LMFDB - Embedded newform 12.11.c.b.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,11,Mod(5,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("12.5");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	12.c (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:	$7.62428703208$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-35}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 9 $ x^2 - x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$0.500000 - 2.95804i$ of defining polynomial
Character	$\chi$	$=$	12.5
Dual form			12.11.c.b.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(117.000 - 212.979i) q^{3} -1277.87i q^{5} -10318.0 q^{7} +(-31671.0 - 49837.1i) q^{9} +O(q^{10})$	\(q+(117.000 - 212.979i) q^{3} -1277.87i q^{5} -10318.0 q^{7} +(-31671.0 - 49837.1i) q^{9} -292633. i q^{11} -256822. q^{13} +(-272160. - 149511. i) q^{15} +557153. i q^{17} +3.19611e6 q^{19} +(-1.20721e6 + 2.19752e6i) q^{21} +8.35474e6i q^{23} +8.13267e6 q^{25} +(-1.43197e7 + 914318. i) q^{27} -3.14906e7i q^{29} +2.31410e7 q^{31} +(-6.23246e7 - 3.42381e7i) q^{33} +1.31851e7i q^{35} +2.97979e7 q^{37} +(-3.00482e7 + 5.46977e7i) q^{39} -948182. i q^{41} +2.47523e8 q^{43} +(-6.36854e7 + 4.04715e7i) q^{45} +3.29553e8i q^{47} -1.76014e8 q^{49} +(1.18662e8 + 6.51869e7i) q^{51} -5.51291e8i q^{53} -3.73948e8 q^{55} +(3.73944e8 - 6.80703e8i) q^{57} -3.59094e8i q^{59} -1.05484e9 q^{61} +(3.26781e8 + 5.14219e8i) q^{63} +3.28186e8i q^{65} -3.61186e8 q^{67} +(1.77938e9 + 9.77504e8i) q^{69} +9.31536e8i q^{71} +3.74437e8 q^{73} +(9.51522e8 - 1.73209e9i) q^{75} +3.01939e9i q^{77} -1.13914e8 q^{79} +(-1.48068e9 + 3.15678e9i) q^{81} -4.91092e9i q^{83} +7.11971e8 q^{85} +(-6.70684e9 - 3.68440e9i) q^{87} -3.28204e9i q^{89} +2.64989e9 q^{91} +(2.70750e9 - 4.92854e9i) q^{93} -4.08422e9i q^{95} +2.80992e9 q^{97} +(-1.45840e10 + 9.26798e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 234 q^{3} - 20636 q^{7} - 63342 q^{9}+O(q^{10}) $ 2 * q + 234 * q^3 - 20636 * q^7 - 63342 * q^9	$ 2 q + 234 q^{3} - 20636 q^{7} - 63342 q^{9} - 513644 q^{13} - 544320 q^{15} + 6392212 q^{19} - 2414412 q^{21} + 16265330 q^{25} - 28639494 q^{27} + 46281988 q^{31} - 124649280 q^{33} + 59595892 q^{37} - 60096348 q^{39} + 495045556 q^{43} - 127370880 q^{45} - 352028250 q^{49} + 237323520 q^{51} - 747895680 q^{55} + 747888804 q^{57} - 2109679532 q^{61} + 653562756 q^{63} - 722372396 q^{67} + 3558764160 q^{69} + 748874788 q^{73} + 1903043610 q^{75} - 227828924 q^{79} - 2961359838 q^{81} + 1423941120 q^{85} - 13413677760 q^{87} + 5299778792 q^{91} + 5414992596 q^{93} + 5619834244 q^{97} - 29167931520 q^{99}+O(q^{100}) $ 2 * q + 234 * q^3 - 20636 * q^7 - 63342 * q^9 - 513644 * q^13 - 544320 * q^15 + 6392212 * q^19 - 2414412 * q^21 + 16265330 * q^25 - 28639494 * q^27 + 46281988 * q^31 - 124649280 * q^33 + 59595892 * q^37 - 60096348 * q^39 + 495045556 * q^43 - 127370880 * q^45 - 352028250 * q^49 + 237323520 * q^51 - 747895680 * q^55 + 747888804 * q^57 - 2109679532 * q^61 + 653562756 * q^63 - 722372396 * q^67 + 3558764160 * q^69 + 748874788 * q^73 + 1903043610 * q^75 - 227828924 * q^79 - 2961359838 * q^81 + 1423941120 * q^85 - 13413677760 * q^87 + 5299778792 * q^91 + 5414992596 * q^93 + 5619834244 * q^97 - 29167931520 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	117.000	−	212.979i	0.481481	−	0.876456i
$3$	117.000	−	212.979i	0.481481	−	0.876456i
$4$		0			0
$5$		−	1277.87i		−	0.408919i	−0.978875	−	0.204460i	$-0.934456\pi$
$5$		−	1277.87i		−	0.408919i	0.978875	−	0.204460i	$-0.0655437\pi$
$6$		0			0
$7$	−10318.0			−0.613911			−0.306955	−	0.951724i	$-0.599310\pi$
$7$	−10318.0			−0.613911			−0.306955	+	0.951724i	$0.599310\pi$
$8$		0			0
$9$	−31671.0	−	49837.1i	−0.536351	−	0.843995i
$10$		0			0
$11$		−	292633.i		−	1.81702i	−0.417863	−	0.908510i	$-0.637221\pi$
$11$		−	292633.i		−	1.81702i	0.417863	−	0.908510i	$-0.362779\pi$
$12$		0			0
$13$	−256822.			−0.691696			−0.345848	−	0.938290i	$-0.612409\pi$
$13$	−256822.			−0.691696			−0.345848	+	0.938290i	$0.612409\pi$
$14$		0			0
$15$	−272160.	−	149511.i	−0.358400	−	0.196887i
$16$		0			0
$17$			557153.i			0.392401i	0.980564	+	0.196200i	$0.0628603\pi$
$17$			557153.i			0.392401i	−0.980564	+	0.196200i	$0.937140\pi$
$18$		0			0
$19$	3.19611e6			1.29078			0.645391	−	0.763852i	$-0.276694\pi$
$19$	3.19611e6			1.29078			0.645391	+	0.763852i	$0.276694\pi$
$20$		0			0
$21$	−1.20721e6	+	2.19752e6i	−0.295587	+	0.538066i
$22$		0			0
$23$			8.35474e6i			1.29806i	0.760764	+	0.649028i	$0.224824\pi$
$23$			8.35474e6i			1.29806i	−0.760764	+	0.649028i	$0.775176\pi$
$24$		0			0
$25$	8.13267e6			0.832785
$26$		0			0
$27$	−1.43197e7	+	914318.i	−0.997968	+	0.0637204i
$28$		0			0
$29$		−	3.14906e7i		−	1.53529i	−0.640873	−	0.767647i	$-0.721428\pi$
$29$		−	3.14906e7i		−	1.53529i	0.640873	−	0.767647i	$-0.278572\pi$
$30$		0			0
$31$	2.31410e7			0.808302			0.404151	−	0.914692i	$-0.367567\pi$
$31$	2.31410e7			0.808302			0.404151	+	0.914692i	$0.367567\pi$
$32$		0			0
$33$	−6.23246e7	−	3.42381e7i	−1.59254	−	0.874862i
$34$		0			0
$35$			1.31851e7i			0.251040i
$36$		0			0
$37$	2.97979e7			0.429712			0.214856	−	0.976646i	$-0.431072\pi$
$37$	2.97979e7			0.429712			0.214856	+	0.976646i	$0.431072\pi$
$38$		0			0
$39$	−3.00482e7	+	5.46977e7i	−0.333039	+	0.606242i
$40$		0			0
$41$		−	948182.i		−	0.00818413i	−0.999992	−	0.00409206i	$-0.998697\pi$
$41$		−	948182.i		−	0.00818413i	0.999992	−	0.00409206i	$-0.00130255\pi$
$42$		0			0
$43$	2.47523e8			1.68373			0.841866	−	0.539687i	$-0.181457\pi$
$43$	2.47523e8			1.68373			0.841866	+	0.539687i	$0.181457\pi$
$44$		0			0
$45$	−6.36854e7	+	4.04715e7i	−0.345126	+	0.219324i
$46$		0			0
$47$			3.29553e8i			1.43693i	0.695562	+	0.718466i	$0.255156\pi$
$47$			3.29553e8i			1.43693i	−0.695562	+	0.718466i	$0.744844\pi$
$48$		0			0
$49$	−1.76014e8			−0.623113
$50$		0			0
$51$	1.18662e8	+	6.51869e7i	0.343922	+	0.188934i
$52$		0			0
$53$		−	5.51291e8i		−	1.31826i	−0.752028	−	0.659131i	$-0.770924\pi$
$53$		−	5.51291e8i		−	1.31826i	0.752028	−	0.659131i	$-0.229076\pi$
$54$		0			0
$55$	−3.73948e8			−0.743015
$56$		0			0
$57$	3.73944e8	−	6.80703e8i	0.621488	−	1.13131i
$58$		0			0
$59$		−	3.59094e8i		−	0.502282i	−0.967950	−	0.251141i	$-0.919194\pi$
$59$		−	3.59094e8i		−	0.502282i	0.967950	−	0.251141i	$-0.0808058\pi$
$60$		0			0
$61$	−1.05484e9			−1.24893			−0.624464	−	0.781054i	$-0.714682\pi$
$61$	−1.05484e9			−1.24893			−0.624464	+	0.781054i	$0.714682\pi$
$62$		0			0
$63$	3.26781e8	+	5.14219e8i	0.329272	+	0.518138i
$64$		0			0
$65$			3.28186e8i			0.282848i
$66$		0			0
$67$	−3.61186e8			−0.267521			−0.133760	−	0.991014i	$-0.542705\pi$
$67$	−3.61186e8			−0.267521			−0.133760	+	0.991014i	$0.542705\pi$
$68$		0			0
$69$	1.77938e9	+	9.77504e8i	1.13769	+	0.624990i
$70$		0			0
$71$			9.31536e8i			0.516307i	0.966104	+	0.258154i	$0.0831140\pi$
$71$			9.31536e8i			0.516307i	−0.966104	+	0.258154i	$0.916886\pi$
$72$		0			0
$73$	3.74437e8			0.180620			0.0903098	−	0.995914i	$-0.471214\pi$
$73$	3.74437e8			0.180620			0.0903098	+	0.995914i	$0.471214\pi$
$74$		0			0
$75$	9.51522e8	−	1.73209e9i	0.400971	−	0.729900i
$76$		0			0
$77$			3.01939e9i			1.11549i
$78$		0			0
$79$	−1.13914e8			−0.0370206			−0.0185103	−	0.999829i	$-0.505892\pi$
$79$	−1.13914e8			−0.0370206			−0.0185103	+	0.999829i	$0.505892\pi$
$80$		0			0
$81$	−1.48068e9	+	3.15678e9i	−0.424655	+	0.905355i
$82$		0			0
$83$		−	4.91092e9i		−	1.24673i	−0.781931	−	0.623365i	$-0.785765\pi$
$83$		−	4.91092e9i		−	1.24673i	0.781931	−	0.623365i	$-0.214235\pi$
$84$		0			0
$85$	7.11971e8			0.160460
$86$		0			0
$87$	−6.70684e9	−	3.68440e9i	−1.34562	−	0.739215i
$88$		0			0
$89$		−	3.28204e9i		−	0.587752i	−0.955844	−	0.293876i	$-0.905055\pi$
$89$		−	3.28204e9i		−	0.587752i	0.955844	−	0.293876i	$-0.0949452\pi$
$90$		0			0
$91$	2.64989e9			0.424640
$92$		0			0
$93$	2.70750e9	−	4.92854e9i	0.389182	−	0.708441i
$94$		0			0
$95$		−	4.08422e9i		−	0.527826i
$96$		0			0
$97$	2.80992e9			0.327216			0.163608	−	0.986525i	$-0.447687\pi$
$97$	2.80992e9			0.327216			0.163608	+	0.986525i	$0.447687\pi$
$98$		0			0
$99$	−1.45840e10	+	9.26798e9i	−1.53356	+	0.974561i
$100$		0			0
$101$			1.28917e10i			1.22660i	0.789849	+	0.613301i	$0.210159\pi$
$101$			1.28917e10i			1.22660i	−0.789849	+	0.613301i	$0.789841\pi$
$102$		0			0
$103$	1.51220e10			1.30443			0.652217	−	0.758032i	$-0.273839\pi$
$103$	1.51220e10			1.30443			0.652217	+	0.758032i	$0.273839\pi$
$104$		0			0
$105$	2.80815e9	+	1.54266e9i	0.220026	+	0.120871i
$106$		0			0
$107$			1.32160e10i			0.942285i	0.882057	+	0.471143i	$0.156158\pi$
$107$			1.32160e10i			0.942285i	−0.882057	+	0.471143i	$0.843842\pi$
$108$		0			0
$109$	1.39846e9			0.0908901			0.0454451	−	0.998967i	$-0.485529\pi$
$109$	1.39846e9			0.0908901			0.0454451	+	0.998967i	$0.485529\pi$
$110$		0			0
$111$	3.48636e9	−	6.34633e9i	0.206898	−	0.376624i
$112$		0			0
$113$		−	1.15787e10i		−	0.628448i	−0.949349	−	0.314224i	$-0.898256\pi$
$113$		−	1.15787e10i		−	0.628448i	0.949349	−	0.314224i	$-0.101744\pi$
$114$		0			0
$115$	1.06763e10			0.530800
$116$		0			0
$117$	8.13381e9	+	1.27993e10i	0.370992	+	0.583788i
$118$		0			0
$119$		−	5.74870e9i		−	0.240899i
$120$		0			0
$121$	−5.96966e10			−2.30156
$122$		0			0
$123$	−2.01943e8	−	1.10937e8i	−0.00717303	−	0.00394051i
$124$		0			0
$125$		−	2.28717e10i		−	0.749461i
$126$		0			0
$127$	8.89747e8			0.0269307			0.0134654	−	0.999909i	$-0.495714\pi$
$127$	8.89747e8			0.0269307			0.0134654	+	0.999909i	$0.495714\pi$
$128$		0			0
$129$	2.89602e10	−	5.27171e10i	0.810686	−	1.47572i
$130$		0			0
$131$			1.05561e10i			0.273619i	0.990597	+	0.136809i	$0.0436848\pi$
$131$			1.05561e10i			0.273619i	−0.990597	+	0.136809i	$0.956315\pi$
$132$		0			0
$133$	−3.29774e10			−0.792426
$134$		0			0
$135$	1.16838e9	+	1.82988e10i	0.0260565	+	0.408088i
$136$		0			0
$137$		−	3.96577e10i		−	0.821722i	−0.911698	−	0.410861i	$-0.865228\pi$
$137$		−	3.96577e10i		−	0.821722i	0.911698	−	0.410861i	$-0.134772\pi$
$138$		0			0
$139$	5.42044e9			0.104463			0.0522313	−	0.998635i	$-0.483367\pi$
$139$	5.42044e9			0.104463			0.0522313	+	0.998635i	$0.483367\pi$
$140$		0			0
$141$	7.01879e10	+	3.85577e10i	1.25941	+	0.691856i
$142$		0			0
$143$			7.51546e10i			1.25683i
$144$		0			0
$145$	−4.02410e10			−0.627811
$146$		0			0
$147$	−2.05937e10	+	3.74873e10i	−0.300018	+	0.546132i
$148$		0			0
$149$			7.71177e10i			1.05008i	0.851077	+	0.525040i	$0.175950\pi$
$149$			7.71177e10i			1.05008i	−0.851077	+	0.525040i	$0.824050\pi$
$150$		0			0
$151$	7.48173e10			0.953053			0.476527	−	0.879160i	$-0.341896\pi$
$151$	7.48173e10			0.953053			0.476527	+	0.879160i	$0.341896\pi$
$152$		0			0
$153$	2.77669e10	−	1.76456e10i	0.331184	−	0.210465i
$154$		0			0
$155$		−	2.95713e10i		−	0.330530i
$156$		0			0
$157$	2.06739e10			0.216732			0.108366	−	0.994111i	$-0.465438\pi$
$157$	2.06739e10			0.216732			0.108366	+	0.994111i	$0.465438\pi$
$158$		0			0
$159$	−1.17413e11	−	6.45011e10i	−1.15540	−	0.634719i
$160$		0			0
$161$		−	8.62042e10i		−	0.796891i
$162$		0			0
$163$	9.57605e10			0.832239			0.416120	−	0.909310i	$-0.363390\pi$
$163$	9.57605e10			0.832239			0.416120	+	0.909310i	$0.363390\pi$
$164$		0			0
$165$	−4.37519e10	+	7.96430e10i	−0.357748	+	0.651220i
$166$		0			0
$167$		−	1.46483e11i		−	1.12773i	−0.825866	−	0.563866i	$-0.809313\pi$
$167$		−	1.46483e11i		−	1.12773i	0.825866	−	0.563866i	$-0.190687\pi$
$168$		0			0
$169$	−7.19010e10			−0.521556
$170$		0			0
$171$	−1.01224e11	−	1.59285e11i	−0.692313	−	1.08941i
$172$		0			0
$173$			2.30251e11i			1.48583i	0.669383	+	0.742917i	$0.266558\pi$
$173$			2.30251e11i			1.48583i	−0.669383	+	0.742917i	$0.733442\pi$
$174$		0			0
$175$	−8.39128e10			−0.511256
$176$		0			0
$177$	−7.64794e10	−	4.20140e10i	−0.440229	−	0.241840i
$178$		0			0
$179$		−	2.27901e11i		−	1.24017i	−0.784536	−	0.620084i	$-0.787099\pi$
$179$		−	2.27901e11i		−	1.24017i	0.784536	−	0.620084i	$-0.212901\pi$
$180$		0			0
$181$	3.45325e11			1.77761			0.888803	−	0.458290i	$-0.151538\pi$
$181$	3.45325e11			1.77761			0.888803	+	0.458290i	$0.151538\pi$
$182$		0			0
$183$	−1.23416e11	+	2.24659e11i	−0.601336	+	1.09463i
$184$		0			0
$185$		−	3.80780e10i		−	0.175718i
$186$		0			0
$187$	1.63041e11			0.713000
$188$		0			0
$189$	1.47751e11	−	9.43394e9i	0.612663	−	0.0391187i
$190$		0			0
$191$			2.05287e11i			0.807596i	0.914848	+	0.403798i	$0.132310\pi$
$191$			2.05287e11i			0.807596i	−0.914848	+	0.403798i	$0.867690\pi$
$192$		0			0
$193$	−1.39964e11			−0.522674			−0.261337	−	0.965248i	$-0.584163\pi$
$193$	−1.39964e11			−0.522674			−0.261337	+	0.965248i	$0.584163\pi$
$194$		0			0
$195$	6.98967e10	+	3.83978e10i	0.247904	+	0.136186i
$196$		0			0
$197$			4.25733e11i			1.43485i	0.696636	+	0.717425i	$0.254679\pi$
$197$			4.25733e11i			1.43485i	−0.696636	+	0.717425i	$0.745321\pi$
$198$		0			0
$199$	−8.32985e10			−0.266914			−0.133457	−	0.991055i	$-0.542608\pi$
$199$	−8.32985e10			−0.266914			−0.133457	+	0.991055i	$0.542608\pi$
$200$		0			0
$201$	−4.22588e10	+	7.69250e10i	−0.128806	+	0.234470i
$202$		0			0
$203$			3.24920e11i			0.942533i
$204$		0			0
$205$	−1.21166e9			−0.00334665
$206$		0			0
$207$	4.16375e11	−	2.64603e11i	1.09555	−	0.696214i
$208$		0			0
$209$		−	9.35286e11i		−	2.34538i
$210$		0			0
$211$	−6.18669e11			−1.47927			−0.739633	−	0.673011i	$-0.765001\pi$
$211$	−6.18669e11			−1.47927			−0.739633	+	0.673011i	$0.765001\pi$
$212$		0			0
$213$	1.98398e11	+	1.08990e11i	0.452521	+	0.248592i
$214$		0			0
$215$		−	3.16303e11i		−	0.688511i
$216$		0			0
$217$	−2.38769e11			−0.496225
$218$		0			0
$219$	4.38092e10	−	7.97473e10i	0.0869650	−	0.158305i
$220$		0			0
$221$		−	1.43089e11i		−	0.271422i
$222$		0			0
$223$	8.45523e10			0.153321			0.0766604	−	0.997057i	$-0.475574\pi$
$223$	8.45523e10			0.153321			0.0766604	+	0.997057i	$0.475574\pi$
$224$		0			0
$225$	−2.57570e11	−	4.05308e11i	−0.446665	−	0.702866i
$226$		0			0
$227$			3.28465e11i			0.544954i	0.962162	+	0.272477i	$0.0878428\pi$
$227$			3.28465e11i			0.544954i	−0.962162	+	0.272477i	$0.912157\pi$
$228$		0			0
$229$	−1.06468e12			−1.69060			−0.845302	−	0.534289i	$-0.820579\pi$
$229$	−1.06468e12			−1.69060			−0.845302	+	0.534289i	$0.820579\pi$
$230$		0			0
$231$	6.43066e11	+	3.53268e11i	0.977677	+	0.537087i
$232$		0			0
$233$			2.81192e11i			0.409471i	0.978817	+	0.204736i	$0.0656335\pi$
$233$			2.81192e11i			0.409471i	−0.978817	+	0.204736i	$0.934367\pi$
$234$		0			0
$235$	4.21127e11			0.587590
$236$		0			0
$237$	−1.33280e10	+	2.42614e10i	−0.0178247	+	0.0324469i
$238$		0			0
$239$		−	4.81414e10i		−	0.0617347i	−0.999523	−	0.0308674i	$-0.990173\pi$
$239$		−	4.81414e10i		−	0.0617347i	0.999523	−	0.0308674i	$-0.00982695\pi$
$240$		0			0
$241$	1.09510e12			1.34700			0.673502	−	0.739186i	$-0.264789\pi$
$241$	1.09510e12			1.34700			0.673502	+	0.739186i	$0.264789\pi$
$242$		0			0
$243$	4.99088e11	+	6.84697e11i	0.589041	+	0.808103i
$244$		0			0
$245$			2.24924e11i			0.254803i
$246$		0			0
$247$	−8.20830e11			−0.892830
$248$		0			0
$249$	−1.04592e12	−	5.74577e11i	−1.09270	−	0.600277i
$250$		0			0
$251$			1.10846e12i			1.11264i	0.830969	+	0.556318i	$0.187786\pi$
$251$			1.10846e12i			1.11264i	−0.830969	+	0.556318i	$0.812214\pi$
$252$		0			0
$253$	2.44487e12			2.35859
$254$		0			0
$255$	8.33006e10	−	1.51635e11i	0.0772586	−	0.140636i
$256$		0			0
$257$			5.66907e10i			0.0505646i	0.999680	+	0.0252823i	$0.00804846\pi$
$257$			5.66907e10i			0.0505646i	−0.999680	+	0.0252823i	$0.991952\pi$
$258$		0			0
$259$	−3.07455e11			−0.263805
$260$		0			0
$261$	−1.56940e12	+	9.97340e11i	−1.29578	+	0.823456i
$262$		0			0
$263$		−	1.24412e11i		−	0.0988740i	−0.998777	−	0.0494370i	$-0.984257\pi$
$263$		−	1.24412e11i		−	0.0988740i	0.998777	−	0.0494370i	$-0.0157427\pi$
$264$		0			0
$265$	−7.04480e11			−0.539063
$266$		0			0
$267$	−6.99005e11	−	3.83999e11i	−0.515139	−	0.282992i
$268$		0			0
$269$		−	2.14333e12i		−	1.52170i	−0.648930	−	0.760848i	$-0.724783\pi$
$269$		−	2.14333e12i		−	1.52170i	0.648930	−	0.760848i	$-0.275217\pi$
$270$		0			0
$271$	5.35797e11			0.366568			0.183284	−	0.983060i	$-0.441327\pi$
$271$	5.35797e11			0.366568			0.183284	+	0.983060i	$0.441327\pi$
$272$		0			0
$273$	3.10037e11	−	5.64370e11i	0.204456	−	0.372178i
$274$		0			0
$275$		−	2.37989e12i		−	1.51319i
$276$		0			0
$277$	1.17533e12			0.720710			0.360355	−	0.932815i	$-0.382656\pi$
$277$	1.17533e12			0.720710			0.360355	+	0.932815i	$0.382656\pi$
$278$		0			0
$279$	−7.32898e11	−	1.15328e12i	−0.433534	−	0.682203i
$280$		0			0
$281$			1.99322e12i			1.13769i	0.822445	+	0.568845i	$0.192610\pi$
$281$			1.99322e12i			1.13769i	−0.822445	+	0.568845i	$0.807390\pi$
$282$		0			0
$283$	−1.41547e12			−0.779773			−0.389886	−	0.920863i	$-0.627486\pi$
$283$	−1.41547e12			−0.779773			−0.389886	+	0.920863i	$0.627486\pi$
$284$		0			0
$285$	−8.69852e11	−	4.77854e11i	−0.462617	−	0.254139i
$286$		0			0
$287$			9.78334e9i			0.00502432i
$288$		0			0
$289$	1.70557e12			0.846022
$290$		0			0
$291$	3.28760e11	−	5.98453e11i	0.157549	−	0.286791i
$292$		0			0
$293$			3.38242e12i			1.56635i	0.621800	+	0.783176i	$0.286402\pi$
$293$			3.38242e12i			1.56635i	−0.621800	+	0.783176i	$0.713598\pi$
$294$		0			0
$295$	−4.58876e11			−0.205393
$296$		0			0
$297$	2.67560e11	+	4.19043e12i	0.115781	+	1.81333i
$298$		0			0
$299$		−	2.14568e12i		−	0.897861i
$300$		0			0
$301$	−2.55394e12			−1.03366
$302$		0			0
$303$	2.74566e12	+	1.50833e12i	1.07506	+	0.590586i
$304$		0			0
$305$			1.34795e12i			0.510711i
$306$		0			0
$307$	2.72469e12			0.999138			0.499569	−	0.866274i	$-0.333492\pi$
$307$	2.72469e12			0.999138			0.499569	+	0.866274i	$0.333492\pi$
$308$		0			0
$309$	1.76927e12	−	3.22066e12i	0.628061	−	1.14328i
$310$		0			0
$311$			2.09948e12i			0.721622i	0.932639	+	0.360811i	$0.117500\pi$
$311$			2.09948e12i			0.721622i	−0.932639	+	0.360811i	$0.882500\pi$
$312$		0			0
$313$	2.15746e12			0.718160			0.359080	−	0.933307i	$-0.383090\pi$
$313$	2.15746e12			0.718160			0.359080	+	0.933307i	$0.383090\pi$
$314$		0			0
$315$	6.57106e11	−	4.17585e11i	0.211877	−	0.134646i
$316$		0			0
$317$		−	2.52312e12i		−	0.788210i	−0.919065	−	0.394105i	$-0.871055\pi$
$317$		−	2.52312e12i		−	0.788210i	0.919065	−	0.394105i	$-0.128945\pi$
$318$		0			0
$319$	−9.21520e12			−2.78966
$320$		0			0
$321$	2.81474e12	+	1.54628e12i	0.825872	+	0.453693i
$322$		0			0
$323$			1.78072e12i			0.506504i
$324$		0			0
$325$	−2.08865e12			−0.576034
$326$		0			0
$327$	1.63619e11	−	2.97842e11i	0.0437619	−	0.0796612i
$328$		0			0
$329$		−	3.40033e12i		−	0.882148i
$330$		0			0
$331$	2.23406e12			0.562283			0.281142	−	0.959666i	$-0.409287\pi$
$331$	2.23406e12			0.562283			0.281142	+	0.959666i	$0.409287\pi$
$332$		0			0
$333$	−9.43731e11	−	1.48504e12i	−0.230477	−	0.362675i
$334$		0			0
$335$			4.61550e11i			0.109394i
$336$		0			0
$337$	−5.32046e12			−1.22405			−0.612026	−	0.790838i	$-0.709645\pi$
$337$	−5.32046e12			−1.22405			−0.612026	+	0.790838i	$0.709645\pi$
$338$		0			0
$339$	−2.46603e12	−	1.35471e12i	−0.550807	−	0.302586i
$340$		0			0
$341$		−	6.77182e12i		−	1.46870i
$342$		0			0
$343$	4.73069e12			0.996447
$344$		0			0
$345$	1.24913e12	−	2.27382e12i	0.255571	−	0.465223i
$346$		0			0
$347$		−	3.39317e11i		−	0.0674463i	−0.999431	−	0.0337232i	$-0.989264\pi$
$347$		−	3.39317e11i		−	0.0674463i	0.999431	−	0.0337232i	$-0.0107365\pi$
$348$		0			0
$349$	−2.82236e12			−0.545111			−0.272555	−	0.962140i	$-0.587869\pi$
$349$	−2.82236e12			−0.545111			−0.272555	+	0.962140i	$0.587869\pi$
$350$		0			0
$351$	3.67763e12	−	2.34817e11i	0.690291	−	0.0440752i
$352$		0			0
$353$			7.34646e12i			1.34031i	0.742222	+	0.670154i	$0.233772\pi$
$353$			7.34646e12i			1.34031i	−0.742222	+	0.670154i	$0.766228\pi$
$354$		0			0
$355$	1.19039e12			0.211128
$356$		0			0
$357$	−1.22435e12	−	6.72598e11i	−0.211137	−	0.115988i
$358$		0			0
$359$			1.03382e11i			0.0173369i	0.999962	+	0.00866847i	$0.00275930\pi$
$359$			1.03382e11i			0.0173369i	−0.999962	+	0.00866847i	$0.997241\pi$
$360$		0			0
$361$	4.08403e12			0.666120
$362$		0			0
$363$	−6.98451e12	+	1.27141e13i	−1.10816	+	2.01722i
$364$		0			0
$365$		−	4.78484e11i		−	0.0738589i
$366$		0			0
$367$	1.09343e13			1.64233			0.821167	−	0.570687i	$-0.193323\pi$
$367$	1.09343e13			1.64233			0.821167	+	0.570687i	$0.193323\pi$
$368$		0			0
$369$	−4.72546e10	+	3.00299e10i	−0.00690736	+	0.00438957i
$370$		0			0
$371$			5.68822e12i			0.809295i
$372$		0			0
$373$	−5.57238e12			−0.771785			−0.385893	−	0.922544i	$-0.626107\pi$
$373$	−5.57238e12			−0.771785			−0.385893	+	0.922544i	$0.626107\pi$
$374$		0			0
$375$	−4.87120e12	−	2.67599e12i	−0.656870	−	0.360852i
$376$		0			0
$377$			8.08749e12i			1.06196i
$378$		0			0
$379$	1.34795e13			1.72376			0.861881	−	0.507110i	$-0.169286\pi$
$379$	1.34795e13			1.72376			0.861881	+	0.507110i	$0.169286\pi$
$380$		0			0
$381$	1.04100e11	−	1.89497e11i	0.0129666	−	0.0236036i
$382$		0			0
$383$		−	8.09167e11i		−	0.0981848i	−0.998794	−	0.0490924i	$-0.984367\pi$
$383$		−	8.09167e11i		−	0.0981848i	0.998794	−	0.0490924i	$-0.0156329\pi$
$384$		0			0
$385$	3.85839e12			0.456145
$386$		0			0
$387$	−7.83929e12	−	1.23358e13i	−0.903071	−	1.42106i
$388$		0			0
$389$		−	1.43807e13i		−	1.61448i	−0.590225	−	0.807239i	$-0.700961\pi$
$389$		−	1.43807e13i		−	1.61448i	0.590225	−	0.807239i	$-0.299039\pi$
$390$		0			0
$391$	−4.65486e12			−0.509358
$392$		0			0
$393$	2.24822e12	+	1.23506e12i	0.239815	+	0.131742i
$394$		0			0
$395$			1.45568e11i			0.0151384i
$396$		0			0
$397$	−2.50553e12			−0.254066			−0.127033	−	0.991898i	$-0.540545\pi$
$397$	−2.50553e12			−0.254066			−0.127033	+	0.991898i	$0.540545\pi$
$398$		0			0
$399$	−3.85836e12	+	7.02349e12i	−0.381538	+	0.694526i
$400$		0			0
$401$		−	4.50020e12i		−	0.434021i	−0.976169	−	0.217010i	$-0.930369\pi$
$401$		−	4.50020e12i		−	0.434021i	0.976169	−	0.217010i	$-0.0696305\pi$
$402$		0			0
$403$	−5.94312e12			−0.559099
$404$		0			0
$405$	4.03396e12	+	1.89212e12i	0.370217	+	0.173650i
$406$		0			0
$407$		−	8.71986e12i		−	0.780796i
$408$		0			0
$409$	−4.13779e12			−0.361537			−0.180768	−	0.983526i	$-0.557858\pi$
$409$	−4.13779e12			−0.361537			−0.180768	+	0.983526i	$0.557858\pi$
$410$		0			0
$411$	−8.44626e12	−	4.63995e12i	−0.720203	−	0.395644i
$412$		0			0
$413$			3.70513e12i			0.308357i
$414$		0			0
$415$	−6.27553e12			−0.509812
$416$		0			0
$417$	6.34191e11	−	1.15444e12i	0.0502968	−	0.0915568i
$418$		0			0
$419$			3.33113e12i			0.257941i	0.991648	+	0.128971i	$0.0411673\pi$
$419$			3.33113e12i			0.257941i	−0.991648	+	0.128971i	$0.958833\pi$
$420$		0			0
$421$	1.73199e12			0.130959			0.0654795	−	0.997854i	$-0.479142\pi$
$421$	1.73199e12			0.130959			0.0654795	+	0.997854i	$0.479142\pi$
$422$		0			0
$423$	1.64240e13	−	1.04373e13i	1.21276	−	0.770700i
$424$		0			0
$425$			4.53114e12i			0.326785i
$426$		0			0
$427$	1.08838e13			0.766730
$428$		0			0
$429$	1.60063e13	+	8.79309e12i	1.10155	+	0.605139i
$430$		0			0
$431$		−	8.04274e12i		−	0.540776i	−0.962751	−	0.270388i	$-0.912848\pi$
$431$		−	8.04274e12i		−	0.540776i	0.962751	−	0.270388i	$-0.0871520\pi$
$432$		0			0
$433$	−1.88870e12			−0.124086			−0.0620430	−	0.998073i	$-0.519762\pi$
$433$	−1.88870e12			−0.124086			−0.0620430	+	0.998073i	$0.519762\pi$
$434$		0			0
$435$	−4.70820e12	+	8.57049e12i	−0.302280	+	0.550249i
$436$		0			0
$437$			2.67026e13i			1.67551i
$438$		0			0
$439$	−2.06976e13			−1.26940			−0.634698	−	0.772760i	$-0.718876\pi$
$439$	−2.06976e13			−1.26940			−0.634698	+	0.772760i	$0.718876\pi$
$440$		0			0
$441$	5.57454e12	+	8.77203e12i	0.334208	+	0.525905i
$442$		0			0
$443$		−	2.36413e12i		−	0.138565i	−0.997597	−	0.0692823i	$-0.977929\pi$
$443$		−	2.36413e12i		−	0.138565i	0.997597	−	0.0692823i	$-0.0220709\pi$
$444$		0			0
$445$	−4.19403e12			−0.240343
$446$		0			0
$447$	1.64244e13	+	9.02277e12i	0.920350	+	0.505594i
$448$		0			0
$449$			1.70932e13i			0.936683i	0.883547	+	0.468342i	$0.155148\pi$
$449$			1.70932e13i			0.936683i	−0.883547	+	0.468342i	$0.844852\pi$
$450$		0			0
$451$	−2.77469e11			−0.0148707
$452$		0			0
$453$	8.75362e12	−	1.59345e13i	0.458877	−	0.835309i
$454$		0			0
$455$		−	3.38622e12i		−	0.173644i
$456$		0			0
$457$	−9.29963e12			−0.466536			−0.233268	−	0.972413i	$-0.574942\pi$
$457$	−9.29963e12			−0.466536			−0.233268	+	0.972413i	$0.574942\pi$
$458$		0			0
$459$	−5.09415e11	−	7.97829e12i	−0.0250039	−	0.391603i
$460$		0			0
$461$			7.49894e12i			0.360160i	0.983652	+	0.180080i	$0.0576356\pi$
$461$			7.49894e12i			0.360160i	−0.983652	+	0.180080i	$0.942364\pi$
$462$		0			0
$463$	−1.01227e13			−0.475762			−0.237881	−	0.971294i	$-0.576453\pi$
$463$	−1.01227e13			−0.475762			−0.237881	+	0.971294i	$0.576453\pi$
$464$		0			0
$465$	−6.29805e12	−	3.45984e12i	−0.289695	−	0.159144i
$466$		0			0
$467$		−	3.34480e13i		−	1.50587i	−0.658097	−	0.752933i	$-0.728638\pi$
$467$		−	3.34480e13i		−	1.50587i	0.658097	−	0.752933i	$-0.271362\pi$
$468$		0			0
$469$	3.72672e12			0.164234
$470$		0			0
$471$	2.41884e12	−	4.40310e12i	0.104353	−	0.189956i
$472$		0			0
$473$		−	7.24333e13i		−	3.05938i
$474$		0			0
$475$	2.59929e13			1.07494
$476$		0			0
$477$	−2.74747e13	+	1.74599e13i	−1.11261	+	0.707051i
$478$		0			0
$479$			4.02680e13i			1.59692i	0.602050	+	0.798458i	$0.294351\pi$
$479$			4.02680e13i			1.59692i	−0.602050	+	0.798458i	$0.705649\pi$
$480$		0			0
$481$	−7.65277e12			−0.297230
$482$		0			0
$483$	−1.83597e13	−	1.00859e13i	−0.698440	−	0.383688i
$484$		0			0
$485$		−	3.59072e12i		−	0.133805i
$486$		0			0
$487$	−3.91707e13			−1.42993			−0.714967	−	0.699158i	$-0.753558\pi$
$487$	−3.91707e13			−1.42993			−0.714967	+	0.699158i	$0.753558\pi$
$488$		0			0
$489$	1.12040e13	−	2.03950e13i	0.400708	−	0.729421i
$490$		0			0
$491$			3.39572e13i			1.18994i	0.803749	+	0.594968i	$0.202835\pi$
$491$			3.39572e13i			1.18994i	−0.803749	+	0.594968i	$0.797165\pi$
$492$		0			0
$493$	1.75451e13			0.602450
$494$		0			0
$495$	1.18433e13	+	1.86365e13i	0.398517	+	0.627101i
$496$		0			0
$497$		−	9.61159e12i		−	0.316967i
$498$		0			0
$499$	4.89256e13			1.58137			0.790685	−	0.612224i	$-0.209725\pi$
$499$	4.89256e13			1.58137			0.790685	+	0.612224i	$0.209725\pi$
$500$		0			0
$501$	−3.11979e13	−	1.71386e13i	−0.988408	−	0.542982i
$502$		0			0
$503$			1.19856e13i			0.372237i	0.982527	+	0.186119i	$0.0595909\pi$
$503$			1.19856e13i			0.372237i	−0.982527	+	0.186119i	$0.940409\pi$
$504$		0			0
$505$	1.64740e13			0.501581
$506$		0			0
$507$	−8.41241e12	+	1.53134e13i	−0.251120	+	0.457121i
$508$		0			0
$509$			3.91544e13i			1.14602i	0.819549	+	0.573009i	$0.194224\pi$
$509$			3.91544e13i			1.14602i	−0.819549	+	0.573009i	$0.805776\pi$
$510$		0			0
$511$	−3.86345e12			−0.110884
$512$		0			0
$513$	−4.57674e13	+	2.92226e12i	−1.28816	+	0.0822492i
$514$		0			0
$515$		−	1.93240e13i		−	0.533409i
$516$		0			0
$517$	9.64382e13			2.61094
$518$		0			0
$519$	4.90385e13	+	2.69393e13i	1.30227	+	0.715402i
$520$		0			0
$521$		−	1.47353e13i		−	0.383857i	−0.981409	−	0.191928i	$-0.938526\pi$
$521$		−	1.47353e13i		−	0.383857i	0.981409	−	0.191928i	$-0.0614741\pi$
$522$		0			0
$523$	−1.61321e13			−0.412271			−0.206136	−	0.978523i	$-0.566089\pi$
$523$	−1.61321e13			−0.412271			−0.206136	+	0.978523i	$0.566089\pi$
$524$		0			0
$525$	−9.81780e12	+	1.78717e13i	−0.246160	+	0.448093i
$526$		0			0
$527$			1.28931e13i			0.317178i
$528$		0			0
$529$	−2.83751e13			−0.684950
$530$		0			0
$531$	−1.78962e13	+	1.13729e13i	−0.423924	+	0.269400i
$532$		0			0
$533$			2.43514e11i			0.00566093i
$534$		0			0
$535$	1.68884e13			0.385319
$536$		0			0
$537$	−4.85380e13	−	2.66644e13i	−1.08695	−	0.597118i
$538$		0			0
$539$			5.15075e13i			1.13221i
$540$		0			0
$541$	−4.23894e13			−0.914684			−0.457342	−	0.889291i	$-0.651198\pi$
$541$	−4.23894e13			−0.914684			−0.457342	+	0.889291i	$0.651198\pi$
$542$		0			0
$543$	4.04030e13	−	7.35469e13i	0.855884	−	1.55799i
$544$		0			0
$545$		−	1.78705e12i		−	0.0371667i
$546$		0			0
$547$	−2.46963e13			−0.504308			−0.252154	−	0.967687i	$-0.581139\pi$
$547$	−2.46963e13			−0.504308			−0.252154	+	0.967687i	$0.581139\pi$
$548$		0			0
$549$	3.34078e13	+	5.25701e13i	0.669864	+	1.05409i
$550$		0			0
$551$		−	1.00647e14i		−	1.98173i
$552$		0			0
$553$	1.17537e12			0.0227273
$554$		0			0
$555$	−8.10981e12	−	4.45513e12i	−0.154009	−	0.0846048i
$556$		0			0
$557$		−	4.65465e13i		−	0.868183i	−0.900869	−	0.434091i	$-0.857069\pi$
$557$		−	4.65465e13i		−	0.868183i	0.900869	−	0.434091i	$-0.142931\pi$
$558$		0			0
$559$	−6.35693e13			−1.16463
$560$		0			0
$561$	1.90758e13	−	3.47243e13i	0.343296	−	0.624913i
$562$		0			0
$563$		−	6.01479e13i		−	1.06335i	−0.846947	−	0.531677i	$-0.821562\pi$
$563$		−	6.01479e13i		−	1.06335i	0.846947	−	0.531677i	$-0.178438\pi$
$564$		0			0
$565$	−1.47962e13			−0.256985
$566$		0			0
$567$	1.52777e13	−	3.25716e13i	0.260700	−	0.555807i
$568$		0			0
$569$			3.39778e13i			0.569684i	0.958574	+	0.284842i	$0.0919412\pi$
$569$			3.39778e13i			0.569684i	−0.958574	+	0.284842i	$0.908059\pi$
$570$		0			0
$571$	2.04262e13			0.336517			0.168258	−	0.985743i	$-0.446186\pi$
$571$	2.04262e13			0.336517			0.168258	+	0.985743i	$0.446186\pi$
$572$		0			0
$573$	4.37217e13	+	2.40185e13i	0.707822	+	0.388842i
$574$		0			0
$575$			6.79463e13i			1.08100i
$576$		0			0
$577$	1.57333e13			0.246003			0.123001	−	0.992407i	$-0.460748\pi$
$577$	1.57333e13			0.246003			0.123001	+	0.992407i	$0.460748\pi$
$578$		0			0
$579$	−1.63758e13	+	2.98094e13i	−0.251658	+	0.458101i
$580$		0			0
$581$			5.06708e13i			0.765381i
$582$		0			0
$583$	−1.61326e14			−2.39531
$584$		0			0
$585$	1.63558e13	−	1.03940e13i	0.238722	−	0.151706i
$586$		0			0
$587$			6.45758e13i			0.926572i	0.886209	+	0.463286i	$0.153330\pi$
$587$			6.45758e13i			0.926572i	−0.886209	+	0.463286i	$0.846670\pi$
$588$		0			0
$589$	7.39611e13			1.04334
$590$		0			0
$591$	9.06722e13	+	4.98108e13i	1.25758	+	0.690854i
$592$		0			0
$593$			9.71953e12i			0.132548i	0.997801	+	0.0662738i	$0.0211111\pi$
$593$			9.71953e12i			0.132548i	−0.997801	+	0.0662738i	$0.978889\pi$
$594$		0			0
$595$	−7.34611e12			−0.0985083
$596$		0			0
$597$	−9.74593e12	+	1.77408e13i	−0.128514	+	0.233939i
$598$		0			0
$599$		−	8.73750e13i		−	1.13306i	−0.824041	−	0.566530i	$-0.808285\pi$
$599$		−	8.73750e13i		−	1.13306i	0.824041	−	0.566530i	$-0.191715\pi$
$600$		0			0
$601$	2.77331e13			0.353693			0.176846	−	0.984238i	$-0.443410\pi$
$601$	2.77331e13			0.353693			0.176846	+	0.984238i	$0.443410\pi$
$602$		0			0
$603$	1.14391e13	+	1.80005e13i	0.143485	+	0.225786i
$604$		0			0
$605$			7.62847e13i			0.941154i
$606$		0			0
$607$	9.77365e13			1.18608			0.593039	−	0.805174i	$-0.297928\pi$
$607$	9.77365e13			1.18608			0.593039	+	0.805174i	$0.297928\pi$
$608$		0			0
$609$	6.92012e13	+	3.80157e13i	0.826089	+	0.453812i
$610$		0			0
$611$		−	8.46365e13i		−	0.993921i
$612$		0			0
$613$	−1.41138e14			−1.63058			−0.815288	−	0.579056i	$-0.803421\pi$
$613$	−1.41138e14			−1.63058			−0.815288	+	0.579056i	$0.803421\pi$
$614$		0			0
$615$	−1.41764e11	+	2.58057e11i	−0.00161135	+	0.00293319i
$616$		0			0
$617$			4.85738e13i			0.543220i	0.962407	+	0.271610i	$0.0875561\pi$
$617$			4.85738e13i			0.543220i	−0.962407	+	0.271610i	$0.912444\pi$
$618$		0			0
$619$	3.95021e13			0.434677			0.217339	−	0.976096i	$-0.430262\pi$
$619$	3.95021e13			0.434677			0.217339	+	0.976096i	$0.430262\pi$
$620$		0			0
$621$	−7.63889e12	−	1.19638e14i	−0.0827127	−	1.29542i
$622$		0			0
$623$			3.38641e13i			0.360827i
$624$		0			0
$625$	5.01934e13			0.526316
$626$		0			0
$627$	−1.99196e14	−	1.09428e14i	−2.05562	−	1.12926i
$628$		0			0
$629$			1.66020e13i			0.168619i
$630$		0			0
$631$	−6.04370e13			−0.604166			−0.302083	−	0.953282i	$-0.597682\pi$
$631$	−6.04370e13			−0.604166			−0.302083	+	0.953282i	$0.597682\pi$
$632$		0			0
$633$	−7.23843e13	+	1.31763e14i	−0.712239	+	1.29651i
$634$		0			0
$635$		−	1.13698e12i		−	0.0110125i
$636$		0			0
$637$	4.52043e13			0.431005
$638$		0			0
$639$	4.64250e13	−	2.95027e13i	0.435761	−	0.276922i
$640$		0			0
$641$		−	1.57323e14i		−	1.45379i	−0.686748	−	0.726896i	$-0.740962\pi$
$641$		−	1.57323e14i		−	1.45379i	0.686748	−	0.726896i	$-0.259038\pi$
$642$		0			0
$643$	1.34823e14			1.22662			0.613310	−	0.789843i	$-0.289838\pi$
$643$	1.34823e14			1.22662			0.613310	+	0.789843i	$0.289838\pi$
$644$		0			0
$645$	−6.73658e13	−	3.70074e13i	−0.603449	−	0.331505i
$646$		0			0
$647$		−	4.02182e13i		−	0.354733i	−0.984145	−	0.177366i	$-0.943242\pi$
$647$		−	4.02182e13i		−	0.354733i	0.984145	−	0.177366i	$-0.0567577\pi$
$648$		0			0
$649$	−1.05083e14			−0.912657
$650$		0			0
$651$	−2.79359e13	+	5.08527e13i	−0.238923	+	0.434920i
$652$		0			0
$653$		−	1.56515e14i		−	1.31823i	−0.752044	−	0.659113i	$-0.770932\pi$
$653$		−	1.56515e14i		−	1.31823i	0.752044	−	0.659113i	$-0.229068\pi$
$654$		0			0
$655$	1.34893e13			0.111888
$656$		0			0
$657$	−1.18588e13	−	1.86609e13i	−0.0968755	−	0.152442i
$658$		0			0
$659$		−	4.35191e12i		−	0.0350149i	−0.999847	−	0.0175074i	$-0.994427\pi$
$659$		−	4.35191e12i		−	0.0350149i	0.999847	−	0.0175074i	$-0.00557308\pi$
$660$		0			0
$661$	−2.58433e13			−0.204805			−0.102403	−	0.994743i	$-0.532653\pi$
$661$	−2.58433e13			−0.204805			−0.102403	+	0.994743i	$0.532653\pi$
$662$		0			0
$663$	−3.04750e13	−	1.67414e13i	−0.237890	−	0.130685i
$664$		0			0
$665$			4.21410e13i			0.324038i
$666$		0			0
$667$	2.63096e14			1.99290
$668$		0			0
$669$	9.89261e12	−	1.80078e13i	0.0738211	−	0.134379i
$670$		0			0
$671$			3.08681e14i			2.26933i
$672$		0			0
$673$	9.33181e13			0.675912			0.337956	−	0.941162i	$-0.390264\pi$
$673$	9.33181e13			0.675912			0.337956	+	0.941162i	$0.390264\pi$
$674$		0			0
$675$	−1.16458e14	+	7.43584e12i	−0.831093	+	0.0530654i
$676$		0			0
$677$		−	7.39555e13i		−	0.520029i	−0.965605	−	0.260014i	$-0.916273\pi$
$677$		−	7.39555e13i		−	0.520029i	0.965605	−	0.260014i	$-0.0837273\pi$
$678$		0			0
$679$	−2.89927e13			−0.200882
$680$		0			0
$681$	6.99561e13	+	3.84304e13i	0.477628	+	0.262385i
$682$		0			0
$683$			1.43414e14i			0.964914i	0.875920	+	0.482457i	$0.160256\pi$
$683$			1.43414e14i			0.964914i	−0.875920	+	0.482457i	$0.839744\pi$
$684$		0			0
$685$	−5.06775e13			−0.336018
$686$		0			0
$687$	−1.24568e14	+	2.26754e14i	−0.813995	+	1.48174i
$688$		0			0
$689$			1.41584e14i			0.911837i
$690$		0			0
$691$	4.15781e13			0.263921			0.131961	−	0.991255i	$-0.457873\pi$
$691$	4.15781e13			0.263921			0.131961	+	0.991255i	$0.457873\pi$
$692$		0			0
$693$	1.50477e14	−	9.56270e13i	0.941467	−	0.598294i
$694$		0			0
$695$		−	6.92663e12i		−	0.0427168i
$696$		0			0
$697$	5.28282e11			0.00321146
$698$		0			0
$699$	5.98880e13	+	3.28995e13i	0.358884	+	0.197153i
$700$		0			0
$701$		−	1.23285e14i		−	0.728317i	−0.931337	−	0.364159i	$-0.881357\pi$
$701$		−	1.23285e14i		−	0.728317i	0.931337	−	0.364159i	$-0.118643\pi$
$702$		0			0
$703$	9.52374e13			0.554665
$704$		0			0
$705$	4.92719e13	−	8.96912e13i	0.282914	−	0.514997i
$706$		0			0
$707$		−	1.33017e14i		−	0.753024i
$708$		0			0
$709$	−2.77906e14			−1.55120			−0.775599	−	0.631225i	$-0.782552\pi$
$709$	−2.77906e14			−1.55120			−0.775599	+	0.631225i	$0.782552\pi$
$710$		0			0
$711$	3.60778e12	+	5.67716e12i	0.0198560	+	0.0312452i
$712$		0			0
$713$			1.93337e14i			1.04922i
$714$		0			0
$715$	9.60380e13			0.513941
$716$		0			0
$717$	−1.02531e13	−	5.63255e12i	−0.0541078	−	0.0297241i
$718$		0			0
$719$		−	2.39434e14i		−	1.24607i	−0.782195	−	0.623034i	$-0.785900\pi$
$719$		−	2.39434e14i		−	1.24607i	0.782195	−	0.623034i	$-0.214100\pi$
$720$		0			0
$721$	−1.56029e14			−0.800807
$722$		0			0
$723$	1.28127e14	−	2.33233e14i	0.648557	−	1.18059i
$724$		0			0
$725$		−	2.56103e14i		−	1.27857i
$726$		0			0
$727$	−1.51463e14			−0.745823			−0.372911	−	0.927867i	$-0.621640\pi$
$727$	−1.51463e14			−0.745823			−0.372911	+	0.927867i	$0.621640\pi$
$728$		0			0
$729$	2.04219e14	−	2.61856e13i	0.991879	−	0.127182i
$730$		0			0
$731$			1.37908e14i			0.660697i
$732$		0			0
$733$	−2.37806e14			−1.12384			−0.561918	−	0.827193i	$-0.689936\pi$
$733$	−2.37806e14			−1.12384			−0.561918	+	0.827193i	$0.689936\pi$
$734$		0			0
$735$	4.79040e13	+	2.63161e13i	0.223324	+	0.122683i
$736$		0			0
$737$			1.05695e14i			0.486090i
$738$		0			0
$739$	−3.58451e14			−1.62633			−0.813164	−	0.582035i	$-0.802257\pi$
$739$	−3.58451e14			−1.62633			−0.813164	+	0.582035i	$0.802257\pi$
$740$		0			0
$741$	−9.60371e13	+	1.74820e14i	−0.429881	+	0.782526i
$742$		0			0
$743$		−	2.11655e14i		−	0.934726i	−0.884065	−	0.467363i	$-0.845204\pi$
$743$		−	2.11655e14i		−	0.934726i	0.884065	−	0.467363i	$-0.154796\pi$
$744$		0			0
$745$	9.85466e13			0.429398
$746$		0			0
$747$	−2.44746e14	+	1.55534e14i	−1.05223	+	0.668685i
$748$		0			0
$749$		−	1.36363e14i		−	0.578479i
$750$		0			0
$751$	1.08945e13			0.0456046			0.0228023	−	0.999740i	$-0.492741\pi$
$751$	1.08945e13			0.0456046			0.0228023	+	0.999740i	$0.492741\pi$
$752$		0			0
$753$	2.36080e14	+	1.29690e14i	0.975177	+	0.535714i
$754$		0			0
$755$		−	9.56070e13i		−	0.389722i
$756$		0			0
$757$	3.51497e14			1.41398			0.706989	−	0.707224i	$-0.250053\pi$
$757$	3.51497e14			1.41398			0.706989	+	0.707224i	$0.250053\pi$
$758$		0			0
$759$	2.86050e14	−	5.20706e14i	1.13562	−	2.06721i
$760$		0			0
$761$			3.08205e14i			1.20758i	0.797144	+	0.603790i	$0.206343\pi$
$761$			3.08205e14i			1.20758i	−0.797144	+	0.603790i	$0.793657\pi$
$762$		0			0
$763$	−1.44293e13			−0.0557984
$764$		0			0
$765$	−2.25488e13	−	3.54825e13i	−0.0860630	−	0.135428i
$766$		0			0
$767$			9.22232e13i			0.347427i
$768$		0			0
$769$	−2.78711e14			−1.03639			−0.518194	−	0.855263i	$-0.673395\pi$
$769$	−2.78711e14			−1.03639			−0.518194	+	0.855263i	$0.673395\pi$
$770$		0			0
$771$	1.20739e13	+	6.63281e12i	0.0443176	+	0.0243459i
$772$		0			0
$773$			4.04348e14i			1.46507i	0.680730	+	0.732534i	$0.261663\pi$
$773$			4.04348e14i			1.46507i	−0.680730	+	0.732534i	$0.738337\pi$
$774$		0			0
$775$	1.88198e14			0.673142
$776$		0			0
$777$	−3.59723e13	+	6.54815e13i	−0.127017	+	0.231214i
$778$		0			0
$779$		−	3.03049e12i		−	0.0105639i
$780$		0			0
$781$	2.72598e14			0.938141
$782$		0			0
$783$	2.87925e13	+	4.50938e14i	0.0978295	+	1.53217i
$784$		0			0
$785$		−	2.64186e13i		−	0.0886260i
$786$		0			0
$787$	−1.25181e14			−0.414634			−0.207317	−	0.978274i	$-0.566473\pi$
$787$	−1.25181e14			−0.414634			−0.207317	+	0.978274i	$0.566473\pi$
$788$		0			0
$789$	−2.64970e13	−	1.45562e13i	−0.0866587	−	0.0476060i
$790$		0			0
$791$			1.19469e14i			0.385811i
$792$		0			0
$793$	2.70906e14			0.863879
$794$		0			0
$795$	−8.24242e13	+	1.50039e14i	−0.259549	+	0.472465i
$796$		0			0
$797$			1.24667e14i			0.387668i	0.981034	+	0.193834i	$0.0620923\pi$
$797$			1.24667e14i			0.387668i	−0.981034	+	0.193834i	$0.937908\pi$
$798$		0			0
$799$	−1.83612e14			−0.563853
$800$		0			0
$801$	−1.63567e14	+	1.03946e14i	−0.496060	+	0.315241i
$802$		0			0
$803$		−	1.09573e14i		−	0.328190i
$804$		0			0
$805$	−1.10158e14			−0.325864
$806$		0			0
$807$	−4.56484e14	−	2.50770e14i	−1.33370	−	0.732668i
$808$		0			0
$809$		−	4.18260e14i		−	1.20699i	−0.797366	−	0.603496i	$-0.793774\pi$
$809$		−	4.18260e14i		−	1.20699i	0.797366	−	0.603496i	$-0.206226\pi$
$810$		0			0
$811$	3.92624e14			1.11911			0.559555	−	0.828793i	$-0.310972\pi$
$811$	3.92624e14			1.11911			0.559555	+	0.828793i	$0.310972\pi$
$812$		0			0
$813$	6.26883e13	−	1.14113e14i	0.176495	−	0.321280i
$814$		0			0
$815$		−	1.22370e14i		−	0.340319i
$816$		0			0
$817$	7.91109e14			2.17333
$818$		0			0
$819$	−8.39246e13	−	1.32063e14i	−0.227756	−	0.358394i
$820$		0			0
$821$		−	1.90066e14i		−	0.509553i	−0.967000	−	0.254777i	$-0.917998\pi$
$821$		−	1.90066e14i		−	0.509553i	0.967000	−	0.254777i	$-0.0820020\pi$
$822$		0			0
$823$	−2.02565e14			−0.536495			−0.268248	−	0.963350i	$-0.586445\pi$
$823$	−2.02565e14			−0.536495			−0.268248	+	0.963350i	$0.586445\pi$
$824$		0			0
$825$	−5.06865e14	−	2.78447e14i	−1.32624	−	0.728572i
$826$		0			0
$827$			1.20987e14i			0.312759i	0.987697	+	0.156380i	$0.0499823\pi$
$827$			1.20987e14i			0.312759i	−0.987697	+	0.156380i	$0.950018\pi$
$828$		0			0
$829$	−2.34411e14			−0.598694			−0.299347	−	0.954144i	$-0.596769\pi$
$829$	−2.34411e14			−0.598694			−0.299347	+	0.954144i	$0.596769\pi$
$830$		0			0
$831$	1.37513e14	−	2.50320e14i	0.347008	−	0.631671i
$832$		0			0
$833$		−	9.80668e13i		−	0.244510i
$834$		0			0
$835$	−1.87187e14			−0.461151
$836$		0			0
$837$	−3.31373e14	+	2.11582e13i	−0.806659	+	0.0515053i
$838$		0			0
$839$		−	5.13382e14i		−	1.23490i	−0.786611	−	0.617449i	$-0.788166\pi$
$839$		−	5.13382e14i		−	1.23490i	0.786611	−	0.617449i	$-0.211834\pi$
$840$		0			0
$841$	−5.70953e14			−1.35713
$842$		0			0
$843$	4.24514e14	+	2.33207e14i	0.997135	+	0.547777i
$844$		0			0
$845$			9.18803e13i			0.213274i
$846$		0			0
$847$	6.15950e14			1.41295
$848$		0			0
$849$	−1.65610e14	+	3.01465e14i	−0.375446	+	0.683437i
$850$		0			0
$851$			2.48954e14i			0.557791i
$852$		0			0
$853$	3.95975e14			0.876844			0.438422	−	0.898769i	$-0.355538\pi$
$853$	3.95975e14			0.876844			0.438422	+	0.898769i	$0.355538\pi$
$854$		0			0
$855$	−2.03545e14	+	1.29351e14i	−0.445483	+	0.283100i
$856$		0			0
$857$		−	2.33139e13i		−	0.0504326i	−0.999682	−	0.0252163i	$-0.991973\pi$
$857$		−	2.33139e13i		−	0.0504326i	0.999682	−	0.0252163i	$-0.00802745\pi$
$858$		0			0
$859$	−4.78130e14			−1.02230			−0.511152	−	0.859490i	$-0.670781\pi$
$859$	−4.78130e14			−1.02230			−0.511152	+	0.859490i	$0.670781\pi$
$860$		0			0
$861$	2.08364e12	+	1.14465e12i	0.00440360	+	0.00241912i
$862$		0			0
$863$			8.30319e14i			1.73457i	0.497815	+	0.867283i	$0.334136\pi$
$863$			8.30319e14i			1.73457i	−0.497815	+	0.867283i	$0.665864\pi$
$864$		0			0
$865$	2.94231e14			0.607587
$866$		0			0
$867$	1.99552e14	−	3.63251e14i	0.407344	−	0.741501i
$868$		0			0
$869$			3.33351e13i			0.0672672i
$870$		0			0
$871$	9.27606e13			0.185043
$872$		0			0
$873$	−8.89929e13	−	1.40038e14i	−0.175503	−	0.276169i
$874$		0			0
$875$			2.35991e14i			0.460102i
$876$		0			0
$877$	7.06641e13			0.136207			0.0681037	−	0.997678i	$-0.478305\pi$
$877$	7.06641e13			0.136207			0.0681037	+	0.997678i	$0.478305\pi$
$878$		0			0
$879$	7.20384e14	+	3.95743e14i	1.37284	+	0.754169i
$880$		0			0
$881$		−	7.25515e14i		−	1.36699i	−0.729953	−	0.683497i	$-0.760458\pi$
$881$		−	7.25515e14i		−	1.36699i	0.729953	−	0.683497i	$-0.239542\pi$
$882$		0			0
$883$	−1.22030e14			−0.227334			−0.113667	−	0.993519i	$-0.536260\pi$
$883$	−1.22030e14			−0.227334			−0.113667	+	0.993519i	$0.536260\pi$
$884$		0			0
$885$	−5.36885e13	+	9.77310e13i	−0.0988929	+	0.180018i
$886$		0			0
$887$			1.77377e14i			0.323056i	0.986868	+	0.161528i	$0.0516423\pi$
$887$			1.77377e14i			0.323056i	−0.986868	+	0.161528i	$0.948358\pi$
$888$		0			0
$889$	−9.18041e12			−0.0165331
$890$		0			0
$891$	9.23778e14	+	4.33296e14i	1.64505	+	0.771607i
$892$		0			0
$893$			1.05329e15i			1.85477i
$894$		0			0
$895$	−2.91228e14			−0.507129
$896$		0			0
$897$	−4.56984e14	−	2.51045e14i	−0.786936	−	0.432303i
$898$		0			0
$899$		−	7.28724e14i		−	1.24098i
$900$		0			0
$901$	3.07153e14			0.517287
$902$		0			0
$903$	−2.98811e14	+	5.43935e14i	−0.497689	+	0.905959i
$904$		0			0
$905$		−	4.41282e14i		−	0.726897i
$906$		0			0
$907$	−3.42190e14			−0.557482			−0.278741	−	0.960366i	$-0.589917\pi$
$907$	−3.42190e14			−0.557482			−0.278741	+	0.960366i	$0.589917\pi$
$908$		0			0
$909$	6.42485e14	−	4.08293e14i	1.03525	−	0.657889i
$910$		0			0
$911$			5.94239e14i			0.947043i	0.880782	+	0.473521i	$0.157017\pi$
$911$			5.94239e14i			0.947043i	−0.880782	+	0.473521i	$0.842983\pi$
$912$		0			0
$913$	−1.43710e15			−2.26533
$914$		0			0
$915$	2.87085e14	+	1.57710e14i	0.447616	+	0.245898i
$916$		0			0
$917$		−	1.08918e14i		−	0.167978i
$918$		0			0
$919$	−6.28087e14			−0.958170			−0.479085	−	0.877769i	$-0.659031\pi$
$919$	−6.28087e14			−0.958170			−0.479085	+	0.877769i	$0.659031\pi$
$920$		0			0
$921$	3.18789e14	−	5.80302e14i	0.481067	−	0.875701i
$922$		0			0
$923$		−	2.39239e14i		−	0.357128i
$924$		0			0
$925$	2.42337e14			0.357858
$926$		0			0
$927$	−4.78928e14	−	7.53635e14i	−0.699635	−	1.10094i
$928$		0			0
$929$		−	1.36253e14i		−	0.196910i	−0.995141	−	0.0984551i	$-0.968610\pi$
$929$		−	1.36253e14i		−	0.196910i	0.995141	−	0.0984551i	$-0.0313901\pi$
$930$		0			0
$931$	−5.62560e14			−0.804304
$932$		0			0
$933$	4.47145e14	+	2.45639e14i	0.632471	+	0.347448i
$934$		0			0
$935$		−	2.08346e14i		−	0.291560i
$936$		0			0
$937$	6.59993e14			0.913780			0.456890	−	0.889523i	$-0.348963\pi$
$937$	6.59993e14			0.913780			0.456890	+	0.889523i	$0.348963\pi$
$938$		0			0
$939$	2.52423e14	−	4.59494e14i	0.345781	−	0.629436i
$940$		0			0
$941$		−	6.64694e14i		−	0.900894i	−0.892803	−	0.450447i	$-0.851265\pi$
$941$		−	6.64694e14i		−	0.900894i	0.892803	−	0.450447i	$-0.148735\pi$
$942$		0			0
$943$	7.92181e12			0.0106235
$944$		0			0
$945$	−1.20554e13	−	1.88807e14i	−0.0159964	−	0.250530i
$946$		0			0
$947$		−	7.98687e14i		−	1.04864i	−0.851521	−	0.524320i	$-0.824319\pi$
$947$		−	7.98687e14i		−	1.04864i	0.851521	−	0.524320i	$-0.175681\pi$
$948$		0			0
$949$	−9.61638e13			−0.124934
$950$		0			0
$951$	−5.37372e14	−	2.95205e14i	−0.690832	−	0.379509i
$952$		0			0
$953$		−	1.82292e14i		−	0.231901i	−0.993255	−	0.115950i	$-0.963009\pi$
$953$		−	1.82292e14i		−	0.231901i	0.993255	−	0.115950i	$-0.0369914\pi$
$954$		0			0
$955$	2.62330e14			0.330242
$956$		0			0
$957$	−1.07818e15	+	1.96264e15i	−1.34317	+	2.44501i
$958$		0			0
$959$			4.09188e14i			0.504464i
$960$		0			0
$961$	−2.84123e14			−0.346648
$962$		0			0
$963$	6.58648e14	−	4.18565e14i	0.795284	−	0.505396i
$964$		0			0
$965$			1.78857e14i			0.213732i
$966$		0			0
$967$	1.13273e15			1.33965			0.669826	−	0.742518i	$-0.266369\pi$
$967$	1.13273e15			1.33965			0.669826	+	0.742518i	$0.266369\pi$
$968$		0			0
$969$	3.79256e14	+	2.08344e14i	0.443929	+	0.243872i
$970$		0			0
$971$			9.18843e14i			1.06450i	0.846588	+	0.532249i	$0.178653\pi$
$971$			9.18843e14i			1.06450i	−0.846588	+	0.532249i	$0.821347\pi$
$972$		0			0
$973$	−5.59281e13			−0.0641307
$974$		0			0
$975$	−2.44372e14	+	4.44838e14i	−0.277350	+	0.504869i
$976$		0			0
$977$			1.73004e15i			1.94350i	0.236017	+	0.971749i	$0.424158\pi$
$977$			1.73004e15i			1.94350i	−0.236017	+	0.971749i	$0.575842\pi$
$978$		0			0
$979$	−9.60433e14			−1.06796
$980$		0			0
$981$	−4.42905e13	−	6.96950e13i	−0.0487490	−	0.0767108i
$982$		0			0
$983$		−	1.29362e15i		−	1.40941i	−0.709498	−	0.704707i	$-0.751078\pi$
$983$		−	1.29362e15i		−	1.40941i	0.709498	−	0.704707i	$-0.248922\pi$
$984$		0			0
$985$	5.44033e14			0.586738
$986$		0			0
$987$	−7.24199e14	−	3.97839e14i	−0.773165	−	0.424738i
$988$		0			0
$989$			2.06799e15i			2.18558i
$990$		0			0
$991$	1.43410e15			1.50041			0.750206	−	0.661205i	$-0.229954\pi$
$991$	1.43410e15			1.50041			0.750206	+	0.661205i	$0.229954\pi$
$992$		0			0
$993$	2.61385e14	−	4.75808e14i	0.270729	−	0.492817i
$994$		0			0
$995$			1.06445e14i			0.109146i
$996$		0			0
$997$	1.70539e15			1.73120			0.865600	−	0.500736i	$-0.166937\pi$
$997$	1.70539e15			1.73120			0.865600	+	0.500736i	$0.166937\pi$
$998$		0			0
$999$	−4.26699e14	+	2.72448e13i	−0.428839	+	0.0273814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.11.c.b.5.1	✓	2
3.2	odd	2	inner	12.11.c.b.5.2	yes	2
4.3	odd	2		48.11.e.b.17.2		2
5.2	odd	4		300.11.b.c.149.1		4
5.3	odd	4		300.11.b.c.149.4		4
5.4	even	2		300.11.g.d.101.2		2
8.3	odd	2		192.11.e.f.65.1		2
8.5	even	2		192.11.e.c.65.2		2
9.2	odd	6		324.11.g.d.53.1		4
9.4	even	3		324.11.g.d.269.1		4
9.5	odd	6		324.11.g.d.269.2		4
9.7	even	3		324.11.g.d.53.2		4
12.11	even	2		48.11.e.b.17.1		2
15.2	even	4		300.11.b.c.149.3		4
15.8	even	4		300.11.b.c.149.2		4
15.14	odd	2		300.11.g.d.101.1		2
24.5	odd	2		192.11.e.c.65.1		2
24.11	even	2		192.11.e.f.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.11.c.b.5.1	✓	2	1.1	even	1	trivial
12.11.c.b.5.2	yes	2	3.2	odd	2	inner
48.11.e.b.17.1		2	12.11	even	2
48.11.e.b.17.2		2	4.3	odd	2
192.11.e.c.65.1		2	24.5	odd	2
192.11.e.c.65.2		2	8.5	even	2
192.11.e.f.65.1		2	8.3	odd	2
192.11.e.f.65.2		2	24.11	even	2
300.11.b.c.149.1		4	5.2	odd	4
300.11.b.c.149.2		4	15.8	even	4
300.11.b.c.149.3		4	15.2	even	4
300.11.b.c.149.4		4	5.3	odd	4
300.11.g.d.101.1		2	15.14	odd	2
300.11.g.d.101.2		2	5.4	even	2
324.11.g.d.53.1		4	9.2	odd	6
324.11.g.d.53.2		4	9.7	even	3
324.11.g.d.269.1		4	9.4	even	3
324.11.g.d.269.2		4	9.5	odd	6

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	12.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(117.000 - 212.979i) q^{3} -1277.87i q^{5} -10318.0 q^{7} +(-31671.0 - 49837.1i) q^{9} +O(q^{10})\)	\(q+(117.000 - 212.979i) q^{3} -1277.87i q^{5} -10318.0 q^{7} +(-31671.0 - 49837.1i) q^{9} -292633. i q^{11} -256822. q^{13} +(-272160. - 149511. i) q^{15} +557153. i q^{17} +3.19611e6 q^{19} +(-1.20721e6 + 2.19752e6i) q^{21} +8.35474e6i q^{23} +8.13267e6 q^{25} +(-1.43197e7 + 914318. i) q^{27} -3.14906e7i q^{29} +2.31410e7 q^{31} +(-6.23246e7 - 3.42381e7i) q^{33} +1.31851e7i q^{35} +2.97979e7 q^{37} +(-3.00482e7 + 5.46977e7i) q^{39} -948182. i q^{41} +2.47523e8 q^{43} +(-6.36854e7 + 4.04715e7i) q^{45} +3.29553e8i q^{47} -1.76014e8 q^{49} +(1.18662e8 + 6.51869e7i) q^{51} -5.51291e8i q^{53} -3.73948e8 q^{55} +(3.73944e8 - 6.80703e8i) q^{57} -3.59094e8i q^{59} -1.05484e9 q^{61} +(3.26781e8 + 5.14219e8i) q^{63} +3.28186e8i q^{65} -3.61186e8 q^{67} +(1.77938e9 + 9.77504e8i) q^{69} +9.31536e8i q^{71} +3.74437e8 q^{73} +(9.51522e8 - 1.73209e9i) q^{75} +3.01939e9i q^{77} -1.13914e8 q^{79} +(-1.48068e9 + 3.15678e9i) q^{81} -4.91092e9i q^{83} +7.11971e8 q^{85} +(-6.70684e9 - 3.68440e9i) q^{87} -3.28204e9i q^{89} +2.64989e9 q^{91} +(2.70750e9 - 4.92854e9i) q^{93} -4.08422e9i q^{95} +2.80992e9 q^{97} +(-1.45840e10 + 9.26798e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 234 q^{3} - 20636 q^{7} - 63342 q^{9}+O(q^{10}) \) 2 * q + 234 * q^3 - 20636 * q^7 - 63342 * q^9	\( 2 q + 234 q^{3} - 20636 q^{7} - 63342 q^{9} - 513644 q^{13} - 544320 q^{15} + 6392212 q^{19} - 2414412 q^{21} + 16265330 q^{25} - 28639494 q^{27} + 46281988 q^{31} - 124649280 q^{33} + 59595892 q^{37} - 60096348 q^{39} + 495045556 q^{43} - 127370880 q^{45} - 352028250 q^{49} + 237323520 q^{51} - 747895680 q^{55} + 747888804 q^{57} - 2109679532 q^{61} + 653562756 q^{63} - 722372396 q^{67} + 3558764160 q^{69} + 748874788 q^{73} + 1903043610 q^{75} - 227828924 q^{79} - 2961359838 q^{81} + 1423941120 q^{85} - 13413677760 q^{87} + 5299778792 q^{91} + 5414992596 q^{93} + 5619834244 q^{97} - 29167931520 q^{99}+O(q^{100}) \) 2 * q + 234 * q^3 - 20636 * q^7 - 63342 * q^9 - 513644 * q^13 - 544320 * q^15 + 6392212 * q^19 - 2414412 * q^21 + 16265330 * q^25 - 28639494 * q^27 + 46281988 * q^31 - 124649280 * q^33 + 59595892 * q^37 - 60096348 * q^39 + 495045556 * q^43 - 127370880 * q^45 - 352028250 * q^49 + 237323520 * q^51 - 747895680 * q^55 + 747888804 * q^57 - 2109679532 * q^61 + 653562756 * q^63 - 722372396 * q^67 + 3558764160 * q^69 + 748874788 * q^73 + 1903043610 * q^75 - 227828924 * q^79 - 2961359838 * q^81 + 1423941120 * q^85 - 13413677760 * q^87 + 5299778792 * q^91 + 5414992596 * q^93 + 5619834244 * q^97 - 29167931520 * q^99

Introduction

L-functions

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