LMFDB - Embedded newform 48.7.i.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.91573 + 1.15814i) q^{2} +(-26.8410 - 2.92544i) q^{3} +(61.3174 - 18.3351i) q^{4} +(-131.564 + 131.564i) q^{5} +(215.854 - 7.92879i) q^{6} +278.097i q^{7} +(-464.137 + 216.150i) q^{8} +(711.884 + 157.044i) q^{9} +O(q^{10})$	\(q+(-7.91573 + 1.15814i) q^{2} +(-26.8410 - 2.92544i) q^{3} +(61.3174 - 18.3351i) q^{4} +(-131.564 + 131.564i) q^{5} +(215.854 - 7.92879i) q^{6} +278.097i q^{7} +(-464.137 + 216.150i) q^{8} +(711.884 + 157.044i) q^{9} +(889.056 - 1193.80i) q^{10} +(-1280.16 + 1280.16i) q^{11} +(-1699.46 + 312.753i) q^{12} +(-1228.92 + 1228.92i) q^{13} +(-322.077 - 2201.34i) q^{14} +(3916.20 - 3146.44i) q^{15} +(3423.65 - 2248.52i) q^{16} -9226.29i q^{17} +(-5816.95 - 418.653i) q^{18} +(3236.39 - 3236.39i) q^{19} +(-5654.93 + 10479.4i) q^{20} +(813.558 - 7464.42i) q^{21} +(8650.79 - 11616.0i) q^{22} -2724.89 q^{23} +(13090.3 - 4443.88i) q^{24} -18993.3i q^{25} +(8304.55 - 11151.1i) q^{26} +(-18648.3 - 6297.80i) q^{27} +(5098.94 + 17052.2i) q^{28} +(24894.5 + 24894.5i) q^{29} +(-27355.6 + 29441.9i) q^{30} -43110.5 q^{31} +(-24496.6 + 21763.8i) q^{32} +(38105.9 - 30615.8i) q^{33} +(10685.4 + 73032.8i) q^{34} +(-36587.6 - 36587.6i) q^{35} +(46530.3 - 3422.93i) q^{36} +(-23369.5 - 23369.5i) q^{37} +(-21870.2 + 29366.6i) q^{38} +(36580.7 - 29390.5i) q^{39} +(32626.2 - 89501.4i) q^{40} +87187.8 q^{41} +(2204.98 + 60028.5i) q^{42} +(-1473.89 - 1473.89i) q^{43} +(-55024.3 + 101968. i) q^{44} +(-114320. + 72997.0i) q^{45} +(21569.5 - 3155.81i) q^{46} +29064.1i q^{47} +(-98472.2 + 50337.0i) q^{48} +40310.9 q^{49} +(21996.9 + 150345. i) q^{50} +(-26991.0 + 247643. i) q^{51} +(-52822.0 + 97886.8i) q^{52} +(69419.2 - 69419.2i) q^{53} +(154908. + 28254.2i) q^{54} -336847. i q^{55} +(-60110.7 - 129075. i) q^{56} +(-96336.0 + 77400.2i) q^{57} +(-225889. - 168226. i) q^{58} +(32405.9 - 32405.9i) q^{59} +(182441. - 264735. i) q^{60} +(77576.6 - 77576.6i) q^{61} +(341251. - 49928.2i) q^{62} +(-43673.5 + 197973. i) q^{63} +(168702. - 200646. i) q^{64} -323365. i q^{65} +(-266178. + 286478. i) q^{66} +(57061.2 - 57061.2i) q^{67} +(-169165. - 565732. i) q^{68} +(73138.9 + 7971.50i) q^{69} +(331991. + 247244. i) q^{70} -235737. q^{71} +(-364357. + 80983.7i) q^{72} -85743.9i q^{73} +(212051. + 157921. i) q^{74} +(-55563.7 + 509799. i) q^{75} +(139108. - 257787. i) q^{76} +(-356009. - 356009. i) q^{77} +(-255525. + 275012. i) q^{78} -115675. q^{79} +(-154605. + 746254. i) q^{80} +(482115. + 223594. i) q^{81} +(-690155. + 100976. i) q^{82} +(-297884. - 297884. i) q^{83} +(-86975.7 - 472616. i) q^{84} +(1.21385e6 + 1.21385e6i) q^{85} +(13373.9 + 9959.96i) q^{86} +(-595367. - 741021. i) q^{87} +(317463. - 870877. i) q^{88} +682884. q^{89} +(820382. - 710223. i) q^{90} +(-341760. - 341760. i) q^{91} +(-167083. + 49961.1i) q^{92} +(1.15713e6 + 126117. i) q^{93} +(-33660.4 - 230064. i) q^{94} +851586. i q^{95} +(721182. - 512499. i) q^{96} -1.28695e6 q^{97} +(-319090. + 46685.8i) q^{98} +(-1.11237e6 + 710284. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−7.91573	+	1.15814i	−0.989466	+	0.144768i
$2$	−7.91573	+	1.15814i	−0.989466	+	0.144768i
$3$	−26.8410	−	2.92544i	−0.994113	−	0.108350i
$3$	−26.8410	−	2.92544i	−0.994113	−	0.108350i
$4$	61.3174	−	18.3351i	0.958084	−	0.286486i
$5$	−131.564	+	131.564i	−1.05251	+	1.05251i	−0.0539708	+	0.998543i	$0.517188\pi$
$5$	−131.564	+	131.564i	−1.05251	+	1.05251i	−0.998543	+	0.0539708i	$0.982812\pi$
$6$	215.854	−	7.92879i	0.999326	−	0.0367074i
$7$			278.097i			0.810779i	0.914144	+	0.405390i	$0.132864\pi$
$7$			278.097i			0.810779i	−0.914144	+	0.405390i	$0.867136\pi$
$8$	−464.137	+	216.150i	−0.906518	+	0.422168i
$9$	711.884	+	157.044i	0.976521	+	0.215424i
$10$	889.056	−	1193.80i	0.889056	−	1.19380i
$11$	−1280.16	+	1280.16i	−0.961804	+	0.961804i	−0.999297	−	0.0374933i	$-0.988063\pi$
$11$	−1280.16	+	1280.16i	−0.961804	+	0.961804i	0.0374933	+	0.999297i	$0.488063\pi$
$12$	−1699.46	+	312.753i	−0.983485	+	0.180991i
$13$	−1228.92	+	1228.92i	−0.559364	+	0.559364i	−0.929126	−	0.369762i	$-0.879439\pi$
$13$	−1228.92	+	1228.92i	−0.559364	+	0.559364i	0.369762	+	0.929126i	$0.379439\pi$
$14$	−322.077	−	2201.34i	−0.117375	−	0.802238i
$15$	3916.20	−	3146.44i	1.16036	−	0.932277i
$16$	3423.65	−	2248.52i	0.835852	−	0.548955i
$17$		−	9226.29i		−	1.87793i	−0.344006	−	0.938967i	$-0.611784\pi$
$17$		−	9226.29i		−	1.87793i	0.344006	−	0.938967i	$-0.388216\pi$
$18$	−5816.95	−	418.653i	−0.997420	−	0.0717854i
$19$	3236.39	−	3236.39i	0.471846	−	0.471846i	−0.430666	−	0.902512i	$-0.641721\pi$
$19$	3236.39	−	3236.39i	0.471846	−	0.471846i	0.902512	+	0.430666i	$0.141721\pi$
$20$	−5654.93	+	10479.4i	−0.706866	+	1.30993i
$21$	813.558	−	7464.42i	0.0878477	−	0.806006i
$22$	8650.79	−	11616.0i	0.812433	−	1.09091i
$23$	−2724.89			−0.223957			−0.111979	−	0.993711i	$-0.535719\pi$
$23$	−2724.89			−0.223957			−0.111979	+	0.993711i	$0.535719\pi$
$24$	13090.3	−	4443.88i	0.946923	−	0.321462i
$25$		−	18993.3i		−	1.21557i
$26$	8304.55	−	11151.1i	0.472494	−	0.634450i
$27$	−18648.3	−	6297.80i	−0.947431	−	0.319961i
$28$	5098.94	+	17052.2i	0.232277	+	0.776795i
$29$	24894.5	+	24894.5i	1.02073	+	1.02073i	0.999781	+	0.0209452i	$0.00666755\pi$
$29$	24894.5	+	24894.5i	1.02073	+	1.02073i	0.0209452	+	0.999781i	$0.493332\pi$
$30$	−27355.6	+	29441.9i	−1.01317	+	1.09044i
$31$	−43110.5			−1.44710			−0.723550	−	0.690272i	$-0.757491\pi$
$31$	−43110.5			−1.44710			−0.723550	+	0.690272i	$0.757491\pi$
$32$	−24496.6	+	21763.8i	−0.747575	+	0.664177i
$33$	38105.9	−	30615.8i	1.06035	−	0.851930i
$34$	10685.4	+	73032.8i	0.271865	+	1.85815i
$35$	−36587.6	−	36587.6i	−0.853356	−	0.853356i
$36$	46530.3	−	3422.93i	0.997305	−	0.0733653i
$37$	−23369.5	−	23369.5i	−0.461364	−	0.461364i	0.437738	−	0.899102i	$-0.355780\pi$
$37$	−23369.5	−	23369.5i	−0.461364	−	0.461364i	−0.899102	+	0.437738i	$0.855780\pi$
$38$	−21870.2	+	29366.6i	−0.398567	+	0.535183i
$39$	36580.7	−	29390.5i	0.616678	−	0.495464i
$40$	32626.2	−	89501.4i	0.509785	−	1.39846i
$41$	87187.8			1.26504			0.632520	−	0.774544i	$-0.282021\pi$
$41$	87187.8			1.26504			0.632520	+	0.774544i	$0.282021\pi$
$42$	2204.98	+	60028.5i	0.0297616	+	0.810233i
$43$	−1473.89	−	1473.89i	−0.0185379	−	0.0185379i	0.697777	−	0.716315i	$-0.254173\pi$
$43$	−1473.89	−	1473.89i	−0.0185379	−	0.0185379i	−0.716315	+	0.697777i	$0.754173\pi$
$44$	−55024.3	+	101968.i	−0.645946	+	1.19703i
$45$	−114320.	+	72997.0i	−1.25454	+	0.801065i
$46$	21569.5	−	3155.81i	0.221598	−	0.0324218i
$47$			29064.1i			0.279939i	0.990156	+	0.139970i	$0.0447005\pi$
$47$			29064.1i			0.279939i	−0.990156	+	0.139970i	$0.955300\pi$
$48$	−98472.2	+	50337.0i	−0.890410	+	0.455159i
$49$	40310.9			0.342637
$50$	21996.9	+	150345.i	0.175975	+	1.20276i
$51$	−26991.0	+	247643.i	−0.203474	+	1.86688i
$52$	−52822.0	+	97886.8i	−0.375668	+	0.696168i
$53$	69419.2	−	69419.2i	0.466286	−	0.466286i	−0.434423	−	0.900709i	$-0.643048\pi$
$53$	69419.2	−	69419.2i	0.466286	−	0.466286i	0.900709	+	0.434423i	$0.143048\pi$
$54$	154908.	+	28254.2i	0.983770	+	0.179433i
$55$		−	336847.i		−	2.02462i
$56$	−60110.7	−	129075.i	−0.342285	−	0.734986i
$57$	−96336.0	+	77400.2i	−0.520192	+	0.417944i
$58$	−225889.	−	168226.i	−1.15774	−	0.862205i
$59$	32405.9	−	32405.9i	0.157786	−	0.157786i	−0.623799	−	0.781585i	$-0.714412\pi$
$59$	32405.9	−	32405.9i	0.157786	−	0.157786i	0.781585	+	0.623799i	$0.214412\pi$
$60$	182441.	−	264735.i	0.844635	−	1.22563i
$61$	77576.6	−	77576.6i	0.341776	−	0.341776i	−0.515259	−	0.857035i	$-0.672304\pi$
$61$	77576.6	−	77576.6i	0.341776	−	0.341776i	0.857035	+	0.515259i	$0.172304\pi$
$62$	341251.	−	49928.2i	1.43185	−	0.209494i
$63$	−43673.5	+	197973.i	−0.174661	+	0.791743i
$64$	168702.	−	200646.i	0.643549	−	0.765405i
$65$		−	323365.i		−	1.17748i
$66$	−266178.	+	286478.i	−0.925850	+	0.996461i
$67$	57061.2	−	57061.2i	0.189721	−	0.189721i	−0.605854	−	0.795576i	$-0.707169\pi$
$67$	57061.2	−	57061.2i	0.189721	−	0.189721i	0.795576	+	0.605854i	$0.207169\pi$
$68$	−169165.	−	565732.i	−0.538002	−	1.79922i
$69$	73138.9	+	7971.50i	0.222639	+	0.0242657i
$70$	331991.	+	247244.i	0.967905	+	0.720828i
$71$	−235737.			−0.658647			−0.329323	−	0.944217i	$-0.606821\pi$
$71$	−235737.			−0.658647			−0.329323	+	0.944217i	$0.606821\pi$
$72$	−364357.	+	80983.7i	−0.976178	+	0.216970i
$73$		−	85743.9i		−	0.220412i	−0.993909	−	0.110206i	$-0.964849\pi$
$73$		−	85743.9i		−	0.220412i	0.993909	−	0.110206i	$-0.0351510\pi$
$74$	212051.	+	157921.i	0.523294	+	0.389713i
$75$	−55563.7	+	509799.i	−0.131707	+	1.20841i
$76$	139108.	−	257787.i	0.316891	−	0.587245i
$77$	−356009.	−	356009.i	−0.779810	−	0.779810i
$78$	−255525.	+	275012.i	−0.538455	+	0.579520i
$79$	−115675.			−0.234616			−0.117308	−	0.993096i	$-0.537427\pi$
$79$	−115675.			−0.234616			−0.117308	+	0.993096i	$0.537427\pi$
$80$	−154605.	+	746254.i	−0.301962	+	1.45753i
$81$	482115.	+	223594.i	0.907185	+	0.420731i
$82$	−690155.	+	100976.i	−1.25171	+	0.183137i
$83$	−297884.	−	297884.i	−0.520970	−	0.520970i	0.396895	−	0.917864i	$-0.370088\pi$
$83$	−297884.	−	297884.i	−0.520970	−	0.520970i	−0.917864	+	0.396895i	$0.870088\pi$
$84$	−86975.7	−	472616.i	−0.146744	−	0.797389i
$85$	1.21385e6	+	1.21385e6i	1.97655	+	1.97655i
$86$	13373.9	+	9959.96i	0.0210263	+	0.0156589i
$87$	−595367.	−	741021.i	−0.904121	−	1.12531i
$88$	317463.	−	870877.i	0.465849	−	1.27793i
$89$	682884.			0.968672			0.484336	−	0.874882i	$-0.339061\pi$
$89$	682884.			0.968672			0.484336	+	0.874882i	$0.339061\pi$
$90$	820382.	−	710223.i	1.12535	−	0.974243i
$91$	−341760.	−	341760.i	−0.453521	−	0.453521i
$92$	−167083.	+	49961.1i	−0.214570	+	0.0641606i
$93$	1.15713e6	+	126117.i	1.43858	+	0.156793i
$94$	−33660.4	−	230064.i	−0.0405262	−	0.276990i
$95$			851586.i			0.993248i
$96$	721182.	−	512499.i	0.815138	−	0.579267i
$97$	−1.28695e6			−1.41009			−0.705043	−	0.709164i	$-0.749073\pi$
$97$	−1.28695e6			−1.41009			−0.705043	+	0.709164i	$0.749073\pi$
$98$	−319090.	+	46685.8i	−0.339027	+	0.0496029i
$99$	−1.11237e6	+	710284.i	−1.14642	+	0.732026i
$100$	−348243.	−	1.16462e6i	−0.348243	−	1.16462i
$101$	−9552.55	+	9552.55i	−0.00927161	+	0.00927161i	−0.711727	−	0.702456i	$-0.752087\pi$
$101$	−9552.55	+	9552.55i	−0.00927161	+	0.00927161i	0.702456	+	0.711727i	$0.252087\pi$
$102$	−73153.4	−	1.99154e6i	−0.0689341	−	1.87667i
$103$			1.46634e6i			1.34191i	0.741500	+	0.670953i	$0.234115\pi$
$103$			1.46634e6i			1.34191i	−0.741500	+	0.670953i	$0.765885\pi$
$104$	304757.	−	836021.i	0.270928	−	0.743219i
$105$	875015.	+	1.08909e6i	0.755871	+	0.940793i
$106$	−469106.	+	629901.i	−0.393870	+	0.528877i
$107$	−1.00631e6	+	1.00631e6i	−0.821448	+	0.821448i	−0.986316	−	0.164867i	$-0.947280\pi$
$107$	−1.00631e6	+	1.00631e6i	−0.821448	+	0.821448i	0.164867	+	0.986316i	$0.447280\pi$
$108$	−1.25893e6	−	44246.6i	−0.999383	−	0.0351244i
$109$	−210076.	+	210076.i	−0.162217	+	0.162217i	−0.783548	−	0.621331i	$-0.786592\pi$
$109$	−210076.	+	210076.i	−0.162217	+	0.162217i	0.621331	+	0.783548i	$0.286592\pi$
$110$	390117.	+	2.66638e6i	0.293100	+	2.00329i
$111$	558895.	+	695627.i	0.408659	+	0.508636i
$112$	625308.	+	952107.i	0.445082	+	0.677691i
$113$		−	2.45936e6i		−	1.70446i	−0.523165	−	0.852231i	$-0.675249\pi$
$113$		−	2.45936e6i		−	1.70446i	0.523165	−	0.852231i	$-0.324751\pi$
$114$	672929.	−	724250.i	0.454208	−	0.488848i
$115$	358498.	−	358498.i	0.235718	−	0.235718i
$116$	1.98291e6	+	1.07002e6i	1.27037	+	0.685518i
$117$	−1.06785e6	+	681856.i	−0.666731	+	0.425731i
$118$	−218985.	+	294047.i	−0.133281	+	0.178966i
$119$	2.56581e6			1.52259
$120$	−1.13755e6	+	2.30686e6i	−0.658306	+	1.33499i
$121$		−	1.50606e6i		−	0.850132i
$122$	−524230.	+	703920.i	−0.288697	+	0.387654i
$123$	−2.34021e6	−	255063.i	−1.25759	−	0.137067i
$124$	−2.64343e6	+	790436.i	−1.38644	+	0.414573i
$125$	443142.	+	443142.i	0.226889	+	0.226889i
$126$	116426.	−	1.61768e6i	0.0582021	−	0.808688i
$127$	2.07106e6			1.01107			0.505536	−	0.862805i	$-0.331295\pi$
$127$	2.07106e6			1.01107			0.505536	+	0.862805i	$0.331295\pi$
$128$	−1.10302e6	+	1.78364e6i	−0.525963	+	0.850507i
$129$	35249.1	+	43872.6i	0.0164202	+	0.0204374i
$130$	374503.	+	2.55967e6i	0.170461	+	1.16507i
$131$	−1.81780e6	−	1.81780e6i	−0.808599	−	0.808599i	0.175823	−	0.984422i	$-0.443742\pi$
$131$	−1.81780e6	−	1.81780e6i	−0.808599	−	0.808599i	−0.984422	+	0.175823i	$0.943742\pi$
$132$	1.77521e6	−	2.57596e6i	0.771841	−	1.12000i
$133$	900032.	+	900032.i	0.382563	+	0.382563i
$134$	−385595.	+	517766.i	−0.160257	+	0.215188i
$135$	3.28201e6	−	1.62488e6i	1.33395	−	0.660420i
$136$	1.99426e6	+	4.28226e6i	0.792804	+	1.70238i
$137$	−2.25896e6			−0.878509			−0.439255	−	0.898363i	$-0.644757\pi$
$137$	−2.25896e6			−0.878509			−0.439255	+	0.898363i	$0.644757\pi$
$138$	−588179.	+	21605.1i	−0.223806	+	0.00822089i
$139$	435762.	+	435762.i	0.162258	+	0.162258i	0.783566	−	0.621309i	$-0.213399\pi$
$139$	435762.	+	435762.i	0.162258	+	0.162258i	−0.621309	+	0.783566i	$0.713399\pi$
$140$	−2.91430e6	−	1.57262e6i	−1.06206	−	0.573113i
$141$	85025.4	−	780111.i	0.0303313	−	0.278291i
$142$	1.86603e6	−	273017.i	0.651708	−	0.0953510i
$143$		−	3.14644e6i		−	1.07600i
$144$	2.79036e6	−	1.06302e6i	0.934484	−	0.356004i
$145$	−6.55044e6			−2.14865
$146$	99303.8	+	678725.i	0.0319086	+	0.218090i
$147$	−1.08199e6	−	117927.i	−0.340620	−	0.0371246i
$148$	−1.86144e6	−	1.00447e6i	−0.574200	−	0.309851i
$149$	−381544.	+	381544.i	−0.115342	+	0.115342i	−0.762422	−	0.647080i	$-0.775990\pi$
$149$	−381544.	+	381544.i	−0.115342	+	0.115342i	0.647080	+	0.762422i	$0.275990\pi$
$150$	−150594.	−	4.09978e6i	−0.0446203	−	1.21475i
$151$		−	4.15910e6i		−	1.20800i	−0.796983	−	0.604002i	$-0.793572\pi$
$151$		−	4.15910e6i		−	1.20800i	0.796983	−	0.604002i	$-0.206428\pi$
$152$	−802583.	+	2.20167e6i	−0.228538	+	0.626935i
$153$	1.44893e6	−	6.56805e6i	0.404552	−	1.83384i
$154$	3.23038e6	+	2.40576e6i	0.884487	+	0.658704i
$155$	5.67180e6	−	5.67180e6i	1.52309	−	1.52309i
$156$	1.70416e6	−	2.47286e6i	0.448886	−	0.651366i
$157$	1.56821e6	−	1.56821e6i	0.405234	−	0.405234i	−0.474839	−	0.880073i	$-0.657494\pi$
$157$	1.56821e6	−	1.56821e6i	0.405234	−	0.405234i	0.880073	+	0.474839i	$0.157494\pi$
$158$	915651.	−	133968.i	0.232145	−	0.0339649i
$159$	−2.06637e6	+	1.66020e6i	−0.514063	+	0.413019i
$160$	359539.	−	6.08620e6i	0.0877780	−	1.48589i
$161$		−	757784.i		−	0.181580i
$162$	−4.07525e6	−	1.21155e6i	−0.958537	−	0.284968i
$163$	−4.14139e6	+	4.14139e6i	−0.956277	+	0.956277i	−0.999083	−	0.0428064i	$-0.986370\pi$
$163$	−4.14139e6	+	4.14139e6i	−0.956277	+	0.956277i	0.0428064	+	0.999083i	$0.486370\pi$
$164$	5.34613e6	−	1.59860e6i	1.21201	−	0.362416i
$165$	−985425.	+	9.04131e6i	−0.219367	+	2.01270i
$166$	2.70296e6	+	2.01297e6i	0.590901	+	0.440062i
$167$	1.75548e6			0.376918			0.188459	−	0.982081i	$-0.439651\pi$
$167$	1.75548e6			0.376918			0.188459	+	0.982081i	$0.439651\pi$
$168$	1.23583e6	+	3.64037e6i	0.260634	+	0.767745i
$169$			1.80630e6i			0.374223i
$170$	−1.10143e7	−	8.20269e6i	−2.24187	−	1.66959i
$171$	2.81219e6	−	1.79568e6i	0.562414	−	0.359120i
$172$	−117399.	−	63351.4i	−0.0230717	−	0.0124500i
$173$	−83883.3	−	83883.3i	−0.0162008	−	0.0162008i	0.698960	−	0.715161i	$-0.253647\pi$
$173$	−83883.3	−	83883.3i	−0.0162008	−	0.0162008i	−0.715161	+	0.698960i	$0.753647\pi$
$174$	5.57097e6	+	5.17620e6i	1.05751	+	0.982570i
$175$	5.28197e6			0.985558
$176$	−1.50435e6	+	7.26129e6i	−0.275938	+	1.33191i
$177$	−964610.	+	775007.i	−0.173953	+	0.139761i
$178$	−5.40552e6	+	790878.i	−0.958468	+	0.140233i
$179$	−2.58106e6	−	2.58106e6i	−0.450027	−	0.450027i	0.445336	−	0.895363i	$-0.353084\pi$
$179$	−2.58106e6	−	2.58106e6i	−0.450027	−	0.450027i	−0.895363	+	0.445336i	$0.853084\pi$
$180$	−5.67138e6	+	6.57205e6i	−0.972459	+	1.12689i
$181$	−4.30675e6	−	4.30675e6i	−0.726297	−	0.726297i	0.243583	−	0.969880i	$-0.421677\pi$
$181$	−4.30675e6	−	4.30675e6i	−0.726297	−	0.726297i	−0.969880	+	0.243583i	$0.921677\pi$
$182$	3.10109e6	+	2.30947e6i	0.514399	+	0.383088i
$183$	−2.30918e6	+	1.85529e6i	−0.376795	+	0.302732i
$184$	1.26472e6	−	588985.i	0.203021	−	0.0945476i
$185$	6.14917e6			0.971183
$186$	−9.30560e6	+	341815.i	−1.44612	+	0.0531192i
$187$	1.18111e7	+	1.18111e7i	1.80620	+	1.80620i
$188$	532893.	+	1.78214e6i	0.0801986	+	0.268205i
$189$	1.75140e6	−	5.18604e6i	0.259418	−	0.768157i
$190$	−986259.	−	6.74092e6i	−0.143791	−	0.982785i
$191$			1.34954e6i			0.193681i	0.995300	+	0.0968404i	$0.0308736\pi$
$191$			1.34954e6i			0.193681i	−0.995300	+	0.0968404i	$0.969126\pi$
$192$	−5.11513e6	+	4.89203e6i	−0.722691	+	0.691171i
$193$	−6.58298e6			−0.915695			−0.457847	−	0.889031i	$-0.651379\pi$
$193$	−6.58298e6			−0.915695			−0.457847	+	0.889031i	$0.651379\pi$
$194$	1.01871e7	−	1.49047e6i	1.39523	−	0.204135i
$195$	−945984.	+	8.67944e6i	−0.127579	+	1.17054i
$196$	2.47176e6	−	739104.i	0.328275	−	0.0981606i
$197$	−5.28095e6	+	5.28095e6i	−0.690738	+	0.690738i	−0.962394	−	0.271656i	$-0.912429\pi$
$197$	−5.28095e6	+	5.28095e6i	−0.690738	+	0.690738i	0.271656	+	0.962394i	$0.412429\pi$
$198$	7.98258e6	−	6.91069e6i	1.02837	−	0.890279i
$199$		−	1.40252e7i		−	1.77971i	−0.456239	−	0.889857i	$-0.650804\pi$
$199$		−	1.40252e7i		−	1.77971i	0.456239	−	0.889857i	$-0.349196\pi$
$200$	4.10539e6	+	8.81547e6i	0.513174	+	1.10193i
$201$	−1.69851e6	+	1.36465e6i	−0.209161	+	0.168048i
$202$	64552.2	−	86678.6i	0.00783171	−	0.0105162i
$203$	−6.92309e6	+	6.92309e6i	−0.827583	+	0.827583i
$204$	2.88555e6	+	1.56797e7i	0.339889	+	1.84692i
$205$	−1.14708e7	+	1.14708e7i	−1.33147	+	1.33147i
$206$	−1.69823e6	−	1.16071e7i	−0.194265	−	1.32777i
$207$	−1.93980e6	−	427927.i	−0.218699	−	0.0482457i
$208$	−1.44414e6	+	6.97066e6i	−0.160480	+	0.774612i
$209$			8.28620e6i			0.907646i
$210$	−8.18770e6	−	7.60751e6i	−0.884105	−	0.821456i
$211$	−374035.	+	374035.i	−0.0398166	+	0.0398166i	−0.726735	−	0.686918i	$-0.758963\pi$
$211$	−374035.	+	374035.i	−0.0398166	+	0.0398166i	0.686918	+	0.726735i	$0.258963\pi$
$212$	2.98380e6	−	5.52941e6i	0.313157	−	0.580325i
$213$	6.32743e6	+	689635.i	0.654769	+	0.0713642i
$214$	6.80022e6	−	9.13112e6i	0.693876	−	0.931714i
$215$	387823.			0.0390228
$216$	1.00166e7	−	1.10778e6i	0.993940	−	0.109924i
$217$		−	1.19889e7i		−	1.17328i
$218$	1.41961e6	−	1.90620e6i	0.137024	−	0.183992i
$219$	−250839.	+	2.30146e6i	−0.0238816	+	0.219114i
$220$	−6.17611e6	−	2.06546e7i	−0.580026	−	1.93976i
$221$	1.13384e7	+	1.13384e7i	1.05045	+	1.05045i
$222$	−5.22969e6	−	4.85911e6i	−0.477988	−	0.444117i
$223$	1.82824e7			1.64861			0.824305	−	0.566146i	$-0.191566\pi$
$223$	1.82824e7			1.64861			0.824305	+	0.566146i	$0.191566\pi$
$224$	−6.05244e6	−	6.81242e6i	−0.538501	−	0.606119i
$225$	2.98277e6	−	1.35210e7i	0.261862	−	1.18703i
$226$	2.84830e6	+	1.94676e7i	0.246752	+	1.68651i
$227$	−9.03807e6	−	9.03807e6i	−0.772678	−	0.772678i	0.205896	−	0.978574i	$-0.433989\pi$
$227$	−9.03807e6	−	9.03807e6i	−0.772678	−	0.772678i	−0.978574	+	0.205896i	$0.933989\pi$
$228$	−4.48793e6	+	6.51231e6i	−0.378653	+	0.549453i
$229$	−2.10899e6	−	2.10899e6i	−0.175618	−	0.175618i	0.613825	−	0.789442i	$-0.289630\pi$
$229$	−2.10899e6	−	2.10899e6i	−0.175618	−	0.175618i	−0.789442	+	0.613825i	$0.789630\pi$
$230$	−2.42258e6	+	3.25296e6i	−0.199111	+	0.267359i
$231$	8.51417e6	+	1.05971e7i	0.690727	+	0.859712i
$232$	−1.69354e7	−	6.17351e6i	−1.35622	−	0.494388i
$233$	−1.78048e7			−1.40757			−0.703784	−	0.710414i	$-0.748508\pi$
$233$	−1.78048e7			−1.40757			−0.703784	+	0.710414i	$0.748508\pi$
$234$	7.66308e6	−	6.63410e6i	0.598076	−	0.517767i
$235$	−3.82380e6	−	3.82380e6i	−0.294640	−	0.294640i
$236$	1.39288e6	−	2.58121e6i	0.105969	−	0.196376i
$237$	3.10484e6	+	338400.i	0.233235	+	0.0254206i
$238$	−2.03102e7	+	2.97157e6i	−1.50655	+	0.220422i
$239$			2.24763e7i			1.64638i	0.567763	+	0.823192i	$0.307809\pi$
$239$			2.24763e7i			1.64638i	−0.567763	+	0.823192i	$0.692191\pi$
$240$	6.33288e6	−	1.95780e7i	0.458107	−	1.41623i
$241$	2.57254e7			1.83785			0.918927	−	0.394427i	$-0.129057\pi$
$241$	2.57254e7			1.83785			0.918927	+	0.394427i	$0.129057\pi$
$242$	1.74424e6	+	1.19216e7i	0.123072	+	0.841177i
$243$	−1.22864e7	−	7.41190e6i	−0.856258	−	0.516548i
$244$	3.33442e6	−	6.17917e6i	0.229536	−	0.425364i
$245$	−5.30347e6	+	5.30347e6i	−0.360630	+	0.360630i
$246$	1.88199e7	−	691294.i	1.26419	−	0.0464363i
$247$			7.95455e6i			0.527868i
$248$	2.00092e7	−	9.31834e6i	1.31182	−	0.610919i
$249$	7.12407e6	+	8.86695e6i	0.461456	+	0.574350i
$250$	−4.02101e6	−	2.99457e6i	−0.257345	−	0.191652i
$251$	2.09125e6	−	2.09125e6i	0.132247	−	0.132247i	−0.637885	−	0.770132i	$-0.720191\pi$
$251$	2.09125e6	−	2.09125e6i	0.132247	−	0.132247i	0.770132	+	0.637885i	$0.220191\pi$
$252$	951908.	+	1.29399e7i	0.0594830	+	0.808594i
$253$	3.48830e6	−	3.48830e6i	0.215403	−	0.215403i
$254$	−1.63940e7	+	2.39859e6i	−1.00042	+	0.146371i
$255$	−2.90299e7	−	3.61320e7i	−1.75076	−	2.17907i
$256$	6.66552e6	−	1.53963e7i	0.397296	−	0.917690i
$257$		−	1.34901e7i		−	0.794723i	−0.917662	−	0.397361i	$-0.869926\pi$
$257$		−	1.34901e7i		−	0.794723i	0.917662	−	0.397361i	$-0.130074\pi$
$258$	−329833.	−	306460.i	−0.0192059	−	0.0178449i
$259$	6.49899e6	−	6.49899e6i	0.374064	−	0.374064i
$260$	−5.92892e6	−	1.98279e7i	−0.337330	−	1.12812i
$261$	1.38124e7	+	2.16315e7i	0.776871	+	1.21665i
$262$	1.64945e7	+	1.22840e7i	0.917141	+	0.683022i
$263$	1.67302e7			0.919675			0.459837	−	0.888003i	$-0.347908\pi$
$263$	1.67302e7			0.919675			0.459837	+	0.888003i	$0.347908\pi$
$264$	−1.10687e7	+	2.24465e7i	−0.601571	+	1.21994i
$265$			1.82662e7i			0.981544i
$266$	−8.16677e6	−	6.08204e6i	−0.433916	−	0.323150i
$267$	−1.83293e7	−	1.99774e6i	−0.962970	−	0.104955i
$268$	2.45262e6	−	4.54506e6i	0.127417	−	0.236122i
$269$	−1.84354e7	−	1.84354e7i	−0.947098	−	0.947098i	0.0515715	−	0.998669i	$-0.483577\pi$
$269$	−1.84354e7	−	1.84354e7i	−0.947098	−	0.947098i	−0.998669	+	0.0515715i	$0.983577\pi$
$270$	−2.40976e7	+	1.66631e7i	−1.22429	+	0.846576i
$271$	1.03595e7			0.520515			0.260257	−	0.965539i	$-0.416193\pi$
$271$	1.03595e7			0.520515			0.260257	+	0.965539i	$0.416193\pi$
$272$	−2.07455e7	−	3.15876e7i	−1.03090	−	1.56967i
$273$	8.17340e6	+	1.01730e7i	0.401712	+	0.499990i
$274$	1.78813e7	−	2.61620e6i	0.869255	−	0.127180i
$275$	2.43144e7	+	2.43144e7i	1.16914	+	1.16914i
$276$	4.63084e6	−	852216.i	0.220259	−	0.0405343i
$277$	−1.37451e7	−	1.37451e7i	−0.646709	−	0.646709i	0.305487	−	0.952196i	$-0.401181\pi$
$277$	−1.37451e7	−	1.37451e7i	−0.646709	−	0.646709i	−0.952196	+	0.305487i	$0.901181\pi$
$278$	−3.95405e6	−	2.94470e6i	−0.184038	−	0.137059i
$279$	−3.06897e7	−	6.77024e6i	−1.41312	−	0.311739i
$280$	2.48901e7	+	9.07326e6i	1.13384	+	0.413323i
$281$	3.47579e6			0.156651			0.0783257	−	0.996928i	$-0.475043\pi$
$281$	3.47579e6			0.156651			0.0783257	+	0.996928i	$0.475043\pi$
$282$	230443.	+	6.27362e6i	0.0102758	+	0.279750i
$283$	−1.71479e7	−	1.71479e7i	−0.756574	−	0.756574i	0.219123	−	0.975697i	$-0.429680\pi$
$283$	−1.71479e7	−	1.71479e7i	−0.756574	−	0.756574i	−0.975697	+	0.219123i	$0.929680\pi$
$284$	−1.44548e7	+	4.32226e6i	−0.631039	+	0.188693i
$285$	2.49127e6	−	2.28575e7i	0.107618	−	0.987401i
$286$	3.64403e6	+	2.49063e7i	0.155770	+	1.06466i
$287$			2.42467e7i			1.02567i
$288$	−2.08566e7	+	1.16462e7i	−0.873102	+	0.487537i
$289$	−6.09869e7			−2.52664
$290$	5.18515e7	−	7.58635e6i	2.12602	−	0.311056i
$291$	3.45430e7	+	3.76489e6i	1.40179	+	0.152783i
$292$	−1.57212e6	−	5.25760e6i	−0.0631449	−	0.211173i
$293$	3.30448e7	−	3.30448e7i	1.31371	−	1.31371i	0.395051	−	0.918659i	$-0.370727\pi$
$293$	3.30448e7	−	3.30448e7i	1.31371	−	1.31371i	0.918659	−	0.395051i	$-0.129273\pi$
$294$	8.70129e6	−	319617.i	0.342406	−	0.0125773i
$295$			8.52691e6i			0.332143i
$296$	1.58979e7	+	5.79533e6i	0.613008	+	0.223462i
$297$	3.19350e7	−	1.58106e7i	1.21898	−	0.603502i
$298$	2.57832e6	−	3.46208e6i	0.0974288	−	0.130824i
$299$	3.34868e6	−	3.34868e6i	0.125274	−	0.125274i
$300$	5.94019e6	+	3.22783e7i	0.220007	+	1.19549i
$301$	409886.	−	409886.i	0.0150302	−	0.0150302i
$302$	4.81683e6	+	3.29223e7i	0.174880	+	1.19528i
$303$	284346.	−	228455.i	0.0102216	−	0.00821245i
$304$	3.80317e6	−	1.83574e7i	0.135371	−	0.653415i
$305$			2.04126e7i			0.719447i
$306$	−3.86261e6	+	5.36689e7i	−0.134808	+	1.87309i
$307$	2.21460e7	−	2.21460e7i	0.765387	−	0.765387i	−0.211904	−	0.977291i	$-0.567966\pi$
$307$	2.21460e7	−	2.21460e7i	0.765387	−	0.765387i	0.977291	+	0.211904i	$0.0679664\pi$
$308$	−2.83570e7	−	1.53021e7i	−0.970529	−	0.523720i
$309$	4.28968e6	−	3.93580e7i	0.145395	−	1.33401i
$310$	−3.83277e7	+	5.14652e7i	−1.28655	+	1.72754i
$311$	−3.67967e7			−1.22328			−0.611642	−	0.791134i	$-0.709491\pi$
$311$	−3.67967e7			−1.22328			−0.611642	+	0.791134i	$0.709491\pi$
$312$	−1.06257e7	+	2.15481e7i	−0.349861	+	0.709489i
$313$			2.04731e7i			0.667651i	0.942635	+	0.333826i	$0.108340\pi$
$313$			2.04731e7i			0.667651i	−0.942635	+	0.333826i	$0.891660\pi$
$314$	−1.05973e7	+	1.42297e7i	−0.342300	+	0.459630i
$315$	−2.03003e7	−	3.17920e7i	−0.649487	−	1.01715i
$316$	−7.09289e6	+	2.12091e6i	−0.224782	+	0.0672142i
$317$	2.56527e7	+	2.56527e7i	0.805296	+	0.805296i	0.983918	−	0.178622i	$-0.0571638\pi$
$317$	2.56527e7	+	2.56527e7i	0.805296	+	0.805296i	−0.178622	+	0.983918i	$0.557164\pi$
$318$	1.44340e7	−	1.55349e7i	0.448855	−	0.483088i
$319$	−6.37379e7			−1.96348
$320$	4.20268e6	+	4.85931e7i	0.128256	+	1.48294i
$321$	2.99543e7	−	2.40665e7i	0.905616	−	0.727609i
$322$	877623.	+	5.99841e6i	0.0262870	+	0.179667i
$323$	−2.98599e7	−	2.98599e7i	−0.886096	−	0.886096i
$324$	3.36617e7	+	4.87057e6i	0.989694	+	0.143200i
$325$	2.33413e7	+	2.33413e7i	0.679946	+	0.679946i
$326$	2.79858e7	−	3.75785e7i	0.807765	−	1.08464i
$327$	6.25322e6	−	5.02409e6i	0.178838	−	0.143686i
$328$	−4.04671e7	+	1.88456e7i	−1.14678	+	0.534059i
$329$	−8.08265e6			−0.226969
$330$	−2.67079e6	−	7.27098e7i	−0.0743186	−	2.02326i
$331$	1.18356e7	+	1.18356e7i	0.326367	+	0.326367i	0.851203	−	0.524836i	$-0.175873\pi$
$331$	1.18356e7	+	1.18356e7i	0.326367	+	0.326367i	−0.524836	+	0.851203i	$0.675873\pi$
$332$	−2.37272e7	−	1.28037e7i	−0.648383	−	0.349883i
$333$	−1.29663e7	−	2.03064e7i	−0.351143	−	0.549920i
$334$	−1.38959e7	+	2.03310e6i	−0.372947	+	0.0545656i
$335$			1.50144e7i			0.399368i
$336$	−1.39986e7	−	2.73849e7i	−0.369034	−	0.721926i
$337$	1.84717e7			0.482634			0.241317	−	0.970446i	$-0.422421\pi$
$337$	1.84717e7			0.482634			0.241317	+	0.970446i	$0.422421\pi$
$338$	−2.09196e6	−	1.42982e7i	−0.0541755	−	0.370281i
$339$	−7.19473e6	+	6.60119e7i	−0.184678	+	1.69443i
$340$	9.66862e7	+	5.21741e7i	2.45996	+	1.32745i
$341$	5.51884e7	−	5.51884e7i	1.39183	−	1.39183i
$342$	−2.01809e7	+	1.74710e7i	−0.504500	+	0.436757i
$343$			4.39282e7i			1.08858i
$344$	1.00267e6	+	365507.i	0.0246311	+	0.00897883i
$345$	−1.06712e7	+	8.57369e6i	−0.259870	+	0.208790i
$346$	761146.	+	566848.i	0.0183755	+	0.0136848i
$347$	−2.32938e6	+	2.32938e6i	−0.0557508	+	0.0557508i	−0.734433	−	0.678682i	$-0.762552\pi$
$347$	−2.32938e6	+	2.32938e6i	−0.0557508	+	0.0557508i	0.678682	+	0.734433i	$0.262552\pi$
$348$	−5.00930e7	−	3.45214e7i	−1.18861	−	0.819126i
$349$	−1.13692e7	+	1.13692e7i	−0.267458	+	0.267458i	−0.828075	−	0.560617i	$-0.810564\pi$
$349$	−1.13692e7	+	1.13692e7i	−0.267458	+	0.267458i	0.560617	+	0.828075i	$0.310564\pi$
$350$	−4.18107e7	+	6.11728e6i	−0.975176	+	0.142677i
$351$	3.06568e7	−	1.51778e7i	0.708934	−	0.350984i
$352$	3.49842e6	−	5.92206e7i	0.0802129	−	1.35783i
$353$			6.63012e7i			1.50729i	0.657281	+	0.753645i	$0.271706\pi$
$353$			6.63012e7i			1.50729i	−0.657281	+	0.753645i	$0.728294\pi$
$354$	6.73802e6	−	7.25190e6i	0.151888	−	0.163471i
$355$	3.10145e7	−	3.10145e7i	0.693235	−	0.693235i
$356$	4.18727e7	−	1.25207e7i	0.928070	−	0.277511i
$357$	−6.88690e7	−	7.50612e6i	−1.51363	−	0.164972i
$358$	2.34202e7	+	1.74417e7i	0.510436	+	0.380137i
$359$	−4.94579e7			−1.06894			−0.534468	−	0.845189i	$-0.679488\pi$
$359$	−4.94579e7			−1.06894			−0.534468	+	0.845189i	$0.679488\pi$
$360$	3.72817e7	−	5.85908e7i	0.799076	−	1.25580i
$361$			2.60974e7i			0.554723i
$362$	3.90789e7	+	2.91032e7i	0.823790	+	0.613501i
$363$	−4.40589e6	+	4.04243e7i	−0.0921116	+	0.845127i
$364$	−2.72221e7	−	1.46896e7i	−0.564439	−	0.304584i
$365$	1.12808e7	+	1.12808e7i	0.231986	+	0.231986i
$366$	1.61302e7	−	1.73603e7i	0.329000	−	0.354091i
$367$	−1.21858e7			−0.246521			−0.123261	−	0.992374i	$-0.539335\pi$
$367$	−1.21858e7			−0.246521			−0.123261	+	0.992374i	$0.539335\pi$
$368$	−9.32906e6	+	6.12697e6i	−0.187195	+	0.122943i
$369$	6.20676e7	+	1.36923e7i	1.23534	+	0.272520i
$370$	−4.86751e7	+	7.12162e6i	−0.960952	+	0.140596i
$371$	1.93053e7	+	1.93053e7i	0.378055	+	0.378055i
$372$	7.32647e7	−	1.34829e7i	1.42320	−	0.261912i
$373$	−1.71106e7	−	1.71106e7i	−0.329715	−	0.329715i	0.522763	−	0.852478i	$-0.324901\pi$
$373$	−1.71106e7	−	1.71106e7i	−0.329715	−	0.329715i	−0.852478	+	0.522763i	$0.824901\pi$
$374$	−1.07173e8	−	7.98147e7i	−2.04866	−	1.52570i
$375$	−1.05980e7	−	1.31908e7i	−0.200970	−	0.250136i
$376$	−6.28221e6	−	1.34897e7i	−0.118181	−	0.253770i
$377$	−6.11868e7			−1.14192
$378$	−7.85743e6	+	4.30796e7i	−0.145481	+	0.797620i
$379$	3.41634e6	+	3.41634e6i	0.0627542	+	0.0627542i	0.737787	−	0.675033i	$-0.235871\pi$
$379$	3.41634e6	+	3.41634e6i	0.0627542	+	0.0627542i	−0.675033	+	0.737787i	$0.735871\pi$
$380$	1.56139e7	+	5.22170e7i	0.284552	+	0.951616i
$381$	−5.55895e7	−	6.05878e6i	−1.00512	−	0.109549i
$382$	−1.56296e6	−	1.06826e7i	−0.0280388	−	0.191641i
$383$		−	8.04700e7i		−	1.43231i	−0.697940	−	0.716156i	$-0.745900\pi$
$383$		−	8.04700e7i		−	1.43231i	0.697940	−	0.716156i	$-0.254100\pi$
$384$	3.48243e7	−	4.46480e7i	0.615019	−	0.788512i
$385$	9.36761e7			1.64152
$386$	5.21091e7	−	7.62404e6i	0.906049	−	0.132563i
$387$	−817775.	−	1.28071e6i	−0.0141091	−	0.0220962i
$388$	−7.89123e7	+	2.35963e7i	−1.35098	+	0.403970i
$389$	−7.91230e6	+	7.91230e6i	−0.134417	+	0.134417i	−0.771114	−	0.636697i	$-0.780300\pi$
$389$	−7.91230e6	+	7.91230e6i	−0.134417	+	0.134417i	0.636697	+	0.771114i	$0.280300\pi$
$390$	−2.56389e6	−	6.97997e7i	−0.0432221	−	1.17668i
$391$			2.51406e7i			0.420577i
$392$	−1.87098e7	+	8.71320e6i	−0.310606	+	0.144650i
$393$	4.34739e7	+	5.41097e7i	0.716227	+	0.891450i
$394$	3.56865e7	−	4.79187e7i	0.583465	−	0.783459i
$395$	1.52187e7	−	1.52187e7i	0.246937	−	0.246937i
$396$	−5.51843e7	+	6.39481e7i	−0.888649	+	1.02977i
$397$	2.78708e6	−	2.78708e6i	0.0445428	−	0.0445428i	−0.684485	−	0.729027i	$-0.739973\pi$
$397$	2.78708e6	−	2.78708e6i	0.0445428	−	0.0445428i	0.729027	+	0.684485i	$0.239973\pi$
$398$	1.62432e7	+	1.11020e8i	0.257646	+	1.76097i
$399$	−2.15248e7	−	2.67908e7i	−0.338860	−	0.421761i
$400$	−4.27067e7	−	6.50262e7i	−0.667293	−	1.01604i
$401$		−	2.89338e7i		−	0.448717i	−0.974507	−	0.224359i	$-0.927971\pi$
$401$		−	2.89338e7i		−	0.448717i	0.974507	−	0.224359i	$-0.0720287\pi$
$402$	1.18645e7	−	1.27693e7i	0.182629	−	0.196558i
$403$	5.29796e7	−	5.29796e7i	0.809456	−	0.809456i
$404$	−410591.	+	760885.i	−0.00622680	+	0.0115392i
$405$	−9.28461e7	+	3.40122e7i	−1.39765	+	0.511999i
$406$	4.67833e7	−	6.28192e7i	0.699058	−	0.938673i
$407$	5.98333e7			0.887483
$408$	−4.10006e7	−	1.20775e8i	−0.603684	−	1.77826i
$409$		−	8.86436e7i		−	1.29562i	−0.761802	−	0.647810i	$-0.775685\pi$
$409$		−	8.86436e7i		−	1.29562i	0.761802	−	0.647810i	$-0.224315\pi$
$410$	7.75148e7	−	1.04084e8i	1.12469	−	1.51020i
$411$	6.06328e7	+	6.60845e6i	0.873337	+	0.0951862i
$412$	2.68854e7	+	8.99119e7i	0.384437	+	1.28566i
$413$	9.01199e6	+	9.01199e6i	0.127929	+	0.127929i
$414$	1.58506e7	+	1.14078e6i	0.223380	+	0.0160769i
$415$	7.83816e7			1.09666
$416$	3.35840e6	−	5.68504e7i	0.0466501	−	0.789684i
$417$	−1.04215e7	−	1.29711e7i	−0.143722	−	0.178883i
$418$	−9.59661e6	−	6.55913e7i	−0.131398	−	0.898085i
$419$	−4.69670e7	−	4.69670e7i	−0.638485	−	0.638485i	0.311697	−	0.950182i	$-0.399103\pi$
$419$	−4.69670e7	−	4.69670e7i	−0.638485	−	0.638485i	−0.950182	+	0.311697i	$0.899103\pi$
$420$	7.36222e7	+	5.07364e7i	0.993712	+	0.684813i
$421$	−5.98543e7	−	5.98543e7i	−0.802138	−	0.802138i	0.181292	−	0.983429i	$-0.441972\pi$
$421$	−5.98543e7	−	5.98543e7i	−0.802138	−	0.802138i	−0.983429	+	0.181292i	$0.941972\pi$
$422$	2.52757e6	−	3.39394e6i	0.0336330	−	0.0451613i
$423$	−4.56434e6	+	2.06903e7i	−0.0603055	+	0.273366i
$424$	−1.72151e7	+	4.72250e7i	−0.225845	+	0.619547i
$425$	−1.75237e8			−2.28276
$426$	−5.08849e7	+	1.86911e6i	−0.658203	+	0.0241772i
$427$	2.15738e7	+	2.15738e7i	0.277105	+	0.277105i
$428$	−4.32535e7	+	8.01551e7i	−0.551684	+	1.02235i
$429$	−9.20473e6	+	8.44537e7i	−0.116584	+	1.06966i
$430$	−3.06990e6	+	449155.i	−0.0386117	+	0.00564925i
$431$			1.33972e8i			1.67333i	0.547713	+	0.836666i	$0.315499\pi$
$431$			1.33972e8i			1.67333i	−0.547713	+	0.836666i	$0.684501\pi$
$432$	−7.80059e7	+	2.03696e7i	−0.967556	+	0.252657i
$433$	−1.23850e7			−0.152557			−0.0762785	−	0.997087i	$-0.524304\pi$
$433$	−1.23850e7			−0.152557			−0.0762785	+	0.997087i	$0.524304\pi$
$434$	1.38849e7	+	9.49010e7i	0.169853	+	1.16092i
$435$	1.75821e8	+	1.91629e7i	2.13601	+	0.232806i
$436$	−9.02955e6	+	1.67331e7i	−0.108945	+	0.201891i
$437$	−8.81880e6	+	8.81880e6i	−0.105673	+	0.105673i
$438$	−679846.	−	1.85082e7i	−0.00809074	−	0.220263i
$439$			7.38787e7i			0.873223i	0.899650	+	0.436612i	$0.143822\pi$
$439$			7.38787e7i			0.873223i	−0.899650	+	0.436612i	$0.856178\pi$
$440$	7.28094e7	+	1.56343e8i	0.854730	+	1.83536i
$441$	2.86967e7	+	6.33058e6i	0.334592	+	0.0738121i
$442$	−1.02883e8	−	7.66202e7i	−1.19146	−	0.887313i
$443$	1.01790e8	−	1.01790e8i	1.17083	−	1.17083i	0.188820	−	0.982012i	$-0.439534\pi$
$443$	1.01790e8	−	1.01790e8i	1.17083	−	1.17083i	0.982012	−	0.188820i	$-0.0604661\pi$
$444$	4.70244e7	+	3.24066e7i	0.537247	+	0.370242i
$445$	−8.98431e7	+	8.98431e7i	−1.01954	+	1.01954i
$446$	−1.44718e8	+	2.11736e7i	−1.63124	+	0.238666i
$447$	1.13572e7	−	9.12486e6i	0.127160	−	0.102165i
$448$	5.57992e7	+	4.69157e7i	0.620575	+	0.521776i
$449$			2.88985e7i			0.319254i	0.987177	+	0.159627i	$0.0510291\pi$
$449$			2.88985e7i			0.319254i	−0.987177	+	0.159627i	$0.948971\pi$
$450$	−7.95158e6	+	1.10483e8i	−0.0872601	+	1.21243i
$451$	−1.11614e8	+	1.11614e8i	−1.21672	+	1.21672i
$452$	−4.50927e7	−	1.50802e8i	−0.488304	−	1.63302i
$453$	−1.21672e7	+	1.11635e8i	−0.130887	+	1.20089i
$454$	8.20103e7	+	6.10755e7i	0.876397	+	0.652679i
$455$	8.99268e7			0.954674
$456$	2.79830e7	−	5.67473e7i	0.295121	−	0.598482i
$457$			1.30141e7i			0.136353i	0.997673	+	0.0681766i	$0.0217181\pi$
$457$			1.30141e7i			0.136353i	−0.997673	+	0.0681766i	$0.978282\pi$
$458$	1.91367e7	+	1.42517e7i	0.199192	+	0.148344i
$459$	−5.81053e7	+	1.72054e8i	−0.600866	+	1.77921i
$460$	1.54091e7	−	2.85552e7i	0.158308	−	0.293368i
$461$	−6.64262e6	−	6.64262e6i	−0.0678011	−	0.0678011i	0.672393	−	0.740194i	$-0.265266\pi$
$461$	−6.64262e6	−	6.64262e6i	−0.0678011	−	0.0678011i	−0.740194	+	0.672393i	$0.765266\pi$
$462$	−7.96689e7	−	7.40234e7i	−0.807910	−	0.750660i
$463$	−9.96170e7			−1.00367			−0.501834	−	0.864964i	$-0.667341\pi$
$463$	−9.96170e7			−1.00367			−0.501834	+	0.864964i	$0.667341\pi$
$464$	1.41206e8	+	2.92542e7i	1.41351	+	0.292843i
$465$	−1.68830e8	+	1.35645e8i	−1.67915	+	1.34910i
$466$	1.40938e8	−	2.06205e7i	1.39274	−	0.203771i
$467$	−6.15136e6	−	6.15136e6i	−0.0603977	−	0.0603977i	0.676263	−	0.736660i	$-0.263598\pi$
$467$	−6.15136e6	−	6.15136e6i	−0.0603977	−	0.0603977i	−0.736660	+	0.676263i	$0.763598\pi$
$468$	−5.29756e7	+	6.13887e7i	−0.516819	+	0.598895i
$469$	1.58686e7	+	1.58686e7i	0.153822	+	0.153822i
$470$	3.46966e7	+	2.58396e7i	0.334190	+	0.248881i
$471$	−4.66801e7	+	3.75047e7i	−0.446755	+	0.358941i
$472$	−8.03624e6	+	2.20453e7i	−0.0764235	+	0.209648i
$473$	3.77364e6			0.0356597
$474$	−2.49689e7	+	917163.i	−0.234458	+	0.00861215i
$475$	−6.14696e7	−	6.14696e7i	−0.573561	−	0.573561i
$476$	1.57329e8	−	4.70443e7i	1.45877	−	0.436201i
$477$	6.03203e7	−	3.85165e7i	0.555787	−	0.354889i
$478$	−2.60308e7	−	1.77916e8i	−0.238344	−	1.62904i
$479$		−	1.57265e8i		−	1.43095i	−0.698638	−	0.715475i	$-0.746210\pi$
$479$		−	1.57265e8i		−	1.43095i	0.698638	−	0.715475i	$-0.253790\pi$
$480$	−2.74552e7	+	1.62308e8i	−0.248257	+	1.46763i
$481$	5.74386e7			0.516141
$482$	−2.03635e8	+	2.97937e7i	−1.81849	+	0.266063i
$483$	−2.21685e6	+	2.03397e7i	−0.0196741	+	0.180511i
$484$	−2.76138e7	−	9.23478e7i	−0.243551	−	0.814498i
$485$	1.69316e8	−	1.69316e8i	1.48414	−	1.48414i
$486$	1.05840e8	+	4.44411e7i	0.922018	+	0.387147i
$487$		−	1.35851e8i		−	1.17618i	−0.808794	−	0.588092i	$-0.799879\pi$
$487$		−	1.35851e8i		−	1.17618i	0.808794	−	0.588092i	$-0.200121\pi$
$488$	−1.92380e7	+	5.27744e7i	−0.165539	+	0.454112i
$489$	1.23275e8	−	9.90439e7i	1.05426	−	0.847035i
$490$	3.58386e7	−	4.81230e7i	0.304623	−	0.409039i
$491$	1.07002e8	−	1.07002e8i	0.903955	−	0.903955i	−0.0918204	−	0.995776i	$-0.529269\pi$
$491$	1.07002e8	−	1.07002e8i	0.903955	−	0.903955i	0.995776	+	0.0918204i	$0.0292686\pi$
$492$	−1.48172e8	+	2.72682e7i	−1.24415	+	0.228961i
$493$	2.29684e8	−	2.29684e8i	1.91686	−	1.91686i
$494$	−9.21252e6	−	6.29661e7i	−0.0764183	−	0.522307i
$495$	5.28997e7	−	2.39795e8i	0.436152	−	1.97709i
$496$	−1.47595e8	+	9.69349e7i	−1.20956	+	0.794393i
$497$		−	6.55578e7i		−	0.534017i
$498$	−6.66614e7	−	6.19377e7i	−0.539742	−	0.501495i
$499$	−7.02796e7	+	7.02796e7i	−0.565624	+	0.565624i	−0.930899	−	0.365275i	$-0.880975\pi$
$499$	−7.02796e7	+	7.02796e7i	−0.565624	+	0.565624i	0.365275	+	0.930899i	$0.380975\pi$
$500$	3.52974e7	+	1.90473e7i	0.282379	+	0.152378i
$501$	−4.71189e7	−	5.13556e6i	−0.374699	−	0.0408389i
$502$	−1.41318e7	+	1.89757e7i	−0.111708	+	0.149999i
$503$	−7.38304e7			−0.580138			−0.290069	−	0.957006i	$-0.593678\pi$
$503$	−7.38304e7			−0.580138			−0.290069	+	0.957006i	$0.593678\pi$
$504$	−2.25214e7	−	1.01327e8i	−0.175915	−	0.791465i
$505$		−	2.51355e6i		−	0.0195170i
$506$	−2.35724e7	+	3.16523e7i	−0.181950	+	0.244317i
$507$	5.28423e6	−	4.84831e7i	0.0405469	−	0.372020i
$508$	1.26992e8	−	3.79732e7i	0.968693	−	0.289658i
$509$	−1.05329e7	−	1.05329e7i	−0.0798719	−	0.0798719i	0.666042	−	0.745914i	$-0.267987\pi$
$509$	−1.05329e7	−	1.05329e7i	−0.0798719	−	0.0798719i	−0.745914	+	0.666042i	$0.767987\pi$
$510$	2.71639e8	+	2.52390e8i	2.04777	+	1.90267i
$511$	2.38452e7			0.178705
$512$	−3.49313e7	+	1.29592e8i	−0.260259	+	0.965539i
$513$	−8.07352e7	+	3.99710e7i	−0.598014	+	0.296069i
$514$	1.56235e7	+	1.06784e8i	0.115050	+	0.786351i
$515$	−1.92917e8	−	1.92917e8i	−1.41237	−	1.41237i
$516$	2.96579e6	+	2.04386e6i	0.0215869	+	0.0148766i
$517$	−3.72067e7	−	3.72067e7i	−0.269246	−	0.269246i
$518$	−4.39174e7	+	5.89709e7i	−0.315971	+	0.424276i
$519$	2.00612e6	+	2.49691e6i	0.0143501	+	0.0178608i
$520$	6.98952e7	+	1.50085e8i	0.497093	+	1.06740i
$521$	1.52068e8			1.07529			0.537644	−	0.843172i	$-0.319314\pi$
$521$	1.52068e8			1.07529			0.537644	+	0.843172i	$0.319314\pi$
$522$	−1.34388e8	−	1.55232e8i	−0.944819	−	1.09137i
$523$	−3.93597e7	−	3.93597e7i	−0.275135	−	0.275135i	0.556028	−	0.831163i	$-0.312325\pi$
$523$	−3.93597e7	−	3.93597e7i	−0.275135	−	0.275135i	−0.831163	+	0.556028i	$0.812325\pi$
$524$	−1.44793e8	−	7.81335e7i	−1.00636	−	0.543054i
$525$	−1.41774e8	−	1.54521e7i	−0.979756	−	0.106785i
$526$	−1.32432e8	+	1.93760e7i	−0.909987	+	0.133139i
$527$			3.97750e8i			2.71756i
$528$	6.16209e7	−	1.90500e8i	0.418626	−	1.29417i
$529$	−1.40611e8			−0.949843
$530$	−2.11548e7	−	1.44590e8i	−0.142096	−	0.971204i
$531$	2.81584e7	−	1.79801e7i	0.188072	−	0.120090i
$532$	7.16898e7	+	3.86854e7i	0.476126	+	0.256929i
$533$	−1.07147e8	+	1.07147e8i	−0.707618	+	0.707618i
$534$	1.47404e8	−	5.41445e6i	0.968020	−	0.0355574i
$535$		−	2.64789e8i		−	1.72917i
$536$	−1.41504e7	+	3.88180e7i	−0.0918915	+	0.252080i
$537$	6.17276e7	+	7.68291e7i	0.398618	+	0.496138i
$538$	1.67280e8	+	1.24578e8i	1.07423	+	0.800011i
$539$	−5.16044e7	+	5.16044e7i	−0.329549	+	0.329549i
$540$	1.71452e8	−	1.59809e8i	1.08883	−	1.01489i
$541$	7.12615e7	−	7.12615e7i	0.450053	−	0.450053i	−0.445319	−	0.895372i	$-0.646910\pi$
$541$	7.12615e7	−	7.12615e7i	0.450053	−	0.450053i	0.895372	+	0.445319i	$0.146910\pi$
$542$	−8.20033e7	+	1.19978e7i	−0.515031	+	0.0753538i
$543$	1.02999e8	+	1.28197e8i	0.643327	+	0.800715i
$544$	2.00799e8	+	2.26012e8i	1.24728	+	1.40390i
$545$		−	5.52769e7i		−	0.341472i
$546$	−7.64802e7	−	7.10607e7i	−0.469863	−	0.436568i
$547$	4.10273e7	−	4.10273e7i	0.250675	−	0.250675i	−0.570573	−	0.821247i	$-0.693279\pi$
$547$	4.10273e7	−	4.10273e7i	0.250675	−	0.250675i	0.821247	+	0.570573i	$0.193279\pi$
$548$	−1.38513e8	+	4.14182e7i	−0.841686	+	0.251680i
$549$	6.74084e7	−	4.30426e7i	0.407378	−	0.260124i
$550$	−2.20626e8	−	1.64307e8i	−1.32608	−	0.987568i
$551$	1.61137e8			0.963250
$552$	−3.56695e7	+	1.21091e7i	−0.212070	+	0.0719937i
$553$		−	3.21689e7i		−	0.190222i
$554$	1.24721e8	+	9.28837e7i	0.733519	+	0.546274i
$555$	−1.65050e8	−	1.79890e7i	−0.965466	−	0.105227i
$556$	3.47095e7	+	1.87301e7i	0.201941	+	0.108972i
$557$	−1.20060e7	−	1.20060e7i	−0.0694756	−	0.0694756i	0.671515	−	0.740991i	$-0.265644\pi$
$557$	−1.20060e7	−	1.20060e7i	−0.0694756	−	0.0694756i	−0.740991	+	0.671515i	$0.765644\pi$
$558$	2.50772e8	+	1.80483e7i	1.44337	+	0.103881i
$559$	3.62261e6			0.0207389
$560$	−2.07531e8	−	4.29951e7i	−1.18173	−	0.244825i
$561$	−2.82470e8	−	3.51576e8i	−1.59987	−	1.99127i
$562$	−2.75134e7	+	4.02546e6i	−0.155001	+	0.0226781i
$563$	−4.11880e7	−	4.11880e7i	−0.230805	−	0.230805i	0.582223	−	0.813029i	$-0.302183\pi$
$563$	−4.11880e7	−	4.11880e7i	−0.230805	−	0.230805i	−0.813029	+	0.582223i	$0.802183\pi$
$564$	−9.08988e6	−	4.93934e7i	−0.0506665	−	0.275316i
$565$	3.23564e8	+	3.23564e8i	1.79397	+	1.79397i
$566$	1.55598e8	+	1.15878e8i	0.858131	+	0.639076i
$567$	−6.21809e7	+	1.34075e8i	−0.341120	+	0.735527i
$568$	1.09414e8	−	5.09545e7i	0.597075	−	0.278060i
$569$	−2.45376e8			−1.33197			−0.665987	−	0.745963i	$-0.731990\pi$
$569$	−2.45376e8			−1.33197			−0.665987	+	0.745963i	$0.731990\pi$
$570$	6.75205e6	+	1.83819e8i	0.0364595	+	0.992579i
$571$	7.27223e7	+	7.27223e7i	0.390624	+	0.390624i	0.874910	−	0.484286i	$-0.160920\pi$
$571$	7.27223e7	+	7.27223e7i	0.390624	+	0.390624i	−0.484286	+	0.874910i	$0.660920\pi$
$572$	−5.76903e7	−	1.92931e8i	−0.308258	−	1.03090i
$573$	3.94801e6	−	3.62231e7i	0.0209853	−	0.192541i
$574$	−2.80812e7	−	1.91930e8i	−0.148484	−	1.01486i
$575$			5.17545e7i			0.272235i
$576$	1.51607e8	−	1.16343e8i	0.793325	−	0.608798i
$577$	1.27820e8			0.665381			0.332691	−	0.943036i	$-0.392044\pi$
$577$	1.27820e8			0.665381			0.332691	+	0.943036i	$0.392044\pi$
$578$	4.82756e8	−	7.06316e7i	2.50002	−	0.365776i
$579$	1.76694e8	+	1.92581e7i	0.910304	+	0.0992153i
$580$	−4.01656e8	+	1.20103e8i	−2.05859	+	0.615559i
$581$	8.28406e7	−	8.28406e7i	0.422391	−	0.422391i
$582$	−2.77793e8	+	1.02039e7i	−1.40914	+	0.0517606i
$583$			1.77736e8i			0.896951i
$584$	1.85335e7	+	3.97969e7i	0.0930508	+	0.199807i
$585$	5.07824e7	−	2.30198e8i	0.253656	−	1.14983i
$586$	−2.23303e8	+	2.99844e8i	−1.10969	+	1.49005i
$587$	−1.63513e8	+	1.63513e8i	−0.808420	+	0.808420i	−0.984395	−	0.175975i	$-0.943692\pi$
$587$	−1.63513e8	+	1.63513e8i	−0.808420	+	0.808420i	0.175975	+	0.984395i	$0.443692\pi$
$588$	−6.85068e7	+	1.26073e7i	−0.336978	+	0.0620142i
$589$	−1.39523e8	+	1.39523e8i	−0.682808	+	0.682808i
$590$	−9.87539e6	−	6.74967e7i	−0.0480837	−	0.328644i
$591$	1.57195e8	−	1.26297e8i	0.761513	−	0.611831i
$592$	−1.32556e8	−	2.74621e7i	−0.638900	−	0.132364i
$593$			8.80044e7i			0.422027i	0.977483	+	0.211014i	$0.0676764\pi$
$593$			8.80044e7i			0.422027i	−0.977483	+	0.211014i	$0.932324\pi$
$594$	−2.34478e8	+	1.62138e8i	−1.11877	+	0.773614i
$595$	−3.37568e8	+	3.37568e8i	−1.60255	+	1.60255i
$596$	−1.63996e7	+	3.03909e7i	−0.0774633	+	0.143551i
$597$	−4.10300e7	+	3.76452e8i	−0.192832	+	1.76924i
$598$	−2.26290e7	+	3.03855e7i	−0.105818	+	0.142090i
$599$	1.72474e8			0.802495			0.401248	−	0.915970i	$-0.368577\pi$
$599$	1.72474e8			0.802495			0.401248	+	0.915970i	$0.368577\pi$
$600$	−8.44038e7	−	2.48627e8i	−0.390759	−	1.15105i
$601$			2.28854e8i			1.05423i	0.849794	+	0.527114i	$0.176726\pi$
$601$			2.28854e8i			1.05423i	−0.849794	+	0.527114i	$0.823274\pi$
$602$	−2.76984e6	+	3.71925e6i	−0.0126959	+	0.0170477i
$603$	4.95820e7	−	3.16598e7i	0.226137	−	0.144396i
$604$	−7.62575e7	−	2.55025e8i	−0.346076	−	1.15737i
$605$	1.98144e8	+	1.98144e8i	0.894775	+	0.894775i
$606$	−1.98622e6	+	2.13770e6i	−0.00892503	+	0.00960570i
$607$	−3.13382e8			−1.40123			−0.700613	−	0.713541i	$-0.747090\pi$
$607$	−3.13382e8			−1.40123			−0.700613	+	0.713541i	$0.747090\pi$
$608$	−8.84441e6	+	1.49716e8i	−0.0393512	+	0.666129i
$609$	2.06076e8	−	1.65570e8i	0.912380	−	0.733043i
$610$	−2.36407e7	−	1.61581e8i	−0.104153	−	0.711868i
$611$	−3.57176e7	−	3.57176e7i	−0.156588	−	0.156588i
$612$	−3.15810e7	−	4.29302e8i	−0.137775	−	1.87287i
$613$	5.10430e7	+	5.10430e7i	0.221592	+	0.221592i	0.809169	−	0.587576i	$-0.199918\pi$
$613$	5.10430e7	+	5.10430e7i	0.221592	+	0.221592i	−0.587576	+	0.809169i	$0.699918\pi$
$614$	−1.49654e8	+	2.00950e8i	−0.646520	+	0.868127i
$615$	3.41445e8	−	2.74331e8i	1.46790	−	1.17937i
$616$	2.42188e8	+	8.82857e7i	1.03612	+	0.377701i
$617$	2.43754e8			1.03776			0.518879	−	0.854848i	$-0.326350\pi$
$617$	2.43754e8			1.03776			0.518879	+	0.854848i	$0.326350\pi$
$618$	1.16263e7	+	3.16515e8i	0.0492578	+	1.34100i
$619$	−1.29680e8	−	1.29680e8i	−0.546765	−	0.546765i	0.378739	−	0.925504i	$-0.376358\pi$
$619$	−1.29680e8	−	1.29680e8i	−0.546765	−	0.546765i	−0.925504	+	0.378739i	$0.876358\pi$
$620$	2.43787e8	−	4.51773e8i	1.02291	−	1.89559i
$621$	5.08145e7	+	1.71608e7i	0.212184	+	0.0716577i
$622$	2.91272e8	−	4.26159e7i	1.21040	−	0.177092i
$623$			1.89908e8i			0.785380i
$624$	5.91546e7	−	1.82875e8i	0.243464	−	0.752664i
$625$	1.80166e8			0.737962
$626$	−2.37107e7	−	1.62059e8i	−0.0966545	−	0.660618i
$627$	2.42408e7	−	2.22410e8i	0.0983432	−	0.902303i
$628$	6.74053e7	−	1.24912e8i	0.272154	−	0.504342i
$629$	−2.15614e8	+	2.15614e8i	−0.866411	+	0.866411i
$630$	1.97511e8	+	2.28146e8i	0.789896	+	0.912413i
$631$			6.83317e7i			0.271978i	0.990710	+	0.135989i	$0.0434212\pi$
$631$			6.83317e7i			0.271978i	−0.990710	+	0.135989i	$0.956579\pi$
$632$	5.36890e7	−	2.50031e7i	0.212684	−	0.0990474i
$633$	1.11337e7	−	8.94526e6i	0.0438963	−	0.0352681i
$634$	−2.32769e8	−	1.73350e8i	−0.913394	−	0.680232i
$635$	−2.72478e8	+	2.72478e8i	−1.06417	+	1.06417i
$636$	−9.62643e7	+	1.39686e8i	−0.374191	+	0.542978i
$637$	−4.95390e7	+	4.95390e7i	−0.191659	+	0.191659i
$638$	5.04531e8	−	7.38176e7i	1.94279	−	0.284248i
$639$	−1.67817e8	−	3.70210e7i	−0.643182	−	0.141888i
$640$	−8.95450e7	−	3.79782e8i	−0.341587	−	1.44875i
$641$		−	2.44220e8i		−	0.927272i	−0.886026	−	0.463636i	$-0.846544\pi$
$641$		−	2.44220e8i		−	0.927272i	0.886026	−	0.463636i	$-0.153456\pi$
$642$	−2.09238e8	+	2.25195e8i	−0.790742	+	0.851048i
$643$	−1.46844e8	+	1.46844e8i	−0.552362	+	0.552362i	−0.927122	−	0.374760i	$-0.877725\pi$
$643$	−1.46844e8	+	1.46844e8i	−0.552362	+	0.552362i	0.374760	+	0.927122i	$0.377725\pi$
$644$	−1.38940e7	−	4.64654e7i	−0.0520201	−	0.173969i
$645$	−1.04096e7	−	1.13455e6i	−0.0387931	−	0.00422811i
$646$	2.70945e8	+	2.01781e8i	1.00504	+	0.748483i
$647$	−2.77293e8			−1.02383			−0.511914	−	0.859037i	$-0.671063\pi$
$647$	−2.77293e8			−1.02383			−0.511914	+	0.859037i	$0.671063\pi$
$648$	−2.72097e8	+	431014.i	−0.999999	+	0.00158404i
$649$			8.29695e7i			0.303518i
$650$	−2.11796e8	−	1.57730e8i	−0.771217	−	0.574349i
$651$	−3.50729e7	+	3.21795e8i	−0.127124	+	1.16637i
$652$	−1.78007e8	+	3.29872e8i	−0.642234	+	1.19015i
$653$	3.15371e8	+	3.15371e8i	1.13261	+	1.13261i	0.989741	+	0.142872i	$0.0456338\pi$
$653$	3.15371e8	+	3.15371e8i	1.13261	+	1.13261i	0.142872	+	0.989741i	$0.454366\pi$
$654$	−4.36802e7	+	4.70115e7i	−0.156153	+	0.168062i
$655$	4.78316e8			1.70212
$656$	2.98500e8	−	1.96044e8i	1.05739	−	0.694450i
$657$	1.34656e7	−	6.10397e7i	0.0474819	−	0.215237i
$658$	6.39801e7	−	9.36088e6i	0.224578	−	0.0328578i
$659$	−1.35879e8	−	1.35879e8i	−0.474784	−	0.474784i	0.428675	−	0.903459i	$-0.358981\pi$
$659$	−1.35879e8	−	1.35879e8i	−0.474784	−	0.474784i	−0.903459	+	0.428675i	$0.858981\pi$
$660$	1.05350e8	+	5.72458e8i	0.366439	+	1.99118i
$661$	4.33345e7	+	4.33345e7i	0.150048	+	0.150048i	0.778139	−	0.628092i	$-0.216164\pi$
$661$	4.33345e7	+	4.33345e7i	0.150048	+	0.150048i	−0.628092	+	0.778139i	$0.716164\pi$
$662$	−1.07395e8	−	7.99801e7i	−0.370177	−	0.275682i
$663$	−2.71165e8	−	3.37505e8i	−0.930450	−	1.15808i
$664$	2.02646e8	+	7.38713e7i	0.692205	+	0.252332i
$665$	−2.36824e8			−0.805305
$666$	1.26155e8	+	1.45723e8i	0.427054	+	0.493293i
$667$	−6.78347e7	−	6.78347e7i	−0.228599	−	0.228599i
$668$	1.07642e8	−	3.21869e7i	0.361119	−	0.107982i
$669$	−4.90718e8	−	5.34840e7i	−1.63890	−	0.178626i
$670$	−1.73888e7	−	1.18850e8i	−0.0578158	−	0.395161i
$671$			1.98621e8i			0.657442i
$672$	1.42524e8	+	2.00559e8i	0.469658	+	0.660897i
$673$	5.00528e7			0.164204			0.0821019	−	0.996624i	$-0.473837\pi$
$673$	5.00528e7			0.164204			0.0821019	+	0.996624i	$0.473837\pi$
$674$	−1.46217e8	+	2.13929e7i	−0.477550	+	0.0698700i
$675$	−1.19616e8	+	3.54192e8i	−0.388935	+	1.15167i
$676$	3.31187e7	+	1.10758e8i	0.107210	+	0.358537i
$677$	8.17318e7	−	8.17318e7i	0.263406	−	0.263406i	−0.563030	−	0.826436i	$-0.690365\pi$
$677$	8.17318e7	−	8.17318e7i	0.263406	−	0.263406i	0.826436	+	0.563030i	$0.190365\pi$
$678$	−1.94998e7	−	5.30865e8i	−0.0625664	−	1.70331i
$679$		−	3.57897e8i		−	1.14327i
$680$	−8.25766e8	−	3.01019e8i	−2.62622	−	0.957342i
$681$	2.16151e8	+	2.69032e8i	0.684409	+	0.851848i
$682$	−3.72940e8	+	5.00772e8i	−1.17567	+	1.57865i
$683$	3.52733e8	−	3.52733e8i	1.10709	−	1.10709i	0.113563	−	0.993531i	$-0.463774\pi$
$683$	3.52733e8	−	3.52733e8i	1.10709	−	1.10709i	0.993531	−	0.113563i	$-0.0362263\pi$
$684$	1.39512e8	−	1.61668e8i	0.435957	−	0.505191i
$685$	2.97198e8	−	2.97198e8i	0.924643	−	0.924643i
$686$	−5.08752e7	−	3.47724e8i	−0.157592	−	1.07711i
$687$	5.04378e7	+	6.27773e7i	0.155556	+	0.193612i
$688$	−8.36017e6	−	1.73201e6i	−0.0256714	−	0.00531846i
$689$			1.70622e8i			0.521647i
$690$	7.45409e7	−	8.02258e7i	0.226907	−	0.244212i
$691$	4.70485e7	−	4.70485e7i	0.142597	−	0.142597i	−0.632204	−	0.774802i	$-0.717850\pi$
$691$	4.70485e7	−	4.70485e7i	0.142597	−	0.142597i	0.774802	+	0.632204i	$0.217850\pi$
$692$	−6.68151e6	−	3.60550e6i	−0.0201631	−	0.0108805i
$693$	−1.97528e8	−	3.09346e8i	−0.593511	−	0.929491i
$694$	1.57409e7	−	2.11364e7i	0.0470926	−	0.0632344i
$695$	−1.14661e8			−0.341556
$696$	4.36503e8	+	2.15247e8i	1.29467	+	0.638424i
$697$		−	8.04420e8i		−	2.37566i
$698$	7.68285e7	−	1.03163e8i	0.225921	−	0.303359i
$699$	4.77899e8	+	5.20869e7i	1.39928	+	0.152510i
$700$	3.23877e8	−	9.68455e7i	0.944248	−	0.282348i
$701$	−2.27629e8	−	2.27629e8i	−0.660805	−	0.660805i	0.294765	−	0.955570i	$-0.404759\pi$
$701$	−2.27629e8	−	2.27629e8i	−0.660805	−	0.660805i	−0.955570	+	0.294765i	$0.904759\pi$
$702$	−2.25093e8	+	1.55648e8i	−0.650654	+	0.449918i
$703$	−1.51265e8			−0.435385
$704$	4.08934e7	+	4.72826e8i	0.117202	+	1.35514i
$705$	9.14484e7	+	1.13821e8i	0.260981	+	0.324829i
$706$	−7.67863e7	−	5.24822e8i	−0.218207	−	1.49141i
$707$	−2.65654e6	−	2.65654e6i	−0.00751723	−	0.00751723i
$708$	−4.49376e7	+	6.52076e7i	−0.126622	+	0.183738i
$709$	2.17211e8	+	2.17211e8i	0.609456	+	0.609456i	0.942804	−	0.333348i	$-0.108178\pi$
$709$	2.17211e8	+	2.17211e8i	0.609456	+	0.609456i	−0.333348	+	0.942804i	$0.608178\pi$
$710$	−2.09583e8	+	2.81422e8i	−0.585574	+	0.786290i
$711$	−8.23471e7	−	1.81660e7i	−0.229108	−	0.0505419i
$712$	−3.16952e8	+	1.47605e8i	−0.878119	+	0.408942i
$713$	1.17471e8			0.324088
$714$	5.53841e8	−	2.03438e7i	1.52156	−	0.0558903i
$715$	4.13959e8	+	4.13959e8i	1.13250	+	1.13250i
$716$	−2.05588e8	−	1.10940e8i	−0.560091	−	0.302238i
$717$	6.57531e7	−	6.03287e8i	0.178385	−	1.63669i
$718$	3.91495e8	−	5.72793e7i	1.05768	−	0.154748i
$719$		−	4.83068e7i		−	0.129963i	−0.997886	−	0.0649817i	$-0.979301\pi$
$719$		−	4.83068e7i		−	0.129963i	0.997886	−	0.0649817i	$-0.0206989\pi$
$720$	−2.27255e8	+	5.06966e8i	−0.608858	+	1.35826i
$721$	−4.07784e8			−1.08799
$722$	−3.02246e7	−	2.06580e8i	−0.0803061	−	0.548879i
$723$	−6.90497e8	−	7.52582e7i	−1.82704	−	0.199131i
$724$	−3.43044e8	−	1.85114e8i	−0.903927	−	0.487780i
$725$	4.72827e8	−	4.72827e8i	1.24076	−	1.24076i
$726$	−1.19412e7	−	3.25090e8i	−0.0312061	−	0.849559i
$727$		−	2.58996e8i		−	0.674047i	−0.941496	−	0.337023i	$-0.890580\pi$
$727$		−	2.58996e8i		−	0.674047i	0.941496	−	0.337023i	$-0.109420\pi$
$728$	2.32495e8	+	8.47522e7i	0.602587	+	0.219663i
$729$	3.08096e8	+	2.34886e8i	0.795250	+	0.606282i
$730$	−1.02361e8	−	7.62311e7i	−0.263127	−	0.195958i
$731$	−1.35986e7	+	1.35986e7i	−0.0348130	+	0.0348130i
$732$	−1.07576e8	+	1.56101e8i	−0.274273	+	0.397990i
$733$	−4.55339e8	+	4.55339e8i	−1.15617	+	1.15617i	−0.170881	+	0.985292i	$0.554661\pi$
$733$	−4.55339e8	+	4.55339e8i	−1.15617	+	1.15617i	−0.985292	+	0.170881i	$0.945339\pi$
$734$	9.64591e7	−	1.41129e7i	0.243924	−	0.0356884i
$735$	1.57866e8	−	1.26836e8i	0.397581	−	0.319433i
$736$	6.67504e7	−	5.93038e7i	0.167425	−	0.148747i
$737$			1.46095e8i			0.364949i
$738$	−5.07167e8	−	3.65014e7i	−1.26178	−	0.0908114i
$739$	4.84080e8	−	4.84080e8i	1.19946	−	1.19946i	0.225126	−	0.974330i	$-0.427721\pi$
$739$	4.84080e8	−	4.84080e8i	1.19946	−	1.19946i	0.974330	−	0.225126i	$-0.0722792\pi$
$740$	3.77051e8	−	1.12746e8i	0.930476	−	0.278230i
$741$	2.32706e7	−	2.13509e8i	0.0571943	−	0.524760i
$742$	−1.75174e8	−	1.30457e8i	−0.428802	−	0.319342i
$743$	1.77242e8			0.432115			0.216057	−	0.976381i	$-0.430680\pi$
$743$	1.77242e8			0.432115			0.216057	+	0.976381i	$0.430680\pi$
$744$	−5.64328e8	+	1.91578e8i	−1.37029	+	0.465187i
$745$		−	1.00395e8i		−	0.242797i
$746$	1.55259e8	+	1.15626e8i	0.373974	+	0.278509i
$747$	−1.65278e8	−	2.58839e8i	−0.396508	−	0.620967i
$748$	9.40787e8	+	5.07670e8i	2.24795	+	1.21304i
$749$	−2.79852e8	−	2.79852e8i	−0.666013	−	0.666013i
$750$	9.91678e7	+	9.21406e7i	0.235064	+	0.218407i
$751$	−4.07457e8			−0.961970			−0.480985	−	0.876729i	$-0.659721\pi$
$751$	−4.07457e8			−0.961970			−0.480985	+	0.876729i	$0.659721\pi$
$752$	6.53513e7	+	9.95053e7i	0.153674	+	0.233988i
$753$	−6.22491e7	+	5.00135e7i	−0.145797	+	0.117139i
$754$	4.84338e8	−	7.08631e7i	1.12989	−	0.165313i
$755$	5.47188e8	+	5.47188e8i	1.27144	+	1.27144i
$756$	1.23049e7	−	3.50106e8i	0.0284781	−	0.810279i
$757$	−5.08053e8	−	5.08053e8i	−1.17117	−	1.17117i	−0.981930	−	0.189243i	$-0.939397\pi$
$757$	−5.08053e8	−	5.08053e8i	−1.17117	−	1.17117i	−0.189243	−	0.981930i	$-0.560603\pi$
$758$	−3.09994e7	−	2.30862e7i	−0.0711779	−	0.0530083i
$759$	−1.03834e8	+	8.34247e7i	−0.237474	+	0.190796i
$760$	−1.84070e8	−	3.95253e8i	−0.419317	−	0.900397i
$761$	−4.30869e8			−0.977668			−0.488834	−	0.872377i	$-0.662578\pi$
$761$	−4.30869e8			−0.977668			−0.488834	+	0.872377i	$0.662578\pi$
$762$	4.47048e8	−	1.64210e7i	1.01039	−	0.0371138i
$763$	−5.84216e7	−	5.84216e7i	−0.131522	−	0.131522i
$764$	2.47440e7	+	8.27505e7i	0.0554868	+	0.185563i
$765$	6.73492e8	+	1.05475e9i	1.50435	+	2.35594i
$766$	9.31958e7	+	6.36978e8i	0.207353	+	1.41722i
$767$			7.96487e7i			0.176520i
$768$	−2.23951e8	+	3.93753e8i	−0.494389	+	0.869241i
$769$	−6.00972e8			−1.32153			−0.660763	−	0.750595i	$-0.729767\pi$
$769$	−6.00972e8			−1.32153			−0.660763	+	0.750595i	$0.729767\pi$
$770$	−7.41514e8	+	1.08490e8i	−1.62423	+	0.237640i
$771$	−3.94645e7	+	3.62088e8i	−0.0861080	+	0.790044i
$772$	−4.03651e8	+	1.20700e8i	−0.877313	+	0.262334i
$773$	−5.00317e8	+	5.00317e8i	−1.08320	+	1.08320i	−0.0869869	+	0.996209i	$0.527724\pi$
$773$	−5.00317e8	+	5.00317e8i	−1.08320	+	1.08320i	−0.996209	+	0.0869869i	$0.972276\pi$
$774$	7.95652e6	+	9.19062e6i	0.0171593	+	0.0198208i
$775$			8.18809e8i			1.75905i
$776$	5.97320e8	−	2.78174e8i	1.27827	−	0.595293i
$777$	−1.93452e8	+	1.55427e8i	−0.412392	+	0.331332i
$778$	5.34680e7	−	7.17952e7i	0.113542	−	0.152460i
$779$	2.82174e8	−	2.82174e8i	0.596904	−	0.596904i
$780$	1.01133e8	+	5.49546e8i	0.213113	+	1.15803i
$781$	3.01781e8	−	3.01781e8i	0.633489	−	0.633489i
$782$	−2.91165e7	−	1.99006e8i	−0.0608861	−	0.416147i
$783$	−3.07459e8	−	6.21020e8i	−0.640474	−	1.29366i
$784$	1.38010e8	−	9.06399e7i	0.286394	−	0.188092i
$785$			4.12641e8i			0.853028i
$786$	−4.06794e8	−	3.77968e8i	−0.837736	−	0.778373i
$787$	6.61148e8	−	6.61148e8i	1.35636	−	1.35636i	0.477997	−	0.878362i	$-0.341363\pi$
$787$	6.61148e8	−	6.61148e8i	1.35636	−	1.35636i	0.878362	−	0.477997i	$-0.158637\pi$
$788$	−2.26988e8	+	4.20641e8i	−0.463899	+	0.859673i
$789$	−4.49056e8	−	4.89433e7i	−0.914261	−	0.0996465i
$790$	−1.02841e8	+	1.38092e8i	−0.208587	+	0.280084i
$791$	6.83942e8			1.38194
$792$	3.62763e8	−	5.70107e8i	0.730209	−	1.14757i
$793$			1.90671e8i			0.382354i
$794$	−1.88339e7	+	2.52896e7i	−0.0376252	+	0.0505219i
$795$	5.34366e7	−	4.90283e8i	0.106350	−	0.975765i
$796$	−2.57154e8	−	8.59990e8i	−0.509863	−	1.70512i
$797$	1.49477e8	+	1.49477e8i	0.295256	+	0.295256i	0.839152	−	0.543897i	$-0.183052\pi$
$797$	1.49477e8	+	1.49477e8i	0.295256	+	0.295256i	−0.543897	+	0.839152i	$0.683052\pi$
$798$	2.01412e8	+	1.87140e8i	0.396348	+	0.368262i
$799$	2.68154e8			0.525707
$800$	4.13365e8	+	4.65269e8i	0.807353	+	0.908729i
$801$	4.86134e8	+	1.07243e8i	0.945929	+	0.208675i
$802$	3.35095e7	+	2.29032e8i	0.0649599	+	0.443990i
$803$	1.09766e8	+	1.09766e8i	0.211993	+	0.211993i
$804$	−7.91272e7	+	1.14819e8i	−0.152250	+	0.220926i
$805$	9.96972e7	+	9.96972e7i	0.191115	+	0.191115i
$806$	−3.58014e8	+	4.80729e8i	−0.683745	+	0.918112i
$807$	4.40893e8	+	5.48756e8i	0.838904	+	1.04414i
$808$	2.36891e6	−	6.49848e6i	0.00449070	−	0.0123191i
$809$	−1.29211e8			−0.244036			−0.122018	−	0.992528i	$-0.538937\pi$
$809$	−1.29211e8			−0.244036			−0.122018	+	0.992528i	$0.538937\pi$
$810$	6.95553e8	−	3.76760e8i	1.30881	−	0.708941i
$811$	−7.25912e8	−	7.25912e8i	−1.36088	−	1.36088i	−0.872792	−	0.488092i	$-0.837693\pi$
$811$	−7.25912e8	−	7.25912e8i	−1.36088	−	1.36088i	−0.488092	−	0.872792i	$-0.662307\pi$
$812$	−2.97570e8	+	5.51441e8i	−0.555804	+	1.02999i
$813$	−2.78061e8	−	3.03063e7i	−0.517450	−	0.0563976i
$814$	−4.73624e8	+	6.92956e7i	−0.878134	+	0.128479i
$815$		−	1.08972e9i		−	2.01299i
$816$	4.64424e8	+	9.08534e8i	0.854759	+	1.67213i
$817$	−9.54019e6			−0.0174941
$818$	1.02662e8	+	7.01678e8i	0.187564	+	1.28197i
$819$	−1.89622e8	−	2.96965e8i	−0.345174	−	0.540572i
$820$	−4.93041e8	+	9.13677e8i	−0.894214	+	1.65711i
$821$	−4.00224e8	+	4.00224e8i	−0.723225	+	0.723225i	−0.969261	−	0.246036i	$-0.920872\pi$
$821$	−4.00224e8	+	4.00224e8i	−0.723225	+	0.723225i	0.246036	+	0.969261i	$0.420872\pi$
$822$	−4.87606e8	+	1.79108e7i	−0.877917	+	0.0322478i
$823$			4.88436e8i			0.876209i	0.898924	+	0.438105i	$0.144350\pi$
$823$			4.88436e8i			0.876209i	−0.898924	+	0.438105i	$0.855650\pi$
$824$	−3.16948e8	−	6.80581e8i	−0.566509	−	1.21646i
$825$	−5.81494e8	−	7.23755e8i	−1.03558	−	1.28893i
$826$	−8.17736e7	−	6.08993e7i	−0.145102	−	0.108062i
$827$	−1.29960e8	+	1.29960e8i	−0.229771	+	0.229771i	−0.812597	−	0.582826i	$-0.801947\pi$
$827$	−1.29960e8	+	1.29960e8i	−0.229771	+	0.229771i	0.582826	+	0.812597i	$0.301947\pi$
$828$	−1.26790e8	+	9.32711e6i	−0.223354	+	0.0164307i
$829$	2.19888e8	−	2.19888e8i	0.385956	−	0.385956i	−0.487287	−	0.873242i	$-0.662013\pi$
$829$	2.19888e8	−	2.19888e8i	0.385956	−	0.385956i	0.873242	+	0.487287i	$0.162013\pi$
$830$	−6.20448e8	+	9.07772e7i	−1.08510	+	0.158761i
$831$	3.28723e8	+	4.09144e8i	0.572831	+	0.712973i
$832$	3.92567e7	+	4.53901e8i	0.0681623	+	0.788119i
$833$		−	3.71920e8i		−	0.643450i
$834$	9.75162e7	+	9.06061e7i	0.168104	+	0.156192i
$835$	−2.30958e8	+	2.30958e8i	−0.396711	+	0.396711i
$836$	1.51928e8	+	5.08088e8i	0.260028	+	0.869602i
$837$	8.03937e8	+	2.71501e8i	1.37103	+	0.463016i
$838$	4.26172e8	+	3.17383e8i	0.724191	+	0.539327i
$839$	−8.85957e8			−1.50012			−0.750061	−	0.661368i	$-0.769976\pi$
$839$	−8.85957e8			−1.50012			−0.750061	+	0.661368i	$0.769976\pi$
$840$	−6.41533e8	−	3.16350e8i	−1.08238	−	0.533741i
$841$			6.44647e8i			1.08376i
$842$	5.43110e8	+	4.04470e8i	0.909811	+	0.677564i
$843$	−9.32938e7	−	1.01682e7i	−0.155729	−	0.0169731i
$844$	−1.60769e7	+	2.97928e7i	−0.0267408	+	0.0495546i
$845$	−2.37645e8	−	2.37645e8i	−0.393875	−	0.393875i
$846$	1.21678e7	−	1.69065e8i	0.0200955	−	0.279217i
$847$	4.18832e8			0.689270
$848$	8.15764e7	−	3.93758e8i	0.133776	−	0.645716i
$849$	4.10102e8	+	5.10432e8i	0.670145	+	0.834094i
$850$	1.38713e9	−	2.02950e8i	2.25871	−	0.330470i
$851$	6.36792e7	+	6.36792e7i	0.103326	+	0.103326i
$852$	4.00626e8	−	7.37273e7i	0.647769	−	0.119209i
$853$	−7.23223e8	−	7.23223e8i	−1.16527	−	1.16527i	−0.983306	−	0.181961i	$-0.941755\pi$
$853$	−7.23223e8	−	7.23223e8i	−1.16527	−	1.16527i	−0.181961	−	0.983306i	$-0.558245\pi$
$854$	−1.95758e8	−	1.45787e8i	−0.314301	−	0.234070i
$855$	−1.33736e8	+	6.06230e8i	−0.213969	+	0.969927i
$856$	2.49552e8	−	6.84579e8i	0.397868	−	1.09145i
$857$	3.10382e8			0.493122			0.246561	−	0.969127i	$-0.420699\pi$
$857$	3.10382e8			0.493122			0.246561	+	0.969127i	$0.420699\pi$
$858$	−2.49475e7	−	6.79173e8i	−0.0394970	−	1.07527i
$859$	5.19555e8	+	5.19555e8i	0.819695	+	0.819695i	0.986064	−	0.166369i	$-0.0532042\pi$
$859$	5.19555e8	+	5.19555e8i	0.819695	+	0.819695i	−0.166369	+	0.986064i	$0.553204\pi$
$860$	2.37803e7	−	7.11077e6i	0.0373871	−	0.0111795i
$861$	7.09323e7	−	6.50807e8i	0.111131	−	1.01963i
$862$	−1.55159e8	−	1.06049e9i	−0.242245	−	1.65570i
$863$		−	5.32707e8i		−	0.828812i	−0.910092	−	0.414406i	$-0.863989\pi$
$863$		−	5.32707e8i		−	0.828812i	0.910092	−	0.414406i	$-0.136011\pi$
$864$	5.93882e8	−	2.51582e8i	0.920787	−	0.390067i
$865$	2.20721e7			0.0341032
$866$	9.80362e7	−	1.43436e7i	0.150950	−	0.0220854i
$867$	1.63695e9	+	1.78414e8i	2.51176	+	0.273761i
$868$	−2.19818e8	−	7.35130e8i	−0.336128	−	1.12410i
$869$	1.48082e8	−	1.48082e8i	0.225655	−	0.225655i
$870$	−1.41394e9	+	5.19371e7i	−2.14721	+	0.0788715i
$871$			1.40248e8i			0.212247i
$872$	5.20961e7	−	1.42912e8i	0.0785699	−	0.215536i
$873$	−9.16157e8	−	2.02107e8i	−1.37698	−	0.303766i
$874$	5.95938e7	−	8.00207e7i	0.0892620	−	0.119858i
$875$	−1.23237e8	+	1.23237e8i	−0.183957	+	0.183957i
$876$	2.68166e7	+	1.45719e8i	0.0398926	+	0.216772i
$877$	−6.31594e8	+	6.31594e8i	−0.936352	+	0.936352i	−0.998092	−	0.0617404i	$-0.980335\pi$
$877$	−6.31594e8	+	6.31594e8i	−0.936352	+	0.936352i	0.0617404	+	0.998092i	$0.480335\pi$
$878$	−8.55621e7	−	5.84803e8i	−0.126415	−	0.864025i
$879$	−9.83626e8	+	7.90285e8i	−1.44832	+	1.16364i
$880$	−7.57406e8	−	1.15324e9i	−1.11143	−	1.69228i
$881$			6.34080e8i			0.927292i	0.886020	+	0.463646i	$0.153459\pi$
$881$			6.34080e8i			0.927292i	−0.886020	+	0.463646i	$0.846541\pi$
$882$	−2.34487e8	−	1.68763e7i	−0.341753	−	0.0245963i
$883$	4.06667e8	−	4.06667e8i	0.590686	−	0.590686i	−0.347130	−	0.937817i	$-0.612844\pi$
$883$	4.06667e8	−	4.06667e8i	0.590686	−	0.590686i	0.937817	+	0.347130i	$0.112844\pi$
$884$	9.03133e8	+	4.87351e8i	1.30736	+	0.705481i
$885$	2.49450e7	−	2.28871e8i	0.0359876	−	0.330188i
$886$	−6.87855e8	+	9.23630e8i	−0.988999	+	1.32800i
$887$	1.08557e9			1.55556			0.777782	−	0.628534i	$-0.216345\pi$
$887$	1.08557e9			1.55556			0.777782	+	0.628534i	$0.216345\pi$
$888$	−4.09764e8	−	2.02061e8i	−0.585187	−	0.288565i
$889$			5.75957e8i			0.819757i
$890$	6.07122e8	−	8.15224e8i	0.861204	−	1.15640i
$891$	−9.03421e8	+	3.30949e8i	−1.27719	+	0.467873i
$892$	1.12103e9	−	3.35209e8i	1.57951	−	0.472303i
$893$	9.40629e7	+	9.40629e7i	0.132088	+	0.132088i
$894$	−7.93328e7	+	8.53832e7i	−0.111030	+	0.119498i
$895$	6.79150e8			0.947319
$896$	−4.96026e8	−	3.06748e8i	−0.689574	−	0.426440i
$897$	−9.96784e7	+	8.00857e7i	−0.138110	+	0.110963i
$898$	−3.34686e7	−	2.28752e8i	−0.0462177	−	0.315891i
$899$	−1.07321e9	−	1.07321e9i	−1.47709	−	1.47709i
$900$	−6.50126e7	−	8.83761e8i	−0.0891805	−	1.21229i
$901$	−6.40482e8	−	6.40482e8i	−0.875654	−	0.875654i
$902$	7.54243e8	−	1.01277e9i	1.02776	−	1.38004i
$903$	−1.22009e7	+	9.80267e6i	−0.0165702	+	0.0133132i
$904$	5.31591e8	+	1.14148e9i	0.719569	+	1.54513i
$905$	1.13323e9			1.52887
$906$	−3.29766e7	−	8.97760e8i	−0.0443427	−	1.20719i
$907$	9.31714e8	+	9.31714e8i	1.24871	+	1.24871i	0.956291	+	0.292417i	$0.0944596\pi$
$907$	9.31714e8	+	9.31714e8i	1.24871	+	1.24871i	0.292417	+	0.956291i	$0.405540\pi$
$908$	−7.19905e8	−	3.88477e8i	−0.961652	−	0.518929i
$909$	−8.30048e6	+	5.30014e6i	−0.0110512	+	0.00705660i
$910$	−7.11836e8	+	1.04148e8i	−0.944617	+	0.138206i
$911$			1.59649e8i			0.211159i	0.994411	+	0.105580i	$0.0336698\pi$
$911$			1.59649e8i			0.211159i	−0.994411	+	0.105580i	$0.966330\pi$
$912$	−1.55785e8	+	4.81605e8i	−0.205371	+	0.634901i
$913$	7.62678e8			1.00214
$914$	−1.50722e7	−	1.03016e8i	−0.0197396	−	0.134917i
$915$	5.97159e7	−	5.47896e8i	0.0779519	−	0.715212i
$916$	−1.67986e8	−	9.06493e7i	−0.218569	−	0.117945i
$917$	5.05527e8	−	5.05527e8i	0.655596	−	0.655596i
$918$	2.60682e8	−	1.42923e9i	0.336963	−	1.84746i
$919$			9.46045e8i			1.21889i	0.792827	+	0.609446i	$0.208608\pi$
$919$			9.46045e8i			1.21889i	−0.792827	+	0.609446i	$0.791392\pi$
$920$	−8.89028e7	+	2.43881e8i	−0.114170	+	0.313195i
$921$	−6.59210e8	+	5.29636e8i	−0.843810	+	0.677951i
$922$	6.02743e7	+	4.48881e7i	0.0769023	+	0.0572715i
$923$	2.89703e8	−	2.89703e8i	0.368424	−	0.368424i
$924$	7.16367e8	+	4.93681e8i	0.908070	+	0.625793i
$925$	−4.43862e8	+	4.43862e8i	−0.560819	+	0.560819i
$926$	7.88541e8	−	1.15371e8i	0.993096	−	0.145299i
$927$	−2.30279e8	+	1.04386e9i	−0.289078	+	1.31040i
$928$	−1.15163e9	−	6.80316e7i	−1.44101	−	0.0851269i
$929$		−	1.18151e9i		−	1.47364i	−0.676089	−	0.736820i	$-0.736327\pi$
$929$		−	1.18151e9i		−	1.47364i	0.676089	−	0.736820i	$-0.263673\pi$
$930$	1.17931e9	−	1.26925e9i	1.46616	−	1.57797i
$931$	1.30462e8	−	1.30462e8i	0.161672	−	0.161672i
$932$	−1.09174e9	+	3.26453e8i	−1.34857	+	0.403248i
$933$	9.87662e8	+	1.07647e8i	1.21608	+	0.132543i
$934$	5.58166e7	+	4.15683e7i	0.0685051	+	0.0510178i
$935$	−3.10784e9			−3.80211
$936$	3.48244e8	−	5.47289e8i	0.424674	−	0.667405i
$937$			6.79076e8i			0.825467i	0.910852	+	0.412734i	$0.135426\pi$
$937$			6.79076e8i			0.825467i	−0.910852	+	0.412734i	$0.864574\pi$
$938$	−1.43989e8	−	1.07233e8i	−0.174470	−	0.129933i
$939$	5.98927e7	−	5.49518e8i	0.0723398	−	0.663721i
$940$	−3.04575e8	−	1.64356e8i	−0.366700	−	0.197880i
$941$	−6.62319e8	−	6.62319e8i	−0.794874	−	0.794874i	0.187408	−	0.982282i	$-0.439991\pi$
$941$	−6.62319e8	−	6.62319e8i	−0.794874	−	0.794874i	−0.982282	+	0.187408i	$0.939991\pi$
$942$	3.26071e8	−	3.50939e8i	0.390086	−	0.419836i
$943$	−2.37577e8			−0.283315
$944$	3.80811e7	−	1.83812e8i	0.0452682	−	0.218503i
$945$	4.51875e8	+	9.12718e8i	0.535455	+	1.08154i
$946$	−2.98711e7	+	4.37042e6i	−0.0352840	+	0.00516238i
$947$	7.40718e8	+	7.40718e8i	0.872173	+	0.872173i	0.992709	−	0.120536i	$-0.0384612\pi$
$947$	7.40718e8	+	7.40718e8i	0.872173	+	0.872173i	−0.120536	+	0.992709i	$0.538461\pi$
$948$	1.96585e8	−	3.61776e7i	0.230741	−	0.0424634i
$949$	1.05373e8	+	1.05373e8i	0.123291	+	0.123291i
$950$	5.57767e8	+	4.15386e8i	0.650552	+	0.484486i
$951$	−6.13500e8	−	7.63591e8i	−0.713302	−	0.887809i
$952$	−1.19089e9	+	5.54599e8i	−1.38026	+	0.642789i
$953$	−5.23336e8			−0.604648			−0.302324	−	0.953205i	$-0.597762\pi$
$953$	−5.23336e8			−0.604648			−0.302324	+	0.953205i	$0.597762\pi$
$954$	−4.32871e8	+	3.74746e8i	−0.498555	+	0.431610i
$955$	−1.77551e8	−	1.77551e8i	−0.203852	−	0.203852i
$956$	4.12105e8	+	1.37819e9i	0.471666	+	1.57737i
$957$	1.71079e9	+	1.86461e8i	1.95192	+	0.212742i
$958$	1.82135e8	+	1.24486e9i	0.207156	+	1.41588i
$959$		−	6.28210e8i		−	0.712277i
$960$	2.93518e7	−	1.31658e9i	0.0331757	−	1.48811i
$961$	9.71014e8			1.09410
$962$	−4.54668e8	+	6.65221e7i	−0.510704	+	0.0747207i
$963$	−8.74410e8	+	5.58341e8i	−0.979121	+	0.625202i
$964$	1.57742e9	−	4.71678e8i	1.76082	−	0.526519i
$965$	8.66085e8	−	8.66085e8i	0.963781	−	0.963781i
$966$	−6.00831e6	−	1.63571e8i	−0.00666532	−	0.181458i
$967$		−	1.36471e9i		−	1.50925i	−0.656157	−	0.754624i	$-0.727819\pi$
$967$		−	1.36471e9i		−	1.50925i	0.656157	−	0.754624i	$-0.272181\pi$
$968$	3.25535e8	+	6.99019e8i	0.358899	+	0.770660i
$969$	7.14117e8	+	8.88824e8i	0.784871	+	0.976887i
$970$	−1.14417e9	+	1.53635e9i	−1.25365	+	1.68336i
$971$	−1.98275e8	+	1.98275e8i	−0.216576	+	0.216576i	−0.807054	−	0.590478i	$-0.798939\pi$
$971$	−1.98275e8	+	1.98275e8i	−0.216576	+	0.216576i	0.590478	+	0.807054i	$0.298939\pi$
$972$	−8.89266e8	−	2.29206e8i	−0.968351	−	0.249590i
$973$	−1.21184e8	+	1.21184e8i	−0.131555	+	0.131555i
$974$	1.57335e8	+	1.07536e9i	0.170274	+	1.16379i
$975$	−5.58220e8	−	6.94787e8i	−0.602271	−	0.749615i
$976$	9.11624e7	−	4.40028e8i	0.0980542	−	0.473293i
$977$			1.41444e9i			1.51671i	0.651845	+	0.758353i	$0.273995\pi$
$977$			1.41444e9i			1.51671i	−0.651845	+	0.758353i	$0.726005\pi$
$978$	−8.61102e8	+	9.26774e8i	−0.920530	+	0.990735i
$979$	−8.74201e8	+	8.74201e8i	−0.931673	+	0.931673i
$980$	−2.27955e8	+	4.22435e8i	−0.242199	+	0.448829i
$981$	−1.82541e8	+	1.16558e8i	−0.193354	+	0.123463i
$982$	−7.23074e8	+	9.70921e8i	−0.763569	+	1.02530i
$983$	−2.05876e8			−0.216743			−0.108372	−	0.994110i	$-0.534564\pi$
$983$	−2.05876e8			−0.216743			−0.108372	+	0.994110i	$0.534564\pi$
$984$	1.14131e9	−	3.87453e8i	1.19789	−	0.406662i
$985$		−	1.38957e9i		−	1.45402i
$986$	−1.55211e9	+	2.08412e9i	−1.61916	+	2.17416i
$987$	2.16947e8	+	2.36453e7i	0.225633	+	0.0245920i
$988$	1.45847e8	+	4.87753e8i	0.151227	+	0.505742i
$989$	4.01620e6	+	4.01620e6i	0.00415170	+	0.00415170i
$990$	−1.41022e8	+	1.95942e9i	−0.145338	+	2.01940i
$991$	2.33256e8			0.239669			0.119834	−	0.992794i	$-0.461764\pi$
$991$	2.33256e8			0.239669			0.119834	+	0.992794i	$0.461764\pi$
$992$	1.05606e9	−	9.38247e8i	1.08182	−	0.961130i
$993$	−2.83056e8	−	3.52305e8i	−0.289084	−	0.359808i
$994$	7.59254e7	+	5.18938e8i	0.0773086	+	0.528392i
$995$	1.84522e9	+	1.84522e9i	1.87317	+	1.87317i
$996$	5.99406e8	+	4.13078e8i	0.606657	+	0.418075i
$997$	6.06006e8	+	6.06006e8i	0.611493	+	0.611493i	0.943335	−	0.331842i	$-0.107670\pi$
$997$	6.06006e8	+	6.06006e8i	0.611493	+	0.611493i	−0.331842	+	0.943335i	$0.607670\pi$
$998$	4.74920e8	−	6.37708e8i	0.477781	−	0.641550i
$999$	2.88624e8	+	5.82976e8i	0.289492	+	0.584729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.1	✓	92
3.2	odd	2	inner	48.7.i.a.5.46	yes	92
4.3	odd	2		192.7.i.a.113.45		92
12.11	even	2		192.7.i.a.113.22		92
16.3	odd	4		192.7.i.a.17.22		92
16.13	even	4	inner	48.7.i.a.29.46	yes	92
48.29	odd	4	inner	48.7.i.a.29.1	yes	92
48.35	even	4		192.7.i.a.17.45		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.1	✓	92	1.1	even	1	trivial
48.7.i.a.5.46	yes	92	3.2	odd	2	inner
48.7.i.a.29.1	yes	92	48.29	odd	4	inner
48.7.i.a.29.46	yes	92	16.13	even	4	inner
192.7.i.a.17.22		92	16.3	odd	4
192.7.i.a.17.45		92	48.35	even	4
192.7.i.a.113.22		92	12.11	even	2
192.7.i.a.113.45		92	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.91573 + 1.15814i) q^{2} +(-26.8410 - 2.92544i) q^{3} +(61.3174 - 18.3351i) q^{4} +(-131.564 + 131.564i) q^{5} +(215.854 - 7.92879i) q^{6} +278.097i q^{7} +(-464.137 + 216.150i) q^{8} +(711.884 + 157.044i) q^{9} +O(q^{10})\)	\(q+(-7.91573 + 1.15814i) q^{2} +(-26.8410 - 2.92544i) q^{3} +(61.3174 - 18.3351i) q^{4} +(-131.564 + 131.564i) q^{5} +(215.854 - 7.92879i) q^{6} +278.097i q^{7} +(-464.137 + 216.150i) q^{8} +(711.884 + 157.044i) q^{9} +(889.056 - 1193.80i) q^{10} +(-1280.16 + 1280.16i) q^{11} +(-1699.46 + 312.753i) q^{12} +(-1228.92 + 1228.92i) q^{13} +(-322.077 - 2201.34i) q^{14} +(3916.20 - 3146.44i) q^{15} +(3423.65 - 2248.52i) q^{16} -9226.29i q^{17} +(-5816.95 - 418.653i) q^{18} +(3236.39 - 3236.39i) q^{19} +(-5654.93 + 10479.4i) q^{20} +(813.558 - 7464.42i) q^{21} +(8650.79 - 11616.0i) q^{22} -2724.89 q^{23} +(13090.3 - 4443.88i) q^{24} -18993.3i q^{25} +(8304.55 - 11151.1i) q^{26} +(-18648.3 - 6297.80i) q^{27} +(5098.94 + 17052.2i) q^{28} +(24894.5 + 24894.5i) q^{29} +(-27355.6 + 29441.9i) q^{30} -43110.5 q^{31} +(-24496.6 + 21763.8i) q^{32} +(38105.9 - 30615.8i) q^{33} +(10685.4 + 73032.8i) q^{34} +(-36587.6 - 36587.6i) q^{35} +(46530.3 - 3422.93i) q^{36} +(-23369.5 - 23369.5i) q^{37} +(-21870.2 + 29366.6i) q^{38} +(36580.7 - 29390.5i) q^{39} +(32626.2 - 89501.4i) q^{40} +87187.8 q^{41} +(2204.98 + 60028.5i) q^{42} +(-1473.89 - 1473.89i) q^{43} +(-55024.3 + 101968. i) q^{44} +(-114320. + 72997.0i) q^{45} +(21569.5 - 3155.81i) q^{46} +29064.1i q^{47} +(-98472.2 + 50337.0i) q^{48} +40310.9 q^{49} +(21996.9 + 150345. i) q^{50} +(-26991.0 + 247643. i) q^{51} +(-52822.0 + 97886.8i) q^{52} +(69419.2 - 69419.2i) q^{53} +(154908. + 28254.2i) q^{54} -336847. i q^{55} +(-60110.7 - 129075. i) q^{56} +(-96336.0 + 77400.2i) q^{57} +(-225889. - 168226. i) q^{58} +(32405.9 - 32405.9i) q^{59} +(182441. - 264735. i) q^{60} +(77576.6 - 77576.6i) q^{61} +(341251. - 49928.2i) q^{62} +(-43673.5 + 197973. i) q^{63} +(168702. - 200646. i) q^{64} -323365. i q^{65} +(-266178. + 286478. i) q^{66} +(57061.2 - 57061.2i) q^{67} +(-169165. - 565732. i) q^{68} +(73138.9 + 7971.50i) q^{69} +(331991. + 247244. i) q^{70} -235737. q^{71} +(-364357. + 80983.7i) q^{72} -85743.9i q^{73} +(212051. + 157921. i) q^{74} +(-55563.7 + 509799. i) q^{75} +(139108. - 257787. i) q^{76} +(-356009. - 356009. i) q^{77} +(-255525. + 275012. i) q^{78} -115675. q^{79} +(-154605. + 746254. i) q^{80} +(482115. + 223594. i) q^{81} +(-690155. + 100976. i) q^{82} +(-297884. - 297884. i) q^{83} +(-86975.7 - 472616. i) q^{84} +(1.21385e6 + 1.21385e6i) q^{85} +(13373.9 + 9959.96i) q^{86} +(-595367. - 741021. i) q^{87} +(317463. - 870877. i) q^{88} +682884. q^{89} +(820382. - 710223. i) q^{90} +(-341760. - 341760. i) q^{91} +(-167083. + 49961.1i) q^{92} +(1.15713e6 + 126117. i) q^{93} +(-33660.4 - 230064. i) q^{94} +851586. i q^{95} +(721182. - 512499. i) q^{96} -1.28695e6 q^{97} +(-319090. + 46685.8i) q^{98} +(-1.11237e6 + 710284. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Introduction

L-functions

Modular forms

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