LMFDB - Embedded newform 24.4.d.a.13.6

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			13.6
Root			$1.88322 + 0.673417i$ of defining polynomial
Character	$\chi$	$=$	24.13
Dual form			24.4.d.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.55664 + 1.20980i) q^{2} -3.00000i q^{3} +(5.07277 + 6.18604i) q^{4} -0.612661i q^{5} +(3.62940 - 7.66991i) q^{6} -22.7441 q^{7} +(5.48534 + 21.9525i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(2.55664 + 1.20980i) q^{2} -3.00000i q^{3} +(5.07277 + 6.18604i) q^{4} -0.612661i q^{5} +(3.62940 - 7.66991i) q^{6} -22.7441 q^{7} +(5.48534 + 21.9525i) q^{8} -9.00000 q^{9} +(0.741198 - 1.56635i) q^{10} -60.2630i q^{11} +(18.5581 - 15.2183i) q^{12} +52.9062i q^{13} +(-58.1485 - 27.5159i) q^{14} -1.83798 q^{15} +(-12.5341 + 62.7606i) q^{16} +47.1643 q^{17} +(-23.0097 - 10.8882i) q^{18} +29.1643i q^{19} +(3.78994 - 3.10789i) q^{20} +68.2324i q^{21} +(72.9062 - 154.070i) q^{22} +109.488 q^{23} +(65.8574 - 16.4560i) q^{24} +124.625 q^{25} +(-64.0059 + 135.262i) q^{26} +27.0000i q^{27} +(-115.376 - 140.696i) q^{28} -10.4250i q^{29} +(-4.69905 - 2.22359i) q^{30} -220.881 q^{31} +(-107.973 + 145.292i) q^{32} -180.789 q^{33} +(120.582 + 57.0593i) q^{34} +13.9345i q^{35} +(-45.6549 - 55.6743i) q^{36} -408.348i q^{37} +(-35.2829 + 74.5624i) q^{38} +158.718 q^{39} +(13.4494 - 3.36066i) q^{40} -360.742 q^{41} +(-82.5476 + 174.445i) q^{42} +236.414i q^{43} +(372.789 - 305.700i) q^{44} +5.51395i q^{45} +(279.922 + 132.459i) q^{46} +129.113 q^{47} +(188.282 + 37.6023i) q^{48} +174.296 q^{49} +(318.620 + 150.771i) q^{50} -141.493i q^{51} +(-327.279 + 268.381i) q^{52} -117.819i q^{53} +(-32.6646 + 69.0291i) q^{54} -36.9208 q^{55} +(-124.759 - 499.290i) q^{56} +87.4928 q^{57} +(12.6122 - 26.6529i) q^{58} +262.854i q^{59} +(-9.32366 - 11.3698i) q^{60} +273.465i q^{61} +(-564.711 - 267.221i) q^{62} +204.697 q^{63} +(-451.822 + 240.834i) q^{64} +32.4135 q^{65} +(-462.211 - 218.718i) q^{66} +89.4077i q^{67} +(239.253 + 291.760i) q^{68} -328.465i q^{69} +(-16.8579 + 35.6253i) q^{70} -350.521 q^{71} +(-49.3681 - 197.572i) q^{72} +532.610 q^{73} +(494.019 - 1044.00i) q^{74} -373.874i q^{75} +(-180.411 + 147.943i) q^{76} +1370.63i q^{77} +(405.785 + 192.018i) q^{78} -166.561 q^{79} +(38.4510 + 7.67915i) q^{80} +81.0000 q^{81} +(-922.286 - 436.426i) q^{82} -361.934i q^{83} +(-422.088 + 346.127i) q^{84} -28.8957i q^{85} +(-286.013 + 604.423i) q^{86} -31.2750 q^{87} +(1322.92 - 330.563i) q^{88} +40.3285 q^{89} +(-6.67078 + 14.0972i) q^{90} -1203.31i q^{91} +(555.408 + 677.299i) q^{92} +662.642i q^{93} +(330.095 + 156.201i) q^{94} +17.8678 q^{95} +(435.877 + 323.919i) q^{96} -614.921 q^{97} +(445.612 + 210.864i) q^{98} +542.367i 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 $

$2$	2.55664	+	1.20980i	0.903907	+	0.427729i
$2$	2.55664	+	1.20980i	0.903907	+	0.427729i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	5.07277	+	6.18604i	0.634096	+	0.773255i
$5$		−	0.612661i		−	0.0547981i	−0.999625	−	0.0273990i	$-0.991278\pi$
$5$		−	0.612661i		−	0.0547981i	0.999625	−	0.0273990i	$-0.00872248\pi$
$6$	3.62940	−	7.66991i	0.246949	−	0.521871i
$7$	−22.7441			−1.22807			−0.614034	−	0.789279i	$-0.710454\pi$
$7$	−22.7441			−1.22807			−0.614034	+	0.789279i	$0.710454\pi$
$8$	5.48534	+	21.9525i	0.242420	+	0.970171i
$9$	−9.00000			−0.333333
$10$	0.741198	−	1.56635i	0.0234387	−	0.0495324i
$11$		−	60.2630i		−	1.65182i	−0.563805	−	0.825908i	$-0.690663\pi$
$11$		−	60.2630i		−	1.65182i	0.563805	−	0.825908i	$-0.309337\pi$
$12$	18.5581	−	15.2183i	0.446439	−	0.366095i
$13$			52.9062i			1.12873i	0.825524	+	0.564367i	$0.190880\pi$
$13$			52.9062i			1.12873i	−0.825524	+	0.564367i	$0.809120\pi$
$14$	−58.1485	−	27.5159i	−1.11006	−	0.525281i
$15$	−1.83798			−0.0316377
$16$	−12.5341	+	62.7606i	−0.195845	+	0.980635i
$17$	47.1643			0.672883			0.336442	−	0.941704i	$-0.390777\pi$
$17$	47.1643			0.672883			0.336442	+	0.941704i	$0.390777\pi$
$18$	−23.0097	−	10.8882i	−0.301302	−	0.142576i
$19$			29.1643i			0.352144i	0.984377	+	0.176072i	$0.0563392\pi$
$19$			29.1643i			0.352144i	−0.984377	+	0.176072i	$0.943661\pi$
$20$	3.78994	−	3.10789i	0.0423729	−	0.0347472i
$21$			68.2324i			0.709026i
$22$	72.9062	−	154.070i	0.706529	−	1.49309i
$23$	109.488			0.992604			0.496302	−	0.868150i	$-0.334691\pi$
$23$	109.488			0.992604			0.496302	+	0.868150i	$0.334691\pi$
$24$	65.8574	−	16.4560i	0.560129	−	0.139961i
$25$	124.625			0.996997
$26$	−64.0059	+	135.262i	−0.482792	+	1.02027i
$27$			27.0000i			0.192450i
$28$	−115.376	−	140.696i	−0.778713	−	0.949609i
$29$		−	10.4250i		−	0.0667542i	−0.999443	−	0.0333771i	$-0.989374\pi$
$29$		−	10.4250i		−	0.0667542i	0.999443	−	0.0333771i	$-0.0106262\pi$
$30$	−4.69905	−	2.22359i	−0.0285975	−	0.0135324i
$31$	−220.881			−1.27972			−0.639860	−	0.768492i	$-0.721008\pi$
$31$	−220.881			−1.27972			−0.639860	+	0.768492i	$0.721008\pi$
$32$	−107.973	+	145.292i	−0.596472	+	0.802634i
$33$	−180.789			−0.953676
$34$	120.582	+	57.0593i	0.608224	+	0.287812i
$35$			13.9345i			0.0672958i
$36$	−45.6549	−	55.6743i	−0.211365	−	0.257752i
$37$		−	408.348i		−	1.81438i	−0.420725	−	0.907188i	$-0.638224\pi$
$37$		−	408.348i		−	1.81438i	0.420725	−	0.907188i	$-0.361776\pi$
$38$	−35.2829	+	74.5624i	−0.150622	+	0.318306i
$39$	158.718			0.651674
$40$	13.4494	−	3.36066i	0.0531635	−	0.0132842i
$41$	−360.742			−1.37411			−0.687054	−	0.726606i	$-0.741097\pi$
$41$	−360.742			−1.37411			−0.687054	+	0.726606i	$0.741097\pi$
$42$	−82.5476	+	174.445i	−0.303271	+	0.640893i
$43$			236.414i			0.838436i	0.907886	+	0.419218i	$0.137696\pi$
$43$			236.414i			0.838436i	−0.907886	+	0.419218i	$0.862304\pi$
$44$	372.789	−	305.700i	1.27727	−	1.04741i
$45$			5.51395i			0.0182660i
$46$	279.922	+	132.459i	0.897222	+	0.424565i
$47$	129.113			0.400703			0.200352	−	0.979724i	$-0.435792\pi$
$47$	129.113			0.400703			0.200352	+	0.979724i	$0.435792\pi$
$48$	188.282	+	37.6023i	0.566170	+	0.113071i
$49$	174.296			0.508152
$50$	318.620	+	150.771i	0.901193	+	0.426445i
$51$		−	141.493i		−	0.388489i
$52$	−327.279	+	268.381i	−0.872798	+	0.715725i
$53$		−	117.819i		−	0.305353i	−0.988276	−	0.152677i	$-0.951211\pi$
$53$		−	117.819i		−	0.305353i	0.988276	−	0.152677i	$-0.0487893\pi$
$54$	−32.6646	+	69.0291i	−0.0823165	+	0.173957i
$55$	−36.9208			−0.0905163
$56$	−124.759	−	499.290i	−0.297709	−	1.19144i
$57$	87.4928			0.203311
$58$	12.6122	−	26.6529i	0.0285527	−	0.0603396i
$59$			262.854i			0.580012i	0.957025	+	0.290006i	$0.0936574\pi$
$59$			262.854i			0.580012i	−0.957025	+	0.290006i	$0.906343\pi$
$60$	−9.32366	−	11.3698i	−0.0200613	−	0.0244640i
$61$			273.465i			0.573993i	0.957932	+	0.286996i	$0.0926568\pi$
$61$			273.465i			0.573993i	−0.957932	+	0.286996i	$0.907343\pi$
$62$	−564.711	−	267.221i	−1.15675	−	0.547373i
$63$	204.697			0.409356
$64$	−451.822	+	240.834i	−0.882465	+	0.470378i
$65$	32.4135			0.0618524
$66$	−462.211	−	218.718i	−0.862034	−	0.407915i
$67$			89.4077i			0.163028i	0.996672	+	0.0815141i	$0.0259756\pi$
$67$			89.4077i			0.163028i	−0.996672	+	0.0815141i	$0.974024\pi$
$68$	239.253	+	291.760i	0.426672	+	0.520310i
$69$		−	328.465i		−	0.573080i
$70$	−16.8579	+	35.6253i	−0.0287844	+	0.0608291i
$71$	−350.521			−0.585904			−0.292952	−	0.956127i	$-0.594638\pi$
$71$	−350.521			−0.585904			−0.292952	+	0.956127i	$0.594638\pi$
$72$	−49.3681	−	197.572i	−0.0808067	−	0.323390i
$73$	532.610			0.853936			0.426968	−	0.904267i	$-0.359582\pi$
$73$	532.610			0.853936			0.426968	+	0.904267i	$0.359582\pi$
$74$	494.019	−	1044.00i	0.776062	−	1.64003i
$75$		−	373.874i		−	0.575617i
$76$	−180.411	+	147.943i	−0.272297	+	0.223293i
$77$			1370.63i			2.02854i
$78$	405.785	+	192.018i	0.589053	+	0.278740i
$79$	−166.561			−0.237210			−0.118605	−	0.992942i	$-0.537842\pi$
$79$	−166.561			−0.237210			−0.118605	+	0.992942i	$0.537842\pi$
$80$	38.4510	+	7.67915i	0.0537369	+	0.0107319i
$81$	81.0000			0.111111
$82$	−922.286	−	436.426i	−1.24207	−	0.587746i
$83$		−	361.934i		−	0.478644i	−0.970940	−	0.239322i	$-0.923075\pi$
$83$		−	361.934i		−	0.478644i	0.970940	−	0.239322i	$-0.0769252\pi$
$84$	−422.088	+	346.127i	−0.548257	+	0.449590i
$85$		−	28.8957i		−	0.0368727i
$86$	−286.013	+	604.423i	−0.358623	+	0.757868i
$87$	−31.2750			−0.0385405
$88$	1322.92	−	330.563i	1.60254	−	0.400433i
$89$	40.3285			0.0480316			0.0240158	−	0.999712i	$-0.492355\pi$
$89$	40.3285			0.0480316			0.0240158	+	0.999712i	$0.492355\pi$
$90$	−6.67078	+	14.0972i	−0.00781291	+	0.0165108i
$91$		−	1203.31i		−	1.38616i
$92$	555.408	+	677.299i	0.629406	+	0.767535i
$93$			662.642i			0.738846i
$94$	330.095	+	156.201i	0.362199	+	0.171392i
$95$	17.8678			0.0192968
$96$	435.877	+	323.919i	0.463401	+	0.344373i
$97$	−614.921			−0.643667			−0.321834	−	0.946796i	$-0.604299\pi$
$97$	−614.921			−0.643667			−0.321834	+	0.946796i	$0.604299\pi$
$98$	445.612	+	210.864i	0.459322	+	0.217351i
$99$			542.367i			0.550605i
$100$	632.192	+	770.933i	0.632192	+	0.770933i
$101$		−	1664.99i		−	1.64033i	−0.572130	−	0.820163i	$-0.693883\pi$
$101$		−	1664.99i		−	1.64033i	0.572130	−	0.820163i	$-0.306117\pi$
$102$	171.178	−	361.745i	0.166168	−	0.351158i
$103$	396.858			0.379647			0.189823	−	0.981818i	$-0.439208\pi$
$103$	396.858			0.379647			0.189823	+	0.981818i	$0.439208\pi$
$104$	−1161.42	+	290.208i	−1.09506	+	0.273628i
$105$	41.8034			0.0388532
$106$	142.538	−	301.221i	0.130608	−	0.276011i
$107$		−	350.630i		−	0.316791i	−0.987376	−	0.158396i	$-0.949368\pi$
$107$		−	350.630i		−	0.316791i	0.987376	−	0.158396i	$-0.0506321\pi$
$108$	−167.023	+	136.965i	−0.148813	+	0.122032i
$109$			597.009i			0.524615i	0.964984	+	0.262308i	$0.0844835\pi$
$109$			597.009i			0.524615i	−0.964984	+	0.262308i	$0.915516\pi$
$110$	−94.3930	−	44.6668i	−0.0818183	−	0.0387165i
$111$	−1225.04			−1.04753
$112$	285.077	−	1427.44i	0.240511	−	1.20429i
$113$	496.422			0.413270			0.206635	−	0.978418i	$-0.433749\pi$
$113$	496.422			0.413270			0.206635	+	0.978418i	$0.433749\pi$
$114$	223.687	+	105.849i	0.183774	+	0.0869618i
$115$		−	67.0792i		−	0.0543928i
$116$	64.4893	−	52.8835i	0.0516180	−	0.0423285i
$117$		−	476.155i		−	0.376244i
$118$	−318.001	+	672.023i	−0.248088	+	0.524277i
$119$	−1072.71			−0.826346
$120$	−10.0820	−	40.3483i	−0.00766961	−	0.0306940i
$121$	−2300.63			−1.72849
$122$	−330.838	+	699.149i	−0.245513	+	0.518836i
$123$			1082.23i			0.793342i
$124$	−1120.48	−	1366.37i	−0.811465	−	0.989549i
$125$		−	152.935i		−	0.109432i
$126$	523.336	+	247.643i	0.370020	+	0.175094i
$127$	1799.85			1.25756			0.628782	−	0.777581i	$-0.283554\pi$
$127$	1799.85			1.25756			0.628782	+	0.777581i	$0.283554\pi$
$128$	−1446.50	+	69.1093i	−0.998861	+	0.0477223i
$129$	709.241			0.484071
$130$	82.8696	+	39.2139i	0.0559088	+	0.0264561i
$131$			1121.45i			0.747949i	0.927439	+	0.373974i	$0.122005\pi$
$131$			1121.45i			0.747949i	−0.927439	+	0.373974i	$0.877995\pi$
$132$	−917.100	−	1118.37i	−0.604722	−	0.737434i
$133$		−	663.316i		−	0.432457i
$134$	−108.166	+	228.583i	−0.0697319	+	0.147362i
$135$	16.5419			0.0105459
$136$	258.712	+	1035.37i	0.163120	+	0.652812i
$137$	2449.55			1.52759			0.763793	−	0.645461i	$-0.223335\pi$
$137$	2449.55			1.52759			0.763793	+	0.645461i	$0.223335\pi$
$138$	397.377	−	839.765i	0.245123	−	0.518011i
$139$			2457.56i			1.49962i	0.661652	+	0.749811i	$0.269856\pi$
$139$			2457.56i			1.49962i	−0.661652	+	0.749811i	$0.730144\pi$
$140$	−86.1990	+	70.6862i	−0.0520368	+	0.0426720i
$141$		−	387.339i		−	0.231346i
$142$	−896.153	−	424.060i	−0.529602	−	0.250608i
$143$	3188.28			1.86446
$144$	112.807	−	564.846i	0.0652817	−	0.326878i
$145$	−6.38698			−0.00365800
$146$	1361.69	+	644.352i	0.771878	+	0.365253i
$147$		−	522.888i		−	0.293382i
$148$	2526.05	−	2071.45i	1.40297	−	1.15049i
$149$		−	2084.96i		−	1.14635i	−0.819432	−	0.573177i	$-0.805711\pi$
$149$		−	2084.96i		−	1.14635i	0.819432	−	0.573177i	$-0.194289\pi$
$150$	452.313	−	955.859i	0.246208	−	0.520304i
$151$	1057.80			0.570084			0.285042	−	0.958515i	$-0.407992\pi$
$151$	1057.80			0.570084			0.285042	+	0.958515i	$0.407992\pi$
$152$	−640.228	+	159.976i	−0.341640	+	0.0853669i
$153$	−424.478			−0.224294
$154$	−1658.19	+	3504.20i	−0.867666	+	1.83361i
$155$			135.325i			0.0701262i
$156$	805.142	+	981.838i	0.413224	+	0.503910i
$157$			3193.01i			1.62312i	0.584270	+	0.811559i	$0.301381\pi$
$157$			3193.01i			1.62312i	−0.584270	+	0.811559i	$0.698619\pi$
$158$	−425.836	−	201.506i	−0.214416	−	0.101461i
$159$	−353.458			−0.176296
$160$	89.0149	+	66.1508i	0.0439828	+	0.0326855i
$161$	−2490.22			−1.21899
$162$	207.087	+	97.9938i	0.100434	+	0.0475254i
$163$		−	846.854i		−	0.406937i	−0.979081	−	0.203469i	$-0.934779\pi$
$163$		−	846.854i		−	0.406937i	0.979081	−	0.203469i	$-0.0652215\pi$
$164$	−1829.96	−	2231.56i	−0.871316	−	1.06254i
$165$			110.762i			0.0522596i
$166$	437.868	−	925.334i	0.204730	−	0.432650i
$167$	−2630.15			−1.21873			−0.609363	−	0.792892i	$-0.708575\pi$
$167$	−2630.15			−1.21873			−0.609363	+	0.792892i	$0.708575\pi$
$168$	−1497.87	+	374.278i	−0.687876	+	0.171882i
$169$	−602.062			−0.274038
$170$	34.9580	−	73.8758i	0.0157715	−	0.0333295i
$171$		−	262.478i		−	0.117381i
$172$	−1462.46	+	1199.27i	−0.648324	+	0.531648i
$173$			429.843i			0.188904i	0.995529	+	0.0944519i	$0.0301099\pi$
$173$			429.843i			0.188904i	−0.995529	+	0.0944519i	$0.969890\pi$
$174$	−79.9586	−	37.8365i	−0.0348371	−	0.0164849i
$175$	−2834.48			−1.22438
$176$	3782.14	+	755.341i	1.61983	+	0.323500i
$177$	788.563			0.334870
$178$	103.105	+	48.7895i	0.0434161	+	0.0205445i
$179$		−	1516.30i		−	0.633149i	−0.948568	−	0.316574i	$-0.897467\pi$
$179$		−	1516.30i		−	0.633149i	0.948568	−	0.316574i	$-0.102533\pi$
$180$	−34.1095	+	27.9710i	−0.0141243	+	0.0115824i
$181$		−	3380.20i		−	1.38811i	−0.719921	−	0.694056i	$-0.755822\pi$
$181$		−	3380.20i		−	1.38811i	0.719921	−	0.694056i	$-0.244178\pi$
$182$	1455.76	−	3076.41i	0.592901	−	1.25296i
$183$	820.394			0.331395
$184$	600.581	+	2403.54i	0.240627	+	0.962996i
$185$	−250.179			−0.0994244
$186$	−801.664	+	1694.13i	−0.316026	+	0.667849i
$187$		−	2842.26i		−	1.11148i
$188$	654.960	+	798.697i	0.254084	+	0.309846i
$189$		−	614.092i		−	0.236342i
$190$	45.6815	+	21.6165i	0.0174425	+	0.00825381i
$191$	−2799.71			−1.06063			−0.530314	−	0.847801i	$-0.677926\pi$
$191$	−2799.71			−1.06063			−0.530314	+	0.847801i	$0.677926\pi$
$192$	722.501	+	1355.47i	0.271573	+	0.509491i
$193$	624.106			0.232768			0.116384	−	0.993204i	$-0.462870\pi$
$193$	624.106			0.232768			0.116384	+	0.993204i	$0.462870\pi$
$194$	−1572.13	−	743.931i	−0.581816	−	0.275315i
$195$		−	97.2406i		−	0.0357105i
$196$	884.164	+	1078.20i	0.322217	+	0.392931i
$197$			4779.25i			1.72846i	0.503094	+	0.864232i	$0.332195\pi$
$197$			4779.25i			1.72846i	−0.503094	+	0.864232i	$0.667805\pi$
$198$	−656.155	+	1386.63i	−0.235510	+	0.497696i
$199$	2615.92			0.931846			0.465923	−	0.884825i	$-0.345722\pi$
$199$	2615.92			0.931846			0.465923	+	0.884825i	$0.345722\pi$
$200$	683.609	+	2735.82i	0.241692	+	0.967258i
$201$	268.223			0.0941244
$202$	2014.31	−	4256.78i	0.701615	−	1.48270i
$203$			237.107i			0.0819787i
$204$	875.279	−	717.760i	0.300401	−	0.246339i
$205$			221.013i			0.0752985i
$206$	1014.62	+	480.119i	0.343165	+	0.162386i
$207$	−985.395			−0.330868
$208$	−3320.42	−	663.131i	−1.10687	−	0.221057i
$209$	1757.52			0.581677
$210$	106.876	+	50.5737i	0.0351197	+	0.0166187i
$211$		−	1745.78i		−	0.569595i	−0.958588	−	0.284798i	$-0.908074\pi$
$211$		−	1745.78i		−	0.569595i	0.958588	−	0.284798i	$-0.0919264\pi$
$212$	728.834	−	597.670i	0.236116	−	0.193623i
$213$			1051.56i			0.338272i
$214$	424.192	−	896.432i	0.135501	−	0.286350i
$215$	144.841			0.0459447
$216$	−592.717	+	148.104i	−0.186710	+	0.0466538i
$217$	5023.74			1.57158
$218$	−722.261	+	1526.33i	−0.224393	+	0.474203i
$219$		−	1597.83i		−	0.493020i
$220$	−187.290	−	228.393i	−0.0573960	−	0.0699921i
$221$			2495.28i			0.759505i
$222$	−3131.99	−	1482.06i	−0.946870	−	0.448059i
$223$	−3385.60			−1.01667			−0.508333	−	0.861161i	$-0.669738\pi$
$223$	−3385.60			−1.01667			−0.508333	+	0.861161i	$0.669738\pi$
$224$	2455.75	−	3304.55i	0.732508	−	0.985690i
$225$	−1121.62			−0.332332
$226$	1269.17	+	600.572i	0.373557	+	0.176767i
$227$			3847.72i			1.12503i	0.826787	+	0.562515i	$0.190166\pi$
$227$			3847.72i			1.12503i	−0.826787	+	0.562515i	$0.809834\pi$
$228$	443.830	+	541.233i	0.128918	+	0.157211i
$229$			1335.15i			0.385279i	0.981270	+	0.192640i	$0.0617049\pi$
$229$			1335.15i			0.385279i	−0.981270	+	0.192640i	$0.938295\pi$
$230$	81.1525	−	171.497i	0.0232654	−	0.0491660i
$231$	4111.89			1.17118
$232$	228.854	−	57.1846i	0.0647630	−	0.0161826i
$233$	−5146.38			−1.44700			−0.723499	−	0.690325i	$-0.757468\pi$
$233$	−5146.38			−1.44700			−0.723499	+	0.690325i	$0.757468\pi$
$234$	576.053	−	1217.36i	0.160931	−	0.340090i
$235$		−	79.1025i		−	0.0219578i
$236$	−1626.03	+	1333.40i	−0.448497	+	0.367783i
$237$			499.683i			0.136953i
$238$	−2742.53	−	1297.77i	−0.746940	−	0.353452i
$239$	7085.07			1.91755			0.958777	−	0.284160i	$-0.0917146\pi$
$239$	7085.07			1.91755			0.958777	+	0.284160i	$0.0917146\pi$
$240$	23.0374	−	115.353i	0.00619609	−	0.0310250i
$241$	2538.40			0.678476			0.339238	−	0.940701i	$-0.389831\pi$
$241$	2538.40			0.678476			0.339238	+	0.940701i	$0.389831\pi$
$242$	−5881.86	−	2783.30i	−1.56240	−	0.739327i
$243$		−	243.000i		−	0.0641500i
$244$	−1691.66	+	1387.22i	−0.443843	+	0.363966i
$245$		−	106.784i		−	0.0278458i
$246$	−1309.28	+	2766.86i	−0.339335	+	0.717107i
$247$	−1542.97			−0.397477
$248$	−1211.61	−	4848.87i	−0.310230	−	1.24155i
$249$	−1085.80			−0.276345
$250$	185.021	−	391.000i	0.0468071	−	0.0989160i
$251$		−	1696.99i		−	0.426746i	−0.976971	−	0.213373i	$-0.931555\pi$
$251$		−	1696.99i		−	0.426746i	0.976971	−	0.213373i	$-0.0684449\pi$
$252$	1038.38	+	1266.26i	0.259571	+	0.316536i
$253$		−	6598.09i		−	1.63960i
$254$	4601.56	+	2177.46i	1.13672	+	0.537897i
$255$	−86.6871			−0.0212885
$256$	−3781.79	−	1573.29i	−0.923289	−	0.384105i
$257$	−382.902			−0.0929369			−0.0464685	−	0.998920i	$-0.514797\pi$
$257$	−382.902			−0.0929369			−0.0464685	+	0.998920i	$0.514797\pi$
$258$	1813.27	+	858.040i	0.437555	+	0.207051i
$259$			9287.52i			2.22818i
$260$	164.426	+	200.511i	0.0392203	+	0.0478276i
$261$			93.8249i			0.0222514i
$262$	−1356.73	+	2867.13i	−0.319919	+	0.676076i
$263$	−5002.02			−1.17277			−0.586383	−	0.810034i	$-0.699449\pi$
$263$	−5002.02			−1.17277			−0.586383	+	0.810034i	$0.699449\pi$
$264$	−991.689	−	3968.76i	−0.231190	−	0.925229i
$265$	−72.1833			−0.0167328
$266$	802.480	−	1695.86i	0.184974	−	0.390901i
$267$		−	120.986i		−	0.0277311i
$268$	−553.079	+	453.545i	−0.126062	+	0.103376i
$269$		−	6117.47i		−	1.38658i	−0.720661	−	0.693288i	$-0.756161\pi$
$269$		−	6117.47i		−	1.38658i	0.720661	−	0.693288i	$-0.243839\pi$
$270$	42.2915	+	20.0123i	0.00953251	+	0.00451079i
$271$	−3956.12			−0.886780			−0.443390	−	0.896329i	$-0.646224\pi$
$271$	−3956.12			−0.886780			−0.443390	+	0.896329i	$0.646224\pi$
$272$	−591.161	+	2960.06i	−0.131781	+	0.659853i
$273$	−3609.92			−0.800301
$274$	6262.61	+	2963.47i	1.38080	+	0.653393i
$275$		−	7510.25i		−	1.64686i
$276$	2031.90	−	1666.23i	0.443137	−	0.363388i
$277$			4842.17i			1.05032i	0.851004	+	0.525158i	$0.175994\pi$
$277$			4842.17i			1.05032i	−0.851004	+	0.525158i	$0.824006\pi$
$278$	−2973.16	+	6283.09i	−0.641432	+	1.35552i
$279$	1987.92			0.426573
$280$	−305.896	+	76.4353i	−0.0652884	+	0.0163139i
$281$	1878.68			0.398835			0.199417	−	0.979915i	$-0.436095\pi$
$281$	1878.68			0.398835			0.199417	+	0.979915i	$0.436095\pi$
$282$	468.603	−	990.284i	0.0989535	−	0.209115i
$283$			5724.87i			1.20250i	0.799060	+	0.601251i	$0.205331\pi$
$283$			5724.87i			1.20250i	−0.799060	+	0.601251i	$0.794669\pi$
$284$	−1778.11	−	2168.33i	−0.371519	−	0.453053i
$285$		−	53.6034i		−	0.0111410i
$286$	8151.27	+	3857.19i	1.68530	+	0.797483i
$287$	8204.77			1.68750
$288$	971.756	−	1307.63i	0.198824	−	0.267545i
$289$	−2688.53			−0.547228
$290$	−16.3292	−	7.72697i	−0.00330649	−	0.00156463i
$291$			1844.76i			0.371622i
$292$	2701.81	+	3294.75i	0.541477	+	0.660310i
$293$		−	5088.75i		−	1.01464i	−0.861759	−	0.507318i	$-0.830637\pi$
$293$		−	5088.75i		−	1.01464i	0.861759	−	0.507318i	$-0.169363\pi$
$294$	632.591	−	1336.83i	0.125488	−	0.265190i
$295$	161.041			0.0317836
$296$	8964.24	−	2239.93i	1.76026	−	0.439842i
$297$	1627.10			0.317892
$298$	2522.39	−	5330.49i	0.490329	−	1.03620i
$299$			5792.61i			1.12038i
$300$	2312.80	−	1896.58i	0.445098	−	0.364996i
$301$		−	5377.02i		−	1.02966i
$302$	2704.41	+	1279.73i	0.515303	+	0.243841i
$303$	−4994.98			−0.947043
$304$	−1830.37	−	365.547i	−0.345325	−	0.0689657i
$305$	167.541			0.0314537
$306$	−1085.24	−	513.534i	−0.202741	−	0.0959372i
$307$		−	7219.21i		−	1.34209i	−0.741416	−	0.671046i	$-0.765845\pi$
$307$		−	7219.21i		−	1.34209i	0.741416	−	0.671046i	$-0.234155\pi$
$308$	−8478.76	+	6952.88i	−1.56858	+	1.28629i
$309$		−	1190.58i		−	0.219189i
$310$	−163.716	+	345.976i	−0.0299950	+	0.0633875i
$311$	−1537.06			−0.280252			−0.140126	−	0.990134i	$-0.544751\pi$
$311$	−1537.06			−0.280252			−0.140126	+	0.990134i	$0.544751\pi$
$312$	870.625	+	3484.26i	0.157979	+	0.632236i
$313$	−2200.93			−0.397456			−0.198728	−	0.980055i	$-0.563681\pi$
$313$	−2200.93			−0.397456			−0.198728	+	0.980055i	$0.563681\pi$
$314$	−3862.90	+	8163.35i	−0.694255	+	1.46715i
$315$		−	125.410i		−	0.0224319i
$316$	−844.925	−	1030.35i	−0.150414	−	0.183424i
$317$		−	2840.41i		−	0.503260i	−0.967824	−	0.251630i	$-0.919033\pi$
$317$		−	2840.41i		−	0.503260i	0.967824	−	0.251630i	$-0.0809665\pi$
$318$	−903.663	−	427.613i	−0.159355	−	0.0754068i
$319$	−628.240			−0.110266
$320$	147.549	+	276.814i	0.0257758	+	0.0483574i
$321$	−1051.89			−0.182899
$322$	−6366.58	−	3012.67i	−1.10185	−	0.521395i
$323$			1375.51i			0.236952i
$324$	410.894	+	501.069i	0.0704551	+	0.0859172i
$325$			6593.41i			1.12534i
$326$	1024.52	−	2165.10i	0.174059	−	0.367833i
$327$	1791.03			0.302887
$328$	−1978.79	−	7919.18i	−0.333112	−	1.33312i
$329$	−2936.56			−0.492091
$330$	−134.000	+	283.179i	−0.0223530	+	0.0472378i
$331$		−	2118.52i		−	0.351795i	−0.984408	−	0.175898i	$-0.943717\pi$
$331$		−	2118.52i		−	0.351795i	0.984408	−	0.175898i	$-0.0562828\pi$
$332$	2238.94	−	1836.01i	0.370114	−	0.303506i
$333$			3675.13i			0.604792i
$334$	−6724.33	−	3181.96i	−1.10161	−	0.521284i
$335$	54.7766			0.00893364
$336$	−4282.31	−	855.231i	−0.695295	−	0.138859i
$337$	−659.599			−0.106619			−0.0533096	−	0.998578i	$-0.516977\pi$
$337$	−659.599			−0.106619			−0.0533096	+	0.998578i	$0.516977\pi$
$338$	−1539.25	−	728.375i	−0.247705	−	0.117214i
$339$		−	1489.27i		−	0.238601i
$340$	178.750	−	146.581i	0.0285120	−	0.0233808i
$341$			13310.9i			2.11386i
$342$	317.546	−	671.061i	0.0502074	−	0.106102i
$343$	3837.03			0.604023
$344$	−5189.86	+	1296.81i	−0.813426	+	0.203254i
$345$	−201.238			−0.0314037
$346$	−520.024	+	1098.95i	−0.0807996	+	0.170751i
$347$		−	8377.42i		−	1.29603i	−0.761626	−	0.648017i	$-0.775599\pi$
$347$		−	8377.42i		−	1.29603i	0.761626	−	0.648017i	$-0.224401\pi$
$348$	−158.651	−	193.468i	−0.0244384	−	0.0298016i
$349$		−	3254.18i		−	0.499119i	−0.968360	−	0.249559i	$-0.919714\pi$
$349$		−	3254.18i		−	0.499119i	0.968360	−	0.249559i	$-0.0802857\pi$
$350$	−7246.73	−	3429.16i	−1.10673	−	0.523703i
$351$	−1428.47			−0.217225
$352$	8755.74	+	6506.77i	1.32580	+	0.985261i
$353$	11117.5			1.67627			0.838137	−	0.545459i	$-0.183645\pi$
$353$	11117.5			1.67627			0.838137	+	0.545459i	$0.183645\pi$
$354$	2016.07	+	954.004i	0.302692	+	0.143234i
$355$			214.750i			0.0321064i
$356$	204.577	+	249.474i	0.0304566	+	0.0371407i
$357$			3218.13i			0.477091i
$358$	1834.42	−	3876.63i	0.270816	−	0.572308i
$359$	−4756.56			−0.699281			−0.349640	−	0.936884i	$-0.613696\pi$
$359$	−4756.56			−0.699281			−0.349640	+	0.936884i	$0.613696\pi$
$360$	−121.045	+	30.2459i	−0.0177212	+	0.00442805i
$361$	6008.45			0.875994
$362$	4089.37	−	8641.94i	0.593736	−	1.25472i
$363$			6901.88i			0.997946i
$364$	7443.69	−	6104.09i	1.07186	−	0.878959i
$365$		−	326.310i		−	0.0467940i
$366$	2097.45	+	992.513i	0.299550	+	0.141747i
$367$	1837.40			0.261339			0.130670	−	0.991426i	$-0.458287\pi$
$367$	1837.40			0.261339			0.130670	+	0.991426i	$0.458287\pi$
$368$	−1372.34	+	6871.55i	−0.194397	+	0.973382i
$369$	3246.68			0.458036
$370$	−639.616	−	302.666i	−0.0898704	−	0.0425267i
$371$			2679.70i			0.374995i
$372$	−4099.12	+	3361.43i	−0.571316	+	0.468499i
$373$			5598.07i			0.777097i	0.921428	+	0.388549i	$0.127023\pi$
$373$			5598.07i			0.777097i	−0.921428	+	0.388549i	$0.872977\pi$
$374$	3438.56	−	7266.62i	0.475412	−	1.00467i
$375$	−458.806			−0.0631804
$376$	708.229	+	2834.35i	0.0971386	+	0.388751i
$377$	551.546			0.0753476
$378$	742.929	−	1570.01i	0.101090	−	0.213631i
$379$		−	3460.18i		−	0.468965i	−0.972120	−	0.234482i	$-0.924661\pi$
$379$		−	3460.18i		−	0.468965i	0.972120	−	0.234482i	$-0.0753395\pi$
$380$	90.6392	+	110.531i	0.0122360	+	0.0149214i
$381$		−	5399.55i		−	0.726055i
$382$	−7157.84	−	3387.09i	−0.958709	−	0.453661i
$383$	5059.63			0.675027			0.337513	−	0.941321i	$-0.390414\pi$
$383$	5059.63			0.675027			0.337513	+	0.941321i	$0.390414\pi$
$384$	207.328	+	4339.51i	0.0275525	+	0.576692i
$385$	839.732			0.111160
$386$	1595.61	+	755.044i	0.210400	+	0.0995614i
$387$		−	2127.72i		−	0.279479i
$388$	−3119.35	−	3803.92i	−0.408147	−	0.497719i
$389$			2192.22i			0.285732i	0.989742	+	0.142866i	$0.0456318\pi$
$389$			2192.22i			0.285732i	−0.989742	+	0.142866i	$0.954368\pi$
$390$	117.642	−	248.609i	0.0152744	−	0.0322790i
$391$	5163.93			0.667906
$392$	956.074	+	3826.23i	0.123186	+	0.492995i
$393$	3364.34			0.431828
$394$	−5781.93	+	12218.8i	−0.739314	+	1.56237i
$395$			102.045i			0.0129986i
$396$	−3355.10	+	2751.30i	−0.425758	+	0.349136i
$397$			5519.94i			0.697828i	0.937155	+	0.348914i	$0.113449\pi$
$397$			5519.94i			0.697828i	−0.937155	+	0.348914i	$0.886551\pi$
$398$	6687.94	+	3164.73i	0.842302	+	0.398577i
$399$	−1989.95			−0.249679
$400$	−1562.06	+	7821.52i	−0.195257	+	0.977690i
$401$	−7352.64			−0.915645			−0.457822	−	0.889044i	$-0.651370\pi$
$401$	−7352.64			−0.915645			−0.457822	+	0.889044i	$0.651370\pi$
$402$	685.749	+	324.497i	0.0850797	+	0.0402597i
$403$		−	11685.9i		−	1.44446i
$404$	10299.7	−	8446.12i	1.26839	−	1.04012i
$405$		−	49.6256i		−	0.00608868i
$406$	−286.853	+	606.197i	−0.0350647	+	0.0741011i
$407$	−24608.2			−2.99702
$408$	3106.12	−	776.136i	0.376901	−	0.0941776i
$409$	−11311.2			−1.36749			−0.683745	−	0.729721i	$-0.739650\pi$
$409$	−11311.2			−1.36749			−0.683745	+	0.729721i	$0.739650\pi$
$410$	−267.381	+	565.049i	−0.0322074	+	0.0680628i
$411$		−	7348.66i		−	0.881952i
$412$	2013.17	+	2454.98i	0.240732	+	0.293564i
$413$		−	5978.40i		−	0.712295i
$414$	−2519.29	−	1192.13i	−0.299074	−	0.141522i
$415$	−221.743			−0.0262288
$416$	−7686.86	−	5712.43i	−0.905960	−	0.673257i
$417$	7372.68			0.865808
$418$	4493.35	+	2126.25i	0.525782	+	0.248800i
$419$			13042.2i			1.52065i	0.649543	+	0.760325i	$0.274960\pi$
$419$			13042.2i			1.52065i	−0.649543	+	0.760325i	$0.725040\pi$
$420$	212.059	+	258.597i	0.0246367	+	0.0300434i
$421$		−	4544.38i		−	0.526080i	−0.964785	−	0.263040i	$-0.915275\pi$
$421$		−	4544.38i		−	0.526080i	0.964785	−	0.263040i	$-0.0847251\pi$
$422$	2112.05	−	4463.33i	0.243632	−	0.514861i
$423$	−1162.02			−0.133568
$424$	2586.42	−	646.279i	0.296245	−	0.0740238i
$425$	5877.83			0.670863
$426$	−1272.18	+	2688.46i	−0.144689	+	0.305766i
$427$		−	6219.72i		−	0.704903i
$428$	2169.01	−	1778.66i	0.244960	−	0.200876i
$429$		−	9564.85i		−	1.07645i
$430$	370.307	+	175.229i	0.0415297	+	0.0196519i
$431$	7713.83			0.862093			0.431047	−	0.902330i	$-0.358144\pi$
$431$	7713.83			0.862093			0.431047	+	0.902330i	$0.358144\pi$
$432$	−1694.54	−	338.420i	−0.188723	−	0.0376904i
$433$	−15068.3			−1.67237			−0.836183	−	0.548451i	$-0.815218\pi$
$433$	−15068.3			−1.67237			−0.836183	+	0.548451i	$0.815218\pi$
$434$	12843.9	+	6077.72i	1.42057	+	0.672212i
$435$			19.1609i			0.00211195i
$436$	−3693.12	+	3028.49i	−0.405661	+	0.332656i
$437$			3193.14i			0.349540i
$438$	1933.06	−	4085.07i	0.210879	−	0.445644i
$439$	11004.7			1.19642			0.598208	−	0.801341i	$-0.295880\pi$
$439$	11004.7			1.19642			0.598208	+	0.801341i	$0.295880\pi$
$440$	−202.523	−	810.502i	−0.0219430	−	0.0878163i
$441$	−1568.67			−0.169384
$442$	−3018.79	+	6379.52i	−0.324862	+	0.686522i
$443$			2513.04i			0.269522i	0.990878	+	0.134761i	$0.0430266\pi$
$443$			2513.04i			0.269522i	−0.990878	+	0.134761i	$0.956973\pi$
$444$	−6214.36	−	7578.16i	−0.664235	−	0.810008i
$445$		−	24.7077i		−	0.00263204i
$446$	−8655.74	−	4095.90i	−0.918972	−	0.434858i
$447$	−6254.89			−0.661848
$448$	10276.3	−	5477.56i	1.08373	−	0.577657i
$449$	−15752.7			−1.65571			−0.827855	−	0.560942i	$-0.810439\pi$
$449$	−15752.7			−1.65571			−0.827855	+	0.560942i	$0.810439\pi$
$450$	−2867.58	−	1356.94i	−0.300398	−	0.142148i
$451$			21739.4i			2.26977i
$452$	2518.23	+	3070.89i	0.262053	+	0.319563i
$453$		−	3173.40i		−	0.329138i
$454$	−4654.97	+	9837.20i	−0.481208	+	1.01692i
$455$	−737.218			−0.0759590
$456$	479.928	+	1920.68i	0.0492866	+	0.197246i
$457$	−5257.06			−0.538107			−0.269053	−	0.963125i	$-0.586711\pi$
$457$	−5257.06			−0.538107			−0.269053	+	0.963125i	$0.586711\pi$
$458$	−1615.26	+	3413.48i	−0.164795	+	0.348257i
$459$			1273.43i			0.129496i
$460$	414.954	−	340.277i	0.0420595	−	0.0344902i
$461$		−	8066.31i		−	0.814936i	−0.913220	−	0.407468i	$-0.866412\pi$
$461$		−	8066.31i		−	0.814936i	0.913220	−	0.407468i	$-0.133588\pi$
$462$	10512.6	+	4974.56i	1.05864	+	0.500947i
$463$	5683.43			0.570478			0.285239	−	0.958456i	$-0.407927\pi$
$463$	5683.43			0.570478			0.285239	+	0.958456i	$0.407927\pi$
$464$	654.279	+	130.668i	0.0654615	+	0.0130735i
$465$	405.975			0.0404874
$466$	−13157.4	−	6226.09i	−1.30795	−	0.618923i
$467$		−	11139.3i		−	1.10378i	−0.833916	−	0.551891i	$-0.813906\pi$
$467$		−	11139.3i		−	1.10378i	0.833916	−	0.551891i	$-0.186094\pi$
$468$	2945.51	−	2415.43i	0.290933	−	0.238575i
$469$		−	2033.50i		−	0.200210i
$470$	95.6982	−	202.236i	0.00939198	−	0.0198478i
$471$	9579.02			0.937108
$472$	−5770.30	+	1441.85i	−0.562711	+	0.140607i
$473$	14247.0			1.38494
$474$	−604.517	+	1277.51i	−0.0585788	+	0.123793i
$475$			3634.59i			0.351087i
$476$	−5441.61	−	6635.83i	−0.523983	−	0.638976i
$477$			1060.37i			0.101784i
$478$	18114.0	+	8571.53i	1.73329	+	0.820193i
$479$	3477.35			0.331699			0.165850	−	0.986151i	$-0.446963\pi$
$479$	3477.35			0.331699			0.165850	+	0.986151i	$0.446963\pi$
$480$	198.452	−	267.045i	0.0188710	−	0.0253935i
$481$	21604.1			2.04795
$482$	6489.76	+	3070.96i	0.613279	+	0.290204i
$483$			7470.65i			0.703782i
$484$	−11670.5	−	14231.8i	−1.09603	−	1.33657i
$485$			376.738i			0.0352717i
$486$	293.981	−	621.262i	0.0274388	−	0.0579857i
$487$	−478.797			−0.0445510			−0.0222755	−	0.999752i	$-0.507091\pi$
$487$	−478.797			−0.0445510			−0.0222755	+	0.999752i	$0.507091\pi$
$488$	−6003.23	+	1500.05i	−0.556871	+	0.139147i
$489$	−2540.56			−0.234945
$490$	129.188	−	273.009i	0.0119104	−	0.0251700i
$491$			16601.8i			1.52592i	0.646444	+	0.762961i	$0.276255\pi$
$491$			16601.8i			1.52592i	−0.646444	+	0.762961i	$0.723745\pi$
$492$	−6694.69	+	5489.88i	−0.613455	+	0.503055i
$493$		−	491.687i		−	0.0449178i
$494$	−3944.81	−	1866.68i	−0.359282	−	0.170012i
$495$	332.287			0.0301721
$496$	2768.54	−	13862.6i	0.250627	−	1.25494i
$497$	7972.29			0.719530
$498$	−2776.00	−	1313.61i	−0.249790	−	0.118201i
$499$		−	9482.20i		−	0.850664i	−0.905037	−	0.425332i	$-0.860157\pi$
$499$		−	9482.20i		−	0.850664i	0.905037	−	0.425332i	$-0.139843\pi$
$500$	946.063	−	775.805i	0.0846185	−	0.0693901i
$501$			7890.45i			0.703631i
$502$	2053.02	−	4338.59i	0.182532	−	0.385738i
$503$	16561.2			1.46805			0.734023	−	0.679124i	$-0.237640\pi$
$503$	16561.2			1.46805			0.734023	+	0.679124i	$0.237640\pi$
$504$	1122.83	+	4493.61i	0.0992362	+	0.397146i
$505$	−1020.08			−0.0898867
$506$	7982.37	−	16868.9i	0.701304	−	1.48204i
$507$			1806.19i			0.158216i
$508$	9130.21	+	11133.9i	0.797417	+	0.972418i
$509$			4197.35i			0.365509i	0.983159	+	0.182755i	$0.0585014\pi$
$509$			4197.35i			0.365509i	−0.983159	+	0.182755i	$0.941499\pi$
$510$	−221.627	−	104.874i	−0.0192428	−	0.00910569i
$511$	−12113.8			−1.04869
$512$	−7765.29	−	8597.56i	−0.670275	−	0.742113i
$513$	−787.435			−0.0677702
$514$	−978.941	−	463.235i	−0.0840063	−	0.0397518i
$515$		−	243.140i		−	0.0208039i
$516$	3597.81	+	4387.39i	0.306947	+	0.374310i
$517$		−	7780.73i		−	0.661888i
$518$	−11236.0	+	23744.8i	−0.953057	+	2.01407i
$519$	1289.53			0.109064
$520$	177.799	+	711.558i	0.0149943	+	0.0600074i
$521$	−15755.5			−1.32488			−0.662440	−	0.749115i	$-0.730479\pi$
$521$	−15755.5			−1.32488			−0.662440	+	0.749115i	$0.730479\pi$
$522$	−113.509	+	239.876i	−0.00951757	+	0.0201132i
$523$			11555.1i			0.966098i	0.875593	+	0.483049i	$0.160471\pi$
$523$			11555.1i			0.966098i	−0.875593	+	0.483049i	$0.839529\pi$
$524$	−6937.31	+	5688.84i	−0.578355	+	0.474271i
$525$			8503.44i			0.706897i
$526$	−12788.3	−	6051.44i	−1.06007	−	0.501626i
$527$	−10417.7			−0.861102
$528$	2266.02	−	11346.4i	0.186773	−	0.935208i
$529$	−179.314			−0.0147378
$530$	−184.546	−	87.3274i	−0.0151249	−	0.00715709i
$531$		−	2365.69i		−	0.193337i
$532$	4103.30	−	3364.85i	0.334399	−	0.274219i
$533$		−	19085.5i		−	1.55100i
$534$	146.368	−	309.316i	0.0118614	−	0.0250663i
$535$	−214.817			−0.0173595
$536$	−1962.72	+	490.432i	−0.158165	+	0.0395213i
$537$	−4548.90			−0.365549
$538$	7400.92	−	15640.1i	0.593079	−	1.25334i
$539$		−	10503.6i		−	0.839373i
$540$	83.9129	+	102.328i	0.00668711	+	0.00815466i
$541$			7475.65i			0.594091i	0.954863	+	0.297045i	$0.0960013\pi$
$541$			7475.65i			0.594091i	−0.954863	+	0.297045i	$0.903999\pi$
$542$	−10114.4	−	4786.12i	−0.801566	−	0.379301i
$543$	−10140.6			−0.801427
$544$	−5092.46	+	6852.60i	−0.401356	+	0.540079i
$545$	365.764			0.0287479
$546$	−9229.24	−	4367.28i	−0.723397	−	0.342312i
$547$		−	6028.08i		−	0.471192i	−0.971851	−	0.235596i	$-0.924296\pi$
$547$		−	6028.08i		−	0.471192i	0.971851	−	0.235596i	$-0.0757043\pi$
$548$	12426.0	+	15153.0i	0.968636	+	1.18121i
$549$		−	2461.18i		−	0.191331i
$550$	9085.90	−	19201.0i	0.704408	−	1.48860i
$551$	304.037			0.0235071
$552$	7210.62	−	1801.74i	0.555986	−	0.138926i
$553$	3788.29			0.291310
$554$	−5858.06	+	12379.7i	−0.449251	+	0.949389i
$555$			750.536i			0.0574027i
$556$	−15202.6	+	12466.6i	−1.15959	+	0.950904i
$557$			19381.5i			1.47436i	0.675696	+	0.737181i	$0.263843\pi$
$557$			19381.5i			1.47436i	−0.675696	+	0.737181i	$0.736157\pi$
$558$	5082.40	+	2404.99i	0.385583	+	0.182458i
$559$	−12507.7			−0.946370
$560$	−874.535	−	174.656i	−0.0659926	−	0.0131796i
$561$	−8526.77			−0.641712
$562$	4803.10	+	2272.83i	0.360510	+	0.170593i
$563$		−	20565.0i		−	1.53946i	−0.638372	−	0.769728i	$-0.720392\pi$
$563$		−	20565.0i		−	1.53946i	0.638372	−	0.769728i	$-0.279608\pi$
$564$	2396.09	−	1964.88i	0.178889	−	0.146696i
$565$		−	304.139i		−	0.0226464i
$566$	−6925.95	+	14636.4i	−0.514345	+	1.08695i
$567$	−1842.28			−0.136452
$568$	−1922.73	−	7694.80i	−0.142035	−	0.568427i
$569$	15252.9			1.12379			0.561895	−	0.827209i	$-0.310073\pi$
$569$	15252.9			1.12379			0.561895	+	0.827209i	$0.310073\pi$
$570$	64.8494	−	137.044i	0.00476534	−	0.0100705i
$571$		−	16492.8i		−	1.20876i	−0.796697	−	0.604379i	$-0.793421\pi$
$571$		−	16492.8i		−	1.20876i	0.796697	−	0.604379i	$-0.206579\pi$
$572$	16173.4	+	19722.8i	1.18225	+	1.44170i
$573$			8399.13i			0.612354i
$574$	20976.6	+	9926.13i	1.52534	+	0.721792i
$575$	13644.9			0.989623
$576$	4066.40	−	2167.50i	0.294155	−	0.156793i
$577$	−10298.2			−0.743016			−0.371508	−	0.928430i	$-0.621159\pi$
$577$	−10298.2			−0.743016			−0.371508	+	0.928430i	$0.621159\pi$
$578$	−6873.60	−	3252.59i	−0.494644	−	0.234065i
$579$		−	1872.32i		−	0.134388i
$580$	−32.3997	−	39.5101i	−0.00231952	−	0.00282857i
$581$			8231.89i			0.587808i
$582$	−2231.79	+	4716.38i	−0.158953	+	0.335911i
$583$	−7100.14			−0.504387
$584$	2921.55	+	11692.1i	0.207011	+	0.828464i
$585$	−291.722			−0.0206175
$586$	6156.38	−	13010.1i	0.433989	−	0.917136i
$587$		−	13104.8i		−	0.921453i	−0.887542	−	0.460727i	$-0.847589\pi$
$587$		−	13104.8i		−	0.921453i	0.887542	−	0.460727i	$-0.152411\pi$
$588$	3234.61	−	2652.49i	0.226859	−	0.186032i
$589$		−	6441.82i		−	0.450646i
$590$	411.722	+	194.827i	0.0287294	+	0.0135948i
$591$	14337.7			0.997929
$592$	25628.2	+	5118.27i	1.77924	+	0.355337i
$593$	4163.34			0.288310			0.144155	−	0.989555i	$-0.453954\pi$
$593$	4163.34			0.288310			0.144155	+	0.989555i	$0.453954\pi$
$594$	4159.90	+	1968.47i	0.287345	+	0.135972i
$595$			657.208i			0.0452822i
$596$	12897.6	−	10576.5i	0.886423	−	0.726898i
$597$		−	7847.75i		−	0.538001i
$598$	−7007.90	+	14809.6i	−0.479221	+	1.01272i
$599$	−5718.60			−0.390076			−0.195038	−	0.980796i	$-0.562483\pi$
$599$	−5718.60			−0.390076			−0.195038	+	0.980796i	$0.562483\pi$
$600$	8207.46	−	2050.83i	0.558447	−	0.139541i
$601$	17473.0			1.18592			0.592959	−	0.805233i	$-0.297960\pi$
$601$	17473.0			1.18592			0.592959	+	0.805233i	$0.297960\pi$
$602$	6505.13	−	13747.1i	0.440414	−	0.930713i
$603$		−	804.670i		−	0.0543428i
$604$	5365.98	+	6543.60i	0.361488	+	0.440820i
$605$			1409.50i			0.0947181i
$606$	−12770.3	−	6042.93i	−0.856039	−	0.405078i
$607$	−5647.60			−0.377643			−0.188821	−	0.982011i	$-0.560467\pi$
$607$	−5647.60			−0.377643			−0.188821	+	0.982011i	$0.560467\pi$
$608$	−4237.34	−	3148.95i	−0.282643	−	0.210044i
$609$	711.322			0.0473304
$610$	428.342	+	202.691i	0.0284312	+	0.0134537i
$611$			6830.87i			0.452287i
$612$	−2153.28	−	2625.84i	−0.142224	−	0.173437i
$613$			16023.6i			1.05577i	0.849317	+	0.527884i	$0.177014\pi$
$613$			16023.6i			1.05577i	−0.849317	+	0.527884i	$0.822986\pi$
$614$	8733.81	−	18456.9i	0.574052	−	1.21313i
$615$	663.038			0.0434736
$616$	−30088.7	+	7518.37i	−1.96803	+	0.491760i
$617$	−21022.1			−1.37167			−0.685834	−	0.727758i	$-0.740562\pi$
$617$	−21022.1			−1.37167			−0.685834	+	0.727758i	$0.740562\pi$
$618$	1440.36	−	3043.87i	0.0937536	−	0.198127i
$619$			17824.2i			1.15737i	0.815550	+	0.578686i	$0.196434\pi$
$619$			17824.2i			1.15737i	−0.815550	+	0.578686i	$0.803566\pi$
$620$	−837.125	+	686.472i	−0.0542254	+	0.0444667i
$621$			2956.18i			0.191027i
$622$	−3929.69	−	1859.53i	−0.253322	−	0.119872i
$623$	−917.238			−0.0589861
$624$	−1989.39	+	9961.27i	−0.127627	+	0.639055i
$625$	15484.4			0.991001
$626$	−5626.97	−	2662.68i	−0.359263	−	0.170004i
$627$		−	5272.57i		−	0.335831i
$628$	−19752.0	+	16197.4i	−1.25508	+	1.02921i
$629$		−	19259.4i		−	1.22086i
$630$	151.721	−	320.628i	0.00959479	−	0.0202764i
$631$	−22339.0			−1.40935			−0.704677	−	0.709528i	$-0.748908\pi$
$631$	−22339.0			−1.40935			−0.704677	+	0.709528i	$0.748908\pi$
$632$	−913.644	−	3656.42i	−0.0575044	−	0.230134i
$633$	−5237.35			−0.328856
$634$	3436.33	−	7261.89i	0.215259	−	0.454900i
$635$		−	1102.70i		−	0.0689121i
$636$	−1793.01	−	2186.50i	−0.111788	−	0.136322i
$637$			9221.34i			0.573568i
$638$	−1606.18	−	760.046i	−0.0996698	−	0.0471638i
$639$	3154.69			0.195301
$640$	42.3406	+	886.217i	0.00261509	+	0.0547356i
$641$	−5268.43			−0.324634			−0.162317	−	0.986739i	$-0.551897\pi$
$641$	−5268.43			−0.324634			−0.162317	+	0.986739i	$0.551897\pi$
$642$	−2689.30	−	1272.58i	−0.165324	−	0.0782314i
$643$			21965.8i			1.34719i	0.739099	+	0.673597i	$0.235252\pi$
$643$			21965.8i			1.34719i	−0.739099	+	0.673597i	$0.764748\pi$
$644$	−12632.3	−	15404.6i	−0.772953	−	0.942586i
$645$		−	434.524i		−	0.0265262i
$646$	−1664.09	+	3516.68i	−0.101351	+	0.214182i
$647$	3165.40			0.192341			0.0961706	−	0.995365i	$-0.469341\pi$
$647$	3165.40			0.192341			0.0961706	+	0.995365i	$0.469341\pi$
$648$	444.313	+	1778.15i	0.0269356	+	0.107797i
$649$	15840.4			0.958073
$650$	−7976.71	+	16856.9i	−0.481342	+	1.01721i
$651$		−	15071.2i		−	0.907354i
$652$	5238.67	−	4295.89i	0.314666	−	0.258037i
$653$			12094.7i			0.724814i	0.932020	+	0.362407i	$0.118045\pi$
$653$			12094.7i			0.724814i	−0.932020	+	0.362407i	$0.881955\pi$
$654$	4579.00	+	2166.78i	0.273782	+	0.129553i
$655$	687.067			0.0409861
$656$	4521.57	−	22640.4i	0.269112	−	1.34750i
$657$	−4793.49			−0.284645
$658$	−7507.72	−	3552.66i	−0.444805	−	0.210482i
$659$			7523.17i			0.444706i	0.974966	+	0.222353i	$0.0713737\pi$
$659$			7523.17i			0.444706i	−0.974966	+	0.222353i	$0.928626\pi$
$660$	−685.180	+	561.871i	−0.0404100	+	0.0331376i
$661$		−	24141.1i		−	1.42054i	−0.703928	−	0.710271i	$-0.748572\pi$
$661$		−	24141.1i		−	1.42054i	0.703928	−	0.710271i	$-0.251428\pi$
$662$	2562.98	−	5416.28i	0.150473	−	0.317990i
$663$	7485.84			0.438501
$664$	7945.36	−	1985.33i	0.464367	−	0.116033i
$665$	−406.388			−0.0236978
$666$	−4446.17	+	9395.96i	−0.258687	+	0.546676i
$667$		−	1141.41i		−	0.0662604i
$668$	−13342.1	−	16270.2i	−0.772789	−	0.942385i
$669$			10156.8i			0.586972i
$670$	140.044	+	66.2688i	0.00807518	+	0.00382118i
$671$	16479.8			0.948130
$672$	−9913.65	−	7367.26i	−0.569088	−	0.422914i
$673$	944.143			0.0540773			0.0270387	−	0.999634i	$-0.491392\pi$
$673$	944.143			0.0540773			0.0270387	+	0.999634i	$0.491392\pi$
$674$	−1686.35	−	797.983i	−0.0963738	−	0.0456041i
$675$			3364.87i			0.191872i
$676$	−3054.12	−	3724.38i	−0.173766	−	0.211901i
$677$		−	4450.51i		−	0.252654i	−0.991989	−	0.126327i	$-0.959681\pi$
$677$		−	4450.51i		−	0.252654i	0.991989	−	0.126327i	$-0.0403189\pi$
$678$	1801.72	−	3807.51i	0.102057	−	0.215673i
$679$	13985.8			0.790468
$680$	634.332	−	158.503i	0.0357728	−	0.00893869i
$681$	11543.1			0.649536
$682$	−16103.5	+	34031.2i	−0.904160	+	1.91073i
$683$			1726.40i			0.0967189i	0.998830	+	0.0483594i	$0.0153993\pi$
$683$			1726.40i			0.0967189i	−0.998830	+	0.0483594i	$0.984601\pi$
$684$	1623.70	−	1331.49i	0.0907657	−	0.0744310i
$685$		−	1500.75i		−	0.0837088i
$686$	9809.87	+	4642.03i	0.545981	+	0.258358i
$687$	4005.44			0.222441
$688$	−14837.5	−	2963.23i	−0.822199	−	0.164204i
$689$	6233.37			0.344662
$690$	−514.491	−	243.457i	−0.0283860	−	0.0134323i
$691$			683.143i			0.0376092i	0.999823	+	0.0188046i	$0.00598605\pi$
$691$			683.143i			0.0376092i	−0.999823	+	0.0188046i	$0.994014\pi$
$692$	−2659.02	+	2180.49i	−0.146071	+	0.119783i
$693$		−	12335.7i		−	0.676181i
$694$	10135.0	−	21418.0i	0.554351	−	1.17149i
$695$	1505.65			0.0821764
$696$	−171.554	−	686.563i	−0.00934300	−	0.0373909i
$697$	−17014.1			−0.924614
$698$	3936.91	−	8319.76i	0.213487	−	0.451157i
$699$			15439.1i			0.835425i
$700$	−14378.7	−	17534.2i	−0.776375	−	0.946758i
$701$			19533.2i			1.05244i	0.850349	+	0.526220i	$0.176391\pi$
$701$			19533.2i			1.05244i	−0.850349	+	0.526220i	$0.823609\pi$
$702$	−3652.07	−	1728.16i	−0.196351	−	0.0929133i
$703$	11909.2			0.638922
$704$	14513.4	+	27228.1i	0.776978	+	1.45767i
$705$	−237.307			−0.0126773
$706$	28423.4	+	13450.0i	1.51520	+	0.716991i
$707$			37868.8i			2.01443i
$708$	4000.20	+	4878.08i	0.212340	+	0.258940i
$709$		−	26081.9i		−	1.38156i	−0.723066	−	0.690779i	$-0.757268\pi$
$709$		−	26081.9i		−	1.38156i	0.723066	−	0.690779i	$-0.242732\pi$
$710$	−259.805	+	549.038i	−0.0137328	+	0.0290212i
$711$	1499.05			0.0790699
$712$	221.216	+	885.311i	0.0116438	+	0.0465989i
$713$	−24183.8			−1.27025
$714$	−3893.30	+	8227.59i	−0.204066	+	0.431246i
$715$		−	1953.34i		−	0.102169i
$716$	9379.89	−	7691.84i	0.489585	−	0.401477i
$717$		−	21255.2i		−	1.10710i
$718$	−12160.8	−	5754.49i	−0.632085	−	0.299103i
$719$	−30077.3			−1.56007			−0.780036	−	0.625734i	$-0.784800\pi$
$719$	−30077.3			−1.56007			−0.780036	+	0.625734i	$0.784800\pi$
$720$	−346.059	−	69.1123i	−0.0179123	−	0.00357731i
$721$	−9026.21			−0.466232
$722$	15361.4	+	7269.02i	0.791818	+	0.374688i
$723$		−	7615.20i		−	0.391718i
$724$	20910.0	−	17147.0i	1.07336	−	0.880196i
$725$		−	1299.21i		−	0.0665537i
$726$	−8349.89	+	17645.6i	−0.426851	+	0.902051i
$727$	23049.9			1.17589			0.587946	−	0.808900i	$-0.299937\pi$
$727$	23049.9			1.17589			0.587946	+	0.808900i	$0.299937\pi$
$728$	26415.5	−	6600.54i	1.34481	−	0.336033i
$729$	−729.000			−0.0370370
$730$	394.769	−	834.254i	0.0200152	−	0.0422975i
$731$			11150.3i			0.564169i
$732$	4161.67	+	5074.99i	0.210136	+	0.256253i
$733$			4444.57i			0.223962i	0.993710	+	0.111981i	$0.0357195\pi$
$733$			4444.57i			0.223962i	−0.993710	+	0.111981i	$0.964280\pi$
$734$	4697.56	+	2222.89i	0.236226	+	0.111782i
$735$	−320.353			−0.0160768
$736$	−11821.8	+	15907.8i	−0.592060	+	0.796698i
$737$	5387.98			0.269293
$738$	8300.57	+	3927.83i	0.414022	+	0.195915i
$739$		−	28465.1i		−	1.41692i	−0.705749	−	0.708462i	$-0.749390\pi$
$739$		−	28465.1i		−	1.41692i	0.705749	−	0.708462i	$-0.250610\pi$
$740$	−1269.10	−	1547.61i	−0.0630446	−	0.0768803i
$741$			4628.91i			0.229483i
$742$	−3241.90	+	6851.01i	−0.160396	+	0.338960i
$743$	4389.76			0.216749			0.108374	−	0.994110i	$-0.465435\pi$
$743$	4389.76			0.216749			0.108374	+	0.994110i	$0.465435\pi$
$744$	−14546.6	+	3634.82i	−0.716808	+	0.179111i
$745$	−1277.38			−0.0628180
$746$	−6772.55	+	14312.2i	−0.332387	+	0.702423i
$747$			3257.41i			0.159548i
$748$	17582.3	−	14418.1i	0.859456	−	0.704784i
$749$			7974.77i			0.389041i
$750$	−1173.00	−	555.064i	−0.0571092	−	0.0270241i
$751$	14121.9			0.686171			0.343085	−	0.939304i	$-0.388528\pi$
$751$	14121.9			0.686171			0.343085	+	0.939304i	$0.388528\pi$
$752$	−1618.31	+	8103.21i	−0.0784758	+	0.392944i
$753$	−5090.98			−0.246382
$754$	1410.10	+	667.260i	0.0681073	+	0.0322284i
$755$		−	648.074i		−	0.0312395i
$756$	3798.79	−	3115.14i	0.182752	−	0.149863i
$757$		−	17006.3i		−	0.816516i	−0.912866	−	0.408258i	$-0.866136\pi$
$757$		−	17006.3i		−	0.816516i	0.912866	−	0.408258i	$-0.133864\pi$
$758$	4186.13	−	8846.42i	0.200590	−	0.423900i
$759$	−19794.3			−0.946622
$760$	98.0110	+	392.243i	0.00467794	+	0.0187212i
$761$	−4603.38			−0.219280			−0.109640	−	0.993971i	$-0.534970\pi$
$761$	−4603.38			−0.219280			−0.109640	+	0.993971i	$0.534970\pi$
$762$	6532.37	−	13804.7i	0.310555	−	0.656287i
$763$		−	13578.5i		−	0.644264i
$764$	−14202.3	−	17319.1i	−0.672540	−	0.820136i
$765$			260.061i			0.0122909i
$766$	12935.6	+	6121.15i	0.610161	+	0.288728i
$767$	−13906.6			−0.654679
$768$	−4719.88	+	11345.4i	−0.221763	+	0.533061i
$769$	−12459.1			−0.584248			−0.292124	−	0.956380i	$-0.594362\pi$
$769$	−12459.1			−0.584248			−0.292124	+	0.956380i	$0.594362\pi$
$770$	2146.89	+	1015.91i	0.100478	+	0.0475465i
$771$			1148.71i			0.0536571i
$772$	3165.94	+	3860.74i	0.147597	+	0.179989i
$773$		−	27068.1i		−	1.25947i	−0.776808	−	0.629737i	$-0.783163\pi$
$773$		−	27068.1i		−	1.25947i	0.776808	−	0.629737i	$-0.216837\pi$
$774$	2574.12	−	5439.81i	0.119541	−	0.252623i
$775$	−27527.2			−1.27588
$776$	−3373.05	−	13499.0i	−0.156038	−	0.624468i
$777$	27862.6			1.28644
$778$	−2652.15	+	5604.70i	−0.122216	+	0.258275i
$779$		−	10520.8i		−	0.483884i
$780$	601.534	−	493.279i	0.0276133	−	0.0226439i
$781$			21123.4i			0.967804i
$782$	13202.3	+	6247.33i	0.603725	+	0.285683i
$783$	281.475			0.0128468
$784$	−2184.64	+	10938.9i	−0.0995191	+	0.498312i
$785$	1956.23			0.0889438
$786$	8601.39	+	4070.18i	0.390333	+	0.184705i
$787$		−	6986.86i		−	0.316461i	−0.987402	−	0.158230i	$-0.949421\pi$
$787$		−	6986.86i		−	0.316461i	0.987402	−	0.158230i	$-0.0505789\pi$
$788$	−29564.6	+	24244.0i	−1.33654	+	1.09601i
$789$			15006.1i			0.677097i
$790$	−123.455	+	260.893i	−0.00555990	+	0.0117496i
$791$	−11290.7			−0.507523
$792$	−11906.3	+	2975.07i	−0.534181	+	0.133478i
$793$	−14468.0			−0.647885
$794$	−6678.02	+	14112.5i	−0.298481	+	0.630771i
$795$			216.550i			0.00966067i
$796$	13269.9	+	16182.1i	0.590879	+	0.720554i
$797$		−	27271.5i		−	1.21205i	−0.795444	−	0.606027i	$-0.792762\pi$
$797$		−	27271.5i		−	1.21205i	0.795444	−	0.606027i	$-0.207238\pi$
$798$	−5087.57	−	2407.44i	−0.225687	−	0.106795i
$799$	6089.52			0.269627
$800$	−13456.1	+	18107.0i	−0.594681	+	0.800224i
$801$	−362.957			−0.0160105
$802$	−18798.0	−	8895.23i	−0.827658	−	0.391648i
$803$		−	32096.7i		−	1.41054i
$804$	1360.63	+	1659.24i	0.0596839	+	0.0727821i
$805$			1525.66i			0.0667981i
$806$	14137.7	−	29876.7i	0.617838	−	1.30566i
$807$	−18352.4			−0.800540
$808$	36550.7	−	9133.06i	1.59140	−	0.397648i
$809$	23785.9			1.03371			0.516853	−	0.856074i	$-0.327103\pi$
$809$	23785.9			1.03371			0.516853	+	0.856074i	$0.327103\pi$
$810$	60.0370	−	126.874i	0.00260430	−	0.00550360i
$811$			21703.5i			0.939718i	0.882741	+	0.469859i	$0.155695\pi$
$811$			21703.5i			0.939718i	−0.882741	+	0.469859i	$0.844305\pi$
$812$	−1466.75	+	1202.79i	−0.0633904	+	0.0519823i
$813$			11868.4i			0.511982i
$814$	−62914.3	−	29771.1i	−2.70902	−	1.28191i
$815$	−518.835			−0.0222994
$816$	8880.18	+	1773.48i	0.380966	+	0.0760837i
$817$	−6894.83			−0.295250
$818$	−28918.7	−	13684.3i	−1.23608	−	0.584915i
$819$			10829.7i			0.462054i
$820$	−1367.19	+	1121.15i	−0.0582249	+	0.0477465i
$821$			33240.4i			1.41303i	0.707698	+	0.706515i	$0.249734\pi$
$821$			33240.4i			1.41303i	−0.707698	+	0.706515i	$0.750266\pi$
$822$	8890.41	−	18787.8i	0.377237	−	0.797203i
$823$	−17227.5			−0.729665			−0.364832	−	0.931073i	$-0.618874\pi$
$823$	−17227.5			−0.729665			−0.364832	+	0.931073i	$0.618874\pi$
$824$	2176.90	+	8712.02i	0.0920341	+	0.368322i
$825$	−22530.8			−0.950812
$826$	7232.67	−	15284.6i	0.304669	−	0.643848i
$827$			21678.4i			0.911528i	0.890101	+	0.455764i	$0.150634\pi$
$827$			21678.4i			0.911528i	−0.890101	+	0.455764i	$0.849366\pi$
$828$	−4998.68	−	6095.69i	−0.209802	−	0.255845i
$829$			34269.8i			1.43575i	0.696170	+	0.717877i	$0.254886\pi$
$829$			34269.8i			1.43575i	−0.696170	+	0.717877i	$0.745114\pi$
$830$	−566.916	−	268.265i	−0.0237084	−	0.0112188i
$831$	14526.5			0.606401
$832$	−12741.6	−	23904.2i	−0.530931	−	0.996067i
$833$	8220.55			0.341927
$834$	18849.3	+	8919.47i	0.782610	+	0.370331i
$835$			1611.39i			0.0667838i
$836$	8915.51	+	10872.1i	0.368839	+	0.449784i
$837$		−	5963.77i		−	0.246282i
$838$	−15778.4	+	33344.1i	−0.650426	+	1.37453i
$839$	33444.1			1.37618			0.688092	−	0.725623i	$-0.258448\pi$
$839$	33444.1			1.37618			0.688092	+	0.725623i	$0.258448\pi$
$840$	229.306	+	917.687i	0.00941881	+	0.0376943i
$841$	24280.3			0.995544
$842$	5497.80	−	11618.3i	0.225020	−	0.475527i
$843$		−	5636.04i		−	0.230267i
$844$	10799.5	−	8855.95i	0.440442	−	0.361178i
$845$			368.860i			0.0150168i
$846$	−2970.85	−	1405.81i	−0.120733	−	0.0571308i
$847$	52325.8			2.12271
$848$	7394.41	+	1476.76i	0.299440	+	0.0598020i
$849$	17174.6			0.694265
$850$	15027.5	+	7111.00i	0.606397	+	0.286947i
$851$		−	44709.3i		−	1.80096i
$852$	−6505.00	+	5334.33i	−0.261570	+	0.214497i
$853$			37037.3i			1.48667i	0.668917	+	0.743337i	$0.266758\pi$
$853$			37037.3i			1.48667i	−0.668917	+	0.743337i	$0.733242\pi$
$854$	7524.62	−	15901.6i	0.301507	−	0.637166i
$855$	−160.810			−0.00643227
$856$	7697.19	−	1923.32i	0.307342	−	0.0767966i
$857$	35794.2			1.42673			0.713365	−	0.700793i	$-0.247170\pi$
$857$	35794.2			1.42673			0.713365	+	0.700793i	$0.247170\pi$
$858$	11571.6	−	24453.8i	0.460427	−	0.973007i
$859$		−	20582.1i		−	0.817522i	−0.912641	−	0.408761i	$-0.865961\pi$
$859$		−	20582.1i		−	0.817522i	0.912641	−	0.408761i	$-0.134039\pi$
$860$	734.747	+	895.994i	0.0291333	+	0.0355269i
$861$		−	24614.3i		−	0.974278i
$862$	19721.4	+	9332.19i	0.779252	+	0.368742i
$863$	−25677.7			−1.01284			−0.506420	−	0.862287i	$-0.669031\pi$
$863$	−25677.7			−1.01284			−0.506420	+	0.862287i	$0.669031\pi$
$864$	−3922.89	−	2915.27i	−0.154467	−	0.114791i
$865$	263.348			0.0103516
$866$	−38524.0	−	18229.6i	−1.51166	−	0.715319i
$867$			8065.60i			0.315942i
$868$	25484.2	+	31077.0i	0.996534	+	1.21523i
$869$			10037.5i			0.391827i
$870$	−23.1809	+	48.9876i	−0.000903341	+	0.00190900i
$871$	−4730.22			−0.184015
$872$	−13105.8	+	3274.80i	−0.508967	+	0.127177i
$873$	5534.29			0.214556
$874$	−3863.07	+	8163.71i	−0.149508	+	0.315951i
$875$			3478.38i			0.134389i
$876$	9884.24	−	8105.42i	0.381230	−	0.312622i
$877$			32783.0i			1.26226i	0.775676	+	0.631131i	$0.217409\pi$
$877$			32783.0i			1.26226i	−0.775676	+	0.631131i	$0.782591\pi$
$878$	28135.0	+	13313.5i	1.08145	+	0.511742i
$879$	−15266.3			−0.585800
$880$	462.768	−	2317.17i	0.0177272	−	0.0887634i
$881$	26615.7			1.01783			0.508914	−	0.860818i	$-0.330047\pi$
$881$	26615.7			1.01783			0.508914	+	0.860818i	$0.330047\pi$
$882$	−4010.50	−	1897.77i	−0.153107	−	0.0724505i
$883$			19203.4i			0.731875i	0.930639	+	0.365937i	$0.119252\pi$
$883$			19203.4i			0.731875i	−0.930639	+	0.365937i	$0.880748\pi$
$884$	−15435.9	+	12658.0i	−0.587291	+	0.481599i
$885$		−	483.122i		−	0.0183503i
$886$	−3040.28	+	6424.93i	−0.115282	+	0.243623i
$887$	23198.0			0.878144			0.439072	−	0.898452i	$-0.355307\pi$
$887$	23198.0			0.878144			0.439072	+	0.898452i	$0.355307\pi$
$888$	−6719.78	−	26892.7i	−0.253943	−	1.01628i
$889$	−40936.0			−1.54438
$890$	29.8914	−	63.1686i	0.00112580	−	0.00237912i
$891$		−	4881.30i		−	0.183535i
$892$	−17174.4	−	20943.4i	−0.644664	−	0.786142i
$893$			3765.48i			0.141105i
$894$	−15991.5	−	7567.16i	−0.598249	−	0.283091i
$895$	−928.979			−0.0346953
$896$	32899.5	−	1571.83i	1.22667	−	0.0586063i
$897$	17377.8			0.646854
$898$	−40273.8	−	19057.6i	−1.49661	−	0.708195i
$899$			2302.68i			0.0854266i
$900$	−5689.73	−	6938.39i	−0.210731	−	0.256978i
$901$		−	5556.86i		−	0.205467i
$902$	−26300.3	+	55579.7i	−0.970848	+	2.05166i
$903$	−16131.1			−0.594472
$904$	2723.05	+	10897.7i	0.100185	+	0.400942i
$905$	−2070.92			−0.0760659
$906$	3839.19	−	8113.24i	0.140782	−	0.297510i
$907$		−	16151.3i		−	0.591285i	−0.955299	−	0.295643i	$-0.904466\pi$
$907$		−	16151.3i		−	0.591285i	0.955299	−	0.295643i	$-0.0955337\pi$
$908$	−23802.1	+	19518.6i	−0.869935	+	0.713377i
$909$			14984.9i			0.546776i
$910$	−1884.80	−	891.887i	−0.0686599	−	0.0324899i
$911$	−3487.34			−0.126829			−0.0634143	−	0.997987i	$-0.520199\pi$
$911$	−3487.34			−0.126829			−0.0634143	+	0.997987i	$0.520199\pi$
$912$	−1096.64	+	5491.10i	−0.0398174	+	0.199373i
$913$	−21811.2			−0.790632
$914$	−13440.4	−	6359.99i	−0.486398	−	0.230164i
$915$		−	502.624i		−	0.0181598i
$916$	−8259.27	+	6772.89i	−0.297919	+	0.244304i
$917$		−	25506.3i		−	0.918532i
$918$	−1540.60	+	3255.71i	−0.0553894	+	0.117053i
$919$	17055.5			0.612198			0.306099	−	0.952000i	$-0.400976\pi$
$919$	17055.5			0.612198			0.306099	+	0.952000i	$0.400976\pi$
$920$	1472.55	−	367.953i	0.0527703	−	0.0131859i
$921$	−21657.6			−0.774857
$922$	9758.62	−	20622.6i	0.348572	−	0.736626i
$923$		−	18544.7i		−	0.661329i
$924$	20858.7	+	25436.3i	0.742640	+	0.905620i
$925$		−	50890.2i		−	1.80893i
$926$	14530.4	+	6875.81i	0.515659	+	0.244010i
$927$	−3571.73			−0.126549
$928$	1514.67	+	1125.62i	0.0535792	+	0.0398170i
$929$	−55339.3			−1.95438			−0.977192	−	0.212359i	$-0.931885\pi$
$929$	−55339.3			−1.95438			−0.977192	+	0.212359i	$0.931885\pi$
$930$	1037.93	+	491.148i	0.0365968	+	0.0173176i
$931$			5083.22i			0.178943i
$932$	−26106.4	−	31835.7i	−0.917536	−	1.11890i
$933$			4611.17i			0.161804i
$934$	13476.4	−	28479.2i	0.472120	−	0.997717i
$935$	−1741.34			−0.0609069
$936$	10452.8	−	2611.88i	0.365021	−	0.0912092i
$937$	−20457.6			−0.713255			−0.356627	−	0.934247i	$-0.616073\pi$
$937$	−20457.6			−0.713255			−0.356627	+	0.934247i	$0.616073\pi$
$938$	2460.13	−	5198.92i	0.0856356	−	0.180971i
$939$			6602.78i			0.229471i
$940$	489.331	−	401.268i	0.0169789	−	0.0139233i
$941$		−	55891.0i		−	1.93623i	−0.250502	−	0.968116i	$-0.580596\pi$
$941$		−	55891.0i		−	1.93623i	0.250502	−	0.968116i	$-0.419404\pi$
$942$	24490.0	+	11588.7i	0.847058	+	0.400828i
$943$	−39497.0			−1.36395
$944$	−16496.9	−	3294.64i	−0.568780	−	0.113593i
$945$	−376.230			−0.0129511
$946$	36424.3	+	17236.0i	1.25186	+	0.592379i
$947$			54727.0i			1.87792i	0.344027	+	0.938960i	$0.388209\pi$
$947$			54727.0i			1.87792i	−0.344027	+	0.938960i	$0.611791\pi$
$948$	−3091.06	+	2534.77i	−0.105900	+	0.0868414i
$949$			28178.4i			0.963865i
$950$	−4397.12	+	9292.31i	−0.150170	+	0.317350i
$951$	−8521.23			−0.290557
$952$	−5884.19	−	23548.7i	−0.200323	−	0.801698i
$953$	29958.8			1.01832			0.509160	−	0.860672i	$-0.329956\pi$
$953$	29958.8			1.01832			0.509160	+	0.860672i	$0.329956\pi$
$954$	−1282.84	+	2710.99i	−0.0435361	+	0.0920036i
$955$			1715.27i			0.0581204i
$956$	35940.9	+	43828.5i	1.21591	+	1.48276i
$957$			1884.72i			0.0636619i
$958$	8890.31	+	4206.90i	0.299825	+	0.141877i
$959$	−55713.0			−1.87598
$960$	830.441	−	442.648i	0.0279191	−	0.0148817i
$961$	18997.2			0.637682
$962$	55233.8	+	26136.7i	1.85115	+	0.875966i
$963$			3155.67i			0.105597i
$964$	12876.7	+	15702.6i	0.430219	+	0.524634i
$965$		−	382.365i		−	0.0127552i
$966$	−9038.00	+	19099.7i	−0.301028	+	0.636153i
$967$	13498.5			0.448896			0.224448	−	0.974486i	$-0.427942\pi$
$967$	13498.5			0.448896			0.224448	+	0.974486i	$0.427942\pi$
$968$	−12619.7	−	50504.4i	−0.419022	−	1.67694i
$969$	4126.53			0.136804
$970$	−455.778	+	963.182i	−0.0150867	+	0.0318824i
$971$		−	9652.36i		−	0.319010i	−0.987197	−	0.159505i	$-0.949010\pi$
$971$		−	9652.36i		−	0.319010i	0.987197	−	0.159505i	$-0.0509899\pi$
$972$	1503.21	−	1232.68i	0.0496043	−	0.0406773i
$973$		−	55895.1i		−	1.84164i
$974$	−1224.11	−	579.249i	−0.0402700	−	0.0190558i
$975$	19780.2			0.649717
$976$	−17162.8	−	3427.63i	−0.562877	−	0.112414i
$977$	12169.8			0.398511			0.199256	−	0.979948i	$-0.436148\pi$
$977$	12169.8			0.398511			0.199256	+	0.979948i	$0.436148\pi$
$978$	−6495.29	−	3073.57i	−0.212369	−	0.100493i
$979$		−	2430.32i		−	0.0793394i
$980$	660.573	−	541.693i	0.0215319	−	0.0176569i
$981$		−	5373.08i		−	0.174872i
$982$	−20084.8	+	42444.7i	−0.652681	+	1.37929i
$983$	47545.2			1.54268			0.771341	−	0.636423i	$-0.219587\pi$
$983$	47545.2			1.54268			0.771341	+	0.636423i	$0.219587\pi$
$984$	−23757.5	+	5936.38i	−0.769678	+	0.192322i
$985$	2928.06			0.0947165
$986$	594.843	−	1257.06i	0.0192126	−	0.0406015i
$987$			8809.69i			0.284109i
$988$	−7827.12	−	9544.86i	−0.252038	−	0.307351i
$989$			25884.5i			0.832234i
$990$	849.537	+	402.001i	0.0272728	+	0.0129055i
$991$	−892.350			−0.0286039			−0.0143019	−	0.999898i	$-0.504553\pi$
$991$	−892.350			−0.0286039			−0.0143019	+	0.999898i	$0.504553\pi$
$992$	23849.1	−	32092.2i	0.763317	−	1.02715i
$993$	−6355.55			−0.203109
$994$	20382.2	+	9644.88i	0.650388	+	0.307764i
$995$		−	1602.67i		−	0.0510634i
$996$	−5508.03	−	6716.82i	−0.175229	−	0.213685i
$997$		−	4458.57i		−	0.141629i	−0.997489	−	0.0708146i	$-0.977440\pi$
$997$		−	4458.57i		−	0.141629i	0.997489	−	0.0708146i	$-0.0225599\pi$
$998$	11471.6	−	24242.5i	0.363854	−	0.768921i
$999$	11025.4			0.349177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.4.d.a.13.6	yes	6
3.2	odd	2		72.4.d.d.37.1		6
4.3	odd	2		96.4.d.a.49.5		6
8.3	odd	2		96.4.d.a.49.2		6
8.5	even	2	inner	24.4.d.a.13.5	✓	6
12.11	even	2		288.4.d.d.145.4		6
16.3	odd	4		768.4.a.q.1.2		3
16.5	even	4		768.4.a.r.1.2		3
16.11	odd	4		768.4.a.t.1.2		3
16.13	even	4		768.4.a.s.1.2		3
24.5	odd	2		72.4.d.d.37.2		6
24.11	even	2		288.4.d.d.145.3		6
48.5	odd	4		2304.4.a.bt.1.2		3
48.11	even	4		2304.4.a.bu.1.2		3
48.29	odd	4		2304.4.a.bv.1.2		3
48.35	even	4		2304.4.a.bw.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.4.d.a.13.5	✓	6	8.5	even	2	inner
24.4.d.a.13.6	yes	6	1.1	even	1	trivial
72.4.d.d.37.1		6	3.2	odd	2
72.4.d.d.37.2		6	24.5	odd	2
96.4.d.a.49.2		6	8.3	odd	2
96.4.d.a.49.5		6	4.3	odd	2
288.4.d.d.145.3		6	24.11	even	2
288.4.d.d.145.4		6	12.11	even	2
768.4.a.q.1.2		3	16.3	odd	4
768.4.a.r.1.2		3	16.5	even	4
768.4.a.s.1.2		3	16.13	even	4
768.4.a.t.1.2		3	16.11	odd	4
2304.4.a.bt.1.2		3	48.5	odd	4
2304.4.a.bu.1.2		3	48.11	even	4
2304.4.a.bv.1.2		3	48.29	odd	4
2304.4.a.bw.1.2		3	48.35	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)

\(f(q)\)	\(=\)	\(q+(2.55664 + 1.20980i) q^{2} -3.00000i q^{3} +(5.07277 + 6.18604i) q^{4} -0.612661i q^{5} +(3.62940 - 7.66991i) q^{6} -22.7441 q^{7} +(5.48534 + 21.9525i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(2.55664 + 1.20980i) q^{2} -3.00000i q^{3} +(5.07277 + 6.18604i) q^{4} -0.612661i q^{5} +(3.62940 - 7.66991i) q^{6} -22.7441 q^{7} +(5.48534 + 21.9525i) q^{8} -9.00000 q^{9} +(0.741198 - 1.56635i) q^{10} -60.2630i q^{11} +(18.5581 - 15.2183i) q^{12} +52.9062i q^{13} +(-58.1485 - 27.5159i) q^{14} -1.83798 q^{15} +(-12.5341 + 62.7606i) q^{16} +47.1643 q^{17} +(-23.0097 - 10.8882i) q^{18} +29.1643i q^{19} +(3.78994 - 3.10789i) q^{20} +68.2324i q^{21} +(72.9062 - 154.070i) q^{22} +109.488 q^{23} +(65.8574 - 16.4560i) q^{24} +124.625 q^{25} +(-64.0059 + 135.262i) q^{26} +27.0000i q^{27} +(-115.376 - 140.696i) q^{28} -10.4250i q^{29} +(-4.69905 - 2.22359i) q^{30} -220.881 q^{31} +(-107.973 + 145.292i) q^{32} -180.789 q^{33} +(120.582 + 57.0593i) q^{34} +13.9345i q^{35} +(-45.6549 - 55.6743i) q^{36} -408.348i q^{37} +(-35.2829 + 74.5624i) q^{38} +158.718 q^{39} +(13.4494 - 3.36066i) q^{40} -360.742 q^{41} +(-82.5476 + 174.445i) q^{42} +236.414i q^{43} +(372.789 - 305.700i) q^{44} +5.51395i q^{45} +(279.922 + 132.459i) q^{46} +129.113 q^{47} +(188.282 + 37.6023i) q^{48} +174.296 q^{49} +(318.620 + 150.771i) q^{50} -141.493i q^{51} +(-327.279 + 268.381i) q^{52} -117.819i q^{53} +(-32.6646 + 69.0291i) q^{54} -36.9208 q^{55} +(-124.759 - 499.290i) q^{56} +87.4928 q^{57} +(12.6122 - 26.6529i) q^{58} +262.854i q^{59} +(-9.32366 - 11.3698i) q^{60} +273.465i q^{61} +(-564.711 - 267.221i) q^{62} +204.697 q^{63} +(-451.822 + 240.834i) q^{64} +32.4135 q^{65} +(-462.211 - 218.718i) q^{66} +89.4077i q^{67} +(239.253 + 291.760i) q^{68} -328.465i q^{69} +(-16.8579 + 35.6253i) q^{70} -350.521 q^{71} +(-49.3681 - 197.572i) q^{72} +532.610 q^{73} +(494.019 - 1044.00i) q^{74} -373.874i q^{75} +(-180.411 + 147.943i) q^{76} +1370.63i q^{77} +(405.785 + 192.018i) q^{78} -166.561 q^{79} +(38.4510 + 7.67915i) q^{80} +81.0000 q^{81} +(-922.286 - 436.426i) q^{82} -361.934i q^{83} +(-422.088 + 346.127i) q^{84} -28.8957i q^{85} +(-286.013 + 604.423i) q^{86} -31.2750 q^{87} +(1322.92 - 330.563i) q^{88} +40.3285 q^{89} +(-6.67078 + 14.0972i) q^{90} -1203.31i q^{91} +(555.408 + 677.299i) q^{92} +662.642i q^{93} +(330.095 + 156.201i) q^{94} +17.8678 q^{95} +(435.877 + 323.919i) q^{96} -614.921 q^{97} +(445.612 + 210.864i) q^{98} +542.367i 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

Modular forms

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