LMFDB - Embedded newform 72.4.d.d.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,4,Mod(37,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, 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("72.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	72.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:	$4.24813752041$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.3
Root			$-0.641412 + 1.89436i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.4.d.d.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25295 - 2.53577i) q^{2} +(-4.86025 + 6.35436i) q^{4} +9.15486i q^{5} +27.4175 q^{7} +(22.2028 + 4.36281i) q^{8} +O(q^{10})$	\(q+(-1.25295 - 2.53577i) q^{2} +(-4.86025 + 6.35436i) q^{4} +9.15486i q^{5} +27.4175 q^{7} +(22.2028 + 4.36281i) q^{8} +(23.2146 - 11.4705i) q^{10} +20.5252i q^{11} -32.0471i q^{13} +(-34.3526 - 69.5243i) q^{14} +(-16.7559 - 61.7676i) q^{16} +111.764 q^{17} +129.764i q^{19} +(-58.1733 - 44.4950i) q^{20} +(52.0471 - 25.7169i) q^{22} -9.16510 q^{23} +41.1885 q^{25} +(-81.2641 + 40.1533i) q^{26} +(-133.256 + 174.220i) q^{28} +41.0606i q^{29} -187.606 q^{31} +(-135.634 + 119.880i) q^{32} +(-140.034 - 283.408i) q^{34} +251.003i q^{35} -114.127i q^{37} +(329.052 - 162.587i) q^{38} +(-39.9409 + 203.264i) q^{40} -282.915 q^{41} +89.3870i q^{43} +(-130.424 - 99.7576i) q^{44} +(11.4834 + 23.2406i) q^{46} +54.6464 q^{47} +408.717 q^{49} +(-51.6070 - 104.445i) q^{50} +(203.639 + 155.757i) q^{52} -726.878i q^{53} -187.905 q^{55} +(608.745 + 119.617i) q^{56} +(104.120 - 51.4467i) q^{58} -216.579i q^{59} -754.222i q^{61} +(235.060 + 475.726i) q^{62} +(473.932 + 193.734i) q^{64} +293.387 q^{65} +379.433i q^{67} +(-543.202 + 710.189i) q^{68} +(636.486 - 314.493i) q^{70} -302.080 q^{71} -504.396 q^{73} +(-289.401 + 142.995i) q^{74} +(-824.568 - 630.686i) q^{76} +562.748i q^{77} +301.780 q^{79} +(565.474 - 153.398i) q^{80} +(354.477 + 717.408i) q^{82} -599.003i q^{83} +1023.18i q^{85} +(226.665 - 111.997i) q^{86} +(-89.5475 + 455.717i) q^{88} +277.528 q^{89} -878.651i q^{91} +(44.5447 - 58.2383i) q^{92} +(-68.4689 - 138.571i) q^{94} -1187.97 q^{95} -765.905 q^{97} +(-512.100 - 1036.41i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 76 * q^8	$ 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8} + 60 q^{10} + 100 q^{14} + 56 q^{16} - 52 q^{17} - 56 q^{20} + 224 q^{22} - 328 q^{23} - 106 q^{25} - 56 q^{26} - 352 q^{28} - 636 q^{31} + 248 q^{32} - 548 q^{34} + 776 q^{38} + 232 q^{40} - 236 q^{41} - 1152 q^{44} + 328 q^{46} + 408 q^{47} + 654 q^{49} - 1970 q^{50} - 368 q^{52} + 1024 q^{55} + 1864 q^{56} + 140 q^{58} + 2108 q^{62} + 832 q^{64} + 1744 q^{65} - 2976 q^{68} + 1352 q^{70} + 1704 q^{71} + 956 q^{73} - 1568 q^{74} - 1744 q^{76} - 44 q^{79} + 2112 q^{80} - 2236 q^{82} + 760 q^{86} + 1856 q^{88} + 220 q^{89} - 1728 q^{92} + 2088 q^{94} - 5104 q^{95} - 2444 q^{97} - 3354 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 76 * q^8 + 60 * q^10 + 100 * q^14 + 56 * q^16 - 52 * q^17 - 56 * q^20 + 224 * q^22 - 328 * q^23 - 106 * q^25 - 56 * q^26 - 352 * q^28 - 636 * q^31 + 248 * q^32 - 548 * q^34 + 776 * q^38 + 232 * q^40 - 236 * q^41 - 1152 * q^44 + 328 * q^46 + 408 * q^47 + 654 * q^49 - 1970 * q^50 - 368 * q^52 + 1024 * q^55 + 1864 * q^56 + 140 * q^58 + 2108 * q^62 + 832 * q^64 + 1744 * q^65 - 2976 * q^68 + 1352 * q^70 + 1704 * q^71 + 956 * q^73 - 1568 * q^74 - 1744 * q^76 - 44 * q^79 + 2112 * q^80 - 2236 * q^82 + 760 * q^86 + 1856 * q^88 + 220 * q^89 - 1728 * q^92 + 2088 * q^94 - 5104 * q^95 - 2444 * q^97 - 3354 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$	−4.86025	+	6.35436i	−0.607532	+	0.794295i
$5$			9.15486i			0.818836i	0.912347	+	0.409418i	$0.134268\pi$
$5$			9.15486i			0.818836i	−0.912347	+	0.409418i	$0.865732\pi$
$6$		0			0
$7$	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
$9$		0			0
$10$	23.2146	−	11.4705i	0.734111	−	0.362730i
$11$			20.5252i			0.562598i	0.959620	+	0.281299i	$0.0907652\pi$
$11$			20.5252i			0.562598i	−0.959620	+	0.281299i	$0.909235\pi$
$12$		0			0
$13$		−	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
$15$		0			0
$16$	−16.7559	−	61.7676i	−0.261810	−	0.965119i
$17$	111.764			1.59452			0.797258	−	0.603639i	$-0.206283\pi$
$17$	111.764			1.59452			0.797258	+	0.603639i	$0.206283\pi$
$18$		0			0
$19$			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
$21$		0			0
$22$	52.0471	−	25.7169i	0.504386	−	0.249221i
$23$	−9.16510			−0.0830893			−0.0415447	−	0.999137i	$-0.513228\pi$
$23$	−9.16510			−0.0830893			−0.0415447	+	0.999137i	$0.513228\pi$
$24$		0			0
$25$	41.1885			0.329508
$26$	−81.2641	+	40.1533i	−0.612970	+	0.302874i
$27$		0			0
$28$	−133.256	+	174.220i	−0.899392	+	1.17588i
$29$			41.0606i			0.262923i	0.991321	+	0.131461i	$0.0419669\pi$
$29$			41.0606i			0.262923i	−0.991321	+	0.131461i	$0.958033\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	−140.034	−	283.408i	−0.706344	−	1.42953i
$35$			251.003i			1.21221i
$36$		0			0
$37$		−	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
$39$		0			0
$40$	−39.9409	+	203.264i	−0.157880	+	0.803471i
$41$	−282.915			−1.07766			−0.538828	−	0.842416i	$-0.681133\pi$
$41$	−282.915			−1.07766			−0.538828	+	0.842416i	$0.681133\pi$
$42$		0			0
$43$			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
$45$		0			0
$46$	11.4834	+	23.2406i	0.0368072	+	0.0744921i
$47$	54.6464			0.169596			0.0847978	−	0.996398i	$-0.472976\pi$
$47$	54.6464			0.169596			0.0847978	+	0.996398i	$0.472976\pi$
$48$		0			0
$49$	408.717			1.19159
$50$	−51.6070	−	104.445i	−0.145967	−	0.295414i
$51$		0			0
$52$	203.639	+	155.757i	0.543070	+	0.415378i
$53$		−	726.878i		−	1.88386i	−0.335815	−	0.941928i	$-0.609012\pi$
$53$		−	726.878i		−	1.88386i	0.335815	−	0.941928i	$-0.390988\pi$
$54$		0			0
$55$	−187.905			−0.460675
$56$	608.745	+	119.617i	1.45262	+	0.285438i
$57$		0			0
$58$	104.120	−	51.4467i	0.235718	−	0.116470i
$59$		−	216.579i		−	0.477900i	−0.971032	−	0.238950i	$-0.923197\pi$
$59$		−	216.579i		−	0.477900i	0.971032	−	0.238950i	$-0.0768033\pi$
$60$		0			0
$61$		−	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
$63$		0			0
$64$	473.932	+	193.734i	0.925648	+	0.378386i
$65$	293.387			0.559849
$66$		0			0
$67$			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
$69$		0			0
$70$	636.486	−	314.493i	1.08678	−	0.536987i
$71$	−302.080			−0.504933			−0.252467	−	0.967606i	$-0.581242\pi$
$71$	−302.080			−0.504933			−0.252467	+	0.967606i	$0.581242\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	−824.568	−	630.686i	−1.24453	−	0.951904i
$77$			562.748i			0.832872i
$78$		0			0
$79$	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
$81$		0			0
$82$	354.477	+	717.408i	0.477384	+	0.966151i
$83$		−	599.003i		−	0.792158i	−0.918216	−	0.396079i	$-0.870371\pi$
$83$		−	599.003i		−	0.792158i	0.918216	−	0.396079i	$-0.129629\pi$
$84$		0			0
$85$			1023.18i			1.30565i
$86$	226.665	−	111.997i	0.284208	−	0.140430i
$87$		0			0
$88$	−89.5475	+	455.717i	−0.108475	+	0.552041i
$89$	277.528			0.330538			0.165269	−	0.986248i	$-0.447151\pi$
$89$	277.528			0.330538			0.165269	+	0.986248i	$0.447151\pi$
$90$		0			0
$91$		−	878.651i		−	1.01217i
$92$	44.5447	−	58.2383i	0.0504794	−	0.0659975i
$93$		0			0
$94$	−68.4689	−	138.571i	−0.0751280	−	0.152048i
$95$	−1187.97			−1.28298
$96$		0			0
$97$	−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
$99$		0			0
$100$	−200.187	+	261.727i	−0.200187	+	0.261727i
$101$			201.253i			0.198272i	0.995074	+	0.0991360i	$0.0316079\pi$
$101$			201.253i			0.198272i	−0.995074	+	0.0991360i	$0.968392\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	−1843.20	+	910.739i	−1.68893	+	0.834517i
$107$			457.252i			0.413123i	0.978434	+	0.206562i	$0.0662274\pi$
$107$			457.252i			0.413123i	−0.978434	+	0.206562i	$0.933773\pi$
$108$		0			0
$109$		−	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
$111$		0			0
$112$	−459.403	−	1693.51i	−0.387585	−	1.42877i
$113$	−981.151			−0.816805			−0.408402	−	0.912802i	$-0.633914\pi$
$113$	−981.151			−0.816805			−0.408402	+	0.912802i	$0.633914\pi$
$114$		0			0
$115$		−	83.9052i		−	0.0680365i
$116$	−260.914	−	199.565i	−0.208838	−	0.159734i
$117$		0			0
$118$	−549.193	+	271.361i	−0.428452	+	0.211702i
$119$	3064.29			2.36053
$120$		0			0
$121$	909.717			0.683484
$122$	−1912.53	+	944.999i	−1.41928	+	0.701280i
$123$		0			0
$124$	911.813	−	1192.12i	0.660348	−	0.863349i
$125$			1521.43i			1.08865i
$126$		0			0
$127$	−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
$129$		0			0
$130$	−367.598	−	743.962i	−0.248004	−	0.501921i
$131$			1110.85i			0.740884i	0.928856	+	0.370442i	$0.120794\pi$
$131$			1110.85i			0.740884i	−0.928856	+	0.370442i	$0.879206\pi$
$132$		0			0
$133$			3557.80i			2.31955i
$134$	962.155	−	475.409i	0.620280	−	0.306486i
$135$		0			0
$136$	2481.48	+	487.606i	1.56460	+	0.307440i
$137$	466.765			0.291084			0.145542	−	0.989352i	$-0.453507\pi$
$137$	466.765			0.291084			0.145542	+	0.989352i	$0.453507\pi$
$138$		0			0
$139$		−	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
$141$		0			0
$142$	378.489	+	766.005i	0.223677	+	0.452688i
$143$	657.773			0.384656
$144$		0			0
$145$	−375.904			−0.215291
$146$	631.981	+	1279.03i	0.358240	+	0.725023i
$147$		0			0
$148$	725.207	+	554.688i	0.402781	+	0.308075i
$149$		−	1290.49i		−	0.709540i	−0.934954	−	0.354770i	$-0.884559\pi$
$149$		−	1290.49i		−	0.709540i	0.934954	−	0.354770i	$-0.115441\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	1427.00	−	705.093i	0.746694	−	0.368948i
$155$		−	1717.51i		−	0.890022i
$156$		0			0
$157$			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
$159$		0			0
$160$	−1097.49	−	1241.71i	−0.542276	−	0.613538i
$161$	−251.284			−0.123006
$162$		0			0
$163$		−	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
$165$		0			0
$166$	−1518.93	+	750.518i	−0.710193	+	0.350913i
$167$	−45.8012			−0.0212228			−0.0106114	−	0.999944i	$-0.503378\pi$
$167$	−45.8012			−0.0212228			−0.0106114	+	0.999944i	$0.503378\pi$
$168$		0			0
$169$	1169.98			0.532536
$170$	2594.56	−	1281.99i	1.17055	−	0.578379i
$171$		0			0
$172$	−567.998	−	434.444i	−0.251799	−	0.192593i
$173$			2455.02i			1.07891i	0.842014	+	0.539455i	$0.181370\pi$
$173$			2455.02i			1.07891i	−0.842014	+	0.539455i	$0.818630\pi$
$174$		0			0
$175$	1129.28			0.487805
$176$	1267.79	−	343.917i	0.542974	−	0.147294i
$177$		0			0
$178$	−347.728	−	703.747i	−0.146423	−	0.296338i
$179$		−	1026.28i		−	0.428533i	−0.976775	−	0.214267i	$-0.931264\pi$
$179$		−	1026.28i		−	0.428533i	0.976775	−	0.214267i	$-0.0687362\pi$
$180$		0			0
$181$		−	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
$183$		0			0
$184$	−203.491	−	39.9856i	−0.0815302	−	0.0160205i
$185$	1044.82			0.415226
$186$		0			0
$187$			2293.98i			0.897071i
$188$	−265.595	+	347.243i	−0.103035	+	0.134709i
$189$		0			0
$190$	1488.46	+	3012.42i	0.568340	+	1.15023i
$191$	−5108.93			−1.93544			−0.967721	−	0.252023i	$-0.918904\pi$
$191$	−5108.93			−1.93544			−0.967721	+	0.252023i	$0.918904\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−1986.47	+	2597.13i	−0.723931	+	0.946477i
$197$		−	2816.66i		−	1.01867i	−0.860567	−	0.509337i	$-0.829891\pi$
$197$		−	2816.66i		−	1.01867i	0.860567	−	0.509337i	$-0.170109\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	510.332	−	252.160i	0.177757	−	0.0878311i
$203$			1125.78i			0.389232i
$204$		0			0
$205$		−	2590.05i		−	0.882424i
$206$	−855.060	−	1730.51i	−0.289198	−	0.585293i
$207$		0			0
$208$	−1979.48	+	536.977i	−0.659865	+	0.179003i
$209$	−2663.43			−0.881499
$210$		0			0
$211$			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
$213$		0			0
$214$	1159.49	−	572.912i	0.370377	−	0.183007i
$215$	−818.326			−0.259578
$216$		0			0
$217$	−5143.68			−1.60910
$218$	−1586.91	+	784.108i	−0.493025	+	0.243608i
$219$		0			0
$220$	913.267	−	1194.02i	0.279875	−	0.365912i
$221$		−	3581.72i		−	1.09019i
$222$		0			0
$223$	−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
$225$		0			0
$226$	1229.33	+	2487.97i	0.361831	+	0.732290i
$227$		−	2897.47i		−	0.847189i	−0.905852	−	0.423594i	$-0.860768\pi$
$227$		−	2897.47i		−	0.847189i	0.905852	−	0.423594i	$-0.139232\pi$
$228$		0			0
$229$			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
$231$		0			0
$232$	−179.140	+	911.662i	−0.0506944	+	0.257989i
$233$	1054.02			0.296355			0.148178	−	0.988961i	$-0.452659\pi$
$233$	1054.02			0.296355			0.148178	+	0.988961i	$0.452659\pi$
$234$		0			0
$235$			500.280i			0.138871i
$236$	1376.22	+	1052.63i	0.379594	+	0.290340i
$237$		0			0
$238$	−3839.38	−	7770.32i	−1.04567	−	2.11628i
$239$	654.700			0.177192			0.0885962	−	0.996068i	$-0.471762\pi$
$239$	654.700			0.177192			0.0885962	+	0.996068i	$0.471762\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	4792.60	+	3665.71i	1.25744	+	0.961774i
$245$			3741.74i			0.975719i
$246$		0			0
$247$	4158.57			1.07127
$248$	−4165.38	−	818.490i	−1.06654	−	0.209573i
$249$		0			0
$250$	3858.00	−	1906.27i	0.976006	−	0.482253i
$251$			5042.90i			1.26815i	0.773273	+	0.634074i	$0.218618\pi$
$251$			5042.90i			1.26815i	−0.773273	+	0.634074i	$0.781382\pi$
$252$		0			0
$253$		−	188.115i		−	0.0467459i
$254$	1012.45	+	2049.04i	0.250105	+	0.506174i
$255$		0			0
$256$	−3534.48	+	2069.94i	−0.862911	+	0.505356i
$257$	5166.64			1.25403			0.627016	−	0.779007i	$-0.284276\pi$
$257$	5166.64			1.25403			0.627016	+	0.779007i	$0.284276\pi$
$258$		0			0
$259$		−	3129.08i		−	0.750702i
$260$	−1425.94	+	1864.29i	−0.340126	+	0.444685i
$261$		0			0
$262$	2816.87	−	1391.84i	0.664225	−	0.328199i
$263$	7366.11			1.72705			0.863524	−	0.504308i	$-0.168252\pi$
$263$	7366.11			1.72705			0.863524	+	0.504308i	$0.168252\pi$
$264$		0			0
$265$	6654.47			1.54257
$266$	9021.76	−	4457.73i	2.07955	−	1.02752i
$267$		0			0
$268$	−2411.06	−	1844.14i	−0.549548	−	0.420332i
$269$		−	7877.80i		−	1.78557i	−0.450484	−	0.892784i	$-0.648749\pi$
$269$		−	7877.80i		−	1.78557i	0.450484	−	0.892784i	$-0.351251\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	−584.832	−	1183.61i	−0.128945	−	0.260965i
$275$			845.402i			0.185381i
$276$		0			0
$277$		−	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
$279$		0			0
$280$	−1095.08	+	5572.98i	−0.233727	+	1.18946i
$281$	−8068.94			−1.71300			−0.856499	−	0.516148i	$-0.827365\pi$
$281$	−8068.94			−1.71300			−0.856499	+	0.516148i	$0.827365\pi$
$282$		0			0
$283$			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
$285$		0			0
$286$	−824.154	−	1667.96i	−0.170396	−	0.344855i
$287$	−7756.81			−1.59537
$288$		0			0
$289$	7578.21			1.54248
$290$	470.987	+	953.206i	0.0953701	+	0.193014i
$291$		0			0
$292$	2451.49	−	3205.11i	0.491311	−	0.642346i
$293$			6372.75i			1.27065i	0.772246	+	0.635324i	$0.219133\pi$
$293$			6372.75i			1.27065i	−0.772246	+	0.635324i	$0.780867\pi$
$294$		0			0
$295$	1982.75			0.391322
$296$	497.916	−	2533.95i	0.0977730	−	0.497577i
$297$		0			0
$298$	−3272.40	+	1616.92i	−0.636124	+	0.314314i
$299$			293.715i			0.0568093i
$300$		0			0
$301$			2450.76i			0.469301i
$302$	−1472.85	−	2980.83i	−0.280639	−	0.567971i
$303$		0			0
$304$	8015.22	−	2174.31i	1.51219	−	0.410214i
$305$	6904.79			1.29629
$306$		0			0
$307$			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
$309$		0			0
$310$	−4355.20	+	2151.94i	−0.797932	+	0.394265i
$311$	8106.73			1.47810			0.739052	−	0.673648i	$-0.235274\pi$
$311$	8106.73			1.47810			0.739052	+	0.673648i	$0.235274\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	−1466.73	+	1917.62i	−0.261108	+	0.341376i
$317$			5828.98i			1.03277i	0.856357	+	0.516385i	$0.172723\pi$
$317$			5828.98i			1.03277i	−0.856357	+	0.516385i	$0.827277\pi$
$318$		0			0
$319$	−842.776			−0.147920
$320$	−1773.60	+	4338.78i	−0.309836	+	0.757953i
$321$		0			0
$322$	314.845	+	637.197i	0.0544895	+	0.110278i
$323$			14503.0i			2.49835i
$324$		0			0
$325$		−	1319.97i		−	0.225289i
$326$	−9197.16	+	4544.40i	−1.56253	+	0.772058i
$327$		0			0
$328$	−6281.52	−	1234.31i	−1.05744	−	0.207784i
$329$	1498.26			0.251070
$330$		0			0
$331$		−	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
$333$		0			0
$334$	57.3864	+	116.141i	0.00940133	+	0.0190269i
$335$	−3473.66			−0.566526
$336$		0			0
$337$	−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
$339$		0			0
$340$	−6501.69	−	4972.94i	−1.03707	−	0.793222i
$341$		−	3850.65i		−	0.611508i
$342$		0			0
$343$	1801.78			0.283636
$344$	−389.979	+	1984.65i	−0.0611228	+	0.311061i
$345$		0			0
$346$	6225.36	−	3076.00i	0.967276	−	0.477939i
$347$		−	10148.2i		−	1.56999i	−0.619505	−	0.784993i	$-0.712667\pi$
$347$		−	10148.2i		−	1.56999i	0.619505	−	0.784993i	$-0.287333\pi$
$348$		0			0
$349$			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
$351$		0			0
$352$	−2460.57	−	2783.92i	−0.372582	−	0.421544i
$353$	−2813.56			−0.424223			−0.212111	−	0.977245i	$-0.568034\pi$
$353$	−2813.56			−0.424223			−0.212111	+	0.977245i	$0.568034\pi$
$354$		0			0
$355$		−	2765.50i		−	0.413457i
$356$	−1348.86	+	1763.51i	−0.200813	+	0.262545i
$357$		0			0
$358$	−2602.40	+	1285.87i	−0.384193	+	0.189833i
$359$	2427.25			0.356839			0.178419	−	0.983955i	$-0.442902\pi$
$359$	2427.25			0.356839			0.178419	+	0.983955i	$0.442902\pi$
$360$		0			0
$361$	−9979.71			−1.45498
$362$	−9379.95	+	4634.71i	−1.36188	+	0.672915i
$363$		0			0
$364$	5583.27	+	4270.47i	0.803963	+	0.614926i
$365$		−	4617.67i		−	0.662192i
$366$		0			0
$367$	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
$369$		0			0
$370$	−1309.10	−	2649.42i	−0.183938	−	0.372262i
$371$		−	19929.1i		−	2.78887i
$372$		0			0
$373$		−	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
$375$		0			0
$376$	1213.30	+	238.412i	0.166413	+	0.0326999i
$377$	1315.87			0.179764
$378$		0			0
$379$		−	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
$381$		0			0
$382$	6401.22	+	12955.1i	0.857368	+	1.73518i
$383$	−7350.18			−0.980618			−0.490309	−	0.871549i	$-0.663116\pi$
$383$	−7350.18			−0.980618			−0.490309	+	0.871549i	$0.663116\pi$
$384$		0			0
$385$	−5151.88			−0.681985
$386$	1771.83	+	3585.92i	0.233637	+	0.472846i
$387$		0			0
$388$	3722.49	−	4866.84i	0.487064	−	0.636795i
$389$			13009.1i			1.69560i	0.530317	+	0.847800i	$0.322073\pi$
$389$			13009.1i			1.69560i	−0.530317	+	0.847800i	$0.677927\pi$
$390$		0			0
$391$	−1024.33			−0.132487
$392$	9074.67	+	1783.15i	1.16923	+	0.229752i
$393$		0			0
$394$	−7142.41	+	3529.13i	−0.913272	+	0.451256i
$395$			2762.76i			0.351923i
$396$		0			0
$397$			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
$399$		0			0
$400$	−690.149	−	2544.12i	−0.0862686	−	0.318015i
$401$	−5552.33			−0.691446			−0.345723	−	0.938337i	$-0.612366\pi$
$401$	−5552.33			−0.691446			−0.345723	+	0.938337i	$0.612366\pi$
$402$		0			0
$403$			6012.23i			0.743153i
$404$	−1278.84	−	978.143i	−0.157486	−	0.120456i
$405$		0			0
$406$	2854.71	−	1410.54i	0.348958	−	0.172423i
$407$	2342.49			0.285289
$408$		0			0
$409$	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
$411$		0			0
$412$	−3316.83	+	4336.47i	−0.396623	+	0.518550i
$413$		−	5938.03i		−	0.707485i
$414$		0			0
$415$	5483.79			0.648647
$416$	3841.83	+	4346.69i	0.452791	+	0.512293i
$417$		0			0
$418$	3337.13	+	6753.85i	0.390489	+	0.790291i
$419$			10461.0i			1.21970i	0.792518	+	0.609849i	$0.208770\pi$
$419$			10461.0i			1.21970i	−0.792518	+	0.609849i	$0.791230\pi$
$420$		0			0
$421$		−	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
$423$		0			0
$424$	3171.23	−	16138.8i	0.363228	−	1.84851i
$425$	4603.40			0.525406
$426$		0			0
$427$		−	20678.8i		−	2.34360i
$428$	−2905.54	−	2222.36i	−0.328142	−	0.250986i
$429$		0			0
$430$	1025.32	+	2075.09i	0.114989	+	0.232720i
$431$	−12490.7			−1.39595			−0.697975	−	0.716122i	$-0.745915\pi$
$431$	−12490.7			−1.39595			−0.697975	+	0.716122i	$0.745915\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	3976.64	+	3041.60i	0.436803	+	0.334097i
$437$		−	1189.30i		−	0.130188i
$438$		0			0
$439$	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
$441$		0			0
$442$	−9082.41	+	4487.70i	−0.977390	+	0.482937i
$443$		−	7601.37i		−	0.815241i	−0.913151	−	0.407621i	$-0.866359\pi$
$443$		−	7601.37i		−	0.815241i	0.913151	−	0.407621i	$-0.133641\pi$
$444$		0			0
$445$			2540.73i			0.270657i
$446$	5752.25	+	11641.7i	0.610710	+	1.23598i
$447$		0			0
$448$	12994.0	+	5311.68i	1.37033	+	0.560164i
$449$	−10708.8			−1.12557			−0.562785	−	0.826603i	$-0.690270\pi$
$449$	−10708.8			−1.12557			−0.562785	+	0.826603i	$0.690270\pi$
$450$		0			0
$451$		−	5806.89i		−	0.606287i
$452$	4768.64	−	6234.59i	0.496235	−	0.648784i
$453$		0			0
$454$	−7347.32	+	3630.37i	−0.759530	+	0.375290i
$455$	8043.92			0.828802
$456$		0			0
$457$	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
$459$		0			0
$460$	533.164	+	407.801i	0.0540411	+	0.0413343i
$461$		−	981.307i		−	0.0991410i	−0.998771	−	0.0495705i	$-0.984215\pi$
$461$		−	981.307i		−	0.0991410i	0.998771	−	0.0495705i	$-0.0157853\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	−1320.62	−	2672.74i	−0.131280	−	0.265692i
$467$		−	9286.49i		−	0.920188i	−0.887870	−	0.460094i	$-0.847816\pi$
$467$		−	9286.49i		−	0.920188i	0.887870	−	0.460094i	$-0.152184\pi$
$468$		0			0
$469$			10403.1i			1.02424i
$470$	1268.59	−	626.824i	0.124502	−	0.0615175i
$471$		0			0
$472$	944.892	−	4808.66i	0.0921444	−	0.468933i
$473$	−1834.68			−0.178349
$474$		0			0
$475$			5344.79i			0.516286i
$476$	−14893.2	+	19471.6i	−1.43409	+	1.87496i
$477$		0			0
$478$	−820.303	−	1660.17i	−0.0784933	−	0.158858i
$479$	19409.3			1.85143			0.925715	−	0.378222i	$-0.123464\pi$
$479$	19409.3			1.85143			0.925715	+	0.378222i	$0.123464\pi$
$480$		0			0
$481$	−3657.46			−0.346706
$482$	−4001.90	−	8099.24i	−0.378178	−	0.765374i
$483$		0			0
$484$	−4421.46	+	5780.67i	−0.415238	+	0.542888i
$485$		−	7011.76i		−	0.656469i
$486$		0			0
$487$	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
$489$		0			0
$490$	9488.20	−	4688.20i	0.874762	−	0.432227i
$491$			5100.69i			0.468820i	0.972138	+	0.234410i	$0.0753159\pi$
$491$			5100.69i			0.468820i	−0.972138	+	0.234410i	$0.924684\pi$
$492$		0			0
$493$			4589.10i			0.419235i
$494$	−5210.46	−	10545.2i	−0.474554	−	0.960424i
$495$		0			0
$496$	3143.50	+	11588.0i	0.284571	+	1.04902i
$497$	−8282.26			−0.747505
$498$		0			0
$499$		−	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
$501$		0			0
$502$	12787.6	−	6318.48i	1.13693	−	0.561768i
$503$	12287.2			1.08918			0.544592	−	0.838701i	$-0.316684\pi$
$503$	12287.2			1.08918			0.544592	+	0.838701i	$0.316684\pi$
$504$		0			0
$505$	−1842.45			−0.162352
$506$	−477.017	+	235.698i	−0.0419091	+	0.0207076i
$507$		0			0
$508$	3927.35	−	5134.67i	0.343008	−	0.448453i
$509$			450.441i			0.0392248i	0.999808	+	0.0196124i	$0.00624322\pi$
$509$			450.441i			0.0392248i	−0.999808	+	0.0196124i	$0.993757\pi$
$510$		0			0
$511$	−13829.2			−1.19720
$512$	9677.40	+	6369.11i	0.835322	+	0.549761i
$513$		0			0
$514$	−6473.52	−	13101.4i	−0.555515	−	1.12428i
$515$			6247.64i			0.534571i
$516$		0			0
$517$			1121.63i			0.0954141i
$518$	−7934.63	+	3920.57i	−0.673026	+	0.332548i
$519$		0			0
$520$	6514.02	+	1279.99i	0.549344	+	0.107945i
$521$	15088.1			1.26876			0.634378	−	0.773023i	$-0.281256\pi$
$521$	15088.1			1.26876			0.634378	+	0.773023i	$0.281256\pi$
$522$		0			0
$523$			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
$525$		0			0
$526$	−9229.33	−	18678.7i	−0.765053	−	1.54835i
$527$	−20967.6			−1.73314
$528$		0			0
$529$	−12083.0			−0.993096
$530$	−8337.69	−	16874.2i	−0.683332	−	1.38296i
$531$		0			0
$532$	−22607.6	−	17291.8i	−1.84241	−	1.40920i
$533$			9066.62i			0.736808i
$534$		0			0
$535$	−4186.08			−0.338280
$536$	−1655.40	+	8424.50i	−0.133400	+	0.678886i
$537$		0			0
$538$	−19976.3	+	9870.46i	−1.60082	+	0.790977i
$539$			8388.98i			0.670388i
$540$		0			0
$541$		−	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
$543$		0			0
$544$	−15159.0	+	13398.3i	−1.19474	+	1.05597i
$545$	5729.22			0.450299
$546$		0			0
$547$		−	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
$549$		0			0
$550$	2143.74	−	1059.24i	0.166199	−	0.0821205i
$551$	−5328.19			−0.411957
$552$		0			0
$553$	8274.05			0.636254
$554$	−11198.1	+	5533.10i	−0.858779	+	0.424330i
$555$		0			0
$556$	2235.29	+	1709.70i	0.170499	+	0.130409i
$557$			16555.5i			1.25938i	0.776845	+	0.629692i	$0.216819\pi$
$557$			16555.5i			1.25938i	−0.776845	+	0.629692i	$0.783181\pi$
$558$		0			0
$559$	2864.60			0.216743
$560$	15503.9	−	4205.77i	1.16992	−	0.317368i
$561$		0			0
$562$	10109.9	+	20461.0i	0.758830	+	1.53575i
$563$			12580.7i			0.941766i	0.882196	+	0.470883i	$0.156065\pi$
$563$			12580.7i			0.941766i	−0.882196	+	0.470883i	$0.843935\pi$
$564$		0			0
$565$		−	8982.30i		−	0.668829i
$566$	13290.3	−	6566.86i	0.986985	−	0.487678i
$567$		0			0
$568$	−6707.03	−	1317.92i	−0.495459	−	0.0973567i
$569$	−2657.93			−0.195828			−0.0979141	−	0.995195i	$-0.531217\pi$
$569$	−2657.93			−0.195828			−0.0979141	+	0.995195i	$0.531217\pi$
$570$		0			0
$571$			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
$573$		0			0
$574$	9718.86	+	19669.5i	0.706721	+	1.43029i
$575$	−377.497			−0.0273786
$576$		0			0
$577$	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
$579$		0			0
$580$	1826.99	−	2388.63i	0.130796	−	0.171004i
$581$		−	16423.1i		−	1.17271i
$582$		0			0
$583$	14919.3			1.05985
$584$	−11199.0	−	2200.59i	−0.793525	−	0.155926i
$585$		0			0
$586$	16159.8	−	7984.70i	1.13917	−	0.562876i
$587$			4096.53i			0.288044i	0.989574	+	0.144022i	$0.0460036\pi$
$587$			4096.53i			0.288044i	−0.989574	+	0.144022i	$0.953996\pi$
$588$		0			0
$589$		−	24344.5i		−	1.70305i
$590$	−2484.27	−	5027.79i	−0.173349	−	0.350832i
$591$		0			0
$592$	−7049.38	+	1912.30i	−0.489405	+	0.132762i
$593$	21988.3			1.52269			0.761343	−	0.648349i	$-0.224540\pi$
$593$	21988.3			1.52269			0.761343	+	0.648349i	$0.224540\pi$
$594$		0			0
$595$			28053.1i			1.93288i
$596$	8200.27	+	6272.13i	0.563584	+	0.431068i
$597$		0			0
$598$	744.794	−	368.009i	0.0509312	−	0.0251656i
$599$	−20767.7			−1.41660			−0.708302	−	0.705909i	$-0.750539\pi$
$599$	−20767.7			−1.41660			−0.708302	+	0.705909i	$0.750539\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	−5713.28	+	7469.62i	−0.384884	+	0.503203i
$605$			8328.33i			0.559661i
$606$		0			0
$607$	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
$609$		0			0
$610$	−8651.33	−	17509.0i	−0.574233	−	1.16216i
$611$		−	1751.26i		−	0.115955i
$612$		0			0
$613$			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
$615$		0			0
$616$	−2455.17	+	12494.6i	−0.160587	+	0.817243i
$617$	51.5882			0.00336607			0.00168303	−	0.999999i	$-0.499464\pi$
$617$	51.5882			0.00336607			0.00168303	+	0.999999i	$0.499464\pi$
$618$		0			0
$619$		−	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
$621$		0			0
$622$	−10157.3	−	20556.8i	−0.654775	−	1.32516i
$623$	7609.11			0.489330
$624$		0			0
$625$	−8779.94			−0.561916
$626$	701.629	+	1419.99i	0.0447967	+	0.0906616i
$627$		0			0
$628$	−6939.53	−	5307.83i	−0.440951	−	0.337270i
$629$		−	12755.3i		−	0.808567i
$630$		0			0
$631$	−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
$633$		0			0
$634$	14780.9	−	7303.39i	0.925909	−	0.457500i
$635$		−	7397.63i		−	0.462309i
$636$		0			0
$637$		−	13098.2i		−	0.814709i
$638$	1055.95	+	2137.09i	0.0655260	+	0.132615i
$639$		0			0
$640$	13224.4	−	938.802i	0.816780	−	0.0579835i
$641$	20406.3			1.25741			0.628705	−	0.777644i	$-0.283585\pi$
$641$	20406.3			1.25741			0.628705	+	0.777644i	$0.283585\pi$
$642$		0			0
$643$		−	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
$645$		0			0
$646$	36776.2	−	18171.4i	2.23984	−	1.10673i
$647$	8167.12			0.496264			0.248132	−	0.968726i	$-0.420183\pi$
$647$	8167.12			0.496264			0.248132	+	0.968726i	$0.420183\pi$
$648$		0			0
$649$	4445.31			0.268866
$650$	−3347.15	+	1653.86i	−0.201978	+	0.0997993i
$651$		0			0
$652$	23047.1	+	17628.0i	1.38435	+	1.05884i
$653$			7444.93i			0.446160i	0.974800	+	0.223080i	$0.0716111\pi$
$653$			7444.93i			0.446160i	−0.974800	+	0.223080i	$0.928389\pi$
$654$		0			0
$655$	−10169.7			−0.606662
$656$	4740.49	+	17475.0i	0.282142	+	1.04007i
$657$		0			0
$658$	−1877.24	−	3799.25i	−0.111220	−	0.225092i
$659$		−	23780.4i		−	1.40569i	−0.711342	−	0.702846i	$-0.751912\pi$
$659$		−	23780.4i		−	1.40569i	0.711342	−	0.702846i	$-0.248088\pi$
$660$		0			0
$661$		−	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
$663$		0			0
$664$	2613.34	−	13299.6i	0.152737	−	0.777294i
$665$	−32571.2			−1.89933
$666$		0			0
$667$		−	376.324i		−	0.0218461i
$668$	222.605	−	291.037i	0.0128935	−	0.0168571i
$669$		0			0
$670$	4352.31	+	8808.40i	0.250962	+	0.507908i
$671$	15480.5			0.890640
$672$		0			0
$673$	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
$675$		0			0
$676$	−5686.41	+	7434.49i	−0.323532	+	0.422991i
$677$		−	24191.5i		−	1.37335i	−0.726966	−	0.686673i	$-0.759070\pi$
$677$		−	24191.5i		−	1.37335i	0.726966	−	0.686673i	$-0.240930\pi$
$678$		0			0
$679$	−20999.2			−1.18685
$680$	−4463.96	+	22717.6i	−0.251743	+	1.28115i
$681$		0			0
$682$	−9764.35	+	4824.65i	−0.548235	+	0.270888i
$683$			13965.2i			0.782376i	0.920311	+	0.391188i	$0.127936\pi$
$683$			13965.2i			0.782376i	−0.920311	+	0.391188i	$0.872064\pi$
$684$		0			0
$685$			4273.17i			0.238350i
$686$	−2257.54	−	4568.91i	−0.125646	−	0.254288i
$687$		0			0
$688$	5521.23	−	1497.76i	0.305952	−	0.0829962i
$689$	−23294.4			−1.28802
$690$		0			0
$691$			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
$693$		0			0
$694$	−25733.5	+	12715.2i	−1.40754	+	0.695477i
$695$	3220.43			0.175767
$696$		0			0
$697$	−31619.7			−1.71834
$698$	24130.3	−	11923.0i	1.30852	−	0.646550i
$699$		0			0
$700$	−5488.61	+	7175.88i	−0.296357	+	0.387461i
$701$		−	25942.2i		−	1.39775i	−0.715243	−	0.698876i	$-0.753684\pi$
$701$		−	25942.2i		−	1.39775i	0.715243	−	0.698876i	$-0.246316\pi$
$702$		0			0
$703$	14809.6			0.794532
$704$	−3976.42	+	9727.53i	−0.212879	+	0.520767i
$705$		0			0
$706$	3525.24	+	7134.54i	0.187924	+	0.380329i
$707$			5517.86i			0.293522i
$708$		0			0
$709$			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
$711$		0			0
$712$	6161.91	+	1210.80i	0.324336	+	0.0637314i
$713$	1719.43			0.0903128
$714$		0			0
$715$			6021.82i			0.314970i
$716$	6521.33	+	4987.96i	0.340382	+	0.260348i
$717$		0			0
$718$	−3041.21	−	6154.94i	−0.158074	−	0.319917i
$719$	−17141.2			−0.889094			−0.444547	−	0.895756i	$-0.646635\pi$
$719$	−17141.2			−0.889094			−0.444547	+	0.895756i	$0.646635\pi$
$720$		0			0
$721$	18710.8			0.966470
$722$	12504.0	+	25306.3i	0.644532	+	1.30443i
$723$		0			0
$724$	23505.1	+	17978.3i	1.20658	+	0.922873i
$725$			1691.23i			0.0866352i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−11709.4	+	5785.69i	−0.593675	+	0.293340i
$731$			9990.26i			0.505476i
$732$		0			0
$733$		−	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
$735$		0			0
$736$	1243.10	−	1098.72i	0.0622572	−	0.0550261i
$737$	−7787.94			−0.389243
$738$		0			0
$739$		−	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
$741$		0			0
$742$	−50535.7	+	24970.1i	−2.50030	+	1.23542i
$743$	1772.73			0.0875303			0.0437652	−	0.999042i	$-0.486065\pi$
$743$	1772.73			0.0875303			0.0437652	+	0.999042i	$0.486065\pi$
$744$		0			0
$745$	11814.3			0.580997
$746$	−8069.82	+	3987.37i	−0.396055	+	0.195694i
$747$		0			0
$748$	−14576.8	−	11149.3i	−0.712539	−	0.544999i
$749$			12536.7i			0.611589i
$750$		0			0
$751$	−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
$753$		0			0
$754$	−1648.72	−	3336.75i	−0.0796324	−	0.161164i
$755$			10761.6i			0.518750i
$756$		0			0
$757$			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
$759$		0			0
$760$	−26376.3	−	5182.90i	−1.25891	−	0.247373i
$761$	−18393.5			−0.876166			−0.438083	−	0.898934i	$-0.644342\pi$
$761$	−18393.5			−0.876166			−0.438083	+	0.898934i	$0.644342\pi$
$762$		0			0
$763$		−	17158.2i		−	0.814112i
$764$	24830.7	−	32464.0i	1.17584	−	1.53731i
$765$		0			0
$766$	9209.38	+	18638.4i	0.434397	+	0.879153i
$767$	−6940.72			−0.326747
$768$		0			0
$769$	−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
$771$		0			0
$772$	6873.05	−	8985.92i	0.320423	−	0.418925i
$773$			16256.4i			0.756405i	0.925723	+	0.378202i	$0.123458\pi$
$773$			16256.4i			0.756405i	−0.925723	+	0.378202i	$0.876542\pi$
$774$		0			0
$775$	−7727.21			−0.358154
$776$	−17005.3	−	3341.50i	−0.786667	−	0.154578i
$777$		0			0
$778$	32988.1	−	16299.7i	1.52016	−	0.751122i
$779$		−	36712.2i		−	1.68851i
$780$		0			0
$781$		−	6200.24i		−	0.284074i
$782$	1283.43	+	2597.46i	0.0586896	+	0.118779i
$783$		0			0
$784$	−6848.40	−	25245.5i	−0.311971	−	1.15003i
$785$	−9997.92			−0.454575
$786$		0			0
$787$		−	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
$789$		0			0
$790$	7005.72	−	3461.59i	0.315509	−	0.155896i
$791$	−26900.7			−1.20920
$792$		0			0
$793$	−24170.6			−1.08238
$794$	12369.2	−	6111.72i	0.552853	−	0.273170i
$795$		0			0
$796$	4610.22	−	6027.47i	0.205283	−	0.268389i
$797$			32966.9i			1.46518i	0.680672	+	0.732589i	$0.261688\pi$
$797$			32966.9i			1.46518i	−0.680672	+	0.732589i	$0.738312\pi$
$798$		0			0
$799$	6107.50			0.270423
$800$	−5586.58	+	4937.70i	−0.246894	+	0.218218i
$801$		0			0
$802$	6956.76	+	14079.4i	0.306299	+	0.619902i
$803$		−	10352.8i		−	0.454973i
$804$		0			0
$805$		−	2300.47i		−	0.100721i
$806$	15245.6	−	7533.00i	0.666259	−	0.329204i
$807$		0			0
$808$	−878.031	+	4468.40i	−0.0382290	+	0.194552i
$809$	41700.3			1.81224			0.906122	−	0.423017i	$-0.139029\pi$
$809$	41700.3			1.81224			0.906122	+	0.423017i	$0.139029\pi$
$810$		0			0
$811$			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
$813$		0			0
$814$	−2935.01	−	5940.00i	−0.126378	−	0.255770i
$815$	33204.4			1.42712
$816$		0			0
$817$	−11599.2			−0.496702
$818$	−8757.18	−	17723.2i	−0.374312	−	0.757551i
$819$		0			0
$820$	16458.1	+	12588.3i	0.700905	+	0.536100i
$821$		−	9846.06i		−	0.418550i	−0.977857	−	0.209275i	$-0.932890\pi$
$821$		−	9846.06i		−	0.418550i	0.977857	−	0.209275i	$-0.0671104\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	−15057.5	+	7440.03i	−0.634282	+	0.313404i
$827$		−	21727.4i		−	0.913587i	−0.889573	−	0.456794i	$-0.848998\pi$
$827$		−	21727.4i		−	0.913587i	0.889573	−	0.456794i	$-0.151002\pi$
$828$		0			0
$829$			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
$831$		0			0
$832$	6208.61	−	15188.2i	0.258708	−	0.632878i
$833$	45679.8			1.90002
$834$		0			0
$835$		−	419.304i		−	0.0173780i
$836$	12945.0	−	16924.4i	0.535539	−	0.700171i
$837$		0			0
$838$	26526.7	−	13107.1i	1.09350	−	0.540306i
$839$	−11010.4			−0.453064			−0.226532	−	0.974004i	$-0.572739\pi$
$839$	−11010.4			−0.453064			−0.226532	+	0.974004i	$0.572739\pi$
$840$		0			0
$841$	22703.0			0.930872
$842$	−11787.7	+	5824.39i	−0.482458	+	0.238387i
$843$		0			0
$844$	−28513.8	−	21809.3i	−1.16290	−	0.889465i
$845$			10711.0i			0.436059i
$846$		0			0
$847$	24942.1			1.01183
$848$	−44897.5	+	12179.5i	−1.81815	+	0.493213i
$849$		0			0
$850$	−5767.81	−	11673.2i	−0.232746	−	0.471042i
$851$			1045.99i			0.0421340i
$852$		0			0
$853$			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
$855$		0			0
$856$	−1994.90	+	10152.3i	−0.0796547	+	0.405372i
$857$	−8848.01			−0.352675			−0.176337	−	0.984330i	$-0.556425\pi$
$857$	−8848.01			−0.352675			−0.176337	+	0.984330i	$0.556425\pi$
$858$		0			0
$859$			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
$861$		0			0
$862$	15650.1	+	31673.5i	0.618382	+	1.25151i
$863$	33669.9			1.32808			0.664042	−	0.747695i	$-0.268839\pi$
$863$	33669.9			1.32808			0.664042	+	0.747695i	$0.268839\pi$
$864$		0			0
$865$	−22475.3			−0.883450
$866$	−11835.8	−	23953.8i	−0.464430	−	0.939936i
$867$		0			0
$868$	24999.6	−	32684.8i	0.977582	−	1.27810i
$869$			6194.10i			0.241796i
$870$		0			0
$871$	12159.7			0.473039
$872$	2730.30	−	13894.8i	0.106032	−	0.539607i
$873$		0			0
$874$	−3015.79	+	1490.13i	−0.116717	+	0.0576709i
$875$			41713.8i			1.61164i
$876$		0			0
$877$			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
$879$		0			0
$880$	3148.51	+	11606.5i	0.120609	+	0.444606i
$881$	−18716.9			−0.715766			−0.357883	−	0.933766i	$-0.616501\pi$
$881$	−18716.9			−0.715766			−0.357883	+	0.933766i	$0.616501\pi$
$882$		0			0
$883$		−	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
$885$		0			0
$886$	−19275.3	+	9524.10i	−0.730888	+	0.361138i
$887$	15544.6			0.588429			0.294215	−	0.955739i	$-0.404942\pi$
$887$	15544.6			0.588429			0.294215	+	0.955739i	$0.404942\pi$
$888$		0			0
$889$	−22154.8			−0.835825
$890$	6442.71	−	3183.40i	0.242652	−	0.119896i
$891$		0			0
$892$	22313.3	−	29172.7i	0.837562	−	1.09504i
$893$			7091.14i			0.265729i
$894$		0			0
$895$	9395.42			0.350898
$896$	−2811.57	−	39605.0i	−0.104830	−	1.47669i
$897$		0			0
$898$	13417.6	+	27155.1i	0.498609	+	1.00911i
$899$		−	7703.21i		−	0.285780i
$900$		0			0
$901$		−	81238.8i		−	3.00384i
$902$	−14724.9	+	7275.71i	−0.543555	+	0.268575i
$903$		0			0
$904$	−21784.3	−	4280.58i	−0.801478	−	0.157489i
$905$	33864.3			1.24385
$906$		0			0
$907$		−	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
$909$		0			0
$910$	−10078.6	−	20397.5i	−0.367145	−	0.743046i
$911$	−1975.97			−0.0718627			−0.0359313	−	0.999354i	$-0.511440\pi$
$911$	−1975.97			−0.0718627			−0.0359313	+	0.999354i	$0.511440\pi$
$912$		0			0
$913$	12294.6			0.445666
$914$	−292.988	−	592.964i	−0.0106031	−	0.0214590i
$915$		0			0
$916$	−220.047	−	168.307i	−0.00793730	−	0.00607099i
$917$			30456.8i			1.09681i
$918$		0			0
$919$	−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
$921$		0			0
$922$	−2488.37	+	1229.52i	−0.0888829	+	0.0439178i
$923$			9680.79i			0.345230i
$924$		0			0
$925$		−	4700.74i		−	0.167091i
$926$	17644.9	+	35710.6i	0.626185	+	1.26730i
$927$		0			0
$928$	−4922.36	−	5569.23i	−0.174121	−	0.197003i
$929$	−12506.8			−0.441697			−0.220848	−	0.975308i	$-0.570883\pi$
$929$	−12506.8			−0.441697			−0.220848	+	0.975308i	$0.570883\pi$
$930$		0			0
$931$			53036.7i			1.86703i
$932$	−5122.78	+	6697.59i	−0.180045	+	0.235394i
$933$		0			0
$934$	−23548.4	+	11635.5i	−0.824976	+	0.407628i
$935$	−21001.0			−0.734554
$936$		0			0
$937$	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
$939$		0			0
$940$	−3178.96	−	2431.49i	−0.110305	−	0.0843685i
$941$		−	23727.2i		−	0.821981i	−0.911640	−	0.410991i	$-0.865183\pi$
$941$		−	23727.2i		−	0.821981i	0.911640	−	0.410991i	$-0.134817\pi$
$942$		0			0
$943$	2592.94			0.0895418
$944$	−13377.5	+	3628.96i	−0.461231	+	0.125119i
$945$		0			0
$946$	2298.76	+	4652.34i	0.0790054	+	0.159895i
$947$			23399.8i			0.802948i	0.915870	+	0.401474i	$0.131502\pi$
$947$			23399.8i			0.802948i	−0.915870	+	0.401474i	$0.868498\pi$
$948$		0			0
$949$			16164.4i			0.552919i
$950$	13553.2	−	6696.73i	0.462866	−	0.228706i
$951$		0			0
$952$	68035.8	+	13368.9i	2.31623	+	0.455135i
$953$	−41497.1			−1.41052			−0.705258	−	0.708950i	$-0.749169\pi$
$953$	−41497.1			−1.41052			−0.705258	+	0.708950i	$0.749169\pi$
$954$		0			0
$955$		−	46771.6i		−	1.58481i
$956$	−3182.01	+	4160.20i	−0.107650	+	0.140743i
$957$		0			0
$958$	−24318.8	−	49217.6i	−0.820152	−	1.65986i
$959$	12797.5			0.430921
$960$		0			0
$961$	5405.00			0.181431
$962$	4582.59	+	9274.46i	0.153585	+	0.310832i
$963$		0			0
$964$	−15523.6	+	20295.8i	−0.518654	+	0.678096i
$965$		−	12946.2i		−	0.431868i
$966$		0			0
$967$	−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
$969$		0			0
$970$	−17780.2	+	8785.35i	−0.588544	+	0.290805i
$971$		−	20346.8i		−	0.672462i	−0.941780	−	0.336231i	$-0.890848\pi$
$971$		−	20346.8i		−	0.672462i	0.941780	−	0.336231i	$-0.109152\pi$
$972$		0			0
$973$		−	9644.71i		−	0.317775i
$974$	−15191.7	−	30745.6i	−0.499766	−	1.01145i
$975$		0			0
$976$	−46586.5	+	12637.6i	−1.52787	+	0.414468i
$977$	−40602.1			−1.32955			−0.664777	−	0.747042i	$-0.731474\pi$
$977$	−40602.1			−1.32955			−0.664777	+	0.747042i	$0.731474\pi$
$978$		0			0
$979$			5696.32i			0.185960i
$980$	−23776.4	−	18185.8i	−0.775009	−	0.592781i
$981$		0			0
$982$	12934.2	−	6390.89i	0.420312	−	0.207680i
$983$	−50425.9			−1.63615			−0.818075	−	0.575112i	$-0.804959\pi$
$983$	−50425.9			−1.63615			−0.818075	+	0.575112i	$0.804959\pi$
$984$		0			0
$985$	25786.2			0.834127
$986$	11636.9	−	5749.89i	0.375856	−	0.185714i
$987$		0			0
$988$	−20211.7	+	26425.0i	−0.650829	+	0.850903i
$989$		−	819.241i		−	0.0263401i
$990$		0			0
$991$	−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
$993$		0			0
$994$	10377.2	+	21001.9i	0.331132	+	0.670161i
$995$		−	8683.90i		−	0.276681i
$996$		0			0
$997$			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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.4.d.a.13.3	✓	6	24.5	odd	2
24.4.d.a.13.4	yes	6	3.2	odd	2
72.4.d.d.37.3		6	1.1	even	1	trivial
72.4.d.d.37.4		6	8.5	even	2	inner
96.4.d.a.49.1		6	12.11	even	2
96.4.d.a.49.6		6	24.11	even	2
288.4.d.d.145.2		6	8.3	odd	2
288.4.d.d.145.5		6	4.3	odd	2
768.4.a.q.1.3		3	48.11	even	4
768.4.a.r.1.1		3	48.29	odd	4
768.4.a.s.1.3		3	48.5	odd	4
768.4.a.t.1.1		3	48.35	even	4
2304.4.a.bt.1.3		3	16.13	even	4
2304.4.a.bu.1.3		3	16.3	odd	4
2304.4.a.bv.1.1		3	16.5	even	4
2304.4.a.bw.1.1		3	16.11	odd	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25295 - 2.53577i) q^{2} +(-4.86025 + 6.35436i) q^{4} +9.15486i q^{5} +27.4175 q^{7} +(22.2028 + 4.36281i) q^{8} +O(q^{10})\)	\(q+(-1.25295 - 2.53577i) q^{2} +(-4.86025 + 6.35436i) q^{4} +9.15486i q^{5} +27.4175 q^{7} +(22.2028 + 4.36281i) q^{8} +(23.2146 - 11.4705i) q^{10} +20.5252i q^{11} -32.0471i q^{13} +(-34.3526 - 69.5243i) q^{14} +(-16.7559 - 61.7676i) q^{16} +111.764 q^{17} +129.764i q^{19} +(-58.1733 - 44.4950i) q^{20} +(52.0471 - 25.7169i) q^{22} -9.16510 q^{23} +41.1885 q^{25} +(-81.2641 + 40.1533i) q^{26} +(-133.256 + 174.220i) q^{28} +41.0606i q^{29} -187.606 q^{31} +(-135.634 + 119.880i) q^{32} +(-140.034 - 283.408i) q^{34} +251.003i q^{35} -114.127i q^{37} +(329.052 - 162.587i) q^{38} +(-39.9409 + 203.264i) q^{40} -282.915 q^{41} +89.3870i q^{43} +(-130.424 - 99.7576i) q^{44} +(11.4834 + 23.2406i) q^{46} +54.6464 q^{47} +408.717 q^{49} +(-51.6070 - 104.445i) q^{50} +(203.639 + 155.757i) q^{52} -726.878i q^{53} -187.905 q^{55} +(608.745 + 119.617i) q^{56} +(104.120 - 51.4467i) q^{58} -216.579i q^{59} -754.222i q^{61} +(235.060 + 475.726i) q^{62} +(473.932 + 193.734i) q^{64} +293.387 q^{65} +379.433i q^{67} +(-543.202 + 710.189i) q^{68} +(636.486 - 314.493i) q^{70} -302.080 q^{71} -504.396 q^{73} +(-289.401 + 142.995i) q^{74} +(-824.568 - 630.686i) q^{76} +562.748i q^{77} +301.780 q^{79} +(565.474 - 153.398i) q^{80} +(354.477 + 717.408i) q^{82} -599.003i q^{83} +1023.18i q^{85} +(226.665 - 111.997i) q^{86} +(-89.5475 + 455.717i) q^{88} +277.528 q^{89} -878.651i q^{91} +(44.5447 - 58.2383i) q^{92} +(-68.4689 - 138.571i) q^{94} -1187.97 q^{95} -765.905 q^{97} +(-512.100 - 1036.41i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 76 * q^8	\( 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8} + 60 q^{10} + 100 q^{14} + 56 q^{16} - 52 q^{17} - 56 q^{20} + 224 q^{22} - 328 q^{23} - 106 q^{25} - 56 q^{26} - 352 q^{28} - 636 q^{31} + 248 q^{32} - 548 q^{34} + 776 q^{38} + 232 q^{40} - 236 q^{41} - 1152 q^{44} + 328 q^{46} + 408 q^{47} + 654 q^{49} - 1970 q^{50} - 368 q^{52} + 1024 q^{55} + 1864 q^{56} + 140 q^{58} + 2108 q^{62} + 832 q^{64} + 1744 q^{65} - 2976 q^{68} + 1352 q^{70} + 1704 q^{71} + 956 q^{73} - 1568 q^{74} - 1744 q^{76} - 44 q^{79} + 2112 q^{80} - 2236 q^{82} + 760 q^{86} + 1856 q^{88} + 220 q^{89} - 1728 q^{92} + 2088 q^{94} - 5104 q^{95} - 2444 q^{97} - 3354 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 76 * q^8 + 60 * q^10 + 100 * q^14 + 56 * q^16 - 52 * q^17 - 56 * q^20 + 224 * q^22 - 328 * q^23 - 106 * q^25 - 56 * q^26 - 352 * q^28 - 636 * q^31 + 248 * q^32 - 548 * q^34 + 776 * q^38 + 232 * q^40 - 236 * q^41 - 1152 * q^44 + 328 * q^46 + 408 * q^47 + 654 * q^49 - 1970 * q^50 - 368 * q^52 + 1024 * q^55 + 1864 * q^56 + 140 * q^58 + 2108 * q^62 + 832 * q^64 + 1744 * q^65 - 2976 * q^68 + 1352 * q^70 + 1704 * q^71 + 956 * q^73 - 1568 * q^74 - 1744 * q^76 - 44 * q^79 + 2112 * q^80 - 2236 * q^82 + 760 * q^86 + 1856 * q^88 + 220 * q^89 - 1728 * q^92 + 2088 * q^94 - 5104 * q^95 - 2444 * q^97 - 3354 * q^98

Introduction

L-functions

Modular forms

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