LMFDB - Embedded newform 45.9.d.a.44.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,9,Mod(44,45)]

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([1, 1]))

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

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

chi := DirichletCharacter("45.44");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	45.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.3320374528$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1982 x^{14} + 1579736 x^{12} + 654647506 x^{10} + 151540734566 x^{8} + 19474609444738 x^{6} + \cdots + 29\!\cdots\!09 $ x^16 + 1982x^14 + 1579736x^12 + 654647506x^10 + 151540734566x^8 + 19474609444738x^6 + 1288318886608936x^4 + 36624709707917870*x^2 + 296773539014178009
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{42}\cdot 5^{10}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			44.12
Root			$-3.60184i$ of defining polynomial
Character	$\chi$	$=$	45.44
Dual form			45.9.d.a.44.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+13.0310 q^{2} -86.1932 q^{4} +(86.8741 + 618.933i) q^{5} -1918.88i q^{7} -4459.12 q^{8} +O(q^{10})$	\(q+13.0310 q^{2} -86.1932 q^{4} +(86.8741 + 618.933i) q^{5} -1918.88i q^{7} -4459.12 q^{8} +(1132.06 + 8065.31i) q^{10} -7407.11i q^{11} -44920.9i q^{13} -25004.9i q^{14} -36041.3 q^{16} -122036. q^{17} -146641. q^{19} +(-7487.95 - 53347.8i) q^{20} -96522.1i q^{22} +345961. q^{23} +(-375531. + 107538. i) q^{25} -585364. i q^{26} +165395. i q^{28} -453681. i q^{29} -1.17653e6 q^{31} +671880. q^{32} -1.59025e6 q^{34} +(1.18766e6 - 166701. i) q^{35} +1.32581e6i q^{37} -1.91088e6 q^{38} +(-387382. - 2.75989e6i) q^{40} -1.74823e6i q^{41} -1.07161e6i q^{43} +638443. i q^{44} +4.50822e6 q^{46} -3.34039e6 q^{47} +2.08269e6 q^{49} +(-4.89354e6 + 1.40133e6i) q^{50} +3.87187e6i q^{52} +6.15049e6 q^{53} +(4.58451e6 - 643486. i) q^{55} +8.55652e6i q^{56} -5.91192e6i q^{58} +1.31715e7i q^{59} +4.80050e6 q^{61} -1.53314e7 q^{62} +1.79818e7 q^{64} +(2.78030e7 - 3.90246e6i) q^{65} +3.65129e7i q^{67} +1.05187e7 q^{68} +(1.54764e7 - 2.17228e6i) q^{70} -798301. i q^{71} -7.40621e6i q^{73} +1.72767e7i q^{74} +1.26395e7 q^{76} -1.42134e7 q^{77} -6.47230e7 q^{79} +(-3.13105e6 - 2.23071e7i) q^{80} -2.27811e7i q^{82} -2.15820e7 q^{83} +(-1.06018e7 - 7.55322e7i) q^{85} -1.39641e7i q^{86} +3.30292e7i q^{88} -3.11064e7i q^{89} -8.61978e7 q^{91} -2.98195e7 q^{92} -4.35286e7 q^{94} +(-1.27393e7 - 9.07611e7i) q^{95} +9.43227e7i q^{97} +2.71396e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 1572 q^{4}+O(q^{10}) $ 16 * q + 1572 * q^4	$ 16 q + 1572 q^{4} + 16280 q^{10} - 12844 q^{16} + 263600 q^{19} + 1124860 q^{25} - 4312984 q^{31} + 2439352 q^{34} + 10217140 q^{40} - 5376344 q^{46} - 7338968 q^{49} + 5658120 q^{55} + 26097968 q^{61} - 123290756 q^{64} + 27888840 q^{70} + 222695760 q^{76} - 262645864 q^{79} + 202172900 q^{85} + 350561736 q^{91} - 789068384 q^{94}+O(q^{100}) $ 16 * q + 1572 * q^4 + 16280 * q^10 - 12844 * q^16 + 263600 * q^19 + 1124860 * q^25 - 4312984 * q^31 + 2439352 * q^34 + 10217140 * q^40 - 5376344 * q^46 - 7338968 * q^49 + 5658120 * q^55 + 26097968 * q^61 - 123290756 * q^64 + 27888840 * q^70 + 222695760 * q^76 - 262645864 * q^79 + 202172900 * q^85 + 350561736 * q^91 - 789068384 * q^94

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 $

$2$	13.0310			0.814437			0.407219	−	0.913331i	$-0.366499\pi$
$2$	13.0310			0.814437			0.407219	+	0.913331i	$0.366499\pi$
$3$		0			0
$3$		0			0
$4$	−86.1932			−0.336692
$5$	86.8741	+	618.933i	0.138999	+	0.990293i
$5$	86.8741	+	618.933i	0.138999	+	0.990293i
$6$		0			0
$7$		−	1918.88i		−	0.799201i	−0.916689	−	0.399601i	$-0.869149\pi$
$7$		−	1918.88i		−	0.799201i	0.916689	−	0.399601i	$-0.130851\pi$
$8$	−4459.12			−1.08865
$9$		0			0
$10$	1132.06	+	8065.31i	0.113206	+	0.806531i
$11$		−	7407.11i		−	0.505916i	−0.967477	−	0.252958i	$-0.918597\pi$
$11$		−	7407.11i		−	0.505916i	0.967477	−	0.252958i	$-0.0814034\pi$
$12$		0			0
$13$		−	44920.9i		−	1.57280i	−0.617715	−	0.786402i	$-0.711941\pi$
$13$		−	44920.9i		−	1.57280i	0.617715	−	0.786402i	$-0.288059\pi$
$14$		−	25004.9i		−	0.650899i
$15$		0			0
$16$	−36041.3			−0.549946
$17$	−122036.			−1.46114			−0.730572	−	0.682836i	$-0.760746\pi$
$17$	−122036.			−1.46114			−0.730572	+	0.682836i	$0.760746\pi$
$18$		0			0
$19$	−146641.			−1.12523			−0.562616	−	0.826718i	$-0.690205\pi$
$19$	−146641.			−1.12523			−0.562616	+	0.826718i	$0.690205\pi$
$20$	−7487.95	−	53347.8i	−0.0467997	−	0.333424i
$21$		0			0
$22$		−	96522.1i		−	0.412037i
$23$	345961.			1.23628			0.618139	−	0.786069i	$-0.287887\pi$
$23$	345961.			1.23628			0.618139	+	0.786069i	$0.287887\pi$
$24$		0			0
$25$	−375531.	+	107538.i	−0.961359	+	0.275298i
$26$		−	585364.i		−	1.28095i
$27$		0			0
$28$			165395.i			0.269085i
$29$		−	453681.i		−	0.641444i	−0.947173	−	0.320722i	$-0.896074\pi$
$29$		−	453681.i		−	0.641444i	0.947173	−	0.320722i	$-0.103926\pi$
$30$		0			0
$31$	−1.17653e6			−1.27396			−0.636982	−	0.770878i	$-0.719818\pi$
$31$	−1.17653e6			−1.27396			−0.636982	+	0.770878i	$0.719818\pi$
$32$	671880.			0.640755
$33$		0			0
$34$	−1.59025e6			−1.19001
$35$	1.18766e6	−	166701.i	0.791443	−	0.111088i
$36$		0			0
$37$			1.32581e6i			0.707417i	0.935356	+	0.353709i	$0.115080\pi$
$37$			1.32581e6i			0.707417i	−0.935356	+	0.353709i	$0.884920\pi$
$38$	−1.91088e6			−0.916430
$39$		0			0
$40$	−387382.	−	2.75989e6i	−0.151321	−	1.07808i
$41$		−	1.74823e6i		−	0.618675i	−0.950952	−	0.309337i	$-0.899893\pi$
$41$		−	1.74823e6i		−	0.618675i	0.950952	−	0.309337i	$-0.100107\pi$
$42$		0			0
$43$		−	1.07161e6i		−	0.313445i	−0.987643	−	0.156722i	$-0.949907\pi$
$43$		−	1.07161e6i		−	0.313445i	0.987643	−	0.156722i	$-0.0500928\pi$
$44$			638443.i			0.170338i
$45$		0			0
$46$	4.50822e6			1.00687
$47$	−3.34039e6			−0.684551			−0.342276	−	0.939600i	$-0.611198\pi$
$47$	−3.34039e6			−0.684551			−0.342276	+	0.939600i	$0.611198\pi$
$48$		0			0
$49$	2.08269e6			0.361278
$50$	−4.89354e6	+	1.40133e6i	−0.782966	+	0.224213i
$51$		0			0
$52$			3.87187e6i			0.529551i
$53$	6.15049e6			0.779482			0.389741	−	0.920924i	$-0.372564\pi$
$53$	6.15049e6			0.779482			0.389741	+	0.920924i	$0.372564\pi$
$54$		0			0
$55$	4.58451e6	−	643486.i	0.501005	−	0.0703216i
$56$			8.55652e6i			0.870052i
$57$		0			0
$58$		−	5.91192e6i		−	0.522416i
$59$			1.31715e7i			1.08699i	0.839412	+	0.543495i	$0.182899\pi$
$59$			1.31715e7i			1.08699i	−0.839412	+	0.543495i	$0.817101\pi$
$60$		0			0
$61$	4.80050e6			0.346711			0.173355	−	0.984859i	$-0.444539\pi$
$61$	4.80050e6			0.346711			0.173355	+	0.984859i	$0.444539\pi$
$62$	−1.53314e7			−1.03756
$63$		0			0
$64$	1.79818e7			1.07180
$65$	2.78030e7	−	3.90246e6i	1.55754	−	0.218617i
$66$		0			0
$67$			3.65129e7i			1.81195i	0.423329	+	0.905976i	$0.360861\pi$
$67$			3.65129e7i			1.81195i	−0.423329	+	0.905976i	$0.639139\pi$
$68$	1.05187e7			0.491956
$69$		0			0
$70$	1.54764e7	−	2.17228e6i	0.644581	−	0.0904740i
$71$		−	798301.i		−	0.0314147i	−0.999877	−	0.0157074i	$-0.995000\pi$
$71$		−	798301.i		−	0.0314147i	0.999877	−	0.0157074i	$-0.00500001\pi$
$72$		0			0
$73$		−	7.40621e6i		−	0.260798i	−0.991462	−	0.130399i	$-0.958374\pi$
$73$		−	7.40621e6i		−	0.260798i	0.991462	−	0.130399i	$-0.0416258\pi$
$74$			1.72767e7i			0.576147i
$75$		0			0
$76$	1.26395e7			0.378857
$77$	−1.42134e7			−0.404329
$78$		0			0
$79$	−6.47230e7			−1.66169			−0.830845	−	0.556503i	$-0.812143\pi$
$79$	−6.47230e7			−1.66169			−0.830845	+	0.556503i	$0.812143\pi$
$80$	−3.13105e6	−	2.23071e7i	−0.0764417	−	0.544608i
$81$		0			0
$82$		−	2.27811e7i		−	0.503872i
$83$	−2.15820e7			−0.454757			−0.227378	−	0.973806i	$-0.573015\pi$
$83$	−2.15820e7			−0.454757			−0.227378	+	0.973806i	$0.573015\pi$
$84$		0			0
$85$	−1.06018e7	−	7.55322e7i	−0.203097	−	1.44696i
$86$		−	1.39641e7i		−	0.255281i
$87$		0			0
$88$			3.30292e7i			0.550766i
$89$		−	3.11064e7i		−	0.495781i	−0.968788	−	0.247891i	$-0.920263\pi$
$89$		−	3.11064e7i		−	0.495781i	0.968788	−	0.247891i	$-0.0797374\pi$
$90$		0			0
$91$	−8.61978e7			−1.25699
$92$	−2.98195e7			−0.416245
$93$		0			0
$94$	−4.35286e7			−0.557524
$95$	−1.27393e7	−	9.07611e7i	−0.156406	−	1.11431i
$96$		0			0
$97$			9.43227e7i			1.06544i	0.846291	+	0.532720i	$0.178830\pi$
$97$			9.43227e7i			1.06544i	−0.846291	+	0.532720i	$0.821170\pi$
$98$	2.71396e7			0.294238
$99$		0			0
$100$	3.23682e7	−	9.26908e6i	0.323682	−	0.0926908i
$101$		−	1.68846e8i		−	1.62258i	−0.584647	−	0.811288i	$-0.698767\pi$
$101$		−	1.68846e8i		−	1.62258i	0.584647	−	0.811288i	$-0.301233\pi$
$102$		0			0
$103$		−	1.85101e8i		−	1.64460i	−0.569057	−	0.822298i	$-0.692692\pi$
$103$		−	1.85101e8i		−	1.64460i	0.569057	−	0.822298i	$-0.307308\pi$
$104$			2.00307e8i			1.71224i
$105$		0			0
$106$	8.01470e7			0.634839
$107$	6.02130e7			0.459362			0.229681	−	0.973266i	$-0.426232\pi$
$107$	6.02130e7			0.459362			0.229681	+	0.973266i	$0.426232\pi$
$108$		0			0
$109$	−2.23264e8			−1.58166			−0.790830	−	0.612036i	$-0.790351\pi$
$109$	−2.23264e8			−1.58166			−0.790830	+	0.612036i	$0.790351\pi$
$110$	5.97407e7	−	8.38526e6i	0.408037	−	0.0572725i
$111$		0			0
$112$			6.91590e7i			0.439518i
$113$	3.21005e7			0.196879			0.0984393	−	0.995143i	$-0.468615\pi$
$113$	3.21005e7			0.196879			0.0984393	+	0.995143i	$0.468615\pi$
$114$		0			0
$115$	3.00551e7	+	2.14127e8i	0.171841	+	1.22428i
$116$			3.91042e7i			0.215969i
$117$		0			0
$118$			1.71637e8i			0.885286i
$119$			2.34173e8i			1.16775i
$120$		0			0
$121$	1.59494e8			0.744049
$122$	6.25553e7			0.282374
$123$		0			0
$124$	1.01409e8			0.428934
$125$	−9.91830e7	−	2.23086e8i	−0.406253	−	0.913760i
$126$		0			0
$127$		−	4.80589e8i		−	1.84739i	−0.383126	−	0.923696i	$-0.625153\pi$
$127$		−	4.80589e8i		−	1.84739i	0.383126	−	0.923696i	$-0.374847\pi$
$128$	6.23198e7			0.232159
$129$		0			0
$130$	3.62301e8	−	5.08529e7i	1.26852	−	0.178050i
$131$		−	2.98566e7i		−	0.101381i	−0.998714	−	0.0506904i	$-0.983858\pi$
$131$		−	2.98566e7i		−	0.101381i	0.998714	−	0.0506904i	$-0.0161422\pi$
$132$		0			0
$133$			2.81387e8i			0.899286i
$134$			4.75799e8i			1.47572i
$135$		0			0
$136$	5.44174e8			1.59068
$137$	−2.90456e8			−0.824515			−0.412257	−	0.911067i	$-0.635260\pi$
$137$	−2.90456e8			−0.824515			−0.412257	+	0.911067i	$0.635260\pi$
$138$		0			0
$139$	−3.12159e8			−0.836212			−0.418106	−	0.908398i	$-0.637306\pi$
$139$	−3.12159e8			−0.836212			−0.418106	+	0.908398i	$0.637306\pi$
$140$	−1.02368e8	+	1.43685e7i	−0.266473	+	0.0374024i
$141$		0			0
$142$		−	1.04027e7i		−	0.0255853i
$143$	−3.32734e8			−0.795707
$144$		0			0
$145$	2.80798e8	−	3.94131e7i	0.635217	−	0.0891598i
$146$		−	9.65102e7i		−	0.212404i
$147$		0			0
$148$		−	1.14276e8i		−	0.238182i
$149$			8.72146e8i			1.76947i	0.466091	+	0.884737i	$0.345662\pi$
$149$			8.72146e8i			1.76947i	−0.466091	+	0.884737i	$0.654338\pi$
$150$		0			0
$151$	−2.42967e8			−0.467347			−0.233673	−	0.972315i	$-0.575075\pi$
$151$	−2.42967e8			−0.467347			−0.233673	+	0.972315i	$0.575075\pi$
$152$	6.53891e8			1.22499
$153$		0			0
$154$	−1.85214e8			−0.329300
$155$	−1.02210e8	−	7.28195e8i	−0.177079	−	1.26160i
$156$		0			0
$157$		−	5.05078e8i		−	0.831304i	−0.909524	−	0.415652i	$-0.863553\pi$
$157$		−	5.05078e8i		−	0.831304i	0.909524	−	0.415652i	$-0.136447\pi$
$158$	−8.43405e8			−1.35334
$159$		0			0
$160$	5.83690e7	+	4.15849e8i	0.0890640	+	0.634535i
$161$		−	6.63859e8i		−	0.988035i
$162$		0			0
$163$			1.92088e8i			0.272114i	0.990701	+	0.136057i	$0.0434430\pi$
$163$			1.92088e8i			0.272114i	−0.990701	+	0.136057i	$0.956557\pi$
$164$			1.50685e8i			0.208303i
$165$		0			0
$166$	−2.81235e8			−0.370371
$167$	1.26266e9			1.62338			0.811690	−	0.584088i	$-0.198548\pi$
$167$	1.26266e9			1.62338			0.811690	+	0.584088i	$0.198548\pi$
$168$		0			0
$169$	−1.20215e9			−1.47371
$170$	−1.38152e8	−	9.84260e8i	−0.165410	−	1.17846i
$171$		0			0
$172$			9.23651e7i			0.105534i
$173$	1.67194e9			1.86653			0.933265	−	0.359189i	$-0.116946\pi$
$173$	1.67194e9			1.86653			0.933265	+	0.359189i	$0.116946\pi$
$174$		0			0
$175$	2.06354e8	+	7.20599e8i	0.220019	+	0.768319i
$176$			2.66962e8i			0.278227i
$177$		0			0
$178$		−	4.05348e8i		−	0.403783i
$179$		−	2.38184e8i		−	0.232007i	−0.993249	−	0.116003i	$-0.962992\pi$
$179$		−	2.38184e8i		−	0.232007i	0.993249	−	0.116003i	$-0.0370083\pi$
$180$		0			0
$181$	−3.21450e8			−0.299502			−0.149751	−	0.988724i	$-0.547847\pi$
$181$	−3.21450e8			−0.299502			−0.149751	+	0.988724i	$0.547847\pi$
$182$	−1.12324e9			−1.02374
$183$		0			0
$184$	−1.54268e9			−1.34588
$185$	−8.20590e8	+	1.15179e8i	−0.700550	+	0.0983299i
$186$		0			0
$187$			9.03936e8i			0.739216i
$188$	2.87919e8			0.230483
$189$		0			0
$190$	−1.66006e8	−	1.18271e9i	−0.127382	−	0.907534i
$191$		−	8.26431e8i		−	0.620973i	−0.950578	−	0.310487i	$-0.899508\pi$
$191$		−	8.26431e8i		−	0.620973i	0.950578	−	0.310487i	$-0.100492\pi$
$192$		0			0
$193$		−	3.42380e8i		−	0.246763i	−0.992359	−	0.123381i	$-0.960626\pi$
$193$		−	3.42380e8i		−	0.246763i	0.992359	−	0.123381i	$-0.0393738\pi$
$194$			1.22912e9i			0.867735i
$195$		0			0
$196$	−1.79514e8			−0.121639
$197$	−1.16560e9			−0.773902			−0.386951	−	0.922100i	$-0.626472\pi$
$197$	−1.16560e9			−0.773902			−0.386951	+	0.922100i	$0.626472\pi$
$198$		0			0
$199$	3.49071e8			0.222588			0.111294	−	0.993788i	$-0.464500\pi$
$199$	3.49071e8			0.222588			0.111294	+	0.993788i	$0.464500\pi$
$200$	1.67454e9	−	4.79527e8i	1.04658	−	0.299704i
$201$		0			0
$202$		−	2.20023e9i		−	1.32149i
$203$	−8.70561e8			−0.512643
$204$		0			0
$205$	1.08204e9	−	1.51876e8i	0.612669	−	0.0859949i
$206$		−	2.41205e9i		−	1.33942i
$207$		0			0
$208$			1.61901e9i			0.864958i
$209$			1.08619e9i			0.569273i
$210$		0			0
$211$	1.88697e9			0.951995			0.475998	−	0.879447i	$-0.342087\pi$
$211$	1.88697e9			0.951995			0.475998	+	0.879447i	$0.342087\pi$
$212$	−5.30130e8			−0.262446
$213$		0			0
$214$	7.84636e8			0.374122
$215$	6.63252e8	−	9.30947e7i	0.310402	−	0.0435684i
$216$		0			0
$217$			2.25763e9i			1.01815i
$218$	−2.90935e9			−1.28816
$219$		0			0
$220$	−3.95153e8	+	5.54641e7i	−0.168684	+	0.0236767i
$221$			5.48197e9i			2.29809i
$222$		0			0
$223$		−	3.00252e9i		−	1.21414i	−0.794650	−	0.607068i	$-0.792346\pi$
$223$		−	3.00252e9i		−	1.21414i	0.794650	−	0.607068i	$-0.207654\pi$
$224$		−	1.28926e9i		−	0.512092i
$225$		0			0
$226$	4.18302e8			0.160345
$227$	−7.55931e8			−0.284694			−0.142347	−	0.989817i	$-0.545465\pi$
$227$	−7.55931e8			−0.284694			−0.142347	+	0.989817i	$0.545465\pi$
$228$		0			0
$229$	3.80872e9			1.38496			0.692479	−	0.721438i	$-0.256518\pi$
$229$	3.80872e9			1.38496			0.692479	+	0.721438i	$0.256518\pi$
$230$	3.91647e8	+	2.79029e9i	0.139954	+	0.997097i
$231$		0			0
$232$			2.02302e9i			0.698309i
$233$	2.90545e9			0.985801			0.492900	−	0.870086i	$-0.335937\pi$
$233$	2.90545e9			0.985801			0.492900	+	0.870086i	$0.335937\pi$
$234$		0			0
$235$	−2.90193e8	−	2.06748e9i	−0.0951516	−	0.677906i
$236$		−	1.13529e9i		−	0.365981i
$237$		0			0
$238$			3.05151e9i			0.951057i
$239$			3.35229e9i			1.02742i	0.857963	+	0.513712i	$0.171730\pi$
$239$			3.35229e9i			1.02742i	−0.857963	+	0.513712i	$0.828270\pi$
$240$		0			0
$241$	3.45448e9			1.02403			0.512017	−	0.858975i	$-0.328899\pi$
$241$	3.45448e9			1.02403			0.512017	+	0.858975i	$0.328899\pi$
$242$	2.07836e9			0.605981
$243$		0			0
$244$	−4.13770e8			−0.116735
$245$	1.80932e8	+	1.28905e9i	0.0502170	+	0.357770i
$246$		0			0
$247$			6.58726e9i			1.76977i
$248$	5.24630e9			1.38690
$249$		0			0
$250$	−1.29245e9	−	2.90703e9i	−0.330868	−	0.744200i
$251$		−	1.34472e9i		−	0.338794i	−0.985548	−	0.169397i	$-0.945818\pi$
$251$		−	1.34472e9i		−	0.338794i	0.985548	−	0.169397i	$-0.0541820\pi$
$252$		0			0
$253$		−	2.56258e9i		−	0.625453i
$254$		−	6.26255e9i		−	1.50458i
$255$		0			0
$256$	−3.79126e9			−0.882722
$257$	−5.38058e9			−1.23338			−0.616689	−	0.787207i	$-0.711527\pi$
$257$	−5.38058e9			−1.23338			−0.616689	+	0.787207i	$0.711527\pi$
$258$		0			0
$259$	2.54408e9			0.565369
$260$	−2.39643e9	+	3.36365e8i	−0.524410	+	0.0736068i
$261$		0			0
$262$		−	3.89062e8i		−	0.0825683i
$263$	−1.59261e9			−0.332878			−0.166439	−	0.986052i	$-0.553227\pi$
$263$	−1.59261e9			−0.332878			−0.166439	+	0.986052i	$0.553227\pi$
$264$		0			0
$265$	5.34318e8	+	3.80674e9i	0.108347	+	0.771916i
$266$			3.66676e9i			0.732412i
$267$		0			0
$268$		−	3.14716e9i		−	0.610070i
$269$		−	1.03270e10i		−	1.97226i	−0.165977	−	0.986130i	$-0.553078\pi$
$269$		−	1.03270e10i		−	1.97226i	0.165977	−	0.986130i	$-0.446922\pi$
$270$		0			0
$271$	−7.47903e9			−1.38665			−0.693327	−	0.720623i	$-0.743856\pi$
$271$	−7.47903e9			−1.38665			−0.693327	+	0.720623i	$0.743856\pi$
$272$	4.39834e9			0.803551
$273$		0			0
$274$	−3.78493e9			−0.671516
$275$	7.96549e8	+	2.78160e9i	0.139278	+	0.486367i
$276$		0			0
$277$		−	8.73280e9i		−	1.48332i	−0.670777	−	0.741660i	$-0.734039\pi$
$277$		−	8.73280e9i		−	1.48332i	0.670777	−	0.741660i	$-0.265961\pi$
$278$	−4.06774e9			−0.681042
$279$		0			0
$280$	−5.29591e9	+	7.43340e8i	−0.861606	+	0.120936i
$281$			2.27147e9i			0.364319i	0.983269	+	0.182159i	$0.0583087\pi$
$281$			2.27147e9i			0.364319i	−0.983269	+	0.182159i	$0.941691\pi$
$282$		0			0
$283$		−	4.90950e9i		−	0.765406i	−0.923872	−	0.382703i	$-0.874993\pi$
$283$		−	4.90950e9i		−	0.765406i	0.923872	−	0.382703i	$-0.125007\pi$
$284$			6.88081e7i			0.0105771i
$285$		0			0
$286$	−4.33586e9			−0.648053
$287$	−3.35464e9			−0.494446
$288$		0			0
$289$	7.91708e9			1.13494
$290$	3.65908e9	−	5.13592e8i	0.517345	−	0.0726150i
$291$		0			0
$292$			6.38364e8i			0.0878086i
$293$	−5.24948e9			−0.712271			−0.356136	−	0.934434i	$-0.615906\pi$
$293$	−5.24948e9			−0.712271			−0.356136	+	0.934434i	$0.615906\pi$
$294$		0			0
$295$	−8.15225e9	+	1.14426e9i	−1.07644	+	0.151090i
$296$		−	5.91196e9i		−	0.770131i
$297$		0			0
$298$			1.13649e10i			1.44112i
$299$		−	1.55409e10i		−	1.94442i
$300$		0			0
$301$	−2.05628e9			−0.250505
$302$	−3.16610e9			−0.380625
$303$		0			0
$304$	5.28514e9			0.618817
$305$	4.17039e8	+	2.97119e9i	0.0481922	+	0.343345i
$306$		0			0
$307$		−	4.33898e9i		−	0.488466i	−0.969717	−	0.244233i	$-0.921464\pi$
$307$		−	4.33898e9i		−	0.488466i	0.969717	−	0.244233i	$-0.0785362\pi$
$308$	1.22510e9			0.136134
$309$		0			0
$310$	−1.33190e9	−	9.48910e9i	−0.144220	−	1.02749i
$311$			1.02901e10i			1.09996i	0.835178	+	0.549980i	$0.185365\pi$
$311$			1.02901e10i			1.09996i	−0.835178	+	0.549980i	$0.814635\pi$
$312$		0			0
$313$			6.45458e9i			0.672497i	0.941773	+	0.336249i	$0.109158\pi$
$313$			6.45458e9i			0.672497i	−0.941773	+	0.336249i	$0.890842\pi$
$314$		−	6.58167e9i		−	0.677045i
$315$		0			0
$316$	5.57868e9			0.559478
$317$	1.40779e10			1.39412			0.697059	−	0.717013i	$-0.254491\pi$
$317$	1.40779e10			1.39412			0.697059	+	0.717013i	$0.254491\pi$
$318$		0			0
$319$	−3.36047e9			−0.324517
$320$	1.56216e9	+	1.11295e10i	0.148979	+	1.06140i
$321$		0			0
$322$		−	8.65074e9i		−	0.804692i
$323$	1.78955e10			1.64413
$324$		0			0
$325$	4.83072e9	+	1.68692e10i	0.432991	+	1.51203i
$326$			2.50310e9i			0.221620i
$327$		0			0
$328$			7.79555e9i			0.673521i
$329$			6.40982e9i			0.547094i
$330$		0			0
$331$	−1.04281e10			−0.868747			−0.434374	−	0.900733i	$-0.643030\pi$
$331$	−1.04281e10			−0.868747			−0.434374	+	0.900733i	$0.643030\pi$
$332$	1.86022e9			0.153113
$333$		0			0
$334$	1.64537e10			1.32214
$335$	−2.25990e10	+	3.17202e9i	−1.79436	+	0.251859i
$336$		0			0
$337$			4.20998e9i			0.326408i	0.986592	+	0.163204i	$0.0521828\pi$
$337$			4.20998e9i			0.326408i	−0.986592	+	0.163204i	$0.947817\pi$
$338$	−1.56653e10			−1.20025
$339$		0			0
$340$	9.13801e8	+	6.51036e9i	0.0683811	+	0.487180i
$341$			8.71472e9i			0.644519i
$342$		0			0
$343$		−	1.50584e10i		−	1.08793i
$344$			4.77841e9i			0.341232i
$345$		0			0
$346$	2.17870e10			1.52017
$347$	1.61293e10			1.11249			0.556246	−	0.831017i	$-0.312241\pi$
$347$	1.61293e10			1.11249			0.556246	+	0.831017i	$0.312241\pi$
$348$		0			0
$349$	1.41858e10			0.956207			0.478104	−	0.878303i	$-0.341324\pi$
$349$	1.41858e10			0.956207			0.478104	+	0.878303i	$0.341324\pi$
$350$	2.68899e9	+	9.39012e9i	0.179191	+	0.625748i
$351$		0			0
$352$		−	4.97669e9i		−	0.324168i
$353$	−7.51852e9			−0.484210			−0.242105	−	0.970250i	$-0.577838\pi$
$353$	−7.51852e9			−0.484210			−0.242105	+	0.970250i	$0.577838\pi$
$354$		0			0
$355$	4.94095e8	−	6.93516e7i	0.0311098	−	0.00436660i
$356$			2.68116e9i			0.166926i
$357$		0			0
$358$		−	3.10378e9i		−	0.188955i
$359$		−	1.71611e10i		−	1.03316i	−0.856239	−	0.516581i	$-0.827205\pi$
$359$		−	1.71611e10i		−	1.03316i	0.856239	−	0.516581i	$-0.172795\pi$
$360$		0			0
$361$	4.52011e9			0.266146
$362$	−4.18881e9			−0.243925
$363$		0			0
$364$	7.42967e9			0.423218
$365$	4.58394e9	−	6.43407e8i	0.258266	−	0.0362505i
$366$		0			0
$367$			6.96880e9i			0.384144i	0.981381	+	0.192072i	$0.0615207\pi$
$367$			6.96880e9i			0.384144i	−0.981381	+	0.192072i	$0.938479\pi$
$368$	−1.24689e10			−0.679887
$369$		0			0
$370$	−1.06931e10	+	1.50089e9i	−0.570554	+	0.0800836i
$371$		−	1.18021e10i		−	0.622963i
$372$		0			0
$373$		−	5.84873e9i		−	0.302152i	−0.988522	−	0.151076i	$-0.951726\pi$
$373$		−	5.84873e9i		−	0.302152i	0.988522	−	0.151076i	$-0.0482739\pi$
$374$			1.17792e10i			0.602045i
$375$		0			0
$376$	1.48952e10			0.745238
$377$	−2.03798e10			−1.00887
$378$		0			0
$379$	−2.17986e10			−1.05651			−0.528253	−	0.849087i	$-0.677153\pi$
$379$	−2.17986e10			−1.05651			−0.528253	+	0.849087i	$0.677153\pi$
$380$	1.09804e9	+	7.82299e9i	0.0526605	+	0.375179i
$381$		0			0
$382$		−	1.07692e10i		−	0.505744i
$383$	1.63885e10			0.761631			0.380816	−	0.924651i	$-0.375643\pi$
$383$	1.63885e10			0.761631			0.380816	+	0.924651i	$0.375643\pi$
$384$		0			0
$385$	−1.23477e9	−	8.79713e9i	−0.0562011	−	0.400404i
$386$		−	4.46155e9i		−	0.200973i
$387$		0			0
$388$		−	8.12998e9i		−	0.358726i
$389$			8.17971e9i			0.357223i	0.983920	+	0.178612i	$0.0571605\pi$
$389$			8.17971e9i			0.357223i	−0.983920	+	0.178612i	$0.942839\pi$
$390$		0			0
$391$	−4.22198e10			−1.80638
$392$	−9.28697e9			−0.393305
$393$		0			0
$394$	−1.51890e10			−0.630294
$395$	−5.62275e9	−	4.00592e10i	−0.230973	−	1.64556i
$396$		0			0
$397$		−	1.00785e10i		−	0.405729i	−0.979207	−	0.202864i	$-0.934975\pi$
$397$		−	1.00785e10i		−	0.405729i	0.979207	−	0.202864i	$-0.0650250\pi$
$398$	4.54875e9			0.181284
$399$		0			0
$400$	1.35346e10	−	3.87582e9i	0.528696	−	0.151399i
$401$			1.95831e9i			0.0757364i	0.999283	+	0.0378682i	$0.0120567\pi$
$401$			1.95831e9i			0.0757364i	−0.999283	+	0.0378682i	$0.987943\pi$
$402$		0			0
$403$			5.28509e10i			2.00370i
$404$			1.45534e10i			0.546308i
$405$		0			0
$406$	−1.13443e10			−0.417515
$407$	9.82045e9			0.357894
$408$		0			0
$409$	−1.16686e10			−0.416990			−0.208495	−	0.978023i	$-0.566857\pi$
$409$	−1.16686e10			−0.416990			−0.208495	+	0.978023i	$0.566857\pi$
$410$	1.41000e10	−	1.97909e9i	0.498980	−	0.0700374i
$411$		0			0
$412$			1.59544e10i			0.553722i
$413$	2.52745e10			0.868724
$414$		0			0
$415$	−1.87492e9	−	1.33578e10i	−0.0632105	−	0.450342i
$416$		−	3.01815e10i		−	1.00778i
$417$		0			0
$418$			1.41541e10i			0.463637i
$419$		−	3.48051e10i		−	1.12924i	−0.825351	−	0.564621i	$-0.809022\pi$
$419$		−	3.48051e10i		−	1.12924i	0.825351	−	0.564621i	$-0.190978\pi$
$420$		0			0
$421$	1.15892e9			0.0368914			0.0184457	−	0.999830i	$-0.494128\pi$
$421$	1.15892e9			0.0368914			0.0184457	+	0.999830i	$0.494128\pi$
$422$	2.45891e10			0.775340
$423$		0			0
$424$	−2.74258e10			−0.848585
$425$	4.58284e10	−	1.31236e10i	1.40468	−	0.402251i
$426$		0			0
$427$		−	9.21159e9i		−	0.277091i
$428$	−5.18995e9			−0.154664
$429$		0			0
$430$	8.64283e9	−	1.21312e9i	0.252803	−	0.0354837i
$431$			4.74653e9i			0.137552i	0.997632	+	0.0687760i	$0.0219094\pi$
$431$			4.74653e9i			0.137552i	−0.997632	+	0.0687760i	$0.978091\pi$
$432$		0			0
$433$		−	5.86356e10i		−	1.66805i	−0.551725	−	0.834026i	$-0.686030\pi$
$433$		−	5.86356e10i		−	1.66805i	0.551725	−	0.834026i	$-0.313970\pi$
$434$			2.94191e10i			0.829222i
$435$		0			0
$436$	1.92439e10			0.532532
$437$	−5.07322e10			−1.39110
$438$		0			0
$439$	−5.06896e10			−1.36477			−0.682387	−	0.730991i	$-0.739058\pi$
$439$	−5.06896e10			−1.36477			−0.682387	+	0.730991i	$0.739058\pi$
$440$	−2.04429e10	+	2.86938e9i	−0.545420	+	0.0765557i
$441$		0			0
$442$			7.14355e10i			1.87165i
$443$	−4.34873e10			−1.12914			−0.564570	−	0.825385i	$-0.690958\pi$
$443$	−4.34873e10			−1.12914			−0.564570	+	0.825385i	$0.690958\pi$
$444$		0			0
$445$	1.92528e10	−	2.70234e9i	0.490969	−	0.0689129i
$446$		−	3.91259e10i		−	0.988837i
$447$		0			0
$448$		−	3.45050e10i		−	0.856585i
$449$			7.22137e10i			1.77678i	0.459087	+	0.888391i	$0.348177\pi$
$449$			7.22137e10i			1.77678i	−0.459087	+	0.888391i	$0.651823\pi$
$450$		0			0
$451$	−1.29493e10			−0.312997
$452$	−2.76685e9			−0.0662875
$453$		0			0
$454$	−9.85053e9			−0.231866
$455$	−7.48836e9	−	5.33507e10i	−0.174719	−	1.24479i
$456$		0			0
$457$			6.46241e10i			1.48160i	0.671728	+	0.740798i	$0.265552\pi$
$457$			6.46241e10i			1.48160i	−0.671728	+	0.740798i	$0.734448\pi$
$458$	4.96314e10			1.12796
$459$		0			0
$460$	−2.59054e9	−	1.84563e10i	−0.0578575	−	0.412204i
$461$			6.89816e10i			1.52732i	0.645620	+	0.763659i	$0.276599\pi$
$461$			6.89816e10i			1.52732i	−0.645620	+	0.763659i	$0.723401\pi$
$462$		0			0
$463$		−	5.82360e10i		−	1.26727i	−0.773634	−	0.633633i	$-0.781563\pi$
$463$		−	5.82360e10i		−	1.26727i	0.773634	−	0.633633i	$-0.218437\pi$
$464$			1.63513e10i			0.352760i
$465$		0			0
$466$	3.78608e10			0.802873
$467$	−4.24626e10			−0.892768			−0.446384	−	0.894841i	$-0.647288\pi$
$467$	−4.24626e10			−0.892768			−0.446384	+	0.894841i	$0.647288\pi$
$468$		0			0
$469$	7.00639e10			1.44811
$470$	−3.78151e9	−	2.69413e10i	−0.0774950	−	0.552112i
$471$		0			0
$472$		−	5.87331e10i		−	1.18335i
$473$	−7.93750e9			−0.158577
$474$		0			0
$475$	5.50683e10	−	1.57696e10i	1.08175	−	0.309774i
$476$		−	2.01841e10i		−	0.393172i
$477$		0			0
$478$			4.36837e10i			0.836773i
$479$			5.67715e10i			1.07842i	0.842171	+	0.539210i	$0.181277\pi$
$479$			5.67715e10i			1.07842i	−0.842171	+	0.539210i	$0.818723\pi$
$480$		0			0
$481$	5.95567e10			1.11263
$482$	4.50153e10			0.834011
$483$		0			0
$484$	−1.37473e10			−0.250515
$485$	−5.83794e10	+	8.19420e9i	−1.05510	+	0.148095i
$486$		0			0
$487$		−	2.01211e9i		−	0.0357715i	−0.999840	−	0.0178857i	$-0.994306\pi$
$487$		−	2.01211e9i		−	0.0357715i	0.999840	−	0.0178857i	$-0.00569351\pi$
$488$	−2.14060e10			−0.377447
$489$		0			0
$490$	2.35772e9	+	1.67976e10i	0.0408986	+	0.291382i
$491$		−	4.44540e10i		−	0.764866i	−0.923983	−	0.382433i	$-0.875086\pi$
$491$		−	4.44540e10i		−	0.764866i	0.923983	−	0.382433i	$-0.124914\pi$
$492$		0			0
$493$			5.53655e10i			0.937242i
$494$			8.58385e10i			1.44137i
$495$		0			0
$496$	4.24038e10			0.700612
$497$	−1.53185e9			−0.0251067
$498$		0			0
$499$	−3.00108e10			−0.484034			−0.242017	−	0.970272i	$-0.577809\pi$
$499$	−3.00108e10			−0.484034			−0.242017	+	0.970272i	$0.577809\pi$
$500$	8.54890e9	+	1.92285e10i	0.136782	+	0.307656i
$501$		0			0
$502$		−	1.75230e10i		−	0.275926i
$503$	2.63318e10			0.411347			0.205673	−	0.978621i	$-0.434062\pi$
$503$	2.63318e10			0.411347			0.205673	+	0.978621i	$0.434062\pi$
$504$		0			0
$505$	1.04504e11	−	1.46683e10i	1.60682	−	0.225536i
$506$		−	3.33929e10i		−	0.509392i
$507$		0			0
$508$			4.14235e10i			0.622002i
$509$			1.71042e10i			0.254819i	0.991850	+	0.127410i	$0.0406663\pi$
$509$			1.71042e10i			0.254819i	−0.991850	+	0.127410i	$0.959334\pi$
$510$		0			0
$511$	−1.42116e10			−0.208430
$512$	−6.53578e10			−0.951081
$513$		0			0
$514$	−7.01143e10			−1.00451
$515$	1.14565e11	−	1.60805e10i	1.62863	−	0.228596i
$516$		0			0
$517$			2.47427e10i			0.346325i
$518$	3.31519e10			0.460457
$519$		0			0
$520$	−1.23977e11	+	1.74015e10i	−1.69562	+	0.237998i
$521$			1.00723e11i			1.36703i	0.729937	+	0.683514i	$0.239549\pi$
$521$			1.00723e11i			1.36703i	−0.729937	+	0.683514i	$0.760451\pi$
$522$		0			0
$523$			3.74201e10i			0.500148i	0.968227	+	0.250074i	$0.0804549\pi$
$523$			3.74201e10i			0.500148i	−0.968227	+	0.250074i	$0.919545\pi$
$524$			2.57344e9i			0.0341341i
$525$		0			0
$526$	−2.07532e10			−0.271108
$527$	1.43580e11			1.86145
$528$		0			0
$529$	4.13783e10			0.528384
$530$	6.96270e9	+	4.96056e10i	0.0882417	+	0.628677i
$531$		0			0
$532$		−	2.42537e10i		−	0.302783i
$533$	−7.85319e10			−0.973054
$534$		0			0
$535$	5.23095e9	+	3.72678e10i	0.0638507	+	0.454903i
$536$		−	1.62815e11i		−	1.97258i
$537$		0			0
$538$		−	1.34571e11i		−	1.60628i
$539$		−	1.54267e10i		−	0.182776i
$540$		0			0
$541$	−5.67222e9			−0.0662162			−0.0331081	−	0.999452i	$-0.510541\pi$
$541$	−5.67222e9			−0.0662162			−0.0331081	+	0.999452i	$0.510541\pi$
$542$	−9.74592e10			−1.12934
$543$		0			0
$544$	−8.19937e10			−0.936235
$545$	−1.93959e10	−	1.38186e11i	−0.219848	−	1.56631i
$546$		0			0
$547$		−	1.13867e11i		−	1.27189i	−0.771735	−	0.635944i	$-0.780611\pi$
$547$		−	1.13867e11i		−	1.27189i	0.771735	−	0.635944i	$-0.219389\pi$
$548$	2.50354e10			0.277608
$549$		0			0
$550$	1.03798e10	+	3.62470e10i	0.113433	+	0.396115i
$551$			6.65284e10i			0.721773i
$552$		0			0
$553$			1.24196e11i			1.32803i
$554$		−	1.13797e11i		−	1.20807i
$555$		0			0
$556$	2.69060e10			0.281546
$557$	1.20812e11			1.25513			0.627565	−	0.778564i	$-0.284052\pi$
$557$	1.20812e11			1.25513			0.627565	+	0.778564i	$0.284052\pi$
$558$		0			0
$559$	−4.81374e10			−0.492987
$560$	−4.28048e10	+	6.00812e9i	−0.435251	+	0.0610923i
$561$		0			0
$562$			2.95995e10i			0.296715i
$563$	−1.33228e11			−1.32605			−0.663027	−	0.748596i	$-0.730728\pi$
$563$	−1.33228e11			−1.32605			−0.663027	+	0.748596i	$0.730728\pi$
$564$		0			0
$565$	2.78870e9	+	1.98681e10i	0.0273658	+	0.194967i
$566$		−	6.39757e10i		−	0.623375i
$567$		0			0
$568$			3.55972e9i			0.0341997i
$569$			9.24293e8i			0.00881781i	0.999990	+	0.00440891i	$0.00140340\pi$
$569$			9.24293e8i			0.00881781i	−0.999990	+	0.00440891i	$0.998597\pi$
$570$		0			0
$571$	−1.74424e11			−1.64082			−0.820411	−	0.571775i	$-0.806255\pi$
$571$	−1.74424e11			−1.64082			−0.820411	+	0.571775i	$0.806255\pi$
$572$	2.86794e10			0.267908
$573$		0			0
$574$	−4.37143e10			−0.402695
$575$	−1.29919e11	+	3.72041e10i	−1.18851	+	0.340345i
$576$		0			0
$577$		−	1.86635e11i		−	1.68380i	−0.539637	−	0.841898i	$-0.681439\pi$
$577$		−	1.86635e11i		−	1.68380i	0.539637	−	0.841898i	$-0.318561\pi$
$578$	1.03167e11			0.924338
$579$		0			0
$580$	−2.42029e10	+	3.39714e9i	−0.213873	+	0.0300194i
$581$			4.14133e10i			0.363442i
$582$		0			0
$583$		−	4.55574e10i		−	0.394353i
$584$			3.30251e10i			0.283918i
$585$		0			0
$586$	−6.84059e10			−0.580100
$587$	−4.03447e10			−0.339809			−0.169904	−	0.985461i	$-0.554346\pi$
$587$	−4.03447e10			−0.339809			−0.169904	+	0.985461i	$0.554346\pi$
$588$		0			0
$589$	1.72528e11			1.43351
$590$	−1.06232e11	+	1.49108e10i	−0.876692	+	0.123053i
$591$		0			0
$592$		−	4.77840e10i		−	0.389041i
$593$	1.32300e11			1.06989			0.534946	−	0.844886i	$-0.320332\pi$
$593$	1.32300e11			1.06989			0.534946	+	0.844886i	$0.320332\pi$
$594$		0			0
$595$	−1.44937e11	+	2.03436e10i	−1.15641	+	0.162315i
$596$		−	7.51730e10i		−	0.595768i
$597$		0			0
$598$		−	2.02513e11i		−	1.58361i
$599$		−	1.69478e11i		−	1.31646i	−0.752818	−	0.658228i	$-0.771306\pi$
$599$		−	1.69478e11i		−	1.31646i	0.752818	−	0.658228i	$-0.228694\pi$
$600$		0			0
$601$	1.97703e10			0.151535			0.0757677	−	0.997125i	$-0.475859\pi$
$601$	1.97703e10			0.151535			0.0757677	+	0.997125i	$0.475859\pi$
$602$	−2.67954e10			−0.204021
$603$		0			0
$604$	2.09421e10			0.157352
$605$	1.38559e10	+	9.87158e10i	0.103422	+	0.736826i
$606$		0			0
$607$			1.84942e11i			1.36232i	0.732133	+	0.681161i	$0.238525\pi$
$607$			1.84942e11i			1.36232i	−0.732133	+	0.681161i	$0.761475\pi$
$608$	−9.85254e10			−0.720998
$609$		0			0
$610$	5.43443e9	+	3.87175e10i	0.0392496	+	0.279633i
$611$			1.50053e11i			1.07667i
$612$		0			0
$613$			1.98997e11i			1.40930i	0.709554	+	0.704651i	$0.248896\pi$
$613$			1.98997e11i			1.40930i	−0.709554	+	0.704651i	$0.751104\pi$
$614$		−	5.65413e10i		−	0.397825i
$615$		0			0
$616$	6.33791e10			0.440173
$617$	6.55893e10			0.452577			0.226289	−	0.974060i	$-0.427341\pi$
$617$	6.55893e10			0.452577			0.226289	+	0.974060i	$0.427341\pi$
$618$		0			0
$619$	8.30730e10			0.565845			0.282923	−	0.959143i	$-0.408696\pi$
$619$	8.30730e10			0.565845			0.282923	+	0.959143i	$0.408696\pi$
$620$	8.80982e9	+	6.27654e10i	0.0596212	+	0.424770i
$621$		0			0
$622$			1.34090e11i			0.895849i
$623$	−5.96896e10			−0.396229
$624$		0			0
$625$	1.29459e11	−	8.07680e10i	0.848422	−	0.529321i
$626$			8.41096e10i			0.547707i
$627$		0			0
$628$			4.35343e10i			0.279894i
$629$		−	1.61797e11i		−	1.03364i
$630$		0			0
$631$	−3.46002e10			−0.218254			−0.109127	−	0.994028i	$-0.534805\pi$
$631$	−3.46002e10			−0.218254			−0.109127	+	0.994028i	$0.534805\pi$
$632$	2.88607e11			1.80900
$633$		0			0
$634$	1.83449e11			1.13542
$635$	2.97452e11	−	4.17507e10i	1.82946	−	0.256785i
$636$		0			0
$637$		−	9.35564e10i		−	0.568219i
$638$	−4.37903e10			−0.264299
$639$		0			0
$640$	5.41398e9	+	3.85718e10i	0.0322698	+	0.229906i
$641$			2.85486e11i			1.69104i	0.533947	+	0.845518i	$0.320708\pi$
$641$			2.85486e11i			1.69104i	−0.533947	+	0.845518i	$0.679292\pi$
$642$		0			0
$643$			7.11481e10i			0.416217i	0.978106	+	0.208108i	$0.0667306\pi$
$643$			7.11481e10i			0.416217i	−0.978106	+	0.208108i	$0.933269\pi$
$644$			5.72201e10i			0.332664i
$645$		0			0
$646$	2.33197e11			1.33904
$647$	−2.20623e11			−1.25903			−0.629513	−	0.776990i	$-0.716745\pi$
$647$	−2.20623e11			−1.25903			−0.629513	+	0.776990i	$0.716745\pi$
$648$		0			0
$649$	9.75625e10			0.549926
$650$	6.29491e10	+	2.19822e11i	0.352644	+	1.23145i
$651$		0			0
$652$		−	1.65567e10i		−	0.0916186i
$653$	−1.22498e10			−0.0673718			−0.0336859	−	0.999432i	$-0.510725\pi$
$653$	−1.22498e10			−0.0673718			−0.0336859	+	0.999432i	$0.510725\pi$
$654$		0			0
$655$	1.84793e10	−	2.59377e9i	0.100397	−	0.0140918i
$656$			6.30083e10i			0.340238i
$657$		0			0
$658$			8.35263e10i			0.445574i
$659$		−	7.01341e10i		−	0.371867i	−0.982562	−	0.185934i	$-0.940469\pi$
$659$		−	7.01341e10i		−	0.371867i	0.982562	−	0.185934i	$-0.0595309\pi$
$660$		0			0
$661$	−1.27159e11			−0.666105			−0.333053	−	0.942908i	$-0.608079\pi$
$661$	−1.27159e11			−0.666105			−0.333053	+	0.942908i	$0.608079\pi$
$662$	−1.35889e11			−0.707540
$663$		0			0
$664$	9.62366e10			0.495072
$665$	−1.74160e11	+	2.44453e10i	−0.890557	+	0.124999i
$666$		0			0
$667$		−	1.56956e11i		−	0.793003i
$668$	−1.08833e11			−0.546579
$669$		0			0
$670$	−2.94488e11	+	4.13346e10i	−1.46140	+	0.205123i
$671$		−	3.55578e10i		−	0.175406i
$672$		0			0
$673$		−	1.08256e11i		−	0.527703i	−0.964563	−	0.263852i	$-0.915007\pi$
$673$		−	1.08256e11i		−	0.527703i	0.964563	−	0.263852i	$-0.0849929\pi$
$674$			5.48602e10i			0.265839i
$675$		0			0
$676$	1.03617e11			0.496188
$677$	−1.06487e11			−0.506923			−0.253461	−	0.967346i	$-0.581569\pi$
$677$	−1.06487e11			−0.506923			−0.253461	+	0.967346i	$0.581569\pi$
$678$		0			0
$679$	1.80994e11			0.851502
$680$	4.72746e10	+	3.36807e11i	0.221102	+	1.57524i
$681$		0			0
$682$			1.13561e11i			0.524920i
$683$	3.30690e11			1.51963			0.759815	−	0.650139i	$-0.225289\pi$
$683$	3.30690e11			1.51963			0.759815	+	0.650139i	$0.225289\pi$
$684$		0			0
$685$	−2.52331e10	−	1.79773e11i	−0.114606	−	0.816511i
$686$		−	1.96226e11i		−	0.886054i
$687$		0			0
$688$			3.86220e10i			0.172378i
$689$		−	2.76285e11i		−	1.22597i
$690$		0			0
$691$	−1.23710e11			−0.542615			−0.271308	−	0.962493i	$-0.587456\pi$
$691$	−1.23710e11			−0.542615			−0.271308	+	0.962493i	$0.587456\pi$
$692$	−1.44109e11			−0.628446
$693$		0			0
$694$	2.10181e11			0.906055
$695$	−2.71185e10	−	1.93205e11i	−0.116232	−	0.828095i
$696$		0			0
$697$			2.13347e11i			0.903973i
$698$	1.84855e11			0.778771
$699$		0			0
$700$	−1.77863e10	−	6.21107e10i	−0.0740786	−	0.258687i
$701$		−	7.23976e10i		−	0.299814i	−0.988700	−	0.149907i	$-0.952103\pi$
$701$		−	7.23976e10i		−	0.299814i	0.988700	−	0.149907i	$-0.0478974\pi$
$702$		0			0
$703$		−	1.94419e11i		−	0.796008i
$704$		−	1.33194e11i		−	0.542241i
$705$		0			0
$706$	−9.79737e10			−0.394358
$707$	−3.23995e11			−1.29676
$708$		0			0
$709$	−2.92209e11			−1.15640			−0.578200	−	0.815895i	$-0.696245\pi$
$709$	−2.92209e11			−1.15640			−0.578200	+	0.815895i	$0.696245\pi$
$710$	6.43854e9	−	9.03721e8i	0.0253369	−	0.00355632i
$711$		0			0
$712$			1.38707e11i			0.539733i
$713$	−4.07035e11			−1.57497
$714$		0			0
$715$	−2.89060e10	−	2.05940e11i	−0.110602	−	0.787983i
$716$			2.05298e10i			0.0781148i
$717$		0			0
$718$		−	2.23627e11i		−	0.841445i
$719$		−	3.76304e11i		−	1.40807i	−0.710166	−	0.704034i	$-0.751380\pi$
$719$		−	3.76304e11i		−	1.40807i	0.710166	−	0.704034i	$-0.248620\pi$
$720$		0			0
$721$	−3.55186e11			−1.31436
$722$	5.89015e10			0.216759
$723$		0			0
$724$	2.77068e10			0.100840
$725$	4.87882e10	+	1.70371e11i	0.176589	+	0.616658i
$726$		0			0
$727$			2.88082e11i			1.03129i	0.856804	+	0.515643i	$0.172447\pi$
$727$			2.88082e11i			1.03129i	−0.856804	+	0.515643i	$0.827553\pi$
$728$	3.84366e11			1.36842
$729$		0			0
$730$	5.97333e10	−	8.38424e9i	0.210342	−	0.0295238i
$731$			1.30775e11i			0.457988i
$732$		0			0
$733$		−	2.35415e11i		−	0.815488i	−0.913096	−	0.407744i	$-0.866316\pi$
$733$		−	2.35415e11i		−	0.815488i	0.913096	−	0.407744i	$-0.133684\pi$
$734$			9.08104e10i			0.312861i
$735$		0			0
$736$	2.32445e11			0.792152
$737$	2.70455e11			0.916695
$738$		0			0
$739$	−1.40233e11			−0.470190			−0.235095	−	0.971972i	$-0.575540\pi$
$739$	−1.40233e11			−0.470190			−0.235095	+	0.971972i	$0.575540\pi$
$740$	7.07292e10	−	9.92763e9i	0.235870	−	0.0331069i
$741$		0			0
$742$		−	1.53793e11i		−	0.507364i
$743$	−9.10790e10			−0.298857			−0.149428	−	0.988773i	$-0.547743\pi$
$743$	−9.10790e10			−0.298857			−0.149428	+	0.988773i	$0.547743\pi$
$744$		0			0
$745$	−5.39800e11	+	7.57669e10i	−1.75230	+	0.245954i
$746$		−	7.62147e10i		−	0.246084i
$747$		0			0
$748$		−	7.79131e10i		−	0.248888i
$749$		−	1.15542e11i		−	0.367123i
$750$		0			0
$751$	−3.21915e11			−1.01200			−0.506001	−	0.862533i	$-0.668877\pi$
$751$	−3.21915e11			−1.01200			−0.506001	+	0.862533i	$0.668877\pi$
$752$	1.20392e11			0.376466
$753$		0			0
$754$	−2.65569e11			−0.821658
$755$	−2.11075e10	−	1.50380e11i	−0.0649605	−	0.462810i
$756$		0			0
$757$			3.25603e11i			0.991527i	0.868458	+	0.495763i	$0.165112\pi$
$757$			3.25603e11i			0.991527i	−0.868458	+	0.495763i	$0.834888\pi$
$758$	−2.84058e11			−0.860458
$759$		0			0
$760$	5.68062e10	+	4.04715e11i	0.170271	+	1.21309i
$761$			4.36690e10i			0.130207i	0.997879	+	0.0651035i	$0.0207378\pi$
$761$			4.36690e10i			0.130207i	−0.997879	+	0.0651035i	$0.979262\pi$
$762$		0			0
$763$			4.28418e11i			1.26406i
$764$			7.12327e10i			0.209077i
$765$		0			0
$766$	2.13559e11			0.620301
$767$	5.91673e11			1.70962
$768$		0			0
$769$	−9.02382e10			−0.258039			−0.129019	−	0.991642i	$-0.541183\pi$
$769$	−9.02382e10			−0.258039			−0.129019	+	0.991642i	$0.541183\pi$
$770$	−1.60903e10	−	1.14635e11i	−0.0457722	−	0.326104i
$771$		0			0
$772$			2.95108e10i			0.0830830i
$773$	2.31272e11			0.647747			0.323873	−	0.946100i	$-0.395015\pi$
$773$	2.31272e11			0.647747			0.323873	+	0.946100i	$0.395015\pi$
$774$		0			0
$775$	4.41824e11	−	1.26523e11i	1.22474	−	0.350720i
$776$		−	4.20596e11i		−	1.15989i
$777$		0			0
$778$			1.06590e11i			0.290936i
$779$			2.56362e11i			0.696152i
$780$		0			0
$781$	−5.91311e9			−0.0158932
$782$	−5.50166e11			−1.47118
$783$		0			0
$784$	−7.50629e10			−0.198683
$785$	3.12610e11	−	4.38782e10i	0.823235	−	0.115550i
$786$		0			0
$787$		−	6.09405e11i		−	1.58857i	−0.607544	−	0.794286i	$-0.707845\pi$
$787$		−	6.09405e11i		−	1.58857i	0.607544	−	0.794286i	$-0.292155\pi$
$788$	1.00467e11			0.260567
$789$		0			0
$790$	−7.32700e10	−	5.22011e11i	−0.188113	−	1.34021i
$791$		−	6.15971e10i		−	0.157346i
$792$		0			0
$793$		−	2.15643e11i		−	0.545308i
$794$		−	1.31333e11i		−	0.330440i
$795$		0			0
$796$	−3.00876e10			−0.0749437
$797$	−1.10929e11			−0.274923			−0.137461	−	0.990507i	$-0.543894\pi$
$797$	−1.10929e11			−0.274923			−0.137461	+	0.990507i	$0.543894\pi$
$798$		0			0
$799$	4.07649e11			1.00023
$800$	−2.52312e11	+	7.22530e10i	−0.615996	+	0.176399i
$801$		0			0
$802$			2.55188e10i			0.0616825i
$803$	−5.48586e10			−0.131942
$804$		0			0
$805$	4.10884e11	−	5.76721e10i	0.978444	−	0.137335i
$806$			6.88700e11i			1.63189i
$807$		0			0
$808$			7.52903e11i			1.76642i
$809$			4.36316e10i			0.101861i	0.998702	+	0.0509303i	$0.0162186\pi$
$809$			4.36316e10i			0.101861i	−0.998702	+	0.0509303i	$0.983781\pi$
$810$		0			0
$811$	8.84218e10			0.204398			0.102199	−	0.994764i	$-0.467412\pi$
$811$	8.84218e10			0.204398			0.102199	+	0.994764i	$0.467412\pi$
$812$	7.50364e10			0.172603
$813$		0			0
$814$	1.27970e11			0.291482
$815$	−1.18890e11	+	1.66875e10i	−0.269472	+	0.0378234i
$816$		0			0
$817$			1.57142e11i			0.352698i
$818$	−1.52054e11			−0.339612
$819$		0			0
$820$	−9.32640e10	+	1.30906e10i	−0.206281	+	0.0289538i
$821$			3.18098e10i			0.0700145i	0.999387	+	0.0350072i	$0.0111454\pi$
$821$			3.18098e10i			0.0700145i	−0.999387	+	0.0350072i	$0.988855\pi$
$822$		0			0
$823$			2.98230e11i			0.650058i	0.945704	+	0.325029i	$0.105374\pi$
$823$			2.98230e11i			0.650058i	−0.945704	+	0.325029i	$0.894626\pi$
$824$			8.25386e11i			1.79039i
$825$		0			0
$826$	3.29352e11			0.707521
$827$	−4.80677e11			−1.02762			−0.513808	−	0.857905i	$-0.671766\pi$
$827$	−4.80677e11			−1.02762			−0.513808	+	0.857905i	$0.671766\pi$
$828$		0			0
$829$	1.96280e11			0.415583			0.207792	−	0.978173i	$-0.433372\pi$
$829$	1.96280e11			0.415583			0.207792	+	0.978173i	$0.433372\pi$
$830$	−2.44320e10	−	1.74065e11i	−0.0514810	−	0.366775i
$831$		0			0
$832$		−	8.07760e11i		−	1.68573i
$833$	−2.54164e11			−0.527878
$834$		0			0
$835$	1.09692e11	+	7.81501e11i	0.225647	+	1.60762i
$836$		−	9.36221e10i		−	0.191670i
$837$		0			0
$838$		−	4.53545e11i		−	0.919696i
$839$			9.37646e11i			1.89230i	0.323721	+	0.946152i	$0.395066\pi$
$839$			9.37646e11i			1.89230i	−0.323721	+	0.946152i	$0.604934\pi$
$840$		0			0
$841$	2.94420e11			0.588549
$842$	1.51019e10			0.0300457
$843$		0			0
$844$	−1.62644e11			−0.320529
$845$	−1.04436e11	−	7.44053e11i	−0.204844	−	1.45941i
$846$		0			0
$847$		−	3.06049e11i		−	0.594645i
$848$	−2.21672e11			−0.428673
$849$		0			0
$850$	5.97189e11	−	1.71013e11i	1.14403	−	0.327608i
$851$			4.58680e11i			0.874565i
$852$		0			0
$853$		−	6.26886e11i		−	1.18411i	−0.805897	−	0.592056i	$-0.798317\pi$
$853$		−	6.26886e11i		−	1.18411i	0.805897	−	0.592056i	$-0.201683\pi$
$854$		−	1.20036e11i		−	0.225674i
$855$		0			0
$856$	−2.68497e11			−0.500086
$857$	1.01708e11			0.188552			0.0942759	−	0.995546i	$-0.469946\pi$
$857$	1.01708e11			0.188552			0.0942759	+	0.995546i	$0.469946\pi$
$858$		0			0
$859$	−2.13233e11			−0.391635			−0.195817	−	0.980640i	$-0.562736\pi$
$859$	−2.13233e11			−0.391635			−0.195817	+	0.980640i	$0.562736\pi$
$860$	−5.71678e10	+	8.02413e9i	−0.104510	+	0.0146691i
$861$		0			0
$862$			6.18520e10i			0.112027i
$863$	5.24346e11			0.945311			0.472655	−	0.881247i	$-0.343296\pi$
$863$	5.24346e11			0.945311			0.472655	+	0.881247i	$0.343296\pi$
$864$		0			0
$865$	1.45248e11	+	1.03482e12i	0.259445	+	1.84841i
$866$		−	7.64080e11i		−	1.35852i
$867$		0			0
$868$		−	1.94592e11i		−	0.342804i
$869$			4.79411e11i			0.840676i
$870$		0			0
$871$	1.64019e12			2.84985
$872$	9.95561e11			1.72188
$873$		0			0
$874$	−6.61091e11			−1.13296
$875$	−4.28076e11	+	1.90320e11i	−0.730278	+	0.324678i
$876$		0			0
$877$			1.14765e11i			0.194005i	0.995284	+	0.0970023i	$0.0309254\pi$
$877$			1.14765e11i			0.194005i	−0.995284	+	0.0970023i	$0.969075\pi$
$878$	−6.60536e11			−1.11152
$879$		0			0
$880$	−1.65231e11	+	2.31921e10i	−0.275526	+	0.0386731i
$881$		−	7.06861e11i		−	1.17336i	−0.809820	−	0.586679i	$-0.800435\pi$
$881$		−	7.06861e11i		−	1.17336i	0.809820	−	0.586679i	$-0.199565\pi$
$882$		0			0
$883$			1.23511e11i			0.203171i	0.994827	+	0.101586i	$0.0323916\pi$
$883$			1.23511e11i			0.203171i	−0.994827	+	0.101586i	$0.967608\pi$
$884$		−	4.72509e11i		−	0.773750i
$885$		0			0
$886$	−5.66683e11			−0.919613
$887$	7.99657e11			1.29184			0.645921	−	0.763405i	$-0.276474\pi$
$887$	7.99657e11			1.29184			0.645921	+	0.763405i	$0.276474\pi$
$888$		0			0
$889$	−9.22194e11			−1.47644
$890$	2.50883e11	−	3.52142e10i	0.399863	−	0.0561252i
$891$		0			0
$892$			2.58797e11i			0.408790i
$893$	4.89839e11			0.770279
$894$		0			0
$895$	1.47420e11	−	2.06920e10i	0.229755	−	0.0322486i
$896$		−	1.19584e11i		−	0.185542i
$897$		0			0
$898$			9.41016e11i			1.44708i
$899$			5.33771e11i			0.817177i
$900$		0			0
$901$	−7.50583e11			−1.13894
$902$	−1.68742e11			−0.254917
$903$		0			0
$904$	−1.43140e11			−0.214332
$905$	−2.79257e10	−	1.98956e11i	−0.0416303	−	0.296594i
$906$		0			0
$907$		−	3.05478e11i		−	0.451389i	−0.974198	−	0.225694i	$-0.927535\pi$
$907$		−	3.05478e11i		−	0.451389i	0.974198	−	0.225694i	$-0.0724651\pi$
$908$	6.51561e10			0.0958543
$909$		0			0
$910$	−9.75807e10	−	6.95212e11i	−0.142298	−	1.01380i
$911$			6.34054e11i			0.920562i	0.887773	+	0.460281i	$0.152251\pi$
$911$			6.34054e11i			0.920562i	−0.887773	+	0.460281i	$0.847749\pi$
$912$		0			0
$913$			1.59860e11i			0.230069i
$914$			8.42116e11i			1.20667i
$915$		0			0
$916$	−3.28286e11			−0.466305
$917$	−5.72914e10			−0.0810237
$918$		0			0
$919$	−1.51061e10			−0.0211783			−0.0105892	−	0.999944i	$-0.503371\pi$
$919$	−1.51061e10			−0.0211783			−0.0105892	+	0.999944i	$0.503371\pi$
$920$	−1.34019e11	−	9.54817e11i	−0.187075	−	1.33281i
$921$		0			0
$922$			8.98899e11i			1.24390i
$923$	−3.58604e10			−0.0494092
$924$		0			0
$925$	−1.42576e11	−	4.97884e11i	−0.194751	−	0.680082i
$926$		−	7.58873e11i		−	1.03211i
$927$		0			0
$928$		−	3.04820e11i		−	0.411009i
$929$		−	8.37421e10i		−	0.112430i	−0.998419	−	0.0562149i	$-0.982097\pi$
$929$		−	8.37421e10i		−	0.112430i	0.998419	−	0.0562149i	$-0.0179032\pi$
$930$		0			0
$931$	−3.05409e11			−0.406521
$932$	−2.50430e11			−0.331911
$933$		0			0
$934$	−5.53329e11			−0.727104
$935$	−5.59476e11	+	7.85286e10i	−0.732040	+	0.102750i
$936$		0			0
$937$		−	8.11620e11i		−	1.05292i	−0.850201	−	0.526458i	$-0.823520\pi$
$937$		−	8.11620e11i		−	1.05292i	0.850201	−	0.526458i	$-0.176480\pi$
$938$	9.13002e11			1.17940
$939$		0			0
$940$	2.50127e10	+	1.78203e11i	0.0320368	+	0.228246i
$941$		−	7.45393e11i		−	0.950664i	−0.879807	−	0.475332i	$-0.842328\pi$
$941$		−	7.45393e11i		−	0.950664i	0.879807	−	0.475332i	$-0.157672\pi$
$942$		0			0
$943$		−	6.04819e11i		−	0.764854i
$944$		−	4.74716e11i		−	0.597787i
$945$		0			0
$946$	−1.03434e11			−0.129151
$947$	−6.69046e11			−0.831872			−0.415936	−	0.909394i	$-0.636546\pi$
$947$	−6.69046e11			−0.831872			−0.415936	+	0.909394i	$0.636546\pi$
$948$		0			0
$949$	−3.32693e11			−0.410184
$950$	7.17595e11	−	2.05493e11i	0.881018	−	0.252292i
$951$		0			0
$952$		−	1.04421e12i		−	1.27127i
$953$	−6.00889e11			−0.728489			−0.364244	−	0.931303i	$-0.618673\pi$
$953$	−6.00889e11			−0.728489			−0.364244	+	0.931303i	$0.618673\pi$
$954$		0			0
$955$	5.11505e11	−	7.17954e10i	0.614945	−	0.0863144i
$956$		−	2.88945e11i		−	0.345926i
$957$		0			0
$958$			7.39789e11i			0.878306i
$959$			5.57351e11i			0.658953i
$960$		0			0
$961$	5.31339e11			0.622986
$962$	7.76083e11			0.906166
$963$		0			0
$964$	−2.97752e11			−0.344784
$965$	2.11910e11	−	2.97439e10i	0.244367	−	0.0342996i
$966$		0			0
$967$			1.25476e12i			1.43501i	0.696555	+	0.717503i	$0.254715\pi$
$967$			1.25476e12i			1.43501i	−0.696555	+	0.717503i	$0.745285\pi$
$968$	−7.11200e11			−0.810010
$969$		0			0
$970$	−7.60742e11	+	1.06779e11i	−0.859311	+	0.120614i
$971$		−	9.39290e11i		−	1.05663i	−0.849049	−	0.528315i	$-0.822824\pi$
$971$		−	9.39290e11i		−	1.05663i	0.849049	−	0.528315i	$-0.177176\pi$
$972$		0			0
$973$			5.98996e11i			0.668302i
$974$		−	2.62198e10i		−	0.0291336i
$975$		0			0
$976$	−1.73016e11			−0.190672
$977$	−3.92709e11			−0.431015			−0.215508	−	0.976502i	$-0.569141\pi$
$977$	−3.92709e11			−0.431015			−0.215508	+	0.976502i	$0.569141\pi$
$978$		0			0
$979$	−2.30409e11			−0.250824
$980$	−1.55951e10	−	1.11107e11i	−0.0169077	−	0.120458i
$981$		0			0
$982$		−	5.79280e11i		−	0.622935i
$983$	−1.01412e12			−1.08611			−0.543056	−	0.839696i	$-0.682733\pi$
$983$	−1.01412e12			−1.08611			−0.543056	+	0.839696i	$0.682733\pi$
$984$		0			0
$985$	−1.01261e11	−	7.21430e11i	−0.107571	−	0.766389i
$986$			7.21468e11i			0.763325i
$987$		0			0
$988$		−	5.67777e11i		−	0.595867i
$989$		−	3.70734e11i		−	0.387505i
$990$		0			0
$991$	9.73017e11			1.00885			0.504424	−	0.863456i	$-0.331705\pi$
$991$	9.73017e11			1.00885			0.504424	+	0.863456i	$0.331705\pi$
$992$	−7.90489e11			−0.816299
$993$		0			0
$994$	−1.99615e10			−0.0204478
$995$	3.03253e10	+	2.16052e11i	0.0309394	+	0.220427i
$996$		0			0
$997$		−	3.28222e11i		−	0.332191i	−0.986110	−	0.166095i	$-0.946884\pi$
$997$		−	3.28222e11i		−	0.332191i	0.986110	−	0.166095i	$-0.0531160\pi$
$998$	−3.91071e11			−0.394215
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.9.d.a.44.12	yes	16
3.2	odd	2	inner	45.9.d.a.44.5	✓	16
5.2	odd	4		225.9.c.e.26.12		16
5.3	odd	4		225.9.c.e.26.5		16
5.4	even	2	inner	45.9.d.a.44.6	yes	16
15.2	even	4		225.9.c.e.26.6		16
15.8	even	4		225.9.c.e.26.11		16
15.14	odd	2	inner	45.9.d.a.44.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.9.d.a.44.5	✓	16	3.2	odd	2	inner
45.9.d.a.44.6	yes	16	5.4	even	2	inner
45.9.d.a.44.11	yes	16	15.14	odd	2	inner
45.9.d.a.44.12	yes	16	1.1	even	1	trivial
225.9.c.e.26.5		16	5.3	odd	4
225.9.c.e.26.6		16	15.2	even	4
225.9.c.e.26.11		16	15.8	even	4
225.9.c.e.26.12		16	5.2	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	45.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+13.0310 q^{2} -86.1932 q^{4} +(86.8741 + 618.933i) q^{5} -1918.88i q^{7} -4459.12 q^{8} +O(q^{10})\)	\(q+13.0310 q^{2} -86.1932 q^{4} +(86.8741 + 618.933i) q^{5} -1918.88i q^{7} -4459.12 q^{8} +(1132.06 + 8065.31i) q^{10} -7407.11i q^{11} -44920.9i q^{13} -25004.9i q^{14} -36041.3 q^{16} -122036. q^{17} -146641. q^{19} +(-7487.95 - 53347.8i) q^{20} -96522.1i q^{22} +345961. q^{23} +(-375531. + 107538. i) q^{25} -585364. i q^{26} +165395. i q^{28} -453681. i q^{29} -1.17653e6 q^{31} +671880. q^{32} -1.59025e6 q^{34} +(1.18766e6 - 166701. i) q^{35} +1.32581e6i q^{37} -1.91088e6 q^{38} +(-387382. - 2.75989e6i) q^{40} -1.74823e6i q^{41} -1.07161e6i q^{43} +638443. i q^{44} +4.50822e6 q^{46} -3.34039e6 q^{47} +2.08269e6 q^{49} +(-4.89354e6 + 1.40133e6i) q^{50} +3.87187e6i q^{52} +6.15049e6 q^{53} +(4.58451e6 - 643486. i) q^{55} +8.55652e6i q^{56} -5.91192e6i q^{58} +1.31715e7i q^{59} +4.80050e6 q^{61} -1.53314e7 q^{62} +1.79818e7 q^{64} +(2.78030e7 - 3.90246e6i) q^{65} +3.65129e7i q^{67} +1.05187e7 q^{68} +(1.54764e7 - 2.17228e6i) q^{70} -798301. i q^{71} -7.40621e6i q^{73} +1.72767e7i q^{74} +1.26395e7 q^{76} -1.42134e7 q^{77} -6.47230e7 q^{79} +(-3.13105e6 - 2.23071e7i) q^{80} -2.27811e7i q^{82} -2.15820e7 q^{83} +(-1.06018e7 - 7.55322e7i) q^{85} -1.39641e7i q^{86} +3.30292e7i q^{88} -3.11064e7i q^{89} -8.61978e7 q^{91} -2.98195e7 q^{92} -4.35286e7 q^{94} +(-1.27393e7 - 9.07611e7i) q^{95} +9.43227e7i q^{97} +2.71396e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 1572 q^{4}+O(q^{10}) \) 16 * q + 1572 * q^4	\( 16 q + 1572 q^{4} + 16280 q^{10} - 12844 q^{16} + 263600 q^{19} + 1124860 q^{25} - 4312984 q^{31} + 2439352 q^{34} + 10217140 q^{40} - 5376344 q^{46} - 7338968 q^{49} + 5658120 q^{55} + 26097968 q^{61} - 123290756 q^{64} + 27888840 q^{70} + 222695760 q^{76} - 262645864 q^{79} + 202172900 q^{85} + 350561736 q^{91} - 789068384 q^{94}+O(q^{100}) \) 16 * q + 1572 * q^4 + 16280 * q^10 - 12844 * q^16 + 263600 * q^19 + 1124860 * q^25 - 4312984 * q^31 + 2439352 * q^34 + 10217140 * q^40 - 5376344 * q^46 - 7338968 * q^49 + 5658120 * q^55 + 26097968 * q^61 - 123290756 * q^64 + 27888840 * q^70 + 222695760 * q^76 - 262645864 * q^79 + 202172900 * q^85 + 350561736 * q^91 - 789068384 * q^94

Introduction

L-functions

Modular forms

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Database

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