LMFDB - Embedded newform 17.10.b.a.16.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,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, 10, names="a")

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
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:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 122690 x^{10} + 5157152560 x^{8} + 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 $ x^12 + 122690x^10 + 5157152560x^8 + 87983684680032x^6 + 612743619071665152x^4 + 1335826553351738886144*x^2 + 203949399568932198678528
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.10
Root			$225.146i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.10.b.a.16.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+25.8215 q^{2} +225.146i q^{3} +154.751 q^{4} +96.4328i q^{5} +5813.61i q^{6} +1385.77i q^{7} -9224.72 q^{8} -31007.8 q^{9} +O(q^{10})$	\(q+25.8215 q^{2} +225.146i q^{3} +154.751 q^{4} +96.4328i q^{5} +5813.61i q^{6} +1385.77i q^{7} -9224.72 q^{8} -31007.8 q^{9} +2490.04i q^{10} +33833.7i q^{11} +34841.5i q^{12} +138558. q^{13} +35782.8i q^{14} -21711.5 q^{15} -317429. q^{16} +(177982. + 294805. i) q^{17} -800668. q^{18} +429726. q^{19} +14923.1i q^{20} -312001. q^{21} +873638. i q^{22} -352831. i q^{23} -2.07691e6i q^{24} +1.94383e6 q^{25} +3.57778e6 q^{26} -2.54973e6i q^{27} +214449. i q^{28} -508224. i q^{29} -560623. q^{30} -8.73026e6i q^{31} -3.47343e6 q^{32} -7.61753e6 q^{33} +(4.59577e6 + 7.61232e6i) q^{34} -133634. q^{35} -4.79848e6 q^{36} +1.62218e7i q^{37} +1.10962e7 q^{38} +3.11958e7i q^{39} -889565. i q^{40} -1.12435e7i q^{41} -8.05635e6 q^{42} -2.43795e7 q^{43} +5.23579e6i q^{44} -2.99017e6i q^{45} -9.11064e6i q^{46} -1.11673e7 q^{47} -7.14678e7i q^{48} +3.84332e7 q^{49} +5.01925e7 q^{50} +(-6.63743e7 + 4.00720e7i) q^{51} +2.14420e7 q^{52} +3.54297e7 q^{53} -6.58378e7i q^{54} -3.26268e6 q^{55} -1.27834e7i q^{56} +9.67510e7i q^{57} -1.31231e7i q^{58} +5.03437e7 q^{59} -3.35987e6 q^{60} +1.53033e8i q^{61} -2.25429e8i q^{62} -4.29697e7i q^{63} +7.28341e7 q^{64} +1.33615e7i q^{65} -1.96696e8 q^{66} -2.44023e8 q^{67} +(2.75429e7 + 4.56214e7i) q^{68} +7.94386e7 q^{69} -3.45063e6 q^{70} -3.78713e8i q^{71} +2.86038e8 q^{72} +1.38738e7i q^{73} +4.18871e8i q^{74} +4.37645e8i q^{75} +6.65004e7 q^{76} -4.68858e7 q^{77} +8.05523e8i q^{78} -5.65164e8i q^{79} -3.06105e7i q^{80} -3.62648e7 q^{81} -2.90325e8i q^{82} -5.68408e8 q^{83} -4.82825e7 q^{84} +(-2.84289e7 + 1.71633e7i) q^{85} -6.29517e8 q^{86} +1.14425e8 q^{87} -3.12106e8i q^{88} +2.61194e8 q^{89} -7.72106e7i q^{90} +1.92010e8i q^{91} -5.46009e7i q^{92} +1.96558e9 q^{93} -2.88357e8 q^{94} +4.14396e7i q^{95} -7.82030e8i q^{96} -1.04492e9i q^{97} +9.92405e8 q^{98} -1.04911e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9}+O(q^{10}) $ 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9	$ 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9} - 63204 q^{13} - 243480 q^{15} + 38978 q^{16} - 105960 q^{17} + 547706 q^{18} + 1110672 q^{19} - 172580 q^{21} - 4441796 q^{25} + 1336332 q^{26} - 500496 q^{30} - 1934850 q^{32} - 6557404 q^{33} - 15085546 q^{34} + 3519864 q^{35} + 30244102 q^{36} + 28748136 q^{38} - 11901296 q^{42} + 10004616 q^{43} - 112552440 q^{47} + 121354720 q^{49} - 164889018 q^{50} - 52506472 q^{51} - 59093180 q^{52} + 76804272 q^{53} + 300732568 q^{55} + 11618904 q^{59} + 101609232 q^{60} - 260062974 q^{64} + 18429632 q^{66} - 304208752 q^{67} - 444301206 q^{68} - 211308236 q^{69} + 460311456 q^{70} + 493218954 q^{72} + 416024248 q^{76} + 138357828 q^{77} - 363335792 q^{81} - 845042136 q^{83} + 958037984 q^{84} - 388949632 q^{85} + 127952904 q^{86} + 610860648 q^{87} - 938223804 q^{89} + 1635779524 q^{93} - 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) $ 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9 - 63204 * q^13 - 243480 * q^15 + 38978 * q^16 - 105960 * q^17 + 547706 * q^18 + 1110672 * q^19 - 172580 * q^21 - 4441796 * q^25 + 1336332 * q^26 - 500496 * q^30 - 1934850 * q^32 - 6557404 * q^33 - 15085546 * q^34 + 3519864 * q^35 + 30244102 * q^36 + 28748136 * q^38 - 11901296 * q^42 + 10004616 * q^43 - 112552440 * q^47 + 121354720 * q^49 - 164889018 * q^50 - 52506472 * q^51 - 59093180 * q^52 + 76804272 * q^53 + 300732568 * q^55 + 11618904 * q^59 + 101609232 * q^60 - 260062974 * q^64 + 18429632 * q^66 - 304208752 * q^67 - 444301206 * q^68 - 211308236 * q^69 + 460311456 * q^70 + 493218954 * q^72 + 416024248 * q^76 + 138357828 * q^77 - 363335792 * q^81 - 845042136 * q^83 + 958037984 * q^84 - 388949632 * q^85 + 127952904 * q^86 + 610860648 * q^87 - 938223804 * q^89 + 1635779524 * q^93 - 238629952 * q^94 - 152046078 * 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 $

$2$	25.8215			1.14116			0.570580	−	0.821242i	$-0.306718\pi$
$2$	25.8215			1.14116			0.570580	+	0.821242i	$0.306718\pi$
$3$			225.146i			1.60479i	0.596792	+	0.802396i	$0.296442\pi$
$3$			225.146i			1.60479i	−0.596792	+	0.802396i	$0.703558\pi$
$4$	154.751			0.302248
$5$			96.4328i			0.0690017i	0.999405	+	0.0345009i	$0.0109841\pi$
$5$			96.4328i			0.0690017i	−0.999405	+	0.0345009i	$0.989016\pi$
$6$			5813.61i			1.83133i
$7$			1385.77i			0.218148i	0.994034	+	0.109074i	$0.0347885\pi$
$7$			1385.77i			0.218148i	−0.994034	+	0.109074i	$0.965211\pi$
$8$	−9224.72			−0.796248
$9$	−31007.8			−1.57536
$10$			2490.04i			0.0787420i
$11$			33833.7i			0.696759i	0.937354	+	0.348379i	$0.113268\pi$
$11$			33833.7i			0.696759i	−0.937354	+	0.348379i	$0.886732\pi$
$12$			34841.5i			0.485045i
$13$	138558.			1.34551			0.672755	−	0.739866i	$-0.265111\pi$
$13$	138558.			1.34551			0.672755	+	0.739866i	$0.265111\pi$
$14$			35782.8i			0.248942i
$15$	−21711.5			−0.110733
$16$	−317429.			−1.21089
$17$	177982.	+	294805.i	0.516840	+	0.856082i
$17$	177982.	+	294805.i	0.516840	+	0.856082i
$18$	−800668.			−1.79774
$19$	429726.			0.756484			0.378242	−	0.925707i	$-0.376529\pi$
$19$	429726.			0.756484			0.378242	+	0.925707i	$0.376529\pi$
$20$			14923.1i			0.0208556i
$21$	−312001.			−0.350082
$22$			873638.i			0.795114i
$23$		−	352831.i		−	0.262901i	−0.991323	−	0.131450i	$-0.958037\pi$
$23$		−	352831.i		−	0.262901i	0.991323	−	0.131450i	$-0.0419634\pi$
$24$		−	2.07691e6i		−	1.27781i
$25$	1.94383e6			0.995239
$26$	3.57778e6			1.53544
$27$		−	2.54973e6i		−	0.923330i
$28$			214449.i			0.0659347i
$29$		−	508224.i		−	0.133433i	−0.997772	−	0.0667166i	$-0.978748\pi$
$29$		−	508224.i		−	0.133433i	0.997772	−	0.0667166i	$-0.0212523\pi$
$30$	−560623.			−0.126365
$31$		−	8.73026e6i		−	1.69785i	−0.528513	−	0.848925i	$-0.677250\pi$
$31$		−	8.73026e6i		−	1.69785i	0.528513	−	0.848925i	$-0.322750\pi$
$32$	−3.47343e6			−0.585577
$33$	−7.61753e6			−1.11815
$34$	4.59577e6	+	7.61232e6i	0.589798	+	0.976927i
$35$	−133634.			−0.0150526
$36$	−4.79848e6			−0.476148
$37$			1.62218e7i			1.42295i	0.702710	+	0.711476i	$0.251973\pi$
$37$			1.62218e7i			1.42295i	−0.702710	+	0.711476i	$0.748027\pi$
$38$	1.10962e7			0.863270
$39$			3.11958e7i			2.15926i
$40$		−	889565.i		−	0.0549424i
$41$		−	1.12435e7i		−	0.621406i	−0.950507	−	0.310703i	$-0.899436\pi$
$41$		−	1.12435e7i		−	0.621406i	0.950507	−	0.310703i	$-0.100564\pi$
$42$	−8.05635e6			−0.399500
$43$	−2.43795e7			−1.08747			−0.543735	−	0.839257i	$-0.682990\pi$
$43$	−2.43795e7			−1.08747			−0.543735	+	0.839257i	$0.682990\pi$
$44$			5.23579e6i			0.210594i
$45$		−	2.99017e6i		−	0.108702i
$46$		−	9.11064e6i		−	0.300012i
$47$	−1.11673e7			−0.333817			−0.166909	−	0.985972i	$-0.553379\pi$
$47$	−1.11673e7			−0.333817			−0.166909	+	0.985972i	$0.553379\pi$
$48$		−	7.14678e7i		−	1.94323i
$49$	3.84332e7			0.952412
$50$	5.01925e7			1.13573
$51$	−6.63743e7	+	4.00720e7i	−1.37383	+	0.829421i
$52$	2.14420e7			0.406677
$53$	3.54297e7			0.616774			0.308387	−	0.951261i	$-0.400211\pi$
$53$	3.54297e7			0.616774			0.308387	+	0.951261i	$0.400211\pi$
$54$		−	6.58378e7i		−	1.05367i
$55$	−3.26268e6			−0.0480775
$56$		−	1.27834e7i		−	0.173700i
$57$			9.67510e7i			1.21400i
$58$		−	1.31231e7i		−	0.152269i
$59$	5.03437e7			0.540893			0.270446	−	0.962735i	$-0.412829\pi$
$59$	5.03437e7			0.540893			0.270446	+	0.962735i	$0.412829\pi$
$60$	−3.35987e6			−0.0334689
$61$			1.53033e8i			1.41515i	0.706639	+	0.707574i	$0.250211\pi$
$61$			1.53033e8i			1.41515i	−0.706639	+	0.707574i	$0.749789\pi$
$62$		−	2.25429e8i		−	1.93752i
$63$		−	4.29697e7i		−	0.343661i
$64$	7.28341e7			0.542656
$65$			1.33615e7i			0.0928425i
$66$	−1.96696e8			−1.27599
$67$	−2.44023e8			−1.47943			−0.739713	−	0.672922i	$-0.765039\pi$
$67$	−2.44023e8			−1.47943			−0.739713	+	0.672922i	$0.765039\pi$
$68$	2.75429e7	+	4.56214e7i	0.156214	+	0.258749i
$69$	7.94386e7			0.421901
$70$	−3.45063e6			−0.0171774
$71$		−	3.78713e8i		−	1.76867i	−0.466850	−	0.884337i	$-0.654611\pi$
$71$		−	3.78713e8i		−	1.76867i	0.466850	−	0.884337i	$-0.345389\pi$
$72$	2.86038e8			1.25437
$73$			1.38738e7i			0.0571798i	0.999591	+	0.0285899i	$0.00910169\pi$
$73$			1.38738e7i			0.0571798i	−0.999591	+	0.0285899i	$0.990898\pi$
$74$			4.18871e8i			1.62382i
$75$			4.37645e8i			1.59715i
$76$	6.65004e7			0.228646
$77$	−4.68858e7			−0.151996
$78$			8.05523e8i			2.46407i
$79$		−	5.65164e8i		−	1.63250i	−0.577700	−	0.816250i	$-0.696049\pi$
$79$		−	5.65164e8i		−	1.63250i	0.577700	−	0.816250i	$-0.303951\pi$
$80$		−	3.06105e7i		−	0.0835537i
$81$	−3.62648e7			−0.0936057
$82$		−	2.90325e8i		−	0.709124i
$83$	−5.68408e8			−1.31465			−0.657323	−	0.753609i	$-0.728311\pi$
$83$	−5.68408e8			−1.31465			−0.657323	+	0.753609i	$0.728311\pi$
$84$	−4.82825e7			−0.105811
$85$	−2.84289e7	+	1.71633e7i	−0.0590711	+	0.0356629i
$86$	−6.29517e8			−1.24098
$87$	1.14425e8			0.214133
$88$		−	3.12106e8i		−	0.554792i
$89$	2.61194e8			0.441275			0.220637	−	0.975356i	$-0.429186\pi$
$89$	2.61194e8			0.441275			0.220637	+	0.975356i	$0.429186\pi$
$90$		−	7.72106e7i		−	0.124047i
$91$			1.92010e8i			0.293520i
$92$		−	5.46009e7i		−	0.0794611i
$93$	1.96558e9			2.72470
$94$	−2.88357e8			−0.380939
$95$			4.14396e7i			0.0521987i
$96$		−	7.82030e8i		−	0.939730i
$97$		−	1.04492e9i		−	1.19842i	−0.800590	−	0.599212i	$-0.795481\pi$
$97$		−	1.04492e9i		−	1.19842i	0.800590	−	0.599212i	$-0.204519\pi$
$98$	9.92405e8			1.08685
$99$		−	1.04911e9i		−	1.09764i
$100$	3.00809e8			0.300809
$101$	2.97630e7			0.0284597			0.0142299	−	0.999899i	$-0.495470\pi$
$101$	2.97630e7			0.0284597			0.0142299	+	0.999899i	$0.495470\pi$
$102$	−1.71388e9	+	1.03472e9i	−1.56776	+	0.946503i
$103$	1.60523e9			1.40530			0.702650	−	0.711536i	$-0.252000\pi$
$103$	1.60523e9			1.40530			0.702650	+	0.711536i	$0.252000\pi$
$104$	−1.27816e9			−1.07136
$105$		−	3.00872e7i		−	0.0241562i
$106$	9.14849e8			0.703838
$107$			2.35483e9i			1.73673i	0.495925	+	0.868365i	$0.334829\pi$
$107$			2.35483e9i			1.73673i	−0.495925	+	0.868365i	$0.665171\pi$
$108$		−	3.94572e8i		−	0.279074i
$109$		−	1.68886e9i		−	1.14597i	−0.819566	−	0.572985i	$-0.805785\pi$
$109$		−	1.68886e9i		−	1.14597i	0.819566	−	0.572985i	$-0.194215\pi$
$110$	−8.42473e7			−0.0548642
$111$	−3.65227e9			−2.28354
$112$		−	4.39884e8i		−	0.264154i
$113$			2.39661e9i			1.38275i	0.722496	+	0.691375i	$0.242995\pi$
$113$			2.39661e9i			1.38275i	−0.722496	+	0.691375i	$0.757005\pi$
$114$			2.49826e9i			1.38537i
$115$	3.40245e7			0.0181406
$116$		−	7.86480e7i		−	0.0403299i
$117$	−4.29638e9			−2.11966
$118$	1.29995e9			0.617245
$119$	−4.08533e8	+	2.46643e8i	−0.186752	+	0.112748i
$120$	2.00282e8			0.0881712
$121$	1.21323e9			0.514527
$122$			3.95156e9i			1.61491i
$123$	2.53144e9			0.997227
$124$		−	1.35101e9i		−	0.513171i
$125$			3.75794e8i			0.137675i
$126$		−	1.10954e9i		−	0.392172i
$127$	4.20715e9			1.43506			0.717532	−	0.696526i	$-0.245272\pi$
$127$	4.20715e9			1.43506			0.717532	+	0.696526i	$0.245272\pi$
$128$	3.65909e9			1.20484
$129$		−	5.48896e9i		−	1.74516i
$130$			3.45015e8i			0.105948i
$131$		−	1.46332e9i		−	0.434129i	−0.976157	−	0.217064i	$-0.930352\pi$
$131$		−	1.46332e9i		−	0.434129i	0.976157	−	0.217064i	$-0.0696481\pi$
$132$	−1.17882e9			−0.337959
$133$			5.95502e8i			0.165025i
$134$	−6.30103e9			−1.68826
$135$	2.45877e8			0.0637113
$136$	−1.64184e9	−	2.71950e9i	−0.411533	−	0.681653i
$137$	−4.13890e9			−1.00379			−0.501894	−	0.864929i	$-0.667363\pi$
$137$	−4.13890e9			−1.00379			−0.501894	+	0.864929i	$0.667363\pi$
$138$	2.05122e9			0.481457
$139$		−	1.74238e9i		−	0.395892i	−0.980213	−	0.197946i	$-0.936573\pi$
$139$		−	1.74238e9i		−	0.395892i	0.980213	−	0.197946i	$-0.0634271\pi$
$140$	−2.06800e7			−0.00454960
$141$		−	2.51428e9i		−	0.535708i
$142$		−	9.77895e9i		−	2.01834i
$143$			4.68793e9i			0.937496i
$144$	9.84275e9			1.90759
$145$	4.90094e7			0.00920712
$146$			3.58243e8i			0.0652514i
$147$			8.65309e9i			1.52842i
$148$			2.51033e9i			0.430084i
$149$	4.80220e9			0.798183			0.399092	−	0.916911i	$-0.369326\pi$
$149$	4.80220e9			0.798183			0.399092	+	0.916911i	$0.369326\pi$
$150$			1.13007e10i			1.82261i
$151$	1.22756e9			0.192152			0.0960762	−	0.995374i	$-0.469371\pi$
$151$	1.22756e9			0.192152			0.0960762	+	0.995374i	$0.469371\pi$
$152$	−3.96410e9			−0.602349
$153$	−5.51883e9	−	9.14126e9i	−0.814208	−	1.34864i
$154$	−1.21066e9			−0.173452
$155$	8.41883e8			0.117155
$156$			4.82758e9i			0.652632i
$157$	1.72654e9			0.226792			0.113396	−	0.993550i	$-0.463827\pi$
$157$	1.72654e9			0.226792			0.113396	+	0.993550i	$0.463827\pi$
$158$		−	1.45934e10i		−	1.86294i
$159$			7.97686e9i			0.989794i
$160$		−	3.34953e8i		−	0.0404058i
$161$	4.88944e8			0.0573512
$162$	−9.36411e8			−0.106819
$163$		−	2.27451e9i		−	0.252374i	−0.992006	−	0.126187i	$-0.959726\pi$
$163$		−	2.27451e9i		−	0.252374i	0.992006	−	0.126187i	$-0.0402739\pi$
$164$		−	1.73995e9i		−	0.187818i
$165$		−	7.34580e8i		−	0.0771545i
$166$	−1.46772e10			−1.50022
$167$			1.42586e10i			1.41857i	0.704921	+	0.709286i	$0.250982\pi$
$167$			1.42586e10i			1.41857i	−0.704921	+	0.709286i	$0.749018\pi$
$168$	2.87812e9			0.278752
$169$	8.59384e9			0.810396
$170$	−7.34078e8	+	4.43183e8i	−0.0674096	+	0.0406971i
$171$	−1.33248e10			−1.19173
$172$	−3.77275e9			−0.328685
$173$		−	6.92744e9i		−	0.587984i	−0.955808	−	0.293992i	$-0.905016\pi$
$173$		−	6.92744e9i		−	0.587984i	0.955808	−	0.293992i	$-0.0949839\pi$
$174$	2.95462e9			0.244360
$175$			2.69370e9i			0.217109i
$176$		−	1.07398e10i		−	0.843701i
$177$			1.13347e10i			0.868020i
$178$	6.74444e9			0.503565
$179$	1.32700e10			0.966120			0.483060	−	0.875587i	$-0.339525\pi$
$179$	1.32700e10			0.966120			0.483060	+	0.875587i	$0.339525\pi$
$180$		−	4.62731e8i		−	0.0328550i
$181$			8.95066e9i			0.619871i	0.950758	+	0.309936i	$0.100308\pi$
$181$			8.95066e9i			0.619871i	−0.950758	+	0.309936i	$0.899692\pi$
$182$			4.95799e9i			0.334953i
$183$	−3.44549e10			−2.27102
$184$			3.25477e9i			0.209334i
$185$	−1.56431e9			−0.0981861
$186$	5.07544e10			3.10932
$187$	−9.97436e9	+	6.02180e9i	−0.596483	+	0.360113i
$188$	−1.72815e9			−0.100896
$189$	3.53334e9			0.201422
$190$			1.07003e9i			0.0595671i
$191$	−2.10560e9			−0.114479			−0.0572394	−	0.998360i	$-0.518230\pi$
$191$	−2.10560e9			−0.114479			−0.0572394	+	0.998360i	$0.518230\pi$
$192$			1.63983e10i			0.870851i
$193$			5.10730e9i			0.264962i	0.991186	+	0.132481i	$0.0422944\pi$
$193$			5.10730e9i			0.264962i	−0.991186	+	0.132481i	$0.957706\pi$
$194$		−	2.69815e10i		−	1.36760i
$195$	−3.00830e9			−0.148993
$196$	5.94758e9			0.287864
$197$		−	1.85517e10i		−	0.877578i	−0.898590	−	0.438789i	$-0.855408\pi$
$197$		−	1.85517e10i		−	0.877578i	0.898590	−	0.438789i	$-0.144592\pi$
$198$		−	2.70896e10i		−	1.25259i
$199$		−	1.37208e10i		−	0.620211i	−0.950702	−	0.310105i	$-0.899636\pi$
$199$		−	1.37208e10i		−	0.620211i	0.950702	−	0.310105i	$-0.100364\pi$
$200$	−1.79312e10			−0.792456
$201$		−	5.49407e10i		−	2.37417i
$202$	7.68527e8			0.0324771
$203$	7.04282e8			0.0291082
$204$	−1.02715e10	+	6.20117e9i	−0.415238	+	0.250691i
$205$	1.08425e9			0.0428781
$206$	4.14494e10			1.60367
$207$			1.09405e10i			0.414163i
$208$	−4.39823e10			−1.62927
$209$			1.45392e10i			0.527087i
$210$		−	7.76896e8i		−	0.0275662i
$211$		−	6.12032e9i		−	0.212570i	−0.994336	−	0.106285i	$-0.966104\pi$
$211$		−	6.12032e9i		−	0.212570i	0.994336	−	0.106285i	$-0.0338957\pi$
$212$	5.48278e9			0.186419
$213$	8.52658e10			2.83835
$214$			6.08053e10i			1.98189i
$215$		−	2.35099e9i		−	0.0750373i
$216$			2.35205e10i			0.735199i
$217$	1.20982e10			0.370382
$218$		−	4.36088e10i		−	1.30774i
$219$	−3.12363e9			−0.0917617
$220$	−5.04902e8			−0.0145313
$221$	2.46609e10	+	4.08477e10i	0.695414	+	1.15187i
$222$	−9.43071e10			−2.60589
$223$	−6.31228e9			−0.170928			−0.0854642	−	0.996341i	$-0.527237\pi$
$223$	−6.31228e9			−0.170928			−0.0854642	+	0.996341i	$0.527237\pi$
$224$		−	4.81339e9i		−	0.127742i
$225$	−6.02737e10			−1.56786
$226$			6.18840e10i			1.57794i
$227$			5.43032e10i			1.35740i	0.734413	+	0.678702i	$0.237457\pi$
$227$			5.43032e10i			1.35740i	−0.734413	+	0.678702i	$0.762543\pi$
$228$			1.49723e10i			0.366929i
$229$	−1.03751e10			−0.249306			−0.124653	−	0.992200i	$-0.539782\pi$
$229$	−1.03751e10			−0.249306			−0.124653	+	0.992200i	$0.539782\pi$
$230$	8.78564e8			0.0207013
$231$		−	1.05562e10i		−	0.243923i
$232$			4.68822e9i			0.106246i
$233$		−	5.93158e10i		−	1.31846i	−0.751939	−	0.659232i	$-0.770881\pi$
$233$		−	5.93158e10i		−	1.31846i	0.751939	−	0.659232i	$-0.229119\pi$
$234$	−1.10939e11			−2.41887
$235$		−	1.07690e9i		−	0.0230340i
$236$	7.79073e9			0.163484
$237$	1.27245e11			2.61982
$238$	−1.05489e10	+	6.36869e9i	−0.213114	+	0.128663i
$239$	−6.57143e10			−1.30278			−0.651388	−	0.758745i	$-0.725813\pi$
$239$	−6.57143e10			−1.30278			−0.651388	+	0.758745i	$0.725813\pi$
$240$	6.89184e9			0.134086
$241$		−	2.02970e10i		−	0.387574i	−0.981044	−	0.193787i	$-0.937923\pi$
$241$		−	2.02970e10i		−	0.387574i	0.981044	−	0.193787i	$-0.0620771\pi$
$242$	3.13274e10			0.587158
$243$		−	5.83511e10i		−	1.07355i
$244$			2.36820e10i			0.427725i
$245$			3.70623e9i			0.0657180i
$246$	6.53655e10			1.13800
$247$	5.95420e10			1.01786
$248$			8.05342e10i			1.35191i
$249$		−	1.27975e11i		−	2.10974i
$250$			9.70357e9i			0.157109i
$251$	−8.71654e10			−1.38616			−0.693078	−	0.720863i	$-0.743746\pi$
$251$	−8.71654e10			−1.38616			−0.693078	+	0.720863i	$0.743746\pi$
$252$		−	6.64960e9i		−	0.103871i
$253$	1.19376e10			0.183178
$254$	1.08635e11			1.63764
$255$	−3.86426e9	−	6.40066e9i	−0.0572315	−	0.0947968i
$256$	5.71921e10			0.832254
$257$	−1.20306e10			−0.172023			−0.0860115	−	0.996294i	$-0.527412\pi$
$257$	−1.20306e10			−0.172023			−0.0860115	+	0.996294i	$0.527412\pi$
$258$		−	1.41733e11i		−	1.99151i
$259$	−2.24797e10			−0.310414
$260$			2.06771e9i			0.0280614i
$261$			1.57589e10i			0.210205i
$262$		−	3.77851e10i		−	0.495411i
$263$	3.51365e10			0.452853			0.226426	−	0.974028i	$-0.427296\pi$
$263$	3.51365e10			0.452853			0.226426	+	0.974028i	$0.427296\pi$
$264$	7.02695e10			0.890327
$265$			3.41659e9i			0.0425585i
$266$			1.53768e10i			0.188321i
$267$			5.88069e10i			0.708154i
$268$	−3.77627e10			−0.447153
$269$			8.30055e10i			0.966544i	0.875470	+	0.483272i	$0.160552\pi$
$269$			8.30055e10i			0.966544i	−0.875470	+	0.483272i	$0.839448\pi$
$270$	6.34893e9			0.0727048
$271$	−5.57473e10			−0.627858			−0.313929	−	0.949446i	$-0.601645\pi$
$271$	−5.57473e10			−0.627858			−0.313929	+	0.949446i	$0.601645\pi$
$272$	−5.64966e10	−	9.35797e10i	−0.625839	−	1.03662i
$273$	−4.32303e10			−0.471038
$274$	−1.06873e11			−1.14548
$275$			6.57668e10i			0.693441i
$276$	1.22932e10			0.127519
$277$		−	1.84969e11i		−	1.88773i	−0.330333	−	0.943864i	$-0.607161\pi$
$277$		−	1.84969e11i		−	1.88773i	0.330333	−	0.943864i	$-0.392839\pi$
$278$		−	4.49910e10i		−	0.451777i
$279$			2.70706e11i			2.67472i
$280$	1.23274e9			0.0119856
$281$	−1.35823e11			−1.29956			−0.649778	−	0.760124i	$-0.725138\pi$
$281$	−1.35823e11			−1.29956			−0.649778	+	0.760124i	$0.725138\pi$
$282$		−	6.49225e10i		−	0.611328i
$283$			5.85987e10i			0.543062i	0.962430	+	0.271531i	$0.0875299\pi$
$283$			5.85987e10i			0.543062i	−0.962430	+	0.271531i	$0.912470\pi$
$284$		−	5.86061e10i		−	0.534577i
$285$	−9.32997e9			−0.0837681
$286$			1.21050e11i			1.06983i
$287$	1.55810e10			0.135558
$288$	1.07703e11			0.922493
$289$	−5.52326e10	+	1.04940e11i	−0.465752	+	0.884915i
$290$	1.26550e9			0.0105068
$291$	2.35260e11			1.92322
$292$			2.14698e9i			0.0172825i
$293$	−5.48232e10			−0.434571			−0.217285	−	0.976108i	$-0.569720\pi$
$293$	−5.48232e10			−0.434571			−0.217285	+	0.976108i	$0.569720\pi$
$294$			2.23436e11i			1.74418i
$295$			4.85478e9i			0.0373225i
$296$		−	1.49641e11i		−	1.13302i
$297$	8.62667e10			0.643338
$298$	1.24000e11			0.910855
$299$		−	4.88876e10i		−	0.353735i
$300$			6.77259e10i			0.482735i
$301$		−	3.37845e10i		−	0.237229i
$302$	3.16974e10			0.219277
$303$			6.70103e9i			0.0456720i
$304$	−1.36407e11			−0.916023
$305$	−1.47574e10			−0.0976477
$306$	−1.42505e11	−	2.36041e11i	−0.929143	−	1.53901i
$307$	−1.88055e11			−1.20826			−0.604132	−	0.796884i	$-0.706480\pi$
$307$	−1.88055e11			−1.20826			−0.604132	+	0.796884i	$0.706480\pi$
$308$	−7.25562e9			−0.0459406
$309$			3.61411e11i			2.25521i
$310$	2.17387e10			0.133692
$311$		−	1.81717e11i		−	1.10147i	−0.834679	−	0.550737i	$-0.814347\pi$
$311$		−	1.81717e11i		−	1.10147i	0.834679	−	0.550737i	$-0.185653\pi$
$312$		−	2.87773e11i		−	1.71931i
$313$		−	2.21549e11i		−	1.30473i	−0.757905	−	0.652364i	$-0.773777\pi$
$313$		−	2.21549e11i		−	1.30473i	0.757905	−	0.652364i	$-0.226223\pi$
$314$	4.45819e10			0.258807
$315$	4.14369e9			0.0237132
$316$		−	8.74597e10i		−	0.493419i
$317$			2.66841e11i			1.48418i	0.670301	+	0.742089i	$0.266165\pi$
$317$			2.66841e11i			1.48418i	−0.670301	+	0.742089i	$0.733835\pi$
$318$			2.05975e11i			1.12951i
$319$	1.71951e10			0.0929708
$320$			7.02360e9i			0.0374442i
$321$	−5.30181e11			−2.78709
$322$	1.26253e10			0.0654469
$323$	7.64835e10	+	1.26685e11i	0.390982	+	0.647613i
$324$	−5.61200e9			−0.0282921
$325$	2.69333e11			1.33910
$326$		−	5.87314e10i		−	0.287999i
$327$	3.80239e11			1.83904
$328$			1.03718e11i			0.494793i
$329$		−	1.54754e10i		−	0.0728215i
$330$		−	1.89680e10i		−	0.0880456i
$331$	3.46276e11			1.58561			0.792804	−	0.609476i	$-0.208620\pi$
$331$	3.46276e11			1.58561			0.792804	+	0.609476i	$0.208620\pi$
$332$	−8.79617e10			−0.397349
$333$		−	5.03001e11i		−	2.24166i
$334$			3.68177e11i			1.61882i
$335$		−	2.35318e10i		−	0.102083i
$336$	9.90381e10			0.423912
$337$		−	2.14440e11i		−	0.905671i	−0.891594	−	0.452836i	$-0.850412\pi$
$337$		−	2.14440e11i		−	0.905671i	0.891594	−	0.452836i	$-0.149588\pi$
$338$	2.21906e11			0.924792
$339$	−5.39586e11			−2.21903
$340$	−4.39940e9	+	2.65604e9i	−0.0178541	+	0.0107790i
$341$	2.95377e11			1.18299
$342$	−3.44067e11			−1.35996
$343$			1.09181e11i			0.425914i
$344$	2.24894e11			0.865896
$345$			7.66048e9i			0.0291119i
$346$		−	1.78877e11i		−	0.670984i
$347$		−	2.25675e11i		−	0.835603i	−0.908538	−	0.417801i	$-0.862801\pi$
$347$		−	2.25675e11i		−	0.835603i	0.908538	−	0.417801i	$-0.137199\pi$
$348$	1.77073e10			0.0647211
$349$	−3.13210e10			−0.113011			−0.0565055	−	0.998402i	$-0.517996\pi$
$349$	−3.13210e10			−0.113011			−0.0565055	+	0.998402i	$0.517996\pi$
$350$			6.95554e10i			0.247756i
$351$		−	3.53285e11i		−	1.24235i
$352$		−	1.17519e11i		−	0.408006i
$353$	1.67054e11			0.572625			0.286312	−	0.958136i	$-0.407571\pi$
$353$	1.67054e11			0.572625			0.286312	+	0.958136i	$0.407571\pi$
$354$			2.92679e11i			0.990551i
$355$	3.65204e10			0.122041
$356$	4.04201e10			0.133374
$357$	−5.55307e10	−	9.19797e10i	−0.180936	−	0.299699i
$358$	3.42650e11			1.10250
$359$	−5.25130e11			−1.66856			−0.834280	−	0.551341i	$-0.814116\pi$
$359$	−5.25130e11			−1.66856			−0.834280	+	0.551341i	$0.814116\pi$
$360$			2.75834e10i			0.0865540i
$361$	−1.38024e11			−0.427731
$362$			2.31120e11i			0.707373i
$363$			2.73154e11i			0.825709i
$364$			2.97137e10i			0.0887157i
$365$	−1.33789e9			−0.00394551
$366$	−8.89677e11			−2.59160
$367$		−	9.23982e10i		−	0.265868i	−0.991125	−	0.132934i	$-0.957560\pi$
$367$		−	9.23982e10i		−	0.265868i	0.991125	−	0.132934i	$-0.0424399\pi$
$368$			1.11999e11i			0.318345i
$369$			3.48637e11i			0.978936i
$370$	−4.03929e10			−0.112046
$371$			4.90975e10i			0.134548i
$372$	3.04176e11			0.823533
$373$	1.27208e11			0.340272			0.170136	−	0.985421i	$-0.445579\pi$
$373$	1.27208e11			0.340272			0.170136	+	0.985421i	$0.445579\pi$
$374$	−2.57553e11	+	1.55492e11i	−0.680682	+	0.410947i
$375$	−8.46085e10			−0.220940
$376$	1.03015e11			0.265801
$377$		−	7.04185e10i		−	0.179536i
$378$	9.12363e10			0.229855
$379$		−	4.08652e11i		−	1.01737i	−0.860954	−	0.508683i	$-0.830132\pi$
$379$		−	4.08652e11i		−	1.01737i	0.860954	−	0.508683i	$-0.169868\pi$
$380$			6.41282e9i			0.0157769i
$381$			9.47223e11i			2.30298i
$382$	−5.43697e10			−0.130639
$383$	2.61140e11			0.620123			0.310062	−	0.950716i	$-0.399650\pi$
$383$	2.61140e11			0.620123			0.310062	+	0.950716i	$0.399650\pi$
$384$			8.23829e11i			1.93351i
$385$		−	4.52133e9i		−	0.0104880i
$386$			1.31878e11i			0.302364i
$387$	7.55955e11			1.71316
$388$		−	1.61702e11i		−	0.362221i
$389$	−3.51283e11			−0.777829			−0.388914	−	0.921274i	$-0.627150\pi$
$389$	−3.51283e11			−0.777829			−0.388914	+	0.921274i	$0.627150\pi$
$390$	−7.76789e10			−0.170025
$391$	1.04017e11	−	6.27977e10i	0.225064	−	0.135878i
$392$	−3.54536e11			−0.758355
$393$	3.29461e11			0.696686
$394$		−	4.79033e11i		−	1.00146i
$395$	5.45004e10			0.112645
$396$		−	1.62350e11i		−	0.331760i
$397$			4.17307e11i			0.843137i	0.906797	+	0.421569i	$0.138520\pi$
$397$			4.17307e11i			0.843137i	−0.906797	+	0.421569i	$0.861480\pi$
$398$		−	3.54291e11i		−	0.707760i
$399$	−1.34075e11			−0.264831
$400$	−6.17026e11			−1.20513
$401$			4.93060e11i			0.952248i	0.879378	+	0.476124i	$0.157959\pi$
$401$			4.93060e11i			0.952248i	−0.879378	+	0.476124i	$0.842041\pi$
$402$		−	1.41865e12i		−	2.70931i
$403$		−	1.20965e12i		−	2.28447i
$404$	4.60585e9			0.00860189
$405$		−	3.49711e9i		−	0.00645895i
$406$	1.81856e10			0.0332171
$407$	−5.48842e11			−0.991454
$408$	6.12284e11	−	3.69653e11i	1.09391	−	0.660425i
$409$	2.79374e11			0.493663			0.246831	−	0.969058i	$-0.420611\pi$
$409$	2.79374e11			0.493663			0.246831	+	0.969058i	$0.420611\pi$
$410$	2.79969e10			0.0489308
$411$		−	9.31857e11i		−	1.61087i
$412$	2.48410e11			0.424748
$413$			6.97649e10i			0.117995i
$414$			2.82500e11i			0.472626i
$415$		−	5.48132e10i		−	0.0907129i
$416$	−4.81272e11			−0.787900
$417$	3.92291e11			0.635325
$418$			3.75424e11i			0.601491i
$419$		−	4.89354e10i		−	0.0775640i	−0.999248	−	0.0387820i	$-0.987652\pi$
$419$		−	4.89354e10i		−	0.0775640i	0.999248	−	0.0387820i	$-0.0123478\pi$
$420$		−	4.65601e9i		−	0.00730117i
$421$	9.73572e11			1.51042			0.755211	−	0.655481i	$-0.227534\pi$
$421$	9.73572e11			1.51042			0.755211	+	0.655481i	$0.227534\pi$
$422$		−	1.58036e11i		−	0.242577i
$423$	3.46274e11			0.525882
$424$	−3.26829e11			−0.491105
$425$	3.45966e11	+	5.73050e11i	0.514380	+	0.852006i
$426$	2.20169e12			3.23902
$427$	−2.12070e11			−0.308712
$428$			3.64412e11i			0.524923i
$429$	−1.05547e12			−1.50449
$430$		−	6.07061e10i		−	0.0856296i
$431$			3.60887e11i			0.503760i	0.967758	+	0.251880i	$0.0810489\pi$
$431$			3.60887e11i			0.503760i	−0.967758	+	0.251880i	$0.918951\pi$
$432$			8.09356e11i			1.11805i
$433$	−1.32088e12			−1.80579			−0.902895	−	0.429862i	$-0.858562\pi$
$433$	−1.32088e12			−1.80579			−0.902895	+	0.429862i	$0.858562\pi$
$434$	3.12393e11			0.422666
$435$			1.10343e10i			0.0147755i
$436$		−	2.61352e11i		−	0.346367i
$437$		−	1.51621e11i		−	0.198880i
$438$	−8.06570e10			−0.104715
$439$		−	4.29288e11i		−	0.551643i	−0.961209	−	0.275822i	$-0.911050\pi$
$439$		−	4.29288e11i		−	0.551643i	0.961209	−	0.275822i	$-0.0889499\pi$
$440$	3.00973e10			0.0382816
$441$	−1.19173e12			−1.50039
$442$	6.36781e11	+	1.05475e12i	0.793579	+	1.31446i
$443$	−9.88207e11			−1.21908			−0.609538	−	0.792757i	$-0.708645\pi$
$443$	−9.88207e11			−1.21908			−0.609538	+	0.792757i	$0.708645\pi$
$444$	−5.65191e11			−0.690195
$445$			2.51877e10i			0.0304487i
$446$	−1.62993e11			−0.195057
$447$			1.08120e12i			1.28092i
$448$			1.00932e11i			0.118379i
$449$		−	5.27610e11i		−	0.612639i	−0.951929	−	0.306319i	$-0.900902\pi$
$449$		−	5.27610e11i		−	0.612639i	0.951929	−	0.306319i	$-0.0990975\pi$
$450$	−1.55636e12			−1.78918
$451$	3.80410e11			0.432970
$452$			3.70877e11i			0.417933i
$453$			2.76380e11i			0.308365i
$454$			1.40219e12i			1.54902i
$455$	−1.85161e10			−0.0202534
$456$		−	8.92501e11i		−	0.966645i
$457$	1.13024e11			0.121213			0.0606064	−	0.998162i	$-0.480697\pi$
$457$	1.13024e11			0.121213			0.0606064	+	0.998162i	$0.480697\pi$
$458$	−2.67901e11			−0.284498
$459$	7.51673e11	−	4.53806e11i	0.790446	−	0.477214i
$460$	5.26532e9			0.00548295
$461$	1.11660e12			1.15145			0.575725	−	0.817643i	$-0.304720\pi$
$461$	1.11660e12			1.15145			0.575725	+	0.817643i	$0.304720\pi$
$462$		−	2.72576e11i		−	0.278355i
$463$	−3.92248e11			−0.396685			−0.198343	−	0.980133i	$-0.563556\pi$
$463$	−3.92248e11			−0.396685			−0.198343	+	0.980133i	$0.563556\pi$
$464$			1.61325e11i			0.161573i
$465$			1.89547e11i			0.188009i
$466$		−	1.53162e12i		−	1.50458i
$467$	1.59510e11			0.155189			0.0775946	−	0.996985i	$-0.475276\pi$
$467$	1.59510e11			0.155189			0.0775946	+	0.996985i	$0.475276\pi$
$468$	−6.64868e11			−0.640662
$469$		−	3.38160e11i		−	0.322734i
$470$		−	2.78071e10i		−	0.0262855i
$471$			3.88724e11i			0.363955i
$472$	−4.64406e11			−0.430684
$473$		−	8.24850e11i		−	0.757705i
$474$	3.28565e12			2.98964
$475$	8.35312e11			0.752883
$476$	−6.32209e10	+	3.81682e10i	−0.0564455	+	0.0340777i
$477$	−1.09860e12			−0.971640
$478$	−1.69684e12			−1.48668
$479$			4.37040e11i			0.379325i	0.981849	+	0.189662i	$0.0607393\pi$
$479$			4.37040e11i			0.379325i	−0.981849	+	0.189662i	$0.939261\pi$
$480$	7.54134e10			0.0648429
$481$			2.24766e12i			1.91460i
$482$		−	5.24099e11i		−	0.442284i
$483$			1.10084e11i			0.0920367i
$484$	1.87748e11			0.155515
$485$	1.00765e11			0.0826933
$486$		−	1.50672e12i		−	1.22509i
$487$			1.05048e12i			0.846270i	0.906067	+	0.423135i	$0.139070\pi$
$487$			1.05048e12i			0.846270i	−0.906067	+	0.423135i	$0.860930\pi$
$488$		−	1.41169e12i		−	1.12681i
$489$	5.12097e11			0.405007
$490$			9.57004e10i			0.0749948i
$491$	1.77945e12			1.38172			0.690859	−	0.722990i	$-0.257233\pi$
$491$	1.77945e12			1.38172			0.690859	+	0.722990i	$0.257233\pi$
$492$	3.91742e11			0.301410
$493$	1.49827e11	−	9.04548e10i	0.114230	−	0.0689637i
$494$	1.53746e12			1.16154
$495$	1.01168e11			0.0757393
$496$			2.77123e12i			2.05592i
$497$	5.24810e11			0.385832
$498$		−	3.30451e12i		−	2.40755i
$499$		−	1.14978e12i		−	0.830162i	−0.909785	−	0.415081i	$-0.863753\pi$
$499$		−	1.14978e12i		−	0.830162i	0.909785	−	0.415081i	$-0.136247\pi$
$500$			5.81544e10i			0.0416119i
$501$	−3.21026e12			−2.27651
$502$	−2.25074e12			−1.58183
$503$		−	1.33344e12i		−	0.928788i	−0.885629	−	0.464394i	$-0.846272\pi$
$503$		−	1.33344e12i		−	0.928788i	0.885629	−	0.464394i	$-0.153728\pi$
$504$			3.96383e11i			0.273639i
$505$			2.87013e9i			0.00196377i
$506$	3.08247e11			0.209036
$507$			1.93487e12i			1.30052i
$508$	6.51059e11			0.433744
$509$	−2.18589e12			−1.44344			−0.721721	−	0.692185i	$-0.756648\pi$
$509$	−2.18589e12			−1.44344			−0.721721	+	0.692185i	$0.756648\pi$
$510$	−9.97809e10	−	1.65275e11i	−0.0653103	−	0.108178i
$511$	−1.92259e10			−0.0124737
$512$	−3.96666e11			−0.255100
$513$		−	1.09568e12i		−	0.698484i
$514$	−3.10647e11			−0.196306
$515$			1.54797e11i			0.0969681i
$516$		−	8.49421e11i		−	0.527472i
$517$		−	3.77832e11i		−	0.232590i
$518$	−5.80459e11			−0.354232
$519$	1.55969e12			0.943592
$520$		−	1.23256e11i		−	0.0739256i
$521$			9.81356e11i			0.583521i	0.956491	+	0.291761i	$0.0942411\pi$
$521$			9.81356e11i			0.583521i	−0.956491	+	0.291761i	$0.905759\pi$
$522$			4.06918e11i			0.239878i
$523$	1.01562e11			0.0593572			0.0296786	−	0.999559i	$-0.490552\pi$
$523$	1.01562e11			0.0593572			0.0296786	+	0.999559i	$0.490552\pi$
$524$		−	2.26450e11i		−	0.131214i
$525$	−6.06476e11			−0.348415
$526$	9.07277e11			0.516778
$527$	2.57373e12	−	1.55383e12i	1.45350	−	0.877518i
$528$	2.41802e12			1.35396
$529$	1.67666e12			0.930883
$530$			8.82214e10i			0.0485660i
$531$	−1.56105e12			−0.852099
$532$			9.21544e10i			0.0498785i
$533$		−	1.55788e12i		−	0.836107i
$534$			1.51848e12i			0.808117i
$535$	−2.27083e11			−0.119837
$536$	2.25104e12			1.17799
$537$			2.98768e12i			1.55042i
$538$			2.14333e12i			1.10298i
$539$			1.30034e12i			0.663601i
$540$	3.80497e10			0.0192566
$541$			2.29392e12i			1.15131i	0.817694	+	0.575653i	$0.195252\pi$
$541$			2.29392e12i			1.15131i	−0.817694	+	0.575653i	$0.804748\pi$
$542$	−1.43948e12			−0.716487
$543$	−2.01521e12			−0.994765
$544$	−6.18209e11	−	1.02399e12i	−0.302650	−	0.501302i
$545$	1.62861e11			0.0790739
$546$	−1.11627e12			−0.537531
$547$			4.31625e10i			0.0206140i	0.999947	+	0.0103070i	$0.00328088\pi$
$547$			4.31625e10i			0.0206140i	−0.999947	+	0.0103070i	$0.996719\pi$
$548$	−6.40498e11			−0.303393
$549$		−	4.74522e12i		−	2.22937i
$550$			1.69820e12i			0.791328i
$551$		−	2.18397e11i		−	0.100940i
$552$	−7.32798e11			−0.335938
$553$	7.83189e11			0.356126
$554$		−	4.77618e12i		−	2.15420i
$555$		−	3.52198e11i		−	0.157568i
$556$		−	2.69635e11i		−	0.119658i
$557$	−1.26017e12			−0.554730			−0.277365	−	0.960765i	$-0.589461\pi$
$557$	−1.26017e12			−0.554730			−0.277365	+	0.960765i	$0.589461\pi$
$558$			6.99003e12i			3.05229i
$559$	−3.37798e12			−1.46320
$560$	4.24192e10			0.0182271
$561$	−1.35578e12	−	2.24569e12i	−0.577907	−	0.957231i
$562$	−3.50716e12			−1.48300
$563$	1.57680e12			0.661436			0.330718	−	0.943730i	$-0.392709\pi$
$563$	1.57680e12			0.661436			0.330718	+	0.943730i	$0.392709\pi$
$564$		−	3.89087e11i		−	0.161916i
$565$	−2.31111e11			−0.0954121
$566$			1.51311e12i			0.619721i
$567$		−	5.02547e10i		−	0.0204199i
$568$			3.49352e12i			1.40830i
$569$	4.44023e12			1.77583			0.887913	−	0.460012i	$-0.152155\pi$
$569$	4.44023e12			1.77583			0.887913	+	0.460012i	$0.152155\pi$
$570$	−2.40914e11			−0.0955928
$571$			2.59026e11i			0.101972i	0.998699	+	0.0509860i	$0.0162364\pi$
$571$			2.59026e11i			0.101972i	−0.998699	+	0.0509860i	$0.983764\pi$
$572$			7.25461e11i			0.283356i
$573$		−	4.74067e11i		−	0.183715i
$574$	4.02324e11			0.154694
$575$		−	6.85842e11i		−	0.261649i
$576$	−2.25842e12			−0.854878
$577$	2.66713e12			1.00173			0.500867	−	0.865524i	$-0.333015\pi$
$577$	2.66713e12			1.00173			0.500867	+	0.865524i	$0.333015\pi$
$578$	−1.42619e12	+	2.70972e12i	−0.531498	+	1.00983i
$579$	−1.14989e12			−0.425209
$580$	7.58425e9			0.00278283
$581$		−	7.87685e11i		−	0.286787i
$582$	6.07477e12			2.19471
$583$			1.19872e12i			0.429743i
$584$		−	1.27982e11i		−	0.0455293i
$585$		−	4.14312e11i		−	0.146260i
$586$	−1.41562e12			−0.495915
$587$	−4.82084e12			−1.67591			−0.837956	−	0.545738i	$-0.816249\pi$
$587$	−4.82084e12			−1.67591			−0.837956	+	0.545738i	$0.816249\pi$
$588$			1.33907e12i			0.461962i
$589$		−	3.75162e12i		−	1.28440i
$590$			1.25358e11i			0.0425910i
$591$	4.17684e12			1.40833
$592$		−	5.14925e12i		−	1.72304i
$593$	2.49924e12			0.829968			0.414984	−	0.909829i	$-0.363787\pi$
$593$	2.49924e12			0.829968			0.414984	+	0.909829i	$0.363787\pi$
$594$	2.22754e12			0.734152
$595$	−2.37845e10	−	3.93960e10i	−0.00777977	−	0.0128862i
$596$	7.43145e11			0.241249
$597$	3.08918e12			0.995310
$598$		−	1.26235e12i		−	0.403669i
$599$	−3.23334e12			−1.02620			−0.513098	−	0.858330i	$-0.671502\pi$
$599$	−3.23334e12			−1.02620			−0.513098	+	0.858330i	$0.671502\pi$
$600$		−	4.03715e12i		−	1.27173i
$601$		−	5.50244e12i		−	1.72036i	−0.509988	−	0.860181i	$-0.670350\pi$
$601$		−	5.50244e12i		−	1.72036i	0.509988	−	0.860181i	$-0.329650\pi$
$602$		−	8.72367e11i		−	0.270717i
$603$	7.56660e12			2.33063
$604$	1.89966e11			0.0580776
$605$			1.16995e11i			0.0355032i
$606$			1.73031e11i			0.0521191i
$607$			3.65674e12i			1.09331i	0.837357	+	0.546657i	$0.184100\pi$
$607$			3.65674e12i			1.09331i	−0.837357	+	0.546657i	$0.815900\pi$
$608$	−1.49262e12			−0.442980
$609$			1.58566e11i			0.0467125i
$610$	−3.81060e11			−0.111432
$611$	−1.54732e12			−0.449155
$612$	−8.54043e11	−	1.41462e12i	−0.246093	−	0.407622i
$613$	1.17726e12			0.336743			0.168372	−	0.985724i	$-0.446149\pi$
$613$	1.17726e12			0.336743			0.168372	+	0.985724i	$0.446149\pi$
$614$	−4.85586e12			−1.37882
$615$			2.44114e11i			0.0688104i
$616$	4.32508e11			0.121027
$617$			3.74523e12i			1.04039i	0.854048	+	0.520194i	$0.174141\pi$
$617$			3.74523e12i			1.04039i	−0.854048	+	0.520194i	$0.825859\pi$
$618$			9.33217e12i			2.57356i
$619$		−	6.72874e12i		−	1.84215i	−0.389381	−	0.921077i	$-0.627311\pi$
$619$		−	6.72874e12i		−	1.84215i	0.389381	−	0.921077i	$-0.372689\pi$
$620$	1.30282e11			0.0354097
$621$	−8.99623e11			−0.242744
$622$		−	4.69221e12i		−	1.25696i
$623$			3.61956e11i			0.0962631i
$624$		−	9.90244e12i		−	2.61464i
$625$	3.76030e12			0.985739
$626$		−	5.72073e12i		−	1.48891i
$627$	−3.27345e12			−0.845865
$628$	2.67184e11			0.0685475
$629$	−4.78226e12	+	2.88718e12i	−1.21816	+	0.735439i
$630$	1.06996e11			0.0270605
$631$	−4.61439e12			−1.15873			−0.579365	−	0.815068i	$-0.696700\pi$
$631$	−4.61439e12			−1.15873			−0.579365	+	0.815068i	$0.696700\pi$
$632$			5.21348e12i			1.29987i
$633$	1.37797e12			0.341131
$634$			6.89024e12i			1.69369i
$635$			4.05707e11i			0.0990218i
$636$			1.23443e12i			0.299163i
$637$	5.32524e12			1.28148
$638$	4.44003e11			0.106095
$639$			1.17430e13i			2.78629i
$640$			3.52856e11i			0.0831357i
$641$			7.42031e12i			1.73605i	0.496524	+	0.868023i	$0.334609\pi$
$641$			7.42031e12i			1.73605i	−0.496524	+	0.868023i	$0.665391\pi$
$642$	−1.36901e13			−3.18052
$643$		−	6.05336e12i		−	1.39652i	−0.715845	−	0.698260i	$-0.753958\pi$
$643$		−	6.05336e12i		−	1.39652i	0.715845	−	0.698260i	$-0.246042\pi$
$644$	7.56644e10			0.0173343
$645$	5.29316e11			0.120419
$646$	1.97492e12	+	3.27121e12i	0.446173	+	0.739030i
$647$	−4.28077e12			−0.960402			−0.480201	−	0.877159i	$-0.659436\pi$
$647$	−4.28077e12			−0.960402			−0.480201	+	0.877159i	$0.659436\pi$
$648$	3.34532e11			0.0745333
$649$			1.70331e12i			0.376872i
$650$	6.95458e12			1.52813
$651$			2.72385e12i			0.594387i
$652$		−	3.51983e11i		−	0.0762793i
$653$			2.02322e12i			0.435445i	0.976011	+	0.217723i	$0.0698629\pi$
$653$			2.02322e12i			0.435445i	−0.976011	+	0.217723i	$0.930137\pi$
$654$	9.81835e12			2.09864
$655$	1.41112e11			0.0299556
$656$			3.56902e12i			0.752457i
$657$		−	4.30196e11i		−	0.0900787i
$658$		−	3.99598e11i		−	0.0831011i
$659$	−2.09148e12			−0.431985			−0.215993	−	0.976395i	$-0.569299\pi$
$659$	−2.09148e12			−0.431985			−0.215993	+	0.976395i	$0.569299\pi$
$660$		−	1.13677e11i		−	0.0233198i
$661$	−3.66578e12			−0.746895			−0.373448	−	0.927651i	$-0.621824\pi$
$661$	−3.66578e12			−0.746895			−0.373448	+	0.927651i	$0.621824\pi$
$662$	8.94136e12			1.80943
$663$	−9.19669e12	+	5.55230e12i	−1.84851	+	1.11599i
$664$	5.24341e12			1.04678
$665$	−5.74259e10			−0.0113870
$666$		−	1.29882e13i		−	2.55809i
$667$	−1.79317e11			−0.0350797
$668$			2.20652e12i			0.428760i
$669$		−	1.42118e12i		−	0.274305i
$670$		−	6.07626e11i		−	0.116493i
$671$	−5.17769e12			−0.986017
$672$	1.08372e12			0.205000
$673$		−	4.12814e12i		−	0.775686i	−0.921725	−	0.387843i	$-0.873220\pi$
$673$		−	4.12814e12i		−	0.775686i	0.921725	−	0.387843i	$-0.126780\pi$
$674$		−	5.53716e12i		−	1.03352i
$675$		−	4.95622e12i		−	0.918933i
$676$	1.32990e12			0.244940
$677$		−	3.86753e12i		−	0.707594i	−0.935322	−	0.353797i	$-0.884890\pi$
$677$		−	3.86753e12i		−	0.707594i	0.935322	−	0.353797i	$-0.115110\pi$
$678$	−1.39329e13			−2.53226
$679$	1.44802e12			0.261434
$680$	2.62249e11	−	1.58327e11i	0.0470352	−	0.0283965i
$681$	−1.22262e13			−2.17835
$682$	7.62708e12			1.34998
$683$			6.60671e12i			1.16170i	0.814012	+	0.580848i	$0.197279\pi$
$683$			6.60671e12i			1.16170i	−0.814012	+	0.580848i	$0.802721\pi$
$684$	−2.06203e12			−0.360199
$685$		−	3.99126e11i		−	0.0692631i
$686$			2.81921e12i			0.486037i
$687$		−	2.33591e12i		−	0.400084i
$688$	7.73876e12			1.31681
$689$	4.90907e12			0.829875
$690$			1.97805e11i			0.0332213i
$691$		−	8.12202e12i		−	1.35523i	−0.735417	−	0.677615i	$-0.763014\pi$
$691$		−	8.12202e12i		−	1.35523i	0.735417	−	0.677615i	$-0.236986\pi$
$692$		−	1.07203e12i		−	0.177717i
$693$	1.45382e12			0.239449
$694$		−	5.82726e12i		−	0.953557i
$695$	1.68023e11			0.0273172
$696$	−1.05553e12			−0.170503
$697$	3.31465e12	−	2.00115e12i	0.531974	−	0.321168i
$698$	−8.08755e11			−0.128964
$699$	1.33547e13			2.11586
$700$			4.16852e11i			0.0656207i
$701$	6.09018e12			0.952574			0.476287	−	0.879290i	$-0.341982\pi$
$701$	6.09018e12			0.952574			0.476287	+	0.879290i	$0.341982\pi$
$702$		−	9.12236e12i		−	1.41772i
$703$			6.97091e12i			1.07644i
$704$			2.46425e12i			0.378101i
$705$	2.42459e11			0.0369647
$706$	4.31358e12			0.653457
$707$			4.12448e10i			0.00620843i
$708$			1.75405e12i			0.262357i
$709$			1.24847e12i			0.185553i	0.995687	+	0.0927767i	$0.0295743\pi$
$709$			1.24847e12i			0.185553i	−0.995687	+	0.0927767i	$0.970426\pi$
$710$	9.43011e11			0.139269
$711$			1.75245e13i			2.57177i
$712$	−2.40944e12			−0.351364
$713$	−3.08031e12			−0.446366
$714$	−1.43389e12	−	2.37505e12i	−0.206478	−	0.342004i
$715$	−4.52071e11			−0.0646888
$716$	2.05354e12			0.292007
$717$		−	1.47953e13i		−	2.09068i
$718$	−1.35596e13			−1.90409
$719$			4.85534e12i			0.677547i	0.940868	+	0.338774i	$0.110012\pi$
$719$			4.85534e12i			0.677547i	−0.940868	+	0.338774i	$0.889988\pi$
$720$			9.49164e11i			0.131627i
$721$			2.22448e12i			0.306563i
$722$	−3.56398e12			−0.488110
$723$	4.56979e12			0.621976
$724$			1.38512e12i			0.187355i
$725$		−	9.87898e11i		−	0.132798i
$726$			7.05324e12i			0.942267i
$727$	3.36183e12			0.446345			0.223173	−	0.974779i	$-0.428359\pi$
$727$	3.36183e12			0.446345			0.223173	+	0.974779i	$0.428359\pi$
$728$		−	1.77124e12i		−	0.233715i
$729$	1.24237e13			1.62921
$730$	−3.45464e10			−0.00450246
$731$	−4.33912e12	−	7.18722e12i	−0.562049	−	0.930964i
$732$	−5.33192e12			−0.686410
$733$	−1.02897e13			−1.31654			−0.658271	−	0.752781i	$-0.728712\pi$
$733$	−1.02897e13			−1.31654			−0.658271	+	0.752781i	$0.728712\pi$
$734$		−	2.38586e12i		−	0.303398i
$735$	−8.34442e11			−0.105464
$736$			1.22554e12i			0.153949i
$737$		−	8.25619e12i		−	1.03080i
$738$			9.00233e12i			1.11712i
$739$	−1.10714e12			−0.136553			−0.0682766	−	0.997666i	$-0.521750\pi$
$739$	−1.10714e12			−0.136553			−0.0682766	+	0.997666i	$0.521750\pi$
$740$	−2.42078e11			−0.0296765
$741$			1.34056e13i			1.63345i
$742$			1.26777e12i			0.153541i
$743$		−	5.80468e12i		−	0.698761i	−0.936981	−	0.349380i	$-0.886392\pi$
$743$		−	5.80468e12i		−	0.698761i	0.936981	−	0.349380i	$-0.113608\pi$
$744$	−1.81320e13			−2.16953
$745$			4.63090e11i			0.0550760i
$746$	3.28471e12			0.388305
$747$	1.76251e13			2.07104
$748$	−1.54354e12	+	9.31878e11i	−0.180285	+	0.108843i
$749$	−3.26326e12			−0.378864
$750$	−2.18472e12			−0.252128
$751$			8.01566e12i			0.919517i	0.888044	+	0.459758i	$0.152064\pi$
$751$			8.01566e12i			0.919517i	−0.888044	+	0.459758i	$0.847936\pi$
$752$	3.54483e12			0.404218
$753$		−	1.96249e13i		−	2.22449i
$754$		−	1.81831e12i		−	0.204879i
$755$			1.18377e11i			0.0132588i
$756$	5.46788e11			0.0608794
$757$	−4.40521e12			−0.487568			−0.243784	−	0.969829i	$-0.578389\pi$
$757$	−4.40521e12			−0.487568			−0.243784	+	0.969829i	$0.578389\pi$
$758$		−	1.05520e13i		−	1.16098i
$759$			2.68770e12i			0.293963i
$760$		−	3.82269e11i		−	0.0415631i
$761$	−1.23860e13			−1.33875			−0.669377	−	0.742923i	$-0.733439\pi$
$761$	−1.23860e13			−1.33875			−0.669377	+	0.742923i	$0.733439\pi$
$762$			2.44587e13i			2.62807i
$763$	2.34037e12			0.249991
$764$	−3.25843e11			−0.0346009
$765$	8.81517e11	−	5.32196e11i	0.0930581	−	0.0561818i
$766$	6.74302e12			0.707660
$767$	6.97553e12			0.727776
$768$			1.28766e13i			1.33560i
$769$	−1.34212e13			−1.38396			−0.691978	−	0.721919i	$-0.743260\pi$
$769$	−1.34212e13			−1.38396			−0.691978	+	0.721919i	$0.743260\pi$
$770$		−	1.16748e11i		−	0.0119685i
$771$		−	2.70863e12i		−	0.276061i
$772$			7.90359e11i			0.0800842i
$773$	3.10743e12			0.313036			0.156518	−	0.987675i	$-0.449973\pi$
$773$	3.10743e12			0.313036			0.156518	+	0.987675i	$0.449973\pi$
$774$	1.95199e13			1.95499
$775$		−	1.69701e13i		−	1.68977i
$776$			9.63910e12i			0.954243i
$777$		−	5.06121e12i		−	0.498150i
$778$	−9.07066e12			−0.887628
$779$		−	4.83163e12i		−	0.470084i
$780$	−4.65537e11			−0.0450327
$781$	1.28133e13			1.23234
$782$	2.68586e12	−	1.62153e12i	0.256835	−	0.155058i
$783$	−1.29583e12			−0.123203
$784$	−1.21998e13			−1.15327
$785$			1.66495e11i			0.0156491i
$786$	8.50718e12			0.795031
$787$			4.60263e12i			0.427681i	0.976869	+	0.213840i	$0.0685973\pi$
$787$			4.60263e12i			0.427681i	−0.976869	+	0.213840i	$0.931403\pi$
$788$		−	2.87089e12i		−	0.265246i
$789$			7.91084e12i			0.726735i
$790$	1.40728e12			0.128546
$791$	−3.32115e12			−0.301644
$792$			9.67772e12i			0.873997i
$793$			2.12040e13i			1.90410i
$794$			1.07755e13i			0.962155i
$795$	−7.69231e11			−0.0682975
$796$		−	2.12330e12i		−	0.187457i
$797$	1.39540e13			1.22500			0.612502	−	0.790469i	$-0.290163\pi$
$797$	1.39540e13			1.22500			0.612502	+	0.790469i	$0.290163\pi$
$798$	−3.46202e12			−0.302215
$799$	−1.98759e12	−	3.29219e12i	−0.172530	−	0.285775i
$800$	−6.75175e12			−0.582789
$801$	−8.09906e12			−0.695165
$802$			1.27316e13i			1.08667i
$803$	−4.69402e11			−0.0398405
$804$		−	8.50212e12i		−	0.717588i
$805$			4.71502e10i			0.00395733i
$806$		−	3.12349e13i		−	2.60695i
$807$	−1.86884e13			−1.55110
$808$	−2.74556e11			−0.0226610
$809$		−	2.10896e13i		−	1.73101i	−0.500896	−	0.865507i	$-0.666996\pi$
$809$		−	2.10896e13i		−	1.73101i	0.500896	−	0.865507i	$-0.333004\pi$
$810$		−	9.03008e10i		−	0.00737070i
$811$			3.64082e12i			0.295533i	0.989022	+	0.147766i	$0.0472084\pi$
$811$			3.64082e12i			0.295533i	−0.989022	+	0.147766i	$0.952792\pi$
$812$	1.08988e11			0.00879787
$813$		−	1.25513e13i		−	1.00758i
$814$	−1.41719e13			−1.13141
$815$	2.19338e11			0.0174142
$816$	2.10691e13	−	1.27200e13i	1.66357	−	1.00434i
$817$	−1.04765e13			−0.822655
$818$	7.21385e12			0.563349
$819$		−	5.95380e12i		−	0.462399i
$820$	1.67788e11			0.0129598
$821$			1.79752e13i			1.38080i	0.723429	+	0.690399i	$0.242565\pi$
$821$			1.79752e13i			1.38080i	−0.723429	+	0.690399i	$0.757435\pi$
$822$		−	2.40620e13i		−	1.83826i
$823$		−	4.92718e12i		−	0.374368i	−0.982325	−	0.187184i	$-0.940064\pi$
$823$		−	4.92718e12i		−	0.374368i	0.982325	−	0.187184i	$-0.0599361\pi$
$824$	−1.48078e13			−1.11897
$825$	−1.48071e13			−1.11283
$826$			1.80144e12i			0.134651i
$827$			5.12459e12i			0.380964i	0.981691	+	0.190482i	$0.0610051\pi$
$827$			5.12459e12i			0.380964i	−0.981691	+	0.190482i	$0.938995\pi$
$828$			1.69305e12i			0.125180i
$829$	1.91602e13			1.40898			0.704490	−	0.709714i	$-0.251176\pi$
$829$	1.91602e13			1.40898			0.704490	+	0.709714i	$0.251176\pi$
$830$		−	1.41536e12i		−	0.103518i
$831$	4.16450e13			3.02941
$832$	1.00918e13			0.730149
$833$	6.84043e12	+	1.13303e13i	0.492245	+	0.815342i
$834$	1.01295e13			0.725008
$835$	−1.37499e12			−0.0978839
$836$			2.24995e12i			0.159311i
$837$	−2.22598e13			−1.56768
$838$		−	1.26359e12i		−	0.0885130i
$839$			9.27849e12i			0.646470i	0.946319	+	0.323235i	$0.104770\pi$
$839$			9.27849e12i			0.646470i	−0.946319	+	0.323235i	$0.895230\pi$
$840$			2.77546e11i			0.0192343i
$841$	1.42489e13			0.982196
$842$	2.51391e13			1.72364
$843$		−	3.05800e13i		−	2.08552i
$844$		−	9.47124e11i		−	0.0642489i
$845$			8.28729e11i			0.0559187i
$846$	8.94132e12			0.600116
$847$			1.68126e12i			0.112243i
$848$	−1.12464e13			−0.746848
$849$	−1.31933e13			−0.871501
$850$	8.93338e12	+	1.47970e13i	0.586990	+	0.972276i
$851$	5.72354e12			0.374095
$852$	1.31949e13			0.857886
$853$			1.45073e13i			0.938244i	0.883133	+	0.469122i	$0.155429\pi$
$853$			1.45073e13i			0.938244i	−0.883133	+	0.469122i	$0.844571\pi$
$854$	−5.47596e12			−0.352289
$855$		−	1.28495e12i		−	0.0822317i
$856$		−	2.17226e13i		−	1.38287i
$857$			6.75756e12i			0.427933i	0.976841	+	0.213967i	$0.0686384\pi$
$857$			6.75756e12i			0.427933i	−0.976841	+	0.213967i	$0.931362\pi$
$858$	−2.72538e13			−1.71686
$859$	−6.20315e11			−0.0388726			−0.0194363	−	0.999811i	$-0.506187\pi$
$859$	−6.20315e11			−0.0388726			−0.0194363	+	0.999811i	$0.506187\pi$
$860$		−	3.63817e11i		−	0.0226799i
$861$			3.50800e12i			0.217543i
$862$			9.31866e12i			0.574871i
$863$	1.36639e12			0.0838542			0.0419271	−	0.999121i	$-0.486650\pi$
$863$	1.36639e12			0.0838542			0.0419271	+	0.999121i	$0.486650\pi$
$864$			8.85631e12i			0.540681i
$865$	6.68033e11			0.0405719
$866$	−3.41071e13			−2.06070
$867$	−2.36269e13	−	1.24354e13i	−1.42010	−	0.747435i
$868$	1.87220e12			0.111947
$869$	1.91216e13			1.13746
$870$			2.84922e11i			0.0168612i
$871$	−3.38113e13			−1.99058
$872$			1.55792e13i			0.912476i
$873$			3.24007e13i			1.88795i
$874$		−	3.91507e12i		−	0.226954i
$875$	−5.20765e11			−0.0300335
$876$	−4.83385e11			−0.0277348
$877$			1.47910e13i			0.844304i	0.906525	+	0.422152i	$0.138725\pi$
$877$			1.47910e13i			0.844304i	−0.906525	+	0.422152i	$0.861275\pi$
$878$		−	1.10849e13i		−	0.629514i
$879$		−	1.23432e13i		−	0.697396i
$880$	1.03567e12			0.0582168
$881$			1.90695e12i			0.106647i	0.998577	+	0.0533234i	$0.0169814\pi$
$881$			1.90695e12i			0.106647i	−0.998577	+	0.0533234i	$0.983019\pi$
$882$	−3.07723e13			−1.71218
$883$	9.34392e12			0.517256			0.258628	−	0.965977i	$-0.416730\pi$
$883$	9.34392e12			0.517256			0.258628	+	0.965977i	$0.416730\pi$
$884$	3.81629e12	+	6.32121e12i	0.210187	+	0.348149i
$885$	−1.09304e12			−0.0598949
$886$	−2.55170e13			−1.39116
$887$			6.67058e12i			0.361832i	0.983499	+	0.180916i	$0.0579063\pi$
$887$			6.67058e12i			0.361832i	−0.983499	+	0.180916i	$0.942094\pi$
$888$	3.36911e13			1.81826
$889$			5.83015e12i			0.313056i
$890$			6.50385e11i			0.0347469i
$891$		−	1.22697e12i		−	0.0652206i
$892$	−9.76830e11			−0.0516627
$893$	−4.79889e12			−0.252528
$894$			2.79182e13i			1.46173i
$895$			1.27966e12i			0.0666639i
$896$			5.07066e12i			0.262832i
$897$	1.10069e13			0.567672
$898$		−	1.36237e13i		−	0.699119i
$899$	−4.43692e12			−0.226550
$900$	−9.32740e12			−0.473881
$901$	6.30586e12	+	1.04449e13i	0.318774	+	0.528009i
$902$	9.82277e12			0.494088
$903$	7.60645e12			0.380704
$904$		−	2.21080e13i		−	1.10101i
$905$	−8.63138e11			−0.0427722
$906$			7.13655e12i			0.351893i
$907$			2.25953e13i			1.10863i	0.832308	+	0.554313i	$0.187019\pi$
$907$			2.25953e13i			1.10863i	−0.832308	+	0.554313i	$0.812981\pi$
$908$			8.40347e12i			0.410272i
$909$	−9.22885e11			−0.0448343
$910$	−4.78113e11			−0.0231124
$911$			2.70620e13i			1.30175i	0.759186	+	0.650873i	$0.225597\pi$
$911$			2.70620e13i			1.30175i	−0.759186	+	0.650873i	$0.774403\pi$
$912$		−	3.07115e13i		−	1.47003i
$913$		−	1.92314e13i		−	0.915992i
$914$	2.91846e12			0.138323
$915$		−	3.32258e12i		−	0.156704i
$916$	−1.60555e12			−0.0753521
$917$	2.02783e12			0.0947042
$918$	1.94093e13	−	1.17180e13i	0.902026	−	0.544578i
$919$	1.59897e13			0.739468			0.369734	−	0.929138i	$-0.379449\pi$
$919$	1.59897e13			0.739468			0.369734	+	0.929138i	$0.379449\pi$
$920$	−3.13866e11			−0.0144444
$921$		−	4.23398e13i		−	1.93901i
$922$	2.88324e13			1.31399
$923$		−	5.24738e13i		−	2.37977i
$924$		−	1.63357e12i		−	0.0737250i
$925$			3.15323e13i			1.41618i
$926$	−1.01284e13			−0.452682
$927$	−4.97745e13			−2.21385
$928$			1.76528e12i			0.0781354i
$929$			9.00625e12i			0.396710i	0.980130	+	0.198355i	$0.0635599\pi$
$929$			9.00625e12i			0.396710i	−0.980130	+	0.198355i	$0.936440\pi$
$930$			4.89438e12i			0.214548i
$931$	1.65157e13			0.720485
$932$		−	9.17916e12i		−	0.398503i
$933$	4.09129e13			1.76764
$934$	4.11879e12			0.177096
$935$	−5.80699e11	−	9.61855e11i	−0.0248484	−	0.0411583i
$936$	3.96329e13			1.68777
$937$	−4.00157e13			−1.69591			−0.847954	−	0.530071i	$-0.822165\pi$
$937$	−4.00157e13			−1.69591			−0.847954	+	0.530071i	$0.822165\pi$
$938$		−	8.73180e12i		−	0.368291i
$939$	4.98809e13			2.09382
$940$		−	1.66651e11i		−	0.00696196i
$941$		−	2.42260e13i		−	1.00723i	−0.863928	−	0.503615i	$-0.832003\pi$
$941$		−	2.42260e13i		−	1.00723i	0.863928	−	0.503615i	$-0.167997\pi$
$942$			1.00374e13i			0.415331i
$943$	−3.96707e12			−0.163368
$944$	−1.59805e13			−0.654964
$945$			3.40730e11i			0.0138985i
$946$		−	2.12989e13i		−	0.864663i
$947$		−	3.52100e13i		−	1.42263i	−0.702875	−	0.711313i	$-0.748101\pi$
$947$		−	3.52100e13i		−	1.42263i	0.702875	−	0.711313i	$-0.251899\pi$
$948$	1.96912e13			0.791835
$949$			1.92233e12i			0.0769360i
$950$	2.15690e13			0.859160
$951$	−6.00782e13			−2.38180
$952$	3.76860e12	−	2.27521e12i	0.148701	−	0.0897750i
$953$	9.99226e12			0.392415			0.196208	−	0.980562i	$-0.437137\pi$
$953$	9.99226e12			0.392415			0.196208	+	0.980562i	$0.437137\pi$
$954$	−2.83674e13			−1.10880
$955$		−	2.03049e11i		−	0.00789923i
$956$	−1.01693e13			−0.393761
$957$			3.87141e12i			0.149199i
$958$			1.12850e13i			0.432870i
$959$		−	5.73557e12i		−	0.218974i
$960$	−1.58134e12			−0.0600902
$961$	−4.97778e13			−1.88270
$962$			5.80379e13i			2.18486i
$963$		−	7.30180e13i		−	2.73597i
$964$		−	3.14097e12i		−	0.117143i
$965$	−4.92511e11			−0.0182828
$966$			2.84253e12i			0.105029i
$967$	3.17277e12			0.116686			0.0583431	−	0.998297i	$-0.481418\pi$
$967$	3.17277e12			0.116686			0.0583431	+	0.998297i	$0.481418\pi$
$968$	−1.11917e13			−0.409691
$969$	−2.85227e13	+	1.72200e13i	−1.03928	+	0.627444i
$970$	2.60190e12			0.0943664
$971$	2.55138e13			0.921061			0.460531	−	0.887644i	$-0.347659\pi$
$971$	2.55138e13			0.921061			0.460531	+	0.887644i	$0.347659\pi$
$972$		−	9.02989e12i		−	0.324477i
$973$	2.41455e12			0.0863630
$974$			2.71251e13i			0.965730i
$975$			6.06392e13i			2.14898i
$976$		−	4.85772e13i		−	1.71359i
$977$	−4.02976e12			−0.141499			−0.0707496	−	0.997494i	$-0.522539\pi$
$977$	−4.02976e12			−0.141499			−0.0707496	+	0.997494i	$0.522539\pi$
$978$	1.32231e13			0.462178
$979$			8.83718e12i			0.307462i
$980$			5.73541e11i			0.0198631i
$981$			5.23676e13i			1.80531i
$982$	4.59481e13			1.57676
$983$			9.84380e12i			0.336258i	0.985765	+	0.168129i	$0.0537724\pi$
$983$			9.84380e12i			0.336258i	−0.985765	+	0.168129i	$0.946228\pi$
$984$	−2.33518e13			−0.794040
$985$	1.78899e12			0.0605544
$986$	3.86876e12	−	2.33568e12i	0.130354	−	0.0786986i
$987$	3.48422e12			0.116863
$988$	9.21417e12			0.307645
$989$			8.60186e12i			0.285897i
$990$	2.61232e12			0.0864307
$991$			7.10324e12i			0.233951i	0.993135	+	0.116976i	$0.0373199\pi$
$991$			7.10324e12i			0.233951i	−0.993135	+	0.116976i	$0.962680\pi$
$992$			3.03240e13i			0.994222i
$993$			7.79626e13i			2.54457i
$994$	1.35514e13			0.440297
$995$	1.32313e12			0.0427956
$996$		−	1.98042e13i		−	0.637663i
$997$			3.04471e13i			0.975928i	0.872864	+	0.487964i	$0.162260\pi$
$997$			3.04471e13i			0.975928i	−0.872864	+	0.487964i	$0.837740\pi$
$998$		−	2.96891e13i		−	0.947348i
$999$	4.13611e13			1.31385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.b.a.16.10	yes	12
3.2	odd	2		153.10.d.b.118.3		12
4.3	odd	2		272.10.b.c.33.1		12
17.4	even	4		289.10.a.c.1.4		12
17.13	even	4		289.10.a.c.1.3		12
17.16	even	2	inner	17.10.b.a.16.9	✓	12
51.50	odd	2		153.10.d.b.118.4		12
68.67	odd	2		272.10.b.c.33.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.9	✓	12	17.16	even	2	inner
17.10.b.a.16.10	yes	12	1.1	even	1	trivial
153.10.d.b.118.3		12	3.2	odd	2
153.10.d.b.118.4		12	51.50	odd	2
272.10.b.c.33.1		12	4.3	odd	2
272.10.b.c.33.12		12	68.67	odd	2
289.10.a.c.1.3		12	17.13	even	4
289.10.a.c.1.4		12	17.4	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+25.8215 q^{2} +225.146i q^{3} +154.751 q^{4} +96.4328i q^{5} +5813.61i q^{6} +1385.77i q^{7} -9224.72 q^{8} -31007.8 q^{9} +O(q^{10})\)	\(q+25.8215 q^{2} +225.146i q^{3} +154.751 q^{4} +96.4328i q^{5} +5813.61i q^{6} +1385.77i q^{7} -9224.72 q^{8} -31007.8 q^{9} +2490.04i q^{10} +33833.7i q^{11} +34841.5i q^{12} +138558. q^{13} +35782.8i q^{14} -21711.5 q^{15} -317429. q^{16} +(177982. + 294805. i) q^{17} -800668. q^{18} +429726. q^{19} +14923.1i q^{20} -312001. q^{21} +873638. i q^{22} -352831. i q^{23} -2.07691e6i q^{24} +1.94383e6 q^{25} +3.57778e6 q^{26} -2.54973e6i q^{27} +214449. i q^{28} -508224. i q^{29} -560623. q^{30} -8.73026e6i q^{31} -3.47343e6 q^{32} -7.61753e6 q^{33} +(4.59577e6 + 7.61232e6i) q^{34} -133634. q^{35} -4.79848e6 q^{36} +1.62218e7i q^{37} +1.10962e7 q^{38} +3.11958e7i q^{39} -889565. i q^{40} -1.12435e7i q^{41} -8.05635e6 q^{42} -2.43795e7 q^{43} +5.23579e6i q^{44} -2.99017e6i q^{45} -9.11064e6i q^{46} -1.11673e7 q^{47} -7.14678e7i q^{48} +3.84332e7 q^{49} +5.01925e7 q^{50} +(-6.63743e7 + 4.00720e7i) q^{51} +2.14420e7 q^{52} +3.54297e7 q^{53} -6.58378e7i q^{54} -3.26268e6 q^{55} -1.27834e7i q^{56} +9.67510e7i q^{57} -1.31231e7i q^{58} +5.03437e7 q^{59} -3.35987e6 q^{60} +1.53033e8i q^{61} -2.25429e8i q^{62} -4.29697e7i q^{63} +7.28341e7 q^{64} +1.33615e7i q^{65} -1.96696e8 q^{66} -2.44023e8 q^{67} +(2.75429e7 + 4.56214e7i) q^{68} +7.94386e7 q^{69} -3.45063e6 q^{70} -3.78713e8i q^{71} +2.86038e8 q^{72} +1.38738e7i q^{73} +4.18871e8i q^{74} +4.37645e8i q^{75} +6.65004e7 q^{76} -4.68858e7 q^{77} +8.05523e8i q^{78} -5.65164e8i q^{79} -3.06105e7i q^{80} -3.62648e7 q^{81} -2.90325e8i q^{82} -5.68408e8 q^{83} -4.82825e7 q^{84} +(-2.84289e7 + 1.71633e7i) q^{85} -6.29517e8 q^{86} +1.14425e8 q^{87} -3.12106e8i q^{88} +2.61194e8 q^{89} -7.72106e7i q^{90} +1.92010e8i q^{91} -5.46009e7i q^{92} +1.96558e9 q^{93} -2.88357e8 q^{94} +4.14396e7i q^{95} -7.82030e8i q^{96} -1.04492e9i q^{97} +9.92405e8 q^{98} -1.04911e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9}+O(q^{10}) \) 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9	\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9} - 63204 q^{13} - 243480 q^{15} + 38978 q^{16} - 105960 q^{17} + 547706 q^{18} + 1110672 q^{19} - 172580 q^{21} - 4441796 q^{25} + 1336332 q^{26} - 500496 q^{30} - 1934850 q^{32} - 6557404 q^{33} - 15085546 q^{34} + 3519864 q^{35} + 30244102 q^{36} + 28748136 q^{38} - 11901296 q^{42} + 10004616 q^{43} - 112552440 q^{47} + 121354720 q^{49} - 164889018 q^{50} - 52506472 q^{51} - 59093180 q^{52} + 76804272 q^{53} + 300732568 q^{55} + 11618904 q^{59} + 101609232 q^{60} - 260062974 q^{64} + 18429632 q^{66} - 304208752 q^{67} - 444301206 q^{68} - 211308236 q^{69} + 460311456 q^{70} + 493218954 q^{72} + 416024248 q^{76} + 138357828 q^{77} - 363335792 q^{81} - 845042136 q^{83} + 958037984 q^{84} - 388949632 q^{85} + 127952904 q^{86} + 610860648 q^{87} - 938223804 q^{89} + 1635779524 q^{93} - 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) \) 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9 - 63204 * q^13 - 243480 * q^15 + 38978 * q^16 - 105960 * q^17 + 547706 * q^18 + 1110672 * q^19 - 172580 * q^21 - 4441796 * q^25 + 1336332 * q^26 - 500496 * q^30 - 1934850 * q^32 - 6557404 * q^33 - 15085546 * q^34 + 3519864 * q^35 + 30244102 * q^36 + 28748136 * q^38 - 11901296 * q^42 + 10004616 * q^43 - 112552440 * q^47 + 121354720 * q^49 - 164889018 * q^50 - 52506472 * q^51 - 59093180 * q^52 + 76804272 * q^53 + 300732568 * q^55 + 11618904 * q^59 + 101609232 * q^60 - 260062974 * q^64 + 18429632 * q^66 - 304208752 * q^67 - 444301206 * q^68 - 211308236 * q^69 + 460311456 * q^70 + 493218954 * q^72 + 416024248 * q^76 + 138357828 * q^77 - 363335792 * q^81 - 845042136 * q^83 + 958037984 * q^84 - 388949632 * q^85 + 127952904 * q^86 + 610860648 * q^87 - 938223804 * q^89 + 1635779524 * q^93 - 238629952 * q^94 - 152046078 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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