LMFDB - Embedded newform 48.7.i.a.5.3

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			5.3
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.81038 - 1.73145i) q^{2} +(-5.41236 - 26.4520i) q^{3} +(58.0042 + 27.0465i) q^{4} +(-54.1549 + 54.1549i) q^{5} +(-3.52753 + 215.971i) q^{6} -639.122i q^{7} +(-406.205 - 311.675i) q^{8} +(-670.413 + 286.335i) q^{9} +O(q^{10})$	\(q+(-7.81038 - 1.73145i) q^{2} +(-5.41236 - 26.4520i) q^{3} +(58.0042 + 27.0465i) q^{4} +(-54.1549 + 54.1549i) q^{5} +(-3.52753 + 215.971i) q^{6} -639.122i q^{7} +(-406.205 - 311.675i) q^{8} +(-670.413 + 286.335i) q^{9} +(516.737 - 329.204i) q^{10} +(865.761 - 865.761i) q^{11} +(401.494 - 1680.71i) q^{12} +(-1382.53 + 1382.53i) q^{13} +(-1106.60 + 4991.79i) q^{14} +(1725.61 + 1139.40i) q^{15} +(2632.97 + 3137.62i) q^{16} +894.209i q^{17} +(5731.95 - 1075.60i) q^{18} +(-5724.27 + 5724.27i) q^{19} +(-4605.91 + 1676.51i) q^{20} +(-16906.0 + 3459.16i) q^{21} +(-8260.95 + 5262.91i) q^{22} -6298.37 q^{23} +(-6045.88 + 12431.8i) q^{24} +9759.49i q^{25} +(13191.9 - 8404.33i) q^{26} +(11202.6 + 16184.0i) q^{27} +(17286.0 - 37071.7i) q^{28} +(18594.2 + 18594.2i) q^{29} +(-11504.9 - 11886.9i) q^{30} -6159.23 q^{31} +(-15131.9 - 29064.9i) q^{32} +(-27586.9 - 18215.3i) q^{33} +(1548.28 - 6984.12i) q^{34} +(34611.6 + 34611.6i) q^{35} +(-46631.1 - 1523.69i) q^{36} +(2390.27 + 2390.27i) q^{37} +(54620.0 - 34797.5i) q^{38} +(44053.5 + 29087.9i) q^{39} +(38876.7 - 5119.29i) q^{40} -65647.4 q^{41} +(138032. + 2254.52i) q^{42} +(-99064.2 - 99064.2i) q^{43} +(73633.6 - 26801.9i) q^{44} +(20799.7 - 51812.6i) q^{45} +(49192.7 + 10905.3i) q^{46} +54149.8i q^{47} +(68745.7 - 86629.2i) q^{48} -290827. q^{49} +(16898.0 - 76225.4i) q^{50} +(23653.6 - 4839.78i) q^{51} +(-117585. + 42800.0i) q^{52} +(181923. - 181923. i) q^{53} +(-59475.3 - 145800. i) q^{54} +93770.4i q^{55} +(-199198. + 259615. i) q^{56} +(182400. + 120436. i) q^{57} +(-113033. - 177423. i) q^{58} +(-114825. + 114825. i) q^{59} +(69275.8 + 112762. i) q^{60} +(16629.9 - 16629.9i) q^{61} +(48106.0 + 10664.4i) q^{62} +(183003. + 428475. i) q^{63} +(67861.6 + 253208. i) q^{64} -149742. i q^{65} +(183925. + 190033. i) q^{66} +(92916.9 - 92916.9i) q^{67} +(-24185.2 + 51867.9i) q^{68} +(34089.1 + 166604. i) q^{69} +(-210402. - 330258. i) q^{70} -678777. q^{71} +(361569. + 92639.9i) q^{72} -66507.2i q^{73} +(-14530.3 - 22807.5i) q^{74} +(258158. - 52821.9i) q^{75} +(-486853. + 177210. i) q^{76} +(-553327. - 553327. i) q^{77} +(-293710. - 303464. i) q^{78} +615607. q^{79} +(-312506. - 27329.4i) q^{80} +(367465. - 383926. i) q^{81} +(512731. + 113665. i) q^{82} +(520347. + 520347. i) q^{83} +(-1.07418e6 - 256603. i) q^{84} +(-48425.8 - 48425.8i) q^{85} +(602205. + 945254. i) q^{86} +(391215. - 592492. i) q^{87} +(-621513. + 81840.8i) q^{88} -868822. q^{89} +(-252164. + 368663. i) q^{90} +(883606. + 883606. i) q^{91} +(-365332. - 170349. i) q^{92} +(33336.0 + 162924. i) q^{93} +(93757.5 - 422931. i) q^{94} -619994. i q^{95} +(-686924. + 557578. i) q^{96} -1.04625e6 q^{97} +(2.27147e6 + 503552. i) q^{98} +(-332519. + 828315. 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 $

$2$	−7.81038	−	1.73145i	−0.976298	−	0.216431i
$2$	−7.81038	−	1.73145i	−0.976298	−	0.216431i
$3$	−5.41236	−	26.4520i	−0.200458	−	0.979702i
$3$	−5.41236	−	26.4520i	−0.200458	−	0.979702i
$4$	58.0042	+	27.0465i	0.906315	+	0.422602i
$5$	−54.1549	+	54.1549i	−0.433239	+	0.433239i	−0.889729	−	0.456490i	$-0.849107\pi$
$5$	−54.1549	+	54.1549i	−0.433239	+	0.433239i	0.456490	+	0.889729i	$0.349107\pi$
$6$	−3.52753	+	215.971i	−0.0163311	+	0.999867i
$7$		−	639.122i		−	1.86333i	−0.363321	−	0.931664i	$-0.618357\pi$
$7$		−	639.122i		−	1.86333i	0.363321	−	0.931664i	$-0.381643\pi$
$8$	−406.205	−	311.675i	−0.793370	−	0.608740i
$9$	−670.413	+	286.335i	−0.919633	+	0.392778i
$10$	516.737	−	329.204i	0.516737	−	0.329204i
$11$	865.761	−	865.761i	0.650459	−	0.650459i	−0.302644	−	0.953104i	$-0.597869\pi$
$11$	865.761	−	865.761i	0.650459	−	0.650459i	0.953104	+	0.302644i	$0.0978695\pi$
$12$	401.494	−	1680.71i	0.232346	−	0.972633i
$13$	−1382.53	+	1382.53i	−0.629282	+	0.629282i	−0.947887	−	0.318606i	$-0.896785\pi$
$13$	−1382.53	+	1382.53i	−0.629282	+	0.629282i	0.318606	+	0.947887i	$0.396785\pi$
$14$	−1106.60	+	4991.79i	−0.403282	+	1.81916i
$15$	1725.61	+	1139.40i	0.511292	+	0.337599i
$16$	2632.97	+	3137.62i	0.642815	+	0.766021i
$17$			894.209i			0.182009i	0.995850	+	0.0910044i	$0.0290077\pi$
$17$			894.209i			0.182009i	−0.995850	+	0.0910044i	$0.970992\pi$
$18$	5731.95	−	1075.60i	0.982845	−	0.184432i
$19$	−5724.27	+	5724.27i	−0.834563	+	0.834563i	−0.988137	−	0.153574i	$-0.950922\pi$
$19$	−5724.27	+	5724.27i	−0.834563	+	0.834563i	0.153574	+	0.988137i	$0.450922\pi$
$20$	−4605.91	+	1676.51i	−0.575739	+	0.209564i
$21$	−16906.0	+	3459.16i	−1.82551	+	0.373519i
$22$	−8260.95	+	5262.91i	−0.775821	+	0.494263i
$23$	−6298.37			−0.517660			−0.258830	−	0.965923i	$-0.583337\pi$
$23$	−6298.37			−0.517660			−0.258830	+	0.965923i	$0.583337\pi$
$24$	−6045.88	+	12431.8i	−0.437347	+	0.899293i
$25$			9759.49i			0.624607i
$26$	13191.9	−	8404.33i	0.750563	−	0.478171i
$27$	11202.6	+	16184.0i	0.569153	+	0.822231i
$28$	17286.0	−	37071.7i	0.787446	−	1.68876i
$29$	18594.2	+	18594.2i	0.762402	+	0.762402i	0.976756	−	0.214354i	$-0.0687647\pi$
$29$	18594.2	+	18594.2i	0.762402	+	0.762402i	−0.214354	+	0.976756i	$0.568765\pi$
$30$	−11504.9	−	11886.9i	−0.426106	−	0.440257i
$31$	−6159.23			−0.206748			−0.103374	−	0.994643i	$-0.532964\pi$
$31$	−6159.23			−0.206748			−0.103374	+	0.994643i	$0.532964\pi$
$32$	−15131.9	−	29064.9i	−0.461789	−	0.886990i
$33$	−27586.9	−	18215.3i	−0.767646	−	0.506867i
$34$	1548.28	−	6984.12i	0.0393923	−	0.177695i
$35$	34611.6	+	34611.6i	0.807267	+	0.807267i
$36$	−46631.1	−	1523.69i	−0.999467	−	0.0326579i
$37$	2390.27	+	2390.27i	0.0471891	+	0.0471891i	0.730308	−	0.683118i	$-0.239377\pi$
$37$	2390.27	+	2390.27i	0.0471891	+	0.0471891i	−0.683118	+	0.730308i	$0.739377\pi$
$38$	54620.0	−	34797.5i	0.995407	−	0.634157i
$39$	44053.5	+	29087.9i	0.742653	+	0.490364i
$40$	38876.7	−	5119.29i	0.607449	−	0.0799889i
$41$	−65647.4			−0.952502			−0.476251	−	0.879309i	$-0.658005\pi$
$41$	−65647.4			−0.952502			−0.476251	+	0.879309i	$0.658005\pi$
$42$	138032.	+	2254.52i	1.86308	+	0.0304303i
$43$	−99064.2	−	99064.2i	−1.24598	−	1.24598i	−0.957480	−	0.288501i	$-0.906843\pi$
$43$	−99064.2	−	99064.2i	−1.24598	−	1.24598i	−0.288501	−	0.957480i	$-0.593157\pi$
$44$	73633.6	−	26801.9i	0.864406	−	0.314636i
$45$	20799.7	−	51812.6i	0.228254	−	0.568588i
$46$	49192.7	+	10905.3i	0.505390	+	0.112038i
$47$			54149.8i			0.521559i	0.965398	+	0.260779i	$0.0839795\pi$
$47$			54149.8i			0.521559i	−0.965398	+	0.260779i	$0.916020\pi$
$48$	68745.7	−	86629.2i	0.621615	−	0.783323i
$49$	−290827.			−2.47199
$50$	16898.0	−	76225.4i	0.135184	−	0.609803i
$51$	23653.6	−	4839.78i	0.178314	−	0.0364851i
$52$	−117585.	+	42800.0i	−0.836264	+	0.304392i
$53$	181923.	−	181923.i	1.22197	−	1.22197i	0.255038	−	0.966931i	$-0.417912\pi$
$53$	181923.	−	181923.i	1.22197	−	1.22197i	0.966931	−	0.255038i	$-0.0820879\pi$
$54$	−59475.3	−	145800.i	−0.377707	−	0.925925i
$55$			93770.4i			0.563609i
$56$	−199198.	+	259615.i	−1.13428	+	1.47831i
$57$	182400.	+	120436.i	0.984918	+	0.650328i
$58$	−113033.	−	177423.i	−0.579324	−	0.909338i
$59$	−114825.	+	114825.i	−0.559088	+	0.559088i	−0.929048	−	0.369959i	$-0.879372\pi$
$59$	−114825.	+	114825.i	−0.559088	+	0.559088i	0.369959	+	0.929048i	$0.379372\pi$
$60$	69275.8	+	112762.i	0.320721	+	0.522044i
$61$	16629.9	−	16629.9i	0.0732654	−	0.0732654i	−0.669525	−	0.742790i	$-0.733502\pi$
$61$	16629.9	−	16629.9i	0.0732654	−	0.0732654i	0.742790	+	0.669525i	$0.233502\pi$
$62$	48106.0	+	10664.4i	0.201848	+	0.0447467i
$63$	183003.	+	428475.i	0.731875	+	1.71358i
$64$	67861.6	+	253208.i	0.258871	+	0.965912i
$65$		−	149742.i		−	0.545259i
$66$	183925.	+	190033.i	0.639750	+	0.660995i
$67$	92916.9	−	92916.9i	0.308937	−	0.308937i	−0.535560	−	0.844497i	$-0.679899\pi$
$67$	92916.9	−	92916.9i	0.308937	−	0.308937i	0.844497	+	0.535560i	$0.179899\pi$
$68$	−24185.2	+	51867.9i	−0.0769172	+	0.164957i
$69$	34089.1	+	166604.i	0.103769	+	0.507153i
$70$	−210402.	−	330258.i	−0.613416	−	0.962851i
$71$	−678777.			−1.89650			−0.948249	−	0.317528i	$-0.897147\pi$
$71$	−678777.			−1.89650			−0.948249	+	0.317528i	$0.897147\pi$
$72$	361569.	+	92639.9i	0.968709	+	0.248199i
$73$		−	66507.2i		−	0.170962i	−0.996340	−	0.0854810i	$-0.972757\pi$
$73$		−	66507.2i		−	0.170962i	0.996340	−	0.0854810i	$-0.0272427\pi$
$74$	−14530.3	−	22807.5i	−0.0358574	−	0.0562837i
$75$	258158.	−	52821.9i	0.611929	−	0.125208i
$76$	−486853.	+	177210.i	−1.10907	+	0.403689i
$77$	−553327.	−	553327.i	−1.21202	−	1.21202i
$78$	−293710.	−	303464.i	−0.618921	−	0.639475i
$79$	615607.			1.24860			0.624299	−	0.781186i	$-0.285385\pi$
$79$	615607.			1.24860			0.624299	+	0.781186i	$0.285385\pi$
$80$	−312506.	−	27329.4i	−0.610363	−	0.0533777i
$81$	367465.	−	383926.i	0.691451	−	0.722424i
$82$	512731.	+	113665.i	0.929925	+	0.206151i
$83$	520347.	+	520347.i	0.910037	+	0.910037i	0.996275	−	0.0862380i	$-0.0274845\pi$
$83$	520347.	+	520347.i	0.910037	+	0.910037i	−0.0862380	+	0.996275i	$0.527485\pi$
$84$	−1.07418e6	−	256603.i	−1.81233	−	0.432937i
$85$	−48425.8	−	48425.8i	−0.0788533	−	0.0788533i
$86$	602205.	+	945254.i	0.946780	+	1.48612i
$87$	391215.	−	592492.i	0.594097	−	0.899756i
$88$	−621513.	+	81840.8i	−0.912015	+	0.120094i
$89$	−868822.			−1.23243			−0.616213	−	0.787580i	$-0.711334\pi$
$89$	−868822.			−1.23243			−0.616213	+	0.787580i	$0.711334\pi$
$90$	−252164.	+	368663.i	−0.345904	+	0.505710i
$91$	883606.	+	883606.i	1.17256	+	1.17256i
$92$	−365332.	−	170349.i	−0.469163	−	0.218764i
$93$	33336.0	+	162924.i	0.0414443	+	0.202552i
$94$	93757.5	−	422931.i	0.112881	−	0.509197i
$95$		−	619994.i		−	0.723131i
$96$	−686924.	+	557578.i	−0.776417	+	0.630219i
$97$	−1.04625e6			−1.14636			−0.573180	−	0.819429i	$-0.694290\pi$
$97$	−1.04625e6			−1.14636			−0.573180	+	0.819429i	$0.694290\pi$
$98$	2.27147e6	+	503552.i	2.41340	+	0.535015i
$99$	−332519.	+	828315.i	−0.342698	+	0.853670i
$100$	−263960.	+	566091.i	−0.263960	+	0.566091i
$101$	660309.	−	660309.i	0.640889	−	0.640889i	−0.309885	−	0.950774i	$-0.600291\pi$
$101$	660309.	−	660309.i	0.640889	−	0.640889i	0.950774	+	0.309885i	$0.100291\pi$
$102$	−193123.	−	3154.35i	−0.181984	−	0.00297241i
$103$		−	1.55470e6i		−	1.42277i	−0.702802	−	0.711386i	$-0.748068\pi$
$103$		−	1.55470e6i		−	1.42277i	0.702802	−	0.711386i	$-0.251932\pi$
$104$	992492.	−	130691.i	0.882322	−	0.116184i
$105$	728214.	−	1.10287e6i	0.629058	−	0.952704i
$106$	−1.73588e6	+	1.10590e6i	−1.45748	+	0.928534i
$107$	164503.	−	164503.i	0.134284	−	0.134284i	−0.636770	−	0.771054i	$-0.719730\pi$
$107$	164503.	−	164503.i	0.134284	−	0.134284i	0.771054	+	0.636770i	$0.219730\pi$
$108$	212080.	+	1.24173e6i	0.168356	+	0.985726i
$109$	203158.	−	203158.i	0.156876	−	0.156876i	−0.624305	−	0.781181i	$-0.714618\pi$
$109$	203158.	−	203158.i	0.156876	−	0.156876i	0.781181	+	0.624305i	$0.214618\pi$
$110$	162358.	−	732383.i	0.121982	−	0.550250i
$111$	50290.3	−	76164.3i	0.0367718	−	0.0556907i
$112$	2.00532e6	−	1.68279e6i	1.42735	−	1.19778i
$113$			263339.i			0.182507i	0.995828	+	0.0912535i	$0.0290874\pi$
$113$			263339.i			0.182507i	−0.995828	+	0.0912535i	$0.970913\pi$
$114$	−1.21608e6	−	1.25647e6i	−0.820822	−	0.848081i
$115$	341088.	−	341088.i	0.224271	−	0.224271i
$116$	575633.	+	1.58145e6i	0.368784	+	1.01317i
$117$	530999.	−	1.32273e6i	0.331540	−	0.825877i
$118$	1.09564e6	−	698014.i	0.666841	−	0.424833i
$119$	571508.			0.339142
$120$	−345830.	−	1.00066e6i	−0.200133	−	0.579085i
$121$			272477.i			0.153806i
$122$	−158679.	+	101092.i	−0.0873858	+	0.0556720i
$123$	355307.	+	1.73650e6i	0.190936	+	0.933168i
$124$	−357261.	−	166586.i	−0.187379	−	0.0873722i
$125$	−1.37469e6	−	1.37469e6i	−0.703844	−	0.703844i
$126$	−687442.	−	3.66342e6i	−0.343656	−	1.83136i
$127$	−1.00694e6			−0.491576			−0.245788	−	0.969324i	$-0.579047\pi$
$127$	−1.00694e6			−0.491576			−0.245788	+	0.969324i	$0.579047\pi$
$128$	−91608.7	−	2.09515e6i	−0.0436824	−	0.999045i
$129$	−2.08427e6	+	3.15661e6i	−0.970924	+	1.47046i
$130$	−259270.	+	1.16954e6i	−0.118011	+	0.532335i
$131$	−1.85710e6	−	1.85710e6i	−0.826079	−	0.826079i	0.160892	−	0.986972i	$-0.448563\pi$
$131$	−1.85710e6	−	1.85710e6i	−0.826079	−	0.826079i	−0.986972	+	0.160892i	$0.948563\pi$
$132$	−1.10750e6	−	1.80269e6i	−0.481527	−	0.783790i
$133$	3.65850e6	+	3.65850e6i	1.55506	+	1.55506i
$134$	−886597.	+	564836.i	−0.368478	+	0.234751i
$135$	−1.48312e6	−	269764.i	−0.602802	−	0.109643i
$136$	278702.	−	363232.i	0.110796	−	0.144400i
$137$	326184.			0.126853			0.0634265	−	0.997987i	$-0.479797\pi$
$137$	326184.			0.126853			0.0634265	+	0.997987i	$0.479797\pi$
$138$	22217.7	−	1.36027e6i	0.00845398	−	0.517591i
$139$	253984.	+	253984.i	0.0945718	+	0.0945718i	0.752810	−	0.658238i	$-0.228698\pi$
$139$	253984.	+	253984.i	0.0945718	+	0.0945718i	−0.658238	+	0.752810i	$0.728698\pi$
$140$	1.07149e6	+	2.94374e6i	0.390486	+	1.07279i
$141$	1.43237e6	−	293078.i	0.510972	−	0.104551i
$142$	5.30151e6	+	1.17527e6i	1.85155	+	0.410461i
$143$			2.39389e6i			0.818644i
$144$	−2.66359e6	−	1.34959e6i	−0.892031	−	0.451975i
$145$	−2.01394e6			−0.660605
$146$	−115154.	+	519446.i	−0.0370015	+	0.166910i
$147$	1.57406e6	+	7.69296e6i	0.495530	+	2.42182i
$148$	73997.1	+	203294.i	0.0228260	+	0.0627104i
$149$	−1.54443e6	+	1.54443e6i	−0.466884	+	0.466884i	−0.900903	−	0.434020i	$-0.857095\pi$
$149$	−1.54443e6	+	1.54443e6i	−0.466884	+	0.466884i	0.434020	+	0.900903i	$0.357095\pi$
$150$	−2.10777e6	−	34426.9i	−0.624524	−	0.0102006i
$151$		−	4.78499e6i		−	1.38979i	−0.719109	−	0.694897i	$-0.755450\pi$
$151$		−	4.78499e6i		−	1.38979i	0.719109	−	0.694897i	$-0.244550\pi$
$152$	4.10934e6	−	541118.i	1.17015	−	0.154085i
$153$	−256044.	−	599489.i	−0.0714891	−	0.167381i
$154$	3.36364e6	+	5.27975e6i	0.920973	+	1.44561i
$155$	333553.	−	333553.i	0.0895714	−	0.0895714i
$156$	1.76856e6	+	2.87871e6i	0.465849	+	0.758272i
$157$	−903031.	+	903031.i	−0.233348	+	0.233348i	−0.814089	−	0.580741i	$-0.802763\pi$
$157$	−903031.	+	903031.i	−0.233348	+	0.233348i	0.580741	+	0.814089i	$0.302763\pi$
$158$	−4.80813e6	−	1.06589e6i	−1.21900	−	0.270235i
$159$	−5.79686e6	−	3.82759e6i	−1.44212	−	0.952212i
$160$	2.39347e6	+	754540.i	0.584344	+	0.184214i
$161$			4.02542e6i			0.964570i
$162$	−3.53479e6	+	2.36236e6i	−0.831417	+	0.555650i
$163$	−5.14300e6	+	5.14300e6i	−1.18756	+	1.18756i	−0.209814	+	0.977741i	$0.567286\pi$
$163$	−5.14300e6	+	5.14300e6i	−1.18756	+	1.18756i	−0.977741	+	0.209814i	$0.932714\pi$
$164$	−3.80782e6	−	1.77553e6i	−0.863267	−	0.402529i
$165$	2.48041e6	−	507520.i	0.552169	−	0.112980i
$166$	−3.16316e6	−	4.96506e6i	−0.691507	−	1.08543i
$167$	−8.41258e6			−1.80626			−0.903129	−	0.429369i	$-0.858736\pi$
$167$	−8.41258e6			−1.80626			−0.903129	+	0.429369i	$0.858736\pi$
$168$	7.94545e6	+	3.86405e6i	1.67568	+	0.814921i
$169$			1.00402e6i			0.208009i
$170$	294377.	+	462071.i	0.0599181	+	0.0940506i
$171$	2.19856e6	−	5.47668e6i	0.439694	−	1.09529i
$172$	−3.06680e6	−	8.42548e6i	−0.602698	−	1.65581i
$173$	1.90824e6	+	1.90824e6i	0.368548	+	0.368548i	0.866948	−	0.498399i	$-0.166079\pi$
$173$	1.90824e6	+	1.90824e6i	0.368548	+	0.368548i	−0.498399	+	0.866948i	$0.666079\pi$
$174$	−4.08141e6	+	3.95022e6i	−0.774751	+	0.749849i
$175$	6.23750e6			1.16385
$176$	4.99596e6	+	436908.i	0.916391	+	0.0801405i
$177$	3.65882e6	+	2.41587e6i	0.659814	+	0.435667i
$178$	6.78583e6	+	1.50432e6i	1.20321	+	0.266735i
$179$	−1.57581e6	−	1.57581e6i	−0.274754	−	0.274754i	0.556257	−	0.831010i	$-0.312237\pi$
$179$	−1.57581e6	−	1.57581e6i	−0.274754	−	0.274754i	−0.831010	+	0.556257i	$0.812237\pi$
$180$	2.60782e6	−	2.44279e6i	0.447157	−	0.418859i
$181$	−1.37922e6	−	1.37922e6i	−0.232594	−	0.232594i	0.581180	−	0.813775i	$-0.302591\pi$
$181$	−1.37922e6	−	1.37922e6i	−0.232594	−	0.232594i	−0.813775	+	0.581180i	$0.802591\pi$
$182$	−5.37139e6	−	8.43122e6i	−0.890989	−	1.39854i
$183$	−529899.	−	349886.i	−0.0864649	−	0.0570917i
$184$	2.55843e6	+	1.96304e6i	0.410696	+	0.315120i
$185$	−258889.			−0.0408883
$186$	21726.9	−	1.33022e6i	0.00337643	−	0.206721i
$187$	774171.	+	774171.i	0.118389	+	0.118389i
$188$	−1.46456e6	+	3.14092e6i	−0.220412	+	0.472697i
$189$	1.03435e7	−	7.15985e6i	1.53209	−	1.06052i
$190$	−1.07349e6	+	4.84239e6i	−0.156508	+	0.705991i
$191$		−	6.82181e6i		−	0.979038i	−0.871993	−	0.489519i	$-0.837172\pi$
$191$		−	6.82181e6i		−	0.979038i	0.871993	−	0.489519i	$-0.162828\pi$
$192$	6.33056e6	−	3.16552e6i	0.894413	−	0.447241i
$193$	−9.27545e6			−1.29022			−0.645109	−	0.764091i	$-0.723188\pi$
$193$	−9.27545e6			−1.29022			−0.645109	+	0.764091i	$0.723188\pi$
$194$	8.17163e6	+	1.81153e6i	1.11919	+	0.248108i
$195$	−3.96096e6	+	810457.i	−0.534192	+	0.109302i
$196$	−1.68692e7	−	7.86587e6i	−2.24040	−	1.04467i
$197$	2.26852e6	−	2.26852e6i	0.296718	−	0.296718i	−0.543009	−	0.839727i	$-0.682715\pi$
$197$	2.26852e6	−	2.26852e6i	0.296718	−	0.296718i	0.839727	+	0.543009i	$0.182715\pi$
$198$	4.03129e6	−	5.89372e6i	0.519336	−	0.759266i
$199$		−	4.45625e6i		−	0.565471i	−0.959198	−	0.282735i	$-0.908758\pi$
$199$		−	4.45625e6i		−	0.565471i	0.959198	−	0.282735i	$-0.0912418\pi$
$200$	3.04179e6	−	3.96436e6i	0.380224	−	0.495545i
$201$	−2.96073e6	−	1.95493e6i	−0.364595	−	0.240738i
$202$	−6.30055e6	+	4.01398e6i	−0.764407	+	0.486991i
$203$	1.18840e7	−	1.18840e7i	1.42060	−	1.42060i
$204$	1.50291e6	+	359019.i	0.177028	+	0.0422890i
$205$	3.55513e6	−	3.55513e6i	0.412661	−	0.412661i
$206$	−2.69188e6	+	1.21428e7i	−0.307932	+	1.38905i
$207$	4.22251e6	−	1.80344e6i	0.476057	−	0.203325i
$208$	−7.97803e6	−	697698.i	−0.886555	−	0.0775313i
$209$			9.91170e6i			1.08570i
$210$	−7.59720e6	+	7.35301e6i	−0.820343	+	0.793976i
$211$	7.88389e6	−	7.88389e6i	0.839253	−	0.839253i	−0.149507	−	0.988761i	$-0.547769\pi$
$211$	7.88389e6	−	7.88389e6i	0.839253	−	0.839253i	0.988761	+	0.149507i	$0.0477688\pi$
$212$	1.54727e7	−	5.63191e6i	1.62390	−	0.591083i
$213$	3.67379e6	+	1.79550e7i	0.380168	+	1.85800i
$214$	−1.56966e6	+	1.00001e6i	−0.160164	+	0.102038i
$215$	1.07296e7			1.07962
$216$	493565.	−	1.00656e7i	0.0489760	−	0.998800i
$217$			3.93650e6i			0.385240i
$218$	−1.93850e6	+	1.23499e6i	−0.187110	+	0.119205i
$219$	−1.75924e6	+	359961.i	−0.167492	+	0.0342707i
$220$	−2.53616e6	+	5.43908e6i	−0.238182	+	0.510807i
$221$	−1.23627e6	−	1.23627e6i	−0.114535	−	0.114535i
$222$	−524661.	+	507797.i	−0.0479534	+	0.0464121i
$223$	2.07836e6			0.187416			0.0937081	−	0.995600i	$-0.470128\pi$
$223$	2.07836e6			0.187416			0.0937081	+	0.995600i	$0.470128\pi$
$224$	−1.85760e7	+	9.67112e6i	−1.65275	+	0.860464i
$225$	−2.79449e6	−	6.54289e6i	−0.245332	−	0.574410i
$226$	455957.	−	2.05678e6i	0.0395002	−	0.178181i
$227$	4.31998e6	+	4.31998e6i	0.369321	+	0.369321i	0.867230	−	0.497909i	$-0.165898\pi$
$227$	4.31998e6	+	4.31998e6i	0.369321	+	0.369321i	−0.497909	+	0.867230i	$0.665898\pi$
$228$	7.32258e6	+	1.19191e7i	0.617816	+	1.00563i
$229$	6.53571e6	+	6.53571e6i	0.544235	+	0.544235i	0.924768	−	0.380532i	$-0.124259\pi$
$229$	6.53571e6	+	6.53571e6i	0.544235	+	0.544235i	−0.380532	+	0.924768i	$0.624259\pi$
$230$	−3.25460e6	+	2.07345e6i	−0.267494	+	0.170416i
$231$	−1.16418e7	+	1.76314e7i	−0.944459	+	1.43038i
$232$	−1.75772e6	−	1.33484e7i	−0.140762	−	1.06897i
$233$	−5.57558e6			−0.440780			−0.220390	−	0.975412i	$-0.570733\pi$
$233$	−5.57558e6			−0.440780			−0.220390	+	0.975412i	$0.570733\pi$
$234$	−6.43755e6	+	9.41167e6i	−0.502427	+	0.734546i
$235$	−2.93248e6	−	2.93248e6i	−0.225960	−	0.225960i
$236$	−9.76595e6	+	3.55471e6i	−0.742982	+	0.270439i
$237$	−3.33189e6	−	1.62840e7i	−0.250291	−	1.22325i
$238$	−4.46370e6	−	989536.i	−0.331104	−	0.0734008i
$239$			2.45763e6i			0.180021i	0.995941	+	0.0900104i	$0.0286900\pi$
$239$			2.45763e6i			0.180021i	−0.995941	+	0.0900104i	$0.971310\pi$
$240$	968480.	+	8.41431e6i	0.0700579	+	0.608674i
$241$	−7.17023e6			−0.512250			−0.256125	−	0.966644i	$-0.582446\pi$
$241$	−7.17023e6			−0.512250			−0.256125	+	0.966644i	$0.582446\pi$
$242$	471779.	−	2.12815e6i	0.0332883	−	0.150160i
$243$	−1.21444e7	−	7.64223e6i	−0.846367	−	0.532600i
$244$	1.41438e6	−	514821.i	0.0973637	−	0.0354395i
$245$	1.57497e7	−	1.57497e7i	1.07096	−	1.07096i
$246$	231573.	−	1.41779e7i	0.0155554	−	0.952375i
$247$		−	1.58280e7i		−	1.05035i
$248$	2.50191e6	+	1.91968e6i	0.164028	+	0.125856i
$249$	1.09479e7	−	1.65805e7i	0.709141	−	1.07399i
$250$	8.35668e6	+	1.31171e7i	0.534828	+	0.839495i
$251$	−2.04131e7	+	2.04131e7i	−1.29089	+	1.29089i	−0.356648	+	0.934239i	$0.616080\pi$
$251$	−2.04131e7	+	2.04131e7i	−1.29089	+	1.29089i	−0.934239	+	0.356648i	$0.883920\pi$
$252$	−973822.	+	2.98030e7i	−0.0608524	+	1.86233i
$253$	−5.45288e6	+	5.45288e6i	−0.336717	+	0.336717i
$254$	7.86456e6	+	1.74346e6i	0.479925	+	0.106392i
$255$	−1.01886e6	+	1.54306e6i	−0.0614460	+	0.0930596i
$256$	−2.91214e6	+	1.65225e7i	−0.173577	+	0.984820i
$257$		−	4.16117e6i		−	0.245141i	−0.992460	−	0.122570i	$-0.960886\pi$
$257$		−	4.16117e6i		−	0.245141i	0.992460	−	0.122570i	$-0.0391137\pi$
$258$	2.17445e7	−	2.10456e7i	1.26616	−	1.22547i
$259$	1.52767e6	−	1.52767e6i	0.0879287	−	0.0879287i
$260$	4.05000e6	−	8.68565e6i	0.230428	−	0.494177i
$261$	−1.77900e7	−	7.14162e6i	−1.00058	−	0.401675i
$262$	1.12892e7	+	1.77201e7i	0.627711	+	0.985289i
$263$	776996.			0.0427122			0.0213561	−	0.999772i	$-0.493202\pi$
$263$	776996.			0.0427122			0.0213561	+	0.999772i	$0.493202\pi$
$264$	5.52870e6	+	1.59973e7i	0.300477	+	0.869429i
$265$			1.97041e7i			1.05881i
$266$	−2.22398e7	−	3.49088e7i	−1.18164	−	1.85477i
$267$	4.70238e6	+	2.29820e7i	0.247049	+	1.20741i
$268$	7.90264e6	−	2.87649e6i	0.410552	−	0.149437i
$269$	1.41758e7	+	1.41758e7i	0.728267	+	0.728267i	0.970274	−	0.242008i	$-0.0778059\pi$
$269$	1.41758e7	+	1.41758e7i	0.728267	+	0.728267i	−0.242008	+	0.970274i	$0.577806\pi$
$270$	1.11167e7	+	4.67490e6i	0.564785	+	0.237510i
$271$	−5.83230e6			−0.293043			−0.146522	−	0.989207i	$-0.546808\pi$
$271$	−5.83230e6			−0.293043			−0.146522	+	0.989207i	$0.546808\pi$
$272$	−2.80569e6	+	2.35443e6i	−0.139423	+	0.116998i
$273$	1.85907e7	−	2.81555e7i	0.913710	−	1.38381i
$274$	−2.54762e6	−	564769.i	−0.123846	−	0.0274549i
$275$	8.44939e6	+	8.44939e6i	0.406282	+	0.406282i
$276$	−2.52876e6	+	1.05857e7i	−0.120276	+	0.503493i
$277$	−1.66030e7	−	1.66030e7i	−0.781173	−	0.781173i	0.198856	−	0.980029i	$-0.436277\pi$
$277$	−1.66030e7	−	1.66030e7i	−0.781173	−	0.781173i	−0.980029	+	0.198856i	$0.936277\pi$
$278$	−1.54395e6	−	2.42347e6i	−0.0718620	−	0.112799i
$279$	4.12923e6	−	1.76361e6i	0.190132	−	0.0812061i
$280$	−3.27185e6	−	2.48470e7i	−0.149046	−	1.13188i
$281$	−2.00660e7			−0.904361			−0.452181	−	0.891926i	$-0.649354\pi$
$281$	−2.00660e7			−0.904361			−0.452181	+	0.891926i	$0.649354\pi$
$282$	−1.16948e7	−	191015.i	−0.521489	−	0.00851765i
$283$	9.24801e6	+	9.24801e6i	0.408027	+	0.408027i	0.881050	−	0.473023i	$-0.156837\pi$
$283$	9.24801e6	+	9.24801e6i	0.408027	+	0.408027i	−0.473023	+	0.881050i	$0.656837\pi$
$284$	−3.93719e7	−	1.83586e7i	−1.71883	−	0.801464i
$285$	−1.64001e7	+	3.35563e6i	−0.708453	+	0.144957i
$286$	4.14488e6	−	1.86972e7i	0.177180	−	0.799241i
$287$			4.19567e7i			1.77482i
$288$	1.84669e7	+	1.51527e7i	0.773066	+	0.634325i
$289$	2.33380e7			0.966873
$290$	1.57296e7	+	3.48702e6i	0.644947	+	0.142975i
$291$	5.66270e6	+	2.76754e7i	0.229797	+	1.12309i
$292$	1.79879e6	−	3.85769e6i	0.0722489	−	0.154946i
$293$	1.17434e7	−	1.17434e7i	0.466863	−	0.466863i	−0.434034	−	0.900897i	$-0.642910\pi$
$293$	1.17434e7	−	1.17434e7i	0.466863	−	0.466863i	0.900897	+	0.434034i	$0.142910\pi$
$294$	1.02590e6	−	6.28104e7i	0.0403705	−	2.47166i
$295$		−	1.24367e7i		−	0.484438i
$296$	−225953.	−	1.71593e6i	−0.00871251	−	0.0661642i
$297$	2.37103e7	+	4.31264e6i	0.905039	+	0.164617i
$298$	1.47367e7	−	9.38847e6i	0.556865	−	0.354769i
$299$	8.70770e6	−	8.70770e6i	0.325754	−	0.325754i
$300$	1.64029e7	+	3.91838e6i	0.607514	+	0.145125i
$301$	−6.33141e7	+	6.33141e7i	−2.32167	+	2.32167i
$302$	−8.28496e6	+	3.73726e7i	−0.300794	+	1.35685i
$303$	−2.10403e7	−	1.38926e7i	−0.756352	−	0.499409i
$304$	−3.30324e7	−	2.88876e6i	−1.17576	−	0.102823i
$305$			1.80118e6i			0.0634829i
$306$	961815.	+	5.12556e6i	0.0335681	+	0.178886i
$307$	2.39376e7	−	2.39376e7i	0.827304	−	0.827304i	−0.159839	−	0.987143i	$-0.551097\pi$
$307$	2.39376e7	−	2.39376e7i	0.827304	−	0.827304i	0.987143	+	0.159839i	$0.0510974\pi$
$308$	−1.71297e7	−	4.70608e7i	−0.586270	−	1.61067i
$309$	−4.11249e7	+	8.41461e6i	−1.39389	+	0.285206i
$310$	−3.18270e6	+	2.02765e6i	−0.106834	+	0.0680624i
$311$	3.21416e7			1.06853			0.534265	−	0.845317i	$-0.320588\pi$
$311$	3.21416e7			1.06853			0.534265	+	0.845317i	$0.320588\pi$
$312$	−8.82877e6	−	2.55460e7i	−0.290694	−	0.841123i
$313$		−	1.50760e7i		−	0.491648i	−0.969314	−	0.245824i	$-0.920941\pi$
$313$		−	1.50760e7i		−	0.491648i	0.969314	−	0.245824i	$-0.0790585\pi$
$314$	8.61656e6	−	5.48947e6i	0.278321	−	0.177313i
$315$	−3.31145e7	−	1.32935e7i	−1.05947	−	0.425313i
$316$	3.57078e7	+	1.66500e7i	1.13162	+	0.527660i
$317$	−1.31600e7	−	1.31600e7i	−0.413122	−	0.413122i	0.469702	−	0.882825i	$-0.344361\pi$
$317$	−1.31600e7	−	1.31600e7i	−0.413122	−	0.413122i	−0.882825	+	0.469702i	$0.844361\pi$
$318$	3.86484e7	+	3.99319e7i	1.20185	+	1.24176i
$319$	3.21963e7			0.991822
$320$	−1.73875e7	−	1.00374e7i	−0.530624	−	0.306318i
$321$	−5.24179e6	−	3.46109e6i	−0.158476	−	0.104640i
$322$	6.96980e6	−	3.14401e7i	0.208763	−	0.941708i
$323$	−5.11869e6	−	5.11869e6i	−0.151898	−	0.151898i
$324$	3.16984e7	−	1.23306e7i	0.931970	−	0.362535i
$325$	−1.34928e7	−	1.34928e7i	−0.393054	−	0.393054i
$326$	4.90737e7	−	3.12640e7i	1.41643	−	0.902384i
$327$	−6.47351e6	−	4.27437e6i	−0.185138	−	0.122244i
$328$	2.66663e7	+	2.04606e7i	0.755686	+	0.579826i
$329$	3.46083e7			0.971835
$330$	−2.02517e7	−	330778.i	−0.563534	−	0.00920437i
$331$	−521955.	−	521955.i	−0.0143929	−	0.0143929i	0.699874	−	0.714267i	$-0.253240\pi$
$331$	−521955.	−	521955.i	−0.0143929	−	0.0143929i	−0.714267	+	0.699874i	$0.753240\pi$
$332$	1.61087e7	+	4.42559e7i	0.440197	+	1.20936i
$333$	−2.28688e6	−	918048.i	−0.0619315	−	0.0248618i
$334$	6.57055e7	+	1.45659e7i	1.76345	+	0.390930i
$335$			1.00638e7i			0.267687i
$336$	−5.53666e7	−	4.39369e7i	−1.45959	−	1.15827i
$337$	−2.55151e7			−0.666666			−0.333333	−	0.942809i	$-0.608173\pi$
$337$	−2.55151e7			−0.666666			−0.333333	+	0.942809i	$0.608173\pi$
$338$	1.73840e6	−	7.84177e6i	0.0450195	−	0.203079i
$339$	6.96583e6	−	1.42529e6i	0.178803	−	0.0365850i
$340$	−1.49915e6	−	4.11865e6i	−0.0381424	−	0.104790i
$341$	−5.33242e6	+	5.33242e6i	−0.134481	+	0.134481i
$342$	−2.66542e7	+	3.89683e7i	−0.666327	+	0.974166i
$343$			1.10682e8i			2.74281i
$344$	9.36458e6	+	7.11162e7i	0.230045	+	1.74700i
$345$	−1.08685e7	−	7.17634e6i	−0.264675	−	0.174762i
$346$	−1.16001e7	−	1.82081e7i	−0.280048	−	0.439578i
$347$	−4.48669e6	+	4.48669e6i	−0.107383	+	0.107383i	−0.758757	−	0.651374i	$-0.774193\pi$
$347$	−4.48669e6	+	4.48669e6i	−0.107383	+	0.107383i	0.651374	+	0.758757i	$0.274193\pi$
$348$	3.87169e7	−	2.37860e7i	0.918678	−	0.564396i
$349$	4.41155e7	−	4.41155e7i	1.03780	−	1.03780i	0.0385466	−	0.999257i	$-0.487727\pi$
$349$	4.41155e7	−	4.41155e7i	1.03780	−	1.03780i	0.999257	−	0.0385466i	$-0.0122728\pi$
$350$	−4.87173e7	−	1.07999e7i	−1.13626	−	0.251893i
$351$	−3.78629e7	−	6.88685e6i	−0.875573	−	0.159257i
$352$	−3.82638e7	−	1.20626e7i	−0.877325	−	0.276576i
$353$		−	5.78167e6i		−	0.131440i	−0.997838	−	0.0657202i	$-0.979066\pi$
$353$		−	5.78167e6i		−	0.131440i	0.997838	−	0.0657202i	$-0.0209345\pi$
$354$	−2.43938e7	−	2.52039e7i	−0.549883	−	0.568144i
$355$	3.67591e7	−	3.67591e7i	0.821637	−	0.821637i
$356$	−5.03953e7	−	2.34986e7i	−1.11697	−	0.520825i
$357$	−3.09321e6	−	1.51175e7i	−0.0679837	−	0.332258i
$358$	9.57922e6	+	1.50361e7i	0.208776	+	0.327707i
$359$	6.71218e7			1.45071			0.725354	−	0.688376i	$-0.241676\pi$
$359$	6.71218e7			1.45071			0.725354	+	0.688376i	$0.241676\pi$
$360$	−2.45976e7	+	1.45638e7i	−0.527212	+	0.312153i
$361$		−	1.84886e7i		−	0.392990i
$362$	8.38422e6	+	1.31603e7i	0.176741	+	0.277422i
$363$	7.20754e6	−	1.47474e6i	0.150684	−	0.0308316i
$364$	2.73544e7	+	7.51513e7i	0.567182	+	1.55823i
$365$	3.60169e6	+	3.60169e6i	0.0740675	+	0.0740675i
$366$	3.53291e6	+	3.65023e6i	0.0720591	+	0.0744521i
$367$	1.56094e7			0.315783			0.157892	−	0.987456i	$-0.449530\pi$
$367$	1.56094e7			0.315783			0.157892	+	0.987456i	$0.449530\pi$
$368$	−1.65834e7	−	1.97619e7i	−0.332760	−	0.396538i
$369$	4.40108e7	−	1.87972e7i	0.875952	−	0.374122i
$370$	2.02203e6	+	448253.i	0.0399192	+	0.00884949i
$371$	−1.16271e8	−	1.16271e8i	−2.27693	−	2.27693i
$372$	−2.47289e6	+	1.03519e7i	−0.0480371	+	0.201090i
$373$	3.76070e6	+	3.76070e6i	0.0724674	+	0.0724674i	0.742412	−	0.669944i	$-0.233682\pi$
$373$	3.76070e6	+	3.76070e6i	0.0724674	+	0.0724674i	−0.669944	+	0.742412i	$0.733682\pi$
$374$	−4.70614e6	−	7.38701e6i	−0.0899601	−	0.141206i
$375$	−2.89230e7	+	4.38037e7i	−0.548466	+	0.830648i
$376$	1.68771e7	−	2.19959e7i	0.317494	−	0.413789i
$377$	−5.14142e7			−0.959531
$378$	−9.31839e7	+	3.80119e7i	−1.72530	+	0.703792i
$379$	−4.95457e7	−	4.95457e7i	−0.910099	−	0.910099i	0.0861807	−	0.996280i	$-0.472534\pi$
$379$	−4.95457e7	−	4.95457e7i	−0.910099	−	0.910099i	−0.996280	+	0.0861807i	$0.972534\pi$
$380$	1.67687e7	−	3.59623e7i	0.305596	−	0.655385i
$381$	5.44991e6	+	2.66355e7i	0.0985404	+	0.481599i
$382$	−1.18116e7	+	5.32810e7i	−0.211894	+	0.955833i
$383$			7.85845e7i			1.39875i	0.714754	+	0.699376i	$0.246539\pi$
$383$			7.85845e7i			1.39875i	−0.714754	+	0.699376i	$0.753461\pi$
$384$	−5.49250e7	+	1.37629e7i	−0.970011	+	0.243062i
$385$	5.99307e7			1.05019
$386$	7.24448e7	+	1.60599e7i	1.25964	+	0.279243i
$387$	9.47795e7	+	3.80483e7i	1.63524	+	0.656451i
$388$	−6.06870e7	−	2.82975e7i	−1.03896	−	0.484454i
$389$	−2.55716e7	+	2.55716e7i	−0.434419	+	0.434419i	−0.890129	−	0.455710i	$-0.849386\pi$
$389$	−2.55716e7	+	2.55716e7i	−0.434419	+	0.434419i	0.455710	+	0.890129i	$0.349386\pi$
$390$	3.23399e7	+	528218.i	0.545186	+	0.00890470i
$391$		−	5.63206e6i		−	0.0942186i
$392$	1.18136e8	+	9.06436e7i	1.96120	+	1.50480i
$393$	−3.90727e7	+	5.91753e7i	−0.643718	+	0.974906i
$394$	−2.16458e7	+	1.37902e7i	−0.353904	+	0.225466i
$395$	−3.33381e7	+	3.33381e7i	−0.540941	+	0.540941i
$396$	−4.16906e7	+	3.90523e7i	−0.671355	+	0.628869i
$397$	1.43736e7	−	1.43736e7i	0.229718	−	0.229718i	−0.582857	−	0.812575i	$-0.698065\pi$
$397$	1.43736e7	−	1.43736e7i	0.229718	−	0.229718i	0.812575	+	0.582857i	$0.198065\pi$
$398$	−7.71575e6	+	3.48050e7i	−0.122385	+	0.552068i
$399$	7.69734e7	−	1.16576e8i	1.21178	−	1.83523i
$400$	−3.06216e7	+	2.56965e7i	−0.478463	+	0.401507i
$401$		−	5.30328e7i		−	0.822454i	−0.911533	−	0.411227i	$-0.865100\pi$
$401$		−	5.30328e7i		−	0.822454i	0.911533	−	0.411227i	$-0.134900\pi$
$402$	1.97396e7	+	2.03951e7i	0.303851	+	0.313941i
$403$	8.51534e6	−	8.51534e6i	0.130103	−	0.130103i
$404$	5.61597e7	−	2.04416e7i	0.851689	−	0.310007i
$405$	891406.	+	4.06915e7i	0.0134187	+	0.612546i
$406$	−1.13395e8	+	7.22419e7i	−1.69440	+	1.07947i
$407$	4.13880e6			0.0613891
$408$	−1.11167e7	−	5.40628e6i	−0.163679	−	0.0796009i
$409$			1.19806e8i			1.75110i	0.483131	+	0.875548i	$0.339499\pi$
$409$			1.19806e8i			1.75110i	−0.483131	+	0.875548i	$0.660501\pi$
$410$	−3.39224e7	+	2.16114e7i	−0.492193	+	0.313568i
$411$	−1.76542e6	−	8.62820e6i	−0.0254287	−	0.124278i
$412$	4.20493e7	−	9.01792e7i	0.601266	−	1.28948i
$413$	7.33872e7	+	7.33872e7i	1.04177	+	1.04177i
$414$	−3.61020e7	+	6.77455e6i	−0.508780	+	0.0954728i
$415$	−5.63587e7			−0.788527
$416$	6.11035e7	+	1.92628e7i	0.848762	+	0.267572i
$417$	5.34372e6	−	8.09303e6i	0.0736946	−	0.111610i
$418$	1.71616e7	−	7.74141e7i	0.234979	−	1.05996i
$419$	−3.57905e7	−	3.57905e7i	−0.486548	−	0.486548i	0.420667	−	0.907215i	$-0.361796\pi$
$419$	−3.57905e7	−	3.57905e7i	−0.486548	−	0.486548i	−0.907215	+	0.420667i	$0.861796\pi$
$420$	7.20684e7	−	4.42757e7i	0.972740	−	0.597609i
$421$	1.76240e7	+	1.76240e7i	0.236189	+	0.236189i	0.815270	−	0.579081i	$-0.196589\pi$
$421$	1.76240e7	+	1.76240e7i	0.236189	+	0.236189i	−0.579081	+	0.815270i	$0.696589\pi$
$422$	−7.52267e7	+	4.79257e7i	−1.00100	+	0.637721i
$423$	−1.55050e7	−	3.63027e7i	−0.204857	−	0.479643i
$424$	−1.30599e8	+	1.71973e7i	−1.71333	+	0.225612i
$425$	−8.72703e6			−0.113684
$426$	2.39441e6	−	1.46596e8i	0.0309720	−	1.89624i
$427$	−1.06285e7	−	1.06285e7i	−0.136518	−	0.136518i
$428$	1.39911e7	−	5.09264e6i	0.178452	−	0.0649549i
$429$	6.33230e7	−	1.29566e7i	0.802028	−	0.164104i
$430$	−8.38025e7	−	1.85778e7i	−1.05403	−	0.233662i
$431$		−	1.05377e8i		−	1.31617i	−0.752942	−	0.658086i	$-0.771366\pi$
$431$		−	1.05377e8i		−	1.31617i	0.752942	−	0.658086i	$-0.228634\pi$
$432$	−2.12830e7	+	7.77616e7i	−0.263986	+	0.964526i
$433$	7.23384e7			0.891056			0.445528	−	0.895268i	$-0.353016\pi$
$433$	7.23384e7			0.891056			0.445528	+	0.895268i	$0.353016\pi$
$434$	6.81584e6	−	3.07456e7i	0.0833777	−	0.376109i
$435$	1.09002e7	+	5.32726e7i	0.132423	+	0.647196i
$436$	1.72788e7	−	6.28931e6i	0.208475	−	0.0758829i
$437$	3.60535e7	−	3.60535e7i	0.432020	−	0.432020i
$438$	1.43636e7	+	234606.i	0.170939	+	0.00279201i
$439$		−	9.35132e6i		−	0.110530i	−0.998472	−	0.0552649i	$-0.982400\pi$
$439$		−	9.35132e6i		−	0.110530i	0.998472	−	0.0552649i	$-0.0176003\pi$
$440$	2.92259e7	−	3.80900e7i	0.343091	−	0.447150i
$441$	1.94974e8	−	8.32742e7i	2.27333	−	0.970945i
$442$	7.51522e6	+	1.17963e7i	0.0870312	+	0.136609i
$443$	8.39110e7	−	8.39110e7i	0.965178	−	0.965178i	−0.0342354	−	0.999414i	$-0.510900\pi$
$443$	8.39110e7	−	8.39110e7i	0.965178	−	0.965178i	0.999414	+	0.0342354i	$0.0108996\pi$
$444$	4.97702e6	−	3.05767e6i	0.0568618	−	0.0349335i
$445$	4.70510e7	−	4.70510e7i	0.533935	−	0.533935i
$446$	−1.62328e7	−	3.59858e6i	−0.182974	−	0.0405626i
$447$	4.92121e7	+	3.24941e7i	0.550997	+	0.363816i
$448$	1.61831e8	−	4.33718e7i	1.79981	−	0.482362i
$449$		−	1.58902e7i		−	0.175546i	−0.996141	−	0.0877729i	$-0.972025\pi$
$449$		−	1.58902e7i		−	0.175546i	0.996141	−	0.0877729i	$-0.0279750\pi$
$450$	1.04974e7	+	5.59410e7i	0.115197	+	0.613893i
$451$	−5.68349e7	+	5.68349e7i	−0.619563	+	0.619563i
$452$	−7.12240e6	+	1.52748e7i	−0.0771279	+	0.165409i
$453$	−1.26573e8	+	2.58981e7i	−1.36159	+	0.278595i
$454$	−2.62609e7	−	4.12205e7i	−0.280635	−	0.440500i
$455$	−9.57032e7			−1.01600
$456$	−3.65549e7	−	1.05771e8i	−0.385523	−	1.11551i
$457$		−	1.62779e8i		−	1.70550i	−0.522322	−	0.852748i	$-0.674934\pi$
$457$		−	1.62779e8i		−	1.70550i	0.522322	−	0.852748i	$-0.325066\pi$
$458$	−3.97302e7	−	6.23627e7i	−0.413546	−	0.649125i
$459$	−1.44719e7	+	1.00175e7i	−0.149653	+	0.103591i
$460$	2.90097e7	−	1.05593e7i	0.298037	−	0.108483i
$461$	−5.20012e7	−	5.20012e7i	−0.530775	−	0.530775i	0.390028	−	0.920803i	$-0.372465\pi$
$461$	−5.20012e7	−	5.20012e7i	−0.530775	−	0.530775i	−0.920803	+	0.390028i	$0.872465\pi$
$462$	1.21454e8	−	1.17551e8i	1.23165	−	1.19206i
$463$	−1.46215e8			−1.47315			−0.736576	−	0.676355i	$-0.763559\pi$
$463$	−1.46215e8			−1.47315			−0.736576	+	0.676355i	$0.763559\pi$
$464$	−9.38361e6	+	1.07300e8i	−0.0939325	+	1.07410i
$465$	−1.06284e7	−	7.01782e6i	−0.105709	−	0.0697980i
$466$	4.35474e7	+	9.65381e6i	0.430333	+	0.0953984i
$467$	−9.72232e7	−	9.72232e7i	−0.954595	−	0.954595i	0.0444179	−	0.999013i	$-0.485857\pi$
$467$	−9.72232e7	−	9.72232e7i	−0.954595	−	0.954595i	−0.999013	+	0.0444179i	$0.985857\pi$
$468$	6.65756e7	−	6.23625e7i	0.649497	−	0.608395i
$469$	−5.93852e7	−	5.93852e7i	−0.575651	−	0.575651i
$470$	1.78263e7	+	2.79812e7i	0.171699	+	0.269509i
$471$	2.87745e7	+	1.89994e7i	0.275388	+	0.181835i
$472$	8.24306e7	−	1.08545e7i	0.783903	−	0.103224i
$473$	−1.71532e8			−1.62092
$474$	−2.17157e6	+	1.32953e8i	−0.0203910	+	1.24843i
$475$	−5.58659e7	−	5.58659e7i	−0.521274	−	0.521274i
$476$	3.31499e7	+	1.54573e7i	0.307370	+	0.143322i
$477$	−6.98725e7	+	1.74055e8i	−0.643801	+	1.60373i
$478$	4.25526e6	−	1.91950e7i	0.0389621	−	0.175754i
$479$			1.02079e8i			0.928821i	0.885620	+	0.464410i	$0.153734\pi$
$479$			1.02079e8i			0.928821i	−0.885620	+	0.464410i	$0.846266\pi$
$480$	7.00473e6	−	6.73959e7i	0.0633385	−	0.609410i
$481$	−6.60924e6			−0.0593904
$482$	5.60023e7	+	1.24149e7i	0.500109	+	0.110867i
$483$	1.06480e8	−	2.17871e7i	0.944992	−	0.193356i
$484$	−7.36954e6	+	1.58048e7i	−0.0649987	+	0.139397i
$485$	5.66597e7	−	5.66597e7i	0.496648	−	0.496648i
$486$	8.16206e7	+	8.07162e7i	0.711035	+	0.703156i
$487$			2.92309e7i			0.253078i	0.991962	+	0.126539i	$0.0403869\pi$
$487$			2.92309e7i			0.253078i	−0.991962	+	0.126539i	$0.959613\pi$
$488$	−1.19382e7	+	1.57203e6i	−0.102726	+	0.0135270i
$489$	1.63878e8	+	1.08207e8i	1.40151	+	0.925396i
$490$	−1.50281e8	+	9.57416e7i	−1.27737	+	0.813791i
$491$	8.27929e7	−	8.27929e7i	0.699437	−	0.699437i	−0.264852	−	0.964289i	$-0.585323\pi$
$491$	8.27929e7	−	8.27929e7i	0.699437	−	0.699437i	0.964289	+	0.264852i	$0.0853232\pi$
$492$	−2.63570e7	+	1.10334e8i	−0.221310	+	0.926435i
$493$	−1.66271e7	+	1.66271e7i	−0.138764	+	0.138764i
$494$	−2.74053e7	+	1.23622e8i	−0.227328	+	1.02546i
$495$	−2.68498e7	−	6.28649e7i	−0.221373	−	0.518313i
$496$	−1.62171e7	−	1.93254e7i	−0.132901	−	0.158373i
$497$			4.33821e8i			3.53380i
$498$	−1.14216e8	+	1.10544e8i	−0.924777	+	0.895053i
$499$	−1.37980e8	+	1.37980e8i	−1.11049	+	1.11049i	−0.117403	+	0.993084i	$0.537457\pi$
$499$	−1.37980e8	+	1.37980e8i	−1.11049	+	1.11049i	−0.993084	+	0.117403i	$0.962543\pi$
$500$	−4.25573e7	−	1.16919e8i	−0.340459	−	0.935350i
$501$	4.55320e7	+	2.22529e8i	0.362079	+	1.76960i
$502$	1.94778e8	−	1.24090e8i	1.53968	−	0.980902i
$503$	1.85417e8			1.45696			0.728478	−	0.685070i	$-0.240228\pi$
$503$	1.85417e8			1.45696			0.728478	+	0.685070i	$0.240228\pi$
$504$	5.92081e7	−	2.31086e8i	0.462477	−	1.80502i
$505$			7.15179e7i			0.555317i
$506$	5.20305e7	−	3.31477e7i	0.401612	−	0.255860i
$507$	2.65583e7	−	5.43411e6i	0.203787	−	0.0416970i
$508$	−5.84066e7	−	2.72341e7i	−0.445523	−	0.207741i
$509$	−7.06640e7	−	7.06640e7i	−0.535852	−	0.535852i	0.386456	−	0.922308i	$-0.373699\pi$
$509$	−7.06640e7	−	7.06640e7i	−0.535852	−	0.535852i	−0.922308	+	0.386456i	$0.873699\pi$
$510$	1.06294e7	−	1.02878e7i	0.0801306	−	0.0775551i
$511$	−4.25062e7			−0.318558
$512$	5.13528e7	−	1.24005e8i	0.382608	−	0.923911i
$513$	−1.56768e8	−	2.85145e7i	−1.16120	−	0.211209i
$514$	−7.20484e6	+	3.25003e7i	−0.0530560	+	0.239330i
$515$	8.41947e7	+	8.41947e7i	0.616401	+	0.616401i
$516$	−2.06272e8	+	1.26725e8i	−1.50138	+	0.922384i
$517$	4.68808e7	+	4.68808e7i	0.339253	+	0.339253i
$518$	−1.45768e7	+	9.28662e6i	−0.104875	+	0.0668141i
$519$	4.01486e7	−	6.08048e7i	0.287189	−	0.434946i
$520$	−4.66708e7	+	6.08259e7i	−0.331921	+	0.432592i
$521$	−2.53784e8			−1.79453			−0.897265	−	0.441492i	$-0.854449\pi$
$521$	−2.53784e8			−1.79453			−0.897265	+	0.441492i	$0.854449\pi$
$522$	1.26581e8	+	8.65812e7i	0.889934	+	0.608712i
$523$	1.39866e8	+	1.39866e8i	0.977706	+	0.977706i	0.999757	−	0.0220506i	$-0.00701948\pi$
$523$	1.39866e8	+	1.39866e8i	0.977706	+	0.977706i	−0.0220506	+	0.999757i	$0.507019\pi$
$524$	−5.74915e7	−	1.57948e8i	−0.399586	−	1.09779i
$525$	−3.37596e7	−	1.64994e8i	−0.233303	−	1.14023i
$526$	−6.06864e6	−	1.34533e6i	−0.0416998	−	0.00924423i
$527$		−	5.50764e6i		−	0.0376300i
$528$	−1.54829e7	−	1.34518e8i	−0.105184	−	0.913855i
$529$	−1.08366e8			−0.732028
$530$	3.41165e7	−	1.53896e8i	0.229159	−	1.03371i
$531$	4.41017e7	−	1.09859e8i	0.294559	−	0.733754i
$532$	1.13259e8	+	3.11158e8i	0.752206	+	2.06655i
$533$	9.07596e7	−	9.07596e7i	0.599392	−	0.599392i
$534$	3.06479e6	−	1.87640e8i	0.0201269	−	1.23226i
$535$			1.78173e7i			0.116354i
$536$	−6.67032e7	+	8.78347e6i	−0.433164	+	0.0570390i
$537$	−3.31543e7	+	5.02120e7i	−0.214100	+	0.324253i
$538$	−8.61737e7	−	1.35263e8i	−0.553386	−	0.868625i
$539$	−2.51787e8	+	2.51787e8i	−1.60793	+	1.60793i
$540$	−7.87310e7	−	5.57607e7i	−0.499994	−	0.354117i
$541$	−1.18197e7	+	1.18197e7i	−0.0746474	+	0.0746474i	−0.743445	−	0.668797i	$-0.766809\pi$
$541$	−1.18197e7	+	1.18197e7i	−0.0746474	+	0.0746474i	0.668797	+	0.743445i	$0.266809\pi$
$542$	4.55525e7	+	1.00983e7i	0.286098	+	0.0634236i
$543$	−2.90183e7	+	4.39481e7i	−0.181248	+	0.274499i
$544$	2.59901e7	−	1.35311e7i	0.161440	−	0.0840496i
$545$			2.20041e7i			0.135929i
$546$	−1.93950e8	+	1.87717e8i	−1.19155	+	1.15325i
$547$	−7.42213e7	+	7.42213e7i	−0.453489	+	0.453489i	−0.896511	−	0.443022i	$-0.853906\pi$
$547$	−7.42213e7	+	7.42213e7i	−0.453489	+	0.453489i	0.443022	+	0.896511i	$0.353906\pi$
$548$	1.89200e7	+	8.82213e6i	0.114969	+	0.0536083i
$549$	−6.38715e6	+	1.59106e7i	−0.0386003	+	0.0961544i
$550$	−5.13633e7	−	8.06226e7i	−0.308720	−	0.484584i
$551$	−2.12876e8			−1.27254
$552$	3.80792e7	−	7.83002e7i	0.226397	−	0.465528i
$553$		−	3.93448e8i		−	2.32655i
$554$	1.00929e8	+	1.58423e8i	0.593587	+	0.931727i
$555$	1.40120e6	+	6.84813e6i	0.00819638	+	0.0400584i
$556$	7.86275e6	+	2.16015e7i	0.0457457	+	0.125678i
$557$	7.66566e7	+	7.66566e7i	0.443592	+	0.443592i	0.893217	−	0.449625i	$-0.148442\pi$
$557$	7.66566e7	+	7.66566e7i	0.443592	+	0.443592i	−0.449625	+	0.893217i	$0.648442\pi$
$558$	−3.53044e7	+	6.62490e6i	−0.203201	+	0.0381309i
$559$	2.73919e8			1.56815
$560$	−1.74668e7	+	1.99729e8i	−0.0994602	+	1.13731i
$561$	1.62883e7	−	2.46684e7i	0.0922542	−	0.139718i
$562$	1.56723e8	+	3.47432e7i	0.882926	+	0.195732i
$563$	8.92546e7	+	8.92546e7i	0.500156	+	0.500156i	0.911486	−	0.411330i	$-0.134936\pi$
$563$	8.92546e7	+	8.92546e7i	0.500156	+	0.500156i	−0.411330	+	0.911486i	$0.634936\pi$
$564$	9.10101e7	+	2.17408e7i	0.507285	+	0.121182i
$565$	−1.42611e7	−	1.42611e7i	−0.0790692	−	0.0790692i
$566$	−5.62181e7	−	8.82430e7i	−0.310046	−	0.486666i
$567$	−2.45375e8	−	2.34855e8i	−1.34611	−	1.28840i
$568$	2.75723e8	+	2.11558e8i	1.50462	+	1.15447i
$569$	2.27051e8			1.23250			0.616249	−	0.787551i	$-0.288651\pi$
$569$	2.27051e8			1.23250			0.616249	+	0.787551i	$0.288651\pi$
$570$	1.33901e8	+	2.18705e6i	0.723034	+	0.0118096i
$571$	2.02563e8	+	2.02563e8i	1.08806	+	1.08806i	0.995728	+	0.0923309i	$0.0294318\pi$
$571$	2.02563e8	+	2.02563e8i	1.08806	+	1.08806i	0.0923309	+	0.995728i	$0.470568\pi$
$572$	−6.47463e7	+	1.38855e8i	−0.345961	+	0.741950i
$573$	−1.80450e8	+	3.69221e7i	−0.959166	+	0.196256i
$574$	7.26457e7	−	3.27698e8i	0.384126	−	1.73276i
$575$		−	6.14689e7i		−	0.323334i
$576$	−1.17998e8	−	1.50323e8i	−0.617456	−	0.786606i
$577$	7.35353e7			0.382797			0.191399	−	0.981512i	$-0.438698\pi$
$577$	7.35353e7			0.382797			0.191399	+	0.981512i	$0.438698\pi$
$578$	−1.82278e8	−	4.04084e7i	−0.943956	−	0.209261i
$579$	5.02021e7	+	2.45354e8i	0.258634	+	1.26403i
$580$	−1.16817e8	−	5.44700e7i	−0.598716	−	0.279173i
$581$	3.32565e8	−	3.32565e8i	1.69570	−	1.69570i
$582$	3.69068e6	−	2.25960e8i	0.0187214	−	1.14621i
$583$		−	3.15004e8i		−	1.58968i
$584$	−2.07286e7	+	2.70156e7i	−0.104071	+	0.135636i
$585$	4.28764e7	+	1.00389e8i	0.214166	+	0.501438i
$586$	−1.12053e8	+	7.13871e7i	−0.556841	+	0.354754i
$587$	1.71201e8	−	1.71201e8i	0.846434	−	0.846434i	−0.143252	−	0.989686i	$-0.545756\pi$
$587$	1.71201e8	−	1.71201e8i	0.846434	−	0.846434i	0.989686	+	0.143252i	$0.0457559\pi$
$588$	−1.16765e8	+	4.88797e8i	−0.574358	+	2.40434i
$589$	3.52571e7	−	3.52571e7i	0.172544	−	0.172544i
$590$	−2.15334e7	+	9.71352e7i	−0.104847	+	0.472956i
$591$	−7.22848e7	−	4.77287e7i	−0.350174	−	0.231216i
$592$	−1.20625e6	+	1.37933e7i	−0.00581398	+	0.0664817i
$593$		−	3.61729e8i		−	1.73468i	−0.497715	−	0.867341i	$-0.665827\pi$
$593$		−	3.61729e8i		−	1.73468i	0.497715	−	0.867341i	$-0.334173\pi$
$594$	−1.77719e8	−	7.47365e7i	−0.847959	−	0.356593i
$595$	−3.09500e7	+	3.09500e7i	−0.146930	+	0.146930i
$596$	−1.31355e8	+	4.78119e7i	−0.620450	+	0.225838i
$597$	−1.17876e8	+	2.41188e7i	−0.553993	+	0.113353i
$598$	−8.30874e7	+	5.29335e7i	−0.388536	+	0.247530i
$599$	1.12092e8			0.521548			0.260774	−	0.965400i	$-0.416022\pi$
$599$	1.12092e8			0.521548			0.260774	+	0.965400i	$0.416022\pi$
$600$	−1.21328e8	−	5.90047e7i	−0.561705	−	0.273170i
$601$			1.91486e8i			0.882090i	0.897485	+	0.441045i	$0.145392\pi$
$601$			1.91486e8i			0.882090i	−0.897485	+	0.441045i	$0.854608\pi$
$602$	6.04132e8	−	3.84882e8i	2.76912	−	1.76416i
$603$	−3.56873e7	+	8.88980e7i	−0.162765	+	0.405453i
$604$	1.29417e8	−	2.77550e8i	0.587330	−	1.25959i
$605$	−1.47559e7	−	1.47559e7i	−0.0666348	−	0.0666348i
$606$	1.40278e8	+	1.44937e8i	0.630337	+	0.651270i
$607$	−1.28820e8			−0.575993			−0.287997	−	0.957631i	$-0.592989\pi$
$607$	−1.28820e8			−0.575993			−0.287997	+	0.957631i	$0.592989\pi$
$608$	2.52994e8	+	7.97562e7i	1.12564	+	0.354857i
$609$	−3.78674e8	−	2.50034e8i	−1.67654	−	1.10700i
$610$	3.11864e6	−	1.40679e7i	0.0137397	−	0.0619782i
$611$	−7.48638e7	−	7.48638e7i	−0.328208	−	0.328208i
$612$	1.36250e6	−	4.16980e7i	0.00594403	−	0.181912i
$613$	1.44668e8	+	1.44668e8i	0.628045	+	0.628045i	0.947576	−	0.319531i	$-0.103525\pi$
$613$	1.44668e8	+	1.44668e8i	0.628045	+	0.628045i	−0.319531	+	0.947576i	$0.603525\pi$
$614$	−2.28408e8	+	1.45515e8i	−0.986750	+	0.628641i
$615$	−1.13282e8	−	7.47985e7i	−0.487006	−	0.321564i
$616$	5.23062e7	+	3.97222e8i	0.223775	+	1.69938i
$617$	1.83676e8			0.781984			0.390992	−	0.920394i	$-0.372132\pi$
$617$	1.83676e8			0.781984			0.390992	+	0.920394i	$0.372132\pi$
$618$	3.35771e8	+	5.48425e6i	1.42258	+	0.0232355i
$619$	−5.65764e6	−	5.65764e6i	−0.0238541	−	0.0238541i	0.695079	−	0.718933i	$-0.255369\pi$
$619$	−5.65764e6	−	5.65764e6i	−0.0238541	−	0.0238541i	−0.718933	+	0.695079i	$0.755369\pi$
$620$	2.83689e7	−	1.03260e7i	0.119033	−	0.0433269i
$621$	−7.05584e7	−	1.01933e8i	−0.294628	−	0.425636i
$622$	−2.51039e8	−	5.56515e7i	−1.04320	−	0.231263i
$623$			5.55283e8i			2.29641i
$624$	2.47245e7	+	2.14811e8i	0.101759	+	0.884102i
$625$	−3.59913e6			−0.0147420
$626$	−2.61034e7	+	1.17750e8i	−0.106408	+	0.479995i
$627$	2.62184e8	−	5.36457e7i	1.06366	−	0.217637i
$628$	−7.68034e7	+	2.79557e7i	−0.310100	+	0.112873i
$629$	−2.13740e6	+	2.13740e6i	−0.00858882	+	0.00858882i
$630$	2.35620e8	+	1.61164e8i	0.942304	+	0.644533i
$631$		−	2.01683e8i		−	0.802752i	−0.915913	−	0.401376i	$-0.868532\pi$
$631$		−	2.01683e8i		−	0.802752i	0.915913	−	0.401376i	$-0.131468\pi$
$632$	−2.50063e8	−	1.91869e8i	−0.990599	−	0.760071i
$633$	−2.51215e8	−	1.65874e8i	−0.990453	−	0.653983i
$634$	7.99989e7	+	1.25571e8i	0.313918	+	0.492743i
$635$	5.45306e7	−	5.45306e7i	0.212970	−	0.212970i
$636$	−2.32719e8	−	3.78801e8i	−0.904608	−	1.47245i
$637$	4.02078e8	−	4.02078e8i	1.55558	−	1.55558i
$638$	−2.51465e8	−	5.57462e7i	−0.968314	−	0.214661i
$639$	4.55061e8	−	1.94358e8i	1.74408	−	0.744903i
$640$	1.18424e8	+	1.08502e8i	0.451751	+	0.413901i
$641$			8.70474e7i			0.330508i	0.986251	+	0.165254i	$0.0528443\pi$
$641$			8.70474e7i			0.330508i	−0.986251	+	0.165254i	$0.947156\pi$
$642$	3.49477e7	+	3.61083e7i	0.132073	+	0.136459i
$643$	−1.24757e8	+	1.24757e8i	−0.469280	+	0.469280i	−0.901681	−	0.432401i	$-0.857666\pi$
$643$	−1.24757e8	+	1.24757e8i	−0.469280	+	0.469280i	0.432401	+	0.901681i	$0.357666\pi$
$644$	−1.08874e8	+	2.33491e8i	−0.407629	+	0.874205i
$645$	−5.80726e7	−	2.83820e8i	−0.216417	−	1.05770i
$646$	3.11162e7	+	4.88417e7i	0.115422	+	0.181173i
$647$	4.94931e7			0.182739			0.0913696	−	0.995817i	$-0.470876\pi$
$647$	4.94931e7			0.182739			0.0913696	+	0.995817i	$0.470876\pi$
$648$	−2.68926e8	+	4.14229e7i	−0.988344	+	0.152235i
$649$			1.98822e8i			0.727328i
$650$	8.20220e7	+	1.28746e8i	0.298669	+	0.468807i
$651$	1.04128e8	−	2.13058e7i	0.377420	−	0.0772243i
$652$	−4.37416e8	+	1.59215e8i	−1.57816	+	0.574437i
$653$	−2.55431e8	−	2.55431e8i	−0.917347	−	0.917347i	0.0794891	−	0.996836i	$-0.474671\pi$
$653$	−2.55431e8	−	2.55431e8i	−0.917347	−	0.917347i	−0.996836	+	0.0794891i	$0.974671\pi$
$654$	4.31597e7	+	4.45930e7i	0.154293	+	0.159417i
$655$	2.01142e8			0.715780
$656$	−1.72848e8	−	2.05977e8i	−0.612283	−	0.729637i
$657$	1.90433e7	+	4.45872e7i	0.0671502	+	0.157222i
$658$	−2.70304e8	−	5.99224e7i	−0.948801	−	0.210335i
$659$	1.63412e8	+	1.63412e8i	0.570990	+	0.570990i	0.932405	−	0.361415i	$-0.117706\pi$
$659$	1.63412e8	+	1.63412e8i	0.570990	+	0.570990i	−0.361415	+	0.932405i	$0.617706\pi$
$660$	1.57601e8	+	3.76483e7i	0.548185	+	0.130952i
$661$	2.22895e8	+	2.22895e8i	0.771784	+	0.771784i	0.978418	−	0.206634i	$-0.0662509\pi$
$661$	2.22895e8	+	2.22895e8i	0.771784	+	0.771784i	−0.206634	+	0.978418i	$0.566251\pi$
$662$	3.17293e6	+	4.98041e6i	0.0109367	+	0.0171669i
$663$	−2.60107e7	+	3.93930e7i	−0.0892506	+	0.135169i
$664$	−4.91887e7	−	3.73547e8i	−0.168020	−	1.27597i
$665$	−3.96252e8			−1.34743
$666$	1.62719e7	+	1.11299e7i	0.0550827	+	0.0376764i
$667$	−1.17113e8	−	1.17113e8i	−0.394665	−	0.394665i
$668$	−4.87965e8	−	2.27531e8i	−1.63704	−	0.763328i
$669$	−1.12489e7	−	5.49768e7i	−0.0375690	−	0.183612i
$670$	1.74249e7	−	7.86022e7i	0.0579358	−	0.261343i
$671$		−	2.87950e7i		−	0.0953123i
$672$	3.56360e8	+	4.39028e8i	1.17431	+	1.44672i
$673$	−1.25817e8			−0.412758			−0.206379	−	0.978472i	$-0.566168\pi$
$673$	−1.25817e8			−0.412758			−0.206379	+	0.978472i	$0.566168\pi$
$674$	1.99283e8	+	4.41781e7i	0.650864	+	0.144287i
$675$	−1.57947e8	+	1.09332e8i	−0.513572	+	0.355497i
$676$	−2.71552e7	+	5.82373e7i	−0.0879049	+	0.188522i
$677$	−7.60961e7	+	7.60961e7i	−0.245243	+	0.245243i	−0.819015	−	0.573772i	$-0.805479\pi$
$677$	−7.60961e7	+	7.60961e7i	−0.245243	+	0.245243i	0.573772	+	0.819015i	$0.305479\pi$
$678$	−5.68736e7	−	928935.i	−0.182483	−	0.00298055i
$679$			6.68682e8i			2.13605i
$680$	4.57771e6	+	3.47639e7i	0.0145587	+	0.110561i
$681$	9.08906e7	−	1.37653e8i	0.287791	−	0.435858i
$682$	5.08811e7	−	3.24155e7i	0.160400	−	0.102188i
$683$	2.18348e7	−	2.18348e7i	0.0685311	−	0.0685311i	−0.672010	−	0.740542i	$-0.734569\pi$
$683$	2.18348e7	−	2.18348e7i	0.0685311	−	0.0685311i	0.740542	+	0.672010i	$0.234569\pi$
$684$	2.75651e8	−	2.58207e8i	0.861373	−	0.806863i
$685$	−1.76644e7	+	1.76644e7i	−0.0549577	+	0.0549577i
$686$	1.91640e8	−	8.64470e8i	0.593628	−	2.67780i
$687$	1.37509e8	−	2.08256e8i	0.424092	−	0.642285i
$688$	4.99929e7	−	5.71659e8i	0.153512	−	1.75538i
$689$			5.03029e8i			1.53793i
$690$	7.24619e7	+	7.48683e7i	0.220578	+	0.227903i
$691$	3.11619e8	−	3.11619e8i	0.944473	−	0.944473i	−0.0540640	−	0.998537i	$-0.517218\pi$
$691$	3.11619e8	−	3.11619e8i	0.944473	−	0.944473i	0.998537	+	0.0540640i	$0.0172175\pi$
$692$	5.90746e7	+	1.62297e8i	0.178272	+	0.489770i
$693$	5.29394e8	+	2.12520e8i	1.59067	+	0.638558i
$694$	4.28112e7	−	2.72743e7i	0.128079	−	0.0815972i
$695$	−2.75090e7			−0.0819445
$696$	−3.43578e8	+	1.18742e8i	−1.01906	+	0.352189i
$697$		−	5.87025e7i		−	0.173364i
$698$	−4.20943e8	+	2.68175e8i	−1.23782	+	0.788593i
$699$	3.01770e7	+	1.47485e8i	0.0883579	+	0.431833i
$700$	3.61801e8	+	1.68703e8i	1.05481	+	0.491845i
$701$	4.32090e8	+	4.32090e8i	1.25435	+	1.25435i	0.953748	+	0.300607i	$0.0971892\pi$
$701$	4.32090e8	+	4.32090e8i	1.25435	+	1.25435i	0.300607	+	0.953748i	$0.402811\pi$
$702$	2.83799e8	+	1.19347e8i	0.820352	+	0.344984i
$703$	−2.73651e7			−0.0787645
$704$	2.77970e8	+	1.60466e8i	0.796671	+	0.459901i
$705$	−6.16982e7	+	9.34414e7i	−0.176078	+	0.266669i
$706$	−1.00106e7	+	4.51570e7i	−0.0284478	+	0.128325i
$707$	−4.22018e8	−	4.22018e8i	−1.19419	−	1.19419i
$708$	1.46886e8	+	2.39089e8i	0.413886	+	0.673690i
$709$	−7.92574e7	−	7.92574e7i	−0.222383	−	0.222383i	0.587118	−	0.809501i	$-0.300262\pi$
$709$	−7.92574e7	−	7.92574e7i	−0.222383	−	0.222383i	−0.809501	+	0.587118i	$0.800262\pi$
$710$	−3.50749e8	+	2.23456e8i	−0.979990	+	0.624335i
$711$	−4.12711e8	+	1.76270e8i	−1.14825	+	0.490422i
$712$	3.52920e8	+	2.70790e8i	0.977769	+	0.750227i
$713$	3.87931e7			0.107025
$714$	−2.01601e6	+	1.23429e8i	−0.00553858	+	0.339097i
$715$	−1.29641e8	−	1.29641e8i	−0.354669	−	0.354669i
$716$	−4.87833e7	−	1.34023e8i	−0.132902	−	0.365125i
$717$	6.50092e7	−	1.33016e7i	0.176367	−	0.0360866i
$718$	−5.24247e8	−	1.16218e8i	−1.41632	−	0.313978i
$719$			2.73029e8i			0.734551i	0.930112	+	0.367275i	$0.119709\pi$
$719$			2.73029e8i			0.734551i	−0.930112	+	0.367275i	$0.880291\pi$
$720$	2.17333e8	−	7.11595e7i	0.582276	−	0.190649i
$721$	−9.93643e8			−2.65109
$722$	−3.20120e7	+	1.44403e8i	−0.0850553	+	0.383676i
$723$	3.88079e7	+	1.89667e8i	0.102685	+	0.501853i
$724$	−4.26976e7	−	1.17304e8i	−0.112509	−	0.309099i
$725$	−1.81470e8	+	1.81470e8i	−0.476202	+	0.476202i
$726$	−5.88471e7	−	961168.i	−0.153785	−	0.00251183i
$727$		−	1.27655e8i		−	0.332226i	−0.986107	−	0.166113i	$-0.946878\pi$
$727$		−	1.27655e8i		−	0.332226i	0.986107	−	0.166113i	$-0.0531217\pi$
$728$	−8.35277e7	−	6.34323e8i	−0.216489	−	1.64406i
$729$	−1.36422e8	+	3.62607e8i	−0.352129	+	0.935952i
$730$	−2.18944e7	−	3.43667e7i	−0.0562814	−	0.0883424i
$731$	8.85841e7	−	8.85841e7i	0.226779	−	0.226779i
$732$	−2.12732e7	−	3.46268e7i	−0.0542374	−	0.0882833i
$733$	−5.90748e7	+	5.90748e7i	−0.150000	+	0.150000i	−0.778118	−	0.628118i	$-0.783825\pi$
$733$	−5.90748e7	+	5.90748e7i	−0.150000	+	0.150000i	0.628118	+	0.778118i	$0.283825\pi$
$734$	−1.21916e8	−	2.70269e7i	−0.308298	−	0.0683452i
$735$	−5.01855e8	−	3.31368e8i	−1.26391	−	0.834543i
$736$	9.53062e7	+	1.83061e8i	0.239049	+	0.459159i
$737$		−	1.60888e8i		−	0.401902i
$738$	−3.76288e8	+	7.06106e7i	−0.936162	+	0.175671i
$739$	−3.68974e7	+	3.68974e7i	−0.0914244	+	0.0914244i	−0.751340	−	0.659915i	$-0.770592\pi$
$739$	−3.68974e7	+	3.68974e7i	−0.0914244	+	0.0914244i	0.659915	+	0.751340i	$0.270592\pi$
$740$	−1.50167e7	−	7.00206e6i	−0.0370577	−	0.0172795i
$741$	−4.18681e8	+	8.56667e7i	−1.02903	+	0.210551i
$742$	7.06804e8	+	1.10944e9i	1.73016	+	2.71576i
$743$	3.71772e8			0.906380			0.453190	−	0.891414i	$-0.350286\pi$
$743$	3.71772e8			0.906380			0.453190	+	0.891414i	$0.350286\pi$
$744$	3.72380e7	−	7.65705e7i	0.0904206	−	0.185927i
$745$		−	1.67277e8i		−	0.404545i
$746$	−2.28611e7	−	3.58840e7i	−0.0550656	−	0.0864339i
$747$	−4.97841e8	−	1.99854e8i	−1.19434	−	0.479457i
$748$	2.39665e7	+	6.58438e7i	0.0572665	+	0.157330i
$749$	−1.05138e8	−	1.05138e8i	−0.250215	−	0.250215i
$750$	3.01744e8	−	2.92045e8i	0.715244	−	0.692255i
$751$	−4.62464e8			−1.09184			−0.545918	−	0.837838i	$-0.683819\pi$
$751$	−4.62464e8			−1.09184			−0.545918	+	0.837838i	$0.683819\pi$
$752$	−1.69902e8	+	1.42575e8i	−0.399525	+	0.335266i
$753$	6.50450e8	+	4.29484e8i	1.52345	+	1.00592i
$754$	4.01565e8	+	8.90209e7i	0.936788	+	0.207672i
$755$	2.59131e8	+	2.59131e8i	0.602114	+	0.602114i
$756$	7.93617e8	−	1.35545e8i	1.83673	−	0.313702i
$757$	−3.31871e8	−	3.31871e8i	−0.765036	−	0.765036i	0.212192	−	0.977228i	$-0.431940\pi$
$757$	−3.31871e8	−	3.31871e8i	−0.765036	−	0.765036i	−0.977228	+	0.212192i	$0.931940\pi$
$758$	3.01185e8	+	4.72757e8i	0.691554	+	1.08550i
$759$	1.73752e8	+	1.14726e8i	0.397380	+	0.262385i
$760$	−1.93237e8	+	2.51845e8i	−0.440199	+	0.573710i
$761$	4.94510e8			1.12207			0.561036	−	0.827791i	$-0.310403\pi$
$761$	4.94510e8			1.12207			0.561036	+	0.827791i	$0.310403\pi$
$762$	3.55200e6	−	2.17469e8i	0.00802800	−	0.491511i
$763$	−1.29843e8	−	1.29843e8i	−0.292311	−	0.292311i
$764$	1.84506e8	−	3.95694e8i	0.413743	−	0.887317i
$765$	4.63313e7	+	1.85993e7i	0.103488	+	0.0415443i
$766$	1.36065e8	−	6.13775e8i	0.302733	−	1.36560i
$767$		−	3.17499e8i		−	0.703648i
$768$	4.52815e8	−	1.23941e7i	0.999626	−	0.0273610i
$769$	5.83761e8			1.28368			0.641838	−	0.766840i	$-0.278172\pi$
$769$	5.83761e8			1.28368			0.641838	+	0.766840i	$0.278172\pi$
$770$	−4.68082e8	−	1.03767e8i	−1.02530	−	0.227293i
$771$	−1.10071e8	+	2.25217e7i	−0.240165	+	0.0491404i
$772$	−5.38015e8	−	2.50869e8i	−1.16934	−	0.545248i
$773$	−1.44988e8	+	1.44988e8i	−0.313903	+	0.313903i	−0.846419	−	0.532517i	$-0.821246\pi$
$773$	−1.44988e8	+	1.44988e8i	−0.313903	+	0.313903i	0.532517	+	0.846419i	$0.321246\pi$
$774$	−6.74385e8	−	4.61278e8i	−1.45440	−	0.994808i
$775$		−	6.01110e7i		−	0.129136i
$776$	4.24993e8	+	3.26090e8i	0.909488	+	0.697835i
$777$	−4.86782e7	−	3.21416e7i	−0.103770	−	0.0685180i
$778$	2.44000e8	−	1.55448e8i	0.518144	−	0.330101i
$779$	3.75783e8	−	3.75783e8i	0.794923	−	0.794923i
$780$	−2.51673e8	−	6.01204e7i	−0.530337	−	0.126689i
$781$	−5.87659e8	+	5.87659e8i	−1.23359	+	1.23359i
$782$	−9.75161e6	+	4.39885e7i	−0.0203918	+	0.0919855i
$783$	−9.26240e7	+	5.09233e8i	−0.192947	+	1.06079i
$784$	−7.65740e8	−	9.12507e8i	−1.58903	−	1.89360i
$785$		−	9.78071e7i		−	0.202191i
$786$	4.07631e8	−	3.94530e8i	0.839460	−	0.812478i
$787$	−3.36905e8	+	3.36905e8i	−0.691167	+	0.691167i	−0.962489	−	0.271322i	$-0.912539\pi$
$787$	−3.36905e8	+	3.36905e8i	−0.691167	+	0.691167i	0.271322	+	0.962489i	$0.412539\pi$
$788$	1.92939e8	−	7.02280e7i	0.394313	−	0.143526i
$789$	−4.20539e6	−	2.05531e7i	−0.00856199	−	0.0418452i
$790$	3.18107e8	−	2.02660e8i	0.645196	−	0.411043i
$791$	1.68306e8			0.340071
$792$	3.93236e8	−	2.32828e8i	0.791549	−	0.468662i
$793$			4.59826e7i			0.0922092i
$794$	−1.37151e8	+	8.73765e7i	−0.273991	+	0.174555i
$795$	5.21211e8	−	1.06645e8i	1.03732	−	0.212247i
$796$	1.20526e8	−	2.58481e8i	0.238969	−	0.512495i
$797$	3.16006e8	+	3.16006e8i	0.624195	+	0.624195i	0.946601	−	0.322406i	$-0.104492\pi$
$797$	3.16006e8	+	3.16006e8i	0.624195	+	0.624195i	−0.322406	+	0.946601i	$0.604492\pi$
$798$	−8.03037e8	+	7.77226e8i	−1.58025	+	1.52946i
$799$	−4.84212e7			−0.0949283
$800$	2.83659e8	−	1.47680e8i	0.554021	−	0.288437i
$801$	5.82469e8	−	2.48774e8i	1.13338	−	0.484070i
$802$	−9.18235e7	+	4.14207e8i	−0.178004	+	0.802960i
$803$	−5.75793e7	−	5.75793e7i	−0.111204	−	0.111204i
$804$	−1.18861e8	−	1.93472e8i	−0.228702	−	0.372263i
$805$	−2.17996e8	−	2.17996e8i	−0.417890	−	0.417890i
$806$	−8.12519e7	+	5.17642e7i	−0.155177	+	0.0988609i
$807$	2.98253e8	−	4.51702e8i	0.567498	−	0.859471i
$808$	−4.74023e8	+	6.24193e7i	−0.898597	+	0.118327i
$809$	4.59516e8			0.867870			0.433935	−	0.900944i	$-0.357125\pi$
$809$	4.59516e8			0.867870			0.433935	+	0.900944i	$0.357125\pi$
$810$	6.34929e7	−	3.19360e8i	0.119473	−	0.600932i
$811$	−6.66651e7	−	6.66651e7i	−0.124979	−	0.124979i	0.641851	−	0.766830i	$-0.278167\pi$
$811$	−6.66651e7	−	6.66651e7i	−0.124979	−	0.124979i	−0.766830	+	0.641851i	$0.778167\pi$
$812$	1.01074e9	−	3.67900e8i	1.88787	−	0.687166i
$813$	3.15665e7	+	1.54276e8i	0.0587429	+	0.287095i
$814$	−3.23256e7	−	7.16611e6i	−0.0599341	−	0.0132865i
$815$		−	5.57038e8i		−	1.02899i
$816$	7.74646e7	+	6.14730e7i	0.142572	+	0.113139i
$817$	1.13414e9			2.07970
$818$	2.07438e8	−	9.35733e8i	0.378991	−	1.70959i
$819$	−8.45388e8	−	3.39373e8i	−1.53888	−	0.617769i
$820$	3.02366e8	−	1.10058e8i	0.548393	−	0.199610i
$821$	−3.00661e8	+	3.00661e8i	−0.543310	+	0.543310i	−0.924498	−	0.381187i	$-0.875515\pi$
$821$	−3.00661e8	+	3.00661e8i	−0.543310	+	0.543310i	0.381187	+	0.924498i	$0.375515\pi$
$822$	−1.15062e6	+	7.04463e7i	−0.00207165	+	0.126836i
$823$		−	3.18716e8i		−	0.571748i	−0.958267	−	0.285874i	$-0.907716\pi$
$823$		−	3.18716e8i		−	0.571748i	0.958267	−	0.285874i	$-0.0922839\pi$
$824$	−4.84561e8	+	6.31528e8i	−0.866098	+	1.12878i
$825$	1.77772e8	−	2.69234e8i	0.316593	−	0.479477i
$826$	−4.46116e8	−	7.00248e8i	−0.791603	−	1.24254i
$827$	−6.35683e8	+	6.35683e8i	−1.12389	+	1.12389i	−0.132739	+	0.991151i	$0.542377\pi$
$827$	−6.35683e8	+	6.35683e8i	−1.12389	+	1.12389i	−0.991151	+	0.132739i	$0.957623\pi$
$828$	2.93700e8	+	9.59675e6i	0.517384	+	0.0169057i
$829$	−9.32191e7	+	9.32191e7i	−0.163622	+	0.163622i	−0.784169	−	0.620547i	$-0.786911\pi$
$829$	−9.32191e7	+	9.32191e7i	−0.163622	+	0.163622i	0.620547	+	0.784169i	$0.286911\pi$
$830$	4.40183e8	+	9.75821e7i	0.769837	+	0.170662i
$831$	−3.49320e8	+	5.29043e8i	−0.608724	+	0.921909i
$832$	−4.43889e8	−	2.56247e8i	−0.770734	−	0.444928i
$833$		−	2.60061e8i		−	0.449924i
$834$	−5.57492e7	+	5.39573e7i	−0.0961037	+	0.0930148i
$835$	4.55583e8	−	4.55583e8i	0.782542	−	0.782542i
$836$	−2.68077e8	+	5.74920e8i	−0.458818	+	0.983985i
$837$	−6.89997e7	−	9.96809e7i	−0.117671	−	0.169995i
$838$	2.17568e8	+	3.41507e8i	0.369712	+	0.580320i
$839$	−5.12235e8			−0.867329			−0.433664	−	0.901075i	$-0.642780\pi$
$839$	−5.12235e8			−0.867329			−0.433664	+	0.901075i	$0.642780\pi$
$840$	−6.39542e8	+	2.21028e8i	−1.07903	+	0.372914i
$841$			9.66662e7i			0.162512i
$842$	−1.07135e8	−	1.68166e8i	−0.179472	−	0.281709i
$843$	1.08605e8	+	5.30785e8i	0.181286	+	0.886005i
$844$	6.70530e8	−	2.44067e8i	1.11530	−	0.405958i
$845$	−5.43725e7	−	5.43725e7i	−0.0901176	−	0.0901176i
$846$	5.82438e7	+	3.10384e8i	0.0961919	+	0.512612i
$847$	1.74146e8			0.286591
$848$	1.04980e9	+	9.18078e7i	1.72155	+	0.150554i
$849$	1.94574e8	−	2.94682e8i	0.317953	−	0.481537i
$850$	6.81614e7	+	1.51104e7i	0.110989	+	0.0246047i
$851$	−1.50548e7	−	1.50548e7i	−0.0244279	−	0.0244279i
$852$	−2.72525e8	+	1.14083e9i	−0.440644	+	1.84460i
$853$	2.00534e8	+	2.00534e8i	0.323103	+	0.323103i	0.849956	−	0.526853i	$-0.176628\pi$
$853$	2.00534e8	+	2.00534e8i	0.323103	+	0.323103i	−0.526853	+	0.849956i	$0.676628\pi$
$854$	6.46100e7	+	1.01415e8i	0.103735	+	0.162828i
$855$	1.77526e8	+	4.15652e8i	0.284030	+	0.665015i
$856$	−1.18094e8	+	1.55506e7i	−0.188281	+	0.0247928i
$857$	−1.14605e9			−1.82079			−0.910395	−	0.413739i	$-0.864222\pi$
$857$	−1.14605e9			−1.82079			−0.910395	+	0.413739i	$0.864222\pi$
$858$	−5.17010e8	−	8.44449e6i	−0.818535	−	0.0133694i
$859$	1.66318e8	+	1.66318e8i	0.262397	+	0.262397i	0.826027	−	0.563630i	$-0.190596\pi$
$859$	1.66318e8	+	1.66318e8i	0.262397	+	0.262397i	−0.563630	+	0.826027i	$0.690596\pi$
$860$	6.22363e8	+	2.90199e8i	0.978472	+	0.456248i
$861$	1.10984e9	−	2.27085e8i	1.73880	−	0.355777i
$862$	−1.82454e8	+	8.23033e8i	−0.284860	+	1.28498i
$863$		−	9.25526e8i		−	1.43998i	−0.693984	−	0.719990i	$-0.744146\pi$
$863$		−	9.25526e8i		−	1.43998i	0.693984	−	0.719990i	$-0.255854\pi$
$864$	3.00868e8	−	5.70498e8i	0.466482	−	0.884530i
$865$	−2.06681e8			−0.319339
$866$	−5.64990e8	−	1.25250e8i	−0.869936	−	0.192852i
$867$	−1.26314e8	−	6.17335e8i	−0.193817	−	0.947248i
$868$	−1.06469e8	+	2.28333e8i	−0.162803	+	0.349149i
$869$	5.32969e8	−	5.32969e8i	0.812161	−	0.812161i
$870$	7.10421e6	−	4.34952e8i	0.0107884	−	0.660517i
$871$			2.56921e8i			0.388817i
$872$	−1.45843e8	+	1.92047e7i	−0.219957	+	0.0289639i
$873$	7.01421e8	−	2.99579e8i	1.05423	−	0.450265i
$874$	−3.44017e8	+	2.19167e8i	−0.515282	+	0.328278i
$875$	−8.78597e8	+	8.78597e8i	−1.31149	+	1.31149i
$876$	−1.11779e8	−	2.67022e7i	−0.166283	−	0.0397224i
$877$	−4.22785e8	+	4.22785e8i	−0.626788	+	0.626788i	−0.947259	−	0.320470i	$-0.896159\pi$
$877$	−4.22785e8	+	4.22785e8i	−0.626788	+	0.626788i	0.320470	+	0.947259i	$0.396159\pi$
$878$	−1.61913e7	+	7.30374e7i	−0.0239220	+	0.107910i
$879$	−3.74194e8	−	2.47075e8i	−0.550973	−	0.363800i
$880$	−2.94216e8	+	2.46895e8i	−0.431736	+	0.362296i
$881$			4.79696e8i			0.701517i	0.936466	+	0.350759i	$0.114076\pi$
$881$			4.79696e8i			0.701517i	−0.936466	+	0.350759i	$0.885924\pi$
$882$	−1.66701e9	+	3.12815e8i	−2.42959	+	0.455913i
$883$	4.07684e8	−	4.07684e8i	0.592163	−	0.592163i	−0.346052	−	0.938215i	$-0.612478\pi$
$883$	4.07684e8	−	4.07684e8i	0.592163	−	0.592163i	0.938215	+	0.346052i	$0.112478\pi$
$884$	−3.82721e7	−	1.05146e8i	−0.0554020	−	0.152207i
$885$	−3.28975e8	+	6.73118e7i	−0.474605	+	0.0971094i
$886$	−8.00664e8	+	5.10090e8i	−1.15120	+	0.733407i
$887$	−2.31553e8			−0.331802			−0.165901	−	0.986142i	$-0.553053\pi$
$887$	−2.31553e8			−0.331802			−0.165901	+	0.986142i	$0.553053\pi$
$888$	−4.41667e7	+	1.52641e7i	−0.0630748	+	0.0217988i
$889$			6.43555e8i			0.915968i
$890$	−4.48952e8	+	2.86020e8i	−0.636840	+	0.405720i
$891$	−1.42507e7	−	6.50525e8i	−0.0201467	−	0.919667i
$892$	1.20554e8	+	5.62125e7i	0.169858	+	0.0792024i
$893$	−3.09968e8	−	3.09968e8i	−0.435274	−	0.435274i
$894$	−3.28104e8	−	3.39000e8i	−0.459197	−	0.474446i
$895$	1.70675e8			0.238068
$896$	−1.33906e9	+	5.85491e7i	−1.86155	+	0.0813947i
$897$	−2.77465e8	−	1.83206e8i	−0.384442	−	0.253842i
$898$	−2.75130e7	+	1.24109e8i	−0.0379935	+	0.171385i
$899$	−1.14526e8	−	1.14526e8i	−0.157625	−	0.157625i
$900$	1.48704e7	−	4.55096e8i	0.0203984	−	0.624274i
$901$	1.62677e8	+	1.62677e8i	0.222409	+	0.222409i
$902$	5.42309e8	−	3.45496e8i	0.738971	−	0.470786i
$903$	2.01746e9	+	1.33210e9i	2.73994	+	1.80915i
$904$	8.20761e7	−	1.06970e8i	0.111099	−	0.144796i
$905$	1.49384e8			0.201538
$906$	1.03342e9	+	1.68792e7i	1.38961	+	0.0226969i
$907$	−4.03477e8	−	4.03477e8i	−0.540751	−	0.540751i	0.382998	−	0.923749i	$-0.374892\pi$
$907$	−4.03477e8	−	4.03477e8i	−0.540751	−	0.540751i	−0.923749	+	0.382998i	$0.874892\pi$
$908$	1.33736e8	+	3.67417e8i	0.178646	+	0.490797i
$909$	−2.53610e8	+	6.31749e8i	−0.337656	+	0.841110i
$910$	7.47479e8	+	1.65705e8i	0.991916	+	0.219893i
$911$		−	3.97215e8i		−	0.525376i	−0.964881	−	0.262688i	$-0.915391\pi$
$911$		−	3.97215e8i		−	0.525376i	0.964881	−	0.262688i	$-0.0846090\pi$
$912$	1.02370e8	+	8.89407e8i	0.134955	+	1.17251i
$913$	9.00992e8			1.18388
$914$	−2.81844e8	+	1.27137e9i	−0.369122	+	1.66507i
$915$	4.76447e7	−	9.74862e6i	0.0621943	−	0.0127256i
$916$	2.02330e8	+	5.55867e8i	0.263254	+	0.723243i
$917$	−1.18691e9	+	1.18691e9i	−1.53926	+	1.53926i
$918$	1.30376e8	−	5.31833e7i	0.168526	−	0.0687460i
$919$			5.52490e8i			0.711833i	0.934518	+	0.355917i	$0.115831\pi$
$919$			5.52490e8i			0.711833i	−0.934518	+	0.355917i	$0.884169\pi$
$920$	−2.44860e8	+	3.22432e7i	−0.314452	+	0.0414070i
$921$	−7.62755e8	−	5.03637e8i	−0.976352	−	0.644672i
$922$	3.16112e8	+	4.96187e8i	0.403319	+	0.633071i
$923$	9.38432e8	−	9.38432e8i	1.19343	−	1.19343i
$924$	−1.15214e9	+	7.07824e8i	−1.46046	+	0.897242i
$925$	−2.33278e7	+	2.33278e7i	−0.0294746	+	0.0294746i
$926$	1.14199e9	+	2.53163e8i	1.43824	+	0.318836i
$927$	4.45166e8	+	1.04229e9i	0.558834	+	1.30843i
$928$	2.59073e8	−	8.21804e8i	0.324174	−	1.02831i
$929$		−	9.36995e8i		−	1.16867i	−0.811514	−	0.584333i	$-0.801356\pi$
$929$		−	9.36995e8i		−	1.16867i	0.811514	−	0.584333i	$-0.198644\pi$
$930$	7.08612e7	+	7.32144e7i	0.0880967	+	0.0910223i
$931$	1.66477e9	−	1.66477e9i	2.06303	−	2.06303i
$932$	−3.23407e8	−	1.50800e8i	−0.399486	−	0.186275i
$933$	−1.73962e8	−	8.50209e8i	−0.214195	−	1.04684i
$934$	5.91014e8	+	9.27687e8i	0.725366	+	1.13857i
$935$	−8.38504e7			−0.102582
$936$	−6.27958e8	+	3.71803e8i	−0.765778	+	0.453404i
$937$			1.32821e8i			0.161453i	0.996736	+	0.0807267i	$0.0257241\pi$
$937$			1.32821e8i			0.161453i	−0.996736	+	0.0807267i	$0.974276\pi$
$938$	3.60999e8	+	5.66643e8i	0.437419	+	0.686596i
$939$	−3.98791e8	+	8.15970e7i	−0.481669	+	0.0985547i
$940$	−9.07827e7	−	2.49409e8i	−0.109300	−	0.300282i
$941$	−6.81919e8	−	6.81919e8i	−0.818397	−	0.818397i	0.167479	−	0.985876i	$-0.446437\pi$
$941$	−6.81919e8	−	6.81919e8i	−0.818397	−	0.818397i	−0.985876	+	0.167479i	$0.946437\pi$
$942$	−1.91843e8	−	1.98214e8i	−0.229506	−	0.237127i
$943$	4.13471e8			0.493072
$944$	−6.62609e8	−	5.79467e7i	−0.787664	−	0.0688831i
$945$	−1.72412e8	+	9.47894e8i	−0.204301	+	1.12322i
$946$	1.33973e9	+	2.96998e8i	1.58250	+	0.350817i
$947$	−7.22398e7	−	7.22398e7i	−0.0850602	−	0.0850602i	0.663296	−	0.748357i	$-0.269157\pi$
$947$	−7.22398e7	−	7.22398e7i	−0.0850602	−	0.0850602i	−0.748357	+	0.663296i	$0.769157\pi$
$948$	2.47162e8	−	1.03466e9i	0.290107	−	1.21443i
$949$	9.19483e7	+	9.19483e7i	0.107583	+	0.107583i
$950$	3.39606e8	+	5.33063e8i	0.396099	+	0.621739i
$951$	−2.76882e8	+	4.19335e8i	−0.321923	+	0.487551i
$952$	−2.32150e8	−	1.78125e8i	−0.269065	−	0.206449i
$953$	−3.02852e8			−0.349906			−0.174953	−	0.984577i	$-0.555977\pi$
$953$	−3.02852e8			−0.349906			−0.174953	+	0.984577i	$0.555977\pi$
$954$	8.47097e8	−	1.23845e9i	0.975637	−	1.42638i
$955$	3.69434e8	+	3.69434e8i	0.424158	+	0.424158i
$956$	−6.64704e7	+	1.42553e8i	−0.0760772	+	0.163156i
$957$	−1.74258e8	−	8.51655e8i	−0.198819	−	0.971690i
$958$	1.76745e8	−	7.97280e8i	0.201025	−	0.906806i
$959$		−	2.08471e8i		−	0.236369i
$960$	−1.71402e8	+	5.14259e8i	−0.193732	+	0.581257i
$961$	−8.49568e8			−0.957255
$962$	5.16207e7	+	1.14436e7i	0.0579828	+	0.0128539i
$963$	−6.31820e7	+	1.57388e8i	−0.0707481	+	0.176236i
$964$	−4.15903e8	−	1.93930e8i	−0.464260	−	0.216478i
$965$	5.02311e8	−	5.02311e8i	0.558973	−	0.558973i
$966$	−8.69375e8	−	1.41998e7i	−0.964442	−	0.0157525i
$967$		−	1.00088e9i		−	1.10689i	−0.832887	−	0.553443i	$-0.813314\pi$
$967$		−	1.00088e9i		−	1.10689i	0.832887	−	0.553443i	$-0.186686\pi$
$968$	8.49241e7	−	1.10681e8i	0.0936278	−	0.122025i
$969$	−1.07695e8	+	1.63104e8i	−0.118365	+	0.179264i
$970$	−5.40637e8	+	3.44431e8i	−0.592367	+	0.377387i
$971$	−4.71338e8	+	4.71338e8i	−0.514843	+	0.514843i	−0.916006	−	0.401164i	$-0.868606\pi$
$971$	−4.71338e8	+	4.71338e8i	−0.514843	+	0.514843i	0.401164	+	0.916006i	$0.368606\pi$
$972$	−4.97733e8	−	7.71746e8i	−0.541997	−	0.840380i
$973$	1.62327e8	−	1.62327e8i	0.176218	−	0.176218i
$974$	5.06117e7	−	2.28304e8i	0.0547739	−	0.247080i
$975$	−2.83883e8	+	4.29939e8i	−0.306285	+	0.463867i
$976$	9.59642e7	+	8.39229e6i	0.103219	+	0.00902674i
$977$		−	1.75602e9i		−	1.88298i	−0.337040	−	0.941490i	$-0.609426\pi$
$977$		−	1.75602e9i		−	1.88298i	0.337040	−	0.941490i	$-0.390574\pi$
$978$	−1.09260e9	−	1.12888e9i	−1.16800	−	1.20679i
$979$	−7.52192e8	+	7.52192e8i	−0.801642	+	0.801642i
$980$	1.33953e9	−	4.87575e8i	1.42322	−	0.518040i
$981$	−7.80286e7	+	1.94371e8i	−0.0826507	+	0.205885i
$982$	−7.89995e8	+	5.03293e8i	−0.834238	+	0.531479i
$983$	−9.19157e8			−0.967674			−0.483837	−	0.875158i	$-0.660757\pi$
$983$	−9.19157e8			−0.967674			−0.483837	+	0.875158i	$0.660757\pi$
$984$	3.96896e8	−	8.16117e8i	0.416574	−	0.856578i
$985$			2.45703e8i			0.257100i
$986$	1.58653e8	−	1.01075e8i	0.165508	−	0.105442i
$987$	−1.87313e8	−	9.15458e8i	−0.194812	−	0.952109i
$988$	4.28091e8	−	9.18088e8i	0.443880	−	0.951949i
$989$	6.23943e8	+	6.23943e8i	0.644994	+	0.644994i
$990$	1.00860e8	+	5.37488e8i	0.103947	+	0.553940i
$991$	1.62214e9			1.66674			0.833370	−	0.552715i	$-0.186408\pi$
$991$	1.62214e9			1.66674			0.833370	+	0.552715i	$0.186408\pi$
$992$	9.32008e7	+	1.79017e8i	0.0954739	+	0.183384i
$993$	−1.09817e7	+	1.66317e7i	−0.0112156	+	0.0169860i
$994$	7.51138e8	−	3.38831e9i	0.764823	−	3.45004i
$995$	2.41328e8	+	2.41328e8i	0.244984	+	0.244984i
$996$	1.08347e9	−	6.65636e8i	1.09658	−	0.673688i
$997$	−1.37098e9	−	1.37098e9i	−1.38340	−	1.38340i	−0.838510	−	0.544887i	$-0.816573\pi$
$997$	−1.37098e9	−	1.37098e9i	−1.38340	−	1.38340i	−0.544887	−	0.838510i	$-0.683427\pi$
$998$	1.31658e9	−	8.38770e8i	1.32451	−	0.843823i
$999$	−1.19067e7	+	6.54614e7i	−0.0119425	+	0.0656581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.3	✓	92
3.2	odd	2	inner	48.7.i.a.5.44	yes	92
4.3	odd	2		192.7.i.a.113.25		92
12.11	even	2		192.7.i.a.113.3		92
16.3	odd	4		192.7.i.a.17.3		92
16.13	even	4	inner	48.7.i.a.29.44	yes	92
48.29	odd	4	inner	48.7.i.a.29.3	yes	92
48.35	even	4		192.7.i.a.17.25		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.3	✓	92	1.1	even	1	trivial
48.7.i.a.5.44	yes	92	3.2	odd	2	inner
48.7.i.a.29.3	yes	92	48.29	odd	4	inner
48.7.i.a.29.44	yes	92	16.13	even	4	inner
192.7.i.a.17.3		92	16.3	odd	4
192.7.i.a.17.25		92	48.35	even	4
192.7.i.a.113.3		92	12.11	even	2
192.7.i.a.113.25		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)

\(f(q)\)	\(=\)	\(q+(-7.81038 - 1.73145i) q^{2} +(-5.41236 - 26.4520i) q^{3} +(58.0042 + 27.0465i) q^{4} +(-54.1549 + 54.1549i) q^{5} +(-3.52753 + 215.971i) q^{6} -639.122i q^{7} +(-406.205 - 311.675i) q^{8} +(-670.413 + 286.335i) q^{9} +O(q^{10})\)	\(q+(-7.81038 - 1.73145i) q^{2} +(-5.41236 - 26.4520i) q^{3} +(58.0042 + 27.0465i) q^{4} +(-54.1549 + 54.1549i) q^{5} +(-3.52753 + 215.971i) q^{6} -639.122i q^{7} +(-406.205 - 311.675i) q^{8} +(-670.413 + 286.335i) q^{9} +(516.737 - 329.204i) q^{10} +(865.761 - 865.761i) q^{11} +(401.494 - 1680.71i) q^{12} +(-1382.53 + 1382.53i) q^{13} +(-1106.60 + 4991.79i) q^{14} +(1725.61 + 1139.40i) q^{15} +(2632.97 + 3137.62i) q^{16} +894.209i q^{17} +(5731.95 - 1075.60i) q^{18} +(-5724.27 + 5724.27i) q^{19} +(-4605.91 + 1676.51i) q^{20} +(-16906.0 + 3459.16i) q^{21} +(-8260.95 + 5262.91i) q^{22} -6298.37 q^{23} +(-6045.88 + 12431.8i) q^{24} +9759.49i q^{25} +(13191.9 - 8404.33i) q^{26} +(11202.6 + 16184.0i) q^{27} +(17286.0 - 37071.7i) q^{28} +(18594.2 + 18594.2i) q^{29} +(-11504.9 - 11886.9i) q^{30} -6159.23 q^{31} +(-15131.9 - 29064.9i) q^{32} +(-27586.9 - 18215.3i) q^{33} +(1548.28 - 6984.12i) q^{34} +(34611.6 + 34611.6i) q^{35} +(-46631.1 - 1523.69i) q^{36} +(2390.27 + 2390.27i) q^{37} +(54620.0 - 34797.5i) q^{38} +(44053.5 + 29087.9i) q^{39} +(38876.7 - 5119.29i) q^{40} -65647.4 q^{41} +(138032. + 2254.52i) q^{42} +(-99064.2 - 99064.2i) q^{43} +(73633.6 - 26801.9i) q^{44} +(20799.7 - 51812.6i) q^{45} +(49192.7 + 10905.3i) q^{46} +54149.8i q^{47} +(68745.7 - 86629.2i) q^{48} -290827. q^{49} +(16898.0 - 76225.4i) q^{50} +(23653.6 - 4839.78i) q^{51} +(-117585. + 42800.0i) q^{52} +(181923. - 181923. i) q^{53} +(-59475.3 - 145800. i) q^{54} +93770.4i q^{55} +(-199198. + 259615. i) q^{56} +(182400. + 120436. i) q^{57} +(-113033. - 177423. i) q^{58} +(-114825. + 114825. i) q^{59} +(69275.8 + 112762. i) q^{60} +(16629.9 - 16629.9i) q^{61} +(48106.0 + 10664.4i) q^{62} +(183003. + 428475. i) q^{63} +(67861.6 + 253208. i) q^{64} -149742. i q^{65} +(183925. + 190033. i) q^{66} +(92916.9 - 92916.9i) q^{67} +(-24185.2 + 51867.9i) q^{68} +(34089.1 + 166604. i) q^{69} +(-210402. - 330258. i) q^{70} -678777. q^{71} +(361569. + 92639.9i) q^{72} -66507.2i q^{73} +(-14530.3 - 22807.5i) q^{74} +(258158. - 52821.9i) q^{75} +(-486853. + 177210. i) q^{76} +(-553327. - 553327. i) q^{77} +(-293710. - 303464. i) q^{78} +615607. q^{79} +(-312506. - 27329.4i) q^{80} +(367465. - 383926. i) q^{81} +(512731. + 113665. i) q^{82} +(520347. + 520347. i) q^{83} +(-1.07418e6 - 256603. i) q^{84} +(-48425.8 - 48425.8i) q^{85} +(602205. + 945254. i) q^{86} +(391215. - 592492. i) q^{87} +(-621513. + 81840.8i) q^{88} -868822. q^{89} +(-252164. + 368663. i) q^{90} +(883606. + 883606. i) q^{91} +(-365332. - 170349. i) q^{92} +(33336.0 + 162924. i) q^{93} +(93757.5 - 422931. i) q^{94} -619994. i q^{95} +(-686924. + 557578. i) q^{96} -1.04625e6 q^{97} +(2.27147e6 + 503552. i) q^{98} +(-332519. + 828315. 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more