LMFDB - Embedded newform 37.6.b.a.36.10

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			36.10
Root			$2.85171i$ of defining polynomial
Character	$\chi$	$=$	37.36
Dual form			37.6.b.a.36.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.85171i q^{2} -12.3080 q^{3} +23.8677 q^{4} +38.2713i q^{5} -35.0990i q^{6} -96.3094 q^{7} +159.319i q^{8} -91.5127 q^{9} +O(q^{10})$	\(q+2.85171i q^{2} -12.3080 q^{3} +23.8677 q^{4} +38.2713i q^{5} -35.0990i q^{6} -96.3094 q^{7} +159.319i q^{8} -91.5127 q^{9} -109.139 q^{10} -564.497 q^{11} -293.764 q^{12} +678.423i q^{13} -274.647i q^{14} -471.044i q^{15} +309.435 q^{16} -2074.76i q^{17} -260.968i q^{18} +2693.06i q^{19} +913.449i q^{20} +1185.38 q^{21} -1609.78i q^{22} +3071.93i q^{23} -1960.90i q^{24} +1660.31 q^{25} -1934.67 q^{26} +4117.19 q^{27} -2298.69 q^{28} -2966.43i q^{29} +1343.28 q^{30} -5199.33i q^{31} +5980.62i q^{32} +6947.84 q^{33} +5916.63 q^{34} -3685.89i q^{35} -2184.20 q^{36} +(7849.71 + 2779.56i) q^{37} -7679.83 q^{38} -8350.04i q^{39} -6097.34 q^{40} -6499.88 q^{41} +3380.36i q^{42} +8586.79i q^{43} -13473.3 q^{44} -3502.31i q^{45} -8760.27 q^{46} -8498.42 q^{47} -3808.54 q^{48} -7531.50 q^{49} +4734.72i q^{50} +25536.2i q^{51} +16192.4i q^{52} +22725.8 q^{53} +11741.0i q^{54} -21604.0i q^{55} -15343.9i q^{56} -33146.2i q^{57} +8459.41 q^{58} +23622.9i q^{59} -11242.7i q^{60} +14456.4i q^{61} +14827.0 q^{62} +8813.53 q^{63} -7153.11 q^{64} -25964.1 q^{65} +19813.3i q^{66} -4980.51 q^{67} -49519.8i q^{68} -37809.4i q^{69} +10511.1 q^{70} -7644.87 q^{71} -14579.7i q^{72} +76611.5 q^{73} +(-7926.51 + 22385.1i) q^{74} -20435.1 q^{75} +64277.1i q^{76} +54366.4 q^{77} +23811.9 q^{78} -43134.5i q^{79} +11842.5i q^{80} -28436.9 q^{81} -18535.8i q^{82} -48677.9 q^{83} +28292.3 q^{84} +79403.8 q^{85} -24487.1 q^{86} +36510.9i q^{87} -89935.0i q^{88} +46571.1i q^{89} +9987.59 q^{90} -65338.5i q^{91} +73320.0i q^{92} +63993.5i q^{93} -24235.1i q^{94} -103067. q^{95} -73609.6i q^{96} +135193. i q^{97} -21477.7i q^{98} +51658.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.85171i			0.504117i	0.967712	+	0.252058i	$0.0811075\pi$
$2$			2.85171i			0.504117i	−0.967712	+	0.252058i	$0.918893\pi$
$3$	−12.3080			−0.789560			−0.394780	−	0.918776i	$-0.629179\pi$
$3$	−12.3080			−0.789560			−0.394780	+	0.918776i	$0.629179\pi$
$4$	23.8677			0.745866
$5$			38.2713i			0.684618i	0.939587	+	0.342309i	$0.111209\pi$
$5$			38.2713i			0.684618i	−0.939587	+	0.342309i	$0.888791\pi$
$6$		−	35.0990i		−	0.398030i
$7$	−96.3094			−0.742888			−0.371444	−	0.928455i	$-0.621137\pi$
$7$	−96.3094			−0.742888			−0.371444	+	0.928455i	$0.621137\pi$
$8$			159.319i			0.880120i
$9$	−91.5127			−0.376595
$10$	−109.139			−0.345127
$11$	−564.497			−1.40663			−0.703315	−	0.710878i	$-0.748298\pi$
$11$	−564.497			−1.40663			−0.703315	+	0.710878i	$0.748298\pi$
$12$	−293.764			−0.588906
$13$			678.423i			1.11338i	0.830721	+	0.556688i	$0.187928\pi$
$13$			678.423i			1.11338i	−0.830721	+	0.556688i	$0.812072\pi$
$14$		−	274.647i		−	0.374502i
$15$		−	471.044i		−	0.540547i
$16$	309.435			0.302183
$17$		−	2074.76i		−	1.74119i	−0.492002	−	0.870594i	$-0.663735\pi$
$17$		−	2074.76i		−	1.74119i	0.492002	−	0.870594i	$-0.336265\pi$
$18$		−	260.968i		−	0.189848i
$19$			2693.06i			1.71144i	0.517440	+	0.855719i	$0.326885\pi$
$19$			2693.06i			1.71144i	−0.517440	+	0.855719i	$0.673115\pi$
$20$			913.449i			0.510634i
$21$	1185.38			0.586555
$22$		−	1609.78i		−	0.709106i
$23$			3071.93i			1.21085i	0.795901	+	0.605427i	$0.206998\pi$
$23$			3071.93i			1.21085i	−0.795901	+	0.605427i	$0.793002\pi$
$24$		−	1960.90i		−	0.694908i
$25$	1660.31			0.531298
$26$	−1934.67			−0.561272
$27$	4117.19			1.08690
$28$	−2298.69			−0.554095
$29$		−	2966.43i		−	0.654996i	−0.944852	−	0.327498i	$-0.893794\pi$
$29$		−	2966.43i		−	0.654996i	0.944852	−	0.327498i	$-0.106206\pi$
$30$	1343.28			0.272499
$31$		−	5199.33i		−	0.971725i	−0.874035	−	0.485863i	$-0.838506\pi$
$31$		−	5199.33i		−	0.971725i	0.874035	−	0.485863i	$-0.161494\pi$
$32$			5980.62i			1.03246i
$33$	6947.84			1.11062
$34$	5916.63			0.877762
$35$		−	3685.89i		−	0.508595i
$36$	−2184.20			−0.280890
$37$	7849.71	+	2779.56i	0.942648	+	0.333789i
$37$	7849.71	+	2779.56i	0.942648	+	0.333789i
$38$	−7679.83			−0.862765
$39$		−	8350.04i		−	0.879078i
$40$	−6097.34			−0.602546
$41$	−6499.88			−0.603873			−0.301937	−	0.953328i	$-0.597633\pi$
$41$	−6499.88			−0.603873			−0.301937	+	0.953328i	$0.597633\pi$
$42$			3380.36i			0.295692i
$43$			8586.79i			0.708206i	0.935206	+	0.354103i	$0.115214\pi$
$43$			8586.79i			0.708206i	−0.935206	+	0.354103i	$0.884786\pi$
$44$	−13473.3			−1.04916
$45$		−	3502.31i		−	0.257824i
$46$	−8760.27			−0.610412
$47$	−8498.42			−0.561169			−0.280584	−	0.959829i	$-0.590528\pi$
$47$	−8498.42			−0.561169			−0.280584	+	0.959829i	$0.590528\pi$
$48$	−3808.54			−0.238591
$49$	−7531.50			−0.448117
$50$			4734.72i			0.267836i
$51$			25536.2i			1.37477i
$52$			16192.4i			0.830430i
$53$	22725.8			1.11130			0.555648	−	0.831418i	$-0.312470\pi$
$53$	22725.8			1.11130			0.555648	+	0.831418i	$0.312470\pi$
$54$			11741.0i			0.547927i
$55$		−	21604.0i		−	0.963004i
$56$		−	15343.9i		−	0.653831i
$57$		−	33146.2i		−	1.35128i
$58$	8459.41			0.330195
$59$			23622.9i			0.883492i	0.897140	+	0.441746i	$0.145641\pi$
$59$			23622.9i			0.883492i	−0.897140	+	0.441746i	$0.854359\pi$
$60$		−	11242.7i		−	0.403176i
$61$			14456.4i			0.497435i	0.968576	+	0.248718i	$0.0800091\pi$
$61$			14456.4i			0.497435i	−0.968576	+	0.248718i	$0.919991\pi$
$62$	14827.0			0.489863
$63$	8813.53			0.279768
$64$	−7153.11			−0.218295
$65$	−25964.1			−0.762238
$66$			19813.3i			0.559881i
$67$	−4980.51			−0.135546			−0.0677730	−	0.997701i	$-0.521589\pi$
$67$	−4980.51			−0.135546			−0.0677730	+	0.997701i	$0.521589\pi$
$68$		−	49519.8i		−	1.29869i
$69$		−	37809.4i		−	0.956042i
$70$	10511.1			0.256391
$71$	−7644.87			−0.179980			−0.0899900	−	0.995943i	$-0.528684\pi$
$71$	−7644.87			−0.179980			−0.0899900	+	0.995943i	$0.528684\pi$
$72$		−	14579.7i		−	0.331449i
$73$	76611.5			1.68262			0.841312	−	0.540550i	$-0.181784\pi$
$73$	76611.5			1.68262			0.841312	+	0.540550i	$0.181784\pi$
$74$	−7926.51	+	22385.1i	−0.168268	+	0.475205i
$75$	−20435.1			−0.419492
$76$			64277.1i			1.27650i
$77$	54366.4			1.04497
$78$	23811.9			0.443158
$79$		−	43134.5i		−	0.777601i	−0.921322	−	0.388800i	$-0.872890\pi$
$79$		−	43134.5i		−	0.777601i	0.921322	−	0.388800i	$-0.127110\pi$
$80$			11842.5i			0.206880i
$81$	−28436.9			−0.481581
$82$		−	18535.8i		−	0.304423i
$83$	−48677.9			−0.775599			−0.387799	−	0.921744i	$-0.626765\pi$
$83$	−48677.9			−0.775599			−0.387799	+	0.921744i	$0.626765\pi$
$84$	28292.3			0.437491
$85$	79403.8			1.19205
$86$	−24487.1			−0.357019
$87$			36510.9i			0.517159i
$88$		−	89935.0i		−	1.23800i
$89$			46571.1i			0.623220i	0.950210	+	0.311610i	$0.100868\pi$
$89$			46571.1i			0.623220i	−0.950210	+	0.311610i	$0.899132\pi$
$90$	9987.59			0.129973
$91$		−	65338.5i		−	0.827114i
$92$			73320.0i			0.903135i
$93$			63993.5i			0.767235i
$94$		−	24235.1i		−	0.282894i
$95$	−103067.			−1.17168
$96$		−	73609.6i		−	0.815186i
$97$			135193.i			1.45889i	0.684038	+	0.729446i	$0.260222\pi$
$97$			135193.i			1.45889i	−0.684038	+	0.729446i	$0.739778\pi$
$98$		−	21477.7i		−	0.225903i
$99$	51658.6			0.529730
$100$	39627.7			0.396277
$101$	−200856.			−1.95921			−0.979605	−	0.200933i	$-0.935603\pi$
$101$	−200856.			−1.95921			−0.979605	+	0.200933i	$0.935603\pi$
$102$	−72821.9			−0.693046
$103$			62474.9i			0.580247i	0.956989	+	0.290123i	$0.0936963\pi$
$103$			62474.9i			0.580247i	−0.956989	+	0.290123i	$0.906304\pi$
$104$	−108086.			−0.979906
$105$			45366.0i			0.401566i
$106$			64807.6i			0.560223i
$107$	−39477.9			−0.333345			−0.166673	−	0.986012i	$-0.553302\pi$
$107$	−39477.9			−0.333345			−0.166673	+	0.986012i	$0.553302\pi$
$108$	98267.9			0.810685
$109$		−	117545.i		−	0.947628i	−0.880625	−	0.473814i	$-0.842877\pi$
$109$		−	117545.i		−	0.947628i	0.880625	−	0.473814i	$-0.157123\pi$
$110$	61608.6			0.485467
$111$	−96614.4	−	34210.9i	−0.744277	−	0.263546i
$112$	−29801.5			−0.224488
$113$		−	158580.i		−	1.16830i	−0.811647	−	0.584148i	$-0.801429\pi$
$113$		−	158580.i		−	1.16830i	0.811647	−	0.584148i	$-0.198571\pi$
$114$	94523.5			0.681205
$115$	−117567.			−0.828972
$116$		−	70801.9i		−	0.488540i
$117$		−	62084.3i		−	0.419292i
$118$	−67365.7			−0.445383
$119$			199819.i			1.29351i
$120$	75046.2			0.475746
$121$	157606.			0.978608
$122$	−41225.6			−0.250765
$123$	80000.7			0.476794
$124$		−	124096.i		−	0.724777i
$125$			183140.i			1.04835i
$126$			25133.7i			0.141036i
$127$	77966.9			0.428944			0.214472	−	0.976730i	$-0.431197\pi$
$127$	77966.9			0.428944			0.214472	+	0.976730i	$0.431197\pi$
$128$			170981.i			0.922409i
$129$		−	105686.i		−	0.559171i
$130$		−	74042.3i		−	0.384257i
$131$			160530.i			0.817294i	0.912693	+	0.408647i	$0.133999\pi$
$131$			160530.i			0.817294i	−0.912693	+	0.408647i	$0.866001\pi$
$132$	165829.			0.828373
$133$		−	259367.i		−	1.27141i
$134$		−	14203.0i		−	0.0683310i
$135$			157570.i			0.744114i
$136$	330548.			1.53246
$137$	51981.2			0.236616			0.118308	−	0.992977i	$-0.462253\pi$
$137$	51981.2			0.236616			0.118308	+	0.992977i	$0.462253\pi$
$138$	107822.			0.481957
$139$	−402175.			−1.76554			−0.882771	−	0.469803i	$-0.844325\pi$
$139$	−402175.			−1.76554			−0.882771	+	0.469803i	$0.844325\pi$
$140$		−	87973.7i		−	0.379344i
$141$	104599.			0.443076
$142$		−	21801.0i		−	0.0907309i
$143$		−	382968.i		−	1.56611i
$144$	−28317.2			−0.113801
$145$	113529.			0.448422
$146$			218474.i			0.848239i
$147$	92697.9			0.353815
$148$	187355.	+	66341.8i	0.703089	+	0.248962i
$149$	33622.9			0.124071			0.0620353	−	0.998074i	$-0.480241\pi$
$149$	33622.9			0.124071			0.0620353	+	0.998074i	$0.480241\pi$
$150$		−	58275.0i		−	0.211473i
$151$	46126.5			0.164630			0.0823148	−	0.996606i	$-0.473769\pi$
$151$	46126.5			0.164630			0.0823148	+	0.996606i	$0.473769\pi$
$152$	−429055.			−1.50627
$153$			189867.i			0.655723i
$154$			155037.i			0.526786i
$155$	198985.			0.665261
$156$		−	199296.i		−	0.655674i
$157$	−189721.			−0.614281			−0.307140	−	0.951664i	$-0.599372\pi$
$157$	−189721.			−0.614281			−0.307140	+	0.951664i	$0.599372\pi$
$158$	123007.			0.392002
$159$	−279710.			−0.877435
$160$	−228886.			−0.706838
$161$		−	295856.i		−	0.899529i
$162$		−	81093.8i		−	0.242773i
$163$		−	89298.7i		−	0.263255i	−0.991299	−	0.131627i	$-0.957980\pi$
$163$		−	89298.7i		−	0.263255i	0.991299	−	0.131627i	$-0.0420202\pi$
$164$	−155137.			−0.450409
$165$			265903.i			0.760350i
$166$		−	138816.i		−	0.390992i
$167$			84828.3i			0.235369i	0.993051	+	0.117685i	$0.0375472\pi$
$167$			84828.3i			0.235369i	−0.993051	+	0.117685i	$0.962453\pi$
$168$			188853.i			0.516239i
$169$	−88964.7			−0.239608
$170$			226437.i			0.600932i
$171$		−	246449.i		−	0.644520i
$172$			204947.i			0.528227i
$173$	352138.			0.894536			0.447268	−	0.894400i	$-0.352397\pi$
$173$	352138.			0.894536			0.447268	+	0.894400i	$0.352397\pi$
$174$	−104119.			−0.260708
$175$	−159903.			−0.394695
$176$	−174675.			−0.425059
$177$		−	290751.i		−	0.697570i
$178$	−132808.			−0.314176
$179$			167857.i			0.391568i	0.980647	+	0.195784i	$0.0627252\pi$
$179$			167857.i			0.391568i	−0.980647	+	0.195784i	$0.937275\pi$
$180$		−	83592.1i		−	0.192302i
$181$	416443.			0.944842			0.472421	−	0.881373i	$-0.343380\pi$
$181$	416443.			0.944842			0.472421	+	0.881373i	$0.343380\pi$
$182$	186327.			0.416962
$183$		−	177930.i		−	0.392755i
$184$	−489416.			−1.06570
$185$	−106377.	+	300419.i	−0.228518	+	0.645354i
$186$	−182491.			−0.386776
$187$			1.17120e6i			2.44921i
$188$	−202838.			−0.418557
$189$	−396524.			−0.807448
$190$		−	293917.i		−	0.590664i
$191$		−	713843.i		−	1.41586i	−0.706284	−	0.707929i	$-0.749630\pi$
$191$		−	713843.i		−	1.41586i	0.706284	−	0.707929i	$-0.250370\pi$
$192$	88040.6			0.172357
$193$			133580.i			0.258136i	0.991636	+	0.129068i	$0.0411986\pi$
$193$			133580.i			0.258136i	−0.991636	+	0.129068i	$0.958801\pi$
$194$	−385531.			−0.735452
$195$	319567.			0.601832
$196$	−179760.			−0.334235
$197$	637649.			1.17062			0.585310	−	0.810809i	$-0.300973\pi$
$197$	637649.			1.17062			0.585310	+	0.810809i	$0.300973\pi$
$198$			147316.i			0.267046i
$199$			363643.i			0.650942i	0.945552	+	0.325471i	$0.105523\pi$
$199$			363643.i			0.650942i	−0.945552	+	0.325471i	$0.894477\pi$
$200$			264518.i			0.467606i
$201$	61300.2			0.107022
$202$		−	572784.i		−	0.987671i
$203$			285695.i			0.486589i
$204$			609491.i			1.02540i
$205$		−	248759.i		−	0.413423i
$206$	−178161.			−0.292512
$207$		−	281120.i		−	0.456002i
$208$			209928.i			0.336443i
$209$		−	1.52022e6i		−	2.40736i
$210$	−129371.			−0.202436
$211$	1.19996e6			1.85550			0.927752	−	0.373197i	$-0.121738\pi$
$211$	1.19996e6			1.85550			0.927752	+	0.373197i	$0.121738\pi$
$212$	542413.			0.828878
$213$	94093.2			0.142105
$214$		−	112580.i		−	0.168045i
$215$	−328628.			−0.484851
$216$			655946.i			0.956607i
$217$			500745.i			0.721883i
$218$	335205.			0.477715
$219$	−942936.			−1.32853
$220$		−	515639.i		−	0.718272i
$221$	1.40757e6			1.93860
$222$	97559.7	−	275517.i	0.132858	−	0.375202i
$223$	−54778.0			−0.0737640			−0.0368820	−	0.999320i	$-0.511743\pi$
$223$	−54778.0			−0.0737640			−0.0368820	+	0.999320i	$0.511743\pi$
$224$		−	575990.i		−	0.766999i
$225$	−151939.			−0.200084
$226$	452225.			0.588957
$227$		−	802415.i		−	1.03356i	−0.856119	−	0.516778i	$-0.827131\pi$
$227$		−	802415.i		−	1.03356i	0.856119	−	0.516778i	$-0.172869\pi$
$228$		−	791124.i		−	1.00788i
$229$	710586.			0.895423			0.447711	−	0.894178i	$-0.352239\pi$
$229$	710586.			0.895423			0.447711	+	0.894178i	$0.352239\pi$
$230$		−	335267.i		−	0.417899i
$231$	−669142.			−0.825065
$232$	472608.			0.576476
$233$	307185.			0.370689			0.185345	−	0.982674i	$-0.440660\pi$
$233$	307185.			0.370689			0.185345	+	0.982674i	$0.440660\pi$
$234$	177047.			0.211372
$235$		−	325246.i		−	0.384186i
$236$			563824.i			0.658967i
$237$			530900.i			0.613962i
$238$	−569827.			−0.652079
$239$			1.34121e6i			1.51881i	0.650621	+	0.759403i	$0.274509\pi$
$239$			1.34121e6i			1.51881i	−0.650621	+	0.759403i	$0.725491\pi$
$240$		−	145758.i		−	0.163344i
$241$			1.02266e6i			1.13420i	0.823650	+	0.567099i	$0.191934\pi$
$241$			1.02266e6i			1.13420i	−0.823650	+	0.567099i	$0.808066\pi$
$242$			449447.i			0.493333i
$243$	−650475.			−0.706668
$244$			345042.i			0.371020i
$245$		−	288241.i		−	0.306789i
$246$			228139.i			0.240360i
$247$	−1.82703e6			−1.90548
$248$	828352.			0.855235
$249$	599129.			0.612381
$250$	−522263.			−0.528493
$251$		−	25154.5i		−	0.0252018i	−0.999921	−	0.0126009i	$-0.995989\pi$
$251$		−	25154.5i		−	0.0252018i	0.999921	−	0.0126009i	$-0.00401110\pi$
$252$	210359.			0.208670
$253$		−	1.73410e6i		−	1.70322i
$254$			222339.i			0.216238i
$255$	−977304.			−0.941194
$256$	−716489.			−0.683298
$257$			815697.i			0.770364i	0.922841	+	0.385182i	$0.125861\pi$
$257$			815697.i			0.770364i	−0.922841	+	0.385182i	$0.874139\pi$
$258$	301387.			0.281888
$259$	−756001.	−	267698.i	−0.700282	−	0.247968i
$260$	−619705.			−0.568527
$261$			271466.i			0.246669i
$262$	−457786.			−0.412011
$263$	323462.			0.288359			0.144180	−	0.989552i	$-0.453946\pi$
$263$	323462.			0.288359			0.144180	+	0.989552i	$0.453946\pi$
$264$			1.10692e6i			0.977478i
$265$			869747.i			0.760813i
$266$	739640.			0.640938
$267$		−	573198.i		−	0.492070i
$268$	−118873.			−0.101099
$269$	866044.			0.729725			0.364863	−	0.931061i	$-0.381116\pi$
$269$	866044.			0.729725			0.364863	+	0.931061i	$0.381116\pi$
$270$	−449345.			−0.375120
$271$	120109.			0.0993463			0.0496732	−	0.998766i	$-0.484182\pi$
$271$	120109.			0.0993463			0.0496732	+	0.998766i	$0.484182\pi$
$272$		−	642004.i		−	0.526157i
$273$			804187.i			0.653056i
$274$			148236.i			0.119282i
$275$	−937238.			−0.747340
$276$		−	902424.i		−	0.713079i
$277$		−	1.46087e6i		−	1.14397i	−0.820265	−	0.571983i	$-0.806174\pi$
$277$		−	1.46087e6i		−	1.14397i	0.820265	−	0.571983i	$-0.193826\pi$
$278$		−	1.14689e6i		−	0.890039i
$279$			475805.i			0.365947i
$280$	587231.			0.447625
$281$		−	755744.i		−	0.570964i	−0.958384	−	0.285482i	$-0.907846\pi$
$281$		−	755744.i		−	0.570964i	0.958384	−	0.285482i	$-0.0921537\pi$
$282$			298286.i			0.223362i
$283$			2.59322e6i			1.92474i	0.271735	+	0.962372i	$0.412402\pi$
$283$			2.59322e6i			1.92474i	−0.271735	+	0.962372i	$0.587598\pi$
$284$	−182466.			−0.134241
$285$	1.26855e6			0.925113
$286$	1.09211e6			0.789502
$287$	626000.			0.448610
$288$		−	547303.i		−	0.388818i
$289$	−2.88477e6			−2.03174
$290$			323753.i			0.226057i
$291$		−	1.66395e6i		−	1.15188i
$292$	1.82854e6			1.25501
$293$	−433664.			−0.295111			−0.147555	−	0.989054i	$-0.547140\pi$
$293$	−433664.			−0.295111			−0.147555	+	0.989054i	$0.547140\pi$
$294$			264348.i			0.178364i
$295$	−904078.			−0.604854
$296$	−442836.	+	1.25061e6i	−0.293774	+	0.829644i
$297$	−2.32414e6			−1.52887
$298$			95882.8i			0.0625461i
$299$	−2.08407e6			−1.34814
$300$	−487739.			−0.312885
$301$		−	826988.i		−	0.526118i
$302$			131540.i			0.0829925i
$303$	2.47214e6			1.54691
$304$			833326.i			0.517167i
$305$	−553267.			−0.340553
$306$	−541446.			−0.330561
$307$	1.00344e6			0.607641			0.303820	−	0.952729i	$-0.401738\pi$
$307$	1.00344e6			0.607641			0.303820	+	0.952729i	$0.401738\pi$
$308$	1.29760e6			0.779407
$309$		−	768943.i		−	0.458139i
$310$			567449.i			0.335369i
$311$		−	1.51587e6i		−	0.888714i	−0.895850	−	0.444357i	$-0.853432\pi$
$311$		−	1.51587e6i		−	0.888714i	0.895850	−	0.444357i	$-0.146568\pi$
$312$	1.33032e6			0.773694
$313$			141947.i			0.0818963i	0.999161	+	0.0409482i	$0.0130378\pi$
$313$			141947.i			0.0818963i	−0.999161	+	0.0409482i	$0.986962\pi$
$314$		−	541031.i		−	0.309669i
$315$			337305.i			0.191534i
$316$		−	1.02952e6i		−	0.579986i
$317$	1.48491e6			0.829948			0.414974	−	0.909833i	$-0.363791\pi$
$317$	1.48491e6			0.829948			0.414974	+	0.909833i	$0.363791\pi$
$318$		−	797653.i		−	0.442330i
$319$			1.67454e6i			0.921338i
$320$		−	273759.i		−	0.149449i
$321$	485895.			0.263196
$322$	843696.			0.453468
$323$	5.58745e6			2.97994
$324$	−678723.			−0.359195
$325$			1.12639e6i			0.591535i
$326$	254655.			0.132711
$327$			1.44675e6i			0.748209i
$328$		−	1.03555e6i		−	0.531481i
$329$	818477.			0.416886
$330$	−758279.			−0.383305
$331$		−	2.66337e6i		−	1.33617i	−0.744085	−	0.668085i	$-0.767114\pi$
$331$		−	2.66337e6i		−	1.33617i	0.744085	−	0.668085i	$-0.232886\pi$
$332$	−1.16183e6			−0.578493
$333$	−718348.	−	254365.i	−0.354997	−	0.125703i
$334$	−241906.			−0.118654
$335$		−	190611.i		−	0.0927973i
$336$	366798.			0.177247
$337$	−2.02951e6			−0.973458			−0.486729	−	0.873553i	$-0.661810\pi$
$337$	−2.02951e6			−0.973458			−0.486729	+	0.873553i	$0.661810\pi$
$338$		−	253702.i		−	0.120790i
$339$			1.95181e6i			0.922439i
$340$	1.89519e6			0.889109
$341$			2.93501e6i			1.36686i
$342$	702801.			0.324913
$343$	2.34403e6			1.07579
$344$	−1.36804e6			−0.623307
$345$	1.44701e6			0.654523
$346$			1.00420e6i			0.450951i
$347$		−	3.16483e6i		−	1.41100i	−0.708710	−	0.705500i	$-0.750723\pi$
$347$		−	3.16483e6i		−	1.41100i	0.708710	−	0.705500i	$-0.249277\pi$
$348$			871431.i			0.385731i
$349$	−1.43841e6			−0.632147			−0.316073	−	0.948735i	$-0.602365\pi$
$349$	−1.43841e6			−0.632147			−0.316073	+	0.948735i	$0.602365\pi$
$350$		−	455998.i		−	0.198972i
$351$			2.79319e6i			1.21013i
$352$		−	3.37604e6i		−	1.45228i
$353$		−	677495.i		−	0.289381i	−0.989477	−	0.144690i	$-0.953781\pi$
$353$		−	677495.i		−	0.289381i	0.989477	−	0.144690i	$-0.0462186\pi$
$354$	829138.			0.351657
$355$		−	292579.i		−	0.123218i
$356$			1.11155e6i			0.464839i
$357$		−	2.45938e6i		−	1.02130i
$358$	−478681.			−0.197396
$359$	−1.97222e6			−0.807642			−0.403821	−	0.914838i	$-0.632318\pi$
$359$	−1.97222e6			−0.807642			−0.403821	+	0.914838i	$0.632318\pi$
$360$	557984.			0.226916
$361$	−4.77645e6			−1.92902
$362$			1.18758e6i			0.476311i
$363$	−1.93982e6			−0.772670
$364$		−	1.55948e6i		−	0.616917i
$365$			2.93202e6i			1.15195i
$366$	507406.			0.197994
$367$	−2.97537e6			−1.15312			−0.576562	−	0.817053i	$-0.695606\pi$
$367$	−2.97537e6			−1.15312			−0.576562	+	0.817053i	$0.695606\pi$
$368$			950563.i			0.365899i
$369$	594821.			0.227416
$370$	−856709.	−	303358.i	−0.325334	−	0.115200i
$371$	−2.18871e6			−0.825569
$372$			1.52738e6i			0.572255i
$373$	−2.19422e6			−0.816597			−0.408299	−	0.912848i	$-0.633878\pi$
$373$	−2.19422e6			−0.816597			−0.408299	+	0.912848i	$0.633878\pi$
$374$	−3.33992e6			−1.23469
$375$		−	2.25409e6i		−	0.827738i
$376$		−	1.35396e6i		−	0.493896i
$377$	2.01249e6			0.729258
$378$		−	1.13077e6i		−	0.407048i
$379$	2.44142e6			0.873061			0.436530	−	0.899689i	$-0.356207\pi$
$379$	2.44142e6			0.873061			0.436530	+	0.899689i	$0.356207\pi$
$380$	−2.45997e6			−0.873918
$381$	−959618.			−0.338677
$382$	2.03568e6			0.713757
$383$			685919.i			0.238933i	0.992838	+	0.119466i	$0.0381184\pi$
$383$			685919.i			0.238933i	−0.992838	+	0.119466i	$0.961882\pi$
$384$		−	2.10444e6i		−	0.728297i
$385$			2.08067e6i			0.715405i
$386$	−380933.			−0.130131
$387$		−	785800.i		−	0.266707i
$388$			3.22674e6i			1.08814i
$389$			4.07598e6i			1.36571i	0.730554	+	0.682855i	$0.239262\pi$
$389$			4.07598e6i			1.36571i	−0.730554	+	0.682855i	$0.760738\pi$
$390$			911314.i			0.303394i
$391$	6.37352e6			2.10832
$392$		−	1.19991e6i		−	0.394397i
$393$		−	1.97581e6i		−	0.645302i
$394$			1.81839e6i			0.590129i
$395$	1.65081e6			0.532360
$396$	1.23297e6			0.395108
$397$	862797.			0.274746			0.137373	−	0.990519i	$-0.456134\pi$
$397$	862797.			0.274746			0.137373	+	0.990519i	$0.456134\pi$
$398$	−1.03701e6			−0.328151
$399$			3.19229e6i			1.00385i
$400$	513757.			0.160549
$401$		−	121613.i		−	0.0377676i	−0.999822	−	0.0188838i	$-0.993989\pi$
$401$		−	121613.i		−	0.0377676i	0.999822	−	0.0188838i	$-0.00601125\pi$
$402$			174811.i			0.0539514i
$403$	3.52735e6			1.08190
$404$	−4.79397e6			−1.46131
$405$		−	1.08832e6i		−	0.329699i
$406$	−814720.			−0.245298
$407$	−4.43114e6	−	1.56905e6i	−1.32596	−	0.469517i
$408$	−4.06840e6			−1.20997
$409$		−	5.72992e6i		−	1.69372i	−0.531819	−	0.846858i	$-0.678491\pi$
$409$		−	5.72992e6i		−	1.69372i	0.531819	−	0.846858i	$-0.321509\pi$
$410$	709390.			0.208413
$411$	−639785.			−0.186823
$412$			1.49113e6i			0.432786i
$413$		−	2.27510e6i		−	0.656336i
$414$	801675.			0.229878
$415$		−	1.86297e6i		−	0.530989i
$416$	−4.05739e6			−1.14951
$417$	4.94998e6			1.39400
$418$	4.33524e6			1.21359
$419$	5.11602e6			1.42363			0.711816	−	0.702366i	$-0.247873\pi$
$419$	5.11602e6			1.42363			0.711816	+	0.702366i	$0.247873\pi$
$420$			1.08278e6i			0.299515i
$421$			972912.i			0.267527i	0.991013	+	0.133764i	$0.0427063\pi$
$421$			972912.i			0.267527i	−0.991013	+	0.133764i	$0.957294\pi$
$422$			3.42195e6i			0.935391i
$423$	777713.			0.211333
$424$			3.62065e6i			0.978075i
$425$		−	3.44474e6i		−	0.925090i
$426$			268327.i			0.0716375i
$427$		−	1.39229e6i		−	0.369539i
$428$	−942247.			−0.248631
$429$			4.71357e6i			1.23654i
$430$		−	937152.i		−	0.244421i
$431$			2.25886e6i			0.585728i	0.956154	+	0.292864i	$0.0946084\pi$
$431$			2.25886e6i			0.585728i	−0.956154	+	0.292864i	$0.905392\pi$
$432$	1.27400e6			0.328444
$433$	4.76746e6			1.22199			0.610994	−	0.791635i	$-0.290770\pi$
$433$	4.76746e6			1.22199			0.610994	+	0.791635i	$0.290770\pi$
$434$	−1.42798e6			−0.363913
$435$	−1.39732e6			−0.354056
$436$		−	2.80553e6i		−	0.706804i
$437$	−8.27288e6			−2.07230
$438$		−	2.68898e6i		−	0.669735i
$439$		−	6.47953e6i		−	1.60466i	−0.596882	−	0.802329i	$-0.703594\pi$
$439$		−	6.47953e6i		−	1.60466i	0.596882	−	0.802329i	$-0.296406\pi$
$440$	3.44193e6			0.847560
$441$	689228.			0.168759
$442$			4.01397e6i			0.977280i
$443$	7.13256e6			1.72678			0.863389	−	0.504540i	$-0.168338\pi$
$443$	7.13256e6			1.72678			0.863389	+	0.504540i	$0.168338\pi$
$444$	−2.30597e6	−	816536.i	−0.555131	−	0.196570i
$445$	−1.78234e6			−0.426668
$446$		−	156211.i		−	0.0371856i
$447$	−413831.			−0.0979612
$448$	688911.			0.162169
$449$			6.31912e6i			1.47925i	0.673021	+	0.739624i	$0.264997\pi$
$449$			6.31912e6i			1.47925i	−0.673021	+	0.739624i	$0.735003\pi$
$450$		−	433287.i		−	0.100866i
$451$	3.66916e6			0.849426
$452$		−	3.78495e6i		−	0.871392i
$453$	−567725.			−0.129985
$454$	2.28826e6			0.521033
$455$	2.50059e6			0.566257
$456$	5.28081e6			1.18929
$457$			7.64055e6i			1.71133i	0.517529	+	0.855666i	$0.326852\pi$
$457$			7.64055e6i			1.71133i	−0.517529	+	0.855666i	$0.673148\pi$
$458$			2.02639e6i			0.451398i
$459$		−	8.54218e6i		−	1.89250i
$460$	−2.80605e6			−0.618303
$461$		−	3.92010e6i		−	0.859102i	−0.903043	−	0.429551i	$-0.858672\pi$
$461$		−	3.92010e6i		−	0.859102i	0.903043	−	0.429551i	$-0.141328\pi$
$462$		−	1.90820e6i		−	0.415929i
$463$		−	6.57986e6i		−	1.42647i	−0.700923	−	0.713237i	$-0.747228\pi$
$463$		−	6.57986e6i		−	1.42647i	0.700923	−	0.713237i	$-0.252772\pi$
$464$		−	917917.i		−	0.197929i
$465$	−2.44912e6			−0.525263
$466$			876004.i			0.186871i
$467$		−	3.88545e6i		−	0.824421i	−0.911089	−	0.412211i	$-0.864757\pi$
$467$		−	3.88545e6i		−	0.824421i	0.911089	−	0.412211i	$-0.135243\pi$
$468$		−	1.48181e6i		−	0.312736i
$469$	479670.			0.100696
$470$	927508.			0.193675
$471$	2.33509e6			0.485012
$472$	−3.76357e6			−0.777579
$473$		−	4.84722e6i		−	0.996184i
$474$	−1.51398e6			−0.309509
$475$			4.47130e6i			0.909284i
$476$			4.76922e6i			0.964784i
$477$	−2.07970e6			−0.418509
$478$	−3.82475e6			−0.765656
$479$			752587.i			0.149871i	0.997188	+	0.0749355i	$0.0238751\pi$
$479$			752587.i			0.149871i	−0.997188	+	0.0749355i	$0.976125\pi$
$480$	2.81714e6			0.558091
$481$	−1.88572e6	+	5.32543e6i	−0.371633	+	1.04952i
$482$	−2.91634e6			−0.571768
$483$			3.64140e6i			0.710232i
$484$	3.76169e6			0.729911
$485$	−5.17400e6			−0.998784
$486$		−	1.85497e6i		−	0.356243i
$487$			1.01221e7i			1.93396i	0.254846	+	0.966982i	$0.417975\pi$
$487$			1.01221e7i			1.93396i	−0.254846	+	0.966982i	$0.582025\pi$
$488$	−2.30318e6			−0.437803
$489$			1.09909e6i			0.207855i
$490$	821980.			0.154657
$491$	3.12950e6			0.585829			0.292915	−	0.956139i	$-0.405375\pi$
$491$	3.12950e6			0.585829			0.292915	+	0.956139i	$0.405375\pi$
$492$	1.90943e6			0.355625
$493$	−6.15463e6			−1.14047
$494$		−	5.21017e6i		−	0.960582i
$495$			1.97704e6i			0.362663i
$496$		−	1.60886e6i		−	0.293639i
$497$	736273.			0.133705
$498$			1.70855e6i			0.308712i
$499$			5032.18i			0.000904700i	1.00000		0.000452350i	$0.000143987\pi$
$499$			5032.18i			0.000904700i	−1.00000		0.000452350i	$0.999856\pi$
$500$			4.37113e6i			0.781932i
$501$		−	1.04407e6i		−	0.185838i
$502$	71733.5			0.0127046
$503$			1.88460e6i			0.332123i	0.986115	+	0.166062i	$0.0531050\pi$
$503$			1.88460e6i			0.332123i	−0.986115	+	0.166062i	$0.946895\pi$
$504$			1.40416e6i			0.246230i
$505$		−	7.68702e6i		−	1.34131i
$506$	4.94515e6			0.858624
$507$	1.09498e6			0.189185
$508$	1.86089e6			0.319935
$509$	−6.71398e6			−1.14864			−0.574322	−	0.818629i	$-0.694734\pi$
$509$	−6.71398e6			−1.14864			−0.574322	+	0.818629i	$0.694734\pi$
$510$		−	2.78699e6i		−	0.474472i
$511$	−7.37841e6			−1.25000
$512$			3.42818e6i			0.577948i
$513$			1.10878e7i			1.86017i
$514$	−2.32613e6			−0.388353
$515$	−2.39100e6			−0.397247
$516$		−	2.52249e6i		−	0.417067i
$517$	4.79733e6			0.789357
$518$	763397.	−	2.15590e6i	0.125005	−	0.353024i
$519$	−4.33412e6			−0.706290
$520$		−	4.13658e6i		−	0.670861i
$521$	−3.33825e6			−0.538796			−0.269398	−	0.963029i	$-0.586825\pi$
$521$	−3.33825e6			−0.538796			−0.269398	+	0.963029i	$0.586825\pi$
$522$	−774143.			−0.124350
$523$			5.47242e6i			0.874832i	0.899259	+	0.437416i	$0.144106\pi$
$523$			5.47242e6i			0.874832i	−0.899259	+	0.437416i	$0.855894\pi$
$524$			3.83149e6i			0.609592i
$525$	1.96809e6			0.311635
$526$			922421.i			0.145367i
$527$	−1.07874e7			−1.69196
$528$	2.14991e6			0.335610
$529$	−3.00041e6			−0.466167
$530$	−2.48027e6			−0.383539
$531$		−	2.16179e6i		−	0.332719i
$532$		−	6.19049e6i		−	0.948300i
$533$		−	4.40967e6i		−	0.672338i
$534$	1.63460e6			0.248061
$535$		−	1.51087e6i		−	0.228214i
$536$		−	793489.i		−	0.119297i
$537$		−	2.06599e6i		−	0.309166i
$538$			2.46971e6i			0.367867i
$539$	4.25151e6			0.630335
$540$			3.76084e6i			0.555010i
$541$			850109.i			0.124877i	0.998049	+	0.0624383i	$0.0198877\pi$
$541$			850109.i			0.124877i	−0.998049	+	0.0624383i	$0.980112\pi$
$542$			342516.i			0.0500821i
$543$	−5.12559e6			−0.746010
$544$	1.24084e7			1.79770
$545$	4.49860e6			0.648763
$546$	−2.29331e6			−0.329217
$547$		−	4.42050e6i		−	0.631688i	−0.948811	−	0.315844i	$-0.897712\pi$
$547$		−	4.42050e6i		−	0.631688i	0.948811	−	0.315844i	$-0.102288\pi$
$548$	1.24067e6			0.176484
$549$		−	1.32295e6i		−	0.187332i
$550$		−	2.67274e6i		−	0.376747i
$551$	7.98876e6			1.12099
$552$	6.02375e6			0.841432
$553$			4.15425e6i			0.577670i
$554$	4.16599e6			0.576692
$555$	1.30930e6	−	3.69756e6i	0.180428	−	0.509545i
$556$	−9.59900e6			−1.31686
$557$			5.79127e6i			0.790926i	0.918482	+	0.395463i	$0.129416\pi$
$557$			5.79127e6i			0.790926i	−0.918482	+	0.395463i	$0.870584\pi$
$558$	−1.35686e6			−0.184480
$559$	−5.82547e6			−0.788500
$560$		−	1.14054e6i		−	0.153689i
$561$		−	1.44151e7i		−	1.93380i
$562$	2.15517e6			0.287833
$563$			5.05335e6i			0.671906i	0.941879	+	0.335953i	$0.109058\pi$
$563$			5.05335e6i			0.671906i	−0.941879	+	0.335953i	$0.890942\pi$
$564$	2.49653e6			0.330476
$565$	6.06907e6			0.799836
$566$	−7.39512e6			−0.970296
$567$	2.73874e6			0.357761
$568$		−	1.21797e6i		−	0.158404i
$569$		−	3.57229e6i		−	0.462558i	−0.972888	−	0.231279i	$-0.925709\pi$
$569$		−	3.57229e6i		−	0.462558i	0.972888	−	0.231279i	$-0.0742910\pi$
$570$			3.61754e6i			0.466365i
$571$	1.29233e7			1.65876			0.829380	−	0.558684i	$-0.188694\pi$
$571$	1.29233e7			1.65876			0.829380	+	0.558684i	$0.188694\pi$
$572$		−	9.14057e6i		−	1.16811i
$573$			8.78600e6i			1.11790i
$574$			1.78517e6i			0.226152i
$575$			5.10035e6i			0.643324i
$576$	654600.			0.0822090
$577$		−	1.61007e6i		−	0.201329i	−0.994920	−	0.100664i	$-0.967903\pi$
$577$		−	1.61007e6i		−	0.201329i	0.994920	−	0.100664i	$-0.0320968\pi$
$578$		−	8.22656e6i		−	1.02423i
$579$		−	1.64411e6i		−	0.203814i
$580$	2.70968e6			0.334463
$581$	4.68814e6			0.576183
$582$	4.74512e6			0.580684
$583$	−1.28287e7			−1.56318
$584$			1.22057e7i			1.48091i
$585$	2.37605e6			0.287055
$586$		−	1.23669e6i		−	0.148770i
$587$			4.70903e6i			0.564075i	0.959403	+	0.282037i	$0.0910102\pi$
$587$			4.70903e6i			0.564075i	−0.959403	+	0.282037i	$0.908990\pi$
$588$	2.21249e6			0.263899
$589$	1.40021e7			1.66305
$590$		−	2.57817e6i		−	0.304917i
$591$	−7.84820e6			−0.924275
$592$	2.42898e6	+	860094.i	0.284852	+	0.100865i
$593$	6.00154e6			0.700851			0.350426	−	0.936591i	$-0.386037\pi$
$593$	6.00154e6			0.700851			0.350426	+	0.936591i	$0.386037\pi$
$594$		−	6.62779e6i		−	0.770730i
$595$	−7.64733e6			−0.885559
$596$	802501.			0.0925401
$597$		−	4.47572e6i		−	0.513958i
$598$		−	5.94317e6i		−	0.679618i
$599$	1.17352e7			1.33636			0.668179	−	0.744000i	$-0.267074\pi$
$599$	1.17352e7			1.33636			0.668179	+	0.744000i	$0.267074\pi$
$600$		−	3.25569e6i		−	0.369203i
$601$	−9.96280e6			−1.12511			−0.562555	−	0.826760i	$-0.690182\pi$
$601$	−9.96280e6			−1.12511			−0.562555	+	0.826760i	$0.690182\pi$
$602$	2.35833e6			0.265225
$603$	455780.			0.0510460
$604$	1.10093e6			0.122792
$605$			6.03178e6i			0.669973i
$606$			7.04983e6i			0.779825i
$607$		−	1.17448e6i		−	0.129382i	−0.997905	−	0.0646908i	$-0.979394\pi$
$607$		−	1.17448e6i		−	0.129382i	0.997905	−	0.0646908i	$-0.0206061\pi$
$608$	−1.61062e7			−1.76699
$609$		−	3.51634e6i		−	0.384191i
$610$		−	1.57776e6i		−	0.171679i
$611$		−	5.76552e6i		−	0.624792i
$612$			4.53169e6i			0.489082i
$613$	−1.45455e7			−1.56343			−0.781715	−	0.623636i	$-0.785655\pi$
$613$	−1.45455e7			−1.56343			−0.781715	+	0.623636i	$0.785655\pi$
$614$			2.86153e6i			0.306322i
$615$			3.06173e6i			0.326422i
$616$			8.66158e6i			0.919699i
$617$	8.19052e6			0.866161			0.433081	−	0.901355i	$-0.357427\pi$
$617$	8.19052e6			0.866161			0.433081	+	0.901355i	$0.357427\pi$
$618$	2.19281e6			0.230956
$619$	595920.			0.0625117			0.0312558	−	0.999511i	$-0.490049\pi$
$619$	595920.			0.0625117			0.0312558	+	0.999511i	$0.490049\pi$
$620$	4.74933e6			0.496195
$621$			1.26477e7i			1.31608i
$622$	4.32284e6			0.448016
$623$		−	4.48524e6i		−	0.462983i
$624$		−	2.58380e6i		−	0.265642i
$625$	−1.82055e6			−0.186424
$626$	−404791.			−0.0412853
$627$			1.87109e7i			1.90076i
$628$	−4.52822e6			−0.458171
$629$	5.76692e6	−	1.62863e7i	0.581189	−	1.64133i
$630$	−961898.			−0.0965557
$631$			2.68979e6i			0.268934i	0.990918	+	0.134467i	$0.0429322\pi$
$631$			2.68979e6i			0.268934i	−0.990918	+	0.134467i	$0.957068\pi$
$632$	6.87213e6			0.684382
$633$	−1.47692e7			−1.46503
$634$			4.23453e6i			0.418390i
$635$			2.98390e6i			0.293663i
$636$	−6.67604e6			−0.654449
$637$		−	5.10954e6i		−	0.498923i
$638$	−4.77531e6			−0.464462
$639$	699602.			0.0677796
$640$	−6.54368e6			−0.631498
$641$	1.40540e6			0.135100			0.0675498	−	0.997716i	$-0.478482\pi$
$641$	1.40540e6			0.135100			0.0675498	+	0.997716i	$0.478482\pi$
$642$			1.38563e6i			0.132682i
$643$		−	1.06168e7i		−	1.01267i	−0.862337	−	0.506335i	$-0.831000\pi$
$643$		−	1.06168e7i		−	1.01267i	0.862337	−	0.506335i	$-0.169000\pi$
$644$		−	7.06140e6i		−	0.670928i
$645$	4.04476e6			0.382819
$646$			1.59338e7i			1.50224i
$647$			2.90444e6i			0.272773i	0.990656	+	0.136387i	$0.0435489\pi$
$647$			2.90444e6i			0.272773i	−0.990656	+	0.136387i	$0.956451\pi$
$648$		−	4.53053e6i		−	0.423849i
$649$		−	1.33350e7i		−	1.24275i
$650$	−3.21214e6			−0.298203
$651$		−	6.16317e6i		−	0.569970i
$652$		−	2.13136e6i		−	0.196353i
$653$			6.64094e6i			0.609462i	0.952438	+	0.304731i	$0.0985666\pi$
$653$			6.64094e6i			0.609462i	−0.952438	+	0.304731i	$0.901433\pi$
$654$	−4.12571e6			−0.377185
$655$	−6.14370e6			−0.559534
$656$	−2.01129e6			−0.182480
$657$	−7.01092e6			−0.633668
$658$			2.33406e6i			0.210159i
$659$	1.05401e6			0.0945431			0.0472716	−	0.998882i	$-0.484947\pi$
$659$	1.05401e6			0.0945431			0.0472716	+	0.998882i	$0.484947\pi$
$660$			6.34650e6i			0.567119i
$661$		−	6.02242e6i		−	0.536126i	−0.963401	−	0.268063i	$-0.913616\pi$
$661$		−	6.02242e6i		−	0.536126i	0.963401	−	0.268063i	$-0.0863836\pi$
$662$	7.59518e6			0.673586
$663$	−1.73243e7			−1.53064
$664$		−	7.75531e6i		−	0.682620i
$665$	9.92630e6			0.870429
$666$	725376.	−	2.04852e6i	0.0633691	−	0.178960i
$667$	9.11266e6			0.793105
$668$			2.02466e6i			0.175554i
$669$	674209.			0.0582411
$670$	543567.			0.0467807
$671$		−	8.16061e6i		−	0.699707i
$672$			7.08930e6i			0.605592i
$673$	6.71709e6			0.571667			0.285834	−	0.958279i	$-0.407730\pi$
$673$	6.71709e6			0.571667			0.285834	+	0.958279i	$0.407730\pi$
$674$		−	5.78759e6i		−	0.490736i
$675$	6.83580e6			0.577470
$676$	−2.12338e6			−0.178715
$677$	−1.24184e7			−1.04134			−0.520670	−	0.853758i	$-0.674318\pi$
$677$	−1.24184e7			−1.04134			−0.520670	+	0.853758i	$0.674318\pi$
$678$	−5.56600e6			−0.465017
$679$		−	1.30203e7i		−	1.08379i
$680$			1.26505e7i			1.04915i
$681$			9.87613e6i			0.816055i
$682$	−8.36981e6			−0.689056
$683$			1.47559e6i			0.121036i	0.998167	+	0.0605180i	$0.0192753\pi$
$683$			1.47559e6i			0.121036i	−0.998167	+	0.0605180i	$0.980725\pi$
$684$		−	5.88217e6i		−	0.480726i
$685$			1.98939e6i			0.161992i
$686$			6.68449e6i			0.542323i
$687$	−8.74591e6			−0.706990
$688$			2.65706e6i			0.214008i
$689$			1.54177e7i			1.23729i
$690$			4.12647e6i			0.329956i
$691$	−7.94552e6			−0.633034			−0.316517	−	0.948587i	$-0.602513\pi$
$691$	−7.94552e6			−0.633034			−0.316517	+	0.948587i	$0.602513\pi$
$692$	8.40473e6			0.667204
$693$	−4.97521e6			−0.393530
$694$	9.02520e6			0.711308
$695$		−	1.53918e7i		−	1.20872i
$696$	−5.81687e6			−0.455162
$697$			1.34857e7i			1.05146i
$698$		−	4.10192e6i		−	0.318676i
$699$	−3.78084e6			−0.292681
$700$	−3.81652e6			−0.294390
$701$		−	1.46257e7i		−	1.12414i	−0.827088	−	0.562072i	$-0.810004\pi$
$701$		−	1.46257e7i		−	1.12414i	0.827088	−	0.562072i	$-0.189996\pi$
$702$	−7.96540e6			−0.610049
$703$	−7.48551e6	+	2.11397e7i	−0.571259	+	1.61328i
$704$	4.03791e6			0.307061
$705$			4.00313e6i			0.303338i
$706$	1.93202e6			0.145882
$707$	1.93443e7			1.45547
$708$		−	6.93956e6i		−	0.520294i
$709$			2.36304e7i			1.76545i	0.469892	+	0.882724i	$0.344293\pi$
$709$			2.36304e7i			1.76545i	−0.469892	+	0.882724i	$0.655707\pi$
$710$	834352.			0.0621160
$711$			3.94735e6i			0.292841i
$712$	−7.41966e6			−0.548509
$713$	1.59720e7			1.17662
$714$	7.01344e6			0.514855
$715$	1.46567e7			1.07219
$716$			4.00637e6i			0.292057i
$717$		−	1.65076e7i		−	1.19919i
$718$		−	5.62421e6i		−	0.407146i
$719$	−5.85300e6			−0.422237			−0.211118	−	0.977460i	$-0.567711\pi$
$719$	−5.85300e6			−0.422237			−0.211118	+	0.977460i	$0.567711\pi$
$720$		−	1.08374e6i		−	0.0779100i
$721$		−	6.01692e6i		−	0.431058i
$722$		−	1.36211e7i		−	0.972453i
$723$		−	1.25869e7i		−	0.895517i
$724$	9.93955e6			0.704726
$725$		−	4.92518e6i		−	0.347998i
$726$		−	5.53180e6i		−	0.389516i
$727$		−	636687.i		−	0.0446776i	−0.999750	−	0.0223388i	$-0.992889\pi$
$727$		−	636687.i		−	0.0446776i	0.999750	−	0.0223388i	$-0.00711126\pi$
$728$	1.04097e7			0.727960
$729$	1.49162e7			1.03954
$730$	−8.36129e6			−0.580719
$731$	1.78155e7			1.23312
$732$		−	4.24678e6i		−	0.292943i
$733$	1.67411e7			1.15087			0.575433	−	0.817849i	$-0.304833\pi$
$733$	1.67411e7			1.15087			0.575433	+	0.817849i	$0.304833\pi$
$734$		−	8.48491e6i		−	0.581309i
$735$			3.54767e6i			0.242228i
$736$	−1.83721e7			−1.25015
$737$	2.81148e6			0.190663
$738$			1.69626e6i			0.114644i
$739$	1.36468e7			0.919217			0.459609	−	0.888122i	$-0.347990\pi$
$739$	1.36468e7			0.919217			0.459609	+	0.888122i	$0.347990\pi$
$740$	−2.53899e6	+	7.17031e6i	−0.170444	+	0.481348i
$741$	2.24871e7			1.50449
$742$		−	6.24158e6i		−	0.416183i
$743$	−1.59940e6			−0.106288			−0.0531440	−	0.998587i	$-0.516924\pi$
$743$	−1.59940e6			−0.106288			−0.0531440	+	0.998587i	$0.516924\pi$
$744$	−1.01954e7			−0.675259
$745$			1.28679e6i			0.0849410i
$746$		−	6.25729e6i		−	0.411660i
$747$	4.45465e6			0.292087
$748$			2.79538e7i			1.82678i
$749$	3.80209e6			0.247638
$750$	6.42802e6			0.417277
$751$	−1.94616e6			−0.125915			−0.0629575	−	0.998016i	$-0.520053\pi$
$751$	−1.94616e6			−0.125915			−0.0629575	+	0.998016i	$0.520053\pi$
$752$	−2.62971e6			−0.169576
$753$			309602.i			0.0198983i
$754$			5.73906e6i			0.367631i
$755$			1.76532e6i			0.112708i
$756$	−9.46412e6			−0.602249
$757$		−	2.01297e7i		−	1.27673i	−0.769735	−	0.638364i	$-0.779611\pi$
$757$		−	2.01297e7i		−	1.27673i	0.769735	−	0.638364i	$-0.220389\pi$
$758$			6.96223e6i			0.440125i
$759$			2.13433e7i			1.34480i
$760$		−	1.64205e7i		−	1.03122i
$761$	7.09820e6			0.444310			0.222155	−	0.975011i	$-0.428691\pi$
$761$	7.09820e6			0.444310			0.222155	+	0.975011i	$0.428691\pi$
$762$		−	2.73656e6i		−	0.170733i
$763$			1.13207e7i			0.703982i
$764$		−	1.70378e7i		−	1.05604i
$765$	−7.26645e6			−0.448920
$766$	−1.95604e6			−0.120450
$767$	−1.60263e7			−0.983659
$768$	8.81857e6			0.539504
$769$		−	6.44116e6i		−	0.392779i	−0.980526	−	0.196389i	$-0.937078\pi$
$769$		−	6.44116e6i		−	0.392779i	0.980526	−	0.196389i	$-0.0629217\pi$
$770$	−5.93348e6			−0.360647
$771$		−	1.00396e7i		−	0.608248i
$772$			3.18826e6i			0.192535i
$773$	−9.51628e6			−0.572820			−0.286410	−	0.958107i	$-0.592462\pi$
$773$	−9.51628e6			−0.572820			−0.286410	+	0.958107i	$0.592462\pi$
$774$	2.24088e6			0.134451
$775$		−	8.63249e6i		−	0.516276i
$776$	−2.15387e7			−1.28400
$777$	9.30488e6	+	3.29483e6i	0.552915	+	0.195785i
$778$	−1.16235e7			−0.688477
$779$		−	1.75045e7i		−	1.03349i
$780$	7.62734e6			0.448886
$781$	4.31550e6			0.253165
$782$			1.81755e7i			1.06284i
$783$		−	1.22133e7i		−	0.711918i
$784$	−2.33051e6			−0.135413
$785$		−	7.26088e6i		−	0.420548i
$786$	5.63444e6			0.325308
$787$	−2.72531e7			−1.56848			−0.784241	−	0.620457i	$-0.786947\pi$
$787$	−2.72531e7			−1.56848			−0.784241	+	0.620457i	$0.786947\pi$
$788$	1.52192e7			0.873126
$789$	−3.98118e6			−0.227677
$790$			4.70765e6i			0.268371i
$791$			1.52728e7i			0.867913i
$792$			8.23019e6i			0.466226i
$793$	−9.80757e6			−0.553833
$794$			2.46045e6i			0.138504i
$795$		−	1.07049e7i		−	0.600708i
$796$			8.67932e6i			0.485516i
$797$			2.81998e7i			1.57253i	0.617888	+	0.786266i	$0.287988\pi$
$797$			2.81998e7i			1.57253i	−0.617888	+	0.786266i	$0.712012\pi$
$798$	−9.10350e6			−0.506059
$799$			1.76322e7i			0.977100i
$800$			9.92967e6i			0.548542i
$801$		−	4.26185e6i		−	0.234702i
$802$	346806.			0.0190393
$803$	−4.32470e7			−2.36683
$804$	1.46310e6			0.0798239
$805$	1.13228e7			0.615834
$806$			1.00590e7i			0.545402i
$807$	−1.06593e7			−0.576162
$808$		−	3.20001e7i		−	1.72434i
$809$		−	1.93886e7i		−	1.04154i	−0.853698	−	0.520768i	$-0.825646\pi$
$809$		−	1.93886e7i		−	1.04154i	0.853698	−	0.520768i	$-0.174354\pi$
$810$	3.10357e6			0.166207
$811$	4.62132e6			0.246725			0.123363	−	0.992362i	$-0.460632\pi$
$811$	4.62132e6			0.246725			0.123363	+	0.992362i	$0.460632\pi$
$812$			6.81889e6i			0.362930i
$813$	−1.47830e6			−0.0784399
$814$	4.47449e6	−	1.26363e7i	0.236692	−	0.668437i
$815$	3.41758e6			0.180229
$816$			7.90180e6i			0.415433i
$817$	−2.31247e7			−1.21205
$818$	1.63401e7			0.853831
$819$			5.97930e6i			0.311487i
$820$		−	5.93731e6i		−	0.308358i
$821$	−2.53220e7			−1.31111			−0.655557	−	0.755145i	$-0.727566\pi$
$821$	−2.53220e7			−1.31111			−0.655557	+	0.755145i	$0.727566\pi$
$822$		−	1.82449e6i		−	0.0941805i
$823$	3.21181e7			1.65291			0.826457	−	0.563001i	$-0.190353\pi$
$823$	3.21181e7			1.65291			0.826457	+	0.563001i	$0.190353\pi$
$824$	−9.95343e6			−0.510687
$825$	1.15355e7			0.590070
$826$	6.48795e6			0.330870
$827$			1.20543e7i			0.612883i	0.951889	+	0.306442i	$0.0991384\pi$
$827$			1.20543e7i			0.612883i	−0.951889	+	0.306442i	$0.900862\pi$
$828$		−	6.70971e6i		−	0.340116i
$829$			1.95634e7i			0.988684i	0.869267	+	0.494342i	$0.164591\pi$
$829$			1.95634e7i			0.988684i	−0.869267	+	0.494342i	$0.835409\pi$
$830$	5.31266e6			0.267680
$831$			1.79805e7i			0.903230i
$832$		−	4.85283e6i		−	0.243045i
$833$			1.56261e7i			0.780256i
$834$			1.41159e7i			0.702739i
$835$	−3.24649e6			−0.161138
$836$		−	3.62842e7i		−	1.79557i
$837$		−	2.14066e7i		−	1.05617i
$838$			1.45894e7i			0.717676i
$839$	−1.14371e7			−0.560931			−0.280466	−	0.959864i	$-0.590489\pi$
$839$	−1.14371e7			−0.560931			−0.280466	+	0.959864i	$0.590489\pi$
$840$	−7.22765e6			−0.353426
$841$	1.17115e7			0.570980
$842$	−2.77447e6			−0.134865
$843$			9.30171e6i			0.450810i
$844$	2.86404e7			1.38396
$845$		−	3.40479e6i		−	0.164040i
$846$			2.21781e6i			0.106537i
$847$	−1.51789e7			−0.726996
$848$	7.03217e6			0.335815
$849$		−	3.19174e7i		−	1.51970i
$850$	9.82341e6			0.466353
$851$	−8.53861e6	+	2.41138e7i	−0.404169	+	1.14141i
$852$	2.24579e6			0.105991
$853$			1.88357e7i			0.886359i	0.896433	+	0.443180i	$0.146150\pi$
$853$			1.88357e7i			0.886359i	−0.896433	+	0.443180i	$0.853850\pi$
$854$	3.97041e6			0.186291
$855$	9.43192e6			0.441250
$856$		−	6.28957e6i		−	0.293384i
$857$		−	1.22399e7i		−	0.569280i	−0.958635	−	0.284640i	$-0.908126\pi$
$857$		−	1.22399e7i		−	0.569280i	0.958635	−	0.284640i	$-0.0918740\pi$
$858$	−1.34418e7			−0.623359
$859$		−	2.16729e7i		−	1.00216i	−0.865402	−	0.501078i	$-0.832937\pi$
$859$		−	2.16729e7i		−	1.00216i	0.865402	−	0.501078i	$-0.167063\pi$
$860$	−7.84359e6			−0.361634
$861$	−7.70482e6			−0.354205
$862$	−6.44162e6			−0.295275
$863$	−4.04170e7			−1.84730			−0.923649	−	0.383240i	$-0.874808\pi$
$863$	−4.04170e7			−1.84730			−0.923649	+	0.383240i	$0.874808\pi$
$864$			2.46234e7i			1.12218i
$865$			1.34768e7i			0.612415i
$866$			1.35954e7i			0.616025i
$867$	3.55059e7			1.60418
$868$			1.19516e7i			0.538428i
$869$			2.43493e7i			1.09380i
$870$		−	3.98475e6i		−	0.178486i
$871$		−	3.37889e6i		−	0.150914i
$872$	1.87271e7			0.834027
$873$		−	1.23718e7i		−	0.549412i
$874$		−	2.35919e7i		−	1.04468i
$875$		−	1.76381e7i		−	0.778810i
$876$	−2.25057e7			−0.990907
$877$	−1.77282e7			−0.778333			−0.389166	−	0.921167i	$-0.627237\pi$
$877$	−1.77282e7			−0.778333			−0.389166	+	0.921167i	$0.627237\pi$
$878$	1.84778e7			0.808935
$879$	5.33755e6			0.233007
$880$		−	6.68505e6i		−	0.291003i
$881$	−2.08301e7			−0.904172			−0.452086	−	0.891974i	$-0.649320\pi$
$881$	−2.08301e7			−0.904172			−0.452086	+	0.891974i	$0.649320\pi$
$882$			1.96548e6i			0.0850741i
$883$			1.01542e7i			0.438270i	0.975695	+	0.219135i	$0.0703236\pi$
$883$			1.01542e7i			0.438270i	−0.975695	+	0.219135i	$0.929676\pi$
$884$	3.35954e7			1.44594
$885$	1.11274e7			0.477569
$886$			2.03400e7i			0.870497i
$887$	−3.19961e7			−1.36549			−0.682744	−	0.730657i	$-0.739214\pi$
$887$	−3.19961e7			−1.36549			−0.682744	+	0.730657i	$0.739214\pi$
$888$	5.45044e6	−	1.53925e7i	0.231952	−	0.655053i
$889$	−7.50894e6			−0.318658
$890$		−	5.08272e6i		−	0.215090i
$891$	1.60525e7			0.677406
$892$	−1.30743e6			−0.0550181
$893$		−	2.28867e7i		−	0.960406i
$894$		−	1.18013e6i		−	0.0493839i
$895$	−6.42411e6			−0.268075
$896$		−	1.64671e7i		−	0.685247i
$897$	2.56507e7			1.06443
$898$	−1.80203e7			−0.745713
$899$	−1.54235e7			−0.636476
$900$	−3.62644e6			−0.149236
$901$		−	4.71506e7i		−	1.93498i
$902$			1.04634e7i			0.428210i
$903$			1.01786e7i			0.415402i
$904$	2.52648e7			1.02824
$905$			1.59378e7i			0.646856i
$906$		−	1.61899e6i		−	0.0655275i
$907$		−	1.27218e7i		−	0.513486i	−0.966480	−	0.256743i	$-0.917351\pi$
$907$		−	1.27218e7i		−	0.513486i	0.966480	−	0.256743i	$-0.0826494\pi$
$908$		−	1.91518e7i		−	0.770895i
$909$	1.83808e7			0.737829
$910$			7.13097e6i			0.285460i
$911$			1.63465e7i			0.652571i	0.945271	+	0.326285i	$0.105797\pi$
$911$			1.63465e7i			0.652571i	−0.945271	+	0.326285i	$0.894203\pi$
$912$		−	1.02566e7i		−	0.408335i
$913$	2.74786e7			1.09098
$914$	−2.17887e7			−0.862711
$915$	6.80962e6			0.268887
$916$	1.69601e7			0.667866
$917$		−	1.54606e7i		−	0.607158i
$918$	2.43599e7			0.954043
$919$			3.39032e7i			1.32419i	0.749418	+	0.662097i	$0.230333\pi$
$919$			3.39032e7i			1.32419i	−0.749418	+	0.662097i	$0.769667\pi$
$920$		−	1.87306e7i		−	0.729596i
$921$	−1.23504e7			−0.479769
$922$	1.11790e7			0.433088
$923$		−	5.18645e6i		−	0.200385i
$924$	−1.59709e7			−0.615389
$925$	1.30329e7	+	4.61492e6i	0.500827	+	0.177341i
$926$	1.87639e7			0.719110
$927$		−	5.71725e6i		−	0.218518i
$928$	1.77411e7			0.676255
$929$	4.54616e7			1.72824			0.864122	−	0.503282i	$-0.167874\pi$
$929$	4.54616e7			1.72824			0.864122	+	0.503282i	$0.167874\pi$
$930$		−	6.98418e6i		−	0.264794i
$931$		−	2.02828e7i		−	0.766925i
$932$	7.33180e6			0.276485
$933$			1.86574e7i			0.701693i
$934$	1.10802e7			0.415605
$935$	−4.48232e7			−1.67677
$936$	9.89119e6			0.369028
$937$	−1.11969e6			−0.0416629			−0.0208314	−	0.999783i	$-0.506631\pi$
$937$	−1.11969e6			−0.0416629			−0.0208314	+	0.999783i	$0.506631\pi$
$938$			1.36788e6i			0.0507623i
$939$		−	1.74708e6i		−	0.0646620i
$940$		−	7.76287e6i		−	0.286551i
$941$	2.25114e7			0.828760			0.414380	−	0.910104i	$-0.363999\pi$
$941$	2.25114e7			0.828760			0.414380	+	0.910104i	$0.363999\pi$
$942$			6.65902e6i			0.244502i
$943$		−	1.99672e7i		−	0.731202i
$944$			7.30975e6i			0.266976i
$945$		−	1.51755e7i		−	0.552794i
$946$	1.38229e7			0.502193
$947$			3.50838e7i			1.27125i	0.771997	+	0.635626i	$0.219258\pi$
$947$			3.50838e7i			1.27125i	−0.771997	+	0.635626i	$0.780742\pi$
$948$			1.26714e7i			0.457934i
$949$			5.19750e7i			1.87339i
$950$	−1.27509e7			−0.458385
$951$	−1.82762e7			−0.655293
$952$	−3.18349e7			−1.13844
$953$	8.82460e6			0.314748			0.157374	−	0.987539i	$-0.449697\pi$
$953$	8.82460e6			0.314748			0.157374	+	0.987539i	$0.449697\pi$
$954$		−	5.93071e6i		−	0.210977i
$955$	2.73197e7			0.969322
$956$			3.20116e7i			1.13283i
$957$		−	2.06103e7i		−	0.727451i
$958$	−2.14616e6			−0.0755525
$959$	−5.00628e6			−0.175779
$960$			3.36943e6i			0.117999i
$961$	1.59608e6			0.0557501
$962$	−1.51866e7	−	5.37753e6i	−0.529082	−	0.187346i
$963$	3.61273e6			0.125536
$964$			2.44086e7i			0.845960i
$965$	−5.11229e6			−0.176725
$966$	−1.03842e7			−0.358040
$967$		−	2.91030e7i		−	1.00086i	−0.865778	−	0.500428i	$-0.833176\pi$
$967$		−	2.91030e7i		−	1.00086i	0.865778	−	0.500428i	$-0.166824\pi$
$968$			2.51096e7i			0.861293i
$969$	−6.87704e7			−2.35284
$970$		−	1.47548e7i		−	0.503504i
$971$	−1.31598e7			−0.447921			−0.223961	−	0.974598i	$-0.571899\pi$
$971$	−1.31598e7			−0.447921			−0.223961	+	0.974598i	$0.571899\pi$
$972$	−1.55254e7			−0.527080
$973$	3.87332e7			1.31160
$974$	−2.88653e7			−0.974943
$975$		−	1.38636e7i		−	0.467052i
$976$			4.47333e6i			0.150316i
$977$		−	3.87316e7i		−	1.29816i	−0.760720	−	0.649080i	$-0.775154\pi$
$977$		−	3.87316e7i		−	1.29816i	0.760720	−	0.649080i	$-0.224846\pi$
$978$	−3.13429e6			−0.104783
$979$		−	2.62893e7i		−	0.876641i
$980$		−	6.87964e6i		−	0.228824i
$981$			1.07569e7i			0.356872i
$982$			8.92444e6i			0.295326i
$983$	−1.63230e7			−0.538788			−0.269394	−	0.963030i	$-0.586823\pi$
$983$	−1.63230e7			−0.538788			−0.269394	+	0.963030i	$0.586823\pi$
$984$			1.27456e7i			0.419636i
$985$			2.44037e7i			0.801428i
$986$		−	1.75512e7i		−	0.574931i
$987$	−1.00738e7			−0.329156
$988$	−4.36071e7			−1.42123
$989$	−2.63780e7			−0.857534
$990$	−5.63796e6			−0.182824
$991$		−	1.49634e7i		−	0.484001i	−0.970276	−	0.242000i	$-0.922196\pi$
$991$		−	1.49634e7i		−	0.484001i	0.970276	−	0.242000i	$-0.0778035\pi$
$992$	3.10953e7			1.00326
$993$			3.27808e7i			1.05499i
$994$			2.09964e6i			0.0674029i
$995$	−1.39171e7			−0.445647
$996$	1.42998e7			0.456755
$997$			2.63578e7i			0.839791i	0.907572	+	0.419896i	$0.137933\pi$
$997$			2.63578e7i			0.839791i	−0.907572	+	0.419896i	$0.862067\pi$
$998$	−14350.3			−0.000456074
$999$	3.23187e7	+	1.14440e7i	1.02457	+	0.362796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.b.a.36.10	yes	16
3.2	odd	2		333.6.c.d.73.7		16
4.3	odd	2		592.6.g.c.369.12		16
37.36	even	2	inner	37.6.b.a.36.7	✓	16
111.110	odd	2		333.6.c.d.73.10		16
148.147	odd	2		592.6.g.c.369.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.b.a.36.7	✓	16	37.36	even	2	inner
37.6.b.a.36.10	yes	16	1.1	even	1	trivial
333.6.c.d.73.7		16	3.2	odd	2
333.6.c.d.73.10		16	111.110	odd	2
592.6.g.c.369.11		16	148.147	odd	2
592.6.g.c.369.12		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.85171i q^{2} -12.3080 q^{3} +23.8677 q^{4} +38.2713i q^{5} -35.0990i q^{6} -96.3094 q^{7} +159.319i q^{8} -91.5127 q^{9} +O(q^{10})\)	\(q+2.85171i q^{2} -12.3080 q^{3} +23.8677 q^{4} +38.2713i q^{5} -35.0990i q^{6} -96.3094 q^{7} +159.319i q^{8} -91.5127 q^{9} -109.139 q^{10} -564.497 q^{11} -293.764 q^{12} +678.423i q^{13} -274.647i q^{14} -471.044i q^{15} +309.435 q^{16} -2074.76i q^{17} -260.968i q^{18} +2693.06i q^{19} +913.449i q^{20} +1185.38 q^{21} -1609.78i q^{22} +3071.93i q^{23} -1960.90i q^{24} +1660.31 q^{25} -1934.67 q^{26} +4117.19 q^{27} -2298.69 q^{28} -2966.43i q^{29} +1343.28 q^{30} -5199.33i q^{31} +5980.62i q^{32} +6947.84 q^{33} +5916.63 q^{34} -3685.89i q^{35} -2184.20 q^{36} +(7849.71 + 2779.56i) q^{37} -7679.83 q^{38} -8350.04i q^{39} -6097.34 q^{40} -6499.88 q^{41} +3380.36i q^{42} +8586.79i q^{43} -13473.3 q^{44} -3502.31i q^{45} -8760.27 q^{46} -8498.42 q^{47} -3808.54 q^{48} -7531.50 q^{49} +4734.72i q^{50} +25536.2i q^{51} +16192.4i q^{52} +22725.8 q^{53} +11741.0i q^{54} -21604.0i q^{55} -15343.9i q^{56} -33146.2i q^{57} +8459.41 q^{58} +23622.9i q^{59} -11242.7i q^{60} +14456.4i q^{61} +14827.0 q^{62} +8813.53 q^{63} -7153.11 q^{64} -25964.1 q^{65} +19813.3i q^{66} -4980.51 q^{67} -49519.8i q^{68} -37809.4i q^{69} +10511.1 q^{70} -7644.87 q^{71} -14579.7i q^{72} +76611.5 q^{73} +(-7926.51 + 22385.1i) q^{74} -20435.1 q^{75} +64277.1i q^{76} +54366.4 q^{77} +23811.9 q^{78} -43134.5i q^{79} +11842.5i q^{80} -28436.9 q^{81} -18535.8i q^{82} -48677.9 q^{83} +28292.3 q^{84} +79403.8 q^{85} -24487.1 q^{86} +36510.9i q^{87} -89935.0i q^{88} +46571.1i q^{89} +9987.59 q^{90} -65338.5i q^{91} +73320.0i q^{92} +63993.5i q^{93} -24235.1i q^{94} -103067. q^{95} -73609.6i q^{96} +135193. i q^{97} -21477.7i q^{98} +51658.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 18 q^{3} - 268 q^{4} + 190 q^{7} + 1394 q^{9}+O(q^{10}) \) 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