.175131i
$456$		0			0
$457$	8.61654e8	+	1.49243e9i	0.0197546	+	0.0342160i	0.875734	−	0.482794i	$-0.160378\pi$
$457$	8.61654e8	+	1.49243e9i	0.0197546	+	0.0342160i	−0.855979	+	0.517010i	$0.827045\pi$
$458$	4.98314e10	+	2.87702e10i	1.13251	+	0.653853i
$459$		0			0
$460$	−1.11365e10	+	6.42969e9i	−0.248725	+	0.143601i
$461$		−	5.62647e10i		−	1.24575i	−0.782320	−	0.622877i	$-0.785964\pi$
$461$		−	5.62647e10i		−	1.24575i	0.782320	−	0.622877i	$-0.214036\pi$
$462$		0			0
$463$	5.75300e10			1.25190			0.625951	−	0.779863i	$-0.284711\pi$
$463$	5.75300e10			1.25190			0.625951	+	0.779863i	$0.284711\pi$
$464$	−5.68237e8	−	9.84216e8i	−0.0122591	−	0.0212333i
$465$		0			0
$466$	3.12909e9	−	5.41974e9i	0.0663551	−	0.114930i
$467$	2.55815e10	−	1.47695e10i	0.537846	−	0.310525i	−0.206360	−	0.978476i	$-0.566162\pi$
$467$	2.55815e10	−	1.47695e10i	0.537846	−	0.310525i	0.744205	+	0.667951i	$0.232828\pi$
$468$		0			0
$469$	3.08489e9	−	6.01838e8i	0.0637599	−	0.0124391i
$470$	1.39097e10			0.285053
$471$		0			0
$472$	−1.01269e8	−	5.84679e7i	−0.00204037	−	0.00117801i
$473$	−3.72846e9	+	6.45789e9i	−0.0744878	+	0.129017i
$474$		0			0
$475$		−	3.63114e10i		−	0.713294i
$476$	−8.23558e9	−	2.82942e9i	−0.160423	−	0.0551149i
$477$		0			0
$478$	−1.45297e10	−	2.51662e10i	−0.278320	−	0.482065i
$479$	7.73386e9	+	4.46515e9i	0.146911	+	0.0848191i	0.571654	−	0.820495i	$-0.306302\pi$
$479$	7.73386e9	+	4.46515e9i	0.146911	+	0.0848191i	−0.424743	+	0.905314i	$0.639635\pi$
$480$		0			0
$481$	−1.23475e10	+	7.12884e9i	−0.230674	+	0.133180i
$482$		−	4.76126e10i		−	0.882132i
$483$		0			0
$484$	−2.05727e10			−0.374894
$485$	−4.94448e9	−	8.56410e9i	−0.0893622	−	0.154780i
$486$		0			0
$487$	4.76628e10	−	8.25545e10i	0.847352	−	1.46766i	−0.0362103	−	0.999344i	$-0.511529\pi$
$487$	4.76628e10	−	8.25545e10i	0.847352	−	1.46766i	0.883563	−	0.468313i	$-0.155138\pi$
$488$	4.84203e9	−	2.79555e9i	0.0853785	−	0.0492933i
$489$		0			0
$490$	−1.24401e10	+	1.59677e10i	−0.215795	+	0.276987i
$491$	8.27002e10			1.42292			0.711461	−	0.702726i	$-0.248034\pi$
$491$	8.27002e10			1.42292			0.711461	+	0.702726i	$0.248034\pi$
$492$		0			0
$493$	−1.70212e9	−	9.82718e8i	−0.0288139	−	0.0166357i
$494$	−7.43373e9	+	1.28756e10i	−0.124824	+	0.216202i
$495$		0			0
$496$		−	1.11009e10i		−	0.183414i
$497$	−6.15110e10	−	7.06623e10i	−1.00815	−	1.15814i
$498$		0			0
$499$	2.16835e10	+	3.75570e10i	0.349726	+	0.605743i	0.986201	−	0.165554i	$-0.0529414\pi$
$499$	2.16835e10	+	3.75570e10i	0.349726	+	0.605743i	−0.636475	+	0.771298i	$0.719608\pi$
$500$	2.35637e10	+	1.36045e10i	0.377020	+	0.217673i
$501$		0			0
$502$	−3.39173e10	+	1.95822e10i	−0.534080	+	0.308351i
$503$		−	1.03115e11i		−	1.61083i	−0.592712	−	0.805415i	$-0.701943\pi$
$503$		−	1.03115e11i		−	1.61083i	0.592712	−	0.805415i	$-0.298057\pi$
$504$		0			0
$505$	−5.94348e9			−0.0913850
$506$	−1.34107e10	−	2.32280e10i	−0.204574	−	0.354332i
$507$		0			0
$508$	−1.12860e10	+	1.95480e10i	−0.169468	+	0.293526i
$509$	6.42743e10	−	3.71088e10i	0.957560	−	0.552847i	0.0621387	−	0.998068i	$-0.480208\pi$
$509$	6.42743e10	−	3.71088e10i	0.957560	−	0.552847i	0.895421	+	0.445220i	$0.146875\pi$
$510$		0			0
$511$	−6.32429e9	−	3.24169e10i	−0.0927530	−	0.475431i
$512$	3.03700e9			0.0441942
$513$		0			0
$514$	−7.32332e10	−	4.22812e10i	−1.04919	−	0.605752i
$515$	−1.97329e10	+	3.41784e10i	−0.280519	+	0.485873i
$516$		0			0
$517$			2.90121e10i			0.406085i
$518$	−3.56900e10	+	6.96285e9i	−0.495710	+	0.0967093i
$519$		0			0
$520$	−2.39348e9	−	4.14563e9i	−0.0327353	−	0.0566992i
$521$	1.02678e11	+	5.92814e10i	1.39357	+	0.804577i	0.993708	−	0.111999i	$-0.0357254\pi$
$521$	1.02678e11	+	5.92814e10i	1.39357	+	0.804577i	0.399860	+	0.916576i	$0.369059\pi$
$522$		0			0
$523$	7.82719e10	−	4.51903e10i	1.04616	−	0.604002i	0.124590	−	0.992208i	$-0.460239\pi$
$523$	7.82719e10	−	4.51903e10i	1.04616	−	0.604002i	0.921572	+	0.388207i	$0.126905\pi$
$524$		−	5.57573e10i		−	0.739565i
$525$		0			0
$526$	−5.53034e10			−0.722452
$527$	−9.59907e9	−	1.66261e10i	−0.124448	−	0.215550i
$528$		0			0
$529$	−1.32378e10	+	2.29285e10i	−0.169041	+	0.292788i
$530$	4.10681e10	−	2.37107e10i	0.520476	−	0.300497i
$531$		0			0
$532$	−2.86001e10	+	2.48961e10i	−0.357043	+	0.310803i
$533$	−1.07461e9			−0.0133150
$534$		0			0
$535$	7.96456e9	+	4.59834e9i	0.0972180	+	0.0561289i
$536$	−9.47858e8	+	1.64174e9i	−0.0114838	+	0.0198905i
$537$		0			0
$538$		−	6.32135e10i		−	0.754538i
$539$	−3.33047e10	−	2.59470e10i	−0.394594	−	0.307420i
$540$		0			0
$541$	7.39222e10	+	1.28037e11i	0.862951	+	1.49467i	0.869068	+	0.494693i	$0.164720\pi$
$541$	7.39222e10	+	1.28037e11i	0.862951	+	1.49467i	−0.00611676	+	0.999981i	$0.501947\pi$
$542$	−8.08944e9	−	4.67044e9i	−0.0937392	−	0.0541204i
$543$		0			0
$544$	4.54857e9	−	2.62612e9i	0.0519373	−	0.0299860i
$545$		−	1.97376e10i		−	0.223722i
$546$		0			0
$547$	5.79541e10			0.647343			0.323672	−	0.946170i	$-0.395083\pi$
$547$	5.79541e10			0.647343			0.323672	+	0.946170i	$0.395083\pi$
$548$	−6.00699e9	−	1.04044e10i	−0.0666092	−	0.115371i
$549$		0			0
$550$	−1.21926e10	+	2.11183e10i	−0.133244	+	0.230785i
$551$	−7.41165e9	+	4.27912e9i	−0.0804097	+	0.0464245i
$552$		0			0
$553$	−3.97673e10	+	1.15750e11i	−0.425231	+	1.23772i
$554$	1.40099e10			0.148729
$555$		0			0
$556$	−5.22754e10	−	3.01812e10i	−0.547014	−	0.315819i
$557$	−7.53965e10	+	1.30591e11i	−0.783304	+	1.35672i	0.146702	+	0.989181i	$0.453134\pi$
$557$	−7.53965e10	+	1.30591e11i	−0.783304	+	1.35672i	−0.930007	+	0.367542i	$0.880199\pi$
$558$		0			0
$559$			1.08448e10i			0.111065i
$560$	−2.33775e9	−	1.19828e10i	−0.0237709	−	0.121844i
$561$		0			0
$562$	3.42444e10	+	5.93131e10i	0.343277	+	0.594573i
$563$	1.25319e11	+	7.23527e10i	1.24733	+	0.720147i	0.970576	−	0.240793i	$-0.0774076\pi$
$563$	1.25319e11	+	7.23527e10i	1.24733	+	0.720147i	0.276755	+	0.960941i	$0.410741\pi$
$564$		0			0
$565$	−1.68486e10	+	9.72756e9i	−0.165337	+	0.0954575i
$566$			5.62755e10i			0.548345i
$567$		0			0
$568$	5.65054e10			0.542871
$569$	−4.75705e10	−	8.23945e10i	−0.453825	−	0.786048i	0.544795	−	0.838569i	$-0.316608\pi$
$569$	−4.75705e10	−	8.23945e10i	−0.453825	−	0.786048i	−0.998620	+	0.0525213i	$0.983274\pi$
$570$		0			0
$571$	7.80806e10	−	1.35240e11i	0.734512	−	1.27221i	−0.220425	−	0.975404i	$-0.570745\pi$
$571$	7.80806e10	−	1.35240e11i	0.734512	−	1.27221i	0.954937	−	0.296808i	$-0.0959222\pi$
$572$	8.64674e9	−	4.99220e9i	0.0807733	−	0.0466345i
$573$		0			0
$574$	−2.59198e9	−	8.90503e8i	−0.0238773	−	0.00820329i
$575$	9.52689e10			0.871525
$576$		0			0
$577$	−1.51443e10	−	8.74358e9i	−0.136630	−	0.0788835i	0.430127	−	0.902768i	$-0.358469\pi$
$577$	−1.51443e10	−	8.74358e9i	−0.136630	−	0.0788835i	−0.566757	+	0.823885i	$0.691802\pi$
$578$	−3.49192e10	+	6.04818e10i	−0.312862	+	0.541893i
$579$		0			0
$580$		−	2.75554e9i		−	0.0243498i
$581$	−1.24974e11	+	1.08788e11i	−1.09677	+	0.954725i
$582$		0			0
$583$	4.94545e10	+	8.56577e10i	0.428087	+	0.741468i
$584$	1.72519e10	+	9.96037e9i	0.148315	+	0.0856296i
$585$		0			0
$586$	−3.21093e9	+	1.85383e9i	−0.0272295	+	0.0157210i
$587$		−	7.87793e10i		−	0.663528i	−0.943362	−	0.331764i	$-0.892356\pi$
$587$		−	7.87793e10i		−	0.663528i	0.943362	−	0.331764i	$-0.107644\pi$
$588$		0			0
$589$	−8.35958e10			−0.694581
$590$	−1.41764e8	−	2.45542e8i	−0.00116992	−	0.00202636i
$591$		0			0
$592$	1.09661e10	−	1.89938e10i	0.0892821	−	0.154641i
$593$	1.49011e11	−	8.60313e10i	1.20503	−	0.695725i	0.243362	−	0.969936i	$-0.421750\pi$
$593$	1.49011e11	−	8.60313e10i	1.20503	−	0.695725i	0.961670	+	0.274210i	$0.0884165\pi$
$594$		0			0
$595$	−1.38629e10	−	1.59254e10i	−0.110608	−	0.127064i
$596$	−4.03125e10			−0.319488
$597$		0			0
$598$	−3.37813e10	−	1.95036e10i	−0.264162	−	0.152514i
$599$	−9.01078e10	+	1.56071e11i	−0.699930	+	1.21232i	0.268560	+	0.963263i	$0.413452\pi$
$599$	−9.01078e10	+	1.56071e11i	−0.699930	+	1.21232i	−0.968490	+	0.249052i	$0.919881\pi$
$600$		0			0
$601$			1.78947e11i			1.37159i	0.727793	+	0.685797i	$0.240546\pi$
$601$			1.78947e11i			1.37159i	−0.727793	+	0.685797i	$0.759454\pi$
$602$	−8.98687e9	+	2.61581e10i	−0.0684262	+	0.199168i
$603$		0			0
$604$	−3.66824e9	−	6.35357e9i	−0.0275619	−	0.0477386i
$605$	−4.31985e10	−	2.49406e10i	−0.322438	−	0.186160i
$606$		0			0
$607$	2.01237e11	−	1.16184e11i	1.48236	−	0.855838i	0.482556	−	0.875865i	$-0.339708\pi$
$607$	2.01237e11	−	1.16184e11i	1.48236	−	0.855838i	0.999799	+	0.0200268i	$0.00637515\pi$
$608$		−	2.28702e10i		−	0.167361i
$609$		0			0
$610$	1.35564e10			0.0979095
$611$	2.10966e10	+	3.65404e10i	0.151373	+	0.262186i
$612$		0			0
$613$	−8.71275e10	+	1.50909e11i	−0.617040	+	1.06874i	0.372983	+	0.927838i	$0.378335\pi$
$613$	−8.71275e10	+	1.50909e11i	−0.617040	+	1.06874i	−0.990023	+	0.140906i	$0.954998\pi$
$614$	−7.94383e10	+	4.58637e10i	−0.558928	+	0.322698i
$615$		0			0
$616$	2.49931e10	−	4.87596e9i	0.173579	−	0.0338639i
$617$	−2.09739e11			−1.44724			−0.723618	−	0.690200i	$-0.757522\pi$
$617$	−2.09739e11			−1.44724			−0.723618	+	0.690200i	$0.757522\pi$
$618$		0			0
$619$	9.51908e10	+	5.49584e10i	0.648384	+	0.374345i	0.787837	−	0.615884i	$-0.211201\pi$
$619$	9.51908e10	+	5.49584e10i	0.648384	+	0.374345i	−0.139453	+	0.990229i	$0.544534\pi$
$620$	1.34579e10	−	2.33098e10i	0.0910773	−	0.157751i
$621$		0			0
$622$			2.04389e9i			0.0136551i
$623$	−2.52386e11	−	8.67098e10i	−1.67538	−	0.575594i
$624$		0			0
$625$	−2.44954e10	−	4.24274e10i	−0.160533	−	0.278052i
$626$	1.38678e11	+	8.00656e10i	0.903045	+	0.521373i
$627$		0			0
$628$	−4.34251e10	+	2.50715e10i	−0.279192	+	0.161191i
$629$		−	3.79298e10i		−	0.242314i
$630$		0			0
$631$	−1.78221e11			−1.12420			−0.562098	−	0.827071i	$-0.690006\pi$
$631$	−1.78221e11			−1.12420			−0.562098	+	0.827071i	$0.690006\pi$
$632$	−3.69099e10	−	6.39298e10i	−0.231353	−	0.400714i
$633$		0			0
$634$	−5.66793e9	+	9.81714e9i	−0.0350806	+	0.0607614i
$635$	−4.73968e10	+	2.73646e10i	−0.291511	+	0.168304i
$636$		0			0
$637$	−6.08146e10	−	8.46187e9i	−0.369360	−	0.0513935i
$638$	5.74737e9			0.0346885
$639$		0			0
$640$	6.37709e9	+	3.68182e9i	0.0380104	+	0.0219453i
$641$	−1.26336e11	+	2.18820e11i	−0.748333	+	1.29615i	0.200289	+	0.979737i	$0.435812\pi$
$641$	−1.26336e11	+	2.18820e11i	−0.748333	+	1.29615i	−0.948621	+	0.316413i	$0.897521\pi$
$642$		0			0
$643$		−	2.10234e11i		−	1.22987i	−0.788578	−	0.614934i	$-0.789183\pi$
$643$		−	2.10234e11i		−	1.22987i	0.788578	−	0.614934i	$-0.210817\pi$
$644$	−6.53191e10	−	7.50370e10i	−0.379749	−	0.436247i
$645$		0			0
$646$	−1.97760e10	−	3.42531e10i	−0.113556	−	0.196684i
$647$	3.02203e11	+	1.74477e11i	1.72457	+	0.995684i	0.908694	+	0.417463i	$0.137081\pi$
$647$	3.02203e11	+	1.74477e11i	1.72457	+	0.995684i	0.815881	+	0.578220i	$0.196253\pi$
$648$		0			0
$649$	5.12138e8	−	2.95683e8i	0.00288674	−	0.00166666i
$650$			3.54643e10i			0.198672i
$651$		0			0
$652$	3.77190e10			0.208723
$653$	2.26857e10	+	3.92928e10i	0.124767	+	0.216103i	0.921642	−	0.388042i	$-0.126848\pi$
$653$	2.26857e10	+	3.92928e10i	0.124767	+	0.216103i	−0.796875	+	0.604144i	$0.793515\pi$
$654$		0			0
$655$	6.75957e10	−	1.17079e11i	0.367243	−	0.636084i
$656$	1.43157e9	−	8.26518e8i	0.00773033	−	0.00446311i
$657$		0			0
$658$	2.06054e10	+	1.05619e11i	0.109920	+	0.563427i
$659$	−3.26397e11			−1.73063			−0.865315	−	0.501228i	$-0.832882\pi$
$659$	−3.26397e11			−1.73063			−0.865315	+	0.501228i	$0.832882\pi$
$660$		0			0
$661$	−2.04253e11	−	1.17926e11i	−1.06995	−	0.617735i	−0.141781	−	0.989898i	$-0.545283\pi$
$661$	−2.04253e11	−	1.17926e11i	−1.06995	−	0.617735i	−0.928167	+	0.372163i	$0.878616\pi$
$662$	−1.33274e11	+	2.30838e11i	−0.693928	+	1.20192i
$663$		0			0
$664$		−	9.99356e10i		−	0.514100i
$665$	−9.02365e10	+	1.76045e10i	−0.461419	+	0.0900194i
$666$		0			0
$667$	−1.12270e10	−	1.94457e10i	−0.0567230	−	0.0982471i
$668$	−7.32504e10	−	4.22911e10i	−0.367878	−	0.212395i
$669$		0			0
$670$	−3.98063e9	+	2.29822e9i	−0.0197539	+	0.0114049i
$671$			2.82752e10i			0.139481i
$672$		0			0
$673$	−1.87469e11			−0.913836			−0.456918	−	0.889509i	$-0.651047\pi$
$673$	−1.87469e11			−0.913836			−0.456918	+	0.889509i	$0.651047\pi$
$674$	8.09741e10	+	1.40251e11i	0.392380	+	0.679622i
$675$		0			0
$676$	−4.49465e10	+	7.78496e10i	−0.215233	+	0.372794i
$677$	−1.30893e11	+	7.55712e10i	−0.623106	+	0.359751i	−0.778077	−	0.628168i	$-0.783805\pi$
$677$	−1.30893e11	+	7.55712e10i	−0.623106	+	0.359751i	0.154971	+	0.987919i	$0.450472\pi$
$678$		0			0
$679$	5.77041e10	−	5.02309e10i	0.271474	−	0.236316i
$680$	1.27348e10			0.0595602
$681$		0			0
$682$	4.86183e10	+	2.80698e10i	0.224731	+	0.129748i
$683$	−2.83371e10	+	4.90813e10i	−0.130219	+	0.225545i	−0.923761	−	0.382970i	$-0.874901\pi$
$683$	−2.83371e10	+	4.90813e10i	−0.130219	+	0.225545i	0.793542	+	0.608515i	$0.208235\pi$
$684$		0			0
$685$		−	2.91295e10i		−	0.132304i
$686$	−1.39674e11	−	7.08059e10i	−0.630696	−	0.319722i
$687$		0			0
$688$	−8.34115e9	−	1.44473e10i	−0.0372282	−	0.0644811i
$689$	1.24575e11	+	7.19232e10i	0.552781	+	0.319148i
$690$		0			0
$691$	3.04629e11	−	1.75878e11i	1.33616	−	0.771435i	0.349928	−	0.936777i	$-0.386206\pi$
$691$	3.04629e11	−	1.75878e11i	1.33616	−	0.771435i	0.986236	+	0.165342i	$0.0528728\pi$
$692$		−	9.82403e10i		−	0.428415i
$693$		0			0
$694$	2.50952e11			1.08181
$695$	−7.31786e10	−	1.26749e11i	−0.313650	−	0.543257i
$696$		0			0
$697$	1.42939e9	−	2.47578e9i	0.00605649	−	0.0104901i
$698$	1.16132e11	−	6.70487e10i	0.489248	−	0.282467i
$699$		0			0
$700$	−2.93884e10	+	8.55407e10i	−0.122401	+	0.356271i
$701$	2.98966e11			1.23808			0.619041	−	0.785359i	$-0.287521\pi$
$701$	2.98966e11			1.23808			0.619041	+	0.785359i	$0.287521\pi$
$702$		0			0
$703$	−1.43033e11	−	8.25802e10i	−0.585619	−	0.338107i
$704$	−7.67934e9	+	1.33010e10i	−0.0312632	+	0.0541494i
$705$		0			0
$706$		−	1.02162e11i		−	0.411217i
$707$	−8.80449e9	−	4.51299e10i	−0.0352392	−	0.180629i
$708$		0			0
$709$	4.36899e10	+	7.56732e10i	0.172901	+	0.299473i	0.939433	−	0.342733i	$-0.111353\pi$
$709$	4.36899e10	+	7.56732e10i	0.172901	+	0.299473i	−0.766532	+	0.642206i	$0.778019\pi$
$710$	1.18650e11	+	6.85026e10i	0.466911	+	0.269571i
$711$		0			0
$712$	1.39395e11	−	8.04795e10i	0.542408	−	0.313159i
$713$		−	2.19327e11i		−	0.848662i
$714$		0			0
$715$	2.42085e10			0.0926285
$716$	−6.09219e10	−	1.05520e11i	−0.231804	−	0.401497i
$717$		0			0
$718$	5.11604e10	−	8.86124e10i	0.192502	−	0.333424i
$719$	1.77517e11	−	1.02489e11i	0.664239	−	0.383499i	−0.129651	−	0.991560i	$-0.541386\pi$
$719$	1.77517e11	−	1.02489e11i	0.664239	−	0.383499i	0.793890	+	0.608061i	$0.208052\pi$
$720$		0			0
$721$	−2.88755e11	−	9.92047e10i	−1.06853	−	0.367106i
$722$	1.99230e10			0.0733174
$723$		0			0
$724$	9.99005e10	+	5.76776e10i	0.363591	+	0.209920i
$725$	−1.02072e10	+	1.76794e10i	−0.0369450	+	0.0639907i
$726$		0			0
$727$			7.18474e10i			0.257201i	0.991696	+	0.128601i	$0.0410485\pi$
$727$			7.18474e10i			0.257201i	−0.991696	+	0.128601i	$0.958951\pi$
$728$	2.79329e10	−	2.43153e10i	0.0994466	−	0.0865674i
$729$		0			0
$730$	2.41503e10	+	4.18296e10i	0.0850416	+	0.147296i
$731$	−2.49854e10	−	1.44253e10i	−0.0875016	−	0.0505191i
$732$		0			0
$733$	−2.02189e11	+	1.16734e11i	−0.700391	+	0.404371i	−0.807493	−	0.589877i	$-0.799176\pi$
$733$	−2.02189e11	+	1.16734e11i	−0.700391	+	0.404371i	0.107102	+	0.994248i	$0.465843\pi$
$734$		−	1.31666e11i		−	0.453618i
$735$		0			0
$736$	6.00037e10			0.204487
$737$	−4.79350e9	−	8.30258e9i	−0.0162474	−	0.0281412i
$738$		0			0
$739$	−1.36191e11	+	2.35889e11i	−0.456636	+	0.790917i	−0.998781	−	0.0493684i	$-0.984279\pi$
$739$	−1.36191e11	+	2.35889e11i	−0.456636	+	0.790917i	0.542145	+	0.840285i	$0.317612\pi$
$740$	4.60531e10	−	2.65888e10i	0.153579	−	0.0886690i
$741$		0			0
$742$	2.40876e11	+	2.76713e11i	0.794655	+	0.912880i
$743$	1.83116e11			0.600858			0.300429	−	0.953804i	$-0.402870\pi$
$743$	1.83116e11			0.600858			0.300429	+	0.953804i	$0.402870\pi$
$744$		0			0
$745$	−8.46483e10	−	4.88717e10i	−0.274785	−	0.158647i
$746$	−5.80395e10	+	1.00527e11i	−0.187399	+	0.324585i
$747$		0			0
$748$			2.65616e10i			0.0848491i
$749$	−2.31176e10	+	6.72882e10i	−0.0734539	+	0.213802i
$750$		0			0
$751$	−2.10829e11	−	3.65166e11i	−0.662781	−	1.14797i	−0.979882	−	0.199579i	$-0.936043\pi$
$751$	−2.10829e11	−	3.65166e11i	−0.662781	−	1.14797i	0.317101	−	0.948392i	$-0.397291\pi$
$752$	−5.62090e10	−	3.24523e10i	−0.175766	−	0.101478i
$753$		0			0
$754$	7.23874e9	−	4.17929e9i	0.0223964	−	0.0129305i
$755$		−	1.77883e10i		−	0.0547453i
$756$		0			0
$757$	−2.97619e11			−0.906310			−0.453155	−	0.891432i	$-0.649702\pi$
$757$	−2.97619e11			−0.906310			−0.453155	+	0.891432i	$0.649702\pi$
$758$	−2.70128e10	−	4.67876e10i	−0.0818263	−	0.141727i
$759$		0			0
$760$	2.77260e10	−	4.80228e10i	0.0831060	−	0.143944i
$761$	4.74647e11	−	2.74037e11i	1.41525	−	0.817093i	0.419370	−	0.907816i	$-0.362251\pi$
$761$	4.74647e11	−	2.74037e11i	1.41525	−	0.817093i	0.995876	+	0.0907229i	$0.0289178\pi$
$762$		0			0
$763$	1.49871e11	−	2.92387e10i	0.442201	−	0.0862700i
$764$	1.89952e11			0.557533
$765$		0			0
$766$	7.68353e9	+	4.43609e9i	0.0223175	+	0.0128850i
$767$	4.30021e8	−	7.44818e8i	0.00124253	−	0.00215213i
$768$		0			0
$769$			2.79249e11i			0.798521i	0.916837	+	0.399261i	$0.130733\pi$
$769$			2.79249e11i			0.798521i	−0.916837	+	0.399261i	$0.869267\pi$
$770$	5.83917e10	+	2.00611e10i	0.166107	+	0.0570678i
$771$		0			0
$772$	5.74365e10	+	9.94830e10i	0.161703	+	0.280078i
$773$	3.95527e11	+	2.28358e11i	1.10779	+	0.639584i	0.938257	−	0.345940i	$-0.112440\pi$
$773$	3.95527e11	+	2.28358e11i	1.10779	+	0.639584i	0.169536	+	0.985524i	$0.445773\pi$
$774$		0			0
$775$	−1.72691e11	+	9.97030e10i	−0.478698	+	0.276377i
$776$			4.61433e10i			0.127251i
$777$		0			0
$778$	4.97320e11			1.35743
$779$	−6.22411e9	−	1.07805e10i	−0.0169016	−	0.0292744i
$780$		0			0
$781$	−1.42879e11	+	2.47474e11i	−0.384030	+	0.665159i
$782$	8.98686e10	−	5.18856e10i	0.240315	−	0.138746i
$783$		0			0
$784$	8.75244e10	−	3.55019e10i	0.231667	−	0.0939696i
$785$	−1.21579e11			−0.320169
$786$		0			0
$787$	3.95367e11	+	2.28266e11i	1.03063	+	0.595033i	0.917165	−	0.398509i	$-0.130472\pi$
$787$	3.95367e11	+	2.28266e11i	1.03063	+	0.595033i	0.113464	+	0.993542i	$0.463805\pi$
$788$	3.17998e10	−	5.50790e10i	0.0824746	−	0.142850i
$789$		0			0
$790$		−	1.78986e11i		−	0.459527i
$791$	−9.88221e10	−	1.13524e11i	−0.252434	−	0.289990i
$792$		0			0
$793$	2.05608e10	+	3.56123e10i	0.0519932	+	0.0900549i
$794$	−1.21599e11	−	7.02054e10i	−0.305949	−	0.176640i
$795$		0			0
$796$	−2.32067e11	+	1.33984e11i	−0.578045	+	0.333734i
$797$		−	4.37964e11i		−	1.08544i	−0.839914	−	0.542719i	$-0.817395\pi$
$797$		−	4.37964e11i		−	1.08544i	0.839914	−	0.542719i	$-0.182605\pi$
$798$		0			0
$799$	−1.12247e11			−0.275415
$800$	−2.72768e10	−	4.72448e10i	−0.0665937	−	0.115344i
$801$		0			0
$802$	−1.21474e11	+	2.10399e11i	−0.293619	+	0.508564i
$803$	−8.72460e10	+	5.03715e10i	−0.209838	+	0.121150i
$804$		0			0
$805$	−4.61882e10	−	2.36750e11i	−0.109989	−	0.563777i
$806$	8.16455e10			0.193460
$807$		0			0
$808$	2.40176e10	+	1.38665e10i	0.0563487	+	0.0325329i
$809$	7.57959e10	−	1.31282e11i	0.176950	−	0.306487i	−0.763884	−	0.645353i	$-0.776710\pi$
$809$	7.57959e10	−	1.31282e11i	0.176950	−	0.306487i	0.940835	+	0.338866i	$0.110043\pi$
$810$		0			0
$811$			3.72055e11i			0.860050i	0.902817	+	0.430025i	$0.141495\pi$
$811$			3.72055e11i			0.860050i	−0.902817	+	0.430025i	$0.858505\pi$
$812$	2.09233e10	−	4.08198e9i	0.0481289	−	0.00938959i
$813$		0			0
$814$	5.54575e10	+	9.60553e10i	0.126317	+	0.218788i
$815$	7.92023e10	+	4.57275e10i	0.179518	+	0.103645i
$816$		0			0
$817$	−1.08795e11	+	6.28131e10i	−0.244187	+	0.140981i
$818$		−	3.32666e10i		−	0.0743011i
$819$		0			0
$820$	4.00802e9			0.00886491
$821$	−3.40400e11	−	5.89590e11i	−0.749233	−	1.29771i	−0.948191	−	0.317702i	$-0.897089\pi$
$821$	−3.40400e11	−	5.89590e11i	−0.749233	−	1.29771i	0.198957	−	0.980008i	$-0.436244\pi$
$822$		0			0
$823$	3.69730e11	−	6.40392e11i	0.805908	−	1.39587i	−0.109768	−	0.993957i	$-0.535011\pi$
$823$	3.69730e11	−	6.40392e11i	0.805908	−	1.39587i	0.915676	−	0.401917i	$-0.131656\pi$
$824$	1.59481e11	−	9.20766e10i	0.345940	−	0.199729i
$825$		0			0
$826$	1.65444e9	−	1.44017e9i	0.00355410	−	0.00309382i
$827$	5.52152e11			1.18042			0.590210	−	0.807250i	$-0.299045\pi$
$827$	5.52152e11			1.18042			0.590210	+	0.807250i	$0.299045\pi$
$828$		0			0
$829$	2.24396e11	+	1.29555e11i	0.475113	+	0.274306i	0.718377	−	0.695654i	$-0.244885\pi$
$829$	2.24396e11	+	1.29555e11i	0.475113	+	0.274306i	−0.243265	+	0.969960i	$0.578218\pi$
$830$	1.21154e11	−	2.09845e11i	0.255285	−	0.442166i
$831$		0			0
$832$			2.23366e10i			0.0466148i
$833$	1.00388e11	−	1.28855e11i	0.208498	−	0.267621i
$834$		0			0
$835$	−1.02541e11	−	1.77606e11i	−0.210936	−	0.365352i
$836$	1.00163e11	+	5.78294e10i	0.205061	+	0.118392i
$837$		0			0
$838$	−4.21858e11	+	2.43560e11i	−0.855441	+	0.493889i
$839$		−	5.93133e11i		−	1.19703i	−0.801113	−	0.598514i	$-0.795758\pi$
$839$		−	5.93133e11i		−	1.19703i	0.801113	−	0.598514i	$-0.204242\pi$
$840$		0			0
$841$	−4.95435e11			−0.990382
$842$	2.04470e11	+	3.54153e11i	0.406801	+	0.704600i
$843$		0			0
$844$	−2.42055e10	+	4.19251e10i	−0.0477027	+	0.0826236i
$845$	−1.88757e11	+	1.08979e11i	−0.370234	+	0.213755i
$846$		0			0
$847$	1.25386e11	−	3.64960e11i	0.243621	−	0.709107i
$848$	−2.21275e11			−0.427906
$849$		0			0
$850$	−8.17059e10	−	4.71729e10i	−0.156523	−	0.0903685i
$851$	2.16663e11	−	3.75271e11i	0.413110	−	0.715528i
$852$		0			0
$853$			5.33930e11i			1.00853i	0.863549	+	0.504265i	$0.168236\pi$
$853$			5.33930e11i			1.00853i	−0.863549	+	0.504265i	$0.831764\pi$
$854$	2.00820e10	+	1.02936e11i	0.0377552	+	0.193525i
$855$		0			0
$856$	−2.14565e10	−	3.71638e10i	−0.0399635	−	0.0692189i
$857$	2.65771e10	+	1.53443e10i	0.0492702	+	0.0284462i	0.524433	−	0.851452i	$-0.324277\pi$
$857$	2.65771e10	+	1.53443e10i	0.0492702	+	0.0284462i	−0.475163	+	0.879898i	$0.657611\pi$
$858$		0			0
$859$	3.65042e11	−	2.10757e11i	0.670456	−	0.387088i	−0.125793	−	0.992056i	$-0.540148\pi$
$859$	3.65042e11	−	2.10757e11i	0.670456	−	0.387088i	0.796249	+	0.604968i	$0.206814\pi$
$860$		−	4.04485e10i		−	0.0739450i
$861$		0			0
$862$	4.55706e11			0.825383
$863$	1.57987e11	+	2.73641e11i	0.284825	+	0.493331i	0.972567	−	0.232624i	$-0.0747312\pi$
$863$	1.57987e11	+	2.73641e11i	0.284825	+	0.493331i	−0.687742	+	0.725955i	$0.741398\pi$
$864$		0			0
$865$	1.19099e11	−	2.06285e11i	0.212737	−	0.368471i
$866$	1.69506e9	−	9.78644e8i	0.00301379	−	0.00174002i
$867$		0			0
$868$	1.96931e11	+	6.76578e10i	0.346925	+	0.119190i
$869$	3.73320e11			0.654640
$870$		0			0
$871$	−1.20747e10	−	6.97134e9i	−0.0209799	−	0.0121128i
$872$	−4.60492e10	+	7.97595e10i	−0.0796445	+	0.137948i
$873$		0			0
$874$		−	4.51858e11i		−	0.774384i
$875$	−3.84961e11	+	3.35105e11i	−0.656726	+	0.571675i
$876$		0			0
$877$	1.07631e11	+	1.86422e11i	0.181944	+	0.315136i	0.942543	−	0.334086i	$-0.108428\pi$
$877$	1.07631e11	+	1.86422e11i	0.181944	+	0.315136i	−0.760598	+	0.649223i	$0.775094\pi$
$878$	−3.10102e11	−	1.79037e11i	−0.521827	−	0.301277i
$879$		0			0
$880$	−3.22502e10	+	1.86196e10i	−0.0537776	+	0.0310485i
$881$			5.75323e11i			0.955010i	0.878629	+	0.477505i	$0.158459\pi$
$881$			5.75323e11i			0.955010i	−0.878629	+	0.477505i	$0.841541\pi$
$882$		0			0
$883$	1.66564e11			0.273992			0.136996	−	0.990572i	$-0.456255\pi$
$883$	1.66564e11			0.273992			0.136996	+	0.990572i	$0.456255\pi$
$884$	1.93146e10	+	3.34540e10i	0.0316284	+	0.0547821i
$885$		0			0
$886$	−9.51674e10	+	1.64835e11i	−0.154438	+	0.267494i
$887$	−2.84479e11	+	1.64244e11i	−0.459574	+	0.265335i	−0.711865	−	0.702316i	$-0.752149\pi$
$887$	−2.84479e11	+	1.64244e11i	−0.459574	+	0.265335i	0.252291	+	0.967651i	$0.418816\pi$
$888$		0			0
$889$	−2.77996e11	−	3.19355e11i	−0.445074	−	0.511290i
$890$	3.90268e11			0.622017
$891$		0			0
$892$	−2.22266e11	−	1.28325e11i	−0.351086	−	0.202700i
$893$	−2.44382e11	+	4.23283e11i	−0.384294	+	0.665617i
$894$		0			0
$895$		−	2.95428e11i		−	0.460425i
$896$	−1.85098e10	+	5.38765e10i	−0.0287191	+	0.0835925i
$897$		0			0
$898$	−3.05900e11	−	5.29835e11i	−0.470408	−	0.814770i
$899$	4.07015e10	+	2.34990e10i	0.0623120	+	0.0359758i
$900$		0			0
$901$	−3.31407e11	+	1.91338e11i	−0.502878	+	0.290337i
$902$			8.35972e9i			0.0126289i
$903$		0			0
$904$	9.07803e10			0.135931
$905$	1.39847e11	+	2.42223e11i	0.208478	+	0.361094i
$906$		0			0
$907$	2.17195e11	−	3.76192e11i	0.320937	−	0.555880i	−0.659744	−	0.751490i	$-0.729335\pi$
$907$	2.17195e11	−	3.76192e11i	0.320937	−	0.555880i	0.980682	+	0.195610i	$0.0626688\pi$
$908$	−4.20631e11	+	2.42852e11i	−0.618811	+	0.357271i
$909$		0			0
$910$	8.81313e10	−	1.71937e10i	0.128518	−	0.0250729i
$911$	−5.37011e11			−0.779667			−0.389834	−	0.920885i	$-0.627467\pi$
$911$	−5.37011e11			−0.779667			−0.389834	+	0.920885i	$0.627467\pi$
$912$		0			0
$913$	4.37683e11	+	2.52697e11i	0.629908	+	0.363677i
$914$	9.74851e9	−	1.68849e10i	0.0139686	−	0.0241943i
$915$		0			0
$916$		−	6.50994e11i		−	0.924688i
$917$	9.89137e11	+	3.39828e11i	1.39888	+	0.480598i
$918$		0			0
$919$	1.40134e10	+	2.42719e10i	0.0196463	+	0.0340284i	0.875681	−	0.482889i	$-0.160413\pi$
$919$	1.40134e10	+	2.42719e10i	0.0196463	+	0.0340284i	−0.856035	+	0.516918i	$0.827079\pi$
$920$	1.25996e11	+	7.27436e10i	0.175875	+	0.101542i
$921$		0			0
$922$	−5.51279e11	+	3.18281e11i	−0.762865	+	0.440440i
$923$			4.15587e11i			0.572606i
$924$		0			0
$925$	−3.93967e11			−0.538137
$926$	−3.25439e11	−	5.63676e11i	−0.442614	−	0.766630i
$927$		0			0
$928$	−6.42887e9	+	1.11351e10i	−0.00866848	+	0.0150142i
$929$	−5.67238e11	+	3.27495e11i	−0.761557	+	0.439685i	−0.829854	−	0.557980i	$-0.811577\pi$
$929$	−5.67238e11	+	3.27495e11i	−0.761557	+	0.439685i	0.0682978	+	0.997665i	$0.478243\pi$
$930$		0			0
$931$	−2.67347e11	−	6.59103e11i	−0.355858	−	0.877313i
$932$	−7.08032e10			−0.0938403
$933$		0			0
$934$	−2.89421e11	−	1.67097e11i	−0.380314	−	0.219575i
$935$	−3.22011e10	+	5.57739e10i	−0.0421332	+	0.0729768i
$936$		0			0
$937$			9.51137e11i			1.23391i	0.786997	+	0.616957i	$0.211635\pi$
$937$			9.51137e11i			1.23391i	−0.786997	+	0.616957i	$0.788365\pi$
$938$	−2.33475e10	−	2.68211e10i	−0.0301599	−	0.0346469i
$939$		0			0
$940$	−7.86851e10	−	1.36287e11i	−0.100782	−	0.174559i
$941$	−1.23430e12	−	7.12622e11i	−1.57421	−	0.908868i	−0.995645	−	0.0932284i	$-0.970281\pi$
$941$	−1.23430e12	−	7.12622e11i	−1.57421	−	0.908868i	−0.578561	−	0.815639i	$-0.696385\pi$
$942$		0			0
$943$	2.82843e10	−	1.63300e10i	0.0357684	−	0.0206509i
$944$			1.32298e9i			0.00166596i
$945$		0			0
$946$	8.43655e10			0.105342
$947$	2.50503e11	+	4.33885e11i	0.311468	+	0.539479i	0.978680	−	0.205389i	$-0.0658459\pi$
$947$	2.50503e11	+	4.33885e11i	0.311468	+	0.539479i	−0.667212	+	0.744868i	$0.732513\pi$
$948$		0			0
$949$	−7.32568e10	+	1.26885e11i	−0.0903199	+	0.156439i
$950$	−3.55777e11	+	2.05408e11i	−0.436801	+	0.252187i
$951$		0			0
$952$	1.88649e10	+	9.66974e10i	0.0229672	+	0.117725i
$953$	−6.02406e11			−0.730327			−0.365164	−	0.930943i	$-0.618987\pi$
$953$	−6.02406e11			−0.730327			−0.365164	+	0.930943i	$0.618987\pi$
$954$		0			0
$955$	3.98862e11	+	2.30283e11i	0.479522	+	0.276852i
$956$	−1.64385e11	+	2.84723e11i	−0.196802	+	0.340871i
$957$		0			0
$958$		−	1.01035e11i		−	0.119952i
$959$	2.21186e11	−	4.31517e10i	0.261507	−	0.0510180i
$960$		0			0
$961$	−1.96910e11	−	3.41058e11i	−0.230874	−	0.399885i
$962$	1.39696e11	+	8.06536e10i	0.163111	+	0.0941724i
$963$		0			0
$964$	−4.66506e11	+	2.69338e11i	−0.540194	+	0.311881i
$965$			2.78526e11i			0.321186i
$966$		0			0
$967$	3.88014e11			0.443753			0.221877	−	0.975075i	$-0.428782\pi$
$967$	3.88014e11			0.443753			0.221877	+	0.975075i	$0.428782\pi$
$968$	1.16377e11	+	2.01570e11i	0.132545	+	0.229575i
$969$		0			0
$970$	−5.59405e10	+	9.68917e10i	−0.0631886	+	0.109446i
$971$	−1.18626e11	+	6.84889e10i	−0.133445	+	0.0770448i	−0.565237	−	0.824929i	$-0.691215\pi$
$971$	−1.18626e11	+	6.84889e10i	−0.133445	+	0.0770448i	0.431791	+	0.901974i	$0.357882\pi$
$972$		0			0
$973$	8.54024e11	−	7.43421e11i	0.952837	−	0.829437i
$974$	−1.07849e12			−1.19834
$975$		0			0
$976$	−5.47813e10	−	3.16280e10i	−0.0603717	−	0.0348556i
$977$	−3.01842e11	+	5.22806e11i	−0.331285	+	0.573802i	−0.982764	−	0.184864i	$-0.940815\pi$
$977$	−3.01842e11	+	5.22806e11i	−0.331285	+	0.573802i	0.651479	+	0.758666i	$0.274149\pi$
$978$		0			0
$979$			8.14000e11i			0.886122i
$980$	2.26823e11	+	3.15606e10i	0.245914	+	0.0342170i
$981$		0			0
$982$	−4.67823e11	−	8.10294e11i	−0.503079	−	0.871358i
$983$	−1.37063e12	−	7.91333e11i	−1.46793	−	0.847510i	−0.468576	−	0.883423i	$-0.655233\pi$
$983$	−1.37063e12	−	7.91333e11i	−1.46793	−	0.847510i	−0.999355	+	0.0359127i	$0.988566\pi$
$984$		0			0
$985$	1.33547e11	−	7.71032e10i	0.141869	−	0.0819082i
$986$			2.22364e10i			0.0235264i
$987$		0			0
$988$	1.68206e11			0.176528
$989$	−1.64801e11	−	2.85443e11i	−0.172256	−	0.298355i
$990$		0			0
$991$	−2.12570e11	+	3.68183e11i	−0.220398	+	0.381741i	−0.954929	−	0.296834i	$-0.904069\pi$
$991$	−2.12570e11	+	3.68183e11i	−0.220398	+	0.381741i	0.734531	+	0.678576i	$0.237402\pi$
$992$	−1.08767e11	+	6.27964e10i	−0.112318	+	0.0648467i
$993$		0			0
$994$	−3.44388e11	+	1.00241e12i	−0.352779	+	1.02683i
$995$	−6.49726e11			−0.662885
$996$		0			0
$997$	1.64710e12	+	9.50953e11i	1.66701	+	0.962450i	0.969235	+	0.246136i	$0.0791611\pi$
$997$	1.64710e12	+	9.50953e11i	1.66701	+	0.962450i	0.697778	+	0.716314i	$0.254172\pi$
$998$	2.45321e11	−	4.24909e11i	0.247294	−	0.428325i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.n.d.73.2	yes	20
3.2	odd	2	inner	126.9.n.d.73.9	yes	20
7.5	odd	6	inner	126.9.n.d.19.2	✓	20
21.5	even	6	inner	126.9.n.d.19.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.n.d.19.2	✓	20	7.5	odd	6	inner
126.9.n.d.19.9	yes	20	21.5	even	6	inner
126.9.n.d.73.2	yes	20	1.1	even	1	trivial
126.9.n.d.73.9	yes	20	3.2	odd	2	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-268.774 + 155.177i) q^{5} +(-1576.44 - 1810.98i) q^{7} +1448.15 q^{8} +O(q^{10})\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(-268.774 + 155.177i) q^{5} +(-1576.44 - 1810.98i) q^{7} +1448.15 q^{8} +(3040.83 + 1755.63i) q^{10} +(-3661.80 + 6342.42i) q^{11} +10650.9i q^{13} +(-8826.18 + 25690.3i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-24538.6 - 14167.4i) q^{17} +(-106850. + 61689.9i) q^{19} -39725.3i q^{20} +82857.0 q^{22} +(-161854. - 280339. i) q^{23} +(-147153. + 254876. i) q^{25} +(104357. - 60250.8i) q^{26} +(301641. - 58847.9i) q^{28} +69364.9 q^{29} +(586773. + 338774. i) q^{31} +(-92681.9 + 160530. i) q^{32} +320571. i q^{34} +(704729. + 242117. i) q^{35} +(669316. + 1.15929e6i) q^{37} +(1.20887e6 + 697942. i) q^{38} +(-389227. + 224720. i) q^{40} +100893. i q^{41} +1.01821e6 q^{43} +(-468710. - 811829. i) q^{44} +(-1.83117e6 + 3.17167e6i) q^{46} +(3.43073e6 - 1.98073e6i) q^{47} +(-794472. + 5.70979e6i) q^{49} +3.32969e6 q^{50} +(-1.18067e6 - 681659. i) q^{52} +(6.75277e6 - 1.16961e7i) q^{53} -2.27290e6i q^{55} +(-2.28293e6 - 2.62257e6i) q^{56} +(-392387. - 679634. i) q^{58} +(-69929.9 - 40374.0i) q^{59} +(3.34359e6 - 1.93042e6i) q^{61} -7.66558e6i q^{62} +2.09715e6 q^{64} +(-1.65278e6 - 2.86270e6i) q^{65} +(-654528. + 1.13368e6i) q^{67} +(3.14094e6 - 1.81342e6i) q^{68} +(-1.61430e6 - 8.27452e6i) q^{70} +3.90189e7 q^{71} +(1.19130e7 + 6.87798e6i) q^{73} +(7.57245e6 - 1.31159e7i) q^{74} -1.57926e7i q^{76} +(1.72586e7 - 3.36701e6i) q^{77} +(-2.54875e7 - 4.41457e7i) q^{79} +(4.40360e6 + 2.54242e6i) q^{80} +(988549. - 570739. i) q^{82} -6.90089e7i q^{83} +8.79380e6 q^{85} +(-5.75984e6 - 9.97634e6i) q^{86} +(-5.30285e6 + 9.18480e6i) q^{88} +(9.62567e7 - 5.55738e7i) q^{89} +(1.92886e7 - 1.67906e7i) q^{91} +4.14346e7 q^{92} +(-3.88142e7 - 2.24094e7i) q^{94} +(1.91457e7 - 3.31613e7i) q^{95} +3.18635e7i q^{97} +(6.04385e7 - 2.45153e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) \) 20 * q - 1280 * q^4 + 4186 * q^7	\( 20 q - 1280 q^{4} + 4186 q^{7} - 17664 q^{10} - 163840 q^{16} - 250890 q^{19} + 420864 q^{22} + 258962 q^{25} - 1189888 q^{28} + 342762 q^{31} - 4806598 q^{37} + 2260992 q^{40} + 6968252 q^{43} - 4357632 q^{46} - 26046538 q^{49} + 2075904 q^{52} + 2455296 q^{58} - 15410424 q^{61} + 41943040 q^{64} - 70041074 q^{67} - 25804800 q^{70} + 220264098 q^{73} + 12860578 q^{79} + 12085248 q^{82} + 29161632 q^{85} - 26935296 q^{88} - 311022894 q^{91} + 332230656 q^{94}+O(q^{100}) \) 20 * q - 1280 * q^4 + 4186 * q^7 - 17664 * q^10 - 163840 * q^16 - 250890 * q^19 + 420864 * q^22 + 258962 * q^25 - 1189888 * q^28 + 342762 * q^31 - 4806598 * q^37 + 2260992 * q^40 + 6968252 * q^43 - 4357632 * q^46 - 26046538 * q^49 + 2075904 * q^52 + 2455296 * q^58 - 15410424 * q^61 + 41943040 * q^64 - 70041074 * q^67 - 25804800 * q^70 + 220264098 * q^73 + 12860578 * q^79 + 12085248 * q^82 + 29161632 * q^85 - 26935296 * q^88 - 311022894 * q^91 + 332230656 * q^94

Introduction

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