LMFDB - Embedded newform 196.8.e.d.177.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,8,Mod(165,196)] 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("196.165"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,14,0,-42] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$61.2274649949$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{3529})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 883x^{2} + 882x + 777924 $ x^4 - x^3 + 883x^2 + 882x + 777924
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.2
Root			$15.1013 + 26.1563i$ of defining polynomial
Character	$\chi$	$=$	196.177
Dual form			196.8.e.d.165.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(33.2027 + 57.5088i) q^{3} +(78.6081 - 136.153i) q^{5} +(-1111.34 + 1924.89i) q^{9} +(-3104.51 - 5377.17i) q^{11} +5380.35 q^{13} +10440.0 q^{15} +(5497.46 + 9521.87i) q^{17} +(-5851.53 + 10135.1i) q^{19} +(-53070.5 + 91920.8i) q^{23} +(26704.0 + 46252.8i) q^{25} -2369.04 q^{27} -51562.7 q^{29} +(123778. + 214390. i) q^{31} +(206156. - 357073. i) q^{33} +(-216839. + 375576. i) q^{37} +(178642. + 309417. i) q^{39} +322819. q^{41} +878703. q^{43} +(174720. + 302624. i) q^{45} +(-327563. + 567356. i) q^{47} +(-365061. + 632304. i) q^{51} +(222418. + 385240. i) q^{53} -976159. q^{55} -777146. q^{57} +(-1.07273e6 - 1.85802e6i) q^{59} +(-296451. + 513468. i) q^{61} +(422939. - 732552. i) q^{65} +(-864332. - 1.49707e6i) q^{67} -7.04833e6 q^{69} +1.58060e6 q^{71} +(2.16582e6 + 3.75131e6i) q^{73} +(-1.77329e6 + 3.07143e6i) q^{75} +(3.04259e6 - 5.26992e6i) q^{79} +(2.35184e6 + 4.07350e6i) q^{81} -8.10357e6 q^{83} +1.72858e6 q^{85} +(-1.71202e6 - 2.96531e6i) q^{87} +(-4.93016e6 + 8.53929e6i) q^{89} +(-8.21955e6 + 1.42367e7i) q^{93} +(919955. + 1.59341e6i) q^{95} -171786. q^{97} +1.38007e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 14 q^{3} - 42 q^{5} - 2782 q^{9} - 7428 q^{11} + 23660 q^{13} + 41760 q^{15} - 15792 q^{17} - 26614 q^{19} - 32640 q^{23} + 91846 q^{25} - 175336 q^{27} - 316032 q^{29} + 180740 q^{31} + 348432 q^{33}+ \cdots + 28964904 q^{99}+O(q^{100}) $ 4 * q + 14 * q^3 - 42 * q^5 - 2782 * q^9 - 7428 * q^11 + 23660 * q^13 + 41760 * q^15 - 15792 * q^17 - 26614 * q^19 - 32640 * q^23 + 91846 * q^25 - 175336 * q^27 - 316032 * q^29 + 180740 * q^31 + 348432 * q^33 + 45824 * q^37 + 19288 * q^39 - 643440 * q^41 + 2047736 * q^43 + 238014 * q^45 - 1665972 * q^47 - 2133900 * q^51 + 410628 * q^53 - 1466640 * q^55 + 8536 * q^57 - 1702134 * q^59 + 547526 * q^61 - 438996 * q^65 + 2590616 * q^67 - 21800352 * q^69 + 8258544 * q^71 + 8008868 * q^73 - 1532230 * q^75 - 2470456 * q^79 + 10397042 * q^81 - 19801572 * q^83 + 14129928 * q^85 + 2154684 * q^87 - 15423492 * q^89 - 19940648 * q^93 - 1130592 * q^95 - 34754944 * q^97 + 28964904 * q^99

Character values

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

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	33.2027	+	57.5088i	0.709985	+	1.22973i	0.964862	+	0.262756i	$0.0846315\pi$
$3$	33.2027	+	57.5088i	0.709985	+	1.22973i	−0.254878	+	0.966973i	$0.582035\pi$
$4$		0			0
$5$	78.6081	−	136.153i	0.281237	−	0.487116i	−0.690453	−	0.723377i	$-0.742589\pi$
$5$	78.6081	−	136.153i	0.281237	−	0.487116i	0.971690	+	0.236261i	$0.0759220\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1111.34	+	1924.89i	−0.508156	+	0.880152i
$10$		0			0
$11$	−3104.51	−	5377.17i	−0.703265	−	1.21809i	−0.967314	−	0.253582i	$-0.918391\pi$
$11$	−3104.51	−	5377.17i	−0.703265	−	1.21809i	0.264049	−	0.964509i	$-0.414942\pi$
$12$		0			0
$13$	5380.35			0.679218			0.339609	−	0.940567i	$-0.389705\pi$
$13$	5380.35			0.679218			0.339609	+	0.940567i	$0.389705\pi$
$14$		0			0
$15$	10440.0			0.798695
$16$		0			0
$17$	5497.46	+	9521.87i	0.271388	+	0.470058i	0.969217	−	0.246206i	$-0.0791840\pi$
$17$	5497.46	+	9521.87i	0.271388	+	0.470058i	−0.697830	+	0.716264i	$0.745851\pi$
$18$		0			0
$19$	−5851.53	+	10135.1i	−0.195718	+	0.338994i	−0.947136	−	0.320833i	$-0.896037\pi$
$19$	−5851.53	+	10135.1i	−0.195718	+	0.338994i	0.751417	+	0.659827i	$0.229371\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−53070.5	+	91920.8i	−0.909506	+	1.57531i	−0.0947540	+	0.995501i	$0.530206\pi$
$23$	−53070.5	+	91920.8i	−0.909506	+	1.57531i	−0.814752	+	0.579810i	$0.803127\pi$
$24$		0			0
$25$	26704.0	+	46252.8i	0.341812	+	0.592035i
$26$		0			0
$27$	−2369.04			−0.0231632
$28$		0			0
$29$	−51562.7			−0.392593			−0.196297	−	0.980545i	$-0.562892\pi$
$29$	−51562.7			−0.392593			−0.196297	+	0.980545i	$0.562892\pi$
$30$		0			0
$31$	123778.	+	214390.i	0.746240	+	1.29253i	0.949613	+	0.313425i	$0.101476\pi$
$31$	123778.	+	214390.i	0.746240	+	1.29253i	−0.203373	+	0.979101i	$0.565190\pi$
$32$		0			0
$33$	206156.	−	357073.i	0.998615	−	1.72965i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−216839.	+	375576.i	−0.703771	+	1.21897i	0.263363	+	0.964697i	$0.415168\pi$
$37$	−216839.	+	375576.i	−0.703771	+	1.21897i	−0.967133	+	0.254270i	$0.918165\pi$
$38$		0			0
$39$	178642.	+	309417.i	0.482234	+	0.835254i
$40$		0			0
$41$	322819.			0.731501			0.365751	−	0.930713i	$-0.380812\pi$
$41$	322819.			0.731501			0.365751	+	0.930713i	$0.380812\pi$
$42$		0			0
$43$	878703.			1.68540			0.842699	−	0.538385i	$-0.180965\pi$
$43$	878703.			1.68540			0.842699	+	0.538385i	$0.180965\pi$
$44$		0			0
$45$	174720.	+	302624.i	0.285824	+	0.495063i
$46$		0			0
$47$	−327563.	+	567356.i	−0.460206	+	0.797101i	−0.998971	−	0.0453557i	$-0.985558\pi$
$47$	−327563.	+	567356.i	−0.460206	+	0.797101i	0.538765	+	0.842456i	$0.318891\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−365061.	+	632304.i	−0.385363	+	0.667468i
$52$		0			0
$53$	222418.	+	385240.i	0.205213	+	0.355439i	0.950201	−	0.311639i	$-0.100878\pi$
$53$	222418.	+	385240.i	0.205213	+	0.355439i	−0.744988	+	0.667078i	$0.767545\pi$
$54$		0			0
$55$	−976159.			−0.791136
$56$		0			0
$57$	−777146.			−0.555828
$58$		0			0
$59$	−1.07273e6	−	1.85802e6i	−0.679996	−	1.17779i	−0.974981	−	0.222286i	$-0.928648\pi$
$59$	−1.07273e6	−	1.85802e6i	−0.679996	−	1.17779i	0.294985	−	0.955502i	$-0.404685\pi$
$60$		0			0
$61$	−296451.	+	513468.i	−0.167224	+	0.289640i	−0.937443	−	0.348139i	$-0.886814\pi$
$61$	−296451.	+	513468.i	−0.167224	+	0.289640i	0.770219	+	0.637780i	$0.220147\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	422939.	−	732552.i	0.191021	−	0.330858i
$66$		0			0
$67$	−864332.	−	1.49707e6i	−0.351090	−	0.608106i	0.635351	−	0.772224i	$-0.280856\pi$
$67$	−864332.	−	1.49707e6i	−0.351090	−	0.608106i	−0.986441	+	0.164118i	$0.947522\pi$
$68$		0			0
$69$	−7.04833e6			−2.58294
$70$		0			0
$71$	1.58060e6			0.524105			0.262052	−	0.965054i	$-0.415601\pi$
$71$	1.58060e6			0.524105			0.262052	+	0.965054i	$0.415601\pi$
$72$		0			0
$73$	2.16582e6	+	3.75131e6i	0.651617	+	1.12863i	0.982731	+	0.185042i	$0.0592423\pi$
$73$	2.16582e6	+	3.75131e6i	0.651617	+	1.12863i	−0.331114	+	0.943591i	$0.607424\pi$
$74$		0			0
$75$	−1.77329e6	+	3.07143e6i	−0.485362	+	0.840672i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.04259e6	−	5.26992e6i	0.694302	−	1.20257i	−0.276113	−	0.961125i	$-0.589046\pi$
$79$	3.04259e6	−	5.26992e6i	0.694302	−	1.20257i	0.970415	−	0.241442i	$-0.0776202\pi$
$80$		0			0
$81$	2.35184e6	+	4.07350e6i	0.491711	+	0.851668i
$82$		0			0
$83$	−8.10357e6			−1.55562			−0.777809	−	0.628500i	$-0.783669\pi$
$83$	−8.10357e6			−1.55562			−0.777809	+	0.628500i	$0.783669\pi$
$84$		0			0
$85$	1.72858e6			0.305297
$86$		0			0
$87$	−1.71202e6	−	2.96531e6i	−0.278735	−	0.482783i
$88$		0			0
$89$	−4.93016e6	+	8.53929e6i	−0.741303	+	1.28398i	0.210599	+	0.977573i	$0.432459\pi$
$89$	−4.93016e6	+	8.53929e6i	−0.741303	+	1.28398i	−0.951902	+	0.306403i	$0.900875\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−8.21955e6	+	1.42367e7i	−1.05964	+	1.83535i
$94$		0			0
$95$	919955.	+	1.59341e6i	0.110086	+	0.190675i
$96$		0			0
$97$	−171786.			−0.0191111			−0.00955555	−	0.999954i	$-0.503042\pi$
$97$	−171786.			−0.0191111			−0.00955555	+	0.999954i	$0.503042\pi$
$98$		0			0
$99$	1.38007e7			1.42947
$100$		0			0
$101$	−750685.	−	1.30022e6i	−0.0724991	−	0.125572i	0.827497	−	0.561470i	$-0.189764\pi$
$101$	−750685.	−	1.30022e6i	−0.0724991	−	0.125572i	−0.899996	+	0.435898i	$0.856431\pi$
$102$		0			0
$103$	7.00495e6	−	1.21329e7i	0.631648	−	1.09405i	−0.355567	−	0.934651i	$-0.615712\pi$
$103$	7.00495e6	−	1.21329e7i	0.631648	−	1.09405i	0.987215	−	0.159395i	$-0.0509544\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.18255e7	+	2.04824e7i	−0.933203	+	1.61636i	−0.155397	+	0.987852i	$0.549666\pi$
$107$	−1.18255e7	+	2.04824e7i	−0.933203	+	1.61636i	−0.777807	+	0.628504i	$0.783668\pi$
$108$		0			0
$109$	9.12277e6	+	1.58011e7i	0.674736	+	1.16868i	0.976546	+	0.215309i	$0.0690759\pi$
$109$	9.12277e6	+	1.58011e7i	0.674736	+	1.16868i	−0.301810	+	0.953368i	$0.597591\pi$
$110$		0			0
$111$	−2.87985e7			−1.99867
$112$		0			0
$113$	6.85019e6			0.446610			0.223305	−	0.974749i	$-0.428315\pi$
$113$	6.85019e6			0.446610			0.223305	+	0.974749i	$0.428315\pi$
$114$		0			0
$115$	8.34354e6	+	1.44514e7i	0.511573	+	0.886071i
$116$		0			0
$117$	−5.97939e6	+	1.03566e7i	−0.345149	+	0.597815i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−9.53242e6	+	1.65106e7i	−0.489164	+	0.847257i
$122$		0			0
$123$	1.07184e7	+	1.85649e7i	0.519355	+	0.899549i
$124$		0			0
$125$	2.06791e7			0.946994
$126$		0			0
$127$	2.93488e7			1.27139			0.635693	−	0.771942i	$-0.280714\pi$
$127$	2.93488e7			1.27139			0.635693	+	0.771942i	$0.280714\pi$
$128$		0			0
$129$	2.91753e7	+	5.05331e7i	1.19661	+	2.07258i
$130$		0			0
$131$	5.15465e6	−	8.92812e6i	0.200332	−	0.346985i	−0.748304	−	0.663356i	$-0.769131\pi$
$131$	5.15465e6	−	8.92812e6i	0.200332	−	0.346985i	0.948635	+	0.316372i	$0.102465\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−186226.	+	322552.i	−0.00651435	+	0.0112832i
$136$		0			0
$137$	−5.67534e6	−	9.82998e6i	−0.188569	−	0.326611i	0.756204	−	0.654335i	$-0.227052\pi$
$137$	−5.67534e6	−	9.82998e6i	−0.188569	−	0.326611i	−0.944773	+	0.327724i	$0.893718\pi$
$138$		0			0
$139$	−5.67661e7			−1.79282			−0.896412	−	0.443222i	$-0.853835\pi$
$139$	−5.67661e7			−1.79282			−0.896412	+	0.443222i	$0.853835\pi$
$140$		0			0
$141$	−4.35039e7			−1.30696
$142$		0			0
$143$	−1.67034e7	−	2.89311e7i	−0.477670	−	0.827349i
$144$		0			0
$145$	−4.05325e6	+	7.02043e6i	−0.110412	+	0.191239i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.35563e7	+	2.34802e7i	−0.335729	+	0.581500i	−0.983625	−	0.180229i	$-0.942316\pi$
$149$	−1.35563e7	+	2.34802e7i	−0.335729	+	0.581500i	0.647895	+	0.761729i	$0.275649\pi$
$150$		0			0
$151$	−1.61793e6	−	2.80234e6i	−0.0382420	−	0.0662370i	0.846271	−	0.532753i	$-0.178842\pi$
$151$	−1.61793e6	−	2.80234e6i	−0.0382420	−	0.0662370i	−0.884513	+	0.466516i	$0.845509\pi$
$152$		0			0
$153$	−2.44381e7			−0.551630
$154$		0			0
$155$	3.89199e7			0.839481
$156$		0			0
$157$	−4.21922e7	−	7.30790e7i	−0.870127	−	1.50711i	−0.861864	−	0.507139i	$-0.830703\pi$
$157$	−4.21922e7	−	7.30790e7i	−0.870127	−	1.50711i	−0.00826332	−	0.999966i	$-0.502630\pi$
$158$		0			0
$159$	−1.47698e7	+	2.55820e7i	−0.291396	+	0.504713i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	3.14398e7	−	5.44554e7i	0.568622	−	0.984882i	−0.428081	−	0.903740i	$-0.640810\pi$
$163$	3.14398e7	−	5.44554e7i	0.568622	−	0.984882i	0.996703	−	0.0811413i	$-0.0258565\pi$
$164$		0			0
$165$	−3.24111e7	−	5.61377e7i	−0.561695	−	0.972883i
$166$		0			0
$167$	7.14808e7			1.18763			0.593816	−	0.804601i	$-0.297621\pi$
$167$	7.14808e7			1.18763			0.593816	+	0.804601i	$0.297621\pi$
$168$		0			0
$169$	−3.38003e7			−0.538663
$170$		0			0
$171$	−1.30060e7	−	2.25271e7i	−0.198911	−	0.344524i
$172$		0			0
$173$	−3.30065e7	+	5.71690e7i	−0.484662	+	0.839459i	−0.999845	−	0.0176216i	$-0.994391\pi$
$173$	−3.30065e7	+	5.71690e7i	−0.484662	+	0.839459i	0.515183	+	0.857080i	$0.327724\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.12348e7	−	1.23382e8i	0.965574	−	1.67242i
$178$		0			0
$179$	4.71103e6	+	8.15974e6i	0.0613946	+	0.106339i	0.895089	−	0.445887i	$-0.147112\pi$
$179$	4.71103e6	+	8.15974e6i	0.0613946	+	0.106339i	−0.833694	+	0.552226i	$0.813779\pi$
$180$		0			0
$181$	3.65024e7			0.457558			0.228779	−	0.973478i	$-0.426527\pi$
$181$	3.65024e7			0.457558			0.228779	+	0.973478i	$0.426527\pi$
$182$		0			0
$183$	−3.93719e7			−0.474906
$184$		0			0
$185$	3.40906e7	+	5.90466e7i	0.395852	+	0.685637i
$186$		0			0
$187$	3.41339e7	−	5.91216e7i	0.381715	−	0.661150i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.20307e7	−	7.27993e7i	0.436465	−	0.755980i	−0.560949	−	0.827850i	$-0.689564\pi$
$191$	4.20307e7	−	7.27993e7i	0.436465	−	0.755980i	0.997414	+	0.0718707i	$0.0228969\pi$
$192$		0			0
$193$	3.33711e7	+	5.78004e7i	0.334133	+	0.578735i	0.983318	−	0.181895i	$-0.0582232\pi$
$193$	3.33711e7	+	5.78004e7i	0.334133	+	0.578735i	−0.649185	+	0.760631i	$0.724890\pi$
$194$		0			0
$195$	5.61709e7			0.542488
$196$		0			0
$197$	−5.11607e7			−0.476765			−0.238383	−	0.971171i	$-0.576617\pi$
$197$	−5.11607e7			−0.476765			−0.238383	+	0.971171i	$0.576617\pi$
$198$		0			0
$199$	−5.90834e7	−	1.02335e8i	−0.531471	−	0.920535i	−0.999325	−	0.0367292i	$-0.988306\pi$
$199$	−5.90834e7	−	1.02335e8i	−0.531471	−	0.920535i	0.467854	−	0.883806i	$-0.345027\pi$
$200$		0			0
$201$	5.73963e7	−	9.94133e7i	0.498537	−	0.863492i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.53762e7	−	4.39528e7i	0.205725	−	0.356326i
$206$		0			0
$207$	−1.17958e8	−	2.04310e8i	−0.924342	−	1.60101i
$208$		0			0
$209$	7.26646e7			0.550568
$210$		0			0
$211$	−8.10808e7			−0.594196			−0.297098	−	0.954847i	$-0.596019\pi$
$211$	−8.10808e7			−0.594196			−0.297098	+	0.954847i	$0.596019\pi$
$212$		0			0
$213$	5.24802e7	+	9.08984e7i	0.372106	+	0.644507i
$214$		0			0
$215$	6.90731e7	−	1.19638e8i	0.473996	−	0.820985i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.43822e8	+	2.49107e8i	−0.925276	+	1.60262i
$220$		0			0
$221$	2.95782e7	+	5.12310e7i	0.184331	+	0.319271i
$222$		0			0
$223$	2.40244e8			1.45072			0.725362	−	0.688368i	$-0.241672\pi$
$223$	2.40244e8			1.45072			0.725362	+	0.688368i	$0.241672\pi$
$224$		0			0
$225$	−1.18709e8			−0.694775
$226$		0			0
$227$	−3.81697e7	−	6.61118e7i	−0.216585	−	0.375136i	0.737177	−	0.675700i	$-0.236158\pi$
$227$	−3.81697e7	−	6.61118e7i	−0.216585	−	0.375136i	−0.953762	+	0.300564i	$0.902825\pi$
$228$		0			0
$229$	3.46250e7	−	5.99723e7i	0.190531	−	0.330009i	−0.754895	−	0.655845i	$-0.772312\pi$
$229$	3.46250e7	−	5.99723e7i	0.190531	−	0.330009i	0.945426	+	0.325836i	$0.105646\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.07631e7	−	5.32832e7i	0.159325	−	0.275959i	−0.775300	−	0.631593i	$-0.782402\pi$
$233$	3.07631e7	−	5.32832e7i	0.159325	−	0.275959i	0.934625	+	0.355633i	$0.115735\pi$
$234$		0			0
$235$	5.14982e7	+	8.91975e7i	0.258854	+	0.448348i
$236$		0			0
$237$	4.04089e8			1.97178
$238$		0			0
$239$	−9.93248e7			−0.470614			−0.235307	−	0.971921i	$-0.575610\pi$
$239$	−9.93248e7			−0.470614			−0.235307	+	0.971921i	$0.575610\pi$
$240$		0			0
$241$	7.73023e7	+	1.33892e8i	0.355740	+	0.616160i	0.987244	−	0.159213i	$-0.0508955\pi$
$241$	7.73023e7	+	1.33892e8i	0.355740	+	0.616160i	−0.631504	+	0.775372i	$0.717562\pi$
$242$		0			0
$243$	−1.58765e8	+	2.74989e8i	−0.709796	+	1.22940i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.14833e7	+	5.45306e7i	−0.132935	+	0.230251i
$248$		0			0
$249$	−2.69060e8	−	4.66026e8i	−1.10447	−	1.91299i
$250$		0			0
$251$	8.53238e7			0.340575			0.170287	−	0.985394i	$-0.445530\pi$
$251$	8.53238e7			0.340575			0.170287	+	0.985394i	$0.445530\pi$
$252$		0			0
$253$	6.59032e8			2.55850
$254$		0			0
$255$	5.73934e7	+	9.94084e7i	0.216756	+	0.375433i
$256$		0			0
$257$	2.13862e8	−	3.70419e8i	0.785900	−	1.36122i	−0.142560	−	0.989786i	$-0.545534\pi$
$257$	2.13862e8	−	3.70419e8i	0.785900	−	1.36122i	0.928460	−	0.371432i	$-0.121133\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5.73036e7	−	9.92527e7i	0.199499	−	0.345542i
$262$		0			0
$263$	2.33554e8	+	4.04528e8i	0.791667	+	1.37121i	0.924934	+	0.380128i	$0.124120\pi$
$263$	2.33554e8	+	4.04528e8i	0.791667	+	1.37121i	−0.133267	+	0.991080i	$0.542547\pi$
$264$		0			0
$265$	6.99355e7			0.230854
$266$		0			0
$267$	−6.54778e8			−2.10526
$268$		0			0
$269$	−1.00001e8	−	1.73207e8i	−0.313237	−	0.542542i	0.665824	−	0.746109i	$-0.268080\pi$
$269$	−1.00001e8	−	1.73207e8i	−0.313237	−	0.542542i	−0.979061	+	0.203567i	$0.934747\pi$
$270$		0			0
$271$	1.16453e8	−	2.01702e8i	0.355432	−	0.615627i	−0.631760	−	0.775164i	$-0.717667\pi$
$271$	1.16453e8	−	2.01702e8i	0.355432	−	0.615627i	0.987192	+	0.159538i	$0.0510004\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.65806e8	−	2.87185e8i	0.480769	−	0.832716i
$276$		0			0
$277$	−2.23409e7	−	3.86955e7i	−0.0631569	−	0.109391i	0.832718	−	0.553697i	$-0.186784\pi$
$277$	−2.23409e7	−	3.86955e7i	−0.0631569	−	0.109391i	−0.895875	+	0.444306i	$0.853450\pi$
$278$		0			0
$279$	−5.50238e8			−1.51683
$280$		0			0
$281$	−1.38876e8			−0.373385			−0.186692	−	0.982418i	$-0.559777\pi$
$281$	−1.38876e8			−0.373385			−0.186692	+	0.982418i	$0.559777\pi$
$282$		0			0
$283$	−1.64264e8	−	2.84513e8i	−0.430814	−	0.746191i	0.566130	−	0.824316i	$-0.308440\pi$
$283$	−1.64264e8	−	2.84513e8i	−0.430814	−	0.746191i	−0.996944	+	0.0781251i	$0.975107\pi$
$284$		0			0
$285$	−6.10899e7	+	1.05811e8i	−0.156319	+	0.270753i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.44725e8	−	2.50672e8i	0.352697	−	0.610889i
$290$		0			0
$291$	−5.70375e6	−	9.87918e6i	−0.0135686	−	0.0235015i
$292$		0			0
$293$	−1.91796e8			−0.445455			−0.222727	−	0.974881i	$-0.571496\pi$
$293$	−1.91796e8			−0.445455			−0.222727	+	0.974881i	$0.571496\pi$
$294$		0			0
$295$	−3.37300e8			−0.764960
$296$		0			0
$297$	7.35472e6	+	1.27387e7i	0.0162899	+	0.0282149i
$298$		0			0
$299$	−2.85538e8	+	4.94566e8i	−0.617752	+	1.06998i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	4.98495e7	−	8.63419e7i	0.102947	−	0.178309i
$304$		0			0
$305$	4.66069e7	+	8.07255e7i	0.0940591	+	0.162915i
$306$		0			0
$307$	1.98092e8			0.390734			0.195367	−	0.980730i	$-0.437410\pi$
$307$	1.98092e8			0.390734			0.195367	+	0.980730i	$0.437410\pi$
$308$		0			0
$309$	9.30333e8			1.79384
$310$		0			0
$311$	−2.00359e8	−	3.47033e8i	−0.377701	−	0.654198i	0.613026	−	0.790063i	$-0.289952\pi$
$311$	−2.00359e8	−	3.47033e8i	−0.377701	−	0.654198i	−0.990727	+	0.135865i	$0.956619\pi$
$312$		0			0
$313$	−2.65671e8	+	4.60156e8i	−0.489711	+	0.848203i	−0.999930	−	0.0118408i	$-0.996231\pi$
$313$	−2.65671e8	+	4.60156e8i	−0.489711	+	0.848203i	0.510219	+	0.860044i	$0.329564\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.19124e7	−	3.79533e7i	0.0386351	−	0.0669180i	−0.846061	−	0.533086i	$-0.821032\pi$
$317$	2.19124e7	−	3.79533e7i	0.0386351	−	0.0669180i	0.884696	+	0.466168i	$0.154366\pi$
$318$		0			0
$319$	1.60077e8	+	2.77262e8i	0.276097	+	0.478214i
$320$		0			0
$321$	−1.57055e9			−2.65024
$322$		0			0
$323$	−1.28674e8			−0.212462
$324$		0			0
$325$	1.43677e8	+	2.48856e8i	0.232165	+	0.402121i
$326$		0			0
$327$	−6.05801e8	+	1.04928e9i	−0.958104	+	1.65949i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.82233e8	+	3.15637e8i	−0.276204	+	0.478399i	−0.970438	−	0.241350i	$-0.922410\pi$
$331$	−1.82233e8	+	3.15637e8i	−0.276204	+	0.478399i	0.694234	+	0.719749i	$0.255743\pi$
$332$		0			0
$333$	−4.81962e8	−	8.34784e8i	−0.715251	−	1.23885i
$334$		0			0
$335$	−2.71774e8			−0.394958
$336$		0			0
$337$	9.00453e8			1.28161			0.640806	−	0.767703i	$-0.278600\pi$
$337$	9.00453e8			1.28161			0.640806	+	0.767703i	$0.278600\pi$
$338$		0			0
$339$	2.27445e8	+	3.93946e8i	0.317086	+	0.549209i
$340$		0			0
$341$	7.68543e8	−	1.33116e9i	1.04961	−	1.81798i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−5.54056e8	+	9.59653e8i	−0.726418	+	1.25819i
$346$		0			0
$347$	1.34815e8	+	2.33506e8i	0.173215	+	0.300017i	0.939542	−	0.342434i	$-0.111251\pi$
$347$	1.34815e8	+	2.33506e8i	0.173215	+	0.300017i	−0.766327	+	0.642450i	$0.777918\pi$
$348$		0			0
$349$	6.42732e8			0.809358			0.404679	−	0.914459i	$-0.367383\pi$
$349$	6.42732e8			0.809358			0.404679	+	0.914459i	$0.367383\pi$
$350$		0			0
$351$	−1.27463e7			−0.0157329
$352$		0			0
$353$	4.98523e8	+	8.63466e8i	0.603217	+	1.04480i	0.992331	+	0.123612i	$0.0394479\pi$
$353$	4.98523e8	+	8.63466e8i	0.603217	+	1.04480i	−0.389114	+	0.921190i	$0.627219\pi$
$354$		0			0
$355$	1.24248e8	−	2.15204e8i	0.147398	−	0.255300i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.30674e8	+	1.43877e9i	−0.947545	+	1.64120i	−0.196972	+	0.980409i	$0.563111\pi$
$359$	−8.30674e8	+	1.43877e9i	−0.947545	+	1.64120i	−0.750573	+	0.660787i	$0.770223\pi$
$360$		0			0
$361$	3.78455e8	+	6.55504e8i	0.423389	+	0.733331i
$362$		0			0
$363$	−1.26601e9			−1.38919
$364$		0			0
$365$	6.81004e8			0.733034
$366$		0			0
$367$	−3.60430e8	−	6.24283e8i	−0.380618	−	0.659250i	0.610532	−	0.791991i	$-0.290956\pi$
$367$	−3.60430e8	−	6.24283e8i	−0.380618	−	0.659250i	−0.991151	+	0.132741i	$0.957622\pi$
$368$		0			0
$369$	−3.58761e8	+	6.21392e8i	−0.371717	+	0.643833i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.39439e8	−	4.14721e8i	0.238899	−	0.413785i	−0.721500	−	0.692415i	$-0.756547\pi$
$373$	2.39439e8	−	4.14721e8i	0.238899	−	0.413785i	0.960399	+	0.278630i	$0.0898802\pi$
$374$		0			0
$375$	6.86603e8	+	1.18923e9i	0.672351	+	1.16455i
$376$		0			0
$377$	−2.77426e8			−0.266656
$378$		0			0
$379$	−1.03267e9			−0.974373			−0.487186	−	0.873298i	$-0.661977\pi$
$379$	−1.03267e9			−0.974373			−0.487186	+	0.873298i	$0.661977\pi$
$380$		0			0
$381$	9.74460e8	+	1.68781e9i	0.902665	+	1.56346i
$382$		0			0
$383$	2.96721e8	−	5.13937e8i	0.269869	−	0.467427i	−0.698959	−	0.715162i	$-0.746353\pi$
$383$	2.96721e8	−	5.13937e8i	0.269869	−	0.467427i	0.968828	+	0.247735i	$0.0796862\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.76536e8	+	1.69141e9i	−0.856445	+	1.48341i
$388$		0			0
$389$	1.07662e9	+	1.86476e9i	0.927340	+	1.60620i	0.787754	+	0.615990i	$0.211244\pi$
$389$	1.07662e9	+	1.86476e9i	0.927340	+	1.60620i	0.139586	+	0.990210i	$0.455423\pi$
$390$		0			0
$391$	−1.16701e9			−0.987316
$392$		0			0
$393$	6.84593e8			0.568930
$394$		0			0
$395$	−4.78344e8	−	8.28517e8i	−0.390527	−	0.676412i
$396$		0			0
$397$	−9.41231e7	+	1.63026e8i	−0.0754969	+	0.130765i	−0.901302	−	0.433191i	$-0.857388\pi$
$397$	−9.41231e7	+	1.63026e8i	−0.0754969	+	0.130765i	0.825805	+	0.563955i	$0.190721\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.79082e8	−	6.56590e8i	0.293581	−	0.508498i	−0.681073	−	0.732216i	$-0.738486\pi$
$401$	3.79082e8	−	6.56590e8i	0.293581	−	0.508498i	0.974654	+	0.223718i	$0.0718196\pi$
$402$		0			0
$403$	6.65971e8	+	1.15350e9i	0.506860	+	0.877906i
$404$		0			0
$405$	7.39494e8			0.553149
$406$		0			0
$407$	2.69272e9			1.97975
$408$		0			0
$409$	7.53535e8	+	1.30516e9i	0.544593	+	0.943262i	0.998632	+	0.0522808i	$0.0166491\pi$
$409$	7.53535e8	+	1.30516e9i	0.544593	+	0.943262i	−0.454040	+	0.890981i	$0.650018\pi$
$410$		0			0
$411$	3.76873e8	−	6.52764e8i	0.267762	−	0.463778i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.37006e8	+	1.10333e9i	−0.437497	+	0.757767i
$416$		0			0
$417$	−1.88479e9	−	3.26455e9i	−1.27288	−	2.20469i
$418$		0			0
$419$	1.51449e9			1.00581			0.502907	−	0.864341i	$-0.332264\pi$
$419$	1.51449e9			1.00581			0.502907	+	0.864341i	$0.332264\pi$
$420$		0			0
$421$	−1.05648e9			−0.690037			−0.345019	−	0.938596i	$-0.612127\pi$
$421$	−1.05648e9			−0.690037			−0.345019	+	0.938596i	$0.612127\pi$
$422$		0			0
$423$	−7.28067e8	−	1.26105e9i	−0.467713	−	0.810103i
$424$		0			0
$425$	−2.93609e8	+	5.08545e8i	−0.185527	+	0.321342i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.10919e9	−	1.92118e9i	0.678277	−	1.17481i
$430$		0			0
$431$	−1.26232e9	−	2.18640e9i	−0.759450	−	1.31541i	−0.943131	−	0.332420i	$-0.892135\pi$
$431$	−1.26232e9	−	2.18640e9i	−0.759450	−	1.31541i	0.183681	−	0.982986i	$-0.441199\pi$
$432$		0			0
$433$	4.25297e8			0.251759			0.125879	−	0.992046i	$-0.459825\pi$
$433$	4.25297e8			0.251759			0.125879	+	0.992046i	$0.459825\pi$
$434$		0			0
$435$	−5.38315e8			−0.313562
$436$		0			0
$437$	−6.21087e8	−	1.07575e9i	−0.356014	−	0.616634i
$438$		0			0
$439$	−5.36614e8	+	9.29443e8i	−0.302717	+	0.524321i	−0.976750	−	0.214380i	$-0.931227\pi$
$439$	−5.36614e8	+	9.29443e8i	−0.302717	+	0.524321i	0.674034	+	0.738701i	$0.264560\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.89589e8	−	5.01584e8i	0.158259	−	0.274113i	−0.775982	−	0.630756i	$-0.782745\pi$
$443$	2.89589e8	−	5.01584e8i	0.158259	−	0.274113i	0.934241	+	0.356642i	$0.116078\pi$
$444$		0			0
$445$	7.75101e8	+	1.34251e9i	0.416964	+	0.722202i
$446$		0			0
$447$	−1.80042e9			−0.953450
$448$		0			0
$449$	−2.44352e9			−1.27396			−0.636978	−	0.770882i	$-0.719816\pi$
$449$	−2.44352e9			−1.27396			−0.636978	+	0.770882i	$0.719816\pi$
$450$		0			0
$451$	−1.00219e9	−	1.73585e9i	−0.514439	−	0.891035i
$452$		0			0
$453$	1.07439e8	−	1.86090e8i	0.0543024	−	0.0940545i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.86749e8	−	4.96664e8i	0.140538	−	0.243420i	−0.787161	−	0.616747i	$-0.788450\pi$
$457$	2.86749e8	−	4.96664e8i	0.140538	−	0.243420i	0.927700	+	0.373328i	$0.121783\pi$
$458$		0			0
$459$	−1.30237e7	−	2.25577e7i	−0.00628622	−	0.0108881i
$460$		0			0
$461$	4.58794e8			0.218105			0.109052	−	0.994036i	$-0.465218\pi$
$461$	4.58794e8			0.218105			0.109052	+	0.994036i	$0.465218\pi$
$462$		0			0
$463$	−3.14598e8			−0.147307			−0.0736533	−	0.997284i	$-0.523466\pi$
$463$	−3.14598e8			−0.147307			−0.0736533	+	0.997284i	$0.523466\pi$
$464$		0			0
$465$	1.29225e9	+	2.23824e9i	0.596019	+	1.03233i
$466$		0			0
$467$	−4.71062e8	+	8.15903e8i	−0.214027	+	0.370706i	−0.952971	−	0.303061i	$-0.901991\pi$
$467$	−4.71062e8	+	8.15903e8i	−0.214027	+	0.370706i	0.738944	+	0.673767i	$0.235325\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.80179e9	−	4.85284e9i	1.23555	−	2.14004i
$472$		0			0
$473$	−2.72794e9	−	4.72494e9i	−1.18528	−	2.05297i
$474$		0			0
$475$	−6.25038e8			−0.267595
$476$		0			0
$477$	−9.88727e8			−0.417121
$478$		0			0
$479$	−1.55182e9	−	2.68783e9i	−0.645160	−	1.11745i	−0.984265	−	0.176701i	$-0.943457\pi$
$479$	−1.55182e9	−	2.68783e9i	−0.645160	−	1.11745i	0.339105	−	0.940749i	$-0.389876\pi$
$480$		0			0
$481$	−1.16667e9	+	2.02073e9i	−0.478013	+	0.827944i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.35037e7	+	2.33892e7i	−0.00537475	+	0.00930934i
$486$		0			0
$487$	9.49669e8	+	1.64488e9i	0.372581	+	0.645330i	0.989962	−	0.141335i	$-0.0451395\pi$
$487$	9.49669e8	+	1.64488e9i	0.372581	+	0.645330i	−0.617381	+	0.786665i	$0.711806\pi$
$488$		0			0
$489$	4.17555e9			1.61485
$490$		0			0
$491$	−1.74671e9			−0.665940			−0.332970	−	0.942937i	$-0.608051\pi$
$491$	−1.74671e9			−0.665940			−0.332970	+	0.942937i	$0.608051\pi$
$492$		0			0
$493$	−2.83464e8	−	4.90974e8i	−0.106545	−	0.184541i
$494$		0			0
$495$	1.08484e9	−	1.87900e9i	0.402021	−	0.696320i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.90379e9	−	3.29746e9i	0.685910	−	1.18803i	−0.287240	−	0.957859i	$-0.592738\pi$
$499$	1.90379e9	−	3.29746e9i	0.685910	−	1.18803i	0.973150	−	0.230172i	$-0.0739288\pi$
$500$		0			0
$501$	2.37336e9	+	4.11077e9i	0.843201	+	1.46047i
$502$		0			0
$503$	−3.25718e8			−0.114118			−0.0570589	−	0.998371i	$-0.518172\pi$
$503$	−3.25718e8			−0.114118			−0.0570589	+	0.998371i	$0.518172\pi$
$504$		0			0
$505$	−2.36040e8			−0.0815577
$506$		0			0
$507$	−1.12226e9	−	1.94382e9i	−0.382443	−	0.662410i
$508$		0			0
$509$	1.95090e9	−	3.37907e9i	0.655728	−	1.13575i	−0.325983	−	0.945376i	$-0.605695\pi$
$509$	1.95090e9	−	3.37907e9i	0.655728	−	1.13575i	0.981711	−	0.190379i	$-0.0609716\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	1.38625e7	−	2.40106e7i	0.00453347	−	0.00785220i
$514$		0			0
$515$	−1.10129e9	−	1.90749e9i	−0.355285	−	0.615372i
$516$		0			0
$517$	4.06770e9			1.29459
$518$		0			0
$519$	−4.38362e9			−1.37641
$520$		0			0
$521$	1.46434e9	+	2.53631e9i	0.453638	+	0.785724i	0.998609	−	0.0527313i	$-0.0167927\pi$
$521$	1.46434e9	+	2.53631e9i	0.453638	+	0.785724i	−0.544971	+	0.838455i	$0.683459\pi$
$522$		0			0
$523$	2.24897e9	−	3.89532e9i	0.687428	−	1.19066i	−0.285239	−	0.958456i	$-0.592073\pi$
$523$	2.24897e9	−	3.89532e9i	0.687428	−	1.19066i	0.972667	−	0.232204i	$-0.0745936\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.36093e9	+	2.35720e9i	−0.405041	+	0.701552i
$528$		0			0
$529$	−3.93054e9	−	6.80789e9i	−1.15440	−	1.99948i
$530$		0			0
$531$	4.76864e9			1.38218
$532$		0			0
$533$	1.73688e9			0.496849
$534$		0			0
$535$	1.85916e9	+	3.22016e9i	0.524902	+	0.909158i
$536$		0			0
$537$	−3.12838e8	+	5.41851e8i	−0.0871785	+	0.150998i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−5.88858e8	+	1.01993e9i	−0.159889	+	0.276937i	−0.934829	−	0.355099i	$-0.884447\pi$
$541$	−5.88858e8	+	1.01993e9i	−0.159889	+	0.276937i	0.774939	+	0.632036i	$0.217780\pi$
$542$		0			0
$543$	1.21198e9	+	2.09921e9i	0.324859	+	0.562672i
$544$		0			0
$545$	2.86849e9			0.759042
$546$		0			0
$547$	3.94940e9			1.03175			0.515877	−	0.856663i	$-0.327466\pi$
$547$	3.94940e9			1.03175			0.515877	+	0.856663i	$0.327466\pi$
$548$		0			0
$549$	−6.58915e8	−	1.14127e9i	−0.169952	−	0.294365i
$550$		0			0
$551$	3.01721e8	−	5.22595e8i	0.0768377	−	0.133087i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.26380e9	+	3.92101e9i	−0.562098	+	0.973583i
$556$		0			0
$557$	2.10372e9	+	3.64374e9i	0.515815	+	0.893418i	0.999831	+	0.0183590i	$0.00584416\pi$
$557$	2.10372e9	+	3.64374e9i	0.515815	+	0.893418i	−0.484016	+	0.875059i	$0.660823\pi$
$558$		0			0
$559$	4.72773e9			1.14475
$560$		0			0
$561$	4.53334e9			1.08405
$562$		0			0
$563$	−1.98661e9	−	3.44091e9i	−0.469174	−	0.812632i	0.530205	−	0.847869i	$-0.322115\pi$
$563$	−1.98661e9	−	3.44091e9i	−0.469174	−	0.812632i	−0.999379	+	0.0352368i	$0.988781\pi$
$564$		0			0
$565$	5.38480e8	−	9.32675e8i	0.125603	−	0.217551i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.53009e9	+	4.38225e9i	−0.575763	+	0.997250i	0.420196	+	0.907434i	$0.361961\pi$
$569$	−2.53009e9	+	4.38225e9i	−0.575763	+	0.997250i	−0.995958	+	0.0898168i	$0.971372\pi$
$570$		0			0
$571$	−2.12052e8	−	3.67285e8i	−0.0476668	−	0.0825613i	0.841208	−	0.540712i	$-0.181845\pi$
$571$	−2.12052e8	−	3.67285e8i	−0.0476668	−	0.0825613i	−0.888874	+	0.458151i	$0.848512\pi$
$572$		0			0
$573$	5.58213e9			1.23953
$574$		0			0
$575$	−5.66878e9			−1.24352
$576$		0			0
$577$	2.51195e9	+	4.35082e9i	0.544371	+	0.942878i	0.998646	+	0.0520169i	$0.0165650\pi$
$577$	2.51195e9	+	4.35082e9i	0.544371	+	0.942878i	−0.454275	+	0.890861i	$0.650102\pi$
$578$		0			0
$579$	−2.21602e9	+	3.83826e9i	−0.474459	+	0.821786i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.38100e9	−	2.39196e9i	0.288638	−	0.499936i
$584$		0			0
$585$	9.40056e8	+	1.62823e9i	0.194137	+	0.336255i
$586$		0			0
$587$	−8.56543e9			−1.74790			−0.873948	−	0.486019i	$-0.838449\pi$
$587$	−8.56543e9			−1.74790			−0.873948	+	0.486019i	$0.838449\pi$
$588$		0			0
$589$	−2.89717e9			−0.584212
$590$		0			0
$591$	−1.69867e9	−	2.94219e9i	−0.338496	−	0.586293i
$592$		0			0
$593$	2.89605e9	−	5.01611e9i	0.570315	−	0.987815i	−0.426218	−	0.904621i	$-0.640154\pi$
$593$	2.89605e9	−	5.01611e9i	0.570315	−	0.987815i	0.996533	−	0.0831947i	$-0.0265123\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.92346e9	−	6.79562e9i	0.754673	−	1.30713i
$598$		0			0
$599$	−8.72232e8	−	1.51075e9i	−0.165820	−	0.287210i	0.771126	−	0.636683i	$-0.219694\pi$
$599$	−8.72232e8	−	1.51075e9i	−0.165820	−	0.287210i	−0.936946	+	0.349473i	$0.886361\pi$
$600$		0			0
$601$	−8.05605e9			−1.51378			−0.756888	−	0.653545i	$-0.773281\pi$
$601$	−8.05605e9			−1.51378			−0.756888	+	0.653545i	$0.773281\pi$
$602$		0			0
$603$	3.84226e9			0.713635
$604$		0			0
$605$	1.49865e9	+	2.59574e9i	0.275142	+	0.476559i
$606$		0			0
$607$	−2.34963e9	+	4.06967e9i	−0.426421	+	0.738583i	−0.996552	−	0.0829709i	$-0.973559\pi$
$607$	−2.34963e9	+	4.06967e9i	−0.426421	+	0.738583i	0.570131	+	0.821554i	$0.306892\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.76240e9	+	3.05257e9i	−0.312580	+	0.541405i
$612$		0			0
$613$	−1.15331e9	−	1.99759e9i	−0.202225	−	0.350263i	0.747020	−	0.664801i	$-0.231484\pi$
$613$	−1.15331e9	−	1.99759e9i	−0.202225	−	0.350263i	−0.949245	+	0.314538i	$0.898150\pi$
$614$		0			0
$615$	3.37023e9			0.584247
$616$		0			0
$617$	−8.81255e9			−1.51044			−0.755220	−	0.655471i	$-0.772470\pi$
$617$	−8.81255e9			−1.51044			−0.755220	+	0.655471i	$0.772470\pi$
$618$		0			0
$619$	2.75824e9	+	4.77742e9i	0.467428	+	0.809610i	0.999307	−	0.0372106i	$-0.0118472\pi$
$619$	2.75824e9	+	4.77742e9i	0.467428	+	0.809610i	−0.531879	+	0.846820i	$0.678514\pi$
$620$		0			0
$621$	1.25726e8	−	2.17764e8i	0.0210671	−	0.0364893i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−4.60707e8	+	7.97967e8i	−0.0754822	+	0.130739i
$626$		0			0
$627$	2.41266e9	+	4.17885e9i	0.390895	+	0.677049i
$628$		0			0
$629$	−4.76825e9			−0.763980
$630$		0			0
$631$	4.00663e9			0.634857			0.317429	−	0.948282i	$-0.397181\pi$
$631$	4.00663e9			0.634857			0.317429	+	0.948282i	$0.397181\pi$
$632$		0			0
$633$	−2.69210e9	−	4.66286e9i	−0.421870	−	0.730700i
$634$		0			0
$635$	2.30705e9	−	3.99593e9i	0.357561	−	0.619313i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.75658e9	+	3.04249e9i	−0.266327	+	0.461292i
$640$		0			0
$641$	−3.76178e9	−	6.51560e9i	−0.564145	−	0.977128i	−0.997129	−	0.0757261i	$-0.975873\pi$
$641$	−3.76178e9	−	6.51560e9i	−0.564145	−	0.977128i	0.432984	−	0.901402i	$-0.357461\pi$
$642$		0			0
$643$	−1.08744e10			−1.61311			−0.806557	−	0.591156i	$-0.798672\pi$
$643$	−1.08744e10			−1.61311			−0.806557	+	0.591156i	$0.798672\pi$
$644$		0			0
$645$	9.17366e9			1.34612
$646$		0			0
$647$	1.58668e9	+	2.74821e9i	0.230316	+	0.398919i	0.957901	−	0.287098i	$-0.0926907\pi$
$647$	1.58668e9	+	2.74821e9i	0.230316	+	0.398919i	−0.727585	+	0.686018i	$0.759357\pi$
$648$		0			0
$649$	−6.66058e9	+	1.15365e10i	−0.956435	+	1.65659i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.97427e9	−	6.88363e9i	0.558549	−	0.967434i	−0.439069	−	0.898453i	$-0.644692\pi$
$653$	3.97427e9	−	6.88363e9i	0.558549	−	0.967434i	0.997618	−	0.0689813i	$-0.0219749\pi$
$654$		0			0
$655$	−8.10394e8	−	1.40364e9i	−0.112681	−	0.195170i
$656$		0			0
$657$	−9.62783e9			−1.32449
$658$		0			0
$659$	−1.08219e10			−1.47301			−0.736504	−	0.676433i	$-0.763525\pi$
$659$	−1.08219e10			−1.47301			−0.736504	+	0.676433i	$0.763525\pi$
$660$		0			0
$661$	−4.93054e9	−	8.53995e9i	−0.664033	−	1.15014i	−0.979547	−	0.201217i	$-0.935510\pi$
$661$	−4.93054e9	−	8.53995e9i	−0.664033	−	1.15014i	0.315514	−	0.948921i	$-0.397823\pi$
$662$		0			0
$663$	−1.96416e9	+	3.40202e9i	−0.261745	+	0.453356i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.73646e9	−	4.73968e9i	0.357066	−	0.618456i
$668$		0			0
$669$	7.97673e9	+	1.38161e10i	1.02999	+	1.78400i
$670$		0			0
$671$	3.68135e9			0.470411
$672$		0			0
$673$	1.48659e10			1.87992			0.939959	−	0.341288i	$-0.110863\pi$
$673$	1.48659e10			1.87992			0.939959	+	0.341288i	$0.110863\pi$
$674$		0			0
$675$	−6.32629e7	−	1.09575e8i	−0.00791746	−	0.0137135i
$676$		0			0
$677$	2.85564e9	−	4.94611e9i	0.353706	−	0.612637i	−0.633190	−	0.773997i	$-0.718255\pi$
$677$	2.85564e9	−	4.94611e9i	0.353706	−	0.612637i	0.986896	+	0.161360i	$0.0515880\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.53467e9	−	4.39018e9i	0.307544	−	0.532681i
$682$		0			0
$683$	−4.70337e9	−	8.14647e9i	−0.564854	−	0.978356i	−0.997063	−	0.0765825i	$-0.975599\pi$
$683$	−4.70337e9	−	8.14647e9i	−0.564854	−	0.978356i	0.432209	−	0.901773i	$-0.357734\pi$
$684$		0			0
$685$	−1.78451e9			−0.212130
$686$		0			0
$687$	4.59857e9			0.541096
$688$		0			0
$689$	1.19669e9	+	2.07273e9i	0.139384	+	0.241421i
$690$		0			0
$691$	−8.15556e9	+	1.41258e10i	−0.940331	+	1.62870i	−0.175490	+	0.984481i	$0.556151\pi$
$691$	−8.15556e9	+	1.41258e10i	−0.940331	+	1.62870i	−0.764841	+	0.644219i	$0.777182\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.46228e9	+	7.72889e9i	−0.504208	+	0.873314i
$696$		0			0
$697$	1.77468e9	+	3.07384e9i	0.198521	+	0.343848i
$698$		0			0
$699$	4.08567e9			0.452473
$700$		0			0
$701$	1.18926e10			1.30396			0.651979	−	0.758237i	$-0.273939\pi$
$701$	1.18926e10			1.30396			0.651979	+	0.758237i	$0.273939\pi$
$702$		0			0
$703$	−2.53768e9	−	4.39539e9i	−0.275482	−	0.477148i
$704$		0			0
$705$	−3.41976e9	+	5.92320e9i	−0.367565	+	0.636640i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−7.49704e9	+	1.29853e10i	−0.790002	+	1.36832i	0.135963	+	0.990714i	$0.456587\pi$
$709$	−7.49704e9	+	1.29853e10i	−0.790002	+	1.36832i	−0.925965	+	0.377609i	$0.876746\pi$
$710$		0			0
$711$	6.76269e9	+	1.17133e10i	0.705628	+	1.22218i
$712$		0			0
$713$	−2.62759e10			−2.71484
$714$		0			0
$715$	−5.25208e9			−0.537354
$716$		0			0
$717$	−3.29785e9	−	5.71204e9i	−0.334129	−	0.578728i
$718$		0			0
$719$	−2.17818e9	+	3.77272e9i	−0.218546	+	0.378533i	−0.954364	−	0.298647i	$-0.903465\pi$
$719$	−2.17818e9	+	3.77272e9i	−0.218546	+	0.378533i	0.735817	+	0.677180i	$0.236798\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−5.13329e9	+	8.89112e9i	−0.505140	+	0.874928i
$724$		0			0
$725$	−1.37693e9	−	2.38492e9i	−0.134193	−	0.232429i
$726$		0			0
$727$	4.64655e9			0.448498			0.224249	−	0.974532i	$-0.428007\pi$
$727$	4.64655e9			0.448498			0.224249	+	0.974532i	$0.428007\pi$
$728$		0			0
$729$	−1.07988e10			−1.03235
$730$		0			0
$731$	4.83063e9	+	8.36690e9i	0.457397	+	0.792234i
$732$		0			0
$733$	8.35641e9	−	1.44737e10i	0.783710	−	1.35743i	−0.146056	−	0.989276i	$-0.546658\pi$
$733$	8.35641e9	−	1.44737e10i	0.783710	−	1.35743i	0.929766	−	0.368150i	$-0.120009\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.36666e9	+	9.29533e9i	−0.493819	+	0.855320i
$738$		0			0
$739$	5.20893e9	+	9.02213e9i	0.474781	+	0.822344i	0.999583	−	0.0288800i	$-0.00919406\pi$
$739$	5.20893e9	+	9.02213e9i	0.474781	+	0.822344i	−0.524802	+	0.851224i	$0.675861\pi$
$740$		0			0
$741$	−4.18132e9			−0.377528
$742$		0			0
$743$	1.42061e8			0.0127061			0.00635307	−	0.999980i	$-0.497978\pi$
$743$	1.42061e8			0.0127061			0.00635307	+	0.999980i	$0.497978\pi$
$744$		0			0
$745$	2.13127e9	+	3.69147e9i	0.188839	+	0.327078i
$746$		0			0
$747$	9.00580e9	−	1.55985e10i	0.790497	−	1.36918i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.34693e9	−	2.33295e9i	0.116039	−	0.200986i	−0.802155	−	0.597115i	$-0.796314\pi$
$751$	1.34693e9	−	2.33295e9i	0.116039	−	0.200986i	0.918195	+	0.396129i	$0.129647\pi$
$752$		0			0
$753$	2.83298e9	+	4.90687e9i	0.241803	+	0.418815i
$754$		0			0
$755$	−5.08729e8			−0.0430202
$756$		0			0
$757$	−4.63791e8			−0.0388585			−0.0194293	−	0.999811i	$-0.506185\pi$
$757$	−4.63791e8			−0.0388585			−0.0194293	+	0.999811i	$0.506185\pi$
$758$		0			0
$759$	2.18816e10	+	3.79001e10i	1.81649	+	3.14626i
$760$		0			0
$761$	8.57486e9	−	1.48521e10i	0.705311	−	1.22163i	−0.261268	−	0.965266i	$-0.584141\pi$
$761$	8.57486e9	−	1.48521e10i	0.705311	−	1.22163i	0.966579	−	0.256369i	$-0.0825261\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.92103e9	+	3.32733e9i	−0.155139	+	0.268708i
$766$		0			0
$767$	−5.77164e9	−	9.99677e9i	−0.461865	−	0.799974i
$768$		0			0
$769$	2.83370e9			0.224705			0.112352	−	0.993668i	$-0.464161\pi$
$769$	2.83370e9			0.224705			0.112352	+	0.993668i	$0.464161\pi$
$770$		0			0
$771$	2.84031e10			2.23191
$772$		0			0
$773$	−3.60180e9	−	6.23849e9i	−0.280473	−	0.485793i	0.691028	−	0.722828i	$-0.257158\pi$
$773$	−3.60180e9	−	6.23849e9i	−0.280473	−	0.485793i	−0.971501	+	0.237034i	$0.923825\pi$
$774$		0			0
$775$	−6.61076e9	+	1.14502e10i	−0.510147	+	0.883601i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.88898e9	+	3.27181e9i	−0.143168	+	0.247975i
$780$		0			0
$781$	−4.90700e9	−	8.49917e9i	−0.368585	−	0.638407i
$782$		0			0
$783$	1.22154e8			0.00909373
$784$		0			0
$785$	−1.32666e10			−0.978848
$786$		0			0
$787$	3.41031e9	+	5.90683e9i	0.249392	+	0.431960i	0.963357	−	0.268222i	$-0.0864359\pi$
$787$	3.41031e9	+	5.90683e9i	0.249392	+	0.431960i	−0.713965	+	0.700181i	$0.753103\pi$
$788$		0			0
$789$	−1.55093e10	+	2.68628e10i	−1.12414	+	1.94707i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.59501e9	+	2.76264e9i	−0.113581	+	0.196729i
$794$		0			0
$795$	2.32205e9	+	4.02190e9i	0.163903	+	0.283888i
$796$		0			0
$797$	1.38571e10			0.969544			0.484772	−	0.874641i	$-0.338903\pi$
$797$	1.38571e10			0.969544			0.484772	+	0.874641i	$0.338903\pi$
$798$		0			0
$799$	−7.20306e9			−0.499578
$800$		0			0
$801$	−1.09581e10	−	1.89801e10i	−0.753396	−	1.30492i
$802$		0			0
$803$	1.34476e10	−	2.32920e10i	0.916519	−	1.58746i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.64063e9	−	1.15019e10i	0.444787	−	0.770393i
$808$		0			0
$809$	2.60291e9	+	4.50837e9i	0.172838	+	0.299364i	0.939411	−	0.342793i	$-0.111373\pi$
$809$	2.60291e9	+	4.50837e9i	0.172838	+	0.299364i	−0.766573	+	0.642157i	$0.778040\pi$
$810$		0			0
$811$	1.44908e9			0.0953938			0.0476969	−	0.998862i	$-0.484812\pi$
$811$	1.44908e9			0.0953938			0.0476969	+	0.998862i	$0.484812\pi$
$812$		0			0
$813$	1.54662e10			1.00941
$814$		0			0
$815$	−4.94285e9	−	8.56126e9i	−0.319835	−	0.553970i
$816$		0			0
$817$	−5.14175e9	+	8.90578e9i	−0.329863	+	0.571340i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.34721e10	+	2.33344e10i	−0.849638	+	1.47162i	0.0318930	+	0.999491i	$0.489846\pi$
$821$	−1.34721e10	+	2.33344e10i	−0.849638	+	1.47162i	−0.881531	+	0.472125i	$0.843487\pi$
$822$		0			0
$823$	5.60170e9	+	9.70243e9i	0.350284	+	0.606710i	0.986299	−	0.164967i	$-0.0527517\pi$
$823$	5.60170e9	+	9.70243e9i	0.350284	+	0.606710i	−0.636015	+	0.771677i	$0.719418\pi$
$824$		0			0
$825$	2.20208e10			1.36535
$826$		0			0
$827$	−7.78707e9			−0.478746			−0.239373	−	0.970928i	$-0.576942\pi$
$827$	−7.78707e9			−0.478746			−0.239373	+	0.970928i	$0.576942\pi$
$828$		0			0
$829$	5.44374e9	+	9.42883e9i	0.331861	+	0.574800i	0.982877	−	0.184264i	$-0.0589901\pi$
$829$	5.44374e9	+	9.42883e9i	0.331861	+	0.574800i	−0.651016	+	0.759064i	$0.725657\pi$
$830$		0			0
$831$	1.48355e9	−	2.56959e9i	0.0896809	−	0.155332i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	5.61897e9	−	9.73235e9i	0.334006	−	0.578515i
$836$		0			0
$837$	−2.93236e8	−	5.07899e8i	−0.0172853	−	0.0299391i
$838$		0			0
$839$	−8.20806e9			−0.479815			−0.239907	−	0.970796i	$-0.577117\pi$
$839$	−8.20806e9			−0.479815			−0.239907	+	0.970796i	$0.577117\pi$
$840$		0			0
$841$	−1.45912e10			−0.845871
$842$		0			0
$843$	−4.61107e9	−	7.98661e9i	−0.265097	−	0.459162i
$844$		0			0
$845$	−2.65698e9	+	4.60202e9i	−0.151492	+	0.262392i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.09080e10	−	1.88932e10i	0.611742	−	1.05957i
$850$		0			0
$851$	−2.30155e10	−	3.98640e10i	−1.28017	−	2.21731i
$852$		0			0
$853$	4.95254e9			0.273216			0.136608	−	0.990625i	$-0.456380\pi$
$853$	4.95254e9			0.273216			0.136608	+	0.990625i	$0.456380\pi$
$854$		0			0
$855$	−4.08952e9			−0.223764
$856$		0			0
$857$	−1.69082e10	−	2.92859e10i	−0.917625	−	1.58937i	−0.803011	−	0.595964i	$-0.796770\pi$
$857$	−1.69082e10	−	2.92859e10i	−0.917625	−	1.58937i	−0.114614	−	0.993410i	$-0.536563\pi$
$858$		0			0
$859$	3.24901e9	−	5.62746e9i	0.174894	−	0.302926i	−0.765230	−	0.643756i	$-0.777375\pi$
$859$	3.24901e9	−	5.62746e9i	0.174894	−	0.302926i	0.940125	+	0.340831i	$0.110708\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.07004e10	−	1.85336e10i	0.566709	−	0.981569i	−0.430179	−	0.902744i	$-0.641550\pi$
$863$	1.07004e10	−	1.85336e10i	0.566709	−	0.981569i	0.996888	−	0.0788258i	$-0.0251171\pi$
$864$		0			0
$865$	5.18916e9	+	8.98789e9i	0.272609	+	0.472173i
$866$		0			0
$867$	1.92211e10			1.00164
$868$		0			0
$869$	−3.77830e10			−1.95311
$870$		0			0
$871$	−4.65041e9	−	8.05475e9i	−0.238467	−	0.413036i
$872$		0			0
$873$	1.90912e8	−	3.30669e8i	0.00971143	−	0.0168207i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.40547e10	−	2.43434e10i	0.703595	−	1.21866i	−0.263601	−	0.964632i	$-0.584910\pi$
$877$	1.40547e10	−	2.43434e10i	0.703595	−	1.21866i	0.967196	−	0.254031i	$-0.0817564\pi$
$878$		0			0
$879$	−6.36816e9	−	1.10300e10i	−0.316266	−	0.547789i
$880$		0			0
$881$	8.82922e9			0.435017			0.217509	−	0.976058i	$-0.430207\pi$
$881$	8.82922e9			0.435017			0.217509	+	0.976058i	$0.430207\pi$
$882$		0			0
$883$	2.59216e10			1.26707			0.633534	−	0.773715i	$-0.281604\pi$
$883$	2.59216e10			1.26707			0.633534	+	0.773715i	$0.281604\pi$
$884$		0			0
$885$	−1.11993e10	−	1.93977e10i	−0.543110	−	0.940694i
$886$		0			0
$887$	9.46987e9	−	1.64023e10i	0.455629	−	0.789173i	−0.543095	−	0.839671i	$-0.682748\pi$
$887$	9.46987e9	−	1.64023e10i	0.455629	−	0.789173i	0.998724	+	0.0504984i	$0.0160810\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.46026e10	−	2.52925e10i	0.691606	−	1.19790i
$892$		0			0
$893$	−3.83349e9	−	6.63980e9i	−0.180142	−	0.312014i
$894$		0			0
$895$	1.48130e9			0.0690657
$896$		0			0
$897$	−3.79225e10			−1.75438
$898$		0			0
$899$	−6.38235e9	−	1.10545e10i	−0.292969	−	0.507437i
$900$		0			0
$901$	−2.44547e9	+	4.23568e9i	−0.111385	+	0.192924i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.86938e9	−	4.96991e9i	0.128682	−	0.222884i
$906$		0			0
$907$	−4.51010e9	−	7.81172e9i	−0.200706	−	0.347633i	0.748050	−	0.663642i	$-0.230990\pi$
$907$	−4.51010e9	−	7.81172e9i	−0.200706	−	0.347633i	−0.948756	+	0.316009i	$0.897657\pi$
$908$		0			0
$909$	3.33706e9			0.147364
$910$		0			0
$911$	3.38470e10			1.48322			0.741610	−	0.670831i	$-0.234062\pi$
$911$	3.38470e10			1.48322			0.741610	+	0.670831i	$0.234062\pi$
$912$		0			0
$913$	2.51576e10	+	4.35743e10i	1.09401	+	1.89489i
$914$		0			0
$915$	−3.09495e9	+	5.36061e9i	−0.133561	+	0.231334i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.75389e10	−	3.03783e10i	0.745415	−	1.29110i	−0.204585	−	0.978849i	$-0.565585\pi$
$919$	1.75389e10	−	3.03783e10i	0.745415	−	1.29110i	0.950001	−	0.312248i	$-0.101082\pi$
$920$		0			0
$921$	6.57717e9	+	1.13920e10i	0.277415	+	0.480497i
$922$		0			0
$923$	8.50419e9			0.355981
$924$		0			0
$925$	−2.31619e10			−0.962228
$926$		0			0
$927$	1.55697e10	+	2.69676e10i	0.641951	+	1.11189i
$928$		0			0
$929$	1.18689e10	−	2.05575e10i	0.485685	−	0.841230i	−0.514180	−	0.857682i	$-0.671904\pi$
$929$	1.18689e10	−	2.05575e10i	0.485685	−	0.841230i	0.999865	+	0.0164520i	$0.00523706\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.33049e10	−	2.30448e10i	0.536324	−	0.928941i
$934$		0			0
$935$	−5.36639e9	−	9.29487e9i	−0.214705	−	0.371880i
$936$		0			0
$937$	2.48298e9			0.0986017			0.0493009	−	0.998784i	$-0.484301\pi$
$937$	2.48298e9			0.0986017			0.0493009	+	0.998784i	$0.484301\pi$
$938$		0			0
$939$	−3.52840e10			−1.39075
$940$		0			0
$941$	−8.52745e9	−	1.47700e10i	−0.333623	−	0.577851i	0.649597	−	0.760279i	$-0.274938\pi$
$941$	−8.52745e9	−	1.47700e10i	−0.333623	−	0.577851i	−0.983219	+	0.182428i	$0.941604\pi$
$942$		0			0
$943$	−1.71321e10	+	2.96737e10i	−0.665305	+	1.15234i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.77604e9	+	1.69326e10i	−0.374057	+	0.647886i	−0.990185	−	0.139760i	$-0.955367\pi$
$947$	−9.77604e9	+	1.69326e10i	−0.374057	+	0.647886i	0.616128	+	0.787646i	$0.288700\pi$
$948$		0			0
$949$	1.16529e10	+	2.01834e10i	0.442590	+	0.766588i
$950$		0			0
$951$	2.91020e9			0.109721
$952$		0			0
$953$	1.99979e10			0.748444			0.374222	−	0.927339i	$-0.377910\pi$
$953$	1.99979e10			0.748444			0.374222	+	0.927339i	$0.377910\pi$
$954$		0			0
$955$	−6.60790e9	−	1.14452e10i	−0.245500	−	0.425219i
$956$		0			0
$957$	−1.06300e10	+	1.84117e10i	−0.392049	+	0.679049i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−1.68858e10	+	2.92471e10i	−0.613749	+	1.06304i
$962$		0			0
$963$	−2.62843e10	−	4.55257e10i	−0.948426	−	1.64272i
$964$		0			0
$965$	1.04929e10			0.375882
$966$		0			0
$967$	2.36717e10			0.841853			0.420927	−	0.907095i	$-0.361705\pi$
$967$	2.36717e10			0.841853			0.420927	+	0.907095i	$0.361705\pi$
$968$		0			0
$969$	−4.27233e9	−	7.39989e9i	−0.150845	−	0.261271i
$970$		0			0
$971$	2.74938e10	−	4.76207e10i	0.963757	−	1.66928i	0.250839	−	0.968029i	$-0.419293\pi$
$971$	2.74938e10	−	4.76207e10i	0.963757	−	1.66928i	0.712918	−	0.701248i	$-0.247373\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−9.54093e9	+	1.65254e10i	−0.329666	+	0.570999i
$976$		0			0
$977$	2.72177e9	+	4.71424e9i	0.0933727	+	0.161726i	0.908928	−	0.416952i	$-0.136902\pi$
$977$	2.72177e9	+	4.71424e9i	0.0933727	+	0.161726i	−0.815556	+	0.578679i	$0.803569\pi$
$978$		0			0
$979$	6.12230e10			2.08533
$980$		0			0
$981$	−4.05539e10			−1.37149
$982$		0			0
$983$	−1.83178e10	−	3.17273e10i	−0.615086	−	1.06536i	−0.990369	−	0.138450i	$-0.955788\pi$
$983$	−1.83178e10	−	3.17273e10i	−0.615086	−	1.06536i	0.375284	−	0.926910i	$-0.377545\pi$
$984$		0			0
$985$	−4.02165e9	+	6.96569e9i	−0.134084	+	0.232240i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.66332e10	+	8.07710e10i	−1.53288	+	2.65502i
$990$		0			0
$991$	−6.84498e8	−	1.18559e9i	−0.0223416	−	0.0386968i	0.854638	−	0.519224i	$-0.173779\pi$
$991$	−6.84498e8	−	1.18559e9i	−0.0223416	−	0.0386968i	−0.876980	+	0.480527i	$0.840445\pi$
$992$		0			0
$993$	−2.42025e10			−0.784401
$994$		0			0
$995$	−1.85777e10			−0.597877
$996$		0			0
$997$	−6.81654e9	−	1.18066e10i	−0.217837	−	0.377304i	0.736310	−	0.676645i	$-0.236567\pi$
$997$	−6.81654e9	−	1.18066e10i	−0.217837	−	0.377304i	−0.954146	+	0.299341i	$0.903233\pi$
$998$		0			0
$999$	5.13700e8	−	8.89755e8i	0.0163016	−	0.0282352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.8.e.d.177.2		4
7.2	even	3		28.8.a.a.1.1	✓	2
7.3	odd	6		196.8.e.a.165.1		4
7.4	even	3	inner	196.8.e.d.165.2		4
7.5	odd	6		196.8.a.b.1.2		2
7.6	odd	2		196.8.e.a.177.1		4
21.2	odd	6		252.8.a.e.1.2		2
28.23	odd	6		112.8.a.i.1.2		2
56.37	even	6		448.8.a.p.1.2		2
56.51	odd	6		448.8.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.8.a.a.1.1	✓	2	7.2	even	3
112.8.a.i.1.2		2	28.23	odd	6
196.8.a.b.1.2		2	7.5	odd	6
196.8.e.a.165.1		4	7.3	odd	6
196.8.e.a.177.1		4	7.6	odd	2
196.8.e.d.165.2		4	7.4	even	3	inner
196.8.e.d.177.2		4	1.1	even	1	trivial
252.8.a.e.1.2		2	21.2	odd	6
448.8.a.n.1.1		2	56.51	odd	6
448.8.a.p.1.2		2	56.37	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(33.2027 + 57.5088i) q^{3} +(78.6081 - 136.153i) q^{5} +(-1111.34 + 1924.89i) q^{9} +(-3104.51 - 5377.17i) q^{11} +5380.35 q^{13} +10440.0 q^{15} +(5497.46 + 9521.87i) q^{17} +(-5851.53 + 10135.1i) q^{19} +(-53070.5 + 91920.8i) q^{23} +(26704.0 + 46252.8i) q^{25} -2369.04 q^{27} -51562.7 q^{29} +(123778. + 214390. i) q^{31} +(206156. - 357073. i) q^{33} +(-216839. + 375576. i) q^{37} +(178642. + 309417. i) q^{39} +322819. q^{41} +878703. q^{43} +(174720. + 302624. i) q^{45} +(-327563. + 567356. i) q^{47} +(-365061. + 632304. i) q^{51} +(222418. + 385240. i) q^{53} -976159. q^{55} -777146. q^{57} +(-1.07273e6 - 1.85802e6i) q^{59} +(-296451. + 513468. i) q^{61} +(422939. - 732552. i) q^{65} +(-864332. - 1.49707e6i) q^{67} -7.04833e6 q^{69} +1.58060e6 q^{71} +(2.16582e6 + 3.75131e6i) q^{73} +(-1.77329e6 + 3.07143e6i) q^{75} +(3.04259e6 - 5.26992e6i) q^{79} +(2.35184e6 + 4.07350e6i) q^{81} -8.10357e6 q^{83} +1.72858e6 q^{85} +(-1.71202e6 - 2.96531e6i) q^{87} +(-4.93016e6 + 8.53929e6i) q^{89} +(-8.21955e6 + 1.42367e7i) q^{93} +(919955. + 1.59341e6i) q^{95} -171786. q^{97} +1.38007e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 14 q^{3} - 42 q^{5} - 2782 q^{9} - 7428 q^{11} + 23660 q^{13} + 41760 q^{15} - 15792 q^{17} - 26614 q^{19} - 32640 q^{23} + 91846 q^{25} - 175336 q^{27} - 316032 q^{29} + 180740 q^{31} + 348432 q^{33}+ \cdots + 28964904 q^{99}+O(q^{100}) \) 4 * q + 14 * q^3 - 42 * q^5 - 2782 * q^9 - 7428 * q^11 + 23660 * q^13 + 41760 * q^15 - 15792 * q^17 - 26614 * q^19 - 32640 * q^23 + 91846 * q^25 - 175336 * q^27 - 316032 * q^29 + 180740 * q^31 + 348432 * q^33 + 45824 * q^37 + 19288 * q^39 - 643440 * q^41 + 2047736 * q^43 + 238014 * q^45 - 1665972 * q^47 - 2133900 * q^51 + 410628 * q^53 - 1466640 * q^55 + 8536 * q^57 - 1702134 * q^59 + 547526 * q^61 - 438996 * q^65 + 2590616 * q^67 - 21800352 * q^69 + 8258544 * q^71 + 8008868 * q^73 - 1532230 * q^75 - 2470456 * q^79 + 10397042 * q^81 - 19801572 * q^83 + 14129928 * q^85 + 2154684 * q^87 - 15423492 * q^89 - 19940648 * q^93 - 1130592 * q^95 - 34754944 * q^97 + 28964904 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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