LMFDB - Embedded newform 196.9.h.b.117.5

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			117.5
Root			$-6.26546 + 10.8521i$ of defining polynomial
Character	$\chi$	$=$	196.117
Dual form			196.9.h.b.129.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(67.7219 - 39.0993i) q^{3} +(594.021 + 342.958i) q^{5} +(-222.993 + 386.236i) q^{9} +(-12258.7 - 21232.7i) q^{11} -275.445i q^{13} +53637.7 q^{15} +(-133739. + 77214.5i) q^{17} +(9691.07 + 5595.14i) q^{19} +(-142793. + 247324. i) q^{23} +(39928.0 + 69157.3i) q^{25} +547936. i q^{27} -266410. q^{29} +(-1.28048e6 + 739287. i) q^{31} +(-1.66037e6 - 958612. i) q^{33} +(1.24589e6 - 2.15795e6i) q^{37} +(-10769.7 - 18653.7i) q^{39} -708210. i q^{41} -1.28062e6 q^{43} +(-264925. + 152955. i) q^{45} +(-1.44828e6 - 836165. i) q^{47} +(-6.03806e6 + 1.04582e7i) q^{51} +(980232. + 1.69781e6i) q^{53} -1.68169e7i q^{55} +875064. q^{57} +(-1.09884e7 + 6.34416e6i) q^{59} +(4.25289e6 + 2.45541e6i) q^{61} +(94466.2 - 163620. i) q^{65} +(-1.33945e7 - 2.31999e7i) q^{67} +2.23323e7i q^{69} -5.66931e6 q^{71} +(3.59285e7 - 2.07433e7i) q^{73} +(5.40800e6 + 3.12231e6i) q^{75} +(-1.42627e7 + 2.47037e7i) q^{79} +(1.99608e7 + 3.45732e7i) q^{81} +6.35086e7i q^{83} -1.05925e8 q^{85} +(-1.80418e7 + 1.04164e7i) q^{87} +(-1.00789e7 - 5.81903e6i) q^{89} +(-5.78112e7 + 1.00132e8i) q^{93} +(3.83780e6 + 6.64726e6i) q^{95} -8.14742e6i q^{97} +1.09344e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	67.7219	−	39.0993i	0.836073	−	0.482707i	−0.0198543	−	0.999803i	$-0.506320\pi$
$3$	67.7219	−	39.0993i	0.836073	−	0.482707i	0.855928	+	0.517096i	$0.172987\pi$
$4$		0			0
$5$	594.021	+	342.958i	0.950433	+	0.548733i	0.893216	−	0.449629i	$-0.148444\pi$
$5$	594.021	+	342.958i	0.950433	+	0.548733i	0.0572178	+	0.998362i	$0.481777\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−222.993	+	386.236i	−0.0339877	+	0.0588685i
$10$		0			0
$11$	−12258.7	−	21232.7i	−0.837286	−	1.45022i	−0.892156	−	0.451728i	$-0.850808\pi$
$11$	−12258.7	−	21232.7i	−0.837286	−	1.45022i	0.0548702	−	0.998493i	$-0.482526\pi$
$12$		0			0
$13$		−	275.445i		−	0.00964410i	−0.999988	−	0.00482205i	$-0.998465\pi$
$13$		−	275.445i		−	0.00964410i	0.999988	−	0.00482205i	$-0.00153491\pi$
$14$		0			0
$15$	53637.7			1.05951
$16$		0			0
$17$	−133739.	+	77214.5i	−1.60127	+	0.924492i	−0.610033	+	0.792376i	$0.708844\pi$
$17$	−133739.	+	77214.5i	−1.60127	+	0.924492i	−0.991234	+	0.132116i	$0.957823\pi$
$18$		0			0
$19$	9691.07	+	5595.14i	0.0743631	+	0.0429336i	0.536721	−	0.843760i	$-0.319663\pi$
$19$	9691.07	+	5595.14i	0.0743631	+	0.0429336i	−0.462357	+	0.886694i	$0.652996\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−142793.	+	247324.i	−0.510263	+	0.883802i	0.489666	+	0.871910i	$0.337119\pi$
$23$	−142793.	+	247324.i	−0.510263	+	0.883802i	−0.999929	+	0.0118918i	$0.996215\pi$
$24$		0			0
$25$	39928.0	+	69157.3i	0.102216	+	0.177043i
$26$		0			0
$27$			547936.i			1.03104i
$28$		0			0
$29$	−266410.			−0.376668			−0.188334	−	0.982105i	$-0.560309\pi$
$29$	−266410.			−0.376668			−0.188334	+	0.982105i	$0.560309\pi$
$30$		0			0
$31$	−1.28048e6	+	739287.i	−1.38652	+	0.800510i	−0.992922	−	0.118771i	$-0.962104\pi$
$31$	−1.28048e6	+	739287.i	−1.38652	+	0.800510i	−0.393602	+	0.919281i	$0.628771\pi$
$32$		0			0
$33$	−1.66037e6	−	958612.i	−1.40006	−	0.808327i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.24589e6	−	2.15795e6i	0.664774	−	1.15142i	−0.314572	−	0.949234i	$-0.601861\pi$
$37$	1.24589e6	−	2.15795e6i	0.664774	−	1.15142i	0.979346	−	0.202189i	$-0.0648056\pi$
$38$		0			0
$39$	−10769.7	−	18653.7i	−0.00465528	−	0.00806318i
$40$		0			0
$41$		−	708210.i		−	0.250626i	−0.992117	−	0.125313i	$-0.960006\pi$
$41$		−	708210.i		−	0.250626i	0.992117	−	0.125313i	$-0.0399936\pi$
$42$		0			0
$43$	−1.28062e6			−0.374582			−0.187291	−	0.982304i	$-0.559971\pi$
$43$	−1.28062e6			−0.374582			−0.187291	+	0.982304i	$0.559971\pi$
$44$		0			0
$45$	−264925.	+	152955.i	−0.0646061	+	0.0373004i
$46$		0			0
$47$	−1.44828e6	−	836165.i	−0.296798	−	0.171356i	0.344205	−	0.938894i	$-0.388148\pi$
$47$	−1.44828e6	−	836165.i	−0.296798	−	0.171356i	−0.641004	+	0.767538i	$0.721482\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−6.03806e6	+	1.04582e7i	−0.892518	+	1.54589i
$52$		0			0
$53$	980232.	+	1.69781e6i	0.124230	+	0.215172i	0.921432	−	0.388541i	$-0.127021\pi$
$53$	980232.	+	1.69781e6i	0.124230	+	0.215172i	−0.797202	+	0.603713i	$0.793687\pi$
$54$		0			0
$55$		−	1.68169e7i		−	1.83778i
$56$		0			0
$57$	875064.			0.0828973
$58$		0			0
$59$	−1.09884e7	+	6.34416e6i	−0.906831	+	0.523559i	−0.879410	−	0.476065i	$-0.842063\pi$
$59$	−1.09884e7	+	6.34416e6i	−0.906831	+	0.523559i	−0.0274209	+	0.999624i	$0.508729\pi$
$60$		0			0
$61$	4.25289e6	+	2.45541e6i	0.307160	+	0.177339i	0.645655	−	0.763629i	$-0.276584\pi$
$61$	4.25289e6	+	2.45541e6i	0.307160	+	0.177339i	−0.338495	+	0.940968i	$0.609918\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	94466.2	−	163620.i	0.00529204	−	0.00916608i
$66$		0			0
$67$	−1.33945e7	−	2.31999e7i	−0.664701	−	1.15130i	−0.979366	−	0.202093i	$-0.935226\pi$
$67$	−1.33945e7	−	2.31999e7i	−0.664701	−	1.15130i	0.314666	−	0.949203i	$-0.398108\pi$
$68$		0			0
$69$			2.23323e7i			0.985231i
$70$		0			0
$71$	−5.66931e6			−0.223098			−0.111549	−	0.993759i	$-0.535581\pi$
$71$	−5.66931e6			−0.223098			−0.111549	+	0.993759i	$0.535581\pi$
$72$		0			0
$73$	3.59285e7	−	2.07433e7i	1.26517	−	0.730444i	0.291097	−	0.956694i	$-0.405980\pi$
$73$	3.59285e7	−	2.07433e7i	1.26517	−	0.730444i	0.974069	+	0.226249i	$0.0726464\pi$
$74$		0			0
$75$	5.40800e6	+	3.12231e6i	0.170920	+	0.0986805i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.42627e7	+	2.47037e7i	−0.366178	+	0.634239i	−0.988964	−	0.148153i	$-0.952667\pi$
$79$	−1.42627e7	+	2.47037e7i	−0.366178	+	0.634239i	0.622786	+	0.782392i	$0.286001\pi$
$80$		0			0
$81$	1.99608e7	+	3.45732e7i	0.463702	+	0.803155i
$82$		0			0
$83$			6.35086e7i			1.33820i	0.743173	+	0.669099i	$0.233320\pi$
$83$			6.35086e7i			1.33820i	−0.743173	+	0.669099i	$0.766680\pi$
$84$		0			0
$85$	−1.05925e8			−2.02920
$86$		0			0
$87$	−1.80418e7	+	1.04164e7i	−0.314922	+	0.181820i
$88$		0			0
$89$	−1.00789e7	−	5.81903e6i	−0.160639	−	0.0927451i	0.417525	−	0.908665i	$-0.362897\pi$
$89$	−1.00789e7	−	5.81903e6i	−0.160639	−	0.0927451i	−0.578165	+	0.815920i	$0.696231\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−5.78112e7	+	1.00132e8i	−0.772823	+	1.33857i
$94$		0			0
$95$	3.83780e6	+	6.64726e6i	0.0471181	+	0.0816110i
$96$		0			0
$97$		−	8.14742e6i		−	0.0920308i	−0.998941	−	0.0460154i	$-0.985348\pi$
$97$		−	8.14742e6i		−	0.0920308i	0.998941	−	0.0460154i	$-0.0146523\pi$
$98$		0			0
$99$	1.09344e7			0.113830
$100$		0			0
$101$	1.37112e8	−	7.91615e7i	1.31762	−	0.760727i	0.334273	−	0.942476i	$-0.391509\pi$
$101$	1.37112e8	−	7.91615e7i	1.31762	−	0.760727i	0.983345	+	0.181750i	$0.0581760\pi$
$102$		0			0
$103$	1.07837e8	+	6.22600e7i	0.958122	+	0.553172i	0.895594	−	0.444871i	$-0.146751\pi$
$103$	1.07837e8	+	6.22600e7i	0.958122	+	0.553172i	0.0625273	+	0.998043i	$0.480084\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.60979e7	+	1.31805e8i	−0.580547	+	1.00554i	0.414867	+	0.909882i	$0.363828\pi$
$107$	−7.60979e7	+	1.31805e8i	−0.580547	+	1.00554i	−0.995415	+	0.0956552i	$0.969505\pi$
$108$		0			0
$109$	−1.33605e8	−	2.31411e8i	−0.946492	−	1.63937i	−0.752735	−	0.658323i	$-0.771266\pi$
$109$	−1.33605e8	−	2.31411e8i	−0.946492	−	1.63937i	−0.193757	−	0.981050i	$-0.562067\pi$
$110$		0			0
$111$		−	1.94854e8i		−	1.28356i
$112$		0			0
$113$	−1.04288e8			−0.639619			−0.319809	−	0.947482i	$-0.603619\pi$
$113$	−1.04288e8			−0.639619			−0.319809	+	0.947482i	$0.603619\pi$
$114$		0			0
$115$	−1.69644e8	+	9.79437e7i	−0.969942	+	0.559997i
$116$		0			0
$117$	106387.	+	61422.5i	0.000567733	+	0.000327781i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.93372e8	+	3.34930e8i	−0.902095	+	1.56247i
$122$		0			0
$123$	−2.76905e7	−	4.79614e7i	−0.120979	−	0.209542i
$124$		0			0
$125$		−	2.13161e8i		−	0.873109i
$126$		0			0
$127$	−4.31517e8			−1.65876			−0.829380	−	0.558685i	$-0.811306\pi$
$127$	−4.31517e8			−1.65876			−0.829380	+	0.558685i	$0.811306\pi$
$128$		0			0
$129$	−8.67262e7	+	5.00714e7i	−0.313178	+	0.180813i
$130$		0			0
$131$	−3.37412e8	−	1.94805e8i	−1.14571	−	0.661478i	−0.197874	−	0.980227i	$-0.563404\pi$
$131$	−3.37412e8	−	1.94805e8i	−1.14571	−	0.661478i	−0.947839	+	0.318750i	$0.896737\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.87919e8	+	3.25486e8i	−0.565765	+	0.979934i
$136$		0			0
$137$	2.21893e8	+	3.84330e8i	0.629886	+	1.09099i	0.987574	+	0.157153i	$0.0502317\pi$
$137$	2.21893e8	+	3.84330e8i	0.629886	+	1.09099i	−0.357688	+	0.933841i	$0.616435\pi$
$138$		0			0
$139$			5.79636e8i			1.55273i	0.630283	+	0.776366i	$0.282939\pi$
$139$			5.79636e8i			1.55273i	−0.630283	+	0.776366i	$0.717061\pi$
$140$		0			0
$141$	−1.30774e8			−0.330860
$142$		0			0
$143$	−5.84844e6	+	3.37660e6i	−0.0139861	+	0.00807487i
$144$		0			0
$145$	−1.58253e8	−	9.13675e7i	−0.357998	−	0.206690i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.06244e7	+	1.05005e8i	−0.122999	+	0.213041i	−0.920949	−	0.389683i	$-0.872585\pi$
$149$	−6.06244e7	+	1.05005e8i	−0.122999	+	0.213041i	0.797950	+	0.602724i	$0.205918\pi$
$150$		0			0
$151$	−9.42994e7	−	1.63331e8i	−0.181385	−	0.314168i	0.760967	−	0.648790i	$-0.224725\pi$
$151$	−9.42994e7	−	1.63331e8i	−0.181385	−	0.314168i	−0.942352	+	0.334622i	$0.891391\pi$
$152$		0			0
$153$		−	6.88733e7i		−	0.125685i
$154$		0			0
$155$	−1.01418e9			−1.75706
$156$		0			0
$157$	−6.60437e8	+	3.81304e8i	−1.08701	+	0.627584i	−0.932778	−	0.360451i	$-0.882623\pi$
$157$	−6.60437e8	+	3.81304e8i	−1.08701	+	0.627584i	−0.154230	+	0.988035i	$0.549290\pi$
$158$		0			0
$159$	1.32766e8	+	7.66528e7i	0.207730	+	0.119933i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.23425e8	+	5.60189e8i	−0.458167	+	0.793569i	−0.998864	−	0.0476488i	$-0.984827\pi$
$163$	−3.23425e8	+	5.60189e8i	−0.458167	+	0.793569i	0.540697	+	0.841217i	$0.318161\pi$
$164$		0			0
$165$	−6.57528e8	−	1.13887e9i	−0.887112	−	1.53652i
$166$		0			0
$167$			5.45334e8i			0.701126i	0.936539	+	0.350563i	$0.114010\pi$
$167$			5.45334e8i			0.701126i	−0.936539	+	0.350563i	$0.885990\pi$
$168$		0			0
$169$	8.15655e8			0.999907
$170$		0			0
$171$	−4.32209e6	+	2.49536e6i	−0.00505486	+	0.00291843i
$172$		0			0
$173$	−5.23771e8	−	3.02400e8i	−0.584733	−	0.337596i	0.178279	−	0.983980i	$-0.442947\pi$
$173$	−5.23771e8	−	3.02400e8i	−0.584733	−	0.337596i	−0.763012	+	0.646384i	$0.776280\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.96104e8	+	8.59277e8i	−0.505451	+	0.875468i
$178$		0			0
$179$	1.53940e8	+	2.66632e8i	0.149947	+	0.259717i	0.931208	−	0.364489i	$-0.118756\pi$
$179$	1.53940e8	+	2.66632e8i	0.149947	+	0.259717i	−0.781260	+	0.624205i	$0.785423\pi$
$180$		0			0
$181$		−	1.25107e9i		−	1.16565i	−0.812598	−	0.582824i	$-0.801948\pi$
$181$		−	1.25107e9i		−	1.16565i	0.812598	−	0.582824i	$-0.198052\pi$
$182$		0			0
$183$	3.84018e8			0.342411
$184$		0			0
$185$	1.48017e9	−	8.54579e8i	1.26365	−	0.729567i
$186$		0			0
$187$	3.27894e9	+	1.89310e9i	2.68144	+	1.54813i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.34642e8	−	5.79616e8i	0.251447	−	0.435519i	−0.712477	−	0.701695i	$-0.752427\pi$
$191$	3.34642e8	−	5.79616e8i	0.251447	−	0.435519i	0.963924	+	0.266176i	$0.0857602\pi$
$192$		0			0
$193$	7.39705e8	+	1.28121e9i	0.533125	+	0.923400i	0.999252	+	0.0386815i	$0.0123158\pi$
$193$	7.39705e8	+	1.28121e9i	0.533125	+	0.923400i	−0.466127	+	0.884718i	$0.654351\pi$
$194$		0			0
$195$		−	1.47742e7i		−	0.0102180i
$196$		0			0
$197$	−1.47444e9			−0.978954			−0.489477	−	0.872016i	$-0.662812\pi$
$197$	−1.47444e9			−0.978954			−0.489477	+	0.872016i	$0.662812\pi$
$198$		0			0
$199$	1.90002e9	−	1.09698e9i	1.21156	−	0.699495i	0.248462	−	0.968642i	$-0.420075\pi$
$199$	1.90002e9	−	1.09698e9i	1.21156	−	0.699495i	0.963099	+	0.269146i	$0.0867415\pi$
$200$		0			0
$201$	−1.81420e9	−	1.04743e9i	−1.11148	−	0.641711i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.42886e8	−	4.20692e8i	0.137527	−	0.238204i
$206$		0			0
$207$	−6.36836e7	−	1.10303e8i	−0.0346854	−	0.0600768i
$208$		0			0
$209$		−	2.74357e8i		−	0.143791i
$210$		0			0
$211$	1.88972e9			0.953382			0.476691	−	0.879071i	$-0.341836\pi$
$211$	1.88972e9			0.953382			0.476691	+	0.879071i	$0.341836\pi$
$212$		0			0
$213$	−3.83936e8	+	2.21666e8i	−0.186527	+	0.107691i
$214$		0			0
$215$	−7.60716e8	−	4.39200e8i	−0.356015	−	0.205546i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.62210e9	−	2.80956e9i	0.705181	−	1.22141i
$220$		0			0
$221$	2.12684e7	+	3.68379e7i	0.00891590	+	0.0154428i
$222$		0			0
$223$			1.22281e9i			0.494470i	0.968956	+	0.247235i	$0.0795220\pi$
$223$			1.22281e9i			0.494470i	−0.968956	+	0.247235i	$0.920478\pi$
$224$		0			0
$225$	−3.56147e7			−0.0138963
$226$		0			0
$227$	2.98893e8	−	1.72566e8i	0.112567	−	0.0649908i	−0.442659	−	0.896690i	$-0.645965\pi$
$227$	2.98893e8	−	1.72566e8i	0.112567	−	0.0649908i	0.555227	+	0.831699i	$0.312632\pi$
$228$		0			0
$229$	6.62134e8	+	3.82283e8i	0.240771	+	0.139009i	0.615531	−	0.788113i	$-0.288942\pi$
$229$	6.62134e8	+	3.82283e8i	0.240771	+	0.139009i	−0.374760	+	0.927122i	$0.622275\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.55495e9	−	4.42530e9i	0.866879	−	1.50148i	0.00170905	−	0.999999i	$-0.499456\pi$
$233$	2.55495e9	−	4.42530e9i	0.866879	−	1.50148i	0.865170	−	0.501479i	$-0.167211\pi$
$234$		0			0
$235$	−5.73539e8	−	9.93399e8i	−0.188058	−	0.325726i
$236$		0			0
$237$			2.23064e9i			0.707027i
$238$		0			0
$239$	2.77466e9			0.850391			0.425196	−	0.905101i	$-0.360205\pi$
$239$	2.77466e9			0.850391			0.425196	+	0.905101i	$0.360205\pi$
$240$		0			0
$241$	−2.84196e9	+	1.64081e9i	−0.842461	+	0.486395i	−0.858100	−	0.513483i	$-0.828355\pi$
$241$	−2.84196e9	+	1.64081e9i	−0.842461	+	0.486395i	0.0156390	+	0.999878i	$0.495022\pi$
$242$		0			0
$243$	−4.09795e8	−	2.36595e8i	−0.117528	−	0.0678549i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.54116e6	−	2.66936e6i	0.000414056	−	0.000717165i
$248$		0			0
$249$	2.48314e9	+	4.30093e9i	0.645958	+	1.11883i
$250$		0			0
$251$		−	2.86848e9i		−	0.722697i	−0.932431	−	0.361349i	$-0.882316\pi$
$251$		−	2.86848e9i		−	0.722697i	0.932431	−	0.361349i	$-0.117684\pi$
$252$		0			0
$253$	7.00180e9			1.70894
$254$		0			0
$255$	−7.17347e9	+	4.14160e9i	−1.69656	+	0.979508i
$256$		0			0
$257$	−3.28758e9	−	1.89809e9i	−0.753606	−	0.435095i	0.0733894	−	0.997303i	$-0.476618\pi$
$257$	−3.28758e9	−	1.89809e9i	−0.753606	−	0.435095i	−0.826995	+	0.562209i	$0.809952\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5.94077e7	−	1.02897e8i	0.0128021	−	0.0221739i
$262$		0			0
$263$	−9.67855e8	−	1.67637e9i	−0.202296	−	0.350387i	0.746972	−	0.664856i	$-0.231507\pi$
$263$	−9.67855e8	−	1.67637e9i	−0.202296	−	0.350387i	−0.949268	+	0.314469i	$0.898174\pi$
$264$		0			0
$265$			1.34471e9i			0.272676i
$266$		0			0
$267$	−9.10080e8			−0.179075
$268$		0			0
$269$	−2.62009e9	+	1.51271e9i	−0.500389	+	0.288900i	−0.728874	−	0.684648i	$-0.759956\pi$
$269$	−2.62009e9	+	1.51271e9i	−0.500389	+	0.288900i	0.228485	+	0.973547i	$0.426623\pi$
$270$		0			0
$271$	−3.04991e8	−	1.76087e8i	−0.0565471	−	0.0326475i	0.471460	−	0.881887i	$-0.343727\pi$
$271$	−3.04991e8	−	1.76087e8i	−0.0565471	−	0.0326475i	−0.528007	+	0.849240i	$0.677061\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.78931e8	−	1.69556e9i	0.171168	−	0.296471i
$276$		0			0
$277$	3.44391e8	+	5.96503e8i	0.0584969	+	0.101320i	0.893791	−	0.448484i	$-0.148036\pi$
$277$	3.44391e8	+	5.96503e8i	0.0584969	+	0.101320i	−0.835294	+	0.549804i	$0.814703\pi$
$278$		0			0
$279$		−	6.59425e8i		−	0.108830i
$280$		0			0
$281$	8.08996e9			1.29754			0.648771	−	0.760984i	$-0.275283\pi$
$281$	8.08996e9			1.29754			0.648771	+	0.760984i	$0.275283\pi$
$282$		0			0
$283$	3.05863e9	−	1.76590e9i	0.476849	−	0.275309i	−0.242254	−	0.970213i	$-0.577887\pi$
$283$	3.05863e9	−	1.76590e9i	0.476849	−	0.275309i	0.719102	+	0.694904i	$0.244553\pi$
$284$		0			0
$285$	5.19806e8	+	3.00110e8i	0.0787884	+	0.0454885i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.43628e9	−	1.46121e10i	1.20937	−	2.09469i
$290$		0			0
$291$	−3.18558e8	−	5.51759e8i	−0.0444239	−	0.0769445i
$292$		0			0
$293$		−	8.15872e9i		−	1.10701i	−0.832846	−	0.553505i	$-0.813290\pi$
$293$		−	8.15872e9i		−	1.10701i	0.832846	−	0.553505i	$-0.186710\pi$
$294$		0			0
$295$	−8.70312e9			−1.14918
$296$		0			0
$297$	1.16342e10	−	6.71699e9i	1.49523	−	0.863274i
$298$		0			0
$299$	6.81242e7	+	3.93315e7i	0.00852348	+	0.00492103i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	6.19032e9	−	1.07219e10i	0.734417	−	1.27205i
$304$		0			0
$305$	1.68420e9	+	2.91712e9i	0.194623	+	0.337097i
$306$		0			0
$307$			3.48446e9i			0.392267i	0.980577	+	0.196134i	$0.0628387\pi$
$307$			3.48446e9i			0.392267i	−0.980577	+	0.196134i	$0.937161\pi$
$308$		0			0
$309$	9.73728e9			1.06808
$310$		0			0
$311$	7.16218e9	−	4.13509e9i	0.765603	−	0.442021i	−0.0657008	−	0.997839i	$-0.520928\pi$
$311$	7.16218e9	−	4.13509e9i	0.765603	−	0.442021i	0.831304	+	0.555818i	$0.187595\pi$
$312$		0			0
$313$	9.69809e9	+	5.59920e9i	1.01044	+	0.583376i	0.911319	−	0.411700i	$-0.135065\pi$
$313$	9.69809e9	+	5.59920e9i	1.01044	+	0.583376i	0.0991170	+	0.995076i	$0.468398\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.58253e9	+	1.48654e10i	−0.849921	+	1.47211i	0.0313580	+	0.999508i	$0.490017\pi$
$317$	−8.58253e9	+	1.48654e10i	−0.849921	+	1.47211i	−0.881278	+	0.472597i	$0.843317\pi$
$318$		0			0
$319$	3.26584e9	+	5.65660e9i	0.315379	+	0.546252i
$320$		0			0
$321$			1.19015e10i			1.12094i
$322$		0			0
$323$	−1.72810e9			−0.158767
$324$		0			0
$325$	1.90491e7	−	1.09980e7i	0.00170742	−	0.000985779i
$326$		0			0
$327$	−1.80960e10	−	1.04477e10i	−1.58267	−	0.913757i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2.07141e9	+	3.58778e9i	−0.172565	+	0.298892i	−0.939316	−	0.343053i	$-0.888539\pi$
$331$	−2.07141e9	+	3.58778e9i	−0.172565	+	0.298892i	0.766751	+	0.641945i	$0.221872\pi$
$332$		0			0
$333$	5.55652e8	+	9.62418e8i	0.0451883	+	0.0782685i
$334$		0			0
$335$		−	1.83750e10i		−	1.45897i
$336$		0			0
$337$	−1.40450e10			−1.08894			−0.544469	−	0.838781i	$-0.683269\pi$
$337$	−1.40450e10			−1.08894			−0.544469	+	0.838781i	$0.683269\pi$
$338$		0			0
$339$	−7.06260e9	+	4.07759e9i	−0.534768	+	0.308749i
$340$		0			0
$341$	3.13941e10	+	1.81254e10i	2.32183	+	1.34051i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−7.65906e9	+	1.32659e10i	−0.540629	+	0.936396i
$346$		0			0
$347$	−4.46784e9	−	7.73853e9i	−0.308163	−	0.533753i	0.669798	−	0.742543i	$-0.266381\pi$
$347$	−4.46784e9	−	7.73853e9i	−0.308163	−	0.533753i	−0.977960	+	0.208790i	$0.933047\pi$
$348$		0			0
$349$			7.14294e9i			0.481477i	0.970590	+	0.240738i	$0.0773896\pi$
$349$			7.14294e9i			0.481477i	−0.970590	+	0.240738i	$0.922610\pi$
$350$		0			0
$351$	1.50926e8			0.00994344
$352$		0			0
$353$	1.09256e9	−	6.30789e8i	0.0703633	−	0.0406243i	−0.464406	−	0.885623i	$-0.653732\pi$
$353$	1.09256e9	−	6.30789e8i	0.0703633	−	0.0406243i	0.534769	+	0.844998i	$0.320399\pi$
$354$		0			0
$355$	−3.36769e9	−	1.94433e9i	−0.212040	−	0.122421i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.16161e8	+	1.06722e9i	−0.0370951	+	0.0642506i	−0.883977	−	0.467531i	$-0.845144\pi$
$359$	−6.16161e8	+	1.06722e9i	−0.0370951	+	0.0642506i	0.846882	+	0.531781i	$0.178477\pi$
$360$		0			0
$361$	−8.42917e9	−	1.45998e10i	−0.496313	−	0.859640i
$362$		0			0
$363$			3.02428e10i			1.74179i
$364$		0			0
$365$	2.84564e10			1.60328
$366$		0			0
$367$	1.01355e10	−	5.85176e9i	0.558705	−	0.322569i	−0.193920	−	0.981017i	$-0.562120\pi$
$367$	1.01355e10	−	5.85176e9i	0.558705	−	0.322569i	0.752626	+	0.658449i	$0.228787\pi$
$368$		0			0
$369$	2.73536e8	+	1.57926e8i	0.0147540	+	0.00851822i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−6.35740e9	+	1.10113e10i	−0.328431	+	0.568860i	−0.982201	−	0.187834i	$-0.939853\pi$
$373$	−6.35740e9	+	1.10113e10i	−0.328431	+	0.568860i	0.653769	+	0.756694i	$0.273187\pi$
$374$		0			0
$375$	−8.33446e9	−	1.44357e10i	−0.421456	−	0.729983i
$376$		0			0
$377$			7.33814e7i			0.00363262i
$378$		0			0
$379$	−3.32897e10			−1.61344			−0.806720	−	0.590934i	$-0.798759\pi$
$379$	−3.32897e10			−1.61344			−0.806720	+	0.590934i	$0.798759\pi$
$380$		0			0
$381$	−2.92232e10	+	1.68720e10i	−1.38684	+	0.800695i
$382$		0			0
$383$	−2.06925e10	−	1.19468e10i	−0.961653	−	0.555210i	−0.0649714	−	0.997887i	$-0.520696\pi$
$383$	−2.06925e10	−	1.19468e10i	−0.961653	−	0.555210i	−0.896681	+	0.442677i	$0.854029\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.85570e8	−	4.94622e8i	0.0127312	−	0.0220511i
$388$		0			0
$389$	1.07117e10	+	1.85532e10i	0.467799	+	0.810251i	0.999323	−	0.0367921i	$-0.0117139\pi$
$389$	1.07117e10	+	1.85532e10i	0.467799	+	0.810251i	−0.531524	+	0.847043i	$0.678381\pi$
$390$		0			0
$391$		−	4.41026e10i		−	1.88694i
$392$		0			0
$393$	−3.04670e10			−1.27720
$394$		0			0
$395$	−1.69446e10	+	9.78299e9i	−0.696056	+	0.401868i
$396$		0			0
$397$	−3.18830e10	−	1.84077e10i	−1.28351	−	0.741032i	−0.306018	−	0.952026i	$-0.598997\pi$
$397$	−3.18830e10	−	1.84077e10i	−1.28351	−	0.741032i	−0.977488	+	0.210993i	$0.932330\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.84595e10	+	3.19729e10i	−0.713910	+	1.23653i	0.249468	+	0.968383i	$0.419744\pi$
$401$	−1.84595e10	+	3.19729e10i	−0.713910	+	1.23653i	−0.963378	+	0.268146i	$0.913589\pi$
$402$		0			0
$403$	2.03633e8	+	3.52703e8i	0.00772020	+	0.0133718i
$404$		0			0
$405$			2.73829e10i			1.01779i
$406$		0			0
$407$	−6.10922e10			−2.22642
$408$		0			0
$409$	3.27839e10	−	1.89278e10i	1.17157	−	0.676405i	0.217519	−	0.976056i	$-0.430204\pi$
$409$	3.27839e10	−	1.89278e10i	1.17157	−	0.676405i	0.954049	+	0.299651i	$0.0968702\pi$
$410$		0			0
$411$	3.00541e10	+	1.73517e10i	1.05326	+	0.608101i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.17808e10	+	3.77254e10i	−0.734313	+	1.27187i
$416$		0			0
$417$	2.26634e10	+	3.92541e10i	0.749515	+	1.29820i
$418$		0			0
$419$			1.32942e9i			0.0431326i	0.999767	+	0.0215663i	$0.00686529\pi$
$419$			1.32942e9i			0.0431326i	−0.999767	+	0.0215663i	$0.993135\pi$
$420$		0			0
$421$	3.33376e10			1.06122			0.530611	−	0.847616i	$-0.321963\pi$
$421$	3.33376e10			1.06122			0.530611	+	0.847616i	$0.321963\pi$
$422$		0			0
$423$	6.45914e8	−	3.72919e8i	0.0201750	−	0.0116480i
$424$		0			0
$425$	−1.06799e10	−	6.16604e9i	−0.327349	−	0.188995i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.64045e8	+	4.57340e8i	−0.00779559	+	0.0135024i
$430$		0			0
$431$	−2.65259e10	−	4.59442e10i	−0.768707	−	1.33144i	−0.938265	−	0.345919i	$-0.887567\pi$
$431$	−2.65259e10	−	4.59442e10i	−0.768707	−	1.33144i	0.169558	−	0.985520i	$-0.445766\pi$
$432$		0			0
$433$		−	6.87668e10i		−	1.95626i	−0.207990	−	0.978131i	$-0.566692\pi$
$433$		−	6.87668e10i		−	1.95626i	0.207990	−	0.978131i	$-0.433308\pi$
$434$		0			0
$435$	−1.42896e10			−0.399083
$436$		0			0
$437$	−2.76763e9	+	1.59789e9i	−0.0758895	+	0.0438148i
$438$		0			0
$439$	−5.25587e9	−	3.03448e9i	−0.141510	−	0.0817007i	0.427574	−	0.903981i	$-0.359369\pi$
$439$	−5.25587e9	−	3.03448e9i	−0.141510	−	0.0817007i	−0.569083	+	0.822280i	$0.692702\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.02667e10	+	1.77825e10i	−0.266574	+	0.461720i	−0.967975	−	0.251047i	$-0.919225\pi$
$443$	−1.02667e10	+	1.77825e10i	−0.266574	+	0.461720i	0.701401	+	0.712767i	$0.252558\pi$
$444$		0			0
$445$	−3.99137e9	−	6.91325e9i	−0.101785	−	0.176296i
$446$		0			0
$447$			9.48148e9i			0.237490i
$448$		0			0
$449$	8.27711e9			0.203654			0.101827	−	0.994802i	$-0.467531\pi$
$449$	8.27711e9			0.203654			0.101827	+	0.994802i	$0.467531\pi$
$450$		0			0
$451$	−1.50372e10	+	8.68174e9i	−0.363464	+	0.209846i
$452$		0			0
$453$	−1.27723e10	−	7.37408e9i	−0.303302	−	0.175112i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.14518e9	−	1.58399e10i	0.209666	−	0.363152i	−0.741943	−	0.670462i	$-0.766096\pi$
$457$	9.14518e9	−	1.58399e10i	0.209666	−	0.363152i	0.951609	+	0.307311i	$0.0994291\pi$
$458$		0			0
$459$	−4.23086e10	−	7.32807e10i	−0.953187	−	1.65097i
$460$		0			0
$461$			1.74969e10i			0.387398i	0.981061	+	0.193699i	$0.0620485\pi$
$461$			1.74969e10i			0.387398i	−0.981061	+	0.193699i	$0.937952\pi$
$462$		0			0
$463$	1.40067e10			0.304797			0.152399	−	0.988319i	$-0.451300\pi$
$463$	1.40067e10			0.304797			0.152399	+	0.988319i	$0.451300\pi$
$464$		0			0
$465$	−6.86821e10	+	3.96536e10i	−1.46903	+	0.848147i
$466$		0			0
$467$	5.86513e10	+	3.38623e10i	1.23313	+	0.711950i	0.967682	−	0.252174i	$-0.0811456\pi$
$467$	5.86513e10	+	3.38623e10i	1.23313	+	0.711950i	0.265452	+	0.964124i	$0.414479\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.98174e10	+	5.16452e10i	−0.605879	+	1.04941i
$472$		0			0
$473$	1.56988e10	+	2.71910e10i	0.313632	+	0.543227i
$474$		0			0
$475$			8.93612e8i			0.0175539i
$476$		0			0
$477$	−8.74342e8			−0.0168891
$478$		0			0
$479$	6.06493e10	−	3.50159e10i	1.15208	−	0.665156i	0.202689	−	0.979243i	$-0.435032\pi$
$479$	6.06493e10	−	3.50159e10i	1.15208	−	0.665156i	0.949394	+	0.314087i	$0.101698\pi$
$480$		0			0
$481$	−5.94398e8	−	3.43176e8i	−0.0111044	−	0.00641115i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.79422e9	−	4.83974e9i	0.0505003	−	0.0874692i
$486$		0			0
$487$	1.52789e10	+	2.64639e10i	0.271629	+	0.470476i	0.969279	−	0.245963i	$-0.0791042\pi$
$487$	1.52789e10	+	2.64639e10i	0.271629	+	0.470476i	−0.697650	+	0.716439i	$0.745771\pi$
$488$		0			0
$489$			5.05828e10i			0.884642i
$490$		0			0
$491$	−7.30623e10			−1.25709			−0.628546	−	0.777772i	$-0.716350\pi$
$491$	−7.30623e10			−1.25709			−0.628546	+	0.777772i	$0.716350\pi$
$492$		0			0
$493$	3.56295e10	−	2.05707e10i	0.603146	−	0.348226i
$494$		0			0
$495$	6.49528e9	+	3.75005e9i	0.108188	+	0.0624621i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.23165e10	−	2.13328e10i	0.198649	−	0.344069i	−0.749442	−	0.662070i	$-0.769678\pi$
$499$	1.23165e10	−	2.13328e10i	0.198649	−	0.344069i	0.948090	+	0.318001i	$0.103011\pi$
$500$		0			0
$501$	2.13221e10	+	3.69310e10i	0.338439	+	0.586193i
$502$		0			0
$503$			7.46256e10i			1.16578i	0.812552	+	0.582889i	$0.198078\pi$
$503$			7.46256e10i			1.16578i	−0.812552	+	0.582889i	$0.801922\pi$
$504$		0			0
$505$	1.08596e11			1.66974
$506$		0			0
$507$	5.52377e10	−	3.18915e10i	0.835995	−	0.482662i
$508$		0			0
$509$	−2.11793e10	−	1.22279e10i	−0.315530	−	0.182171i	0.333868	−	0.942620i	$-0.391646\pi$
$509$	−2.11793e10	−	1.22279e10i	−0.315530	−	0.182171i	−0.649398	+	0.760448i	$0.724979\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−3.06578e9	+	5.31009e9i	−0.0442662	+	0.0766712i
$514$		0			0
$515$	4.27051e10	+	7.39675e10i	0.607087	+	1.05151i
$516$		0			0
$517$			4.10012e10i			0.573897i
$518$		0			0
$519$	−4.72944e10			−0.651839
$520$		0			0
$521$	5.17214e10	−	2.98613e10i	0.701971	−	0.405283i	−0.106110	−	0.994354i	$-0.533840\pi$
$521$	5.17214e10	−	2.98613e10i	0.701971	−	0.405283i	0.808081	+	0.589071i	$0.200506\pi$
$522$		0			0
$523$	4.67456e9	+	2.69886e9i	0.0624790	+	0.0360723i	0.530914	−	0.847426i	$-0.321849\pi$
$523$	4.67456e9	+	2.69886e9i	0.0624790	+	0.0360723i	−0.468435	+	0.883498i	$0.655182\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.14167e11	−	1.97744e11i	1.48013	−	2.56366i
$528$		0			0
$529$	−1.62394e9	−	2.81275e9i	−0.0207371	−	0.0359178i
$530$		0			0
$531$		−	5.65882e9i		−	0.0711783i
$532$		0			0
$533$	−1.95073e8			−0.00241707
$534$		0			0
$535$	−9.04075e10	+	5.21968e10i	−1.10354	+	0.637131i
$536$		0			0
$537$	2.08502e10	+	1.20379e10i	0.250734	+	0.144761i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.88609e9	−	8.46295e9i	0.0570390	−	0.0987945i	−0.836096	−	0.548583i	$-0.815167\pi$
$541$	4.88609e9	−	8.46295e9i	0.0570390	−	0.0987945i	0.893135	+	0.449789i	$0.148501\pi$
$542$		0			0
$543$	−4.89160e10	−	8.47249e10i	−0.562667	−	0.974567i
$544$		0			0
$545$		−	1.83284e11i		−	2.07749i
$546$		0			0
$547$	1.72001e10			0.192124			0.0960620	−	0.995375i	$-0.469375\pi$
$547$	1.72001e10			0.192124			0.0960620	+	0.995375i	$0.469375\pi$
$548$		0			0
$549$	−1.89673e9	+	1.09508e9i	−0.0208793	+	0.0120547i
$550$		0			0
$551$	−2.58180e9	−	1.49060e9i	−0.0280102	−	0.0161717i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	6.68268e10	−	1.15747e11i	0.704334	−	1.21994i
$556$		0			0
$557$	3.75938e10	+	6.51143e10i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$557$	3.75938e10	+	6.51143e10i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$558$		0			0
$559$			3.52741e8i			0.00361251i
$560$		0			0
$561$	2.96075e11			2.98917
$562$		0			0
$563$	4.79026e10	−	2.76566e10i	0.476788	−	0.275274i	−0.242289	−	0.970204i	$-0.577898\pi$
$563$	4.79026e10	−	2.76566e10i	0.476788	−	0.275274i	0.719077	+	0.694930i	$0.244565\pi$
$564$		0			0
$565$	−6.19493e10	−	3.57665e10i	−0.607915	−	0.350980i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.49212e10	+	1.12447e11i	−0.619352	+	1.07275i	0.370252	+	0.928931i	$0.379271\pi$
$569$	−6.49212e10	+	1.12447e11i	−0.619352	+	1.07275i	−0.989604	+	0.143818i	$0.954062\pi$
$570$		0			0
$571$	−6.84703e10	−	1.18594e11i	−0.644107	−	1.11563i	−0.984507	−	0.175345i	$-0.943896\pi$
$571$	−6.84703e10	−	1.18594e11i	−0.644107	−	1.11563i	0.340400	−	0.940281i	$-0.389437\pi$
$572$		0			0
$573$		−	5.23370e10i		−	0.485501i
$574$		0			0
$575$	−2.28057e10			−0.208628
$576$		0			0
$577$	5.08263e10	−	2.93446e10i	0.458548	−	0.264743i	−0.252885	−	0.967496i	$-0.581380\pi$
$577$	5.08263e10	−	2.93446e10i	0.458548	−	0.264743i	0.711434	+	0.702753i	$0.248046\pi$
$578$		0			0
$579$	1.00188e11	+	5.78438e10i	0.891463	+	0.514686i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.40327e10	−	4.16259e10i	0.208032	−	0.360321i
$584$		0			0
$585$	4.21307e7	+	7.29725e7i	0.000359729	+	0.000623068i
$586$		0			0
$587$			6.05036e10i			0.509600i	0.966994	+	0.254800i	$0.0820096\pi$
$587$			6.05036e10i			0.509600i	−0.966994	+	0.254800i	$0.917990\pi$
$588$		0			0
$589$	−1.65457e10			−0.137475
$590$		0			0
$591$	−9.98520e10	+	5.76496e10i	−0.818478	+	0.472548i
$592$		0			0
$593$	6.76283e9	+	3.90452e9i	0.0546902	+	0.0315754i	0.527096	−	0.849806i	$-0.323281\pi$
$593$	6.76283e9	+	3.90452e9i	0.0546902	+	0.0315754i	−0.472406	+	0.881381i	$0.656614\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.57819e10	−	1.48579e11i	0.675303	−	1.16966i
$598$		0			0
$599$	1.03537e11	+	1.79332e11i	0.804247	+	1.39300i	0.916798	+	0.399350i	$0.130764\pi$
$599$	1.03537e11	+	1.79332e11i	0.804247	+	1.39300i	−0.112552	+	0.993646i	$0.535902\pi$
$600$		0			0
$601$		−	2.04173e11i		−	1.56495i	−0.622680	−	0.782476i	$-0.713956\pi$
$601$		−	2.04173e11i		−	1.56495i	0.622680	−	0.782476i	$-0.286044\pi$
$602$		0			0
$603$	1.19475e10			0.0903666
$604$		0			0
$605$	−2.29734e11	+	1.32637e11i	−1.71476	+	0.990018i
$606$		0			0
$607$	−6.20308e10	−	3.58135e10i	−0.456933	−	0.263810i	0.253821	−	0.967251i	$-0.418313\pi$
$607$	−6.20308e10	−	3.58135e10i	−0.456933	−	0.263810i	−0.710754	+	0.703441i	$0.751646\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.30318e8	+	3.98922e8i	−0.00165258	+	0.00286235i
$612$		0			0
$613$	4.93732e10	+	8.55169e10i	0.349663	+	0.605634i	0.986189	−	0.165621i	$-0.0529628\pi$
$613$	4.93732e10	+	8.55169e10i	0.349663	+	0.605634i	−0.636527	+	0.771255i	$0.719630\pi$
$614$		0			0
$615$		−	3.79867e10i		−	0.265541i
$616$		0			0
$617$	2.68662e11			1.85381			0.926906	−	0.375294i	$-0.122458\pi$
$617$	2.68662e11			1.85381			0.926906	+	0.375294i	$0.122458\pi$
$618$		0			0
$619$	−1.34653e11	+	7.77420e10i	−0.917178	+	0.529533i	−0.882734	−	0.469874i	$-0.844300\pi$
$619$	−1.34653e11	+	7.77420e10i	−0.917178	+	0.529533i	−0.0344445	+	0.999407i	$0.510966\pi$
$620$		0			0
$621$	−1.35518e11	−	7.82412e10i	−0.911234	−	0.526101i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	8.87023e10	−	1.53637e11i	0.581320	−	1.00688i
$626$		0			0
$627$	−1.07271e10	−	1.85800e10i	−0.0694087	−	0.120219i
$628$		0			0
$629$			3.84804e11i			2.45831i
$630$		0			0
$631$	−1.48914e11			−0.939327			−0.469663	−	0.882846i	$-0.655625\pi$
$631$	−1.48914e11			−0.939327			−0.469663	+	0.882846i	$0.655625\pi$
$632$		0			0
$633$	1.27975e11	−	7.38866e10i	0.797097	−	0.460204i
$634$		0			0
$635$	−2.56330e11	−	1.47992e11i	−1.57654	−	0.910216i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.26422e9	−	2.18969e9i	0.00758261	−	0.0131335i
$640$		0			0
$641$	1.32267e10	+	2.29093e10i	0.0783463	+	0.135700i	0.902537	−	0.430613i	$-0.141703\pi$
$641$	1.32267e10	+	2.29093e10i	0.0783463	+	0.135700i	−0.824190	+	0.566313i	$0.808369\pi$
$642$		0			0
$643$			1.31229e11i			0.767689i	0.923398	+	0.383845i	$0.125400\pi$
$643$			1.31229e11i			0.767689i	−0.923398	+	0.383845i	$0.874600\pi$
$644$		0			0
$645$	−6.86895e10			−0.396873
$646$		0			0
$647$	5.00024e10	−	2.88689e10i	0.285347	−	0.164745i	−0.350494	−	0.936565i	$-0.613986\pi$
$647$	5.00024e10	−	2.88689e10i	0.285347	−	0.164745i	0.635842	+	0.771819i	$0.280653\pi$
$648$		0			0
$649$	2.69407e11	+	1.55542e11i	1.51855	+	0.876737i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.86237e10	−	4.95778e10i	0.157425	−	0.272668i	−0.776514	−	0.630099i	$-0.783014\pi$
$653$	2.86237e10	−	4.95778e10i	0.157425	−	0.272668i	0.933939	+	0.357431i	$0.116347\pi$
$654$		0			0
$655$	−1.33620e11	−	2.31437e11i	−0.725949	−	1.25738i
$656$		0			0
$657$			1.85025e10i			0.0993045i
$658$		0			0
$659$	−7.42215e10			−0.393539			−0.196770	−	0.980450i	$-0.563045\pi$
$659$	−7.42215e10			−0.393539			−0.196770	+	0.980450i	$0.563045\pi$
$660$		0			0
$661$	2.04993e11	−	1.18353e11i	1.07382	−	0.619973i	0.144601	−	0.989490i	$-0.453810\pi$
$661$	2.04993e11	−	1.18353e11i	1.07382	−	0.619973i	0.929224	+	0.369517i	$0.120477\pi$
$662$		0			0
$663$	2.88067e9	+	1.66316e9i	0.0149087	+	0.00860753i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.80414e10	−	6.58896e10i	0.192200	−	0.332900i
$668$		0			0
$669$	4.78111e10	+	8.28112e10i	0.238684	+	0.413413i
$670$		0			0
$671$		−	1.20400e11i		−	0.593933i
$672$		0			0
$673$	−3.95895e10			−0.192983			−0.0964917	−	0.995334i	$-0.530762\pi$
$673$	−3.95895e10			−0.192983			−0.0964917	+	0.995334i	$0.530762\pi$
$674$		0			0
$675$	−3.78938e10	+	2.18780e10i	−0.182538	+	0.105388i
$676$		0			0
$677$	8.58629e10	+	4.95730e10i	0.408743	+	0.235988i	0.690250	−	0.723571i	$-0.257501\pi$
$677$	8.58629e10	+	4.95730e10i	0.408743	+	0.235988i	−0.281506	+	0.959559i	$0.590834\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.34944e10	−	2.33730e10i	0.0627430	−	0.108674i
$682$		0			0
$683$	5.00961e9	+	8.67690e9i	0.0230208	+	0.0398733i	0.877306	−	0.479931i	$-0.159338\pi$
$683$	5.00961e9	+	8.67690e9i	0.0230208	+	0.0398733i	−0.854285	+	0.519804i	$0.826005\pi$
$684$		0			0
$685$			3.04400e11i			1.38256i
$686$		0			0
$687$	5.97880e10			0.268403
$688$		0			0
$689$	4.67654e8	−	2.70000e8i	0.00207514	−	0.00119808i
$690$		0			0
$691$	7.96091e10	+	4.59623e10i	0.349181	+	0.201600i	0.664324	−	0.747444i	$-0.268719\pi$
$691$	7.96091e10	+	4.59623e10i	0.349181	+	0.201600i	−0.315144	+	0.949044i	$0.602053\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.98791e11	+	3.44316e11i	−0.852035	+	1.47577i
$696$		0			0
$697$	5.46841e10	+	9.47156e10i	0.231702	+	0.401320i
$698$		0			0
$699$		−	3.99586e11i		−	1.67379i
$700$		0			0
$701$	7.64528e10			0.316608			0.158304	−	0.987390i	$-0.449397\pi$
$701$	7.64528e10			0.316608			0.158304	+	0.987390i	$0.449397\pi$
$702$		0			0
$703$	2.41481e10	−	1.39419e10i	0.0988693	−	0.0570822i
$704$		0			0
$705$	−7.76824e10	−	4.48499e10i	−0.314460	−	0.181554i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−8.34054e10	+	1.44462e11i	−0.330072	+	0.571702i	−0.982526	−	0.186127i	$-0.940406\pi$
$709$	−8.34054e10	+	1.44462e11i	−0.330072	+	0.571702i	0.652453	+	0.757829i	$0.273740\pi$
$710$		0			0
$711$	−6.36096e9	−	1.10175e10i	−0.0248911	−	0.0431127i
$712$		0			0
$713$		−	4.22259e11i		−	1.63388i
$714$		0			0
$715$	−4.63213e9			−0.0177238
$716$		0			0
$717$	1.87906e11	−	1.08487e11i	0.710989	−	0.410490i
$718$		0			0
$719$	3.84062e11	+	2.21738e11i	1.43710	+	0.829708i	0.997647	−	0.0685600i	$-0.0218405\pi$
$719$	3.84062e11	+	2.21738e11i	1.43710	+	0.829708i	0.439449	+	0.898268i	$0.355174\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.28309e11	+	2.22237e11i	−0.469573	+	0.813324i
$724$		0			0
$725$	−1.06372e10	−	1.84242e10i	−0.0385014	−	0.0666863i
$726$		0			0
$727$			1.75400e11i			0.627902i	0.949439	+	0.313951i	$0.101653\pi$
$727$			1.75400e11i			0.627902i	−0.949439	+	0.313951i	$0.898347\pi$
$728$		0			0
$729$	−2.98929e11			−1.05842
$730$		0			0
$731$	1.71270e11	−	9.88826e10i	0.599806	−	0.346298i
$732$		0			0
$733$	4.03417e10	+	2.32913e10i	0.139746	+	0.0806823i	0.568243	−	0.822861i	$-0.307623\pi$
$733$	4.03417e10	+	2.32913e10i	0.139746	+	0.0806823i	−0.428497	+	0.903543i	$0.640957\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.28397e11	+	5.68801e11i	−1.11309	+	1.92793i
$738$		0			0
$739$	−1.77446e11	−	3.07346e11i	−0.594962	−	1.03051i	−0.993552	−	0.113376i	$-0.963834\pi$
$739$	−1.77446e11	−	3.07346e11i	−0.594962	−	1.03051i	0.398590	−	0.917129i	$-0.369500\pi$
$740$		0			0
$741$		−	2.41032e8i		−	0.000799470i
$742$		0			0
$743$	−1.71203e11			−0.561767			−0.280884	−	0.959742i	$-0.590628\pi$
$743$	−1.71203e11			−0.561767			−0.280884	+	0.959742i	$0.590628\pi$
$744$		0			0
$745$	−7.20243e10	+	4.15833e10i	−0.233805	+	0.134988i
$746$		0			0
$747$	−2.45293e10	−	1.41620e10i	−0.0787776	−	0.0454823i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.68250e10	−	1.33065e11i	0.241514	−	0.418315i	−0.719632	−	0.694356i	$-0.755689\pi$
$751$	7.68250e10	−	1.33065e11i	0.241514	−	0.418315i	0.961146	+	0.276041i	$0.0890226\pi$
$752$		0			0
$753$	−1.12155e11	−	1.94259e11i	−0.348851	−	0.604228i
$754$		0			0
$755$		−	1.29363e11i		−	0.398128i
$756$		0			0
$757$	−7.15192e10			−0.217791			−0.108895	−	0.994053i	$-0.534731\pi$
$757$	−7.15192e10			−0.217791			−0.108895	+	0.994053i	$0.534731\pi$
$758$		0			0
$759$	4.74176e11	−	2.73765e11i	1.42880	−	0.824920i
$760$		0			0
$761$	−2.84305e10	−	1.64144e10i	−0.0847707	−	0.0489424i	0.457015	−	0.889459i	$-0.348918\pi$
$761$	−2.84305e10	−	1.64144e10i	−0.0847707	−	0.0489424i	−0.541786	+	0.840516i	$0.682252\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.36207e10	−	4.09122e10i	0.0689678	−	0.119456i
$766$		0			0
$767$	1.74747e9	+	3.02670e9i	0.00504926	+	0.00874557i
$768$		0			0
$769$			3.53063e11i			1.00960i	0.863238	+	0.504798i	$0.168433\pi$
$769$			3.53063e11i			1.00960i	−0.863238	+	0.504798i	$0.831567\pi$
$770$		0			0
$771$	−2.96855e11			−0.840093
$772$		0			0
$773$	−4.97675e11	+	2.87333e11i	−1.39389	+	0.804762i	−0.993743	−	0.111689i	$-0.964374\pi$
$773$	−4.97675e11	+	2.87333e11i	−1.39389	+	0.804762i	−0.400146	+	0.916452i	$0.631040\pi$
$774$		0			0
$775$	−1.02254e11	−	5.90366e10i	−0.283449	−	0.163649i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.96254e9	−	6.86332e9i	0.0107603	−	0.0186373i
$780$		0			0
$781$	6.94983e10	+	1.20375e11i	0.186797	+	0.323542i
$782$		0			0
$783$		−	1.45976e11i		−	0.388359i
$784$		0			0
$785$	−5.23085e11			−1.37751
$786$		0			0
$787$	−3.50120e11	+	2.02142e11i	−0.912680	+	0.526936i	−0.881292	−	0.472571i	$-0.843326\pi$
$787$	−3.50120e11	+	2.02142e11i	−0.912680	+	0.526936i	−0.0313876	+	0.999507i	$0.509993\pi$
$788$		0			0
$789$	−1.31090e11	−	7.56849e10i	−0.338269	−	0.195300i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.76330e8	−	1.17144e9i	0.00171027	−	0.00296228i
$794$		0			0
$795$	5.25774e10	+	9.10667e10i	0.131623	+	0.227977i
$796$		0			0
$797$			1.43229e11i			0.354975i	0.984123	+	0.177488i	$0.0567969\pi$
$797$			1.43229e11i			0.354975i	−0.984123	+	0.177488i	$0.943203\pi$
$798$		0			0
$799$	2.58256e11			0.633671
$800$		0			0
$801$	4.49504e9	−	2.59521e9i	0.0109195	−	0.00630439i
$802$		0			0
$803$	−8.80873e11	−	5.08572e11i	−2.11861	−	1.22318i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.18292e11	+	2.04888e11i	−0.278908	+	0.483083i
$808$		0			0
$809$	1.64053e10	+	2.84147e10i	0.0382991	+	0.0663360i	0.884540	−	0.466465i	$-0.154473\pi$
$809$	1.64053e10	+	2.84147e10i	0.0382991	+	0.0663360i	−0.846240	+	0.532801i	$0.821139\pi$
$810$		0			0
$811$			6.27249e11i			1.44996i	0.688769	+	0.724981i	$0.258151\pi$
$811$			6.27249e11i			1.44996i	−0.688769	+	0.724981i	$0.741849\pi$
$812$		0			0
$813$	−2.75395e10			−0.0630367
$814$		0			0
$815$	−3.84243e11	+	2.21843e11i	−0.870914	+	0.502823i
$816$		0			0
$817$	−1.24106e10	−	7.16526e9i	−0.0278551	−	0.0160821i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.42590e11	+	5.93384e11i	−0.754054	+	1.30606i	0.191789	+	0.981436i	$0.438571\pi$
$821$	−3.42590e11	+	5.93384e11i	−0.754054	+	1.30606i	−0.945843	+	0.324623i	$0.894762\pi$
$822$		0			0
$823$	2.20407e11	+	3.81756e11i	0.480425	+	0.832121i	0.999748	−	0.0224571i	$-0.00714891\pi$
$823$	2.20407e11	+	3.81756e11i	0.480425	+	0.832121i	−0.519322	+	0.854578i	$0.673816\pi$
$824$		0			0
$825$		−	1.53102e11i		−	0.330495i
$826$		0			0
$827$	−3.10595e11			−0.664007			−0.332004	−	0.943278i	$-0.607725\pi$
$827$	−3.10595e11			−0.664007			−0.332004	+	0.943278i	$0.607725\pi$
$828$		0			0
$829$	−6.95885e11	+	4.01770e11i	−1.47340	+	0.850666i	−0.999552	−	0.0299427i	$-0.990468\pi$
$829$	−6.95885e11	+	4.01770e11i	−1.47340	+	0.850666i	−0.473845	+	0.880608i	$0.657134\pi$
$830$		0			0
$831$	4.66457e10	+	2.69309e10i	0.0978154	+	0.0564738i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.87027e11	+	3.23940e11i	−0.384731	+	0.666374i
$836$		0			0
$837$	−4.05082e11	−	7.01623e11i	−0.825356	−	1.42956i
$838$		0			0
$839$			2.60770e11i			0.526271i	0.964759	+	0.263136i	$0.0847567\pi$
$839$			2.60770e11i			0.526271i	−0.964759	+	0.263136i	$0.915243\pi$
$840$		0			0
$841$	−4.29272e11			−0.858121
$842$		0			0
$843$	5.47868e11	−	3.16312e11i	1.08484	−	0.626332i
$844$		0			0
$845$	4.84516e11	+	2.79735e11i	0.950345	+	0.548682i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.38091e11	−	2.39180e11i	0.265787	−	0.460356i
$850$		0			0
$851$	3.55809e11	+	6.16279e11i	0.678420	+	1.17506i
$852$		0			0
$853$		−	2.90865e11i		−	0.549409i	−0.961529	−	0.274704i	$-0.911420\pi$
$853$		−	2.90865e11i		−	0.549409i	0.961529	−	0.274704i	$-0.0885800\pi$
$854$		0			0
$855$	−3.42322e9			−0.00640575
$856$		0			0
$857$	5.96952e10	−	3.44650e10i	0.110666	−	0.0638933i	−0.443645	−	0.896203i	$-0.646315\pi$
$857$	5.96952e10	−	3.44650e10i	0.110666	−	0.0638933i	0.554312	+	0.832309i	$0.312982\pi$
$858$		0			0
$859$	2.30322e11	+	1.32976e11i	0.423022	+	0.244232i	0.696369	−	0.717684i	$-0.254798\pi$
$859$	2.30322e11	+	1.32976e11i	0.423022	+	0.244232i	−0.273347	+	0.961915i	$0.588131\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.41523e11	+	4.18331e11i	−0.435427	+	0.754182i	−0.997330	−	0.0730207i	$-0.976736\pi$
$863$	−2.41523e11	+	4.18331e11i	−0.435427	+	0.754182i	0.561903	+	0.827203i	$0.310069\pi$
$864$		0			0
$865$	−2.07421e11	−	3.59263e11i	−0.370500	−	0.641724i
$866$		0			0
$867$		−	1.31941e12i		−	2.33509i
$868$		0			0
$869$	6.99367e11			1.22638
$870$		0			0
$871$	−6.39030e9	+	3.68944e9i	−0.0111032	+	0.00641044i
$872$		0			0
$873$	3.14683e9	+	1.81682e9i	0.00541771	+	0.00312792i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.38694e11	+	2.40226e11i	−0.234456	+	0.406089i	−0.959114	−	0.283019i	$-0.908664\pi$
$877$	−1.38694e11	+	2.40226e11i	−0.234456	+	0.406089i	0.724659	+	0.689108i	$0.241997\pi$
$878$		0			0
$879$	−3.19000e11	−	5.52524e11i	−0.534361	−	0.925541i
$880$		0			0
$881$			2.40890e11i			0.399866i	0.979810	+	0.199933i	$0.0640725\pi$
$881$			2.40890e11i			0.399866i	−0.979810	+	0.199933i	$0.935928\pi$
$882$		0			0
$883$	7.97420e11			1.31173			0.655865	−	0.754879i	$-0.272304\pi$
$883$	7.97420e11			1.31173			0.655865	+	0.754879i	$0.272304\pi$
$884$		0			0
$885$	−5.89392e11	+	3.40286e11i	−0.960796	+	0.554716i
$886$		0			0
$887$	1.78784e10	+	1.03221e10i	0.0288825	+	0.0166753i	0.514372	−	0.857567i	$-0.328025\pi$
$887$	1.78784e10	+	1.03221e10i	0.0288825	+	0.0166753i	−0.485489	+	0.874243i	$0.661358\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.89388e11	−	8.47645e11i	0.776502	−	1.34494i
$892$		0			0
$893$	−9.35693e9	−	1.62067e10i	−0.0147139	−	0.0254852i
$894$		0			0
$895$			2.11180e11i			0.329124i
$896$		0			0
$897$	6.15134e9			0.00950167
$898$		0			0
$899$	3.41134e11	−	1.96954e11i	0.522259	−	0.301526i
$900$		0			0
$901$	−2.62191e11	−	1.51376e11i	−0.397850	−	0.229699i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.29065e11	−	7.43162e11i	0.639630	−	1.10787i
$906$		0			0
$907$	−4.03438e11	−	6.98775e11i	−0.596139	−	1.03254i	−0.993385	−	0.114831i	$-0.963367\pi$
$907$	−4.03438e11	−	6.98775e11i	−0.596139	−	1.03254i	0.397246	−	0.917712i	$-0.369966\pi$
$908$		0			0
$909$			7.06100e10i			0.103421i
$910$		0			0
$911$	−4.47775e11			−0.650109			−0.325054	−	0.945695i	$-0.605383\pi$
$911$	−4.47775e11			−0.650109			−0.325054	+	0.945695i	$0.605383\pi$
$912$		0			0
$913$	1.34846e12	−	7.78533e11i	1.94068	−	1.12045i
$914$		0			0
$915$	2.28115e11	+	1.31702e11i	0.325439	+	0.187892i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	2.80924e11	−	4.86575e11i	0.393846	−	0.682162i	−0.599107	−	0.800669i	$-0.704478\pi$
$919$	2.80924e11	−	4.86575e11i	0.393846	−	0.682162i	0.992953	+	0.118507i	$0.0378108\pi$
$920$		0			0
$921$	1.36240e11	+	2.35975e11i	0.189350	+	0.327964i
$922$		0			0
$923$			1.56158e9i			0.00215158i
$924$		0			0
$925$	1.98984e11			0.271802
$926$		0			0
$927$	−4.80941e10	+	2.77671e10i	−0.0651287	+	0.0376021i
$928$		0			0
$929$	4.59844e11	+	2.65491e11i	0.617374	+	0.356441i	0.775846	−	0.630923i	$-0.217323\pi$
$929$	4.59844e11	+	2.65491e11i	0.617374	+	0.356441i	−0.158472	+	0.987363i	$0.550657\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	3.23358e11	−	5.60072e11i	0.426733	−	0.739124i
$934$		0			0
$935$	1.29851e12	+	2.24908e12i	1.69902	+	2.94278i
$936$		0			0
$937$		−	1.19762e12i		−	1.55368i	−0.629699	−	0.776839i	$-0.716822\pi$
$937$		−	1.19762e12i		−	1.55368i	0.629699	−	0.776839i	$-0.283178\pi$
$938$		0			0
$939$	8.75698e11			1.12640
$940$		0			0
$941$	1.18102e12	−	6.81860e11i	1.50625	−	0.869635i	0.506278	−	0.862370i	$-0.331021\pi$
$941$	1.18102e12	−	6.81860e11i	1.50625	−	0.869635i	0.999974	−	0.00726500i	$-0.00231254\pi$
$942$		0			0
$943$	1.75157e11	+	1.01127e11i	0.221504	+	0.127885i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.47927e11	+	7.75832e11i	−0.556938	+	0.964645i	0.440812	+	0.897600i	$0.354691\pi$
$947$	−4.47927e11	+	7.75832e11i	−0.556938	+	0.964645i	−0.997750	+	0.0670457i	$0.978643\pi$
$948$		0			0
$949$	−5.71365e9	−	9.89633e9i	−0.00704448	−	0.0122014i
$950$		0			0
$951$			1.34228e12i			1.64105i
$952$		0			0
$953$	−1.10721e12			−1.34232			−0.671161	−	0.741311i	$-0.734204\pi$
$953$	−1.10721e12			−1.34232			−0.671161	+	0.741311i	$0.734204\pi$
$954$		0			0
$955$	3.97568e11	−	2.29536e11i	0.477967	−	0.275955i
$956$		0			0
$957$	4.42338e11	+	2.55384e11i	0.527359	+	0.304471i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	6.66646e11	−	1.15467e12i	0.781631	−	1.35383i
$962$		0			0
$963$	−3.39387e10	−	5.87835e10i	−0.0394629	−	0.0683518i
$964$		0			0
$965$			1.01475e12i			1.17017i
$966$		0			0
$967$	4.92082e11			0.562771			0.281385	−	0.959595i	$-0.409206\pi$
$967$	4.92082e11			0.562771			0.281385	+	0.959595i	$0.409206\pi$
$968$		0			0
$969$	−1.17031e11	+	6.75676e10i	−0.132741	+	0.0766379i
$970$		0			0
$971$	−4.27322e11	−	2.46714e11i	−0.480704	−	0.277535i	0.240006	−	0.970771i	$-0.422851\pi$
$971$	−4.27322e11	−	2.46714e11i	−0.480704	−	0.277535i	−0.720710	+	0.693237i	$0.756184\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	8.60026e8	−	1.48961e9i	0.000951685	−	0.00164837i
$976$		0			0
$977$	5.67571e11	+	9.83062e11i	0.622934	+	1.07895i	0.988937	+	0.148339i	$0.0473928\pi$
$977$	5.67571e11	+	9.83062e11i	0.622934	+	1.07895i	−0.366003	+	0.930614i	$0.619274\pi$
$978$		0			0
$979$			2.85335e11i			0.310616i
$980$		0			0
$981$	1.19172e11			0.128676
$982$		0			0
$983$	−1.02512e12	+	5.91855e11i	−1.09790	+	0.633872i	−0.935668	−	0.352881i	$-0.885202\pi$
$983$	−1.02512e12	+	5.91855e11i	−1.09790	+	0.633872i	−0.162230	+	0.986753i	$0.551869\pi$
$984$		0			0
$985$	−8.75849e11	−	5.05671e11i	−0.930431	−	0.537185i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.82863e11	−	3.16728e11i	0.191135	−	0.331056i
$990$		0			0
$991$	−4.89231e11	−	8.47373e11i	−0.507247	−	0.878577i	−0.999965	−	0.00838831i	$-0.997330\pi$
$991$	−4.89231e11	−	8.47373e11i	−0.507247	−	0.878577i	0.492718	−	0.870189i	$-0.336003\pi$
$992$		0			0
$993$			3.23962e11i			0.333194i
$994$		0			0
$995$	1.50487e12			1.53534
$996$		0			0
$997$	−2.64794e11	+	1.52879e11i	−0.267995	+	0.154727i	−0.627976	−	0.778233i	$-0.716116\pi$
$997$	−2.64794e11	+	1.52879e11i	−0.267995	+	0.154727i	0.359981	+	0.932960i	$0.382783\pi$
$998$		0			0
$999$	1.18242e12	+	6.82670e11i	1.18716	+	0.685408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.9.h.b.117.5		12
7.2	even	3		28.9.b.a.13.5	yes	6
7.3	odd	6	inner	196.9.h.b.129.5		12
7.4	even	3	inner	196.9.h.b.129.2		12
7.5	odd	6		28.9.b.a.13.2	✓	6
7.6	odd	2	inner	196.9.h.b.117.2		12
21.2	odd	6		252.9.d.b.181.5		6
21.5	even	6		252.9.d.b.181.2		6
28.19	even	6		112.9.c.d.97.5		6
28.23	odd	6		112.9.c.d.97.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.b.a.13.2	✓	6	7.5	odd	6
28.9.b.a.13.5	yes	6	7.2	even	3
112.9.c.d.97.2		6	28.23	odd	6
112.9.c.d.97.5		6	28.19	even	6
196.9.h.b.117.2		12	7.6	odd	2	inner
196.9.h.b.117.5		12	1.1	even	1	trivial
196.9.h.b.129.2		12	7.4	even	3	inner
196.9.h.b.129.5		12	7.3	odd	6	inner
252.9.d.b.181.2		6	21.5	even	6
252.9.d.b.181.5		6	21.2	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 $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(67.7219 - 39.0993i) q^{3} +(594.021 + 342.958i) q^{5} +(-222.993 + 386.236i) q^{9} +(-12258.7 - 21232.7i) q^{11} -275.445i q^{13} +53637.7 q^{15} +(-133739. + 77214.5i) q^{17} +(9691.07 + 5595.14i) q^{19} +(-142793. + 247324. i) q^{23} +(39928.0 + 69157.3i) q^{25} +547936. i q^{27} -266410. q^{29} +(-1.28048e6 + 739287. i) q^{31} +(-1.66037e6 - 958612. i) q^{33} +(1.24589e6 - 2.15795e6i) q^{37} +(-10769.7 - 18653.7i) q^{39} -708210. i q^{41} -1.28062e6 q^{43} +(-264925. + 152955. i) q^{45} +(-1.44828e6 - 836165. i) q^{47} +(-6.03806e6 + 1.04582e7i) q^{51} +(980232. + 1.69781e6i) q^{53} -1.68169e7i q^{55} +875064. q^{57} +(-1.09884e7 + 6.34416e6i) q^{59} +(4.25289e6 + 2.45541e6i) q^{61} +(94466.2 - 163620. i) q^{65} +(-1.33945e7 - 2.31999e7i) q^{67} +2.23323e7i q^{69} -5.66931e6 q^{71} +(3.59285e7 - 2.07433e7i) q^{73} +(5.40800e6 + 3.12231e6i) q^{75} +(-1.42627e7 + 2.47037e7i) q^{79} +(1.99608e7 + 3.45732e7i) q^{81} +6.35086e7i q^{83} -1.05925e8 q^{85} +(-1.80418e7 + 1.04164e7i) q^{87} +(-1.00789e7 - 5.81903e6i) q^{89} +(-5.78112e7 + 1.00132e8i) q^{93} +(3.83780e6 + 6.64726e6i) q^{95} -8.14742e6i q^{97} +1.09344e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18234 q^{9} - 24492 q^{11} - 306816 q^{15} + 11604 q^{23} + 678714 q^{25} + 2528664 q^{29} - 3184332 q^{37} - 5634240 q^{39} - 15566760 q^{43} - 6877824 q^{51} + 8340660 q^{53} - 35901696 q^{57}+ \cdots - 1191795624 q^{99}+O(q^{100}) \) 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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