LMFDB - Embedded newform 252.9.z.d.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(73,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$102.659409735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 $ x^12 - 3x^11 + 148097x^10 + 46071824x^9 + 21578502553x^8 + 3561445462121x^7 + 576413321817541x^6 + 47217566733462528x^5 + 5214056955297543333x^4 + 358752845334081085965x^3 + 30962072851910211245661x^2 + 1221542968331193193318500*x + 45396580558961892385326096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{10}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.2
Root			$221.993 - 384.503i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.d.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-632.551 + 365.204i) q^{5} +(984.437 - 2189.91i) q^{7} +O(q^{10})$	$q+(-632.551 + 365.204i) q^{5} +(984.437 - 2189.91i) q^{7} +(-6353.95 + 11005.4i) q^{11} -21176.4i q^{13} +(82551.9 + 47661.3i) q^{17} +(-133336. + 76981.8i) q^{19} +(47111.5 + 81599.5i) q^{23} +(71435.0 - 123729. i) q^{25} -541664. q^{29} +(-185730. - 107231. i) q^{31} +(177055. + 1.74475e6i) q^{35} +(-370376. - 641510. i) q^{37} -782599. i q^{41} -221324. q^{43} +(-7.13230e6 + 4.11784e6i) q^{47} +(-3.82657e6 - 4.31165e6i) q^{49} +(-659083. + 1.14157e6i) q^{53} -9.28194e6i q^{55} +(7.52865e6 + 4.34667e6i) q^{59} +(1.31192e7 - 7.57439e6i) q^{61} +(7.73369e6 + 1.33951e7i) q^{65} +(1.99100e7 - 3.44851e7i) q^{67} +9.34713e6 q^{71} +(2.94520e7 + 1.70041e7i) q^{73} +(1.78456e7 + 2.47486e7i) q^{77} +(2.26450e7 + 3.92223e7i) q^{79} -6.58893e7i q^{83} -6.96244e7 q^{85} +(1.09902e7 - 6.34517e6i) q^{89} +(-4.63742e7 - 2.08468e7i) q^{91} +(5.62280e7 - 9.73898e7i) q^{95} +6.15780e6i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) $ 12 * q - 285 * q^5 + 198 * q^7	$ 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) $ 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−632.551	+	365.204i	−1.01208	+	0.584326i	−0.911801	−	0.410633i	$-0.865308\pi$
$5$	−632.551	+	365.204i	−1.01208	+	0.584326i	−0.100282	+	0.994959i	$0.531974\pi$
$6$		0			0
$7$	984.437	−	2189.91i	0.410011	−	0.912080i
$7$	984.437	−	2189.91i	0.410011	−	0.912080i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−6353.95	+	11005.4i	−0.433983	+	0.751681i	−0.997212	−	0.0746198i	$-0.976226\pi$
$11$	−6353.95	+	11005.4i	−0.433983	+	0.751681i	0.563229	+	0.826301i	$0.309559\pi$
$12$		0			0
$13$		−	21176.4i		−	0.741444i	−0.928744	−	0.370722i	$-0.879110\pi$
$13$		−	21176.4i		−	0.741444i	0.928744	−	0.370722i	$-0.120890\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	82551.9	+	47661.3i	0.988397	+	0.570651i	0.904795	−	0.425848i	$-0.140024\pi$
$17$	82551.9	+	47661.3i	0.988397	+	0.570651i	0.0836020	+	0.996499i	$0.473358\pi$
$18$		0			0
$19$	−133336.	+	76981.8i	−1.02314	+	0.590709i	−0.915011	−	0.403428i	$-0.867818\pi$
$19$	−133336.	+	76981.8i	−1.02314	+	0.590709i	−0.108126	+	0.994137i	$0.534485\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	47111.5	+	81599.5i	0.168351	+	0.291593i	0.937840	−	0.347067i	$-0.112822\pi$
$23$	47111.5	+	81599.5i	0.168351	+	0.291593i	−0.769489	+	0.638660i	$0.779489\pi$
$24$		0			0
$25$	71435.0	−	123729.i	0.182874	−	0.316746i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−541664.			−0.765840			−0.382920	−	0.923782i	$-0.625081\pi$
$29$	−541664.			−0.765840			−0.382920	+	0.923782i	$0.625081\pi$
$30$		0			0
$31$	−185730.	−	107231.i	−0.201110	−	0.116111i	0.396063	−	0.918223i	$-0.370376\pi$
$31$	−185730.	−	107231.i	−0.201110	−	0.116111i	−0.597173	+	0.802112i	$0.703710\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	177055.	+	1.74475e6i	0.117987	+	1.16268i
$36$		0			0
$37$	−370376.	−	641510.i	−0.197622	−	0.342292i	0.750135	−	0.661285i	$-0.229989\pi$
$37$	−370376.	−	641510.i	−0.197622	−	0.342292i	−0.947757	+	0.318993i	$0.896655\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	782599.i		−	0.276952i	−0.990366	−	0.138476i	$-0.955780\pi$
$41$		−	782599.i		−	0.276952i	0.990366	−	0.138476i	$-0.0442203\pi$
$42$		0			0
$43$	−221324.			−0.0647373			−0.0323687	−	0.999476i	$-0.510305\pi$
$43$	−221324.			−0.0647373			−0.0323687	+	0.999476i	$0.510305\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.13230e6	+	4.11784e6i	−1.46163	+	0.843874i	−0.999087	−	0.0427209i	$-0.986397\pi$
$47$	−7.13230e6	+	4.11784e6i	−1.46163	+	0.843874i	−0.462546	+	0.886595i	$0.653064\pi$
$48$		0			0
$49$	−3.82657e6	−	4.31165e6i	−0.663782	−	0.747926i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−659083.	+	1.14157e6i	−0.0835289	+	0.144676i	−0.904763	−	0.425915i	$-0.859952\pi$
$53$	−659083.	+	1.14157e6i	−0.0835289	+	0.144676i	0.821235	+	0.570591i	$0.193286\pi$
$54$		0			0
$55$		−	9.28194e6i		−	1.01435i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.52865e6	+	4.34667e6i	0.621311	+	0.358714i	0.777379	−	0.629032i	$-0.216549\pi$
$59$	7.52865e6	+	4.34667e6i	0.621311	+	0.358714i	−0.156068	+	0.987746i	$0.549882\pi$
$60$		0			0
$61$	1.31192e7	−	7.57439e6i	0.947521	−	0.547052i	0.0552112	−	0.998475i	$-0.482417\pi$
$61$	1.31192e7	−	7.57439e6i	0.947521	−	0.547052i	0.892310	+	0.451423i	$0.149083\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.73369e6	+	1.33951e7i	0.433245	+	0.750402i
$66$		0			0
$67$	1.99100e7	−	3.44851e7i	0.988033	−	1.71132i	0.360436	−	0.932784i	$-0.382628\pi$
$67$	1.99100e7	−	3.44851e7i	0.988033	−	1.71132i	0.627596	−	0.778539i	$-0.284039\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.34713e6			0.367828			0.183914	−	0.982942i	$-0.441123\pi$
$71$	9.34713e6			0.367828			0.183914	+	0.982942i	$0.441123\pi$
$72$		0			0
$73$	2.94520e7	+	1.70041e7i	1.03711	+	0.598774i	0.919012	−	0.394229i	$-0.128988\pi$
$73$	2.94520e7	+	1.70041e7i	1.03711	+	0.598774i	0.118094	+	0.993002i	$0.462321\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.78456e7	+	2.47486e7i	0.507656	+	0.704025i
$78$		0			0
$79$	2.26450e7	+	3.92223e7i	0.581385	+	1.00699i	0.995316	+	0.0966799i	$0.0308223\pi$
$79$	2.26450e7	+	3.92223e7i	0.581385	+	1.00699i	−0.413931	+	0.910308i	$0.635844\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	6.58893e7i		−	1.38836i	−0.719801	−	0.694180i	$-0.755767\pi$
$83$		−	6.58893e7i		−	1.38836i	0.719801	−	0.694180i	$-0.244233\pi$
$84$		0			0
$85$	−6.96244e7			−1.33378
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.09902e7	−	6.34517e6i	0.175164	−	0.101131i	−0.409855	−	0.912151i	$-0.634421\pi$
$89$	1.09902e7	−	6.34517e6i	0.175164	−	0.101131i	0.585018	+	0.811020i	$0.301087\pi$
$90$		0			0
$91$	−4.63742e7	−	2.08468e7i	−0.676256	−	0.304000i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.62280e7	−	9.73898e7i	0.690333	−	1.19569i
$96$		0			0
$97$			6.15780e6i			0.0695566i	0.999395	+	0.0347783i	$0.0110725\pi$
$97$			6.15780e6i			0.0695566i	−0.999395	+	0.0347783i	$0.988927\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.15329e8	−	6.65855e7i	−1.10829	−	0.639874i	−0.169907	−	0.985460i	$-0.554347\pi$
$101$	−1.15329e8	−	6.65855e7i	−1.10829	−	0.639874i	−0.938387	+	0.345587i	$0.887680\pi$
$102$		0			0
$103$	4.81925e7	−	2.78240e7i	0.428184	−	0.247212i	−0.270389	−	0.962751i	$-0.587152\pi$
$103$	4.81925e7	−	2.78240e7i	0.428184	−	0.247212i	0.698573	+	0.715539i	$0.253819\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.23667e6	−	1.25343e7i	−0.0552082	−	0.0956234i	0.837101	−	0.547049i	$-0.184249\pi$
$107$	−7.23667e6	−	1.25343e7i	−0.0552082	−	0.0956234i	−0.892309	+	0.451426i	$0.850916\pi$
$108$		0			0
$109$	−9.01793e7	+	1.56195e8i	−0.638853	+	1.10653i	0.346832	+	0.937927i	$0.387257\pi$
$109$	−9.01793e7	+	1.56195e8i	−0.638853	+	1.10653i	−0.985685	+	0.168598i	$0.946076\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.21791e7			0.136028			0.0680142	−	0.997684i	$-0.478334\pi$
$113$	2.21791e7			0.136028			0.0680142	+	0.997684i	$0.478334\pi$
$114$		0			0
$115$	−5.96009e7	−	3.44106e7i	−0.340770	−	0.196744i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.85641e8	−	1.33861e8i	0.925733	−	0.667524i
$120$		0			0
$121$	2.64341e7	+	4.57852e7i	0.123317	+	0.213591i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	1.80962e8i		−	0.741221i
$126$		0			0
$127$	1.77711e8			0.683123			0.341561	−	0.939859i	$-0.389044\pi$
$127$	1.77711e8			0.683123			0.341561	+	0.939859i	$0.389044\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.83164e8	−	2.78955e8i	1.64062	−	0.947215i	0.660012	−	0.751255i	$-0.270551\pi$
$131$	4.83164e8	−	2.78955e8i	1.64062	−	0.947215i	0.980612	−	0.195960i	$-0.0627823\pi$
$132$		0			0
$133$	3.73216e7	+	3.67778e8i	0.119276	+	1.17538i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.96914e8	−	3.41064e8i	0.558977	−	0.968176i	−0.438606	−	0.898680i	$-0.644528\pi$
$137$	1.96914e8	−	3.41064e8i	0.558977	−	0.968176i	0.997582	−	0.0694962i	$-0.0221392\pi$
$138$		0			0
$139$		−	4.85677e8i		−	1.30103i	−0.759492	−	0.650516i	$-0.774553\pi$
$139$		−	4.85677e8i		−	1.30103i	0.759492	−	0.650516i	$-0.225447\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.33054e8	+	1.34554e8i	0.557329	+	0.321774i
$144$		0			0
$145$	3.42630e8	−	1.97818e8i	0.775093	−	0.447500i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.60563e8	−	2.78103e8i	−0.325762	−	0.564236i	0.655905	−	0.754844i	$-0.272287\pi$
$149$	−1.60563e8	−	2.78103e8i	−0.325762	−	0.564236i	−0.981666	+	0.190608i	$0.938954\pi$
$150$		0			0
$151$	4.12702e8	−	7.14822e8i	0.793833	−	1.37496i	−0.129744	−	0.991547i	$-0.541416\pi$
$151$	4.12702e8	−	7.14822e8i	0.793833	−	1.37496i	0.923577	−	0.383412i	$-0.125251\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.56645e8			0.271387
$156$		0			0
$157$	9.15549e8	+	5.28592e8i	1.50689	+	0.870006i	0.999968	+	0.00801653i	$0.00255177\pi$
$157$	9.15549e8	+	5.28592e8i	1.50689	+	0.870006i	0.506926	+	0.861989i	$0.330782\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.25074e8	−	2.28402e7i	0.334982	−	0.0339935i
$162$		0			0
$163$	−5.67831e8	−	9.83512e8i	−0.804394	−	1.39325i	−0.916699	−	0.399577i	$-0.869157\pi$
$163$	−5.67831e8	−	9.83512e8i	−0.804394	−	1.39325i	0.112306	−	0.993674i	$-0.464176\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			1.00076e9i			1.28666i	0.765591	+	0.643328i	$0.222447\pi$
$167$			1.00076e9i			1.28666i	−0.765591	+	0.643328i	$0.777553\pi$
$168$		0			0
$169$	3.67292e8			0.450261
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.46649e8	−	3.15608e8i	0.610273	−	0.352341i	−0.162799	−	0.986659i	$-0.552052\pi$
$173$	5.46649e8	−	3.15608e8i	0.610273	−	0.352341i	0.773072	+	0.634318i	$0.218719\pi$
$174$		0			0
$175$	−2.00632e8	−	2.78239e8i	−0.213918	−	0.296665i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.77342e8	−	9.99986e8i	0.562369	−	0.974052i	−0.434920	−	0.900469i	$-0.643223\pi$
$179$	5.77342e8	−	9.99986e8i	0.562369	−	0.974052i	0.997289	−	0.0735826i	$-0.0234433\pi$
$180$		0			0
$181$		−	1.42212e9i		−	1.32502i	−0.749052	−	0.662511i	$-0.769491\pi$
$181$		−	1.42212e9i		−	1.32502i	0.749052	−	0.662511i	$-0.230509\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.68564e8	+	2.70525e8i	0.400020	+	0.230952i
$186$		0			0
$187$	−1.04906e9	+	6.05676e8i	−0.857895	+	0.495306i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.05844e8	−	5.29737e8i	−0.229809	−	0.398040i	0.727943	−	0.685638i	$-0.240477\pi$
$191$	−3.05844e8	−	5.29737e8i	−0.229809	−	0.398040i	−0.957751	+	0.287598i	$0.907143\pi$
$192$		0			0
$193$	9.49542e8	−	1.64465e9i	0.684360	−	1.18535i	−0.289277	−	0.957245i	$-0.593415\pi$
$193$	9.49542e8	−	1.64465e9i	0.684360	−	1.18535i	0.973637	−	0.228101i	$-0.0732518\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.00843e9			−0.669544			−0.334772	−	0.942299i	$-0.608659\pi$
$197$	−1.00843e9			−0.669544			−0.334772	+	0.942299i	$0.608659\pi$
$198$		0			0
$199$	2.76255e8	+	1.59496e8i	0.176156	+	0.101704i	0.585485	−	0.810683i	$-0.300904\pi$
$199$	2.76255e8	+	1.59496e8i	0.176156	+	0.101704i	−0.409329	+	0.912387i	$0.634237\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.33234e8	+	1.18619e9i	−0.314003	+	0.698507i
$204$		0			0
$205$	2.85808e8	+	4.95034e8i	0.161830	+	0.280298i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	1.95655e9i		−	1.02543i
$210$		0			0
$211$	−1.39969e9			−0.706160			−0.353080	−	0.935593i	$-0.614866\pi$
$211$	−1.39969e9			−0.706160			−0.353080	+	0.935593i	$0.614866\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.39999e8	−	8.08283e7i	0.0655195	−	0.0378277i
$216$		0			0
$217$	−4.17665e8	+	3.01168e8i	−0.188360	+	0.135822i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.00929e9	−	1.74815e9i	0.423106	−	0.732840i
$222$		0			0
$223$			3.09118e9i			1.24999i	0.780630	+	0.624993i	$0.214898\pi$
$223$			3.09118e9i			1.24999i	−0.780630	+	0.624993i	$0.785102\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.27805e9	+	1.89258e9i	1.23456	+	0.712774i	0.967977	−	0.251038i	$-0.0807719\pi$
$227$	3.27805e9	+	1.89258e9i	1.23456	+	0.712774i	0.266583	+	0.963812i	$0.414105\pi$
$228$		0			0
$229$	−2.74391e9	+	1.58420e9i	−0.997763	+	0.576059i	−0.907586	−	0.419867i	$-0.862077\pi$
$229$	−2.74391e9	+	1.58420e9i	−0.997763	+	0.576059i	−0.0901773	+	0.995926i	$0.528743\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.76314e9	−	4.78590e9i	−0.937518	−	1.62383i	−0.770081	−	0.637946i	$-0.779784\pi$
$233$	−2.76314e9	−	4.78590e9i	−0.937518	−	1.62383i	−0.167437	−	0.985883i	$-0.553549\pi$
$234$		0			0
$235$	3.00770e9	−	5.20949e9i	0.986195	−	1.70814i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.93530e9			1.20611			0.603054	−	0.797701i	$-0.293951\pi$
$239$	3.93530e9			1.20611			0.603054	+	0.797701i	$0.293951\pi$
$240$		0			0
$241$	5.76301e9	+	3.32727e9i	1.70837	+	0.986326i	0.936586	+	0.350437i	$0.113967\pi$
$241$	5.76301e9	+	3.32727e9i	1.70837	+	0.986326i	0.771780	+	0.635889i	$0.219367\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.99513e9	+	1.32986e9i	1.10883	+	0.369098i
$246$		0			0
$247$	1.63019e9	+	2.82358e9i	0.437977	+	0.758599i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	4.25680e9i		−	1.07248i	−0.844066	−	0.536239i	$-0.819845\pi$
$251$		−	4.25680e9i		−	1.07248i	0.844066	−	0.536239i	$-0.180155\pi$
$252$		0			0
$253$	−1.19738e9			−0.292246
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.63398e9	−	1.52073e9i	0.603782	−	0.348593i	−0.166746	−	0.986000i	$-0.553326\pi$
$257$	2.63398e9	−	1.52073e9i	0.603782	−	0.348593i	0.770528	+	0.637406i	$0.219993\pi$
$258$		0			0
$259$	−1.76946e9	+	1.79562e8i	−0.393225	+	0.0399039i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.20815e9	+	7.28873e9i	−0.879566	+	1.52345i	−0.0277486	+	0.999615i	$0.508834\pi$
$263$	−4.20815e9	+	7.28873e9i	−0.879566	+	1.52345i	−0.851818	+	0.523838i	$0.824500\pi$
$264$		0			0
$265$		−	9.62798e8i		−	0.195232i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.40038e9	−	3.69526e9i	−1.22235	−	0.705726i	−0.256934	−	0.966429i	$-0.582712\pi$
$269$	−6.40038e9	−	3.69526e9i	−1.22235	−	0.705726i	−0.965419	+	0.260703i	$0.916046\pi$
$270$		0			0
$271$	−3.72934e9	+	2.15314e9i	−0.691441	+	0.399204i	−0.804152	−	0.594424i	$-0.797380\pi$
$271$	−3.72934e9	+	2.15314e9i	−0.691441	+	0.399204i	0.112711	+	0.993628i	$0.464047\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.07789e8	+	1.57234e9i	0.158728	+	0.274925i
$276$		0			0
$277$	−2.54312e7	+	4.40481e7i	−0.00431964	+	0.00748183i	−0.868177	−	0.496254i	$-0.834708\pi$
$277$	−2.54312e7	+	4.40481e7i	−0.00431964	+	0.00748183i	0.863858	+	0.503736i	$0.168042\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.03421e10			−1.65877			−0.829383	−	0.558680i	$-0.811308\pi$
$281$	−1.03421e10			−1.65877			−0.829383	+	0.558680i	$0.811308\pi$
$282$		0			0
$283$	−2.55984e9	−	1.47792e9i	−0.399086	−	0.230412i	0.287003	−	0.957930i	$-0.407341\pi$
$283$	−2.55984e9	−	1.47792e9i	−0.399086	−	0.230412i	−0.686090	+	0.727517i	$0.740674\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.71382e9	−	7.70419e8i	−0.252602	−	0.113553i
$288$		0			0
$289$	1.05533e9	+	1.82788e9i	0.151285	+	0.262034i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			4.22563e9i			0.573351i	0.958028	+	0.286676i	$0.0925502\pi$
$293$			4.22563e9i			0.573351i	−0.958028	+	0.286676i	$0.907450\pi$
$294$		0			0
$295$	−6.34968e9			−0.838424
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.72798e9	−	9.97651e8i	0.216199	−	0.124823i
$300$		0			0
$301$	−2.17880e8	+	4.84679e8i	−0.0265430	+	0.0590456i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.53239e9	+	9.58238e9i	−0.639313	+	1.10732i
$306$		0			0
$307$			2.96070e9i			0.333304i	0.986016	+	0.166652i	$0.0532956\pi$
$307$			2.96070e9i			0.333304i	−0.986016	+	0.166652i	$0.946704\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.74956e9	+	4.47421e9i	0.828391	+	0.478272i	0.853302	−	0.521418i	$-0.174597\pi$
$311$	7.74956e9	+	4.47421e9i	0.828391	+	0.478272i	−0.0249101	+	0.999690i	$0.507930\pi$
$312$		0			0
$313$	−5.04664e9	+	2.91368e9i	−0.525806	+	0.303574i	−0.739307	−	0.673369i	$-0.764847\pi$
$313$	−5.04664e9	+	2.91368e9i	−0.525806	+	0.303574i	0.213501	+	0.976943i	$0.431513\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.50614e9	−	4.34076e9i	−0.248181	−	0.429861i	0.714840	−	0.699288i	$-0.246499\pi$
$317$	−2.50614e9	−	4.34076e9i	−0.248181	−	0.429861i	−0.963021	+	0.269426i	$0.913166\pi$
$318$		0			0
$319$	3.44171e9	−	5.96121e9i	0.332362	−	0.575667i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.46762e10			−1.34835
$324$		0			0
$325$	−2.62013e9	−	1.51273e9i	−0.234850	−	0.135590i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.99637e9	+	1.96728e10i	0.170395	+	1.67912i
$330$		0			0
$331$	4.78357e9	+	8.28539e9i	0.398511	+	0.690242i	0.993542	−	0.113461i	$-0.0361937\pi$
$331$	4.78357e9	+	8.28539e9i	0.398511	+	0.690242i	−0.595031	+	0.803703i	$0.702860\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			2.90848e10i			2.30933i
$336$		0			0
$337$	2.32884e9			0.180560			0.0902798	−	0.995916i	$-0.471224\pi$
$337$	2.32884e9			0.180560			0.0902798	+	0.995916i	$0.471224\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.36023e9	−	1.36268e9i	0.174557	−	0.100781i
$342$		0			0
$343$	−1.32091e10	+	4.13528e9i	−0.954327	+	0.298764i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.04233e10	+	1.80536e10i	−0.718928	+	1.24522i	0.242497	+	0.970152i	$0.422034\pi$
$347$	−1.04233e10	+	1.80536e10i	−0.718928	+	1.24522i	−0.961425	+	0.275068i	$0.911300\pi$
$348$		0			0
$349$		−	2.91490e10i		−	1.96482i	−0.186745	−	0.982409i	$-0.559794\pi$
$349$		−	2.91490e10i		−	1.96482i	0.186745	−	0.982409i	$-0.440206\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.78829e8	−	5.65127e8i	−0.0630388	−	0.0363955i	0.468149	−	0.883649i	$-0.344921\pi$
$353$	−9.78829e8	−	5.65127e8i	−0.0630388	−	0.0363955i	−0.531188	+	0.847254i	$0.678254\pi$
$354$		0			0
$355$	−5.91254e9	+	3.41361e9i	−0.372272	+	0.214932i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.49405e9	−	9.51597e9i	−0.330761	−	0.572896i	0.651900	−	0.758305i	$-0.273972\pi$
$359$	−5.49405e9	−	9.51597e9i	−0.330761	−	0.572896i	−0.982661	+	0.185409i	$0.940639\pi$
$360$		0			0
$361$	3.36060e9	−	5.82073e9i	0.197874	−	0.342727i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.48399e10			−1.39952
$366$		0			0
$367$	−2.47539e9	−	1.42917e9i	−0.136452	−	0.0787805i	0.430220	−	0.902724i	$-0.358436\pi$
$367$	−2.47539e9	−	1.42917e9i	−0.136452	−	0.0787805i	−0.566672	+	0.823944i	$0.691769\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.85109e9	+	2.56713e9i	0.0977086	+	0.135504i
$372$		0			0
$373$	8.91785e9	+	1.54462e10i	0.460707	+	0.797968i	0.998996	−	0.0447919i	$-0.0142625\pi$
$373$	8.91785e9	+	1.54462e10i	0.460707	+	0.797968i	−0.538289	+	0.842760i	$0.680929\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			1.14705e10i			0.567827i
$378$		0			0
$379$	3.25934e10			1.57969			0.789847	−	0.613303i	$-0.210160\pi$
$379$	3.25934e10			1.57969			0.789847	+	0.613303i	$0.210160\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.90349e10	−	1.09898e10i	0.884619	−	0.510735i	0.0124407	−	0.999923i	$-0.496040\pi$
$383$	1.90349e10	−	1.09898e10i	0.884619	−	0.510735i	0.872179	+	0.489187i	$0.162707\pi$
$384$		0			0
$385$	−2.03266e10	−	9.13749e9i	−0.925170	−	0.415895i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.09555e10	−	1.89755e10i	0.478448	−	0.828695i	−0.521247	−	0.853406i	$-0.674533\pi$
$389$	1.09555e10	−	1.89755e10i	0.478448	−	0.828695i	0.999695	+	0.0247103i	$0.00786634\pi$
$390$		0			0
$391$			8.98159e9i			0.384279i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.86482e10	−	1.65401e10i	−1.17682	−	0.679437i
$396$		0			0
$397$	−4.10594e10	+	2.37057e10i	−1.65292	+	0.954312i	−0.677052	+	0.735936i	$0.736743\pi$
$397$	−4.10594e10	+	2.37057e10i	−1.65292	+	0.954312i	−0.975865	+	0.218376i	$0.929924\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.47336e8	−	1.12122e9i	−0.0250353	−	0.0433623i	0.853236	−	0.521524i	$-0.174636\pi$
$401$	−6.47336e8	−	1.12122e9i	−0.0250353	−	0.0433623i	−0.878272	+	0.478162i	$0.841303\pi$
$402$		0			0
$403$	−2.27076e9	+	3.93308e9i	−0.0860898	+	0.149112i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	9.41340e9			0.343059
$408$		0			0
$409$	1.05517e10	+	6.09204e9i	0.377077	+	0.217705i	0.676546	−	0.736401i	$-0.263476\pi$
$409$	1.05517e10	+	6.09204e9i	0.377077	+	0.217705i	−0.299469	+	0.954106i	$0.596809\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.69303e10	−	1.22080e10i	0.581921	−	0.419609i
$414$		0			0
$415$	2.40630e10	+	4.16783e10i	0.811255	+	1.40514i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	2.83249e9i		−	0.0918992i	−0.998944	−	0.0459496i	$-0.985369\pi$
$419$		−	2.83249e9i		−	0.0918992i	0.998944	−	0.0459496i	$-0.0146314\pi$
$420$		0			0
$421$	1.47344e10			0.469033			0.234517	−	0.972112i	$-0.424649\pi$
$421$	1.47344e10			0.469033			0.234517	+	0.972112i	$0.424649\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.17942e10	−	6.80938e9i	0.361503	−	0.208714i
$426$		0			0
$427$	−3.67214e9	−	3.61864e10i	−0.110461	−	1.08851i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.99404e10	+	3.45377e10i	−0.577862	+	1.00089i	0.417862	+	0.908510i	$0.362780\pi$
$431$	−1.99404e10	+	3.45377e10i	−0.577862	+	1.00089i	−0.995724	+	0.0923761i	$0.970554\pi$
$432$		0			0
$433$			3.77901e10i			1.07505i	0.843249	+	0.537523i	$0.180640\pi$
$433$			3.77901e10i			1.07505i	−0.843249	+	0.537523i	$0.819360\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.25634e10	−	7.25345e9i	−0.344493	−	0.198893i
$438$		0			0
$439$	7.02545e9	−	4.05614e9i	0.189154	−	0.109208i	−0.402432	−	0.915450i	$-0.631835\pi$
$439$	7.02545e9	−	4.05614e9i	0.189154	−	0.109208i	0.591587	+	0.806242i	$0.298502\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.85877e10	−	4.95154e10i	−0.742274	−	1.28566i	−0.951457	−	0.307780i	$-0.900414\pi$
$443$	−2.85877e10	−	4.95154e10i	−0.742274	−	1.28566i	0.209183	−	0.977876i	$-0.432919\pi$
$444$		0			0
$445$	−4.63456e9	+	8.02729e9i	−0.118187	+	0.204705i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.27811e10			1.54470			0.772349	−	0.635199i	$-0.219082\pi$
$449$	6.27811e10			1.54470			0.772349	+	0.635199i	$0.219082\pi$
$450$		0			0
$451$	8.61279e9	+	4.97259e9i	0.208179	+	0.120192i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.69474e10	−	3.74937e9i	0.862062	−	0.0874809i
$456$		0			0
$457$	−8.34859e9	−	1.44602e10i	−0.191403	−	0.331519i	0.754313	−	0.656515i	$-0.227970\pi$
$457$	−8.34859e9	−	1.44602e10i	−0.191403	−	0.331519i	−0.945715	+	0.324996i	$0.894637\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	1.39906e10i		−	0.309766i	−0.987933	−	0.154883i	$-0.950500\pi$
$461$		−	1.39906e10i		−	0.309766i	0.987933	−	0.154883i	$-0.0495001\pi$
$462$		0			0
$463$	−2.56476e10			−0.558114			−0.279057	−	0.960274i	$-0.590022\pi$
$463$	−2.56476e10			−0.558114			−0.279057	+	0.960274i	$0.590022\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.36726e10	−	1.94409e10i	0.707960	−	0.408741i	−0.102345	−	0.994749i	$-0.532635\pi$
$467$	3.36726e10	−	1.94409e10i	0.707960	−	0.408741i	0.810305	+	0.586008i	$0.199301\pi$
$468$		0			0
$469$	−5.59189e10	−	7.75493e10i	−1.15576	−	1.60283i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.40628e9	−	2.43575e9i	0.0280949	−	0.0486618i
$474$		0			0
$475$			2.19968e10i			0.432100i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.40797e9	−	3.69965e9i	−0.121725	−	0.0702778i	0.437901	−	0.899023i	$-0.355722\pi$
$479$	−6.40797e9	−	3.69965e9i	−0.121725	−	0.0702778i	−0.559626	+	0.828745i	$0.689055\pi$
$480$		0			0
$481$	−1.35849e10	+	7.84322e9i	−0.253790	+	0.146526i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.24885e9	−	3.89512e9i	−0.0406437	−	0.0703970i
$486$		0			0
$487$	−1.11183e10	+	1.92575e10i	−0.197662	+	0.342361i	−0.947770	−	0.318954i	$-0.896668\pi$
$487$	−1.11183e10	+	1.92575e10i	−0.197662	+	0.342361i	0.750108	+	0.661316i	$0.230002\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.62576e10			−0.623839			−0.311920	−	0.950109i	$-0.600972\pi$
$491$	−3.62576e10			−0.623839			−0.311920	+	0.950109i	$0.600972\pi$
$492$		0			0
$493$	−4.47154e10	−	2.58164e10i	−0.756953	−	0.437027i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.20166e9	−	2.04693e10i	0.150814	−	0.335489i
$498$		0			0
$499$	3.67859e10	+	6.37151e10i	0.593307	+	1.02764i	0.993783	+	0.111331i	$0.0355114\pi$
$499$	3.67859e10	+	6.37151e10i	0.593307	+	1.02764i	−0.400476	+	0.916307i	$0.631155\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			5.49729e10i			0.858770i	0.903122	+	0.429385i	$0.141270\pi$
$503$			5.49729e10i			0.858770i	−0.903122	+	0.429385i	$0.858730\pi$
$504$		0			0
$505$	9.72691e10			1.49558
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.64437e10	−	3.25878e10i	0.840900	−	0.485494i	−0.0166697	−	0.999861i	$-0.505306\pi$
$509$	5.64437e10	−	3.25878e10i	0.840900	−	0.485494i	0.857570	+	0.514367i	$0.171973\pi$
$510$		0			0
$511$	6.62311e10	−	4.77576e10i	0.971355	−	0.700421i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.03228e10	+	3.52002e10i	−0.288905	+	0.500398i
$516$		0			0
$517$		−	1.04658e11i		−	1.46491i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.65862e9	−	3.84435e9i	−0.0903718	−	0.0521762i	0.454133	−	0.890934i	$-0.349949\pi$
$521$	−6.65862e9	−	3.84435e9i	−0.0903718	−	0.0521762i	−0.544505	+	0.838758i	$0.683282\pi$
$522$		0			0
$523$	1.07896e11	−	6.22937e10i	1.44211	−	0.832602i	0.444119	−	0.895968i	$-0.353517\pi$
$523$	1.07896e11	−	6.22937e10i	1.44211	−	0.832602i	0.997990	+	0.0633652i	$0.0201833\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.02215e10	−	1.77042e10i	−0.132518	−	0.229528i
$528$		0			0
$529$	3.47165e10	−	6.01307e10i	0.443316	−	0.767846i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.65726e10			−0.205344
$534$		0			0
$535$	9.15513e9	+	5.28572e9i	0.111750	+	0.0645191i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.17651e10	−	1.47168e10i	0.850272	−	0.174365i
$540$		0			0
$541$	−4.97811e10	−	8.62233e10i	−0.581132	−	1.00655i	−0.995346	−	0.0963708i	$-0.969277\pi$
$541$	−4.97811e10	−	8.62233e10i	−0.581132	−	1.00655i	0.414213	−	0.910180i	$-0.364057\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	1.31735e11i		−	1.49319i
$546$		0			0
$547$	−2.34938e10			−0.262424			−0.131212	−	0.991354i	$-0.541887\pi$
$547$	−2.34938e10			−0.262424			−0.131212	+	0.991354i	$0.541887\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.22235e10	−	4.16982e10i	0.783559	−	0.452388i
$552$		0			0
$553$	1.08186e11	−	1.09785e10i	1.15683	−	0.117393i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.24108e10	+	2.14962e10i	−0.128938	+	0.223327i	−0.923265	−	0.384163i	$-0.874490\pi$
$557$	−1.24108e10	+	2.14962e10i	−0.128938	+	0.223327i	0.794328	+	0.607490i	$0.207823\pi$
$558$		0			0
$559$			4.68684e9i			0.0479991i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.47632e11	+	8.52355e10i	1.46942	+	0.848373i	0.999412	−	0.0342868i	$-0.0109160\pi$
$563$	1.47632e11	+	8.52355e10i	1.46942	+	0.848373i	0.470013	+	0.882660i	$0.344249\pi$
$564$		0			0
$565$	−1.40294e10	+	8.09988e9i	−0.137672	+	0.0794849i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.03247e10	+	3.52033e10i	0.193898	+	0.335842i	0.946539	−	0.322590i	$-0.104553\pi$
$569$	2.03247e10	+	3.52033e10i	0.193898	+	0.335842i	−0.752640	+	0.658432i	$0.771220\pi$
$570$		0			0
$571$	4.24414e9	−	7.35107e9i	0.0399250	−	0.0691522i	−0.845372	−	0.534177i	$-0.820621\pi$
$571$	4.24414e9	−	7.35107e9i	0.0399250	−	0.0691522i	0.885297	+	0.465025i	$0.153955\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.34616e10			0.123148
$576$		0			0
$577$	−5.94782e10	−	3.43397e10i	−0.536604	−	0.309809i	0.207097	−	0.978320i	$-0.433598\pi$
$577$	−5.94782e10	−	3.43397e10i	−0.536604	−	0.309809i	−0.743702	+	0.668512i	$0.766932\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.44291e11	−	6.48638e10i	−1.26630	−	0.569243i
$582$		0			0
$583$	−8.37556e9	−	1.45069e10i	−0.0725003	−	0.125574i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			1.43383e11i			1.20766i	0.797114	+	0.603829i	$0.206359\pi$
$587$			1.43383e11i			1.20766i	−0.797114	+	0.603829i	$0.793641\pi$
$588$		0			0
$589$	3.30193e10			0.274351
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.30721e11	−	7.54720e10i	1.05713	−	0.610333i	0.132491	−	0.991184i	$-0.457702\pi$
$593$	1.30721e11	−	7.54720e10i	1.05713	−	0.610333i	0.924636	+	0.380851i	$0.124369\pi$
$594$		0			0
$595$	−6.85408e10	+	1.52471e11i	−0.546867	+	1.21652i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.29322e10	−	1.43643e11i	0.644193	−	1.11577i	−0.340294	−	0.940319i	$-0.610527\pi$
$599$	8.29322e10	−	1.43643e11i	0.644193	−	1.11577i	0.984487	−	0.175456i	$-0.0561399\pi$
$600$		0			0
$601$			7.04035e10i			0.539630i	0.962912	+	0.269815i	$0.0869625\pi$
$601$			7.04035e10i			0.539630i	−0.962912	+	0.269815i	$0.913037\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.34418e10	−	1.93076e10i	−0.249614	−	0.144115i
$606$		0			0
$607$	−5.15559e10	+	2.97658e10i	−0.379773	+	0.219262i	−0.677719	−	0.735321i	$-0.737032\pi$
$607$	−5.15559e10	+	2.97658e10i	−0.379773	+	0.219262i	0.297947	+	0.954583i	$0.403698\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.72009e10	+	1.51036e11i	0.625685	+	1.08372i
$612$		0			0
$613$	1.14654e11	−	1.98587e11i	0.811986	−	1.40640i	−0.0994852	−	0.995039i	$-0.531720\pi$
$613$	1.14654e11	−	1.98587e11i	0.811986	−	1.40640i	0.911472	−	0.411363i	$-0.134947\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.93904e11			−1.33797			−0.668986	−	0.743275i	$-0.733272\pi$
$617$	−1.93904e11			−1.33797			−0.668986	+	0.743275i	$0.733272\pi$
$618$		0			0
$619$	1.77090e10	+	1.02243e10i	0.120623	+	0.0696418i	0.559098	−	0.829102i	$-0.311148\pi$
$619$	1.77090e10	+	1.02243e10i	0.120623	+	0.0696418i	−0.438474	+	0.898744i	$0.644481\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.07621e9	−	3.03138e10i	−0.0204203	−	0.201228i
$624$		0			0
$625$	9.39923e10	+	1.62799e11i	0.615988	+	1.06692i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	7.06105e10i		−	0.451094i
$630$		0			0
$631$	−1.43159e11			−0.903030			−0.451515	−	0.892263i	$-0.649116\pi$
$631$	−1.43159e11			−0.903030			−0.451515	+	0.892263i	$0.649116\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.12411e11	+	6.49006e10i	−0.691377	+	0.399166i
$636$		0			0
$637$	−9.13050e10	+	8.10328e10i	−0.554545	+	0.492157i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.32450e11	−	2.29411e11i	0.784551	−	1.35888i	−0.144716	−	0.989473i	$-0.546227\pi$
$641$	1.32450e11	−	2.29411e11i	0.784551	−	1.35888i	0.929267	−	0.369409i	$-0.120440\pi$
$642$		0			0
$643$		−	1.18901e9i		−	0.00695572i	−0.999994	−	0.00347786i	$-0.998893\pi$
$643$		−	1.18901e9i		−	0.00695572i	0.999994	−	0.00347786i	$-0.00110704\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.24205e10	+	4.75855e10i	0.470347	+	0.271555i	0.716385	−	0.697705i	$-0.245796\pi$
$647$	8.24205e10	+	4.75855e10i	0.470347	+	0.271555i	−0.246038	+	0.969260i	$0.579129\pi$
$648$		0			0
$649$	−9.56733e10	+	5.52370e10i	−0.539277	+	0.311352i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.66756e11	−	2.88829e11i	−0.917124	−	1.58850i	−0.803762	−	0.594951i	$-0.797171\pi$
$653$	−1.66756e11	−	2.88829e11i	−0.917124	−	1.58850i	−0.113362	−	0.993554i	$-0.536162\pi$
$654$		0			0
$655$	−2.03751e11	+	3.52906e11i	−1.10696	+	1.91732i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.17025e11			−0.620493			−0.310246	−	0.950656i	$-0.600412\pi$
$659$	−1.17025e11			−0.620493			−0.310246	+	0.950656i	$0.600412\pi$
$660$		0			0
$661$	2.68769e10	+	1.55174e10i	0.140791	+	0.0812855i	0.568741	−	0.822517i	$-0.307431\pi$
$661$	2.68769e10	+	1.55174e10i	0.140791	+	0.0812855i	−0.427950	+	0.903802i	$0.640764\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.57922e11	−	2.19008e11i	−0.807523	−	1.11989i
$666$		0			0
$667$	−2.55186e10	−	4.41995e10i	−0.128930	−	0.223313i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			1.92509e11i			0.949645i
$672$		0			0
$673$	−2.12193e11			−1.03436			−0.517179	−	0.855877i	$-0.673018\pi$
$673$	−2.12193e11			−1.03436			−0.517179	+	0.855877i	$0.673018\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.30441e10	+	5.37191e10i	−0.442929	+	0.255725i	−0.704839	−	0.709367i	$-0.748981\pi$
$677$	−9.30441e10	+	5.37191e10i	−0.442929	+	0.255725i	0.261910	+	0.965092i	$0.415648\pi$
$678$		0			0
$679$	1.34850e10	+	6.06196e9i	0.0634412	+	0.0285190i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.88995e10	+	1.02017e11i	−0.270663	+	0.468802i	−0.969032	−	0.246936i	$-0.920576\pi$
$683$	−5.88995e10	+	1.02017e11i	−0.270663	+	0.468802i	0.698369	+	0.715738i	$0.253909\pi$
$684$		0			0
$685$			2.87654e11i			1.30650i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.41742e10	+	1.39570e10i	0.107269	+	0.0619320i
$690$		0			0
$691$	2.96618e11	−	1.71253e11i	1.30103	−	0.751148i	0.320446	−	0.947267i	$-0.396167\pi$
$691$	2.96618e11	−	1.71253e11i	1.30103	−	0.751148i	0.980580	+	0.196119i	$0.0628339\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.77371e11	+	3.07215e11i	0.760227	+	1.31675i
$696$		0			0
$697$	3.72997e10	−	6.46050e10i	0.158043	−	0.273738i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.15900e11			0.479967			0.239984	−	0.970777i	$-0.422858\pi$
$701$	1.15900e11			0.479967			0.239984	+	0.970777i	$0.422858\pi$
$702$		0			0
$703$	9.87691e10	+	5.70244e10i	0.404390	+	0.233474i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.59351e11	+	1.87011e11i	−1.03803	+	0.748498i
$708$		0			0
$709$	−7.71407e10	−	1.33612e11i	−0.305280	−	0.528761i	0.672044	−	0.740512i	$-0.265417\pi$
$709$	−7.71407e10	−	1.33612e11i	−0.305280	−	0.528761i	−0.977324	+	0.211751i	$0.932083\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	2.02073e10i		−	0.0781897i
$714$		0			0
$715$	−1.96558e11			−0.752084
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.82639e11	+	1.05447e11i	−0.683404	+	0.394564i	−0.801136	−	0.598482i	$-0.795771\pi$
$719$	−1.82639e11	+	1.05447e11i	−0.683404	+	0.394564i	0.117732	+	0.993045i	$0.462438\pi$
$720$		0			0
$721$	−1.34893e10	−	1.32928e11i	−0.0499172	−	0.491898i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.86938e10	+	6.70195e10i	−0.140052	+	0.242577i
$726$		0			0
$727$			2.28475e10i			0.0817900i	0.999163	+	0.0408950i	$0.0130209\pi$
$727$			2.28475e10i			0.0817900i	−0.999163	+	0.0408950i	$0.986979\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.82707e10	−	1.05486e10i	−0.0639861	−	0.0369424i
$732$		0			0
$733$	3.90685e11	−	2.25562e11i	1.35335	−	0.781358i	0.364634	−	0.931151i	$-0.381194\pi$
$733$	3.90685e11	−	2.25562e11i	1.35335	−	0.781358i	0.988717	+	0.149793i	$0.0478609\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.53014e11	+	4.38233e11i	0.857579	+	1.48537i
$738$		0			0
$739$	8.06607e10	−	1.39708e11i	0.270448	−	0.468430i	−0.698528	−	0.715582i	$-0.746161\pi$
$739$	8.06607e10	−	1.39708e11i	0.270448	−	0.468430i	0.968977	+	0.247152i	$0.0794948\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.11855e11			0.695159			0.347579	−	0.937651i	$-0.387004\pi$
$743$	2.11855e11			0.695159			0.347579	+	0.937651i	$0.387004\pi$
$744$		0			0
$745$	2.03129e11	+	1.17276e11i	0.659395	+	0.380702i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.45729e10	+	3.50841e9i	−0.109852	+	0.0111477i
$750$		0			0
$751$	−2.80633e11	−	4.86071e11i	−0.882224	−	1.52806i	−0.848862	−	0.528614i	$-0.822712\pi$
$751$	−2.80633e11	−	4.86071e11i	−0.882224	−	1.52806i	−0.0333617	−	0.999443i	$-0.510621\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			6.02882e11i			1.85543i
$756$		0			0
$757$	−2.12454e11			−0.646967			−0.323483	−	0.946234i	$-0.604854\pi$
$757$	−2.12454e11			−0.646967			−0.323483	+	0.946234i	$0.604854\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.11683e11	+	1.79950e11i	−0.929338	+	0.536554i	−0.886602	−	0.462533i	$-0.846941\pi$
$761$	−3.11683e11	+	1.79950e11i	−0.929338	+	0.536554i	−0.0427362	+	0.999086i	$0.513607\pi$
$762$		0			0
$763$	2.53277e11	+	3.51248e11i	0.747304	+	1.03637i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.20467e10	−	1.59429e11i	0.265966	−	0.460667i
$768$		0			0
$769$			1.74232e11i			0.498222i	0.968475	+	0.249111i	$0.0801385\pi$
$769$			1.74232e11i			0.498222i	−0.968475	+	0.249111i	$0.919862\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.44377e11	−	1.41091e11i	−0.684450	−	0.395168i	0.117079	−	0.993123i	$-0.462647\pi$
$773$	−2.44377e11	−	1.41091e11i	−0.684450	−	0.395168i	−0.801530	+	0.597955i	$0.795980\pi$
$774$		0			0
$775$	−2.65352e10	+	1.53201e10i	−0.0735555	+	0.0424673i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.02458e10	+	1.04349e11i	0.163598	+	0.283360i
$780$		0			0
$781$	−5.93912e10	+	1.02869e11i	−0.159631	+	0.276490i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.72175e11			−2.03347
$786$		0			0
$787$	5.01252e11	+	2.89398e11i	1.30664	+	0.754391i	0.981535	−	0.191285i	$-0.0612654\pi$
$787$	5.01252e11	+	2.89398e11i	1.30664	+	0.754391i	0.325110	+	0.945676i	$0.394599\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.18339e10	−	4.85701e10i	0.0557732	−	0.124069i
$792$		0			0
$793$	−1.60398e11	−	2.77818e11i	−0.405608	−	0.702534i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			1.44708e11i			0.358640i	0.983791	+	0.179320i	$0.0573898\pi$
$797$			1.44708e11i			0.358640i	−0.983791	+	0.179320i	$0.942610\pi$
$798$		0			0
$799$	−7.85047e11			−1.92623
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.74273e11	+	2.16087e11i	−0.900174	+	0.519716i
$804$		0			0
$805$	−1.34029e11	+	9.66453e10i	−0.319166	+	0.230143i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.04878e11	−	1.81654e11i	0.244844	−	0.424083i	−0.717244	−	0.696823i	$-0.754596\pi$
$809$	1.04878e11	−	1.81654e11i	0.244844	−	0.424083i	0.962088	+	0.272740i	$0.0879298\pi$
$810$		0			0
$811$		−	5.06101e10i		−	0.116991i	−0.998288	−	0.0584957i	$-0.981370\pi$
$811$		−	5.06101e10i		−	0.116991i	0.998288	−	0.0584957i	$-0.0186304\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	7.18365e11	+	4.14748e11i	1.62823	+	0.940056i
$816$		0			0
$817$	2.95105e10	−	1.70379e10i	0.0662352	−	0.0382409i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.52706e10	+	6.10905e10i	0.0776319	+	0.134462i	0.902228	−	0.431260i	$-0.141931\pi$
$821$	3.52706e10	+	6.10905e10i	0.0776319	+	0.134462i	−0.824596	+	0.565722i	$0.808597\pi$
$822$		0			0
$823$	−1.72986e11	+	2.99621e11i	−0.377061	+	0.653089i	−0.990633	−	0.136550i	$-0.956399\pi$
$823$	−1.72986e11	+	2.99621e11i	−0.377061	+	0.653089i	0.613572	+	0.789639i	$0.289732\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.36661e11			−1.57487			−0.787436	−	0.616396i	$-0.788592\pi$
$827$	−7.36661e11			−1.57487			−0.787436	+	0.616396i	$0.788592\pi$
$828$		0			0
$829$	−5.55082e10	−	3.20477e10i	−0.117527	−	0.0678545i	0.440084	−	0.897957i	$-0.354949\pi$
$829$	−5.55082e10	−	3.20477e10i	−0.117527	−	0.0678545i	−0.557611	+	0.830102i	$0.688282\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.10392e11	−	5.38314e11i	−0.229275	−	1.11804i
$834$		0			0
$835$	−3.65480e11	−	6.33029e11i	−0.751826	−	1.30220i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			3.78990e11i			0.764857i	0.923985	+	0.382428i	$0.124912\pi$
$839$			3.78990e11i			0.764857i	−0.923985	+	0.382428i	$0.875088\pi$
$840$		0			0
$841$	−2.06847e11			−0.413489
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.32331e11	+	1.34136e11i	−0.455701	+	0.263099i
$846$		0			0
$847$	1.26288e11	−	1.28155e10i	0.245374	−	0.0249002i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.48980e10	−	6.04450e10i	0.0665398	−	0.115250i
$852$		0			0
$853$			3.34365e11i			0.631575i	0.948830	+	0.315787i	$0.102269\pi$
$853$			3.34365e11i			0.631575i	−0.948830	+	0.315787i	$0.897731\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.45660e11	+	1.41832e11i	0.455419	+	0.262937i	0.710116	−	0.704084i	$-0.248642\pi$
$857$	2.45660e11	+	1.41832e11i	0.455419	+	0.262937i	−0.254697	+	0.967021i	$0.581976\pi$
$858$		0			0
$859$	4.58194e11	−	2.64539e11i	0.841544	−	0.485866i	−0.0162447	−	0.999868i	$-0.505171\pi$
$859$	4.58194e11	−	2.64539e11i	0.841544	−	0.485866i	0.857789	+	0.514002i	$0.171838\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8.74072e10	−	1.51394e11i	−0.157581	−	0.272938i	0.776415	−	0.630222i	$-0.217036\pi$
$863$	−8.74072e10	−	1.51394e11i	−0.157581	−	0.272938i	−0.933996	+	0.357284i	$0.883703\pi$
$864$		0			0
$865$	−2.30522e11	+	3.99276e11i	−0.411764	+	0.713197i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.75541e11			−1.00925
$870$		0			0
$871$	−7.30269e11	−	4.21621e11i	−1.26885	−	0.732571i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.96290e11	−	1.78146e11i	−0.676053	−	0.303909i
$876$		0			0
$877$	2.49143e11	+	4.31528e11i	0.421162	+	0.729475i	0.996053	−	0.0887553i	$-0.0282889\pi$
$877$	2.49143e11	+	4.31528e11i	0.421162	+	0.729475i	−0.574891	+	0.818230i	$0.694956\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	2.65089e11i		−	0.440035i	−0.975496	−	0.220018i	$-0.929389\pi$
$881$		−	2.65089e11i		−	0.440035i	0.975496	−	0.220018i	$-0.0706115\pi$
$882$		0			0
$883$	2.64089e11			0.434418			0.217209	−	0.976125i	$-0.430305\pi$
$883$	2.64089e11			0.434418			0.217209	+	0.976125i	$0.430305\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.00397e12	−	5.79640e11i	1.62190	−	0.936406i	0.635491	−	0.772108i	$-0.280798\pi$
$887$	1.00397e12	−	5.79640e11i	1.62190	−	0.936406i	0.986411	−	0.164297i	$-0.0525357\pi$
$888$		0			0
$889$	1.74945e11	−	3.89170e11i	0.280088	−	0.623063i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.33997e11	−	1.09811e12i	0.996968	−	1.72680i
$894$		0			0
$895$			8.43390e11i			1.31443i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.00603e11	+	5.80832e10i	0.154018	+	0.0889225i
$900$		0			0
$901$	−1.08817e11	+	6.28256e10i	−0.165119	+	0.0953317i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.19365e11	+	8.99566e11i	0.774244	+	1.34103i
$906$		0			0
$907$	−2.24197e9	+	3.88320e9i	−0.00331284	+	0.00573801i	−0.867677	−	0.497128i	$-0.834388\pi$
$907$	−2.24197e9	+	3.88320e9i	−0.00331284	+	0.00573801i	0.864364	+	0.502866i	$0.167721\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.14100e11			1.18196			0.590982	−	0.806685i	$-0.298740\pi$
$911$	8.14100e11			1.18196			0.590982	+	0.806685i	$0.298740\pi$
$912$		0			0
$913$	7.25135e11	+	4.18657e11i	1.04360	+	0.602525i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.35240e11	−	1.33270e12i	−0.191262	−	1.88475i
$918$		0			0
$919$	5.26562e11	+	9.12032e11i	0.738222	+	1.27864i	0.953295	+	0.302041i	$0.0976679\pi$
$919$	5.26562e11	+	9.12032e11i	0.738222	+	1.27864i	−0.215073	+	0.976598i	$0.568999\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	1.97938e11i		−	0.272724i
$924$		0			0
$925$	−1.05831e11			−0.144560
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.96093e11	−	5.17360e11i	1.20307	−	0.694592i	0.241832	−	0.970318i	$-0.422252\pi$
$929$	8.96093e11	−	5.17360e11i	1.20307	−	0.694592i	0.961236	+	0.275726i	$0.0889182\pi$
$930$		0			0
$931$	8.42139e11	+	2.80323e11i	1.12095	+	0.373130i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.42390e11	−	7.66242e11i	0.578840	−	1.00258i
$936$		0			0
$937$		−	8.31714e11i		−	1.07899i	−0.841990	−	0.539493i	$-0.818616\pi$
$937$		−	8.31714e11i		−	1.07899i	0.841990	−	0.539493i	$-0.181384\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.14487e12	+	6.60992e11i	1.46015	+	0.843020i	0.999018	−	0.0443103i	$-0.0141090\pi$
$941$	1.14487e12	+	6.60992e11i	1.46015	+	0.843020i	0.461135	+	0.887330i	$0.347442\pi$
$942$		0			0
$943$	6.38597e10	−	3.68694e10i	0.0807570	−	0.0466251i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.20176e11	−	3.81357e11i	−0.273760	−	0.474167i	0.696061	−	0.717982i	$-0.254934\pi$
$947$	−2.20176e11	−	3.81357e11i	−0.273760	−	0.474167i	−0.969822	+	0.243815i	$0.921601\pi$
$948$		0			0
$949$	3.60086e11	−	6.23687e11i	0.443957	−	0.768956i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−7.16416e11			−0.868547			−0.434274	−	0.900781i	$-0.642995\pi$
$953$	−7.16416e11			−0.868547			−0.434274	+	0.900781i	$0.642995\pi$
$954$		0			0
$955$	3.86924e11	+	2.23391e11i	0.465171	+	0.268566i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.53050e11	−	7.66979e11i	−0.653868	−	0.906795i
$960$		0			0
$961$	−4.03449e11	−	6.98793e11i	−0.473036	−	0.819323i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			1.38710e12i			1.59956i
$966$		0			0
$967$	1.18405e12			1.35414			0.677070	−	0.735919i	$-0.263249\pi$
$967$	1.18405e12			1.35414			0.677070	+	0.735919i	$0.263249\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.17425e12	−	6.77952e11i	1.32094	−	0.762645i	0.337061	−	0.941483i	$-0.390567\pi$
$971$	1.17425e12	−	6.77952e11i	1.32094	−	0.762645i	0.983879	+	0.178838i	$0.0572338\pi$
$972$		0			0
$973$	−1.06359e12	−	4.78118e11i	−1.18665	−	0.533438i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.61277e11	+	4.52545e11i	−0.286763	+	0.496688i	−0.973035	−	0.230657i	$-0.925913\pi$
$977$	−2.61277e11	+	4.52545e11i	−0.286763	+	0.496688i	0.686272	+	0.727345i	$0.259246\pi$
$978$		0			0
$979$			1.61268e11i			0.175556i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.35501e12	−	7.82318e11i	−1.45121	−	0.837855i	−0.452658	−	0.891684i	$-0.649524\pi$
$983$	−1.35501e12	−	7.82318e11i	−1.45121	−	0.837855i	−0.998550	+	0.0538289i	$0.982857\pi$
$984$		0			0
$985$	6.37882e11	−	3.68281e11i	0.677634	−	0.391232i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.04269e10	−	1.80599e10i	−0.0108986	−	0.0188769i
$990$		0			0
$991$	−1.30845e11	+	2.26630e11i	−0.135663	+	0.234975i	−0.925851	−	0.377890i	$-0.876650\pi$
$991$	−1.30845e11	+	2.26630e11i	−0.135663	+	0.234975i	0.790187	+	0.612865i	$0.209983\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.32994e11			−0.237713
$996$		0			0
$997$	−1.55089e12	−	8.95405e11i	−1.56964	−	0.906231i	−0.996211	−	0.0869745i	$-0.972280\pi$
$997$	−1.55089e12	−	8.95405e11i	−1.56964	−	0.906231i	−0.573427	−	0.819256i	$-0.694387\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.d.73.2		12
3.2	odd	2		84.9.m.b.73.5	yes	12
7.5	odd	6	inner	252.9.z.d.145.2		12
21.5	even	6		84.9.m.b.61.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.m.b.61.5	✓	12	21.5	even	6
84.9.m.b.73.5	yes	12	3.2	odd	2
252.9.z.d.73.2		12	1.1	even	1	trivial
252.9.z.d.145.2		12	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-632.551 + 365.204i) q^{5} +(984.437 - 2189.91i) q^{7} +O(q^{10})\)	\(q+(-632.551 + 365.204i) q^{5} +(984.437 - 2189.91i) q^{7} +(-6353.95 + 11005.4i) q^{11} -21176.4i q^{13} +(82551.9 + 47661.3i) q^{17} +(-133336. + 76981.8i) q^{19} +(47111.5 + 81599.5i) q^{23} +(71435.0 - 123729. i) q^{25} -541664. q^{29} +(-185730. - 107231. i) q^{31} +(177055. + 1.74475e6i) q^{35} +(-370376. - 641510. i) q^{37} -782599. i q^{41} -221324. q^{43} +(-7.13230e6 + 4.11784e6i) q^{47} +(-3.82657e6 - 4.31165e6i) q^{49} +(-659083. + 1.14157e6i) q^{53} -9.28194e6i q^{55} +(7.52865e6 + 4.34667e6i) q^{59} +(1.31192e7 - 7.57439e6i) q^{61} +(7.73369e6 + 1.33951e7i) q^{65} +(1.99100e7 - 3.44851e7i) q^{67} +9.34713e6 q^{71} +(2.94520e7 + 1.70041e7i) q^{73} +(1.78456e7 + 2.47486e7i) q^{77} +(2.26450e7 + 3.92223e7i) q^{79} -6.58893e7i q^{83} -6.96244e7 q^{85} +(1.09902e7 - 6.34517e6i) q^{89} +(-4.63742e7 - 2.08468e7i) q^{91} +(5.62280e7 - 9.73898e7i) q^{95} +6.15780e6i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) 12 * q - 285 * q^5 + 198 * q^7	\( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more