LMFDB - Embedded newform 64.22.e.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,22,Mod(17,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("64.17");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	64.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$178.865500344$
Analytic rank:	$0$
Dimension:	$82$
Relative dimension:	$41$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	64.49
Dual form			64.22.e.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-117950. + 117950. i) q^{3} +(2.07522e7 + 2.07522e7i) q^{5} +1.29970e9i q^{7} -1.73642e10i q^{9} +O(q^{10})$	\(q+(-117950. + 117950. i) q^{3} +(2.07522e7 + 2.07522e7i) q^{5} +1.29970e9i q^{7} -1.73642e10i q^{9} +(-5.54435e10 - 5.54435e10i) q^{11} +(5.16123e11 - 5.16123e11i) q^{13} -4.89545e12 q^{15} +9.53487e12 q^{17} +(9.83239e12 - 9.83239e12i) q^{19} +(-1.53300e14 - 1.53300e14i) q^{21} +2.30915e12i q^{23} +3.84467e14i q^{25} +(8.14309e14 + 8.14309e14i) q^{27} +(-6.33852e14 + 6.33852e14i) q^{29} +5.23093e15 q^{31} +1.30792e16 q^{33} +(-2.69716e16 + 2.69716e16i) q^{35} +(3.18380e16 + 3.18380e16i) q^{37} +1.21754e17i q^{39} +2.66193e15i q^{41} +(2.83749e15 + 2.83749e15i) q^{43} +(3.60344e17 - 3.60344e17i) q^{45} +1.54686e17 q^{47} -1.13067e18 q^{49} +(-1.12464e18 + 1.12464e18i) q^{51} +(6.19582e17 + 6.19582e17i) q^{53} -2.30114e18i q^{55} +2.31947e18i q^{57} +(2.28518e18 + 2.28518e18i) q^{59} +(5.87506e18 - 5.87506e18i) q^{61} +2.25682e19 q^{63} +2.14213e19 q^{65} +(-1.94499e18 + 1.94499e18i) q^{67} +(-2.72365e17 - 2.72365e17i) q^{69} +3.58026e19i q^{71} -3.87758e19i q^{73} +(-4.53480e19 - 4.53480e19i) q^{75} +(7.20599e19 - 7.20599e19i) q^{77} +1.23530e20 q^{79} -1.04604e19 q^{81} +(4.84009e19 - 4.84009e19i) q^{83} +(1.97869e20 + 1.97869e20i) q^{85} -1.49526e20i q^{87} -7.40615e19i q^{89} +(6.70805e20 + 6.70805e20i) q^{91} +(-6.16989e20 + 6.16989e20i) q^{93} +4.08086e20 q^{95} -6.30147e20 q^{97} +(-9.62731e20 + 9.62731e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 2 q^{3} - 2 q^{5}+O(q^{10}) $ 82 * q + 2 * q^3 - 2 * q^5	$ 82 q + 2 q^{3} - 2 q^{5} - 67333320738 q^{11} - 2 q^{13} - 4613203124996 q^{15} - 4 q^{17} + 46007763621434 q^{19} + 20920706404 q^{21} - 11\!\cdots\!20 q^{27}+ \cdots - 27\!\cdots\!38 q^{99}+O(q^{100}) $ 82 * q + 2 * q^3 - 2 * q^5 - 67333320738 * q^11 - 2 * q^13 - 4613203124996 * q^15 - 4 * q^17 + 46007763621434 * q^19 + 20920706404 * q^21 - 1147760716556920 * q^27 - 2433173450216602 * q^29 + 9835539443769616 * q^31 - 4 * q^33 + 19253478556034884 * q^35 - 7245708527119386 * q^37 - 215332019803969386 * q^43 + 953653395699842 * q^45 - 1051982644716600976 * q^47 - 5585458640832840074 * q^49 - 3238772068175213124 * q^51 + 1889987679210147606 * q^53 - 3631979197965016922 * q^59 + 10385362452353654062 * q^61 + 17464422381302680956 * q^63 - 9364161130572538716 * q^65 + 17102217044572669130 * q^67 - 3951842785111207532 * q^69 - 145960939174166395366 * q^75 - 82041801652678580764 * q^77 - 204448210818924484480 * q^79 - 802405920297757300870 * q^81 - 317463236552669319678 * q^83 + 323656241286464843748 * q^85 - 144326756239046079748 * q^91 - 669717759565183008560 * q^93 + 1411330138695550130700 * q^95 - 4 * q^97 - 2710306841526615010238 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−117950.	+	117950.i	−1.15326	+	1.15326i	−0.167360	+	0.985896i	$0.553524\pi$
$3$	−117950.	+	117950.i	−1.15326	+	1.15326i	−0.985896	+	0.167360i	$0.946476\pi$
$4$		0			0
$5$	2.07522e7	+	2.07522e7i	0.950338	+	0.950338i	0.998824	−	0.0484857i	$-0.0154395\pi$
$5$	2.07522e7	+	2.07522e7i	0.950338	+	0.950338i	−0.0484857	+	0.998824i	$0.515440\pi$
$6$		0			0
$7$			1.29970e9i			1.73906i	0.493883	+	0.869528i	$0.335577\pi$
$7$			1.29970e9i			1.73906i	−0.493883	+	0.869528i	$0.664423\pi$
$8$		0			0
$9$		−	1.73642e10i		−	1.66000i
$10$		0			0
$11$	−5.54435e10	−	5.54435e10i	−0.644507	−	0.644507i	0.307153	−	0.951660i	$-0.400624\pi$
$11$	−5.54435e10	−	5.54435e10i	−0.644507	−	0.644507i	−0.951660	+	0.307153i	$0.900624\pi$
$12$		0			0
$13$	5.16123e11	−	5.16123e11i	1.03836	−	1.03836i	0.0391257	−	0.999234i	$-0.487543\pi$
$13$	5.16123e11	−	5.16123e11i	1.03836	−	1.03836i	0.999234	−	0.0391257i	$-0.0124573\pi$
$14$		0			0
$15$	−4.89545e12			−2.19197
$16$		0			0
$17$	9.53487e12			1.14710			0.573550	−	0.819171i	$-0.305566\pi$
$17$	9.53487e12			1.14710			0.573550	+	0.819171i	$0.305566\pi$
$18$		0			0
$19$	9.83239e12	−	9.83239e12i	0.367914	−	0.367914i	−0.498802	−	0.866716i	$-0.666227\pi$
$19$	9.83239e12	−	9.83239e12i	0.367914	−	0.367914i	0.866716	+	0.498802i	$0.166227\pi$
$20$		0			0
$21$	−1.53300e14	−	1.53300e14i	−2.00558	−	2.00558i
$22$		0			0
$23$			2.30915e12i			0.0116228i	0.999983	+	0.00581140i	$0.00184984\pi$
$23$			2.30915e12i			0.0116228i	−0.999983	+	0.00581140i	$0.998150\pi$
$24$		0			0
$25$			3.84467e14i			0.806285i
$26$		0			0
$27$	8.14309e14	+	8.14309e14i	0.761149	+	0.761149i
$28$		0			0
$29$	−6.33852e14	+	6.33852e14i	−0.279775	+	0.279775i	−0.833019	−	0.553244i	$-0.813390\pi$
$29$	−6.33852e14	+	6.33852e14i	−0.279775	+	0.279775i	0.553244	+	0.833019i	$0.313390\pi$
$30$		0			0
$31$	5.23093e15			1.14625			0.573127	−	0.819466i	$-0.305730\pi$
$31$	5.23093e15			1.14625			0.573127	+	0.819466i	$0.305730\pi$
$32$		0			0
$33$	1.30792e16			1.48656
$34$		0			0
$35$	−2.69716e16	+	2.69716e16i	−1.65269	+	1.65269i
$36$		0			0
$37$	3.18380e16	+	3.18380e16i	1.08850	+	1.08850i	0.995683	+	0.0928149i	$0.0295865\pi$
$37$	3.18380e16	+	3.18380e16i	1.08850	+	1.08850i	0.0928149	+	0.995683i	$0.470414\pi$
$38$		0			0
$39$			1.21754e17i			2.39499i
$40$		0			0
$41$			2.66193e15i			0.0309717i	0.999880	+	0.0154859i	$0.00492950\pi$
$41$			2.66193e15i			0.0309717i	−0.999880	+	0.0154859i	$0.995071\pi$
$42$		0			0
$43$	2.83749e15	+	2.83749e15i	0.0200224	+	0.0200224i	0.717047	−	0.697025i	$-0.245493\pi$
$43$	2.83749e15	+	2.83749e15i	0.0200224	+	0.0200224i	−0.697025	+	0.717047i	$0.745493\pi$
$44$		0			0
$45$	3.60344e17	−	3.60344e17i	1.57756	−	1.57756i
$46$		0			0
$47$	1.54686e17			0.428968			0.214484	−	0.976728i	$-0.431193\pi$
$47$	1.54686e17			0.428968			0.214484	+	0.976728i	$0.431193\pi$
$48$		0			0
$49$	−1.13067e18			−2.02432
$50$		0			0
$51$	−1.12464e18	+	1.12464e18i	−1.32290	+	1.32290i
$52$		0			0
$53$	6.19582e17	+	6.19582e17i	0.486634	+	0.486634i	0.907242	−	0.420608i	$-0.138183\pi$
$53$	6.19582e17	+	6.19582e17i	0.486634	+	0.486634i	−0.420608	+	0.907242i	$0.638183\pi$
$54$		0			0
$55$		−	2.30114e18i		−	1.22500i
$56$		0			0
$57$			2.31947e18i			0.848598i
$58$		0			0
$59$	2.28518e18	+	2.28518e18i	0.582067	+	0.582067i	0.935471	−	0.353403i	$-0.114976\pi$
$59$	2.28518e18	+	2.28518e18i	0.582067	+	0.582067i	−0.353403	+	0.935471i	$0.614976\pi$
$60$		0			0
$61$	5.87506e18	−	5.87506e18i	1.05451	−	1.05451i	0.0560804	−	0.998426i	$-0.482140\pi$
$61$	5.87506e18	−	5.87506e18i	1.05451	−	1.05451i	0.998426	−	0.0560804i	$-0.0178603\pi$
$62$		0			0
$63$	2.25682e19			2.88683
$64$		0			0
$65$	2.14213e19			1.97359
$66$		0			0
$67$	−1.94499e18	+	1.94499e18i	−0.130356	+	0.130356i	−0.769275	−	0.638918i	$-0.779382\pi$
$67$	−1.94499e18	+	1.94499e18i	−0.130356	+	0.130356i	0.638918	+	0.769275i	$0.279382\pi$
$68$		0			0
$69$	−2.72365e17	−	2.72365e17i	−0.0134041	−	0.0134041i
$70$		0			0
$71$			3.58026e19i			1.30527i	0.757671	+	0.652636i	$0.226337\pi$
$71$			3.58026e19i			1.30527i	−0.757671	+	0.652636i	$0.773663\pi$
$72$		0			0
$73$		−	3.87758e19i		−	1.05602i	−0.849240	−	0.528008i	$-0.822939\pi$
$73$		−	3.87758e19i		−	1.05602i	0.849240	−	0.528008i	$-0.177061\pi$
$74$		0			0
$75$	−4.53480e19	−	4.53480e19i	−0.929853	−	0.929853i
$76$		0			0
$77$	7.20599e19	−	7.20599e19i	1.12083	−	1.12083i
$78$		0			0
$79$	1.23530e20			1.46788			0.733938	−	0.679216i	$-0.237680\pi$
$79$	1.23530e20			1.46788			0.733938	+	0.679216i	$0.237680\pi$
$80$		0			0
$81$	−1.04604e19			−0.0955999
$82$		0			0
$83$	4.84009e19	−	4.84009e19i	0.342400	−	0.342400i	−0.514869	−	0.857269i	$-0.672159\pi$
$83$	4.84009e19	−	4.84009e19i	0.342400	−	0.342400i	0.857269	+	0.514869i	$0.172159\pi$
$84$		0			0
$85$	1.97869e20	+	1.97869e20i	1.09013	+	1.09013i
$86$		0			0
$87$		−	1.49526e20i		−	0.645304i
$88$		0			0
$89$		−	7.40615e19i		−	0.251766i	−0.992045	−	0.125883i	$-0.959824\pi$
$89$		−	7.40615e19i		−	0.251766i	0.992045	−	0.125883i	$-0.0401764\pi$
$90$		0			0
$91$	6.70805e20	+	6.70805e20i	1.80577	+	1.80577i
$92$		0			0
$93$	−6.16989e20	+	6.16989e20i	−1.32192	+	1.32192i
$94$		0			0
$95$	4.08086e20			0.699285
$96$		0			0
$97$	−6.30147e20			−0.867638			−0.433819	−	0.901000i	$-0.642834\pi$
$97$	−6.30147e20			−0.867638			−0.433819	+	0.901000i	$0.642834\pi$
$98$		0			0
$99$	−9.62731e20	+	9.62731e20i	−1.06988	+	1.06988i
$100$		0			0
$101$	1.38335e21	+	1.38335e21i	1.24612	+	1.24612i	0.957420	+	0.288698i	$0.0932223\pi$
$101$	1.38335e21	+	1.38335e21i	1.24612	+	1.24612i	0.288698	+	0.957420i	$0.406778\pi$
$102$		0			0
$103$			2.43181e20i			0.178295i	0.996018	+	0.0891474i	$0.0284142\pi$
$103$			2.43181e20i			0.178295i	−0.996018	+	0.0891474i	$0.971586\pi$
$104$		0			0
$105$		−	6.36261e21i		−	3.81195i
$106$		0			0
$107$	−4.13829e20	−	4.13829e20i	−0.203372	−	0.203372i	0.598071	−	0.801443i	$-0.295934\pi$
$107$	−4.13829e20	−	4.13829e20i	−0.203372	−	0.203372i	−0.801443	+	0.598071i	$0.795934\pi$
$108$		0			0
$109$	1.45196e21	−	1.45196e21i	0.587457	−	0.587457i	−0.349485	−	0.936942i	$-0.613643\pi$
$109$	1.45196e21	−	1.45196e21i	0.587457	−	0.587457i	0.936942	+	0.349485i	$0.113643\pi$
$110$		0			0
$111$	−7.51060e21			−2.51063
$112$		0			0
$113$	−5.07545e21			−1.40653			−0.703267	−	0.710925i	$-0.748276\pi$
$113$	−5.07545e21			−1.40653			−0.703267	+	0.710925i	$0.748276\pi$
$114$		0			0
$115$	−4.79199e19	+	4.79199e19i	−0.0110456	+	0.0110456i
$116$		0			0
$117$	−8.96205e21	−	8.96205e21i	−1.72368	−	1.72368i
$118$		0			0
$119$			1.23925e22i			1.99487i
$120$		0			0
$121$		−	1.25229e21i		−	0.169222i
$122$		0			0
$123$	−3.13975e20	−	3.13975e20i	−0.0357183	−	0.0357183i
$124$		0			0
$125$	1.91689e21	−	1.91689e21i	0.184095	−	0.184095i
$126$		0			0
$127$	1.36511e20			0.0110976			0.00554878	−	0.999985i	$-0.498234\pi$
$127$	1.36511e20			0.0110976			0.00554878	+	0.999985i	$0.498234\pi$
$128$		0			0
$129$	−6.69366e20			−0.0461819
$130$		0			0
$131$	8.71584e21	−	8.71584e21i	0.511635	−	0.511635i	−0.403392	−	0.915027i	$-0.632169\pi$
$131$	8.71584e21	−	8.71584e21i	0.511635	−	0.511635i	0.915027	+	0.403392i	$0.132169\pi$
$132$		0			0
$133$	1.27792e22	+	1.27792e22i	0.639823	+	0.639823i
$134$		0			0
$135$			3.37973e22i			1.44670i
$136$		0			0
$137$			3.16170e22i			1.15973i	0.814714	+	0.579863i	$0.196894\pi$
$137$			3.16170e22i			1.15973i	−0.814714	+	0.579863i	$0.803106\pi$
$138$		0			0
$139$	8.96656e21	+	8.96656e21i	0.282469	+	0.282469i	0.834093	−	0.551624i	$-0.185992\pi$
$139$	8.96656e21	+	8.96656e21i	0.282469	+	0.282469i	−0.551624	+	0.834093i	$0.685992\pi$
$140$		0			0
$141$	−1.82453e22	+	1.82453e22i	−0.494709	+	0.494709i
$142$		0			0
$143$	−5.72313e22			−1.33846
$144$		0			0
$145$	−2.63076e22			−0.531762
$146$		0			0
$147$	1.33363e23	−	1.33363e23i	2.33456	−	2.33456i
$148$		0			0
$149$	7.87874e22	+	7.87874e22i	1.19674	+	1.19674i	0.975136	+	0.221608i	$0.0711304\pi$
$149$	7.87874e22	+	7.87874e22i	1.19674	+	1.19674i	0.221608	+	0.975136i	$0.428870\pi$
$150$		0			0
$151$			3.05673e22i			0.403644i	0.979422	+	0.201822i	$0.0646863\pi$
$151$			3.05673e22i			0.403644i	−0.979422	+	0.201822i	$0.935314\pi$
$152$		0			0
$153$		−	1.65565e23i		−	1.90419i
$154$		0			0
$155$	1.08553e23	+	1.08553e23i	1.08933	+	1.08933i
$156$		0			0
$157$	4.60981e20	−	4.60981e20i	0.00404330	−	0.00404330i	−0.705082	−	0.709126i	$-0.749090\pi$
$157$	4.60981e20	−	4.60981e20i	0.00404330	−	0.00404330i	0.709126	+	0.705082i	$0.249090\pi$
$158$		0			0
$159$	−1.46160e23			−1.12243
$160$		0			0
$161$	−3.00121e21			−0.0202127
$162$		0			0
$163$	−1.07648e23	+	1.07648e23i	−0.636851	+	0.636851i	−0.949777	−	0.312927i	$-0.898691\pi$
$163$	−1.07648e23	+	1.07648e23i	−0.636851	+	0.636851i	0.312927	+	0.949777i	$0.398691\pi$
$164$		0			0
$165$	2.71421e23	+	2.71421e23i	1.41274	+	1.41274i
$166$		0			0
$167$		−	2.53670e23i		−	1.16345i	−0.813387	−	0.581723i	$-0.802379\pi$
$167$		−	2.53670e23i		−	1.16345i	0.813387	−	0.581723i	$-0.197621\pi$
$168$		0			0
$169$		−	2.85701e23i		−	1.15638i
$170$		0			0
$171$	−1.70731e23	−	1.70731e23i	−0.610737	−	0.610737i
$172$		0			0
$173$	−2.66174e23	+	2.66174e23i	−0.842716	+	0.842716i	−0.989211	−	0.146496i	$-0.953201\pi$
$173$	−2.66174e23	+	2.66174e23i	−0.842716	+	0.842716i	0.146496	+	0.989211i	$0.453201\pi$
$174$		0			0
$175$	−4.99691e23			−1.40218
$176$		0			0
$177$	−5.39074e23			−1.34255
$178$		0			0
$179$	4.42654e23	−	4.42654e23i	0.979733	−	0.979733i	−0.0200661	−	0.999799i	$-0.506388\pi$
$179$	4.42654e23	−	4.42654e23i	0.979733	−	0.979733i	0.999799	+	0.0200661i	$0.00638767\pi$
$180$		0			0
$181$	1.34665e23	+	1.34665e23i	0.265234	+	0.265234i	0.827176	−	0.561943i	$-0.189946\pi$
$181$	1.34665e23	+	1.34665e23i	0.265234	+	0.265234i	−0.561943	+	0.827176i	$0.689946\pi$
$182$		0			0
$183$			1.38593e24i			2.43223i
$184$		0			0
$185$			1.32141e24i			2.06888i
$186$		0			0
$187$	−5.28647e23	−	5.28647e23i	−0.739314	−	0.739314i
$188$		0			0
$189$	−1.05836e24	+	1.05836e24i	−1.32368	+	1.32368i
$190$		0			0
$191$	3.50649e23			0.392665			0.196332	−	0.980537i	$-0.437097\pi$
$191$	3.50649e23			0.392665			0.196332	+	0.980537i	$0.437097\pi$
$192$		0			0
$193$	−1.12826e24			−1.13255			−0.566277	−	0.824215i	$-0.691617\pi$
$193$	−1.12826e24			−1.13255			−0.566277	+	0.824215i	$0.691617\pi$
$194$		0			0
$195$	−2.52665e24	+	2.52665e24i	−2.27605	+	2.27605i
$196$		0			0
$197$	−2.43517e23	−	2.43517e23i	−0.197076	−	0.197076i	0.601669	−	0.798745i	$-0.294502\pi$
$197$	−2.43517e23	−	2.43517e23i	−0.197076	−	0.197076i	−0.798745	+	0.601669i	$0.794502\pi$
$198$		0			0
$199$		−	2.05413e24i		−	1.49510i	−0.664207	−	0.747549i	$-0.731230\pi$
$199$		−	2.05413e24i		−	1.49510i	0.664207	−	0.747549i	$-0.268770\pi$
$200$		0			0
$201$		−	4.58824e23i		−	0.300668i
$202$		0			0
$203$	−8.23817e23	−	8.23817e23i	−0.486544	−	0.486544i
$204$		0			0
$205$	−5.52407e22	+	5.52407e22i	−0.0294336	+	0.0294336i
$206$		0			0
$207$	4.00966e22			0.0192938
$208$		0			0
$209$	−1.09028e24			−0.474246
$210$		0			0
$211$	−1.84034e24	+	1.84034e24i	−0.724322	+	0.724322i	−0.969483	−	0.245160i	$-0.921159\pi$
$211$	−1.84034e24	+	1.84034e24i	−0.724322	+	0.724322i	0.245160	+	0.969483i	$0.421159\pi$
$212$		0			0
$213$	−4.22292e24	−	4.22292e24i	−1.50531	−	1.50531i
$214$		0			0
$215$			1.17768e23i			0.0380561i
$216$		0			0
$217$			6.79864e24i			1.99340i
$218$		0			0
$219$	4.57361e24	+	4.57361e24i	1.21786	+	1.21786i
$220$		0			0
$221$	4.92117e24	−	4.92117e24i	1.19110	−	1.19110i
$222$		0			0
$223$	−3.34145e24			−0.735757			−0.367878	−	0.929874i	$-0.619916\pi$
$223$	−3.34145e24			−0.735757			−0.367878	+	0.929874i	$0.619916\pi$
$224$		0			0
$225$	6.67595e24			1.33843
$226$		0			0
$227$	3.45036e23	−	3.45036e23i	0.0630367	−	0.0630367i	−0.674886	−	0.737922i	$-0.735807\pi$
$227$	3.45036e23	−	3.45036e23i	0.0630367	−	0.0630367i	0.737922	+	0.674886i	$0.235807\pi$
$228$		0			0
$229$	2.40999e24	+	2.40999e24i	0.401553	+	0.401553i	0.878780	−	0.477227i	$-0.158358\pi$
$229$	2.40999e24	+	2.40999e24i	0.401553	+	0.401553i	−0.477227	+	0.878780i	$0.658358\pi$
$230$		0			0
$231$			1.69990e25i			2.58522i
$232$		0			0
$233$			9.46245e23i			0.131452i	0.997838	+	0.0657259i	$0.0209363\pi$
$233$			9.46245e23i			0.131452i	−0.997838	+	0.0657259i	$0.979064\pi$
$234$		0			0
$235$	3.21007e24	+	3.21007e24i	0.407664	+	0.407664i
$236$		0			0
$237$	−1.45704e25	+	1.45704e25i	−1.69284	+	1.69284i
$238$		0			0
$239$	1.27355e25			1.35468			0.677340	−	0.735670i	$-0.263132\pi$
$239$	1.27355e25			1.35468			0.677340	+	0.735670i	$0.263132\pi$
$240$		0			0
$241$	−1.57571e24			−0.153566			−0.0767832	−	0.997048i	$-0.524465\pi$
$241$	−1.57571e24			−0.153566			−0.0767832	+	0.997048i	$0.524465\pi$
$242$		0			0
$243$	−7.28415e24	+	7.28415e24i	−0.650898	+	0.650898i
$244$		0			0
$245$	−2.34639e25	−	2.34639e25i	−1.92379	−	1.92379i
$246$		0			0
$247$		−	1.01494e25i		−	0.764054i
$248$		0			0
$249$			1.14178e25i			0.789749i
$250$		0			0
$251$	−1.06981e25	−	1.06981e25i	−0.680349	−	0.680349i	0.279729	−	0.960079i	$-0.409755\pi$
$251$	−1.06981e25	−	1.06981e25i	−0.680349	−	0.680349i	−0.960079	+	0.279729i	$0.909755\pi$
$252$		0			0
$253$	1.28028e23	−	1.28028e23i	0.00749097	−	0.00749097i
$254$		0			0
$255$	−4.66774e25			−2.51440
$256$		0			0
$257$	1.91045e25			0.948063			0.474031	−	0.880508i	$-0.342798\pi$
$257$	1.91045e25			0.948063			0.474031	+	0.880508i	$0.342798\pi$
$258$		0			0
$259$	−4.13799e25	+	4.13799e25i	−1.89296	+	1.89296i
$260$		0			0
$261$	1.10063e25	+	1.10063e25i	0.464426	+	0.464426i
$262$		0			0
$263$			9.46080e24i			0.368462i	0.982883	+	0.184231i	$0.0589794\pi$
$263$			9.46080e24i			0.368462i	−0.982883	+	0.184231i	$0.941021\pi$
$264$		0			0
$265$			2.57153e25i			0.924934i
$266$		0			0
$267$	8.73558e24	+	8.73558e24i	0.290351	+	0.290351i
$268$		0			0
$269$	1.08512e25	−	1.08512e25i	0.333487	−	0.333487i	−0.520422	−	0.853909i	$-0.674225\pi$
$269$	1.08512e25	−	1.08512e25i	0.333487	−	0.333487i	0.853909	+	0.520422i	$0.174225\pi$
$270$		0			0
$271$	5.19043e25			1.47579			0.737897	−	0.674913i	$-0.235819\pi$
$271$	5.19043e25			1.47579			0.737897	+	0.674913i	$0.235819\pi$
$272$		0			0
$273$	−1.58243e26			−4.16502
$274$		0			0
$275$	2.13162e25	−	2.13162e25i	0.519656	−	0.519656i
$276$		0			0
$277$	5.50134e25	+	5.50134e25i	1.24288	+	1.24288i	0.958799	+	0.284085i	$0.0916898\pi$
$277$	5.50134e25	+	5.50134e25i	1.24288	+	1.24288i	0.284085	+	0.958799i	$0.408310\pi$
$278$		0			0
$279$		−	9.08308e25i		−	1.90278i
$280$		0			0
$281$			5.58752e24i			0.108593i	0.998525	+	0.0542966i	$0.0172917\pi$
$281$			5.58752e24i			0.108593i	−0.998525	+	0.0542966i	$0.982708\pi$
$282$		0			0
$283$	−6.70923e25	−	6.70923e25i	−1.21036	−	1.21036i	−0.970908	−	0.239453i	$-0.923032\pi$
$283$	−6.70923e25	−	6.70923e25i	−1.21036	−	1.21036i	−0.239453	−	0.970908i	$-0.576968\pi$
$284$		0			0
$285$	−4.81339e25	+	4.81339e25i	−0.806455	+	0.806455i
$286$		0			0
$287$	−3.45970e24			−0.0538616
$288$		0			0
$289$	2.18219e25			0.315838
$290$		0			0
$291$	7.43260e25	−	7.43260e25i	1.00061	−	1.00061i
$292$		0			0
$293$	2.79412e25	+	2.79412e25i	0.350054	+	0.350054i	0.860130	−	0.510076i	$-0.170383\pi$
$293$	2.79412e25	+	2.79412e25i	0.350054	+	0.350054i	−0.510076	+	0.860130i	$0.670383\pi$
$294$		0			0
$295$			9.48446e25i			1.10632i
$296$		0			0
$297$		−	9.02963e25i		−	0.981131i
$298$		0			0
$299$	1.19181e24	+	1.19181e24i	0.0120686	+	0.0120686i
$300$		0			0
$301$	−3.68789e24	+	3.68789e24i	−0.0348201	+	0.0348201i
$302$		0			0
$303$	−3.26334e26			−2.87419
$304$		0			0
$305$	2.43840e26			2.00428
$306$		0			0
$307$	1.71083e26	−	1.71083e26i	1.31297	−	1.31297i	0.393751	−	0.919217i	$-0.371177\pi$
$307$	1.71083e26	−	1.71083e26i	1.31297	−	1.31297i	0.919217	−	0.393751i	$-0.128823\pi$
$308$		0			0
$309$	−2.86833e25	−	2.86833e25i	−0.205620	−	0.205620i
$310$		0			0
$311$			3.53460e25i			0.236786i	0.992967	+	0.118393i	$0.0377742\pi$
$311$			3.53460e25i			0.236786i	−0.992967	+	0.118393i	$0.962226\pi$
$312$		0			0
$313$		−	1.68100e26i		−	1.05282i	−0.850232	−	0.526408i	$-0.823538\pi$
$313$		−	1.68100e26i		−	1.05282i	0.850232	−	0.526408i	$-0.176462\pi$
$314$		0			0
$315$	4.68339e26	+	4.68339e26i	2.74347	+	2.74347i
$316$		0			0
$317$	1.19615e26	−	1.19615e26i	0.655636	−	0.655636i	−0.298709	−	0.954344i	$-0.596556\pi$
$317$	1.19615e26	−	1.19615e26i	0.655636	−	0.655636i	0.954344	+	0.298709i	$0.0965559\pi$
$318$		0			0
$319$	7.02859e25			0.360634
$320$		0			0
$321$	9.76226e25			0.469081
$322$		0			0
$323$	9.37505e25	−	9.37505e25i	0.422034	−	0.422034i
$324$		0			0
$325$	1.98432e26	+	1.98432e26i	0.837214	+	0.837214i
$326$		0			0
$327$			3.42518e26i			1.35498i
$328$		0			0
$329$			2.01046e26i			0.745999i
$330$		0			0
$331$	−3.82099e25	−	3.82099e25i	−0.133040	−	0.133040i	0.637451	−	0.770491i	$-0.279989\pi$
$331$	−3.82099e25	−	3.82099e25i	−0.133040	−	0.133040i	−0.770491	+	0.637451i	$0.779989\pi$
$332$		0			0
$333$	5.52841e26	−	5.52841e26i	1.80691	−	1.80691i
$334$		0			0
$335$	−8.07254e25			−0.247765
$336$		0			0
$337$	−1.01328e26			−0.292156			−0.146078	−	0.989273i	$-0.546665\pi$
$337$	−1.01328e26			−0.292156			−0.146078	+	0.989273i	$0.546665\pi$
$338$		0			0
$339$	5.98650e26	−	5.98650e26i	1.62210	−	1.62210i
$340$		0			0
$341$	−2.90021e26	−	2.90021e26i	−0.738769	−	0.738769i
$342$		0			0
$343$		−	7.43595e26i		−	1.78135i
$344$		0			0
$345$		−	1.13043e25i		−	0.0254768i
$346$		0			0
$347$	−4.43008e26	−	4.43008e26i	−0.939619	−	0.939619i	0.0586586	−	0.998278i	$-0.481318\pi$
$347$	−4.43008e26	−	4.43008e26i	−0.939619	−	0.939619i	−0.998278	+	0.0586586i	$0.981318\pi$
$348$		0			0
$349$	−4.37193e25	+	4.37193e25i	−0.0872983	+	0.0872983i	−0.749407	−	0.662109i	$-0.769662\pi$
$349$	−4.37193e25	+	4.37193e25i	−0.0872983	+	0.0872983i	0.662109	+	0.749407i	$0.269662\pi$
$350$		0			0
$351$	8.40567e26			1.58069
$352$		0			0
$353$	−4.81801e26			−0.853558			−0.426779	−	0.904356i	$-0.640352\pi$
$353$	−4.81801e26			−0.853558			−0.426779	+	0.904356i	$0.640352\pi$
$354$		0			0
$355$	−7.42980e26	+	7.42980e26i	−1.24045	+	1.24045i
$356$		0			0
$357$	−1.46170e27	−	1.46170e27i	−2.30060	−	2.30060i
$358$		0			0
$359$		−	9.78541e26i		−	1.45240i	−0.687481	−	0.726202i	$-0.741284\pi$
$359$		−	9.78541e26i		−	1.45240i	0.687481	−	0.726202i	$-0.258716\pi$
$360$		0			0
$361$			5.20858e26i			0.729279i
$362$		0			0
$363$	1.47708e26	+	1.47708e26i	0.195157	+	0.195157i
$364$		0			0
$365$	8.04681e26	−	8.04681e26i	1.00357	−	1.00357i
$366$		0			0
$367$	−3.99488e26			−0.470446			−0.235223	−	0.971941i	$-0.575582\pi$
$367$	−3.99488e26			−0.470446			−0.235223	+	0.971941i	$0.575582\pi$
$368$		0			0
$369$	4.62222e25			0.0514131
$370$		0			0
$371$	−8.05271e26	+	8.05271e26i	−0.846284	+	0.846284i
$372$		0			0
$373$	6.71339e26	+	6.71339e26i	0.666805	+	0.666805i	0.956975	−	0.290170i	$-0.0937118\pi$
$373$	6.71339e26	+	6.71339e26i	0.666805	+	0.666805i	−0.290170	+	0.956975i	$0.593712\pi$
$374$		0			0
$375$			4.52194e26i			0.424617i
$376$		0			0
$377$			6.54291e26i			0.581014i
$378$		0			0
$379$	5.91699e26	+	5.91699e26i	0.497038	+	0.497038i	0.910515	−	0.413477i	$-0.135686\pi$
$379$	5.91699e26	+	5.91699e26i	0.497038	+	0.497038i	−0.413477	+	0.910515i	$0.635686\pi$
$380$		0			0
$381$	−1.61015e25	+	1.61015e25i	−0.0127983	+	0.0127983i
$382$		0			0
$383$	1.88449e26			0.141777			0.0708885	−	0.997484i	$-0.477417\pi$
$383$	1.88449e26			0.141777			0.0708885	+	0.997484i	$0.477417\pi$
$384$		0			0
$385$	2.99080e27			2.13034
$386$		0			0
$387$	4.92707e25	−	4.92707e25i	0.0332372	−	0.0332372i
$388$		0			0
$389$	−2.05407e26	−	2.05407e26i	−0.131263	−	0.131263i	0.638423	−	0.769686i	$-0.279587\pi$
$389$	−2.05407e26	−	2.05407e26i	−0.131263	−	0.131263i	−0.769686	+	0.638423i	$0.779587\pi$
$390$		0			0
$391$			2.20175e25i			0.0133325i
$392$		0			0
$393$			2.05607e27i			1.18009i
$394$		0			0
$395$	2.56352e27	+	2.56352e27i	1.39498	+	1.39498i
$396$		0			0
$397$	1.66401e27	−	1.66401e27i	0.858728	−	0.858728i	−0.132461	−	0.991188i	$-0.542288\pi$
$397$	1.66401e27	−	1.66401e27i	0.858728	−	0.858728i	0.991188	+	0.132461i	$0.0422878\pi$
$398$		0			0
$399$	−3.01461e27			−1.47576
$400$		0			0
$401$	−1.50575e27			−0.699417			−0.349709	−	0.936859i	$-0.613719\pi$
$401$	−1.50575e27			−0.699417			−0.349709	+	0.936859i	$0.613719\pi$
$402$		0			0
$403$	2.69980e27	−	2.69980e27i	1.19022	−	1.19022i
$404$		0			0
$405$	−2.17077e26	−	2.17077e26i	−0.0908522	−	0.0908522i
$406$		0			0
$407$		−	3.53042e27i		−	1.40309i
$408$		0			0
$409$			1.28059e27i			0.483409i	0.970350	+	0.241704i	$0.0777065\pi$
$409$			1.28059e27i			0.483409i	−0.970350	+	0.241704i	$0.922294\pi$
$410$		0			0
$411$	−3.72924e27	−	3.72924e27i	−1.33746	−	1.33746i
$412$		0			0
$413$	−2.97004e27	+	2.97004e27i	−1.01225	+	1.01225i
$414$		0			0
$415$	2.00885e27			0.650791
$416$		0			0
$417$	−2.11522e27			−0.651518
$418$		0			0
$419$	1.02195e27	−	1.02195e27i	0.299351	−	0.299351i	−0.541408	−	0.840760i	$-0.682109\pi$
$419$	1.02195e27	−	1.02195e27i	0.299351	−	0.299351i	0.840760	+	0.541408i	$0.182109\pi$
$420$		0			0
$421$	−9.46928e26	−	9.46928e26i	−0.263849	−	0.263849i	0.562767	−	0.826616i	$-0.309737\pi$
$421$	−9.46928e26	−	9.46928e26i	−0.263849	−	0.263849i	−0.826616	+	0.562767i	$0.809737\pi$
$422$		0			0
$423$		−	2.68600e27i		−	0.712086i
$424$		0			0
$425$			3.66584e27i			0.924890i
$426$		0			0
$427$	7.63582e27	+	7.63582e27i	1.83385	+	1.83385i
$428$		0			0
$429$	6.75045e27	−	6.75045e27i	1.54359	−	1.54359i
$430$		0			0
$431$	−7.13993e27			−1.55483			−0.777414	−	0.628989i	$-0.783469\pi$
$431$	−7.13993e27			−1.55483			−0.777414	+	0.628989i	$0.783469\pi$
$432$		0			0
$433$	1.39228e27			0.288804			0.144402	−	0.989519i	$-0.453874\pi$
$433$	1.39228e27			0.288804			0.144402	+	0.989519i	$0.453874\pi$
$434$		0			0
$435$	3.10299e27	−	3.10299e27i	0.613257	−	0.613257i
$436$		0			0
$437$	2.27045e25	+	2.27045e25i	0.00427619	+	0.00427619i
$438$		0			0
$439$			2.95011e27i			0.529615i	0.964301	+	0.264808i	$0.0853084\pi$
$439$			2.95011e27i			0.529615i	−0.964301	+	0.264808i	$0.914692\pi$
$440$		0			0
$441$			1.96332e28i			3.36037i
$442$		0			0
$443$	−1.63439e27	−	1.63439e27i	−0.266757	−	0.266757i	0.561035	−	0.827792i	$-0.310403\pi$
$443$	−1.63439e27	−	1.63439e27i	−0.266757	−	0.266757i	−0.827792	+	0.561035i	$0.810403\pi$
$444$		0			0
$445$	1.53694e27	−	1.53694e27i	0.239263	−	0.239263i
$446$		0			0
$447$	−1.85860e28			−2.76030
$448$		0			0
$449$	−1.06818e28			−1.51377			−0.756883	−	0.653551i	$-0.773279\pi$
$449$	−1.06818e28			−1.51377			−0.756883	+	0.653551i	$0.773279\pi$
$450$		0			0
$451$	1.47586e26	−	1.47586e26i	0.0199615	−	0.0199615i
$452$		0			0
$453$	−3.60542e27	−	3.60542e27i	−0.465505	−	0.465505i
$454$		0			0
$455$			2.78413e28i			3.43218i
$456$		0			0
$457$		−	9.83403e27i		−	1.15774i	−0.815419	−	0.578871i	$-0.803494\pi$
$457$		−	9.83403e27i		−	1.15774i	0.815419	−	0.578871i	$-0.196506\pi$
$458$		0			0
$459$	7.76433e27	+	7.76433e27i	0.873114	+	0.873114i
$460$		0			0
$461$	−1.04097e28	+	1.04097e28i	−1.11836	+	1.11836i	−0.126373	+	0.991983i	$0.540333\pi$
$461$	−1.04097e28	+	1.04097e28i	−1.11836	+	1.11836i	−0.991983	+	0.126373i	$0.959667\pi$
$462$		0			0
$463$	−1.83612e28			−1.88496			−0.942479	−	0.334265i	$-0.891512\pi$
$463$	−1.83612e28			−1.88496			−0.942479	+	0.334265i	$0.891512\pi$
$464$		0			0
$465$	−2.56077e28			−2.51255
$466$		0			0
$467$	−3.81569e27	+	3.81569e27i	−0.357887	+	0.357887i	−0.863034	−	0.505147i	$-0.831438\pi$
$467$	−3.81569e27	+	3.81569e27i	−0.357887	+	0.357887i	0.505147	+	0.863034i	$0.331438\pi$
$468$		0			0
$469$	−2.52790e27	−	2.52790e27i	−0.226697	−	0.226697i
$470$		0			0
$471$			1.08746e26i			0.00932593i
$472$		0			0
$473$		−	3.14641e26i		−	0.0258091i
$474$		0			0
$475$	3.78022e27	+	3.78022e27i	0.296643	+	0.296643i
$476$		0			0
$477$	1.07585e28	−	1.07585e28i	0.807812	−	0.807812i
$478$		0			0
$479$	−2.01231e27			−0.144601			−0.0723007	−	0.997383i	$-0.523034\pi$
$479$	−2.01231e27			−0.144601			−0.0723007	+	0.997383i	$0.523034\pi$
$480$		0			0
$481$	3.28646e28			2.26051
$482$		0			0
$483$	3.53993e26	−	3.53993e26i	0.0233104	−	0.0233104i
$484$		0			0
$485$	−1.30769e28	−	1.30769e28i	−0.824549	−	0.824549i
$486$		0			0
$487$		−	2.38673e28i		−	1.44128i	−0.693307	−	0.720642i	$-0.743847\pi$
$487$		−	2.38673e28i		−	1.44128i	0.693307	−	0.720642i	$-0.256153\pi$
$488$		0			0
$489$		−	2.53943e28i		−	1.46890i
$490$		0			0
$491$	3.23472e27	+	3.23472e27i	0.179259	+	0.179259i	0.791033	−	0.611774i	$-0.209544\pi$
$491$	3.23472e27	+	3.23472e27i	0.179259	+	0.179259i	−0.611774	+	0.791033i	$0.709544\pi$
$492$		0			0
$493$	−6.04370e27	+	6.04370e27i	−0.320930	+	0.320930i
$494$		0			0
$495$	−3.99575e28			−2.03350
$496$		0			0
$497$	−4.65326e28			−2.26994
$498$		0			0
$499$	8.27092e27	−	8.27092e27i	0.386810	−	0.386810i	−0.486738	−	0.873548i	$-0.661813\pi$
$499$	8.27092e27	−	8.27092e27i	0.386810	−	0.386810i	0.873548	+	0.486738i	$0.161813\pi$
$500$		0			0
$501$	2.99205e28	+	2.99205e28i	1.34175	+	1.34175i
$502$		0			0
$503$			1.13744e28i			0.489176i	0.969627	+	0.244588i	$0.0786527\pi$
$503$			1.13744e28i			0.489176i	−0.969627	+	0.244588i	$0.921347\pi$
$504$		0			0
$505$			5.74152e28i			2.36847i
$506$		0			0
$507$	3.36985e28	+	3.36985e28i	1.33361	+	1.33361i
$508$		0			0
$509$	1.96241e28	−	1.96241e28i	0.745165	−	0.745165i	−0.228402	−	0.973567i	$-0.573350\pi$
$509$	1.96241e28	−	1.96241e28i	0.745165	−	0.745165i	0.973567	+	0.228402i	$0.0733500\pi$
$510$		0			0
$511$	5.03969e28			1.83647
$512$		0			0
$513$	1.60132e28			0.560074
$514$		0			0
$515$	−5.04653e27	+	5.04653e27i	−0.169440	+	0.169440i
$516$		0			0
$517$	−8.57635e27	−	8.57635e27i	−0.276472	−	0.276472i
$518$		0			0
$519$		−	6.27905e28i		−	1.94373i
$520$		0			0
$521$		−	2.16639e28i		−	0.644081i	−0.946726	−	0.322041i	$-0.895631\pi$
$521$		−	2.16639e28i		−	0.644081i	0.946726	−	0.322041i	$-0.104369\pi$
$522$		0			0
$523$	−2.10665e28	−	2.10665e28i	−0.601623	−	0.601623i	0.339120	−	0.940743i	$-0.389871\pi$
$523$	−2.10665e28	−	2.10665e28i	−0.601623	−	0.601623i	−0.940743	+	0.339120i	$0.889871\pi$
$524$		0			0
$525$	5.89387e28	−	5.89387e28i	1.61707	−	1.61707i
$526$		0			0
$527$	4.98762e28			1.31487
$528$		0			0
$529$	3.94663e28			0.999865
$530$		0			0
$531$	3.96802e28	−	3.96802e28i	0.966232	−	0.966232i
$532$		0			0
$533$	1.37388e27	+	1.37388e27i	0.0321598	+	0.0321598i
$534$		0			0
$535$		−	1.71757e28i		−	0.386545i
$536$		0			0
$537$			1.04422e29i			2.25977i
$538$		0			0
$539$	6.26885e28	+	6.26885e28i	1.30469	+	1.30469i
$540$		0			0
$541$	−4.93820e28	+	4.93820e28i	−0.988547	+	0.988547i	−0.999935	−	0.0113880i	$-0.996375\pi$
$541$	−4.93820e28	+	4.93820e28i	−0.988547	+	0.988547i	0.0113880	+	0.999935i	$0.496375\pi$
$542$		0			0
$543$	−3.17675e28			−0.611765
$544$		0			0
$545$	6.02626e28			1.11657
$546$		0			0
$547$	−7.36301e28	+	7.36301e28i	−1.31277	+	1.31277i	−0.393404	+	0.919366i	$0.628703\pi$
$547$	−7.36301e28	+	7.36301e28i	−1.31277	+	1.31277i	−0.919366	+	0.393404i	$0.871297\pi$
$548$		0			0
$549$	−1.02016e29	−	1.02016e29i	−1.75048	−	1.75048i
$550$		0			0
$551$			1.24646e28i			0.205866i
$552$		0			0
$553$			1.60552e29i			2.55272i
$554$		0			0
$555$	−1.55861e29	−	1.55861e29i	−2.38595	−	2.38595i
$556$		0			0
$557$	8.16810e28	−	8.16810e28i	1.20404	−	1.20404i	0.231114	−	0.972927i	$-0.425763\pi$
$557$	8.16810e28	−	8.16810e28i	1.20404	−	1.20404i	0.972927	−	0.231114i	$-0.0742372\pi$
$558$		0			0
$559$	2.92899e27			0.0415809
$560$		0			0
$561$	1.24708e29			1.70524
$562$		0			0
$563$	9.60185e28	−	9.60185e28i	1.26479	−	1.26479i	0.316040	−	0.948746i	$-0.397647\pi$
$563$	9.60185e28	−	9.60185e28i	1.26479	−	1.26479i	0.948746	−	0.316040i	$-0.102353\pi$
$564$		0			0
$565$	−1.05326e29	−	1.05326e29i	−1.33668	−	1.33668i
$566$		0			0
$567$		−	1.35954e28i		−	0.166254i
$568$		0			0
$569$		−	1.54818e28i		−	0.182450i	−0.995830	−	0.0912249i	$-0.970922\pi$
$569$		−	1.54818e28i		−	0.182450i	0.995830	−	0.0912249i	$-0.0290782\pi$
$570$		0			0
$571$	1.84809e28	+	1.84809e28i	0.209915	+	0.209915i	0.804232	−	0.594316i	$-0.202577\pi$
$571$	1.84809e28	+	1.84809e28i	0.209915	+	0.209915i	−0.594316	+	0.804232i	$0.702577\pi$
$572$		0			0
$573$	−4.13591e28	+	4.13591e28i	−0.452843	+	0.452843i
$574$		0			0
$575$	−8.87793e26			−0.00937129
$576$		0			0
$577$	−1.14856e29			−1.16898			−0.584490	−	0.811401i	$-0.698705\pi$
$577$	−1.14856e29			−1.16898			−0.584490	+	0.811401i	$0.698705\pi$
$578$		0			0
$579$	1.33079e29	−	1.33079e29i	1.30613	−	1.30613i
$580$		0			0
$581$	6.29066e28	+	6.29066e28i	0.595452	+	0.595452i
$582$		0			0
$583$		−	6.87036e28i		−	0.627278i
$584$		0			0
$585$		−	3.71964e29i		−	3.27615i
$586$		0			0
$587$	6.71971e28	+	6.71971e28i	0.571019	+	0.571019i	0.932413	−	0.361394i	$-0.117699\pi$
$587$	6.71971e28	+	6.71971e28i	0.571019	+	0.571019i	−0.361394	+	0.932413i	$0.617699\pi$
$588$		0			0
$589$	5.14325e28	−	5.14325e28i	0.421723	−	0.421723i
$590$		0			0
$591$	5.74457e28			0.454558
$592$		0			0
$593$	−2.57735e29			−1.96834			−0.984170	−	0.177230i	$-0.943286\pi$
$593$	−2.57735e29			−1.96834			−0.984170	+	0.177230i	$0.943286\pi$
$594$		0			0
$595$	−2.57171e29	+	2.57171e29i	−1.89580	+	1.89580i
$596$		0			0
$597$	2.42285e29	+	2.42285e29i	1.72423	+	1.72423i
$598$		0			0
$599$			2.23242e28i			0.153389i	0.997055	+	0.0766946i	$0.0244366\pi$
$599$			2.23242e28i			0.153389i	−0.997055	+	0.0766946i	$0.975563\pi$
$600$		0			0
$601$		−	2.49910e29i		−	1.65807i	−0.559198	−	0.829034i	$-0.688891\pi$
$601$		−	2.49910e29i		−	1.65807i	0.559198	−	0.829034i	$-0.311109\pi$
$602$		0			0
$603$	3.37732e28	+	3.37732e28i	0.216391	+	0.216391i
$604$		0			0
$605$	2.59876e28	−	2.59876e28i	0.160818	−	0.160818i
$606$		0			0
$607$	−2.05976e29			−1.23122			−0.615609	−	0.788052i	$-0.711090\pi$
$607$	−2.05976e29			−1.23122			−0.615609	+	0.788052i	$0.711090\pi$
$608$		0			0
$609$	1.94339e29			1.12222
$610$		0			0
$611$	7.98372e28	−	7.98372e28i	0.445423	−	0.445423i
$612$		0			0
$613$	−3.90133e28	−	3.90133e28i	−0.210319	−	0.210319i	0.594084	−	0.804403i	$-0.297515\pi$
$613$	−3.90133e28	−	3.90133e28i	−0.210319	−	0.210319i	−0.804403	+	0.594084i	$0.797515\pi$
$614$		0			0
$615$		−	1.30313e28i		−	0.0678890i
$616$		0			0
$617$			1.03005e29i			0.518638i	0.965792	+	0.259319i	$0.0834980\pi$
$617$			1.03005e29i			0.518638i	−0.965792	+	0.259319i	$0.916502\pi$
$618$		0			0
$619$	1.77536e29	+	1.77536e29i	0.864039	+	0.864039i	0.991804	−	0.127765i	$-0.0407804\pi$
$619$	1.77536e29	+	1.77536e29i	0.864039	+	0.864039i	−0.127765	+	0.991804i	$0.540780\pi$
$620$		0			0
$621$	−1.88036e27	+	1.88036e27i	−0.00884668	+	0.00884668i
$622$		0			0
$623$	9.62578e28			0.437836
$624$		0			0
$625$	2.62887e29			1.15619
$626$		0			0
$627$	1.28599e29	−	1.28599e29i	0.546927	−	0.546927i
$628$		0			0
$629$	3.03571e29	+	3.03571e29i	1.24862	+	1.24862i
$630$		0			0
$631$			2.74477e29i			1.09194i	0.837806	+	0.545968i	$0.183838\pi$
$631$			2.74477e29i			1.09194i	−0.837806	+	0.545968i	$0.816162\pi$
$632$		0			0
$633$		−	4.34137e29i		−	1.67066i
$634$		0			0
$635$	2.83289e27	+	2.83289e27i	0.0105464	+	0.0105464i
$636$		0			0
$637$	−5.83567e29	+	5.83567e29i	−2.10197	+	2.10197i
$638$		0			0
$639$	6.21682e29			2.16675
$640$		0			0
$641$	−2.24406e29			−0.756878			−0.378439	−	0.925626i	$-0.623539\pi$
$641$	−2.24406e29			−0.756878			−0.378439	+	0.925626i	$0.623539\pi$
$642$		0			0
$643$	−1.34630e29	+	1.34630e29i	−0.439468	+	0.439468i	−0.891833	−	0.452365i	$-0.850580\pi$
$643$	−1.34630e29	+	1.34630e29i	−0.439468	+	0.439468i	0.452365	+	0.891833i	$0.350580\pi$
$644$		0			0
$645$	−1.38908e28	−	1.38908e28i	−0.0438884	−	0.0438884i
$646$		0			0
$647$			2.14995e28i			0.0657558i	0.999459	+	0.0328779i	$0.0104672\pi$
$647$			2.14995e28i			0.0657558i	−0.999459	+	0.0328779i	$0.989533\pi$
$648$		0			0
$649$		−	2.53396e29i		−	0.750293i
$650$		0			0
$651$	−8.01901e29	−	8.01901e29i	−2.29890	−	2.29890i
$652$		0			0
$653$	5.01413e28	−	5.01413e28i	0.139190	−	0.139190i	−0.634079	−	0.773268i	$-0.718621\pi$
$653$	5.01413e28	−	5.01413e28i	0.139190	−	0.139190i	0.773268	+	0.634079i	$0.218621\pi$
$654$		0			0
$655$	3.61745e29			0.972453
$656$		0			0
$657$	−6.73310e29			−1.75299
$658$		0			0
$659$	1.43753e29	−	1.43753e29i	0.362510	−	0.362510i	−0.502226	−	0.864736i	$-0.667486\pi$
$659$	1.43753e29	−	1.43753e29i	0.362510	−	0.362510i	0.864736	+	0.502226i	$0.167486\pi$
$660$		0			0
$661$	6.37847e28	+	6.37847e28i	0.155812	+	0.155812i	0.780708	−	0.624896i	$-0.214859\pi$
$661$	6.37847e28	+	6.37847e28i	0.155812	+	0.155812i	−0.624896	+	0.780708i	$0.714859\pi$
$662$		0			0
$663$			1.16091e30i			2.74729i
$664$		0			0
$665$			5.30390e29i			1.21610i
$666$		0			0
$667$	−1.46366e27	−	1.46366e27i	−0.00325177	−	0.00325177i
$668$		0			0
$669$	3.94125e29	−	3.94125e29i	0.848516	−	0.848516i
$670$		0			0
$671$	−6.51468e29			−1.35927
$672$		0			0
$673$	4.59335e29			0.928904			0.464452	−	0.885598i	$-0.346251\pi$
$673$	4.59335e29			0.928904			0.464452	+	0.885598i	$0.346251\pi$
$674$		0			0
$675$	−3.13075e29	+	3.13075e29i	−0.613703	+	0.613703i
$676$		0			0
$677$	4.17769e29	+	4.17769e29i	0.793881	+	0.793881i	0.982123	−	0.188242i	$-0.0602788\pi$
$677$	4.17769e29	+	4.17769e29i	0.793881	+	0.793881i	−0.188242	+	0.982123i	$0.560279\pi$
$678$		0			0
$679$		−	8.19001e29i		−	1.50887i
$680$		0			0
$681$			8.13943e28i			0.145395i
$682$		0			0
$683$	1.27677e29	+	1.27677e29i	0.221154	+	0.221154i	0.808984	−	0.587830i	$-0.200018\pi$
$683$	1.27677e29	+	1.27677e29i	0.221154	+	0.221154i	−0.587830	+	0.808984i	$0.700018\pi$
$684$		0			0
$685$	−6.56122e29	+	6.56122e29i	−1.10213	+	1.10213i
$686$		0			0
$687$	−5.68518e29			−0.926186
$688$		0			0
$689$	6.39561e29			1.01060
$690$		0			0
$691$	−3.42973e29	+	3.42973e29i	−0.525703	+	0.525703i	−0.919288	−	0.393585i	$-0.871235\pi$
$691$	−3.42973e29	+	3.42973e29i	−0.525703	+	0.525703i	0.393585	+	0.919288i	$0.371235\pi$
$692$		0			0
$693$	−1.25126e30	−	1.25126e30i	−1.86058	−	1.86058i
$694$		0			0
$695$			3.72151e29i			0.536882i
$696$		0			0
$697$			2.53811e28i			0.0355277i
$698$		0			0
$699$	−1.11610e29	−	1.11610e29i	−0.151598	−	0.151598i
$700$		0			0
$701$	−5.90044e29	+	5.90044e29i	−0.777759	+	0.777759i	−0.979449	−	0.201691i	$-0.935356\pi$
$701$	−5.90044e29	+	5.90044e29i	−0.777759	+	0.777759i	0.201691	+	0.979449i	$0.435356\pi$
$702$		0			0
$703$	6.26087e29			0.800947
$704$		0			0
$705$	−7.57258e29			−0.940283
$706$		0			0
$707$	−1.79795e30	+	1.79795e30i	−2.16707	+	2.16707i
$708$		0			0
$709$	5.66215e29	+	5.66215e29i	0.662515	+	0.662515i	0.955972	−	0.293457i	$-0.0948059\pi$
$709$	5.66215e29	+	5.66215e29i	0.662515	+	0.662515i	−0.293457	+	0.955972i	$0.594806\pi$
$710$		0			0
$711$		−	2.14500e30i		−	2.43667i
$712$		0			0
$713$			1.20790e28i			0.0133227i
$714$		0			0
$715$	−1.18767e30	−	1.18767e30i	−1.27199	−	1.27199i
$716$		0			0
$717$	−1.50215e30	+	1.50215e30i	−1.56229	+	1.56229i
$718$		0			0
$719$	−1.82495e30			−1.84330			−0.921651	−	0.388019i	$-0.873159\pi$
$719$	−1.82495e30			−1.84330			−0.921651	+	0.388019i	$0.873159\pi$
$720$		0			0
$721$	−3.16062e29			−0.310065
$722$		0			0
$723$	1.85855e29	−	1.85855e29i	0.177101	−	0.177101i
$724$		0			0
$725$	−2.43695e29	−	2.43695e29i	−0.225578	−	0.225578i
$726$		0			0
$727$			1.10055e30i			0.989685i	0.868983	+	0.494842i	$0.164774\pi$
$727$			1.10055e30i			0.989685i	−0.868983	+	0.494842i	$0.835226\pi$
$728$		0			0
$729$		−	1.82775e30i		−	1.59690i
$730$		0			0
$731$	2.70551e28	+	2.70551e28i	0.0229677	+	0.0229677i
$732$		0			0
$733$	−9.08004e29	+	9.08004e29i	−0.749024	+	0.749024i	−0.974296	−	0.225272i	$-0.927673\pi$
$733$	−9.08004e29	+	9.08004e29i	−0.749024	+	0.749024i	0.225272	+	0.974296i	$0.427673\pi$
$734$		0			0
$735$	5.53515e30			4.43724
$736$		0			0
$737$	2.15674e29			0.168031
$738$		0			0
$739$	1.32785e30	−	1.32785e30i	1.00550	−	1.00550i	0.00551559	−	0.999985i	$-0.498244\pi$
$739$	1.32785e30	−	1.32785e30i	1.00550	−	1.00550i	0.999985	−	0.00551559i	$-0.00175567\pi$
$740$		0			0
$741$	1.19713e30	+	1.19713e30i	0.881150	+	0.881150i
$742$		0			0
$743$			1.00349e30i			0.718012i	0.933335	+	0.359006i	$0.116884\pi$
$743$			1.00349e30i			0.718012i	−0.933335	+	0.359006i	$0.883116\pi$
$744$		0			0
$745$			3.27002e30i			2.27462i
$746$		0			0
$747$	−8.40442e29	−	8.40442e29i	−0.568383	−	0.568383i
$748$		0			0
$749$	5.37854e29	−	5.37854e29i	0.353676	−	0.353676i
$750$		0			0
$751$	5.79250e29			0.370379			0.185190	−	0.982703i	$-0.440710\pi$
$751$	5.79250e29			0.370379			0.185190	+	0.982703i	$0.440710\pi$
$752$		0			0
$753$	2.52368e30			1.56923
$754$		0			0
$755$	−6.34337e29	+	6.34337e29i	−0.383598	+	0.383598i
$756$		0			0
$757$	−7.66624e29	−	7.66624e29i	−0.450895	−	0.450895i	0.444756	−	0.895652i	$-0.353290\pi$
$757$	−7.66624e29	−	7.66624e29i	−0.450895	−	0.450895i	−0.895652	+	0.444756i	$0.853290\pi$
$758$		0			0
$759$			3.02018e28i			0.0172780i
$760$		0			0
$761$			2.64624e30i			1.47262i	0.676644	+	0.736310i	$0.263434\pi$
$761$			2.64624e30i			1.47262i	−0.676644	+	0.736310i	$0.736566\pi$
$762$		0			0
$763$	1.88711e30	+	1.88711e30i	1.02162	+	1.02162i
$764$		0			0
$765$	3.43584e30	−	3.43584e30i	1.80962	−	1.80962i
$766$		0			0
$767$	2.35886e30			1.20879
$768$		0			0
$769$	4.02533e29			0.200713			0.100356	−	0.994952i	$-0.468002\pi$
$769$	4.02533e29			0.200713			0.100356	+	0.994952i	$0.468002\pi$
$770$		0			0
$771$	−2.25338e30	+	2.25338e30i	−1.09336	+	1.09336i
$772$		0			0
$773$	5.58851e29	+	5.58851e29i	0.263883	+	0.263883i	0.826629	−	0.562747i	$-0.190255\pi$
$773$	5.58851e29	+	5.58851e29i	0.263883	+	0.263883i	−0.562747	+	0.826629i	$0.690255\pi$
$774$		0			0
$775$			2.01112e30i			0.924208i
$776$		0			0
$777$		−	9.76153e30i		−	4.36614i
$778$		0			0
$779$	2.61731e28	+	2.61731e28i	0.0113949	+	0.0113949i
$780$		0			0
$781$	1.98502e30	−	1.98502e30i	0.841257	−	0.841257i
$782$		0			0
$783$	−1.03230e30			−0.425901
$784$		0			0
$785$	1.91327e28			0.00768501
$786$		0			0
$787$	8.09039e29	−	8.09039e29i	0.316399	−	0.316399i	−0.530983	−	0.847382i	$-0.678177\pi$
$787$	8.09039e29	−	8.09039e29i	0.316399	−	0.316399i	0.847382	+	0.530983i	$0.178177\pi$
$788$		0			0
$789$	−1.11590e30	−	1.11590e30i	−0.424931	−	0.424931i
$790$		0			0
$791$		−	6.59656e30i		−	2.44604i
$792$		0			0
$793$		−	6.06451e30i		−	2.18992i
$794$		0			0
$795$	−3.03313e30	−	3.03313e30i	−1.06669	−	1.06669i
$796$		0			0
$797$	2.08417e30	−	2.08417e30i	0.713874	−	0.713874i	−0.253469	−	0.967343i	$-0.581572\pi$
$797$	2.08417e30	−	2.08417e30i	0.713874	−	0.713874i	0.967343	+	0.253469i	$0.0815717\pi$
$798$		0			0
$799$	1.47491e30			0.492069
$800$		0			0
$801$	−1.28602e30			−0.417932
$802$		0			0
$803$	−2.14986e30	+	2.14986e30i	−0.680609	+	0.680609i
$804$		0			0
$805$	−6.22815e28	−	6.22815e28i	−0.0192089	−	0.0192089i
$806$		0			0
$807$			2.55981e30i			0.769192i
$808$		0			0
$809$			2.83522e30i			0.830093i	0.909800	+	0.415046i	$0.136235\pi$
$809$			2.83522e30i			0.830093i	−0.909800	+	0.415046i	$0.863765\pi$
$810$		0			0
$811$	3.27698e30	+	3.27698e30i	0.934878	+	0.934878i	0.998005	−	0.0631273i	$-0.0201074\pi$
$811$	3.27698e30	+	3.27698e30i	0.934878	+	0.934878i	−0.0631273	+	0.998005i	$0.520107\pi$
$812$		0			0
$813$	−6.12213e30	+	6.12213e30i	−1.70197	+	1.70197i
$814$		0			0
$815$	−4.46787e30			−1.21045
$816$		0			0
$817$	5.57986e28			0.0147330
$818$		0			0
$819$	1.16480e31	−	1.16480e31i	2.99757	−	2.99757i
$820$		0			0
$821$	2.77097e30	+	2.77097e30i	0.695069	+	0.695069i	0.963343	−	0.268273i	$-0.0864531\pi$
$821$	2.77097e30	+	2.77097e30i	0.695069	+	0.695069i	−0.268273	+	0.963343i	$0.586453\pi$
$822$		0			0
$823$			6.70276e30i			1.63891i	0.573142	+	0.819456i	$0.305724\pi$
$823$			6.70276e30i			1.63891i	−0.573142	+	0.819456i	$0.694276\pi$
$824$		0			0
$825$			5.02850e30i			1.19859i
$826$		0			0
$827$	4.46161e30	+	4.46161e30i	1.03677	+	1.03677i	0.999298	+	0.0374752i	$0.0119315\pi$
$827$	4.46161e30	+	4.46161e30i	1.03677	+	1.03677i	0.0374752	+	0.999298i	$0.488068\pi$
$828$		0			0
$829$	−1.60098e30	+	1.60098e30i	−0.362713	+	0.362713i	−0.864811	−	0.502098i	$-0.832562\pi$
$829$	−1.60098e30	+	1.60098e30i	−0.362713	+	0.362713i	0.502098	+	0.864811i	$0.332562\pi$
$830$		0			0
$831$	−1.29777e31			−2.86673
$832$		0			0
$833$	−1.07808e31			−2.32209
$834$		0			0
$835$	5.26420e30	−	5.26420e30i	1.10567	−	1.10567i
$836$		0			0
$837$	4.25959e30	+	4.25959e30i	0.872470	+	0.872470i
$838$		0			0
$839$		−	3.61125e30i		−	0.721369i	−0.932688	−	0.360684i	$-0.882543\pi$
$839$		−	3.61125e30i		−	0.721369i	0.932688	−	0.360684i	$-0.117457\pi$
$840$		0			0
$841$			4.32931e30i			0.843452i
$842$		0			0
$843$	−6.59050e29	−	6.59050e29i	−0.125236	−	0.125236i
$844$		0			0
$845$	5.92892e30	−	5.92892e30i	1.09895	−	1.09895i
$846$		0			0
$847$	1.62760e30			0.294287
$848$		0			0
$849$	1.58271e31			2.79171
$850$		0			0
$851$	−7.35189e28	+	7.35189e28i	−0.0126514	+	0.0126514i
$852$		0			0
$853$	−1.64861e30	−	1.64861e30i	−0.276792	−	0.276792i	0.555035	−	0.831827i	$-0.312705\pi$
$853$	−1.64861e30	−	1.64861e30i	−0.276792	−	0.276792i	−0.831827	+	0.555035i	$0.812705\pi$
$854$		0			0
$855$		−	7.08609e30i		−	1.16081i
$856$		0			0
$857$		−	4.03522e30i		−	0.645013i	−0.946567	−	0.322507i	$-0.895475\pi$
$857$		−	4.03522e30i		−	0.645013i	0.946567	−	0.322507i	$-0.104525\pi$
$858$		0			0
$859$	−2.52601e30	−	2.52601e30i	−0.394009	−	0.394009i	0.482105	−	0.876114i	$-0.339872\pi$
$859$	−2.52601e30	−	2.52601e30i	−0.394009	−	0.394009i	−0.876114	+	0.482105i	$0.839872\pi$
$860$		0			0
$861$	4.08073e29	−	4.08073e29i	0.0621162	−	0.0621162i
$862$		0			0
$863$	−6.04849e30			−0.898532			−0.449266	−	0.893398i	$-0.648314\pi$
$863$	−6.04849e30			−0.898532			−0.449266	+	0.893398i	$0.648314\pi$
$864$		0			0
$865$	−1.10474e31			−1.60173
$866$		0			0
$867$	−2.57389e30	+	2.57389e30i	−0.364242	+	0.364242i
$868$		0			0
$869$	−6.84896e30	−	6.84896e30i	−0.946056	−	0.946056i
$870$		0			0
$871$			2.00771e30i			0.270713i
$872$		0			0
$873$			1.09420e31i			1.44028i
$874$		0			0
$875$	2.49138e30	+	2.49138e30i	0.320151	+	0.320151i
$876$		0			0
$877$	6.80664e29	−	6.80664e29i	0.0853960	−	0.0853960i	−0.663118	−	0.748514i	$-0.730767\pi$
$877$	6.80664e29	−	6.80664e29i	0.0853960	−	0.0853960i	0.748514	+	0.663118i	$0.230767\pi$
$878$		0			0
$879$	−6.59135e30			−0.807404
$880$		0			0
$881$	1.10724e31			1.32433			0.662163	−	0.749360i	$-0.269639\pi$
$881$	1.10724e31			1.32433			0.662163	+	0.749360i	$0.269639\pi$
$882$		0			0
$883$	1.00000e31	−	1.00000e31i	1.16792	−	1.16792i	0.185229	−	0.982695i	$-0.440697\pi$
$883$	1.00000e31	−	1.00000e31i	1.16792	−	1.16792i	0.982695	−	0.185229i	$-0.0593026\pi$
$884$		0			0
$885$	−1.11869e31	−	1.11869e31i	−1.27587	−	1.27587i
$886$		0			0
$887$		−	6.82940e30i		−	0.760650i	−0.924853	−	0.380325i	$-0.875812\pi$
$887$		−	6.82940e30i		−	0.760650i	0.924853	−	0.380325i	$-0.124188\pi$
$888$		0			0
$889$			1.77423e29i			0.0192993i
$890$		0			0
$891$	5.79964e29	+	5.79964e29i	0.0616148	+	0.0616148i
$892$		0			0
$893$	1.52094e30	−	1.52094e30i	0.157823	−	0.157823i
$894$		0			0
$895$	1.83720e31			1.86215
$896$		0			0
$897$	−2.81148e29			−0.0278365
$898$		0			0
$899$	−3.31563e30	+	3.31563e30i	−0.320693	+	0.320693i
$900$		0			0
$901$	5.90764e30	+	5.90764e30i	0.558218	+	0.558218i
$902$		0			0
$903$		−	8.69975e29i		−	0.0803129i
$904$		0			0
$905$			5.58916e30i			0.504123i
$906$		0			0
$907$	−8.18722e30	−	8.18722e30i	−0.721540	−	0.721540i	0.247379	−	0.968919i	$-0.420431\pi$
$907$	−8.18722e30	−	8.18722e30i	−0.721540	−	0.721540i	−0.968919	+	0.247379i	$0.920431\pi$
$908$		0			0
$909$	2.40208e31	−	2.40208e31i	2.06856	−	2.06856i
$910$		0			0
$911$	5.09309e30			0.428586			0.214293	−	0.976769i	$-0.431255\pi$
$911$	5.09309e30			0.428586			0.214293	+	0.976769i	$0.431255\pi$
$912$		0			0
$913$	−5.36703e30			−0.441358
$914$		0			0
$915$	−2.87611e31	+	2.87611e31i	−2.31144	+	2.31144i
$916$		0			0
$917$	1.13280e31	+	1.13280e31i	0.889763	+	0.889763i
$918$		0			0
$919$			1.08438e31i			0.832473i	0.909256	+	0.416236i	$0.136651\pi$
$919$			1.08438e31i			0.832473i	−0.909256	+	0.416236i	$0.863349\pi$
$920$		0			0
$921$			4.03586e31i			3.02838i
$922$		0			0
$923$	1.84785e31	+	1.84785e31i	1.35534	+	1.35534i
$924$		0			0
$925$	−1.22407e31	+	1.22407e31i	−0.877640	+	0.877640i
$926$		0			0
$927$	4.22264e30			0.295969
$928$		0			0
$929$	5.22129e30			0.357777			0.178889	−	0.983869i	$-0.442750\pi$
$929$	5.22129e30			0.357777			0.178889	+	0.983869i	$0.442750\pi$
$930$		0			0
$931$	−1.11172e31	+	1.11172e31i	−0.744774	+	0.744774i
$932$		0			0
$933$	−4.16907e30	−	4.16907e30i	−0.273075	−	0.273075i
$934$		0			0
$935$		−	2.19411e31i		−	1.40520i
$936$		0			0
$937$		−	1.39575e31i		−	0.874060i	−0.899447	−	0.437030i	$-0.856030\pi$
$937$		−	1.39575e31i		−	0.874060i	0.899447	−	0.437030i	$-0.143970\pi$
$938$		0			0
$939$	1.98275e31	+	1.98275e31i	1.21417	+	1.21417i
$940$		0			0
$941$	1.31784e29	−	1.31784e29i	0.00789171	−	0.00789171i	−0.703150	−	0.711042i	$-0.748224\pi$
$941$	1.31784e29	−	1.31784e29i	0.00789171	−	0.00789171i	0.711042	+	0.703150i	$0.248224\pi$
$942$		0			0
$943$	−6.14679e27			−0.000359978
$944$		0			0
$945$	−4.39264e31			−2.51589
$946$		0			0
$947$	6.13269e30	−	6.13269e30i	0.343539	−	0.343539i	−0.514157	−	0.857696i	$-0.671895\pi$
$947$	6.13269e30	−	6.13269e30i	0.343539	−	0.343539i	0.857696	+	0.514157i	$0.171895\pi$
$948$		0			0
$949$	−2.00131e31	−	2.00131e31i	−1.09652	−	1.09652i
$950$		0			0
$951$			2.82172e31i			1.51223i
$952$		0			0
$953$			1.04436e31i			0.547486i	0.961803	+	0.273743i	$0.0882618\pi$
$953$			1.04436e31i			0.547486i	−0.961803	+	0.273743i	$0.911738\pi$
$954$		0			0
$955$	7.27672e30	+	7.27672e30i	0.373164	+	0.373164i
$956$		0			0
$957$	−8.29025e30	+	8.29025e30i	−0.415903	+	0.415903i
$958$		0			0
$959$	−4.10927e31			−2.01683
$960$		0			0
$961$	6.53710e30			0.313899
$962$		0			0
$963$	−7.18581e30	+	7.18581e30i	−0.337598	+	0.337598i
$964$		0			0
$965$	−2.34139e31	−	2.34139e31i	−1.07631	−	1.07631i
$966$		0			0
$967$		−	2.06396e31i		−	0.928376i	−0.885737	−	0.464188i	$-0.846346\pi$
$967$		−	2.06396e31i		−	0.928376i	0.885737	−	0.464188i	$-0.153654\pi$
$968$		0			0
$969$			2.21158e31i			0.973426i
$970$		0			0
$971$	−2.43293e31	−	2.43293e31i	−1.04792	−	1.04792i	−0.998793	−	0.0491267i	$-0.984356\pi$
$971$	−2.43293e31	−	2.43293e31i	−1.04792	−	1.04792i	−0.0491267	−	0.998793i	$-0.515644\pi$
$972$		0			0
$973$	−1.16538e31	+	1.16538e31i	−0.491229	+	0.491229i
$974$		0			0
$975$	−4.68102e31			−1.93105
$976$		0			0
$977$	2.68432e31			1.08378			0.541890	−	0.840450i	$-0.317709\pi$
$977$	2.68432e31			1.08378			0.541890	+	0.840450i	$0.317709\pi$
$978$		0			0
$979$	−4.10623e30	+	4.10623e30i	−0.162265	+	0.162265i
$980$		0			0
$981$	−2.52121e31	−	2.52121e31i	−0.975179	−	0.975179i
$982$		0			0
$983$			1.95315e31i			0.739474i	0.929137	+	0.369737i	$0.120552\pi$
$983$			1.95315e31i			0.739474i	−0.929137	+	0.369737i	$0.879448\pi$
$984$		0			0
$985$		−	1.01070e31i		−	0.374577i
$986$		0			0
$987$	−2.37134e31	−	2.37134e31i	−0.860328	−	0.860328i
$988$		0			0
$989$	−6.55220e27	+	6.55220e27i	−0.000232716	+	0.000232716i
$990$		0			0
$991$	−3.72730e31			−1.29605			−0.648023	−	0.761620i	$-0.724404\pi$
$991$	−3.72730e31			−1.29605			−0.648023	+	0.761620i	$0.724404\pi$
$992$		0			0
$993$	9.01375e30			0.306859
$994$		0			0
$995$	4.26275e31	−	4.26275e31i	1.42085	−	1.42085i
$996$		0			0
$997$	2.35585e31	+	2.35585e31i	0.768863	+	0.768863i	0.977906	−	0.209043i	$-0.0670349\pi$
$997$	2.35585e31	+	2.35585e31i	0.768863	+	0.768863i	−0.209043	+	0.977906i	$0.567035\pi$
$998$		0			0
$999$			5.18519e31i			1.65702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.22.e.a.49.4		82
4.3	odd	2		16.22.e.a.5.8	✓	82
16.3	odd	4		16.22.e.a.13.8	yes	82
16.13	even	4	inner	64.22.e.a.17.4		82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.22.e.a.5.8	✓	82	4.3	odd	2
16.22.e.a.13.8	yes	82	16.3	odd	4
64.22.e.a.17.4		82	16.13	even	4	inner
64.22.e.a.49.4		82	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-117950. + 117950. i) q^{3} +(2.07522e7 + 2.07522e7i) q^{5} +1.29970e9i q^{7} -1.73642e10i q^{9} +O(q^{10})\)	\(q+(-117950. + 117950. i) q^{3} +(2.07522e7 + 2.07522e7i) q^{5} +1.29970e9i q^{7} -1.73642e10i q^{9} +(-5.54435e10 - 5.54435e10i) q^{11} +(5.16123e11 - 5.16123e11i) q^{13} -4.89545e12 q^{15} +9.53487e12 q^{17} +(9.83239e12 - 9.83239e12i) q^{19} +(-1.53300e14 - 1.53300e14i) q^{21} +2.30915e12i q^{23} +3.84467e14i q^{25} +(8.14309e14 + 8.14309e14i) q^{27} +(-6.33852e14 + 6.33852e14i) q^{29} +5.23093e15 q^{31} +1.30792e16 q^{33} +(-2.69716e16 + 2.69716e16i) q^{35} +(3.18380e16 + 3.18380e16i) q^{37} +1.21754e17i q^{39} +2.66193e15i q^{41} +(2.83749e15 + 2.83749e15i) q^{43} +(3.60344e17 - 3.60344e17i) q^{45} +1.54686e17 q^{47} -1.13067e18 q^{49} +(-1.12464e18 + 1.12464e18i) q^{51} +(6.19582e17 + 6.19582e17i) q^{53} -2.30114e18i q^{55} +2.31947e18i q^{57} +(2.28518e18 + 2.28518e18i) q^{59} +(5.87506e18 - 5.87506e18i) q^{61} +2.25682e19 q^{63} +2.14213e19 q^{65} +(-1.94499e18 + 1.94499e18i) q^{67} +(-2.72365e17 - 2.72365e17i) q^{69} +3.58026e19i q^{71} -3.87758e19i q^{73} +(-4.53480e19 - 4.53480e19i) q^{75} +(7.20599e19 - 7.20599e19i) q^{77} +1.23530e20 q^{79} -1.04604e19 q^{81} +(4.84009e19 - 4.84009e19i) q^{83} +(1.97869e20 + 1.97869e20i) q^{85} -1.49526e20i q^{87} -7.40615e19i q^{89} +(6.70805e20 + 6.70805e20i) q^{91} +(-6.16989e20 + 6.16989e20i) q^{93} +4.08086e20 q^{95} -6.30147e20 q^{97} +(-9.62731e20 + 9.62731e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 82 * q + 2 * q^3 - 2 * q^5	\( 82 q + 2 q^{3} - 2 q^{5} - 67333320738 q^{11} - 2 q^{13} - 4613203124996 q^{15} - 4 q^{17} + 46007763621434 q^{19} + 20920706404 q^{21} - 11\!\cdots\!20 q^{27}+ \cdots - 27\!\cdots\!38 q^{99}+O(q^{100}) \) 82 * q + 2 * q^3 - 2 * q^5 - 67333320738 * q^11 - 2 * q^13 - 4613203124996 * q^15 - 4 * q^17 + 46007763621434 * q^19 + 20920706404 * q^21 - 1147760716556920 * q^27 - 2433173450216602 * q^29 + 9835539443769616 * q^31 - 4 * q^33 + 19253478556034884 * q^35 - 7245708527119386 * q^37 - 215332019803969386 * q^43 + 953653395699842 * q^45 - 1051982644716600976 * q^47 - 5585458640832840074 * q^49 - 3238772068175213124 * q^51 + 1889987679210147606 * q^53 - 3631979197965016922 * q^59 + 10385362452353654062 * q^61 + 17464422381302680956 * q^63 - 9364161130572538716 * q^65 + 17102217044572669130 * q^67 - 3951842785111207532 * q^69 - 145960939174166395366 * q^75 - 82041801652678580764 * q^77 - 204448210818924484480 * q^79 - 802405920297757300870 * q^81 - 317463236552669319678 * q^83 + 323656241286464843748 * q^85 - 144326756239046079748 * q^91 - 669717759565183008560 * q^93 + 1411330138695550130700 * q^95 - 4 * q^97 - 2710306841526615010238 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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