LMFDB - Embedded newform 37.6.b.a.36.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,6,Mod(36,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("37.36");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	37.b (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:	$5.93420133308$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 390 x^{14} + 60701 x^{12} + 4799932 x^{10} + 203487156 x^{8} + 4519465040 x^{6} + \cdots + 178006118400 $ x^16 + 390x^14 + 60701x^12 + 4799932x^10 + 203487156x^8 + 4519465040x^6 + 48993644736x^4 + 211923220224*x^2 + 178006118400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			36.15
Root			$9.87320i$ of defining polynomial
Character	$\chi$	$=$	37.36
Dual form			37.6.b.a.36.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.87320i q^{2} -2.75305 q^{3} -65.4800 q^{4} -100.817i q^{5} -27.1814i q^{6} -37.8971 q^{7} -330.555i q^{8} -235.421 q^{9} +O(q^{10})$	\(q+9.87320i q^{2} -2.75305 q^{3} -65.4800 q^{4} -100.817i q^{5} -27.1814i q^{6} -37.8971 q^{7} -330.555i q^{8} -235.421 q^{9} +995.382 q^{10} -284.206 q^{11} +180.270 q^{12} +736.146i q^{13} -374.166i q^{14} +277.553i q^{15} +1168.27 q^{16} -1303.38i q^{17} -2324.35i q^{18} -2224.12i q^{19} +6601.47i q^{20} +104.333 q^{21} -2806.02i q^{22} +2543.87i q^{23} +910.033i q^{24} -7038.98 q^{25} -7268.11 q^{26} +1317.12 q^{27} +2481.50 q^{28} +606.649i q^{29} -2740.33 q^{30} +5882.99i q^{31} +956.815i q^{32} +782.432 q^{33} +12868.6 q^{34} +3820.66i q^{35} +15415.3 q^{36} +(-3504.92 - 7553.78i) q^{37} +21959.2 q^{38} -2026.65i q^{39} -33325.4 q^{40} -9705.95 q^{41} +1030.10i q^{42} -5693.02i q^{43} +18609.8 q^{44} +23734.3i q^{45} -25116.2 q^{46} +25290.9 q^{47} -3216.31 q^{48} -15370.8 q^{49} -69497.2i q^{50} +3588.28i q^{51} -48202.8i q^{52} +9013.32 q^{53} +13004.1i q^{54} +28652.6i q^{55} +12527.1i q^{56} +6123.11i q^{57} -5989.57 q^{58} -15172.6i q^{59} -18174.2i q^{60} +29053.1i q^{61} -58083.9 q^{62} +8921.77 q^{63} +27937.8 q^{64} +74215.7 q^{65} +7725.10i q^{66} -149.609 q^{67} +85345.6i q^{68} -7003.41i q^{69} -37722.1 q^{70} -39655.1 q^{71} +77819.4i q^{72} -39371.7 q^{73} +(74579.9 - 34604.7i) q^{74} +19378.7 q^{75} +145635. i q^{76} +10770.6 q^{77} +20009.5 q^{78} -83704.0i q^{79} -117781. i q^{80} +53581.2 q^{81} -95828.7i q^{82} -36443.3 q^{83} -6831.70 q^{84} -131403. q^{85} +56208.3 q^{86} -1670.14i q^{87} +93945.5i q^{88} +63406.6i q^{89} -234333. q^{90} -27897.8i q^{91} -166573. i q^{92} -16196.1i q^{93} +249702. i q^{94} -224228. q^{95} -2634.16i q^{96} -16855.7i q^{97} -151759. i q^{98} +66907.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 18 q^{3} - 268 q^{4} + 190 q^{7} + 1394 q^{9}+O(q^{10}) $ 16 * q - 18 * q^3 - 268 * q^4 + 190 * q^7 + 1394 * q^9	$ 16 q - 18 q^{3} - 268 q^{4} + 190 q^{7} + 1394 q^{9} - 74 q^{10} - 1110 q^{11} + 1402 q^{12} + 2900 q^{16} - 7010 q^{21} - 12052 q^{25} + 4902 q^{26} + 4266 q^{27} - 16824 q^{28} + 19280 q^{30} - 2478 q^{33} + 20556 q^{34} - 51402 q^{36} - 11400 q^{37} + 12108 q^{38} + 16966 q^{40} + 3918 q^{41} + 125394 q^{44} + 17470 q^{46} + 3822 q^{47} - 78034 q^{48} - 32618 q^{49} - 24126 q^{53} - 164718 q^{58} - 81426 q^{62} + 219268 q^{63} + 158076 q^{64} + 98976 q^{65} + 23560 q^{67} - 222404 q^{70} - 50046 q^{71} - 196274 q^{73} + 141216 q^{74} + 214054 q^{75} - 239574 q^{77} - 90822 q^{78} + 317312 q^{81} - 215814 q^{83} + 438572 q^{84} - 346472 q^{85} + 197640 q^{86} - 857612 q^{90} - 132504 q^{95} - 574860 q^{99}+O(q^{100}) $ 16 * q - 18 * q^3 - 268 * q^4 + 190 * q^7 + 1394 * q^9 - 74 * q^10 - 1110 * q^11 + 1402 * q^12 + 2900 * q^16 - 7010 * q^21 - 12052 * q^25 + 4902 * q^26 + 4266 * q^27 - 16824 * q^28 + 19280 * q^30 - 2478 * q^33 + 20556 * q^34 - 51402 * q^36 - 11400 * q^37 + 12108 * q^38 + 16966 * q^40 + 3918 * q^41 + 125394 * q^44 + 17470 * q^46 + 3822 * q^47 - 78034 * q^48 - 32618 * q^49 - 24126 * q^53 - 164718 * q^58 - 81426 * q^62 + 219268 * q^63 + 158076 * q^64 + 98976 * q^65 + 23560 * q^67 - 222404 * q^70 - 50046 * q^71 - 196274 * q^73 + 141216 * q^74 + 214054 * q^75 - 239574 * q^77 - 90822 * q^78 + 317312 * q^81 - 215814 * q^83 + 438572 * q^84 - 346472 * q^85 + 197640 * q^86 - 857612 * q^90 - 132504 * q^95 - 574860 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			9.87320i			1.74535i	0.488301	+	0.872675i	$0.337617\pi$
$2$			9.87320i			1.74535i	−0.488301	+	0.872675i	$0.662383\pi$
$3$	−2.75305			−0.176608			−0.0883041	−	0.996094i	$-0.528145\pi$
$3$	−2.75305			−0.176608			−0.0883041	+	0.996094i	$0.528145\pi$
$4$	−65.4800			−2.04625
$5$		−	100.817i		−	1.80346i	−0.432298	−	0.901731i	$-0.642297\pi$
$5$		−	100.817i		−	1.80346i	0.432298	−	0.901731i	$-0.357703\pi$
$6$		−	27.1814i		−	0.308243i
$7$	−37.8971			−0.292322			−0.146161	−	0.989261i	$-0.546692\pi$
$7$	−37.8971			−0.292322			−0.146161	+	0.989261i	$0.546692\pi$
$8$		−	330.555i		−	1.82607i
$9$	−235.421			−0.968810
$10$	995.382			3.14767
$11$	−284.206			−0.708192			−0.354096	−	0.935209i	$-0.615211\pi$
$11$	−284.206			−0.708192			−0.354096	+	0.935209i	$0.615211\pi$
$12$	180.270			0.361384
$13$			736.146i			1.20811i	0.796944	+	0.604054i	$0.206449\pi$
$13$			736.146i			1.20811i	−0.796944	+	0.604054i	$0.793551\pi$
$14$		−	374.166i		−	0.510204i
$15$			277.553i			0.318506i
$16$	1168.27			1.14089
$17$		−	1303.38i		−	1.09383i	−0.837188	−	0.546916i	$-0.815802\pi$
$17$		−	1303.38i		−	1.09383i	0.837188	−	0.546916i	$-0.184198\pi$
$18$		−	2324.35i		−	1.69091i
$19$		−	2224.12i		−	1.41343i	−0.707499	−	0.706715i	$-0.750176\pi$
$19$		−	2224.12i		−	1.41343i	0.707499	−	0.706715i	$-0.249824\pi$
$20$			6601.47i			3.69033i
$21$	104.333			0.0516264
$22$		−	2806.02i		−	1.23604i
$23$			2543.87i			1.00271i	0.865241	+	0.501356i	$0.167165\pi$
$23$			2543.87i			1.00271i	−0.865241	+	0.501356i	$0.832835\pi$
$24$			910.033i			0.322499i
$25$	−7038.98			−2.25247
$26$	−7268.11			−2.10857
$27$	1317.12			0.347708
$28$	2481.50			0.598163
$29$			606.649i			0.133950i	0.997755	+	0.0669750i	$0.0213348\pi$
$29$			606.649i			0.133950i	−0.997755	+	0.0669750i	$0.978665\pi$
$30$	−2740.33			−0.555905
$31$			5882.99i			1.09950i	0.835331	+	0.549748i	$0.185276\pi$
$31$			5882.99i			1.09950i	−0.835331	+	0.549748i	$0.814724\pi$
$32$			956.815i			0.165178i
$33$	782.432			0.125072
$34$	12868.6			1.90912
$35$			3820.66i			0.527191i
$36$	15415.3			1.98243
$37$	−3504.92	−	7553.78i	−0.420895	−	0.907110i
$37$	−3504.92	−	7553.78i	−0.420895	−	0.907110i
$38$	21959.2			2.46693
$39$		−	2026.65i		−	0.213362i
$40$	−33325.4			−3.29325
$41$	−9705.95			−0.901734			−0.450867	−	0.892591i	$-0.648885\pi$
$41$	−9705.95			−0.901734			−0.450867	+	0.892591i	$0.648885\pi$
$42$			1030.10i			0.0901062i
$43$		−	5693.02i		−	0.469539i	−0.972051	−	0.234770i	$-0.924566\pi$
$43$		−	5693.02i		−	0.469539i	0.972051	−	0.234770i	$-0.0754335\pi$
$44$	18609.8			1.44914
$45$			23734.3i			1.74721i
$46$	−25116.2			−1.75008
$47$	25290.9			1.67001			0.835004	−	0.550243i	$-0.185465\pi$
$47$	25290.9			1.67001			0.835004	+	0.550243i	$0.185465\pi$
$48$	−3216.31			−0.201490
$49$	−15370.8			−0.914548
$50$		−	69497.2i		−	3.93136i
$51$			3588.28i			0.193180i
$52$		−	48202.8i		−	2.47209i
$53$	9013.32			0.440753			0.220376	−	0.975415i	$-0.429271\pi$
$53$	9013.32			0.440753			0.220376	+	0.975415i	$0.429271\pi$
$54$			13004.1i			0.606872i
$55$			28652.6i			1.27720i
$56$			12527.1i			0.533801i
$57$			6123.11i			0.249623i
$58$	−5989.57			−0.233790
$59$		−	15172.6i		−	0.567452i	−0.958905	−	0.283726i	$-0.908429\pi$
$59$		−	15172.6i		−	0.567452i	0.958905	−	0.283726i	$-0.0915706\pi$
$60$		−	18174.2i		−	0.651743i
$61$			29053.1i			0.999695i	0.866113	+	0.499847i	$0.166611\pi$
$61$			29053.1i			0.999695i	−0.866113	+	0.499847i	$0.833389\pi$
$62$	−58083.9			−1.91901
$63$	8921.77			0.283204
$64$	27937.8			0.852595
$65$	74215.7			2.17878
$66$			7725.10i			0.218295i
$67$	−149.609			−0.00407165			−0.00203582	−	0.999998i	$-0.500648\pi$
$67$	−149.609			−0.00407165			−0.00203582	+	0.999998i	$0.500648\pi$
$68$			85345.6i			2.23825i
$69$		−	7003.41i		−	0.177087i
$70$	−37722.1			−0.920133
$71$	−39655.1			−0.933584			−0.466792	−	0.884367i	$-0.654590\pi$
$71$	−39655.1			−0.933584			−0.466792	+	0.884367i	$0.654590\pi$
$72$			77819.4i			1.76912i
$73$	−39371.7			−0.864723			−0.432361	−	0.901700i	$-0.642319\pi$
$73$	−39371.7			−0.864723			−0.432361	+	0.901700i	$0.642319\pi$
$74$	74579.9	−	34604.7i	1.58322	−	0.734609i
$75$	19378.7			0.397805
$76$			145635.i			2.89223i
$77$	10770.6			0.207020
$78$	20009.5			0.372391
$79$		−	83704.0i		−	1.50896i	−0.656322	−	0.754481i	$-0.727889\pi$
$79$		−	83704.0i		−	1.50896i	0.656322	−	0.754481i	$-0.272111\pi$
$80$		−	117781.i		−	2.05755i
$81$	53581.2			0.907402
$82$		−	95828.7i		−	1.57384i
$83$	−36443.3			−0.580660			−0.290330	−	0.956927i	$-0.593765\pi$
$83$	−36443.3			−0.580660			−0.290330	+	0.956927i	$0.593765\pi$
$84$	−6831.70			−0.105641
$85$	−131403.			−1.97268
$86$	56208.3			0.819510
$87$		−	1670.14i		−	0.0236567i
$88$			93945.5i			1.29321i
$89$			63406.6i			0.848515i	0.905542	+	0.424258i	$0.139465\pi$
$89$			63406.6i			0.848515i	−0.905542	+	0.424258i	$0.860535\pi$
$90$	−234333.			−3.04950
$91$		−	27897.8i		−	0.353156i
$92$		−	166573.i		−	2.05180i
$93$		−	16196.1i		−	0.194180i
$94$			249702.i			2.91475i
$95$	−224228.			−2.54907
$96$		−	2634.16i		−	0.0291718i
$97$		−	16855.7i		−	0.181893i	−0.995856	−	0.0909467i	$-0.971011\pi$
$97$		−	16855.7i		−	0.181893i	0.995856	−	0.0909467i	$-0.0289893\pi$
$98$		−	151759.i		−	1.59621i
$99$	66907.9			0.686103
$100$	460912.			4.60912
$101$	119645.			1.16706			0.583528	−	0.812093i	$-0.301672\pi$
$101$	119645.			1.16706			0.583528	+	0.812093i	$0.301672\pi$
$102$	−35427.8			−0.337166
$103$		−	160054.i		−	1.48652i	−0.669000	−	0.743262i	$-0.733277\pi$
$103$		−	160054.i		−	1.48652i	0.669000	−	0.743262i	$-0.266723\pi$
$104$	243336.			2.20609
$105$		−	10518.5i		−	0.0931063i
$106$			88990.2i			0.769268i
$107$	95588.2			0.807133			0.403566	−	0.914950i	$-0.367770\pi$
$107$	95588.2			0.807133			0.403566	+	0.914950i	$0.367770\pi$
$108$	−86244.7			−0.711497
$109$		−	82980.7i		−	0.668976i	−0.942400	−	0.334488i	$-0.891437\pi$
$109$		−	82980.7i		−	0.668976i	0.942400	−	0.334488i	$-0.108563\pi$
$110$	−282893.			−2.22916
$111$	9649.21	+	20795.9i	0.0743334	+	0.160203i
$112$	−44274.1			−0.333507
$113$			51762.8i			0.381348i	0.981653	+	0.190674i	$0.0610674\pi$
$113$			51762.8i			0.381348i	−0.981653	+	0.190674i	$0.938933\pi$
$114$	−60454.7			−0.435680
$115$	256465.			1.80835
$116$		−	39723.4i		−	0.274095i
$117$		−	173304.i		−	1.17043i
$118$	149802.			0.990403
$119$			49394.5i			0.319751i
$120$	91746.4			0.581615
$121$	−80278.2			−0.498464
$122$	−286847.			−1.74482
$123$	26721.0			0.159254
$124$		−	385218.i		−	2.24984i
$125$			394594.i			2.25879i
$126$			88086.4i			0.494291i
$127$	−239395.			−1.31706			−0.658530	−	0.752555i	$-0.728821\pi$
$127$	−239395.			−1.31706			−0.658530	+	0.752555i	$0.728821\pi$
$128$			306454.i			1.65326i
$129$			15673.2i			0.0829244i
$130$			732746.i			3.80273i
$131$		−	294446.i		−	1.49909i	−0.661953	−	0.749545i	$-0.730272\pi$
$131$		−	294446.i		−	1.49909i	0.661953	−	0.749545i	$-0.269728\pi$
$132$	−51233.6			−0.255929
$133$			84287.8i			0.413176i
$134$		−	1477.12i		−	0.00710645i
$135$		−	132787.i		−	0.627078i
$136$	−430840.			−1.99742
$137$	−157240.			−0.715752			−0.357876	−	0.933769i	$-0.616499\pi$
$137$	−157240.			−0.715752			−0.357876	+	0.933769i	$0.616499\pi$
$138$	69146.0			0.309079
$139$	208395.			0.914852			0.457426	−	0.889248i	$-0.348771\pi$
$139$	208395.			0.914852			0.457426	+	0.889248i	$0.348771\pi$
$140$		−	250177.i		−	1.07876i
$141$	−69626.9			−0.294937
$142$		−	391523.i		−	1.62943i
$143$		−	209217.i		−	0.855572i
$144$	−275035.			−1.10530
$145$	61160.3			0.241574
$146$		−	388724.i		−	1.50924i
$147$	42316.6			0.161517
$148$	229502.	+	494621.i	0.861256	+	1.85617i
$149$	324029.			1.19569			0.597844	−	0.801612i	$-0.296024\pi$
$149$	324029.			1.19569			0.597844	+	0.801612i	$0.296024\pi$
$150$			191329.i			0.694310i
$151$	118246.			0.422032			0.211016	−	0.977483i	$-0.432323\pi$
$151$	118246.			0.422032			0.211016	+	0.977483i	$0.432323\pi$
$152$	−735193.			−2.58103
$153$			306844.i			1.05971i
$154$			106340.i			0.361322i
$155$	593102.			1.98290
$156$			132705.i			0.436591i
$157$	−572427.			−1.85341			−0.926704	−	0.375792i	$-0.877371\pi$
$157$	−572427.			−1.85341			−0.926704	+	0.375792i	$0.877371\pi$
$158$	826426.			2.63367
$159$	−24814.1			−0.0778405
$160$	96462.8			0.297893
$161$		−	96405.5i		−	0.293114i
$162$			529017.i			1.58373i
$163$			271637.i			0.800792i	0.916342	+	0.400396i	$0.131127\pi$
$163$			271637.i			0.800792i	−0.916342	+	0.400396i	$0.868873\pi$
$164$	635546.			1.84517
$165$		−	78882.1i		−	0.225563i
$166$		−	359812.i		−	1.01346i
$167$		−	13718.7i		−	0.0380647i	−0.999819	−	0.0190323i	$-0.993941\pi$
$167$		−	13718.7i		−	0.0380647i	0.999819	−	0.0190323i	$-0.00605855\pi$
$168$		−	34487.6i		−	0.0942736i
$169$	−170618.			−0.459523
$170$		−	1.29737e6i		−	3.44302i
$171$			523604.i			1.36934i
$172$			372779.i			0.960794i
$173$	195002.			0.495364			0.247682	−	0.968841i	$-0.420331\pi$
$173$	195002.			0.495364			0.247682	+	0.968841i	$0.420331\pi$
$174$	16489.6			0.0412892
$175$	266757.			0.658447
$176$	−332029.			−0.807968
$177$			41770.8i			0.100217i
$178$	−626026.			−1.48096
$179$			226757.i			0.528966i	0.964390	+	0.264483i	$0.0852013\pi$
$179$			226757.i			0.528966i	−0.964390	+	0.264483i	$0.914799\pi$
$180$		−	1.55412e6i		−	3.57523i
$181$	117568.			0.266742			0.133371	−	0.991066i	$-0.457420\pi$
$181$	117568.			0.266742			0.133371	+	0.991066i	$0.457420\pi$
$182$	275441.			0.616381
$183$		−	79984.5i		−	0.176554i
$184$	840889.			1.83102
$185$	−761546.	+	353354.i	−1.63594	+	0.759067i
$186$	159908.			0.338912
$187$			370429.i			0.774642i
$188$	−1.65604e6			−3.41726
$189$	−49914.9			−0.101643
$190$		−	2.21385e6i		−	4.44901i
$191$		−	487344.i		−	0.966611i	−0.875452	−	0.483306i	$-0.839436\pi$
$191$		−	487344.i		−	0.966611i	0.875452	−	0.483306i	$-0.160564\pi$
$192$	−76914.2			−0.150575
$193$		−	341504.i		−	0.659938i	−0.943992	−	0.329969i	$-0.892962\pi$
$193$		−	341504.i		−	0.659938i	0.943992	−	0.329969i	$-0.107038\pi$
$194$	166419.			0.317468
$195$	−204319.			−0.384789
$196$	1.00648e6			1.87139
$197$	−651239.			−1.19557			−0.597785	−	0.801657i	$-0.703952\pi$
$197$	−651239.			−1.19557			−0.597785	+	0.801657i	$0.703952\pi$
$198$			660595.i			1.19749i
$199$		−	779867.i		−	1.39601i	−0.716094	−	0.698004i	$-0.754072\pi$
$199$		−	779867.i		−	1.39601i	0.716094	−	0.698004i	$-0.245928\pi$
$200$			2.32677e6i			4.11318i
$201$	411.880			0.000719086
$202$			1.18128e6i			2.03692i
$203$		−	22990.3i		−	0.0391565i
$204$		−	234961.i		−	0.395294i
$205$			978520.i			1.62624i
$206$	1.58024e6			2.59451
$207$		−	598881.i		−	0.971436i
$208$			860017.i			1.37832i
$209$			632107.i			1.00098i
$210$	103851.			0.162503
$211$	−1.15677e6			−1.78871			−0.894356	−	0.447356i	$-0.852366\pi$
$211$	−1.15677e6			−1.78871			−0.894356	+	0.447356i	$0.852366\pi$
$212$	−590192.			−0.901890
$213$	109173.			0.164879
$214$			943761.i			1.40873i
$215$	−573951.			−0.846796
$216$		−	435379.i		−	0.634940i
$217$		−	222948.i		−	0.321407i
$218$	819284.			1.16760
$219$	108392.			0.152717
$220$		−	1.87617e6i		−	2.61346i
$221$	959481.			1.32147
$222$	−205322.	+	95268.5i	−0.279610	+	0.129738i
$223$	−759581.			−1.02285			−0.511425	−	0.859328i	$-0.670882\pi$
$223$	−759581.			−1.02285			−0.511425	+	0.859328i	$0.670882\pi$
$224$		−	36260.5i		−	0.0482852i
$225$	1.65712e6			2.18222
$226$	−511065.			−0.665587
$227$			49088.1i			0.0632283i	0.999500	+	0.0316142i	$0.0100648\pi$
$227$			49088.1i			0.0632283i	−0.999500	+	0.0316142i	$0.989935\pi$
$228$		−	400941.i		−	0.510792i
$229$	−1.16335e6			−1.46596			−0.732978	−	0.680252i	$-0.761870\pi$
$229$	−1.16335e6			−1.46596			−0.732978	+	0.680252i	$0.761870\pi$
$230$			2.53213e6i			3.15621i
$231$	−29651.9			−0.0365614
$232$	200531.			0.244603
$233$	−386330.			−0.466196			−0.233098	−	0.972453i	$-0.574886\pi$
$233$	−386330.			−0.466196			−0.233098	+	0.972453i	$0.574886\pi$
$234$	1.71106e6			2.04280
$235$		−	2.54974e6i		−	3.01180i
$236$			993500.i			1.16115i
$237$			230441.i			0.266495i
$238$	−487682.			−0.558077
$239$			690828.i			0.782303i	0.920326	+	0.391152i	$0.127923\pi$
$239$			690828.i			0.782303i	−0.920326	+	0.391152i	$0.872077\pi$
$240$			324257.i			0.363380i
$241$			1.38199e6i			1.53272i	0.642410	+	0.766362i	$0.277935\pi$
$241$			1.38199e6i			1.53272i	−0.642410	+	0.766362i	$0.722065\pi$
$242$		−	792602.i		−	0.869995i
$243$	−467571.			−0.507962
$244$		−	1.90240e6i		−	2.04563i
$245$			1.54963e6i			1.64935i
$246$			263821.i			0.277953i
$247$	1.63728e6			1.70757
$248$	1.94465e6			2.00776
$249$	100330.			0.102549
$250$	−3.89590e6			−3.94238
$251$			60032.8i			0.0601457i	0.999548	+	0.0300728i	$0.00957393\pi$
$251$			60032.8i			0.0601457i	−0.999548	+	0.0300728i	$0.990426\pi$
$252$	−584197.			−0.579506
$253$		−	722983.i		−	0.710112i
$254$		−	2.36359e6i		−	2.29873i
$255$	361758.			0.348392
$256$	−2.13167e6			−2.03292
$257$		−	371424.i		−	0.350782i	−0.984499	−	0.175391i	$-0.943881\pi$
$257$		−	371424.i		−	0.350782i	0.984499	−	0.175391i	$-0.0561189\pi$
$258$	−154744.			−0.144732
$259$	132826.	+	286266.i	0.123037	+	0.265168i
$260$	−4.85964e6			−4.45832
$261$		−	142818.i		−	0.129772i
$262$	2.90712e6			2.61644
$263$	732517.			0.653022			0.326511	−	0.945193i	$-0.394127\pi$
$263$	732517.			0.653022			0.326511	+	0.945193i	$0.394127\pi$
$264$		−	258636.i		−	0.228391i
$265$		−	908691.i		−	0.794880i
$266$	−832190.			−0.721138
$267$		−	174562.i		−	0.149855i
$268$	9796.38			0.00833160
$269$	116693.			0.0983252			0.0491626	−	0.998791i	$-0.484345\pi$
$269$	116693.			0.0983252			0.0491626	+	0.998791i	$0.484345\pi$
$270$	1.31103e6			1.09447
$271$	1.13684e6			0.940317			0.470158	−	0.882582i	$-0.344197\pi$
$271$	1.13684e6			0.940317			0.470158	+	0.882582i	$0.344197\pi$
$272$		−	1.52271e6i		−	1.24794i
$273$			76804.1i			0.0623703i
$274$		−	1.55246e6i		−	1.24924i
$275$	2.00052e6			1.59518
$276$			458583.i			0.362364i
$277$			715969.i			0.560654i	0.959905	+	0.280327i	$0.0904429\pi$
$277$			715969.i			0.560654i	−0.959905	+	0.280327i	$0.909557\pi$
$278$			2.05753e6i			1.59674i
$279$		−	1.38498e6i		−	1.06520i
$280$	1.26294e6			0.962690
$281$		−	139202.i		−	0.105167i	−0.998617	−	0.0525836i	$-0.983254\pi$
$281$		−	139202.i		−	0.105167i	0.998617	−	0.0525836i	$-0.0167456\pi$
$282$		−	687441.i		−	0.514769i
$283$			572225.i			0.424718i	0.977192	+	0.212359i	$0.0681146\pi$
$283$			572225.i			0.424718i	−0.977192	+	0.212359i	$0.931885\pi$
$284$	2.59662e6			1.91035
$285$	617311.			0.450186
$286$	2.06564e6			1.49327
$287$	367828.			0.263596
$288$		−	225254.i		−	0.160026i
$289$	−278955.			−0.196467
$290$			603848.i			0.421631i
$291$			46404.5i			0.0321239i
$292$	2.57806e6			1.76944
$293$	−1.62064e6			−1.10285			−0.551425	−	0.834224i	$-0.685916\pi$
$293$	−1.62064e6			−1.10285			−0.551425	+	0.834224i	$0.685916\pi$
$294$			417800.i			0.281903i
$295$	−1.52965e6			−1.02338
$296$	−2.49694e6	+	1.15857e6i	−1.65645	+	0.768584i
$297$	−374332.			−0.246244
$298$			3.19920e6i			2.08690i
$299$	−1.87266e6			−1.21138
$300$	−1.26891e6			−0.814009
$301$			215749.i			0.137257i
$302$			1.16747e6i			0.736594i
$303$	−329389.			−0.206112
$304$		−	2.59837e6i		−	1.61257i
$305$	2.92903e6			1.80291
$306$	−3.02953e6			−1.84957
$307$	1.74662e6			1.05768			0.528839	−	0.848722i	$-0.322628\pi$
$307$	1.74662e6			1.05768			0.528839	+	0.848722i	$0.322628\pi$
$308$	−705257.			−0.423614
$309$			440635.i			0.262532i
$310$			5.85582e6i			3.46085i
$311$			1.86359e6i			1.09257i	0.837600	+	0.546284i	$0.183958\pi$
$311$			1.86359e6i			1.09257i	−0.837600	+	0.546284i	$0.816042\pi$
$312$	−669917.			−0.389614
$313$		−	2.96662e6i		−	1.71159i	−0.517311	−	0.855797i	$-0.673067\pi$
$313$		−	2.96662e6i		−	1.71159i	0.517311	−	0.855797i	$-0.326933\pi$
$314$		−	5.65169e6i		−	3.23485i
$315$		−	899462.i		−	0.510748i
$316$			5.48094e6i			3.08771i
$317$	950355.			0.531175			0.265587	−	0.964087i	$-0.414434\pi$
$317$	950355.			0.531175			0.265587	+	0.964087i	$0.414434\pi$
$318$		−	244994.i		−	0.135859i
$319$		−	172413.i		−	0.0948623i
$320$		−	2.81660e6i		−	1.53762i
$321$	−263159.			−0.142546
$322$	951830.			0.511587
$323$	−2.89888e6			−1.54605
$324$	−3.50849e6			−1.85677
$325$		−	5.18172e6i		−	2.72123i
$326$	−2.68192e6			−1.39766
$327$			228450.i			0.118147i
$328$			3.20835e6i			1.64663i
$329$	−958451.			−0.488180
$330$	778818.			0.393687
$331$			1.92675e6i			0.966618i	0.875450	+	0.483309i	$0.160565\pi$
$331$			1.92675e6i			0.966618i	−0.875450	+	0.483309i	$0.839435\pi$
$332$	2.38631e6			1.18818
$333$	825130.	+	1.77832e6i	0.407767	+	0.878816i
$334$	135448.			0.0664363
$335$			15083.0i			0.00734306i
$336$	121889.			0.0589000
$337$	−2.20780e6			−1.05897			−0.529485	−	0.848319i	$-0.677615\pi$
$337$	−2.20780e6			−1.05897			−0.529485	+	0.848319i	$0.677615\pi$
$338$		−	1.68454e6i		−	0.802030i
$339$		−	142506.i		−	0.0673492i
$340$	8.60425e6			4.03660
$341$		−	1.67198e6i		−	0.778654i
$342$	−5.16964e6			−2.38999
$343$	1.21945e6			0.559664
$344$	−1.88185e6			−0.857413
$345$	−706060.			−0.319370
$346$			1.92530e6i			0.864584i
$347$		−	1.78913e6i		−	0.797662i	−0.917024	−	0.398831i	$-0.869416\pi$
$347$		−	1.78913e6i		−	0.797662i	0.917024	−	0.398831i	$-0.130584\pi$
$348$			109360.i			0.0484075i
$349$	−593448.			−0.260807			−0.130403	−	0.991461i	$-0.541627\pi$
$349$	−593448.			−0.260807			−0.130403	+	0.991461i	$0.541627\pi$
$350$			2.63374e6i			1.14922i
$351$			969589.i			0.420068i
$352$		−	271932.i		−	0.116978i
$353$		−	1.18246e6i		−	0.505066i	−0.967588	−	0.252533i	$-0.918736\pi$
$353$		−	1.18246e6i		−	0.505066i	0.967588	−	0.252533i	$-0.0812636\pi$
$354$	−412412.			−0.174913
$355$			3.99789e6i			1.68368i
$356$		−	4.15187e6i		−	1.73627i
$357$		−	135986.i		−	0.0564706i
$358$	−2.23881e6			−0.923231
$359$	1.64233e6			0.672549			0.336275	−	0.941764i	$-0.390833\pi$
$359$	1.64233e6			0.672549			0.336275	+	0.941764i	$0.390833\pi$
$360$	7.84548e6			3.19053
$361$	−2.47061e6			−0.997783
$362$			1.16077e6i			0.465559i
$363$	221010.			0.0880329
$364$			1.82675e6i			0.722646i
$365$			3.96932e6i			1.55949i
$366$	789703.			0.308149
$367$	3.30858e6			1.28226			0.641131	−	0.767432i	$-0.278466\pi$
$367$	3.30858e6			1.28226			0.641131	+	0.767432i	$0.278466\pi$
$368$			2.97193e6i			1.14398i
$369$	2.28498e6			0.873608
$370$	−3.48873e6	−	7.51889e6i	−1.32484	−	2.85528i
$371$	−341579.			−0.128842
$372$			1.06052e6i			0.397341i
$373$	−3.59546e6			−1.33808			−0.669041	−	0.743225i	$-0.733295\pi$
$373$	−3.59546e6			−1.33808			−0.669041	+	0.743225i	$0.733295\pi$
$374$	−3.65732e6			−1.35202
$375$		−	1.08634e6i		−	0.398920i
$376$		−	8.36001e6i		−	3.04956i
$377$	−446582.			−0.161826
$378$		−	492820.i		−	0.177402i
$379$	−1.61202e6			−0.576463			−0.288232	−	0.957561i	$-0.593067\pi$
$379$	−1.61202e6			−0.576463			−0.288232	+	0.957561i	$0.593067\pi$
$380$	1.46825e7			5.21603
$381$	659066.			0.232603
$382$	4.81164e6			1.68708
$383$		−	2.35743e6i		−	0.821185i	−0.911819	−	0.410592i	$-0.865322\pi$
$383$		−	2.35743e6i		−	0.821185i	0.911819	−	0.410592i	$-0.134678\pi$
$384$		−	843682.i		−	0.291978i
$385$		−	1.08585e6i		−	0.373352i
$386$	3.37174e6			1.15182
$387$			1.34026e6i			0.454894i
$388$			1.10371e6i			0.372199i
$389$			1.24614e6i			0.417534i	0.977965	+	0.208767i	$0.0669450\pi$
$389$			1.24614e6i			0.417534i	−0.977965	+	0.208767i	$0.933055\pi$
$390$		−	2.01729e6i		−	0.671593i
$391$	3.31565e6			1.09680
$392$			5.08089e6i			1.67003i
$393$			810625.i			0.264752i
$394$		−	6.42981e6i		−	2.08669i
$395$	−8.43875e6			−2.72136
$396$	−4.38113e6			−1.40394
$397$	2.29513e6			0.730856			0.365428	−	0.930840i	$-0.380923\pi$
$397$	2.29513e6			0.730856			0.365428	+	0.930840i	$0.380923\pi$
$398$	7.69978e6			2.43652
$399$		−	232048.i		−	0.0729703i
$400$	−8.22343e6			−2.56982
$401$		−	1.93165e6i		−	0.599884i	−0.953958	−	0.299942i	$-0.903033\pi$
$401$		−	1.93165e6i		−	0.599884i	0.953958	−	0.299942i	$-0.0969672\pi$
$402$			4066.57i			0.00125506i
$403$	−4.33074e6			−1.32831
$404$	−7.83436e6			−2.38809
$405$		−	5.40187e6i		−	1.63646i
$406$	226987.			0.0683418
$407$	996117.	+	2.14682e6i	0.298074	+	0.642407i
$408$	1.18612e6			0.352760
$409$			706587.i			0.208861i	0.994532	+	0.104431i	$0.0333020\pi$
$409$			706587.i			0.208861i	−0.994532	+	0.104431i	$0.966698\pi$
$410$	−9.66112e6			−2.83836
$411$	432890.			0.126408
$412$			1.04803e7i			3.04180i
$413$			574997.i			0.165879i
$414$	5.91287e6			1.69550
$415$			3.67409e6i			1.04720i
$416$	−704356.			−0.199553
$417$	−573723.			−0.161570
$418$	−6.24092e6			−1.74706
$419$	2.20124e6			0.612538			0.306269	−	0.951945i	$-0.400919\pi$
$419$	2.20124e6			0.612538			0.306269	+	0.951945i	$0.400919\pi$
$420$			688749.i			0.190519i
$421$		−	1.32734e6i		−	0.364988i	−0.983207	−	0.182494i	$-0.941583\pi$
$421$		−	1.32734e6i		−	0.364988i	0.983207	−	0.182494i	$-0.0584170\pi$
$422$		−	1.14210e7i		−	3.12193i
$423$	−5.95399e6			−1.61792
$424$		−	2.97939e6i		−	0.804847i
$425$			9.17450e6i			2.46383i
$426$			1.07788e6i			0.287771i
$427$		−	1.10103e6i		−	0.292233i
$428$	−6.25912e6			−1.65160
$429$			575984.i			0.151101i
$430$		−	5.66673e6i		−	1.47796i
$431$			5.50972e6i			1.42868i	0.699797	+	0.714342i	$0.253274\pi$
$431$			5.50972e6i			1.42868i	−0.699797	+	0.714342i	$0.746726\pi$
$432$	1.53875e6			0.396696
$433$	4.94787e6			1.26823			0.634116	−	0.773238i	$-0.281364\pi$
$433$	4.94787e6			1.26823			0.634116	+	0.773238i	$0.281364\pi$
$434$	2.20121e6			0.560967
$435$	−168377.			−0.0426639
$436$			5.43357e6i			1.36889i
$437$	5.65788e6			1.41726
$438$			1.07018e6i			0.266545i
$439$			1.57962e6i			0.391194i	0.980684	+	0.195597i	$0.0626645\pi$
$439$			1.57962e6i			0.391194i	−0.980684	+	0.195597i	$0.937336\pi$
$440$	9.47126e6			2.33225
$441$	3.61861e6			0.886023
$442$			9.47315e6i			2.30642i
$443$	262118.			0.0634583			0.0317291	−	0.999497i	$-0.489899\pi$
$443$	262118.			0.0634583			0.0317291	+	0.999497i	$0.489899\pi$
$444$	−631830.	−	1.36172e6i	−0.152105	−	0.327815i
$445$	6.39244e6			1.53026
$446$		−	7.49949e6i		−	1.78523i
$447$	−892067.			−0.211168
$448$	−1.05876e6			−0.249232
$449$			448765.i			0.105052i	0.998620	+	0.0525259i	$0.0167272\pi$
$449$			448765.i			0.105052i	−0.998620	+	0.0525259i	$0.983273\pi$
$450$			1.63611e7i			3.80874i
$451$	2.75848e6			0.638600
$452$		−	3.38943e6i		−	0.780334i
$453$	−325538.			−0.0745343
$454$	−484656.			−0.110356
$455$	−2.81256e6			−0.636903
$456$	2.02402e6			0.455830
$457$		−	239106.i		−	0.0535551i	−0.999641	−	0.0267775i	$-0.991475\pi$
$457$		−	239106.i		−	0.0535551i	0.999641	−	0.0267775i	$-0.00852457\pi$
$458$		−	1.14860e7i		−	2.55861i
$459$		−	1.71671e6i		−	0.380334i
$460$	−1.67933e7			−3.70034
$461$		−	7.68350e6i		−	1.68386i	−0.539585	−	0.841931i	$-0.681419\pi$
$461$		−	7.68350e6i		−	1.68386i	0.539585	−	0.841931i	$-0.318581\pi$
$462$		−	292759.i		−	0.0638125i
$463$		−	5.61085e6i		−	1.21640i	−0.793784	−	0.608200i	$-0.791892\pi$
$463$		−	5.61085e6i		−	1.21640i	0.793784	−	0.608200i	$-0.208108\pi$
$464$			708730.i			0.152822i
$465$	−1.63284e6			−0.350196
$466$		−	3.81431e6i		−	0.813676i
$467$			4.46838e6i			0.948109i	0.880496	+	0.474054i	$0.157210\pi$
$467$			4.46838e6i			0.948109i	−0.880496	+	0.474054i	$0.842790\pi$
$468$			1.13479e7i			2.39498i
$469$	5669.74			0.00119023
$470$	2.51740e7			5.25664
$471$	1.57592e6			0.327327
$472$	−5.01536e6			−1.03621
$473$			1.61799e6i			0.332524i
$474$	−2.27519e6			−0.465127
$475$			1.56555e7i			3.18371i
$476$		−	3.23435e6i		−	0.654290i
$477$	−2.12192e6			−0.427005
$478$	−6.82068e6			−1.36539
$479$			1.44578e6i			0.287915i	0.989584	+	0.143957i	$0.0459828\pi$
$479$			1.44578e6i			0.287915i	−0.989584	+	0.143957i	$0.954017\pi$
$480$	−265567.			−0.0526103
$481$	5.56068e6	−	2.58013e6i	1.09589	−	0.508486i
$482$	−1.36447e7			−2.67514
$483$			265409.i			0.0517664i
$484$	5.25662e6			1.01998
$485$	−1.69933e6			−0.328038
$486$		−	4.61642e6i		−	0.886573i
$487$		−	2.94284e6i		−	0.562270i	−0.959668	−	0.281135i	$-0.909289\pi$
$487$		−	2.94284e6i		−	0.562270i	0.959668	−	0.281135i	$-0.0907108\pi$
$488$	9.60363e6			1.82552
$489$		−	747829.i		−	0.141426i
$490$	−1.52998e7			−2.87870
$491$	−2.50545e6			−0.469010			−0.234505	−	0.972115i	$-0.575347\pi$
$491$	−2.50545e6			−0.469010			−0.234505	+	0.972115i	$0.575347\pi$
$492$	−1.74969e6			−0.325873
$493$	790698.			0.146519
$494$			1.61652e7i			2.98032i
$495$		−	6.74542e6i		−	1.23736i
$496$			6.87292e6i			1.25440i
$497$	1.50282e6			0.272907
$498$			990579.i			0.178985i
$499$		−	2.64448e6i		−	0.475433i	−0.971335	−	0.237716i	$-0.923601\pi$
$499$		−	2.64448e6i		−	0.475433i	0.971335	−	0.237716i	$-0.0763989\pi$
$500$		−	2.58380e7i		−	4.62204i
$501$			37768.3i			0.00672254i
$502$	−592716.			−0.104975
$503$		−	1.50302e6i		−	0.264878i	−0.991191	−	0.132439i	$-0.957719\pi$
$503$		−	1.50302e6i		−	0.264878i	0.991191	−	0.132439i	$-0.0422808\pi$
$504$		−	2.94913e6i		−	0.517152i
$505$		−	1.20622e7i		−	2.10474i
$506$	7.13815e6			1.23939
$507$	469719.			0.0811556
$508$	1.56756e7			2.69503
$509$	−2.14855e6			−0.367580			−0.183790	−	0.982966i	$-0.558837\pi$
$509$	−2.14855e6			−0.367580			−0.183790	+	0.982966i	$0.558837\pi$
$510$			3.57171e6i			0.608066i
$511$	1.49207e6			0.252777
$512$		−	1.12398e7i		−	1.89490i
$513$		−	2.92942e6i		−	0.491461i
$514$	3.66714e6			0.612237
$515$	−1.61360e7			−2.68089
$516$		−	1.02628e6i		−	0.169684i
$517$	−7.18780e6			−1.18269
$518$	−2.82636e6	+	1.31142e6i	−0.462811	+	0.214742i
$519$	−536851.			−0.0874853
$520$		−	2.45323e7i		−	3.97860i
$521$	−4.84841e6			−0.782537			−0.391269	−	0.920277i	$-0.627964\pi$
$521$	−4.84841e6			−0.782537			−0.391269	+	0.920277i	$0.627964\pi$
$522$	1.41007e6			0.226498
$523$			9.46409e6i			1.51295i	0.654023	+	0.756475i	$0.273080\pi$
$523$			9.46409e6i			1.51295i	−0.654023	+	0.756475i	$0.726920\pi$
$524$			1.92803e7i			3.06751i
$525$	−734395.			−0.116287
$526$			7.23228e6i			1.13975i
$527$	7.66780e6			1.20266
$528$	914092.			0.142694
$529$	−34949.8			−0.00543007
$530$	8.97169e6			1.38735
$531$			3.57194e6i			0.549753i
$532$		−	5.51916e6i		−	0.845462i
$533$		−	7.14499e6i		−	1.08939i
$534$	1.72348e6			0.261549
$535$		−	9.63687e6i		−	1.45563i
$536$			49453.9i			0.00743512i
$537$		−	624272.i		−	0.0934197i
$538$			1.15213e6i			0.171612i
$539$	4.36847e6			0.647675
$540$			8.69490e6i			1.28316i
$541$			7.78843e6i			1.14408i	0.820226	+	0.572040i	$0.193848\pi$
$541$			7.78843e6i			1.14408i	−0.820226	+	0.572040i	$0.806152\pi$
$542$			1.12242e7i			1.64118i
$543$	−323670.			−0.0471089
$544$	1.24710e6			0.180677
$545$	−8.36582e6			−1.20647
$546$	−758302.			−0.108858
$547$		−	2.41496e6i		−	0.345098i	−0.985001	−	0.172549i	$-0.944800\pi$
$547$		−	2.41496e6i		−	0.345098i	0.985001	−	0.172549i	$-0.0552002\pi$
$548$	1.02961e7			1.46461
$549$		−	6.83969e6i		−	0.968514i
$550$			1.97515e7i			2.78415i
$551$	1.34926e6			0.189329
$552$	−2.31501e6			−0.323374
$553$			3.17214e6i			0.441103i
$554$	−7.06890e6			−0.978538
$555$	2.09657e6	−	972800.i	0.288920	−	0.134057i
$556$	−1.36457e7			−1.87202
$557$			464341.i			0.0634161i	0.999497	+	0.0317080i	$0.0100947\pi$
$557$			464341.i			0.0634161i	−0.999497	+	0.0317080i	$0.989905\pi$
$558$	1.36741e7			1.85915
$559$	4.19090e6			0.567254
$560$			4.46356e6i			0.601467i
$561$		−	1.01981e6i		−	0.136808i
$562$	1.37437e6			0.183554
$563$			5.16246e6i			0.686413i	0.939260	+	0.343207i	$0.111513\pi$
$563$			5.16246e6i			0.686413i	−0.939260	+	0.343207i	$0.888487\pi$
$564$	4.55917e6			0.603515
$565$	5.21855e6			0.687747
$566$	−5.64969e6			−0.741282
$567$	−2.03057e6			−0.265253
$568$			1.31082e7i			1.70479i
$569$		−	6.84241e6i		−	0.885989i	−0.896524	−	0.442994i	$-0.853916\pi$
$569$		−	6.84241e6i		−	0.885989i	0.896524	−	0.442994i	$-0.146084\pi$
$570$			6.09483e6i			0.785732i
$571$	1.37986e7			1.77111			0.885554	−	0.464537i	$-0.153779\pi$
$571$	1.37986e7			1.77111			0.885554	+	0.464537i	$0.153779\pi$
$572$			1.36995e7i			1.75071i
$573$			1.34168e6i			0.170711i
$574$			3.63163e6i			0.460068i
$575$		−	1.79063e7i		−	2.25858i
$576$	−6.57714e6			−0.826002
$577$			6.17747e6i			0.772451i	0.922404	+	0.386226i	$0.126221\pi$
$577$			6.17747e6i			0.772451i	−0.922404	+	0.386226i	$0.873779\pi$
$578$		−	2.75418e6i		−	0.342904i
$579$			940178.i			0.116550i
$580$	−4.00478e6			−0.494320
$581$	1.38110e6			0.169740
$582$	−458161.			−0.0560674
$583$	−2.56163e6			−0.312137
$584$			1.30145e7i			1.57905i
$585$	−1.74719e7			−2.11082
$586$		−	1.60009e7i		−	1.92486i
$587$		−	383466.i		−	0.0459338i	−0.999736	−	0.0229669i	$-0.992689\pi$
$587$		−	383466.i		−	0.0459338i	0.999736	−	0.0229669i	$-0.00731123\pi$
$588$	−2.77089e6			−0.330503
$589$	1.30845e7			1.55406
$590$		−	1.51025e7i		−	1.78615i
$591$	1.79289e6			0.211147
$592$	−4.09469e6	−	8.82485e6i	−0.480194	−	1.03491i
$593$	408757.			0.0477340			0.0238670	−	0.999715i	$-0.492402\pi$
$593$	408757.			0.0477340			0.0238670	+	0.999715i	$0.492402\pi$
$594$		−	3.69585e6i		−	0.429782i
$595$	4.97979e6			0.576658
$596$	−2.12174e7			−2.44668
$597$			2.14701e6i			0.246546i
$598$		−	1.84892e7i		−	2.11429i
$599$	−2.89241e6			−0.329377			−0.164688	−	0.986346i	$-0.552662\pi$
$599$	−2.89241e6			−0.329377			−0.164688	+	0.986346i	$0.552662\pi$
$600$		−	6.40570e6i		−	0.726421i
$601$	−2.65283e6			−0.299587			−0.149793	−	0.988717i	$-0.547861\pi$
$601$	−2.65283e6			−0.299587			−0.149793	+	0.988717i	$0.547861\pi$
$602$	−2.13013e6			−0.239561
$603$	35221.0			0.00394465
$604$	−7.74277e6			−0.863583
$605$			8.09337e6i			0.898961i
$606$		−	3.25212e6i		−	0.359737i
$607$		−	1.35595e7i		−	1.49373i	−0.664975	−	0.746866i	$-0.731558\pi$
$607$		−	1.35595e7i		−	1.49373i	0.664975	−	0.746866i	$-0.268442\pi$
$608$	2.12807e6			0.233468
$609$			63293.3i			0.00691536i
$610$			2.89189e7i			3.14671i
$611$			1.86178e7i			2.01755i
$612$		−	2.00921e7i		−	2.16844i
$613$	−1.43925e7			−1.54698			−0.773489	−	0.633809i	$-0.781490\pi$
$613$	−1.43925e7			−1.54698			−0.773489	+	0.633809i	$0.781490\pi$
$614$			1.72448e7i			1.84602i
$615$		−	2.69391e6i		−	0.287208i
$616$		−	3.56026e6i		−	0.378034i
$617$	3.48129e6			0.368152			0.184076	−	0.982912i	$-0.441071\pi$
$617$	3.48129e6			0.368152			0.184076	+	0.982912i	$0.441071\pi$
$618$	−4.35048e6			−0.458211
$619$	7.64539e6			0.801997			0.400999	−	0.916079i	$-0.368663\pi$
$619$	7.64539e6			0.801997			0.400999	+	0.916079i	$0.368663\pi$
$620$	−3.88363e7			−4.05751
$621$			3.35058e6i			0.348651i
$622$	−1.83996e7			−1.90692
$623$		−	2.40293e6i		−	0.248039i
$624$		−	2.36767e6i		−	0.243422i
$625$	1.77848e7			1.82116
$626$	2.92900e7			2.98733
$627$		−	1.74022e6i		−	0.176781i
$628$	3.74825e7			3.79254
$629$	−9.84548e6	+	4.56826e6i	−0.992225	+	0.460388i
$630$	8.88057e6			0.891434
$631$			1.47961e7i			1.47936i	0.672958	+	0.739681i	$0.265023\pi$
$631$			1.47961e7i			1.47936i	−0.672958	+	0.739681i	$0.734977\pi$
$632$	−2.76687e7			−2.75548
$633$	3.18464e6			0.315901
$634$			9.38304e6i			0.927087i
$635$			2.41350e7i			2.37527i
$636$	1.62483e6			0.159281
$637$		−	1.13152e7i		−	1.10487i
$638$	1.70227e6			0.165568
$639$	9.33564e6			0.904465
$640$	3.08956e7			2.98158
$641$	1.65084e6			0.158693			0.0793467	−	0.996847i	$-0.474717\pi$
$641$	1.65084e6			0.158693			0.0793467	+	0.996847i	$0.474717\pi$
$642$		−	2.59822e6i		−	0.248793i
$643$		−	8.15538e6i		−	0.777888i	−0.921261	−	0.388944i	$-0.872840\pi$
$643$		−	8.15538e6i		−	0.777888i	0.921261	−	0.388944i	$-0.127160\pi$
$644$			6.31263e6i			0.599785i
$645$	1.58011e6			0.149551
$646$		−	2.86213e7i		−	2.69841i
$647$		−	9.93861e6i		−	0.933394i	−0.884417	−	0.466697i	$-0.845444\pi$
$647$		−	9.93861e6i		−	0.933394i	0.884417	−	0.466697i	$-0.154556\pi$
$648$		−	1.77115e7i		−	1.65698i
$649$			4.31213e6i			0.401865i
$650$	5.11601e7			4.74950
$651$			613788.i			0.0567630i
$652$		−	1.77868e7i		−	1.63862i
$653$		−	1.49370e7i		−	1.37082i	−0.728157	−	0.685410i	$-0.759623\pi$
$653$		−	1.49370e7i		−	1.37082i	0.728157	−	0.685410i	$-0.240377\pi$
$654$	−2.25553e6			−0.206207
$655$	−2.96850e7			−2.70355
$656$	−1.13392e7			−1.02878
$657$	9.26891e6			0.837751
$658$		−	9.46297e6i		−	0.852045i
$659$	2.84687e6			0.255361			0.127681	−	0.991815i	$-0.459247\pi$
$659$	2.84687e6			0.255361			0.127681	+	0.991815i	$0.459247\pi$
$660$			5.16520e6i			0.461559i
$661$			9.70917e6i			0.864328i	0.901795	+	0.432164i	$0.142250\pi$
$661$			9.70917e6i			0.864328i	−0.901795	+	0.432164i	$0.857750\pi$
$662$	−1.90232e7			−1.68709
$663$	−2.64150e6			−0.233382
$664$			1.20465e7i			1.06033i
$665$	8.49760e6			0.745148
$666$	−1.75577e7	+	8.14667e6i	−1.53384	+	0.711696i
$667$	−1.54324e6			−0.134313
$668$			898302.i			0.0778899i
$669$	2.09116e6			0.180644
$670$	−148918.			−0.0128162
$671$		−	8.25704e6i		−	0.707976i
$672$			99827.1i			0.00852757i
$673$	2.68585e6			0.228583			0.114291	−	0.993447i	$-0.463540\pi$
$673$	2.68585e6			0.228583			0.114291	+	0.993447i	$0.463540\pi$
$674$		−	2.17980e7i		−	1.84828i
$675$	−9.27115e6			−0.783203
$676$	1.11721e7			0.940300
$677$	9.96835e6			0.835894			0.417947	−	0.908471i	$-0.362750\pi$
$677$	9.96835e6			0.835894			0.417947	+	0.908471i	$0.362750\pi$
$678$	1.40699e6			0.117548
$679$			638782.i			0.0531714i
$680$			4.34358e7i			3.60226i
$681$		−	135142.i		−	0.0111666i
$682$	1.65078e7			1.35902
$683$		−	9.53625e6i		−	0.782214i	−0.920345	−	0.391107i	$-0.872092\pi$
$683$		−	9.53625e6i		−	0.782214i	0.920345	−	0.391107i	$-0.127908\pi$
$684$		−	3.42856e7i		−	2.80202i
$685$			1.58524e7i			1.29083i
$686$			1.20398e7i			0.976810i
$687$	3.20276e6			0.258900
$688$		−	6.65099e6i		−	0.535692i
$689$			6.63512e6i			0.532476i
$690$		−	6.97106e6i		−	0.557412i
$691$	2.11608e7			1.68592			0.842959	−	0.537977i	$-0.180811\pi$
$691$	2.11608e7			1.68592			0.842959	+	0.537977i	$0.180811\pi$
$692$	−1.27687e7			−1.01364
$693$	−2.53562e6			−0.200563
$694$	1.76645e7			1.39220
$695$		−	2.10097e7i		−	1.64990i
$696$	−552071.			−0.0431988
$697$			1.26506e7i			0.986345i
$698$		−	5.85923e6i		−	0.455200i
$699$	1.06359e6			0.0823340
$700$	−1.74673e7			−1.34735
$701$			1.53923e7i			1.18306i	0.806282	+	0.591531i	$0.201476\pi$
$701$			1.53923e7i			1.18306i	−0.806282	+	0.591531i	$0.798524\pi$
$702$	−9.57295e6			−0.733167
$703$	−1.68005e7	+	7.79535e6i	−1.28214	+	0.594905i
$704$	−7.94009e6			−0.603801
$705$			7.01955e6i			0.531908i
$706$	1.16746e7			0.881517
$707$	−4.53421e6			−0.341156
$708$		−	2.73515e6i		−	0.205068i
$709$			3.65791e6i			0.273286i	0.990620	+	0.136643i	$0.0436313\pi$
$709$			3.65791e6i			0.273286i	−0.990620	+	0.136643i	$0.956369\pi$
$710$	−3.94720e7			−2.93862
$711$			1.97057e7i			1.46190i
$712$	2.09594e7			1.54945
$713$	−1.49656e7			−1.10248
$714$	1.34261e6			0.0985610
$715$	−2.10925e7			−1.54299
$716$		−	1.48480e7i		−	1.08240i
$717$		−	1.90188e6i		−	0.138161i
$718$			1.62150e7i			1.17383i
$719$	9.26542e6			0.668410			0.334205	−	0.942500i	$-0.391532\pi$
$719$	9.26542e6			0.668410			0.334205	+	0.942500i	$0.391532\pi$
$720$			2.77281e7i			1.99337i
$721$			6.06557e6i			0.434544i
$722$		−	2.43928e7i		−	1.74148i
$723$		−	3.80470e6i		−	0.270691i
$724$	−7.69834e6			−0.545822
$725$		−	4.27019e6i		−	0.301719i
$726$			2.18207e6i			0.153648i
$727$		−	5.28381e6i		−	0.370776i	−0.982665	−	0.185388i	$-0.940646\pi$
$727$		−	5.28381e6i		−	0.370776i	0.982665	−	0.185388i	$-0.0593541\pi$
$728$	−9.22175e6			−0.644889
$729$	−1.17330e7			−0.817691
$730$	−3.91898e7			−2.72186
$731$	−7.42020e6			−0.513597
$732$			5.23739e6i			0.361274i
$733$	−1.60458e7			−1.10306			−0.551532	−	0.834154i	$-0.685957\pi$
$733$	−1.60458e7			−1.10306			−0.551532	+	0.834154i	$0.685957\pi$
$734$			3.26663e7i			2.23800i
$735$		−	4.26621e6i		−	0.291289i
$736$	−2.43402e6			−0.165626
$737$	42519.6			0.00288351
$738$			2.25601e7i			1.52475i
$739$	9.45250e6			0.636701			0.318350	−	0.947973i	$-0.396871\pi$
$739$	9.45250e6			0.636701			0.318350	+	0.947973i	$0.396871\pi$
$740$	4.98660e7	−	2.31376e7i	3.34754	−	1.55324i
$741$	−4.50750e6			−0.301572
$742$		−	3.37247e6i		−	0.224874i
$743$	2.54624e7			1.69211			0.846053	−	0.533099i	$-0.178973\pi$
$743$	2.54624e7			1.69211			0.846053	+	0.533099i	$0.178973\pi$
$744$	−5.35371e6			−0.354587
$745$		−	3.26675e7i		−	2.15638i
$746$		−	3.54987e7i		−	2.33542i
$747$	8.57950e6			0.562549
$748$		−	2.42557e7i		−	1.58511i
$749$	−3.62252e6			−0.235942
$750$	1.07256e7			0.696256
$751$	−2.61898e7			−1.69446			−0.847231	−	0.531225i	$-0.821732\pi$
$751$	−2.61898e7			−1.69446			−0.847231	+	0.531225i	$0.821732\pi$
$752$	2.95466e7			1.90529
$753$		−	165273.i		−	0.0106222i
$754$		−	4.40920e6i		−	0.282443i
$755$		−	1.19212e7i		−	0.761119i
$756$	3.26843e6			0.207986
$757$			1.11682e7i			0.708345i	0.935180	+	0.354173i	$0.115237\pi$
$757$			1.11682e7i			0.708345i	−0.935180	+	0.354173i	$0.884763\pi$
$758$		−	1.59158e7i		−	1.00613i
$759$			1.99041e6i			0.125412i
$760$			7.41196e7i			4.65478i
$761$	−5.61182e6			−0.351271			−0.175636	−	0.984455i	$-0.556198\pi$
$761$	−5.61182e6			−0.351271			−0.175636	+	0.984455i	$0.556198\pi$
$762$			6.50708e6i			0.405975i
$763$			3.14473e6i			0.195556i
$764$			3.19113e7i			1.97793i
$765$	3.09349e7			1.91115
$766$	2.32753e7			1.43326
$767$	1.11692e7			0.685543
$768$	5.86858e6			0.359030
$769$			1.21930e7i			0.743522i	0.928329	+	0.371761i	$0.121246\pi$
$769$			1.21930e7i			0.743522i	−0.928329	+	0.371761i	$0.878754\pi$
$770$	1.07208e7			0.651631
$771$			1.02255e6i			0.0619509i
$772$			2.23617e7i			1.35040i
$773$	−1.18645e7			−0.714166			−0.357083	−	0.934073i	$-0.616229\pi$
$773$	−1.18645e7			−0.714166			−0.357083	+	0.934073i	$0.616229\pi$
$774$	−1.32326e7			−0.793950
$775$		−	4.14102e7i		−	2.47658i
$776$	−5.57172e6			−0.332151
$777$	−365677.	−	788105.i	−0.0217293	−	0.0468308i
$778$	−1.23034e7			−0.728743
$779$			2.15872e7i			1.27454i
$780$	1.33788e7			0.787375
$781$	1.12702e7			0.661157
$782$			3.27360e7i			1.91430i
$783$			799027.i			0.0465755i
$784$	−1.79573e7			−1.04340
$785$			5.77101e7i			3.34255i
$786$	−8.00346e6			−0.462084
$787$	−2.50476e7			−1.44155			−0.720773	−	0.693171i	$-0.756213\pi$
$787$	−2.50476e7			−1.44155			−0.720773	+	0.693171i	$0.756213\pi$
$788$	4.26431e7			2.44643
$789$	−2.01665e6			−0.115329
$790$		−	8.33174e7i		−	4.74972i
$791$		−	1.96166e6i		−	0.111476i
$792$		−	2.21167e7i		−	1.25287i
$793$	−2.13873e7			−1.20774
$794$			2.26603e7i			1.27560i
$795$			2.50167e6i			0.140382i
$796$			5.10657e7i			2.85658i
$797$		−	5.81614e6i		−	0.324331i	−0.986764	−	0.162166i	$-0.948152\pi$
$797$		−	5.81614e6i		−	0.324331i	0.986764	−	0.162166i	$-0.0518479\pi$
$798$	2.29106e6			0.127359
$799$		−	3.29637e7i		−	1.82671i
$800$		−	6.73500e6i		−	0.372060i
$801$		−	1.49272e7i		−	0.822050i
$802$	1.90715e7			1.04701
$803$	1.11896e7			0.612389
$804$	−26969.9			−0.00147143
$805$	−9.71927e6			−0.528620
$806$		−	4.27582e7i		−	2.31837i
$807$	−321262.			−0.0173650
$808$		−	3.95492e7i		−	2.13113i
$809$		−	2.04340e7i		−	1.09770i	−0.835922	−	0.548848i	$-0.815067\pi$
$809$		−	2.04340e7i		−	1.09770i	0.835922	−	0.548848i	$-0.184933\pi$
$810$	5.33337e7			2.85620
$811$	−1.77391e7			−0.947066			−0.473533	−	0.880776i	$-0.657022\pi$
$811$	−1.77391e7			−0.947066			−0.473533	+	0.880776i	$0.657022\pi$
$812$			1.50540e6i			0.0801240i
$813$	−3.12976e6			−0.166068
$814$	−2.11960e7	+	9.83486e6i	−1.12123	+	0.520244i
$815$	2.73855e7			1.44420
$816$			4.19208e6i			0.220396i
$817$	−1.26620e7			−0.663660
$818$	−6.97627e6			−0.364536
$819$			6.56772e6i			0.342141i
$820$		−	6.40735e7i		−	3.32770i
$821$	−1.04128e7			−0.539153			−0.269576	−	0.962979i	$-0.586884\pi$
$821$	−1.04128e7			−0.539153			−0.269576	+	0.962979i	$0.586884\pi$
$822$			4.27401e6i			0.220626i
$823$	7.39694e6			0.380673			0.190337	−	0.981719i	$-0.439042\pi$
$823$	7.39694e6			0.380673			0.190337	+	0.981719i	$0.439042\pi$
$824$	−5.29064e7			−2.71450
$825$	−5.50752e6			−0.281722
$826$	−5.67706e6			−0.289516
$827$		−	2.32075e6i		−	0.117995i	−0.998258	−	0.0589977i	$-0.981210\pi$
$827$		−	2.32075e6i		−	0.117995i	0.998258	−	0.0589977i	$-0.0187905\pi$
$828$			3.92147e7i			1.98780i
$829$		−	2.91531e7i		−	1.47333i	−0.676260	−	0.736663i	$-0.736401\pi$
$829$		−	2.91531e7i		−	1.47333i	0.676260	−	0.736663i	$-0.263599\pi$
$830$	−3.62750e7			−1.82773
$831$		−	1.97110e6i		−	0.0990161i
$832$			2.05663e7i			1.03003i
$833$			2.00341e7i			1.00036i
$834$		−	5.66448e6i		−	0.281997i
$835$	−1.38307e6			−0.0686482
$836$		−	4.13904e7i		−	2.04825i
$837$			7.74857e6i			0.382303i
$838$			2.17333e7i			1.06909i
$839$	−3.42013e7			−1.67740			−0.838702	−	0.544591i	$-0.816685\pi$
$839$	−3.42013e7			−1.67740			−0.838702	+	0.544591i	$0.816685\pi$
$840$	−3.47692e6			−0.170019
$841$	2.01431e7			0.982057
$842$	1.31051e7			0.637032
$843$			383230.i			0.0185734i
$844$	7.57452e7			3.66015
$845$			1.72011e7i			0.828733i
$846$		−	5.87849e7i		−	2.82384i
$847$	3.04231e6			0.145712
$848$	1.05300e7			0.502850
$849$		−	1.57536e6i		−	0.0750087i
$850$	−9.05816e7			−4.30024
$851$	1.92158e7	−	8.91606e6i	0.909569	−	0.422036i
$852$	−7.14862e6			−0.337383
$853$		−	1.32406e6i		−	0.0623067i	−0.999515	−	0.0311533i	$-0.990082\pi$
$853$		−	1.32406e6i		−	0.0623067i	0.999515	−	0.0311533i	$-0.00991802\pi$
$854$	1.08707e7			0.510048
$855$	5.27879e7			2.46956
$856$		−	3.15971e7i		−	1.47388i
$857$			2.78886e6i			0.129710i	0.997895	+	0.0648551i	$0.0206585\pi$
$857$			2.78886e6i			0.129710i	−0.997895	+	0.0648551i	$0.979341\pi$
$858$	−5.68680e6			−0.263724
$859$			624964.i			0.0288983i	0.999896	+	0.0144491i	$0.00459947\pi$
$859$			624964.i			0.0288983i	−0.999896	+	0.0144491i	$0.995401\pi$
$860$	3.75823e7			1.73276
$861$	−1.01265e6			−0.0465533
$862$	−5.43985e7			−2.49355
$863$	4.16503e7			1.90367			0.951833	−	0.306617i	$-0.0991969\pi$
$863$	4.16503e7			1.90367			0.951833	+	0.306617i	$0.0991969\pi$
$864$			1.26024e6i			0.0574338i
$865$		−	1.96595e7i		−	0.893370i
$866$			4.88513e7i			2.21351i
$867$	767977.			0.0346977
$868$			1.45987e7i			0.657678i
$869$			2.37891e7i			1.06863i
$870$		−	1.66242e6i		−	0.0744634i
$871$		−	110134.i		−	0.00491899i
$872$	−2.74296e7			−1.22160
$873$			3.96818e6i			0.176220i
$874$			5.58614e7i			2.47362i
$875$		−	1.49540e7i		−	0.660293i
$876$	−7.09752e6			−0.312497
$877$	3.26671e6			0.143421			0.0717103	−	0.997426i	$-0.477154\pi$
$877$	3.26671e6			0.143421			0.0717103	+	0.997426i	$0.477154\pi$
$878$	−1.55959e7			−0.682771
$879$	4.46169e6			0.194772
$880$			3.34740e7i			1.45714i
$881$	2.15378e7			0.934890			0.467445	−	0.884022i	$-0.345175\pi$
$881$	2.15378e7			0.934890			0.467445	+	0.884022i	$0.345175\pi$
$882$			3.57272e7i			1.54642i
$883$			2.95246e7i			1.27433i	0.770727	+	0.637165i	$0.219893\pi$
$883$			2.95246e7i			1.27433i	−0.770727	+	0.637165i	$0.780107\pi$
$884$	−6.28268e7			−2.70405
$885$	4.21119e6			0.180737
$886$			2.58795e6i			0.110757i
$887$	1.97635e7			0.843439			0.421720	−	0.906726i	$-0.361427\pi$
$887$	1.97635e7			0.843439			0.421720	+	0.906726i	$0.361427\pi$
$888$	6.87418e6	−	3.18959e6i	0.292542	−	0.135738i
$889$	9.07238e6			0.385005
$890$			6.31138e7i			2.67085i
$891$	−1.52281e7			−0.642614
$892$	4.97374e7			2.09301
$893$		−	5.62499e7i		−	2.36044i
$894$		−	8.80755e6i		−	0.368563i
$895$	2.28608e7			0.953969
$896$		−	1.16137e7i		−	0.483283i
$897$	5.15553e6			0.213940
$898$	−4.43074e6			−0.183352
$899$	−3.56891e6			−0.147277
$900$	−1.08508e8			−4.46536
$901$		−	1.17478e7i		−	0.482109i
$902$			2.72351e7i			1.11458i
$903$		−	593968.i		−	0.0242406i
$904$	1.71104e7			0.696370
$905$		−	1.18528e7i		−	0.481060i
$906$		−	3.21410e6i		−	0.130089i
$907$			1.61434e7i			0.651593i	0.945440	+	0.325796i	$0.105632\pi$
$907$			1.61434e7i			0.651593i	−0.945440	+	0.325796i	$0.894368\pi$
$908$		−	3.21429e6i		−	0.129381i
$909$	−2.81669e7			−1.13065
$910$		−	2.77690e7i		−	1.11162i
$911$		−	4.35170e7i		−	1.73725i	−0.495467	−	0.868627i	$-0.665003\pi$
$911$		−	4.35170e7i		−	1.73725i	0.495467	−	0.868627i	$-0.334997\pi$
$912$			7.15345e6i			0.284792i
$913$	1.03574e7			0.411219
$914$	2.36074e6			0.0934724
$915$	−8.06376e6			−0.318409
$916$	7.61761e7			2.99971
$917$			1.11587e7i			0.438217i
$918$	1.69494e7			0.663816
$919$			2.20543e7i			0.861398i	0.902496	+	0.430699i	$0.141733\pi$
$919$			2.20543e7i			0.861398i	−0.902496	+	0.430699i	$0.858267\pi$
$920$		−	8.47755e7i		−	3.30218i
$921$	−4.80854e6			−0.186794
$922$	7.58607e7			2.93893
$923$		−	2.91920e7i		−	1.12787i
$924$	1.94161e6			0.0748138
$925$	2.46710e7	+	5.31709e7i	0.948054	+	2.04324i
$926$	5.53970e7			2.12304
$927$			3.76799e7i			1.44016i
$928$	−580451.			−0.0221256
$929$	−4.05513e7			−1.54158			−0.770788	−	0.637091i	$-0.780137\pi$
$929$	−4.05513e7			−1.54158			−0.770788	+	0.637091i	$0.780137\pi$
$930$		−	1.61214e7i		−	0.611215i
$931$			3.41865e7i			1.29265i
$932$	2.52969e7			0.953954
$933$		−	5.13055e6i		−	0.192957i
$934$	−4.41172e7			−1.65478
$935$	3.73454e7			1.39704
$936$	−5.72864e7			−2.13728
$937$	−1.56270e6			−0.0581469			−0.0290734	−	0.999577i	$-0.509256\pi$
$937$	−1.56270e6			−0.0581469			−0.0290734	+	0.999577i	$0.509256\pi$
$938$			55978.5i			0.00207737i
$939$			8.16725e6i			0.302282i
$940$			1.66957e8i			6.16289i
$941$	1.60631e7			0.591364			0.295682	−	0.955286i	$-0.404453\pi$
$941$	1.60631e7			0.591364			0.295682	+	0.955286i	$0.404453\pi$
$942$			1.55594e7i			0.571301i
$943$		−	2.46907e7i		−	0.904179i
$944$		−	1.77257e7i		−	0.647400i
$945$			5.03225e6i			0.183308i
$946$	−1.59747e7			−0.580371
$947$		−	2.24583e7i		−	0.813769i	−0.913480	−	0.406885i	$-0.866615\pi$
$947$		−	2.24583e7i		−	0.813769i	0.913480	−	0.406885i	$-0.133385\pi$
$948$		−	1.50893e7i		−	0.545316i
$949$		−	2.89833e7i		−	1.04468i
$950$	−1.54570e8			−5.55670
$951$	−2.61637e6			−0.0938098
$952$	1.63276e7			0.583888
$953$	−1.58089e7			−0.563856			−0.281928	−	0.959435i	$-0.590974\pi$
$953$	−1.58089e7			−0.563856			−0.281928	+	0.959435i	$0.590974\pi$
$954$		−	2.09501e7i		−	0.745274i
$955$	−4.91323e7			−1.74325
$956$		−	4.52354e7i		−	1.60079i
$957$			474662.i			0.0167535i
$958$	−1.42745e7			−0.502512
$959$	5.95896e6			0.209230
$960$			7.75423e6i			0.271557i
$961$	−5.98038e6			−0.208891
$962$	2.54741e7	+	5.49017e7i	0.887486	+	1.91271i
$963$	−2.25034e7			−0.781958
$964$		−	9.04930e7i		−	3.13633i
$965$	−3.44293e7			−1.19017
$966$	−2.62044e6			−0.0903505
$967$		−	3.63358e6i		−	0.124959i	−0.998046	−	0.0624796i	$-0.980099\pi$
$967$		−	3.63358e6i		−	0.124959i	0.998046	−	0.0624796i	$-0.0199008\pi$
$968$			2.65363e7i			0.910233i
$969$	7.98077e6			0.273046
$970$		−	1.67778e7i		−	0.572541i
$971$	−5.02464e6			−0.171024			−0.0855120	−	0.996337i	$-0.527253\pi$
$971$	−5.02464e6			−0.171024			−0.0855120	+	0.996337i	$0.527253\pi$
$972$	3.06165e7			1.03942
$973$	−7.89758e6			−0.267431
$974$	2.90553e7			0.981358
$975$			1.42655e7i			0.480591i
$976$			3.39418e7i			1.14054i
$977$		−	5.10227e7i		−	1.71012i	−0.518528	−	0.855060i	$-0.673520\pi$
$977$		−	5.10227e7i		−	1.71012i	0.518528	−	0.855060i	$-0.326480\pi$
$978$	7.38347e6			0.246839
$979$		−	1.80205e7i		−	0.600911i
$980$		−	1.01470e8i		−	3.37499i
$981$			1.95354e7i			0.648110i
$982$		−	2.47368e7i		−	0.818586i
$983$	1.38574e6			0.0457404			0.0228702	−	0.999738i	$-0.492720\pi$
$983$	1.38574e6			0.0457404			0.0228702	+	0.999738i	$0.492720\pi$
$984$		−	8.83273e6i		−	0.290809i
$985$			6.56557e7i			2.15616i
$986$			7.80671e6i			0.255727i
$987$	2.63866e6			0.0862166
$988$	−1.07209e8			−3.49412
$989$	1.44823e7			0.470812
$990$	6.65989e7			2.15963
$991$		−	2.87127e7i		−	0.928732i	−0.885643	−	0.464366i	$-0.846282\pi$
$991$		−	2.87127e7i		−	0.928732i	0.885643	−	0.464366i	$-0.153718\pi$
$992$	−5.62893e6			−0.181613
$993$		−	5.30443e6i		−	0.170713i
$994$			1.48376e7i			0.476318i
$995$	−7.86235e7			−2.51764
$996$	−6.56962e6			−0.209842
$997$		−	3.96980e7i		−	1.26483i	−0.774631	−	0.632413i	$-0.782064\pi$
$997$		−	3.96980e7i		−	1.26483i	0.774631	−	0.632413i	$-0.217936\pi$
$998$	2.61095e7			0.829797
$999$	−4.61638e6	−	9.94920e6i	−0.146348	−	0.315409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.b.a.36.15	yes	16
3.2	odd	2		333.6.c.d.73.2		16
4.3	odd	2		592.6.g.c.369.9		16
37.36	even	2	inner	37.6.b.a.36.2	✓	16
111.110	odd	2		333.6.c.d.73.15		16
148.147	odd	2		592.6.g.c.369.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.b.a.36.2	✓	16	37.36	even	2	inner
37.6.b.a.36.15	yes	16	1.1	even	1	trivial
333.6.c.d.73.2		16	3.2	odd	2
333.6.c.d.73.15		16	111.110	odd	2
592.6.g.c.369.9		16	4.3	odd	2
592.6.g.c.369.10		16	148.147	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	37.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+9.87320i q^{2} -2.75305 q^{3} -65.4800 q^{4} -100.817i q^{5} -27.1814i q^{6} -37.8971 q^{7} -330.555i q^{8} -235.421 q^{9} +O(q^{10})\)	\(q+9.87320i q^{2} -2.75305 q^{3} -65.4800 q^{4} -100.817i q^{5} -27.1814i q^{6} -37.8971 q^{7} -330.555i q^{8} -235.421 q^{9} +995.382 q^{10} -284.206 q^{11} +180.270 q^{12} +736.146i q^{13} -374.166i q^{14} +277.553i q^{15} +1168.27 q^{16} -1303.38i q^{17} -2324.35i q^{18} -2224.12i q^{19} +6601.47i q^{20} +104.333 q^{21} -2806.02i q^{22} +2543.87i q^{23} +910.033i q^{24} -7038.98 q^{25} -7268.11 q^{26} +1317.12 q^{27} +2481.50 q^{28} +606.649i q^{29} -2740.33 q^{30} +5882.99i q^{31} +956.815i q^{32} +782.432 q^{33} +12868.6 q^{34} +3820.66i q^{35} +15415.3 q^{36} +(-3504.92 - 7553.78i) q^{37} +21959.2 q^{38} -2026.65i q^{39} -33325.4 q^{40} -9705.95 q^{41} +1030.10i q^{42} -5693.02i q^{43} +18609.8 q^{44} +23734.3i q^{45} -25116.2 q^{46} +25290.9 q^{47} -3216.31 q^{48} -15370.8 q^{49} -69497.2i q^{50} +3588.28i q^{51} -48202.8i q^{52} +9013.32 q^{53} +13004.1i q^{54} +28652.6i q^{55} +12527.1i q^{56} +6123.11i q^{57} -5989.57 q^{58} -15172.6i q^{59} -18174.2i q^{60} +29053.1i q^{61} -58083.9 q^{62} +8921.77 q^{63} +27937.8 q^{64} +74215.7 q^{65} +7725.10i q^{66} -149.609 q^{67} +85345.6i q^{68} -7003.41i q^{69} -37722.1 q^{70} -39655.1 q^{71} +77819.4i q^{72} -39371.7 q^{73} +(74579.9 - 34604.7i) q^{74} +19378.7 q^{75} +145635. i q^{76} +10770.6 q^{77} +20009.5 q^{78} -83704.0i q^{79} -117781. i q^{80} +53581.2 q^{81} -95828.7i q^{82} -36443.3 q^{83} -6831.70 q^{84} -131403. q^{85} +56208.3 q^{86} -1670.14i q^{87} +93945.5i q^{88} +63406.6i q^{89} -234333. q^{90} -27897.8i q^{91} -166573. i q^{92} -16196.1i q^{93} +249702. i q^{94} -224228. q^{95} -2634.16i q^{96} -16855.7i q^{97} -151759. i q^{98} +66907.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 18 q^{3} - 268 q^{4} + 190 q^{7} + 1394 q^{9}+O(q^{10}) \) 16 * q - 18 * q^3 - 268 * q^4 + 190 * q^7 + 1394 * q^9	\( 16 q - 18 q^{3} - 268 q^{4} + 190 q^{7} + 1394 q^{9} - 74 q^{10} - 1110 q^{11} + 1402 q^{12} + 2900 q^{16} - 7010 q^{21} - 12052 q^{25} + 4902 q^{26} + 4266 q^{27} - 16824 q^{28} + 19280 q^{30} - 2478 q^{33} + 20556 q^{34} - 51402 q^{36} - 11400 q^{37} + 12108 q^{38} + 16966 q^{40} + 3918 q^{41} + 125394 q^{44} + 17470 q^{46} + 3822 q^{47} - 78034 q^{48} - 32618 q^{49} - 24126 q^{53} - 164718 q^{58} - 81426 q^{62} + 219268 q^{63} + 158076 q^{64} + 98976 q^{65} + 23560 q^{67} - 222404 q^{70} - 50046 q^{71} - 196274 q^{73} + 141216 q^{74} + 214054 q^{75} - 239574 q^{77} - 90822 q^{78} + 317312 q^{81} - 215814 q^{83} + 438572 q^{84} - 346472 q^{85} + 197640 q^{86} - 857612 q^{90} - 132504 q^{95} - 574860 q^{99}+O(q^{100}) \) 16 * q - 18 * q^3 - 268 * q^4 + 190 * q^7 + 1394 * q^9 - 74 * q^10 - 1110 * q^11 + 1402 * q^12 + 2900 * q^16 - 7010 * q^21 - 12052 * q^25 + 4902 * q^26 + 4266 * q^27 - 16824 * q^28 + 19280 * q^30 - 2478 * q^33 + 20556 * q^34 - 51402 * q^36 - 11400 * q^37 + 12108 * q^38 + 16966 * q^40 + 3918 * q^41 + 125394 * q^44 + 17470 * q^46 + 3822 * q^47 - 78034 * q^48 - 32618 * q^49 - 24126 * q^53 - 164718 * q^58 - 81426 * q^62 + 219268 * q^63 + 158076 * q^64 + 98976 * q^65 + 23560 * q^67 - 222404 * q^70 - 50046 * q^71 - 196274 * q^73 + 141216 * q^74 + 214054 * q^75 - 239574 * q^77 - 90822 * q^78 + 317312 * q^81 - 215814 * q^83 + 438572 * q^84 - 346472 * q^85 + 197640 * q^86 - 857612 * q^90 - 132504 * q^95 - 574860 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more