LMFDB - Embedded newform 17.16.b.a.16.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,16,Mod(16,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	17.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:	$24.2578958670$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.16
Character	$\chi$	$=$	17.16
Dual form			17.16.b.a.16.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+158.526 q^{2} -159.452i q^{3} -7637.56 q^{4} +199360. i q^{5} -25277.2i q^{6} -4.18240e6i q^{7} -6.40533e6 q^{8} +1.43235e7 q^{9} +O(q^{10})$	\(q+158.526 q^{2} -159.452i q^{3} -7637.56 q^{4} +199360. i q^{5} -25277.2i q^{6} -4.18240e6i q^{7} -6.40533e6 q^{8} +1.43235e7 q^{9} +3.16037e7i q^{10} +2.18585e7i q^{11} +1.21782e6i q^{12} +3.46297e8 q^{13} -6.63018e8i q^{14} +3.17883e7 q^{15} -7.65142e8 q^{16} +(1.58871e9 + 5.81735e8i) q^{17} +2.27064e9 q^{18} +2.94794e9 q^{19} -1.52262e9i q^{20} -6.66890e8 q^{21} +3.46514e9i q^{22} -1.44407e10i q^{23} +1.02134e9i q^{24} -9.22682e9 q^{25} +5.48970e10 q^{26} -4.57186e9i q^{27} +3.19433e10i q^{28} -2.64369e9i q^{29} +5.03926e9 q^{30} -1.40061e11i q^{31} +8.85950e10 q^{32} +3.48538e9 q^{33} +(2.51852e11 + 9.22200e10i) q^{34} +8.33803e11 q^{35} -1.09397e11 q^{36} -8.75378e11i q^{37} +4.67325e11 q^{38} -5.52176e10i q^{39} -1.27697e12i q^{40} +2.04844e12i q^{41} -1.05719e11 q^{42} +1.79994e12 q^{43} -1.66946e11i q^{44} +2.85553e12i q^{45} -2.28922e12i q^{46} -2.86172e12 q^{47} +1.22003e11i q^{48} -1.27449e13 q^{49} -1.46269e12 q^{50} +(9.27585e10 - 2.53323e11i) q^{51} -2.64487e12 q^{52} +6.85277e12 q^{53} -7.24757e11i q^{54} -4.35772e12 q^{55} +2.67896e13i q^{56} -4.70054e11i q^{57} -4.19093e11i q^{58} -2.14930e13 q^{59} -2.42785e11 q^{60} -6.73864e12i q^{61} -2.22033e13i q^{62} -5.99065e13i q^{63} +3.91168e13 q^{64} +6.90377e13i q^{65} +5.52522e11 q^{66} +1.21139e12 q^{67} +(-1.21339e13 - 4.44304e12i) q^{68} -2.30259e12 q^{69} +1.32179e14 q^{70} +7.71221e12i q^{71} -9.17466e13 q^{72} +1.22093e14i q^{73} -1.38770e14i q^{74} +1.47123e12i q^{75} -2.25151e13 q^{76} +9.14211e13 q^{77} -8.75341e12i q^{78} -2.38004e14i q^{79} -1.52539e14i q^{80} +2.04797e14 q^{81} +3.24731e14i q^{82} -9.16560e13 q^{83} +5.09341e12 q^{84} +(-1.15975e14 + 3.16726e14i) q^{85} +2.85337e14 q^{86} -4.21541e11 q^{87} -1.40011e14i q^{88} +2.05833e14 q^{89} +4.52675e14i q^{90} -1.44835e15i q^{91} +1.10292e14i q^{92} -2.23330e13 q^{93} -4.53657e14 q^{94} +5.87702e14i q^{95} -1.41266e13i q^{96} +7.88714e14i q^{97} -2.02039e15 q^{98} +3.13090e14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9}+O(q^{10}) $ 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9	$ 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9} + 702506672 q^{13} - 1787378376 q^{15} + 3524081474 q^{16} - 2245058454 q^{17} + 6803778314 q^{18} + 9958891784 q^{19} - 4168893668 q^{21} - 238696683970 q^{25} - 33467295588 q^{26} - 62541989808 q^{30} - 43445086338 q^{32} + 213283309748 q^{33} + 521524562854 q^{34} - 467785613304 q^{35} - 2300588654186 q^{36} + 3162083165688 q^{38} - 3011205093968 q^{42} - 2215728209008 q^{43} - 7793870107128 q^{47} - 1555224751482 q^{49} + 30118817411766 q^{50} - 21451923375880 q^{51} + 51163160044372 q^{52} - 6062965973460 q^{53} - 11679154373592 q^{55} + 22772194849344 q^{59} - 86295684546192 q^{60} - 28567749560318 q^{64} + 251781147903680 q^{66} + 153875904272808 q^{67} - 48849686100870 q^{68} + 60664072036996 q^{69} - 150925771647648 q^{70} - 293782759569702 q^{72} - 388479948338264 q^{76} - 622427249887884 q^{77} + 983865215787034 q^{81} - 15\!\cdots\!44 q^{83}+ \cdots + 26\!\cdots\!90 q^{98}+O(q^{100}) $ 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9 + 702506672 * q^13 - 1787378376 * q^15 + 3524081474 * q^16 - 2245058454 * q^17 + 6803778314 * q^18 + 9958891784 * q^19 - 4168893668 * q^21 - 238696683970 * q^25 - 33467295588 * q^26 - 62541989808 * q^30 - 43445086338 * q^32 + 213283309748 * q^33 + 521524562854 * q^34 - 467785613304 * q^35 - 2300588654186 * q^36 + 3162083165688 * q^38 - 3011205093968 * q^42 - 2215728209008 * q^43 - 7793870107128 * q^47 - 1555224751482 * q^49 + 30118817411766 * q^50 - 21451923375880 * q^51 + 51163160044372 * q^52 - 6062965973460 * q^53 - 11679154373592 * q^55 + 22772194849344 * q^59 - 86295684546192 * q^60 - 28567749560318 * q^64 + 251781147903680 * q^66 + 153875904272808 * q^67 - 48849686100870 * q^68 + 60664072036996 * q^69 - 150925771647648 * q^70 - 293782759569702 * q^72 - 388479948338264 * q^76 - 622427249887884 * q^77 + 983865215787034 * q^81 - 1541046988482144 * q^83 + 1542636638603936 * q^84 + 94526232685248 * q^85 + 102594718370712 * q^86 - 428830075363560 * q^87 - 894061425316800 * q^89 + 2342465228549812 * q^93 + 2620489835637760 * q^94 + 2662999543720290 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	158.526			0.875740			0.437870	−	0.899038i	$-0.355733\pi$
$2$	158.526			0.875740			0.437870	+	0.899038i	$0.355733\pi$
$3$		−	159.452i		−	0.0420939i	−0.999778	−	0.0210470i	$-0.993300\pi$
$3$		−	159.452i		−	0.0420939i	0.999778	−	0.0210470i	$-0.00669995\pi$
$4$	−7637.56			−0.233080
$5$			199360.i			1.14120i	0.821227	+	0.570602i	$0.193290\pi$
$5$			199360.i			1.14120i	−0.821227	+	0.570602i	$0.806710\pi$
$6$		−	25277.2i		−	0.0368633i
$7$		−	4.18240e6i		−	1.91951i	−0.280842	−	0.959754i	$-0.590614\pi$
$7$		−	4.18240e6i		−	1.91951i	0.280842	−	0.959754i	$-0.409386\pi$
$8$	−6.40533e6			−1.07986
$9$	1.43235e7			0.998228
$10$			3.16037e7i			0.999397i
$11$			2.18585e7i			0.338202i	0.985599	+	0.169101i	$0.0540864\pi$
$11$			2.18585e7i			0.338202i	−0.985599	+	0.169101i	$0.945914\pi$
$12$			1.21782e6i			0.00981125i
$13$	3.46297e8			1.53064			0.765321	−	0.643649i	$-0.222580\pi$
$13$	3.46297e8			1.53064			0.765321	+	0.643649i	$0.222580\pi$
$14$		−	6.63018e8i		−	1.68099i
$15$	3.17883e7			0.0480377
$16$	−7.65142e8			−0.712594
$17$	1.58871e9	+	5.81735e8i	0.939028	+	0.343841i
$17$	1.58871e9	+	5.81735e8i	0.939028	+	0.343841i
$18$	2.27064e9			0.874188
$19$	2.94794e9			0.756601			0.378301	−	0.925683i	$-0.376509\pi$
$19$	2.94794e9			0.756601			0.378301	+	0.925683i	$0.376509\pi$
$20$		−	1.52262e9i		−	0.265992i
$21$	−6.66890e8			−0.0807996
$22$			3.46514e9i			0.296177i
$23$		−	1.44407e10i		−	0.884359i	−0.896927	−	0.442179i	$-0.854205\pi$
$23$		−	1.44407e10i		−	0.884359i	0.896927	−	0.442179i	$-0.145795\pi$
$24$			1.02134e9i			0.0454554i
$25$	−9.22682e9			−0.302345
$26$	5.48970e10			1.34044
$27$		−	4.57186e9i		−	0.0841132i
$28$			3.19433e10i			0.447399i
$29$		−	2.64369e9i		−	0.0284594i	−0.999899	−	0.0142297i	$-0.995470\pi$
$29$		−	2.64369e9i		−	0.0284594i	0.999899	−	0.0142297i	$-0.00452961\pi$
$30$	5.03926e9			0.0420685
$31$		−	1.40061e11i		−	0.914334i	−0.889381	−	0.457167i	$-0.848864\pi$
$31$		−	1.40061e11i		−	0.914334i	0.889381	−	0.457167i	$-0.151136\pi$
$32$	8.85950e10			0.455810
$33$	3.48538e9			0.0142362
$34$	2.51852e11	+	9.22200e10i	0.822344	+	0.301115i
$35$	8.33803e11			2.19055
$36$	−1.09397e11			−0.232667
$37$		−	8.75378e11i		−	1.51594i	−0.652288	−	0.757971i	$-0.726191\pi$
$37$		−	8.75378e11i		−	1.51594i	0.652288	−	0.757971i	$-0.273809\pi$
$38$	4.67325e11			0.662586
$39$		−	5.52176e10i		−	0.0644307i
$40$		−	1.27697e12i		−	1.23234i
$41$			2.04844e12i			1.64265i	0.570461	+	0.821324i	$0.306764\pi$
$41$			2.04844e12i			1.64265i	−0.570461	+	0.821324i	$0.693236\pi$
$42$	−1.05719e11			−0.0707594
$43$	1.79994e12			1.00982			0.504911	−	0.863171i	$-0.331525\pi$
$43$	1.79994e12			1.00982			0.504911	+	0.863171i	$0.331525\pi$
$44$		−	1.66946e11i		−	0.0788281i
$45$			2.85553e12i			1.13918i
$46$		−	2.28922e12i		−	0.774468i
$47$	−2.86172e12			−0.823937			−0.411968	−	0.911198i	$-0.635159\pi$
$47$	−2.86172e12			−0.823937			−0.411968	+	0.911198i	$0.635159\pi$
$48$			1.22003e11i			0.0299959i
$49$	−1.27449e13			−2.68451
$50$	−1.46269e12			−0.264775
$51$	9.27585e10	−	2.53323e11i	0.0144736	−	0.0395273i
$52$	−2.64487e12			−0.356762
$53$	6.85277e12			0.801303			0.400652	−	0.916231i	$-0.368784\pi$
$53$	6.85277e12			0.801303			0.400652	+	0.916231i	$0.368784\pi$
$54$		−	7.24757e11i		−	0.0736613i
$55$	−4.35772e12			−0.385957
$56$			2.67896e13i			2.07279i
$57$		−	4.70054e11i		−	0.0318483i
$58$		−	4.19093e11i		−	0.0249230i
$59$	−2.14930e13			−1.12436			−0.562181	−	0.827014i	$-0.690038\pi$
$59$	−2.14930e13			−1.12436			−0.562181	+	0.827014i	$0.690038\pi$
$60$	−2.42785e11			−0.0111966
$61$		−	6.73864e12i		−	0.274536i	−0.990534	−	0.137268i	$-0.956168\pi$
$61$		−	6.73864e12i		−	0.274536i	0.990534	−	0.137268i	$-0.0438321\pi$
$62$		−	2.22033e13i		−	0.800718i
$63$		−	5.99065e13i		−	1.91611i
$64$	3.91168e13			1.11177
$65$			6.90377e13i			1.74677i
$66$	5.52522e11			0.0124672
$67$	1.21139e12			0.0244187			0.0122093	−	0.999925i	$-0.496114\pi$
$67$	1.21139e12			0.0244187			0.0122093	+	0.999925i	$0.496114\pi$
$68$	−1.21339e13	−	4.44304e12i	−0.218869	−	0.0801425i
$69$	−2.30259e12			−0.0372261
$70$	1.32179e14			1.91835
$71$			7.71221e12i			0.100633i	0.998733	+	0.0503166i	$0.0160230\pi$
$71$			7.71221e12i			0.100633i	−0.998733	+	0.0503166i	$0.983977\pi$
$72$	−9.17466e13			−1.07794
$73$			1.22093e14i			1.29350i	0.762701	+	0.646752i	$0.223873\pi$
$73$			1.22093e14i			1.29350i	−0.762701	+	0.646752i	$0.776127\pi$
$74$		−	1.38770e14i		−	1.32757i
$75$			1.47123e12i			0.0127269i
$76$	−2.25151e13			−0.176349
$77$	9.14211e13			0.649181
$78$		−	8.75341e12i		−	0.0564245i
$79$		−	2.38004e14i		−	1.39438i	−0.716887	−	0.697189i	$-0.754434\pi$
$79$		−	2.38004e14i		−	1.39438i	0.716887	−	0.697189i	$-0.245566\pi$
$80$		−	1.52539e14i		−	0.813214i
$81$	2.04797e14			0.994687
$82$			3.24731e14i			1.43853i
$83$	−9.16560e13			−0.370745			−0.185372	−	0.982668i	$-0.559349\pi$
$83$	−9.16560e13			−0.370745			−0.185372	+	0.982668i	$0.559349\pi$
$84$	5.09341e12			0.0188328
$85$	−1.15975e14	+	3.16726e14i	−0.392393	+	1.07162i
$86$	2.85337e14			0.884342
$87$	−4.21541e11			−0.00119797
$88$		−	1.40011e14i		−	0.365210i
$89$	2.05833e14			0.493276			0.246638	−	0.969108i	$-0.420674\pi$
$89$	2.05833e14			0.493276			0.246638	+	0.969108i	$0.420674\pi$
$90$			4.52675e14i			0.997626i
$91$		−	1.44835e15i		−	2.93808i
$92$			1.10292e14i			0.206126i
$93$	−2.23330e13			−0.0384879
$94$	−4.53657e14			−0.721554
$95$			5.87702e14i			0.863435i
$96$		−	1.41266e13i		−	0.0191868i
$97$			7.88714e14i			0.991132i	0.868570	+	0.495566i	$0.165039\pi$
$97$			7.88714e14i			0.991132i	−0.868570	+	0.495566i	$0.834961\pi$
$98$	−2.02039e15			−2.35093
$99$			3.13090e14i			0.337603i
$100$	7.04705e13			0.0704705
$101$	6.38862e14			0.592921			0.296460	−	0.955045i	$-0.404194\pi$
$101$	6.38862e14			0.592921			0.296460	+	0.955045i	$0.404194\pi$
$102$	1.47046e13	−	4.01582e13i	0.0126751	−	0.0346157i
$103$	−5.25891e14			−0.421324			−0.210662	−	0.977559i	$-0.567562\pi$
$103$	−5.25891e14			−0.421324			−0.210662	+	0.977559i	$0.567562\pi$
$104$	−2.21814e15			−1.65287
$105$		−	1.32951e14i		−	0.0922088i
$106$	1.08634e15			0.701733
$107$			1.03719e15i			0.624422i	0.950013	+	0.312211i	$0.101070\pi$
$107$			1.03719e15i			0.624422i	−0.950013	+	0.312211i	$0.898930\pi$
$108$			3.49178e13i			0.0196051i
$109$		−	1.61211e15i		−	0.844690i	−0.906435	−	0.422345i	$-0.861207\pi$
$109$		−	1.61211e15i		−	0.844690i	0.906435	−	0.422345i	$-0.138793\pi$
$110$	−6.90811e14			−0.337998
$111$	−1.39580e14			−0.0638120
$112$			3.20013e15i			1.36783i
$113$		−	1.38840e15i		−	0.555170i	−0.960701	−	0.277585i	$-0.910466\pi$
$113$		−	1.38840e15i		−	0.555170i	0.960701	−	0.277585i	$-0.0895340\pi$
$114$		−	7.45157e13i		−	0.0278908i
$115$	2.87889e15			1.00923
$116$			2.01914e13i			0.00663332i
$117$	4.96018e15			1.52793
$118$	−3.40719e15			−0.984649
$119$	2.43305e15	−	6.64463e15i	0.660006	−	1.80247i
$120$	−2.03614e14			−0.0518738
$121$	3.69945e15			0.885619
$122$		−	1.06825e15i		−	0.240422i
$123$	3.26627e14			0.0691455
$124$			1.06973e15i			0.213113i
$125$			4.24452e15i			0.796167i
$126$		−	9.49673e15i		−	1.67801i
$127$	7.48064e15			1.24569			0.622847	−	0.782344i	$-0.285976\pi$
$127$	7.48064e15			1.24569			0.622847	+	0.782344i	$0.285976\pi$
$128$	3.29794e15			0.517806
$129$		−	2.87004e14i		−	0.0425074i
$130$			1.09443e16i			1.52972i
$131$			1.20476e16i			1.58989i	0.606683	+	0.794944i	$0.292500\pi$
$131$			1.20476e16i			1.58989i	−0.606683	+	0.794944i	$0.707500\pi$
$132$	−2.66198e13			−0.00331818
$133$		−	1.23295e16i		−	1.45230i
$134$	1.92036e14			0.0213844
$135$	9.11445e14			0.0959903
$136$	−1.01762e16	−	3.72620e15i	−1.01402	−	0.371299i
$137$	−1.03293e16			−0.974244			−0.487122	−	0.873334i	$-0.661953\pi$
$137$	−1.03293e16			−0.974244			−0.487122	+	0.873334i	$0.661953\pi$
$138$	−3.65019e14			−0.0326004
$139$		−	1.09962e16i		−	0.930314i	−0.885228	−	0.465157i	$-0.845998\pi$
$139$		−	1.09962e16i		−	0.930314i	0.885228	−	0.465157i	$-0.154002\pi$
$140$	−6.36822e15			−0.510573
$141$			4.56306e14i			0.0346827i
$142$			1.22258e15i			0.0881284i
$143$			7.56955e15i			0.517666i
$144$	−1.09595e16			−0.711331
$145$	5.27046e14			0.0324780
$146$			1.93548e16i			1.13277i
$147$			2.03219e15i			0.113002i
$148$			6.68576e15i			0.353336i
$149$	−9.75044e15			−0.489922			−0.244961	−	0.969533i	$-0.578775\pi$
$149$	−9.75044e15			−0.489922			−0.244961	+	0.969533i	$0.578775\pi$
$150$			2.33228e14i			0.0111454i
$151$	−2.61100e16			−1.18708			−0.593540	−	0.804805i	$-0.702270\pi$
$151$	−2.61100e16			−1.18708			−0.593540	+	0.804805i	$0.702270\pi$
$152$	−1.88825e16			−0.817021
$153$	2.27559e16	+	8.33247e15i	0.937364	+	0.343232i
$154$	1.44926e16			0.568514
$155$	2.79226e16			1.04344
$156$			4.21728e14i			0.0150175i
$157$	5.25667e15			0.178428			0.0892141	−	0.996012i	$-0.471564\pi$
$157$	5.25667e15			0.178428			0.0892141	+	0.996012i	$0.471564\pi$
$158$		−	3.77297e16i		−	1.22111i
$159$		−	1.09268e15i		−	0.0337300i
$160$			1.76623e16i			0.520172i
$161$	−6.03966e16			−1.69753
$162$	3.24657e16			0.871087
$163$		−	5.03998e16i		−	1.29128i	−0.763640	−	0.645642i	$-0.776590\pi$
$163$		−	5.03998e16i		−	1.29128i	0.763640	−	0.645642i	$-0.223410\pi$
$164$		−	1.56451e16i		−	0.382869i
$165$			6.94845e14i			0.0162464i
$166$	−1.45298e16			−0.324676
$167$			1.69822e16i			0.362760i	0.983413	+	0.181380i	$0.0580564\pi$
$167$			1.69822e16i			0.362760i	−0.983413	+	0.181380i	$0.941944\pi$
$168$	4.27164e15			0.0872520
$169$	6.87357e16			1.34286
$170$	−1.83850e16	+	5.02092e16i	−0.343634	+	0.938461i
$171$	4.22248e16			0.755260
$172$	−1.37472e16			−0.235369
$173$			6.89017e16i			1.12950i	0.825264	+	0.564748i	$0.191026\pi$
$173$			6.89017e16i			1.12950i	−0.825264	+	0.564748i	$0.808974\pi$
$174$	−6.68251e13			−0.00104911
$175$			3.85902e16i			0.580353i
$176$		−	1.67249e16i		−	0.241001i
$177$			3.42709e15i			0.0473288i
$178$	3.26299e16			0.431982
$179$	−6.76787e16			−0.859120			−0.429560	−	0.903038i	$-0.641331\pi$
$179$	−6.76787e16			−0.859120			−0.429560	+	0.903038i	$0.641331\pi$
$180$		−	2.18093e16i		−	0.265520i
$181$		−	1.25875e17i		−	1.47011i	−0.678005	−	0.735057i	$-0.737155\pi$
$181$		−	1.25875e17i		−	1.47011i	0.678005	−	0.735057i	$-0.262845\pi$
$182$		−	2.29601e17i		−	2.57299i
$183$	−1.07449e15			−0.0115563
$184$			9.24972e16i			0.954981i
$185$	1.74515e17			1.73000
$186$	−3.54035e15			−0.0337054
$187$	−1.27159e16	+	3.47269e16i	−0.116288	+	0.317581i
$188$	2.18566e16			0.192043
$189$	−1.91213e16			−0.161456
$190$			9.31659e16i			0.756145i
$191$	−4.16351e16			−0.324870			−0.162435	−	0.986719i	$-0.551935\pi$
$191$	−4.16351e16			−0.324870			−0.162435	+	0.986719i	$0.551935\pi$
$192$		−	6.23723e15i		−	0.0467985i
$193$			7.70094e16i			0.555730i	0.960620	+	0.277865i	$0.0896268\pi$
$193$			7.70094e16i			0.555730i	−0.960620	+	0.277865i	$0.910373\pi$
$194$			1.25032e17i			0.867974i
$195$	1.10082e16			0.0735285
$196$	9.73399e16			0.625706
$197$		−	1.81285e17i		−	1.12167i	−0.827927	−	0.560836i	$-0.810480\pi$
$197$		−	1.81285e17i		−	1.12167i	0.827927	−	0.560836i	$-0.189520\pi$
$198$			4.96329e16i			0.295652i
$199$		−	3.50540e16i		−	0.201066i	−0.994934	−	0.100533i	$-0.967945\pi$
$199$		−	3.50540e16i		−	0.201066i	0.994934	−	0.100533i	$-0.0320549\pi$
$200$	5.91008e16			0.326489
$201$		−	1.93158e14i		−	0.00102788i
$202$	1.01276e17			0.519244
$203$	−1.10570e16			−0.0546281
$204$	−7.08449e14	+	1.93477e15i	−0.00337351	+	0.00921303i
$205$	−4.08377e17			−1.87460
$206$	−8.33673e16			−0.368970
$207$		−	2.06841e17i		−	0.882792i
$208$	−2.64966e17			−1.09073
$209$			6.44377e16i			0.255884i
$210$		−	2.10762e16i		−	0.0807509i
$211$			1.77202e17i			0.655165i	0.944823	+	0.327582i	$0.106234\pi$
$211$			1.77202e17i			0.655165i	−0.944823	+	0.327582i	$0.893766\pi$
$212$	−5.23384e16			−0.186768
$213$	1.22972e15			0.00423604
$214$			1.64421e17i			0.546831i
$215$			3.58836e17i			1.15241i
$216$			2.92842e16i			0.0908303i
$217$	−5.85791e17			−1.75507
$218$		−	2.55562e17i		−	0.739728i
$219$	1.94678e16			0.0544486
$220$	3.32824e16			0.0899589
$221$	5.50166e17	+	2.01453e17i	1.43731	+	0.526298i
$222$	−2.21271e16			−0.0558827
$223$	−1.44465e17			−0.352757			−0.176379	−	0.984322i	$-0.556438\pi$
$223$	−1.44465e17			−0.352757			−0.176379	+	0.984322i	$0.556438\pi$
$224$		−	3.70539e17i		−	0.874932i
$225$	−1.32160e17			−0.301809
$226$		−	2.20097e17i		−	0.486184i
$227$			1.91458e17i			0.409148i	0.978851	+	0.204574i	$0.0655809\pi$
$227$			1.91458e17i			0.409148i	−0.978851	+	0.204574i	$0.934419\pi$
$228$			3.59007e15i			0.00742320i
$229$	−7.35122e17			−1.47093			−0.735467	−	0.677561i	$-0.763037\pi$
$229$	−7.35122e17			−1.47093			−0.735467	+	0.677561i	$0.763037\pi$
$230$	4.56379e17			0.883826
$231$		−	1.45772e16i		−	0.0273266i
$232$			1.69337e16i			0.0307321i
$233$			9.80178e17i			1.72241i	0.508261	+	0.861203i	$0.330288\pi$
$233$			9.80178e17i			1.72241i	−0.508261	+	0.861203i	$0.669712\pi$
$234$	7.86316e17			1.33807
$235$		−	5.70513e17i		−	0.940279i
$236$	1.64154e17			0.262066
$237$	−3.79501e16			−0.0586948
$238$	3.85701e17	−	1.05334e18i	0.577994	−	1.57850i
$239$	8.48489e17			1.23215			0.616073	−	0.787689i	$-0.288723\pi$
$239$	8.48489e17			1.23215			0.616073	+	0.787689i	$0.288723\pi$
$240$	−2.43225e16			−0.0342314
$241$			5.93140e17i			0.809151i	0.914505	+	0.404575i	$0.132581\pi$
$241$			5.93140e17i			0.809151i	−0.914505	+	0.404575i	$0.867419\pi$
$242$	5.86459e17			0.775572
$243$		−	9.82564e16i		−	0.125984i
$244$			5.14668e16i			0.0639887i
$245$		−	2.54082e18i		−	3.06357i
$246$	5.17788e16			0.0605535
$247$	1.02086e18			1.15809
$248$			8.97137e17i			0.987350i
$249$			1.46147e16i			0.0156061i
$250$			6.72867e17i			0.697235i
$251$	−1.07688e18			−1.08296			−0.541480	−	0.840714i	$-0.682136\pi$
$251$	−1.07688e18			−1.08296			−0.541480	+	0.840714i	$0.682136\pi$
$252$			4.57540e17i			0.446606i
$253$	3.15652e17			0.299092
$254$	1.18588e18			1.09090
$255$	5.05024e16	+	1.84923e16i	0.0451087	+	0.0165173i
$256$	−7.58970e17			−0.658301
$257$	1.81287e18			1.52710			0.763550	−	0.645748i	$-0.223455\pi$
$257$	1.81287e18			1.52710			0.763550	+	0.645748i	$0.223455\pi$
$258$		−	4.54975e16i		−	0.0372254i
$259$	−3.66118e18			−2.90986
$260$		−	5.27280e17i		−	0.407138i
$261$		−	3.78669e16i		−	0.0284090i
$262$			1.90986e18i			1.39233i
$263$	−1.06776e18			−0.756496			−0.378248	−	0.925704i	$-0.623473\pi$
$263$	−1.06776e18			−0.756496			−0.378248	+	0.925704i	$0.623473\pi$
$264$	−2.23250e16			−0.0153731
$265$			1.36617e18i			0.914450i
$266$		−	1.95454e18i		−	1.27184i
$267$		−	3.28204e16i		−	0.0207639i
$268$	−9.25206e15			−0.00569151
$269$			4.36489e17i			0.261115i	0.991441	+	0.130557i	$0.0416767\pi$
$269$			4.36489e17i			0.261115i	−0.991441	+	0.130557i	$0.958323\pi$
$270$	1.44488e17			0.0840625
$271$	8.06135e16			0.0456182			0.0228091	−	0.999740i	$-0.492739\pi$
$271$	8.06135e16			0.0456182			0.0228091	+	0.999740i	$0.492739\pi$
$272$	−1.21559e18	−	4.45109e17i	−0.669145	−	0.245019i
$273$	−2.30942e17			−0.123675
$274$	−1.63746e18			−0.853184
$275$		−	2.01685e17i		−	0.102254i
$276$	1.75862e16			0.00867666
$277$			2.74184e18i			1.31657i	0.752769	+	0.658285i	$0.228718\pi$
$277$			2.74184e18i			1.31657i	−0.752769	+	0.658285i	$0.771282\pi$
$278$		−	1.74317e18i		−	0.814713i
$279$		−	2.00616e18i		−	0.912714i
$280$	−5.34078e18			−2.36548
$281$	−8.12207e17			−0.350243			−0.175122	−	0.984547i	$-0.556032\pi$
$281$	−8.12207e17			−0.350243			−0.175122	+	0.984547i	$0.556032\pi$
$282$			7.23363e16i			0.0303730i
$283$			2.65807e18i			1.08685i	0.839458	+	0.543424i	$0.182872\pi$
$283$			2.65807e18i			1.08685i	−0.839458	+	0.543424i	$0.817128\pi$
$284$		−	5.89025e16i		−	0.0234556i
$285$	9.37099e16			0.0363454
$286$			1.19997e18i			0.453341i
$287$	8.56740e18			3.15308
$288$	1.26899e18			0.455003
$289$	2.18559e18	+	1.84842e18i	0.763546	+	0.645753i
$290$	8.35505e16			0.0284422
$291$	1.25762e17			0.0417206
$292$		−	9.32490e17i		−	0.301490i
$293$	−2.14496e18			−0.675947			−0.337973	−	0.941156i	$-0.609741\pi$
$293$	−2.14496e18			−0.675947			−0.337973	+	0.941156i	$0.609741\pi$
$294$			3.22155e17i			0.0989600i
$295$		−	4.28484e18i		−	1.28313i
$296$			5.60708e18i			1.63700i
$297$	9.99341e16			0.0284473
$298$	−1.54570e18			−0.429045
$299$		−	5.00076e18i		−	1.35364i
$300$		−	1.12366e16i		−	0.00296638i
$301$		−	7.52807e18i		−	1.93836i
$302$	−4.13911e18			−1.03957
$303$		−	1.01867e17i		−	0.0249584i
$304$	−2.25559e18			−0.539149
$305$	1.34342e18			0.313301
$306$	3.60740e18	+	1.32091e18i	0.820887	+	0.300582i
$307$	4.41885e17			0.0981232			0.0490616	−	0.998796i	$-0.484377\pi$
$307$	4.41885e17			0.0981232			0.0490616	+	0.998796i	$0.484377\pi$
$308$	−6.98235e17			−0.151311
$309$			8.38541e16i			0.0177352i
$310$	4.42645e18			0.913782
$311$			5.66509e18i			1.14157i	0.821099	+	0.570786i	$0.193362\pi$
$311$			5.66509e18i			1.14157i	−0.821099	+	0.570786i	$0.806638\pi$
$312$			3.53686e17i			0.0695759i
$313$			1.37869e18i			0.264779i	0.991198	+	0.132389i	$0.0422649\pi$
$313$			1.37869e18i			0.264779i	−0.991198	+	0.132389i	$0.957735\pi$
$314$	8.33318e17			0.156257
$315$	1.19430e19			2.18667
$316$			1.81777e18i			0.325002i
$317$		−	4.79332e18i		−	0.836935i	−0.908232	−	0.418467i	$-0.862567\pi$
$317$		−	4.79332e18i		−	0.836935i	0.908232	−	0.418467i	$-0.137433\pi$
$318$		−	1.73219e17i		−	0.0295387i
$319$	5.77873e16			0.00962503
$320$			7.79832e18i			1.26875i
$321$	1.65381e17			0.0262844
$322$	−9.57442e18			−1.48660
$323$	4.68343e18	+	1.71492e18i	0.710469	+	0.260151i
$324$	−1.56415e18			−0.231842
$325$	−3.19522e18			−0.462781
$326$		−	7.98967e18i		−	1.13083i
$327$	−2.57054e17			−0.0355563
$328$		−	1.31209e19i		−	1.77383i
$329$			1.19689e19i			1.58155i
$330$			1.10151e17i			0.0142277i
$331$	−7.17534e18			−0.906010			−0.453005	−	0.891508i	$-0.649648\pi$
$331$	−7.17534e18			−0.906010			−0.453005	+	0.891508i	$0.649648\pi$
$332$	7.00028e17			0.0864132
$333$		−	1.25385e19i		−	1.51326i
$334$			2.69211e18i			0.317684i
$335$			2.41502e17i			0.0278667i
$336$	5.10265e17			0.0575773
$337$		−	1.11853e19i		−	1.23431i	−0.786841	−	0.617156i	$-0.788285\pi$
$337$		−	1.11853e19i		−	1.23431i	0.786841	−	0.617156i	$-0.211715\pi$
$338$	1.08964e19			1.17600
$339$	−2.21382e17			−0.0233693
$340$	8.85764e17	−	2.41901e18i	0.0914589	−	0.249773i
$341$	3.06153e18			0.309229
$342$	6.69372e18			0.661412
$343$			3.34480e19i			3.23343i
$344$	−1.15292e19			−1.09046
$345$		−	4.59044e17i		−	0.0424826i
$346$			1.09227e19i			0.989144i
$347$		−	1.10292e19i		−	0.977404i	−0.872451	−	0.488702i	$-0.837470\pi$
$347$		−	1.10292e19i		−	0.977404i	0.872451	−	0.488702i	$-0.162530\pi$
$348$	3.21954e15			0.000279222
$349$	−5.14133e18			−0.436400			−0.218200	−	0.975904i	$-0.570019\pi$
$349$	−5.14133e18			−0.436400			−0.218200	+	0.975904i	$0.570019\pi$
$350$			6.11755e18i			0.508238i
$351$		−	1.58322e18i		−	0.128747i
$352$			1.93656e18i			0.154156i
$353$	−3.53875e18			−0.275766			−0.137883	−	0.990449i	$-0.544030\pi$
$353$	−3.53875e18			−0.275766			−0.137883	+	0.990449i	$0.544030\pi$
$354$			5.43282e17i			0.0414477i
$355$	−1.53751e18			−0.114843
$356$	−1.57206e18			−0.114973
$357$	−1.05950e18	−	3.87953e17i	−0.0758731	−	0.0277822i
$358$	−1.07288e19			−0.752366
$359$	−6.12634e18			−0.420720			−0.210360	−	0.977624i	$-0.567464\pi$
$359$	−6.12634e18			−0.420720			−0.210360	+	0.977624i	$0.567464\pi$
$360$		−	1.82906e19i		−	1.23015i
$361$	−6.49076e18			−0.427555
$362$		−	1.99545e19i		−	1.28744i
$363$		−	5.89883e17i		−	0.0372792i
$364$			1.10619e19i			0.684807i
$365$	−2.43404e19			−1.47615
$366$	−1.70334e17			−0.0101203
$367$			1.09320e19i			0.636364i	0.948030	+	0.318182i	$0.103072\pi$
$367$			1.09320e19i			0.636364i	−0.948030	+	0.318182i	$0.896928\pi$
$368$			1.10492e19i			0.630189i
$369$			2.93408e19i			1.63974i
$370$	2.76652e19			1.51503
$371$		−	2.86610e19i		−	1.53811i
$372$	1.70569e17			0.00897075
$373$	−1.27810e19			−0.658790			−0.329395	−	0.944192i	$-0.606845\pi$
$373$	−1.27810e19			−0.658790			−0.329395	+	0.944192i	$0.606845\pi$
$374$	−2.01579e18	+	5.50512e18i	−0.101838	+	0.278118i
$375$	6.76796e17			0.0335138
$376$	1.83303e19			0.889734
$377$		−	9.15503e17i		−	0.0435612i
$378$	−3.03122e18			−0.141393
$379$		−	2.38725e18i		−	0.109170i	−0.998509	−	0.0545850i	$-0.982616\pi$
$379$		−	2.38725e18i		−	0.109170i	0.998509	−	0.0545850i	$-0.0173836\pi$
$380$		−	4.48861e18i		−	0.201250i
$381$		−	1.19280e18i		−	0.0524361i
$382$	−6.60024e18			−0.284501
$383$	−4.29754e19			−1.81647			−0.908237	−	0.418456i	$-0.862571\pi$
$383$	−4.29754e19			−1.81647			−0.908237	+	0.418456i	$0.862571\pi$
$384$		−	5.25861e17i		−	0.0217965i
$385$			1.82257e19i			0.740848i
$386$			1.22080e19i			0.486675i
$387$	2.57814e19			1.00803
$388$		−	6.02386e18i		−	0.231013i
$389$	5.07229e18			0.190801			0.0954007	−	0.995439i	$-0.469587\pi$
$389$	5.07229e18			0.190801			0.0954007	+	0.995439i	$0.469587\pi$
$390$	1.74508e18			0.0643918
$391$	8.40064e18	−	2.29421e19i	0.304079	−	0.830438i
$392$	8.16351e19			2.89889
$393$	1.92101e18			0.0669246
$394$		−	2.87384e19i		−	0.982292i
$395$	4.74484e19			1.59127
$396$		−	2.39125e18i		−	0.0786884i
$397$		−	1.74130e19i		−	0.562270i	−0.959668	−	0.281135i	$-0.909289\pi$
$397$		−	1.74130e19i		−	0.562270i	0.959668	−	0.281135i	$-0.0907108\pi$
$398$		−	5.55696e18i		−	0.176082i
$399$	−1.96595e18			−0.0611331
$400$	7.05983e18			0.215449
$401$			9.00313e18i			0.269656i	0.990869	+	0.134828i	$0.0430482\pi$
$401$			9.00313e18i			0.269656i	−0.990869	+	0.134828i	$0.956952\pi$
$402$		−	3.06205e16i		−	0.000900154i
$403$		−	4.85027e19i		−	1.39952i
$404$	−4.87935e18			−0.138198
$405$			4.08284e19i			1.13514i
$406$	−1.75282e18			−0.0478400
$407$	1.91345e19			0.512695
$408$	−5.94148e17	+	1.62261e18i	−0.0156294	+	0.0426839i
$409$	9.77434e18			0.252442			0.126221	−	0.992002i	$-0.459715\pi$
$409$	9.77434e18			0.252442			0.126221	+	0.992002i	$0.459715\pi$
$410$	−6.47384e19			−1.64166
$411$			1.64703e18i			0.0410097i
$412$	4.01653e18			0.0982022
$413$			8.98921e19i			2.15822i
$414$		−	3.27896e19i		−	0.773096i
$415$		−	1.82725e19i		−	0.423095i
$416$	3.06802e19			0.697682
$417$	−1.75335e18			−0.0391606
$418$			1.02150e19i			0.224088i
$419$		−	7.33145e19i		−	1.57974i	−0.613277	−	0.789868i	$-0.710149\pi$
$419$		−	7.33145e19i		−	1.57974i	0.613277	−	0.789868i	$-0.289851\pi$
$420$			1.01542e18i			0.0214920i
$421$	1.38405e19			0.287763			0.143882	−	0.989595i	$-0.454042\pi$
$421$	1.38405e19			0.287763			0.143882	+	0.989595i	$0.454042\pi$
$422$			2.80911e19i			0.573754i
$423$	−4.09898e19			−0.822477
$424$	−4.38942e19			−0.865293
$425$	−1.46588e19	−	5.36756e18i	−0.283910	−	0.103959i
$426$	1.94943e17			0.00370967
$427$	−2.81837e19			−0.526973
$428$		−	7.92158e18i		−	0.145540i
$429$	1.20698e18			0.0217906
$430$			5.68848e19i			1.00921i
$431$			5.65020e19i			0.985110i	0.870281	+	0.492555i	$0.163937\pi$
$431$			5.65020e19i			0.985110i	−0.870281	+	0.492555i	$0.836063\pi$
$432$			3.49812e18i			0.0599386i
$433$	−1.52687e19			−0.257125			−0.128562	−	0.991701i	$-0.541036\pi$
$433$	−1.52687e19			−0.257125			−0.128562	+	0.991701i	$0.541036\pi$
$434$	−9.28630e19			−1.53699
$435$		−	8.40384e16i		−	0.00136712i
$436$			1.23126e19i			0.196880i
$437$		−	4.25703e19i		−	0.669107i
$438$	3.08615e18			0.0476828
$439$			6.89727e19i			1.04760i	0.851843	+	0.523798i	$0.175485\pi$
$439$			6.89727e19i			1.04760i	−0.851843	+	0.523798i	$0.824515\pi$
$440$	2.79126e19			0.416779
$441$	−1.82551e20			−2.67975
$442$	8.72156e19	+	3.19355e19i	1.25871	+	0.460900i
$443$	−6.71973e17			−0.00953507			−0.00476753	−	0.999989i	$-0.501518\pi$
$443$	−6.71973e17			−0.00953507			−0.00476753	+	0.999989i	$0.501518\pi$
$444$	1.06605e18			0.0148733
$445$			4.10349e19i			0.562929i
$446$	−2.29014e19			−0.308924
$447$			1.55472e18i			0.0206227i
$448$		−	1.63602e20i		−	2.13404i
$449$		−	7.09136e19i		−	0.909666i	−0.890577	−	0.454833i	$-0.849699\pi$
$449$		−	7.09136e19i		−	0.909666i	0.890577	−	0.454833i	$-0.150301\pi$
$450$	−2.09508e19			−0.264306
$451$	−4.47760e19			−0.555547
$452$			1.06040e19i			0.129399i
$453$			4.16328e18i			0.0499688i
$454$			3.03511e19i			0.358307i
$455$	2.88743e20			3.35294
$456$			3.01085e18i			0.0343916i
$457$	−2.72465e19			−0.306154			−0.153077	−	0.988214i	$-0.548918\pi$
$457$	−2.72465e19			−0.306154			−0.153077	+	0.988214i	$0.548918\pi$
$458$	−1.16536e20			−1.28816
$459$	2.65961e18	−	7.26337e18i	0.0289216	−	0.0789847i
$460$	−2.19877e19			−0.235232
$461$	−4.53406e19			−0.477232			−0.238616	−	0.971114i	$-0.576694\pi$
$461$	−4.53406e19			−0.477232			−0.238616	+	0.971114i	$0.576694\pi$
$462$		−	2.31087e18i		−	0.0239310i
$463$	1.67356e20			1.70523			0.852616	−	0.522537i	$-0.175015\pi$
$463$	1.67356e20			1.70523			0.852616	+	0.522537i	$0.175015\pi$
$464$			2.02280e18i			0.0202800i
$465$		−	4.45230e18i		−	0.0439225i
$466$			1.55384e20i			1.50838i
$467$	6.06907e19			0.579757			0.289878	−	0.957064i	$-0.406385\pi$
$467$	6.06907e19			0.579757			0.289878	+	0.957064i	$0.406385\pi$
$468$	−3.78837e19			−0.356130
$469$		−	5.06651e18i		−	0.0468719i
$470$		−	9.04411e19i		−	0.823440i
$471$		−	8.38184e17i		−	0.00751074i
$472$	1.37669e20			1.21415
$473$			3.93441e19i			0.341524i
$474$	−6.01607e18			−0.0514014
$475$	−2.72001e19			−0.228754
$476$	−1.85825e19	+	5.07488e19i	−0.153834	+	0.420120i
$477$	9.81555e19			0.799883
$478$	1.34507e20			1.07904
$479$		−	5.85305e19i		−	0.462238i	−0.972925	−	0.231119i	$-0.925761\pi$
$479$		−	5.85305e19i		−	0.462238i	0.972925	−	0.231119i	$-0.0742387\pi$
$480$	2.81628e18			0.0218961
$481$		−	3.03141e20i		−	2.32037i
$482$			9.40280e19i			0.708605i
$483$			9.63033e18i			0.0714558i
$484$	−2.82548e19			−0.206420
$485$	−1.57238e20			−1.13108
$486$		−	1.55762e19i		−	0.110329i
$487$			5.33368e19i			0.372015i	0.982548	+	0.186007i	$0.0595548\pi$
$487$			5.33368e19i			0.372015i	−0.982548	+	0.186007i	$0.940445\pi$
$488$			4.31632e19i			0.296459i
$489$	−8.03632e18			−0.0543552
$490$		−	4.02786e20i		−	2.68289i
$491$	3.54728e19			0.232694			0.116347	−	0.993209i	$-0.462882\pi$
$491$	3.54728e19			0.232694			0.116347	+	0.993209i	$0.462882\pi$
$492$	−2.49464e18			−0.0161164
$493$	1.53793e18	−	4.20007e18i	0.00978552	−	0.0267242i
$494$	1.61833e20			1.01418
$495$	−6.24177e19			−0.385273
$496$			1.07167e20i			0.651549i
$497$	3.22555e19			0.193166
$498$			2.31680e18i			0.0136669i
$499$			1.97873e20i			1.14983i	0.818214	+	0.574913i	$0.194964\pi$
$499$			1.97873e20i			1.14983i	−0.818214	+	0.574913i	$0.805036\pi$
$500$		−	3.24178e19i		−	0.185570i
$501$	2.70783e18			0.0152700
$502$	−1.70713e20			−0.948391
$503$			8.88278e19i			0.486171i	0.970005	+	0.243086i	$0.0781596\pi$
$503$			8.88278e19i			0.486171i	−0.970005	+	0.243086i	$0.921840\pi$
$504$			3.83721e20i			2.06912i
$505$			1.27363e20i			0.676643i
$506$	5.00390e19			0.261927
$507$		−	1.09600e19i		−	0.0565264i
$508$	−5.71339e19			−0.290346
$509$	−3.27395e20			−1.63941			−0.819707	−	0.572783i	$-0.805864\pi$
$509$	−3.27395e20			−1.63941			−0.819707	+	0.572783i	$0.805864\pi$
$510$	8.00593e18	+	2.93151e18i	0.0395035	+	0.0144649i
$511$	5.10639e20			2.48289
$512$	−2.28383e20			−1.09431
$513$		−	1.34776e19i		−	0.0636402i
$514$	2.87386e20			1.33734
$515$		−	1.04842e20i		−	0.480816i
$516$			2.19201e18i			0.00990762i
$517$		−	6.25531e19i		−	0.278657i
$518$	−5.80392e20			−2.54828
$519$	1.09865e19			0.0475449
$520$		−	4.42209e20i		−	1.88627i
$521$		−	2.27732e20i		−	0.957504i	−0.877950	−	0.478752i	$-0.841089\pi$
$521$		−	2.27732e20i		−	0.957504i	0.877950	−	0.478752i	$-0.158911\pi$
$522$		−	6.00288e18i		−	0.0248789i
$523$	3.01779e20			1.23289			0.616447	−	0.787396i	$-0.288572\pi$
$523$	3.01779e20			1.23289			0.616447	+	0.787396i	$0.288572\pi$
$524$		−	9.20145e19i		−	0.370571i
$525$	6.15327e18			0.0244293
$526$	−1.69268e20			−0.662493
$527$	8.14784e19	−	2.22517e20i	0.314386	−	0.858585i
$528$	−2.66681e18			−0.0101447
$529$	5.81023e19			0.217909
$530$			2.16573e20i			0.800820i
$531$	−3.07854e20			−1.12237
$532$			9.41671e19i			0.338503i
$533$			7.09369e20i			2.51431i
$534$		−	5.20288e18i		−	0.0181838i
$535$	−2.06773e20			−0.712593
$536$	−7.75934e18			−0.0263687
$537$			1.07915e19i			0.0361637i
$538$			6.91948e19i			0.228669i
$539$		−	2.78585e20i		−	0.907907i
$540$	−6.96122e18			−0.0223734
$541$			5.34089e20i			1.69291i	0.532459	+	0.846456i	$0.321268\pi$
$541$			5.34089e20i			1.69291i	−0.532459	+	0.846456i	$0.678732\pi$
$542$	1.27793e19			0.0399496
$543$	−2.00710e19			−0.0618829
$544$	1.40752e20	+	5.15388e19i	0.428019	+	0.156726i
$545$	3.21391e20			0.963962
$546$	−3.66102e19			−0.108307
$547$		−	3.73979e20i		−	1.09129i	−0.838015	−	0.545647i	$-0.816284\pi$
$547$		−	3.73979e20i		−	1.09129i	0.838015	−	0.545647i	$-0.183716\pi$
$548$	7.88909e19			0.227077
$549$		−	9.65208e19i		−	0.274049i
$550$		−	3.19723e19i		−	0.0895475i
$551$		−	7.79345e18i		−	0.0215324i
$552$	1.47488e19			0.0401989
$553$	−9.95426e20			−2.67652
$554$			4.34653e20i			1.15297i
$555$		−	2.78267e19i		−	0.0728224i
$556$			8.39838e19i			0.216838i
$557$	1.40186e20			0.357101			0.178551	−	0.983931i	$-0.442859\pi$
$557$	1.40186e20			0.357101			0.178551	+	0.983931i	$0.442859\pi$
$558$		−	3.18029e20i		−	0.799300i
$559$	6.23315e20			1.54568
$560$	−6.37977e20			−1.56097
$561$	5.53726e18	+	2.02757e18i	0.0133682	+	0.00489501i
$562$	−1.28756e20			−0.306722
$563$	−1.34470e20			−0.316090			−0.158045	−	0.987432i	$-0.550519\pi$
$563$	−1.34470e20			−0.316090			−0.158045	+	0.987432i	$0.550519\pi$
$564$		−	3.48507e18i		−	0.00808384i
$565$	2.76791e20			0.633561
$566$			4.21373e20i			0.951796i
$567$		−	8.56544e20i		−	1.90931i
$568$		−	4.93992e19i		−	0.108669i
$569$	−4.22113e20			−0.916404			−0.458202	−	0.888848i	$-0.651506\pi$
$569$	−4.22113e20			−0.916404			−0.458202	+	0.888848i	$0.651506\pi$
$570$	1.48554e19			0.0318291
$571$		−	4.17975e20i		−	0.883851i	−0.897052	−	0.441925i	$-0.854296\pi$
$571$		−	4.17975e20i		−	0.883851i	0.897052	−	0.441925i	$-0.145704\pi$
$572$		−	5.78129e19i		−	0.120658i
$573$			6.63878e18i			0.0136750i
$574$	1.35815e21			2.76128
$575$			1.33241e20i			0.267381i
$576$	5.60288e20			1.10980
$577$	−5.38797e20			−1.05343			−0.526716	−	0.850041i	$-0.676577\pi$
$577$	−5.38797e20			−1.05343			−0.526716	+	0.850041i	$0.676577\pi$
$578$	3.46473e20	+	2.93022e20i	0.668668	+	0.565512i
$579$	1.22793e19			0.0233928
$580$	−4.02535e18			−0.00756996
$581$			3.83342e20i			0.711648i
$582$	1.99365e19			0.0365364
$583$			1.49791e20i			0.271002i
$584$		−	7.82042e20i		−	1.39680i
$585$			9.88861e20i			1.74368i
$586$	−3.40032e20			−0.591954
$587$	7.93873e20			1.36447			0.682237	−	0.731131i	$-0.261007\pi$
$587$	7.93873e20			1.36447			0.682237	+	0.731131i	$0.261007\pi$
$588$		−	1.55210e19i		−	0.0263384i
$589$		−	4.12892e20i		−	0.691786i
$590$		−	6.79257e20i		−	1.12368i
$591$	−2.89062e19			−0.0472155
$592$			6.69788e20i			1.08025i
$593$	2.57974e20			0.410834			0.205417	−	0.978675i	$-0.434145\pi$
$593$	2.57974e20			0.410834			0.205417	+	0.978675i	$0.434145\pi$
$594$	1.58421e19			0.0249124
$595$	1.32467e21	+	4.85052e20i	2.05699	+	0.753201i
$596$	7.44696e19			0.114191
$597$	−5.58941e18			−0.00846367
$598$		−	7.92749e20i		−	1.18543i
$599$	−6.95261e20			−1.02671			−0.513354	−	0.858177i	$-0.671597\pi$
$599$	−6.95261e20			−1.02671			−0.513354	+	0.858177i	$0.671597\pi$
$600$		−	9.42371e18i		−	0.0137432i
$601$		−	1.09980e21i		−	1.58400i	−0.610521	−	0.792000i	$-0.709040\pi$
$601$		−	1.09980e21i		−	1.58400i	0.610521	−	0.792000i	$-0.290960\pi$
$602$		−	1.19339e21i		−	1.69750i
$603$	1.73513e19			0.0243754
$604$	1.99417e20			0.276684
$605$			7.37523e20i			1.01067i
$606$		−	1.61486e19i		−	0.0218570i
$607$			8.91626e20i			1.19198i	0.802993	+	0.595988i	$0.203239\pi$
$607$			8.91626e20i			1.19198i	−0.802993	+	0.595988i	$0.796761\pi$
$608$	2.61173e20			0.344867
$609$			1.76305e18i			0.00229951i
$610$	2.12966e20			0.274370
$611$	−9.91006e20			−1.26115
$612$	−1.73800e20	−	6.36398e19i	−0.218481	−	0.0800005i
$613$	−5.36538e20			−0.666265			−0.333132	−	0.942880i	$-0.608106\pi$
$613$	−5.36538e20			−0.666265			−0.333132	+	0.942880i	$0.608106\pi$
$614$	7.00502e19			0.0859303
$615$			6.51164e19i			0.0789091i
$616$	−5.85582e20			−0.701023
$617$			1.07802e21i			1.27494i	0.770476	+	0.637469i	$0.220018\pi$
$617$			1.07802e21i			1.27494i	−0.770476	+	0.637469i	$0.779982\pi$
$618$			1.32930e19i			0.0155314i
$619$			6.31132e19i			0.0728519i	0.999336	+	0.0364259i	$0.0115973\pi$
$619$			6.31132e19i			0.0728519i	−0.999336	+	0.0364259i	$0.988403\pi$
$620$	−2.13260e20			−0.243205
$621$	−6.60207e19			−0.0743863
$622$			8.98062e20i			0.999721i
$623$		−	8.60876e20i		−	0.946848i
$624$			4.22493e19i			0.0459129i
$625$	−1.12777e21			−1.21093
$626$			2.18557e20i			0.231877i
$627$	1.02747e19			0.0107712
$628$	−4.01482e19			−0.0415880
$629$	5.09238e20	−	1.39072e21i	0.521244	−	1.42351i
$630$	1.89327e21			1.91495
$631$	−1.38840e21			−1.38769			−0.693846	−	0.720123i	$-0.744085\pi$
$631$	−1.38840e21			−1.38769			−0.693846	+	0.720123i	$0.744085\pi$
$632$			1.52449e21i			1.50573i
$633$	2.82551e19			0.0275784
$634$		−	7.59864e20i		−	0.732937i
$635$			1.49134e21i			1.42159i
$636$			8.34544e18i			0.00786178i
$637$	−4.41351e21			−4.10902
$638$	9.16077e18			0.00842902
$639$			1.10466e20i			0.100455i
$640$			6.57476e20i			0.590922i
$641$		−	8.31924e20i		−	0.739007i	−0.929229	−	0.369503i	$-0.879528\pi$
$641$		−	8.31924e20i		−	0.739007i	0.929229	−	0.369503i	$-0.120472\pi$
$642$	2.62171e19			0.0230183
$643$		−	8.86554e19i		−	0.0769348i	−0.999260	−	0.0384674i	$-0.987752\pi$
$643$		−	8.86554e19i		−	0.0769348i	0.999260	−	0.0384674i	$-0.0122476\pi$
$644$	4.61283e20			0.395661
$645$	5.72170e19			0.0485096
$646$	7.42445e20	+	2.71859e20i	0.622186	+	0.227824i
$647$	1.12655e21			0.933183			0.466591	−	0.884473i	$-0.345482\pi$
$647$	1.12655e21			0.933183			0.466591	+	0.884473i	$0.345482\pi$
$648$	−1.31179e21			−1.07412
$649$		−	4.69805e20i		−	0.380262i
$650$	−5.06525e20			−0.405276
$651$			9.34053e19i			0.0738778i
$652$			3.84932e20i			0.300972i
$653$		−	1.03373e21i		−	0.799019i	−0.916729	−	0.399510i	$-0.869180\pi$
$653$		−	1.03373e21i		−	0.799019i	0.916729	−	0.399510i	$-0.130820\pi$
$654$	−4.07497e19			−0.0311380
$655$	−2.40181e21			−1.81438
$656$		−	1.56735e21i		−	1.17054i
$657$			1.74879e21i			1.29121i
$658$			1.89737e21i			1.38503i
$659$	2.52058e21			1.81912			0.909558	−	0.415577i	$-0.136420\pi$
$659$	2.52058e21			1.81912			0.909558	+	0.415577i	$0.136420\pi$
$660$		−	5.30692e18i		−	0.00378672i
$661$	1.97056e21			1.39021			0.695103	−	0.718910i	$-0.255359\pi$
$661$	1.97056e21			1.39021			0.695103	+	0.718910i	$0.255359\pi$
$662$	−1.13748e21			−0.793429
$663$	3.21220e19	−	8.77248e19i	0.0221539	−	0.0605022i
$664$	5.87086e20			0.400351
$665$	2.45800e21			1.65737
$666$		−	1.98767e21i		−	1.32522i
$667$	−3.81767e19			−0.0251683
$668$		−	1.29702e20i		−	0.0845522i
$669$			2.30352e19i			0.0148489i
$670$			3.82844e19i			0.0244040i
$671$	1.47297e20			0.0928485
$672$	−5.90831e19			−0.0368293
$673$			4.85098e20i			0.299031i	0.988759	+	0.149516i	$0.0477714\pi$
$673$			4.85098e20i			0.299031i	−0.988759	+	0.149516i	$0.952229\pi$
$674$		−	1.77317e21i		−	1.08094i
$675$			4.21837e19i			0.0254312i
$676$	−5.24973e20			−0.312995
$677$		−	2.37013e21i		−	1.39752i	−0.715358	−	0.698758i	$-0.753736\pi$
$677$		−	2.37013e21i		−	1.39752i	0.715358	−	0.698758i	$-0.246264\pi$
$678$	−3.50948e19			−0.0204654
$679$	3.29872e21			1.90249
$680$	7.42855e20	−	2.02873e21i	0.423728	−	1.15720i
$681$	3.05283e19			0.0172226
$682$	4.85332e20			0.270805
$683$			6.43817e20i			0.355310i	0.984093	+	0.177655i	$0.0568511\pi$
$683$			6.43817e20i			0.355310i	−0.984093	+	0.177655i	$0.943149\pi$
$684$	−3.22495e20			−0.176036
$685$		−	2.05925e21i		−	1.11181i
$686$			5.30237e21i			2.83165i
$687$			1.17216e20i			0.0619174i
$688$	−1.37721e21			−0.719593
$689$	2.37309e21			1.22651
$690$		−	7.27703e19i		−	0.0372037i
$691$			3.19949e21i			1.61806i	0.587766	+	0.809031i	$0.300007\pi$
$691$			3.19949e21i			1.61806i	−0.587766	+	0.809031i	$0.699993\pi$
$692$		−	5.26241e20i		−	0.263263i
$693$	1.30947e21			0.648031
$694$		−	1.74842e21i		−	0.855952i
$695$	2.19219e21			1.06168
$696$	2.70011e18			0.00129363
$697$	−1.19165e21	+	3.25439e21i	−0.564811	+	1.54249i
$698$	−8.15034e20			−0.382173
$699$	1.56291e20			0.0725028
$700$		−	2.94735e20i		−	0.135269i
$701$	−1.15174e21			−0.522962			−0.261481	−	0.965209i	$-0.584211\pi$
$701$	−1.15174e21			−0.522962			−0.261481	+	0.965209i	$0.584211\pi$
$702$		−	2.50981e20i		−	0.112749i
$703$		−	2.58056e21i		−	1.14696i
$704$			8.55035e20i			0.376001i
$705$	−9.09692e19			−0.0395800
$706$	−5.60984e20			−0.241499
$707$		−	2.67197e21i		−	1.13812i
$708$		−	2.61746e19i		−	0.0110314i
$709$			6.65190e20i			0.277395i	0.990335	+	0.138698i	$0.0442916\pi$
$709$			6.65190e20i			0.277395i	−0.990335	+	0.138698i	$0.955708\pi$
$710$	−2.43734e20			−0.100572
$711$		−	3.40904e21i		−	1.39191i
$712$	−1.31843e21			−0.532668
$713$	−2.02258e21			−0.808599
$714$	−1.67957e20	−	6.15005e19i	−0.0664451	−	0.0243300i
$715$	−1.50906e21			−0.590762
$716$	5.16900e20			0.200244
$717$		−	1.35293e20i		−	0.0518658i
$718$	−9.71183e20			−0.368441
$719$		−	8.08899e20i		−	0.303688i	−0.988404	−	0.151844i	$-0.951479\pi$
$719$		−	8.08899e20i		−	0.303688i	0.988404	−	0.151844i	$-0.0485212\pi$
$720$		−	2.18488e21i		−	0.811773i
$721$			2.19948e21i			0.808735i
$722$	−1.02895e21			−0.374427
$723$	9.45771e19			0.0340603
$724$			9.61381e20i			0.342654i
$725$			2.43929e19i			0.00860455i
$726$		−	9.35117e19i		−	0.0326469i
$727$	−1.06374e21			−0.367558			−0.183779	−	0.982968i	$-0.558833\pi$
$727$	−1.06374e21			−0.367558			−0.183779	+	0.982968i	$0.558833\pi$
$728$			9.27716e21i			3.17271i
$729$	2.92295e21			0.989384
$730$	−3.85858e21			−1.29272
$731$	2.85959e21	+	1.04709e21i	0.948252	+	0.347219i
$732$	8.20646e18			0.00269354
$733$	−2.40283e21			−0.780626			−0.390313	−	0.920682i	$-0.627633\pi$
$733$	−2.40283e21			−0.780626			−0.390313	+	0.920682i	$0.627633\pi$
$734$			1.73301e21i			0.557289i
$735$	−4.05138e20			−0.128958
$736$		−	1.27937e21i		−	0.403100i
$737$			2.64792e19i			0.00825845i
$738$			4.65128e21i			1.43598i
$739$	1.77876e21			0.543605			0.271802	−	0.962353i	$-0.412380\pi$
$739$	1.77876e21			0.543605			0.271802	+	0.962353i	$0.412380\pi$
$740$	−1.33287e21			−0.403228
$741$		−	1.62778e20i		−	0.0487483i
$742$		−	4.54351e21i		−	1.34698i
$743$		−	3.40116e21i		−	0.998184i	−0.866549	−	0.499092i	$-0.833667\pi$
$743$		−	3.40116e21i		−	0.998184i	0.866549	−	0.499092i	$-0.166333\pi$
$744$	1.43050e20			0.0415614
$745$		−	1.94385e21i		−	0.559101i
$746$	−2.02611e21			−0.576929
$747$	−1.31283e21			−0.370088
$748$	9.71183e19	−	2.65229e20i	0.0271044	−	0.0740218i
$749$	4.33792e21			1.19858
$750$	1.07290e20			0.0293493
$751$			3.76738e21i			1.02033i	0.860077	+	0.510164i	$0.170415\pi$
$751$			3.76738e21i			1.02033i	−0.860077	+	0.510164i	$0.829585\pi$
$752$	2.18962e21			0.587132
$753$			1.71709e20i			0.0455860i
$754$		−	1.45131e20i		−	0.0381482i
$755$		−	5.20529e21i		−	1.35470i
$756$	1.46040e20			0.0376322
$757$	2.53621e21			0.647092			0.323546	−	0.946212i	$-0.395125\pi$
$757$	2.53621e21			0.647092			0.323546	+	0.946212i	$0.395125\pi$
$758$		−	3.78440e20i		−	0.0956045i
$759$		−	5.03312e19i		−	0.0125899i
$760$		−	3.76442e21i		−	0.932387i
$761$	−3.27640e21			−0.803548			−0.401774	−	0.915739i	$-0.631606\pi$
$761$	−3.27640e21			−0.803548			−0.401774	+	0.915739i	$0.631606\pi$
$762$		−	1.89090e20i		−	0.0459204i
$763$	−6.74250e21			−1.62139
$764$	3.17991e20			0.0757206
$765$	−1.66116e21	+	4.53662e21i	−0.391697	+	1.06972i
$766$	−6.81271e21			−1.59076
$767$	−7.44295e21			−1.72100
$768$			1.21019e20i			0.0277105i
$769$	8.18449e21			1.85585			0.927927	−	0.372762i	$-0.121589\pi$
$769$	8.18449e21			1.85585			0.927927	+	0.372762i	$0.121589\pi$
$770$			2.88925e21i			0.648790i
$771$		−	2.89064e20i		−	0.0642816i
$772$		−	5.88164e20i		−	0.129529i
$773$	3.54902e21			0.774038			0.387019	−	0.922072i	$-0.373505\pi$
$773$	3.54902e21			0.774038			0.387019	+	0.922072i	$0.373505\pi$
$774$	4.08702e21			0.882775
$775$			1.29232e21i			0.276444i
$776$		−	5.05197e21i		−	1.07028i
$777$			5.83781e20i			0.122488i
$778$	8.04088e20			0.167092
$779$			6.03869e21i			1.24283i
$780$	−8.40756e19			−0.0171380
$781$	−1.68578e20			−0.0340343
$782$	1.33172e21	−	3.63691e21i	0.266294	−	0.727247i
$783$	−1.20866e19			−0.00239381
$784$	9.75164e21			1.91297
$785$			1.04797e21i			0.203623i
$786$	3.04530e20			0.0586085
$787$			8.85630e21i			1.68827i	0.536131	+	0.844135i	$0.319885\pi$
$787$			8.85630e21i			1.68827i	−0.536131	+	0.844135i	$0.680115\pi$
$788$			1.38458e21i			0.261439i
$789$			1.70256e20i			0.0318439i
$790$	7.52180e21			1.39354
$791$	−5.80683e21			−1.06565
$792$		−	2.00545e21i		−	0.364563i
$793$		−	2.33357e21i		−	0.420216i
$794$		−	2.76041e21i		−	0.492402i
$795$	2.17837e20			0.0384928
$796$			2.67727e20i			0.0468646i
$797$	−3.22338e21			−0.558952			−0.279476	−	0.960153i	$-0.590161\pi$
$797$	−3.22338e21			−0.558952			−0.279476	+	0.960153i	$0.590161\pi$
$798$	−3.11654e20			−0.0535366
$799$	−4.54646e21	−	1.66476e21i	−0.773699	−	0.283303i
$800$	−8.17450e20			−0.137812
$801$	2.94825e21			0.492402
$802$			1.42723e21i			0.236149i
$803$	−2.66877e21			−0.437465
$804$			1.47525e18i			0.000239578i
$805$		−	1.20407e22i		−	1.93723i
$806$		−	7.68893e21i		−	1.22561i
$807$	6.95989e19			0.0109913
$808$	−4.09212e21			−0.640270
$809$		−	2.25752e21i		−	0.349959i	−0.984572	−	0.174979i	$-0.944014\pi$
$809$		−	2.25752e21i		−	0.349959i	0.984572	−	0.174979i	$-0.0559859\pi$
$810$			6.47235e21i			0.994088i
$811$			5.09331e21i			0.775074i	0.921854	+	0.387537i	$0.126674\pi$
$811$			5.09331e21i			0.775074i	−0.921854	+	0.387537i	$0.873326\pi$
$812$	8.44483e19			0.0127327
$813$		−	1.28539e19i		−	0.00192025i
$814$	3.03331e21			0.448987
$815$	1.00477e22			1.47362
$816$	−7.09734e19	+	1.93828e20i	−0.0103138	+	0.0281669i
$817$	5.30613e21			0.764033
$818$	1.54948e21			0.221074
$819$		−	2.07454e22i		−	2.93287i
$820$	3.11901e21			0.436931
$821$		−	2.40115e20i		−	0.0333308i	−0.999861	−	0.0166654i	$-0.994695\pi$
$821$		−	2.40115e20i		−	0.0333308i	0.999861	−	0.0166654i	$-0.00530501\pi$
$822$			2.61096e20i			0.0359138i
$823$			9.92633e21i			1.35298i	0.736454	+	0.676488i	$0.236499\pi$
$823$			9.92633e21i			1.35298i	−0.736454	+	0.676488i	$0.763501\pi$
$824$	3.36850e21			0.454970
$825$	−3.21590e19			−0.00430425
$826$			1.42502e22i			1.89004i
$827$			1.14002e22i			1.49838i	0.662354	+	0.749191i	$0.269558\pi$
$827$			1.14002e22i			1.49838i	−0.662354	+	0.749191i	$0.730442\pi$
$828$			1.57976e21i			0.205761i
$829$	4.99461e21			0.644678			0.322339	−	0.946624i	$-0.395531\pi$
$829$	4.99461e21			0.644678			0.322339	+	0.946624i	$0.395531\pi$
$830$		−	2.89667e21i		−	0.370521i
$831$	4.37191e20			0.0554196
$832$	1.35460e22			1.70171
$833$	−2.02480e22	−	7.41414e21i	−2.52083	−	0.923046i
$834$	−2.77952e20			−0.0342945
$835$	−3.38557e21			−0.413983
$836$		−	4.92147e20i		−	0.0596414i
$837$	−6.40339e20			−0.0769076
$838$		−	1.16222e22i		−	1.38344i
$839$			9.98972e21i			1.17852i	0.807942	+	0.589262i	$0.200581\pi$
$839$			9.98972e21i			1.17852i	−0.807942	+	0.589262i	$0.799419\pi$
$840$			8.51595e20i			0.0995723i
$841$	8.62220e21			0.999190
$842$	2.19407e21			0.252006
$843$			1.29508e20i			0.0147431i
$844$		−	1.35339e21i		−	0.152706i
$845$			1.37031e22i			1.53248i
$846$	−6.49795e21			−0.720275
$847$		−	1.54726e22i		−	1.69995i
$848$	−5.24334e21			−0.571004
$849$	4.23834e20			0.0457497
$850$	−2.32379e21	−	8.50897e20i	−0.248631	−	0.0910406i
$851$	−1.26410e22			−1.34064
$852$	−9.39209e18			−0.000987337
$853$			4.07624e21i			0.424758i	0.977187	+	0.212379i	$0.0681212\pi$
$853$			4.07624e21i			0.424758i	−0.977187	+	0.212379i	$0.931879\pi$
$854$	−4.46784e21			−0.461491
$855$			8.41793e21i			0.861906i
$856$		−	6.64352e21i		−	0.674287i
$857$		−	1.27495e22i		−	1.28273i	−0.767234	−	0.641367i	$-0.778368\pi$
$857$		−	1.27495e22i		−	1.28273i	0.767234	−	0.641367i	$-0.221632\pi$
$858$	1.91337e20			0.0190829
$859$	−2.48668e21			−0.245851			−0.122925	−	0.992416i	$-0.539228\pi$
$859$	−2.48668e21			−0.245851			−0.122925	+	0.992416i	$0.539228\pi$
$860$		−	2.74064e21i		−	0.268604i
$861$		−	1.36608e21i		−	0.132725i
$862$			8.95703e21i			0.862700i
$863$	−1.26687e22			−1.20962			−0.604811	−	0.796369i	$-0.706751\pi$
$863$	−1.26687e22			−1.20962			−0.604811	+	0.796369i	$0.706751\pi$
$864$		−	4.05043e20i		−	0.0383397i
$865$	−1.37362e22			−1.28898
$866$	−2.42049e21			−0.225174
$867$	2.94733e20	−	3.48496e20i	0.0271823	−	0.0321406i
$868$	4.47402e21			0.409072
$869$	5.20242e21			0.471582
$870$		−	1.33222e19i		−	0.00119725i
$871$	4.19500e20			0.0373763
$872$			1.03261e22i			0.912144i
$873$			1.12971e22i			0.989376i
$874$		−	6.74849e21i		−	0.585963i
$875$	1.77523e22			1.52825
$876$	−1.48687e20			−0.0126909
$877$			2.41152e21i			0.204077i	0.994780	+	0.102038i	$0.0325364\pi$
$877$			2.41152e21i			0.204077i	−0.994780	+	0.102038i	$0.967464\pi$
$878$			1.09340e22i			0.917421i
$879$			3.42018e20i			0.0284532i
$880$	3.33427e21			0.275031
$881$			1.33784e22i			1.09417i	0.837077	+	0.547085i	$0.184263\pi$
$881$			1.33784e22i			1.09417i	−0.837077	+	0.547085i	$0.815737\pi$
$882$	−2.89391e22			−2.34677
$883$	−1.14532e22			−0.920920			−0.460460	−	0.887680i	$-0.652316\pi$
$883$	−1.14532e22			−0.920920			−0.460460	+	0.887680i	$0.652316\pi$
$884$	−4.20193e21	−	1.53861e21i	−0.335009	−	0.122669i
$885$	−6.83224e20			−0.0540118
$886$	−1.06525e20			−0.00835024
$887$			1.69923e22i			1.32076i	0.750931	+	0.660381i	$0.229605\pi$
$887$			1.69923e22i			1.32076i	−0.750931	+	0.660381i	$0.770395\pi$
$888$	8.94058e20			0.0689078
$889$		−	3.12870e22i		−	2.39112i
$890$			6.50509e21i			0.492979i
$891$			4.47657e21i			0.336405i
$892$	1.10336e21			0.0822207
$893$	−8.43620e21			−0.623391
$894$			2.46464e20i			0.0180602i
$895$		−	1.34924e22i		−	0.980431i
$896$		−	1.37933e22i		−	0.993933i
$897$	−7.97379e20			−0.0569798
$898$		−	1.12416e22i		−	0.796631i
$899$	−3.70278e20			−0.0260214
$900$	1.00938e21			0.0703456
$901$	1.08871e22	+	3.98649e21i	0.752446	+	0.275521i
$902$	−7.09815e21			−0.486515
$903$	−1.20036e21			−0.0815933
$904$			8.89314e21i			0.599504i
$905$	2.50945e22			1.67770
$906$			6.59987e20i			0.0437597i
$907$		−	8.55443e20i		−	0.0562518i	−0.999604	−	0.0281259i	$-0.991046\pi$
$907$		−	8.55443e20i		−	0.0562518i	0.999604	−	0.0281259i	$-0.00895394\pi$
$908$		−	1.46227e21i		−	0.0953641i
$909$	9.15073e21			0.591870
$910$	4.57733e22			2.93631
$911$		−	6.54832e21i		−	0.416622i	−0.978063	−	0.208311i	$-0.933203\pi$
$911$		−	6.54832e21i		−	0.416622i	0.978063	−	0.208311i	$-0.0667966\pi$
$912$			3.59658e20i			0.0226949i
$913$		−	2.00347e21i		−	0.125387i
$914$	−4.31927e21			−0.268111
$915$		−	2.14210e20i		−	0.0131881i
$916$	5.61454e21			0.342845
$917$	5.03879e22			3.05180
$918$	4.21616e20	−	1.15143e21i	0.0253278	−	0.0691700i
$919$	−6.25595e21			−0.372758			−0.186379	−	0.982478i	$-0.559675\pi$
$919$	−6.25595e21			−0.372758			−0.186379	+	0.982478i	$0.559675\pi$
$920$	−1.84402e22			−1.08983
$921$		−	7.04592e19i		−	0.00413039i
$922$	−7.18765e21			−0.417931
$923$			2.67071e21i			0.154033i
$924$			1.11335e20i			0.00636928i
$925$			8.07696e21i			0.458337i
$926$	2.65302e22			1.49334
$927$	−7.53259e21			−0.420578
$928$		−	2.34218e20i		−	0.0129721i
$929$		−	2.98003e22i		−	1.63721i	−0.574360	−	0.818603i	$-0.694749\pi$
$929$		−	2.98003e22i		−	1.63721i	0.574360	−	0.818603i	$-0.305251\pi$
$930$		−	7.05804e20i		−	0.0384647i
$931$	−3.75712e22			−2.03110
$932$		−	7.48617e21i		−	0.401458i
$933$	9.03307e20			0.0480533
$934$	9.62105e21			0.507716
$935$	−6.92316e21	−	2.53504e21i	−0.362424	−	0.132708i
$936$	−3.17716e22			−1.64995
$937$	3.15821e22			1.62702			0.813511	−	0.581549i	$-0.197553\pi$
$937$	3.15821e22			1.62702			0.813511	+	0.581549i	$0.197553\pi$
$938$		−	8.03172e20i		−	0.0410476i
$939$	2.19834e20			0.0111456
$940$			4.35733e21i			0.219160i
$941$		−	6.57865e21i		−	0.328257i	−0.986439	−	0.164129i	$-0.947519\pi$
$941$		−	6.57865e21i		−	0.328257i	0.986439	−	0.164129i	$-0.0524812\pi$
$942$		−	1.32874e20i		−	0.00657745i
$943$	2.95809e22			1.45269
$944$	1.64452e22			0.801214
$945$		−	3.81203e21i		−	0.184254i
$946$			6.23706e21i			0.299086i
$947$		−	3.39373e22i		−	1.61455i	−0.590172	−	0.807277i	$-0.700940\pi$
$947$		−	3.39373e22i		−	1.61455i	0.590172	−	0.807277i	$-0.299060\pi$
$948$	2.89846e20			0.0136806
$949$			4.22803e22i			1.97989i
$950$	−4.31192e21			−0.200329
$951$	−7.64301e20			−0.0352298
$952$	−1.55844e22	+	4.25610e22i	−0.712712	+	1.94641i
$953$	−1.32569e22			−0.601512			−0.300756	−	0.953701i	$-0.597239\pi$
$953$	−1.32569e22			−0.601512			−0.300756	+	0.953701i	$0.597239\pi$
$954$	1.55602e22			0.700490
$955$		−	8.30037e21i		−	0.370742i
$956$	−6.48039e21			−0.287188
$957$		−	9.21427e18i		−	0.000405155i
$958$		−	9.27859e21i		−	0.404800i
$959$			4.32013e22i			1.87007i
$960$	1.24345e21			0.0534066
$961$	3.84816e21			0.163994
$962$		−	4.80556e22i		−	2.03204i
$963$			1.48561e22i			0.623316i
$964$		−	4.53014e21i		−	0.188597i
$965$	−1.53526e22			−0.634201
$966$			1.52666e21i			0.0625767i
$967$	2.10811e22			0.857422			0.428711	−	0.903442i	$-0.358968\pi$
$967$	2.10811e22			0.857422			0.428711	+	0.903442i	$0.358968\pi$
$968$	−2.36962e22			−0.956342
$969$	2.73447e20	−	7.46780e20i	0.0109508	−	0.0299064i
$970$	−2.49263e22			−0.990535
$971$	−2.70400e22			−1.06626			−0.533129	−	0.846034i	$-0.678984\pi$
$971$	−2.70400e22			−1.06626			−0.533129	+	0.846034i	$0.678984\pi$
$972$			7.50439e20i			0.0293642i
$973$	−4.59903e22			−1.78575
$974$			8.45526e21i			0.325788i
$975$			5.09483e20i			0.0194803i
$976$			5.15602e21i			0.195632i
$977$	−3.83644e22			−1.44451			−0.722254	−	0.691628i	$-0.756894\pi$
$977$	−3.83644e22			−1.44451			−0.722254	+	0.691628i	$0.756894\pi$
$978$	−1.27396e21			−0.0476010
$979$			4.49921e21i			0.166827i
$980$			1.94057e22i			0.714058i
$981$		−	2.30911e22i		−	0.843193i
$982$	5.62336e21			0.203779
$983$			6.55814e21i			0.235847i	0.993023	+	0.117923i	$0.0376237\pi$
$983$			6.55814e21i			0.235847i	−0.993023	+	0.117923i	$0.962376\pi$
$984$	−2.09215e21			−0.0746673
$985$	3.61410e22			1.28005
$986$	2.43801e20	−	6.65819e20i	0.00856957	−	0.0234034i
$987$	1.90845e21			0.0665737
$988$	−7.79691e21			−0.269926
$989$		−	2.59924e22i		−	0.893046i
$990$	−9.89482e21			−0.337399
$991$			9.42665e20i			0.0319011i	0.999873	+	0.0159505i	$0.00507743\pi$
$991$			9.42665e20i			0.0319011i	−0.999873	+	0.0159505i	$0.994923\pi$
$992$		−	1.24087e22i		−	0.416763i
$993$			1.14412e21i			0.0381375i
$994$	5.11333e21			0.169163
$995$	6.98836e21			0.229458
$996$		−	1.11621e20i		−	0.00363747i
$997$		−	1.27851e22i		−	0.413514i	−0.978392	−	0.206757i	$-0.933709\pi$
$997$		−	1.27851e22i		−	0.413514i	0.978392	−	0.206757i	$-0.0662909\pi$
$998$			3.13680e22i			1.00695i
$999$	−4.00210e21			−0.127511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.16.b.a.16.16	yes	22
17.16	even	2	inner	17.16.b.a.16.15	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.16.b.a.16.15	✓	22	17.16	even	2	inner
17.16.b.a.16.16	yes	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+158.526 q^{2} -159.452i q^{3} -7637.56 q^{4} +199360. i q^{5} -25277.2i q^{6} -4.18240e6i q^{7} -6.40533e6 q^{8} +1.43235e7 q^{9} +O(q^{10})\)	\(q+158.526 q^{2} -159.452i q^{3} -7637.56 q^{4} +199360. i q^{5} -25277.2i q^{6} -4.18240e6i q^{7} -6.40533e6 q^{8} +1.43235e7 q^{9} +3.16037e7i q^{10} +2.18585e7i q^{11} +1.21782e6i q^{12} +3.46297e8 q^{13} -6.63018e8i q^{14} +3.17883e7 q^{15} -7.65142e8 q^{16} +(1.58871e9 + 5.81735e8i) q^{17} +2.27064e9 q^{18} +2.94794e9 q^{19} -1.52262e9i q^{20} -6.66890e8 q^{21} +3.46514e9i q^{22} -1.44407e10i q^{23} +1.02134e9i q^{24} -9.22682e9 q^{25} +5.48970e10 q^{26} -4.57186e9i q^{27} +3.19433e10i q^{28} -2.64369e9i q^{29} +5.03926e9 q^{30} -1.40061e11i q^{31} +8.85950e10 q^{32} +3.48538e9 q^{33} +(2.51852e11 + 9.22200e10i) q^{34} +8.33803e11 q^{35} -1.09397e11 q^{36} -8.75378e11i q^{37} +4.67325e11 q^{38} -5.52176e10i q^{39} -1.27697e12i q^{40} +2.04844e12i q^{41} -1.05719e11 q^{42} +1.79994e12 q^{43} -1.66946e11i q^{44} +2.85553e12i q^{45} -2.28922e12i q^{46} -2.86172e12 q^{47} +1.22003e11i q^{48} -1.27449e13 q^{49} -1.46269e12 q^{50} +(9.27585e10 - 2.53323e11i) q^{51} -2.64487e12 q^{52} +6.85277e12 q^{53} -7.24757e11i q^{54} -4.35772e12 q^{55} +2.67896e13i q^{56} -4.70054e11i q^{57} -4.19093e11i q^{58} -2.14930e13 q^{59} -2.42785e11 q^{60} -6.73864e12i q^{61} -2.22033e13i q^{62} -5.99065e13i q^{63} +3.91168e13 q^{64} +6.90377e13i q^{65} +5.52522e11 q^{66} +1.21139e12 q^{67} +(-1.21339e13 - 4.44304e12i) q^{68} -2.30259e12 q^{69} +1.32179e14 q^{70} +7.71221e12i q^{71} -9.17466e13 q^{72} +1.22093e14i q^{73} -1.38770e14i q^{74} +1.47123e12i q^{75} -2.25151e13 q^{76} +9.14211e13 q^{77} -8.75341e12i q^{78} -2.38004e14i q^{79} -1.52539e14i q^{80} +2.04797e14 q^{81} +3.24731e14i q^{82} -9.16560e13 q^{83} +5.09341e12 q^{84} +(-1.15975e14 + 3.16726e14i) q^{85} +2.85337e14 q^{86} -4.21541e11 q^{87} -1.40011e14i q^{88} +2.05833e14 q^{89} +4.52675e14i q^{90} -1.44835e15i q^{91} +1.10292e14i q^{92} -2.23330e13 q^{93} -4.53657e14 q^{94} +5.87702e14i q^{95} -1.41266e13i q^{96} +7.88714e14i q^{97} -2.02039e15 q^{98} +3.13090e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9}+O(q^{10}) \) 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9	\( 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9} + 702506672 q^{13} - 1787378376 q^{15} + 3524081474 q^{16} - 2245058454 q^{17} + 6803778314 q^{18} + 9958891784 q^{19} - 4168893668 q^{21} - 238696683970 q^{25} - 33467295588 q^{26} - 62541989808 q^{30} - 43445086338 q^{32} + 213283309748 q^{33} + 521524562854 q^{34} - 467785613304 q^{35} - 2300588654186 q^{36} + 3162083165688 q^{38} - 3011205093968 q^{42} - 2215728209008 q^{43} - 7793870107128 q^{47} - 1555224751482 q^{49} + 30118817411766 q^{50} - 21451923375880 q^{51} + 51163160044372 q^{52} - 6062965973460 q^{53} - 11679154373592 q^{55} + 22772194849344 q^{59} - 86295684546192 q^{60} - 28567749560318 q^{64} + 251781147903680 q^{66} + 153875904272808 q^{67} - 48849686100870 q^{68} + 60664072036996 q^{69} - 150925771647648 q^{70} - 293782759569702 q^{72} - 388479948338264 q^{76} - 622427249887884 q^{77} + 983865215787034 q^{81} - 15\!\cdots\!44 q^{83}+ \cdots + 26\!\cdots\!90 q^{98}+O(q^{100}) \) 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9 + 702506672 * q^13 - 1787378376 * q^15 + 3524081474 * q^16 - 2245058454 * q^17 + 6803778314 * q^18 + 9958891784 * q^19 - 4168893668 * q^21 - 238696683970 * q^25 - 33467295588 * q^26 - 62541989808 * q^30 - 43445086338 * q^32 + 213283309748 * q^33 + 521524562854 * q^34 - 467785613304 * q^35 - 2300588654186 * q^36 + 3162083165688 * q^38 - 3011205093968 * q^42 - 2215728209008 * q^43 - 7793870107128 * q^47 - 1555224751482 * q^49 + 30118817411766 * q^50 - 21451923375880 * q^51 + 51163160044372 * q^52 - 6062965973460 * q^53 - 11679154373592 * q^55 + 22772194849344 * q^59 - 86295684546192 * q^60 - 28567749560318 * q^64 + 251781147903680 * q^66 + 153875904272808 * q^67 - 48849686100870 * q^68 + 60664072036996 * q^69 - 150925771647648 * q^70 - 293782759569702 * q^72 - 388479948338264 * q^76 - 622427249887884 * q^77 + 983865215787034 * q^81 - 1541046988482144 * q^83 + 1542636638603936 * q^84 + 94526232685248 * q^85 + 102594718370712 * q^86 - 428830075363560 * q^87 - 894061425316800 * q^89 + 2342465228549812 * q^93 + 2620489835637760 * q^94 + 2662999543720290 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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