LMFDB - Embedded newform 196.9.h.b.117.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,9,Mod(117,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.117"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	196.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$79.8462075720$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 720x^{10} + 409912x^{8} + 71803008x^{6} + 9498639424x^{4} + 342190245888x^{2} + 9948826238976 $ x^12 + 720x^10 + 409912x^8 + 71803008x^6 + 9498639424x^4 + 342190245888*x^2 + 9948826238976
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{7}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			117.6
Root			$11.4531 - 19.8373i$ of defining polynomial
Character	$\chi$	$=$	196.117
Dual form			196.9.h.b.129.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(127.153 - 73.4116i) q^{3} +(-834.906 - 482.033i) q^{5} +(7498.03 - 12987.0i) q^{9} +(-5928.09 - 10267.8i) q^{11} -28897.2i q^{13} -141547. q^{15} +(39852.8 - 23009.0i) q^{17} +(-16883.1 - 9747.47i) q^{19} +(65822.6 - 114008. i) q^{23} +(269399. + 466614. i) q^{25} -1.23846e6i q^{27} +1.22466e6 q^{29} +(-941455. + 543550. i) q^{31} +(-1.50755e6 - 870382. i) q^{33} +(-1.24453e6 + 2.15559e6i) q^{37} +(-2.12139e6 - 3.67436e6i) q^{39} +26466.8i q^{41} -4.08031e6 q^{43} +(-1.25203e7 + 7.22860e6i) q^{45} +(-6.01939e6 - 3.47530e6i) q^{47} +(3.37826e6 - 5.85132e6i) q^{51} +(4.38991e6 + 7.60356e6i) q^{53} +1.14302e7i q^{55} -2.86231e6 q^{57} +(-3.24161e6 + 1.87154e6i) q^{59} +(-1.21938e7 - 7.04007e6i) q^{61} +(-1.39294e7 + 2.41265e7i) q^{65} +(3.81126e6 + 6.60129e6i) q^{67} -1.93286e7i q^{69} +158650. q^{71} +(3.36551e7 - 1.94308e7i) q^{73} +(6.85097e7 + 3.95541e7i) q^{75} +(-5.65086e6 + 9.78758e6i) q^{79} +(-4.17231e7 - 7.22665e7i) q^{81} -5.38238e6i q^{83} -4.43645e7 q^{85} +(1.55719e8 - 8.99046e7i) q^{87} +(9.42793e6 + 5.44322e6i) q^{89} +(-7.98057e7 + 1.38228e8i) q^{93} +(9.39721e6 + 1.62764e7i) q^{95} -5.55681e7i q^{97} -1.77796e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18234 q^{9} - 24492 q^{11} - 306816 q^{15} + 11604 q^{23} + 678714 q^{25} + 2528664 q^{29} - 3184332 q^{37} - 5634240 q^{39} - 15566760 q^{43} - 6877824 q^{51} + 8340660 q^{53} - 35901696 q^{57}+ \cdots - 1191795624 q^{99}+O(q^{100}) $ 12 * q + 18234 * q^9 - 24492 * q^11 - 306816 * q^15 + 11604 * q^23 + 678714 * q^25 + 2528664 * q^29 - 3184332 * q^37 - 5634240 * q^39 - 15566760 * q^43 - 6877824 * q^51 + 8340660 * q^53 - 35901696 * q^57 - 84095232 * q^65 - 16579500 * q^67 - 124177704 * q^71 - 186114540 * q^79 - 131284998 * q^81 - 526421760 * q^85 - 638128512 * q^93 - 85912896 * q^95 - 1191795624 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	127.153	−	73.4116i	1.56979	−	0.906316i	0.573593	−	0.819140i	$-0.305549\pi$
$3$	127.153	−	73.4116i	1.56979	−	0.906316i	0.996193	−	0.0871760i	$-0.0277842\pi$
$4$		0			0
$5$	−834.906	−	482.033i	−1.33585	−	0.771253i	−0.349660	−	0.936876i	$-0.613703\pi$
$5$	−834.906	−	482.033i	−1.33585	−	0.771253i	−0.986189	+	0.165623i	$0.947036\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	7498.03	−	12987.0i	1.14282	−	1.97942i
$10$		0			0
$11$	−5928.09	−	10267.8i	−0.404897	−	0.701302i	0.589413	−	0.807832i	$-0.299359\pi$
$11$	−5928.09	−	10267.8i	−0.404897	−	0.701302i	−0.994309	+	0.106530i	$0.966026\pi$
$12$		0			0
$13$		−	28897.2i		−	1.01177i	−0.862600	−	0.505886i	$-0.831166\pi$
$13$		−	28897.2i		−	1.01177i	0.862600	−	0.505886i	$-0.168834\pi$
$14$		0			0
$15$	−141547.			−2.79600
$16$		0			0
$17$	39852.8	−	23009.0i	0.477159	−	0.275488i	−0.242073	−	0.970258i	$-0.577827\pi$
$17$	39852.8	−	23009.0i	0.477159	−	0.275488i	0.719232	+	0.694770i	$0.244494\pi$
$18$		0			0
$19$	−16883.1	−	9747.47i	−0.129550	−	0.0747959i	0.433824	−	0.900997i	$-0.357164\pi$
$19$	−16883.1	−	9747.47i	−0.129550	−	0.0747959i	−0.563375	+	0.826202i	$0.690497\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	65822.6	−	114008.i	0.235214	−	0.407403i	−0.724121	−	0.689673i	$-0.757754\pi$
$23$	65822.6	−	114008.i	0.235214	−	0.407403i	0.959335	+	0.282270i	$0.0910875\pi$
$24$		0			0
$25$	269399.	+	466614.i	0.689663	+	1.19453i
$26$		0			0
$27$		−	1.23846e6i		−	2.33039i
$28$		0			0
$29$	1.22466e6			1.73151			0.865755	−	0.500468i	$-0.166839\pi$
$29$	1.22466e6			1.73151			0.865755	+	0.500468i	$0.166839\pi$
$30$		0			0
$31$	−941455.	+	543550.i	−1.01942	+	0.588562i	−0.913936	−	0.405859i	$-0.866972\pi$
$31$	−941455.	+	543550.i	−1.01942	+	0.588562i	−0.105484	+	0.994421i	$0.533639\pi$
$32$		0			0
$33$	−1.50755e6	−	870382.i	−1.27120	−	0.733929i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.24453e6	+	2.15559e6i	−0.664047	+	1.15016i	0.315495	+	0.948927i	$0.397829\pi$
$37$	−1.24453e6	+	2.15559e6i	−0.664047	+	1.15016i	−0.979543	+	0.201237i	$0.935504\pi$
$38$		0			0
$39$	−2.12139e6	−	3.67436e6i	−0.916985	−	1.58826i
$40$		0			0
$41$			26466.8i			0.00936627i	0.999989	+	0.00468314i	$0.00149069\pi$
$41$			26466.8i			0.00936627i	−0.999989	+	0.00468314i	$0.998509\pi$
$42$		0			0
$43$	−4.08031e6			−1.19349			−0.596746	−	0.802430i	$-0.703540\pi$
$43$	−4.08031e6			−1.19349			−0.596746	+	0.802430i	$0.703540\pi$
$44$		0			0
$45$	−1.25203e7	+	7.22860e6i	−3.05327	+	1.76280i
$46$		0			0
$47$	−6.01939e6	−	3.47530e6i	−1.23356	−	0.712198i	−0.265792	−	0.964030i	$-0.585634\pi$
$47$	−6.01939e6	−	3.47530e6i	−1.23356	−	0.712198i	−0.967771	+	0.251832i	$0.918967\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.37826e6	−	5.85132e6i	0.499358	−	0.864914i
$52$		0			0
$53$	4.38991e6	+	7.60356e6i	0.556356	+	0.963636i	0.997797	+	0.0663461i	$0.0211341\pi$
$53$	4.38991e6	+	7.60356e6i	0.556356	+	0.963636i	−0.441441	+	0.897290i	$0.645533\pi$
$54$		0			0
$55$			1.14302e7i			1.24911i
$56$		0			0
$57$	−2.86231e6			−0.271155
$58$		0			0
$59$	−3.24161e6	+	1.87154e6i	−0.267517	+	0.154451i	−0.627759	−	0.778408i	$-0.716028\pi$
$59$	−3.24161e6	+	1.87154e6i	−0.267517	+	0.154451i	0.360241	+	0.932859i	$0.382694\pi$
$60$		0			0
$61$	−1.21938e7	−	7.04007e6i	−0.880680	−	0.508461i	−0.00979722	−	0.999952i	$-0.503119\pi$
$61$	−1.21938e7	−	7.04007e6i	−0.880680	−	0.508461i	−0.870882	+	0.491491i	$0.836452\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.39294e7	+	2.41265e7i	−0.780332	+	1.35157i
$66$		0			0
$67$	3.81126e6	+	6.60129e6i	0.189134	+	0.327589i	0.944962	−	0.327181i	$-0.106099\pi$
$67$	3.81126e6	+	6.60129e6i	0.189134	+	0.327589i	−0.755828	+	0.654770i	$0.772765\pi$
$68$		0			0
$69$		−	1.93286e7i		−	0.852714i
$70$		0			0
$71$	158650.			0.00624319			0.00312159	−	0.999995i	$-0.499006\pi$
$71$	158650.			0.00624319			0.00312159	+	0.999995i	$0.499006\pi$
$72$		0			0
$73$	3.36551e7	−	1.94308e7i	1.18511	−	0.684225i	0.227920	−	0.973680i	$-0.426807\pi$
$73$	3.36551e7	−	1.94308e7i	1.18511	−	0.684225i	0.957192	+	0.289455i	$0.0934741\pi$
$74$		0			0
$75$	6.85097e7	+	3.95541e7i	2.16525	+	1.25011i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−5.65086e6	+	9.78758e6i	−0.145080	+	0.251285i	−0.929403	−	0.369067i	$-0.879677\pi$
$79$	−5.65086e6	+	9.78758e6i	−0.145080	+	0.251285i	0.784323	+	0.620353i	$0.213010\pi$
$80$		0			0
$81$	−4.17231e7	−	7.22665e7i	−0.969251	−	1.67879i
$82$		0			0
$83$		−	5.38238e6i		−	0.113413i	−0.998391	−	0.0567064i	$-0.981940\pi$
$83$		−	5.38238e6i		−	0.113413i	0.998391	−	0.0567064i	$-0.0180599\pi$
$84$		0			0
$85$	−4.43645e7			−0.849884
$86$		0			0
$87$	1.55719e8	−	8.99046e7i	2.71810	−	1.56930i
$88$		0			0
$89$	9.42793e6	+	5.44322e6i	0.150264	+	0.0867552i	0.573247	−	0.819383i	$-0.305684\pi$
$89$	9.42793e6	+	5.44322e6i	0.150264	+	0.0867552i	−0.422983	+	0.906138i	$0.639017\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−7.98057e7	+	1.38228e8i	−1.06685	+	1.84783i
$94$		0			0
$95$	9.39721e6	+	1.62764e7i	0.115373	+	0.199832i
$96$		0			0
$97$		−	5.55681e7i		−	0.627681i	−0.949476	−	0.313840i	$-0.898384\pi$
$97$		−	5.55681e7i		−	0.627681i	0.949476	−	0.313840i	$-0.101616\pi$
$98$		0			0
$99$	−1.77796e8			−1.85089
$100$		0			0
$101$	−6.63105e7	+	3.82844e7i	−0.637231	+	0.367905i	−0.783547	−	0.621332i	$-0.786592\pi$
$101$	−6.63105e7	+	3.82844e7i	−0.637231	+	0.367905i	0.146316	+	0.989238i	$0.453258\pi$
$102$		0			0
$103$	1.10175e8	+	6.36096e7i	0.978891	+	0.565163i	0.901935	−	0.431871i	$-0.142147\pi$
$103$	1.10175e8	+	6.36096e7i	0.978891	+	0.565163i	0.0769560	+	0.997034i	$0.475480\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.75020e7	+	1.16917e8i	−0.514969	+	0.891953i	0.484880	+	0.874581i	$0.338863\pi$
$107$	−6.75020e7	+	1.16917e8i	−0.514969	+	0.891953i	−0.999849	+	0.0173723i	$0.994470\pi$
$108$		0			0
$109$	3.85089e7	+	6.66994e7i	0.272807	+	0.472515i	0.969579	−	0.244777i	$-0.0787147\pi$
$109$	3.85089e7	+	6.66994e7i	0.272807	+	0.472515i	−0.696773	+	0.717292i	$0.745381\pi$
$110$		0			0
$111$			3.65452e8i			2.40735i
$112$		0			0
$113$	9.20801e7			0.564745			0.282372	−	0.959305i	$-0.408879\pi$
$113$	9.20801e7			0.564745			0.282372	+	0.959305i	$0.408879\pi$
$114$		0			0
$115$	−1.09911e8	+	6.34573e7i	−0.628421	+	0.362819i
$116$		0			0
$117$	−3.75287e8	−	2.16672e8i	−2.00272	−	1.15627i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.68948e7	−	6.39037e7i	0.172117	−	0.298116i
$122$		0			0
$123$	1.94297e6	+	3.36533e6i	0.00848881	+	0.0147030i
$124$		0			0
$125$		−	1.42850e8i		−	0.585112i
$126$		0			0
$127$	−3.72776e8			−1.43296			−0.716479	−	0.697609i	$-0.754247\pi$
$127$	−3.72776e8			−1.43296			−0.716479	+	0.697609i	$0.754247\pi$
$128$		0			0
$129$	−5.18822e8	+	2.99542e8i	−1.87353	+	1.08168i
$130$		0			0
$131$	2.02519e8	+	1.16924e8i	0.687671	+	0.397027i	0.802739	−	0.596331i	$-0.203375\pi$
$131$	2.02519e8	+	1.16924e8i	0.687671	+	0.397027i	−0.115068	+	0.993358i	$0.536709\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−5.96981e8	+	1.03400e9i	−1.79732	+	3.11305i
$136$		0			0
$137$	−3.39126e8	−	5.87384e8i	−0.962673	−	1.66740i	−0.715740	−	0.698366i	$-0.753911\pi$
$137$	−3.39126e8	−	5.87384e8i	−0.962673	−	1.66740i	−0.246933	−	0.969033i	$-0.579423\pi$
$138$		0			0
$139$		−	4.09826e8i		−	1.09784i	−0.835874	−	0.548921i	$-0.815039\pi$
$139$		−	4.09826e8i		−	1.09784i	0.835874	−	0.548921i	$-0.184961\pi$
$140$		0			0
$141$	−1.02051e9			−2.58191
$142$		0			0
$143$	−2.96710e8	+	1.71305e8i	−0.709557	+	0.409663i
$144$		0			0
$145$	−1.02248e9	−	5.90329e8i	−2.31304	−	1.33543i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.32479e8	+	4.02666e8i	−0.471671	+	0.816958i	−0.999475	−	0.0324084i	$-0.989682\pi$
$149$	−2.32479e8	+	4.02666e8i	−0.471671	+	0.816958i	0.527804	+	0.849366i	$0.323016\pi$
$150$		0			0
$151$	−2.12626e8	−	3.68280e8i	−0.408987	−	0.708386i	0.585790	−	0.810463i	$-0.300785\pi$
$151$	−2.12626e8	−	3.68280e8i	−0.408987	−	0.708386i	−0.994777	+	0.102077i	$0.967451\pi$
$152$		0			0
$153$		−	6.90090e8i		−	1.25933i
$154$		0			0
$155$	1.04804e9			1.81572
$156$		0			0
$157$	7.91338e8	−	4.56879e8i	1.30246	−	0.751974i	0.321633	−	0.946865i	$-0.395768\pi$
$157$	7.91338e8	−	4.56879e8i	1.30246	−	0.751974i	0.980825	+	0.194890i	$0.0624351\pi$
$158$		0			0
$159$	1.11638e9	+	6.44542e8i	1.74672	+	1.00847i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.96853e8	−	5.14164e8i	0.420524	−	0.728368i	−0.575467	−	0.817825i	$-0.695180\pi$
$163$	2.96853e8	−	5.14164e8i	0.420524	−	0.728368i	0.995991	+	0.0894567i	$0.0285131\pi$
$164$		0			0
$165$	8.39106e8	+	1.45337e9i	1.13209	+	1.96084i
$166$		0			0
$167$			6.97081e8i			0.896225i	0.893977	+	0.448113i	$0.147904\pi$
$167$			6.97081e8i			0.896225i	−0.893977	+	0.448113i	$0.852096\pi$
$168$		0			0
$169$	−1.93178e7			−0.0236816
$170$		0			0
$171$	−2.53180e8	+	1.46174e8i	−0.296105	+	0.170956i
$172$		0			0
$173$	4.04103e8	+	2.33309e8i	0.451136	+	0.260463i	0.708310	−	0.705902i	$-0.249458\pi$
$173$	4.04103e8	+	2.33309e8i	0.451136	+	0.260463i	−0.257174	+	0.966365i	$0.582791\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.74786e8	+	4.75943e8i	−0.279963	+	0.484911i
$178$		0			0
$179$	−4.26118e8	−	7.38058e8i	−0.415066	−	0.718916i	0.580369	−	0.814354i	$-0.302908\pi$
$179$	−4.26118e8	−	7.38058e8i	−0.415066	−	0.718916i	−0.995435	+	0.0954374i	$0.969575\pi$
$180$		0			0
$181$		−	7.41085e8i		−	0.690484i	−0.938514	−	0.345242i	$-0.887797\pi$
$181$		−	7.41085e8i		−	0.690484i	0.938514	−	0.345242i	$-0.112203\pi$
$182$		0			0
$183$	−2.06729e9			−1.84330
$184$		0			0
$185$	2.07813e9	−	1.19981e9i	1.77413	−	1.02430i
$186$		0			0
$187$	−4.72502e8	−	2.72799e8i	−0.386400	−	0.223088i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.73865e8	+	3.01143e8i	−0.130641	+	0.226277i	−0.923924	−	0.382577i	$-0.875037\pi$
$191$	−1.73865e8	+	3.01143e8i	−0.130641	+	0.226277i	0.793283	+	0.608853i	$0.208370\pi$
$192$		0			0
$193$	2.48677e8	+	4.30722e8i	0.179228	+	0.310433i	0.941617	−	0.336687i	$-0.109307\pi$
$193$	2.48677e8	+	4.30722e8i	0.179228	+	0.310433i	−0.762388	+	0.647120i	$0.775973\pi$
$194$		0			0
$195$			4.09032e9i			2.82891i
$196$		0			0
$197$	−2.99473e8			−0.198835			−0.0994175	−	0.995046i	$-0.531698\pi$
$197$	−2.99473e8			−0.198835			−0.0994175	+	0.995046i	$0.531698\pi$
$198$		0			0
$199$	−5.97731e7	+	3.45100e7i	−0.0381148	+	0.0220056i	−0.518936	−	0.854813i	$-0.673672\pi$
$199$	−5.97731e7	+	3.45100e7i	−0.0381148	+	0.0220056i	0.480822	+	0.876818i	$0.340338\pi$
$200$		0			0
$201$	9.69223e8	+	5.59581e8i	0.593799	+	0.342830i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.27579e7	−	2.20973e7i	0.00722377	−	0.0125119i
$206$		0			0
$207$	−9.87080e8	−	1.70967e9i	−0.537614	−	0.931175i
$208$		0			0
$209$			2.31136e8i			0.121138i
$210$		0			0
$211$	1.38118e9			0.696820			0.348410	−	0.937342i	$-0.386722\pi$
$211$	1.38118e9			0.696820			0.348410	+	0.937342i	$0.386722\pi$
$212$		0			0
$213$	2.01728e7	−	1.16467e7i	0.00980047	−	0.00565830i
$214$		0			0
$215$	3.40668e9	+	1.96685e9i	1.59433	+	0.920484i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2.85289e9	−	4.94135e9i	1.24025	−	2.14817i
$220$		0			0
$221$	−6.64897e8	−	1.15163e9i	−0.278731	−	0.482776i
$222$		0			0
$223$		−	3.59070e9i		−	1.45198i	−0.687707	−	0.725989i	$-0.741383\pi$
$223$		−	3.59070e9i		−	1.45198i	0.687707	−	0.725989i	$-0.258617\pi$
$224$		0			0
$225$	8.07987e9			3.15264
$226$		0			0
$227$	−1.25764e9	+	7.26100e8i	−0.473646	+	0.273460i	−0.717765	−	0.696286i	$-0.754835\pi$
$227$	−1.25764e9	+	7.26100e8i	−0.473646	+	0.273460i	0.244119	+	0.969745i	$0.421501\pi$
$228$		0			0
$229$	−3.80290e9	−	2.19560e9i	−1.38284	−	0.798384i	−0.390347	−	0.920668i	$-0.627645\pi$
$229$	−3.80290e9	−	2.19560e9i	−1.38284	−	0.798384i	−0.992495	+	0.122283i	$0.960978\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.25662e9	+	2.17653e9i	−0.426364	+	0.738485i	−0.996547	−	0.0830333i	$-0.973539\pi$
$233$	−1.25662e9	+	2.17653e9i	−0.426364	+	0.738485i	0.570182	+	0.821518i	$0.306873\pi$
$234$		0			0
$235$	3.35042e9	+	5.80310e9i	1.09857	+	1.90278i
$236$		0			0
$237$			1.65936e9i			0.525952i
$238$		0			0
$239$	−1.38734e9			−0.425198			−0.212599	−	0.977140i	$-0.568193\pi$
$239$	−1.38734e9			−0.425198			−0.212599	+	0.977140i	$0.568193\pi$
$240$		0			0
$241$	1.73691e9	−	1.00280e9i	0.514882	−	0.297267i	−0.219956	−	0.975510i	$-0.570591\pi$
$241$	1.73691e9	−	1.00280e9i	0.514882	−	0.297267i	0.734838	+	0.678242i	$0.237258\pi$
$242$		0			0
$243$	−3.57345e9	−	2.06313e9i	−1.02486	−	0.591701i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.81675e8	+	4.87875e8i	−0.0756763	+	0.131075i
$248$		0			0
$249$	−3.95129e8	−	6.84384e8i	−0.102788	−	0.178034i
$250$		0			0
$251$		−	7.22678e9i		−	1.82075i	−0.413786	−	0.910374i	$-0.635794\pi$
$251$		−	7.22678e9i		−	1.82075i	0.413786	−	0.910374i	$-0.364206\pi$
$252$		0			0
$253$	−1.56081e9			−0.380950
$254$		0			0
$255$	−5.64106e9	+	3.25687e9i	−1.33414	+	0.770264i
$256$		0			0
$257$	6.62531e8	+	3.82512e8i	0.151871	+	0.0876825i	0.574010	−	0.818849i	$-0.305387\pi$
$257$	6.62531e8	+	3.82512e8i	0.151871	+	0.0876825i	−0.422139	+	0.906531i	$0.638721\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	9.18258e9	−	1.59047e10i	1.97880	−	3.42739i
$262$		0			0
$263$	3.08764e9	+	5.34796e9i	0.645363	+	1.11780i	0.984217	+	0.176963i	$0.0566273\pi$
$263$	3.08764e9	+	5.34796e9i	0.645363	+	1.11780i	−0.338854	+	0.940839i	$0.610039\pi$
$264$		0			0
$265$		−	8.46434e9i		−	1.71636i
$266$		0			0
$267$	1.59838e9			0.314511
$268$		0			0
$269$	−5.55561e9	+	3.20753e9i	−1.06102	+	0.612579i	−0.925714	−	0.378225i	$-0.876535\pi$
$269$	−5.55561e9	+	3.20753e9i	−1.06102	+	0.612579i	−0.135304	+	0.990804i	$0.543201\pi$
$270$		0			0
$271$	−4.47050e9	−	2.58104e9i	−0.828855	−	0.478540i	0.0246053	−	0.999697i	$-0.492167\pi$
$271$	−4.47050e9	−	2.58104e9i	−0.828855	−	0.478540i	−0.853461	+	0.521157i	$0.825500\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.19405e9	−	5.53226e9i	0.558485	−	0.967324i
$276$		0			0
$277$	−3.16804e9	−	5.48720e9i	−0.538110	−	0.932034i	−0.999006	−	0.0445796i	$-0.985805\pi$
$277$	−3.16804e9	−	5.48720e9i	−0.538110	−	0.932034i	0.460896	−	0.887454i	$-0.347528\pi$
$278$		0			0
$279$			1.63022e10i			2.69048i
$280$		0			0
$281$	2.11288e9			0.338883			0.169441	−	0.985540i	$-0.445804\pi$
$281$	2.11288e9			0.338883			0.169441	+	0.985540i	$0.445804\pi$
$282$		0			0
$283$	4.45489e9	−	2.57203e9i	0.694530	−	0.400987i	−0.110777	−	0.993845i	$-0.535334\pi$
$283$	4.45489e9	−	2.57203e9i	0.694530	−	0.400987i	0.805307	+	0.592858i	$0.202001\pi$
$284$		0			0
$285$	2.38976e9	+	1.37973e9i	0.362222	+	0.209129i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2.42905e9	+	4.20723e9i	−0.348213	+	0.603122i
$290$		0			0
$291$	−4.07935e9	−	7.06564e9i	−0.568877	−	0.985325i
$292$		0			0
$293$			7.60278e9i			1.03158i	0.856716	+	0.515789i	$0.172501\pi$
$293$			7.60278e9i			1.03158i	−0.856716	+	0.515789i	$0.827499\pi$
$294$		0			0
$295$	3.60858e9			0.476484
$296$		0			0
$297$	−1.27163e10	+	7.34173e9i	−1.63431	+	0.943567i
$298$		0			0
$299$	−3.29451e9	−	1.90209e9i	−0.412199	−	0.237983i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−5.62104e9	+	9.73592e9i	−0.666877	+	1.15507i
$304$		0			0
$305$	6.78709e9	+	1.17556e10i	0.784304	+	1.35845i
$306$		0			0
$307$		−	1.31307e10i		−	1.47820i	−0.673593	−	0.739102i	$-0.735250\pi$
$307$		−	1.31307e10i		−	1.47820i	0.673593	−	0.739102i	$-0.264750\pi$
$308$		0			0
$309$	1.86787e10			2.04887
$310$		0			0
$311$	1.29974e10	−	7.50404e9i	1.38936	−	0.802146i	0.396115	−	0.918201i	$-0.370358\pi$
$311$	1.29974e10	−	7.50404e9i	1.38936	−	0.802146i	0.993243	+	0.116055i	$0.0370248\pi$
$312$		0			0
$313$	7.07342e9	+	4.08384e9i	0.736974	+	0.425492i	0.820968	−	0.570974i	$-0.193434\pi$
$313$	7.07342e9	+	4.08384e9i	0.736974	+	0.425492i	−0.0839939	+	0.996466i	$0.526768\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.80008e9	−	3.11783e9i	0.178260	−	0.308756i	−0.763025	−	0.646369i	$-0.776286\pi$
$317$	1.80008e9	−	3.11783e9i	0.178260	−	0.308756i	0.941285	+	0.337614i	$0.109620\pi$
$318$		0			0
$319$	−7.25993e9	−	1.25746e10i	−0.701083	−	1.21431i
$320$		0			0
$321$			1.98217e10i			1.86690i
$322$		0			0
$323$	−8.97120e8			−0.0824214
$324$		0			0
$325$	1.34838e10	−	7.78489e9i	1.20859	−	0.697781i
$326$		0			0
$327$	9.79302e9	+	5.65400e9i	0.856496	+	0.494498i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.52697e9	−	1.47692e10i	0.710367	−	1.23039i	−0.254352	−	0.967112i	$-0.581862\pi$
$331$	8.52697e9	−	1.47692e10i	0.710367	−	1.23039i	0.964719	−	0.263281i	$-0.0848045\pi$
$332$		0			0
$333$	1.86631e10	+	3.23254e10i	1.51777	+	2.62886i
$334$		0			0
$335$		−	7.34861e9i		−	0.583480i
$336$		0			0
$337$	−2.14873e9			−0.166595			−0.0832976	−	0.996525i	$-0.526545\pi$
$337$	−2.14873e9			−0.166595			−0.0832976	+	0.996525i	$0.526545\pi$
$338$		0			0
$339$	1.17082e10	−	6.75975e9i	0.886528	−	0.511837i
$340$		0			0
$341$	1.11621e10	+	6.44443e9i	0.825520	+	0.476614i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−9.31701e9	+	1.61375e10i	−0.657658	+	1.13910i
$346$		0			0
$347$	−1.10714e10	−	1.91762e10i	−0.763631	−	1.32265i	−0.940967	−	0.338498i	$-0.890081\pi$
$347$	−1.10714e10	−	1.91762e10i	−0.763631	−	1.32265i	0.177336	−	0.984150i	$-0.443252\pi$
$348$		0			0
$349$			5.06835e8i			0.0341637i	0.999854	+	0.0170818i	$0.00543758\pi$
$349$			5.06835e8i			0.0341637i	−0.999854	+	0.0170818i	$0.994562\pi$
$350$		0			0
$351$	−3.57882e10			−2.35782
$352$		0			0
$353$	1.89369e10	−	1.09332e10i	1.21958	−	0.704124i	0.254751	−	0.967007i	$-0.418006\pi$
$353$	1.89369e10	−	1.09332e10i	1.21958	−	0.704124i	0.964828	+	0.262882i	$0.0846731\pi$
$354$		0			0
$355$	−1.32458e8	−	7.64745e7i	−0.00833996	−	0.00481508i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.26180e9	−	1.43099e10i	0.497390	−	0.861504i	−0.502606	−	0.864516i	$-0.667625\pi$
$359$	8.26180e9	−	1.43099e10i	0.497390	−	0.861504i	0.999995	+	0.00301141i	$0.000958563\pi$
$360$		0			0
$361$	−8.30176e9	−	1.43791e10i	−0.488811	−	0.846646i
$362$		0			0
$363$		−	1.08340e10i		−	0.623970i
$364$		0			0
$365$	−3.74651e10			−2.11084
$366$		0			0
$367$	7.32875e9	−	4.23125e9i	0.403985	−	0.233241i	−0.284217	−	0.958760i	$-0.591734\pi$
$367$	7.32875e9	−	4.23125e9i	0.403985	−	0.233241i	0.688202	+	0.725519i	$0.258400\pi$
$368$		0			0
$369$	3.43724e8	+	1.98449e8i	0.0185398	+	0.0107040i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.27113e10	+	2.20167e10i	−0.656684	+	1.13741i	0.324785	+	0.945788i	$0.394708\pi$
$373$	−1.27113e10	+	2.20167e10i	−0.656684	+	1.13741i	−0.981469	+	0.191622i	$0.938625\pi$
$374$		0			0
$375$	−1.04868e10	−	1.81637e10i	−0.530296	−	0.918500i
$376$		0			0
$377$		−	3.53894e10i		−	1.75189i
$378$		0			0
$379$	3.76359e9			0.182409			0.0912044	−	0.995832i	$-0.470928\pi$
$379$	3.76359e9			0.182409			0.0912044	+	0.995832i	$0.470928\pi$
$380$		0			0
$381$	−4.73995e10	+	2.73661e10i	−2.24944	+	1.29871i
$382$		0			0
$383$	−1.38377e10	−	7.98919e9i	−0.643085	−	0.371285i	0.142717	−	0.989764i	$-0.454416\pi$
$383$	−1.38377e10	−	7.98919e9i	−0.643085	−	0.371285i	−0.785802	+	0.618478i	$0.787749\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.05943e10	+	5.29909e10i	−1.36394	+	2.36242i
$388$		0			0
$389$	1.02289e10	+	1.77170e10i	0.446716	+	0.773734i	0.998170	−	0.0604707i	$-0.0192602\pi$
$389$	1.02289e10	+	1.77170e10i	0.446716	+	0.773734i	−0.551454	+	0.834205i	$0.685927\pi$
$390$		0			0
$391$		−	6.05805e9i		−	0.259195i
$392$		0			0
$393$	3.43344e10			1.43933
$394$		0			0
$395$	9.43588e9	−	5.44781e9i	0.387609	−	0.223786i
$396$		0			0
$397$	6.29042e9	+	3.63177e9i	0.253231	+	0.146203i	0.621243	−	0.783618i	$-0.286628\pi$
$397$	6.29042e9	+	3.63177e9i	0.253231	+	0.146203i	−0.368012	+	0.929821i	$0.619961\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.10853e9	+	1.92003e9i	−0.0428716	+	0.0742558i	−0.886665	−	0.462412i	$-0.846984\pi$
$401$	−1.10853e9	+	1.92003e9i	−0.0428716	+	0.0742558i	0.843793	+	0.536668i	$0.180317\pi$
$402$		0			0
$403$	1.57071e10	+	2.72054e10i	0.595490	+	1.03142i
$404$		0			0
$405$			8.04476e10i			2.99015i
$406$		0			0
$407$	2.95108e10			1.07548
$408$		0			0
$409$	−2.93161e10	+	1.69256e10i	−1.04764	+	0.604856i	−0.921988	−	0.387218i	$-0.873436\pi$
$409$	−2.93161e10	+	1.69256e10i	−1.04764	+	0.604856i	−0.125653	+	0.992074i	$0.540103\pi$
$410$		0			0
$411$	−8.62416e10	−	4.97916e10i	−3.02238	−	1.74497i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.59449e9	+	4.49378e9i	−0.0874700	+	0.151502i
$416$		0			0
$417$	−3.00860e10	−	5.21104e10i	−0.994993	−	1.72338i
$418$		0			0
$419$		−	3.14074e10i		−	1.01900i	−0.860469	−	0.509502i	$-0.829830\pi$
$419$		−	3.14074e10i		−	1.01900i	0.860469	−	0.509502i	$-0.170170\pi$
$420$		0			0
$421$	1.95780e10			0.623217			0.311608	−	0.950211i	$-0.399132\pi$
$421$	1.95780e10			0.623217			0.311608	+	0.950211i	$0.399132\pi$
$422$		0			0
$423$	−9.02672e10	+	5.21158e10i	−2.81948	+	1.62783i
$424$		0			0
$425$	2.14727e10	+	1.23972e10i	0.658158	+	0.379988i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.51516e10	+	4.35639e10i	−0.742569	+	1.28617i
$430$		0			0
$431$	9.90486e9	+	1.71557e10i	0.287038	+	0.497164i	0.973101	−	0.230377i	$-0.0739961\pi$
$431$	9.90486e9	+	1.71557e10i	0.287038	+	0.497164i	−0.686063	+	0.727542i	$0.740663\pi$
$432$		0			0
$433$		−	1.98951e10i		−	0.565972i	−0.959124	−	0.282986i	$-0.908675\pi$
$433$		−	1.98951e10i		−	0.565972i	0.959124	−	0.282986i	$-0.0913250\pi$
$434$		0			0
$435$	−1.73348e11			−4.84130
$436$		0			0
$437$	−2.22258e9	+	1.28321e9i	−0.0609441	+	0.0351861i
$438$		0			0
$439$	5.83968e10	+	3.37154e10i	1.57228	+	0.907759i	0.995888	+	0.0905878i	$0.0288746\pi$
$439$	5.83968e10	+	3.37154e10i	1.57228	+	0.907759i	0.576396	+	0.817171i	$0.304459\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.57082e10	+	4.45279e10i	−0.667508	+	1.15616i	0.311091	+	0.950380i	$0.399306\pi$
$443$	−2.57082e10	+	4.45279e10i	−0.667508	+	1.15616i	−0.978599	+	0.205778i	$0.934028\pi$
$444$		0			0
$445$	−5.24762e9	−	9.08915e9i	−0.133821	−	0.231784i
$446$		0			0
$447$			6.82667e10i			1.70993i
$448$		0			0
$449$	−2.77031e9			−0.0681620			−0.0340810	−	0.999419i	$-0.510850\pi$
$449$	−2.77031e9			−0.0681620			−0.0340810	+	0.999419i	$0.510850\pi$
$450$		0			0
$451$	2.71755e8	−	1.56898e8i	0.00656858	−	0.00379237i
$452$		0			0
$453$	−5.40720e10	−	3.12185e10i	−1.28404	−	0.741343i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.86662e10	−	3.23309e10i	0.427949	−	0.741229i	−0.568742	−	0.822516i	$-0.692570\pi$
$457$	1.86662e10	−	3.23309e10i	0.427949	−	0.741229i	0.996691	+	0.0812869i	$0.0259030\pi$
$458$		0			0
$459$	−2.84959e10	−	4.93563e10i	−0.641994	−	1.11197i
$460$		0			0
$461$		−	3.50363e10i		−	0.775736i	−0.921715	−	0.387868i	$-0.873212\pi$
$461$		−	3.50363e10i		−	0.775736i	0.921715	−	0.387868i	$-0.126788\pi$
$462$		0			0
$463$	−7.33892e10			−1.59701			−0.798506	−	0.601986i	$-0.794376\pi$
$463$	−7.33892e10			−1.59701			−0.798506	+	0.601986i	$0.794376\pi$
$464$		0			0
$465$	1.33261e11	−	7.69380e10i	2.85029	−	1.64562i
$466$		0			0
$467$	−4.16603e10	−	2.40526e10i	−0.875901	−	0.505702i	−0.00659622	−	0.999978i	$-0.502100\pi$
$467$	−4.16603e10	−	2.40526e10i	−0.875901	−	0.505702i	−0.869305	+	0.494277i	$0.835433\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	6.70805e10	−	1.16187e11i	1.36305	−	2.36088i
$472$		0			0
$473$	2.41885e10	+	4.18957e10i	0.483241	+	0.836998i
$474$		0			0
$475$		−	1.05039e10i		−	0.206336i
$476$		0			0
$477$	1.31663e11			2.54326
$478$		0			0
$479$	2.74061e10	−	1.58229e10i	0.520602	−	0.300570i	−0.216579	−	0.976265i	$-0.569490\pi$
$479$	2.74061e10	−	1.58229e10i	0.520602	−	0.300570i	0.737181	+	0.675696i	$0.236157\pi$
$480$		0			0
$481$	6.22906e10	+	3.59635e10i	1.16370	+	0.671864i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.67857e10	+	4.63942e10i	−0.484101	+	0.838487i
$486$		0			0
$487$	1.32231e10	+	2.29032e10i	0.235082	+	0.407173i	0.959296	−	0.282401i	$-0.0911309\pi$
$487$	1.32231e10	+	2.29032e10i	0.235082	+	0.407173i	−0.724215	+	0.689575i	$0.757798\pi$
$488$		0			0
$489$		−	8.71697e10i		−	1.52451i
$490$		0			0
$491$	8.51063e9			0.146432			0.0732159	−	0.997316i	$-0.476674\pi$
$491$	8.51063e9			0.146432			0.0732159	+	0.997316i	$0.476674\pi$
$492$		0			0
$493$	4.88063e10	−	2.81783e10i	0.826206	−	0.477010i
$494$		0			0
$495$	1.48443e11	+	8.57037e10i	2.47252	+	1.42751i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−3.21633e10	+	5.57084e10i	−0.518750	+	0.898501i	0.481013	+	0.876714i	$0.340269\pi$
$499$	−3.21633e10	+	5.57084e10i	−0.518750	+	0.898501i	−0.999763	+	0.0217874i	$0.993064\pi$
$500$		0			0
$501$	5.11738e10	+	8.86357e10i	0.812264	+	1.40688i
$502$		0			0
$503$		−	1.04123e10i		−	0.162658i	−0.996687	−	0.0813292i	$-0.974083\pi$
$503$		−	1.04123e10i		−	0.162658i	0.996687	−	0.0813292i	$-0.0259165\pi$
$504$		0			0
$505$	7.38174e10			1.13499
$506$		0			0
$507$	−2.45631e9	+	1.41815e9i	−0.0371751	+	0.0214631i
$508$		0			0
$509$	1.18781e10	+	6.85785e9i	0.176961	+	0.102168i	0.585864	−	0.810409i	$-0.300755\pi$
$509$	1.18781e10	+	6.85785e9i	0.176961	+	0.102168i	−0.408903	+	0.912578i	$0.634089\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.20719e10	+	2.09091e10i	−0.174303	+	0.301902i
$514$		0			0
$515$	−6.13239e10	−	1.06216e11i	−0.871768	−	1.50995i
$516$		0			0
$517$			8.24076e10i			1.15347i
$518$		0			0
$519$	6.85103e10			0.944249
$520$		0			0
$521$	7.79914e10	−	4.50284e10i	1.05851	−	0.611132i	0.133492	−	0.991050i	$-0.457381\pi$
$521$	7.79914e10	−	4.50284e10i	1.05851	−	0.611132i	0.925020	+	0.379918i	$0.124048\pi$
$522$		0			0
$523$	3.81036e10	+	2.19992e10i	0.509284	+	0.294035i	0.732539	−	0.680725i	$-0.238335\pi$
$523$	3.81036e10	+	2.19992e10i	0.509284	+	0.294035i	−0.223255	+	0.974760i	$0.571668\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.50131e10	+	4.33240e10i	−0.324284	+	0.561676i
$528$		0			0
$529$	3.04903e10	+	5.28107e10i	0.389349	+	0.674372i
$530$		0			0
$531$			5.61315e10i			0.706039i
$532$		0			0
$533$	7.64818e8			0.00947653
$534$		0			0
$535$	1.12716e11	−	6.50764e10i	1.37584	−	0.794344i
$536$		0			0
$537$	−1.08364e11	−	6.25640e10i	−1.30313	−	0.752363i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.90766e10	−	8.50031e10i	0.572908	−	0.992306i	−0.423357	−	0.905963i	$-0.639148\pi$
$541$	4.90766e10	−	8.50031e10i	0.572908	−	0.992306i	0.996265	−	0.0863435i	$-0.0275183\pi$
$542$		0			0
$543$	−5.44042e10	−	9.42309e10i	−0.625797	−	1.08391i
$544$		0			0
$545$		−	7.42503e10i		−	0.841612i
$546$		0			0
$547$	−9.97101e8			−0.0111376			−0.00556878	−	0.999984i	$-0.501773\pi$
$547$	−9.97101e8			−0.0111376			−0.00556878	+	0.999984i	$0.501773\pi$
$548$		0			0
$549$	−1.82858e11	+	1.05573e11i	−2.01291	+	1.16216i
$550$		0			0
$551$	−2.06762e10	−	1.19374e10i	−0.224318	−	0.129510i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.76160e11	−	3.05118e11i	1.85667	−	3.21585i
$556$		0			0
$557$	−1.76931e10	−	3.06454e10i	−0.183816	−	0.318379i	0.759361	−	0.650670i	$-0.225512\pi$
$557$	−1.76931e10	−	3.06454e10i	−0.183816	−	0.318379i	−0.943177	+	0.332291i	$0.892178\pi$
$558$		0			0
$559$			1.17910e11i			1.20754i
$560$		0			0
$561$	−8.01066e10			−0.808755
$562$		0			0
$563$	−1.54756e11	+	8.93482e10i	−1.54033	+	0.889308i	−0.541509	+	0.840695i	$0.682147\pi$
$563$	−1.54756e11	+	8.93482e10i	−1.54033	+	0.889308i	−0.998818	+	0.0486136i	$0.984520\pi$
$564$		0			0
$565$	−7.68783e10	−	4.43857e10i	−0.754414	−	0.435561i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.58381e10	−	7.93940e10i	0.437298	−	0.757423i	−0.560182	−	0.828370i	$-0.689269\pi$
$569$	4.58381e10	−	7.93940e10i	0.437298	−	0.757423i	0.997480	+	0.0709466i	$0.0226020\pi$
$570$		0			0
$571$	−8.30890e9	−	1.43914e10i	−0.0781626	−	0.135382i	0.824295	−	0.566161i	$-0.191572\pi$
$571$	−8.30890e9	−	1.43914e10i	−0.0781626	−	0.135382i	−0.902457	+	0.430779i	$0.858239\pi$
$572$		0			0
$573$			5.10549e10i			0.473608i
$574$		0			0
$575$	7.09303e10			0.648874
$576$		0			0
$577$	−1.17744e11	+	6.79795e10i	−1.06227	+	0.613303i	−0.926060	−	0.377377i	$-0.876826\pi$
$577$	−1.17744e11	+	6.79795e10i	−1.06227	+	0.613303i	−0.136212	+	0.990680i	$0.543493\pi$
$578$		0			0
$579$	6.32400e10	+	3.65116e10i	0.562701	+	0.324875i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	5.20477e10	−	9.01492e10i	0.450533	−	0.780347i
$584$		0			0
$585$	2.08886e11	+	3.61802e11i	1.78356	+	3.08921i
$586$		0			0
$587$			2.24512e10i			0.189098i	0.995520	+	0.0945491i	$0.0301409\pi$
$587$			2.24512e10i			0.189098i	−0.995520	+	0.0945491i	$0.969859\pi$
$588$		0			0
$589$	2.11929e10			0.176088
$590$		0			0
$591$	−3.80788e10	+	2.19848e10i	−0.312128	+	0.180207i
$592$		0			0
$593$	−2.08225e11	−	1.20219e11i	−1.68389	−	0.972196i	−0.959031	−	0.283301i	$-0.908571\pi$
$593$	−2.08225e11	−	1.20219e11i	−1.68389	−	0.972196i	−0.724861	−	0.688895i	$-0.758096\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.06687e9	+	8.77608e9i	−0.0398880	+	0.0690881i
$598$		0			0
$599$	1.81295e10	+	3.14012e10i	0.140825	+	0.243915i	0.927807	−	0.373060i	$-0.121691\pi$
$599$	1.81295e10	+	3.14012e10i	0.140825	+	0.243915i	−0.786983	+	0.616975i	$0.788358\pi$
$600$		0			0
$601$		−	1.88260e11i		−	1.44298i	−0.692426	−	0.721488i	$-0.743458\pi$
$601$		−	1.88260e11i		−	1.44298i	0.692426	−	0.721488i	$-0.256542\pi$
$602$		0			0
$603$	1.14308e11			0.864582
$604$		0			0
$605$	−6.16074e10	+	3.55691e10i	−0.459845	+	0.265492i
$606$		0			0
$607$	−2.56421e10	−	1.48045e10i	−0.188886	−	0.109053i	0.402575	−	0.915387i	$-0.368115\pi$
$607$	−2.56421e10	−	1.48045e10i	−0.188886	−	0.109053i	−0.591461	+	0.806334i	$0.701449\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.00426e11	+	1.73944e11i	−0.720582	+	1.24808i
$612$		0			0
$613$	−1.14545e11	−	1.98398e11i	−0.811211	−	1.40506i	−0.912017	−	0.410152i	$-0.865476\pi$
$613$	−1.14545e11	−	1.98398e11i	−0.811211	−	1.40506i	0.100806	−	0.994906i	$-0.467858\pi$
$614$		0			0
$615$		−	3.74631e9i		−	0.0261881i
$616$		0			0
$617$	2.19299e11			1.51320			0.756598	−	0.653880i	$-0.226860\pi$
$617$	2.19299e11			1.51320			0.756598	+	0.653880i	$0.226860\pi$
$618$		0			0
$619$	−5.21137e10	+	3.00878e10i	−0.354968	+	0.204941i	−0.666871	−	0.745173i	$-0.732367\pi$
$619$	−5.21137e10	+	3.00878e10i	−0.354968	+	0.204941i	0.311903	+	0.950114i	$0.399034\pi$
$620$		0			0
$621$	−1.41195e11	−	8.15189e10i	−0.949407	−	0.548140i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	3.63760e10	−	6.30050e10i	0.238393	−	0.412910i
$626$		0			0
$627$	1.69681e10	+	2.93895e10i	0.109790	+	0.190161i
$628$		0			0
$629$			1.14542e11i			0.731748i
$630$		0			0
$631$	−1.82301e11			−1.14993			−0.574965	−	0.818178i	$-0.694984\pi$
$631$	−1.82301e11			−1.14993			−0.574965	+	0.818178i	$0.694984\pi$
$632$		0			0
$633$	1.75621e11	−	1.01395e11i	1.09386	−	0.631540i
$634$		0			0
$635$	3.11233e11	+	1.79691e11i	1.91422	+	1.10517i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.18956e9	−	2.06038e9i	0.00713483	−	0.0123579i
$640$		0			0
$641$	1.19484e11	+	2.06952e11i	0.707746	+	1.22585i	0.965691	+	0.259693i	$0.0836213\pi$
$641$	1.19484e11	+	2.06952e11i	0.707746	+	1.22585i	−0.257945	+	0.966160i	$0.583045\pi$
$642$		0			0
$643$		−	2.67685e11i		−	1.56596i	−0.622046	−	0.782980i	$-0.713698\pi$
$643$		−	2.67685e11i		−	1.56596i	0.622046	−	0.782980i	$-0.286302\pi$
$644$		0			0
$645$	5.77557e11			3.33700
$646$		0			0
$647$	1.69051e9	−	9.76018e8i	0.00964720	−	0.00556981i	−0.495169	−	0.868797i	$-0.664894\pi$
$647$	1.69051e9	−	9.76018e8i	0.00964720	−	0.00556981i	0.504816	+	0.863227i	$0.331560\pi$
$648$		0			0
$649$	3.84331e10	+	2.21894e10i	0.216634	+	0.125074i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.26140e11	−	2.18481e11i	0.693744	−	1.20160i	−0.276858	−	0.960911i	$-0.589293\pi$
$653$	1.26140e11	−	2.18481e11i	0.693744	−	1.20160i	0.970602	−	0.240690i	$-0.0773736\pi$
$654$		0			0
$655$	−1.12723e11	−	1.95242e11i	−0.612417	−	1.06074i
$656$		0			0
$657$		−	5.82770e11i		−	3.12778i
$658$		0			0
$659$	−2.72053e11			−1.44249			−0.721244	−	0.692681i	$-0.756429\pi$
$659$	−2.72053e11			−1.44249			−0.721244	+	0.692681i	$0.756429\pi$
$660$		0			0
$661$	−2.10482e11	+	1.21522e11i	−1.10258	+	0.636574i	−0.936897	−	0.349605i	$-0.886316\pi$
$661$	−2.10482e11	+	1.21522e11i	−1.10258	+	0.636574i	−0.165682	+	0.986179i	$0.552982\pi$
$662$		0			0
$663$	−1.69087e11	−	9.76223e10i	−0.875096	−	0.505237i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.06106e10	−	1.39622e11i	0.407276	−	0.705422i
$668$		0			0
$669$	−2.63599e11	−	4.56567e11i	−1.31595	−	2.27929i
$670$		0			0
$671$			1.66937e11i			0.823496i
$672$		0			0
$673$	4.27524e9			0.0208401			0.0104201	−	0.999946i	$-0.496683\pi$
$673$	4.27524e9			0.0208401			0.0104201	+	0.999946i	$0.496683\pi$
$674$		0			0
$675$	5.77884e11	−	3.33642e11i	2.78372	−	1.60718i
$676$		0			0
$677$	1.72104e11	+	9.93640e10i	0.819285	+	0.473014i	0.850170	−	0.526508i	$-0.176499\pi$
$677$	1.72104e11	+	9.93640e10i	0.819285	+	0.473014i	−0.0308848	+	0.999523i	$0.509832\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.06608e11	+	1.84651e11i	−0.495682	+	0.858546i
$682$		0			0
$683$	8.36179e10	+	1.44830e11i	0.384252	+	0.665544i	0.991665	−	0.128842i	$-0.0411260\pi$
$683$	8.36179e10	+	1.44830e11i	0.384252	+	0.665544i	−0.607413	+	0.794386i	$0.707793\pi$
$684$		0			0
$685$			6.53880e11i			2.96986i
$686$		0			0
$687$	−6.44731e11			−2.89436
$688$		0			0
$689$	2.19722e11	−	1.26856e11i	0.974980	−	0.562905i
$690$		0			0
$691$	−2.09552e11	−	1.20985e11i	−0.919135	−	0.530663i	−0.0357762	−	0.999360i	$-0.511390\pi$
$691$	−2.09552e11	−	1.20985e11i	−0.919135	−	0.530663i	−0.883359	+	0.468697i	$0.844724\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.97550e11	+	3.42166e11i	−0.846714	+	1.46655i
$696$		0			0
$697$	6.08976e8	+	1.05478e9i	0.00258030	+	0.00446920i
$698$		0			0
$699$			3.69003e11i			1.54568i
$700$		0			0
$701$	−3.65999e11			−1.51568			−0.757840	−	0.652441i	$-0.773745\pi$
$701$	−3.65999e11			−1.51568			−0.757840	+	0.652441i	$0.773745\pi$
$702$		0			0
$703$	4.20231e10	−	2.42621e10i	0.172055	−	0.0993360i
$704$		0			0
$705$	8.52029e11	+	4.91919e11i	3.44904	+	1.99130i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.87001e11	+	3.23895e11i	−0.740045	+	1.28180i	0.212429	+	0.977176i	$0.431863\pi$
$709$	−1.87001e11	+	3.23895e11i	−0.740045	+	1.28180i	−0.952474	+	0.304619i	$0.901471\pi$
$710$		0			0
$711$	8.47407e10	+	1.46775e11i	0.331599	+	0.574347i
$712$		0			0
$713$			1.43111e11i			0.553753i
$714$		0			0
$715$	3.30300e11			1.26382
$716$		0			0
$717$	−1.76404e11	+	1.01847e11i	−0.667470	+	0.385364i
$718$		0			0
$719$	9.07180e9	+	5.23760e9i	0.0339451	+	0.0195982i	0.516877	−	0.856060i	$-0.327095\pi$
$719$	9.07180e9	+	5.23760e9i	0.0339451	+	0.0195982i	−0.482931	+	0.875658i	$0.660428\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.47235e11	−	2.55018e11i	0.538837	−	0.933292i
$724$		0			0
$725$	3.29924e11	+	5.71445e11i	1.19416	+	2.06834i
$726$		0			0
$727$		−	4.11284e11i		−	1.47233i	−0.676804	−	0.736163i	$-0.736636\pi$
$727$		−	4.11284e11i		−	1.47233i	0.676804	−	0.736163i	$-0.263364\pi$
$728$		0			0
$729$	−5.83421e10			−0.206572
$730$		0			0
$731$	−1.62612e11	+	9.38840e10i	−0.569485	+	0.328793i
$732$		0			0
$733$	−4.22981e11	−	2.44208e11i	−1.46523	−	0.845950i	−0.465982	−	0.884794i	$-0.654299\pi$
$733$	−4.22981e11	−	2.44208e11i	−1.46523	−	0.845950i	−0.999245	+	0.0388444i	$0.987632\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.51870e10	−	7.82661e10i	0.153159	−	0.265280i
$738$		0			0
$739$	1.44034e11	+	2.49474e11i	0.482932	+	0.836463i	0.999808	−	0.0195972i	$-0.00623838\pi$
$739$	1.44034e11	+	2.49474e11i	0.482932	+	0.836463i	−0.516876	+	0.856060i	$0.672905\pi$
$740$		0			0
$741$			8.27128e10i			0.274347i
$742$		0			0
$743$	2.14288e11			0.703142			0.351571	−	0.936161i	$-0.385648\pi$
$743$	2.14288e11			0.703142			0.351571	+	0.936161i	$0.385648\pi$
$744$		0			0
$745$	3.88197e11	−	2.24125e11i	1.26016	−	0.727555i
$746$		0			0
$747$	−6.99009e10	−	4.03573e10i	−0.224492	−	0.129610i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−9.27393e10	+	1.60629e11i	−0.291544	+	0.504969i	−0.974175	−	0.225794i	$-0.927502\pi$
$751$	−9.27393e10	+	1.60629e11i	−0.291544	+	0.504969i	0.682631	+	0.730763i	$0.260836\pi$
$752$		0			0
$753$	−5.30530e11	−	9.18904e11i	−1.65017	−	2.85819i
$754$		0			0
$755$			4.09972e11i			1.26173i
$756$		0			0
$757$	6.69254e10			0.203802			0.101901	−	0.994795i	$-0.467508\pi$
$757$	6.69254e10			0.203802			0.101901	+	0.994795i	$0.467508\pi$
$758$		0			0
$759$	−1.98461e11	+	1.14582e11i	−0.598010	+	0.345261i
$760$		0			0
$761$	−3.95980e10	−	2.28619e10i	−0.118069	−	0.0681670i	0.439803	−	0.898094i	$-0.355048\pi$
$761$	−3.95980e10	−	2.28619e10i	−0.118069	−	0.0681670i	−0.557871	+	0.829927i	$0.688382\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3.32646e11	+	5.76160e11i	−0.971263	+	1.68228i
$766$		0			0
$767$	5.40823e10	+	9.36733e10i	0.156269	+	0.270667i
$768$		0			0
$769$			4.25562e11i			1.21691i	0.793589	+	0.608454i	$0.208210\pi$
$769$			4.25562e11i			1.21691i	−0.793589	+	0.608454i	$0.791790\pi$
$770$		0			0
$771$	1.12323e11			0.317872
$772$		0			0
$773$	−1.40014e11	+	8.08370e10i	−0.392151	+	0.226408i	−0.683092	−	0.730333i	$-0.739365\pi$
$773$	−1.40014e11	+	8.08370e10i	−0.392151	+	0.226408i	0.290941	+	0.956741i	$0.406032\pi$
$774$		0			0
$775$	−5.07255e11	−	2.92864e11i	−1.40611	−	0.811819i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.57985e8	−	4.46843e8i	0.000700558	−	0.00121340i
$780$		0			0
$781$	−9.40491e8	−	1.62898e9i	−0.00252785	−	0.00437836i
$782$		0			0
$783$		−	1.51670e12i		−	4.03509i
$784$		0			0
$785$	−8.80924e11			−2.31985
$786$		0			0
$787$	−2.69667e11	+	1.55692e11i	−0.702957	+	0.405852i	−0.808448	−	0.588568i	$-0.799692\pi$
$787$	−2.69667e11	+	1.55692e11i	−0.702957	+	0.405852i	0.105491	+	0.994420i	$0.466359\pi$
$788$		0			0
$789$	7.85204e11	+	4.53338e11i	2.02616	+	1.16981i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.03438e11	+	3.52365e11i	−0.514446	+	0.891047i
$794$		0			0
$795$	−6.21381e11	−	1.07626e12i	−1.55557	−	2.69432i
$796$		0			0
$797$			5.39201e11i			1.33634i	0.744008	+	0.668171i	$0.232922\pi$
$797$			5.39201e11i			1.33634i	−0.744008	+	0.668171i	$0.767078\pi$
$798$		0			0
$799$	−3.19853e11			−0.784808
$800$		0			0
$801$	1.41382e11	−	8.16269e10i	0.343450	−	0.198291i
$802$		0			0
$803$	−3.99021e11	−	2.30375e11i	−0.959696	−	0.554081i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4.70941e11	+	8.15693e11i	−1.11038	+	1.92324i
$808$		0			0
$809$	1.86129e11	+	3.22384e11i	0.434530	+	0.752627i	0.997257	−	0.0740152i	$-0.0235813\pi$
$809$	1.86129e11	+	3.22384e11i	0.434530	+	0.752627i	−0.562728	+	0.826642i	$0.690248\pi$
$810$		0			0
$811$		−	6.84823e11i		−	1.58305i	−0.611137	−	0.791525i	$-0.709287\pi$
$811$		−	6.84823e11i		−	1.58305i	0.611137	−	0.791525i	$-0.290713\pi$
$812$		0			0
$813$	−7.57914e11			−1.73483
$814$		0			0
$815$	−4.95688e11	+	2.86186e11i	−1.12351	+	0.648660i
$816$		0			0
$817$	6.88884e10	+	3.97727e10i	0.154617	+	0.0892683i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.03381e11	+	3.52267e11i	−0.447650	+	0.775353i	−0.998233	−	0.0594279i	$-0.981072\pi$
$821$	−2.03381e11	+	3.52267e11i	−0.447650	+	0.775353i	0.550582	+	0.834781i	$0.314406\pi$
$822$		0			0
$823$	−2.80981e11	−	4.86673e11i	−0.612459	−	1.06081i	−0.990825	−	0.135154i	$-0.956847\pi$
$823$	−2.80981e11	−	4.86673e11i	−0.612459	−	1.06081i	0.378366	−	0.925656i	$-0.376486\pi$
$824$		0			0
$825$		−	9.37922e11i		−	2.02465i
$826$		0			0
$827$	−1.56518e11			−0.334612			−0.167306	−	0.985905i	$-0.553507\pi$
$827$	−1.56518e11			−0.334612			−0.167306	+	0.985905i	$0.553507\pi$
$828$		0			0
$829$	−5.91496e11	+	3.41500e11i	−1.25237	+	0.723058i	−0.971580	−	0.236710i	$-0.923931\pi$
$829$	−5.91496e11	+	3.41500e11i	−1.25237	+	0.723058i	−0.280793	+	0.959768i	$0.590597\pi$
$830$		0			0
$831$	−8.05648e11	−	4.65141e11i	−1.68944	−	0.975396i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	3.36016e11	−	5.81997e11i	0.691216	−	1.19722i
$836$		0			0
$837$	6.73167e11	+	1.16596e12i	1.37158	+	2.37564i
$838$		0			0
$839$			6.02058e11i			1.21504i	0.794304	+	0.607520i	$0.207836\pi$
$839$			6.02058e11i			1.21504i	−0.794304	+	0.607520i	$0.792164\pi$
$840$		0			0
$841$	9.99557e11			1.99813
$842$		0			0
$843$	2.68658e11	−	1.55110e11i	0.531974	−	0.307135i
$844$		0			0
$845$	1.61286e10	+	9.31184e9i	0.0316351	+	0.0182645i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	3.77634e11	−	6.54081e11i	0.726842	−	1.25893i
$850$		0			0
$851$	1.63837e11	+	2.83773e11i	0.312387	+	0.541070i
$852$		0			0
$853$			2.62751e11i			0.496305i	0.968721	+	0.248153i	$0.0798235\pi$
$853$			2.62751e11i			0.496305i	−0.968721	+	0.248153i	$0.920177\pi$
$854$		0			0
$855$	2.81842e11			0.527402
$856$		0			0
$857$	4.08594e10	−	2.35902e10i	0.0757476	−	0.0437329i	−0.461648	−	0.887063i	$-0.652742\pi$
$857$	4.08594e10	−	2.35902e10i	0.0757476	−	0.0437329i	0.537395	+	0.843330i	$0.319408\pi$
$858$		0			0
$859$	4.42290e11	+	2.55356e11i	0.812334	+	0.469001i	0.847766	−	0.530371i	$-0.177947\pi$
$859$	4.42290e11	+	2.55356e11i	0.812334	+	0.469001i	−0.0354317	+	0.999372i	$0.511281\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.84748e10	+	3.19993e10i	−0.0333071	+	0.0576896i	−0.882198	−	0.470878i	$-0.843937\pi$
$863$	−1.84748e10	+	3.19993e10i	−0.0333071	+	0.0576896i	0.848891	+	0.528567i	$0.177271\pi$
$864$		0			0
$865$	−2.24925e11	−	3.89582e11i	−0.401767	−	0.695880i
$866$		0			0
$867$			7.13281e11i			1.26236i
$868$		0			0
$869$	1.33995e11			0.234969
$870$		0			0
$871$	1.90759e11	−	1.10135e11i	0.331445	−	0.191360i
$872$		0			0
$873$	−7.21662e11	−	4.16652e11i	−1.24244	−	0.717325i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.84174e11	−	8.38613e11i	0.818470	−	1.41763i	−0.0883394	−	0.996090i	$-0.528156\pi$
$877$	4.84174e11	−	8.38613e11i	0.818470	−	1.41763i	0.906809	−	0.421541i	$-0.138511\pi$
$878$		0			0
$879$	5.58132e11	+	9.66714e11i	0.934936	+	1.61936i
$880$		0			0
$881$		−	9.95652e11i		−	1.65274i	−0.563129	−	0.826369i	$-0.690403\pi$
$881$		−	9.95652e11i		−	1.65274i	0.563129	−	0.826369i	$-0.309597\pi$
$882$		0			0
$883$	5.84931e10			0.0962192			0.0481096	−	0.998842i	$-0.484680\pi$
$883$	5.84931e10			0.0962192			0.0481096	+	0.998842i	$0.484680\pi$
$884$		0			0
$885$	4.58841e11	−	2.64912e11i	0.747978	−	0.431845i
$886$		0			0
$887$	−4.25692e11	−	2.45773e11i	−0.687702	−	0.397045i	0.115048	−	0.993360i	$-0.463298\pi$
$887$	−4.25692e11	−	2.45773e11i	−0.687702	−	0.397045i	−0.802751	+	0.596315i	$0.796631\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.94676e11	+	8.56805e11i	−0.784893	+	1.35947i
$892$		0			0
$893$	6.77508e10	+	1.17348e11i	0.106539	+	0.184531i
$894$		0			0
$895$			8.21612e11i			1.28049i
$896$		0			0
$897$	−5.58542e11			−0.862751
$898$		0			0
$899$	−1.15297e12	+	6.65666e11i	−1.76514	+	1.01910i
$900$		0			0
$901$	3.49901e11	+	2.02015e11i	0.530940	+	0.306539i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.57227e11	+	6.18736e11i	−0.532538	+	0.922383i
$906$		0			0
$907$	−1.85310e11	−	3.20966e11i	−0.273823	−	0.474275i	0.696015	−	0.718027i	$-0.254955\pi$
$907$	−1.85310e11	−	3.20966e11i	−0.273823	−	0.474275i	−0.969837	+	0.243753i	$0.921621\pi$
$908$		0			0
$909$			1.14823e12i			1.68180i
$910$		0			0
$911$	7.13289e11			1.03560			0.517800	−	0.855502i	$-0.326751\pi$
$911$	7.13289e11			1.03560			0.517800	+	0.855502i	$0.326751\pi$
$912$		0			0
$913$	−5.52650e10	+	3.19073e10i	−0.0795366	+	0.0459205i
$914$		0			0
$915$	1.72599e12	+	9.96503e11i	2.46238	+	1.42165i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.78054e11	−	3.08399e11i	0.249626	−	0.432365i	−0.713796	−	0.700354i	$-0.753026\pi$
$919$	1.78054e11	−	3.08399e11i	0.249626	−	0.432365i	0.963422	+	0.267988i	$0.0863589\pi$
$920$		0			0
$921$	−9.63946e11	−	1.66960e12i	−1.33972	−	2.32046i
$922$		0			0
$923$		−	4.58454e9i		−	0.00631668i
$924$		0			0
$925$	−1.34110e12			−1.83187
$926$		0			0
$927$	1.65219e12	−	9.53894e11i	2.23739	−	1.29176i
$928$		0			0
$929$	1.06799e12	+	6.16605e11i	1.43385	+	0.827836i	0.997412	−	0.0718969i	$-0.0229053\pi$
$929$	1.06799e12	+	6.16605e11i	1.43385	+	0.827836i	0.436441	+	0.899733i	$0.356239\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.10177e12	−	1.90832e12i	1.45400	−	2.51840i
$934$		0			0
$935$	2.62997e11	+	4.55524e11i	0.344115	+	0.596025i
$936$		0			0
$937$			1.10549e12i			1.43415i	0.696994	+	0.717077i	$0.254521\pi$
$937$			1.10549e12i			1.43415i	−0.696994	+	0.717077i	$0.745479\pi$
$938$		0			0
$939$	1.19921e12			1.54252
$940$		0			0
$941$	6.51461e11	−	3.76121e11i	0.830864	−	0.479700i	−0.0232842	−	0.999729i	$-0.507412\pi$
$941$	6.51461e11	−	3.76121e11i	0.830864	−	0.479700i	0.854149	+	0.520029i	$0.174079\pi$
$942$		0			0
$943$	3.01743e9	+	1.74212e9i	0.00381585	+	0.00220308i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.50836e11	+	7.80870e11i	−0.560555	+	0.970910i	0.436893	+	0.899513i	$0.356079\pi$
$947$	−4.50836e11	+	7.80870e11i	−0.560555	+	0.970910i	−0.997448	+	0.0713963i	$0.977255\pi$
$948$		0			0
$949$	−5.61495e11	−	9.72538e11i	−0.692279	−	1.19906i
$950$		0			0
$951$		−	5.28587e11i		−	0.646240i
$952$		0			0
$953$	5.66082e11			0.686290			0.343145	−	0.939282i	$-0.388508\pi$
$953$	5.66082e11			0.686290			0.343145	+	0.939282i	$0.388508\pi$
$954$		0			0
$955$	2.90322e11	−	1.67618e11i	0.349033	−	0.201514i
$956$		0			0
$957$	−1.84624e12	−	1.06593e12i	−2.20110	−	1.27081i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.64447e11	−	2.84830e11i	0.192811	−	0.333958i
$962$		0			0
$963$	1.01226e12	+	1.75329e12i	1.17703	+	2.03868i
$964$		0			0
$965$		−	4.79483e11i		−	0.552922i
$966$		0			0
$967$	8.41824e11			0.962754			0.481377	−	0.876514i	$-0.340137\pi$
$967$	8.41824e11			0.962754			0.481377	+	0.876514i	$0.340137\pi$
$968$		0			0
$969$	−1.14071e11	+	6.58590e10i	−0.129384	+	0.0746999i
$970$		0			0
$971$	3.65564e11	+	2.11059e11i	0.411232	+	0.237425i	0.691319	−	0.722550i	$-0.257030\pi$
$971$	3.65564e11	+	2.11059e11i	0.411232	+	0.237425i	−0.280087	+	0.959975i	$0.590363\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.14300e12	−	1.97974e12i	1.26482	−	2.19073i
$976$		0			0
$977$	7.19959e10	+	1.24701e11i	0.0790187	+	0.136864i	0.902827	−	0.430004i	$-0.141488\pi$
$977$	7.19959e10	+	1.24701e11i	0.0790187	+	0.136864i	−0.823808	+	0.566869i	$0.808155\pi$
$978$		0			0
$979$		−	1.29072e11i		−	0.140508i
$980$		0			0
$981$	1.15496e12			1.24707
$982$		0			0
$983$	1.46173e12	−	8.43932e11i	1.56550	−	0.903844i	0.568820	−	0.822462i	$-0.307400\pi$
$983$	1.46173e12	−	8.43932e11i	1.56550	−	0.903844i	0.996683	−	0.0813819i	$-0.0259334\pi$
$984$		0			0
$985$	2.50032e11	+	1.44356e11i	0.265614	+	0.153352i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.68577e11	+	4.65188e11i	−0.280726	+	0.486232i
$990$		0			0
$991$	3.04469e11	+	5.27355e11i	0.315681	+	0.546775i	0.979582	−	0.201045i	$-0.0644339\pi$
$991$	3.04469e11	+	5.27355e11i	0.315681	+	0.546775i	−0.663901	+	0.747820i	$0.731101\pi$
$992$		0			0
$993$		−	2.50392e12i		−	2.57527i
$994$		0			0
$995$	6.65399e10			0.0678875
$996$		0			0
$997$	−5.55067e11	+	3.20468e11i	−0.561778	+	0.324343i	−0.753859	−	0.657036i	$-0.771810\pi$
$997$	−5.55067e11	+	3.20468e11i	−0.561778	+	0.324343i	0.192081	+	0.981379i	$0.438476\pi$
$998$		0			0
$999$	2.66962e12	+	1.54131e12i	2.68033	+	1.54749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.9.h.b.117.6		12
7.2	even	3		28.9.b.a.13.6	yes	6
7.3	odd	6	inner	196.9.h.b.129.6		12
7.4	even	3	inner	196.9.h.b.129.1		12
7.5	odd	6		28.9.b.a.13.1	✓	6
7.6	odd	2	inner	196.9.h.b.117.1		12
21.2	odd	6		252.9.d.b.181.1		6
21.5	even	6		252.9.d.b.181.6		6
28.19	even	6		112.9.c.d.97.6		6
28.23	odd	6		112.9.c.d.97.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.b.a.13.1	✓	6	7.5	odd	6
28.9.b.a.13.6	yes	6	7.2	even	3
112.9.c.d.97.1		6	28.23	odd	6
112.9.c.d.97.6		6	28.19	even	6
196.9.h.b.117.1		12	7.6	odd	2	inner
196.9.h.b.117.6		12	1.1	even	1	trivial
196.9.h.b.129.1		12	7.4	even	3	inner
196.9.h.b.129.6		12	7.3	odd	6	inner
252.9.d.b.181.1		6	21.2	odd	6
252.9.d.b.181.6		6	21.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	196.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(127.153 - 73.4116i) q^{3} +(-834.906 - 482.033i) q^{5} +(7498.03 - 12987.0i) q^{9} +(-5928.09 - 10267.8i) q^{11} -28897.2i q^{13} -141547. q^{15} +(39852.8 - 23009.0i) q^{17} +(-16883.1 - 9747.47i) q^{19} +(65822.6 - 114008. i) q^{23} +(269399. + 466614. i) q^{25} -1.23846e6i q^{27} +1.22466e6 q^{29} +(-941455. + 543550. i) q^{31} +(-1.50755e6 - 870382. i) q^{33} +(-1.24453e6 + 2.15559e6i) q^{37} +(-2.12139e6 - 3.67436e6i) q^{39} +26466.8i q^{41} -4.08031e6 q^{43} +(-1.25203e7 + 7.22860e6i) q^{45} +(-6.01939e6 - 3.47530e6i) q^{47} +(3.37826e6 - 5.85132e6i) q^{51} +(4.38991e6 + 7.60356e6i) q^{53} +1.14302e7i q^{55} -2.86231e6 q^{57} +(-3.24161e6 + 1.87154e6i) q^{59} +(-1.21938e7 - 7.04007e6i) q^{61} +(-1.39294e7 + 2.41265e7i) q^{65} +(3.81126e6 + 6.60129e6i) q^{67} -1.93286e7i q^{69} +158650. q^{71} +(3.36551e7 - 1.94308e7i) q^{73} +(6.85097e7 + 3.95541e7i) q^{75} +(-5.65086e6 + 9.78758e6i) q^{79} +(-4.17231e7 - 7.22665e7i) q^{81} -5.38238e6i q^{83} -4.43645e7 q^{85} +(1.55719e8 - 8.99046e7i) q^{87} +(9.42793e6 + 5.44322e6i) q^{89} +(-7.98057e7 + 1.38228e8i) q^{93} +(9.39721e6 + 1.62764e7i) q^{95} -5.55681e7i q^{97} -1.77796e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18234 q^{9} - 24492 q^{11} - 306816 q^{15} + 11604 q^{23} + 678714 q^{25} + 2528664 q^{29} - 3184332 q^{37} - 5634240 q^{39} - 15566760 q^{43} - 6877824 q^{51} + 8340660 q^{53} - 35901696 q^{57}+ \cdots - 1191795624 q^{99}+O(q^{100}) \) 12 * q + 18234 * q^9 - 24492 * q^11 - 306816 * q^15 + 11604 * q^23 + 678714 * q^25 + 2528664 * q^29 - 3184332 * q^37 - 5634240 * q^39 - 15566760 * q^43 - 6877824 * q^51 + 8340660 * q^53 - 35901696 * q^57 - 84095232 * q^65 - 16579500 * q^67 - 124177704 * q^71 - 186114540 * q^79 - 131284998 * q^81 - 526421760 * q^85 - 638128512 * q^93 - 85912896 * q^95 - 1191795624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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