LMFDB - Embedded newform 45.10.b.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,10,Mod(19,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("45.19");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	45.b (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:	$23.1766126274$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.49740556.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 45x^{2} + 304 $ x^4 + 45*x^2 + 304
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$-2.87724i$ of defining polynomial
Character	$\chi$	$=$	45.19
Dual form			45.10.b.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-41.3193i q^{2} -1195.29 q^{4} +(-1138.29 - 810.818i) q^{5} +5315.22i q^{7} +28233.0i q^{8} +O(q^{10})$	\(q-41.3193i q^{2} -1195.29 q^{4} +(-1138.29 - 810.818i) q^{5} +5315.22i q^{7} +28233.0i q^{8} +(-33502.5 + 47033.3i) q^{10} -10426.2 q^{11} -79655.1i q^{13} +219621. q^{14} +554581. q^{16} +313750. i q^{17} +246945. q^{19} +(1.36058e6 + 969161. i) q^{20} +430806. i q^{22} -721761. i q^{23} +(638273. + 1.84589e6i) q^{25} -3.29130e6 q^{26} -6.35321e6i q^{28} +2.56903e6 q^{29} -3.29543e6 q^{31} -8.45965e6i q^{32} +1.29639e7 q^{34} +(4.30967e6 - 6.05025e6i) q^{35} -1.40463e7i q^{37} -1.02036e7i q^{38} +(2.28918e7 - 3.21373e7i) q^{40} -1.70412e7 q^{41} +2.92261e7i q^{43} +1.24624e7 q^{44} -2.98227e7 q^{46} +4.10316e7i q^{47} +1.21021e7 q^{49} +(7.62709e7 - 2.63730e7i) q^{50} +9.52108e7i q^{52} +5.67230e7i q^{53} +(1.18681e7 + 8.45379e6i) q^{55} -1.50065e8 q^{56} -1.06150e8i q^{58} +1.60408e8 q^{59} +5.33033e7 q^{61} +1.36165e8i q^{62} -6.56012e7 q^{64} +(-6.45858e7 + 9.06705e7i) q^{65} +2.80916e8i q^{67} -3.75022e8i q^{68} +(-2.49992e8 - 1.78073e8i) q^{70} +8.97228e7 q^{71} -7.60225e7i q^{73} -5.80383e8 q^{74} -2.95170e8 q^{76} -5.54178e7i q^{77} -4.10672e8 q^{79} +(-6.31273e8 - 4.49665e8i) q^{80} +7.04131e8i q^{82} +5.21969e8i q^{83} +(2.54394e8 - 3.57138e8i) q^{85} +1.20760e9 q^{86} -2.94364e8i q^{88} +2.37312e8 q^{89} +4.23384e8 q^{91} +8.62712e8i q^{92} +1.69540e9 q^{94} +(-2.81094e8 - 2.00227e8i) q^{95} +6.03778e8i q^{97} -5.00050e8i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1368 q^{4} - 1140 q^{5}+O(q^{10}) $ 4 * q - 1368 * q^4 - 1140 * q^5	$ 4 q - 1368 q^{4} - 1140 q^{5} - 69160 q^{10} - 109968 q^{11} + 424536 q^{14} + 1631264 q^{16} - 636880 q^{19} + 3302280 q^{20} - 1337900 q^{25} - 6618768 q^{26} + 3531720 q^{29} - 10587712 q^{31} + 26434624 q^{34} - 13629840 q^{35} + 43578400 q^{40} + 16788552 q^{41} - 20638944 q^{44} - 61250072 q^{46} - 46921028 q^{49} + 150092400 q^{50} - 26907120 q^{55} - 315178080 q^{56} + 460829040 q^{59} + 360490568 q^{61} + 134995072 q^{64} - 183895680 q^{65} - 508341960 q^{70} + 47611872 q^{71} - 1176861744 q^{74} - 1168489440 q^{76} - 728043520 q^{79} - 965843040 q^{80} + 1275419840 q^{85} + 2375904552 q^{86} + 1582700760 q^{89} + 473322528 q^{91} + 3327101704 q^{94} - 1204791600 q^{95}+O(q^{100}) $ 4 * q - 1368 * q^4 - 1140 * q^5 - 69160 * q^10 - 109968 * q^11 + 424536 * q^14 + 1631264 * q^16 - 636880 * q^19 + 3302280 * q^20 - 1337900 * q^25 - 6618768 * q^26 + 3531720 * q^29 - 10587712 * q^31 + 26434624 * q^34 - 13629840 * q^35 + 43578400 * q^40 + 16788552 * q^41 - 20638944 * q^44 - 61250072 * q^46 - 46921028 * q^49 + 150092400 * q^50 - 26907120 * q^55 - 315178080 * q^56 + 460829040 * q^59 + 360490568 * q^61 + 134995072 * q^64 - 183895680 * q^65 - 508341960 * q^70 + 47611872 * q^71 - 1176861744 * q^74 - 1168489440 * q^76 - 728043520 * q^79 - 965843040 * q^80 + 1275419840 * q^85 + 2375904552 * q^86 + 1582700760 * q^89 + 473322528 * q^91 + 3327101704 * q^94 - 1204791600 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	41.3193i		−	1.82607i	−0.407877	−	0.913037i	$-0.633731\pi$
$2$		−	41.3193i		−	1.82607i	0.407877	−	0.913037i	$-0.366269\pi$
$3$		0			0
$3$		0			0
$4$	−1195.29			−2.33455
$5$	−1138.29	−	810.818i	−0.814492	−	0.580174i
$5$	−1138.29	−	810.818i	−0.814492	−	0.580174i
$6$		0			0
$7$			5315.22i			0.836719i	0.908281	+	0.418360i	$0.137395\pi$
$7$			5315.22i			0.836719i	−0.908281	+	0.418360i	$0.862605\pi$
$8$			28233.0i			2.43698i
$9$		0			0
$10$	−33502.5	+	47033.3i	−1.05944	+	1.48732i
$11$	−10426.2			−0.214714			−0.107357	−	0.994221i	$-0.534239\pi$
$11$	−10426.2			−0.214714			−0.107357	+	0.994221i	$0.534239\pi$
$12$		0			0
$13$		−	79655.1i		−	0.773515i	−0.922181	−	0.386758i	$-0.873595\pi$
$13$		−	79655.1i		−	0.773515i	0.922181	−	0.386758i	$-0.126405\pi$
$14$	219621.			1.52791
$15$		0			0
$16$	554581.			2.11556
$17$			313750.i			0.911095i	0.890212	+	0.455547i	$0.150556\pi$
$17$			313750.i			0.911095i	−0.890212	+	0.455547i	$0.849444\pi$
$18$		0			0
$19$	246945.			0.434719			0.217360	−	0.976092i	$-0.430256\pi$
$19$	246945.			0.434719			0.217360	+	0.976092i	$0.430256\pi$
$20$	1.36058e6	+	969161.i	1.90147	+	1.35444i
$21$		0			0
$22$			430806.i			0.392084i
$23$		−	721761.i		−	0.537797i	−0.963169	−	0.268898i	$-0.913340\pi$
$23$		−	721761.i		−	0.537797i	0.963169	−	0.268898i	$-0.0866595\pi$
$24$		0			0
$25$	638273.	+	1.84589e6i	0.326796	+	0.945095i
$26$	−3.29130e6			−1.41250
$27$		0			0
$28$		−	6.35321e6i		−	1.95336i
$29$	2.56903e6			0.674493			0.337247	−	0.941416i	$-0.390504\pi$
$29$	2.56903e6			0.674493			0.337247	+	0.941416i	$0.390504\pi$
$30$		0			0
$31$	−3.29543e6			−0.640891			−0.320445	−	0.947267i	$-0.603833\pi$
$31$	−3.29543e6			−0.640891			−0.320445	+	0.947267i	$0.603833\pi$
$32$		−	8.45965e6i		−	1.42619i
$33$		0			0
$34$	1.29639e7			1.66373
$35$	4.30967e6	−	6.05025e6i	0.485443	−	0.681502i
$36$		0			0
$37$		−	1.40463e7i		−	1.23212i	−0.787699	−	0.616060i	$-0.788728\pi$
$37$		−	1.40463e7i		−	1.23212i	0.787699	−	0.616060i	$-0.211272\pi$
$38$		−	1.02036e7i		−	0.793830i
$39$		0			0
$40$	2.28918e7	−	3.21373e7i	1.41387	−	1.98490i
$41$	−1.70412e7			−0.941830			−0.470915	−	0.882178i	$-0.656076\pi$
$41$	−1.70412e7			−0.941830			−0.470915	+	0.882178i	$0.656076\pi$
$42$		0			0
$43$			2.92261e7i			1.30365i	0.758368	+	0.651827i	$0.225997\pi$
$43$			2.92261e7i			1.30365i	−0.758368	+	0.651827i	$0.774003\pi$
$44$	1.24624e7			0.501260
$45$		0			0
$46$	−2.98227e7			−0.982056
$47$			4.10316e7i			1.22653i	0.789878	+	0.613264i	$0.210144\pi$
$47$			4.10316e7i			1.22653i	−0.789878	+	0.613264i	$0.789856\pi$
$48$		0			0
$49$	1.21021e7			0.299901
$50$	7.62709e7	−	2.63730e7i	1.72581	−	0.596753i
$51$		0			0
$52$			9.52108e7i			1.80581i
$53$			5.67230e7i			0.987456i	0.869616	+	0.493728i	$0.164366\pi$
$53$			5.67230e7i			0.987456i	−0.869616	+	0.493728i	$0.835634\pi$
$54$		0			0
$55$	1.18681e7	+	8.45379e6i	0.174883	+	0.124572i
$56$	−1.50065e8			−2.03907
$57$		0			0
$58$		−	1.06150e8i		−	1.23167i
$59$	1.60408e8			1.72342			0.861710	−	0.507402i	$-0.169394\pi$
$59$	1.60408e8			1.72342			0.861710	+	0.507402i	$0.169394\pi$
$60$		0			0
$61$	5.33033e7			0.492912			0.246456	−	0.969154i	$-0.420734\pi$
$61$	5.33033e7			0.492912			0.246456	+	0.969154i	$0.420734\pi$
$62$			1.36165e8i			1.17031i
$63$		0			0
$64$	−6.56012e7			−0.488767
$65$	−6.45858e7	+	9.06705e7i	−0.448773	+	0.630022i
$66$		0			0
$67$			2.80916e8i			1.70310i	0.524276	+	0.851548i	$0.324336\pi$
$67$			2.80916e8i			1.70310i	−0.524276	+	0.851548i	$0.675664\pi$
$68$		−	3.75022e8i		−	2.12699i
$69$		0			0
$70$	−2.49992e8	−	1.78073e8i	−1.24447	−	0.886455i
$71$	8.97228e7			0.419025			0.209513	−	0.977806i	$-0.432812\pi$
$71$	8.97228e7			0.419025			0.209513	+	0.977806i	$0.432812\pi$
$72$		0			0
$73$		−	7.60225e7i		−	0.313321i	−0.987653	−	0.156660i	$-0.949927\pi$
$73$		−	7.60225e7i		−	0.313321i	0.987653	−	0.156660i	$-0.0500728\pi$
$74$	−5.80383e8			−2.24994
$75$		0			0
$76$	−2.95170e8			−1.01487
$77$		−	5.54178e7i		−	0.179656i
$78$		0			0
$79$	−4.10672e8			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$79$	−4.10672e8			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$80$	−6.31273e8	−	4.49665e8i	−1.72311	−	1.22739i
$81$		0			0
$82$			7.04131e8i			1.71985i
$83$			5.21969e8i			1.20724i	0.797272	+	0.603620i	$0.206276\pi$
$83$			5.21969e8i			1.20724i	−0.797272	+	0.603620i	$0.793724\pi$
$84$		0			0
$85$	2.54394e8	−	3.57138e8i	0.528594	−	0.742080i
$86$	1.20760e9			2.38057
$87$		0			0
$88$		−	2.94364e8i		−	0.523254i
$89$	2.37312e8			0.400926			0.200463	−	0.979701i	$-0.435755\pi$
$89$	2.37312e8			0.400926			0.200463	+	0.979701i	$0.435755\pi$
$90$		0			0
$91$	4.23384e8			0.647215
$92$			8.62712e8i			1.25551i
$93$		0			0
$94$	1.69540e9			2.23973
$95$	−2.81094e8	−	2.00227e8i	−0.354076	−	0.252213i
$96$		0			0
$97$			6.03778e8i			0.692476i	0.938147	+	0.346238i	$0.112541\pi$
$97$			6.03778e8i			0.692476i	−0.938147	+	0.346238i	$0.887459\pi$
$98$		−	5.00050e8i		−	0.547641i
$99$		0			0
$100$	−7.62920e8	−	2.20637e9i	−0.762920	−	2.20637i
$101$	2.03606e8			0.194690			0.0973451	−	0.995251i	$-0.468965\pi$
$101$	2.03606e8			0.194690			0.0973451	+	0.995251i	$0.468965\pi$
$102$		0			0
$103$			9.15893e8i			0.801821i	0.916117	+	0.400910i	$0.131306\pi$
$103$			9.15893e8i			0.801821i	−0.916117	+	0.400910i	$0.868694\pi$
$104$	2.24890e9			1.88504
$105$		0			0
$106$	2.34376e9			1.80317
$107$			1.66237e9i			1.22603i	0.790072	+	0.613014i	$0.210043\pi$
$107$			1.66237e9i			1.22603i	−0.790072	+	0.613014i	$0.789957\pi$
$108$		0			0
$109$	−1.73161e9			−1.17498			−0.587491	−	0.809231i	$-0.699884\pi$
$109$	−1.73161e9			−1.17498			−0.587491	+	0.809231i	$0.699884\pi$
$110$	3.49305e8	−	4.90381e8i	0.227477	−	0.319350i
$111$		0			0
$112$			2.94772e9i			1.77013i
$113$		−	6.30956e8i		−	0.364038i	−0.983295	−	0.182019i	$-0.941737\pi$
$113$		−	6.30956e8i		−	0.364038i	0.983295	−	0.182019i	$-0.0582632\pi$
$114$		0			0
$115$	−5.85217e8	+	8.21571e8i	−0.312016	+	0.438031i
$116$	−3.07073e9			−1.57464
$117$		0			0
$118$		−	6.62794e9i		−	3.14709i
$119$	−1.66765e9			−0.762331
$120$		0			0
$121$	−2.24924e9			−0.953898
$122$		−	2.20246e9i		−	0.900094i
$123$		0			0
$124$	3.93898e9			1.49619
$125$	7.70141e8	−	2.61868e9i	0.282147	−	0.959371i
$126$		0			0
$127$		−	2.12104e9i		−	0.723490i	−0.932277	−	0.361745i	$-0.882181\pi$
$127$		−	2.12104e9i		−	0.723490i	0.932277	−	0.361745i	$-0.117819\pi$
$128$		−	1.62074e9i		−	0.533664i
$129$		0			0
$130$	3.74644e9	+	2.66864e9i	1.15047	+	0.819494i
$131$	−5.57686e9			−1.65451			−0.827254	−	0.561828i	$-0.810098\pi$
$131$	−5.57686e9			−1.65451			−0.827254	+	0.561828i	$0.810098\pi$
$132$		0			0
$133$			1.31257e9i			0.363738i
$134$	1.16072e10			3.10998
$135$		0			0
$136$	−8.85810e9			−2.22032
$137$		−	2.57317e9i		−	0.624059i	−0.950072	−	0.312029i	$-0.898991\pi$
$137$		−	2.57317e9i		−	0.624059i	0.950072	−	0.312029i	$-0.101009\pi$
$138$		0			0
$139$	1.62297e9			0.368761			0.184380	−	0.982855i	$-0.440972\pi$
$139$	1.62297e9			0.368761			0.184380	+	0.982855i	$0.440972\pi$
$140$	−5.15130e9	+	7.23179e9i	−1.13329	+	1.59100i
$141$		0			0
$142$		−	3.70729e9i		−	0.765171i
$143$			8.30504e8i			0.166085i
$144$		0			0
$145$	−2.92429e9	−	2.08301e9i	−0.549370	−	0.391324i
$146$	−3.14120e9			−0.572147
$147$		0			0
$148$			1.67893e10i			2.87644i
$149$	−5.98422e9			−0.994647			−0.497324	−	0.867565i	$-0.665684\pi$
$149$	−5.98422e9			−0.994647			−0.497324	+	0.867565i	$0.665684\pi$
$150$		0			0
$151$	−5.95089e9			−0.931505			−0.465753	−	0.884915i	$-0.654216\pi$
$151$	−5.95089e9			−0.931505			−0.465753	+	0.884915i	$0.654216\pi$
$152$			6.97200e9i			1.05940i
$153$		0			0
$154$	−2.28983e9			−0.328064
$155$	3.75114e9	+	2.67199e9i	0.522001	+	0.371828i
$156$		0			0
$157$			2.94325e9i			0.386615i	0.981138	+	0.193308i	$0.0619215\pi$
$157$			2.94325e9i			0.386615i	−0.981138	+	0.193308i	$0.938078\pi$
$158$			1.69687e10i			2.16616i
$159$		0			0
$160$	−6.85923e9	+	9.62951e9i	−0.827438	+	1.16162i
$161$	3.83632e9			0.449985
$162$		0			0
$163$			2.69823e9i			0.299389i	0.988732	+	0.149694i	$0.0478290\pi$
$163$			2.69823e9i			0.299389i	−0.988732	+	0.149694i	$0.952171\pi$
$164$	2.03691e10			2.19875
$165$		0			0
$166$	2.15674e10			2.20451
$167$		−	1.47132e10i		−	1.46380i	−0.681410	−	0.731902i	$-0.738633\pi$
$167$		−	1.47132e10i		−	1.46380i	0.681410	−	0.731902i	$-0.261367\pi$
$168$		0			0
$169$	4.25956e9			0.401675
$170$	−1.47567e10	−	1.05114e10i	−1.35509	−	0.965251i
$171$		0			0
$172$		−	3.49336e10i		−	3.04344i
$173$			1.56605e8i			0.0132923i	0.999978	+	0.00664613i	$0.00211555\pi$
$173$			1.56605e8i			0.0132923i	−0.999978	+	0.00664613i	$0.997884\pi$
$174$		0			0
$175$	−9.81130e9	+	3.39256e9i	−0.790779	+	0.273436i
$176$	−5.78220e9			−0.454241
$177$		0			0
$178$		−	9.80557e9i		−	0.732121i
$179$	−5.35516e9			−0.389883			−0.194941	−	0.980815i	$-0.562452\pi$
$179$	−5.35516e9			−0.389883			−0.194941	+	0.980815i	$0.562452\pi$
$180$		0			0
$181$	−1.52107e9			−0.105341			−0.0526704	−	0.998612i	$-0.516773\pi$
$181$	−1.52107e9			−0.105341			−0.0526704	+	0.998612i	$0.516773\pi$
$182$		−	1.74940e10i		−	1.18186i
$183$		0			0
$184$	2.03775e10			1.31060
$185$	−1.13890e10	+	1.59887e10i	−0.714845	+	1.00355i
$186$		0			0
$187$		−	3.27123e9i		−	0.195625i
$188$		−	4.90445e10i		−	2.86339i
$189$		0			0
$190$	−8.27327e9	+	1.16146e10i	−0.460560	+	0.646568i
$191$	9.28266e9			0.504687			0.252344	−	0.967638i	$-0.418799\pi$
$191$	9.28266e9			0.504687			0.252344	+	0.967638i	$0.418799\pi$
$192$		0			0
$193$			6.94351e9i			0.360223i	0.983646	+	0.180111i	$0.0576458\pi$
$193$			6.94351e9i			0.360223i	−0.983646	+	0.180111i	$0.942354\pi$
$194$	2.49477e10			1.26451
$195$		0			0
$196$	−1.44655e10			−0.700132
$197$			3.60722e10i			1.70637i	0.521606	+	0.853187i	$0.325333\pi$
$197$			3.60722e10i			1.70637i	−0.521606	+	0.853187i	$0.674667\pi$
$198$		0			0
$199$	−2.25173e10			−1.01784			−0.508918	−	0.860815i	$-0.669955\pi$
$199$	−2.25173e10			−1.01784			−0.508918	+	0.860815i	$0.669955\pi$
$200$	−5.21150e10	+	1.80204e10i	−2.30318	+	0.796395i
$201$		0			0
$202$		−	8.41286e9i		−	0.355519i
$203$			1.36549e10i			0.564362i
$204$		0			0
$205$	1.93978e10	+	1.38173e10i	0.767114	+	0.546426i
$206$	3.78441e10			1.46418
$207$		0			0
$208$		−	4.41753e10i		−	1.63642i
$209$	−2.57471e9			−0.0933404
$210$		0			0
$211$	3.62300e10			1.25834			0.629169	−	0.777268i	$-0.283395\pi$
$211$	3.62300e10			1.25834			0.629169	+	0.777268i	$0.283395\pi$
$212$		−	6.78003e10i		−	2.30526i
$213$		0			0
$214$	6.86879e10			2.23882
$215$	2.36970e10	−	3.32677e10i	0.756346	−	1.06182i
$216$		0			0
$217$		−	1.75159e10i		−	0.536246i
$218$			7.15490e10i			2.14560i
$219$		0			0
$220$	−1.41858e10	−	1.01047e10i	−0.408273	−	0.290818i
$221$	2.49918e10			0.704746
$222$		0			0
$223$			4.93834e10i			1.33724i	0.743605	+	0.668619i	$0.233114\pi$
$223$			4.93834e10i			1.33724i	−0.743605	+	0.668619i	$0.766886\pi$
$224$	4.49649e10			1.19332
$225$		0			0
$226$	−2.60707e10			−0.664760
$227$			3.27710e10i			0.819169i	0.912272	+	0.409585i	$0.134326\pi$
$227$			3.27710e10i			0.819169i	−0.912272	+	0.409585i	$0.865674\pi$
$228$		0			0
$229$	−1.35586e10			−0.325803			−0.162902	−	0.986642i	$-0.552085\pi$
$229$	−1.35586e10			−0.325803			−0.162902	+	0.986642i	$0.552085\pi$
$230$	3.39468e10	+	2.41808e10i	0.799877	+	0.569764i
$231$		0			0
$232$			7.25313e10i			1.64373i
$233$			7.99837e9i			0.177787i	0.996041	+	0.0888935i	$0.0283331\pi$
$233$			7.99837e9i			0.177787i	−0.996041	+	0.0888935i	$0.971667\pi$
$234$		0			0
$235$	3.32691e10	−	4.67057e10i	0.711600	−	0.998998i
$236$	−1.91733e11			−4.02340
$237$		0			0
$238$			6.89062e10i			1.39207i
$239$	8.30208e10			1.64587			0.822937	−	0.568133i	$-0.192334\pi$
$239$	8.30208e10			1.64587			0.822937	+	0.568133i	$0.192334\pi$
$240$		0			0
$241$	−6.04789e10			−1.15485			−0.577427	−	0.816442i	$-0.695943\pi$
$241$	−6.04789e10			−1.15485			−0.577427	+	0.816442i	$0.695943\pi$
$242$			9.29372e10i			1.74189i
$243$		0			0
$244$	−6.37128e10			−1.15073
$245$	−1.37756e10	−	9.81258e9i	−0.244267	−	0.173995i
$246$		0			0
$247$		−	1.96704e10i		−	0.336262i
$248$		−	9.30398e10i		−	1.56184i
$249$		0			0
$250$	−1.08202e11	−	3.18217e10i	−1.75188	−	0.515221i
$251$	−1.04682e11			−1.66471			−0.832354	−	0.554244i	$-0.813007\pi$
$251$	−1.04682e11			−1.66471			−0.832354	+	0.554244i	$0.813007\pi$
$252$		0			0
$253$			7.52525e9i			0.115473i
$254$	−8.76400e10			−1.32115
$255$		0			0
$256$	−1.00556e11			−1.46328
$257$		−	7.92751e10i		−	1.13354i	−0.823875	−	0.566771i	$-0.808192\pi$
$257$		−	7.92751e10i		−	1.13354i	0.823875	−	0.566771i	$-0.191808\pi$
$258$		0			0
$259$	7.46590e10			1.03094
$260$	7.71987e10	−	1.08377e11i	1.04768	−	1.47082i
$261$		0			0
$262$			2.30432e11i			3.02126i
$263$			1.04629e8i			0.00134850i	1.00000		0.000674250i	$0.000214620\pi$
$263$			1.04629e8i			0.00134850i	−1.00000		0.000674250i	$0.999785\pi$
$264$		0			0
$265$	4.59920e10	−	6.45671e10i	0.572897	−	0.804275i
$266$	5.42344e10			0.664213
$267$		0			0
$268$		−	3.35775e11i		−	3.97596i
$269$	−7.38735e9			−0.0860208			−0.0430104	−	0.999075i	$-0.513695\pi$
$269$	−7.38735e9			−0.0860208			−0.0430104	+	0.999075i	$0.513695\pi$
$270$		0			0
$271$	1.27706e11			1.43831			0.719153	−	0.694852i	$-0.244530\pi$
$271$	1.27706e11			1.43831			0.719153	+	0.694852i	$0.244530\pi$
$272$			1.74000e11i			1.92748i
$273$		0			0
$274$	−1.06322e11			−1.13958
$275$	−6.65479e9	−	1.92457e10i	−0.0701677	−	0.202925i
$276$		0			0
$277$			3.16563e10i			0.323074i	0.986867	+	0.161537i	$0.0516451\pi$
$277$			3.16563e10i			0.323074i	−0.986867	+	0.161537i	$0.948355\pi$
$278$		−	6.70602e10i		−	0.673385i
$279$		0			0
$280$	1.70817e11	+	1.21675e11i	1.66081	+	1.18302i
$281$	9.50309e10			0.909257			0.454628	−	0.890681i	$-0.349772\pi$
$281$	9.50309e10			0.909257			0.454628	+	0.890681i	$0.349772\pi$
$282$		0			0
$283$		−	4.91862e10i		−	0.455832i	−0.973681	−	0.227916i	$-0.926809\pi$
$283$		−	4.91862e10i		−	0.455832i	0.973681	−	0.227916i	$-0.0731911\pi$
$284$	−1.07245e11			−0.978234
$285$		0			0
$286$	3.43159e10			0.303283
$287$		−	9.05777e10i		−	0.788048i
$288$		0			0
$289$	2.01488e10			0.169906
$290$	−8.60687e10	+	1.20830e11i	−0.714586	+	1.00319i
$291$		0			0
$292$			9.08688e10i			0.731462i
$293$			3.53889e10i			0.280519i	0.990115	+	0.140260i	$0.0447937\pi$
$293$			3.53889e10i			0.280519i	−0.990115	+	0.140260i	$0.955206\pi$
$294$		0			0
$295$	−1.82590e11	−	1.30061e11i	−1.40371	−	0.999883i
$296$	3.96568e11			3.00265
$297$		0			0
$298$			2.47264e11i			1.81630i
$299$	−5.74920e10			−0.415994
$300$		0			0
$301$	−1.55343e11			−1.09079
$302$			2.45887e11i			1.70100i
$303$		0			0
$304$	1.36951e11			0.919675
$305$	−6.06745e10	−	4.32193e10i	−0.401473	−	0.285975i
$306$		0			0
$307$		−	8.30301e10i		−	0.533474i	−0.963769	−	0.266737i	$-0.914055\pi$
$307$		−	8.30301e10i		−	0.533474i	0.963769	−	0.266737i	$-0.0859455\pi$
$308$			6.62402e10i			0.419414i
$309$		0			0
$310$	1.10405e11	−	1.54995e11i	0.678986	−	0.953212i
$311$	−2.13935e10			−0.129676			−0.0648382	−	0.997896i	$-0.520653\pi$
$311$	−2.13935e10			−0.129676			−0.0648382	+	0.997896i	$0.520653\pi$
$312$		0			0
$313$			2.56558e11i			1.51090i	0.655204	+	0.755452i	$0.272582\pi$
$313$			2.56558e11i			1.51090i	−0.655204	+	0.755452i	$0.727418\pi$
$314$	1.21613e11			0.705988
$315$		0			0
$316$	4.90871e11			2.76933
$317$		−	1.26112e11i		−	0.701436i	−0.936481	−	0.350718i	$-0.885938\pi$
$317$		−	1.26112e11i		−	0.701436i	0.936481	−	0.350718i	$-0.114062\pi$
$318$		0			0
$319$	−2.67853e10			−0.144823
$320$	7.46731e10	+	5.31907e10i	0.398097	+	0.283570i
$321$		0			0
$322$		−	1.58514e11i		−	0.821706i
$323$			7.74790e10i			0.396071i
$324$		0			0
$325$	1.47035e11	−	5.08417e10i	0.731045	−	0.252781i
$326$	1.11489e11			0.546706
$327$		0			0
$328$		−	4.81124e11i		−	2.29522i
$329$	−2.18092e11			−1.02626
$330$		0			0
$331$	1.71300e11			0.784389			0.392194	−	0.919882i	$-0.371716\pi$
$331$	1.71300e11			0.784389			0.392194	+	0.919882i	$0.371716\pi$
$332$		−	6.23904e11i		−	2.81836i
$333$		0			0
$334$	−6.07939e11			−2.67301
$335$	2.27771e11	−	3.19763e11i	0.988093	−	1.38716i
$336$		0			0
$337$		−	4.70320e11i		−	1.98637i	−0.116569	−	0.993183i	$-0.537190\pi$
$337$		−	4.70320e11i		−	1.98637i	0.116569	−	0.993183i	$-0.462810\pi$
$338$		−	1.76002e11i		−	0.733487i
$339$		0			0
$340$	−3.04074e11	+	4.26882e11i	−1.23403	+	1.73242i
$341$	3.43589e10			0.137608
$342$		0			0
$343$			2.78813e11i			1.08765i
$344$	−8.25140e11			−3.17698
$345$		0			0
$346$	6.47083e9			0.0242727
$347$			2.86642e11i			1.06135i	0.847576	+	0.530674i	$0.178061\pi$
$347$			2.86642e11i			1.06135i	−0.847576	+	0.530674i	$0.821939\pi$
$348$		0			0
$349$	3.54310e11			1.27841			0.639203	−	0.769038i	$-0.279264\pi$
$349$	3.54310e11			1.27841			0.639203	+	0.769038i	$0.279264\pi$
$350$	1.40178e11	+	4.05396e11i	0.499315	+	1.44402i
$351$		0			0
$352$			8.82023e10i			0.306223i
$353$			2.09491e11i			0.718092i	0.933320	+	0.359046i	$0.116898\pi$
$353$			2.09491e11i			0.718092i	−0.933320	+	0.359046i	$0.883102\pi$
$354$		0			0
$355$	−1.02130e11	−	7.27489e10i	−0.341293	−	0.243108i
$356$	−2.83656e11			−0.935981
$357$		0			0
$358$			2.21272e11i			0.711955i
$359$	2.88081e11			0.915355			0.457678	−	0.889118i	$-0.348681\pi$
$359$	2.88081e11			0.915355			0.457678	+	0.889118i	$0.348681\pi$
$360$		0			0
$361$	−2.61706e11			−0.811019
$362$			6.28498e10i			0.192360i
$363$		0			0
$364$	−5.06066e11			−1.51095
$365$	−6.16404e10	+	8.65355e10i	−0.181781	+	0.255197i
$366$		0			0
$367$		−	1.33587e10i		−	0.0384387i	−0.999815	−	0.0192193i	$-0.993882\pi$
$367$		−	1.33587e10i		−	0.0384387i	0.999815	−	0.0192193i	$-0.00611808\pi$
$368$		−	4.00275e11i		−	1.13774i
$369$		0			0
$370$	6.60642e11	+	4.70585e11i	1.83256	+	1.30536i
$371$	−3.01495e11			−0.826224
$372$		0			0
$373$			4.17763e11i			1.11748i	0.829342	+	0.558741i	$0.188716\pi$
$373$			4.17763e11i			1.11748i	−0.829342	+	0.558741i	$0.811284\pi$
$374$	−1.35165e11			−0.357226
$375$		0			0
$376$	−1.15844e12			−2.98903
$377$		−	2.04636e11i		−	0.521731i
$378$		0			0
$379$	−2.63110e11			−0.655031			−0.327515	−	0.944846i	$-0.606211\pi$
$379$	−2.63110e11			−0.655031			−0.327515	+	0.944846i	$0.606211\pi$
$380$	3.35989e11	+	2.39329e11i	0.826606	+	0.588803i
$381$		0			0
$382$		−	3.83553e11i		−	0.921596i
$383$			7.84146e10i			0.186210i	0.995656	+	0.0931049i	$0.0296792\pi$
$383$			7.84146e10i			0.186210i	−0.995656	+	0.0931049i	$0.970321\pi$
$384$		0			0
$385$	−4.49337e10	+	6.30814e10i	−0.104232	+	0.146328i
$386$	2.86901e11			0.657793
$387$		0			0
$388$		−	7.21688e11i		−	1.61662i
$389$	1.66007e11			0.367581			0.183791	−	0.982965i	$-0.441163\pi$
$389$	1.66007e11			0.367581			0.183791	+	0.982965i	$0.441163\pi$
$390$		0			0
$391$	2.26452e11			0.489984
$392$			3.41678e11i			0.730852i
$393$		0			0
$394$	1.49048e12			3.11596
$395$	4.67462e11	+	3.32980e11i	0.966184	+	0.688226i
$396$		0			0
$397$			4.09536e11i			0.827437i	0.910405	+	0.413719i	$0.135770\pi$
$397$			4.09536e11i			0.827437i	−0.910405	+	0.413719i	$0.864230\pi$
$398$			9.30402e11i			1.85865i
$399$		0			0
$400$	3.53974e11	+	1.02370e12i	0.691356	+	1.99941i
$401$	7.92645e10			0.153084			0.0765419	−	0.997066i	$-0.475612\pi$
$401$	7.92645e10			0.153084			0.0765419	+	0.997066i	$0.475612\pi$
$402$		0			0
$403$			2.62498e11i			0.495739i
$404$	−2.43367e11			−0.454513
$405$		0			0
$406$	5.64213e11			1.03057
$407$			1.46450e11i			0.264554i
$408$		0			0
$409$	−6.85827e11			−1.21188			−0.605940	−	0.795510i	$-0.707203\pi$
$409$	−6.85827e11			−1.21188			−0.605940	+	0.795510i	$0.707203\pi$
$410$	5.70922e11	−	8.01504e11i	0.997814	−	1.40081i
$411$		0			0
$412$		−	1.09476e12i		−	1.87189i
$413$			8.52601e11i			1.44202i
$414$		0			0
$415$	4.23222e11	−	5.94151e11i	0.700410	−	0.983288i
$416$	−6.73854e11			−1.10318
$417$		0			0
$418$			1.06385e11i			0.170447i
$419$	3.31879e11			0.526037			0.263018	−	0.964791i	$-0.415282\pi$
$419$	3.31879e11			0.526037			0.263018	+	0.964791i	$0.415282\pi$
$420$		0			0
$421$	−6.30694e11			−0.978475			−0.489237	−	0.872151i	$-0.662725\pi$
$421$	−6.30694e11			−0.978475			−0.489237	+	0.872151i	$0.662725\pi$
$422$		−	1.49700e12i		−	2.29782i
$423$		0			0
$424$	−1.60146e12			−2.40641
$425$	−5.79148e11	+	2.00258e11i	−0.861071	+	0.297742i
$426$		0			0
$427$			2.83319e11i			0.412429i
$428$		−	1.98701e12i		−	2.86222i
$429$		0			0
$430$	−1.37460e12	−	9.79145e11i	−1.93896	−	1.38114i
$431$	−7.70903e11			−1.07610			−0.538049	−	0.842913i	$-0.680839\pi$
$431$	−7.70903e11			−1.07610			−0.538049	+	0.842913i	$0.680839\pi$
$432$		0			0
$433$			1.07829e12i			1.47415i	0.675811	+	0.737075i	$0.263794\pi$
$433$			1.07829e12i			1.47415i	−0.675811	+	0.737075i	$0.736206\pi$
$434$	−7.23746e11			−0.979225
$435$		0			0
$436$	2.06977e12			2.74305
$437$		−	1.78235e11i		−	0.233791i
$438$		0			0
$439$	9.56419e11			1.22902			0.614508	−	0.788910i	$-0.289354\pi$
$439$	9.56419e11			1.22902			0.614508	+	0.788910i	$0.289354\pi$
$440$	−2.38676e11	+	3.35071e11i	−0.303579	+	0.426187i
$441$		0			0
$442$		−	1.03264e12i		−	1.28692i
$443$		−	2.06392e11i		−	0.254611i	−0.991864	−	0.127305i	$-0.959367\pi$
$443$		−	2.06392e11i		−	0.254611i	0.991864	−	0.127305i	$-0.0406328\pi$
$444$		0			0
$445$	−2.70129e11	−	1.92417e11i	−0.326551	−	0.232607i
$446$	2.04049e12			2.44190
$447$		0			0
$448$		−	3.48685e11i		−	0.408961i
$449$	1.75939e11			0.204293			0.102147	−	0.994769i	$-0.467429\pi$
$449$	1.75939e11			0.204293			0.102147	+	0.994769i	$0.467429\pi$
$450$		0			0
$451$	1.77676e11			0.202224
$452$			7.54174e11i			0.849863i
$453$		0			0
$454$	1.35408e12			1.49586
$455$	−4.81933e11	−	3.43288e11i	−0.527152	−	0.375497i
$456$		0			0
$457$			2.98819e11i			0.320469i	0.987079	+	0.160234i	$0.0512250\pi$
$457$			2.98819e11i			0.320469i	−0.987079	+	0.160234i	$0.948775\pi$
$458$			5.60233e11i			0.594941i
$459$		0			0
$460$	6.99502e11	−	9.82014e11i	0.728415	−	1.02260i
$461$	−4.39422e11			−0.453135			−0.226567	−	0.973995i	$-0.572750\pi$
$461$	−4.39422e11			−0.453135			−0.226567	+	0.973995i	$0.572750\pi$
$462$		0			0
$463$		−	1.16254e12i		−	1.17569i	−0.808973	−	0.587846i	$-0.799976\pi$
$463$		−	1.16254e12i		−	1.17569i	0.808973	−	0.587846i	$-0.200024\pi$
$464$	1.42473e12			1.42693
$465$		0			0
$466$	3.30487e11			0.324652
$467$		−	1.65923e11i		−	0.161429i	−0.996737	−	0.0807144i	$-0.974280\pi$
$467$		−	1.65923e11i		−	0.161429i	0.996737	−	0.0807144i	$-0.0257202\pi$
$468$		0			0
$469$	−1.49313e12			−1.42501
$470$	−1.92985e12	−	1.37466e12i	−1.82425	−	1.29944i
$471$		0			0
$472$			4.52879e12i			4.19994i
$473$		−	3.04718e11i		−	0.279913i
$474$		0			0
$475$	1.57618e11	+	4.55833e11i	0.142064	+	0.410851i
$476$	1.99332e12			1.77970
$477$		0			0
$478$		−	3.43036e12i		−	3.00549i
$479$	1.33180e11			0.115592			0.0577960	−	0.998328i	$-0.481593\pi$
$479$	1.33180e11			0.115592			0.0577960	+	0.998328i	$0.481593\pi$
$480$		0			0
$481$	−1.11886e12			−0.953064
$482$			2.49895e12i			2.10885i
$483$		0			0
$484$	2.68849e12			2.22692
$485$	4.89554e11	−	6.87273e11i	0.401756	−	0.564016i
$486$		0			0
$487$		−	1.43276e12i		−	1.15423i	−0.816662	−	0.577116i	$-0.804178\pi$
$487$		−	1.43276e12i		−	1.15423i	0.816662	−	0.577116i	$-0.195822\pi$
$488$			1.50491e12i			1.20122i
$489$		0			0
$490$	−4.05449e11	+	5.69200e11i	−0.317727	+	0.446049i
$491$	1.05688e12			0.820655			0.410327	−	0.911938i	$-0.365414\pi$
$491$	1.05688e12			0.820655			0.410327	+	0.911938i	$0.365414\pi$
$492$		0			0
$493$			8.06032e11i			0.614527i
$494$	−8.12769e11			−0.614039
$495$		0			0
$496$	−1.82758e12			−1.35584
$497$			4.76896e11i			0.350607i
$498$		0			0
$499$	−1.77897e11			−0.128445			−0.0642223	−	0.997936i	$-0.520457\pi$
$499$	−1.77897e11			−0.128445			−0.0642223	+	0.997936i	$0.520457\pi$
$500$	−9.20541e11	+	3.13007e12i	−0.658685	+	2.23970i
$501$		0			0
$502$			4.32537e12i			3.03988i
$503$		−	1.58467e12i		−	1.10378i	−0.833917	−	0.551889i	$-0.813907\pi$
$503$		−	1.58467e12i		−	1.10378i	0.833917	−	0.551889i	$-0.186093\pi$
$504$		0			0
$505$	−2.31762e11	−	1.65087e11i	−0.158574	−	0.112954i
$506$	3.10939e11			0.210861
$507$		0			0
$508$			2.53525e12i			1.68902i
$509$	−1.93674e12			−1.27891			−0.639456	−	0.768827i	$-0.720841\pi$
$509$	−1.93674e12			−1.27891			−0.639456	+	0.768827i	$0.720841\pi$
$510$		0			0
$511$	4.04076e11			0.262162
$512$			3.32508e12i			2.13839i
$513$		0			0
$514$	−3.27560e12			−2.06993
$515$	7.42623e11	−	1.04255e12i	0.465196	−	0.653077i
$516$		0			0
$517$		−	4.27805e11i		−	0.263353i
$518$		−	3.08486e12i		−	1.88257i
$519$		0			0
$520$	−2.55990e12	−	1.82345e12i	−1.53535	−	1.09365i
$521$	−2.72419e12			−1.61982			−0.809912	−	0.586552i	$-0.800485\pi$
$521$	−2.72419e12			−1.61982			−0.809912	+	0.586552i	$0.800485\pi$
$522$		0			0
$523$			4.86784e11i			0.284497i	0.989831	+	0.142249i	$0.0454333\pi$
$523$			4.86784e11i			0.284497i	−0.989831	+	0.142249i	$0.954567\pi$
$524$	6.66596e12			3.86253
$525$		0			0
$526$	4.32320e9			0.00246246
$527$		−	1.03394e12i		−	0.583912i
$528$		0			0
$529$	1.28021e12			0.710775
$530$	−2.66787e12	−	1.90036e12i	−1.46867	−	1.04615i
$531$		0			0
$532$		−	1.56889e12i		−	0.849164i
$533$			1.35742e12i			0.728520i
$534$		0			0
$535$	1.34788e12	−	1.89225e12i	0.711309	−	0.998590i
$536$	−7.93109e12			−4.15041
$537$		0			0
$538$			3.05240e11i			0.157080i
$539$	−1.26179e11			−0.0643929
$540$		0			0
$541$	1.98233e11			0.0994920			0.0497460	−	0.998762i	$-0.484159\pi$
$541$	1.98233e11			0.0994920			0.0497460	+	0.998762i	$0.484159\pi$
$542$		−	5.27675e12i		−	2.62645i
$543$		0			0
$544$	2.65421e12			1.29939
$545$	1.97107e12	+	1.40402e12i	0.957014	+	0.681694i
$546$		0			0
$547$			4.79532e11i			0.229021i	0.993422	+	0.114510i	$0.0365299\pi$
$547$			4.79532e11i			0.229021i	−0.993422	+	0.114510i	$0.963470\pi$
$548$			3.07567e12i			1.45689i
$549$		0			0
$550$	−7.95219e11	+	2.74972e11i	−0.370557	+	0.128131i
$551$	6.34408e11			0.293215
$552$		0			0
$553$		−	2.18281e12i		−	0.992550i
$554$	1.30802e12			0.589957
$555$		0			0
$556$	−1.93992e12			−0.860889
$557$			1.20856e11i			0.0532011i	0.999646	+	0.0266006i	$0.00846822\pi$
$557$			1.20856e11i			0.0532011i	−0.999646	+	0.0266006i	$0.991532\pi$
$558$		0			0
$559$	2.32801e12			1.00840
$560$	2.39007e12	−	3.35536e12i	1.02698	−	1.44176i
$561$		0			0
$562$		−	3.92662e12i		−	1.66037i
$563$			1.01468e12i			0.425637i	0.977092	+	0.212818i	$0.0682643\pi$
$563$			1.01468e12i			0.425637i	−0.977092	+	0.212818i	$0.931736\pi$
$564$		0			0
$565$	−5.11591e11	+	7.18210e11i	−0.211205	+	0.296506i
$566$	−2.03234e12			−0.832382
$567$		0			0
$568$			2.53314e12i			1.02116i
$569$	1.12630e12			0.450454			0.225227	−	0.974306i	$-0.427688\pi$
$569$	1.12630e12			0.450454			0.225227	+	0.974306i	$0.427688\pi$
$570$		0			0
$571$	−2.75478e12			−1.08449			−0.542243	−	0.840221i	$-0.682425\pi$
$571$	−2.75478e12			−1.08449			−0.542243	+	0.840221i	$0.682425\pi$
$572$		−	9.92691e11i		−	0.387732i
$573$		0			0
$574$	−3.74261e12			−1.43903
$575$	1.33229e12	−	4.60680e11i	0.508269	−	0.175750i
$576$		0			0
$577$			4.14763e12i			1.55779i	0.627155	+	0.778895i	$0.284219\pi$
$577$			4.14763e12i			1.55779i	−0.627155	+	0.778895i	$0.715781\pi$
$578$		−	8.32535e11i		−	0.310261i
$579$		0			0
$580$	3.49537e12	+	2.48980e12i	1.28253	+	0.913563i
$581$	−2.77438e12			−1.01012
$582$		0			0
$583$		−	5.91408e11i		−	0.212021i
$584$	2.14634e12			0.763557
$585$		0			0
$586$	1.46224e12			0.512248
$587$		−	1.38017e12i		−	0.479800i	−0.970798	−	0.239900i	$-0.922885\pi$
$587$		−	1.38017e12i		−	0.479800i	0.970798	−	0.239900i	$-0.0771147\pi$
$588$		0			0
$589$	−8.13789e11			−0.278608
$590$	−5.37405e12	+	7.54450e12i	−1.82586	+	2.56328i
$591$		0			0
$592$		−	7.78980e12i		−	2.60663i
$593$		−	6.90406e11i		−	0.229276i	−0.993407	−	0.114638i	$-0.963429\pi$
$593$		−	6.90406e11i		−	0.229276i	0.993407	−	0.114638i	$-0.0365708\pi$
$594$		0			0
$595$	1.89827e12	+	1.35216e12i	0.620913	+	0.442285i
$596$	7.15286e12			2.32205
$597$		0			0
$598$			2.37553e12i			0.759635i
$599$	1.24239e12			0.394309			0.197155	−	0.980372i	$-0.436830\pi$
$599$	1.24239e12			0.394309			0.197155	+	0.980372i	$0.436830\pi$
$600$		0			0
$601$	2.01140e12			0.628873			0.314437	−	0.949278i	$-0.398184\pi$
$601$	2.01140e12			0.628873			0.314437	+	0.949278i	$0.398184\pi$
$602$			6.41867e12i			1.99187i
$603$		0			0
$604$	7.11302e12			2.17464
$605$	2.56028e12	+	1.82373e12i	0.776943	+	0.553427i
$606$		0			0
$607$		−	2.73579e12i		−	0.817963i	−0.912543	−	0.408981i	$-0.865884\pi$
$607$		−	2.73579e12i		−	0.817963i	0.912543	−	0.408981i	$-0.134116\pi$
$608$		−	2.08907e12i		−	0.619992i
$609$		0			0
$610$	−1.78579e12	+	2.50703e12i	−0.522211	+	0.733120i
$611$	3.26838e12			0.948738
$612$		0			0
$613$		−	1.63707e12i		−	0.468269i	−0.972204	−	0.234135i	$-0.924774\pi$
$613$		−	1.63707e12i		−	0.468269i	0.972204	−	0.234135i	$-0.0752257\pi$
$614$	−3.43075e12			−0.974162
$615$		0			0
$616$	1.56461e12			0.437817
$617$			1.22267e12i			0.339646i	0.985475	+	0.169823i	$0.0543197\pi$
$617$			1.22267e12i			0.339646i	−0.985475	+	0.169823i	$0.945680\pi$
$618$		0			0
$619$	5.78784e12			1.58456			0.792280	−	0.610158i	$-0.208894\pi$
$619$	5.78784e12			1.58456			0.792280	+	0.610158i	$0.208894\pi$
$620$	−4.48370e12	−	3.19380e12i	−1.21863	−	0.868050i
$621$		0			0
$622$			8.83967e11i			0.236799i
$623$			1.26136e12i			0.335463i
$624$		0			0
$625$	−2.99991e12	+	2.35636e12i	−0.786409	+	0.617706i
$626$	1.06008e13			2.75902
$627$		0			0
$628$		−	3.51803e12i		−	0.902571i
$629$	4.40702e12			1.12258
$630$		0			0
$631$	2.00341e12			0.503081			0.251540	−	0.967847i	$-0.419063\pi$
$631$	2.00341e12			0.503081			0.251540	+	0.967847i	$0.419063\pi$
$632$		−	1.15945e13i		−	2.89084i
$633$		0			0
$634$	−5.21084e12			−1.28087
$635$	−1.71978e12	+	2.41435e12i	−0.419750	+	0.589277i
$636$		0			0
$637$		−	9.63992e11i		−	0.231978i
$638$			1.10675e12i			0.264458i
$639$		0			0
$640$	−1.31412e12	+	1.84487e12i	−0.309618	+	0.434666i
$641$	−2.75478e12			−0.644505			−0.322253	−	0.946654i	$-0.604440\pi$
$641$	−2.75478e12			−0.644505			−0.322253	+	0.946654i	$0.604440\pi$
$642$		0			0
$643$		−	7.38857e12i		−	1.70455i	−0.523091	−	0.852277i	$-0.675221\pi$
$643$		−	7.38857e12i		−	1.70455i	0.523091	−	0.852277i	$-0.324779\pi$
$644$	−4.58550e12			−1.05051
$645$		0			0
$646$	3.20138e12			0.723254
$647$			4.12045e12i			0.924432i	0.886767	+	0.462216i	$0.152946\pi$
$647$			4.12045e12i			0.924432i	−0.886767	+	0.462216i	$0.847054\pi$
$648$		0			0
$649$	−1.67245e12			−0.370043
$650$	−2.10075e12	−	6.07537e12i	−0.461598	−	1.33494i
$651$		0			0
$652$		−	3.22517e12i		−	0.698937i
$653$		−	6.51407e12i		−	1.40198i	−0.713170	−	0.700992i	$-0.752741\pi$
$653$		−	6.51407e12i		−	1.40198i	0.713170	−	0.700992i	$-0.247259\pi$
$654$		0			0
$655$	6.34807e12	+	4.52182e12i	1.34758	+	0.959903i
$656$	−9.45073e12			−1.99250
$657$		0			0
$658$			9.01141e12i			1.87403i
$659$	−1.74145e12			−0.359688			−0.179844	−	0.983695i	$-0.557559\pi$
$659$	−1.74145e12			−0.359688			−0.179844	+	0.983695i	$0.557559\pi$
$660$		0			0
$661$	−1.39849e12			−0.284939			−0.142469	−	0.989799i	$-0.545504\pi$
$661$	−1.39849e12			−0.284939			−0.142469	+	0.989799i	$0.545504\pi$
$662$		−	7.07800e12i		−	1.43235i
$663$		0			0
$664$	−1.47368e13			−2.94202
$665$	1.06425e12	−	1.49408e12i	0.211031	−	0.296262i
$666$		0			0
$667$		−	1.85422e12i		−	0.362740i
$668$			1.75865e13i			3.41732i
$669$		0			0
$670$	−1.32124e13	−	9.41137e12i	−2.53306	−	1.80433i
$671$	−5.55753e11			−0.105835
$672$		0			0
$673$			7.23077e12i			1.35868i	0.733824	+	0.679340i	$0.237734\pi$
$673$			7.23077e12i			1.35868i	−0.733824	+	0.679340i	$0.762266\pi$
$674$	−1.94333e13			−3.62725
$675$		0			0
$676$	−5.09140e12			−0.937728
$677$			1.09854e12i			0.200986i	0.994938	+	0.100493i	$0.0320419\pi$
$677$			1.09854e12i			0.200986i	−0.994938	+	0.100493i	$0.967958\pi$
$678$		0			0
$679$	−3.20921e12			−0.579408
$680$	1.00831e13	+	7.18231e12i	1.80843	+	1.28817i
$681$		0			0
$682$		−	1.41969e12i		−	0.251283i
$683$		−	1.51781e12i		−	0.266885i	−0.991057	−	0.133442i	$-0.957397\pi$
$683$		−	1.51781e12i		−	0.266885i	0.991057	−	0.133442i	$-0.0426031\pi$
$684$		0			0
$685$	−2.08637e12	+	2.92900e12i	−0.362063	+	0.508291i
$686$	1.15204e13			1.98613
$687$		0			0
$688$			1.62082e13i			2.75796i
$689$	4.51828e12			0.763812
$690$		0			0
$691$	1.51489e12			0.252772			0.126386	−	0.991981i	$-0.459662\pi$
$691$	1.51489e12			0.252772			0.126386	+	0.991981i	$0.459662\pi$
$692$		−	1.87188e11i		−	0.0310314i
$693$		0			0
$694$	1.18439e13			1.93810
$695$	−1.84741e12	−	1.31594e12i	−0.300353	−	0.213946i
$696$		0			0
$697$		−	5.34668e12i		−	0.858097i
$698$		−	1.46398e13i		−	2.33446i
$699$		0			0
$700$	1.17273e13	−	4.05509e12i	1.84611	−	0.638350i
$701$	−7.62368e12			−1.19243			−0.596216	−	0.802824i	$-0.703330\pi$
$701$	−7.62368e12			−1.19243			−0.596216	+	0.802824i	$0.703330\pi$
$702$		0			0
$703$		−	3.46866e12i		−	0.535627i
$704$	6.83975e11			0.104945
$705$		0			0
$706$	8.65605e12			1.31129
$707$			1.08221e12i			0.162901i
$708$		0			0
$709$	−1.00657e13			−1.49602			−0.748010	−	0.663687i	$-0.768991\pi$
$709$	−1.00657e13			−1.49602			−0.748010	+	0.663687i	$0.768991\pi$
$710$	−3.00594e12	+	4.21996e12i	−0.443933	+	0.623226i
$711$		0			0
$712$			6.70002e12i			0.977049i
$713$			2.37851e12i			0.344669i
$714$		0			0
$715$	6.73388e11	−	9.45353e11i	0.0963580	−	0.135275i
$716$	6.40096e12			0.910199
$717$		0			0
$718$		−	1.19033e13i		−	1.67151i
$719$	8.94464e12			1.24820			0.624098	−	0.781346i	$-0.285466\pi$
$719$	8.94464e12			1.24820			0.624098	+	0.781346i	$0.285466\pi$
$720$		0			0
$721$	−4.86817e12			−0.670899
$722$			1.08135e13i			1.48098i
$723$		0			0
$724$	1.81812e12			0.245923
$725$	1.63974e12	+	4.74214e12i	0.220422	+	0.637460i
$726$		0			0
$727$			1.22168e13i			1.62201i	0.585038	+	0.811006i	$0.301079\pi$
$727$			1.22168e13i			1.62201i	−0.585038	+	0.811006i	$0.698921\pi$
$728$			1.19534e13i			1.57725i
$729$		0			0
$730$	3.57559e12	+	2.54694e12i	0.466009	+	0.331945i
$731$	−9.16968e12			−1.18775
$732$		0			0
$733$		−	1.44452e13i		−	1.84823i	−0.382118	−	0.924114i	$-0.624805\pi$
$733$		−	1.44452e13i		−	1.84823i	0.382118	−	0.924114i	$-0.375195\pi$
$734$	−5.51974e11			−0.0701919
$735$		0			0
$736$	−6.10584e12			−0.767000
$737$		−	2.92889e12i		−	0.365679i
$738$		0			0
$739$	1.11591e13			1.37635			0.688175	−	0.725545i	$-0.258412\pi$
$739$	1.11591e13			1.37635			0.688175	+	0.725545i	$0.258412\pi$
$740$	1.36131e13	−	1.91111e13i	1.66884	−	2.34284i
$741$		0			0
$742$			1.24576e13i			1.50875i
$743$		−	9.35882e12i		−	1.12660i	−0.826251	−	0.563302i	$-0.809531\pi$
$743$		−	9.35882e12i		−	1.12660i	0.826251	−	0.563302i	$-0.190469\pi$
$744$		0			0
$745$	6.81176e12	+	4.85211e12i	0.810133	+	0.577069i
$746$	1.72617e13			2.04061
$747$		0			0
$748$			3.91007e12i			0.456696i
$749$	−8.83585e12			−1.02584
$750$		0			0
$751$	−1.28609e13			−1.47533			−0.737667	−	0.675165i	$-0.764072\pi$
$751$	−1.28609e13			−1.47533			−0.737667	+	0.675165i	$0.764072\pi$
$752$			2.27553e13i			2.59480i
$753$		0			0
$754$	−8.45543e12			−0.952719
$755$	6.77382e12	+	4.82509e12i	0.758704	+	0.540435i
$756$		0			0
$757$			1.42250e13i			1.57442i	0.616684	+	0.787211i	$0.288476\pi$
$757$			1.42250e13i			1.57442i	−0.616684	+	0.787211i	$0.711524\pi$
$758$			1.08716e13i			1.19613i
$759$		0			0
$760$	5.65302e12	−	7.93614e12i	0.614638	−	0.862875i
$761$	−1.65722e13			−1.79122			−0.895610	−	0.444841i	$-0.853260\pi$
$761$	−1.65722e13			−1.79122			−0.895610	+	0.444841i	$0.853260\pi$
$762$		0			0
$763$		−	9.20389e12i		−	0.983130i
$764$	−1.10954e13			−1.17822
$765$		0			0
$766$	3.24004e12			0.340033
$767$		−	1.27773e13i		−	1.33309i
$768$		0			0
$769$	−2.81269e12			−0.290037			−0.145019	−	0.989429i	$-0.546324\pi$
$769$	−2.81269e12			−0.290037			−0.145019	+	0.989429i	$0.546324\pi$
$770$	2.60648e12	+	1.85663e12i	0.267206	+	0.190334i
$771$		0			0
$772$		−	8.29949e12i		−	0.840957i
$773$		−	8.57982e12i		−	0.864311i	−0.901799	−	0.432156i	$-0.857753\pi$
$773$		−	8.57982e12i		−	0.864311i	0.901799	−	0.432156i	$-0.142247\pi$
$774$		0			0
$775$	−2.10338e12	−	6.08299e12i	−0.209440	−	0.605703i
$776$	−1.70465e13			−1.68755
$777$		0			0
$778$		−	6.85930e12i		−	0.671230i
$779$	−4.20824e12			−0.409432
$780$		0			0
$781$	−9.35472e11			−0.0899707
$782$		−	9.35687e12i		−	0.894746i
$783$		0			0
$784$	6.71158e12			0.634458
$785$	2.38644e12	−	3.35027e12i	0.224304	−	0.314895i
$786$		0			0
$787$		−	1.75771e12i		−	0.163328i	−0.996660	−	0.0816642i	$-0.973976\pi$
$787$		−	1.75771e12i		−	0.163328i	0.996660	−	0.0816642i	$-0.0260235\pi$
$788$		−	4.31166e13i		−	3.98361i
$789$		0			0
$790$	1.37585e13	−	1.93152e13i	1.25675	−	1.76432i
$791$	3.35367e12			0.304597
$792$		0			0
$793$		−	4.24588e12i		−	0.381275i
$794$	1.69218e13			1.51096
$795$		0			0
$796$	2.69147e13			2.37619
$797$			2.27115e13i			1.99381i	0.0786130	+	0.996905i	$0.474951\pi$
$797$			2.27115e13i			1.99381i	−0.0786130	+	0.996905i	$0.525049\pi$
$798$		0			0
$799$	−1.28737e13			−1.11748
$800$	1.56156e13	−	5.39956e12i	1.34788	−	0.466073i
$801$		0			0
$802$		−	3.27516e12i		−	0.279542i
$803$			7.92629e11i			0.0672744i
$804$		0			0
$805$	−4.36683e12	−	3.11055e12i	−0.366509	−	0.261070i
$806$	1.08462e13			0.905255
$807$		0			0
$808$			5.74840e12i			0.474456i
$809$	−9.95176e12			−0.816829			−0.408415	−	0.912796i	$-0.633918\pi$
$809$	−9.95176e12			−0.816829			−0.408415	+	0.912796i	$0.633918\pi$
$810$		0			0
$811$	−7.01292e12			−0.569253			−0.284626	−	0.958639i	$-0.591870\pi$
$811$	−7.01292e12			−0.569253			−0.284626	+	0.958639i	$0.591870\pi$
$812$		−	1.63216e13i		−	1.31753i
$813$		0			0
$814$	6.05121e12			0.483095
$815$	2.18778e12	−	3.07137e12i	0.173698	−	0.243850i
$816$		0			0
$817$			7.21723e12i			0.566724i
$818$			2.83379e13i			2.21298i
$819$		0			0
$820$	−2.31859e13	−	1.65157e13i	−1.79086	−	1.27566i
$821$	1.20992e13			0.929420			0.464710	−	0.885463i	$-0.346159\pi$
$821$	1.20992e13			0.929420			0.464710	+	0.885463i	$0.346159\pi$
$822$		0			0
$823$			1.21261e13i			0.921346i	0.887570	+	0.460673i	$0.152392\pi$
$823$			1.21261e13i			0.921346i	−0.887570	+	0.460673i	$0.847608\pi$
$824$	−2.58584e13			−1.95402
$825$		0			0
$826$	3.52289e13			2.63323
$827$		−	1.32495e13i		−	0.984973i	−0.870320	−	0.492486i	$-0.836088\pi$
$827$		−	1.32495e13i		−	0.984973i	0.870320	−	0.492486i	$-0.163912\pi$
$828$		0			0
$829$	1.87106e13			1.37592			0.687960	−	0.725749i	$-0.258507\pi$
$829$	1.87106e13			1.37592			0.687960	+	0.725749i	$0.258507\pi$
$830$	−2.45499e13	−	1.74873e13i	−1.79556	−	1.27900i
$831$		0			0
$832$			5.22548e12i			0.378069i
$833$			3.79702e12i			0.273238i
$834$		0			0
$835$	−1.19297e13	+	1.67478e13i	−0.849261	+	1.19226i
$836$	3.07752e12			0.217908
$837$		0			0
$838$		−	1.37130e13i		−	0.960582i
$839$	1.21346e13			0.845469			0.422734	−	0.906254i	$-0.361070\pi$
$839$	1.21346e13			0.845469			0.422734	+	0.906254i	$0.361070\pi$
$840$		0			0
$841$	−7.90725e12			−0.545059
$842$			2.60599e13i			1.78677i
$843$		0			0
$844$	−4.33053e13			−2.93765
$845$	−4.84860e12	−	3.45373e12i	−0.327161	−	0.233041i
$846$		0			0
$847$		−	1.19552e13i		−	0.798145i
$848$			3.14575e13i			2.08902i
$849$		0			0
$850$	8.27454e12	+	2.39300e13i	0.543699	+	1.57238i
$851$	−1.01380e13			−0.662630
$852$		0			0
$853$			2.34098e13i			1.51401i	0.653411	+	0.757004i	$0.273337\pi$
$853$			2.34098e13i			1.51401i	−0.653411	+	0.757004i	$0.726663\pi$
$854$	1.17065e13			0.753126
$855$		0			0
$856$	−4.69336e13			−2.98780
$857$			1.61008e13i			1.01961i	0.860290	+	0.509805i	$0.170282\pi$
$857$			1.61008e13i			1.01961i	−0.860290	+	0.509805i	$0.829718\pi$
$858$		0			0
$859$	1.34163e13			0.840745			0.420373	−	0.907352i	$-0.361899\pi$
$859$	1.34163e13			0.840745			0.420373	+	0.907352i	$0.361899\pi$
$860$	−2.83248e13	+	3.97644e13i	−1.76573	+	2.47886i
$861$		0			0
$862$			3.18532e13i			1.96504i
$863$			2.03784e13i			1.25061i	0.780381	+	0.625304i	$0.215025\pi$
$863$			2.03784e13i			1.25061i	−0.780381	+	0.625304i	$0.784975\pi$
$864$		0			0
$865$	1.26978e11	−	1.78262e11i	0.00771183	−	0.0108264i
$866$	4.45544e13			2.69191
$867$		0			0
$868$			2.09366e13i			1.25189i
$869$	4.28176e12			0.254703
$870$		0			0
$871$	2.23764e13			1.31737
$872$		−	4.88886e13i		−	2.86341i
$873$		0			0
$874$	−7.36456e12			−0.426919
$875$	1.39188e13	+	4.09347e12i	0.802725	+	0.236078i
$876$		0			0
$877$		−	3.55027e12i		−	0.202658i	−0.994853	−	0.101329i	$-0.967691\pi$
$877$		−	3.55027e12i		−	0.202658i	0.994853	−	0.101329i	$-0.0323094\pi$
$878$		−	3.95186e13i		−	2.24428i
$879$		0			0
$880$	6.58181e12	+	4.68831e12i	0.369976	+	0.263539i
$881$	2.33443e13			1.30554			0.652769	−	0.757557i	$-0.273607\pi$
$881$	2.33443e13			1.30554			0.652769	+	0.757557i	$0.273607\pi$
$882$		0			0
$883$		−	8.70030e12i		−	0.481627i	−0.970571	−	0.240814i	$-0.922586\pi$
$883$		−	8.70030e12i		−	0.481627i	0.970571	−	0.240814i	$-0.0774142\pi$
$884$	−2.98724e13			−1.64526
$885$		0			0
$886$	−8.52799e12			−0.464938
$887$			2.98568e13i			1.61952i	0.586760	+	0.809761i	$0.300403\pi$
$887$			2.98568e13i			1.61952i	−0.586760	+	0.809761i	$0.699597\pi$
$888$		0			0
$889$	1.12738e13			0.605358
$890$	−7.95053e12	+	1.11616e13i	−0.424758	+	0.596307i
$891$		0			0
$892$		−	5.90273e13i		−	3.12184i
$893$			1.01325e13i			0.533196i
$894$		0			0
$895$	6.09572e12	+	4.34206e12i	0.317557	+	0.226200i
$896$	8.61458e12			0.446527
$897$		0			0
$898$		−	7.26969e12i		−	0.373055i
$899$	−8.46604e12			−0.432277
$900$		0			0
$901$	−1.77968e13			−0.899666
$902$		−	7.34144e12i		−	0.369277i
$903$		0			0
$904$	1.78138e13			0.887153
$905$	1.73142e12	+	1.23331e12i	0.0857993	+	0.0611160i
$906$		0			0
$907$		−	2.14293e13i		−	1.05142i	−0.850664	−	0.525709i	$-0.823800\pi$
$907$		−	2.14293e13i		−	1.05142i	0.850664	−	0.525709i	$-0.176200\pi$
$908$		−	3.91708e13i		−	1.91239i
$909$		0			0
$910$	−1.41844e13	+	1.99132e13i	−0.685686	+	0.962618i
$911$	−3.43474e13			−1.65219			−0.826097	−	0.563529i	$-0.809443\pi$
$911$	−3.43474e13			−1.65219			−0.826097	+	0.563529i	$0.809443\pi$
$912$		0			0
$913$		−	5.44218e12i		−	0.259212i
$914$	1.23470e13			0.585200
$915$		0			0
$916$	1.62064e13			0.760603
$917$		−	2.96422e13i		−	1.38436i
$918$		0			0
$919$	−2.05847e13			−0.951975			−0.475987	−	0.879452i	$-0.657909\pi$
$919$	−2.05847e13			−0.951975			−0.475987	+	0.879452i	$0.657909\pi$
$920$	−2.31954e13	−	1.65224e13i	−1.06747	−	0.760376i
$921$		0			0
$922$			1.81566e13i			0.827458i
$923$		−	7.14688e12i		−	0.324122i
$924$		0			0
$925$	2.59278e13	−	8.96535e12i	1.16447	−	0.402652i
$926$	−4.80354e13			−2.14690
$927$		0			0
$928$		−	2.17331e13i		−	0.961955i
$929$	1.78605e13			0.786726			0.393363	−	0.919383i	$-0.371312\pi$
$929$	1.78605e13			0.786726			0.393363	+	0.919383i	$0.371312\pi$
$930$		0			0
$931$	2.98855e12			0.130373
$932$		−	9.56035e12i		−	0.415052i
$933$		0			0
$934$	−6.85583e12			−0.294781
$935$	−2.65238e12	+	3.72361e12i	−0.113497	+	0.159335i
$936$		0			0
$937$			1.00969e13i			0.427917i	0.976843	+	0.213959i	$0.0686358\pi$
$937$			1.00969e13i			0.427917i	−0.976843	+	0.213959i	$0.931364\pi$
$938$			6.16950e13i			2.60218i
$939$		0			0
$940$	−3.97662e13	+	5.58268e13i	−1.66126	+	2.33221i
$941$	2.40159e12			0.0998496			0.0499248	−	0.998753i	$-0.484102\pi$
$941$	2.40159e12			0.0998496			0.0499248	+	0.998753i	$0.484102\pi$
$942$		0			0
$943$			1.22997e13i			0.506513i
$944$	8.89591e13			3.64600
$945$		0			0
$946$	−1.25908e13			−0.511142
$947$		−	2.09609e13i		−	0.846907i	−0.905918	−	0.423453i	$-0.860818\pi$
$947$		−	2.09609e13i		−	0.846907i	0.905918	−	0.423453i	$-0.139182\pi$
$948$		0			0
$949$	−6.05558e12			−0.242358
$950$	1.88347e13	−	6.51268e12i	0.750245	−	0.259420i
$951$		0			0
$952$		−	4.70827e13i		−	1.85779i
$953$			1.23636e12i			0.0485543i	0.999705	+	0.0242771i	$0.00772841\pi$
$953$			1.23636e12i			0.0485543i	−0.999705	+	0.0242771i	$0.992272\pi$
$954$		0			0
$955$	−1.05663e13	−	7.52655e12i	−0.411064	−	0.292806i
$956$	−9.92338e13			−3.84237
$957$		0			0
$958$		−	5.50289e12i		−	0.211080i
$959$	1.36769e13			0.522162
$960$		0			0
$961$	−1.55798e13			−0.589259
$962$			4.62305e13i			1.74037i
$963$		0			0
$964$	7.22897e13			2.69606
$965$	5.62992e12	−	7.90371e12i	0.208992	−	0.293399i
$966$		0			0
$967$			1.93044e13i			0.709966i	0.934873	+	0.354983i	$0.115513\pi$
$967$			1.93044e13i			0.709966i	−0.934873	+	0.354983i	$0.884487\pi$
$968$		−	6.35028e13i		−	2.32463i
$969$		0			0
$970$	−2.83977e13	−	2.02281e13i	−1.02994	−	0.733637i
$971$	2.95198e12			0.106568			0.0532840	−	0.998579i	$-0.483031\pi$
$971$	2.95198e12			0.106568			0.0532840	+	0.998579i	$0.483031\pi$
$972$		0			0
$973$			8.62646e12i			0.308549i
$974$	−5.92007e13			−2.10771
$975$		0			0
$976$	2.95610e13			1.04279
$977$		−	5.39705e13i		−	1.89509i	−0.319617	−	0.947547i	$-0.603554\pi$
$977$		−	5.39705e13i		−	1.89509i	0.319617	−	0.947547i	$-0.396446\pi$
$978$		0			0
$979$	−2.47427e12			−0.0860845
$980$	1.64659e13	+	1.17289e13i	0.570252	+	0.406198i
$981$		0			0
$982$		−	4.36697e13i		−	1.49858i
$983$			2.52782e13i			0.863487i	0.901996	+	0.431743i	$0.142101\pi$
$983$			2.52782e13i			0.863487i	−0.901996	+	0.431743i	$0.857899\pi$
$984$		0			0
$985$	2.92480e13	−	4.10605e13i	0.989994	−	1.38983i
$986$	3.33047e13			1.12217
$987$		0			0
$988$			2.35118e13i			0.785019i
$989$	2.10942e13			0.701101
$990$		0			0
$991$	3.62973e13			1.19548			0.597741	−	0.801689i	$-0.296065\pi$
$991$	3.62973e13			1.19548			0.597741	+	0.801689i	$0.296065\pi$
$992$			2.78781e13i			0.914032i
$993$		0			0
$994$	1.97050e13			0.640234
$995$	2.56312e13	+	1.82575e13i	0.829020	+	0.590523i
$996$		0			0
$997$		−	5.75313e13i		−	1.84406i	−0.387114	−	0.922032i	$-0.626528\pi$
$997$		−	5.75313e13i		−	1.84406i	0.387114	−	0.922032i	$-0.373472\pi$
$998$			7.35058e12i			0.234549i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.10.b.b.19.1		4
3.2	odd	2		5.10.b.a.4.4	yes	4
5.2	odd	4		225.10.a.s.1.4		4
5.3	odd	4		225.10.a.s.1.1		4
5.4	even	2	inner	45.10.b.b.19.4		4
12.11	even	2		80.10.c.c.49.3		4
15.2	even	4		25.10.a.e.1.1		4
15.8	even	4		25.10.a.e.1.4		4
15.14	odd	2		5.10.b.a.4.1	✓	4
60.23	odd	4		400.10.a.ba.1.2		4
60.47	odd	4		400.10.a.ba.1.3		4
60.59	even	2		80.10.c.c.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.10.b.a.4.1	✓	4	15.14	odd	2
5.10.b.a.4.4	yes	4	3.2	odd	2
25.10.a.e.1.1		4	15.2	even	4
25.10.a.e.1.4		4	15.8	even	4
45.10.b.b.19.1		4	1.1	even	1	trivial
45.10.b.b.19.4		4	5.4	even	2	inner
80.10.c.c.49.2		4	60.59	even	2
80.10.c.c.49.3		4	12.11	even	2
225.10.a.s.1.1		4	5.3	odd	4
225.10.a.s.1.4		4	5.2	odd	4
400.10.a.ba.1.2		4	60.23	odd	4
400.10.a.ba.1.3		4	60.47	odd	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-41.3193i q^{2} -1195.29 q^{4} +(-1138.29 - 810.818i) q^{5} +5315.22i q^{7} +28233.0i q^{8} +O(q^{10})\)	\(q-41.3193i q^{2} -1195.29 q^{4} +(-1138.29 - 810.818i) q^{5} +5315.22i q^{7} +28233.0i q^{8} +(-33502.5 + 47033.3i) q^{10} -10426.2 q^{11} -79655.1i q^{13} +219621. q^{14} +554581. q^{16} +313750. i q^{17} +246945. q^{19} +(1.36058e6 + 969161. i) q^{20} +430806. i q^{22} -721761. i q^{23} +(638273. + 1.84589e6i) q^{25} -3.29130e6 q^{26} -6.35321e6i q^{28} +2.56903e6 q^{29} -3.29543e6 q^{31} -8.45965e6i q^{32} +1.29639e7 q^{34} +(4.30967e6 - 6.05025e6i) q^{35} -1.40463e7i q^{37} -1.02036e7i q^{38} +(2.28918e7 - 3.21373e7i) q^{40} -1.70412e7 q^{41} +2.92261e7i q^{43} +1.24624e7 q^{44} -2.98227e7 q^{46} +4.10316e7i q^{47} +1.21021e7 q^{49} +(7.62709e7 - 2.63730e7i) q^{50} +9.52108e7i q^{52} +5.67230e7i q^{53} +(1.18681e7 + 8.45379e6i) q^{55} -1.50065e8 q^{56} -1.06150e8i q^{58} +1.60408e8 q^{59} +5.33033e7 q^{61} +1.36165e8i q^{62} -6.56012e7 q^{64} +(-6.45858e7 + 9.06705e7i) q^{65} +2.80916e8i q^{67} -3.75022e8i q^{68} +(-2.49992e8 - 1.78073e8i) q^{70} +8.97228e7 q^{71} -7.60225e7i q^{73} -5.80383e8 q^{74} -2.95170e8 q^{76} -5.54178e7i q^{77} -4.10672e8 q^{79} +(-6.31273e8 - 4.49665e8i) q^{80} +7.04131e8i q^{82} +5.21969e8i q^{83} +(2.54394e8 - 3.57138e8i) q^{85} +1.20760e9 q^{86} -2.94364e8i q^{88} +2.37312e8 q^{89} +4.23384e8 q^{91} +8.62712e8i q^{92} +1.69540e9 q^{94} +(-2.81094e8 - 2.00227e8i) q^{95} +6.03778e8i q^{97} -5.00050e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1368 q^{4} - 1140 q^{5}+O(q^{10}) \) 4 * q - 1368 * q^4 - 1140 * q^5	\( 4 q - 1368 q^{4} - 1140 q^{5} - 69160 q^{10} - 109968 q^{11} + 424536 q^{14} + 1631264 q^{16} - 636880 q^{19} + 3302280 q^{20} - 1337900 q^{25} - 6618768 q^{26} + 3531720 q^{29} - 10587712 q^{31} + 26434624 q^{34} - 13629840 q^{35} + 43578400 q^{40} + 16788552 q^{41} - 20638944 q^{44} - 61250072 q^{46} - 46921028 q^{49} + 150092400 q^{50} - 26907120 q^{55} - 315178080 q^{56} + 460829040 q^{59} + 360490568 q^{61} + 134995072 q^{64} - 183895680 q^{65} - 508341960 q^{70} + 47611872 q^{71} - 1176861744 q^{74} - 1168489440 q^{76} - 728043520 q^{79} - 965843040 q^{80} + 1275419840 q^{85} + 2375904552 q^{86} + 1582700760 q^{89} + 473322528 q^{91} + 3327101704 q^{94} - 1204791600 q^{95}+O(q^{100}) \) 4 * q - 1368 * q^4 - 1140 * q^5 - 69160 * q^10 - 109968 * q^11 + 424536 * q^14 + 1631264 * q^16 - 636880 * q^19 + 3302280 * q^20 - 1337900 * q^25 - 6618768 * q^26 + 3531720 * q^29 - 10587712 * q^31 + 26434624 * q^34 - 13629840 * q^35 + 43578400 * q^40 + 16788552 * q^41 - 20638944 * q^44 - 61250072 * q^46 - 46921028 * q^49 + 150092400 * q^50 - 26907120 * q^55 - 315178080 * q^56 + 460829040 * q^59 + 360490568 * q^61 + 134995072 * q^64 - 183895680 * q^65 - 508341960 * q^70 + 47611872 * q^71 - 1176861744 * q^74 - 1168489440 * q^76 - 728043520 * q^79 - 965843040 * q^80 + 1275419840 * q^85 + 2375904552 * q^86 + 1582700760 * q^89 + 473322528 * q^91 + 3327101704 * q^94 - 1204791600 * q^95

Introduction

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