LMFDB - Embedded newform 22.7.b.a.21.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,7,Mod(21,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	22.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:	$5.06118983964$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 1781x^{4} + 14500x^{3} + 786532x^{2} - 11444432x + 42080676 $ x^6 - 2x^5 - 1781x^4 + 14500x^3 + 786532x^2 - 11444432*x + 42080676
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.5
Root			$7.52788 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.7.b.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.65685i q^{2} -1.47212 q^{3} -32.0000 q^{4} -147.340 q^{5} -8.32754i q^{6} -44.7193i q^{7} -181.019i q^{8} -726.833 q^{9} +O(q^{10})$	\(q+5.65685i q^{2} -1.47212 q^{3} -32.0000 q^{4} -147.340 q^{5} -8.32754i q^{6} -44.7193i q^{7} -181.019i q^{8} -726.833 q^{9} -833.480i q^{10} +(-669.288 - 1150.48i) q^{11} +47.1077 q^{12} +1580.07i q^{13} +252.971 q^{14} +216.901 q^{15} +1024.00 q^{16} +3815.15i q^{17} -4111.59i q^{18} +9364.20i q^{19} +4714.88 q^{20} +65.8319i q^{21} +(6508.12 - 3786.07i) q^{22} +5777.54 q^{23} +266.481i q^{24} +6084.05 q^{25} -8938.21 q^{26} +2143.15 q^{27} +1431.02i q^{28} -23143.0i q^{29} +1226.98i q^{30} -41047.6 q^{31} +5792.62i q^{32} +(985.269 + 1693.65i) q^{33} -21581.8 q^{34} +6588.94i q^{35} +23258.7 q^{36} -16222.4 q^{37} -52971.9 q^{38} -2326.04i q^{39} +26671.4i q^{40} -111317. i q^{41} -372.402 q^{42} +25271.4i q^{43} +(21417.2 + 36815.5i) q^{44} +107091. q^{45} +32682.7i q^{46} +45719.3 q^{47} -1507.45 q^{48} +115649. q^{49} +34416.6i q^{50} -5616.34i q^{51} -50562.2i q^{52} -134720. q^{53} +12123.5i q^{54} +(98612.9 + 169512. i) q^{55} -8095.06 q^{56} -13785.2i q^{57} +130917. q^{58} -208033. q^{59} -6940.84 q^{60} +267227. i q^{61} -232200. i q^{62} +32503.5i q^{63} -32768.0 q^{64} -232807. i q^{65} +(-9580.71 + 5573.53i) q^{66} -66942.4 q^{67} -122085. i q^{68} -8505.20 q^{69} -37272.7 q^{70} -510244. q^{71} +131571. i q^{72} -658290. i q^{73} -91768.0i q^{74} -8956.42 q^{75} -299654. i q^{76} +(-51448.8 + 29930.1i) q^{77} +13158.1 q^{78} +747441. i q^{79} -150876. q^{80} +526706. q^{81} +629704. q^{82} +981065. i q^{83} -2106.62i q^{84} -562124. i q^{85} -142957. q^{86} +34069.2i q^{87} +(-208260. + 121154. i) q^{88} +94831.2 q^{89} +605801. i q^{90} +70659.5 q^{91} -184881. q^{92} +60426.7 q^{93} +258627. i q^{94} -1.37972e6i q^{95} -8527.40i q^{96} +1.15334e6 q^{97} +654211. i q^{98} +(486461. + 836210. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9}+O(q^{10}) $ 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9	$ 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9} - 1166 q^{11} + 1664 q^{12} + 2208 q^{14} - 6512 q^{15} + 6144 q^{16} - 11776 q^{20} + 1056 q^{22} + 2156 q^{23} + 59862 q^{25} - 1824 q^{26} - 57472 q^{27} - 78468 q^{31} + 142208 q^{33} + 28704 q^{34} + 11072 q^{36} - 205920 q^{37} + 101472 q^{38} - 344160 q^{42} + 37312 q^{44} + 368716 q^{45} + 493460 q^{47} - 53248 q^{48} - 270762 q^{49} - 531700 q^{53} + 274956 q^{55} - 70656 q^{56} + 509184 q^{58} - 833380 q^{59} + 208384 q^{60} - 196608 q^{64} + 193248 q^{66} + 537420 q^{67} + 398860 q^{69} + 96096 q^{70} - 460372 q^{71} - 211428 q^{75} + 249744 q^{77} - 1866912 q^{78} + 376832 q^{80} + 485654 q^{81} + 428640 q^{82} + 1055808 q^{86} - 33792 q^{88} + 2377952 q^{89} - 5068656 q^{91} - 68992 q^{92} + 699868 q^{93} + 1351632 q^{97} - 2470930 q^{99}+O(q^{100}) $ 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9 - 1166 * q^11 + 1664 * q^12 + 2208 * q^14 - 6512 * q^15 + 6144 * q^16 - 11776 * q^20 + 1056 * q^22 + 2156 * q^23 + 59862 * q^25 - 1824 * q^26 - 57472 * q^27 - 78468 * q^31 + 142208 * q^33 + 28704 * q^34 + 11072 * q^36 - 205920 * q^37 + 101472 * q^38 - 344160 * q^42 + 37312 * q^44 + 368716 * q^45 + 493460 * q^47 - 53248 * q^48 - 270762 * q^49 - 531700 * q^53 + 274956 * q^55 - 70656 * q^56 + 509184 * q^58 - 833380 * q^59 + 208384 * q^60 - 196608 * q^64 + 193248 * q^66 + 537420 * q^67 + 398860 * q^69 + 96096 * q^70 - 460372 * q^71 - 211428 * q^75 + 249744 * q^77 - 1866912 * q^78 + 376832 * q^80 + 485654 * q^81 + 428640 * q^82 + 1055808 * q^86 - 33792 * q^88 + 2377952 * q^89 - 5068656 * q^91 - 68992 * q^92 + 699868 * q^93 + 1351632 * q^97 - 2470930 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

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

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 $

$2$			5.65685i			0.707107i
$2$			5.65685i			0.707107i
$3$	−1.47212			−0.0545228			−0.0272614	−	0.999628i	$-0.508679\pi$
$3$	−1.47212			−0.0545228			−0.0272614	+	0.999628i	$0.508679\pi$
$4$	−32.0000			−0.500000
$5$	−147.340			−1.17872			−0.589360	−	0.807871i	$-0.700620\pi$
$5$	−147.340			−1.17872			−0.589360	+	0.807871i	$0.700620\pi$
$6$		−	8.32754i		−	0.0385534i
$7$		−	44.7193i		−	0.130377i	−0.997873	−	0.0651885i	$-0.979235\pi$
$7$		−	44.7193i		−	0.130377i	0.997873	−	0.0651885i	$-0.0207649\pi$
$8$		−	181.019i		−	0.353553i
$9$	−726.833			−0.997027
$10$		−	833.480i		−	0.833480i
$11$	−669.288	−	1150.48i	−0.502846	−	0.864376i
$11$	−669.288	−	1150.48i	−0.502846	−	0.864376i
$12$	47.1077			0.0272614
$13$			1580.07i			0.719193i	0.933108	+	0.359597i	$0.117086\pi$
$13$			1580.07i			0.719193i	−0.933108	+	0.359597i	$0.882914\pi$
$14$	252.971			0.0921904
$15$	216.901			0.0642671
$16$	1024.00			0.250000
$17$			3815.15i			0.776542i	0.921545	+	0.388271i	$0.126928\pi$
$17$			3815.15i			0.776542i	−0.921545	+	0.388271i	$0.873072\pi$
$18$		−	4111.59i		−	0.705005i
$19$			9364.20i			1.36524i	0.730772	+	0.682621i	$0.239160\pi$
$19$			9364.20i			1.36524i	−0.730772	+	0.682621i	$0.760840\pi$
$20$	4714.88			0.589360
$21$			65.8319i			0.00710851i
$22$	6508.12	−	3786.07i	0.611206	−	0.355566i
$23$	5777.54			0.474853			0.237427	−	0.971405i	$-0.423696\pi$
$23$	5777.54			0.474853			0.237427	+	0.971405i	$0.423696\pi$
$24$			266.481i			0.0192767i
$25$	6084.05			0.389379
$26$	−8938.21			−0.508546
$27$	2143.15			0.108883
$28$			1431.02i			0.0651885i
$29$		−	23143.0i		−	0.948913i	−0.880279	−	0.474456i	$-0.842645\pi$
$29$		−	23143.0i		−	0.948913i	0.880279	−	0.474456i	$-0.157355\pi$
$30$			1226.98i			0.0454437i
$31$	−41047.6			−1.37785			−0.688925	−	0.724832i	$-0.741917\pi$
$31$	−41047.6			−1.37785			−0.688925	+	0.724832i	$0.741917\pi$
$32$			5792.62i			0.176777i
$33$	985.269	+	1693.65i	0.0274166	+	0.0471282i
$34$	−21581.8			−0.549098
$35$			6588.94i			0.153678i
$36$	23258.7			0.498514
$37$	−16222.4			−0.320266			−0.160133	−	0.987095i	$-0.551192\pi$
$37$	−16222.4			−0.320266			−0.160133	+	0.987095i	$0.551192\pi$
$38$	−52971.9			−0.965372
$39$		−	2326.04i		−	0.0392124i
$40$			26671.4i			0.416740i
$41$		−	111317.i		−	1.61514i	−0.589772	−	0.807569i	$-0.700783\pi$
$41$		−	111317.i		−	1.61514i	0.589772	−	0.807569i	$-0.299217\pi$
$42$	−372.402			−0.00502648
$43$			25271.4i			0.317851i	0.987291	+	0.158926i	$0.0508030\pi$
$43$			25271.4i			0.317851i	−0.987291	+	0.158926i	$0.949197\pi$
$44$	21417.2	+	36815.5i	0.251423	+	0.432188i
$45$	107091.			1.17522
$46$			32682.7i			0.335772i
$47$	45719.3			0.440358			0.220179	−	0.975459i	$-0.429336\pi$
$47$	45719.3			0.440358			0.220179	+	0.975459i	$0.429336\pi$
$48$	−1507.45			−0.0136307
$49$	115649.			0.983002
$50$			34416.6i			0.275333i
$51$		−	5616.34i		−	0.0423392i
$52$		−	50562.2i		−	0.359597i
$53$	−134720.			−0.904909			−0.452455	−	0.891787i	$-0.649452\pi$
$53$	−134720.			−0.904909			−0.452455	+	0.891787i	$0.649452\pi$
$54$			12123.5i			0.0769923i
$55$	98612.9	+	169512.i	0.592715	+	1.01886i
$56$	−8095.06			−0.0460952
$57$		−	13785.2i		−	0.0744368i
$58$	130917.			0.670983
$59$	−208033.			−1.01292			−0.506462	−	0.862262i	$-0.669047\pi$
$59$	−208033.			−1.01292			−0.506462	+	0.862262i	$0.669047\pi$
$60$	−6940.84			−0.0321335
$61$			267227.i			1.17731i	0.808385	+	0.588655i	$0.200342\pi$
$61$			267227.i			1.17731i	−0.808385	+	0.588655i	$0.799658\pi$
$62$		−	232200.i		−	0.974288i
$63$			32503.5i			0.129989i
$64$	−32768.0			−0.125000
$65$		−	232807.i		−	0.847727i
$66$	−9580.71	+	5573.53i	−0.0333247	+	0.0193864i
$67$	−66942.4			−0.222575			−0.111288	−	0.993788i	$-0.535497\pi$
$67$	−66942.4			−0.222575			−0.111288	+	0.993788i	$0.535497\pi$
$68$		−	122085.i		−	0.388271i
$69$	−8505.20			−0.0258903
$70$	−37272.7			−0.108667
$71$	−510244.			−1.42562			−0.712808	−	0.701359i	$-0.752577\pi$
$71$	−510244.			−1.42562			−0.712808	+	0.701359i	$0.752577\pi$
$72$			131571.i			0.352502i
$73$		−	658290.i		−	1.69219i	−0.533033	−	0.846095i	$-0.678948\pi$
$73$		−	658290.i		−	1.69219i	0.533033	−	0.846095i	$-0.321052\pi$
$74$		−	91768.0i		−	0.226462i
$75$	−8956.42			−0.0212300
$76$		−	299654.i		−	0.682621i
$77$	−51448.8	+	29930.1i	−0.112695	+	0.0655596i
$78$	13158.1			0.0277274
$79$			747441.i			1.51599i	0.652262	+	0.757994i	$0.273820\pi$
$79$			747441.i			1.51599i	−0.652262	+	0.757994i	$0.726180\pi$
$80$	−150876.			−0.294680
$81$	526706.			0.991091
$82$	629704.			1.14208
$83$			981065.i			1.71579i	0.513828	+	0.857893i	$0.328227\pi$
$83$			981065.i			1.71579i	−0.513828	+	0.857893i	$0.671773\pi$
$84$		−	2106.62i		−	0.00355426i
$85$		−	562124.i		−	0.915325i
$86$	−142957.			−0.224755
$87$			34069.2i			0.0517374i
$88$	−208260.	+	121154.i	−0.305603	+	0.177783i
$89$	94831.2			0.134518			0.0672591	−	0.997736i	$-0.478575\pi$
$89$	94831.2			0.134518			0.0672591	+	0.997736i	$0.478575\pi$
$90$			605801.i			0.831003i
$91$	70659.5			0.0937662
$92$	−184881.			−0.237427
$93$	60426.7			0.0751243
$94$			258627.i			0.311380i
$95$		−	1.37972e6i		−	1.60924i
$96$		−	8527.40i		−	0.00963836i
$97$	1.15334e6			1.26370			0.631849	−	0.775092i	$-0.282296\pi$
$97$	1.15334e6			1.26370			0.631849	+	0.775092i	$0.282296\pi$
$98$			654211.i			0.695087i
$99$	486461.	+	836210.i	0.501351	+	0.861806i
$100$	−194690.			−0.194690
$101$		−	118564.i		−	0.115077i	−0.998343	−	0.0575387i	$-0.981675\pi$
$101$		−	118564.i		−	0.115077i	0.998343	−	0.0575387i	$-0.0183253\pi$
$102$	31770.8			0.0299384
$103$	50691.7			0.0463901			0.0231951	−	0.999731i	$-0.492616\pi$
$103$	50691.7			0.0463901			0.0231951	+	0.999731i	$0.492616\pi$
$104$	286023.			0.254273
$105$		−	9699.67i		−	0.00837894i
$106$		−	762092.i		−	0.639867i
$107$		−	1.93360e6i		−	1.57839i	−0.614142	−	0.789196i	$-0.710498\pi$
$107$		−	1.93360e6i		−	1.57839i	0.614142	−	0.789196i	$-0.289502\pi$
$108$	−68580.9			−0.0544417
$109$			350236.i			0.270447i	0.990815	+	0.135223i	$0.0431752\pi$
$109$			350236.i			0.270447i	−0.990815	+	0.135223i	$0.956825\pi$
$110$	−958906.	+	557839.i	−0.720440	+	0.419112i
$111$	23881.3			0.0174618
$112$		−	45792.6i		−	0.0325942i
$113$	−2.72456e6			−1.88825			−0.944127	−	0.329581i	$-0.893092\pi$
$113$	−2.72456e6			−1.88825			−0.944127	+	0.329581i	$0.893092\pi$
$114$	77980.7			0.0526348
$115$	−851262.			−0.559719
$116$			740577.i			0.474456i
$117$		−	1.14845e6i		−	0.717055i
$118$		−	1.17681e6i		−	0.716246i
$119$	170611.			0.101243
$120$		−	39263.3i		−	0.0227218i
$121$	−875667.	+	1.54001e6i	−0.494291	+	0.869296i
$122$	−1.51166e6			−0.832484
$123$			163871.i			0.0880619i
$124$	1.31352e6			0.688925
$125$	1.40576e6			0.719751
$126$	−183867.			−0.0919164
$127$			1.48414e6i			0.724542i	0.932073	+	0.362271i	$0.117999\pi$
$127$			1.48414e6i			0.724542i	−0.932073	+	0.362271i	$0.882001\pi$
$128$		−	185364.i		−	0.0883883i
$129$		−	37202.4i		−	0.0173301i
$130$	1.31696e6			0.599433
$131$		−	332013.i		−	0.147687i	−0.997270	−	0.0738433i	$-0.976474\pi$
$131$		−	332013.i		−	0.147687i	0.997270	−	0.0738433i	$-0.0235265\pi$
$132$	−31528.6	−	54196.7i	−0.0137083	−	0.0235641i
$133$	418760.			0.177996
$134$		−	378683.i		−	0.157384i
$135$	−315772.			−0.128343
$136$	690616.			0.274549
$137$	683346.			0.265753			0.132877	−	0.991133i	$-0.457579\pi$
$137$	683346.			0.265753			0.132877	+	0.991133i	$0.457579\pi$
$138$		−	48112.7i		−	0.0183072i
$139$			303934.i			0.113171i	0.998398	+	0.0565855i	$0.0180214\pi$
$139$			303934.i			0.113171i	−0.998398	+	0.0565855i	$0.981979\pi$
$140$		−	210846.i		−	0.0768389i
$141$	−67304.1			−0.0240096
$142$		−	2.88637e6i		−	1.00806i
$143$	1.81784e6	−	1.05752e6i	0.621653	−	0.361644i
$144$	−744277.			−0.249257
$145$			3.40989e6i			1.11850i
$146$	3.72385e6			1.19656
$147$	−170249.			−0.0535960
$148$	519118.			0.160133
$149$			5.13425e6i			1.55209i	0.630675	+	0.776047i	$0.282778\pi$
$149$			5.13425e6i			1.55209i	−0.630675	+	0.776047i	$0.717222\pi$
$150$		−	50665.2i		−	0.0150119i
$151$			984030.i			0.285810i	0.989736	+	0.142905i	$0.0456443\pi$
$151$			984030.i			0.285810i	−0.989736	+	0.142905i	$0.954356\pi$
$152$	1.69510e6			0.482686
$153$		−	2.77298e6i		−	0.774234i
$154$	−169310.	−	291039.i	−0.0463576	−	0.0796872i
$155$	6.04794e6			1.62410
$156$			74433.3i			0.0196062i
$157$	−5.02351e6			−1.29810			−0.649050	−	0.760746i	$-0.724833\pi$
$157$	−5.02351e6			−1.29810			−0.649050	+	0.760746i	$0.724833\pi$
$158$	−4.22817e6			−1.07197
$159$	198324.			0.0493382
$160$		−	853484.i		−	0.208370i
$161$		−	258367.i		−	0.0619099i
$162$			2.97950e6i			0.700807i
$163$	−7.43461e6			−1.71670			−0.858351	−	0.513062i	$-0.828511\pi$
$163$	−7.43461e6			−1.71670			−0.858351	+	0.513062i	$0.828511\pi$
$164$			3.56214e6i			0.807569i
$165$	−145170.	−	249542.i	−0.0323164	−	0.0555509i
$166$	−5.54974e6			−1.21324
$167$		−	6.05091e6i		−	1.29919i	−0.760282	−	0.649593i	$-0.774939\pi$
$167$		−	6.05091e6i		−	1.29919i	0.760282	−	0.649593i	$-0.225061\pi$
$168$	11916.9			0.00251324
$169$	2.33020e6			0.482761
$170$	3.17985e6			0.647233
$171$		−	6.80621e6i		−	1.36118i
$172$		−	808685.i		−	0.158926i
$173$			2.40729e6i			0.464932i	0.972604	+	0.232466i	$0.0746795\pi$
$173$			2.40729e6i			0.464932i	−0.972604	+	0.232466i	$0.925320\pi$
$174$	−192725.			−0.0365839
$175$		−	272074.i		−	0.0507661i
$176$	−685351.	−	1.17810e6i	−0.125712	−	0.216094i
$177$	306249.			0.0552275
$178$			536446.i			0.0951188i
$179$	3.64304e6			0.635192			0.317596	−	0.948226i	$-0.397124\pi$
$179$	3.64304e6			0.635192			0.317596	+	0.948226i	$0.397124\pi$
$180$	−3.42693e6			−0.587608
$181$	−8.59055e6			−1.44872			−0.724362	−	0.689420i	$-0.757865\pi$
$181$	−8.59055e6			−1.44872			−0.724362	+	0.689420i	$0.757865\pi$
$182$			399711.i			0.0663027i
$183$		−	393389.i		−	0.0641902i
$184$		−	1.04585e6i		−	0.167886i
$185$	2.39021e6			0.377504
$186$			341825.i			0.0531209i
$187$	4.38927e6	−	2.55344e6i	0.671224	−	0.390481i
$188$	−1.46302e6			−0.220179
$189$		−	95840.3i		−	0.0141959i
$190$	7.80488e6			1.13790
$191$	−1.22081e6			−0.175205			−0.0876027	−	0.996155i	$-0.527921\pi$
$191$	−1.22081e6			−0.175205			−0.0876027	+	0.996155i	$0.527921\pi$
$192$	48238.3			0.00681535
$193$		−	1.21731e7i		−	1.69328i	−0.532163	−	0.846642i	$-0.678621\pi$
$193$		−	1.21731e7i		−	1.69328i	0.532163	−	0.846642i	$-0.321379\pi$
$194$			6.52429e6i			0.893569i
$195$			342719.i			0.0462204i
$196$	−3.70077e6			−0.491501
$197$			1.14518e7i			1.49788i	0.662639	+	0.748939i	$0.269436\pi$
$197$			1.14518e7i			1.49788i	−0.662639	+	0.748939i	$0.730564\pi$
$198$	−4.73032e6	+	2.75184e6i	−0.609389	+	0.354509i
$199$	1.14995e7			1.45922			0.729610	−	0.683864i	$-0.239702\pi$
$199$	1.14995e7			1.45922			0.729610	+	0.683864i	$0.239702\pi$
$200$		−	1.10133e6i		−	0.137666i
$201$	98546.9			0.0121354
$202$	670702.			0.0813721
$203$	−1.03494e6			−0.123716
$204$			179723.i			0.0211696i
$205$			1.64014e7i			1.90380i
$206$			286756.i			0.0328028i
$207$	−4.19931e6			−0.473442
$208$			1.61799e6i			0.179798i
$209$	1.07734e7	−	6.26735e6i	1.18008	−	0.686507i
$210$	54869.6			0.00592481
$211$			4.57518e6i			0.487035i	0.969896	+	0.243518i	$0.0783014\pi$
$211$			4.57518e6i			0.487035i	−0.969896	+	0.243518i	$0.921699\pi$
$212$	4.31104e6			0.452455
$213$	751138.			0.0777286
$214$	1.09381e7			1.11609
$215$		−	3.72349e6i		−	0.374658i
$216$		−	387952.i		−	0.0384961i
$217$			1.83562e6i			0.179640i
$218$	−1.98124e6			−0.191235
$219$			969079.i			0.0922629i
$220$	−3.15561e6	−	5.42439e6i	−0.296357	−	0.509428i
$221$	−6.02820e6			−0.558484
$222$			135093.i			0.0123474i
$223$	−1.07721e7			−0.971370			−0.485685	−	0.874134i	$-0.661430\pi$
$223$	−1.07721e7			−0.971370			−0.485685	+	0.874134i	$0.661430\pi$
$224$	259042.			0.0230476
$225$	−4.42209e6			−0.388222
$226$		−	1.54124e7i		−	1.33520i
$227$			1.20991e7i			1.03437i	0.855875	+	0.517183i	$0.173019\pi$
$227$			1.20991e7i			1.03437i	−0.855875	+	0.517183i	$0.826981\pi$
$228$			441126.i			0.0372184i
$229$	7.93649e6			0.660879			0.330440	−	0.943827i	$-0.392803\pi$
$229$	7.93649e6			0.660879			0.330440	+	0.943827i	$0.392803\pi$
$230$		−	4.81547e6i		−	0.395781i
$231$	75738.6	−	44060.6i	0.00614443	−	0.00357449i
$232$	−4.18934e6			−0.335491
$233$		−	1.94922e7i		−	1.54097i	−0.637460	−	0.770483i	$-0.720015\pi$
$233$		−	1.94922e7i		−	1.54097i	0.637460	−	0.770483i	$-0.279985\pi$
$234$	6.49659e6			0.507035
$235$	−6.73628e6			−0.519059
$236$	6.65707e6			0.506462
$237$		−	1.10032e6i		−	0.0826559i
$238$			965121.i			0.0715897i
$239$			1.92872e7i			1.41278i	0.707821	+	0.706392i	$0.249678\pi$
$239$			1.92872e7i			1.41278i	−0.707821	+	0.706392i	$0.750322\pi$
$240$	222107.			0.0160668
$241$		−	1.18172e7i		−	0.844233i	−0.906542	−	0.422116i	$-0.861287\pi$
$241$		−	1.18172e7i		−	0.844233i	0.906542	−	0.422116i	$-0.138713\pi$
$242$	−8.71162e6	−	4.95352e6i	−0.614685	−	0.349517i
$243$	−2.33773e6			−0.162921
$244$		−	8.55126e6i		−	0.588655i
$245$	−1.70397e7			−1.15868
$246$	−926997.			−0.0622691
$247$	−1.47961e7			−0.981873
$248$			7.43040e6i			0.487144i
$249$		−	1.44424e6i		−	0.0935495i
$250$			7.95220e6i			0.508940i
$251$	1.70728e6			0.107965			0.0539825	−	0.998542i	$-0.482808\pi$
$251$	1.70728e6			0.107965			0.0539825	+	0.998542i	$0.482808\pi$
$252$		−	1.04011e6i		−	0.0649947i
$253$	−3.86684e6	−	6.64697e6i	−0.238778	−	0.410452i
$254$	−8.39556e6			−0.512329
$255$			827511.i			0.0499061i
$256$	1.04858e6			0.0625000
$257$	1.32282e7			0.779297			0.389648	−	0.920964i	$-0.372597\pi$
$257$	1.32282e7			0.779297			0.389648	+	0.920964i	$0.372597\pi$
$258$	210449.			0.0122543
$259$			725456.i			0.0417553i
$260$			7.44982e6i			0.423863i
$261$			1.68211e7i			0.946092i
$262$	1.87815e6			0.104430
$263$		−	5.49794e6i		−	0.302226i	−0.988516	−	0.151113i	$-0.951714\pi$
$263$		−	5.49794e6i		−	0.302226i	0.988516	−	0.151113i	$-0.0482858\pi$
$264$	306583.	−	178353.i	0.0166623	−	0.00969322i
$265$	1.98497e7			1.06663
$266$			2.36887e6i			0.125862i
$267$	−139602.			−0.00733431
$268$	2.14216e6			0.111288
$269$	9.78758e6			0.502827			0.251414	−	0.967880i	$-0.419105\pi$
$269$	9.78758e6			0.502827			0.251414	+	0.967880i	$0.419105\pi$
$270$		−	1.78628e6i		−	0.0907523i
$271$			1.30941e7i			0.657913i	0.944345	+	0.328956i	$0.106697\pi$
$271$			1.30941e7i			0.657913i	−0.944345	+	0.328956i	$0.893303\pi$
$272$			3.90671e6i			0.194136i
$273$	−104019.			−0.00511240
$274$			3.86559e6i			0.187916i
$275$	−4.07198e6	−	6.99960e6i	−0.195798	−	0.336570i
$276$	272166.			0.0129452
$277$			753991.i			0.0354753i	0.999843	+	0.0177377i	$0.00564637\pi$
$277$			753991.i			0.0354753i	−0.999843	+	0.0177377i	$0.994354\pi$
$278$	−1.71931e6			−0.0800240
$279$	2.98347e7			1.37375
$280$	1.19272e6			0.0543333
$281$		−	1.57758e7i		−	0.711003i	−0.934676	−	0.355502i	$-0.884310\pi$
$281$		−	1.57758e7i		−	0.711003i	0.934676	−	0.355502i	$-0.115690\pi$
$282$		−	380729.i		−	0.0169773i
$283$		−	1.32700e7i		−	0.585481i	−0.956192	−	0.292740i	$-0.905433\pi$
$283$		−	1.32700e7i		−	0.585481i	0.956192	−	0.292740i	$-0.0945672\pi$
$284$	1.63278e7			0.712808
$285$			2.03111e6i			0.0877401i
$286$	5.98224e6	+	1.02833e7i	0.255721	+	0.439575i
$287$	−4.97802e6			−0.210577
$288$		−	4.21027e6i		−	0.176251i
$289$	9.58219e6			0.396982
$290$	−1.92893e7			−0.790900
$291$	−1.69785e6			−0.0689003
$292$			2.10653e7i			0.846095i
$293$		−	9.33237e6i		−	0.371013i	−0.982643	−	0.185506i	$-0.940607\pi$
$293$		−	9.33237e6i		−	0.371013i	0.982643	−	0.185506i	$-0.0593926\pi$
$294$		−	963073.i		−	0.0378981i
$295$	3.06516e7			1.19395
$296$			2.93658e6i			0.113231i
$297$	−1.43439e6	−	2.46566e6i	−0.0547517	−	0.0941163i
$298$	−2.90437e7			−1.09750
$299$			9.12890e6i			0.341511i
$300$	286606.			0.0106150
$301$	1.13012e6			0.0414405
$302$	−5.56651e6			−0.202098
$303$			174541.i			0.00627434i
$304$			9.58894e6i			0.341311i
$305$		−	3.93732e7i		−	1.38772i
$306$	1.56863e7			0.547466
$307$			2.52648e7i			0.873175i	0.899662	+	0.436587i	$0.143813\pi$
$307$			2.52648e7i			0.873175i	−0.899662	+	0.436587i	$0.856187\pi$
$308$	1.64636e6	−	957763.i	0.0563473	−	0.0327798i
$309$	−74624.1			−0.00252932
$310$			3.42123e7i			1.14841i
$311$	−5.13627e7			−1.70752			−0.853761	−	0.520665i	$-0.825684\pi$
$311$	−5.13627e7			−1.70752			−0.853761	+	0.520665i	$0.825684\pi$
$312$	−421058.			−0.0138637
$313$	2.08676e7			0.680519			0.340259	−	0.940332i	$-0.389485\pi$
$313$	2.08676e7			0.680519			0.340259	+	0.940332i	$0.389485\pi$
$314$		−	2.84172e7i		−	0.917895i
$315$		−	4.78906e6i		−	0.153221i
$316$		−	2.39181e7i		−	0.757994i
$317$	−4.64155e7			−1.45709			−0.728544	−	0.684999i	$-0.759802\pi$
$317$	−4.64155e7			−1.45709			−0.728544	+	0.684999i	$0.759802\pi$
$318$			1.12189e6i			0.0348873i
$319$	−2.66257e7	+	1.54894e7i	−0.820218	+	0.477157i
$320$	4.82803e6			0.147340
$321$			2.84648e6i			0.0860583i
$322$	1.46155e6			0.0437769
$323$	−3.57258e7			−1.06017
$324$	−1.68546e7			−0.495545
$325$			9.61321e6i			0.280039i
$326$		−	4.20565e7i		−	1.21389i
$327$		−	515588.i		−	0.0147455i
$328$	−2.01505e7			−0.571038
$329$		−	2.04454e6i		−	0.0574126i
$330$	1.41162e6	−	821203.i	0.0392804	−	0.0228512i
$331$	3.97574e6			0.109631			0.0548156	−	0.998496i	$-0.482543\pi$
$331$	3.97574e6			0.109631			0.0548156	+	0.998496i	$0.482543\pi$
$332$		−	3.13941e7i		−	0.857893i
$333$	1.17910e7			0.319314
$334$	3.42291e7			0.918663
$335$	9.86328e6			0.262354
$336$			67411.9i			0.00177713i
$337$		−	4.04814e7i		−	1.05771i	−0.848713	−	0.528854i	$-0.822622\pi$
$337$		−	4.04814e7i		−	1.05771i	0.848713	−	0.528854i	$-0.177378\pi$
$338$			1.31816e7i			0.341364i
$339$	4.01086e6			0.102953
$340$			1.79880e7i			0.457663i
$341$	2.74726e7	+	4.72246e7i	0.692847	+	1.19098i
$342$	3.85017e7			0.962502
$343$		−	1.04329e7i		−	0.258538i
$344$	4.57461e6			0.112377
$345$	1.25316e6			0.0305174
$346$	−1.36177e7			−0.328757
$347$			3.80859e7i			0.911539i	0.890098	+	0.455770i	$0.150636\pi$
$347$			3.80859e7i			0.911539i	−0.890098	+	0.455770i	$0.849364\pi$
$348$		−	1.09021e6i		−	0.0258687i
$349$		−	9.49208e6i		−	0.223298i	−0.993748	−	0.111649i	$-0.964387\pi$
$349$		−	9.49208e6i		−	0.223298i	0.993748	−	0.111649i	$-0.0356132\pi$
$350$	1.53909e6			0.0358970
$351$			3.38633e6i			0.0783083i
$352$	6.66432e6	−	3.87693e6i	0.152802	−	0.0888915i
$353$	−2.06638e7			−0.469771			−0.234885	−	0.972023i	$-0.575472\pi$
$353$	−2.06638e7			−0.469771			−0.234885	+	0.972023i	$0.575472\pi$
$354$			1.73241e6i			0.0390517i
$355$	7.51793e7			1.68040
$356$	−3.03460e6			−0.0672591
$357$	−251159.			−0.00552006
$358$			2.06081e7i			0.449148i
$359$		−	5.82503e7i		−	1.25897i	−0.777013	−	0.629484i	$-0.783266\pi$
$359$		−	5.82503e7i		−	1.25897i	0.777013	−	0.629484i	$-0.216734\pi$
$360$		−	1.93856e7i		−	0.415501i
$361$	−4.06423e7			−0.863887
$362$		−	4.85955e7i		−	1.02440i
$363$	1.28908e6	−	2.26707e6i	0.0269501	−	0.0473965i
$364$	−2.26110e6			−0.0468831
$365$			9.69924e7i			1.99462i
$366$	2.22534e6			0.0453893
$367$	−1.87426e6			−0.0379168			−0.0189584	−	0.999820i	$-0.506035\pi$
$367$	−1.87426e6			−0.0379168			−0.0189584	+	0.999820i	$0.506035\pi$
$368$	5.91620e6			0.118713
$369$			8.09089e7i			1.61034i
$370$			1.35211e7i			0.266936i
$371$			6.02459e6i			0.117979i
$372$	−1.93366e6			−0.0375621
$373$		−	1.45277e7i		−	0.279944i	−0.990155	−	0.139972i	$-0.955299\pi$
$373$		−	1.45277e7i		−	0.279944i	0.990155	−	0.139972i	$-0.0447012\pi$
$374$	1.44444e7	+	2.48295e7i	0.276112	+	0.474627i
$375$	−2.06944e6			−0.0392428
$376$		−	8.27608e6i		−	0.155690i
$377$	3.65676e7			0.682452
$378$	542155.			0.0100380
$379$	−2.16915e7			−0.398449			−0.199224	−	0.979954i	$-0.563842\pi$
$379$	−2.16915e7			−0.398449			−0.199224	+	0.979954i	$0.563842\pi$
$380$			4.41510e7i			0.804619i
$381$		−	2.18483e6i		−	0.0395041i
$382$		−	6.90593e6i		−	0.123889i
$383$	8.95790e7			1.59445			0.797223	−	0.603685i	$-0.206301\pi$
$383$	8.95790e7			1.59445			0.797223	+	0.603685i	$0.206301\pi$
$384$			272877.i			0.00481918i
$385$	7.58047e6	−	4.40990e6i	0.132835	−	0.0772763i
$386$	6.88615e7			1.19733
$387$		−	1.83681e7i		−	0.316907i
$388$	−3.69070e7			−0.631849
$389$	−7.80656e7			−1.32620			−0.663102	−	0.748529i	$-0.730761\pi$
$389$	−7.80656e7			−1.32620			−0.663102	+	0.748529i	$0.730761\pi$
$390$	−1.93871e6			−0.0326828
$391$			2.20422e7i			0.368743i
$392$		−	2.09347e7i		−	0.347544i
$393$			488761.i			0.00805228i
$394$	−6.47813e7			−1.05916
$395$		−	1.10128e8i		−	1.78692i
$396$	−1.55667e7	−	2.67587e7i	−0.250676	−	0.430903i
$397$	−2.98130e7			−0.476469			−0.238235	−	0.971208i	$-0.576569\pi$
$397$	−2.98130e7			−0.476469			−0.238235	+	0.971208i	$0.576569\pi$
$398$			6.50511e7i			1.03182i
$399$	−616463.			−0.00970484
$400$	6.23007e6			0.0973448
$401$	3.25930e7			0.505464			0.252732	−	0.967536i	$-0.418671\pi$
$401$	3.25930e7			0.505464			0.252732	+	0.967536i	$0.418671\pi$
$402$			557465.i			0.00858103i
$403$		−	6.48579e7i		−	0.990941i
$404$			3.79406e6i			0.0575387i
$405$	−7.76048e7			−1.16822
$406$		−	5.85451e6i		−	0.0874807i
$407$	1.08575e7	+	1.86637e7i	0.161045	+	0.276830i
$408$	−1.01667e6			−0.0149692
$409$		−	6.83310e7i		−	0.998730i	−0.866392	−	0.499365i	$-0.833567\pi$
$409$		−	6.83310e7i		−	0.998730i	0.866392	−	0.499365i	$-0.166433\pi$
$410$	−9.27805e7			−1.34619
$411$	−1.00596e6			−0.0144896
$412$	−1.62214e6			−0.0231951
$413$			9.30311e6i			0.132062i
$414$		−	2.37549e7i		−	0.334774i
$415$		−	1.44550e8i		−	2.02243i
$416$	−9.15273e6			−0.127137
$417$		−	447426.i		−	0.00617040i
$418$	3.54535e7	+	6.09433e7i	0.485434	+	0.834444i
$419$	−3.97782e7			−0.540759			−0.270379	−	0.962754i	$-0.587149\pi$
$419$	−3.97782e7			−0.540759			−0.270379	+	0.962754i	$0.587149\pi$
$420$			310390.i			0.00418947i
$421$	8.90560e7			1.19348			0.596742	−	0.802433i	$-0.296461\pi$
$421$	8.90560e7			1.19348			0.596742	+	0.802433i	$0.296461\pi$
$422$	−2.58811e7			−0.344386
$423$	−3.32303e7			−0.439049
$424$			2.43870e7i			0.319934i
$425$			2.32116e7i			0.302369i
$426$			4.24908e6i			0.0549624i
$427$	1.19502e7			0.153494
$428$			6.18751e7i			0.789196i
$429$	−2.67607e6	+	1.55679e6i	−0.0338943	+	0.0197178i
$430$	2.10632e7			0.264923
$431$			3.04242e7i			0.380004i	0.981784	+	0.190002i	$0.0608494\pi$
$431$			3.04242e7i			0.380004i	−0.981784	+	0.190002i	$0.939151\pi$
$432$	2.19459e6			0.0272209
$433$	3.36690e7			0.414731			0.207365	−	0.978264i	$-0.433511\pi$
$433$	3.36690e7			0.414731			0.207365	+	0.978264i	$0.433511\pi$
$434$	−1.03838e7			−0.127025
$435$		−	5.01976e6i		−	0.0609838i
$436$		−	1.12076e7i		−	0.135223i
$437$			5.41020e7i			0.648290i
$438$	−5.48194e6			−0.0652397
$439$			1.06022e8i			1.25314i	0.779364	+	0.626572i	$0.215542\pi$
$439$			1.06022e8i			1.25314i	−0.779364	+	0.626572i	$0.784458\pi$
$440$	3.06850e7	−	1.78508e7i	0.360220	−	0.209556i
$441$	−8.40576e7			−0.980080
$442$		−	3.41006e7i		−	0.394908i
$443$	9.40013e7			1.08124			0.540621	−	0.841266i	$-0.318189\pi$
$443$	9.40013e7			1.08124			0.540621	+	0.841266i	$0.318189\pi$
$444$	−764202.			−0.00873090
$445$	−1.39724e7			−0.158559
$446$		−	6.09360e7i		−	0.686862i
$447$		−	7.55821e6i		−	0.0846245i
$448$			1.46536e6i			0.0162971i
$449$	3.89236e7			0.430005			0.215003	−	0.976613i	$-0.431024\pi$
$449$	3.89236e7			0.430005			0.215003	+	0.976613i	$0.431024\pi$
$450$		−	2.50151e7i		−	0.274514i
$451$	−1.28068e8	+	7.45032e7i	−1.39609	+	0.812167i
$452$	8.71858e7			0.944127
$453$		−	1.44860e6i		−	0.0155832i
$454$	−6.84426e7			−0.731407
$455$	−1.04110e7			−0.110524
$456$	−2.49538e6			−0.0263174
$457$		−	4.35145e7i		−	0.455917i	−0.973671	−	0.227958i	$-0.926795\pi$
$457$		−	4.35145e7i		−	0.455917i	0.973671	−	0.227958i	$-0.0732050\pi$
$458$			4.48956e7i			0.467312i
$459$			8.17646e6i			0.0845526i
$460$	2.72404e7			0.279859
$461$			8.05692e7i			0.822368i	0.911552	+	0.411184i	$0.134885\pi$
$461$			8.05692e7i			0.822368i	−0.911552	+	0.411184i	$0.865115\pi$
$462$	249244.	+	428442.i	0.00252755	+	0.00434477i
$463$	1.04911e8			1.05701			0.528505	−	0.848930i	$-0.322753\pi$
$463$	1.04911e8			1.05701			0.528505	+	0.848930i	$0.322753\pi$
$464$		−	2.36985e7i		−	0.237228i
$465$	−8.90327e6			−0.0885504
$466$	1.10265e8			1.08963
$467$	1.88415e8			1.84997			0.924985	−	0.380004i	$-0.124077\pi$
$467$	1.88415e8			1.84997			0.924985	+	0.380004i	$0.124077\pi$
$468$			3.67502e7i			0.358528i
$469$			2.99361e6i			0.0290187i
$470$		−	3.81061e7i		−	0.367030i
$471$	7.39518e6			0.0707760
$472$			3.76581e7i			0.358123i
$473$	2.90744e7	−	1.69139e7i	0.274743	−	0.159830i
$474$	6.22435e6			0.0584465
$475$			5.69722e7i			0.531597i
$476$	−5.45955e6			−0.0506216
$477$	9.79190e7			0.902219
$478$	−1.09105e8			−0.998989
$479$		−	6.24311e7i		−	0.568061i	−0.958815	−	0.284030i	$-0.908328\pi$
$479$		−	6.24311e7i		−	0.568061i	0.958815	−	0.284030i	$-0.0916716\pi$
$480$			1.25643e6i			0.0113609i
$481$		−	2.56326e7i		−	0.230333i
$482$	6.68480e7			0.596963
$483$			380347.i			0.00337550i
$484$	2.80214e7	−	4.92804e7i	0.247146	−	0.434648i
$485$	−1.69933e8			−1.48955
$486$		−	1.32242e7i		−	0.115202i
$487$	−1.54145e8			−1.33458			−0.667288	−	0.744800i	$-0.732545\pi$
$487$	−1.54145e8			−1.33458			−0.667288	+	0.744800i	$0.732545\pi$
$488$	4.83732e7			0.416242
$489$	1.09446e7			0.0935994
$490$		−	9.63913e7i		−	0.819313i
$491$			8.28962e7i			0.700310i	0.936692	+	0.350155i	$0.113871\pi$
$491$			8.28962e7i			0.700310i	−0.936692	+	0.350155i	$0.886129\pi$
$492$		−	5.24389e6i		−	0.0440309i
$493$	8.82942e7			0.736871
$494$		−	8.36992e7i		−	0.694289i
$495$	−7.16751e7	−	1.23207e8i	−0.590953	−	1.01583i
$496$	−4.20327e7			−0.344463
$497$			2.28177e7i			0.185868i
$498$	8.16986e6			0.0661495
$499$	−2.07046e8			−1.66635			−0.833174	−	0.553010i	$-0.813479\pi$
$499$	−2.07046e8			−1.66635			−0.833174	+	0.553010i	$0.813479\pi$
$500$	−4.49844e7			−0.359875
$501$			8.90764e6i			0.0708352i
$502$			9.65782e6i			0.0763428i
$503$			1.65384e8i			1.29954i	0.760131	+	0.649770i	$0.225135\pi$
$503$			1.65384e8i			1.29954i	−0.760131	+	0.649770i	$0.774865\pi$
$504$	5.88375e6			0.0459582
$505$			1.74693e7i			0.135644i
$506$	3.76009e7	−	2.18741e7i	0.290233	−	0.168842i
$507$	−3.43032e6			−0.0263215
$508$		−	4.74925e7i		−	0.362271i
$509$	−8.85216e7			−0.671268			−0.335634	−	0.941993i	$-0.608950\pi$
$509$	−8.85216e7			−0.671268			−0.335634	+	0.941993i	$0.608950\pi$
$510$	−4.68111e6			−0.0352889
$511$	−2.94383e7			−0.220622
$512$			5.93164e6i			0.0441942i
$513$			2.00689e7i			0.148652i
$514$			7.48302e7i			0.551046i
$515$	−7.46892e6			−0.0546809
$516$			1.19048e6i			0.00866507i
$517$	−3.05994e7	−	5.25993e7i	−0.221432	−	0.380635i
$518$	−4.10380e6			−0.0295255
$519$		−	3.54381e6i		−	0.0253494i
$520$	−4.21426e7			−0.299717
$521$	1.25058e7			0.0884300			0.0442150	−	0.999022i	$-0.485921\pi$
$521$	1.25058e7			0.0884300			0.0442150	+	0.999022i	$0.485921\pi$
$522$	−9.51546e7			−0.668988
$523$		−	1.03009e8i		−	0.720061i	−0.932941	−	0.360030i	$-0.882766\pi$
$523$		−	1.03009e8i		−	0.720061i	0.932941	−	0.360030i	$-0.117234\pi$
$524$			1.06244e7i			0.0738433i
$525$			400525.i			0.00276791i
$526$	3.11010e7			0.213706
$527$		−	1.56603e8i		−	1.06996i
$528$	1.00892e6	+	1.73429e6i	0.00685414	+	0.0117820i
$529$	−1.14656e8			−0.774514
$530$			1.12287e8i			0.754224i
$531$	1.51206e8			1.00991
$532$	−1.34003e7			−0.0889981
$533$	1.75888e8			1.16160
$534$		−	789711.i		−	0.00518614i
$535$			2.84896e8i			1.86048i
$536$			1.21179e7i			0.0786922i
$537$	−5.36297e6			−0.0346324
$538$			5.53669e7i			0.355552i
$539$	−7.74026e7	−	1.33053e8i	−0.494299	−	0.849683i
$540$	1.01047e7			0.0641715
$541$		−	2.53556e8i		−	1.60134i	−0.599108	−	0.800669i	$-0.704478\pi$
$541$		−	2.53556e8i		−	1.60134i	0.599108	−	0.800669i	$-0.295522\pi$
$542$	−7.40715e7			−0.465215
$543$	1.26463e7			0.0789884
$544$	−2.20997e7			−0.137275
$545$		−	5.16038e7i		−	0.318781i
$546$		−	588420.i		−	0.00361501i
$547$			2.34110e8i			1.43040i	0.698919	+	0.715201i	$0.253665\pi$
$547$			2.34110e8i			1.43040i	−0.698919	+	0.715201i	$0.746335\pi$
$548$	−2.18671e7			−0.132877
$549$		−	1.94229e8i		−	1.17381i
$550$	3.95957e7	−	2.30346e7i	0.237991	−	0.138450i
$551$	2.16716e8			1.29550
$552$			1.53961e6i			0.00915361i
$553$	3.34250e7			0.197650
$554$	−4.26522e6			−0.0250849
$555$	−3.51867e6			−0.0205826
$556$		−	9.72590e6i		−	0.0565855i
$557$		−	3.32022e7i		−	0.192133i	−0.995375	−	0.0960664i	$-0.969374\pi$
$557$		−	3.32022e7i		−	0.192133i	0.995375	−	0.0960664i	$-0.0306261\pi$
$558$			1.68771e8i			0.971391i
$559$	−3.99305e7			−0.228597
$560$			6.74707e6i			0.0384195i
$561$	−6.46151e6	+	3.75895e6i	−0.0365970	+	0.0212901i
$562$	8.92413e7			0.502755
$563$		−	2.30890e8i		−	1.29384i	−0.762559	−	0.646919i	$-0.776057\pi$
$563$		−	2.30890e8i		−	1.29384i	0.762559	−	0.646919i	$-0.223943\pi$
$564$	2.15373e6			0.0120048
$565$	4.01436e8			2.22572
$566$	7.50667e7			0.413998
$567$		−	2.35539e7i		−	0.129215i
$568$			9.23640e7i			0.504031i
$569$			1.33791e8i			0.726256i	0.931739	+	0.363128i	$0.118291\pi$
$569$			1.33791e8i			0.726256i	−0.931739	+	0.363128i	$0.881709\pi$
$570$	−1.14897e7			−0.0620416
$571$			3.14499e8i			1.68931i	0.535307	+	0.844657i	$0.320196\pi$
$571$			3.14499e8i			1.68931i	−0.535307	+	0.844657i	$0.679804\pi$
$572$	−5.81710e7	+	3.38407e7i	−0.310827	+	0.180822i
$573$	1.79717e6			0.00955268
$574$		−	2.81599e7i		−	0.148900i
$575$	3.51508e7			0.184898
$576$	2.38169e7			0.124628
$577$	4.72751e7			0.246096			0.123048	−	0.992401i	$-0.460733\pi$
$577$	4.72751e7			0.246096			0.123048	+	0.992401i	$0.460733\pi$
$578$			5.42051e7i			0.280709i
$579$			1.79202e7i			0.0923225i
$580$		−	1.09117e8i		−	0.559251i
$581$	4.38725e7			0.223699
$582$		−	9.60451e6i		−	0.0487199i
$583$	9.01666e7	+	1.54993e8i	0.455030	+	0.782182i
$584$	−1.19163e8			−0.598279
$585$			1.69212e8i			0.845207i
$586$	5.27919e7			0.262346
$587$	−2.81860e8			−1.39354			−0.696769	−	0.717296i	$-0.745380\pi$
$587$	−2.81860e8			−1.39354			−0.696769	+	0.717296i	$0.745380\pi$
$588$	5.44797e6			0.0267980
$589$		−	3.84377e8i		−	1.88110i
$590$			1.73392e8i			0.844253i
$591$		−	1.68584e7i		−	0.0816684i
$592$	−1.66118e7			−0.0800665
$593$		−	5.59360e6i		−	0.0268242i	−0.999910	−	0.0134121i	$-0.995731\pi$
$593$		−	5.59360e6i		−	0.0268242i	0.999910	−	0.0134121i	$-0.00426934\pi$
$594$	1.39479e7	−	8.11412e6i	0.0665502	−	0.0387153i
$595$	−2.51378e7			−0.119337
$596$		−	1.64296e8i		−	0.776047i
$597$	−1.69286e7			−0.0795607
$598$	−5.16409e7			−0.241485
$599$	−3.98274e8			−1.85311			−0.926556	−	0.376157i	$-0.877245\pi$
$599$	−3.98274e8			−1.85311			−0.926556	+	0.376157i	$0.877245\pi$
$600$			1.62129e6i			0.00750595i
$601$			3.08323e8i			1.42031i	0.704046	+	0.710154i	$0.251375\pi$
$601$			3.08323e8i			1.42031i	−0.704046	+	0.710154i	$0.748625\pi$
$602$			6.39292e6i			0.0293029i
$603$	4.86559e7			0.221913
$604$		−	3.14889e7i		−	0.142905i
$605$	1.29021e8	−	2.26905e8i	0.582631	−	1.02466i
$606$	−987350.			−0.00443663
$607$			1.00597e8i			0.449798i	0.974382	+	0.224899i	$0.0722053\pi$
$607$			1.00597e8i			0.449798i	−0.974382	+	0.224899i	$0.927795\pi$
$608$	−5.42432e7			−0.241343
$609$	1.52355e6			0.00674536
$610$	2.22728e8			0.981264
$611$			7.22396e7i			0.316703i
$612$			8.87353e7i			0.387117i
$613$		−	3.28587e8i		−	1.42649i	−0.700915	−	0.713245i	$-0.747225\pi$
$613$		−	3.28587e8i		−	1.42649i	0.700915	−	0.713245i	$-0.252775\pi$
$614$	−1.42919e8			−0.617428
$615$		−	2.41448e7i		−	0.103800i
$616$	5.41793e6	+	9.31324e6i	0.0231788	+	0.0398436i
$617$	−2.41203e8			−1.02690			−0.513449	−	0.858120i	$-0.671632\pi$
$617$	−2.41203e8			−1.02690			−0.513449	+	0.858120i	$0.671632\pi$
$618$		−	422138.i		−	0.00178850i
$619$	2.84066e8			1.19770			0.598848	−	0.800862i	$-0.295625\pi$
$619$	2.84066e8			1.19770			0.598848	+	0.800862i	$0.295625\pi$
$620$	−1.93534e8			−0.812050
$621$	1.23822e7			0.0517037
$622$		−	2.90551e8i		−	1.20740i
$623$		−	4.24079e6i		−	0.0175381i
$624$		−	2.38187e6i		−	0.00980310i
$625$	−3.02188e8			−1.23776
$626$			1.18045e8i			0.481200i
$627$	−1.58596e7	+	9.22626e6i	−0.0643414	+	0.0374303i
$628$	1.60752e8			0.649050
$629$		−	6.18911e7i		−	0.248700i
$630$	2.70910e7			0.108344
$631$	−3.60337e8			−1.43424			−0.717118	−	0.696951i	$-0.754539\pi$
$631$	−3.60337e8			−1.43424			−0.717118	+	0.696951i	$0.754539\pi$
$632$	1.35301e8			0.535983
$633$		−	6.73518e6i		−	0.0265545i
$634$		−	2.62566e8i		−	1.03032i
$635$		−	2.18673e8i		−	0.854032i
$636$	−6.34635e6			−0.0246691
$637$			1.82734e8i			0.706968i
$638$	−8.76211e7	−	1.50618e8i	−0.337401	−	0.579981i
$639$	3.70862e8			1.42138
$640$			2.73115e7i			0.104185i
$641$	−2.68774e8			−1.02050			−0.510249	−	0.860027i	$-0.670447\pi$
$641$	−2.68774e8			−1.02050			−0.510249	+	0.860027i	$0.670447\pi$
$642$	−1.61021e7			−0.0608524
$643$	−1.70850e8			−0.642662			−0.321331	−	0.946967i	$-0.604130\pi$
$643$	−1.70850e8			−0.642662			−0.321331	+	0.946967i	$0.604130\pi$
$644$			8.26776e6i			0.0309550i
$645$			5.48140e6i			0.0204274i
$646$		−	2.02096e8i		−	0.749652i
$647$	−3.03849e7			−0.112188			−0.0560938	−	0.998426i	$-0.517865\pi$
$647$	−3.03849e7			−0.112188			−0.0560938	+	0.998426i	$0.517865\pi$
$648$		−	9.53440e7i		−	0.350403i
$649$	1.39234e8	+	2.39339e8i	0.509345	+	0.875548i
$650$	−5.43805e7			−0.198017
$651$		−	2.70224e6i		−	0.00979447i
$652$	2.37907e8			0.858351
$653$	8.58971e7			0.308489			0.154244	−	0.988033i	$-0.450706\pi$
$653$	8.58971e7			0.308489			0.154244	+	0.988033i	$0.450706\pi$
$654$	2.91661e6			0.0104266
$655$			4.89188e7i			0.174081i
$656$		−	1.13989e8i		−	0.403785i
$657$			4.78467e8i			1.68716i
$658$	1.15656e7			0.0405968
$659$			3.24258e7i			0.113301i	0.998394	+	0.0566506i	$0.0180421\pi$
$659$			3.24258e7i			0.113301i	−0.998394	+	0.0566506i	$0.981958\pi$
$660$	4.64542e6	+	7.98533e6i	0.0161582	+	0.0277754i
$661$	−9.62691e7			−0.333336			−0.166668	−	0.986013i	$-0.553301\pi$
$661$	−9.62691e7			−0.333336			−0.166668	+	0.986013i	$0.553301\pi$
$662$			2.24902e7i			0.0775210i
$663$	8.87420e6			0.0304501
$664$	1.77592e8			0.606622
$665$	−6.17001e7			−0.209807
$666$			6.67000e7i			0.225789i
$667$		−	1.33710e8i		−	0.450594i
$668$			1.93629e8i			0.649593i
$669$	1.58577e7			0.0529618
$670$			5.57951e7i			0.185512i
$671$	3.07440e8	−	1.78852e8i	1.01764	−	0.592006i
$672$	−381339.			−0.00125662
$673$			1.90115e8i			0.623694i	0.950132	+	0.311847i	$0.100948\pi$
$673$			1.90115e8i			0.623694i	−0.950132	+	0.311847i	$0.899052\pi$
$674$	2.28997e8			0.747912
$675$	1.30391e7			0.0423970
$676$	−7.45663e7			−0.241381
$677$			4.04304e8i			1.30299i	0.758651	+	0.651497i	$0.225859\pi$
$677$			4.04304e8i			1.30299i	−0.758651	+	0.651497i	$0.774141\pi$
$678$			2.26889e7i			0.0727987i
$679$		−	5.15767e7i		−	0.164757i
$680$	−1.01755e8			−0.323616
$681$		−	1.78112e7i		−	0.0563965i
$682$	−2.67142e8	+	1.55409e8i	−0.842151	+	0.489917i
$683$	2.13802e8			0.671043			0.335521	−	0.942033i	$-0.391087\pi$
$683$	2.13802e8			0.671043			0.335521	+	0.942033i	$0.391087\pi$
$684$			2.17799e8i			0.680592i
$685$	−1.00684e8			−0.313249
$686$	5.90176e7			0.182814
$687$	−1.16834e7			−0.0360330
$688$			2.58779e7i			0.0794629i
$689$		−	2.12867e8i		−	0.650804i
$690$			7.08892e6i			0.0215791i
$691$	2.68742e8			0.814521			0.407260	−	0.913312i	$-0.366484\pi$
$691$	2.68742e8			0.814521			0.407260	+	0.913312i	$0.366484\pi$
$692$		−	7.70332e7i		−	0.232466i
$693$	3.73947e7	−	2.17542e7i	0.112360	−	0.0653647i
$694$	−2.15446e8			−0.644556
$695$		−	4.47817e7i		−	0.133397i
$696$	6.16719e6			0.0182919
$697$	4.24691e8			1.25422
$698$	5.36953e7			0.157896
$699$			2.86948e7i			0.0840178i
$700$			8.70638e6i			0.0253830i
$701$			8.40415e7i			0.243972i	0.992532	+	0.121986i	$0.0389263\pi$
$701$			8.40415e7i			0.243972i	−0.992532	+	0.121986i	$0.961074\pi$
$702$	−1.91560e7			−0.0553723
$703$		−	1.51910e8i		−	0.437241i
$704$	2.19312e7	+	3.76991e7i	0.0628558	+	0.108047i
$705$	9.91658e6			0.0283005
$706$		−	1.16892e8i		−	0.332178i
$707$	−5.30212e6			−0.0150035
$708$	−9.79997e6			−0.0276137
$709$	2.28761e8			0.641865			0.320932	−	0.947102i	$-0.396004\pi$
$709$	2.28761e8			0.641865			0.320932	+	0.947102i	$0.396004\pi$
$710$			4.25278e8i			1.18822i
$711$		−	5.43265e8i		−	1.51148i
$712$		−	1.71663e7i		−	0.0475594i
$713$	−2.37154e8			−0.654277
$714$		−	1.42077e6i		−	0.00390327i
$715$	−2.67841e8	+	1.55815e8i	−0.732755	+	0.426276i
$716$	−1.16577e8			−0.317596
$717$		−	2.83930e7i		−	0.0770289i
$718$	3.29514e8			0.890225
$719$	−9.37476e7			−0.252216			−0.126108	−	0.992016i	$-0.540249\pi$
$719$	−9.37476e7			−0.252216			−0.126108	+	0.992016i	$0.540249\pi$
$720$	1.09662e8			0.293804
$721$		−	2.26690e6i		−	0.00604820i
$722$		−	2.29908e8i		−	0.610860i
$723$			1.73962e7i			0.0460299i
$724$	2.74898e8			0.724362
$725$		−	1.40803e8i		−	0.369487i
$726$	1.28245e7	+	7.29216e6i	0.0335144	+	0.0190566i
$727$	5.77686e8			1.50345			0.751725	−	0.659477i	$-0.229222\pi$
$727$	5.77686e8			1.50345			0.751725	+	0.659477i	$0.229222\pi$
$728$		−	1.27907e7i		−	0.0331514i
$729$	−3.80527e8			−0.982208
$730$	−5.48672e8			−1.41041
$731$	−9.64143e7			−0.246825
$732$			1.25884e7i			0.0320951i
$733$		−	2.92452e8i		−	0.742578i	−0.928517	−	0.371289i	$-0.878916\pi$
$733$		−	2.92452e8i		−	0.742578i	0.928517	−	0.371289i	$-0.121084\pi$
$734$		−	1.06024e7i		−	0.0268112i
$735$	2.50845e7			0.0631746
$736$			3.34671e7i			0.0839430i
$737$	4.48037e7	+	7.70161e7i	0.111921	+	0.192389i
$738$	−4.57690e8			−1.13868
$739$			2.84402e8i			0.704693i	0.935870	+	0.352346i	$0.114616\pi$
$739$			2.84402e8i			0.704693i	−0.935870	+	0.352346i	$0.885384\pi$
$740$	−7.64868e7			−0.188752
$741$	2.17815e7			0.0535345
$742$	−3.40802e7			−0.0834239
$743$			3.24169e8i			0.790323i	0.918612	+	0.395161i	$0.129311\pi$
$743$			3.24169e8i			0.790323i	−0.918612	+	0.395161i	$0.870689\pi$
$744$		−	1.09384e7i		−	0.0265604i
$745$		−	7.56480e8i		−	1.82948i
$746$	8.21811e7			0.197950
$747$		−	7.13070e8i		−	1.71069i
$748$	−1.40457e8	+	8.17100e7i	−0.335612	+	0.195241i
$749$	−8.64691e7			−0.205786
$750$		−	1.17065e7i		−	0.0277489i
$751$	−6.13014e8			−1.44727			−0.723637	−	0.690181i	$-0.757531\pi$
$751$	−6.13014e8			−1.44727			−0.723637	+	0.690181i	$0.757531\pi$
$752$	4.68166e7			0.110090
$753$	−2.51331e6			−0.00588655
$754$			2.06857e8i			0.482566i
$755$		−	1.44987e8i		−	0.336890i
$756$			3.06689e6i			0.00709795i
$757$	−6.70501e8			−1.54565			−0.772826	−	0.634619i	$-0.781157\pi$
$757$	−6.70501e8			−1.54565			−0.772826	+	0.634619i	$0.781157\pi$
$758$		−	1.22706e8i		−	0.281746i
$759$	5.69243e6	+	9.78510e6i	0.0130188	+	0.0223790i
$760$	−2.49756e8			−0.568951
$761$			1.09747e8i			0.249021i	0.992218	+	0.124511i	$0.0397361\pi$
$761$			1.09747e8i			0.249021i	−0.992218	+	0.124511i	$0.960264\pi$
$762$	1.23592e7			0.0279336
$763$	1.56623e7			0.0352600
$764$	3.90659e7			0.0876027
$765$			4.08570e8i			0.912604i
$766$			5.06735e8i			1.12744i
$767$		−	3.28707e8i		−	0.728488i
$768$	−1.54362e6			−0.00340767
$769$			4.32833e8i			0.951791i	0.879502	+	0.475895i	$0.157876\pi$
$769$			4.32833e8i			0.951791i	−0.879502	+	0.475895i	$0.842124\pi$
$770$	2.49462e7	+	4.28816e7i	0.0546426	+	0.0939288i
$771$	−1.94735e7			−0.0424894
$772$			3.89540e8i			0.846642i
$773$	−1.66953e8			−0.361457			−0.180729	−	0.983533i	$-0.557846\pi$
$773$	−1.66953e8			−0.361457			−0.180729	+	0.983533i	$0.557846\pi$
$774$	1.03906e8			0.224087
$775$	−2.49735e8			−0.536506
$776$		−	2.08777e8i		−	0.446785i
$777$		−	1.06795e6i		−	0.00227662i
$778$		−	4.41605e8i		−	0.937768i
$779$	1.04239e9			2.20506
$780$		−	1.09670e7i		−	0.0231102i
$781$	3.41500e8	+	5.87027e8i	0.716866	+	1.23227i
$782$	−1.24689e8			−0.260741
$783$		−	4.95991e7i		−	0.103321i
$784$	1.18425e8			0.245750
$785$	7.40163e8			1.53010
$786$	−2.76485e6			−0.00569382
$787$		−	2.26851e8i		−	0.465389i	−0.972550	−	0.232695i	$-0.925246\pi$
$787$		−	2.26851e8i		−	0.465389i	0.972550	−	0.232695i	$-0.0747542\pi$
$788$		−	3.66459e8i		−	0.748939i
$789$			8.09360e6i			0.0164782i
$790$	6.22978e8			1.26355
$791$			1.21840e8i			0.246185i
$792$	1.51370e8	−	8.80588e7i	0.304695	−	0.177254i
$793$	−4.22237e8			−0.846713
$794$		−	1.68648e8i		−	0.336915i
$795$	−2.92210e7			−0.0581558
$796$	−3.67985e8			−0.729610
$797$	1.16541e7			0.0230199			0.0115099	−	0.999934i	$-0.496336\pi$
$797$	1.16541e7			0.0230199			0.0115099	+	0.999934i	$0.496336\pi$
$798$		−	3.48724e6i		−	0.00686236i
$799$			1.74426e8i			0.341957i
$800$			3.52426e7i			0.0688332i
$801$	−6.89265e7			−0.134118
$802$			1.84374e8i			0.357417i
$803$	−7.57353e8	+	4.40586e8i	−1.46269	+	0.850911i
$804$	−3.15350e6			−0.00606771
$805$			3.80678e7i			0.0729744i
$806$	3.66892e8			0.700701
$807$	−1.44085e7			−0.0274155
$808$	−2.14625e7			−0.0406860
$809$			8.32642e8i			1.57258i	0.617858	+	0.786290i	$0.288001\pi$
$809$			8.32642e8i			1.57258i	−0.617858	+	0.786290i	$0.711999\pi$
$810$		−	4.38999e8i		−	0.826055i
$811$		−	8.70832e8i		−	1.63257i	−0.577650	−	0.816285i	$-0.696030\pi$
$811$		−	8.70832e8i		−	1.63257i	0.577650	−	0.816285i	$-0.303970\pi$
$812$	3.31181e7			0.0618582
$813$		−	1.92761e7i		−	0.0358712i
$814$	−1.05578e8	+	6.14192e7i	−0.195749	+	0.113876i
$815$	1.09541e9			2.02351
$816$		−	5.75113e6i		−	0.0105848i
$817$	−2.36646e8			−0.433944
$818$	3.86539e8			0.706209
$819$	−5.13576e7			−0.0934875
$820$		−	5.24846e8i		−	0.951898i
$821$		−	2.66666e8i		−	0.481880i	−0.970540	−	0.240940i	$-0.922544\pi$
$821$		−	2.66666e8i		−	0.481880i	0.970540	−	0.240940i	$-0.0774557\pi$
$822$		−	5.69059e6i		−	0.0102457i
$823$	1.01515e8			0.182110			0.0910548	−	0.995846i	$-0.470976\pi$
$823$	1.01515e8			0.182110			0.0910548	+	0.995846i	$0.470976\pi$
$824$		−	9.17619e6i		−	0.0164014i
$825$	5.99443e6	+	1.03042e7i	0.0106754	+	0.0183507i
$826$	−5.26263e7			−0.0933819
$827$			1.41527e8i			0.250220i	0.992143	+	0.125110i	$0.0399284\pi$
$827$			1.41527e8i			0.250220i	−0.992143	+	0.125110i	$0.960072\pi$
$828$	1.34378e8			0.236721
$829$	4.71888e8			0.828276			0.414138	−	0.910214i	$-0.364083\pi$
$829$	4.71888e8			0.828276			0.414138	+	0.910214i	$0.364083\pi$
$830$	8.17698e8			1.43007
$831$		−	1.10996e6i		−	0.00193421i
$832$		−	5.17757e7i		−	0.0898992i
$833$			4.41219e8i			0.763342i
$834$	2.53103e6			0.00436313
$835$			8.91540e8i			1.53138i
$836$	−3.44748e8	+	2.00555e8i	−0.590041	+	0.343253i
$837$	−8.79712e7			−0.150025
$838$		−	2.25020e8i		−	0.382374i
$839$	−6.22093e7			−0.105334			−0.0526671	−	0.998612i	$-0.516772\pi$
$839$	−6.22093e7			−0.105334			−0.0526671	+	0.998612i	$0.516772\pi$
$840$	−1.75583e6			−0.00296240
$841$	5.92231e7			0.0995642
$842$			5.03777e8i			0.843921i
$843$			2.32238e7i			0.0387659i
$844$		−	1.46406e8i		−	0.243518i
$845$	−3.43331e8			−0.569040
$846$		−	1.87979e8i		−	0.310455i
$847$	6.88682e7	+	3.91592e7i	0.113336	+	0.0644442i
$848$	−1.37953e8			−0.226227
$849$			1.95350e7i			0.0319221i
$850$	−1.31304e8			−0.213807
$851$	−9.37258e7			−0.152079
$852$	−2.40364e7			−0.0388643
$853$		−	5.80815e8i		−	0.935817i	−0.883777	−	0.467908i	$-0.845008\pi$
$853$		−	5.80815e8i		−	0.935817i	0.883777	−	0.467908i	$-0.154992\pi$
$854$			6.76005e7i			0.108537i
$855$			1.00283e9i			1.60445i
$856$	−3.50019e8			−0.558046
$857$		−	3.77918e8i		−	0.600420i	−0.953873	−	0.300210i	$-0.902943\pi$
$857$		−	3.77918e8i		−	0.600420i	0.953873	−	0.300210i	$-0.0970568\pi$
$858$	−8.80655e6	−	1.51382e7i	−0.0139426	−	0.0239669i
$859$	−2.27236e8			−0.358507			−0.179254	−	0.983803i	$-0.557368\pi$
$859$	−2.27236e8			−0.358507			−0.179254	+	0.983803i	$0.557368\pi$
$860$			1.19152e8i			0.187329i
$861$	7.32821e6			0.0114812
$862$	−1.72105e8			−0.268703
$863$	−7.86361e8			−1.22346			−0.611730	−	0.791067i	$-0.709526\pi$
$863$	−7.86361e8			−1.22346			−0.611730	+	0.791067i	$0.709526\pi$
$864$			1.24145e7i			0.0192481i
$865$		−	3.54690e8i		−	0.548025i
$866$			1.90461e8i			0.293259i
$867$	−1.41061e7			−0.0216446
$868$		−	5.87398e7i		−	0.0898200i
$869$	8.59919e8	−	5.00254e8i	1.31038	−	0.762309i
$870$	2.83960e7			0.0431221
$871$		−	1.05773e8i		−	0.160075i
$872$	6.33995e7			0.0956173
$873$	−8.38288e8			−1.25994
$874$	−3.06047e8			−0.458410
$875$		−	6.28647e7i		−	0.0938389i
$876$		−	3.10105e7i		−	0.0461314i
$877$		−	8.15027e8i		−	1.20830i	−0.796872	−	0.604148i	$-0.793514\pi$
$877$		−	8.15027e8i		−	1.20830i	0.796872	−	0.604148i	$-0.206486\pi$
$878$	−5.99749e8			−0.886106
$879$			1.37383e7i			0.0202287i
$880$	1.00980e8	+	1.73581e8i	0.148179	+	0.254714i
$881$	−4.81351e8			−0.703937			−0.351969	−	0.936012i	$-0.614488\pi$
$881$	−4.81351e8			−0.703937			−0.351969	+	0.936012i	$0.614488\pi$
$882$		−	4.75502e8i		−	0.693021i
$883$	−8.36589e8			−1.21515			−0.607575	−	0.794262i	$-0.707858\pi$
$883$	−8.36589e8			−1.21515			−0.607575	+	0.794262i	$0.707858\pi$
$884$	1.92902e8			0.279242
$885$	−4.51227e7			−0.0650977
$886$			5.31752e8i			0.764553i
$887$		−	3.39904e8i		−	0.487064i	−0.969893	−	0.243532i	$-0.921694\pi$
$887$		−	3.39904e8i		−	0.487064i	0.969893	−	0.243532i	$-0.0783060\pi$
$888$		−	4.32298e6i		−	0.00617368i
$889$	6.63697e7			0.0944636
$890$		−	7.90400e7i		−	0.112118i
$891$	−3.52518e8	−	6.05967e8i	−0.498366	−	0.856675i
$892$	3.44706e8			0.485685
$893$			4.28125e8i			0.601196i
$894$	4.27557e7			0.0598386
$895$	−5.36765e8			−0.748713
$896$	−8.28934e6			−0.0115238
$897$		−	1.34388e7i		−	0.0186201i
$898$			2.20185e8i			0.304060i
$899$			9.49965e8i			1.30746i
$900$	1.41507e8			0.194111
$901$		−	5.13978e8i		−	0.702700i
$902$	−4.21454e8	−	7.24465e8i	−0.574288	−	0.987183i
$903$	−1.66367e6			−0.00225945
$904$			4.93197e8i			0.667599i
$905$	1.26573e9			1.70764
$906$	8.19455e6			0.0110190
$907$	1.06495e9			1.42728			0.713639	−	0.700513i	$-0.247046\pi$
$907$	1.06495e9			1.42728			0.713639	+	0.700513i	$0.247046\pi$
$908$		−	3.87170e8i		−	0.517183i
$909$			8.61765e7i			0.114735i
$910$		−	5.88933e7i		−	0.0781523i
$911$	3.05381e8			0.403912			0.201956	−	0.979395i	$-0.435270\pi$
$911$	3.05381e8			0.403912			0.201956	+	0.979395i	$0.435270\pi$
$912$		−	1.41160e7i		−	0.0186092i
$913$	1.12870e9	−	6.56615e8i	1.48308	−	0.862777i
$914$	2.46155e8			0.322382
$915$			5.79619e7i			0.0756622i
$916$	−2.53968e8			−0.330440
$917$	−1.48474e7			−0.0192549
$918$	−4.62530e7			−0.0597877
$919$		−	9.60565e7i		−	0.123760i	−0.998084	−	0.0618800i	$-0.980290\pi$
$919$		−	9.60565e7i		−	0.123760i	0.998084	−	0.0618800i	$-0.0197096\pi$
$920$			1.54095e8i			0.197890i
$921$		−	3.71927e7i		−	0.0476079i
$922$	−4.55768e8			−0.581502
$923$		−	8.06220e8i		−	1.02529i
$924$	−2.42364e6	+	1.40994e6i	−0.00307221	+	0.00178724i
$925$	−9.86981e7			−0.124705
$926$			5.93468e8i			0.747419i
$927$	−3.68444e7			−0.0462522
$928$	1.34059e8			0.167746
$929$	−6.38585e8			−0.796474			−0.398237	−	0.917283i	$-0.630378\pi$
$929$	−6.38585e8			−0.796474			−0.398237	+	0.917283i	$0.630378\pi$
$930$		−	5.03645e7i		−	0.0626146i
$931$			1.08296e9i			1.34204i
$932$			6.23751e8i			0.770483i
$933$	7.56117e7			0.0930989
$934$			1.06584e9i			1.30813i
$935$	−6.46715e8	+	3.76223e8i	−0.791185	+	0.460268i
$936$	−2.07891e8			−0.253517
$937$		−	9.48308e8i		−	1.15274i	−0.817189	−	0.576369i	$-0.804469\pi$
$937$		−	9.48308e8i		−	1.15274i	0.817189	−	0.576369i	$-0.195531\pi$
$938$	−1.69344e7			−0.0205193
$939$	−3.07196e7			−0.0371038
$940$	2.15561e8			0.259529
$941$		−	1.03062e9i		−	1.23689i	−0.785828	−	0.618446i	$-0.787763\pi$
$941$		−	1.03062e9i		−	1.23689i	0.785828	−	0.618446i	$-0.212237\pi$
$942$			4.18335e7i			0.0500462i
$943$		−	6.43138e8i		−	0.766954i
$944$	−2.13026e8			−0.253231
$945$			1.41211e7i			0.0167330i
$946$	9.56792e7	+	1.64469e8i	0.113017	+	0.194273i
$947$	5.13906e8			0.605109			0.302555	−	0.953132i	$-0.402161\pi$
$947$	5.13906e8			0.605109			0.302555	+	0.953132i	$0.402161\pi$
$948$			3.52102e7i			0.0413279i
$949$	1.04014e9			1.21701
$950$	−3.22284e8			−0.375896
$951$	6.83290e7			0.0794445
$952$		−	3.08839e7i		−	0.0357949i
$953$			6.88249e8i			0.795183i	0.917562	+	0.397592i	$0.130154\pi$
$953$			6.88249e8i			0.795183i	−0.917562	+	0.397592i	$0.869846\pi$
$954$			5.53914e8i			0.637965i
$955$	1.79874e8			0.206518
$956$		−	6.17190e8i		−	0.706392i
$957$	3.91961e7	−	2.28021e7i	0.0447205	−	0.0260159i
$958$	3.53164e8			0.401679
$959$		−	3.05587e7i		−	0.0346481i
$960$	−7.10742e6			−0.00803338
$961$	7.97398e8			0.898473
$962$	1.45000e8			0.162870
$963$			1.40540e9i			1.57370i
$964$			3.78149e8i			0.422116i
$965$			1.79359e9i			1.99591i
$966$	−2.15157e6			−0.00238684
$967$			1.25522e9i			1.38816i	0.719897	+	0.694081i	$0.244189\pi$
$967$			1.25522e9i			1.38816i	−0.719897	+	0.694081i	$0.755811\pi$
$968$	2.78772e8	+	1.58513e8i	0.307343	+	0.174758i
$969$	5.25925e7			0.0578033
$970$		−	9.61289e8i		−	1.05327i
$971$	1.04309e9			1.13937			0.569686	−	0.821862i	$-0.307065\pi$
$971$	1.04309e9			1.13937			0.569686	+	0.821862i	$0.307065\pi$
$972$	7.48074e7			0.0814603
$973$	1.35917e7			0.0147549
$974$		−	8.71977e8i		−	0.943688i
$975$		−	1.41518e7i		−	0.0152685i
$976$			2.73640e8i			0.294327i
$977$	−1.13783e9			−1.22009			−0.610047	−	0.792366i	$-0.708849\pi$
$977$	−1.13783e9			−1.22009			−0.610047	+	0.792366i	$0.708849\pi$
$978$			6.19120e7i			0.0661848i
$979$	−6.34694e7	−	1.09102e8i	−0.0676420	−	0.116274i
$980$	5.45272e8			0.579342
$981$		−	2.54563e8i		−	0.269643i
$982$	−4.68932e8			−0.495194
$983$	−5.92329e8			−0.623594			−0.311797	−	0.950149i	$-0.600931\pi$
$983$	−5.92329e8			−0.623594			−0.311797	+	0.950149i	$0.600931\pi$
$984$	2.96639e7			0.0311346
$985$		−	1.68731e9i		−	1.76558i
$986$			4.99467e8i			0.521046i
$987$			3.00979e6i			0.00313029i
$988$	4.73474e8			0.490937
$989$			1.46007e8i			0.150933i
$990$	6.96965e8	−	4.05456e8i	0.718299	−	0.417867i
$991$	2.92428e8			0.300467			0.150234	−	0.988651i	$-0.451997\pi$
$991$	2.92428e8			0.300467			0.150234	+	0.988651i	$0.451997\pi$
$992$		−	2.37773e8i		−	0.243572i
$993$	−5.85275e6			−0.00597740
$994$	−1.29077e8			−0.131428
$995$	−1.69434e9			−1.72001
$996$			4.62157e7i			0.0467747i
$997$			1.76995e9i			1.78598i	0.450078	+	0.892989i	$0.351396\pi$
$997$			1.76995e9i			1.78598i	−0.450078	+	0.892989i	$0.648604\pi$
$998$		−	1.17123e9i		−	1.17829i
$999$	−3.47672e7			−0.0348717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.7.b.a.21.5	yes	6
3.2	odd	2		198.7.d.a.109.3		6
4.3	odd	2		176.7.h.e.65.4		6
11.10	odd	2	inner	22.7.b.a.21.2	✓	6
33.32	even	2		198.7.d.a.109.6		6
44.43	even	2		176.7.h.e.65.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.7.b.a.21.2	✓	6	11.10	odd	2	inner
22.7.b.a.21.5	yes	6	1.1	even	1	trivial
176.7.h.e.65.3		6	44.43	even	2
176.7.h.e.65.4		6	4.3	odd	2
198.7.d.a.109.3		6	3.2	odd	2
198.7.d.a.109.6		6	33.32	even	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.65685i q^{2} -1.47212 q^{3} -32.0000 q^{4} -147.340 q^{5} -8.32754i q^{6} -44.7193i q^{7} -181.019i q^{8} -726.833 q^{9} +O(q^{10})\)	\(q+5.65685i q^{2} -1.47212 q^{3} -32.0000 q^{4} -147.340 q^{5} -8.32754i q^{6} -44.7193i q^{7} -181.019i q^{8} -726.833 q^{9} -833.480i q^{10} +(-669.288 - 1150.48i) q^{11} +47.1077 q^{12} +1580.07i q^{13} +252.971 q^{14} +216.901 q^{15} +1024.00 q^{16} +3815.15i q^{17} -4111.59i q^{18} +9364.20i q^{19} +4714.88 q^{20} +65.8319i q^{21} +(6508.12 - 3786.07i) q^{22} +5777.54 q^{23} +266.481i q^{24} +6084.05 q^{25} -8938.21 q^{26} +2143.15 q^{27} +1431.02i q^{28} -23143.0i q^{29} +1226.98i q^{30} -41047.6 q^{31} +5792.62i q^{32} +(985.269 + 1693.65i) q^{33} -21581.8 q^{34} +6588.94i q^{35} +23258.7 q^{36} -16222.4 q^{37} -52971.9 q^{38} -2326.04i q^{39} +26671.4i q^{40} -111317. i q^{41} -372.402 q^{42} +25271.4i q^{43} +(21417.2 + 36815.5i) q^{44} +107091. q^{45} +32682.7i q^{46} +45719.3 q^{47} -1507.45 q^{48} +115649. q^{49} +34416.6i q^{50} -5616.34i q^{51} -50562.2i q^{52} -134720. q^{53} +12123.5i q^{54} +(98612.9 + 169512. i) q^{55} -8095.06 q^{56} -13785.2i q^{57} +130917. q^{58} -208033. q^{59} -6940.84 q^{60} +267227. i q^{61} -232200. i q^{62} +32503.5i q^{63} -32768.0 q^{64} -232807. i q^{65} +(-9580.71 + 5573.53i) q^{66} -66942.4 q^{67} -122085. i q^{68} -8505.20 q^{69} -37272.7 q^{70} -510244. q^{71} +131571. i q^{72} -658290. i q^{73} -91768.0i q^{74} -8956.42 q^{75} -299654. i q^{76} +(-51448.8 + 29930.1i) q^{77} +13158.1 q^{78} +747441. i q^{79} -150876. q^{80} +526706. q^{81} +629704. q^{82} +981065. i q^{83} -2106.62i q^{84} -562124. i q^{85} -142957. q^{86} +34069.2i q^{87} +(-208260. + 121154. i) q^{88} +94831.2 q^{89} +605801. i q^{90} +70659.5 q^{91} -184881. q^{92} +60426.7 q^{93} +258627. i q^{94} -1.37972e6i q^{95} -8527.40i q^{96} +1.15334e6 q^{97} +654211. i q^{98} +(486461. + 836210. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9}+O(q^{10}) \) 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9	\( 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9} - 1166 q^{11} + 1664 q^{12} + 2208 q^{14} - 6512 q^{15} + 6144 q^{16} - 11776 q^{20} + 1056 q^{22} + 2156 q^{23} + 59862 q^{25} - 1824 q^{26} - 57472 q^{27} - 78468 q^{31} + 142208 q^{33} + 28704 q^{34} + 11072 q^{36} - 205920 q^{37} + 101472 q^{38} - 344160 q^{42} + 37312 q^{44} + 368716 q^{45} + 493460 q^{47} - 53248 q^{48} - 270762 q^{49} - 531700 q^{53} + 274956 q^{55} - 70656 q^{56} + 509184 q^{58} - 833380 q^{59} + 208384 q^{60} - 196608 q^{64} + 193248 q^{66} + 537420 q^{67} + 398860 q^{69} + 96096 q^{70} - 460372 q^{71} - 211428 q^{75} + 249744 q^{77} - 1866912 q^{78} + 376832 q^{80} + 485654 q^{81} + 428640 q^{82} + 1055808 q^{86} - 33792 q^{88} + 2377952 q^{89} - 5068656 q^{91} - 68992 q^{92} + 699868 q^{93} + 1351632 q^{97} - 2470930 q^{99}+O(q^{100}) \) 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9 - 1166 * q^11 + 1664 * q^12 + 2208 * q^14 - 6512 * q^15 + 6144 * q^16 - 11776 * q^20 + 1056 * q^22 + 2156 * q^23 + 59862 * q^25 - 1824 * q^26 - 57472 * q^27 - 78468 * q^31 + 142208 * q^33 + 28704 * q^34 + 11072 * q^36 - 205920 * q^37 + 101472 * q^38 - 344160 * q^42 + 37312 * q^44 + 368716 * q^45 + 493460 * q^47 - 53248 * q^48 - 270762 * q^49 - 531700 * q^53 + 274956 * q^55 - 70656 * q^56 + 509184 * q^58 - 833380 * q^59 + 208384 * q^60 - 196608 * q^64 + 193248 * q^66 + 537420 * q^67 + 398860 * q^69 + 96096 * q^70 - 460372 * q^71 - 211428 * q^75 + 249744 * q^77 - 1866912 * q^78 + 376832 * q^80 + 485654 * q^81 + 428640 * q^82 + 1055808 * q^86 - 33792 * q^88 + 2377952 * q^89 - 5068656 * q^91 - 68992 * q^92 + 699868 * q^93 + 1351632 * q^97 - 2470930 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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