LMFDB - Embedded newform 126.9.n.d.73.5

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			73.5
Root			$70.5683 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.9.n.d.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(814.617 - 470.320i) q^{5} +(14.7985 + 2400.95i) q^{7} +1448.15 q^{8} +O(q^{10})$	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(814.617 - 470.320i) q^{5} +(14.7985 + 2400.95i) q^{7} +1448.15 q^{8} +(-9216.34 - 5321.06i) q^{10} +(522.290 - 904.633i) q^{11} +47076.6i q^{13} +(23440.7 - 13726.8i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(55462.6 + 32021.4i) q^{17} +(-203421. + 117445. i) q^{19} +120402. i q^{20} -11818.1 q^{22} +(-135729. - 235089. i) q^{23} +(247089. - 427970. i) q^{25} +(461254. - 266305. i) q^{26} +(-267096. - 152021. i) q^{28} -1.26478e6 q^{29} +(143445. + 82818.0i) q^{31} +(-92681.9 + 160530. i) q^{32} -724561. i q^{34} +(1.14127e6 + 1.94890e6i) q^{35} +(-1.35572e6 - 2.34818e6i) q^{37} +(2.30144e6 + 1.32874e6i) q^{38} +(1.17969e6 - 681096. i) q^{40} -1.48329e6i q^{41} -928927. q^{43} +(66853.1 + 115793. i) q^{44} +(-1.53560e6 + 2.65973e6i) q^{46} +(-8.09682e6 + 4.67470e6i) q^{47} +(-5.76436e6 + 71061.3i) q^{49} -5.59098e6 q^{50} +(-5.21850e6 - 3.01290e6i) q^{52} +(-462964. + 801877. i) q^{53} -982573. i q^{55} +(21430.6 + 3.47695e6i) q^{56} +(7.15469e6 + 1.23923e7i) q^{58} +(1.14511e7 + 6.61132e6i) q^{59} +(-1.21666e7 + 7.02438e6i) q^{61} -1.87396e6i q^{62} +2.09715e6 q^{64} +(2.21410e7 + 3.83494e7i) q^{65} +(8.70876e6 - 1.50840e7i) q^{67} +(-7.09922e6 + 4.09874e6i) q^{68} +(1.26392e7 - 2.22068e7i) q^{70} -5.33768e6 q^{71} +(2.95255e7 + 1.70466e7i) q^{73} +(-1.53382e7 + 2.65666e7i) q^{74} -3.00659e7i q^{76} +(2.17971e6 + 1.24061e6i) q^{77} +(1.61504e7 + 2.79734e7i) q^{79} +(-1.33467e7 - 7.70572e6i) q^{80} +(-1.45332e7 + 8.39075e6i) q^{82} +6.53156e7i q^{83} +6.02411e7 q^{85} +(5.25480e6 + 9.10159e6i) q^{86} +(756357. - 1.31005e6i) q^{88} +(-2.58655e7 + 1.49334e7i) q^{89} +(-1.13029e8 + 696665. i) q^{91} +3.47466e7 q^{92} +(9.16051e7 + 5.28882e7i) q^{94} +(-1.10473e8 + 1.91345e8i) q^{95} +5.40321e7i q^{97} +(3.33044e7 + 5.60770e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	814.617	−	470.320i	1.30339	−	0.752511i	0.322404	−	0.946602i	$-0.395509\pi$
$5$	814.617	−	470.320i	1.30339	−	0.752511i	0.980984	+	0.194091i	$0.0621756\pi$
$6$		0			0
$7$	14.7985	+	2400.95i	0.00616349	+	0.999981i
$7$	14.7985	+	2400.95i	0.00616349	+	0.999981i
$8$	1448.15			0.353553
$9$		0			0
$10$	−9216.34	−	5321.06i	−0.921634	−	0.532106i
$11$	522.290	−	904.633i	0.0356731	−	0.0617876i	−0.847638	−	0.530576i	$-0.821976\pi$
$11$	522.290	−	904.633i	0.0356731	−	0.0617876i	0.883311	+	0.468788i	$0.155309\pi$
$12$		0			0
$13$			47076.6i			1.64828i	0.566385	+	0.824141i	$0.308342\pi$
$13$			47076.6i			1.64828i	−0.566385	+	0.824141i	$0.691658\pi$
$14$	23440.7	−	13726.8i	0.610182	−	0.357321i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	55462.6	+	32021.4i	0.664056	+	0.383393i	0.793821	−	0.608152i	$-0.208089\pi$
$17$	55462.6	+	32021.4i	0.664056	+	0.383393i	−0.129765	+	0.991545i	$0.541422\pi$
$18$		0			0
$19$	−203421.	+	117445.i	−1.56092	+	0.901197i	−0.563755	+	0.825942i	$0.690644\pi$
$19$	−203421.	+	117445.i	−1.56092	+	0.901197i	−0.997164	+	0.0752548i	$0.976023\pi$
$20$			120402.i			0.752511i
$21$		0			0
$22$	−11818.1			−0.0504494
$23$	−135729.	−	235089.i	−0.485022	−	0.840082i	0.514830	−	0.857292i	$-0.327855\pi$
$23$	−135729.	−	235089.i	−0.485022	−	0.840082i	−0.999852	+	0.0172101i	$0.994522\pi$
$24$		0			0
$25$	247089.	−	427970.i	0.632547	−	1.09560i
$26$	461254.	−	266305.i	1.00936	−	0.582756i
$27$		0			0
$28$	−267096.	−	152021.i	−0.434545	−	0.247326i
$29$	−1.26478e6			−1.78823			−0.894116	−	0.447836i	$-0.852195\pi$
$29$	−1.26478e6			−1.78823			−0.894116	+	0.447836i	$0.852195\pi$
$30$		0			0
$31$	143445.	+	82818.0i	0.155324	+	0.0896764i	0.575647	−	0.817698i	$-0.304750\pi$
$31$	143445.	+	82818.0i	0.155324	+	0.0896764i	−0.420323	+	0.907374i	$0.638083\pi$
$32$	−92681.9	+	160530.i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	724561.i		−	0.542200i
$35$	1.14127e6	+	1.94890e6i	0.760530	+	1.29873i
$36$		0			0
$37$	−1.35572e6	−	2.34818e6i	−0.723375	−	1.25292i	−0.959639	−	0.281233i	$-0.909257\pi$
$37$	−1.35572e6	−	2.34818e6i	−0.723375	−	1.25292i	0.236265	−	0.971689i	$-0.424077\pi$
$38$	2.30144e6	+	1.32874e6i	1.10374	+	0.637243i
$39$		0			0
$40$	1.17969e6	−	681096.i	0.460817	−	0.266053i
$41$		−	1.48329e6i		−	0.524917i	−0.964943	−	0.262458i	$-0.915467\pi$
$41$		−	1.48329e6i		−	0.524917i	0.964943	−	0.262458i	$-0.0845332\pi$
$42$		0			0
$43$	−928927.			−0.271711			−0.135856	−	0.990729i	$-0.543378\pi$
$43$	−928927.			−0.271711			−0.135856	+	0.990729i	$0.543378\pi$
$44$	66853.1	+	115793.i	0.0178366	+	0.0308938i
$45$		0			0
$46$	−1.53560e6	+	2.65973e6i	−0.342962	+	0.594028i
$47$	−8.09682e6	+	4.67470e6i	−1.65929	+	0.957993i	−0.686251	+	0.727365i	$0.740745\pi$
$47$	−8.09682e6	+	4.67470e6i	−1.65929	+	0.957993i	−0.973042	+	0.230628i	$0.925922\pi$
$48$		0			0
$49$	−5.76436e6	+	71061.3i	−0.999924	+	0.0123268i
$50$	−5.59098e6			−0.894556
$51$		0			0
$52$	−5.21850e6	−	3.01290e6i	−0.713727	−	0.412070i
$53$	−462964.	+	801877.i	−0.0586737	+	0.101626i	−0.893870	−	0.448326i	$-0.852020\pi$
$53$	−462964.	+	801877.i	−0.0586737	+	0.101626i	0.835197	+	0.549952i	$0.185354\pi$
$54$		0			0
$55$		−	982573.i		−	0.107378i
$56$	21430.6	+	3.47695e6i	0.00217912	+	0.353547i
$57$		0			0
$58$	7.15469e6	+	1.23923e7i	0.632235	+	1.09506i
$59$	1.14511e7	+	6.61132e6i	0.945019	+	0.545607i	0.891530	−	0.452961i	$-0.149632\pi$
$59$	1.14511e7	+	6.61132e6i	0.945019	+	0.545607i	0.0534889	+	0.998568i	$0.482966\pi$
$60$		0			0
$61$	−1.21666e7	+	7.02438e6i	−0.878717	+	0.507328i	−0.870235	−	0.492636i	$-0.836033\pi$
$61$	−1.21666e7	+	7.02438e6i	−0.878717	+	0.507328i	−0.00848188	+	0.999964i	$0.502700\pi$
$62$		−	1.87396e6i		−	0.126822i
$63$		0			0
$64$	2.09715e6			0.125000
$65$	2.21410e7	+	3.83494e7i	1.24035	+	2.14835i
$66$		0			0
$67$	8.70876e6	−	1.50840e7i	0.432172	−	0.748544i	−0.564888	−	0.825168i	$-0.691081\pi$
$67$	8.70876e6	−	1.50840e7i	0.432172	−	0.748544i	0.997060	+	0.0766234i	$0.0244139\pi$
$68$	−7.09922e6	+	4.09874e6i	−0.332028	+	0.191697i
$69$		0			0
$70$	1.26392e7	−	2.22068e7i	0.526415	−	0.924897i
$71$	−5.33768e6			−0.210048			−0.105024	−	0.994470i	$-0.533492\pi$
$71$	−5.33768e6			−0.210048			−0.105024	+	0.994470i	$0.533492\pi$
$72$		0			0
$73$	2.95255e7	+	1.70466e7i	1.03970	+	0.600268i	0.919747	−	0.392512i	$-0.128394\pi$
$73$	2.95255e7	+	1.70466e7i	1.03970	+	0.600268i	0.119948	+	0.992780i	$0.461727\pi$
$74$	−1.53382e7	+	2.65666e7i	−0.511503	+	0.885950i
$75$		0			0
$76$		−	3.00659e7i		−	0.901197i
$77$	2.17971e6	+	1.24061e6i	0.0620063	+	0.0352916i
$78$		0			0
$79$	1.61504e7	+	2.79734e7i	0.414644	+	0.718185i	0.995391	−	0.0958993i	$-0.0305727\pi$
$79$	1.61504e7	+	2.79734e7i	0.414644	+	0.718185i	−0.580747	+	0.814084i	$0.697239\pi$
$80$	−1.33467e7	−	7.70572e6i	−0.325847	−	0.188128i
$81$		0			0
$82$	−1.45332e7	+	8.39075e6i	−0.321444	+	0.185586i
$83$			6.53156e7i			1.37627i	0.725582	+	0.688136i	$0.241571\pi$
$83$			6.53156e7i			1.37627i	−0.725582	+	0.688136i	$0.758429\pi$
$84$		0			0
$85$	6.02411e7			1.15403
$86$	5.25480e6	+	9.10159e6i	0.0960645	+	0.166389i
$87$		0			0
$88$	756357.	−	1.31005e6i	0.0126123	−	0.0218452i
$89$	−2.58655e7	+	1.49334e7i	−0.412250	+	0.238012i	−0.691756	−	0.722131i	$-0.743163\pi$
$89$	−2.58655e7	+	1.49334e7i	−0.412250	+	0.238012i	0.279506	+	0.960144i	$0.409829\pi$
$90$		0			0
$91$	−1.13029e8	+	696665.i	−1.64825	+	0.0101592i
$92$	3.47466e7			0.485022
$93$		0			0
$94$	9.16051e7	+	5.28882e7i	1.17330	+	0.677403i
$95$	−1.10473e8	+	1.91345e8i	−1.35632	+	2.34922i
$96$		0			0
$97$			5.40321e7i			0.610330i	0.952299	+	0.305165i	$0.0987116\pi$
$97$			5.40321e7i			0.610330i	−0.952299	+	0.305165i	$0.901288\pi$
$98$	3.33044e7	+	5.60770e7i	0.361075	+	0.607968i
$99$		0			0
$100$	3.16273e7	+	5.47801e7i	0.316273	+	0.547801i
$101$	−8.47958e7	−	4.89569e7i	−0.814871	−	0.470466i	0.0337737	−	0.999430i	$-0.489247\pi$
$101$	−8.47958e7	−	4.89569e7i	−0.814871	−	0.470466i	−0.848644	+	0.528964i	$0.822581\pi$
$102$		0			0
$103$	−1.64140e8	+	9.47665e7i	−1.45837	+	0.841988i	−0.998931	−	0.0462234i	$-0.985281\pi$
$103$	−1.64140e8	+	9.47665e7i	−1.45837	+	0.841988i	−0.459435	+	0.888211i	$0.651948\pi$
$104$			6.81742e7i			0.582756i
$105$		0			0
$106$	1.04757e7			0.0829772
$107$	−3.06326e7	−	5.30573e7i	−0.233695	−	0.404772i	0.725198	−	0.688541i	$-0.241748\pi$
$107$	−3.06326e7	−	5.30573e7i	−0.233695	−	0.404772i	−0.958893	+	0.283769i	$0.908415\pi$
$108$		0			0
$109$	6.66765e7	−	1.15487e8i	0.472353	−	0.818139i	−0.527146	−	0.849774i	$-0.676738\pi$
$109$	6.66765e7	−	1.15487e8i	0.472353	−	0.818139i	0.999499	+	0.0316350i	$0.0100714\pi$
$110$	−9.62721e6	+	5.55827e6i	−0.0657551	+	0.0379637i
$111$		0			0
$112$	3.39458e7	−	1.98786e7i	0.215732	−	0.126332i
$113$	2.67016e8			1.63766			0.818831	−	0.574035i	$-0.194623\pi$
$113$	2.67016e8			1.63766			0.818831	+	0.574035i	$0.194623\pi$
$114$		0			0
$115$	−2.21134e8	−	1.27672e8i	−1.26434	−	0.729968i
$116$	8.09460e7	−	1.40203e8i	0.447058	−	0.774327i
$117$		0			0
$118$		−	1.49597e8i		−	0.771605i
$119$	−7.60611e7	+	1.33637e8i	−0.379293	+	0.666407i
$120$		0			0
$121$	1.06634e8	+	1.84695e8i	0.497455	+	0.861617i
$122$	1.37649e8	+	7.94717e7i	0.621347	+	0.358735i
$123$		0			0
$124$	−1.83610e7	+	1.06007e7i	−0.0776620	+	0.0448382i
$125$		−	9.74051e7i		−	0.398971i
$126$		0			0
$127$	1.08576e8			0.417368			0.208684	−	0.977983i	$-0.433082\pi$
$127$	1.08576e8			0.417368			0.208684	+	0.977983i	$0.433082\pi$
$128$	−1.18633e7	−	2.05478e7i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	2.50497e8	−	4.33874e8i	0.877060	−	1.51911i
$131$	−1.17441e8	+	6.78047e7i	−0.398782	+	0.230237i	−0.685958	−	0.727641i	$-0.740617\pi$
$131$	−1.17441e8	+	6.78047e7i	−0.398782	+	0.230237i	0.287176	+	0.957878i	$0.407283\pi$
$132$		0			0
$133$	−2.84990e8	−	4.86665e8i	−0.910801	−	1.55533i
$134$	−1.97057e8			−0.611184
$135$		0			0
$136$	8.03185e7	+	4.63719e7i	0.234779	+	0.135550i
$137$	2.77423e8	−	4.80510e8i	0.787516	−	1.36402i	−0.139968	−	0.990156i	$-0.544700\pi$
$137$	2.77423e8	−	4.80510e8i	0.787516	−	1.36402i	0.927484	−	0.373862i	$-0.121967\pi$
$138$		0			0
$139$		−	7.11909e7i		−	0.190706i	−0.995444	−	0.0953532i	$-0.969602\pi$
$139$		−	7.11909e7i		−	0.190706i	0.995444	−	0.0953532i	$-0.0303980\pi$
$140$	−2.89079e8	+	1.78177e6i	−0.752497	+	0.00463810i
$141$		0			0
$142$	3.01945e7	+	5.22984e7i	0.0742633	+	0.128628i
$143$	4.25870e7	+	2.45876e7i	0.101843	+	0.0587993i
$144$		0			0
$145$	−1.03031e9	+	5.94852e8i	−2.33076	+	1.34566i
$146$		−	3.85720e8i		−	0.848908i
$147$		0			0
$148$	3.47065e8			0.723375
$149$	−1.42326e8	−	2.46517e8i	−0.288762	−	0.500151i	0.684752	−	0.728776i	$-0.259910\pi$
$149$	−1.42326e8	−	2.46517e8i	−0.288762	−	0.500151i	−0.973515	+	0.228625i	$0.926577\pi$
$150$		0			0
$151$	−2.56501e8	+	4.44273e8i	−0.493380	+	0.854559i	−0.999971	−	0.00762721i	$-0.997572\pi$
$151$	−2.56501e8	+	4.44273e8i	−0.493380	+	0.854559i	0.506591	+	0.862187i	$0.330905\pi$
$152$	−2.94584e8	+	1.70078e8i	−0.551868	+	0.318621i
$153$		0			0
$154$	−174890.	−	2.83747e7i	−0.000310945	−	0.0504484i
$155$	1.55804e8			0.269930
$156$		0			0
$157$	4.41830e8	+	2.55091e8i	0.727204	+	0.419851i	0.817398	−	0.576073i	$-0.195415\pi$
$157$	4.41830e8	+	2.55091e8i	0.727204	+	0.419851i	−0.0901944	+	0.995924i	$0.528749\pi$
$158$	1.82721e8	−	3.16482e8i	0.293198	−	0.507833i
$159$		0			0
$160$			1.74360e8i			0.266053i
$161$	5.62430e8	−	3.29358e8i	0.837077	−	0.490190i
$162$		0			0
$163$	−9.54375e7	−	1.65303e8i	−0.135197	−	0.234169i	0.790475	−	0.612494i	$-0.209834\pi$
$163$	−9.54375e7	−	1.65303e8i	−0.135197	−	0.234169i	−0.925673	+	0.378325i	$0.876500\pi$
$164$	1.64424e8	+	9.49305e7i	0.227296	+	0.131229i
$165$		0			0
$166$	6.39959e8	−	3.69481e8i	0.842791	−	0.486586i
$167$		−	1.37420e9i		−	1.76678i	−0.468636	−	0.883391i	$-0.655254\pi$
$167$		−	1.37420e9i		−	1.76678i	0.468636	−	0.883391i	$-0.344746\pi$
$168$		0			0
$169$	−1.40047e9			−1.71683
$170$	−3.40775e8	−	5.90240e8i	−0.408011	−	0.706696i
$171$		0			0
$172$	5.94513e7	−	1.02973e8i	0.0679278	−	0.117654i
$173$	1.02182e9	−	5.89945e8i	1.14074	−	0.658608i	0.194129	−	0.980976i	$-0.437812\pi$
$173$	1.02182e9	−	5.89945e8i	1.14074	−	0.658608i	0.946615	+	0.322368i	$0.104479\pi$
$174$		0			0
$175$	1.03119e9	+	5.86915e8i	1.09948	+	0.625782i
$176$	−1.71144e7			−0.0178366
$177$		0			0
$178$	2.92634e8	+	1.68952e8i	0.291504	+	0.168300i
$179$	−7.26254e8	+	1.25791e9i	−0.707419	+	1.22529i	0.258393	+	0.966040i	$0.416807\pi$
$179$	−7.26254e8	+	1.25791e9i	−0.707419	+	1.22529i	−0.965811	+	0.259245i	$0.916526\pi$
$180$		0			0
$181$			3.51470e8i			0.327471i	0.986504	+	0.163736i	$0.0523544\pi$
$181$			3.51470e8i			0.327471i	−0.986504	+	0.163736i	$0.947646\pi$
$182$	6.46213e8	+	1.10351e9i	0.588966	+	1.00575i
$183$		0			0
$184$	−1.96556e8	−	3.40446e8i	−0.171481	−	0.297014i
$185$	−2.20879e9	−	1.27524e9i	−1.88568	−	1.08870i
$186$		0			0
$187$	5.79352e7	−	3.34489e7i	0.0473779	−	0.0273536i
$188$		−	1.19672e9i		−	0.957993i
$189$		0			0
$190$	2.49972e9			1.91813
$191$	1.43167e8	+	2.47972e8i	0.107574	+	0.186324i	0.914787	−	0.403936i	$-0.132358\pi$
$191$	1.43167e8	+	2.47972e8i	0.107574	+	0.186324i	−0.807213	+	0.590261i	$0.799025\pi$
$192$		0			0
$193$	1.60498e8	−	2.77991e8i	0.115676	−	0.200356i	−0.802374	−	0.596821i	$-0.796430\pi$
$193$	1.60498e8	−	2.77991e8i	0.115676	−	0.200356i	0.918050	+	0.396466i	$0.129763\pi$
$194$	5.29404e8	−	3.05652e8i	0.373749	−	0.215784i
$195$		0			0
$196$	3.61042e8	−	6.43535e8i	0.244643	−	0.436061i
$197$	9.97043e8			0.661986			0.330993	−	0.943633i	$-0.392616\pi$
$197$	9.97043e8			0.661986			0.330993	+	0.943633i	$0.392616\pi$
$198$		0			0
$199$	9.03419e7	+	5.21589e7i	0.0576072	+	0.0332595i	0.528527	−	0.848917i	$-0.322745\pi$
$199$	9.03419e7	+	5.21589e7i	0.0576072	+	0.0332595i	−0.470920	+	0.882176i	$0.656078\pi$
$200$	3.57822e8	−	6.19767e8i	0.223639	−	0.387354i
$201$		0			0
$202$			1.10777e9i			0.665339i
$203$	−1.87169e7	−	3.03668e9i	−0.0110218	−	1.78820i
$204$		0			0
$205$	−6.97620e8	−	1.20831e9i	−0.395006	−	0.684170i
$206$	1.85704e9	+	1.07216e9i	1.03122	+	0.595375i
$207$		0			0
$208$	6.67968e8	−	3.85651e8i	0.356863	−	0.206035i
$209$			2.45361e8i			0.128594i
$210$		0			0
$211$	−5.58407e8			−0.281722			−0.140861	−	0.990029i	$-0.544987\pi$
$211$	−5.58407e8			−0.281722			−0.140861	+	0.990029i	$0.544987\pi$
$212$	−5.92594e7	−	1.02640e8i	−0.0293369	−	0.0508129i
$213$		0			0
$214$	−3.46569e8	+	6.00275e8i	−0.165247	+	0.286217i
$215$	−7.56720e8	+	4.36893e8i	−0.354145	+	0.204466i
$216$		0			0
$217$	−1.96719e8	+	3.45630e8i	−0.0887173	+	0.155874i
$218$	−1.50872e9			−0.668008
$219$		0			0
$220$	1.08919e8	+	6.28847e7i	0.0464959	+	0.0268444i
$221$	−1.50746e9	+	2.61099e9i	−0.631940	+	1.09455i
$222$		0			0
$223$			1.47205e9i			0.595254i	0.954682	+	0.297627i	$0.0961951\pi$
$223$			1.47205e9i			0.595254i	−0.954682	+	0.297627i	$0.903805\pi$
$224$	−3.86796e8	−	2.20149e8i	−0.153635	−	0.0874431i
$225$		0			0
$226$	−1.51047e9	−	2.61621e9i	−0.579001	−	1.00286i
$227$	1.03779e9	+	5.99169e8i	0.390847	+	0.225656i	0.682527	−	0.730860i	$-0.260881\pi$
$227$	1.03779e9	+	5.99169e8i	0.390847	+	0.225656i	−0.291680	+	0.956516i	$0.594214\pi$
$228$		0			0
$229$	3.13100e7	−	1.80768e7i	0.0113852	−	0.00657326i	−0.494297	−	0.869293i	$-0.664574\pi$
$229$	3.13100e7	−	1.80768e7i	0.0113852	−	0.00657326i	0.505682	+	0.862720i	$0.331241\pi$
$230$			2.88889e9i			1.03233i
$231$		0			0
$232$	−1.83160e9			−0.632235
$233$	1.64329e9	+	2.84627e9i	0.557560	+	0.965722i	0.997699	+	0.0677924i	$0.0215955\pi$
$233$	1.64329e9	+	2.84627e9i	0.557560	+	0.965722i	−0.440140	+	0.897929i	$0.645071\pi$
$234$		0			0
$235$	−4.39721e9	+	7.61619e9i	−1.44180	+	2.49727i
$236$	−1.46575e9	+	8.46249e8i	−0.472510	+	0.272803i
$237$		0			0
$238$	1.73964e9	−	1.07225e7i	0.542189	−	0.00334184i
$239$	3.73479e9			1.14465			0.572327	−	0.820025i	$-0.306041\pi$
$239$	3.73479e9			1.14465			0.572327	+	0.820025i	$0.306041\pi$
$240$		0			0
$241$	1.92362e9	+	1.11060e9i	0.570231	+	0.329223i	0.757241	−	0.653135i	$-0.226547\pi$
$241$	1.92362e9	+	1.11060e9i	0.570231	+	0.329223i	−0.187011	+	0.982358i	$0.559880\pi$
$242$	1.20642e9	−	2.08959e9i	0.351754	−	0.609255i
$243$		0			0
$244$		−	1.79824e9i		−	0.507328i
$245$	−4.66233e9	+	2.76898e9i	−1.29401	+	0.768521i
$246$		0			0
$247$	−5.52890e9	−	9.57634e9i	−1.48543	−	2.57283i
$248$	2.07731e8	+	1.19933e8i	0.0549153	+	0.0317054i
$249$		0			0
$250$	−9.54371e8	+	5.51007e8i	−0.244319	+	0.141058i
$251$			3.49708e9i			0.881069i	0.897736	+	0.440535i	$0.145211\pi$
$251$			3.49708e9i			0.881069i	−0.897736	+	0.440535i	$0.854789\pi$
$252$		0			0
$253$	−2.83559e8			−0.0692089
$254$	−6.14198e8	−	1.06382e9i	−0.147562	−	0.255584i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−7.77094e8	+	4.48656e8i	−0.178132	+	0.102844i	−0.586415	−	0.810011i	$-0.699461\pi$
$257$	−7.77094e8	+	4.48656e8i	−0.178132	+	0.102844i	0.408283	+	0.912855i	$0.366128\pi$
$258$		0			0
$259$	5.61780e9	−	3.28977e9i	1.24844	−	0.731084i
$260$	−5.66810e9			−1.24035
$261$		0			0
$262$	1.32870e9	+	7.67123e8i	0.281981	+	0.162802i
$263$	−1.47398e9	+	2.55300e9i	−0.308083	+	0.533615i	−0.977943	−	0.208872i	$-0.933021\pi$
$263$	−1.47398e9	+	2.55300e9i	−0.308083	+	0.533615i	0.669860	+	0.742487i	$0.266354\pi$
$264$		0			0
$265$			8.70964e8i			0.176611i
$266$	−3.15618e9	+	5.54532e9i	−0.630428	+	1.10764i
$267$		0			0
$268$	1.11472e9	+	1.93075e9i	0.216086	+	0.374272i
$269$	3.58685e9	+	2.07087e9i	0.685021	+	0.395497i	0.801744	−	0.597668i	$-0.203906\pi$
$269$	3.58685e9	+	2.07087e9i	0.685021	+	0.395497i	−0.116723	+	0.993164i	$0.537239\pi$
$270$		0			0
$271$	1.98614e9	−	1.14670e9i	0.368241	−	0.212604i	−0.304449	−	0.952529i	$-0.598472\pi$
$271$	1.98614e9	−	1.14670e9i	0.368241	−	0.212604i	0.672690	+	0.739925i	$0.265139\pi$
$272$		−	1.04928e9i		−	0.191697i
$273$		0			0
$274$	−6.27736e9			−1.11372
$275$	−2.58104e8	−	4.47049e8i	−0.0451298	−	0.0781671i
$276$		0			0
$277$	4.31629e9	−	7.47604e9i	0.733149	−	1.26985i	−0.222382	−	0.974960i	$-0.571383\pi$
$277$	4.31629e9	−	7.47604e9i	0.733149	−	1.26985i	0.955531	−	0.294891i	$-0.0952833\pi$
$278$	−6.97525e8	+	4.02716e8i	−0.116783	+	0.0674249i
$279$		0			0
$280$	1.65274e9	+	2.82231e9i	0.268888	+	0.459169i
$281$	−1.42076e9			−0.227874			−0.113937	−	0.993488i	$-0.536346\pi$
$281$	−1.42076e9			−0.227874			−0.113937	+	0.993488i	$0.536346\pi$
$282$		0			0
$283$	−2.50006e9	−	1.44341e9i	−0.389766	−	0.225032i	0.292293	−	0.956329i	$-0.405582\pi$
$283$	−2.50006e9	−	1.44341e9i	−0.389766	−	0.225032i	−0.682059	+	0.731297i	$0.738915\pi$
$284$	3.41612e8	−	5.91689e8i	0.0525121	−	0.0909536i
$285$		0			0
$286$		−	5.56354e8i		−	0.0831548i
$287$	3.56131e9	−	2.19505e7i	0.524907	−	0.00323532i
$288$		0			0
$289$	−1.43714e9	−	2.48920e9i	−0.206020	−	0.356836i
$290$	1.16567e10	+	6.72998e9i	1.64810	+	0.951528i
$291$		0			0
$292$	−3.77927e9	+	2.18196e9i	−0.519848	+	0.300134i
$293$			9.77296e9i			1.32604i	0.748603	+	0.663019i	$0.230725\pi$
$293$			9.77296e9i			1.32604i	−0.748603	+	0.663019i	$0.769275\pi$
$294$		0			0
$295$	1.24377e10			1.64230
$296$	−1.96329e9	−	3.40052e9i	−0.255752	−	0.442975i
$297$		0			0
$298$	−1.61024e9	+	2.78902e9i	−0.204186	+	0.353660i
$299$	1.10672e10	−	6.38965e9i	1.38469	−	0.799452i
$300$		0			0
$301$	−1.37468e7	−	2.23031e9i	−0.00167469	−	0.271706i
$302$	5.80396e9			0.697745
$303$		0			0
$304$	3.33284e9	+	1.92422e9i	0.390230	+	0.225299i
$305$	−6.60740e9	+	1.14444e10i	−0.763539	+	1.32249i
$306$		0			0
$307$			1.57927e10i			1.77788i	0.458024	+	0.888940i	$0.348557\pi$
$307$			1.57927e10i			1.77788i	−0.458024	+	0.888940i	$0.651443\pi$
$308$	−2.77024e8	+	1.62225e8i	−0.0307833	+	0.0180266i
$309$		0			0
$310$	−8.81359e8	−	1.52656e9i	−0.0954346	−	0.165298i
$311$	−4.52636e9	−	2.61329e9i	−0.483846	−	0.279349i	0.238172	−	0.971223i	$-0.423452\pi$
$311$	−4.52636e9	−	2.61329e9i	−0.483846	−	0.279349i	−0.722018	+	0.691874i	$0.756785\pi$
$312$		0			0
$313$	−8.51493e9	+	4.91610e9i	−0.887164	+	0.512204i	−0.873014	−	0.487695i	$-0.837838\pi$
$313$	−8.51493e9	+	4.91610e9i	−0.887164	+	0.512204i	−0.0141503	+	0.999900i	$0.504504\pi$
$314$		−	5.77204e9i		−	0.593760i
$315$		0			0
$316$	−4.13451e9			−0.414644
$317$	−1.96496e9	−	3.40341e9i	−0.194588	−	0.337036i	0.752177	−	0.658961i	$-0.229004\pi$
$317$	−1.96496e9	−	3.40341e9i	−0.194588	−	0.337036i	−0.946765	+	0.321924i	$0.895670\pi$
$318$		0			0
$319$	−6.60583e8	+	1.14416e9i	−0.0637918	+	0.110491i
$320$	1.70838e9	−	9.86332e8i	0.162923	−	0.0940639i
$321$		0			0
$322$	−6.40862e9	−	3.64754e9i	−0.596130	−	0.339294i
$323$	−1.50430e10			−1.38205
$324$		0			0
$325$	2.01474e10	+	1.16321e10i	1.80586	+	1.04262i
$326$	−1.07975e9	+	1.87018e9i	−0.0955990	+	0.165582i
$327$		0			0
$328$		−	2.14803e9i		−	0.185586i
$329$	−1.13436e10	−	1.93709e10i	−0.968202	−	1.65336i
$330$		0			0
$331$	6.65125e9	+	1.15203e10i	0.554104	+	0.959736i	0.997973	+	0.0636440i	$0.0202722\pi$
$331$	6.65125e9	+	1.15203e10i	0.554104	+	0.959736i	−0.443869	+	0.896092i	$0.646394\pi$
$332$	−7.24031e9	−	4.18020e9i	−0.595943	−	0.344068i
$333$		0			0
$334$	−1.34643e10	+	7.77363e9i	−1.08193	+	0.624652i
$335$		−	1.63836e10i		−	1.30086i
$336$		0			0
$337$	1.53635e10			1.19116			0.595580	−	0.803296i	$-0.296922\pi$
$337$	1.53635e10			1.19116			0.595580	+	0.803296i	$0.296922\pi$
$338$	7.92227e9	+	1.37218e10i	0.606992	+	1.05134i
$339$		0			0
$340$	−3.85543e9	+	6.67780e9i	−0.288508	+	0.499710i
$341$	1.49840e8	−	8.65100e7i	0.0110818	−	0.00639807i
$342$		0			0
$343$	−2.55919e8	−	1.38389e10i	−0.0184895	−	0.999829i
$344$	−1.34523e9			−0.0960645
$345$		0			0
$346$	−1.15605e10	−	6.67447e9i	−0.806627	−	0.465706i
$347$	−1.41386e9	+	2.44888e9i	−0.0975191	+	0.168908i	−0.910657	−	0.413163i	$-0.864424\pi$
$347$	−1.41386e9	+	2.44888e9i	−0.0975191	+	0.168908i	0.813138	+	0.582071i	$0.197757\pi$
$348$		0			0
$349$		−	1.88443e10i		−	1.27022i	−0.772423	−	0.635109i	$-0.780955\pi$
$349$		−	1.88443e10i		−	1.27022i	0.772423	−	0.635109i	$-0.219045\pi$
$350$	−8.27383e7	−	1.34237e10i	−0.00551359	−	0.894539i
$351$		0			0
$352$	9.68136e7	+	1.67686e8i	0.00630617	+	0.0109226i
$353$	1.19955e10	+	6.92562e9i	0.772539	+	0.446026i	0.833780	−	0.552097i	$-0.186172\pi$
$353$	1.19955e10	+	6.92562e9i	0.772539	+	0.446026i	−0.0612403	+	0.998123i	$0.519506\pi$
$354$		0			0
$355$	−4.34817e9	+	2.51042e9i	−0.273775	+	0.158064i
$356$		−	3.82296e9i		−	0.238012i
$357$		0			0
$358$	1.64333e10			1.00044
$359$	2.92238e9	+	5.06172e9i	0.175938	+	0.304733i	0.940485	−	0.339834i	$-0.110371\pi$
$359$	2.92238e9	+	5.06172e9i	0.175938	+	0.304733i	−0.764548	+	0.644567i	$0.777038\pi$
$360$		0			0
$361$	1.90948e10	−	3.30732e10i	1.12431	−	1.94737i
$362$	3.44368e9	−	1.98821e9i	0.200534	−	0.115779i
$363$		0			0
$364$	7.15661e9	−	1.25740e10i	0.407664	−	0.716253i
$365$	3.20693e10			1.80683
$366$		0			0
$367$	4.52947e9	+	2.61509e9i	0.249680	+	0.144153i	0.619618	−	0.784904i	$-0.287288\pi$
$367$	4.52947e9	+	2.61509e9i	0.249680	+	0.144153i	−0.369938	+	0.929057i	$0.620621\pi$
$368$	−2.22378e9	+	3.85170e9i	−0.121255	+	0.210020i
$369$		0			0
$370$			2.88555e10i			1.53965i
$371$	−1.93212e9	−	1.09969e9i	−0.101986	−	0.0580463i
$372$		0			0
$373$	−6.35811e9	−	1.10126e10i	−0.328468	−	0.568922i	0.653740	−	0.756719i	$-0.273199\pi$
$373$	−6.35811e9	−	1.10126e10i	−0.328468	−	0.568922i	−0.982208	+	0.187796i	$0.939865\pi$
$374$	−6.55461e8	−	3.78431e8i	−0.0335012	−	0.0193419i
$375$		0			0
$376$	−1.17254e10	+	6.76969e9i	−0.586649	+	0.338702i
$377$		−	5.95416e10i		−	2.94751i
$378$		0			0
$379$	−1.59283e10			−0.771991			−0.385995	−	0.922501i	$-0.626142\pi$
$379$	−1.59283e10			−0.771991			−0.385995	+	0.922501i	$0.626142\pi$
$380$	−1.41406e10	−	2.44922e10i	−0.678161	−	1.17461i
$381$		0			0
$382$	1.61975e9	−	2.80549e9i	0.0760666	−	0.131751i
$383$	3.16640e9	−	1.82812e9i	0.147154	−	0.0849593i	−0.424615	−	0.905374i	$-0.639591\pi$
$383$	3.16640e9	−	1.82812e9i	0.147154	−	0.0849593i	0.571769	+	0.820415i	$0.306257\pi$
$384$		0			0
$385$	2.35911e9	−	1.45407e7i	0.107376	−	0.000661822i
$386$	−3.63167e9			−0.163590
$387$		0			0
$388$	−5.98952e9	−	3.45805e9i	−0.264281	−	0.152583i
$389$	5.63251e9	−	9.75580e9i	0.245982	−	0.426054i	−0.716425	−	0.697664i	$-0.754223\pi$
$389$	5.63251e9	−	9.75580e9i	0.245982	−	0.426054i	0.962407	+	0.271610i	$0.0875561\pi$
$390$		0			0
$391$		−	1.73849e10i		−	0.743816i
$392$	−8.34769e9	+	1.02908e8i	−0.353527	+	0.00435817i
$393$		0			0
$394$	−5.64013e9	−	9.76898e9i	−0.234047	−	0.405382i
$395$	2.63128e10	+	1.51917e10i	1.08088	+	0.624049i
$396$		0			0
$397$	−2.73124e10	+	1.57688e10i	−1.09951	+	0.634800i	−0.936091	−	0.351757i	$-0.885584\pi$
$397$	−2.73124e10	+	1.57688e10i	−1.09951	+	0.634800i	−0.163415	+	0.986557i	$0.552251\pi$
$398$		−	1.18022e9i		−	0.0470361i
$399$		0			0
$400$	−8.09660e9			−0.316273
$401$	−1.90026e10	−	3.29135e10i	−0.734914	−	1.27291i	−0.954761	−	0.297373i	$-0.903889\pi$
$401$	−1.90026e10	−	3.29135e10i	−0.734914	−	1.27291i	0.219848	−	0.975534i	$-0.429444\pi$
$402$		0			0
$403$	−3.89879e9	+	6.75290e9i	−0.147812	+	0.256018i
$404$	1.08539e10	−	6.26648e9i	0.407435	−	0.235233i
$405$		0			0
$406$	−2.96474e10	+	1.73615e10i	−1.09115	+	0.638973i
$407$	−2.83232e9			−0.103220
$408$		0			0
$409$	9.88374e9	+	5.70638e9i	0.353206	+	0.203924i	0.666096	−	0.745866i	$-0.267964\pi$
$409$	9.88374e9	+	5.70638e9i	0.353206	+	0.203924i	−0.312890	+	0.949789i	$0.601297\pi$
$410$	−7.89267e9	+	1.36705e10i	−0.279311	+	0.483781i
$411$		0			0
$412$		−	2.42602e10i		−	0.841988i
$413$	−1.57040e10	+	2.75915e10i	−0.539772	+	0.948364i
$414$		0			0
$415$	3.07192e10	+	5.32072e10i	1.03566	+	1.79382i
$416$	−7.55719e9	−	4.36315e9i	−0.252341	−	0.145689i
$417$		0			0
$418$	2.40404e9	−	1.38797e9i	0.0787474	−	0.0454648i
$419$		−	7.05049e9i		−	0.228751i	−0.993438	−	0.114376i	$-0.963513\pi$
$419$		−	7.05049e9i		−	0.228751i	0.993438	−	0.114376i	$-0.0364867\pi$
$420$		0			0
$421$	−3.15471e10			−1.00422			−0.502112	−	0.864803i	$-0.667444\pi$
$421$	−3.15471e10			−1.00422			−0.502112	+	0.864803i	$0.667444\pi$
$422$	3.15883e9	+	5.47125e9i	0.0996038	+	0.172519i
$423$		0			0
$424$	−6.70444e8	+	1.16124e9i	−0.0207443	+	0.0359302i
$425$	2.74084e10	−	1.58242e10i	0.840093	−	0.485028i
$426$		0			0
$427$	−1.70453e10	−	2.91074e10i	−0.512734	−	0.875573i
$428$	7.84196e9			0.233695
$429$		0			0
$430$	8.56131e9	+	4.94287e9i	0.250419	+	0.144579i
$431$	−1.60391e10	+	2.77805e10i	−0.464805	+	0.805066i	−0.999193	−	0.0401733i	$-0.987209\pi$
$431$	−1.60391e10	+	2.77805e10i	−0.464805	+	0.805066i	0.534387	+	0.845240i	$0.320542\pi$
$432$		0			0
$433$		−	2.28833e10i		−	0.650979i	−0.945546	−	0.325489i	$-0.894471\pi$
$433$		−	2.28833e10i		−	0.650979i	0.945546	−	0.325489i	$-0.105529\pi$
$434$	4.49929e9	−	2.77319e7i	0.126819	−	0.000781664i
$435$		0			0
$436$	8.53459e9	+	1.47823e10i	0.236177	+	0.409070i
$437$	5.52201e10	+	3.18813e10i	1.51416	+	0.874200i
$438$		0			0
$439$	−2.93893e9	+	1.69679e9i	−0.0791282	+	0.0456847i	−0.539042	−	0.842279i	$-0.681214\pi$
$439$	−2.93893e9	+	1.69679e9i	−0.0791282	+	0.0456847i	0.459914	+	0.887964i	$0.347880\pi$
$440$		−	1.42292e9i		−	0.0379637i
$441$		0			0
$442$	3.41098e10			0.893698
$443$	−2.58531e10	−	4.47789e10i	−0.671271	−	1.16268i	−0.977544	−	0.210732i	$-0.932415\pi$
$443$	−2.58531e10	−	4.47789e10i	−0.671271	−	1.16268i	0.306273	−	0.951944i	$-0.400918\pi$
$444$		0			0
$445$	−1.40470e10	+	2.43301e10i	−0.358214	+	0.620445i
$446$	1.44231e10	−	8.32715e9i	0.364517	−	0.210454i
$447$		0			0
$448$	3.10348e7	+	5.03517e9i	0.000770437	+	0.124998i
$449$	−5.01205e10			−1.23319			−0.616595	−	0.787281i	$-0.711488\pi$
$449$	−5.01205e10			−1.23319			−0.616595	+	0.787281i	$0.711488\pi$
$450$		0			0
$451$	−1.34183e9	−	7.74707e8i	−0.0324334	−	0.0187254i
$452$	−1.70890e10	+	2.95991e10i	−0.409415	+	0.709128i
$453$		0			0
$454$		−	1.35576e10i		−	0.319125i
$455$	−9.17475e10	+	5.37271e10i	−2.14066	+	1.25357i
$456$		0			0
$457$	−3.95560e10	−	6.85130e10i	−0.906875	−	1.57075i	−0.818381	−	0.574677i	$-0.805128\pi$
$457$	−3.95560e10	−	6.85130e10i	−0.906875	−	1.57075i	−0.0884942	−	0.996077i	$-0.528205\pi$
$458$	−3.54232e8	−	2.04516e8i	−0.00805056	−	0.00464799i
$459$		0			0
$460$	2.83052e10	−	1.63420e10i	0.632171	−	0.364984i
$461$			1.40115e10i			0.310228i	0.987897	+	0.155114i	$0.0495745\pi$
$461$			1.40115e10i			0.310228i	−0.987897	+	0.155114i	$0.950426\pi$
$462$		0			0
$463$	6.61893e10			1.44034			0.720168	−	0.693800i	$-0.244065\pi$
$463$	6.61893e10			1.44034			0.720168	+	0.693800i	$0.244065\pi$
$464$	1.03611e10	+	1.79459e10i	0.223529	+	0.387163i
$465$		0			0
$466$	1.85917e10	−	3.22018e10i	0.394254	−	0.682868i
$467$	−3.14542e10	+	1.81601e10i	−0.661319	+	0.381813i	−0.792780	−	0.609509i	$-0.791367\pi$
$467$	−3.14542e10	+	1.81601e10i	−0.661319	+	0.381813i	0.131460	+	0.991321i	$0.458033\pi$
$468$		0			0
$469$	3.63449e10	+	2.06861e10i	0.751194	+	0.427550i
$470$	9.94974e10			2.03902
$471$		0			0
$472$	1.65830e10	+	9.57421e9i	0.334115	+	0.192901i
$473$	−4.85169e8	+	8.40338e8i	−0.00969279	+	0.0167884i
$474$		0			0
$475$			1.16077e11i			2.28020i
$476$	−9.94593e9	−	1.69842e10i	−0.193739	−	0.330840i
$477$		0			0
$478$	−2.11272e10	−	3.65933e10i	−0.404697	−	0.700955i
$479$	6.34734e10	+	3.66464e10i	1.20573	+	0.696128i	0.961823	−	0.273671i	$-0.0882378\pi$
$479$	6.34734e10	+	3.66464e10i	1.20573	+	0.696128i	0.243906	+	0.969799i	$0.421571\pi$
$480$		0			0
$481$	1.10544e11	−	6.38227e10i	2.06517	−	1.19233i
$482$		−	2.51300e10i		−	0.465591i
$483$		0			0
$484$	−2.72983e10			−0.497455
$485$	2.54124e10	+	4.40155e10i	0.459280	+	0.795497i
$486$		0			0
$487$	−3.96063e10	+	6.86001e10i	−0.704123	+	1.21958i	0.262884	+	0.964827i	$0.415326\pi$
$487$	−3.96063e10	+	6.86001e10i	−0.704123	+	1.21958i	−0.967007	+	0.254749i	$0.918007\pi$
$488$	−1.76191e10	+	1.01724e10i	−0.310673	+	0.179367i
$489$		0			0
$490$	5.35045e10	+	3.00176e10i	0.928124	+	0.520705i
$491$	5.63231e10			0.969082			0.484541	−	0.874769i	$-0.338987\pi$
$491$	5.63231e10			0.969082			0.484541	+	0.874769i	$0.338987\pi$
$492$		0			0
$493$	−7.01481e10	−	4.05001e10i	−1.18749	−	0.685595i
$494$	−6.25524e10	+	1.08344e11i	−1.05036	+	1.81927i
$495$		0			0
$496$		−	2.71378e9i		−	0.0448382i
$497$	−7.89900e7	−	1.28155e10i	−0.00129463	−	0.210044i
$498$		0			0
$499$	1.34346e10	+	2.32693e10i	0.216681	+	0.375303i	0.953791	−	0.300470i	$-0.0971434\pi$
$499$	1.34346e10	+	2.32693e10i	0.216681	+	0.375303i	−0.737110	+	0.675773i	$0.763810\pi$
$500$	1.07975e10	+	6.23393e9i	0.172760	+	0.0997428i
$501$		0			0
$502$	3.42642e10	−	1.97824e10i	0.539543	−	0.311505i
$503$		−	4.60200e10i		−	0.718910i	−0.933162	−	0.359455i	$-0.882963\pi$
$503$		−	4.60200e10i		−	0.718910i	0.933162	−	0.359455i	$-0.117037\pi$
$504$		0			0
$505$	−9.21015e10			−1.41612
$506$	1.60405e9	+	2.77830e9i	0.0244690	+	0.0423816i
$507$		0			0
$508$	−6.94886e9	+	1.20358e10i	−0.104342	+	0.180725i
$509$	−9.09077e10	+	5.24856e10i	−1.35435	+	0.781932i	−0.988855	−	0.148882i	$-0.952432\pi$
$509$	−9.09077e10	+	5.24856e10i	−1.35435	+	0.781932i	−0.365492	+	0.930815i	$0.619099\pi$
$510$		0			0
$511$	−4.04911e10	+	7.11417e10i	−0.593849	+	1.04338i
$512$	3.03700e9			0.0441942
$513$		0			0
$514$	8.79182e9	+	5.07596e9i	0.125958	+	0.0727220i
$515$	−8.91411e10	+	1.54397e11i	−1.26721	+	2.19487i
$516$		0			0
$517$			9.76620e9i			0.136698i
$518$	−6.40122e10	−	3.64333e10i	−0.889086	−	0.506033i
$519$		0			0
$520$	3.20636e10	+	5.55359e10i	0.438530	+	0.759557i
$521$	4.56369e10	+	2.63485e10i	0.619391	+	0.357606i	0.776632	−	0.629955i	$-0.216927\pi$
$521$	4.56369e10	+	2.63485e10i	0.619391	+	0.357606i	−0.157241	+	0.987560i	$0.550260\pi$
$522$		0			0
$523$	−3.74118e10	+	2.15997e10i	−0.500037	+	0.288697i	−0.728729	−	0.684802i	$-0.759889\pi$
$523$	−3.74118e10	+	2.15997e10i	−0.500037	+	0.288697i	0.228692	+	0.973499i	$0.426555\pi$
$524$		−	1.73580e10i		−	0.230237i
$525$		0			0
$526$	3.33523e10			0.435695
$527$	5.30389e9	+	9.18661e9i	0.0687626	+	0.119100i
$528$		0			0
$529$	2.31081e9	−	4.00245e9i	0.0295082	−	0.0511096i
$530$	8.53367e9	−	4.92692e9i	0.108151	−	0.0624413i
$531$		0			0
$532$	7.21868e10	−	4.44932e8i	0.901180	−	0.00555452i
$533$	6.98282e10			0.865211
$534$		0			0
$535$	−4.99078e10	−	2.88143e10i	−0.609190	−	0.351716i
$536$	1.26116e10	−	2.18440e10i	0.152796	−	0.264650i
$537$		0			0
$538$		−	4.68584e10i		−	0.559317i
$539$	−2.94638e9	+	5.25175e9i	−0.0349088	+	0.0622227i
$540$		0			0
$541$	−1.65828e10	−	2.87222e10i	−0.193583	−	0.335296i	0.752852	−	0.658190i	$-0.228678\pi$
$541$	−1.65828e10	−	2.87222e10i	−0.193583	−	0.335296i	−0.946435	+	0.322894i	$0.895344\pi$
$542$	−2.24706e10	−	1.29734e10i	−0.260386	−	0.150334i
$543$		0			0
$544$	−1.02808e10	+	5.93560e9i	−0.117390	+	0.0677750i
$545$		−	1.25437e11i		−	1.42180i
$546$		0			0
$547$	−1.44828e11			−1.61772			−0.808860	−	0.588001i	$-0.799915\pi$
$547$	−1.44828e11			−1.61772			−0.808860	+	0.588001i	$0.799915\pi$
$548$	3.55101e10	+	6.15053e10i	0.393758	+	0.682009i
$549$		0			0
$550$	−2.92011e9	+	5.05778e9i	−0.0319116	+	0.0552725i
$551$	2.57283e11	−	1.48542e11i	2.79128	−	1.61155i
$552$		0			0
$553$	−6.69238e10	+	3.91904e10i	−0.715616	+	0.419063i
$554$	−9.76666e10			−1.03683
$555$		0			0
$556$	7.89160e9	+	4.55622e9i	0.0825783	+	0.0476766i
$557$	−9.10260e10	+	1.57662e11i	−0.945682	+	1.63797i	−0.191301	+	0.981531i	$0.561271\pi$
$557$	−9.10260e10	+	1.57662e11i	−0.945682	+	1.63797i	−0.754381	+	0.656437i	$0.772063\pi$
$558$		0			0
$559$		−	4.37307e10i		−	0.447857i
$560$	1.83036e10	−	3.21588e10i	0.186116	−	0.327000i
$561$		0			0
$562$	8.03703e9	+	1.39205e10i	0.0805657	+	0.139544i
$563$	1.36642e11	+	7.88902e10i	1.36003	+	0.785216i	0.989628	−	0.143653i	$-0.0458850\pi$
$563$	1.36642e11	+	7.88902e10i	1.36003	+	0.785216i	0.370407	+	0.928870i	$0.379218\pi$
$564$		0			0
$565$	2.17516e11	−	1.25583e11i	2.13451	−	1.23236i
$566$			3.26606e10i			0.318243i
$567$		0			0
$568$	−7.72979e9			−0.0742633
$569$	7.37347e9	+	1.27712e10i	0.0703433	+	0.121838i	0.899052	−	0.437842i	$-0.144257\pi$
$569$	7.37347e9	+	1.27712e10i	0.0703433	+	0.121838i	−0.828708	+	0.559680i	$0.810924\pi$
$570$		0			0
$571$	2.95716e9	−	5.12196e9i	0.0278183	−	0.0481828i	−0.851781	−	0.523898i	$-0.824477\pi$
$571$	2.95716e9	−	5.12196e9i	0.0278183	−	0.0481828i	0.879599	+	0.475715i	$0.157811\pi$
$572$	−5.45114e9	+	3.14722e9i	−0.0509217	+	0.0293997i
$573$		0			0
$574$	−2.03609e10	−	3.47694e10i	−0.187564	−	0.320295i
$575$	−1.34148e11			−1.22720
$576$		0			0
$577$	−6.08835e10	−	3.51511e10i	−0.549283	−	0.317129i	0.199549	−	0.979888i	$-0.436052\pi$
$577$	−6.08835e10	−	3.51511e10i	−0.549283	−	0.317129i	−0.748833	+	0.662759i	$0.769385\pi$
$578$	−1.62594e10	+	2.81621e10i	−0.145678	+	0.252321i
$579$		0			0
$580$		−	1.52282e11i		−	1.34566i
$581$	−1.56820e11	+	9.66576e8i	−1.37625	+	0.00848264i
$582$		0			0
$583$	4.83603e8	+	8.37625e8i	0.00418615	+	0.00725062i
$584$	4.27575e10	+	2.46861e10i	0.367588	+	0.212227i
$585$		0			0
$586$	9.57551e10	−	5.52842e10i	0.812029	−	0.468825i
$587$		−	1.35170e11i		−	1.13849i	−0.822168	−	0.569245i	$-0.807236\pi$
$587$		−	1.35170e11i		−	1.13849i	0.822168	−	0.569245i	$-0.192764\pi$
$588$		0			0
$589$	−3.89062e10			−0.323264
$590$	−7.03584e10	−	1.21864e11i	−0.580641	−	1.00570i
$591$		0			0
$592$	−2.22121e10	+	3.84725e10i	−0.180844	+	0.313231i
$593$	−5.35885e10	+	3.09393e10i	−0.433364	+	0.250203i	−0.700779	−	0.713379i	$-0.747164\pi$
$593$	−5.35885e10	+	3.09393e10i	−0.433364	+	0.250203i	0.267415	+	0.963582i	$0.413831\pi$
$594$		0			0
$595$	8.91481e8	+	1.44636e11i	0.00711286	+	1.15401i
$596$	3.64356e10			0.288762
$597$		0			0
$598$	−1.25211e11	−	7.22907e10i	−0.979125	−	0.565298i
$599$	5.68987e9	−	9.85515e9i	0.0441972	−	0.0765519i	−0.843081	−	0.537787i	$-0.819260\pi$
$599$	5.68987e9	−	9.85515e9i	0.0441972	−	0.0765519i	0.887278	+	0.461235i	$0.152594\pi$
$600$		0			0
$601$			4.63889e10i			0.355563i	0.984070	+	0.177781i	$0.0568920\pi$
$601$			4.63889e10i			0.355563i	−0.984070	+	0.177781i	$0.943108\pi$
$602$	−2.17747e10	+	1.27512e10i	−0.165793	+	0.0970882i
$603$		0			0
$604$	−3.28322e10	−	5.68670e10i	−0.246690	−	0.427280i
$605$	1.73732e11	+	1.00304e11i	1.29675	+	0.748681i
$606$		0			0
$607$	−1.52237e11	+	8.78940e10i	−1.12141	+	0.647447i	−0.941761	−	0.336284i	$-0.890830\pi$
$607$	−1.52237e11	+	8.78940e10i	−1.12141	+	0.647447i	−0.179650	+	0.983731i	$0.557497\pi$
$608$		−	4.35401e10i		−	0.318621i
$609$		0			0
$610$	1.49508e11			1.07981
$611$	−2.20069e11	−	3.81171e11i	−1.57904	−	2.73498i
$612$		0			0
$613$	1.02160e11	−	1.76947e11i	0.723504	−	1.25315i	−0.236083	−	0.971733i	$-0.575864\pi$
$613$	1.02160e11	−	1.76947e11i	0.723504	−	1.25315i	0.959587	−	0.281412i	$-0.0908029\pi$
$614$	1.54736e11	−	8.93369e10i	1.08872	−	0.628575i
$615$		0			0
$616$	3.15656e9	+	1.79659e9i	0.0219225	+	0.0124775i
$617$	−1.15941e11			−0.800009			−0.400005	−	0.916513i	$-0.630991\pi$
$617$	−1.15941e11			−0.800009			−0.400005	+	0.916513i	$0.630991\pi$
$618$		0			0
$619$	3.73665e10	+	2.15736e10i	0.254519	+	0.146947i	0.621832	−	0.783151i	$-0.286389\pi$
$619$	3.73665e10	+	2.15736e10i	0.254519	+	0.146947i	−0.367313	+	0.930097i	$0.619722\pi$
$620$	−9.97144e9	+	1.72710e10i	−0.0674825	+	0.116883i
$621$		0			0
$622$			5.91321e10i			0.395059i
$623$	−3.62373e10	−	6.18808e10i	−0.240549	−	0.410775i
$624$		0			0
$625$	5.07074e10	+	8.78278e10i	0.332316	+	0.575588i
$626$	9.63355e10	+	5.56193e10i	0.627320	+	0.362183i
$627$		0			0
$628$	−5.65542e10	+	3.26516e10i	−0.363602	+	0.209926i
$629$		−	1.73648e11i		−	1.10935i
$630$		0			0
$631$	−1.09578e11			−0.691204			−0.345602	−	0.938381i	$-0.612325\pi$
$631$	−1.09578e11			−0.691204			−0.345602	+	0.938381i	$0.612325\pi$
$632$	2.33883e10	+	4.05098e10i	0.146599	+	0.253917i
$633$		0			0
$634$	−2.22310e10	+	3.85052e10i	−0.137595	+	0.238321i
$635$	8.84479e10	−	5.10654e10i	0.543992	−	0.314074i
$636$		0			0
$637$	−3.34532e9	−	2.71366e11i	−0.0203180	−	1.64816i
$638$	1.49473e10			0.0902152
$639$		0			0
$640$	−1.93281e10	−	1.11591e10i	−0.115204	−	0.0665132i
$641$	1.02428e11	−	1.77410e11i	0.606718	−	1.05087i	−0.385060	−	0.922892i	$-0.625819\pi$
$641$	1.02428e11	−	1.77410e11i	0.606718	−	1.05087i	0.991778	−	0.127974i	$-0.0408474\pi$
$642$		0			0
$643$			1.78587e11i			1.04474i	0.852720	+	0.522369i	$0.174951\pi$
$643$			1.78587e11i			1.04474i	−0.852720	+	0.522369i	$0.825049\pi$
$644$	5.14199e8	+	8.34250e10i	0.00298943	+	0.485012i
$645$		0			0
$646$	8.50960e10	+	1.47391e11i	0.488629	+	0.846330i
$647$	1.20405e10	+	6.95156e9i	0.0687109	+	0.0396703i	0.533962	−	0.845509i	$-0.320703\pi$
$647$	1.20405e10	+	6.95156e9i	0.0687109	+	0.0396703i	−0.465251	+	0.885179i	$0.654036\pi$
$648$		0			0
$649$	1.19616e10	−	6.90605e9i	0.0674235	−	0.0389270i
$650$		−	2.63204e11i		−	1.47448i
$651$		0			0
$652$	2.44320e10			0.135197
$653$	1.33723e11	+	2.31615e11i	0.735452	+	1.27384i	0.954525	+	0.298131i	$0.0963633\pi$
$653$	1.33723e11	+	2.31615e11i	0.735452	+	1.27384i	−0.219073	+	0.975708i	$0.570303\pi$
$654$		0			0
$655$	−6.37798e10	+	1.10470e11i	−0.346512	+	0.600176i
$656$	−2.10463e10	+	1.21511e10i	−0.113648	+	0.0656146i
$657$		0			0
$658$	−1.25627e11	+	2.20722e11i	−0.670159	+	1.17745i
$659$	2.98246e11			1.58137			0.790684	−	0.612225i	$-0.209725\pi$
$659$	2.98246e11			1.58137			0.790684	+	0.612225i	$0.209725\pi$
$660$		0			0
$661$	−6.89538e10	−	3.98105e10i	−0.361204	−	0.208541i	0.308405	−	0.951255i	$-0.400205\pi$
$661$	−6.89538e10	−	3.98105e10i	−0.361204	−	0.208541i	−0.669609	+	0.742714i	$0.733538\pi$
$662$	7.52503e10	−	1.30337e11i	0.391810	−	0.678636i
$663$		0			0
$664$			9.45870e10i			0.486586i
$665$	−4.61046e11	−	2.62410e11i	−2.35753	−	1.34182i
$666$		0			0
$667$	1.71667e11	+	2.97337e11i	0.867331	+	1.50226i
$668$	1.52331e11	+	8.79486e10i	0.765039	+	0.441696i
$669$		0			0
$670$	−1.60526e11	+	9.26796e10i	−0.796610	+	0.459923i
$671$			1.46750e10i			0.0723918i
$672$		0			0
$673$	2.67506e11			1.30398			0.651992	−	0.758226i	$-0.273933\pi$
$673$	2.67506e11			1.30398			0.651992	+	0.758226i	$0.273933\pi$
$674$	−8.69089e10	−	1.50531e11i	−0.421138	−	0.729433i
$675$		0			0
$676$	8.96303e10	−	1.55244e11i	0.429208	−	0.743410i
$677$	2.29678e11	−	1.32605e11i	1.09336	−	0.631254i	0.158894	−	0.987296i	$-0.449207\pi$
$677$	2.29678e11	−	1.32605e11i	1.09336	−	0.631254i	0.934470	+	0.356041i	$0.115874\pi$
$678$		0			0
$679$	−1.29729e11	+	7.99597e8i	−0.610319	+	0.00376177i
$680$	8.72384e10			0.408011
$681$		0			0
$682$	−1.69524e9	−	9.78749e8i	−0.00783600	−	0.00452412i
$683$	−1.38922e11	+	2.40619e11i	−0.638391	+	1.10573i	0.347394	+	0.937719i	$0.387067\pi$
$683$	−1.38922e11	+	2.40619e11i	−0.638391	+	1.10573i	−0.985786	+	0.168007i	$0.946267\pi$
$684$		0			0
$685$		−	5.21909e11i		−	2.37046i
$686$	−1.34145e11	+	8.07922e10i	−0.605731	+	0.364815i
$687$		0			0
$688$	7.60977e9	+	1.31805e10i	0.0339639	+	0.0588272i
$689$	−3.77496e10	−	2.17948e10i	−0.167508	−	0.0967108i
$690$		0			0
$691$	2.28031e11	−	1.31654e11i	1.00019	−	0.577459i	0.0918837	−	0.995770i	$-0.470711\pi$
$691$	2.28031e11	−	1.31654e11i	1.00019	−	0.577459i	0.908304	+	0.418311i	$0.137378\pi$
$692$			1.51026e11i			0.658608i
$693$		0			0
$694$	3.19921e10			0.137913
$695$	−3.34825e10	−	5.79933e10i	−0.143509	−	0.248564i
$696$		0			0
$697$	4.74969e10	−	8.22671e10i	0.201249	−	0.348574i
$698$	−1.84636e11	+	1.06599e11i	−0.777846	+	0.449090i
$699$		0			0
$700$	−1.31057e11	+	7.67464e10i	−0.545842	+	0.319644i
$701$	3.04779e11			1.26216			0.631078	−	0.775719i	$-0.282613\pi$
$701$	3.04779e11			1.26216			0.631078	+	0.775719i	$0.282613\pi$
$702$		0			0
$703$	5.51563e11	+	3.18445e11i	2.25826	+	1.30381i
$704$	1.09532e9	−	1.89715e9i	0.00445914	−	0.00772345i
$705$		0			0
$706$		−	1.56709e11i		−	0.630776i
$707$	1.16288e11	−	2.04315e11i	0.465434	−	0.817755i
$708$		0			0
$709$	1.59806e11	+	2.76793e11i	0.632425	+	1.09539i	0.987054	+	0.160386i	$0.0512737\pi$
$709$	1.59806e11	+	2.76793e11i	0.632425	+	1.09539i	−0.354629	+	0.935007i	$0.615393\pi$
$710$	4.91939e10	+	2.84021e10i	0.193588	+	0.111768i
$711$		0			0
$712$	−3.74572e10	+	2.16259e10i	−0.145752	+	0.0841501i
$713$		−	4.49632e10i		−	0.173980i
$714$		0			0
$715$	4.62562e10			0.176989
$716$	−9.29606e10	−	1.61012e11i	−0.353709	−	0.612643i
$717$		0			0
$718$	3.30630e10	−	5.72668e10i	0.124407	−	0.215479i
$719$	3.85186e10	−	2.22387e10i	0.144130	−	0.0832136i	−0.426201	−	0.904629i	$-0.640148\pi$
$719$	3.85186e10	−	2.22387e10i	0.144130	−	0.0832136i	0.570331	+	0.821415i	$0.306815\pi$
$720$		0			0
$721$	−2.29959e11	−	3.92691e11i	−0.850961	−	1.45315i
$722$	−4.32067e11			−1.59002
$723$		0			0
$724$	−3.89608e10	−	2.24940e10i	−0.141799	−	0.0818679i
$725$	−3.12513e11	+	5.41289e11i	−1.13114	+	1.95919i
$726$		0			0
$727$			4.83129e10i			0.172952i	0.996254	+	0.0864760i	$0.0275606\pi$
$727$			4.83129e10i			0.172952i	−0.996254	+	0.0864760i	$0.972439\pi$
$728$	−1.63683e11	+	1.00888e9i	−0.582745	+	0.00359181i
$729$		0			0
$730$	−1.81412e11	−	3.14214e11i	−0.638813	−	1.10646i
$731$	−5.15207e10	−	2.97455e10i	−0.180432	−	0.104172i
$732$		0			0
$733$	−7.14347e10	+	4.12428e10i	−0.247453	+	0.142867i	−0.618598	−	0.785708i	$-0.712299\pi$
$733$	−7.14347e10	+	4.12428e10i	−0.247453	+	0.142867i	0.371144	+	0.928575i	$0.378966\pi$
$734$		−	5.91728e10i		−	0.203863i
$735$		0			0
$736$	5.03185e10			0.171481
$737$	−9.09699e9	−	1.57564e10i	−0.0308339	−	0.0534058i
$738$		0			0
$739$	2.42038e11	−	4.19222e11i	0.811532	−	1.40561i	−0.100260	−	0.994961i	$-0.531968\pi$
$739$	2.42038e11	−	4.19222e11i	0.811532	−	1.40561i	0.911792	−	0.410653i	$-0.134699\pi$
$740$	2.82725e11	−	1.63231e11i	0.942838	−	0.544348i
$741$		0			0
$742$	1.55025e8	+	2.51516e10i	0.000511429	+	0.0829756i
$743$	−1.64425e11			−0.539527			−0.269763	−	0.962927i	$-0.586945\pi$
$743$	−1.64425e11			−0.539527			−0.269763	+	0.962927i	$0.586945\pi$
$744$		0			0
$745$	−2.31883e11	−	1.33878e11i	−0.752738	−	0.434594i
$746$	−7.19338e10	+	1.24593e11i	−0.232262	+	0.402289i
$747$		0			0
$748$			8.56291e9i			0.0273536i
$749$	1.26935e11	−	7.43327e10i	0.403323	−	0.236185i
$750$		0			0
$751$	2.10159e11	+	3.64006e11i	0.660675	+	1.14432i	0.980438	+	0.196826i	$0.0630633\pi$
$751$	2.10159e11	+	3.64006e11i	0.660675	+	1.14432i	−0.319763	+	0.947498i	$0.603603\pi$
$752$	1.32658e11	+	7.65903e10i	0.414823	+	0.239498i
$753$		0			0
$754$	−5.83386e11	+	3.36818e11i	−1.80497	+	1.04210i
$755$			4.82550e11i			1.48510i
$756$		0			0
$757$	−2.03317e11			−0.619143			−0.309572	−	0.950876i	$-0.600186\pi$
$757$	−2.03317e11			−0.619143			−0.309572	+	0.950876i	$0.600186\pi$
$758$	9.01040e10	+	1.56065e11i	0.272940	+	0.472746i
$759$		0			0
$760$	−1.59982e11	+	2.77098e11i	−0.479532	+	0.830574i
$761$	1.16599e11	−	6.73185e10i	0.347661	−	0.200722i	−0.315993	−	0.948761i	$-0.602338\pi$
$761$	1.16599e11	−	6.73185e10i	0.347661	−	0.200722i	0.663655	+	0.748039i	$0.269004\pi$
$762$		0			0
$763$	2.78266e11	+	1.58378e11i	0.821035	+	0.467301i
$764$	−3.66507e10			−0.107574
$765$		0			0
$766$	−3.58238e10	−	2.06829e10i	−0.104053	−	0.0600753i
$767$	−3.11238e11	+	5.39080e11i	−0.899314	+	1.55766i
$768$		0			0
$769$			2.56622e11i			0.733817i	0.930257	+	0.366909i	$0.119584\pi$
$769$			2.56622e11i			0.733817i	−0.930257	+	0.366909i	$0.880416\pi$
$770$	−1.34876e10	−	2.30322e10i	−0.0383683	−	0.0655199i
$771$		0			0
$772$	2.05438e10	+	3.55829e10i	0.0578378	+	0.100178i
$773$	1.03389e11	+	5.96919e10i	0.289573	+	0.167185i	0.637749	−	0.770244i	$-0.279866\pi$
$773$	1.03389e11	+	5.96919e10i	0.289573	+	0.167185i	−0.348176	+	0.937429i	$0.613199\pi$
$774$		0			0
$775$	7.08872e10	−	4.09268e10i	0.196499	−	0.113449i
$776$			7.82468e10i			0.215784i
$777$		0			0
$778$	−1.27449e11			−0.347872
$779$	1.74205e11	+	3.01731e11i	0.473053	+	0.819352i
$780$		0			0
$781$	−2.78782e9	+	4.82864e9i	−0.00749308	+	0.0129784i
$782$	−1.70337e11	+	9.83439e10i	−0.455492	+	0.262979i
$783$		0			0
$784$	4.82299e10	+	8.12082e10i	0.127659	+	0.214949i
$785$	4.79896e11			1.26377
$786$		0			0
$787$	−2.33037e11	−	1.34544e11i	−0.607472	−	0.350724i	0.164503	−	0.986377i	$-0.447398\pi$
$787$	−2.33037e11	−	1.34544e11i	−0.607472	−	0.350724i	−0.771975	+	0.635652i	$0.780731\pi$
$788$	−6.38107e10	+	1.10523e11i	−0.165497	+	0.286648i
$789$		0			0
$790$		−	3.43750e11i		−	0.882539i
$791$	3.95145e9	+	6.41094e11i	0.0100937	+	1.63763i
$792$		0			0
$793$	−3.30684e11	−	5.72761e11i	−0.836219	−	1.44837i
$794$	3.09004e11	+	1.78404e11i	0.777468	+	0.448872i
$795$		0			0
$796$	−1.15638e10	+	6.67634e9i	−0.0288036	+	0.0166298i
$797$		−	6.65272e11i		−	1.64879i	−0.566013	−	0.824396i	$-0.691515\pi$
$797$		−	6.65272e11i		−	1.64879i	0.566013	−	0.824396i	$-0.308485\pi$
$798$		0			0
$799$	−5.98761e11			−1.46915
$800$	4.58013e10	+	7.93301e10i	0.111820	+	0.193677i
$801$		0			0
$802$	−2.14990e11	+	3.72374e11i	−0.519662	+	0.900082i
$803$	3.08418e10	−	1.78065e10i	0.0741783	−	0.0428269i
$804$		0			0
$805$	3.03262e11	−	5.32823e11i	0.722162	−	1.26882i
$806$	8.82195e10			0.209038
$807$		0			0
$808$	−1.22797e11	−	7.08971e10i	−0.288100	−	0.166335i
$809$	−5.08703e10	+	8.81100e10i	−0.118760	+	0.205699i	−0.919277	−	0.393612i	$-0.871225\pi$
$809$	−5.08703e10	+	8.81100e10i	−0.118760	+	0.205699i	0.800516	+	0.599311i	$0.204559\pi$
$810$		0			0
$811$			6.79465e11i			1.57067i	0.619074	+	0.785333i	$0.287508\pi$
$811$			6.79465e11i			1.57067i	−0.619074	+	0.785333i	$0.712492\pi$
$812$	3.37818e11	+	1.92273e11i	0.777068	+	0.442277i
$813$		0			0
$814$	1.60220e10	+	2.77509e10i	0.0364938	+	0.0632092i
$815$	−1.55490e11	−	8.97722e10i	−0.352429	−	0.203475i
$816$		0			0
$817$	1.88963e11	−	1.09098e11i	0.424119	−	0.244865i
$818$		−	1.29121e11i		−	0.288391i
$819$		0			0
$820$	1.78591e11			0.395006
$821$	8.29553e10	+	1.43683e11i	0.182588	+	0.316251i	0.942761	−	0.333469i	$-0.108219\pi$
$821$	8.29553e10	+	1.43683e11i	0.182588	+	0.316251i	−0.760173	+	0.649720i	$0.774886\pi$
$822$		0			0
$823$	−2.01168e11	+	3.48433e11i	−0.438489	+	0.759485i	−0.997573	−	0.0696256i	$-0.977820\pi$
$823$	−2.01168e11	+	3.48433e11i	−0.438489	+	0.759485i	0.559084	+	0.829111i	$0.311153\pi$
$824$	−2.37701e11	+	1.37237e11i	−0.515610	+	0.297688i
$825$		0			0
$826$	3.59176e11	−	2.21382e9i	0.771590	−	0.00475578i
$827$	−7.25185e11			−1.55034			−0.775170	−	0.631753i	$-0.782336\pi$
$827$	−7.25185e11			−1.55034			−0.775170	+	0.631753i	$0.782336\pi$
$828$		0			0
$829$	4.13337e11	+	2.38640e11i	0.875158	+	0.505273i	0.869059	−	0.494709i	$-0.164725\pi$
$829$	4.13337e11	+	2.38640e11i	0.875158	+	0.505273i	0.00609923	+	0.999981i	$0.498059\pi$
$830$	3.47548e11	−	6.01971e11i	0.732322	−	1.26842i
$831$		0			0
$832$			9.87267e10i			0.206035i
$833$	−3.21982e11	−	1.80642e11i	−0.668732	−	0.375178i
$834$		0			0
$835$	−6.46312e11	−	1.11944e12i	−1.32952	−	2.30280i
$836$	−2.71986e10	−	1.57031e10i	−0.0556828	−	0.0321485i
$837$		0			0
$838$	−6.90804e10	+	3.98836e10i	−0.140081	+	0.0808758i
$839$		−	4.84023e11i		−	0.976828i	−0.872612	−	0.488414i	$-0.837576\pi$
$839$		−	4.84023e11i		−	0.976828i	0.872612	−	0.488414i	$-0.162424\pi$
$840$		0			0
$841$	1.09943e12			2.19777
$842$	1.78457e11	+	3.09097e11i	0.355047	+	0.614959i
$843$		0			0
$844$	3.57380e10	−	6.19001e10i	0.0704305	−	0.121989i
$845$	−1.14085e12	+	6.58670e11i	−2.23770	+	1.29194i
$846$		0			0
$847$	−4.41867e11	+	2.58756e11i	−0.858535	+	0.502756i
$848$	1.51704e10			0.0293369
$849$		0			0
$850$	−3.10090e11	−	1.79031e11i	−0.594035	−	0.342967i
$851$	−3.68021e11	+	6.37431e11i	−0.701705	+	1.21539i
$852$		0			0
$853$		−	5.15896e10i		−	0.0974464i	−0.998812	−	0.0487232i	$-0.984485\pi$
$853$		−	5.15896e10i		−	0.0974464i	0.998812	−	0.0487232i	$-0.0155152\pi$
$854$	−1.88771e11	+	3.31665e11i	−0.354898	+	0.623546i
$855$		0			0
$856$	−4.43608e10	−	7.68352e10i	−0.0826236	−	0.143108i
$857$	7.06025e11	+	4.07624e11i	1.30887	+	0.755677i	0.981908	−	0.189360i	$-0.0606414\pi$
$857$	7.06025e11	+	4.07624e11i	1.30887	+	0.755677i	0.326963	+	0.945037i	$0.393975\pi$
$858$		0			0
$859$	4.78407e11	−	2.76208e11i	0.878667	−	0.507299i	0.00844851	−	0.999964i	$-0.497311\pi$
$859$	4.78407e11	−	2.76208e11i	0.878667	−	0.507299i	0.870219	+	0.492666i	$0.163977\pi$
$860$		−	1.11844e11i		−	0.204466i
$861$		0			0
$862$	3.62923e11			0.657334
$863$	−1.19370e11	−	2.06755e11i	−0.215205	−	0.372746i	0.738131	−	0.674657i	$-0.235709\pi$
$863$	−1.19370e11	−	2.06755e11i	−0.215205	−	0.372746i	−0.953336	+	0.301912i	$0.902375\pi$
$864$		0			0
$865$	5.54926e11	−	9.61159e11i	0.991221	−	1.71684i
$866$	−2.24209e11	+	1.29447e11i	−0.398641	+	0.230156i
$867$		0			0
$868$	−2.57235e10	−	4.39269e10i	−0.0453160	−	0.0773842i
$869$	3.37408e10			0.0591666
$870$		0			0
$871$	7.10103e11	+	4.09978e11i	1.23381	+	0.712342i
$872$	9.65579e10	−	1.67243e11i	0.167002	−	0.289256i
$873$		0			0
$874$		−	7.21392e11i		−	1.23631i
$875$	2.33865e11	−	1.44145e9i	0.398964	−	0.00245906i
$876$		0			0
$877$	3.70803e10	+	6.42249e10i	0.0626822	+	0.108569i	0.895664	−	0.444732i	$-0.146701\pi$
$877$	3.70803e10	+	6.42249e10i	0.0626822	+	0.108569i	−0.832981	+	0.553301i	$0.813368\pi$
$878$	3.32502e10	+	1.91970e10i	0.0559521	+	0.0323039i
$879$		0			0
$880$	−1.39417e10	+	8.04924e9i	−0.0232479	+	0.0134222i
$881$			1.01123e12i			1.67860i	0.543669	+	0.839300i	$0.317035\pi$
$881$			1.01123e12i			1.67860i	−0.543669	+	0.839300i	$0.682965\pi$
$882$		0			0
$883$	−9.12397e11			−1.50086			−0.750432	−	0.660948i	$-0.770154\pi$
$883$	−9.12397e11			−1.50086			−0.750432	+	0.660948i	$0.770154\pi$
$884$	−1.92954e11	−	3.34207e11i	−0.315970	−	0.547276i
$885$		0			0
$886$	−2.92495e11	+	5.06615e11i	−0.474660	+	0.822136i
$887$	8.38886e11	−	4.84331e11i	1.35522	−	0.782434i	0.366241	−	0.930520i	$-0.380645\pi$
$887$	8.38886e11	−	4.84331e11i	1.35522	−	0.782434i	0.988974	+	0.148086i	$0.0473113\pi$
$888$		0			0
$889$	1.60677e9	+	2.60686e11i	0.00257244	+	0.417360i
$890$	3.17847e11			0.506591
$891$		0			0
$892$	−1.63178e11	−	9.42110e10i	−0.257752	−	0.148813i
$893$	1.09804e12	−	1.90186e12i	1.72668	−	2.99070i
$894$		0			0
$895$			1.36629e12i			2.12936i
$896$	4.91588e10	−	2.87873e10i	0.0762727	−	0.0446651i
$897$		0			0
$898$	2.83524e11	+	4.91078e11i	0.435998	+	0.755171i
$899$	−1.81427e11	−	1.04747e11i	−0.277755	−	0.160362i
$900$		0			0
$901$	−5.13544e10	+	2.96495e10i	−0.0779253	+	0.0449902i
$902$			1.75296e10i			0.0264817i
$903$		0			0
$904$	3.86681e11			0.579001
$905$	1.65303e11	+	2.86313e11i	0.246426	+	0.426822i
$906$		0			0
$907$	−5.82503e11	+	1.00893e12i	−0.860735	+	1.49084i	0.0104860	+	0.999945i	$0.496662\pi$
$907$	−5.82503e11	+	1.00893e12i	−0.860735	+	1.49084i	−0.871221	+	0.490891i	$0.836671\pi$
$908$	−1.32837e11	+	7.66936e10i	−0.195423	+	0.112828i
$909$		0			0
$910$	1.04542e12	+	5.95012e11i	1.52449	+	0.867681i
$911$	3.53799e11			0.513669			0.256835	−	0.966455i	$-0.417320\pi$
$911$	3.53799e11			0.513669			0.256835	+	0.966455i	$0.417320\pi$
$912$		0			0
$913$	5.90866e10	+	3.41137e10i	0.0850366	+	0.0490959i
$914$	−4.47525e11	+	7.75136e11i	−0.641257	+	1.11069i
$915$		0			0
$916$			4.62767e9i			0.00657326i
$917$	−1.64534e11	−	2.80968e11i	−0.232690	−	0.397355i
$918$		0			0
$919$	−2.37089e11	−	4.10651e11i	−0.332392	−	0.575719i	0.650589	−	0.759430i	$-0.274522\pi$
$919$	−2.37089e11	−	4.10651e11i	−0.332392	−	0.575719i	−0.982980	+	0.183711i	$0.941189\pi$
$920$	−3.20237e11	−	1.84889e11i	−0.447013	−	0.258083i
$921$		0			0
$922$	1.37284e11	−	7.92610e10i	0.189975	−	0.109682i
$923$		−	2.51280e11i		−	0.346219i
$924$		0			0
$925$	−1.33993e12			−1.83027
$926$	−3.74423e11	−	6.48520e11i	−0.509235	−	0.882022i
$927$		0			0
$928$	1.17222e11	−	2.03035e11i	0.158059	−	0.273766i
$929$	−3.72827e11	+	2.15252e11i	−0.500546	+	0.288990i	−0.728939	−	0.684579i	$-0.759986\pi$
$929$	−3.72827e11	+	2.15252e11i	−0.500546	+	0.288990i	0.228393	+	0.973569i	$0.426653\pi$
$930$		0			0
$931$	1.16424e12	−	6.91450e11i	1.54969	−	0.920370i
$932$	−4.20683e11			−0.557560
$933$		0			0
$934$	3.55864e11	+	2.05458e11i	0.467623	+	0.269983i
$935$	3.14633e10	−	5.44961e10i	0.0411678	−	0.0713048i
$936$		0			0
$937$			1.06322e12i			1.37932i	0.724134	+	0.689659i	$0.242240\pi$
$937$			1.06322e12i			1.37932i	−0.724134	+	0.689659i	$0.757760\pi$
$938$	−2.91615e9	−	4.73124e11i	−0.00376703	−	0.611172i
$939$		0			0
$940$	−5.62842e11	−	9.74872e11i	−0.720901	−	1.24864i
$941$	−1.26165e12	−	7.28416e11i	−1.60910	−	0.929012i	−0.989573	−	0.144033i	$-0.953993\pi$
$941$	−1.26165e12	−	7.28416e11i	−1.60910	−	0.929012i	−0.619523	−	0.784979i	$-0.712674\pi$
$942$		0			0
$943$	−3.48706e11	+	2.01325e11i	−0.440973	+	0.254596i
$944$		−	2.16640e11i		−	0.272803i
$945$		0			0
$946$	1.09781e10			0.0137077
$947$	−6.32117e11	−	1.09486e12i	−0.785954	−	1.36131i	−0.928427	−	0.371514i	$-0.878839\pi$
$947$	−6.32117e11	−	1.09486e12i	−0.785954	−	1.36131i	0.142473	−	0.989799i	$-0.454495\pi$
$948$		0			0
$949$	−8.02494e11	+	1.38996e12i	−0.989411	+	1.71371i
$950$	1.13732e12	−	6.56632e11i	1.39633	−	0.806171i
$951$		0			0
$952$	−1.10148e11	+	1.93527e11i	−0.134100	+	0.235610i
$953$	7.86324e11			0.953300			0.476650	−	0.879093i	$-0.341851\pi$
$953$	7.86324e11			0.953300			0.476650	+	0.879093i	$0.341851\pi$
$954$		0			0
$955$	2.33253e11	+	1.34668e11i	0.280423	+	0.161902i
$956$	−2.39027e11	+	4.14006e11i	−0.286164	+	0.495650i
$957$		0			0
$958$		−	8.29213e11i		−	0.984474i
$959$	1.15779e12	+	6.58968e11i	1.36885	+	0.779094i
$960$		0			0
$961$	−4.12728e11	−	7.14866e11i	−0.483916	−	0.838168i
$962$	−1.25066e12	−	7.22071e11i	−1.46029	−	0.843102i
$963$		0			0
$964$	−2.46223e11	+	1.42157e11i	−0.285115	+	0.164611i
$965$		−	3.01942e11i		−	0.348189i
$966$		0			0
$967$	2.31465e11			0.264715			0.132358	−	0.991202i	$-0.457745\pi$
$967$	2.31465e11			0.264715			0.132358	+	0.991202i	$0.457745\pi$
$968$	1.54422e11	+	2.67467e11i	0.175877	+	0.304628i
$969$		0			0
$970$	2.87508e11	−	4.97978e11i	0.324760	−	0.562501i
$971$	1.04667e12	−	6.04295e11i	1.17742	−	0.679786i	0.222006	−	0.975045i	$-0.428739\pi$
$971$	1.04667e12	−	6.04295e11i	1.17742	−	0.679786i	0.955417	+	0.295260i	$0.0954061\pi$
$972$		0			0
$973$	1.70926e11	−	1.05352e9i	0.190703	−	0.00117542i
$974$	8.96188e11			0.995780
$975$		0			0
$976$	1.99337e11	+	1.15087e11i	0.219679	+	0.126832i
$977$	5.07309e11	−	8.78684e11i	0.556793	−	0.964394i	−0.440968	−	0.897523i	$-0.645365\pi$
$977$	5.07309e11	−	8.78684e11i	0.556793	−	0.964394i	0.997762	−	0.0668716i	$-0.0213018\pi$
$978$		0			0
$979$			3.11983e10i			0.0339626i
$980$	−8.55591e9	−	6.94040e11i	−0.00927602	−	0.752454i
$981$		0			0
$982$	−3.18612e11	−	5.51851e11i	−0.342622	−	0.593439i
$983$	−2.92626e11	−	1.68948e11i	−0.313400	−	0.180942i	0.335047	−	0.942201i	$-0.391248\pi$
$983$	−2.92626e11	−	1.68948e11i	−0.313400	−	0.180942i	−0.648447	+	0.761260i	$0.724581\pi$
$984$		0			0
$985$	8.12208e11	−	4.68929e11i	0.862825	−	0.498152i
$986$			9.16412e11i			0.969578i
$987$		0			0
$988$	1.41540e12			1.48543
$989$	1.26082e11	+	2.18381e11i	0.131786	+	0.228260i
$990$		0			0
$991$	5.53859e11	−	9.59312e11i	0.574255	−	0.994639i	−0.421867	−	0.906658i	$-0.638625\pi$
$991$	5.53859e11	−	9.59312e11i	0.574255	−	0.994639i	0.996122	−	0.0879813i	$-0.0280416\pi$
$992$	−2.65895e10	+	1.53515e10i	−0.0274577	+	0.0158527i
$993$		0			0
$994$	−1.25119e11	+	7.32695e10i	−0.128168	+	0.0750547i
$995$	9.81254e10			0.100113
$996$		0			0
$997$	−4.16099e11	−	2.40235e11i	−0.421130	−	0.243139i	0.274431	−	0.961607i	$-0.411511\pi$
$997$	−4.16099e11	−	2.40235e11i	−0.421130	−	0.243139i	−0.695561	+	0.718468i	$0.744844\pi$
$998$	1.51995e11	−	2.63263e11i	0.153217	−	0.265379i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.n.d.73.5	yes	20
3.2	odd	2	inner	126.9.n.d.73.6	yes	20
7.5	odd	6	inner	126.9.n.d.19.5	✓	20
21.5	even	6	inner	126.9.n.d.19.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.n.d.19.5	✓	20	7.5	odd	6	inner
126.9.n.d.19.6	yes	20	21.5	even	6	inner
126.9.n.d.73.5	yes	20	1.1	even	1	trivial
126.9.n.d.73.6	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)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(814.617 - 470.320i) q^{5} +(14.7985 + 2400.95i) q^{7} +1448.15 q^{8} +O(q^{10})\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(814.617 - 470.320i) q^{5} +(14.7985 + 2400.95i) q^{7} +1448.15 q^{8} +(-9216.34 - 5321.06i) q^{10} +(522.290 - 904.633i) q^{11} +47076.6i q^{13} +(23440.7 - 13726.8i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(55462.6 + 32021.4i) q^{17} +(-203421. + 117445. i) q^{19} +120402. i q^{20} -11818.1 q^{22} +(-135729. - 235089. i) q^{23} +(247089. - 427970. i) q^{25} +(461254. - 266305. i) q^{26} +(-267096. - 152021. i) q^{28} -1.26478e6 q^{29} +(143445. + 82818.0i) q^{31} +(-92681.9 + 160530. i) q^{32} -724561. i q^{34} +(1.14127e6 + 1.94890e6i) q^{35} +(-1.35572e6 - 2.34818e6i) q^{37} +(2.30144e6 + 1.32874e6i) q^{38} +(1.17969e6 - 681096. i) q^{40} -1.48329e6i q^{41} -928927. q^{43} +(66853.1 + 115793. i) q^{44} +(-1.53560e6 + 2.65973e6i) q^{46} +(-8.09682e6 + 4.67470e6i) q^{47} +(-5.76436e6 + 71061.3i) q^{49} -5.59098e6 q^{50} +(-5.21850e6 - 3.01290e6i) q^{52} +(-462964. + 801877. i) q^{53} -982573. i q^{55} +(21430.6 + 3.47695e6i) q^{56} +(7.15469e6 + 1.23923e7i) q^{58} +(1.14511e7 + 6.61132e6i) q^{59} +(-1.21666e7 + 7.02438e6i) q^{61} -1.87396e6i q^{62} +2.09715e6 q^{64} +(2.21410e7 + 3.83494e7i) q^{65} +(8.70876e6 - 1.50840e7i) q^{67} +(-7.09922e6 + 4.09874e6i) q^{68} +(1.26392e7 - 2.22068e7i) q^{70} -5.33768e6 q^{71} +(2.95255e7 + 1.70466e7i) q^{73} +(-1.53382e7 + 2.65666e7i) q^{74} -3.00659e7i q^{76} +(2.17971e6 + 1.24061e6i) q^{77} +(1.61504e7 + 2.79734e7i) q^{79} +(-1.33467e7 - 7.70572e6i) q^{80} +(-1.45332e7 + 8.39075e6i) q^{82} +6.53156e7i q^{83} +6.02411e7 q^{85} +(5.25480e6 + 9.10159e6i) q^{86} +(756357. - 1.31005e6i) q^{88} +(-2.58655e7 + 1.49334e7i) q^{89} +(-1.13029e8 + 696665. i) q^{91} +3.47466e7 q^{92} +(9.16051e7 + 5.28882e7i) q^{94} +(-1.10473e8 + 1.91345e8i) q^{95} +5.40321e7i q^{97} +(3.33044e7 + 5.60770e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) \) 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

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