LMFDB - Embedded newform 12.9.c.b.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,9,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, 9, names="a")

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

chi := DirichletCharacter("12.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
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:	$4.88854332073$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-110}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 110 $ x^2 + 110
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.2
Root			$10.4881i$ of defining polynomial
Character	$\chi$	$=$	12.5
Dual form			12.9.c.b.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-51.0000 + 62.9285i) q^{3} -1132.71i q^{5} -3094.00 q^{7} +(-1359.00 - 6418.71i) q^{9} +O(q^{10})$	\(q+(-51.0000 + 62.9285i) q^{3} -1132.71i q^{5} -3094.00 q^{7} +(-1359.00 - 6418.71i) q^{9} -1132.71i q^{11} -7294.00 q^{13} +(71280.0 + 57768.4i) q^{15} +58901.1i q^{17} -80326.0 q^{19} +(157794. - 194701. i) q^{21} -97413.4i q^{23} -892415. q^{25} +(473229. + 241834. i) q^{27} -864260. i q^{29} +435914. q^{31} +(71280.0 + 57768.4i) q^{33} +3.50462e6i q^{35} +1.15930e6 q^{37} +(371994. - 459001. i) q^{39} -2.71625e6i q^{41} +990266. q^{43} +(-7.27056e6 + 1.53936e6i) q^{45} -6.70113e6i q^{47} +3.80804e6 q^{49} +(-3.70656e6 - 3.00396e6i) q^{51} +1.00710e7i q^{53} -1.28304e6 q^{55} +(4.09663e6 - 5.05480e6i) q^{57} +1.59826e6i q^{59} +1.93692e7 q^{61} +(4.20475e6 + 1.98595e7i) q^{63} +8.26201e6i q^{65} -2.80243e7 q^{67} +(6.13008e6 + 4.96808e6i) q^{69} -3.36575e7i q^{71} -2.52301e7 q^{73} +(4.55132e7 - 5.61584e7i) q^{75} +3.50462e6i q^{77} -6.34014e7 q^{79} +(-3.93530e7 + 1.74461e7i) q^{81} +4.75434e7i q^{83} +6.67181e7 q^{85} +(5.43866e7 + 4.40773e7i) q^{87} -7.82954e7i q^{89} +2.25676e7 q^{91} +(-2.22316e7 + 2.74314e7i) q^{93} +9.09863e7i q^{95} +1.95503e7 q^{97} +(-7.27056e6 + 1.53936e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 102 q^{3} - 6188 q^{7} - 2718 q^{9}+O(q^{10}) $ 2 * q - 102 * q^3 - 6188 * q^7 - 2718 * q^9	$ 2 q - 102 q^{3} - 6188 q^{7} - 2718 q^{9} - 14588 q^{13} + 142560 q^{15} - 160652 q^{19} + 315588 q^{21} - 1784830 q^{25} + 946458 q^{27} + 871828 q^{31} + 142560 q^{33} + 2318596 q^{37} + 743988 q^{39} + 1980532 q^{43} - 14541120 q^{45} + 7616070 q^{49} - 7413120 q^{51} - 2566080 q^{55} + 8193252 q^{57} + 38738308 q^{61} + 8409492 q^{63} - 56048588 q^{67} + 12260160 q^{69} - 50460284 q^{73} + 91026330 q^{75} - 126802796 q^{79} - 78705918 q^{81} + 133436160 q^{85} + 108773280 q^{87} + 45135272 q^{91} - 44463228 q^{93} + 39100612 q^{97} - 14541120 q^{99}+O(q^{100}) $ 2 * q - 102 * q^3 - 6188 * q^7 - 2718 * q^9 - 14588 * q^13 + 142560 * q^15 - 160652 * q^19 + 315588 * q^21 - 1784830 * q^25 + 946458 * q^27 + 871828 * q^31 + 142560 * q^33 + 2318596 * q^37 + 743988 * q^39 + 1980532 * q^43 - 14541120 * q^45 + 7616070 * q^49 - 7413120 * q^51 - 2566080 * q^55 + 8193252 * q^57 + 38738308 * q^61 + 8409492 * q^63 - 56048588 * q^67 + 12260160 * q^69 - 50460284 * q^73 + 91026330 * q^75 - 126802796 * q^79 - 78705918 * q^81 + 133436160 * q^85 + 108773280 * q^87 + 45135272 * q^91 - 44463228 * q^93 + 39100612 * q^97 - 14541120 * 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
$3$	−51.0000	+	62.9285i	−0.629630	+	0.776895i
$3$	−51.0000	+	62.9285i	−0.629630	+	0.776895i
$4$		0			0
$5$		−	1132.71i		−	1.81234i	−0.422912	−	0.906171i	$-0.638992\pi$
$5$		−	1132.71i		−	1.81234i	0.422912	−	0.906171i	$-0.361008\pi$
$6$		0			0
$7$	−3094.00			−1.28863			−0.644315	−	0.764760i	$-0.722857\pi$
$7$	−3094.00			−1.28863			−0.644315	+	0.764760i	$0.722857\pi$
$8$		0			0
$9$	−1359.00	−	6418.71i	−0.207133	−	0.978313i
$10$		0			0
$11$		−	1132.71i		−	0.0773659i	−0.999252	−	0.0386829i	$-0.987684\pi$
$11$		−	1132.71i		−	0.0773659i	0.999252	−	0.0386829i	$-0.0123162\pi$
$12$		0			0
$13$	−7294.00			−0.255383			−0.127692	−	0.991814i	$-0.540757\pi$
$13$	−7294.00			−0.255383			−0.127692	+	0.991814i	$0.540757\pi$
$14$		0			0
$15$	71280.0	+	57768.4i	1.40800	+	1.14110i
$16$		0			0
$17$			58901.1i			0.705225i	0.935769	+	0.352613i	$0.114707\pi$
$17$			58901.1i			0.705225i	−0.935769	+	0.352613i	$0.885293\pi$
$18$		0			0
$19$	−80326.0			−0.616370			−0.308185	−	0.951326i	$-0.599722\pi$
$19$	−80326.0			−0.616370			−0.308185	+	0.951326i	$0.599722\pi$
$20$		0			0
$21$	157794.	−	194701.i	0.811359	−	1.00113i
$22$		0			0
$23$		−	97413.4i		−	0.348103i	−0.984737	−	0.174051i	$-0.944314\pi$
$23$		−	97413.4i		−	0.348103i	0.984737	−	0.174051i	$-0.0556858\pi$
$24$		0			0
$25$	−892415.			−2.28458
$26$		0			0
$27$	473229.	+	241834.i	0.890464	+	0.455054i
$28$		0			0
$29$		−	864260.i		−	1.22195i	−0.791651	−	0.610974i	$-0.790778\pi$
$29$		−	864260.i		−	1.22195i	0.791651	−	0.610974i	$-0.209222\pi$
$30$		0			0
$31$	435914.			0.472013			0.236007	−	0.971751i	$-0.424161\pi$
$31$	435914.			0.472013			0.236007	+	0.971751i	$0.424161\pi$
$32$		0			0
$33$	71280.0	+	57768.4i	0.0601052	+	0.0487118i
$34$		0			0
$35$			3.50462e6i			2.33544i
$36$		0			0
$37$	1.15930e6			0.618569			0.309285	−	0.950970i	$-0.399910\pi$
$37$	1.15930e6			0.618569			0.309285	+	0.950970i	$0.399910\pi$
$38$		0			0
$39$	371994.	−	459001.i	0.160797	−	0.198406i
$40$		0			0
$41$		−	2.71625e6i		−	0.961244i	−0.876928	−	0.480622i	$-0.840411\pi$
$41$		−	2.71625e6i		−	0.961244i	0.876928	−	0.480622i	$-0.159589\pi$
$42$		0			0
$43$	990266.			0.289653			0.144827	−	0.989457i	$-0.453738\pi$
$43$	990266.			0.289653			0.144827	+	0.989457i	$0.453738\pi$
$44$		0			0
$45$	−7.27056e6	+	1.53936e6i	−1.77304	+	0.375396i
$46$		0			0
$47$		−	6.70113e6i		−	1.37327i	−0.727001	−	0.686636i	$-0.759086\pi$
$47$		−	6.70113e6i		−	1.37327i	0.727001	−	0.686636i	$-0.240914\pi$
$48$		0			0
$49$	3.80804e6			0.660567
$50$		0			0
$51$	−3.70656e6	−	3.00396e6i	−0.547886	−	0.444031i
$52$		0			0
$53$			1.00710e7i			1.27634i	0.769894	+	0.638171i	$0.220309\pi$
$53$			1.00710e7i			1.27634i	−0.769894	+	0.638171i	$0.779691\pi$
$54$		0			0
$55$	−1.28304e6			−0.140213
$56$		0			0
$57$	4.09663e6	−	5.05480e6i	0.388085	−	0.478855i
$58$		0			0
$59$			1.59826e6i			0.131898i	0.997823	+	0.0659491i	$0.0210075\pi$
$59$			1.59826e6i			0.131898i	−0.997823	+	0.0659491i	$0.978992\pi$
$60$		0			0
$61$	1.93692e7			1.39891			0.699457	−	0.714674i	$-0.253425\pi$
$61$	1.93692e7			1.39891			0.699457	+	0.714674i	$0.253425\pi$
$62$		0			0
$63$	4.20475e6	+	1.98595e7i	0.266918	+	1.26068i
$64$		0			0
$65$			8.26201e6i			0.462842i
$66$		0			0
$67$	−2.80243e7			−1.39071			−0.695353	−	0.718668i	$-0.744752\pi$
$67$	−2.80243e7			−1.39071			−0.695353	+	0.718668i	$0.744752\pi$
$68$		0			0
$69$	6.13008e6	+	4.96808e6i	0.270439	+	0.219176i
$70$		0			0
$71$		−	3.36575e7i		−	1.32449i	−0.749289	−	0.662244i	$-0.769604\pi$
$71$		−	3.36575e7i		−	1.32449i	0.749289	−	0.662244i	$-0.230396\pi$
$72$		0			0
$73$	−2.52301e7			−0.888440			−0.444220	−	0.895918i	$-0.646519\pi$
$73$	−2.52301e7			−0.888440			−0.444220	+	0.895918i	$0.646519\pi$
$74$		0			0
$75$	4.55132e7	−	5.61584e7i	1.43844	−	1.77488i
$76$		0			0
$77$			3.50462e6i			0.0996959i
$78$		0			0
$79$	−6.34014e7			−1.62776			−0.813880	−	0.581033i	$-0.802649\pi$
$79$	−6.34014e7			−1.62776			−0.813880	+	0.581033i	$0.802649\pi$
$80$		0			0
$81$	−3.93530e7	+	1.74461e7i	−0.914192	+	0.405282i
$82$		0			0
$83$			4.75434e7i			1.00179i	0.865507	+	0.500896i	$0.166996\pi$
$83$			4.75434e7i			1.00179i	−0.865507	+	0.500896i	$0.833004\pi$
$84$		0			0
$85$	6.67181e7			1.27811
$86$		0			0
$87$	5.43866e7	+	4.40773e7i	0.949326	+	0.769375i
$88$		0			0
$89$		−	7.82954e7i		−	1.24789i	−0.781468	−	0.623945i	$-0.785529\pi$
$89$		−	7.82954e7i		−	1.24789i	0.781468	−	0.623945i	$-0.214471\pi$
$90$		0			0
$91$	2.25676e7			0.329094
$92$		0			0
$93$	−2.22316e7	+	2.74314e7i	−0.297193	+	0.366705i
$94$		0			0
$95$			9.09863e7i			1.11707i
$96$		0			0
$97$	1.95503e7			0.220834			0.110417	−	0.993885i	$-0.464781\pi$
$97$	1.95503e7			0.220834			0.110417	+	0.993885i	$0.464781\pi$
$98$		0			0
$99$	−7.27056e6	+	1.53936e6i	−0.0756880	+	0.0160250i
$100$		0			0
$101$			4.38847e7i			0.421724i	0.977516	+	0.210862i	$0.0676270\pi$
$101$			4.38847e7i			0.421724i	−0.977516	+	0.210862i	$0.932373\pi$
$102$		0			0
$103$	1.13498e8			1.00841			0.504207	−	0.863583i	$-0.331785\pi$
$103$	1.13498e8			1.00841			0.504207	+	0.863583i	$0.331785\pi$
$104$		0			0
$105$	−2.20540e8	−	1.78735e8i	−1.81439	−	1.47046i
$106$		0			0
$107$		−	5.49966e7i		−	0.419567i	−0.977748	−	0.209783i	$-0.932724\pi$
$107$		−	5.49966e7i		−	0.419567i	0.977748	−	0.209783i	$-0.0672759\pi$
$108$		0			0
$109$	1.74355e6			0.0123518			0.00617589	−	0.999981i	$-0.498034\pi$
$109$	1.74355e6			0.0123518			0.00617589	+	0.999981i	$0.498034\pi$
$110$		0			0
$111$	−5.91242e7	+	7.29529e7i	−0.389469	+	0.480563i
$112$		0			0
$113$		−	1.94469e8i		−	1.19271i	−0.802720	−	0.596357i	$-0.796614\pi$
$113$		−	1.94469e8i		−	1.19271i	0.802720	−	0.596357i	$-0.203386\pi$
$114$		0			0
$115$	−1.10341e8			−0.630881
$116$		0			0
$117$	9.91255e6	+	4.68181e7i	0.0528983	+	0.249845i
$118$		0			0
$119$		−	1.82240e8i		−	0.908774i
$120$		0			0
$121$	2.13076e8			0.994015
$122$		0			0
$123$	1.70929e8	+	1.38529e8i	0.746786	+	0.605228i
$124$		0			0
$125$			5.68384e8i			2.32810i
$126$		0			0
$127$	−1.77121e8			−0.680854			−0.340427	−	0.940271i	$-0.610572\pi$
$127$	−1.77121e8			−0.680854			−0.340427	+	0.940271i	$0.610572\pi$
$128$		0			0
$129$	−5.05036e7	+	6.23160e7i	−0.182374	+	0.225030i
$130$		0			0
$131$			1.31133e8i			0.445274i	0.974901	+	0.222637i	$0.0714664\pi$
$131$			1.31133e8i			0.445274i	−0.974901	+	0.222637i	$0.928534\pi$
$132$		0			0
$133$	2.48529e8			0.794273
$134$		0			0
$135$	2.73929e8	−	5.36033e8i	0.824713	−	1.61382i
$136$		0			0
$137$		−	1.76348e8i		−	0.500596i	−0.968169	−	0.250298i	$-0.919471\pi$
$137$		−	1.76348e8i		−	0.500596i	0.968169	−	0.250298i	$-0.0805286\pi$
$138$		0			0
$139$	−2.32285e8			−0.622245			−0.311123	−	0.950370i	$-0.600705\pi$
$139$	−2.32285e8			−0.622245			−0.311123	+	0.950370i	$0.600705\pi$
$140$		0			0
$141$	4.21692e8	+	3.41758e8i	1.06689	+	0.864653i
$142$		0			0
$143$			8.26201e6i			0.0197579i
$144$		0			0
$145$	−9.78960e8			−2.21459
$146$		0			0
$147$	−1.94210e8	+	2.39634e8i	−0.415912	+	0.513191i
$148$		0			0
$149$		−	5.85329e8i		−	1.18756i	−0.804628	−	0.593779i	$-0.797635\pi$
$149$		−	5.85329e8i		−	1.18756i	0.804628	−	0.593779i	$-0.202365\pi$
$150$		0			0
$151$	−4.17368e8			−0.802808			−0.401404	−	0.915901i	$-0.631478\pi$
$151$	−4.17368e8			−0.802808			−0.401404	+	0.915901i	$0.631478\pi$
$152$		0			0
$153$	3.78069e8	−	8.00466e7i	0.689931	−	0.146075i
$154$		0			0
$155$		−	4.93766e8i		−	0.855449i
$156$		0			0
$157$	8.18571e8			1.34728			0.673640	−	0.739060i	$-0.264730\pi$
$157$	8.18571e8			1.34728			0.673640	+	0.739060i	$0.264730\pi$
$158$		0			0
$159$	−6.33750e8	−	5.13619e8i	−0.991585	−	0.803623i
$160$		0			0
$161$			3.01397e8i			0.448575i
$162$		0			0
$163$	3.18429e8			0.451088			0.225544	−	0.974233i	$-0.427584\pi$
$163$	3.18429e8			0.451088			0.225544	+	0.974233i	$0.427584\pi$
$164$		0			0
$165$	6.54350e7	−	8.07398e7i	0.0882825	−	0.108931i
$166$		0			0
$167$			1.16043e9i			1.49195i	0.665976	+	0.745974i	$0.268016\pi$
$167$			1.16043e9i			1.49195i	−0.665976	+	0.745974i	$0.731984\pi$
$168$		0			0
$169$	−7.62528e8			−0.934779
$170$		0			0
$171$	1.09163e8	+	5.15589e8i	0.127671	+	0.603003i
$172$		0			0
$173$			1.41652e9i			1.58139i	0.612213	+	0.790693i	$0.290279\pi$
$173$			1.41652e9i			1.58139i	−0.612213	+	0.790693i	$0.709721\pi$
$174$		0			0
$175$	2.76113e9			2.94398
$176$		0			0
$177$	−1.00576e8	−	8.15112e7i	−0.102471	−	0.0830471i
$178$		0			0
$179$		−	1.56828e9i		−	1.52760i	−0.645451	−	0.763802i	$-0.723331\pi$
$179$		−	1.56828e9i		−	1.52760i	0.645451	−	0.763802i	$-0.276669\pi$
$180$		0			0
$181$	−6.19722e8			−0.577408			−0.288704	−	0.957418i	$-0.593224\pi$
$181$	−6.19722e8			−0.577408			−0.288704	+	0.957418i	$0.593224\pi$
$182$		0			0
$183$	−9.87827e8	+	1.21887e9i	−0.880798	+	1.08681i
$184$		0			0
$185$		−	1.31315e9i		−	1.12106i
$186$		0			0
$187$	6.67181e7			0.0545603
$188$		0			0
$189$	−1.46417e9	−	7.48235e8i	−1.14748	−	0.586396i
$190$		0			0
$191$			4.87719e8i			0.366468i	0.983069	+	0.183234i	$0.0586567\pi$
$191$			4.87719e8i			0.366468i	−0.983069	+	0.183234i	$0.941343\pi$
$192$		0			0
$193$	1.34577e9			0.969933			0.484967	−	0.874533i	$-0.338832\pi$
$193$	1.34577e9			0.969933			0.484967	+	0.874533i	$0.338832\pi$
$194$		0			0
$195$	−5.19916e8	−	4.21363e8i	−0.359580	−	0.291419i
$196$		0			0
$197$		−	1.60057e9i		−	1.06270i	−0.847153	−	0.531349i	$-0.821685\pi$
$197$		−	1.60057e9i		−	1.06270i	0.847153	−	0.531349i	$-0.178315\pi$
$198$		0			0
$199$	−1.41860e9			−0.904579			−0.452289	−	0.891871i	$-0.649393\pi$
$199$	−1.41860e9			−0.904579			−0.452289	+	0.891871i	$0.649393\pi$
$200$		0			0
$201$	1.42924e9	−	1.76353e9i	0.875630	−	1.08043i
$202$		0			0
$203$			2.67402e9i			1.57464i
$204$		0			0
$205$	−3.07673e9			−1.74210
$206$		0			0
$207$	−6.25268e8	+	1.32385e8i	−0.340553	+	0.0721035i
$208$		0			0
$209$			9.09863e7i			0.0476860i
$210$		0			0
$211$	2.70459e9			1.36449			0.682247	−	0.731122i	$-0.261003\pi$
$211$	2.70459e9			1.36449			0.682247	+	0.731122i	$0.261003\pi$
$212$		0			0
$213$	2.11801e9	+	1.71653e9i	1.02899	+	0.833936i
$214$		0			0
$215$		−	1.12169e9i		−	0.524950i
$216$		0			0
$217$	−1.34872e9			−0.608250
$218$		0			0
$219$	1.28674e9	−	1.58770e9i	0.559388	−	0.690225i
$220$		0			0
$221$		−	4.29625e8i		−	0.180103i
$222$		0			0
$223$	1.69115e9			0.683853			0.341927	−	0.939727i	$-0.388921\pi$
$223$	1.69115e9			0.683853			0.341927	+	0.939727i	$0.388921\pi$
$224$		0			0
$225$	1.21279e9	+	5.72815e9i	0.473213	+	2.23504i
$226$		0			0
$227$			6.35028e8i			0.239160i	0.992825	+	0.119580i	$0.0381549\pi$
$227$			6.35028e8i			0.239160i	−0.992825	+	0.119580i	$0.961845\pi$
$228$		0			0
$229$	7.90639e7			0.0287499			0.0143749	−	0.999897i	$-0.495424\pi$
$229$	7.90639e7			0.0287499			0.0143749	+	0.999897i	$0.495424\pi$
$230$		0			0
$231$	−2.20540e8	−	1.78735e8i	−0.0774533	−	0.0627715i
$232$		0			0
$233$			5.72051e9i			1.94094i	0.241229	+	0.970468i	$0.422450\pi$
$233$			5.72051e9i			1.94094i	−0.241229	+	0.970468i	$0.577550\pi$
$234$		0			0
$235$	−7.59046e9			−2.48884
$236$		0			0
$237$	3.23347e9	−	3.98976e9i	1.02489	−	1.26460i
$238$		0			0
$239$		−	4.71043e9i		−	1.44367i	−0.692063	−	0.721837i	$-0.743298\pi$
$239$		−	4.71043e9i		−	1.44367i	0.692063	−	0.721837i	$-0.256702\pi$
$240$		0			0
$241$	1.11857e9			0.331585			0.165793	−	0.986161i	$-0.446982\pi$
$241$	1.11857e9			0.331585			0.165793	+	0.986161i	$0.446982\pi$
$242$		0			0
$243$	9.09146e8	−	3.36617e9i	0.260741	−	0.965409i
$244$		0			0
$245$		−	4.31341e9i		−	1.19717i
$246$		0			0
$247$	5.85898e8			0.157411
$248$		0			0
$249$	−2.99184e9	−	2.42471e9i	−0.778288	−	0.630758i
$250$		0			0
$251$			1.96911e9i			0.496107i	0.968746	+	0.248054i	$0.0797909\pi$
$251$			1.96911e9i			0.496107i	−0.968746	+	0.248054i	$0.920209\pi$
$252$		0			0
$253$	−1.10341e8			−0.0269313
$254$		0			0
$255$	−3.40262e9	+	4.19847e9i	−0.804735	+	0.992957i
$256$		0			0
$257$			1.87262e9i			0.429257i	0.976696	+	0.214628i	$0.0688540\pi$
$257$			1.87262e9i			0.429257i	−0.976696	+	0.214628i	$0.931146\pi$
$258$		0			0
$259$	−3.58687e9			−0.797106
$260$		0			0
$261$	−5.54744e9	+	1.17453e9i	−1.19545	+	0.253106i
$262$		0			0
$263$		−	5.02882e9i		−	1.05110i	−0.850764	−	0.525548i	$-0.823860\pi$
$263$		−	5.02882e9i		−	1.05110i	0.850764	−	0.525548i	$-0.176140\pi$
$264$		0			0
$265$	1.14075e10			2.31317
$266$		0			0
$267$	4.92702e9	+	3.99307e9i	0.969480	+	0.785709i
$268$		0			0
$269$			1.57165e9i			0.300155i	0.988674	+	0.150077i	$0.0479523\pi$
$269$			1.57165e9i			0.300155i	−0.988674	+	0.150077i	$0.952048\pi$
$270$		0			0
$271$	4.27374e9			0.792375			0.396188	−	0.918170i	$-0.370333\pi$
$271$	4.27374e9			0.792375			0.396188	+	0.918170i	$0.370333\pi$
$272$		0			0
$273$	−1.15095e9	+	1.42015e9i	−0.207208	+	0.255672i
$274$		0			0
$275$			1.01085e9i			0.176749i
$276$		0			0
$277$	−2.43619e9			−0.413802			−0.206901	−	0.978362i	$-0.566338\pi$
$277$	−2.43619e9			−0.413802			−0.206901	+	0.978362i	$0.566338\pi$
$278$		0			0
$279$	−5.92407e8	−	2.79801e9i	−0.0977695	−	0.461776i
$280$		0			0
$281$			5.88309e9i			0.943584i	0.881710	+	0.471792i	$0.156393\pi$
$281$			5.88309e9i			0.943584i	−0.881710	+	0.471792i	$0.843607\pi$
$282$		0			0
$283$	5.67732e9			0.885111			0.442555	−	0.896741i	$-0.354072\pi$
$283$	5.67732e9			0.885111			0.442555	+	0.896741i	$0.354072\pi$
$284$		0			0
$285$	−5.72564e9	−	4.64030e9i	−0.867849	−	0.703343i
$286$		0			0
$287$			8.40407e9i			1.23869i
$288$		0			0
$289$	3.50642e9			0.502658
$290$		0			0
$291$	−9.97066e8	+	1.23027e9i	−0.139044	+	0.171565i
$292$		0			0
$293$		−	3.58952e9i		−	0.487041i	−0.969896	−	0.243520i	$-0.921698\pi$
$293$		−	3.58952e9i		−	0.487041i	0.969896	−	0.243520i	$-0.0783023\pi$
$294$		0			0
$295$	1.81037e9			0.239045
$296$		0			0
$297$	2.73929e8	−	5.36033e8i	0.0352056	−	0.0688915i
$298$		0			0
$299$			7.10533e8i			0.0888995i
$300$		0			0
$301$	−3.06388e9			−0.373255
$302$		0			0
$303$	−2.76160e9	−	2.23812e9i	−0.327635	−	0.265530i
$304$		0			0
$305$		−	2.19397e10i		−	2.53531i
$306$		0			0
$307$	−1.43988e10			−1.62096			−0.810480	−	0.585767i	$-0.800794\pi$
$307$	−1.43988e10			−1.62096			−0.810480	+	0.585767i	$0.800794\pi$
$308$		0			0
$309$	−5.78839e9	+	7.14226e9i	−0.634927	+	0.783432i
$310$		0			0
$311$			5.12061e8i			0.0547369i	0.999625	+	0.0273685i	$0.00871274\pi$
$311$			5.12061e8i			0.0547369i	−0.999625	+	0.0273685i	$0.991287\pi$
$312$		0			0
$313$	−9.70528e9			−1.01118			−0.505592	−	0.862772i	$-0.668726\pi$
$313$	−9.70528e9			−1.01118			−0.505592	+	0.862772i	$0.668726\pi$
$314$		0			0
$315$	2.24951e10	−	4.76277e9i	2.28479	−	0.483746i
$316$		0			0
$317$		−	4.26479e9i		−	0.422338i	−0.977450	−	0.211169i	$-0.932273\pi$
$317$		−	4.26479e9i		−	0.422338i	0.977450	−	0.211169i	$-0.0677271\pi$
$318$		0			0
$319$	−9.78960e8			−0.0945370
$320$		0			0
$321$	3.46086e9	+	2.80483e9i	0.325959	+	0.264172i
$322$		0			0
$323$		−	4.73129e9i		−	0.434680i
$324$		0			0
$325$	6.50928e9			0.583444
$326$		0			0
$327$	−8.89213e7	+	1.09719e8i	−0.00777704	+	0.00959604i
$328$		0			0
$329$			2.07333e10i			1.76964i
$330$		0			0
$331$	−5.35245e9			−0.445904			−0.222952	−	0.974829i	$-0.571569\pi$
$331$	−5.35245e9			−0.445904			−0.222952	+	0.974829i	$0.571569\pi$
$332$		0			0
$333$	−1.57549e9	−	7.44120e9i	−0.128126	−	0.605154i
$334$		0			0
$335$			3.17435e10i			2.52044i
$336$		0			0
$337$	−5.99698e9			−0.464957			−0.232479	−	0.972602i	$-0.574684\pi$
$337$	−5.99698e9			−0.464957			−0.232479	+	0.972602i	$0.574684\pi$
$338$		0			0
$339$	1.22376e10	+	9.91791e9i	0.926614	+	0.750968i
$340$		0			0
$341$		−	4.93766e8i		−	0.0365177i
$342$		0			0
$343$	6.05423e9			0.437404
$344$		0			0
$345$	5.62741e9	−	6.94362e9i	0.397221	−	0.490128i
$346$		0			0
$347$		−	2.39763e10i		−	1.65373i	−0.562400	−	0.826865i	$-0.690122\pi$
$347$		−	2.39763e10i		−	1.65373i	0.562400	−	0.826865i	$-0.309878\pi$
$348$		0			0
$349$	2.80408e10			1.89011			0.945057	−	0.326904i	$-0.106005\pi$
$349$	2.80408e10			1.89011			0.945057	+	0.326904i	$0.106005\pi$
$350$		0			0
$351$	−3.45173e9	−	1.76394e9i	−0.227410	−	0.116213i
$352$		0			0
$353$		−	7.50727e9i		−	0.483485i	−0.970340	−	0.241743i	$-0.922281\pi$
$353$		−	7.50727e9i		−	0.483485i	0.970340	−	0.241743i	$-0.0777190\pi$
$354$		0			0
$355$	−3.81243e10			−2.40042
$356$		0			0
$357$	1.14681e10	+	9.29424e9i	0.706022	+	0.572191i
$358$		0			0
$359$		−	1.71973e10i		−	1.03534i	−0.855581	−	0.517669i	$-0.826800\pi$
$359$		−	1.71973e10i		−	1.03534i	0.855581	−	0.517669i	$-0.173200\pi$
$360$		0			0
$361$	−1.05313e10			−0.620088
$362$		0			0
$363$	−1.08669e10	+	1.34085e10i	−0.625861	+	0.772245i
$364$		0			0
$365$			2.85785e10i			1.61016i
$366$		0			0
$367$	1.66397e10			0.917237			0.458619	−	0.888633i	$-0.348344\pi$
$367$	1.66397e10			0.917237			0.458619	+	0.888633i	$0.348344\pi$
$368$		0			0
$369$	−1.74348e10	+	3.69138e9i	−0.940398	+	0.199106i
$370$		0			0
$371$		−	3.11595e10i		−	1.64473i
$372$		0			0
$373$	−1.00036e10			−0.516797			−0.258398	−	0.966038i	$-0.583195\pi$
$373$	−1.00036e10			−0.516797			−0.258398	+	0.966038i	$0.583195\pi$
$374$		0			0
$375$	−3.57676e10	−	2.89876e10i	−1.80869	−	1.46584i
$376$		0			0
$377$			6.30392e9i			0.312065i
$378$		0			0
$379$	3.78010e10			1.83209			0.916044	−	0.401079i	$-0.131365\pi$
$379$	3.78010e10			1.83209			0.916044	+	0.401079i	$0.131365\pi$
$380$		0			0
$381$	9.03315e9	−	1.11459e10i	0.428686	−	0.528952i
$382$		0			0
$383$		−	2.07214e10i		−	0.962997i	−0.876447	−	0.481499i	$-0.840093\pi$
$383$		−	2.07214e10i		−	0.962997i	0.876447	−	0.481499i	$-0.159907\pi$
$384$		0			0
$385$	3.96973e9			0.180683
$386$		0			0
$387$	−1.34577e9	−	6.35623e9i	−0.0599967	−	0.283371i
$388$		0			0
$389$			1.34143e10i			0.585826i	0.956139	+	0.292913i	$0.0946246\pi$
$389$			1.34143e10i			0.585826i	−0.956139	+	0.292913i	$0.905375\pi$
$390$		0			0
$391$	5.73775e9			0.245491
$392$		0			0
$393$	−8.25201e9	−	6.68779e9i	−0.345931	−	0.280358i
$394$		0			0
$395$			7.18156e10i			2.95006i
$396$		0			0
$397$	8.79600e9			0.354098			0.177049	−	0.984202i	$-0.443345\pi$
$397$	8.79600e9			0.354098			0.177049	+	0.984202i	$0.443345\pi$
$398$		0			0
$399$	−1.26750e10	+	1.56395e10i	−0.500098	+	0.617067i
$400$		0			0
$401$		−	3.60295e10i		−	1.39342i	−0.717355	−	0.696708i	$-0.754647\pi$
$401$		−	3.60295e10i		−	1.39342i	0.717355	−	0.696708i	$-0.245353\pi$
$402$		0			0
$403$	−3.17956e9			−0.120544
$404$		0			0
$405$	1.97614e10	+	4.45756e10i	0.734509	+	1.65683i
$406$		0			0
$407$		−	1.31315e9i		−	0.0478561i
$408$		0			0
$409$	9.78141e9			0.349549			0.174775	−	0.984608i	$-0.444080\pi$
$409$	9.78141e9			0.349549			0.174775	+	0.984608i	$0.444080\pi$
$410$		0			0
$411$	1.10973e10	+	8.99373e9i	0.388911	+	0.315190i
$412$		0			0
$413$		−	4.94501e9i		−	0.169968i
$414$		0			0
$415$	5.38530e10			1.81559
$416$		0			0
$417$	1.18465e10	−	1.46173e10i	0.391784	−	0.483420i
$418$		0			0
$419$			2.82806e10i			0.917556i	0.888551	+	0.458778i	$0.151713\pi$
$419$			2.82806e10i			0.917556i	−0.888551	+	0.458778i	$0.848287\pi$
$420$		0			0
$421$	−1.94096e10			−0.617859			−0.308929	−	0.951085i	$-0.599971\pi$
$421$	−1.94096e10			−0.617859			−0.308929	+	0.951085i	$0.599971\pi$
$422$		0			0
$423$	−4.30126e10	+	9.10684e9i	−1.34349	+	0.284450i
$424$		0			0
$425$		−	5.25642e10i		−	1.61114i
$426$		0			0
$427$	−5.99282e10			−1.80268
$428$		0			0
$429$	−5.19916e8	−	4.21363e8i	−0.0153499	−	0.0124402i
$430$		0			0
$431$		−	5.94440e9i		−	0.172266i	−0.996284	−	0.0861329i	$-0.972549\pi$
$431$		−	5.94440e9i		−	0.172266i	0.996284	−	0.0861329i	$-0.0274510\pi$
$432$		0			0
$433$	−2.32206e10			−0.660573			−0.330287	−	0.943881i	$-0.607145\pi$
$433$	−2.32206e10			−0.660573			−0.330287	+	0.943881i	$0.607145\pi$
$434$		0			0
$435$	4.99269e10	−	6.16045e10i	1.39437	−	1.72050i
$436$		0			0
$437$			7.82483e9i			0.214560i
$438$		0			0
$439$	3.09862e10			0.834277			0.417138	−	0.908843i	$-0.363033\pi$
$439$	3.09862e10			0.834277			0.417138	+	0.908843i	$0.363033\pi$
$440$		0			0
$441$	−5.17512e9	−	2.44427e10i	−0.136825	−	0.646241i
$442$		0			0
$443$			3.79891e9i			0.0986379i	0.998783	+	0.0493189i	$0.0157051\pi$
$443$			3.79891e9i			0.0986379i	−0.998783	+	0.0493189i	$0.984295\pi$
$444$		0			0
$445$	−8.86863e10			−2.26160
$446$		0			0
$447$	3.68339e10	+	2.98518e10i	0.922608	+	0.747721i
$448$		0			0
$449$			2.65525e10i			0.653310i	0.945144	+	0.326655i	$0.105922\pi$
$449$			2.65525e10i			0.653310i	−0.945144	+	0.326655i	$0.894078\pi$
$450$		0			0
$451$	−3.07673e9			−0.0743675
$452$		0			0
$453$	2.12858e10	−	2.62644e10i	0.505471	−	0.623698i
$454$		0			0
$455$		−	2.55627e10i		−	0.596432i
$456$		0			0
$457$	−6.93722e10			−1.59045			−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−6.93722e10			−1.59045			−0.795226	+	0.606313i	$0.792648\pi$
$458$		0			0
$459$	−1.42443e10	+	2.78737e10i	−0.320915	+	0.627977i
$460$		0			0
$461$			2.05609e10i			0.455239i	0.973750	+	0.227619i	$0.0730942\pi$
$461$			2.05609e10i			0.455239i	−0.973750	+	0.227619i	$0.926906\pi$
$462$		0			0
$463$	5.34582e9			0.116330			0.0581648	−	0.998307i	$-0.481475\pi$
$463$	5.34582e9			0.116330			0.0581648	+	0.998307i	$0.481475\pi$
$464$		0			0
$465$	3.10719e10	+	2.51821e10i	0.664594	+	0.538616i
$466$		0			0
$467$		−	6.90921e10i		−	1.45265i	−0.687351	−	0.726325i	$-0.741227\pi$
$467$		−	6.90921e10i		−	1.45265i	0.687351	−	0.726325i	$-0.258773\pi$
$468$		0			0
$469$	8.67072e10			1.79211
$470$		0			0
$471$	−4.17471e10	+	5.15115e10i	−0.848287	+	1.04670i
$472$		0			0
$473$		−	1.12169e9i		−	0.0224093i
$474$		0			0
$475$	7.16841e10			1.40815
$476$		0			0
$477$	6.46425e10	−	1.36864e10i	1.24866	−	0.264373i
$478$		0			0
$479$			5.90567e10i			1.12183i	0.827873	+	0.560915i	$0.189551\pi$
$479$			5.90567e10i			1.12183i	−0.827873	+	0.560915i	$0.810449\pi$
$480$		0			0
$481$	−8.45592e9			−0.157972
$482$		0			0
$483$	−1.89665e10	−	1.53712e10i	−0.348496	−	0.282436i
$484$		0			0
$485$		−	2.21449e10i		−	0.400227i
$486$		0			0
$487$	−5.63052e10			−1.00100			−0.500498	−	0.865738i	$-0.666850\pi$
$487$	−5.63052e10			−1.00100			−0.500498	+	0.865738i	$0.666850\pi$
$488$		0			0
$489$	−1.62399e10	+	2.00382e10i	−0.284019	+	0.350449i
$490$		0			0
$491$			1.03299e11i			1.77733i	0.458555	+	0.888666i	$0.348367\pi$
$491$			1.03299e11i			1.77733i	−0.458555	+	0.888666i	$0.651633\pi$
$492$		0			0
$493$	5.09059e10			0.861748
$494$		0			0
$495$	1.74365e9	+	8.23546e9i	0.0290428	+	0.137173i
$496$		0			0
$497$			1.04136e11i			1.70677i
$498$		0			0
$499$	−6.45656e10			−1.04136			−0.520678	−	0.853753i	$-0.674321\pi$
$499$	−6.45656e10			−1.04136			−0.520678	+	0.853753i	$0.674321\pi$
$500$		0			0
$501$	−7.30242e10	−	5.91820e10i	−1.15909	−	0.939374i
$502$		0			0
$503$		−	8.39308e10i		−	1.31114i	−0.755134	−	0.655570i	$-0.772428\pi$
$503$		−	8.39308e10i		−	1.31114i	0.755134	−	0.655570i	$-0.227572\pi$
$504$		0			0
$505$	4.97088e10			0.764307
$506$		0			0
$507$	3.88889e10	−	4.79848e10i	0.588565	−	0.726226i
$508$		0			0
$509$		−	7.78937e10i		−	1.16046i	−0.814452	−	0.580232i	$-0.802962\pi$
$509$		−	7.78937e10i		−	1.16046i	0.814452	−	0.580232i	$-0.197038\pi$
$510$		0			0
$511$	7.80621e10			1.14487
$512$		0			0
$513$	−3.80126e10	−	1.94256e10i	−0.548856	−	0.280482i
$514$		0			0
$515$		−	1.28561e11i		−	1.82759i
$516$		0			0
$517$	−7.59046e9			−0.106244
$518$		0			0
$519$	−8.91394e10	−	7.22424e10i	−1.22857	−	0.995687i
$520$		0			0
$521$		−	1.40022e10i		−	0.190041i	−0.995475	−	0.0950203i	$-0.969708\pi$
$521$		−	1.40022e10i		−	0.190041i	0.995475	−	0.0950203i	$-0.0302916\pi$
$522$		0			0
$523$	−2.95062e10			−0.394372			−0.197186	−	0.980366i	$-0.563180\pi$
$523$	−2.95062e10			−0.394372			−0.197186	+	0.980366i	$0.563180\pi$
$524$		0			0
$525$	−1.40818e11	+	1.73754e11i	−1.85362	+	2.28717i
$526$		0			0
$527$			2.56758e10i			0.332875i
$528$		0			0
$529$	6.88216e10			0.878825
$530$		0			0
$531$	1.02588e10	−	2.17203e9i	0.129038	−	0.0273205i
$532$		0			0
$533$			1.98123e10i			0.245486i
$534$		0			0
$535$	−6.22954e10			−0.760398
$536$		0			0
$537$	9.86894e10	+	7.99821e10i	1.18679	+	0.961824i
$538$		0			0
$539$		−	4.31341e9i		−	0.0511053i
$540$		0			0
$541$	7.00056e10			0.817229			0.408614	−	0.912707i	$-0.366012\pi$
$541$	7.00056e10			0.817229			0.408614	+	0.912707i	$0.366012\pi$
$542$		0			0
$543$	3.16058e10	−	3.89982e10i	0.363553	−	0.448585i
$544$		0			0
$545$		−	1.97495e9i		−	0.0223856i
$546$		0			0
$547$	−9.25123e10			−1.03336			−0.516678	−	0.856180i	$-0.672832\pi$
$547$	−9.25123e10			−1.03336			−0.516678	+	0.856180i	$0.672832\pi$
$548$		0			0
$549$	−2.63227e10	−	1.24325e11i	−0.289762	−	1.36858i
$550$		0			0
$551$			6.94226e10i			0.753172i
$552$		0			0
$553$	1.96164e11			2.09758
$554$		0			0
$555$	8.26348e10	+	6.69708e10i	0.870945	+	0.705852i
$556$		0			0
$557$			9.19422e10i			0.955199i	0.878578	+	0.477600i	$0.158493\pi$
$557$			9.19422e10i			0.955199i	−0.878578	+	0.477600i	$0.841507\pi$
$558$		0			0
$559$	−7.22300e9			−0.0739725
$560$		0			0
$561$	−3.40262e9	+	4.19847e9i	−0.0343528	+	0.0423877i
$562$		0			0
$563$			9.45913e10i			0.941494i	0.882268	+	0.470747i	$0.156016\pi$
$563$			9.45913e10i			0.941494i	−0.882268	+	0.470747i	$0.843984\pi$
$564$		0			0
$565$	−2.20277e11			−2.16160
$566$		0			0
$567$	1.21758e11	−	5.39781e10i	1.17805	−	0.522258i
$568$		0			0
$569$		−	3.17728e10i		−	0.303114i	−0.988448	−	0.151557i	$-0.951571\pi$
$569$		−	3.17728e10i		−	0.303114i	0.988448	−	0.151557i	$-0.0484288\pi$
$570$		0			0
$571$	1.14811e11			1.08003			0.540017	−	0.841654i	$-0.318418\pi$
$571$	1.14811e11			1.08003			0.540017	+	0.841654i	$0.318418\pi$
$572$		0			0
$573$	−3.06915e10	−	2.48737e10i	−0.284708	−	0.230739i
$574$		0			0
$575$			8.69331e10i			0.795269i
$576$		0			0
$577$	−5.54200e10			−0.499993			−0.249996	−	0.968247i	$-0.580429\pi$
$577$	−5.54200e10			−0.499993			−0.249996	+	0.968247i	$0.580429\pi$
$578$		0			0
$579$	−6.86343e10	+	8.46874e10i	−0.610699	+	0.753537i
$580$		0			0
$581$		−	1.47099e11i		−	1.29094i
$582$		0			0
$583$	1.14075e10			0.0987453
$584$		0			0
$585$	5.30315e10	−	1.12281e10i	0.452804	−	0.0958698i
$586$		0			0
$587$		−	1.60567e11i		−	1.35240i	−0.736718	−	0.676200i	$-0.763625\pi$
$587$		−	1.60567e11i		−	1.35240i	0.736718	−	0.676200i	$-0.236375\pi$
$588$		0			0
$589$	−3.50152e10			−0.290935
$590$		0			0
$591$	1.00722e11	+	8.16291e10i	0.825605	+	0.669106i
$592$		0			0
$593$			1.47472e11i			1.19259i	0.802767	+	0.596293i	$0.203360\pi$
$593$			1.47472e11i			1.19259i	−0.802767	+	0.596293i	$0.796640\pi$
$594$		0			0
$595$	−2.06426e11			−1.64701
$596$		0			0
$597$	7.23484e10	−	8.92702e10i	0.569550	−	0.702763i
$598$		0			0
$599$		−	1.76519e11i		−	1.37115i	−0.728002	−	0.685575i	$-0.759551\pi$
$599$		−	1.76519e11i		−	1.37115i	0.728002	−	0.685575i	$-0.240449\pi$
$600$		0			0
$601$	−2.03534e11			−1.56005			−0.780025	−	0.625749i	$-0.784793\pi$
$601$	−2.03534e11			−1.56005			−0.780025	+	0.625749i	$0.784793\pi$
$602$		0			0
$603$	3.80850e10	+	1.79880e11i	0.288061	+	1.36055i
$604$		0			0
$605$		−	2.41354e11i		−	1.80149i
$606$		0			0
$607$	−1.24167e11			−0.914639			−0.457320	−	0.889302i	$-0.651190\pi$
$607$	−1.24167e11			−0.914639			−0.457320	+	0.889302i	$0.651190\pi$
$608$		0			0
$609$	−1.68272e11	−	1.36375e11i	−1.22333	−	0.991439i
$610$		0			0
$611$			4.88781e10i			0.350711i
$612$		0			0
$613$	3.49779e10			0.247715			0.123857	−	0.992300i	$-0.460473\pi$
$613$	3.49779e10			0.247715			0.123857	+	0.992300i	$0.460473\pi$
$614$		0			0
$615$	1.56913e11	−	1.93614e11i	1.09688	−	1.35343i
$616$		0			0
$617$			3.10618e10i			0.214332i	0.994241	+	0.107166i	$0.0341776\pi$
$617$			3.10618e10i			0.214332i	−0.994241	+	0.107166i	$0.965822\pi$
$618$		0			0
$619$	1.65857e11			1.12972			0.564859	−	0.825187i	$-0.308931\pi$
$619$	1.65857e11			1.12972			0.564859	+	0.825187i	$0.308931\pi$
$620$		0			0
$621$	2.35579e10	−	4.60988e10i	0.158405	−	0.309973i
$622$		0			0
$623$			2.42246e11i			1.60807i
$624$		0			0
$625$	2.95217e11			1.93473
$626$		0			0
$627$	−5.72564e9	−	4.64030e9i	−0.0370471	−	0.0300245i
$628$		0			0
$629$			6.82839e10i			0.436230i
$630$		0			0
$631$	−1.14663e11			−0.723280			−0.361640	−	0.932318i	$-0.617783\pi$
$631$	−1.14663e11			−0.723280			−0.361640	+	0.932318i	$0.617783\pi$
$632$		0			0
$633$	−1.37934e11	+	1.70196e11i	−0.859126	+	1.06007i
$634$		0			0
$635$			2.00627e11i			1.23394i
$636$		0			0
$637$	−2.77758e10			−0.168698
$638$		0			0
$639$	−2.16037e11	+	4.57405e10i	−1.29576	+	0.274345i
$640$		0			0
$641$			1.48884e11i			0.881894i	0.897533	+	0.440947i	$0.145357\pi$
$641$			1.48884e11i			0.881894i	−0.897533	+	0.440947i	$0.854643\pi$
$642$		0			0
$643$	2.37607e11			1.39000			0.695000	−	0.719010i	$-0.255404\pi$
$643$	2.37607e11			1.39000			0.695000	+	0.719010i	$0.255404\pi$
$644$		0			0
$645$	7.05862e10	+	5.72061e10i	0.407831	+	0.330524i
$646$		0			0
$647$		−	1.40329e11i		−	0.800814i	−0.916337	−	0.400407i	$-0.868869\pi$
$647$		−	1.40329e11i		−	0.800814i	0.916337	−	0.400407i	$-0.131131\pi$
$648$		0			0
$649$	1.81037e9			0.0102044
$650$		0			0
$651$	6.87846e10	−	8.48728e10i	0.382972	−	0.472547i
$652$		0			0
$653$			3.99459e10i			0.219695i	0.993948	+	0.109847i	$0.0350362\pi$
$653$			3.99459e10i			0.219695i	−0.993948	+	0.109847i	$0.964964\pi$
$654$		0			0
$655$	1.48536e11			0.806988
$656$		0			0
$657$	3.42878e10	+	1.61945e11i	0.184025	+	0.869173i
$658$		0			0
$659$		−	2.73467e11i		−	1.44998i	−0.688757	−	0.724992i	$-0.741843\pi$
$659$		−	2.73467e11i		−	1.44998i	0.688757	−	0.724992i	$-0.258157\pi$
$660$		0			0
$661$	2.01420e11			1.05511			0.527554	−	0.849521i	$-0.323109\pi$
$661$	2.01420e11			1.05511			0.527554	+	0.849521i	$0.323109\pi$
$662$		0			0
$663$	2.70356e10	+	2.19109e10i	0.139921	+	0.113398i
$664$		0			0
$665$		−	2.81512e11i		−	1.43949i
$666$		0			0
$667$	−8.41905e10			−0.425363
$668$		0			0
$669$	−8.62487e10	+	1.06422e11i	−0.430574	+	0.531282i
$670$		0			0
$671$		−	2.19397e10i		−	0.108228i
$672$		0			0
$673$	−5.63035e10			−0.274457			−0.137229	−	0.990539i	$-0.543820\pi$
$673$	−5.63035e10			−0.274457			−0.137229	+	0.990539i	$0.543820\pi$
$674$		0			0
$675$	−4.22317e11	−	2.15817e11i	−2.03434	−	1.03961i
$676$		0			0
$677$			2.30376e11i			1.09668i	0.836254	+	0.548342i	$0.184741\pi$
$677$			2.30376e11i			1.09668i	−0.836254	+	0.548342i	$0.815259\pi$
$678$		0			0
$679$	−6.04886e10			−0.284574
$680$		0			0
$681$	−3.99614e10	−	3.23864e10i	−0.185803	−	0.150582i
$682$		0			0
$683$			6.27237e10i			0.288236i	0.989560	+	0.144118i	$0.0460345\pi$
$683$			6.27237e10i			0.288236i	−0.989560	+	0.144118i	$0.953965\pi$
$684$		0			0
$685$	−1.99751e11			−0.907251
$686$		0			0
$687$	−4.03226e9	+	4.97537e9i	−0.0181018	+	0.0223357i
$688$		0			0
$689$		−	7.34576e10i		−	0.325956i
$690$		0			0
$691$	2.05762e11			0.902511			0.451256	−	0.892395i	$-0.350976\pi$
$691$	2.05762e11			0.902511			0.451256	+	0.892395i	$0.350976\pi$
$692$		0			0
$693$	2.24951e10	−	4.76277e9i	0.0975338	−	0.0206503i
$694$		0			0
$695$			2.63112e11i			1.12772i
$696$		0			0
$697$	1.59990e11			0.677894
$698$		0			0
$699$	−3.59984e11	−	2.91746e11i	−1.50790	−	1.22207i
$700$		0			0
$701$		−	2.57881e11i		−	1.06794i	−0.845504	−	0.533970i	$-0.820700\pi$
$701$		−	2.57881e11i		−	1.06794i	0.845504	−	0.533970i	$-0.179300\pi$
$702$		0			0
$703$	−9.31218e10			−0.381268
$704$		0			0
$705$	3.87114e11	−	4.77657e11i	1.56705	−	1.93357i
$706$		0			0
$707$		−	1.35779e11i		−	0.543446i
$708$		0			0
$709$	−1.09817e11			−0.434595			−0.217297	−	0.976105i	$-0.569724\pi$
$709$	−1.09817e11			−0.434595			−0.217297	+	0.976105i	$0.569724\pi$
$710$		0			0
$711$	8.61625e10	+	4.06955e11i	0.337163	+	1.59246i
$712$		0			0
$713$		−	4.24638e10i		−	0.164309i
$714$		0			0
$715$	9.35849e9			0.0358081
$716$		0			0
$717$	2.96421e11	+	2.40232e11i	1.12158	+	0.908980i
$718$		0			0
$719$		−	2.85970e11i		−	1.07005i	−0.844836	−	0.535025i	$-0.820302\pi$
$719$		−	2.85970e11i		−	1.07005i	0.844836	−	0.535025i	$-0.179698\pi$
$720$		0			0
$721$	−3.51162e11			−1.29947
$722$		0			0
$723$	−5.70471e10	+	7.03900e10i	−0.208776	+	0.257607i
$724$		0			0
$725$			7.71279e11i			2.79164i
$726$		0			0
$727$	−3.23636e11			−1.15856			−0.579280	−	0.815129i	$-0.696666\pi$
$727$	−3.23636e11			−1.15856			−0.579280	+	0.815129i	$0.696666\pi$
$728$		0			0
$729$	1.65462e11	+	2.28886e11i	0.585852	+	0.810418i
$730$		0			0
$731$			5.83278e10i			0.204271i
$732$		0			0
$733$	4.62635e11			1.60259			0.801296	−	0.598269i	$-0.204144\pi$
$733$	4.62635e11			1.60259			0.801296	+	0.598269i	$0.204144\pi$
$734$		0			0
$735$	2.71437e11	+	2.19984e11i	0.930078	+	0.753775i
$736$		0			0
$737$			3.17435e10i			0.107593i
$738$		0			0
$739$	4.79772e11			1.60863			0.804317	−	0.594200i	$-0.202531\pi$
$739$	4.79772e11			1.60863			0.804317	+	0.594200i	$0.202531\pi$
$740$		0			0
$741$	−2.98808e10	+	3.68697e10i	−0.0991104	+	0.122292i
$742$		0			0
$743$		−	5.66358e11i		−	1.85839i	−0.369595	−	0.929193i	$-0.620504\pi$
$743$		−	5.66358e11i		−	1.85839i	0.369595	−	0.929193i	$-0.379496\pi$
$744$		0			0
$745$	−6.63010e11			−2.15226
$746$		0			0
$747$	3.05167e11	−	6.46115e10i	0.980066	−	0.207504i
$748$		0			0
$749$			1.70160e11i			0.540666i
$750$		0			0
$751$	1.77971e11			0.559486			0.279743	−	0.960075i	$-0.409751\pi$
$751$	1.77971e11			0.559486			0.279743	+	0.960075i	$0.409751\pi$
$752$		0			0
$753$	−1.23913e11	−	1.00425e11i	−0.385424	−	0.312364i
$754$		0			0
$755$			4.72758e11i			1.45496i
$756$		0			0
$757$	−2.17313e11			−0.661763			−0.330882	−	0.943672i	$-0.607346\pi$
$757$	−2.17313e11			−0.661763			−0.330882	+	0.943672i	$0.607346\pi$
$758$		0			0
$759$	5.62741e9	−	6.94362e9i	0.0169567	−	0.0209228i
$760$		0			0
$761$		−	2.90514e10i		−	0.0866220i	−0.999062	−	0.0433110i	$-0.986209\pi$
$761$		−	2.90514e10i		−	0.0866220i	0.999062	−	0.0433110i	$-0.0137906\pi$
$762$		0			0
$763$	−5.39456e9			−0.0159169
$764$		0			0
$765$	−9.06699e10	−	4.28244e11i	−0.264739	−	1.25039i
$766$		0			0
$767$		−	1.16577e10i		−	0.0336846i
$768$		0			0
$769$	−1.47894e11			−0.422906			−0.211453	−	0.977388i	$-0.567820\pi$
$769$	−1.47894e11			−0.422906			−0.211453	+	0.977388i	$0.567820\pi$
$770$		0			0
$771$	−1.17841e11	−	9.55036e10i	−0.333488	−	0.270273i
$772$		0			0
$773$		−	3.53522e11i		−	0.990144i	−0.868852	−	0.495072i	$-0.835142\pi$
$773$		−	3.53522e11i		−	0.990144i	0.868852	−	0.495072i	$-0.164858\pi$
$774$		0			0
$775$	−3.89016e11			−1.07835
$776$		0			0
$777$	1.82930e11	−	2.25716e11i	0.501882	−	0.619268i
$778$		0			0
$779$			2.18185e11i			0.592483i
$780$		0			0
$781$	−3.81243e10			−0.102470
$782$		0			0
$783$	2.09008e11	−	4.08993e11i	0.556052	−	1.08810i
$784$		0			0
$785$		−	9.27207e11i		−	2.44173i
$786$		0			0
$787$	−2.10776e11			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$787$	−2.10776e11			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$788$		0			0
$789$	3.16456e11	+	2.56470e11i	0.816592	+	0.661802i
$790$		0			0
$791$			6.01686e11i			1.53697i
$792$		0			0
$793$	−1.41279e11			−0.357259
$794$		0			0
$795$	−5.81783e11	+	7.17858e11i	−1.45644	+	1.79709i
$796$		0			0
$797$		−	3.42870e11i		−	0.849760i	−0.905250	−	0.424880i	$-0.860316\pi$
$797$		−	3.42870e11i		−	0.849760i	0.905250	−	0.424880i	$-0.139684\pi$
$798$		0			0
$799$	3.94704e11			0.968466
$800$		0			0
$801$	−5.02556e11	+	1.06403e11i	−1.22083	+	0.258479i
$802$		0			0
$803$			2.85785e10i			0.0687349i
$804$		0			0
$805$	3.41396e11			0.812972
$806$		0			0
$807$	−9.89014e10	−	8.01539e10i	−0.233189	−	0.188986i
$808$		0			0
$809$			3.70408e11i			0.864740i	0.901696	+	0.432370i	$0.142323\pi$
$809$			3.70408e11i			0.864740i	−0.901696	+	0.432370i	$0.857677\pi$
$810$		0			0
$811$	4.64058e11			1.07273			0.536363	−	0.843987i	$-0.319798\pi$
$811$	4.64058e11			1.07273			0.536363	+	0.843987i	$0.319798\pi$
$812$		0			0
$813$	−2.17961e11	+	2.68940e11i	−0.498903	+	0.615593i
$814$		0			0
$815$		−	3.60688e11i		−	0.817526i
$816$		0			0
$817$	−7.95441e10			−0.178534
$818$		0			0
$819$	−3.06694e10	−	1.44855e11i	−0.0681663	−	0.321957i
$820$		0			0
$821$		−	3.09956e11i		−	0.682225i	−0.940023	−	0.341112i	$-0.889196\pi$
$821$		−	3.09956e11i		−	0.682225i	0.940023	−	0.341112i	$-0.110804\pi$
$822$		0			0
$823$	6.56536e10			0.143106			0.0715532	−	0.997437i	$-0.477204\pi$
$823$	6.56536e10			0.143106			0.0715532	+	0.997437i	$0.477204\pi$
$824$		0			0
$825$	−6.36113e10	−	5.15534e10i	−0.137315	−	0.111286i
$826$		0			0
$827$			2.35294e11i			0.503024i	0.967854	+	0.251512i	$0.0809278\pi$
$827$			2.35294e11i			0.503024i	−0.967854	+	0.251512i	$0.919072\pi$
$828$		0			0
$829$	7.29416e11			1.54439			0.772196	−	0.635385i	$-0.219158\pi$
$829$	7.29416e11			1.54439			0.772196	+	0.635385i	$0.219158\pi$
$830$		0			0
$831$	1.24246e11	−	1.53306e11i	0.260542	−	0.321481i
$832$		0			0
$833$			2.24297e11i			0.465848i
$834$		0			0
$835$	1.31444e12			2.70392
$836$		0			0
$837$	2.06287e11	+	1.05419e11i	0.420311	+	0.214791i
$838$		0			0
$839$			6.85812e11i			1.38407i	0.721866	+	0.692033i	$0.243285\pi$
$839$			6.85812e11i			1.38407i	−0.721866	+	0.692033i	$0.756715\pi$
$840$		0			0
$841$	−2.46700e11			−0.493156
$842$		0			0
$843$	−3.70214e11	−	3.00038e11i	−0.733066	−	0.594108i
$844$		0			0
$845$			8.63726e11i			1.69414i
$846$		0			0
$847$	−6.59257e11			−1.28092
$848$		0			0
$849$	−2.89543e11	+	3.57265e11i	−0.557292	+	0.687639i
$850$		0			0
$851$		−	1.12931e11i		−	0.215325i
$852$		0			0
$853$	−5.80498e11			−1.09649			−0.548245	−	0.836318i	$-0.684704\pi$
$853$	−5.80498e11			−1.09649			−0.548245	+	0.836318i	$0.684704\pi$
$854$		0			0
$855$	5.84015e11	−	1.23650e11i	1.09285	−	0.231383i
$856$		0			0
$857$			3.92709e11i			0.728028i	0.931393	+	0.364014i	$0.118594\pi$
$857$			3.92709e11i			0.728028i	−0.931393	+	0.364014i	$0.881406\pi$
$858$		0			0
$859$	−1.02163e12			−1.87639			−0.938194	−	0.346109i	$-0.887503\pi$
$859$	−1.02163e12			−1.87639			−0.938194	+	0.346109i	$0.887503\pi$
$860$		0			0
$861$	−5.28856e11	−	4.28607e11i	−0.962331	−	0.779915i
$862$		0			0
$863$		−	6.01595e11i		−	1.08458i	−0.840192	−	0.542290i	$-0.817558\pi$
$863$		−	6.01595e11i		−	1.08458i	0.840192	−	0.542290i	$-0.182442\pi$
$864$		0			0
$865$	1.60451e12			2.86601
$866$		0			0
$867$	−1.78827e11	+	2.20654e11i	−0.316488	+	0.390512i
$868$		0			0
$869$			7.18156e10i			0.125933i
$870$		0			0
$871$	2.04409e11			0.355163
$872$		0			0
$873$	−2.65689e10	−	1.25488e11i	−0.0457421	−	0.216045i
$874$		0			0
$875$		−	1.75858e12i		−	3.00006i
$876$		0			0
$877$	1.43691e11			0.242902			0.121451	−	0.992597i	$-0.461245\pi$
$877$	1.43691e11			0.242902			0.121451	+	0.992597i	$0.461245\pi$
$878$		0			0
$879$	2.25883e11	+	1.83065e11i	0.378380	+	0.306655i
$880$		0			0
$881$		−	1.02695e12i		−	1.70469i	−0.522984	−	0.852343i	$-0.675181\pi$
$881$		−	1.02695e12i		−	1.70469i	0.522984	−	0.852343i	$-0.324819\pi$
$882$		0			0
$883$	−1.10181e12			−1.81244			−0.906220	−	0.422807i	$-0.861045\pi$
$883$	−1.10181e12			−1.81244			−0.906220	+	0.422807i	$0.861045\pi$
$884$		0			0
$885$	−9.23288e10	+	1.13924e11i	−0.150510	+	0.185713i
$886$		0			0
$887$			2.12570e10i			0.0343405i	0.999853	+	0.0171703i	$0.00546573\pi$
$887$			2.12570e10i			0.0343405i	−0.999853	+	0.0171703i	$0.994534\pi$
$888$		0			0
$889$	5.48011e11			0.877369
$890$		0			0
$891$	1.97614e10	+	4.45756e10i	0.0313550	+	0.0707272i
$892$		0			0
$893$			5.38275e11i			0.846445i
$894$		0			0
$895$	−1.77641e12			−2.76854
$896$		0			0
$897$	−4.47128e10	−	3.62372e10i	−0.0690657	−	0.0559738i
$898$		0			0
$899$		−	3.76743e11i		−	0.576775i
$900$		0			0
$901$	−5.93190e11			−0.900109
$902$		0			0
$903$	1.56258e11	−	1.92806e11i	0.235013	−	0.289980i
$904$		0			0
$905$			7.01968e11i			1.04646i
$906$		0			0
$907$	4.79910e11			0.709138			0.354569	−	0.935030i	$-0.384628\pi$
$907$	4.79910e11			0.709138			0.354569	+	0.935030i	$0.384628\pi$
$908$		0			0
$909$	2.81683e11	−	5.96393e10i	0.412578	−	0.0873529i
$910$		0			0
$911$			1.10471e12i			1.60389i	0.597398	+	0.801945i	$0.296201\pi$
$911$			1.10471e12i			1.60389i	−0.597398	+	0.801945i	$0.703799\pi$
$912$		0			0
$913$	5.38530e10			0.0775045
$914$		0			0
$915$	1.38063e12	+	1.11892e12i	1.96967	+	1.59631i
$916$		0			0
$917$		−	4.05726e11i		−	0.573793i
$918$		0			0
$919$	5.92307e11			0.830396			0.415198	−	0.909731i	$-0.363712\pi$
$919$	5.92307e11			0.830396			0.415198	+	0.909731i	$0.363712\pi$
$920$		0			0
$921$	7.34338e11	−	9.06094e11i	1.02060	−	1.25932i
$922$		0			0
$923$			2.45497e11i			0.338252i
$924$		0			0
$925$	−1.03457e12			−1.41317
$926$		0			0
$927$	−1.54244e11	−	7.28510e11i	−0.208876	−	0.986544i
$928$		0			0
$929$			1.35709e12i			1.82199i	0.412415	+	0.910996i	$0.364685\pi$
$929$			1.35709e12i			1.82199i	−0.412415	+	0.910996i	$0.635315\pi$
$930$		0			0
$931$	−3.05884e11			−0.407154
$932$		0			0
$933$	−3.22233e10	−	2.61151e10i	−0.0425249	−	0.0344640i
$934$		0			0
$935$		−	7.55725e10i		−	0.0988820i
$936$		0			0
$937$	1.13636e12			1.47420			0.737101	−	0.675783i	$-0.236194\pi$
$937$	1.13636e12			1.47420			0.737101	+	0.675783i	$0.236194\pi$
$938$		0			0
$939$	4.94969e11	−	6.10739e11i	0.636672	−	0.785585i
$940$		0			0
$941$		−	7.44953e11i		−	0.950103i	−0.879958	−	0.475051i	$-0.842429\pi$
$941$		−	7.44953e11i		−	0.950103i	0.879958	−	0.475051i	$-0.157571\pi$
$942$		0			0
$943$	−2.64599e11			−0.334612
$944$		0			0
$945$	−8.47536e11	+	1.65849e12i	−1.06275	+	2.07962i
$946$		0			0
$947$			4.20010e11i			0.522227i	0.965308	+	0.261114i	$0.0840897\pi$
$947$			4.20010e11i			0.522227i	−0.965308	+	0.261114i	$0.915910\pi$
$948$		0			0
$949$	1.84029e11			0.226893
$950$		0			0
$951$	2.68377e11	+	2.17504e11i	0.328113	+	0.265917i
$952$		0			0
$953$		−	5.38419e10i		−	0.0652753i	−0.999467	−	0.0326376i	$-0.989609\pi$
$953$		−	5.38419e10i		−	0.0652753i	0.999467	−	0.0326376i	$-0.0103907\pi$
$954$		0			0
$955$	5.52446e11			0.664166
$956$		0			0
$957$	4.99269e10	−	6.16045e10i	0.0595233	−	0.0734454i
$958$		0			0
$959$			5.45620e11i			0.645083i
$960$		0			0
$961$	−6.62870e11			−0.777204
$962$		0			0
$963$	−3.53007e11	+	7.47404e10i	−0.410468	+	0.0869061i
$964$		0			0
$965$		−	1.52437e12i		−	1.75785i
$966$		0			0
$967$	−5.26299e10			−0.0601904			−0.0300952	−	0.999547i	$-0.509581\pi$
$967$	−5.26299e10			−0.0601904			−0.0300952	+	0.999547i	$0.509581\pi$
$968$		0			0
$969$	2.97733e11	+	2.41296e11i	0.337701	+	0.273687i
$970$		0			0
$971$		−	6.31196e11i		−	0.710047i	−0.934857	−	0.355023i	$-0.884473\pi$
$971$		−	6.31196e11i		−	0.710047i	0.934857	−	0.355023i	$-0.115527\pi$
$972$		0			0
$973$	7.18689e11			0.801844
$974$		0			0
$975$	−3.31973e11	+	4.09619e11i	−0.367354	+	0.453275i
$976$		0			0
$977$		−	6.00940e11i		−	0.659557i	−0.944058	−	0.329779i	$-0.893026\pi$
$977$		−	6.00940e11i		−	0.659557i	0.944058	−	0.329779i	$-0.106974\pi$
$978$		0			0
$979$	−8.86863e10			−0.0965441
$980$		0			0
$981$	−2.36949e9	−	1.11914e10i	−0.00255846	−	0.0120839i
$982$		0			0
$983$		−	9.79004e10i		−	0.104850i	−0.998625	−	0.0524252i	$-0.983305\pi$
$983$		−	9.79004e10i		−	0.104850i	0.998625	−	0.0524252i	$-0.0166951\pi$
$984$		0			0
$985$	−1.81299e12			−1.92597
$986$		0			0
$987$	−1.30472e12	−	1.05740e12i	−1.37483	−	1.11422i
$988$		0			0
$989$		−	9.64651e10i		−	0.100829i
$990$		0			0
$991$	2.73460e10			0.0283530			0.0141765	−	0.999900i	$-0.495487\pi$
$991$	2.73460e10			0.0283530			0.0141765	+	0.999900i	$0.495487\pi$
$992$		0			0
$993$	2.72975e11	−	3.36822e11i	0.280754	−	0.346420i
$994$		0			0
$995$			1.60686e12i			1.63941i
$996$		0			0
$997$	2.97835e11			0.301436			0.150718	−	0.988577i	$-0.451841\pi$
$997$	2.97835e11			0.301436			0.150718	+	0.988577i	$0.451841\pi$
$998$		0			0
$999$	5.48613e11	+	2.80358e11i	0.550813	+	0.281482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.9.c.b.5.2	yes	2
3.2	odd	2	inner	12.9.c.b.5.1	✓	2
4.3	odd	2		48.9.e.c.17.1		2
5.2	odd	4		300.9.b.c.149.4		4
5.3	odd	4		300.9.b.c.149.1		4
5.4	even	2		300.9.g.d.101.1		2
8.3	odd	2		192.9.e.d.65.2		2
8.5	even	2		192.9.e.g.65.1		2
9.2	odd	6		324.9.g.f.53.1		4
9.4	even	3		324.9.g.f.269.1		4
9.5	odd	6		324.9.g.f.269.2		4
9.7	even	3		324.9.g.f.53.2		4
12.11	even	2		48.9.e.c.17.2		2
15.2	even	4		300.9.b.c.149.2		4
15.8	even	4		300.9.b.c.149.3		4
15.14	odd	2		300.9.g.d.101.2		2
24.5	odd	2		192.9.e.g.65.2		2
24.11	even	2		192.9.e.d.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.9.c.b.5.1	✓	2	3.2	odd	2	inner
12.9.c.b.5.2	yes	2	1.1	even	1	trivial
48.9.e.c.17.1		2	4.3	odd	2
48.9.e.c.17.2		2	12.11	even	2
192.9.e.d.65.1		2	24.11	even	2
192.9.e.d.65.2		2	8.3	odd	2
192.9.e.g.65.1		2	8.5	even	2
192.9.e.g.65.2		2	24.5	odd	2
300.9.b.c.149.1		4	5.3	odd	4
300.9.b.c.149.2		4	15.2	even	4
300.9.b.c.149.3		4	15.8	even	4
300.9.b.c.149.4		4	5.2	odd	4
300.9.g.d.101.1		2	5.4	even	2
300.9.g.d.101.2		2	15.14	odd	2
324.9.g.f.53.1		4	9.2	odd	6
324.9.g.f.53.2		4	9.7	even	3
324.9.g.f.269.1		4	9.4	even	3
324.9.g.f.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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	12.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-51.0000 + 62.9285i) q^{3} -1132.71i q^{5} -3094.00 q^{7} +(-1359.00 - 6418.71i) q^{9} +O(q^{10})\)	\(q+(-51.0000 + 62.9285i) q^{3} -1132.71i q^{5} -3094.00 q^{7} +(-1359.00 - 6418.71i) q^{9} -1132.71i q^{11} -7294.00 q^{13} +(71280.0 + 57768.4i) q^{15} +58901.1i q^{17} -80326.0 q^{19} +(157794. - 194701. i) q^{21} -97413.4i q^{23} -892415. q^{25} +(473229. + 241834. i) q^{27} -864260. i q^{29} +435914. q^{31} +(71280.0 + 57768.4i) q^{33} +3.50462e6i q^{35} +1.15930e6 q^{37} +(371994. - 459001. i) q^{39} -2.71625e6i q^{41} +990266. q^{43} +(-7.27056e6 + 1.53936e6i) q^{45} -6.70113e6i q^{47} +3.80804e6 q^{49} +(-3.70656e6 - 3.00396e6i) q^{51} +1.00710e7i q^{53} -1.28304e6 q^{55} +(4.09663e6 - 5.05480e6i) q^{57} +1.59826e6i q^{59} +1.93692e7 q^{61} +(4.20475e6 + 1.98595e7i) q^{63} +8.26201e6i q^{65} -2.80243e7 q^{67} +(6.13008e6 + 4.96808e6i) q^{69} -3.36575e7i q^{71} -2.52301e7 q^{73} +(4.55132e7 - 5.61584e7i) q^{75} +3.50462e6i q^{77} -6.34014e7 q^{79} +(-3.93530e7 + 1.74461e7i) q^{81} +4.75434e7i q^{83} +6.67181e7 q^{85} +(5.43866e7 + 4.40773e7i) q^{87} -7.82954e7i q^{89} +2.25676e7 q^{91} +(-2.22316e7 + 2.74314e7i) q^{93} +9.09863e7i q^{95} +1.95503e7 q^{97} +(-7.27056e6 + 1.53936e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 102 q^{3} - 6188 q^{7} - 2718 q^{9}+O(q^{10}) \) 2 * q - 102 * q^3 - 6188 * q^7 - 2718 * q^9	\( 2 q - 102 q^{3} - 6188 q^{7} - 2718 q^{9} - 14588 q^{13} + 142560 q^{15} - 160652 q^{19} + 315588 q^{21} - 1784830 q^{25} + 946458 q^{27} + 871828 q^{31} + 142560 q^{33} + 2318596 q^{37} + 743988 q^{39} + 1980532 q^{43} - 14541120 q^{45} + 7616070 q^{49} - 7413120 q^{51} - 2566080 q^{55} + 8193252 q^{57} + 38738308 q^{61} + 8409492 q^{63} - 56048588 q^{67} + 12260160 q^{69} - 50460284 q^{73} + 91026330 q^{75} - 126802796 q^{79} - 78705918 q^{81} + 133436160 q^{85} + 108773280 q^{87} + 45135272 q^{91} - 44463228 q^{93} + 39100612 q^{97} - 14541120 q^{99}+O(q^{100}) \) 2 * q - 102 * q^3 - 6188 * q^7 - 2718 * q^9 - 14588 * q^13 + 142560 * q^15 - 160652 * q^19 + 315588 * q^21 - 1784830 * q^25 + 946458 * q^27 + 871828 * q^31 + 142560 * q^33 + 2318596 * q^37 + 743988 * q^39 + 1980532 * q^43 - 14541120 * q^45 + 7616070 * q^49 - 7413120 * q^51 - 2566080 * q^55 + 8193252 * q^57 + 38738308 * q^61 + 8409492 * q^63 - 56048588 * q^67 + 12260160 * q^69 - 50460284 * q^73 + 91026330 * q^75 - 126802796 * q^79 - 78705918 * q^81 + 133436160 * q^85 + 108773280 * q^87 + 45135272 * q^91 - 44463228 * q^93 + 39100612 * q^97 - 14541120 * q^99

Introduction

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