LMFDB - Embedded newform 36.9.d.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,9,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	36.d (of order $2$, degree $1$, 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:	$14.6656299622$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 40x^{6} - 395x^{5} + 403x^{4} + 8998x^{3} + 74584x^{2} + 217224x + 269328 $ x^8 - 3x^7 - 40x^6 - 395x^5 + 403x^4 + 8998x^3 + 74584x^2 + 217224*x + 269328
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-3.64622 - 4.31154i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.9.d.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-13.6476 + 8.35123i) q^{2} +(116.514 - 227.948i) q^{4} -904.196 q^{5} -888.085i q^{7} +(313.513 + 4083.98i) q^{8} +(12340.1 - 7551.15i) q^{10} -14451.0i q^{11} -11609.0 q^{13} +(7416.60 + 12120.2i) q^{14} +(-38385.0 - 53118.4i) q^{16} +128520. q^{17} +225611. i q^{19} +(-105352. + 206110. i) q^{20} +(120684. + 197222. i) q^{22} +441698. i q^{23} +426946. q^{25} +(158435. - 96949.7i) q^{26} +(-202438. - 103474. i) q^{28} -115149. q^{29} -201879. i q^{31} +(967466. + 404376. i) q^{32} +(-1.75398e6 + 1.07330e6i) q^{34} +803004. i q^{35} +2.01233e6 q^{37} +(-1.88413e6 - 3.07905e6i) q^{38} +(-283478. - 3.69272e6i) q^{40} +2.61903e6 q^{41} +1.75420e6i q^{43} +(-3.29409e6 - 1.68375e6i) q^{44} +(-3.68872e6 - 6.02811e6i) q^{46} -4.81199e6i q^{47} +4.97611e6 q^{49} +(-5.82679e6 + 3.56553e6i) q^{50} +(-1.35261e6 + 2.64626e6i) q^{52} -1.23892e6 q^{53} +1.30666e7i q^{55} +(3.62693e6 - 278427. i) q^{56} +(1.57150e6 - 961634. i) q^{58} +1.14062e6i q^{59} -4.60247e6 q^{61} +(1.68594e6 + 2.75517e6i) q^{62} +(-1.65806e7 + 2.56077e6i) q^{64} +1.04968e7 q^{65} -2.33742e7i q^{67} +(1.49743e7 - 2.92958e7i) q^{68} +(-6.70607e6 - 1.09591e7i) q^{70} +3.21271e7i q^{71} +4.89485e7 q^{73} +(-2.74635e7 + 1.68054e7i) q^{74} +(5.14277e7 + 2.62868e7i) q^{76} -1.28338e7 q^{77} +4.23230e6i q^{79} +(3.47076e7 + 4.80294e7i) q^{80} +(-3.57434e7 + 2.18721e7i) q^{82} +1.99136e7i q^{83} -1.16207e8 q^{85} +(-1.46497e7 - 2.39407e7i) q^{86} +(5.90178e7 - 4.53060e6i) q^{88} -8.45908e6 q^{89} +1.03098e7i q^{91} +(1.00684e8 + 5.14639e7i) q^{92} +(4.01860e7 + 6.56721e7i) q^{94} -2.03997e8i q^{95} -8.74596e7 q^{97} +(-6.79119e7 + 4.15566e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 52 q^{4} + 336 q^{5} + 12960 q^{8} + 36628 q^{10} - 2864 q^{13} - 52728 q^{14} + 99440 q^{16} + 193200 q^{17} - 335592 q^{20} - 556968 q^{22} - 579048 q^{25} - 21564 q^{26} - 594672 q^{28}+ \cdots - 691081830 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 - 52 * q^4 + 336 * q^5 + 12960 * q^8 + 36628 * q^10 - 2864 * q^13 - 52728 * q^14 + 99440 * q^16 + 193200 * q^17 - 335592 * q^20 - 556968 * q^22 - 579048 * q^25 - 21564 * q^26 - 594672 * q^28 - 2063472 * q^29 + 3602784 * q^32 + 1568476 * q^34 + 7470352 * q^37 - 3659400 * q^38 + 1749184 * q^40 + 8865456 * q^41 - 2395920 * q^44 - 13649856 * q^46 - 18923896 * q^49 - 14581842 * q^50 + 18592888 * q^52 - 8706672 * q^53 + 45565632 * q^56 - 8816444 * q^58 + 13457296 * q^61 - 80783976 * q^62 + 1268864 * q^64 - 7293408 * q^65 + 117288264 * q^68 - 60373104 * q^70 + 94738960 * q^73 - 119548428 * q^74 + 144621360 * q^76 + 56971392 * q^77 + 163857888 * q^80 - 188383460 * q^82 - 201200416 * q^85 - 240327384 * q^86 + 156323520 * q^88 - 188992272 * q^89 + 387657984 * q^92 - 38749872 * q^94 - 123291632 * q^97 - 691081830 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−13.6476	+	8.35123i	−0.852975	+	0.521952i
$2$	−13.6476	+	8.35123i	−0.852975	+	0.521952i
$3$		0			0
$3$		0			0
$4$	116.514	−	227.948i	0.455133	−	0.890424i
$5$	−904.196			−1.44671			−0.723357	−	0.690474i	$-0.757402\pi$
$5$	−904.196			−1.44671			−0.723357	+	0.690474i	$0.757402\pi$
$6$		0			0
$7$		−	888.085i		−	0.369881i	−0.982750	−	0.184941i	$-0.940791\pi$
$7$		−	888.085i		−	0.369881i	0.982750	−	0.184941i	$-0.0592093\pi$
$8$	313.513	+	4083.98i	0.0765414	+	0.997066i
$9$		0			0
$10$	12340.1	−	7551.15i	1.23401	−	0.755115i
$11$		−	14451.0i		−	0.987026i	−0.869739	−	0.493513i	$-0.835713\pi$
$11$		−	14451.0i		−	0.987026i	0.869739	−	0.493513i	$-0.164287\pi$
$12$		0			0
$13$	−11609.0			−0.406465			−0.203232	−	0.979131i	$-0.565145\pi$
$13$	−11609.0			−0.406465			−0.203232	+	0.979131i	$0.565145\pi$
$14$	7416.60	+	12120.2i	0.193060	+	0.315500i
$15$		0			0
$16$	−38385.0	−	53118.4i	−0.585708	−	0.810522i
$17$	128520.			1.53877			0.769385	−	0.638786i	$-0.220563\pi$
$17$	128520.			1.53877			0.769385	+	0.638786i	$0.220563\pi$
$18$		0			0
$19$			225611.i			1.73120i	0.500740	+	0.865598i	$0.333061\pi$
$19$			225611.i			1.73120i	−0.500740	+	0.865598i	$0.666939\pi$
$20$	−105352.	+	206110.i	−0.658447	+	1.28819i
$21$		0			0
$22$	120684.	+	197222.i	0.515180	+	0.841908i
$23$			441698.i			1.57839i	0.614144	+	0.789194i	$0.289501\pi$
$23$			441698.i			1.57839i	−0.614144	+	0.789194i	$0.710499\pi$
$24$		0			0
$25$	426946.			1.09298
$26$	158435.	−	96949.7i	0.346704	−	0.212155i
$27$		0			0
$28$	−202438.	−	103474.i	−0.329351	−	0.168345i
$29$	−115149.			−0.162805			−0.0814024	−	0.996681i	$-0.525940\pi$
$29$	−115149.			−0.162805			−0.0814024	+	0.996681i	$0.525940\pi$
$30$		0			0
$31$		−	201879.i		−	0.218597i	−0.994009	−	0.109299i	$-0.965139\pi$
$31$		−	201879.i		−	0.218597i	0.994009	−	0.109299i	$-0.0348605\pi$
$32$	967466.	+	404376.i	0.922648	+	0.385643i
$33$		0			0
$34$	−1.75398e6	+	1.07330e6i	−1.31253	+	0.803163i
$35$			803004.i			0.535113i
$36$		0			0
$37$	2.01233e6			1.07372			0.536861	−	0.843671i	$-0.319610\pi$
$37$	2.01233e6			1.07372			0.536861	+	0.843671i	$0.319610\pi$
$38$	−1.88413e6	−	3.07905e6i	−0.903600	−	1.47667i
$39$		0			0
$40$	−283478.	−	3.69272e6i	−0.110733	−	1.44247i
$41$	2.61903e6			0.926839			0.463420	−	0.886139i	$-0.346622\pi$
$41$	2.61903e6			0.926839			0.463420	+	0.886139i	$0.346622\pi$
$42$		0			0
$43$			1.75420e6i			0.513105i	0.966530	+	0.256552i	$0.0825866\pi$
$43$			1.75420e6i			0.513105i	−0.966530	+	0.256552i	$0.917413\pi$
$44$	−3.29409e6	−	1.68375e6i	−0.878871	−	0.449228i
$45$		0			0
$46$	−3.68872e6	−	6.02811e6i	−0.823842	−	1.34633i
$47$		−	4.81199e6i		−	0.986128i	−0.869993	−	0.493064i	$-0.835877\pi$
$47$		−	4.81199e6i		−	0.986128i	0.869993	−	0.493064i	$-0.164123\pi$
$48$		0			0
$49$	4.97611e6			0.863188
$50$	−5.82679e6	+	3.56553e6i	−0.932287	+	0.570484i
$51$		0			0
$52$	−1.35261e6	+	2.64626e6i	−0.184995	+	0.361926i
$53$	−1.23892e6			−0.157014			−0.0785071	−	0.996914i	$-0.525015\pi$
$53$	−1.23892e6			−0.157014			−0.0785071	+	0.996914i	$0.525015\pi$
$54$		0			0
$55$			1.30666e7i			1.42794i
$56$	3.62693e6	−	278427.i	0.368796	−	0.0283112i
$57$		0			0
$58$	1.57150e6	−	961634.i	0.138868	−	0.0849763i
$59$			1.14062e6i			0.0941311i	0.998892	+	0.0470655i	$0.0149870\pi$
$59$			1.14062e6i			0.0941311i	−0.998892	+	0.0470655i	$0.985013\pi$
$60$		0			0
$61$	−4.60247e6			−0.332408			−0.166204	−	0.986091i	$-0.553151\pi$
$61$	−4.60247e6			−0.332408			−0.166204	+	0.986091i	$0.553151\pi$
$62$	1.68594e6	+	2.75517e6i	0.114097	+	0.186458i
$63$		0			0
$64$	−1.65806e7	+	2.56077e6i	−0.988283	+	0.152634i
$65$	1.04968e7			0.588038
$66$		0			0
$67$		−	2.33742e7i		−	1.15995i	−0.814635	−	0.579974i	$-0.803063\pi$
$67$		−	2.33742e7i		−	1.15995i	0.814635	−	0.579974i	$-0.196937\pi$
$68$	1.49743e7	−	2.92958e7i	0.700344	−	1.37016i
$69$		0			0
$70$	−6.70607e6	−	1.09591e7i	−0.279303	−	0.456438i
$71$			3.21271e7i			1.26426i	0.774861	+	0.632132i	$0.217820\pi$
$71$			3.21271e7i			1.26426i	−0.774861	+	0.632132i	$0.782180\pi$
$72$		0			0
$73$	4.89485e7			1.72365			0.861823	−	0.507209i	$-0.169323\pi$
$73$	4.89485e7			1.72365			0.861823	+	0.507209i	$0.169323\pi$
$74$	−2.74635e7	+	1.68054e7i	−0.915858	+	0.560431i
$75$		0			0
$76$	5.14277e7	+	2.62868e7i	1.54150	+	0.787924i
$77$	−1.28338e7			−0.365082
$78$		0			0
$79$			4.23230e6i			0.108660i	0.998523	+	0.0543298i	$0.0173022\pi$
$79$			4.23230e6i			0.108660i	−0.998523	+	0.0543298i	$0.982698\pi$
$80$	3.47076e7	+	4.80294e7i	0.847353	+	1.17259i
$81$		0			0
$82$	−3.57434e7	+	2.18721e7i	−0.790571	+	0.483765i
$83$			1.99136e7i			0.419602i	0.977744	+	0.209801i	$0.0672815\pi$
$83$			1.99136e7i			0.419602i	−0.977744	+	0.209801i	$0.932718\pi$
$84$		0			0
$85$	−1.16207e8			−2.22616
$86$	−1.46497e7	−	2.39407e7i	−0.267816	−	0.437665i
$87$		0			0
$88$	5.90178e7	−	4.53060e6i	0.984130	−	0.0755483i
$89$	−8.45908e6			−0.134823			−0.0674114	−	0.997725i	$-0.521474\pi$
$89$	−8.45908e6			−0.134823			−0.0674114	+	0.997725i	$0.521474\pi$
$90$		0			0
$91$			1.03098e7i			0.150344i
$92$	1.00684e8	+	5.14639e7i	1.40543	+	0.718376i
$93$		0			0
$94$	4.01860e7	+	6.56721e7i	0.514711	+	0.841142i
$95$		−	2.03997e8i		−	2.50455i
$96$		0			0
$97$	−8.74596e7			−0.987917			−0.493959	−	0.869485i	$-0.664451\pi$
$97$	−8.74596e7			−0.987917			−0.493959	+	0.869485i	$0.664451\pi$
$98$	−6.79119e7	+	4.15566e7i	−0.736278	+	0.450542i
$99$		0			0
$100$	4.97452e7	−	9.73217e7i	0.497452	−	0.973217i
$101$	−5.47619e7			−0.526251			−0.263126	−	0.964762i	$-0.584753\pi$
$101$	−5.47619e7			−0.526251			−0.263126	+	0.964762i	$0.584753\pi$
$102$		0			0
$103$		−	9.79588e6i		−	0.0870351i	−0.999053	−	0.0435175i	$-0.986144\pi$
$103$		−	9.79588e6i		−	0.0870351i	0.999053	−	0.0435175i	$-0.0138564\pi$
$104$	−3.63959e6	−	4.74111e7i	−0.0311114	−	0.405272i
$105$		0			0
$106$	1.69082e7	−	1.03465e7i	0.133929	−	0.0819538i
$107$			1.14346e8i			0.872340i	0.899864	+	0.436170i	$0.143665\pi$
$107$			1.14346e8i			0.872340i	−0.899864	+	0.436170i	$0.856335\pi$
$108$		0			0
$109$	4.18346e7			0.296367			0.148183	−	0.988960i	$-0.452657\pi$
$109$	4.18346e7			0.296367			0.148183	+	0.988960i	$0.452657\pi$
$110$	−1.09122e8	−	1.78327e8i	−0.745318	−	1.21800i
$111$		0			0
$112$	−4.71736e7	+	3.40891e7i	−0.299797	+	0.216643i
$113$	−5.24115e7			−0.321449			−0.160725	−	0.986999i	$-0.551383\pi$
$113$	−5.24115e7			−0.321449			−0.160725	+	0.986999i	$0.551383\pi$
$114$		0			0
$115$		−	3.99381e8i		−	2.28348i
$116$	−1.34164e7	+	2.62480e7i	−0.0740978	+	0.144965i
$117$		0			0
$118$	−9.52558e6	−	1.55667e7i	−0.0491319	−	0.0802915i
$119$		−	1.14136e8i		−	0.569162i
$120$		0			0
$121$	5.52626e6			0.0257804
$122$	6.28126e7	−	3.84363e7i	0.283536	−	0.173501i
$123$		0			0
$124$	−4.60181e7	−	2.35218e7i	−0.194644	−	0.0994909i
$125$	−3.28415e7			−0.134519
$126$		0			0
$127$			3.58172e8i			1.37682i	0.725323	+	0.688409i	$0.241690\pi$
$127$			3.58172e8i			1.37682i	−0.725323	+	0.688409i	$0.758310\pi$
$128$	2.04900e8	−	1.73417e8i	0.763313	−	0.646029i
$129$		0			0
$130$	−1.43257e8	+	8.76616e7i	−0.501582	+	0.306928i
$131$			3.12310e8i			1.06048i	0.847848	+	0.530239i	$0.177898\pi$
$131$			3.12310e8i			1.06048i	−0.847848	+	0.530239i	$0.822102\pi$
$132$		0			0
$133$	2.00362e8			0.640337
$134$	1.95204e8	+	3.19002e8i	0.605437	+	0.989406i
$135$		0			0
$136$	4.02926e7	+	5.24872e8i	0.117779	+	1.53426i
$137$	2.02321e8			0.574327			0.287163	−	0.957882i	$-0.407288\pi$
$137$	2.02321e8			0.574327			0.287163	+	0.957882i	$0.407288\pi$
$138$		0			0
$139$			3.56101e8i			0.953924i	0.878924	+	0.476962i	$0.158262\pi$
$139$			3.56101e8i			0.953924i	−0.878924	+	0.476962i	$0.841738\pi$
$140$	1.83043e8	+	9.35611e7i	0.476477	+	0.243547i
$141$		0			0
$142$	−2.68300e8	−	4.38457e8i	−0.659885	−	1.07839i
$143$			1.67763e8i			0.401191i
$144$		0			0
$145$	1.04117e8			0.235532
$146$	−6.68030e8	+	4.08780e8i	−1.47023	+	0.899660i
$147$		0			0
$148$	2.34464e8	−	4.58707e8i	0.488686	−	0.956068i
$149$	4.69207e8			0.951961			0.475981	−	0.879456i	$-0.342093\pi$
$149$	4.69207e8			0.951961			0.475981	+	0.879456i	$0.342093\pi$
$150$		0			0
$151$			4.96132e8i			0.954309i	0.878819	+	0.477155i	$0.158332\pi$
$151$			4.96132e8i			0.954309i	−0.878819	+	0.477155i	$0.841668\pi$
$152$	−9.21392e8	+	7.07321e7i	−1.72612	+	0.132508i
$153$		0			0
$154$	1.75150e8	−	1.07178e8i	0.311406	−	0.190555i
$155$			1.82539e8i			0.316248i
$156$		0			0
$157$	9.86054e8			1.62294			0.811469	−	0.584395i	$-0.198668\pi$
$157$	9.86054e8			1.62294			0.811469	+	0.584395i	$0.198668\pi$
$158$	−3.53449e7	−	5.77607e7i	−0.0567150	−	0.0926839i
$159$		0			0
$160$	−8.74780e8	−	3.65636e8i	−1.33481	−	0.557916i
$161$	3.92265e8			0.583816
$162$		0			0
$163$		−	1.41749e8i		−	0.200803i	−0.994947	−	0.100402i	$-0.967987\pi$
$163$		−	1.41749e8i		−	0.200803i	0.994947	−	0.100402i	$-0.0320128\pi$
$164$	3.05153e8	−	5.97003e8i	0.421835	−	0.825279i
$165$		0			0
$166$	−1.66303e8	−	2.71773e8i	−0.219012	−	0.357910i
$167$		−	6.26762e8i		−	0.805818i	−0.915240	−	0.402909i	$-0.867999\pi$
$167$		−	6.26762e8i		−	0.805818i	0.915240	−	0.402909i	$-0.132001\pi$
$168$		0			0
$169$	−6.80961e8			−0.834787
$170$	1.58595e9	−	9.70471e8i	1.89886	−	1.16195i
$171$		0			0
$172$	3.99868e8	+	2.04389e8i	0.456880	+	0.233531i
$173$	−3.25845e8			−0.363770			−0.181885	−	0.983320i	$-0.558220\pi$
$173$	−3.25845e8			−0.363770			−0.181885	+	0.983320i	$0.558220\pi$
$174$		0			0
$175$		−	3.79165e8i		−	0.404274i
$176$	−7.67616e8	+	5.54703e8i	−0.800006	+	0.578109i
$177$		0			0
$178$	1.15446e8	−	7.06437e7i	0.115000	−	0.0703710i
$179$		−	4.96016e8i		−	0.483152i	−0.970382	−	0.241576i	$-0.922336\pi$
$179$		−	4.96016e8i		−	0.483152i	0.970382	−	0.241576i	$-0.0776642\pi$
$180$		0			0
$181$	−5.63606e8			−0.525123			−0.262562	−	0.964915i	$-0.584567\pi$
$181$	−5.63606e8			−0.525123			−0.262562	+	0.964915i	$0.584567\pi$
$182$	−8.60996e7	−	1.40704e8i	−0.0784722	−	0.128239i
$183$		0			0
$184$	−1.80389e9	+	1.38478e8i	−1.57376	+	0.120812i
$185$	−1.81954e9			−1.55337
$186$		0			0
$187$		−	1.85724e9i		−	1.51880i
$188$	−1.09689e9	−	5.60664e8i	−0.878072	−	0.448819i
$189$		0			0
$190$	1.70362e9	+	2.78407e9i	1.30725	+	2.13631i
$191$			8.54684e8i			0.642203i	0.947045	+	0.321101i	$0.104053\pi$
$191$			8.54684e8i			0.642203i	−0.947045	+	0.321101i	$0.895947\pi$
$192$		0			0
$193$	1.02603e9			0.739489			0.369745	−	0.929133i	$-0.379445\pi$
$193$	1.02603e9			0.739489			0.369745	+	0.929133i	$0.379445\pi$
$194$	1.19361e9	−	7.30395e8i	0.842669	−	0.515645i
$195$		0			0
$196$	5.79786e8	−	1.13430e9i	0.392865	−	0.768603i
$197$	−8.44577e8			−0.560756			−0.280378	−	0.959890i	$-0.590460\pi$
$197$	−8.44577e8			−0.560756			−0.280378	+	0.959890i	$0.590460\pi$
$198$		0			0
$199$			7.72569e8i			0.492635i	0.969189	+	0.246317i	$0.0792206\pi$
$199$			7.72569e8i			0.492635i	−0.969189	+	0.246317i	$0.920779\pi$
$200$	1.33853e8	+	1.74364e9i	0.0836584	+	1.08978i
$201$		0			0
$202$	7.47369e8	−	4.57329e8i	0.448879	−	0.274678i
$203$			1.02262e8i			0.0602185i
$204$		0			0
$205$	−2.36811e9			−1.34087
$206$	8.18076e7	+	1.33690e8i	0.0454281	+	0.0742388i
$207$		0			0
$208$	4.45613e8	+	6.16653e8i	0.238070	+	0.329448i
$209$	3.26032e9			1.70873
$210$		0			0
$211$			2.19966e9i			1.10975i	0.831934	+	0.554875i	$0.187234\pi$
$211$			2.19966e9i			1.10975i	−0.831934	+	0.554875i	$0.812766\pi$
$212$	−1.44351e8	+	2.82409e8i	−0.0714623	+	0.139809i
$213$		0			0
$214$	−9.54930e8	−	1.56055e9i	−0.455320	−	0.744085i
$215$		−	1.58614e9i		−	0.742316i
$216$		0			0
$217$	−1.79286e8			−0.0808551
$218$	−5.70942e8	+	3.49370e8i	−0.252794	+	0.154689i
$219$		0			0
$220$	2.97851e9	+	1.52244e9i	1.27148	+	0.649904i
$221$	−1.49199e9			−0.625455
$222$		0			0
$223$		−	4.61916e9i		−	1.86786i	−0.357459	−	0.933929i	$-0.616357\pi$
$223$		−	4.61916e9i		−	1.86786i	0.357459	−	0.933929i	$-0.383643\pi$
$224$	3.59121e8	−	8.59193e8i	0.142642	−	0.341270i
$225$		0			0
$226$	7.15291e8	−	4.37700e8i	0.274188	−	0.167781i
$227$		−	1.24196e9i		−	0.467738i	−0.972268	−	0.233869i	$-0.924861\pi$
$227$		−	1.24196e9i		−	0.467738i	0.972268	−	0.233869i	$-0.0751388\pi$
$228$		0			0
$229$	−4.83925e9			−1.75969			−0.879845	−	0.475260i	$-0.842354\pi$
$229$	−4.83925e9			−1.75969			−0.879845	+	0.475260i	$0.842354\pi$
$230$	3.33532e9	+	5.45060e9i	1.19186	+	1.94775i
$231$		0			0
$232$	−3.61007e7	−	4.70266e8i	−0.0124613	−	0.162327i
$233$	1.26420e9			0.428936			0.214468	−	0.976731i	$-0.431198\pi$
$233$	1.26420e9			0.428936			0.214468	+	0.976731i	$0.431198\pi$
$234$		0			0
$235$			4.35098e9i			1.42665i
$236$	2.60003e8	+	1.32898e8i	0.0838165	+	0.0428421i
$237$		0			0
$238$	9.53178e8	+	1.55769e9i	0.297075	+	0.485481i
$239$			3.45214e9i			1.05803i	0.848613	+	0.529014i	$0.177438\pi$
$239$			3.45214e9i			1.05803i	−0.848613	+	0.529014i	$0.822562\pi$
$240$		0			0
$241$	2.81376e9			0.834101			0.417050	−	0.908883i	$-0.363064\pi$
$241$	2.81376e9			0.834101			0.417050	+	0.908883i	$0.363064\pi$
$242$	−7.54201e7	+	4.61510e7i	−0.0219900	+	0.0134561i
$243$		0			0
$244$	−5.36252e8	+	1.04913e9i	−0.151290	+	0.295984i
$245$	−4.49938e9			−1.24879
$246$		0			0
$247$		−	2.61913e9i		−	0.703670i
$248$	8.24472e8	−	6.32919e7i	0.217956	−	0.0167317i
$249$		0			0
$250$	4.48208e8	−	2.74267e8i	0.114741	−	0.0702124i
$251$		−	1.02698e9i		−	0.258741i	−0.991596	−	0.129371i	$-0.958704\pi$
$251$		−	1.02698e9i		−	0.258741i	0.991596	−	0.129371i	$-0.0412957\pi$
$252$		0			0
$253$	6.38299e9			1.55791
$254$	−2.99117e9	−	4.88818e9i	−0.718632	−	1.17439i
$255$		0			0
$256$	−1.34815e9	+	4.07790e9i	−0.313891	+	0.949459i
$257$	1.80098e9			0.412834			0.206417	−	0.978464i	$-0.433820\pi$
$257$	1.80098e9			0.412834			0.206417	+	0.978464i	$0.433820\pi$
$258$		0			0
$259$		−	1.78712e9i		−	0.397150i
$260$	1.22303e9	−	2.39274e9i	0.267635	−	0.523603i
$261$		0			0
$262$	−2.60818e9	−	4.26229e9i	−0.553518	−	0.904561i
$263$			6.59493e9i			1.37844i	0.724554	+	0.689219i	$0.242046\pi$
$263$			6.59493e9i			1.37844i	−0.724554	+	0.689219i	$0.757954\pi$
$264$		0			0
$265$	1.12022e9			0.227155
$266$	−2.73446e9	+	1.67327e9i	−0.546191	+	0.334225i
$267$		0			0
$268$	−5.32812e9	−	2.72343e9i	−1.03284	−	0.527930i
$269$	7.85945e8			0.150101			0.0750504	−	0.997180i	$-0.476088\pi$
$269$	7.85945e8			0.150101			0.0750504	+	0.997180i	$0.476088\pi$
$270$		0			0
$271$			4.85570e9i			0.900274i	0.892959	+	0.450137i	$0.148625\pi$
$271$			4.85570e9i			0.900274i	−0.892959	+	0.450137i	$0.851375\pi$
$272$	−4.93322e9	−	6.82675e9i	−0.901270	−	1.24721i
$273$		0			0
$274$	−2.76120e9	+	1.68963e9i	−0.489886	+	0.299771i
$275$		−	6.16982e9i		−	1.07880i
$276$		0			0
$277$	−5.59523e9			−0.950383			−0.475191	−	0.879882i	$-0.657621\pi$
$277$	−5.59523e9			−0.950383			−0.475191	+	0.879882i	$0.657621\pi$
$278$	−2.97388e9	−	4.85992e9i	−0.497902	−	0.813674i
$279$		0			0
$280$	−3.27945e9	+	2.51752e8i	−0.533543	+	0.0409583i
$281$	9.77267e9			1.56743			0.783715	−	0.621121i	$-0.213322\pi$
$281$	9.77267e9			1.56743			0.783715	+	0.621121i	$0.213322\pi$
$282$		0			0
$283$			1.39134e9i			0.216915i	0.994101	+	0.108457i	$0.0345911\pi$
$283$			1.39134e9i			0.216915i	−0.994101	+	0.108457i	$0.965409\pi$
$284$	7.32332e9	+	3.74325e9i	1.12573	+	0.575408i
$285$		0			0
$286$	−1.40102e9	−	2.28956e9i	−0.209402	−	0.342206i
$287$		−	2.32592e9i		−	0.342821i
$288$		0			0
$289$	9.54152e9			1.36781
$290$	−1.42095e9	+	8.69506e8i	−0.200903	+	0.122936i
$291$		0			0
$292$	5.70319e9	−	1.11577e10i	0.784488	−	1.53478i
$293$	−1.31910e10			−1.78981			−0.894904	−	0.446258i	$-0.852756\pi$
$293$	−1.31910e10			−1.78981			−0.894904	+	0.446258i	$0.852756\pi$
$294$		0			0
$295$		−	1.03134e9i		−	0.136181i
$296$	6.30892e8	+	8.21832e9i	0.0821842	+	1.07057i
$297$		0			0
$298$	−6.40355e9	+	3.91845e9i	−0.811999	+	0.496878i
$299$		−	5.12768e9i		−	0.641559i
$300$		0			0
$301$	1.55788e9			0.189788
$302$	−4.14331e9	−	6.77100e9i	−0.498103	−	0.814002i
$303$		0			0
$304$	1.19841e10	−	8.66008e9i	1.40317	−	1.01398i
$305$	4.16154e9			0.480899
$306$		0			0
$307$			1.03003e9i			0.115957i	0.998318	+	0.0579784i	$0.0184654\pi$
$307$			1.03003e9i			0.115957i	−0.998318	+	0.0579784i	$0.981535\pi$
$308$	−1.49531e9	+	2.92544e9i	−0.166161	+	0.325078i
$309$		0			0
$310$	−1.52442e9	−	2.49121e9i	−0.165066	−	0.269752i
$311$		−	1.03275e10i		−	1.10396i	−0.833857	−	0.551981i	$-0.813872\pi$
$311$		−	1.03275e10i		−	1.10396i	0.833857	−	0.551981i	$-0.186128\pi$
$312$		0			0
$313$	−1.75059e9			−0.182393			−0.0911963	−	0.995833i	$-0.529069\pi$
$313$	−1.75059e9			−0.182393			−0.0911963	+	0.995833i	$0.529069\pi$
$314$	−1.34573e10	+	8.23476e9i	−1.38433	+	0.847096i
$315$		0			0
$316$	9.64746e8	+	4.93122e8i	0.0967530	+	0.0494545i
$317$	1.25238e10			1.24022			0.620109	−	0.784515i	$-0.287088\pi$
$317$	1.25238e10			1.24022			0.620109	+	0.784515i	$0.287088\pi$
$318$		0			0
$319$			1.66402e9i			0.160693i
$320$	1.49922e10	−	2.31544e9i	1.42976	−	0.220817i
$321$		0			0
$322$	−5.35348e9	+	3.27590e9i	−0.497981	+	0.304724i
$323$			2.89954e10i			2.66391i
$324$		0			0
$325$	−4.95643e9			−0.444259
$326$	1.18378e9	+	1.93454e9i	0.104810	+	0.171280i
$327$		0			0
$328$	8.21100e8	+	1.06961e10i	0.0709415	+	0.924120i
$329$	−4.27346e9			−0.364750
$330$		0			0
$331$			1.79988e10i			1.49945i	0.661750	+	0.749725i	$0.269814\pi$
$331$			1.79988e10i			1.49945i	−0.661750	+	0.749725i	$0.730186\pi$
$332$	4.53927e9	+	2.32021e9i	0.373623	+	0.190974i
$333$		0			0
$334$	5.23424e9	+	8.55380e9i	0.420598	+	0.687343i
$335$			2.11349e10i			1.67811i
$336$		0			0
$337$	4.52797e9			0.351062			0.175531	−	0.984474i	$-0.443836\pi$
$337$	4.52797e9			0.351062			0.175531	+	0.984474i	$0.443836\pi$
$338$	9.29348e9	−	5.68686e9i	0.712052	−	0.435718i
$339$		0			0
$340$	−1.35397e10	+	2.64892e10i	−1.01320	+	1.98223i
$341$	−2.91737e9			−0.215761
$342$		0			0
$343$		−	9.53884e9i		−	0.689159i
$344$	−7.16414e9	+	5.49966e8i	−0.511599	+	0.0392737i
$345$		0			0
$346$	4.44701e9	−	2.72121e9i	0.310287	−	0.189871i
$347$		−	2.28528e10i		−	1.57624i	−0.615522	−	0.788119i	$-0.711055\pi$
$347$		−	2.28528e10i		−	1.57624i	0.615522	−	0.788119i	$-0.288945\pi$
$348$		0			0
$349$	7.23857e9			0.487922			0.243961	−	0.969785i	$-0.421553\pi$
$349$	7.23857e9			0.487922			0.243961	+	0.969785i	$0.421553\pi$
$350$	3.16649e9	+	5.17469e9i	0.211011	+	0.344835i
$351$		0			0
$352$	5.84366e9	−	1.39809e10i	0.380640	−	0.910677i
$353$	9.02641e9			0.581321			0.290661	−	0.956826i	$-0.406125\pi$
$353$	9.02641e9			0.581321			0.290661	+	0.956826i	$0.406125\pi$
$354$		0			0
$355$		−	2.90492e10i		−	1.82903i
$356$	−9.85601e8	+	1.92823e9i	−0.0613622	+	0.120049i
$357$		0			0
$358$	4.14234e9	+	6.76942e9i	0.252182	+	0.412116i
$359$		−	8.94260e9i		−	0.538377i	−0.963088	−	0.269188i	$-0.913245\pi$
$359$		−	8.94260e9i		−	0.538377i	0.963088	−	0.269188i	$-0.0867554\pi$
$360$		0			0
$361$	−3.39168e10			−1.99704
$362$	7.69187e9	−	4.70680e9i	0.447917	−	0.274089i
$363$		0			0
$364$	2.35011e9	+	1.20124e9i	0.133870	+	0.0684263i
$365$	−4.42591e10			−2.49362
$366$		0			0
$367$		−	9.34134e9i		−	0.514926i	−0.966288	−	0.257463i	$-0.917113\pi$
$367$		−	9.34134e9i		−	0.514926i	0.966288	−	0.257463i	$-0.0828866\pi$
$368$	2.34622e10	−	1.69546e10i	1.27932	−	0.924475i
$369$		0			0
$370$	2.48324e10	−	1.51954e10i	1.32499	−	0.810784i
$371$			1.10026e9i			0.0580766i
$372$		0			0
$373$	−8.10234e9			−0.418577			−0.209288	−	0.977854i	$-0.567115\pi$
$373$	−8.10234e9			−0.418577			−0.209288	+	0.977854i	$0.567115\pi$
$374$	1.55102e10	+	2.53469e10i	0.792743	+	1.29550i
$375$		0			0
$376$	1.96521e10	−	1.50862e9i	0.983235	−	0.0754796i
$377$	1.33677e9			0.0661744
$378$		0			0
$379$		−	2.76442e10i		−	1.33982i	−0.742440	−	0.669912i	$-0.766332\pi$
$379$		−	2.76442e10i		−	1.33982i	0.742440	−	0.669912i	$-0.233668\pi$
$380$	−4.65007e10	−	2.37685e10i	−2.23011	−	1.13990i
$381$		0			0
$382$	−7.13766e9	−	1.16644e10i	−0.335199	−	0.547783i
$383$		−	3.04532e10i		−	1.41526i	−0.706581	−	0.707632i	$-0.749763\pi$
$383$		−	3.04532e10i		−	1.41526i	0.706581	−	0.707632i	$-0.250237\pi$
$384$		0			0
$385$	1.16042e10			0.528170
$386$	−1.40029e10	+	8.56863e9i	−0.630766	+	0.385978i
$387$		0			0
$388$	−1.01903e10	+	1.99363e10i	−0.449633	+	0.879665i
$389$	1.61385e9			0.0704799			0.0352399	−	0.999379i	$-0.488780\pi$
$389$	1.61385e9			0.0704799			0.0352399	+	0.999379i	$0.488780\pi$
$390$		0			0
$391$			5.67668e10i			2.42877i
$392$	1.56008e9	+	2.03223e10i	0.0660696	+	0.860656i
$393$		0			0
$394$	1.15264e10	−	7.05325e9i	0.478311	−	0.292688i
$395$		−	3.82683e9i		−	0.157199i
$396$		0			0
$397$	−3.65388e10			−1.47093			−0.735465	−	0.677563i	$-0.763036\pi$
$397$	−3.65388e10			−1.47093			−0.735465	+	0.677563i	$0.763036\pi$
$398$	−6.45190e9	−	1.05437e10i	−0.257132	−	0.420205i
$399$		0			0
$400$	−1.63883e10	−	2.26787e10i	−0.640169	−	0.885886i
$401$	2.62838e10			1.01651			0.508253	−	0.861208i	$-0.330292\pi$
$401$	2.62838e10			1.01651			0.508253	+	0.861208i	$0.330292\pi$
$402$		0			0
$403$			2.34362e9i			0.0888521i
$404$	−6.38053e9	+	1.24829e10i	−0.239514	+	0.468586i
$405$		0			0
$406$	−8.54013e8	−	1.39563e9i	−0.0314312	−	0.0513649i
$407$		−	2.90802e10i		−	1.05979i
$408$		0			0
$409$	1.69888e10			0.607114			0.303557	−	0.952813i	$-0.401826\pi$
$409$	1.69888e10			0.607114			0.303557	+	0.952813i	$0.401826\pi$
$410$	3.23191e10	−	1.97767e10i	1.14373	−	0.699870i
$411$		0			0
$412$	−2.23295e9	−	1.14136e9i	−0.0774981	−	0.0396125i
$413$	1.01297e9			0.0348173
$414$		0			0
$415$		−	1.80058e10i		−	0.607044i
$416$	−1.12314e10	−	4.69442e9i	−0.375024	−	0.156750i
$417$		0			0
$418$	−4.44955e10	+	2.72276e10i	−1.45751	+	0.891877i
$419$			4.79547e10i			1.55588i	0.628340	+	0.777939i	$0.283735\pi$
$419$			4.79547e10i			1.55588i	−0.628340	+	0.777939i	$0.716265\pi$
$420$		0			0
$421$	3.01561e9			0.0959947			0.0479973	−	0.998847i	$-0.484716\pi$
$421$	3.01561e9			0.0959947			0.0479973	+	0.998847i	$0.484716\pi$
$422$	−1.83698e10	−	3.00201e10i	−0.579236	−	0.946589i
$423$		0			0
$424$	−3.88417e8	−	5.05972e9i	−0.0120181	−	0.156554i
$425$	5.48709e10			1.68185
$426$		0			0
$427$			4.08738e9i			0.122952i
$428$	2.60650e10	+	1.33229e10i	0.776753	+	0.397031i
$429$		0			0
$430$	1.32462e10	+	2.16471e10i	0.387453	+	0.633177i
$431$			1.51705e10i			0.439634i	0.975541	+	0.219817i	$0.0705461\pi$
$431$			1.51705e10i			0.439634i	−0.975541	+	0.219817i	$0.929454\pi$
$432$		0			0
$433$	5.75689e10			1.63771			0.818853	−	0.574003i	$-0.194610\pi$
$433$	5.75689e10			1.63771			0.818853	+	0.574003i	$0.194610\pi$
$434$	2.44682e9	−	1.49726e9i	0.0689674	−	0.0422025i
$435$		0			0
$436$	4.87432e9	−	9.53614e9i	0.134886	−	0.263892i
$437$	−9.96519e10			−2.73250
$438$		0			0
$439$			5.52060e10i			1.48638i	0.669083	+	0.743188i	$0.266687\pi$
$439$			5.52060e10i			1.48638i	−0.669083	+	0.743188i	$0.733313\pi$
$440$	−5.33637e10	+	4.09655e9i	−1.42376	+	0.109297i
$441$		0			0
$442$	2.03621e10	−	1.24599e10i	0.533498	−	0.326457i
$443$			6.97437e10i			1.81088i	0.424473	+	0.905441i	$0.360460\pi$
$443$			6.97437e10i			1.81088i	−0.424473	+	0.905441i	$0.639540\pi$
$444$		0			0
$445$	7.64867e9			0.195050
$446$	3.85757e10	+	6.30405e10i	0.974932	+	1.59324i
$447$		0			0
$448$	2.27418e9	+	1.47250e10i	0.0564563	+	0.365547i
$449$	1.47127e10			0.361998			0.180999	−	0.983483i	$-0.442067\pi$
$449$	1.47127e10			0.361998			0.180999	+	0.983483i	$0.442067\pi$
$450$		0			0
$451$		−	3.78477e10i		−	0.914814i
$452$	−6.10667e9	+	1.19471e10i	−0.146302	+	0.286226i
$453$		0			0
$454$	1.03719e10	+	1.69497e10i	0.244137	+	0.398969i
$455$		−	9.32210e9i		−	0.217504i
$456$		0			0
$457$	6.37221e10			1.46092			0.730458	−	0.682957i	$-0.239306\pi$
$457$	6.37221e10			1.46092			0.730458	+	0.682957i	$0.239306\pi$
$458$	6.60442e10	−	4.04137e10i	1.50097	−	0.918473i
$459$		0			0
$460$	−9.10384e10	−	4.65335e10i	−2.03326	−	1.03928i
$461$	3.93282e10			0.870763			0.435382	−	0.900246i	$-0.356613\pi$
$461$	3.93282e10			0.870763			0.435382	+	0.900246i	$0.356613\pi$
$462$		0			0
$463$		−	6.91241e10i		−	1.50420i	−0.659049	−	0.752100i	$-0.729041\pi$
$463$		−	6.91241e10i		−	1.50420i	0.659049	−	0.752100i	$-0.270959\pi$
$464$	4.41999e9	+	6.11652e9i	0.0953562	+	0.131957i
$465$		0			0
$466$	−1.72533e10	+	1.05576e10i	−0.365872	+	0.223884i
$467$		−	4.48917e10i		−	0.943840i	−0.881641	−	0.471920i	$-0.843561\pi$
$467$		−	4.48917e10i		−	0.943840i	0.881641	−	0.471920i	$-0.156439\pi$
$468$		0			0
$469$	−2.07583e10			−0.429043
$470$	−3.63361e10	−	5.93805e10i	−0.744640	−	1.21689i
$471$		0			0
$472$	−4.65827e9	+	3.57600e8i	−0.0938549	+	0.00720492i
$473$	2.53501e10			0.506447
$474$		0			0
$475$			9.63238e10i			1.89217i
$476$	−2.60172e10	−	1.32985e10i	−0.506795	−	0.259044i
$477$		0			0
$478$	−2.88296e10	−	4.71135e10i	−0.552240	−	0.902471i
$479$			7.56518e10i			1.43707i	0.695492	+	0.718533i	$0.255186\pi$
$479$			7.56518e10i			1.43707i	−0.695492	+	0.718533i	$0.744814\pi$
$480$		0			0
$481$	−2.33612e10			−0.436430
$482$	−3.84010e10	+	2.34983e10i	−0.711467	+	0.435360i
$483$		0			0
$484$	6.43886e8	−	1.25970e9i	0.0117335	−	0.0229555i
$485$	7.90806e10			1.42923
$486$		0			0
$487$			5.39416e10i			0.958977i	0.877548	+	0.479489i	$0.159178\pi$
$487$			5.39416e10i			0.958977i	−0.877548	+	0.479489i	$0.840822\pi$
$488$	−1.44294e9	−	1.87964e10i	−0.0254430	−	0.331433i
$489$		0			0
$490$	6.14057e10	−	3.75753e10i	1.06518	−	0.651806i
$491$		−	9.67425e10i		−	1.66453i	−0.554379	−	0.832264i	$-0.687044\pi$
$491$		−	9.67425e10i		−	1.66453i	0.554379	−	0.832264i	$-0.312956\pi$
$492$		0			0
$493$	−1.47989e10			−0.250519
$494$	2.18729e10	+	3.57448e10i	0.367282	+	0.600213i
$495$		0			0
$496$	−1.07235e10	+	7.74914e9i	−0.177178	+	0.128034i
$497$	2.85316e10			0.467628
$498$		0			0
$499$			1.21097e10i			0.195313i	0.995220	+	0.0976566i	$0.0311347\pi$
$499$			1.21097e10i			0.195313i	−0.995220	+	0.0976566i	$0.968865\pi$
$500$	−3.82650e9	+	7.48618e9i	−0.0612240	+	0.119779i
$501$		0			0
$502$	8.57651e9	+	1.40158e10i	0.135050	+	0.220700i
$503$		−	2.13349e10i		−	0.333286i	−0.986017	−	0.166643i	$-0.946707\pi$
$503$		−	2.13349e10i		−	0.333286i	0.986017	−	0.166643i	$-0.0532928\pi$
$504$		0			0
$505$	4.95155e10			0.761335
$506$	−8.71125e10	+	5.33058e10i	−1.32886	+	0.813153i
$507$		0			0
$508$	8.16447e10	+	4.17320e10i	1.22595	+	0.626635i
$509$	−1.22126e11			−1.81944			−0.909721	−	0.415221i	$-0.863704\pi$
$509$	−1.22126e11			−1.81944			−0.909721	+	0.415221i	$0.863704\pi$
$510$		0			0
$511$		−	4.34705e10i		−	0.637545i
$512$	−1.56564e10	−	6.69122e10i	−0.227830	−	0.973701i
$513$		0			0
$514$	−2.45790e10	+	1.50404e10i	−0.352137	+	0.215480i
$515$			8.85740e9i			0.125915i
$516$		0			0
$517$	−6.95383e10			−0.973333
$518$	1.49246e10	+	2.43899e10i	0.207293	+	0.338759i
$519$		0			0
$520$	3.29090e9	+	4.28690e10i	0.0450092	+	0.586313i
$521$	−8.66914e10			−1.17659			−0.588295	−	0.808646i	$-0.700201\pi$
$521$	−8.66914e10			−1.17659			−0.588295	+	0.808646i	$0.700201\pi$
$522$		0			0
$523$			1.54184e10i			0.206078i	0.994677	+	0.103039i	$0.0328567\pi$
$523$			1.54184e10i			0.206078i	−0.994677	+	0.103039i	$0.967143\pi$
$524$	7.11907e10	+	3.63885e10i	0.944274	+	0.482658i
$525$		0			0
$526$	−5.50757e10	−	9.00049e10i	−0.719478	−	1.17577i
$527$		−	2.59454e10i		−	0.336371i
$528$		0			0
$529$	−1.16786e11			−1.49131
$530$	−1.52884e10	+	9.35525e9i	−0.193757	+	0.118564i
$531$		0			0
$532$	2.33450e10	−	4.56722e10i	0.291438	−	0.570171i
$533$	−3.04044e10			−0.376727
$534$		0			0
$535$		−	1.03391e11i		−	1.26203i
$536$	9.54600e10	−	7.32814e9i	1.15654	−	0.0887840i
$537$		0			0
$538$	−1.07263e10	+	6.56361e9i	−0.128032	+	0.0783454i
$539$		−	7.19099e10i		−	0.851988i
$540$		0			0
$541$	1.38070e10			0.161180			0.0805899	−	0.996747i	$-0.474320\pi$
$541$	1.38070e10			0.161180			0.0805899	+	0.996747i	$0.474320\pi$
$542$	−4.05511e10	−	6.62687e10i	−0.469900	−	0.767912i
$543$		0			0
$544$	1.24338e11	+	5.19703e10i	1.41974	+	0.593416i
$545$	−3.78267e10			−0.428758
$546$		0			0
$547$		−	1.58922e11i		−	1.77514i	−0.460670	−	0.887572i	$-0.652391\pi$
$547$		−	1.58922e11i		−	1.77514i	0.460670	−	0.887572i	$-0.347609\pi$
$548$	2.35732e10	−	4.61188e10i	0.261395	−	0.511394i
$549$		0			0
$550$	5.15256e10	+	8.42032e10i	0.563082	+	0.920191i
$551$		−	2.59788e10i		−	0.281847i
$552$		0			0
$553$	3.75864e9			0.0401911
$554$	7.63614e10	−	4.67270e10i	0.810653	−	0.496054i
$555$		0			0
$556$	8.11726e10	+	4.14907e10i	0.849397	+	0.434162i
$557$	2.99226e10			0.310870			0.155435	−	0.987846i	$-0.450322\pi$
$557$	2.99226e10			0.310870			0.155435	+	0.987846i	$0.450322\pi$
$558$		0			0
$559$		−	2.03646e10i		−	0.208559i
$560$	4.26542e10	−	3.08233e10i	0.433721	−	0.313420i
$561$		0			0
$562$	−1.33374e11	+	8.16138e10i	−1.33698	+	0.818123i
$563$			9.29383e10i			0.925042i	0.886608	+	0.462521i	$0.153055\pi$
$563$			9.29383e10i			0.925042i	−0.886608	+	0.462521i	$0.846945\pi$
$564$		0			0
$565$	4.73903e10			0.465046
$566$	−1.16194e10	−	1.89885e10i	−0.113219	−	0.185023i
$567$		0			0
$568$	−1.31206e11	+	1.00723e10i	−1.26055	+	0.0967685i
$569$	1.27626e11			1.21756			0.608778	−	0.793341i	$-0.291660\pi$
$569$	1.27626e11			1.21756			0.608778	+	0.793341i	$0.291660\pi$
$570$		0			0
$571$			6.17431e10i			0.580823i	0.956902	+	0.290412i	$0.0937923\pi$
$571$			6.17431e10i			0.580823i	−0.956902	+	0.290412i	$0.906208\pi$
$572$	3.82412e10	+	1.95467e10i	0.357230	+	0.182595i
$573$		0			0
$574$	1.94243e10	+	3.17432e10i	0.178936	+	0.292417i
$575$			1.88581e11i			1.72515i
$576$		0			0
$577$	−1.29506e11			−1.16839			−0.584194	−	0.811614i	$-0.698589\pi$
$577$	−1.29506e11			−1.16839			−0.584194	+	0.811614i	$0.698589\pi$
$578$	−1.30219e11	+	7.96834e10i	−1.16671	+	0.713931i
$579$		0			0
$580$	1.21311e10	−	2.37333e10i	0.107198	−	0.209723i
$581$	1.76850e10			0.155203
$582$		0			0
$583$			1.79036e10i			0.154977i
$584$	1.53460e10	+	1.99905e11i	0.131930	+	1.71859i
$585$		0			0
$586$	1.80025e11	−	1.10161e11i	1.52666	−	0.934194i
$587$		−	1.10514e11i		−	0.930820i	−0.885095	−	0.465410i	$-0.845907\pi$
$587$		−	1.10514e11i		−	0.930820i	0.885095	−	0.465410i	$-0.154093\pi$
$588$		0			0
$589$	4.55462e10			0.378435
$590$	8.61300e9	+	1.40754e10i	0.0710798	+	0.116159i
$591$		0			0
$592$	−7.72432e10	−	1.06892e11i	−0.628888	−	0.870275i
$593$	−1.24751e11			−1.00884			−0.504422	−	0.863457i	$-0.668294\pi$
$593$	−1.24751e11			−1.00884			−0.504422	+	0.863457i	$0.668294\pi$
$594$		0			0
$595$			1.03202e11i			0.823415i
$596$	5.46692e10	−	1.06955e11i	0.433269	−	0.847649i
$597$		0			0
$598$	4.28224e10	+	6.99806e10i	0.334863	+	0.547234i
$599$			2.65710e10i			0.206396i	0.994661	+	0.103198i	$0.0329075\pi$
$599$			2.65710e10i			0.206396i	−0.994661	+	0.103198i	$0.967092\pi$
$600$		0			0
$601$	−2.32310e9			−0.0178062			−0.00890308	−	0.999960i	$-0.502834\pi$
$601$	−2.32310e9			−0.0178062			−0.00890308	+	0.999960i	$0.502834\pi$
$602$	−2.12613e10	+	1.30102e10i	−0.161884	+	0.0990601i
$603$		0			0
$604$	1.13092e11	+	5.78063e10i	0.849739	+	0.434337i
$605$	−4.99682e9			−0.0372969
$606$		0			0
$607$			7.34244e10i			0.540861i	0.962739	+	0.270431i	$0.0871661\pi$
$607$			7.34244e10i			0.540861i	−0.962739	+	0.270431i	$0.912834\pi$
$608$	−9.12318e10	+	2.18271e11i	−0.667624	+	1.59728i
$609$		0			0
$610$	−5.67950e10	+	3.47539e10i	−0.410195	+	0.251006i
$611$			5.58626e10i			0.400826i
$612$		0			0
$613$	1.67042e11			1.18300			0.591499	−	0.806306i	$-0.298536\pi$
$613$	1.67042e11			1.18300			0.591499	+	0.806306i	$0.298536\pi$
$614$	−8.60201e9	−	1.40574e10i	−0.0605238	−	0.0989082i
$615$		0			0
$616$	−4.02356e9	−	5.24129e10i	−0.0279439	−	0.364011i
$617$	−5.44122e8			−0.00375453			−0.00187727	−	0.999998i	$-0.500598\pi$
$617$	−5.44122e8			−0.00375453			−0.00187727	+	0.999998i	$0.500598\pi$
$618$		0			0
$619$			1.21943e11i			0.830608i	0.909683	+	0.415304i	$0.136325\pi$
$619$			1.21943e11i			0.830608i	−0.909683	+	0.415304i	$0.863675\pi$
$620$	4.16094e10	+	2.12683e10i	0.281595	+	0.143935i
$621$		0			0
$622$	8.62474e10	+	1.40946e11i	0.576215	+	0.941652i
$623$			7.51239e9i			0.0498684i
$624$		0			0
$625$	−1.37081e11			−0.898372
$626$	2.38914e10	−	1.46196e10i	0.155576	−	0.0952001i
$627$		0			0
$628$	1.14889e11	−	2.24769e11i	0.738652	−	1.44510i
$629$	2.58624e11			1.65221
$630$		0			0
$631$		−	8.33346e10i		−	0.525664i	−0.964842	−	0.262832i	$-0.915344\pi$
$631$		−	8.33346e10i		−	0.525664i	0.964842	−	0.262832i	$-0.0846564\pi$
$632$	−1.72846e10	+	1.32688e9i	−0.108341	+	0.00831695i
$633$		0			0
$634$	−1.70920e11	+	1.04589e11i	−1.05788	+	0.647334i
$635$		−	3.23858e11i		−	1.99186i
$636$		0			0
$637$	−5.77678e10			−0.350855
$638$	−1.38966e10	−	2.27099e10i	−0.0838738	−	0.137067i
$639$		0			0
$640$	−1.85270e11	+	1.56803e11i	−1.10430	+	0.934619i
$641$	−1.00359e11			−0.594461			−0.297230	−	0.954806i	$-0.596063\pi$
$641$	−1.00359e11			−0.594461			−0.297230	+	0.954806i	$0.596063\pi$
$642$		0			0
$643$			1.93698e11i			1.13313i	0.824016	+	0.566566i	$0.191729\pi$
$643$			1.93698e11i			1.13313i	−0.824016	+	0.566566i	$0.808271\pi$
$644$	4.57044e10	−	8.94162e10i	0.265714	−	0.519844i
$645$		0			0
$646$	−2.42148e11	−	3.95718e11i	−1.39043	−	2.27225i
$647$		−	4.50875e10i		−	0.257299i	−0.991690	−	0.128650i	$-0.958936\pi$
$647$		−	4.50875e10i		−	0.257299i	0.991690	−	0.128650i	$-0.0410643\pi$
$648$		0			0
$649$	1.64832e10			0.0929098
$650$	6.76434e10	−	4.13923e10i	0.378942	−	0.231882i
$651$		0			0
$652$	−3.23116e10	−	1.65158e10i	−0.178800	−	0.0913922i
$653$	1.52943e11			0.841156			0.420578	−	0.907256i	$-0.361827\pi$
$653$	1.52943e11			0.841156			0.420578	+	0.907256i	$0.361827\pi$
$654$		0			0
$655$		−	2.82390e11i		−	1.53421i
$656$	−1.00531e11	−	1.39118e11i	−0.542857	−	0.751223i
$657$		0			0
$658$	5.83224e10	−	3.56886e10i	0.311123	−	0.190382i
$659$			2.18458e11i			1.15831i	0.815217	+	0.579156i	$0.196618\pi$
$659$			2.18458e11i			1.15831i	−0.815217	+	0.579156i	$0.803382\pi$
$660$		0			0
$661$	3.70484e11			1.94073			0.970363	−	0.241654i	$-0.0776899\pi$
$661$	3.70484e11			1.94073			0.970363	+	0.241654i	$0.0776899\pi$
$662$	−1.50312e11	−	2.45641e11i	−0.782641	−	1.27899i
$663$		0			0
$664$	−8.13268e10	+	6.24318e9i	−0.418371	+	0.0321169i
$665$	−1.81167e11			−0.926385
$666$		0			0
$667$		−	5.08609e10i		−	0.256969i
$668$	−1.42870e11	−	7.30266e10i	−0.717520	−	0.366754i
$669$		0			0
$670$	−1.76502e11	−	2.88441e11i	−0.875894	−	1.43139i
$671$			6.65105e10i			0.328095i
$672$		0			0
$673$	2.24080e11			1.09230			0.546150	−	0.837687i	$-0.316093\pi$
$673$	2.24080e11			1.09230			0.546150	+	0.837687i	$0.316093\pi$
$674$	−6.17959e10	+	3.78141e10i	−0.299447	+	0.183238i
$675$		0			0
$676$	−7.93415e10	+	1.55224e11i	−0.379939	+	0.743314i
$677$	−1.16058e11			−0.552483			−0.276241	−	0.961088i	$-0.589089\pi$
$677$	−1.16058e11			−0.552483			−0.276241	+	0.961088i	$0.589089\pi$
$678$		0			0
$679$			7.76716e10i			0.365412i
$680$	−3.64324e10	−	4.74587e11i	−0.170393	−	2.21963i
$681$		0			0
$682$	3.98151e10	−	2.43636e10i	0.184039	−	0.112617i
$683$			2.91871e11i			1.34125i	0.741799	+	0.670623i	$0.233973\pi$
$683$			2.91871e11i			1.34125i	−0.741799	+	0.670623i	$0.766027\pi$
$684$		0			0
$685$	−1.82938e11			−0.830887
$686$	7.96610e10	+	1.30182e11i	0.359708	+	0.587835i
$687$		0			0
$688$	9.31804e10	−	6.73350e10i	0.415882	−	0.300530i
$689$	1.43826e10			0.0638207
$690$		0			0
$691$		−	3.60245e11i		−	1.58011i	−0.613039	−	0.790053i	$-0.710053\pi$
$691$		−	3.60245e11i		−	1.58011i	0.613039	−	0.790053i	$-0.289947\pi$
$692$	−3.79655e10	+	7.42760e10i	−0.165564	+	0.323910i
$693$		0			0
$694$	1.90849e11	+	3.11886e11i	0.822721	+	1.34449i
$695$		−	3.21985e11i		−	1.38006i
$696$		0			0
$697$	3.36596e11			1.42619
$698$	−9.87890e10	+	6.04509e10i	−0.416186	+	0.254672i
$699$		0			0
$700$	−8.64300e10	−	4.41780e10i	−0.359975	−	0.183998i
$701$	1.34090e11			0.555297			0.277648	−	0.960683i	$-0.410445\pi$
$701$	1.34090e11			0.555297			0.277648	+	0.960683i	$0.410445\pi$
$702$		0			0
$703$			4.54004e11i			1.85882i
$704$	3.70058e10	+	2.39607e11i	0.150653	+	0.975460i
$705$		0			0
$706$	−1.23189e11	+	7.53816e10i	−0.495853	+	0.303422i
$707$			4.86332e10i			0.194651i
$708$		0			0
$709$	−3.08644e11			−1.22144			−0.610722	−	0.791845i	$-0.709121\pi$
$709$	−3.08644e11			−1.22144			−0.610722	+	0.791845i	$0.709121\pi$
$710$	2.42596e11	+	3.96452e11i	0.954665	+	1.56012i
$711$		0			0
$712$	−2.65204e9	−	3.45468e10i	−0.0103195	−	0.134427i
$713$	8.91696e10			0.345031
$714$		0			0
$715$		−	1.51690e11i		−	0.580409i
$716$	−1.13066e11	−	5.77928e10i	−0.430210	−	0.219898i
$717$		0			0
$718$	7.46817e10	+	1.22045e11i	0.281007	+	0.459222i
$719$		−	1.71505e11i		−	0.641743i	−0.947123	−	0.320872i	$-0.896024\pi$
$719$		−	1.71505e11i		−	0.641743i	0.947123	−	0.320872i	$-0.103976\pi$
$720$		0			0
$721$	−8.69957e9			−0.0321927
$722$	4.62883e11	−	2.83247e11i	1.70342	−	1.04236i
$723$		0			0
$724$	−6.56680e10	+	1.28473e11i	−0.239001	+	0.467582i
$725$	−4.91623e10			−0.177943
$726$		0			0
$727$			3.25160e11i			1.16402i	0.813182	+	0.582009i	$0.197733\pi$
$727$			3.25160e11i			1.16402i	−0.813182	+	0.582009i	$0.802267\pi$
$728$	−4.21051e10	+	3.23226e9i	−0.149903	+	0.0115075i
$729$		0			0
$730$	6.04030e11	−	3.69618e11i	2.12700	−	1.30155i
$731$			2.25449e11i			0.789550i
$732$		0			0
$733$	−2.93827e11			−1.01783			−0.508915	−	0.860817i	$-0.669953\pi$
$733$	−2.93827e11			−1.01783			−0.508915	+	0.860817i	$0.669953\pi$
$734$	7.80117e10	+	1.27487e11i	0.268767	+	0.439219i
$735$		0			0
$736$	−1.78612e11	+	4.27328e11i	−0.608695	+	1.45630i
$737$	−3.37782e11			−1.14490
$738$		0			0
$739$			6.13111e10i			0.205571i	0.994704	+	0.102785i	$0.0327755\pi$
$739$			6.13111e10i			0.205571i	−0.994704	+	0.102785i	$0.967225\pi$
$740$	−2.12002e11	+	4.14761e11i	−0.706989	+	1.38316i
$741$		0			0
$742$	−9.18855e9	−	1.50160e10i	−0.0303132	−	0.0495379i
$743$			1.25399e11i			0.411471i	0.978608	+	0.205735i	$0.0659586\pi$
$743$			1.25399e11i			0.411471i	−0.978608	+	0.205735i	$0.934041\pi$
$744$		0			0
$745$	−4.24255e11			−1.37722
$746$	1.10578e11	−	6.76645e10i	0.357036	−	0.218477i
$747$		0			0
$748$	−4.23355e11	−	2.16395e11i	−1.35238	−	0.691258i
$749$	1.01549e11			0.322663
$750$		0			0
$751$			7.03859e10i			0.221272i	0.993861	+	0.110636i	$0.0352887\pi$
$751$			7.03859e10i			0.221272i	−0.993861	+	0.110636i	$0.964711\pi$
$752$	−2.55605e11	+	1.84708e11i	−0.799278	+	0.577583i
$753$		0			0
$754$	−1.82437e10	+	1.11636e10i	−0.0564451	+	0.0345399i
$755$		−	4.48600e11i		−	1.38061i
$756$		0			0
$757$	2.29777e11			0.699717			0.349859	−	0.936802i	$-0.386230\pi$
$757$	2.29777e11			0.699717			0.349859	+	0.936802i	$0.386230\pi$
$758$	2.30863e11	+	3.77278e11i	0.699324	+	1.14284i
$759$		0			0
$760$	8.33120e11	−	6.39557e10i	2.49720	−	0.191701i
$761$	5.18557e11			1.54617			0.773086	−	0.634301i	$-0.218712\pi$
$761$	5.18557e11			1.54617			0.773086	+	0.634301i	$0.218712\pi$
$762$		0			0
$763$		−	3.71527e10i		−	0.109621i
$764$	1.94824e11	+	9.95826e10i	0.571833	+	0.292287i
$765$		0			0
$766$	2.54322e11	+	4.15613e11i	0.738700	+	1.20719i
$767$		−	1.32415e10i		−	0.0382610i
$768$		0			0
$769$	−3.27159e11			−0.935521			−0.467761	−	0.883855i	$-0.654939\pi$
$769$	−3.27159e11			−0.935521			−0.467761	+	0.883855i	$0.654939\pi$
$770$	−1.58370e11	+	9.69096e10i	−0.450516	+	0.275679i
$771$		0			0
$772$	1.19547e11	−	2.33882e11i	0.336566	−	0.658459i
$773$	4.27537e11			1.19744			0.598722	−	0.800957i	$-0.295675\pi$
$773$	4.27537e11			1.19744			0.598722	+	0.800957i	$0.295675\pi$
$774$		0			0
$775$		−	8.61916e10i		−	0.238923i
$776$	−2.74198e10	−	3.57184e11i	−0.0756165	−	0.985019i
$777$		0			0
$778$	−2.20252e10	+	1.34776e10i	−0.0601176	+	0.0367871i
$779$			5.90881e11i			1.60454i
$780$		0			0
$781$	4.64270e11			1.24786
$782$	−4.74072e11	−	7.74730e11i	−1.26770	−	2.07168i
$783$		0			0
$784$	−1.91008e11	−	2.64323e11i	−0.505576	−	0.699633i
$785$	−8.91586e11			−2.34793
$786$		0			0
$787$		−	6.74861e11i		−	1.75920i	−0.475713	−	0.879601i	$-0.657810\pi$
$787$		−	6.74861e11i		−	1.75920i	0.475713	−	0.879601i	$-0.342190\pi$
$788$	−9.84050e10	+	1.92520e11i	−0.255219	+	0.499311i
$789$		0			0
$790$	3.19587e10	+	5.22270e10i	0.0820505	+	0.134087i
$791$			4.65459e10i			0.118898i
$792$		0			0
$793$	5.34302e10			0.135112
$794$	4.98666e11	−	3.05144e11i	1.25467	−	0.767754i
$795$		0			0
$796$	1.76106e11	+	9.00151e10i	0.438654	+	0.224214i
$797$	1.45915e11			0.361631			0.180816	−	0.983517i	$-0.442126\pi$
$797$	1.45915e11			0.361631			0.180816	+	0.983517i	$0.442126\pi$
$798$		0			0
$799$		−	6.18435e11i		−	1.51742i
$800$	4.13056e11	+	1.72647e11i	1.00844	+	0.421501i
$801$		0			0
$802$	−3.58710e11	+	2.19502e11i	−0.867054	+	0.530567i
$803$		−	7.07357e11i		−	1.70128i
$804$		0			0
$805$	−3.54685e11			−0.844615
$806$	−1.95721e10	−	3.19849e10i	−0.0463765	−	0.0757886i
$807$		0			0
$808$	−1.71686e10	−	2.23647e11i	−0.0402800	−	0.524707i
$809$	−8.40339e11			−1.96183			−0.980913	−	0.194448i	$-0.937709\pi$
$809$	−8.40339e11			−1.96183			−0.980913	+	0.194448i	$0.937709\pi$
$810$		0			0
$811$		−	4.58864e10i		−	0.106072i	−0.998593	−	0.0530360i	$-0.983110\pi$
$811$		−	4.58864e10i		−	0.106072i	0.998593	−	0.0530360i	$-0.0168898\pi$
$812$	2.33105e10	+	1.19149e10i	0.0536200	+	0.0274074i
$813$		0			0
$814$	2.42856e11	+	3.96875e11i	0.553160	+	0.903976i
$815$			1.28169e11i			0.290505i
$816$		0			0
$817$	−3.95768e11			−0.888284
$818$	−2.31857e11	+	1.41878e11i	−0.517853	+	0.316884i
$819$		0			0
$820$	−2.75918e11	+	5.39808e11i	−0.610274	+	1.19394i
$821$	−6.15115e11			−1.35389			−0.676946	−	0.736033i	$-0.736697\pi$
$821$	−6.15115e11			−1.35389			−0.676946	+	0.736033i	$0.736697\pi$
$822$		0			0
$823$			2.81774e11i			0.614188i	0.951679	+	0.307094i	$0.0993566\pi$
$823$			2.81774e11i			0.614188i	−0.951679	+	0.307094i	$0.900643\pi$
$824$	4.00062e10	−	3.07114e9i	0.0867798	−	0.00666178i
$825$		0			0
$826$	−1.38246e10	+	8.45953e9i	−0.0296983	+	0.0181730i
$827$		−	3.61753e10i		−	0.0773375i	−0.999252	−	0.0386688i	$-0.987688\pi$
$827$		−	3.61753e10i		−	0.0773375i	0.999252	−	0.0386688i	$-0.0123117\pi$
$828$		0			0
$829$	3.05903e11			0.647687			0.323843	−	0.946111i	$-0.395025\pi$
$829$	3.05903e11			0.647687			0.323843	+	0.946111i	$0.395025\pi$
$830$	1.50371e11	+	2.45736e11i	0.316848	+	0.517793i
$831$		0			0
$832$	1.92485e11	−	2.97280e10i	0.401702	−	0.0620402i
$833$	6.39527e11			1.32825
$834$		0			0
$835$			5.66716e11i			1.16579i
$836$	3.79872e11	−	7.43184e11i	0.777701	−	1.52150i
$837$		0			0
$838$	−4.00481e11	−	6.54467e11i	−0.812093	−	1.32712i
$839$		−	3.84879e11i		−	0.776741i	−0.921503	−	0.388370i	$-0.873038\pi$
$839$		−	3.84879e11i		−	0.776741i	0.921503	−	0.388370i	$-0.126962\pi$
$840$		0			0
$841$	−4.86987e11			−0.973495
$842$	−4.11559e10	+	2.51841e10i	−0.0818810	+	0.0501046i
$843$		0			0
$844$	5.01409e11	+	2.56291e11i	0.988148	+	0.505084i
$845$	6.15723e11			1.20770
$846$		0			0
$847$		−	4.90779e9i		−	0.00953569i
$848$	4.75558e10	+	6.58092e10i	0.0919645	+	0.127263i
$849$		0			0
$850$	−7.48857e11	+	4.58240e11i	−1.43457	+	0.877843i
$851$			8.88840e11i			1.69475i
$852$		0			0
$853$	1.53208e11			0.289390			0.144695	−	0.989476i	$-0.453780\pi$
$853$	1.53208e11			0.289390			0.144695	+	0.989476i	$0.453780\pi$
$854$	−3.41347e10	−	5.57830e10i	−0.0641748	−	0.104875i
$855$		0			0
$856$	−4.66987e11	+	3.58490e10i	−0.869781	+	0.0667701i
$857$	−1.07815e11			−0.199873			−0.0999365	−	0.994994i	$-0.531864\pi$
$857$	−1.07815e11			−0.199873			−0.0999365	+	0.994994i	$0.531864\pi$
$858$		0			0
$859$		−	1.94089e11i		−	0.356474i	−0.983988	−	0.178237i	$-0.942961\pi$
$859$		−	1.94089e11i		−	0.356474i	0.983988	−	0.178237i	$-0.0570394\pi$
$860$	−3.61559e11	−	1.84808e11i	−0.660976	−	0.337852i
$861$		0			0
$862$	−1.26693e11	−	2.07041e11i	−0.229468	−	0.374997i
$863$		−	9.36925e11i		−	1.68913i	−0.535457	−	0.844563i	$-0.679861\pi$
$863$		−	9.36925e11i		−	1.68913i	0.535457	−	0.844563i	$-0.320139\pi$
$864$		0			0
$865$	2.94628e11			0.526272
$866$	−7.85677e11	+	4.80771e11i	−1.39692	+	0.854804i
$867$		0			0
$868$	−2.08893e10	+	4.08680e10i	−0.0367998	+	0.0719953i
$869$	6.11611e10			0.107250
$870$		0			0
$871$			2.71352e11i			0.471478i
$872$	1.31157e10	+	1.70852e11i	0.0226843	+	0.295498i
$873$		0			0
$874$	1.36001e12	−	8.32216e11i	2.33075	−	1.42623i
$875$			2.91661e10i			0.0497560i
$876$		0			0
$877$	8.90245e11			1.50491			0.752456	−	0.658643i	$-0.228869\pi$
$877$	8.90245e11			1.50491			0.752456	+	0.658643i	$0.228869\pi$
$878$	−4.61038e11	−	7.53430e11i	−0.775816	−	1.26784i
$879$		0			0
$880$	6.94075e11	−	5.01561e11i	1.15738	−	0.836359i
$881$	−2.69111e11			−0.446713			−0.223356	−	0.974737i	$-0.571701\pi$
$881$	−2.69111e11			−0.446713			−0.223356	+	0.974737i	$0.571701\pi$
$882$		0			0
$883$			4.13945e11i			0.680926i	0.940258	+	0.340463i	$0.110584\pi$
$883$			4.13945e11i			0.680926i	−0.940258	+	0.340463i	$0.889416\pi$
$884$	−1.73837e11	+	3.40096e11i	−0.284665	+	0.556920i
$885$		0			0
$886$	−5.82446e11	−	9.51834e11i	−0.945193	−	1.54464i
$887$			3.61899e11i			0.584645i	0.956320	+	0.292323i	$0.0944281\pi$
$887$			3.61899e11i			0.584645i	−0.956320	+	0.292323i	$0.905572\pi$
$888$		0			0
$889$	3.18087e11			0.509259
$890$	−1.04386e11	+	6.38758e10i	−0.166373	+	0.101807i
$891$		0			0
$892$	−1.05293e12	−	5.38197e11i	−1.66318	−	0.850123i
$893$	1.08564e12			1.70718
$894$		0			0
$895$			4.48496e11i			0.698982i
$896$	−1.54009e11	−	1.81969e11i	−0.238954	−	0.282335i
$897$		0			0
$898$	−2.00793e11	+	1.22869e11i	−0.308775	+	0.188945i
$899$			2.32462e10i			0.0355887i
$900$		0			0
$901$	−1.59225e11			−0.241608
$902$	3.16074e11	+	5.16530e11i	0.477489	+	0.780313i
$903$		0			0
$904$	−1.64317e10	−	2.14048e11i	−0.0246042	−	0.320506i
$905$	5.09611e11			0.759704
$906$		0			0
$907$			2.54784e11i			0.376482i	0.982123	+	0.188241i	$0.0602785\pi$
$907$			2.54784e11i			0.376482i	−0.982123	+	0.188241i	$0.939721\pi$
$908$	−2.83102e11	−	1.44705e11i	−0.416485	−	0.212883i
$909$		0			0
$910$	7.78510e10	+	1.27224e11i	0.113527	+	0.185526i
$911$			4.42772e11i			0.642845i	0.946936	+	0.321422i	$0.104161\pi$
$911$			4.42772e11i			0.642845i	−0.946936	+	0.321422i	$0.895839\pi$
$912$		0			0
$913$	2.87772e11			0.414158
$914$	−8.69654e11	+	5.32158e11i	−1.24613	+	0.762528i
$915$		0			0
$916$	−5.63840e11	+	1.10310e12i	−0.800893	+	1.56687i
$917$	2.77358e11			0.392251
$918$		0			0
$919$		−	1.21088e12i		−	1.69761i	−0.528708	−	0.848804i	$-0.677323\pi$
$919$		−	1.21088e12i		−	1.69761i	0.528708	−	0.848804i	$-0.322677\pi$
$920$	1.63107e12	−	1.25211e11i	2.27678	−	0.174780i
$921$		0			0
$922$	−5.36735e11	+	3.28439e11i	−0.742739	+	0.454496i
$923$		−	3.72964e11i		−	0.513879i
$924$		0			0
$925$	8.59156e11			1.17356
$926$	5.77271e11	+	9.43378e11i	0.785120	+	1.28304i
$927$		0			0
$928$	−1.11403e11	−	4.65634e10i	−0.150212	−	0.0627846i
$929$	−1.00636e12			−1.35110			−0.675552	−	0.737313i	$-0.736095\pi$
$929$	−1.00636e12			−1.35110			−0.675552	+	0.737313i	$0.736095\pi$
$930$		0			0
$931$			1.12266e12i			1.49435i
$932$	1.47297e11	−	2.88173e11i	0.195223	−	0.381935i
$933$		0			0
$934$	3.74901e11	+	6.12663e11i	0.492639	+	0.805072i
$935$			1.67931e12i			2.19728i
$936$		0			0
$937$	−9.83820e11			−1.27631			−0.638156	−	0.769907i	$-0.720303\pi$
$937$	−9.83820e11			−1.27631			−0.638156	+	0.769907i	$0.720303\pi$
$938$	2.83301e11	−	1.73357e11i	0.365963	−	0.223940i
$939$		0			0
$940$	9.91800e11	+	5.06950e11i	1.27032	+	0.649313i
$941$	5.99824e11			0.765007			0.382503	−	0.923954i	$-0.375062\pi$
$941$	5.99824e11			0.765007			0.382503	+	0.923954i	$0.375062\pi$
$942$		0			0
$943$			1.15682e12i			1.46291i
$944$	6.05879e10	−	4.37827e10i	0.0762953	−	0.0551334i
$945$		0			0
$946$	−3.45967e11	+	2.11704e11i	−0.431987	+	0.264341i
$947$		−	4.79898e11i		−	0.596690i	−0.954458	−	0.298345i	$-0.903565\pi$
$947$		−	4.79898e11i		−	0.596690i	0.954458	−	0.298345i	$-0.0964347\pi$
$948$		0			0
$949$	−5.68245e11			−0.700601
$950$	−8.04422e11	−	1.31459e12i	−0.987619	−	1.61397i
$951$		0			0
$952$	4.66131e11	−	3.57833e10i	0.567492	−	0.0435644i
$953$	−3.29855e11			−0.399900			−0.199950	−	0.979806i	$-0.564078\pi$
$953$	−3.29855e11			−0.399900			−0.199950	+	0.979806i	$0.564078\pi$
$954$		0			0
$955$		−	7.72802e11i		−	0.929084i
$956$	7.86911e11	+	4.02223e11i	0.942093	+	0.481543i
$957$		0			0
$958$	−6.31785e11	−	1.03246e12i	−0.750080	−	1.22578i
$959$		−	1.79678e11i		−	0.212433i
$960$		0			0
$961$	8.12136e11			0.952215
$962$	3.18824e11	−	1.95095e11i	0.372264	−	0.227795i
$963$		0			0
$964$	3.27842e11	−	6.41391e11i	0.379626	−	0.742703i
$965$	−9.27735e11			−1.06983
$966$		0			0
$967$		−	1.51059e12i		−	1.72759i	−0.503844	−	0.863795i	$-0.668081\pi$
$967$		−	1.51059e12i		−	1.72759i	0.503844	−	0.863795i	$-0.331919\pi$
$968$	1.73256e9	+	2.25691e10i	0.00197327	+	0.0257048i
$969$		0			0
$970$	−1.07926e12	+	6.60421e11i	−1.21910	+	0.745991i
$971$		−	2.03838e11i		−	0.229302i	−0.993406	−	0.114651i	$-0.963425\pi$
$971$		−	2.03838e11i		−	0.229302i	0.993406	−	0.114651i	$-0.0365750\pi$
$972$		0			0
$973$	3.16248e11			0.352839
$974$	−4.50479e11	−	7.36174e11i	−0.500540	−	0.817984i
$975$		0			0
$976$	1.76666e11	+	2.44476e11i	0.194694	+	0.269424i
$977$	6.73129e11			0.738789			0.369394	−	0.929273i	$-0.379565\pi$
$977$	6.73129e11			0.738789			0.369394	+	0.929273i	$0.379565\pi$
$978$		0			0
$979$			1.22243e11i			0.133074i
$980$	−5.24240e11	+	1.02563e12i	−0.568363	+	1.11195i
$981$		0			0
$982$	8.07919e11	+	1.32030e12i	0.868804	+	1.41980i
$983$			1.18974e12i			1.27420i	0.770780	+	0.637101i	$0.219867\pi$
$983$			1.18974e12i			1.27420i	−0.770780	+	0.637101i	$0.780133\pi$
$984$		0			0
$985$	7.63663e11			0.811254
$986$	2.01969e11	−	1.23589e11i	0.213687	−	0.130759i
$987$		0			0
$988$	−5.97026e11	−	3.05165e11i	−0.626564	−	0.320263i
$989$	−7.74827e11			−0.809878
$990$		0			0
$991$		−	1.02703e11i		−	0.106485i	−0.998582	−	0.0532424i	$-0.983044\pi$
$991$		−	1.02703e11i		−	0.106485i	0.998582	−	0.0532424i	$-0.0169556\pi$
$992$	8.16352e10	−	1.95311e11i	0.0843006	−	0.201688i
$993$		0			0
$994$	−3.89388e11	+	2.38274e11i	−0.398875	+	0.244079i
$995$		−	6.98554e11i		−	0.712702i
$996$		0			0
$997$	−6.63905e11			−0.671932			−0.335966	−	0.941874i	$-0.609063\pi$
$997$	−6.63905e11			−0.671932			−0.335966	+	0.941874i	$0.609063\pi$
$998$	−1.01131e11	−	1.65269e11i	−0.101944	−	0.166597i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.9.d.c.19.2		8
3.2	odd	2		12.9.d.a.7.7	✓	8
4.3	odd	2	inner	36.9.d.c.19.1		8
12.11	even	2		12.9.d.a.7.8	yes	8
24.5	odd	2		192.9.g.e.127.1		8
24.11	even	2		192.9.g.e.127.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.9.d.a.7.7	✓	8	3.2	odd	2
12.9.d.a.7.8	yes	8	12.11	even	2
36.9.d.c.19.1		8	4.3	odd	2	inner
36.9.d.c.19.2		8	1.1	even	1	trivial
192.9.g.e.127.1		8	24.5	odd	2
192.9.g.e.127.5		8	24.11	even	2

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.6476 + 8.35123i) q^{2} +(116.514 - 227.948i) q^{4} -904.196 q^{5} -888.085i q^{7} +(313.513 + 4083.98i) q^{8} +(12340.1 - 7551.15i) q^{10} -14451.0i q^{11} -11609.0 q^{13} +(7416.60 + 12120.2i) q^{14} +(-38385.0 - 53118.4i) q^{16} +128520. q^{17} +225611. i q^{19} +(-105352. + 206110. i) q^{20} +(120684. + 197222. i) q^{22} +441698. i q^{23} +426946. q^{25} +(158435. - 96949.7i) q^{26} +(-202438. - 103474. i) q^{28} -115149. q^{29} -201879. i q^{31} +(967466. + 404376. i) q^{32} +(-1.75398e6 + 1.07330e6i) q^{34} +803004. i q^{35} +2.01233e6 q^{37} +(-1.88413e6 - 3.07905e6i) q^{38} +(-283478. - 3.69272e6i) q^{40} +2.61903e6 q^{41} +1.75420e6i q^{43} +(-3.29409e6 - 1.68375e6i) q^{44} +(-3.68872e6 - 6.02811e6i) q^{46} -4.81199e6i q^{47} +4.97611e6 q^{49} +(-5.82679e6 + 3.56553e6i) q^{50} +(-1.35261e6 + 2.64626e6i) q^{52} -1.23892e6 q^{53} +1.30666e7i q^{55} +(3.62693e6 - 278427. i) q^{56} +(1.57150e6 - 961634. i) q^{58} +1.14062e6i q^{59} -4.60247e6 q^{61} +(1.68594e6 + 2.75517e6i) q^{62} +(-1.65806e7 + 2.56077e6i) q^{64} +1.04968e7 q^{65} -2.33742e7i q^{67} +(1.49743e7 - 2.92958e7i) q^{68} +(-6.70607e6 - 1.09591e7i) q^{70} +3.21271e7i q^{71} +4.89485e7 q^{73} +(-2.74635e7 + 1.68054e7i) q^{74} +(5.14277e7 + 2.62868e7i) q^{76} -1.28338e7 q^{77} +4.23230e6i q^{79} +(3.47076e7 + 4.80294e7i) q^{80} +(-3.57434e7 + 2.18721e7i) q^{82} +1.99136e7i q^{83} -1.16207e8 q^{85} +(-1.46497e7 - 2.39407e7i) q^{86} +(5.90178e7 - 4.53060e6i) q^{88} -8.45908e6 q^{89} +1.03098e7i q^{91} +(1.00684e8 + 5.14639e7i) q^{92} +(4.01860e7 + 6.56721e7i) q^{94} -2.03997e8i q^{95} -8.74596e7 q^{97} +(-6.79119e7 + 4.15566e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 52 q^{4} + 336 q^{5} + 12960 q^{8} + 36628 q^{10} - 2864 q^{13} - 52728 q^{14} + 99440 q^{16} + 193200 q^{17} - 335592 q^{20} - 556968 q^{22} - 579048 q^{25} - 21564 q^{26} - 594672 q^{28}+ \cdots - 691081830 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 - 52 * q^4 + 336 * q^5 + 12960 * q^8 + 36628 * q^10 - 2864 * q^13 - 52728 * q^14 + 99440 * q^16 + 193200 * q^17 - 335592 * q^20 - 556968 * q^22 - 579048 * q^25 - 21564 * q^26 - 594672 * q^28 - 2063472 * q^29 + 3602784 * q^32 + 1568476 * q^34 + 7470352 * q^37 - 3659400 * q^38 + 1749184 * q^40 + 8865456 * q^41 - 2395920 * q^44 - 13649856 * q^46 - 18923896 * q^49 - 14581842 * q^50 + 18592888 * q^52 - 8706672 * q^53 + 45565632 * q^56 - 8816444 * q^58 + 13457296 * q^61 - 80783976 * q^62 + 1268864 * q^64 - 7293408 * q^65 + 117288264 * q^68 - 60373104 * q^70 + 94738960 * q^73 - 119548428 * q^74 + 144621360 * q^76 + 56971392 * q^77 + 163857888 * q^80 - 188383460 * q^82 - 201200416 * q^85 - 240327384 * q^86 + 156323520 * q^88 - 188992272 * q^89 + 387657984 * q^92 - 38749872 * q^94 - 123291632 * q^97 - 691081830 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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