LMFDB - Embedded newform 24.4.d.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,4,Mod(13,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("24.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	24.d (of order $2$, degree $1$, 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:	$1.41604584014$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.8248384.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + x^{4} - 12x^{3} + 4x^{2} + 64 $ x^6 + x^4 - 12x^3 + 4x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.4
Root			$-0.641412 - 1.89436i$ of defining polynomial
Character	$\chi$	$=$	24.13
Dual form			24.4.d.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25295 + 2.53577i) q^{2} +3.00000i q^{3} +(-4.86025 + 6.35436i) q^{4} -9.15486i q^{5} +(-7.60731 + 3.75884i) q^{6} +27.4175 q^{7} +(-22.2028 - 4.36281i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(1.25295 + 2.53577i) q^{2} +3.00000i q^{3} +(-4.86025 + 6.35436i) q^{4} -9.15486i q^{5} +(-7.60731 + 3.75884i) q^{6} +27.4175 q^{7} +(-22.2028 - 4.36281i) q^{8} -9.00000 q^{9} +(23.2146 - 11.4705i) q^{10} -20.5252i q^{11} +(-19.0631 - 14.5808i) q^{12} -32.0471i q^{13} +(34.3526 + 69.5243i) q^{14} +27.4646 q^{15} +(-16.7559 - 61.7676i) q^{16} -111.764 q^{17} +(-11.2765 - 22.8219i) q^{18} +129.764i q^{19} +(58.1733 + 44.4950i) q^{20} +82.2524i q^{21} +(52.0471 - 25.7169i) q^{22} +9.16510 q^{23} +(13.0884 - 66.6085i) q^{24} +41.1885 q^{25} +(81.2641 - 40.1533i) q^{26} -27.0000i q^{27} +(-133.256 + 174.220i) q^{28} -41.0606i q^{29} +(34.4116 + 69.6439i) q^{30} -187.606 q^{31} +(135.634 - 119.880i) q^{32} +61.5755 q^{33} +(-140.034 - 283.408i) q^{34} -251.003i q^{35} +(43.7423 - 57.1893i) q^{36} -114.127i q^{37} +(-329.052 + 162.587i) q^{38} +96.1414 q^{39} +(-39.9409 + 203.264i) q^{40} +282.915 q^{41} +(-208.573 + 103.058i) q^{42} +89.3870i q^{43} +(130.424 + 99.7576i) q^{44} +82.3937i q^{45} +(11.4834 + 23.2406i) q^{46} -54.6464 q^{47} +(185.303 - 50.2676i) q^{48} +408.717 q^{49} +(51.6070 + 104.445i) q^{50} -335.292i q^{51} +(203.639 + 155.757i) q^{52} +726.878i q^{53} +(68.4658 - 33.8295i) q^{54} -187.905 q^{55} +(-608.745 - 119.617i) q^{56} -389.292 q^{57} +(104.120 - 51.4467i) q^{58} +216.579i q^{59} +(-133.485 + 174.520i) q^{60} -754.222i q^{61} +(-235.060 - 475.726i) q^{62} -246.757 q^{63} +(473.932 + 193.734i) q^{64} -293.387 q^{65} +(77.1508 + 156.141i) q^{66} +379.433i q^{67} +(543.202 - 710.189i) q^{68} +27.4953i q^{69} +(636.486 - 314.493i) q^{70} +302.080 q^{71} +(199.826 + 39.2653i) q^{72} -504.396 q^{73} +(289.401 - 142.995i) q^{74} +123.566i q^{75} +(-824.568 - 630.686i) q^{76} -562.748i q^{77} +(120.460 + 243.792i) q^{78} +301.780 q^{79} +(-565.474 + 153.398i) q^{80} +81.0000 q^{81} +(354.477 + 717.408i) q^{82} +599.003i q^{83} +(-522.661 - 399.767i) q^{84} +1023.18i q^{85} +(-226.665 + 111.997i) q^{86} +123.182 q^{87} +(-89.5475 + 455.717i) q^{88} -277.528 q^{89} +(-208.932 + 103.235i) q^{90} -878.651i q^{91} +(-44.5447 + 58.2383i) q^{92} -562.818i q^{93} +(-68.4689 - 138.571i) q^{94} +1187.97 q^{95} +(359.641 + 406.903i) q^{96} -765.905 q^{97} +(512.100 + 1036.41i) q^{98} +184.727i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 16 * q^4 - 6 * q^6 + 28 * q^7 - 76 * q^8 - 54 * q^9	$ 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9} + 60 q^{10} - 12 q^{12} - 100 q^{14} - 60 q^{15} + 56 q^{16} + 52 q^{17} - 18 q^{18} + 56 q^{20} + 224 q^{22} + 328 q^{23} + 204 q^{24} - 106 q^{25} + 56 q^{26} - 352 q^{28} + 372 q^{30} - 636 q^{31} - 248 q^{32} - 548 q^{34} - 144 q^{36} - 776 q^{38} + 312 q^{39} + 232 q^{40} + 236 q^{41} - 564 q^{42} + 1152 q^{44} + 328 q^{46} - 408 q^{47} + 576 q^{48} + 654 q^{49} + 1970 q^{50} - 368 q^{52} + 54 q^{54} + 1024 q^{55} - 1864 q^{56} - 168 q^{57} + 140 q^{58} - 1152 q^{60} - 2108 q^{62} - 252 q^{63} + 832 q^{64} - 1744 q^{65} - 1440 q^{66} + 2976 q^{68} + 1352 q^{70} - 1704 q^{71} + 684 q^{72} + 956 q^{73} + 1568 q^{74} - 1744 q^{76} + 1608 q^{78} - 44 q^{79} - 2112 q^{80} + 486 q^{81} - 2236 q^{82} - 1992 q^{84} - 760 q^{86} + 1044 q^{87} + 1856 q^{88} - 220 q^{89} - 540 q^{90} + 1728 q^{92} + 2088 q^{94} + 5104 q^{95} + 2184 q^{96} - 2444 q^{97} + 3354 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 + 16 * q^4 - 6 * q^6 + 28 * q^7 - 76 * q^8 - 54 * q^9 + 60 * q^10 - 12 * q^12 - 100 * q^14 - 60 * q^15 + 56 * q^16 + 52 * q^17 - 18 * q^18 + 56 * q^20 + 224 * q^22 + 328 * q^23 + 204 * q^24 - 106 * q^25 + 56 * q^26 - 352 * q^28 + 372 * q^30 - 636 * q^31 - 248 * q^32 - 548 * q^34 - 144 * q^36 - 776 * q^38 + 312 * q^39 + 232 * q^40 + 236 * q^41 - 564 * q^42 + 1152 * q^44 + 328 * q^46 - 408 * q^47 + 576 * q^48 + 654 * q^49 + 1970 * q^50 - 368 * q^52 + 54 * q^54 + 1024 * q^55 - 1864 * q^56 - 168 * q^57 + 140 * q^58 - 1152 * q^60 - 2108 * q^62 - 252 * q^63 + 832 * q^64 - 1744 * q^65 - 1440 * q^66 + 2976 * q^68 + 1352 * q^70 - 1704 * q^71 + 684 * q^72 + 956 * q^73 + 1568 * q^74 - 1744 * q^76 + 1608 * q^78 - 44 * q^79 - 2112 * q^80 + 486 * q^81 - 2236 * q^82 - 1992 * q^84 - 760 * q^86 + 1044 * q^87 + 1856 * q^88 - 220 * q^89 - 540 * q^90 + 1728 * q^92 + 2088 * q^94 + 5104 * q^95 + 2184 * q^96 - 2444 * q^97 + 3354 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.25295	+	2.53577i	0.442983	+	0.896530i
$2$	1.25295	+	2.53577i	0.442983	+	0.896530i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−4.86025	+	6.35436i	−0.607532	+	0.794295i
$5$		−	9.15486i		−	0.818836i	−0.912347	−	0.409418i	$-0.865732\pi$
$5$		−	9.15486i		−	0.818836i	0.912347	−	0.409418i	$-0.134268\pi$
$6$	−7.60731	+	3.75884i	−0.517612	+	0.255756i
$7$	27.4175			1.48040			0.740202	−	0.672385i	$-0.234730\pi$
$7$	27.4175			1.48040			0.740202	+	0.672385i	$0.234730\pi$
$8$	−22.2028	−	4.36281i	−0.981236	−	0.192811i
$9$	−9.00000			−0.333333
$10$	23.2146	−	11.4705i	0.734111	−	0.362730i
$11$		−	20.5252i		−	0.562598i	−0.959620	−	0.281299i	$-0.909235\pi$
$11$		−	20.5252i		−	0.562598i	0.959620	−	0.281299i	$-0.0907652\pi$
$12$	−19.0631	−	14.5808i	−0.458587	−	0.350759i
$13$		−	32.0471i		−	0.683713i	−0.939752	−	0.341857i	$-0.888944\pi$
$13$		−	32.0471i		−	0.683713i	0.939752	−	0.341857i	$-0.111056\pi$
$14$	34.3526	+	69.5243i	0.655794	+	1.32723i
$15$	27.4646			0.472755
$16$	−16.7559	−	61.7676i	−0.261810	−	0.965119i
$17$	−111.764			−1.59452			−0.797258	−	0.603639i	$-0.793717\pi$
$17$	−111.764			−1.59452			−0.797258	+	0.603639i	$0.793717\pi$
$18$	−11.2765	−	22.8219i	−0.147661	−	0.298843i
$19$			129.764i			1.56684i	0.621494	+	0.783419i	$0.286526\pi$
$19$			129.764i			1.56684i	−0.621494	+	0.783419i	$0.713474\pi$
$20$	58.1733	+	44.4950i	0.650397	+	0.497469i
$21$			82.2524i			0.854711i
$22$	52.0471	−	25.7169i	0.504386	−	0.249221i
$23$	9.16510			0.0830893			0.0415447	−	0.999137i	$-0.486772\pi$
$23$	9.16510			0.0830893			0.0415447	+	0.999137i	$0.486772\pi$
$24$	13.0884	−	66.6085i	0.111319	−	0.566517i
$25$	41.1885			0.329508
$26$	81.2641	−	40.1533i	0.612970	−	0.302874i
$27$		−	27.0000i		−	0.192450i
$28$	−133.256	+	174.220i	−0.899392	+	1.17588i
$29$		−	41.0606i		−	0.262923i	−0.991321	−	0.131461i	$-0.958033\pi$
$29$		−	41.0606i		−	0.262923i	0.991321	−	0.131461i	$-0.0419669\pi$
$30$	34.4116	+	69.6439i	0.209423	+	0.423839i
$31$	−187.606			−1.08694			−0.543468	−	0.839430i	$-0.682889\pi$
$31$	−187.606			−1.08694			−0.543468	+	0.839430i	$0.682889\pi$
$32$	135.634	−	119.880i	0.749281	−	0.662252i
$33$	61.5755			0.324816
$34$	−140.034	−	283.408i	−0.706344	−	1.42953i
$35$		−	251.003i		−	1.21221i
$36$	43.7423	−	57.1893i	0.202511	−	0.264765i
$37$		−	114.127i		−	0.507093i	−0.967323	−	0.253546i	$-0.918403\pi$
$37$		−	114.127i		−	0.507093i	0.967323	−	0.253546i	$-0.0815970\pi$
$38$	−329.052	+	162.587i	−1.40472	+	0.694083i
$39$	96.1414			0.394742
$40$	−39.9409	+	203.264i	−0.157880	+	0.803471i
$41$	282.915			1.07766			0.538828	−	0.842416i	$-0.318867\pi$
$41$	282.915			1.07766			0.538828	+	0.842416i	$0.318867\pi$
$42$	−208.573	+	103.058i	−0.766274	+	0.378623i
$43$			89.3870i			0.317009i	0.987358	+	0.158505i	$0.0506673\pi$
$43$			89.3870i			0.317009i	−0.987358	+	0.158505i	$0.949333\pi$
$44$	130.424	+	99.7576i	0.446869	+	0.341796i
$45$			82.3937i			0.272945i
$46$	11.4834	+	23.2406i	0.0368072	+	0.0744921i
$47$	−54.6464			−0.169596			−0.0847978	−	0.996398i	$-0.527024\pi$
$47$	−54.6464			−0.169596			−0.0847978	+	0.996398i	$0.527024\pi$
$48$	185.303	−	50.2676i	0.557212	−	0.151156i
$49$	408.717			1.19159
$50$	51.6070	+	104.445i	0.145967	+	0.295414i
$51$		−	335.292i		−	0.920594i
$52$	203.639	+	155.757i	0.543070	+	0.415378i
$53$			726.878i			1.88386i	0.335815	+	0.941928i	$0.390988\pi$
$53$			726.878i			1.88386i	−0.335815	+	0.941928i	$0.609012\pi$
$54$	68.4658	−	33.8295i	0.172537	−	0.0852522i
$55$	−187.905			−0.460675
$56$	−608.745	−	119.617i	−1.45262	−	0.285438i
$57$	−389.292			−0.904614
$58$	104.120	−	51.4467i	0.235718	−	0.116470i
$59$			216.579i			0.477900i	0.971032	+	0.238950i	$0.0768033\pi$
$59$			216.579i			0.477900i	−0.971032	+	0.238950i	$0.923197\pi$
$60$	−133.485	+	174.520i	−0.287214	+	0.375507i
$61$		−	754.222i		−	1.58309i	−0.611114	−	0.791543i	$-0.709278\pi$
$61$		−	754.222i		−	1.58309i	0.611114	−	0.791543i	$-0.290722\pi$
$62$	−235.060	−	475.726i	−0.481495	−	0.974471i
$63$	−246.757			−0.493468
$64$	473.932	+	193.734i	0.925648	+	0.378386i
$65$	−293.387			−0.559849
$66$	77.1508	+	156.141i	0.143888	+	0.291207i
$67$			379.433i			0.691868i	0.938259	+	0.345934i	$0.112438\pi$
$67$			379.433i			0.691868i	−0.938259	+	0.345934i	$0.887562\pi$
$68$	543.202	−	710.189i	0.968719	−	1.26652i
$69$			27.4953i			0.0479717i
$70$	636.486	−	314.493i	1.08678	−	0.536987i
$71$	302.080			0.504933			0.252467	−	0.967606i	$-0.418758\pi$
$71$	302.080			0.504933			0.252467	+	0.967606i	$0.418758\pi$
$72$	199.826	+	39.2653i	0.327079	+	0.0642703i
$73$	−504.396			−0.808700			−0.404350	−	0.914604i	$-0.632502\pi$
$73$	−504.396			−0.808700			−0.404350	+	0.914604i	$0.632502\pi$
$74$	289.401	−	142.995i	0.454624	−	0.224634i
$75$			123.566i			0.190242i
$76$	−824.568	−	630.686i	−1.24453	−	0.951904i
$77$		−	562.748i		−	0.832872i
$78$	120.460	+	243.792i	0.174864	+	0.353898i
$79$	301.780			0.429784			0.214892	−	0.976638i	$-0.431060\pi$
$79$	301.780			0.429784			0.214892	+	0.976638i	$0.431060\pi$
$80$	−565.474	+	153.398i	−0.790274	+	0.214380i
$81$	81.0000			0.111111
$82$	354.477	+	717.408i	0.477384	+	0.966151i
$83$			599.003i			0.792158i	0.918216	+	0.396079i	$0.129629\pi$
$83$			599.003i			0.792158i	−0.918216	+	0.396079i	$0.870371\pi$
$84$	−522.661	−	399.767i	−0.678893	−	0.519264i
$85$			1023.18i			1.30565i
$86$	−226.665	+	111.997i	−0.284208	+	0.140430i
$87$	123.182			0.151799
$88$	−89.5475	+	455.717i	−0.108475	+	0.552041i
$89$	−277.528			−0.330538			−0.165269	−	0.986248i	$-0.552849\pi$
$89$	−277.528			−0.330538			−0.165269	+	0.986248i	$0.552849\pi$
$90$	−208.932	+	103.235i	−0.244704	+	0.120910i
$91$		−	878.651i		−	1.01217i
$92$	−44.5447	+	58.2383i	−0.0504794	+	0.0659975i
$93$		−	562.818i		−	0.627543i
$94$	−68.4689	−	138.571i	−0.0751280	−	0.152048i
$95$	1187.97			1.28298
$96$	359.641	+	406.903i	0.382352	+	0.432597i
$97$	−765.905			−0.801710			−0.400855	−	0.916141i	$-0.631287\pi$
$97$	−765.905			−0.801710			−0.400855	+	0.916141i	$0.631287\pi$
$98$	512.100	+	1036.41i	0.527856	+	1.06830i
$99$			184.727i			0.187533i
$100$	−200.187	+	261.727i	−0.200187	+	0.261727i
$101$		−	201.253i		−	0.198272i	−0.995074	−	0.0991360i	$-0.968392\pi$
$101$		−	201.253i		−	0.198272i	0.995074	−	0.0991360i	$-0.0316079\pi$
$102$	850.224	−	420.103i	0.825340	−	0.407808i
$103$	682.440			0.652843			0.326421	−	0.945224i	$-0.394157\pi$
$103$	682.440			0.652843			0.326421	+	0.945224i	$0.394157\pi$
$104$	−139.816	+	711.537i	−0.131827	+	0.670884i
$105$	753.009			0.699868
$106$	−1843.20	+	910.739i	−1.68893	+	0.834517i
$107$		−	457.252i		−	0.413123i	−0.978434	−	0.206562i	$-0.933773\pi$
$107$		−	457.252i		−	0.413123i	0.978434	−	0.206562i	$-0.0662274\pi$
$108$	171.568	+	131.227i	0.152862	+	0.116920i
$109$		−	625.812i		−	0.549926i	−0.961455	−	0.274963i	$-0.911334\pi$
$109$		−	625.812i		−	0.549926i	0.961455	−	0.274963i	$-0.0886655\pi$
$110$	−235.435	−	476.484i	−0.204071	−	0.413009i
$111$	342.382			0.292770
$112$	−459.403	−	1693.51i	−0.387585	−	1.42877i
$113$	981.151			0.816805			0.408402	−	0.912802i	$-0.366086\pi$
$113$	981.151			0.816805			0.408402	+	0.912802i	$0.366086\pi$
$114$	−487.762	−	987.155i	−0.400729	−	0.811014i
$115$		−	83.9052i		−	0.0680365i
$116$	260.914	+	199.565i	0.208838	+	0.159734i
$117$			288.424i			0.227904i
$118$	−549.193	+	271.361i	−0.428452	+	0.211702i
$119$	−3064.29			−2.36053
$120$	−609.792	−	119.823i	−0.463884	−	0.0911523i
$121$	909.717			0.683484
$122$	1912.53	−	944.999i	1.41928	−	0.701280i
$123$			848.745i			0.622185i
$124$	911.813	−	1192.12i	0.660348	−	0.863349i
$125$		−	1521.43i		−	1.08865i
$126$	−309.173	−	625.719i	−0.218598	−	0.442409i
$127$	−808.055			−0.564593			−0.282296	−	0.959327i	$-0.591096\pi$
$127$	−808.055			−0.564593			−0.282296	+	0.959327i	$0.591096\pi$
$128$	102.547	+	1444.52i	0.0708121	+	0.997490i
$129$	−268.161			−0.183025
$130$	−367.598	−	743.962i	−0.248004	−	0.501921i
$131$		−	1110.85i		−	0.740884i	−0.928856	−	0.370442i	$-0.879206\pi$
$131$		−	1110.85i		−	0.740884i	0.928856	−	0.370442i	$-0.120794\pi$
$132$	−299.273	+	391.273i	−0.197336	+	0.258000i
$133$			3557.80i			2.31955i
$134$	−962.155	+	475.409i	−0.620280	+	0.306486i
$135$	−247.181			−0.157585
$136$	2481.48	+	487.606i	1.56460	+	0.307440i
$137$	−466.765			−0.291084			−0.145542	−	0.989352i	$-0.546493\pi$
$137$	−466.765			−0.291084			−0.145542	+	0.989352i	$0.546493\pi$
$138$	−69.7217	+	34.4501i	−0.0430080	+	0.0212506i
$139$		−	351.773i		−	0.214654i	−0.994224	−	0.107327i	$-0.965771\pi$
$139$		−	351.773i		−	0.214654i	0.994224	−	0.107327i	$-0.0342292\pi$
$140$	1594.96	+	1219.94i	0.962850	+	0.736454i
$141$		−	163.939i		−	0.0979161i
$142$	378.489	+	766.005i	0.223677	+	0.452688i
$143$	−657.773			−0.384656
$144$	150.803	+	555.909i	0.0872701	+	0.321706i
$145$	−375.904			−0.215291
$146$	−631.981	−	1279.03i	−0.358240	−	0.725023i
$147$			1226.15i			0.687967i
$148$	725.207	+	554.688i	0.402781	+	0.308075i
$149$			1290.49i			0.709540i	0.934954	+	0.354770i	$0.115441\pi$
$149$			1290.49i			0.709540i	−0.934954	+	0.354770i	$0.884559\pi$
$150$	−313.334	+	154.821i	−0.170557	+	0.0842738i
$151$	1175.51			0.633521			0.316761	−	0.948505i	$-0.397405\pi$
$151$	1175.51			0.633521			0.316761	+	0.948505i	$0.397405\pi$
$152$	566.136	−	2881.13i	0.302103	−	1.53744i
$153$	1005.88			0.531505
$154$	1427.00	−	705.093i	0.746694	−	0.368948i
$155$			1717.51i			0.890022i
$156$	−467.272	+	610.917i	−0.239818	+	0.313542i
$157$			1092.09i			0.555148i	0.960704	+	0.277574i	$0.0895303\pi$
$157$			1092.09i			0.555148i	−0.960704	+	0.277574i	$0.910470\pi$
$158$	378.115	+	765.246i	0.190387	+	0.385314i
$159$	−2180.63			−1.08764
$160$	−1097.49	−	1241.71i	−0.542276	−	0.613538i
$161$	251.284			0.123006
$162$	101.489	+	205.397i	0.0492204	+	0.0996144i
$163$		−	3626.97i		−	1.74286i	−0.490519	−	0.871430i	$-0.663193\pi$
$163$		−	3626.97i		−	1.74286i	0.490519	−	0.871430i	$-0.336807\pi$
$164$	−1375.04	+	1797.75i	−0.654711	+	0.855978i
$165$		−	563.716i		−	0.265971i
$166$	−1518.93	+	750.518i	−0.710193	+	0.350913i
$167$	45.8012			0.0212228			0.0106114	−	0.999944i	$-0.496622\pi$
$167$	45.8012			0.0212228			0.0106114	+	0.999944i	$0.496622\pi$
$168$	358.852	−	1826.24i	0.164798	−	0.838673i
$169$	1169.98			0.532536
$170$	−2594.56	+	1281.99i	−1.17055	+	0.578379i
$171$		−	1167.88i		−	0.522279i
$172$	−567.998	−	434.444i	−0.251799	−	0.192593i
$173$		−	2455.02i		−	1.07891i	−0.842014	−	0.539455i	$-0.818630\pi$
$173$		−	2455.02i		−	1.07891i	0.842014	−	0.539455i	$-0.181370\pi$
$174$	154.340	+	312.361i	0.0672442	+	0.136092i
$175$	1129.28			0.487805
$176$	−1267.79	+	343.917i	−0.542974	+	0.147294i
$177$	−649.736			−0.275916
$178$	−347.728	−	703.747i	−0.146423	−	0.296338i
$179$			1026.28i			0.428533i	0.976775	+	0.214267i	$0.0687362\pi$
$179$			1026.28i			0.428533i	−0.976775	+	0.214267i	$0.931264\pi$
$180$	−523.560	−	400.455i	−0.216799	−	0.165823i
$181$		−	3699.05i		−	1.51905i	−0.650477	−	0.759526i	$-0.725431\pi$
$181$		−	3699.05i		−	1.51905i	0.650477	−	0.759526i	$-0.274569\pi$
$182$	2228.06	−	1100.90i	0.907442	−	0.448375i
$183$	2262.66			0.913995
$184$	−203.491	−	39.9856i	−0.0815302	−	0.0160205i
$185$	−1044.82			−0.415226
$186$	1427.18	−	705.180i	0.562611	−	0.277991i
$187$			2293.98i			0.897071i
$188$	265.595	−	347.243i	0.103035	−	0.134709i
$189$		−	740.271i		−	0.284904i
$190$	1488.46	+	3012.42i	0.568340	+	1.15023i
$191$	5108.93			1.93544			0.967721	−	0.252023i	$-0.0810960\pi$
$191$	5108.93			1.93544			0.967721	+	0.252023i	$0.0810960\pi$
$192$	−581.201	+	1421.80i	−0.218461	+	0.534423i
$193$	−1414.13			−0.527417			−0.263709	−	0.964602i	$-0.584946\pi$
$193$	−1414.13			−0.527417			−0.263709	+	0.964602i	$0.584946\pi$
$194$	−959.638	−	1942.16i	−0.355144	−	0.718757i
$195$		−	880.161i		−	0.323229i
$196$	−1986.47	+	2597.13i	−0.723931	+	0.946477i
$197$			2816.66i			1.01867i	0.860567	+	0.509337i	$0.170109\pi$
$197$			2816.66i			1.01867i	−0.860567	+	0.509337i	$0.829891\pi$
$198$	−468.424	+	231.452i	−0.168129	+	0.0830738i
$199$	−948.556			−0.337896			−0.168948	−	0.985625i	$-0.554037\pi$
$199$	−948.556			−0.337896			−0.168948	+	0.985625i	$0.554037\pi$
$200$	−914.502	−	179.698i	−0.323325	−	0.0635328i
$201$	−1138.30			−0.399450
$202$	510.332	−	252.160i	0.177757	−	0.0878311i
$203$		−	1125.78i		−	0.389232i
$204$	2130.57	+	1629.61i	0.731224	+	0.559290i
$205$		−	2590.05i		−	0.882424i
$206$	855.060	+	1730.51i	0.289198	+	0.585293i
$207$	−82.4859			−0.0276964
$208$	−1979.48	+	536.977i	−0.659865	+	0.179003i
$209$	2663.43			0.881499
$210$	943.479	+	1909.46i	0.310030	+	0.627453i
$211$			4487.28i			1.46406i	0.681271	+	0.732032i	$0.261428\pi$
$211$			4487.28i			1.46406i	−0.681271	+	0.732032i	$0.738572\pi$
$212$	−4618.85	−	3532.81i	−1.49634	−	1.14450i
$213$			906.239i			0.291523i
$214$	1159.49	−	572.912i	0.370377	−	0.183007i
$215$	818.326			0.259578
$216$	−117.796	+	599.477i	−0.0371065	+	0.188839i
$217$	−5143.68			−1.60910
$218$	1586.91	−	784.108i	0.493025	−	0.243608i
$219$		−	1513.19i		−	0.466903i
$220$	913.267	−	1194.02i	0.279875	−	0.365912i
$221$			3581.72i			1.09019i
$222$	428.986	+	868.202i	0.129692	+	0.262477i
$223$	−4590.98			−1.37863			−0.689315	−	0.724462i	$-0.742088\pi$
$223$	−4590.98			−1.37863			−0.689315	+	0.724462i	$0.742088\pi$
$224$	3718.75	−	3286.82i	1.10924	−	0.980401i
$225$	−370.697			−0.109836
$226$	1229.33	+	2487.97i	0.361831	+	0.732290i
$227$			2897.47i			0.847189i	0.905852	+	0.423594i	$0.139232\pi$
$227$			2897.47i			0.847189i	−0.905852	+	0.423594i	$0.860768\pi$
$228$	1892.06	−	2473.70i	0.549582	−	0.718531i
$229$			34.6293i			0.00999288i	0.999988	+	0.00499644i	$0.00159042\pi$
$229$			34.6293i			0.00999288i	−0.999988	+	0.00499644i	$0.998410\pi$
$230$	212.764	−	105.129i	0.0609968	−	0.0301390i
$231$	1688.24			0.480859
$232$	−179.140	+	911.662i	−0.0506944	+	0.257989i
$233$	−1054.02			−0.296355			−0.148178	−	0.988961i	$-0.547341\pi$
$233$	−1054.02			−0.296355			−0.148178	+	0.988961i	$0.547341\pi$
$234$	−731.377	+	361.380i	−0.204323	+	0.100958i
$235$			500.280i			0.138871i
$236$	−1376.22	−	1052.63i	−0.379594	−	0.290340i
$237$			905.341i			0.248136i
$238$	−3839.38	−	7770.32i	−1.04567	−	2.11628i
$239$	−654.700			−0.177192			−0.0885962	−	0.996068i	$-0.528238\pi$
$239$	−654.700			−0.177192			−0.0885962	+	0.996068i	$0.528238\pi$
$240$	−460.193	−	1696.42i	−0.123772	−	0.456265i
$241$	3194.00			0.853707			0.426854	−	0.904321i	$-0.359622\pi$
$241$	3194.00			0.853707			0.426854	+	0.904321i	$0.359622\pi$
$242$	1139.83	+	2306.83i	0.302772	+	0.612764i
$243$			243.000i			0.0641500i
$244$	4792.60	+	3665.71i	1.25744	+	0.961774i
$245$		−	3741.74i		−	0.975719i
$246$	−2152.22	+	1063.43i	−0.557808	+	0.275618i
$247$	4158.57			1.07127
$248$	4165.38	+	818.490i	1.06654	+	0.209573i
$249$	−1797.01			−0.457353
$250$	3858.00	−	1906.27i	0.976006	−	0.482253i
$251$		−	5042.90i		−	1.26815i	−0.773273	−	0.634074i	$-0.781382\pi$
$251$		−	5042.90i		−	1.26815i	0.773273	−	0.634074i	$-0.218618\pi$
$252$	1199.30	−	1567.98i	0.299797	−	0.391959i
$253$		−	188.115i		−	0.0467459i
$254$	−1012.45	−	2049.04i	−0.250105	−	0.506174i
$255$	−3069.55			−0.753815
$256$	−3534.48	+	2069.94i	−0.862911	+	0.505356i
$257$	−5166.64			−1.25403			−0.627016	−	0.779007i	$-0.715724\pi$
$257$	−5166.64			−1.25403			−0.627016	+	0.779007i	$0.715724\pi$
$258$	−335.991	−	679.995i	−0.0810771	−	0.164088i
$259$		−	3129.08i		−	0.750702i
$260$	1425.94	−	1864.29i	0.340126	−	0.444685i
$261$			369.545i			0.0876409i
$262$	2816.87	−	1391.84i	0.664225	−	0.328199i
$263$	−7366.11			−1.72705			−0.863524	−	0.504308i	$-0.831748\pi$
$263$	−7366.11			−1.72705			−0.863524	+	0.504308i	$0.831748\pi$
$264$	−1367.15	−	268.643i	−0.318721	−	0.0626281i
$265$	6654.47			1.54257
$266$	−9021.76	+	4457.73i	−2.07955	+	1.02752i
$267$		−	832.584i		−	0.190836i
$268$	−2411.06	−	1844.14i	−0.549548	−	0.420332i
$269$			7877.80i			1.78557i	0.450484	+	0.892784i	$0.351251\pi$
$269$			7877.80i			1.78557i	−0.450484	+	0.892784i	$0.648749\pi$
$270$	−309.705	−	626.795i	−0.0698075	−	0.141280i
$271$	−5399.92			−1.21041			−0.605206	−	0.796069i	$-0.706909\pi$
$271$	−5399.92			−1.21041			−0.605206	+	0.796069i	$0.706909\pi$
$272$	1872.70	+	6903.40i	0.417461	+	1.53890i
$273$	2635.95			0.584378
$274$	−584.832	−	1183.61i	−0.128945	−	0.260965i
$275$		−	845.402i		−	0.185381i
$276$	−174.715	−	133.634i	−0.0381037	−	0.0291443i
$277$		−	4416.07i		−	0.957892i	−0.877844	−	0.478946i	$-0.841019\pi$
$277$		−	4416.07i		−	0.957892i	0.877844	−	0.478946i	$-0.158981\pi$
$278$	892.014	−	440.752i	0.192444	−	0.0950883i
$279$	1688.45			0.362312
$280$	−1095.08	+	5572.98i	−0.233727	+	1.18946i
$281$	8068.94			1.71300			0.856499	−	0.516148i	$-0.172635\pi$
$281$	8068.94			1.71300			0.856499	+	0.516148i	$0.172635\pi$
$282$	415.712	−	205.407i	0.0877847	−	0.0433752i
$283$			5241.13i			1.10089i	0.834870	+	0.550447i	$0.185543\pi$
$283$			5241.13i			1.10089i	−0.834870	+	0.550447i	$0.814457\pi$
$284$	−1468.18	+	1919.52i	−0.306763	+	0.401066i
$285$			3563.92i			0.740730i
$286$	−824.154	−	1667.96i	−0.170396	−	0.344855i
$287$	7756.81			1.59537
$288$	−1220.71	+	1078.92i	−0.249760	+	0.220751i
$289$	7578.21			1.54248
$290$	−470.987	−	953.206i	−0.0953701	−	0.193014i
$291$		−	2297.72i		−	0.462868i
$292$	2451.49	−	3205.11i	0.491311	−	0.642346i
$293$		−	6372.75i		−	1.27065i	−0.772246	−	0.635324i	$-0.780867\pi$
$293$		−	6372.75i		−	1.27065i	0.772246	−	0.635324i	$-0.219133\pi$
$294$	−3109.23	+	1536.30i	−0.616783	+	0.304758i
$295$	1982.75			0.391322
$296$	−497.916	+	2533.95i	−0.0977730	+	0.497577i
$297$	−554.180			−0.108272
$298$	−3272.40	+	1616.92i	−0.636124	+	0.314314i
$299$		−	293.715i		−	0.0568093i
$300$	−785.180	−	600.560i	−0.151108	−	0.115578i
$301$			2450.76i			0.469301i
$302$	1472.85	+	2980.83i	0.280639	+	0.567971i
$303$	603.760			0.114472
$304$	8015.22	−	2174.31i	1.51219	−	0.410214i
$305$	−6904.79			−1.29629
$306$	1260.31	+	2550.67i	0.235448	+	0.476510i
$307$			3810.22i			0.708342i	0.935181	+	0.354171i	$0.115237\pi$
$307$			3810.22i			0.708342i	−0.935181	+	0.354171i	$0.884763\pi$
$308$	3575.91	+	2735.10i	0.661546	+	0.505996i
$309$			2047.32i			0.376919i
$310$	−4355.20	+	2151.94i	−0.797932	+	0.394265i
$311$	−8106.73			−1.47810			−0.739052	−	0.673648i	$-0.764726\pi$
$311$	−8106.73			−1.47810			−0.739052	+	0.673648i	$0.764726\pi$
$312$	−2134.61	−	419.447i	−0.387335	−	0.0761106i
$313$	−559.983			−0.101125			−0.0505625	−	0.998721i	$-0.516101\pi$
$313$	−559.983			−0.101125			−0.0505625	+	0.998721i	$0.516101\pi$
$314$	−2769.29	+	1368.33i	−0.497707	+	0.245921i
$315$			2259.03i			0.404069i
$316$	−1466.73	+	1917.62i	−0.261108	+	0.341376i
$317$		−	5828.98i		−	1.03277i	−0.856357	−	0.516385i	$-0.827277\pi$
$317$		−	5828.98i		−	1.03277i	0.856357	−	0.516385i	$-0.172723\pi$
$318$	−2732.22	−	5529.59i	−0.481808	−	0.975106i
$319$	−842.776			−0.147920
$320$	1773.60	−	4338.78i	0.309836	−	0.757953i
$321$	1371.76			0.238517
$322$	314.845	+	637.197i	0.0544895	+	0.110278i
$323$		−	14503.0i		−	2.49835i
$324$	−393.681	+	514.703i	−0.0675035	+	0.0882550i
$325$		−	1319.97i		−	0.225289i
$326$	9197.16	−	4544.40i	1.56253	−	0.772058i
$327$	1877.44			0.317500
$328$	−6281.52	−	1234.31i	−1.05744	−	0.207784i
$329$	−1498.26			−0.251070
$330$	1429.45	−	706.305i	0.238451	−	0.117821i
$331$		−	2847.98i		−	0.472928i	−0.971640	−	0.236464i	$-0.924011\pi$
$331$		−	2847.98i		−	0.472928i	0.971640	−	0.236464i	$-0.0759885\pi$
$332$	−3806.28	−	2911.31i	−0.629207	−	0.481261i
$333$			1027.15i			0.169031i
$334$	57.3864	+	116.141i	0.00940133	+	0.0190269i
$335$	3473.66			0.566526
$336$	5080.53	−	1378.21i	0.824898	−	0.223772i
$337$	−10127.8			−1.63707			−0.818537	−	0.574454i	$-0.805214\pi$
$337$	−10127.8			−1.63707			−0.818537	+	0.574454i	$0.805214\pi$
$338$	1465.92	+	2966.80i	0.235904	+	0.477434i
$339$			2943.45i			0.471582i
$340$	−6501.69	−	4972.94i	−1.03707	−	0.793222i
$341$			3850.65i			0.611508i
$342$	2961.47	−	1463.29i	0.468239	−	0.231361i
$343$	1801.78			0.283636
$344$	389.979	−	1984.65i	0.0611228	−	0.311061i
$345$	251.716			0.0392809
$346$	6225.36	−	3076.00i	0.967276	−	0.477939i
$347$			10148.2i			1.56999i	0.619505	+	0.784993i	$0.287333\pi$
$347$			10148.2i			1.56999i	−0.619505	+	0.784993i	$0.712667\pi$
$348$	−598.695	+	782.742i	−0.0922225	+	0.120573i
$349$			9515.96i			1.45954i	0.683695	+	0.729768i	$0.260372\pi$
$349$			9515.96i			1.45954i	−0.683695	+	0.729768i	$0.739628\pi$
$350$	1414.93	+	2863.60i	0.216089	+	0.437332i
$351$	−865.273			−0.131581
$352$	−2460.57	−	2783.92i	−0.372582	−	0.421544i
$353$	2813.56			0.424223			0.212111	−	0.977245i	$-0.431966\pi$
$353$	2813.56			0.424223			0.212111	+	0.977245i	$0.431966\pi$
$354$	−814.083	−	1647.58i	−0.122226	−	0.247367i
$355$		−	2765.50i		−	0.413457i
$356$	1348.86	−	1763.51i	0.200813	−	0.262545i
$357$		−	9192.86i		−	1.36285i
$358$	−2602.40	+	1285.87i	−0.384193	+	0.189833i
$359$	−2427.25			−0.356839			−0.178419	−	0.983955i	$-0.557098\pi$
$359$	−2427.25			−0.356839			−0.178419	+	0.983955i	$0.557098\pi$
$360$	359.469	−	1829.37i	0.0526268	−	0.267824i
$361$	−9979.71			−1.45498
$362$	9379.95	−	4634.71i	1.36188	−	0.672915i
$363$			2729.15i			0.394610i
$364$	5583.27	+	4270.47i	0.803963	+	0.614926i
$365$			4617.67i			0.662192i
$366$	2835.00	+	5737.60i	0.404884	+	0.819423i
$367$	5021.46			0.714219			0.357109	−	0.934063i	$-0.383762\pi$
$367$	5021.46			0.714219			0.357109	+	0.934063i	$0.383762\pi$
$368$	−153.569	−	566.106i	−0.0217536	−	0.0801911i
$369$	−2546.24			−0.359219
$370$	−1309.10	−	2649.42i	−0.183938	−	0.372262i
$371$			19929.1i			2.78887i
$372$	3576.35	+	2735.44i	0.498455	+	0.381252i
$373$		−	3182.40i		−	0.441765i	−0.975300	−	0.220882i	$-0.929106\pi$
$373$		−	3182.40i		−	0.441765i	0.975300	−	0.220882i	$-0.0708937\pi$
$374$	−5817.00	+	2874.23i	−0.804251	+	0.397387i
$375$	4564.30			0.628532
$376$	1213.30	+	238.412i	0.166413	+	0.0326999i
$377$	−1315.87			−0.179764
$378$	1877.16	−	927.520i	0.255425	−	0.126208i
$379$		−	5868.93i		−	0.795426i	−0.917510	−	0.397713i	$-0.869804\pi$
$379$		−	5868.93i		−	0.795426i	0.917510	−	0.397713i	$-0.130196\pi$
$380$	−5773.85	+	7548.81i	−0.779453	+	1.01907i
$381$		−	2424.16i		−	0.325968i
$382$	6401.22	+	12955.1i	0.857368	+	1.73518i
$383$	7350.18			0.980618			0.490309	−	0.871549i	$-0.336884\pi$
$383$	7350.18			0.980618			0.490309	+	0.871549i	$0.336884\pi$
$384$	−4333.56	+	307.641i	−0.575901	+	0.0408834i
$385$	−5151.88			−0.681985
$386$	−1771.83	−	3585.92i	−0.233637	−	0.472846i
$387$		−	804.483i		−	0.105670i
$388$	3722.49	−	4866.84i	0.487064	−	0.636795i
$389$		−	13009.1i		−	1.69560i	−0.530317	−	0.847800i	$-0.677927\pi$
$389$		−	13009.1i		−	1.69560i	0.530317	−	0.847800i	$-0.322073\pi$
$390$	2231.89	−	1102.79i	0.289784	−	0.143185i
$391$	−1024.33			−0.132487
$392$	−9074.67	−	1783.15i	−1.16923	−	0.229752i
$393$	3332.56			0.427750
$394$	−7142.41	+	3529.13i	−0.913272	+	0.451256i
$395$		−	2762.76i		−	0.351923i
$396$	−1173.82	−	897.818i	−0.148956	−	0.113932i
$397$			4877.88i			0.616659i	0.951280	+	0.308330i	$0.0997700\pi$
$397$			4877.88i			0.616659i	−0.951280	+	0.308330i	$0.900230\pi$
$398$	−1188.49	−	2405.32i	−0.149682	−	0.302934i
$399$	−10673.4			−1.33919
$400$	−690.149	−	2544.12i	−0.0862686	−	0.318015i
$401$	5552.33			0.691446			0.345723	−	0.938337i	$-0.387634\pi$
$401$	5552.33			0.691446			0.345723	+	0.938337i	$0.387634\pi$
$402$	−1426.23	−	2886.47i	−0.176950	−	0.358119i
$403$			6012.23i			0.743153i
$404$	1278.84	+	978.143i	0.157486	+	0.120456i
$405$		−	741.544i		−	0.0909817i
$406$	2854.71	−	1410.54i	0.348958	−	0.172423i
$407$	−2342.49			−0.285289
$408$	−1462.82	+	7444.44i	−0.177501	+	0.903320i
$409$	6989.27			0.844981			0.422491	−	0.906367i	$-0.361156\pi$
$409$	6989.27			0.844981			0.422491	+	0.906367i	$0.361156\pi$
$410$	6567.77	−	3245.19i	0.791119	−	0.390899i
$411$		−	1400.30i		−	0.168057i
$412$	−3316.83	+	4336.47i	−0.396623	+	0.518550i
$413$			5938.03i			0.707485i
$414$	−103.350	−	209.165i	−0.0122691	−	0.0248307i
$415$	5483.79			0.648647
$416$	−3841.83	−	4346.69i	−0.452791	−	0.512293i
$417$	1055.32			0.123931
$418$	3337.13	+	6753.85i	0.390489	+	0.790291i
$419$		−	10461.0i		−	1.21970i	−0.792518	−	0.609849i	$-0.791230\pi$
$419$		−	10461.0i		−	1.21970i	0.792518	−	0.609849i	$-0.208770\pi$
$420$	−3659.81	+	4784.89i	−0.425192	+	0.555902i
$421$		−	4648.55i		−	0.538139i	−0.963121	−	0.269070i	$-0.913284\pi$
$421$		−	4648.55i		−	0.538139i	0.963121	−	0.269070i	$-0.0867162\pi$
$422$	−11378.7	+	5622.32i	−1.31258	+	0.648555i
$423$	491.817			0.0565319
$424$	3171.23	−	16138.8i	0.363228	−	1.84851i
$425$	−4603.40			−0.525406
$426$	−2298.01	+	1135.47i	−0.261359	+	0.129140i
$427$		−	20678.8i		−	2.34360i
$428$	2905.54	+	2222.36i	0.328142	+	0.250986i
$429$		−	1973.32i		−	0.222081i
$430$	1025.32	+	2075.09i	0.114989	+	0.232720i
$431$	12490.7			1.39595			0.697975	−	0.716122i	$-0.254085\pi$
$431$	12490.7			1.39595			0.697975	+	0.716122i	$0.254085\pi$
$432$	−1667.73	+	452.408i	−0.185737	+	0.0503854i
$433$	9446.37			1.04842			0.524208	−	0.851590i	$-0.324362\pi$
$433$	9446.37			1.04842			0.524208	+	0.851590i	$0.324362\pi$
$434$	−6444.75	−	13043.2i	−0.712806	−	1.44261i
$435$		−	1127.71i		−	0.124298i
$436$	3976.64	+	3041.60i	0.436803	+	0.334097i
$437$			1189.30i			0.130188i
$438$	3837.10	−	1895.94i	0.418592	−	0.206830i
$439$	2793.60			0.303716			0.151858	−	0.988402i	$-0.451474\pi$
$439$	2793.60			0.303716			0.151858	+	0.988402i	$0.451474\pi$
$440$	4172.03	+	819.795i	0.452031	+	0.0888232i
$441$	−3678.45			−0.397198
$442$	−9082.41	+	4487.70i	−0.977390	+	0.482937i
$443$			7601.37i			0.815241i	0.913151	+	0.407621i	$0.133641\pi$
$443$			7601.37i			0.815241i	−0.913151	+	0.407621i	$0.866359\pi$
$444$	−1664.06	+	2175.62i	−0.177867	+	0.232546i
$445$			2540.73i			0.270657i
$446$	−5752.25	−	11641.7i	−0.610710	−	1.23598i
$447$	−3871.48			−0.409653
$448$	12994.0	+	5311.68i	1.37033	+	0.560164i
$449$	10708.8			1.12557			0.562785	−	0.826603i	$-0.309730\pi$
$449$	10708.8			1.12557			0.562785	+	0.826603i	$0.309730\pi$
$450$	−464.463	−	940.001i	−0.0486555	−	0.0984713i
$451$		−	5806.89i		−	0.606287i
$452$	−4768.64	+	6234.59i	−0.496235	+	0.648784i
$453$			3526.53i			0.365764i
$454$	−7347.32	+	3630.37i	−0.759530	+	0.375290i
$455$	−8043.92			−0.828802
$456$	8643.39	+	1698.41i	0.887640	+	0.174420i
$457$	233.840			0.0239356			0.0119678	−	0.999928i	$-0.496190\pi$
$457$	233.840			0.0239356			0.0119678	+	0.999928i	$0.496190\pi$
$458$	−87.8120	+	43.3887i	−0.00895892	+	0.00442668i
$459$			3017.63i			0.306865i
$460$	533.164	+	407.801i	0.0540411	+	0.0413343i
$461$			981.307i			0.0991410i	0.998771	+	0.0495705i	$0.0157853\pi$
$461$			981.307i			0.0991410i	−0.998771	+	0.0495705i	$0.984215\pi$
$462$	2115.28	+	4281.00i	0.213012	+	0.431104i
$463$	−14082.7			−1.41356			−0.706782	−	0.707431i	$-0.749854\pi$
$463$	−14082.7			−1.41356			−0.706782	+	0.707431i	$0.749854\pi$
$464$	−2536.22	+	688.006i	−0.253752	+	0.0688359i
$465$	−5152.52			−0.513855
$466$	−1320.62	−	2672.74i	−0.131280	−	0.265692i
$467$			9286.49i			0.920188i	0.887870	+	0.460094i	$0.152184\pi$
$467$			9286.49i			0.920188i	−0.887870	+	0.460094i	$0.847816\pi$
$468$	−1832.75	−	1401.81i	−0.181023	−	0.138459i
$469$			10403.1i			1.02424i
$470$	−1268.59	+	626.824i	−0.124502	+	0.0615175i
$471$	−3276.27			−0.320515
$472$	944.892	−	4808.66i	0.0921444	−	0.468933i
$473$	1834.68			0.178349
$474$	−2295.74	+	1134.34i	−0.222461	+	0.109920i
$475$			5344.79i			0.516286i
$476$	14893.2	−	19471.6i	1.43409	−	1.87496i
$477$		−	6541.90i		−	0.627952i
$478$	−820.303	−	1660.17i	−0.0784933	−	0.158858i
$479$	−19409.3			−1.85143			−0.925715	−	0.378222i	$-0.876536\pi$
$479$	−19409.3			−1.85143			−0.925715	+	0.378222i	$0.876536\pi$
$480$	3725.14	−	3292.47i	0.354226	−	0.313083i
$481$	−3657.46			−0.346706
$482$	4001.90	+	8099.24i	0.378178	+	0.765374i
$483$			753.851i			0.0710174i
$484$	−4421.46	+	5780.67i	−0.415238	+	0.542888i
$485$			7011.76i			0.656469i
$486$	−616.192	+	304.466i	−0.0575124	+	0.0284174i
$487$	12124.8			1.12818			0.564091	−	0.825712i	$-0.309227\pi$
$487$	12124.8			1.12818			0.564091	+	0.825712i	$0.309227\pi$
$488$	−3290.53	+	16745.9i	−0.305236	+	1.55338i
$489$	10880.9			1.00624
$490$	9488.20	−	4688.20i	0.874762	−	0.432227i
$491$		−	5100.69i		−	0.468820i	−0.972138	−	0.234410i	$-0.924684\pi$
$491$		−	5100.69i		−	0.468820i	0.972138	−	0.234410i	$-0.0753159\pi$
$492$	−5393.24	−	4125.12i	−0.494199	−	0.377997i
$493$			4589.10i			0.419235i
$494$	5210.46	+	10545.2i	0.474554	+	0.960424i
$495$	1691.15			0.153558
$496$	3143.50	+	11588.0i	0.284571	+	1.04902i
$497$	8282.26			0.747505
$498$	−2251.55	−	4556.80i	−0.202600	−	0.410030i
$499$		−	85.2797i		−	0.00765058i	−0.999993	−	0.00382529i	$-0.998782\pi$
$499$		−	85.2797i		−	0.00765058i	0.999993	−	0.00382529i	$-0.00121763\pi$
$500$	9667.74	+	7394.55i	0.864709	+	0.661389i
$501$			137.404i			0.0122530i
$502$	12787.6	−	6318.48i	1.13693	−	0.561768i
$503$	−12287.2			−1.08918			−0.544592	−	0.838701i	$-0.683316\pi$
$503$	−12287.2			−1.08918			−0.544592	+	0.838701i	$0.683316\pi$
$504$	5478.71	+	1076.55i	0.484208	+	0.0951460i
$505$	−1842.45			−0.162352
$506$	477.017	−	235.698i	0.0419091	−	0.0207076i
$507$			3509.94i			0.307460i
$508$	3927.35	−	5134.67i	0.343008	−	0.448453i
$509$		−	450.441i		−	0.0392248i	−0.999808	−	0.0196124i	$-0.993757\pi$
$509$		−	450.441i		−	0.0392248i	0.999808	−	0.0196124i	$-0.00624322\pi$
$510$	−3845.98	−	7783.68i	−0.333927	−	0.675818i
$511$	−13829.2			−1.19720
$512$	−9677.40	−	6369.11i	−0.835322	−	0.549761i
$513$	3503.63			0.301538
$514$	−6473.52	−	13101.4i	−0.555515	−	1.12428i
$515$		−	6247.64i		−	0.534571i
$516$	1303.33	−	1703.99i	0.111194	−	0.145376i
$517$			1121.63i			0.0954141i
$518$	7934.63	−	3920.57i	0.673026	−	0.332548i
$519$	7365.05			0.622909
$520$	6514.02	+	1279.99i	0.549344	+	0.107945i
$521$	−15088.1			−1.26876			−0.634378	−	0.773023i	$-0.718744\pi$
$521$	−15088.1			−1.26876			−0.634378	+	0.773023i	$0.718744\pi$
$522$	−937.082	+	463.020i	−0.0785727	+	0.0388235i
$523$			17719.4i			1.48149i	0.671789	+	0.740743i	$0.265526\pi$
$523$			17719.4i			1.48149i	−0.671789	+	0.740743i	$0.734474\pi$
$524$	7058.77	+	5399.04i	0.588481	+	0.450111i
$525$			3387.85i			0.281634i
$526$	−9229.33	−	18678.7i	−0.765053	−	1.54835i
$527$	20967.6			1.73314
$528$	−1031.75	−	3803.38i	−0.0850402	−	0.313486i
$529$	−12083.0			−0.993096
$530$	8337.69	+	16874.2i	0.683332	+	1.38296i
$531$		−	1949.21i		−	0.159300i
$532$	−22607.6	−	17291.8i	−1.84241	−	1.40920i
$533$		−	9066.62i		−	0.736808i
$534$	2111.24	−	1043.18i	0.171091	−	0.0845374i
$535$	−4186.08			−0.338280
$536$	1655.40	−	8424.50i	0.133400	−	0.678886i
$537$	−3078.83			−0.247414
$538$	−19976.3	+	9870.46i	−1.60082	+	0.790977i
$539$		−	8388.98i		−	0.670388i
$540$	1201.36	−	1570.68i	0.0957379	−	0.125169i
$541$		−	12244.5i		−	0.973074i	−0.873660	−	0.486537i	$-0.838260\pi$
$541$		−	12244.5i		−	0.973074i	0.873660	−	0.486537i	$-0.161740\pi$
$542$	−6765.80	−	13692.9i	−0.536192	−	1.08517i
$543$	11097.2			0.877025
$544$	−15159.0	+	13398.3i	−1.19474	+	1.05597i
$545$	−5729.22			−0.450299
$546$	3302.70	+	6684.17i	0.258869	+	0.523912i
$547$		−	7822.46i		−	0.611452i	−0.952119	−	0.305726i	$-0.901101\pi$
$547$		−	7822.46i		−	0.611452i	0.952119	−	0.305726i	$-0.0988992\pi$
$548$	2268.60	−	2966.00i	0.176843	−	0.231206i
$549$			6787.99i			0.527695i
$550$	2143.74	−	1059.24i	0.166199	−	0.0821205i
$551$	5328.19			0.411957
$552$	119.957	−	610.473i	0.00924946	−	0.0470715i
$553$	8274.05			0.636254
$554$	11198.1	−	5533.10i	0.858779	−	0.424330i
$555$		−	3134.46i		−	0.239731i
$556$	2235.29	+	1709.70i	0.170499	+	0.130409i
$557$		−	16555.5i		−	1.25938i	−0.776845	−	0.629692i	$-0.783181\pi$
$557$		−	16555.5i		−	1.25938i	0.776845	−	0.629692i	$-0.216819\pi$
$558$	2115.54	+	4281.53i	0.160498	+	0.324824i
$559$	2864.60			0.216743
$560$	−15503.9	+	4205.77i	−1.16992	+	0.317368i
$561$	−6881.93			−0.517924
$562$	10109.9	+	20461.0i	0.758830	+	1.53575i
$563$		−	12580.7i		−	0.941766i	−0.882196	−	0.470883i	$-0.843935\pi$
$563$		−	12580.7i		−	0.941766i	0.882196	−	0.470883i	$-0.156065\pi$
$564$	1041.73	+	796.786i	0.0777743	+	0.0594871i
$565$		−	8982.30i		−	0.668829i
$566$	−13290.3	+	6566.86i	−0.986985	+	0.487678i
$567$	2220.81			0.164489
$568$	−6707.03	−	1317.92i	−0.495459	−	0.0973567i
$569$	2657.93			0.195828			0.0979141	−	0.995195i	$-0.468783\pi$
$569$	2657.93			0.195828			0.0979141	+	0.995195i	$0.468783\pi$
$570$	−9037.27	+	4465.39i	−0.664087	+	0.328131i
$571$			17669.0i			1.29496i	0.762081	+	0.647481i	$0.224178\pi$
$571$			17669.0i			1.29496i	−0.762081	+	0.647481i	$0.775822\pi$
$572$	3196.94	−	4179.73i	0.233691	−	0.305530i
$573$			15326.8i			1.11743i
$574$	9718.86	+	19669.5i	0.706721	+	1.43029i
$575$	377.497			0.0273786
$576$	−4265.39	−	1743.60i	−0.308549	−	0.126129i
$577$	14617.7			1.05467			0.527334	−	0.849658i	$-0.323192\pi$
$577$	14617.7			1.05467			0.527334	+	0.849658i	$0.323192\pi$
$578$	9495.08	+	19216.6i	0.683293	+	1.38288i
$579$		−	4242.40i		−	0.304505i
$580$	1826.99	−	2388.63i	0.130796	−	0.171004i
$581$			16423.1i			1.17271i
$582$	5826.48	−	2878.91i	0.414975	−	0.205043i
$583$	14919.3			1.05985
$584$	11199.0	+	2200.59i	0.793525	+	0.155926i
$585$	2640.48			0.186616
$586$	16159.8	−	7984.70i	1.13917	−	0.562876i
$587$		−	4096.53i		−	0.288044i	−0.989574	−	0.144022i	$-0.953996\pi$
$587$		−	4096.53i		−	0.288044i	0.989574	−	0.144022i	$-0.0460036\pi$
$588$	−7791.40	−	5959.40i	−0.546449	−	0.417962i
$589$		−	24344.5i		−	1.70305i
$590$	2484.27	+	5027.79i	0.173349	+	0.350832i
$591$	−8449.99			−0.588132
$592$	−7049.38	+	1912.30i	−0.489405	+	0.132762i
$593$	−21988.3			−1.52269			−0.761343	−	0.648349i	$-0.775460\pi$
$593$	−21988.3			−1.52269			−0.761343	+	0.648349i	$0.775460\pi$
$594$	−694.357	−	1405.27i	−0.0479627	−	0.0970691i
$595$			28053.1i			1.93288i
$596$	−8200.27	−	6272.13i	−0.563584	−	0.431068i
$597$		−	2845.67i		−	0.195084i
$598$	744.794	−	368.009i	0.0509312	−	0.0251656i
$599$	20767.7			1.41660			0.708302	−	0.705909i	$-0.249461\pi$
$599$	20767.7			1.41660			0.708302	+	0.705909i	$0.249461\pi$
$600$	539.093	−	2743.51i	0.0366807	−	0.186672i
$601$	5382.61			0.365326			0.182663	−	0.983176i	$-0.441528\pi$
$601$	5382.61			0.365326			0.182663	+	0.983176i	$0.441528\pi$
$602$	−6214.57	+	3070.67i	−0.420743	+	0.207893i
$603$		−	3414.90i		−	0.230623i
$604$	−5713.28	+	7469.62i	−0.384884	+	0.503203i
$605$		−	8328.33i		−	0.559661i
$606$	756.479	+	1531.00i	0.0507093	+	0.102628i
$607$	11165.4			0.746607			0.373304	−	0.927709i	$-0.378225\pi$
$607$	11165.4			0.746607			0.373304	+	0.927709i	$0.378225\pi$
$608$	15556.2	+	17600.5i	1.03764	+	1.17400i
$609$	3377.33			0.224723
$610$	−8651.33	−	17509.0i	−0.574233	−	1.16216i
$611$			1751.26i			0.115955i
$612$	−4888.82	+	6391.71i	−0.322906	+	0.422172i
$613$			16413.5i			1.08146i	0.841195	+	0.540731i	$0.181852\pi$
$613$			16413.5i			1.08146i	−0.841195	+	0.540731i	$0.818148\pi$
$614$	−9661.85	+	4774.00i	−0.635050	+	0.313784i
$615$	7770.15			0.509468
$616$	−2455.17	+	12494.6i	−0.160587	+	0.817243i
$617$	−51.5882			−0.00336607			−0.00168303	−	0.999999i	$-0.500536\pi$
$617$	−51.5882			−0.00336607			−0.00168303	+	0.999999i	$0.500536\pi$
$618$	−5191.53	+	2565.18i	−0.337919	+	0.166969i
$619$		−	6349.55i		−	0.412294i	−0.978521	−	0.206147i	$-0.933907\pi$
$619$		−	6349.55i		−	0.412294i	0.978521	−	0.206147i	$-0.0660925\pi$
$620$	−10913.7	−	8347.52i	−0.706941	−	0.540717i
$621$		−	247.458i		−	0.0159906i
$622$	−10157.3	−	20556.8i	−0.654775	−	1.32516i
$623$	−7609.11			−0.489330
$624$	−1610.93	−	5938.43i	−0.103348	−	0.380973i
$625$	−8779.94			−0.561916
$626$	−701.629	−	1419.99i	−0.0447967	−	0.0906616i
$627$			7990.29i			0.508934i
$628$	−6939.53	−	5307.83i	−0.440951	−	0.337270i
$629$			12755.3i			0.808567i
$630$	−5728.37	+	2830.44i	−0.362260	+	0.178996i
$631$	−13379.1			−0.844078			−0.422039	−	0.906578i	$-0.638685\pi$
$631$	−13379.1			−0.844078			−0.422039	+	0.906578i	$0.638685\pi$
$632$	−6700.38	−	1316.61i	−0.421720	−	0.0828671i
$633$	−13461.9			−0.845277
$634$	14780.9	−	7303.39i	0.925909	−	0.457500i
$635$			7397.63i			0.462309i
$636$	10598.4	−	13856.5i	0.660779	−	0.863911i
$637$		−	13098.2i		−	0.814709i
$638$	−1055.95	−	2137.09i	−0.0655260	−	0.132615i
$639$	−2718.72			−0.168311
$640$	13224.4	−	938.802i	0.816780	−	0.0579835i
$641$	−20406.3			−1.25741			−0.628705	−	0.777644i	$-0.716415\pi$
$641$	−20406.3			−1.25741			−0.628705	+	0.777644i	$0.716415\pi$
$642$	1718.74	+	3478.46i	0.105659	+	0.213838i
$643$		−	19415.1i		−	1.19076i	−0.803446	−	0.595378i	$-0.797002\pi$
$643$		−	19415.1i		−	1.19076i	0.803446	−	0.595378i	$-0.202998\pi$
$644$	−1221.30	+	1596.75i	−0.0747299	+	0.0977029i
$645$			2454.98i			0.149868i
$646$	36776.2	−	18171.4i	2.23984	−	1.10673i
$647$	−8167.12			−0.496264			−0.248132	−	0.968726i	$-0.579817\pi$
$647$	−8167.12			−0.496264			−0.248132	+	0.968726i	$0.579817\pi$
$648$	−1798.43	−	353.388i	−0.109026	−	0.0214234i
$649$	4445.31			0.268866
$650$	3347.15	−	1653.86i	0.201978	−	0.0997993i
$651$		−	15431.0i		−	0.929017i
$652$	23047.1	+	17628.0i	1.38435	+	1.05884i
$653$		−	7444.93i		−	0.446160i	−0.974800	−	0.223080i	$-0.928389\pi$
$653$		−	7444.93i		−	0.446160i	0.974800	−	0.223080i	$-0.0716111\pi$
$654$	2352.32	+	4760.74i	0.140647	+	0.284648i
$655$	−10169.7			−0.606662
$656$	−4740.49	−	17475.0i	−0.282142	−	1.04007i
$657$	4539.56			0.269567
$658$	−1877.24	−	3799.25i	−0.111220	−	0.225092i
$659$			23780.4i			1.40569i	0.711342	+	0.702846i	$0.248088\pi$
$659$			23780.4i			1.40569i	−0.711342	+	0.702846i	$0.751912\pi$
$660$	3582.05	+	2739.80i	0.211259	+	0.161586i
$661$		−	2528.90i		−	0.148809i	−0.997228	−	0.0744046i	$-0.976294\pi$
$661$		−	2528.90i		−	0.148809i	0.997228	−	0.0744046i	$-0.0237056\pi$
$662$	7221.82	−	3568.36i	0.423994	−	0.209499i
$663$	−10745.2			−0.629423
$664$	2613.34	−	13299.6i	0.152737	−	0.777294i
$665$	32571.2			1.89933
$666$	−2604.61	+	1286.96i	−0.151541	+	0.0748778i
$667$		−	376.324i		−	0.0218461i
$668$	−222.605	+	291.037i	−0.0128935	+	0.0168571i
$669$		−	13772.9i		−	0.795953i
$670$	4352.31	+	8808.40i	0.250962	+	0.507908i
$671$	−15480.5			−0.890640
$672$	9860.45	+	11156.2i	0.566035	+	0.640419i
$673$	16733.7			0.958447			0.479224	−	0.877693i	$-0.340918\pi$
$673$	16733.7			0.958447			0.479224	+	0.877693i	$0.340918\pi$
$674$	−12689.5	−	25681.6i	−0.725196	−	1.46769i
$675$		−	1112.09i		−	0.0634139i
$676$	−5686.41	+	7434.49i	−0.323532	+	0.422991i
$677$			24191.5i			1.37335i	0.726966	+	0.686673i	$0.240930\pi$
$677$			24191.5i			1.37335i	−0.726966	+	0.686673i	$0.759070\pi$
$678$	−7463.92	+	3687.99i	−0.422788	+	0.208903i
$679$	−20999.2			−1.18685
$680$	4463.96	−	22717.6i	0.251743	−	1.28115i
$681$	−8692.41			−0.489125
$682$	−9764.35	+	4824.65i	−0.548235	+	0.270888i
$683$		−	13965.2i		−	0.782376i	−0.920311	−	0.391188i	$-0.872064\pi$
$683$		−	13965.2i		−	0.782376i	0.920311	−	0.391188i	$-0.127936\pi$
$684$	7421.11	+	5676.18i	0.414844	+	0.317301i
$685$			4273.17i			0.238350i
$686$	2257.54	+	4568.91i	0.125646	+	0.254288i
$687$	−103.888			−0.00576939
$688$	5521.23	−	1497.76i	0.305952	−	0.0829962i
$689$	23294.4			1.28802
$690$	315.386	+	638.293i	0.0174008	+	0.0352165i
$691$			8685.63i			0.478172i	0.970998	+	0.239086i	$0.0768479\pi$
$691$			8685.63i			0.478172i	−0.970998	+	0.239086i	$0.923152\pi$
$692$	15600.1	+	11932.0i	0.856974	+	0.655472i
$693$			5064.73i			0.277624i
$694$	−25733.5	+	12715.2i	−1.40754	+	0.695477i
$695$	−3220.43			−0.175767
$696$	−2734.99	−	537.419i	−0.148950	−	0.0292684i
$697$	−31619.7			−1.71834
$698$	−24130.3	+	11923.0i	−1.30852	+	0.646550i
$699$		−	3162.05i		−	0.171101i
$700$	−5488.61	+	7175.88i	−0.296357	+	0.387461i
$701$			25942.2i			1.39775i	0.715243	+	0.698876i	$0.246316\pi$
$701$			25942.2i			1.39775i	−0.715243	+	0.698876i	$0.753684\pi$
$702$	−1084.14	−	2194.13i	−0.0582880	−	0.117966i
$703$	14809.6			0.794532
$704$	3976.42	−	9727.53i	0.212879	−	0.520767i
$705$	−1500.84			−0.0801772
$706$	3525.24	+	7134.54i	0.187924	+	0.380329i
$707$		−	5517.86i		−	0.293522i
$708$	3157.88	−	4128.66i	0.167628	−	0.219159i
$709$			5487.75i			0.290687i	0.989381	+	0.145343i	$0.0464287\pi$
$709$			5487.75i			0.290687i	−0.989381	+	0.145343i	$0.953571\pi$
$710$	7012.66	−	3465.02i	0.370677	−	0.183155i
$711$	−2716.02			−0.143261
$712$	6161.91	+	1210.80i	0.324336	+	0.0637314i
$713$	−1719.43			−0.0903128
$714$	23311.0	−	11518.2i	1.22184	−	0.603720i
$715$			6021.82i			0.314970i
$716$	−6521.33	−	4987.96i	−0.340382	−	0.260348i
$717$		−	1964.10i		−	0.102302i
$718$	−3041.21	−	6154.94i	−0.158074	−	0.319917i
$719$	17141.2			0.889094			0.444547	−	0.895756i	$-0.353365\pi$
$719$	17141.2			0.889094			0.444547	+	0.895756i	$0.353365\pi$
$720$	5089.27	−	1380.58i	0.263425	−	0.0714599i
$721$	18710.8			0.966470
$722$	−12504.0	−	25306.3i	−0.644532	−	1.30443i
$723$			9581.99i			0.492888i
$724$	23505.1	+	17978.3i	1.20658	+	0.922873i
$725$		−	1691.23i		−	0.0866352i
$726$	−6920.50	+	3419.48i	−0.353779	+	0.174805i
$727$	−15946.4			−0.813508			−0.406754	−	0.913538i	$-0.633339\pi$
$727$	−15946.4			−0.813508			−0.406754	+	0.913538i	$0.633339\pi$
$728$	−3833.39	+	19508.5i	−0.195158	+	0.993179i
$729$	−729.000			−0.0370370
$730$	−11709.4	+	5785.69i	−0.593675	+	0.293340i
$731$		−	9990.26i		−	0.505476i
$732$	−10997.1	+	14377.8i	−0.555281	+	0.725982i
$733$		−	15914.2i		−	0.801917i	−0.916096	−	0.400958i	$-0.868677\pi$
$733$		−	15914.2i		−	0.801917i	0.916096	−	0.400958i	$-0.131323\pi$
$734$	6291.62	+	12733.3i	0.316387	+	0.640318i
$735$	11225.2			0.563332
$736$	1243.10	−	1098.72i	0.0622572	−	0.0550261i
$737$	7787.94			0.389243
$738$	−3190.30	−	6456.67i	−0.159128	−	0.322050i
$739$		−	13555.4i		−	0.674755i	−0.941369	−	0.337377i	$-0.890460\pi$
$739$		−	13555.4i		−	0.674755i	0.941369	−	0.337377i	$-0.109540\pi$
$740$	5078.09	−	6639.17i	0.252263	−	0.329812i
$741$			12475.7i			0.618497i
$742$	−50535.7	+	24970.1i	−2.50030	+	1.23542i
$743$	−1772.73			−0.0875303			−0.0437652	−	0.999042i	$-0.513935\pi$
$743$	−1772.73			−0.0875303			−0.0437652	+	0.999042i	$0.513935\pi$
$744$	−2455.47	+	12496.2i	−0.120997	+	0.615768i
$745$	11814.3			0.580997
$746$	8069.82	−	3987.37i	0.396055	−	0.195694i
$747$		−	5391.03i		−	0.264053i
$748$	−14576.8	−	11149.3i	−0.712539	−	0.544999i
$749$		−	12536.7i		−	0.611589i
$750$	5718.82	+	11574.0i	0.278429	+	0.563497i
$751$	−1006.65			−0.0489124			−0.0244562	−	0.999701i	$-0.507785\pi$
$751$	−1006.65			−0.0489124			−0.0244562	+	0.999701i	$0.507785\pi$
$752$	915.647	+	3375.38i	0.0444019	+	0.163680i
$753$	15128.7			0.732165
$754$	−1648.72	−	3336.75i	−0.0796324	−	0.161164i
$755$		−	10761.6i		−	0.518750i
$756$	4703.95	+	3597.91i	0.226298	+	0.173088i
$757$			28774.0i			1.38152i	0.723086	+	0.690758i	$0.242723\pi$
$757$			28774.0i			1.38152i	−0.723086	+	0.690758i	$0.757277\pi$
$758$	14882.2	−	7353.45i	0.713123	−	0.352360i
$759$	564.346			0.0269887
$760$	−26376.3	−	5182.90i	−1.25891	−	0.247373i
$761$	18393.5			0.876166			0.438083	−	0.898934i	$-0.355658\pi$
$761$	18393.5			0.876166			0.438083	+	0.898934i	$0.355658\pi$
$762$	6147.12	−	3037.35i	0.292240	−	0.144398i
$763$		−	17158.2i		−	0.814112i
$764$	−24830.7	+	32464.0i	−1.17584	+	1.53731i
$765$		−	9208.66i		−	0.435215i
$766$	9209.38	+	18638.4i	0.434397	+	0.879153i
$767$	6940.72			0.326747
$768$	−6209.82	−	10603.4i	−0.291768	−	0.498202i
$769$	−14672.2			−0.688027			−0.344014	−	0.938965i	$-0.611787\pi$
$769$	−14672.2			−0.688027			−0.344014	+	0.938965i	$0.611787\pi$
$770$	−6455.03	−	13064.0i	−0.302108	−	0.611420i
$771$		−	15499.9i		−	0.724016i
$772$	6873.05	−	8985.92i	0.320423	−	0.418925i
$773$		−	16256.4i		−	0.756405i	−0.925723	−	0.378202i	$-0.876542\pi$
$773$		−	16256.4i		−	0.756405i	0.925723	−	0.378202i	$-0.123458\pi$
$774$	2039.98	−	1007.97i	0.0947361	−	0.0468099i
$775$	−7727.21			−0.358154
$776$	17005.3	+	3341.50i	0.786667	+	0.154578i
$777$	9387.25			0.433418
$778$	32988.1	−	16299.7i	1.52016	−	0.751122i
$779$			36712.2i			1.68851i
$780$	5592.86	+	4277.81i	0.256739	+	0.196372i
$781$		−	6200.24i		−	0.284074i
$782$	−1283.43	−	2597.46i	−0.0586896	−	0.118779i
$783$	−1108.64			−0.0505995
$784$	−6848.40	−	25245.5i	−0.311971	−	1.15003i
$785$	9997.92			0.454575
$786$	4175.52	+	8450.62i	0.189486	+	0.383490i
$787$		−	23988.3i		−	1.08652i	−0.839565	−	0.543259i	$-0.817190\pi$
$787$		−	23988.3i		−	1.08652i	0.839565	−	0.543259i	$-0.182810\pi$
$788$	−17898.1	−	13689.7i	−0.809129	−	0.618877i
$789$		−	22098.3i		−	0.997112i
$790$	7005.72	−	3461.59i	0.315509	−	0.155896i
$791$	26900.7			1.20920
$792$	805.928	−	4101.45i	0.0361583	−	0.184014i
$793$	−24170.6			−1.08238
$794$	−12369.2	+	6111.72i	−0.552853	+	0.273170i
$795$			19963.4i			0.890602i
$796$	4610.22	−	6027.47i	0.205283	−	0.268389i
$797$		−	32966.9i		−	1.46518i	−0.680672	−	0.732589i	$-0.738312\pi$
$797$		−	32966.9i		−	1.46518i	0.680672	−	0.732589i	$-0.261688\pi$
$798$	−13373.2	−	27065.3i	−0.593240	−	1.20063i
$799$	6107.50			0.270423
$800$	5586.58	−	4937.70i	0.246894	−	0.218218i
$801$	2497.75			0.110179
$802$	6956.76	+	14079.4i	0.306299	+	0.619902i
$803$			10352.8i			0.454973i
$804$	5532.43	−	7233.17i	0.242679	−	0.317281i
$805$		−	2300.47i		−	0.100721i
$806$	−15245.6	+	7533.00i	−0.666259	+	0.329204i
$807$	−23633.4			−1.03090
$808$	−878.031	+	4468.40i	−0.0382290	+	0.194552i
$809$	−41700.3			−1.81224			−0.906122	−	0.423017i	$-0.860971\pi$
$809$	−41700.3			−1.81224			−0.906122	+	0.423017i	$0.860971\pi$
$810$	1880.38	−	929.114i	0.0815679	−	0.0403034i
$811$			5981.80i			0.259000i	0.991579	+	0.129500i	$0.0413373\pi$
$811$			5981.80i			0.259000i	−0.991579	+	0.129500i	$0.958663\pi$
$812$	7153.60	+	5471.56i	0.309165	+	0.236471i
$813$		−	16199.7i		−	0.698832i
$814$	−2935.01	−	5940.00i	−0.126378	−	0.255770i
$815$	−33204.4			−1.42712
$816$	−20710.2	+	5618.11i	−0.888483	+	0.241021i
$817$	−11599.2			−0.496702
$818$	8757.18	+	17723.2i	0.374312	+	0.757551i
$819$			7907.86i			0.337391i
$820$	16458.1	+	12588.3i	0.700905	+	0.536100i
$821$			9846.06i			0.418550i	0.977857	+	0.209275i	$0.0671104\pi$
$821$			9846.06i			0.418550i	−0.977857	+	0.209275i	$0.932890\pi$
$822$	3550.83	−	1754.50i	0.150668	−	0.0744465i
$823$	47001.9			1.99074			0.995372	−	0.0960935i	$-0.0306348\pi$
$823$	47001.9			1.99074			0.995372	+	0.0960935i	$0.0306348\pi$
$824$	−15152.1	−	2977.36i	−0.640593	−	0.125875i
$825$	2536.21			0.107030
$826$	−15057.5	+	7440.03i	−0.634282	+	0.313404i
$827$			21727.4i			0.913587i	0.889573	+	0.456794i	$0.151002\pi$
$827$			21727.4i			0.913587i	−0.889573	+	0.456794i	$0.848998\pi$
$828$	400.902	−	524.145i	0.0168265	−	0.0219992i
$829$			22772.3i			0.954058i	0.878888	+	0.477029i	$0.158286\pi$
$829$			22772.3i			0.954058i	−0.878888	+	0.477029i	$0.841714\pi$
$830$	6870.89	+	13905.6i	0.287340	+	0.581532i
$831$	13248.2			0.553039
$832$	6208.61	−	15188.2i	0.258708	−	0.632878i
$833$	−45679.8			−1.90002
$834$	1322.26	+	2676.04i	0.0548993	+	0.111108i
$835$		−	419.304i		−	0.0173780i
$836$	−12945.0	+	16924.4i	−0.535539	+	0.700171i
$837$			5065.36i			0.209181i
$838$	26526.7	−	13107.1i	1.09350	−	0.540306i
$839$	11010.4			0.453064			0.226532	−	0.974004i	$-0.427261\pi$
$839$	11010.4			0.453064			0.226532	+	0.974004i	$0.427261\pi$
$840$	−16718.9	−	3285.24i	−0.686736	−	0.134942i
$841$	22703.0			0.930872
$842$	11787.7	−	5824.39i	0.482458	−	0.238387i
$843$			24206.8i			0.989000i
$844$	−28513.8	−	21809.3i	−1.16290	−	0.889465i
$845$		−	10711.0i		−	0.436059i
$846$	616.221	+	1247.14i	0.0250427	+	0.0506825i
$847$	24942.1			1.01183
$848$	44897.5	−	12179.5i	1.81815	−	0.493213i
$849$	−15723.4			−0.635602
$850$	−5767.81	−	11673.2i	−0.232746	−	0.471042i
$851$		−	1045.99i		−	0.0421340i
$852$	−5758.57	−	4404.55i	−0.231556	−	0.177110i
$853$			38177.4i			1.53244i	0.642579	+	0.766219i	$0.277864\pi$
$853$			38177.4i			1.53244i	−0.642579	+	0.766219i	$0.722136\pi$
$854$	52436.8	−	25909.5i	2.10111	−	1.03818i
$855$	−10691.7			−0.427661
$856$	−1994.90	+	10152.3i	−0.0796547	+	0.405372i
$857$	8848.01			0.352675			0.176337	−	0.984330i	$-0.443575\pi$
$857$	8848.01			0.352675			0.176337	+	0.984330i	$0.443575\pi$
$858$	5003.88	−	2472.46i	0.199102	−	0.0983782i
$859$			4347.66i			0.172690i	0.996265	+	0.0863448i	$0.0275187\pi$
$859$			4347.66i			0.172690i	−0.996265	+	0.0863448i	$0.972481\pi$
$860$	−3977.27	+	5199.94i	−0.157702	+	0.206182i
$861$			23270.4i			0.921085i
$862$	15650.1	+	31673.5i	0.618382	+	1.25151i
$863$	−33669.9			−1.32808			−0.664042	−	0.747695i	$-0.731161\pi$
$863$	−33669.9			−1.32808			−0.664042	+	0.747695i	$0.731161\pi$
$864$	−3236.77	−	3662.13i	−0.127451	−	0.144199i
$865$	−22475.3			−0.883450
$866$	11835.8	+	23953.8i	0.464430	+	0.939936i
$867$			22734.6i			0.890552i
$868$	24999.6	−	32684.8i	0.977582	−	1.27810i
$869$		−	6194.10i		−	0.241796i
$870$	2859.62	−	1412.96i	0.111437	−	0.0550620i
$871$	12159.7			0.473039
$872$	−2730.30	+	13894.8i	−0.106032	+	0.539607i
$873$	6893.15			0.267237
$874$	−3015.79	+	1490.13i	−0.116717	+	0.0576709i
$875$		−	41713.8i		−	1.61164i
$876$	9615.34	+	7354.48i	0.370859	+	0.283658i
$877$			50102.0i			1.92910i	0.263892	+	0.964552i	$0.414994\pi$
$877$			50102.0i			1.92910i	−0.263892	+	0.964552i	$0.585006\pi$
$878$	3500.23	+	7083.93i	0.134541	+	0.272291i
$879$	19118.2			0.733609
$880$	3148.51	+	11606.5i	0.120609	+	0.444606i
$881$	18716.9			0.715766			0.357883	−	0.933766i	$-0.383499\pi$
$881$	18716.9			0.715766			0.357883	+	0.933766i	$0.383499\pi$
$882$	−4608.90	−	9327.70i	−0.175952	−	0.356100i
$883$		−	7514.19i		−	0.286379i	−0.989695	−	0.143189i	$-0.954264\pi$
$883$		−	7514.19i		−	0.286379i	0.989695	−	0.143189i	$-0.0457358\pi$
$884$	−22759.5	−	17408.1i	−0.865934	−	0.662326i
$885$			5948.24i			0.225930i
$886$	−19275.3	+	9524.10i	−0.730888	+	0.361138i
$887$	−15544.6			−0.588429			−0.294215	−	0.955739i	$-0.595058\pi$
$887$	−15544.6			−0.588429			−0.294215	+	0.955739i	$0.595058\pi$
$888$	−7601.85	−	1493.75i	−0.287277	−	0.0564493i
$889$	−22154.8			−0.835825
$890$	−6442.71	+	3183.40i	−0.242652	+	0.119896i
$891$		−	1662.54i		−	0.0625109i
$892$	22313.3	−	29172.7i	0.837562	−	1.09504i
$893$		−	7091.14i		−	0.265729i
$894$	−4850.76	−	9817.19i	−0.181469	−	0.367266i
$895$	9395.42			0.350898
$896$	2811.57	+	39605.0i	0.104830	+	1.47669i
$897$	881.145			0.0327989
$898$	13417.6	+	27155.1i	0.498609	+	1.00911i
$899$			7703.21i			0.285780i
$900$	1801.68	−	2355.54i	0.0667289	−	0.0872423i
$901$		−	81238.8i		−	3.00384i
$902$	14724.9	−	7275.71i	0.543555	−	0.268575i
$903$	−7352.29			−0.270951
$904$	−21784.3	−	4280.58i	−0.801478	−	0.157489i
$905$	−33864.3			−1.24385
$906$	−8942.48	+	4418.55i	−0.327918	+	0.162027i
$907$		−	8713.10i		−	0.318979i	−0.987200	−	0.159489i	$-0.949015\pi$
$907$		−	8713.10i		−	0.318979i	0.987200	−	0.159489i	$-0.0509848\pi$
$908$	−18411.6	−	14082.4i	−0.672918	−	0.514694i
$909$			1811.28i			0.0660906i
$910$	−10078.6	−	20397.5i	−0.367145	−	0.743046i
$911$	1975.97			0.0718627			0.0359313	−	0.999354i	$-0.488560\pi$
$911$	1975.97			0.0718627			0.0359313	+	0.999354i	$0.488560\pi$
$912$	6522.92	+	24045.7i	0.236837	+	0.873061i
$913$	12294.6			0.445666
$914$	292.988	+	592.964i	0.0106031	+	0.0214590i
$915$		−	20714.4i		−	0.748411i
$916$	−220.047	−	168.307i	−0.00793730	−	0.00607099i
$917$		−	30456.8i		−	1.09681i
$918$	−7652.01	+	3780.93i	−0.275113	+	0.135936i
$919$	−18430.5			−0.661552			−0.330776	−	0.943709i	$-0.607311\pi$
$919$	−18430.5			−0.661552			−0.330776	+	0.943709i	$0.607311\pi$
$920$	−366.063	+	1862.93i	−0.0131182	+	0.0667599i
$921$	−11430.7			−0.408961
$922$	−2488.37	+	1229.52i	−0.0888829	+	0.0439178i
$923$		−	9680.79i		−	0.345230i
$924$	−8205.30	+	10727.7i	−0.292137	+	0.381944i
$925$		−	4700.74i		−	0.167091i
$926$	−17644.9	−	35710.6i	−0.626185	−	1.26730i
$927$	−6141.96			−0.217614
$928$	−4922.36	−	5569.23i	−0.174121	−	0.197003i
$929$	12506.8			0.441697			0.220848	−	0.975308i	$-0.429117\pi$
$929$	12506.8			0.441697			0.220848	+	0.975308i	$0.429117\pi$
$930$	−6455.83	−	13065.6i	−0.227629	−	0.460686i
$931$			53036.7i			1.86703i
$932$	5122.78	−	6697.59i	0.180045	−	0.235394i
$933$		−	24320.2i		−	0.853384i
$934$	−23548.4	+	11635.5i	−0.824976	+	0.407628i
$935$	21001.0			0.734554
$936$	1258.34	−	6403.83i	0.0439425	−	0.223628i
$937$	39267.5			1.36906			0.684532	−	0.728982i	$-0.260006\pi$
$937$	39267.5			1.36906			0.684532	+	0.728982i	$0.260006\pi$
$938$	−26379.9	+	13034.5i	−0.918265	+	0.453723i
$939$		−	1679.95i		−	0.0583846i
$940$	−3178.96	−	2431.49i	−0.110305	−	0.0843685i
$941$			23727.2i			0.821981i	0.911640	+	0.410991i	$0.134817\pi$
$941$			23727.2i			0.821981i	−0.911640	+	0.410991i	$0.865183\pi$
$942$	−4104.98	−	8307.86i	−0.141983	−	0.287351i
$943$	2592.94			0.0895418
$944$	13377.5	−	3628.96i	0.461231	−	0.125119i
$945$	−6777.08			−0.233289
$946$	2298.76	+	4652.34i	0.0790054	+	0.159895i
$947$		−	23399.8i		−	0.802948i	−0.915870	−	0.401474i	$-0.868498\pi$
$947$		−	23399.8i		−	0.802948i	0.915870	−	0.401474i	$-0.131502\pi$
$948$	−5752.87	−	4400.19i	−0.197093	−	0.150751i
$949$			16164.4i			0.552919i
$950$	−13553.2	+	6696.73i	−0.462866	+	0.228706i
$951$	17486.9			0.596270
$952$	68035.8	+	13368.9i	2.31623	+	0.455135i
$953$	41497.1			1.41052			0.705258	−	0.708950i	$-0.250831\pi$
$953$	41497.1			1.41052			0.705258	+	0.708950i	$0.250831\pi$
$954$	16588.8	−	8196.65i	0.562978	−	0.278172i
$955$		−	46771.6i		−	1.58481i
$956$	3182.01	−	4160.20i	0.107650	−	0.140743i
$957$		−	2528.33i		−	0.0854015i
$958$	−24318.8	−	49217.6i	−0.820152	−	1.65986i
$959$	−12797.5			−0.430921
$960$	13016.3	+	5320.81i	0.437605	+	0.178884i
$961$	5405.00			0.181431
$962$	−4582.59	−	9274.46i	−0.153585	−	0.310832i
$963$			4115.27i			0.137708i
$964$	−15523.6	+	20295.8i	−0.518654	+	0.678096i
$965$			12946.2i			0.431868i
$966$	−1911.59	+	944.534i	−0.0636692	+	0.0314595i
$967$	−49123.6			−1.63362			−0.816808	−	0.576909i	$-0.804259\pi$
$967$	−49123.6			−1.63362			−0.816808	+	0.576909i	$0.804259\pi$
$968$	−20198.3	−	3968.92i	−0.670659	−	0.131783i
$969$	43508.9			1.44242
$970$	−17780.2	+	8785.35i	−0.588544	+	0.290805i
$971$			20346.8i			0.672462i	0.941780	+	0.336231i	$0.109152\pi$
$971$			20346.8i			0.672462i	−0.941780	+	0.336231i	$0.890848\pi$
$972$	−1544.11	−	1181.04i	−0.0509541	−	0.0389732i
$973$		−	9644.71i		−	0.317775i
$974$	15191.7	+	30745.6i	0.499766	+	1.01145i
$975$	3959.92			0.130071
$976$	−46586.5	+	12637.6i	−1.52787	+	0.414468i
$977$	40602.1			1.32955			0.664777	−	0.747042i	$-0.268526\pi$
$977$	40602.1			1.32955			0.664777	+	0.747042i	$0.268526\pi$
$978$	13633.2	+	27591.5i	0.445748	+	0.902125i
$979$			5696.32i			0.185960i
$980$	23776.4	+	18185.8i	0.775009	+	0.592781i
$981$			5632.31i			0.183309i
$982$	12934.2	−	6390.89i	0.420312	−	0.207680i
$983$	50425.9			1.63615			0.818075	−	0.575112i	$-0.195041\pi$
$983$	50425.9			1.63615			0.818075	+	0.575112i	$0.195041\pi$
$984$	3702.92	−	18844.6i	0.119964	−	0.610511i
$985$	25786.2			0.834127
$986$	−11636.9	+	5749.89i	−0.375856	+	0.185714i
$987$		−	4494.79i		−	0.144955i
$988$	−20211.7	+	26425.0i	−0.650829	+	0.850903i
$989$			819.241i			0.0263401i
$990$	2118.91	+	4288.36i	0.0680238	+	0.137670i
$991$	−8511.62			−0.272836			−0.136418	−	0.990651i	$-0.543559\pi$
$991$	−8511.62			−0.272836			−0.136418	+	0.990651i	$0.543559\pi$
$992$	−25445.8	+	22490.3i	−0.814421	+	0.719826i
$993$	8543.94			0.273045
$994$	10377.2	+	21001.9i	0.331132	+	0.670161i
$995$			8683.90i			0.276681i
$996$	8733.92	−	11418.8i	0.277856	−	0.363273i
$997$			25302.1i			0.803738i	0.915697	+	0.401869i	$0.131639\pi$
$997$			25302.1i			0.803738i	−0.915697	+	0.401869i	$0.868361\pi$
$998$	216.250	−	106.851i	0.00685898	−	0.00338908i
$999$	−3081.44			−0.0975900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.4.d.a.13.4	yes	6
3.2	odd	2		72.4.d.d.37.3		6
4.3	odd	2		96.4.d.a.49.1		6
8.3	odd	2		96.4.d.a.49.6		6
8.5	even	2	inner	24.4.d.a.13.3	✓	6
12.11	even	2		288.4.d.d.145.5		6
16.3	odd	4		768.4.a.t.1.1		3
16.5	even	4		768.4.a.s.1.3		3
16.11	odd	4		768.4.a.q.1.3		3
16.13	even	4		768.4.a.r.1.1		3
24.5	odd	2		72.4.d.d.37.4		6
24.11	even	2		288.4.d.d.145.2		6
48.5	odd	4		2304.4.a.bv.1.1		3
48.11	even	4		2304.4.a.bw.1.1		3
48.29	odd	4		2304.4.a.bt.1.3		3
48.35	even	4		2304.4.a.bu.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.4.d.a.13.3	✓	6	8.5	even	2	inner
24.4.d.a.13.4	yes	6	1.1	even	1	trivial
72.4.d.d.37.3		6	3.2	odd	2
72.4.d.d.37.4		6	24.5	odd	2
96.4.d.a.49.1		6	4.3	odd	2
96.4.d.a.49.6		6	8.3	odd	2
288.4.d.d.145.2		6	24.11	even	2
288.4.d.d.145.5		6	12.11	even	2
768.4.a.q.1.3		3	16.11	odd	4
768.4.a.r.1.1		3	16.13	even	4
768.4.a.s.1.3		3	16.5	even	4
768.4.a.t.1.1		3	16.3	odd	4
2304.4.a.bt.1.3		3	48.29	odd	4
2304.4.a.bu.1.3		3	48.35	even	4
2304.4.a.bv.1.1		3	48.5	odd	4
2304.4.a.bw.1.1		3	48.11	even	4

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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	24.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25295 + 2.53577i) q^{2} +3.00000i q^{3} +(-4.86025 + 6.35436i) q^{4} -9.15486i q^{5} +(-7.60731 + 3.75884i) q^{6} +27.4175 q^{7} +(-22.2028 - 4.36281i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(1.25295 + 2.53577i) q^{2} +3.00000i q^{3} +(-4.86025 + 6.35436i) q^{4} -9.15486i q^{5} +(-7.60731 + 3.75884i) q^{6} +27.4175 q^{7} +(-22.2028 - 4.36281i) q^{8} -9.00000 q^{9} +(23.2146 - 11.4705i) q^{10} -20.5252i q^{11} +(-19.0631 - 14.5808i) q^{12} -32.0471i q^{13} +(34.3526 + 69.5243i) q^{14} +27.4646 q^{15} +(-16.7559 - 61.7676i) q^{16} -111.764 q^{17} +(-11.2765 - 22.8219i) q^{18} +129.764i q^{19} +(58.1733 + 44.4950i) q^{20} +82.2524i q^{21} +(52.0471 - 25.7169i) q^{22} +9.16510 q^{23} +(13.0884 - 66.6085i) q^{24} +41.1885 q^{25} +(81.2641 - 40.1533i) q^{26} -27.0000i q^{27} +(-133.256 + 174.220i) q^{28} -41.0606i q^{29} +(34.4116 + 69.6439i) q^{30} -187.606 q^{31} +(135.634 - 119.880i) q^{32} +61.5755 q^{33} +(-140.034 - 283.408i) q^{34} -251.003i q^{35} +(43.7423 - 57.1893i) q^{36} -114.127i q^{37} +(-329.052 + 162.587i) q^{38} +96.1414 q^{39} +(-39.9409 + 203.264i) q^{40} +282.915 q^{41} +(-208.573 + 103.058i) q^{42} +89.3870i q^{43} +(130.424 + 99.7576i) q^{44} +82.3937i q^{45} +(11.4834 + 23.2406i) q^{46} -54.6464 q^{47} +(185.303 - 50.2676i) q^{48} +408.717 q^{49} +(51.6070 + 104.445i) q^{50} -335.292i q^{51} +(203.639 + 155.757i) q^{52} +726.878i q^{53} +(68.4658 - 33.8295i) q^{54} -187.905 q^{55} +(-608.745 - 119.617i) q^{56} -389.292 q^{57} +(104.120 - 51.4467i) q^{58} +216.579i q^{59} +(-133.485 + 174.520i) q^{60} -754.222i q^{61} +(-235.060 - 475.726i) q^{62} -246.757 q^{63} +(473.932 + 193.734i) q^{64} -293.387 q^{65} +(77.1508 + 156.141i) q^{66} +379.433i q^{67} +(543.202 - 710.189i) q^{68} +27.4953i q^{69} +(636.486 - 314.493i) q^{70} +302.080 q^{71} +(199.826 + 39.2653i) q^{72} -504.396 q^{73} +(289.401 - 142.995i) q^{74} +123.566i q^{75} +(-824.568 - 630.686i) q^{76} -562.748i q^{77} +(120.460 + 243.792i) q^{78} +301.780 q^{79} +(-565.474 + 153.398i) q^{80} +81.0000 q^{81} +(354.477 + 717.408i) q^{82} +599.003i q^{83} +(-522.661 - 399.767i) q^{84} +1023.18i q^{85} +(-226.665 + 111.997i) q^{86} +123.182 q^{87} +(-89.5475 + 455.717i) q^{88} -277.528 q^{89} +(-208.932 + 103.235i) q^{90} -878.651i q^{91} +(-44.5447 + 58.2383i) q^{92} -562.818i q^{93} +(-68.4689 - 138.571i) q^{94} +1187.97 q^{95} +(359.641 + 406.903i) q^{96} -765.905 q^{97} +(512.100 + 1036.41i) q^{98} +184.727i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 16 * q^4 - 6 * q^6 + 28 * q^7 - 76 * q^8 - 54 * q^9	\( 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9} + 60 q^{10} - 12 q^{12} - 100 q^{14} - 60 q^{15} + 56 q^{16} + 52 q^{17} - 18 q^{18} + 56 q^{20} + 224 q^{22} + 328 q^{23} + 204 q^{24} - 106 q^{25} + 56 q^{26} - 352 q^{28} + 372 q^{30} - 636 q^{31} - 248 q^{32} - 548 q^{34} - 144 q^{36} - 776 q^{38} + 312 q^{39} + 232 q^{40} + 236 q^{41} - 564 q^{42} + 1152 q^{44} + 328 q^{46} - 408 q^{47} + 576 q^{48} + 654 q^{49} + 1970 q^{50} - 368 q^{52} + 54 q^{54} + 1024 q^{55} - 1864 q^{56} - 168 q^{57} + 140 q^{58} - 1152 q^{60} - 2108 q^{62} - 252 q^{63} + 832 q^{64} - 1744 q^{65} - 1440 q^{66} + 2976 q^{68} + 1352 q^{70} - 1704 q^{71} + 684 q^{72} + 956 q^{73} + 1568 q^{74} - 1744 q^{76} + 1608 q^{78} - 44 q^{79} - 2112 q^{80} + 486 q^{81} - 2236 q^{82} - 1992 q^{84} - 760 q^{86} + 1044 q^{87} + 1856 q^{88} - 220 q^{89} - 540 q^{90} + 1728 q^{92} + 2088 q^{94} + 5104 q^{95} + 2184 q^{96} - 2444 q^{97} + 3354 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 + 16 * q^4 - 6 * q^6 + 28 * q^7 - 76 * q^8 - 54 * q^9 + 60 * q^10 - 12 * q^12 - 100 * q^14 - 60 * q^15 + 56 * q^16 + 52 * q^17 - 18 * q^18 + 56 * q^20 + 224 * q^22 + 328 * q^23 + 204 * q^24 - 106 * q^25 + 56 * q^26 - 352 * q^28 + 372 * q^30 - 636 * q^31 - 248 * q^32 - 548 * q^34 - 144 * q^36 - 776 * q^38 + 312 * q^39 + 232 * q^40 + 236 * q^41 - 564 * q^42 + 1152 * q^44 + 328 * q^46 - 408 * q^47 + 576 * q^48 + 654 * q^49 + 1970 * q^50 - 368 * q^52 + 54 * q^54 + 1024 * q^55 - 1864 * q^56 - 168 * q^57 + 140 * q^58 - 1152 * q^60 - 2108 * q^62 - 252 * q^63 + 832 * q^64 - 1744 * q^65 - 1440 * q^66 + 2976 * q^68 + 1352 * q^70 - 1704 * q^71 + 684 * q^72 + 956 * q^73 + 1568 * q^74 - 1744 * q^76 + 1608 * q^78 - 44 * q^79 - 2112 * q^80 + 486 * q^81 - 2236 * q^82 - 1992 * q^84 - 760 * q^86 + 1044 * q^87 + 1856 * q^88 - 220 * q^89 - 540 * q^90 + 1728 * q^92 + 2088 * q^94 + 5104 * q^95 + 2184 * q^96 - 2444 * q^97 + 3354 * q^98

Introduction

L-functions

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