LMFDB - Embedded newform 17.10.b.a.16.6

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			16.6
Root			$105.759i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.10.b.a.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.15386 q^{2} +105.759i q^{3} -428.207 q^{4} -1752.99i q^{5} -968.101i q^{6} +5869.78i q^{7} +8606.52 q^{8} +8498.07 q^{9} +O(q^{10})$	\(q-9.15386 q^{2} +105.759i q^{3} -428.207 q^{4} -1752.99i q^{5} -968.101i q^{6} +5869.78i q^{7} +8606.52 q^{8} +8498.07 q^{9} +16046.7i q^{10} -57216.5i q^{11} -45286.7i q^{12} +183293. q^{13} -53731.1i q^{14} +185395. q^{15} +140459. q^{16} +(-307867. - 154291. i) q^{17} -77790.1 q^{18} +269437. q^{19} +750644. i q^{20} -620781. q^{21} +523752. i q^{22} -1.82770e6i q^{23} +910216. i q^{24} -1.11987e6 q^{25} -1.67784e6 q^{26} +2.98040e6i q^{27} -2.51348e6i q^{28} -1.33534e6i q^{29} -1.69708e6 q^{30} +5.82494e6i q^{31} -5.69228e6 q^{32} +6.05116e6 q^{33} +(2.81817e6 + 1.41235e6i) q^{34} +1.02897e7 q^{35} -3.63893e6 q^{36} -1.79478e7i q^{37} -2.46639e6 q^{38} +1.93849e7i q^{39} -1.50872e7i q^{40} -1.95813e7i q^{41} +5.68254e6 q^{42} +1.23432e7 q^{43} +2.45005e7i q^{44} -1.48971e7i q^{45} +1.67305e7i q^{46} +3.64169e7 q^{47} +1.48548e7i q^{48} +5.89930e6 q^{49} +1.02511e7 q^{50} +(1.63176e7 - 3.25597e7i) q^{51} -7.84873e7 q^{52} -4.39657e7 q^{53} -2.72821e7i q^{54} -1.00300e8 q^{55} +5.05184e7i q^{56} +2.84954e7i q^{57} +1.22235e7i q^{58} +6.25259e7 q^{59} -7.93873e7 q^{60} +1.82975e8i q^{61} -5.33206e7i q^{62} +4.98818e7i q^{63} -1.98087e7 q^{64} -3.21312e8i q^{65} -5.53914e7 q^{66} +1.37491e8 q^{67} +(1.31831e8 + 6.60683e7i) q^{68} +1.93295e8 q^{69} -9.41904e7 q^{70} +5.84225e7i q^{71} +7.31388e7 q^{72} -1.40109e8i q^{73} +1.64291e8i q^{74} -1.18436e8i q^{75} -1.15375e8 q^{76} +3.35848e8 q^{77} -1.77446e8i q^{78} -1.26401e8i q^{79} -2.46224e8i q^{80} -1.47936e8 q^{81} +1.79245e8i q^{82} +9.17904e7 q^{83} +2.65823e8 q^{84} +(-2.70471e8 + 5.39690e8i) q^{85} -1.12988e8 q^{86} +1.41224e8 q^{87} -4.92435e8i q^{88} -5.55730e8 q^{89} +1.36366e8i q^{90} +1.07589e9i q^{91} +7.82634e8i q^{92} -6.16038e8 q^{93} -3.33355e8 q^{94} -4.72322e8i q^{95} -6.02009e8i q^{96} -6.97429e8i q^{97} -5.40014e7 q^{98} -4.86230e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.15386			−0.404547			−0.202274	−	0.979329i	$-0.564833\pi$
$2$	−9.15386			−0.404547			−0.202274	+	0.979329i	$0.564833\pi$
$3$			105.759i			0.753826i	0.926249	+	0.376913i	$0.123014\pi$
$3$			105.759i			0.753826i	−0.926249	+	0.376913i	$0.876986\pi$
$4$	−428.207			−0.836342
$5$		−	1752.99i		−	1.25434i	−0.778882	−	0.627171i	$-0.784213\pi$
$5$		−	1752.99i		−	1.25434i	0.778882	−	0.627171i	$-0.215787\pi$
$6$		−	968.101i		−	0.304958i
$7$			5869.78i			0.924018i	0.886875	+	0.462009i	$0.152871\pi$
$7$			5869.78i			0.924018i	−0.886875	+	0.462009i	$0.847129\pi$
$8$	8606.52			0.742887
$9$	8498.07			0.431747
$10$			16046.7i			0.507440i
$11$		−	57216.5i		−	1.17830i	−0.808025	−	0.589148i	$-0.799463\pi$
$11$		−	57216.5i		−	1.17830i	0.808025	−	0.589148i	$-0.200537\pi$
$12$		−	45286.7i		−	0.630456i
$13$	183293.			1.77992			0.889960	−	0.456038i	$-0.150732\pi$
$13$	183293.			1.77992			0.889960	+	0.456038i	$0.150732\pi$
$14$		−	53731.1i		−	0.373809i
$15$	185395.			0.945555
$16$	140459.			0.535809
$17$	−307867.	−	154291.i	−0.894012	−	0.448043i
$17$	−307867.	−	154291.i	−0.894012	−	0.448043i
$18$	−77790.1			−0.174662
$19$	269437.			0.474315			0.237157	−	0.971471i	$-0.423784\pi$
$19$	269437.			0.474315			0.237157	+	0.971471i	$0.423784\pi$
$20$			750644.i			1.04906i
$21$	−620781.			−0.696549
$22$			523752.i			0.476677i
$23$		−	1.82770e6i		−	1.36185i	−0.732353	−	0.680925i	$-0.761578\pi$
$23$		−	1.82770e6i		−	1.36185i	0.732353	−	0.680925i	$-0.238422\pi$
$24$			910216.i			0.560007i
$25$	−1.11987e6			−0.573371
$26$	−1.67784e6			−0.720062
$27$			2.98040e6i			1.07929i
$28$		−	2.51348e6i		−	0.772795i
$29$		−	1.33534e6i		−	0.350591i	−0.984516	−	0.175295i	$-0.943912\pi$
$29$		−	1.33534e6i		−	0.350591i	0.984516	−	0.175295i	$-0.0560880\pi$
$30$	−1.69708e6			−0.382522
$31$			5.82494e6i			1.13283i	0.824121	+	0.566413i	$0.191669\pi$
$31$			5.82494e6i			1.13283i	−0.824121	+	0.566413i	$0.808331\pi$
$32$	−5.69228e6			−0.959647
$33$	6.05116e6			0.888230
$34$	2.81817e6	+	1.41235e6i	0.361670	+	0.181254i
$35$	1.02897e7			1.15903
$36$	−3.63893e6			−0.361088
$37$		−	1.79478e7i		−	1.57436i	−0.616726	−	0.787178i	$-0.711541\pi$
$37$		−	1.79478e7i		−	1.57436i	0.616726	−	0.787178i	$-0.288459\pi$
$38$	−2.46639e6			−0.191883
$39$			1.93849e7i			1.34175i
$40$		−	1.50872e7i		−	0.931833i
$41$		−	1.95813e7i		−	1.08222i	−0.840953	−	0.541108i	$-0.818005\pi$
$41$		−	1.95813e7i		−	1.08222i	0.840953	−	0.541108i	$-0.181995\pi$
$42$	5.68254e6			0.281787
$43$	1.23432e7			0.550580			0.275290	−	0.961361i	$-0.411226\pi$
$43$	1.23432e7			0.550580			0.275290	+	0.961361i	$0.411226\pi$
$44$			2.45005e7i			0.985458i
$45$		−	1.48971e7i		−	0.541557i
$46$			1.67305e7i			0.550933i
$47$	3.64169e7			1.08858			0.544292	−	0.838896i	$-0.316798\pi$
$47$	3.64169e7			1.08858			0.544292	+	0.838896i	$0.316798\pi$
$48$			1.48548e7i			0.403907i
$49$	5.89930e6			0.146190
$50$	1.02511e7			0.231956
$51$	1.63176e7	−	3.25597e7i	0.337746	−	0.673930i
$52$	−7.84873e7			−1.48862
$53$	−4.39657e7			−0.765372			−0.382686	−	0.923879i	$-0.625001\pi$
$53$	−4.39657e7			−0.765372			−0.382686	+	0.923879i	$0.625001\pi$
$54$		−	2.72821e7i		−	0.436623i
$55$	−1.00300e8			−1.47799
$56$			5.05184e7i			0.686441i
$57$			2.84954e7i			0.357551i
$58$			1.22235e7i			0.141830i
$59$	6.25259e7			0.671778			0.335889	−	0.941902i	$-0.390963\pi$
$59$	6.25259e7			0.671778			0.335889	+	0.941902i	$0.390963\pi$
$60$	−7.93873e7			−0.790807
$61$			1.82975e8i			1.69203i	0.533163	+	0.846013i	$0.321003\pi$
$61$			1.82975e8i			1.69203i	−0.533163	+	0.846013i	$0.678997\pi$
$62$		−	5.33206e7i		−	0.458282i
$63$			4.98818e7i			0.398942i
$64$	−1.98087e7			−0.147586
$65$		−	3.21312e8i		−	2.23263i
$66$	−5.53914e7			−0.359331
$67$	1.37491e8			0.833560			0.416780	−	0.909007i	$-0.363159\pi$
$67$	1.37491e8			0.833560			0.416780	+	0.909007i	$0.363159\pi$
$68$	1.31831e8	+	6.60683e7i	0.747700	+	0.374717i
$69$	1.93295e8			1.02660
$70$	−9.41904e7			−0.468884
$71$			5.84225e7i			0.272846i	0.990651	+	0.136423i	$0.0435607\pi$
$71$			5.84225e7i			0.272846i	−0.990651	+	0.136423i	$0.956439\pi$
$72$	7.31388e7			0.320739
$73$		−	1.40109e8i		−	0.577450i	−0.957412	−	0.288725i	$-0.906769\pi$
$73$		−	1.40109e8i		−	0.577450i	0.957412	−	0.288725i	$-0.0932313\pi$
$74$			1.64291e8i			0.636901i
$75$		−	1.18436e8i		−	0.432222i
$76$	−1.15375e8			−0.396689
$77$	3.35848e8			1.08877
$78$		−	1.77446e8i		−	0.542801i
$79$		−	1.26401e8i		−	0.365115i	−0.983195	−	0.182558i	$-0.941562\pi$
$79$		−	1.26401e8i		−	0.365115i	0.983195	−	0.182558i	$-0.0584376\pi$
$80$		−	2.46224e8i		−	0.672087i
$81$	−1.47936e8			−0.381848
$82$			1.79245e8i			0.437808i
$83$	9.17904e7			0.212298			0.106149	−	0.994350i	$-0.466148\pi$
$83$	9.17904e7			0.212298			0.106149	+	0.994350i	$0.466148\pi$
$84$	2.65823e8			0.582553
$85$	−2.70471e8	+	5.39690e8i	−0.561998	+	1.12140i
$86$	−1.12988e8			−0.222736
$87$	1.41224e8			0.264284
$88$		−	4.92435e8i		−	0.875341i
$89$	−5.55730e8			−0.938878			−0.469439	−	0.882965i	$-0.655544\pi$
$89$	−5.55730e8			−0.938878			−0.469439	+	0.882965i	$0.655544\pi$
$90$			1.36366e8i			0.219086i
$91$			1.07589e9i			1.64468i
$92$			7.82634e8i			1.13897i
$93$	−6.16038e8			−0.853954
$94$	−3.33355e8			−0.440384
$95$		−	4.72322e8i		−	0.594952i
$96$		−	6.02009e8i		−	0.723407i
$97$		−	6.97429e8i		−	0.799884i	−0.916540	−	0.399942i	$-0.869030\pi$
$97$		−	6.97429e8i		−	0.799884i	0.916540	−	0.399942i	$-0.130970\pi$
$98$	−5.40014e7			−0.0591408
$99$		−	4.86230e8i		−	0.508725i
$100$	4.79534e8			0.479534
$101$	−3.83633e8			−0.366834			−0.183417	−	0.983035i	$-0.558716\pi$
$101$	−3.83633e8			−0.366834			−0.183417	+	0.983035i	$0.558716\pi$
$102$	−1.49369e8	+	2.98047e8i	−0.136634	+	0.272636i
$103$	−1.47116e9			−1.28793			−0.643967	−	0.765054i	$-0.722712\pi$
$103$	−1.47116e9			−1.28793			−0.643967	+	0.765054i	$0.722712\pi$
$104$	1.57751e9			1.32228
$105$			1.08823e9i			0.873710i
$106$	4.02456e8			0.309629
$107$			4.50065e8i			0.331931i	0.986132	+	0.165966i	$0.0530741\pi$
$107$			4.50065e8i			0.331931i	−0.986132	+	0.165966i	$0.946926\pi$
$108$		−	1.27623e9i		−	0.902653i
$109$			3.38904e8i			0.229963i	0.993368	+	0.114981i	$0.0366808\pi$
$109$			3.38904e8i			0.229963i	−0.993368	+	0.114981i	$0.963319\pi$
$110$	9.18135e8			0.597915
$111$	1.89814e9			1.18679
$112$			8.24464e8i			0.495097i
$113$		−	8.15980e7i		−	0.0470789i	−0.999723	−	0.0235395i	$-0.992506\pi$
$113$		−	8.15980e7i		−	0.0470789i	0.999723	−	0.0235395i	$-0.00749354\pi$
$114$		−	2.60843e8i		−	0.144646i
$115$	−3.20395e9			−1.70823
$116$			5.71801e8i			0.293214i
$117$	1.55764e9			0.768475
$118$	−5.72353e8			−0.271766
$119$	9.05652e8	−	1.80711e9i	0.414000	−	0.826084i
$120$	1.59560e9			0.702440
$121$	−9.15786e8			−0.388383
$122$		−	1.67492e9i		−	0.684504i
$123$	2.07090e9			0.815803
$124$		−	2.49428e9i		−	0.947430i
$125$		−	1.46070e9i		−	0.535138i
$126$		−	4.56611e8i		−	0.161391i
$127$	−1.33940e9			−0.456871			−0.228435	−	0.973559i	$-0.573361\pi$
$127$	−1.33940e9			−0.456871			−0.228435	+	0.973559i	$0.573361\pi$
$128$	3.09577e9			1.01935
$129$			1.30540e9i			0.415042i
$130$			2.94124e9i			0.903203i
$131$			3.41422e9i			1.01291i	0.862267	+	0.506455i	$0.169044\pi$
$131$			3.41422e9i			1.01291i	−0.862267	+	0.506455i	$0.830956\pi$
$132$	−2.59115e9			−0.742864
$133$			1.58154e9i			0.438276i
$134$	−1.25857e9			−0.337214
$135$	5.22462e9			1.35379
$136$	−2.64967e9	−	1.32791e9i	−0.664150	−	0.332845i
$137$	−5.41610e9			−1.31354			−0.656771	−	0.754090i	$-0.728078\pi$
$137$	−5.41610e9			−1.31354			−0.656771	+	0.754090i	$0.728078\pi$
$138$	−1.76940e9			−0.415308
$139$			3.28339e9i			0.746030i	0.927825	+	0.373015i	$0.121676\pi$
$139$			3.28339e9i			0.746030i	−0.927825	+	0.373015i	$0.878324\pi$
$140$	−4.40612e9			−0.969348
$141$			3.85141e9i			0.820603i
$142$		−	5.34792e8i		−	0.110379i
$143$		−	1.04874e10i		−	2.09727i
$144$	1.19363e9			0.231334
$145$	−2.34084e9			−0.439760
$146$			1.28254e9i			0.233606i
$147$			6.23903e8i			0.110202i
$148$			7.68536e9i			1.31670i
$149$	−4.20361e8			−0.0698689			−0.0349345	−	0.999390i	$-0.511122\pi$
$149$	−4.20361e8			−0.0698689			−0.0349345	+	0.999390i	$0.511122\pi$
$150$			1.08414e9i			0.174854i
$151$	−1.34993e8			−0.0211307			−0.0105653	−	0.999944i	$-0.503363\pi$
$151$	−1.34993e8			−0.0211307			−0.0105653	+	0.999944i	$0.503363\pi$
$152$	2.31892e9			0.352362
$153$	−2.61628e9	−	1.31117e9i	−0.385987	−	0.193441i
$154$	−3.07431e9			−0.440458
$155$	1.02111e10			1.42095
$156$		−	8.30073e9i		−	1.12216i
$157$	−5.90561e9			−0.775740			−0.387870	−	0.921714i	$-0.626789\pi$
$157$	−5.90561e9			−0.775740			−0.387870	+	0.921714i	$0.626789\pi$
$158$			1.15706e9i			0.147706i
$159$		−	4.64976e9i		−	0.576957i
$160$			9.97854e9i			1.20372i
$161$	1.07282e10			1.25838
$162$	1.35418e9			0.154476
$163$		−	1.60704e10i		−	1.78313i	−0.452890	−	0.891566i	$-0.649607\pi$
$163$		−	1.60704e10i		−	1.78313i	0.452890	−	0.891566i	$-0.350393\pi$
$164$			8.38485e9i			0.905103i
$165$		−	1.06076e10i		−	1.11414i
$166$	−8.40237e8			−0.0858846
$167$			7.33291e9i			0.729546i	0.931097	+	0.364773i	$0.118853\pi$
$167$			7.33291e9i			0.729546i	−0.931097	+	0.364773i	$0.881147\pi$
$168$	−5.34276e9			−0.517457
$169$	2.29918e10			2.16812
$170$	2.47585e9	−	4.94024e9i	0.227355	−	0.453658i
$171$	2.28970e9			0.204784
$172$	−5.28545e9			−0.460473
$173$			1.87691e10i			1.59307i	0.604590	+	0.796537i	$0.293337\pi$
$173$			1.87691e10i			1.59307i	−0.604590	+	0.796537i	$0.706663\pi$
$174$	−1.29274e9			−0.106915
$175$		−	6.57337e9i		−	0.529806i
$176$		−	8.03658e9i		−	0.631342i
$177$			6.61267e9i			0.506404i
$178$	5.08708e9			0.379820
$179$	2.15906e10			1.57190			0.785952	−	0.618287i	$-0.212173\pi$
$179$	2.15906e10			1.57190			0.785952	+	0.618287i	$0.212173\pi$
$180$			6.37903e9i			0.452927i
$181$		−	1.14397e10i		−	0.792249i	−0.918197	−	0.396125i	$-0.870355\pi$
$181$		−	1.14397e10i		−	0.792249i	0.918197	−	0.396125i	$-0.129645\pi$
$182$		−	9.84854e9i		−	0.665350i
$183$	−1.93512e10			−1.27549
$184$		−	1.57301e10i		−	1.01170i
$185$	−3.14624e10			−1.97478
$186$	5.63913e9			0.345465
$187$	−8.82797e9	+	1.76151e10i	−0.527927	+	1.05341i
$188$	−1.55940e10			−0.910428
$189$	−1.74943e10			−0.997281
$190$			4.32357e9i			0.240686i
$191$	−2.88292e9			−0.156741			−0.0783705	−	0.996924i	$-0.524972\pi$
$191$	−2.88292e9			−0.156741			−0.0783705	+	0.996924i	$0.524972\pi$
$192$		−	2.09495e9i		−	0.111254i
$193$			3.11767e10i			1.61742i	0.588209	+	0.808709i	$0.299833\pi$
$193$			3.11767e10i			1.61742i	−0.588209	+	0.808709i	$0.700167\pi$
$194$			6.38417e9i			0.323591i
$195$	3.39815e10			1.68301
$196$	−2.52612e9			−0.122265
$197$		−	3.08413e9i		−	0.145893i	−0.997336	−	0.0729466i	$-0.976760\pi$
$197$		−	3.08413e9i		−	0.145893i	0.997336	−	0.0729466i	$-0.0232403\pi$
$198$			4.45088e9i			0.205803i
$199$		−	1.25130e10i		−	0.565615i	−0.959177	−	0.282808i	$-0.908734\pi$
$199$		−	1.25130e10i		−	0.565615i	0.959177	−	0.282808i	$-0.0912658\pi$
$200$	−9.63815e9			−0.425950
$201$			1.45409e10i			0.628359i
$202$	3.51172e9			0.148402
$203$	7.83814e9			0.323952
$204$	−6.98731e9	+	1.39423e10i	−0.282471	+	0.563635i
$205$	−3.43259e10			−1.35747
$206$	1.34668e10			0.521030
$207$		−	1.55319e10i		−	0.587974i
$208$	2.57452e10			0.953697
$209$		−	1.54163e10i		−	0.558883i
$210$		−	9.96147e9i		−	0.353457i
$211$		−	2.61249e9i		−	0.0907369i	−0.998970	−	0.0453684i	$-0.985554\pi$
$211$		−	2.61249e9i		−	0.0907369i	0.998970	−	0.0453684i	$-0.0144462\pi$
$212$	1.88264e10			0.640112
$213$	−6.17870e9			−0.205678
$214$		−	4.11983e9i		−	0.134282i
$215$		−	2.16376e10i		−	0.690615i
$216$			2.56508e10i			0.801789i
$217$	−3.41911e10			−1.04675
$218$		−	3.10228e9i		−	0.0930308i
$219$	1.48178e10			0.435296
$220$	4.29493e10			1.23610
$221$	−5.64299e10	−	2.82804e10i	−1.59127	−	0.797480i
$222$	−1.73753e10			−0.480113
$223$	5.19850e10			1.40769			0.703843	−	0.710355i	$-0.251466\pi$
$223$	5.19850e10			1.40769			0.703843	+	0.710355i	$0.251466\pi$
$224$		−	3.34124e10i		−	0.886731i
$225$	−9.51670e9			−0.247551
$226$			7.46937e8i			0.0190457i
$227$			6.59252e10i			1.64792i	0.566650	+	0.823958i	$0.308239\pi$
$227$			6.59252e10i			1.64792i	−0.566650	+	0.823958i	$0.691761\pi$
$228$		−	1.22019e10i		−	0.299035i
$229$	7.15519e10			1.71934			0.859669	−	0.510851i	$-0.170670\pi$
$229$	7.15519e10			1.71934			0.859669	+	0.510851i	$0.170670\pi$
$230$	2.93285e10			0.691058
$231$			3.55189e10i			0.820741i
$232$		−	1.14926e10i		−	0.260449i
$233$			1.94101e10i			0.431446i	0.976455	+	0.215723i	$0.0692109\pi$
$233$			1.94101e10i			0.431446i	−0.976455	+	0.215723i	$0.930789\pi$
$234$	−1.42584e10			−0.310884
$235$		−	6.38386e10i		−	1.36546i
$236$	−2.67740e10			−0.561836
$237$	1.33681e10			0.275233
$238$	−8.29021e9	+	1.65421e10i	−0.167482	+	0.334190i
$239$	−9.93587e8			−0.0196977			−0.00984885	−	0.999951i	$-0.503135\pi$
$239$	−9.93587e8			−0.0196977			−0.00984885	+	0.999951i	$0.503135\pi$
$240$	2.60404e10			0.506637
$241$		−	7.36838e9i		−	0.140700i	−0.997522	−	0.0703502i	$-0.977588\pi$
$241$		−	7.36838e9i		−	0.140700i	0.997522	−	0.0703502i	$-0.0224117\pi$
$242$	8.38297e9			0.157119
$243$			4.30176e10i			0.791440i
$244$		−	7.83510e10i		−	1.41511i
$245$		−	1.03414e10i		−	0.183372i
$246$	−1.89567e10			−0.330031
$247$	4.93860e10			0.844243
$248$			5.01324e10i			0.841562i
$249$			9.70765e9i			0.160036i
$250$			1.33710e10i			0.216488i
$251$	−1.14806e11			−1.82571			−0.912855	−	0.408283i	$-0.866128\pi$
$251$	−1.14806e11			−1.82571			−0.912855	+	0.408283i	$0.866128\pi$
$252$		−	2.13597e10i		−	0.333651i
$253$	−1.04575e11			−1.60466
$254$	1.22607e10			0.184826
$255$	−5.70770e10	−	2.86047e10i	−0.845338	−	0.423649i
$256$	−1.81962e10			−0.264790
$257$	−3.12571e10			−0.446940			−0.223470	−	0.974711i	$-0.571738\pi$
$257$	−3.12571e10			−0.446940			−0.223470	+	0.974711i	$0.571738\pi$
$258$		−	1.19495e10i		−	0.167904i
$259$	1.05349e11			1.45473
$260$			1.37588e11i			1.86724i
$261$		−	1.13478e10i		−	0.151366i
$262$		−	3.12533e10i		−	0.409770i
$263$	1.77723e10			0.229057			0.114529	−	0.993420i	$-0.463464\pi$
$263$	1.77723e10			0.229057			0.114529	+	0.993420i	$0.463464\pi$
$264$	5.20794e10			0.659855
$265$			7.70716e10i			0.960037i
$266$		−	1.44772e10i		−	0.177303i
$267$		−	5.87734e10i		−	0.707750i
$268$	−5.88745e10			−0.697141
$269$			7.34859e10i			0.855694i	0.903851	+	0.427847i	$0.140728\pi$
$269$			7.34859e10i			0.855694i	−0.903851	+	0.427847i	$0.859272\pi$
$270$	−4.78254e10			−0.547674
$271$	1.05771e11			1.19125			0.595625	−	0.803263i	$-0.296904\pi$
$271$	1.05771e11			1.19125			0.595625	+	0.803263i	$0.296904\pi$
$272$	−4.32428e10	−	2.16715e10i	−0.479020	−	0.240065i
$273$	−1.13785e11			−1.23980
$274$	4.95782e10			0.531389
$275$			6.40749e10i			0.675602i
$276$	−8.27704e10			−0.858587
$277$		−	1.55982e11i		−	1.59190i	−0.605360	−	0.795952i	$-0.706971\pi$
$277$		−	1.55982e11i		−	1.59190i	0.605360	−	0.795952i	$-0.293029\pi$
$278$		−	3.00557e10i		−	0.301804i
$279$			4.95007e10i			0.489094i
$280$	8.85585e10			0.861031
$281$	−1.55794e10			−0.149064			−0.0745320	−	0.997219i	$-0.523746\pi$
$281$	−1.55794e10			−0.149064			−0.0745320	+	0.997219i	$0.523746\pi$
$282$		−	3.52552e10i		−	0.331973i
$283$		−	1.55832e10i		−	0.144416i	−0.997390	−	0.0722082i	$-0.976995\pi$
$283$		−	1.55832e10i		−	0.144416i	0.997390	−	0.0722082i	$-0.0230046\pi$
$284$		−	2.50169e10i		−	0.228193i
$285$	4.99523e10			0.448491
$286$			9.60001e10i			0.848447i
$287$	1.14938e11			0.999988
$288$	−4.83734e10			−0.414324
$289$	7.09767e10	+	9.50021e10i	0.598516	+	0.801111i
$290$	2.14277e10			0.177904
$291$	7.37593e10			0.602974
$292$			5.99958e10i			0.482945i
$293$	−1.00556e11			−0.797081			−0.398541	−	0.917151i	$-0.630483\pi$
$293$	−1.00556e11			−0.797081			−0.398541	+	0.917151i	$0.630483\pi$
$294$		−	5.71112e9i		−	0.0445819i
$295$		−	1.09608e11i		−	0.842639i
$296$		−	1.54468e11i		−	1.16957i
$297$	1.70528e11			1.27172
$298$	3.84792e9			0.0282653
$299$		−	3.35004e11i		−	2.42399i
$300$			5.07150e10i			0.361485i
$301$			7.24520e10i			0.508746i
$302$	1.23570e9			0.00854836
$303$		−	4.05725e10i		−	0.276529i
$304$	3.78449e10			0.254142
$305$	3.20754e11			2.12238
$306$	2.39490e10	+	1.20023e10i	0.156150	+	0.0782559i
$307$	−1.89792e11			−1.21942			−0.609712	−	0.792623i	$-0.708715\pi$
$307$	−1.89792e11			−1.21942			−0.609712	+	0.792623i	$0.708715\pi$
$308$	−1.43813e11			−0.910581
$309$		−	1.55589e11i		−	0.970877i
$310$	−9.34708e10			−0.574842
$311$			1.73614e10i			0.105236i	0.998615	+	0.0526179i	$0.0167565\pi$
$311$			1.73614e10i			0.105236i	−0.998615	+	0.0526179i	$0.983243\pi$
$312$			1.66836e11i			0.996769i
$313$			2.56822e11i			1.51245i	0.654309	+	0.756227i	$0.272960\pi$
$313$			2.56822e11i			1.51245i	−0.654309	+	0.756227i	$0.727040\pi$
$314$	5.40591e10			0.313823
$315$	8.74425e10			0.500409
$316$			5.41259e10i			0.305361i
$317$			1.00545e11i			0.559232i	0.960112	+	0.279616i	$0.0902072\pi$
$317$			1.00545e11i			0.559232i	−0.960112	+	0.279616i	$0.909793\pi$
$318$			4.25632e10i			0.233406i
$319$	−7.64034e10			−0.413100
$320$			3.47245e10i			0.185124i
$321$	−4.75984e10			−0.250219
$322$	−9.82044e10			−0.509072
$323$	−8.29510e10	−	4.15717e10i	−0.424043	−	0.212513i
$324$	6.33472e10			0.319356
$325$	−2.05264e11			−1.02056
$326$			1.47107e11i			0.721361i
$327$	−3.58421e10			−0.173352
$328$		−	1.68527e11i		−	0.803965i
$329$			2.13759e11i			1.00587i
$330$			9.71009e10i			0.450724i
$331$	−3.48086e11			−1.59390			−0.796950	−	0.604046i	$-0.793554\pi$
$331$	−3.48086e11			−1.59390			−0.796950	+	0.604046i	$0.793554\pi$
$332$	−3.93053e10			−0.177554
$333$		−	1.52521e11i		−	0.679722i
$334$		−	6.71244e10i		−	0.295136i
$335$		−	2.41020e11i		−	1.04557i
$336$	−8.71943e10			−0.373217
$337$			2.40170e10i			0.101434i	0.998713	+	0.0507171i	$0.0161507\pi$
$337$			2.40170e10i			0.101434i	−0.998713	+	0.0507171i	$0.983849\pi$
$338$	−2.10464e11			−0.877106
$339$	8.62971e9			0.0354893
$340$	1.15817e11	−	2.31099e11i	0.470022	−	0.937870i
$341$	3.33283e11			1.33481
$342$	−2.09596e10			−0.0828447
$343$			2.71494e11i			1.05910i
$344$	1.06232e11			0.409019
$345$		−	3.38846e11i		−	1.28770i
$346$		−	1.71810e11i		−	0.644474i
$347$			9.10819e10i			0.337248i	0.985680	+	0.168624i	$0.0539324\pi$
$347$			9.10819e10i			0.337248i	−0.985680	+	0.168624i	$0.946068\pi$
$348$	−6.04730e10			−0.221032
$349$	1.89982e10			0.0685485			0.0342743	−	0.999412i	$-0.489088\pi$
$349$	1.89982e10			0.0685485			0.0342743	+	0.999412i	$0.489088\pi$
$350$			6.01717e10i			0.214331i
$351$			5.46286e11i			1.92105i
$352$			3.25693e11i			1.13075i
$353$	8.47880e10			0.290635			0.145318	−	0.989385i	$-0.453580\pi$
$353$	8.47880e10			0.290635			0.145318	+	0.989385i	$0.453580\pi$
$354$		−	6.05314e10i		−	0.204864i
$355$	1.02414e11			0.342242
$356$	2.37968e11			0.785222
$357$	1.91118e11	+	9.57807e10i	0.622723	+	0.312084i
$358$	−1.97637e11			−0.635909
$359$	3.40209e11			1.08099			0.540494	−	0.841348i	$-0.318237\pi$
$359$	3.40209e11			1.08099			0.540494	+	0.841348i	$0.318237\pi$
$360$		−	1.28212e11i		−	0.402316i
$361$	−2.50091e11			−0.775025
$362$			1.04718e11i			0.320502i
$363$		−	9.68524e10i		−	0.292773i
$364$		−	4.60703e11i		−	1.37551i
$365$	−2.45611e11			−0.724319
$366$	1.77138e11			0.515997
$367$			1.38234e11i			0.397758i	0.980024	+	0.198879i	$0.0637301\pi$
$367$			1.38234e11i			0.397758i	−0.980024	+	0.198879i	$0.936270\pi$
$368$		−	2.56717e11i		−	0.729692i
$369$		−	1.66403e11i		−	0.467243i
$370$	2.88002e11			0.798891
$371$		−	2.58069e11i		−	0.707217i
$372$	2.63792e11			0.714197
$373$	−5.31263e11			−1.42108			−0.710542	−	0.703655i	$-0.751550\pi$
$373$	−5.31263e11			−1.42108			−0.710542	+	0.703655i	$0.751550\pi$
$374$	8.08100e10	−	1.61246e11i	0.213571	−	0.426155i
$375$	1.54482e11			0.403401
$376$	3.13422e11			0.808695
$377$		−	2.44758e11i		−	0.624024i
$378$	1.60140e11			0.403447
$379$			5.46410e11i			1.36032i	0.733062	+	0.680162i	$0.238091\pi$
$379$			5.46410e11i			1.36032i	−0.733062	+	0.680162i	$0.761909\pi$
$380$			2.02252e11i			0.497583i
$381$		−	1.41653e11i		−	0.344401i
$382$	2.63898e10			0.0634091
$383$	−3.55500e11			−0.844200			−0.422100	−	0.906549i	$-0.638707\pi$
$383$	−3.55500e11			−0.844200			−0.422100	+	0.906549i	$0.638707\pi$
$384$			3.27405e11i			0.768414i
$385$		−	5.88741e11i		−	1.36569i
$386$		−	2.85387e11i		−	0.654322i
$387$	1.04894e11			0.237711
$388$			2.98644e11i			0.668976i
$389$	6.89360e11			1.52642			0.763208	−	0.646153i	$-0.223623\pi$
$389$	6.89360e11			1.52642			0.763208	+	0.646153i	$0.223623\pi$
$390$	−3.11062e11			−0.680858
$391$	−2.81997e11	+	5.62689e11i	−0.610167	+	1.21751i
$392$	5.07725e10			0.108603
$393$	−3.61084e11			−0.763557
$394$			2.82317e10i			0.0590207i
$395$	−2.21581e11			−0.457979
$396$			2.08207e11i			0.425468i
$397$		−	8.59801e11i		−	1.73716i	−0.495546	−	0.868582i	$-0.665032\pi$
$397$		−	8.59801e11i		−	1.73716i	0.495546	−	0.868582i	$-0.334968\pi$
$398$			1.14542e11i			0.228818i
$399$	−1.67262e11			−0.330383
$400$	−1.57295e11			−0.307217
$401$			2.49159e11i			0.481202i	0.970624	+	0.240601i	$0.0773445\pi$
$401$			2.49159e11i			0.481202i	−0.970624	+	0.240601i	$0.922656\pi$
$402$		−	1.33105e11i		−	0.254201i
$403$			1.06767e12i			2.01634i
$404$	1.64274e11			0.306798
$405$			2.59331e11i			0.478968i
$406$	−7.17492e10			−0.131054
$407$	−1.02691e12			−1.85506
$408$	1.40438e11	−	2.80226e11i	0.250907	−	0.500653i
$409$	2.46410e11			0.435416			0.217708	−	0.976014i	$-0.430142\pi$
$409$	2.46410e11			0.435416			0.217708	+	0.976014i	$0.430142\pi$
$410$	3.14215e11			0.549160
$411$		−	5.72800e11i		−	0.990181i
$412$	6.29962e11			1.07715
$413$			3.67013e11i			0.620735i
$414$			1.42177e11i			0.237863i
$415$		−	1.60908e11i		−	0.266294i
$416$	−1.04336e12			−1.70810
$417$	−3.47248e11			−0.562377
$418$			1.41118e11i			0.226095i
$419$		−	8.92561e10i		−	0.141473i	−0.997495	−	0.0707367i	$-0.977465\pi$
$419$		−	8.92561e10i		−	0.141473i	0.997495	−	0.0707367i	$-0.0225350\pi$
$420$		−	4.65986e11i		−	0.730720i
$421$	1.44866e11			0.224749			0.112374	−	0.993666i	$-0.464154\pi$
$421$	1.44866e11			0.224749			0.112374	+	0.993666i	$0.464154\pi$
$422$			2.39144e10i			0.0367074i
$423$	3.09473e11			0.469993
$424$	−3.78392e11			−0.568585
$425$	3.44770e11	+	1.72785e11i	0.512601	+	0.256895i
$426$	5.65589e10			0.0832067
$427$	−1.07402e12			−1.56346
$428$		−	1.92721e11i		−	0.277608i
$429$	1.10913e12			1.58098
$430$			1.98068e11i			0.279386i
$431$			7.07364e11i			0.987405i	0.869631	+	0.493702i	$0.164357\pi$
$431$			7.07364e11i			0.987405i	−0.869631	+	0.493702i	$0.835643\pi$
$432$			4.18624e11i			0.578292i
$433$	−2.33937e10			−0.0319818			−0.0159909	−	0.999872i	$-0.505090\pi$
$433$	−2.33937e10			−0.0319818			−0.0159909	+	0.999872i	$0.505090\pi$
$434$	3.12980e11			0.423461
$435$		−	2.47565e11i		−	0.331503i
$436$		−	1.45121e11i		−	0.192327i
$437$		−	4.92451e11i		−	0.645946i
$438$	−1.35640e11			−0.176098
$439$		−	1.22303e12i		−	1.57161i	−0.618474	−	0.785806i	$-0.712249\pi$
$439$		−	1.22303e12i		−	1.57161i	0.618474	−	0.785806i	$-0.287751\pi$
$440$	−8.63237e11			−1.09798
$441$	5.01327e10			0.0631171
$442$	5.16551e11	+	2.58875e11i	0.643744	+	0.322618i
$443$	1.01038e12			1.24643			0.623215	−	0.782050i	$-0.285826\pi$
$443$	1.01038e12			1.24643			0.623215	+	0.782050i	$0.285826\pi$
$444$	−8.12795e11			−0.992562
$445$			9.74192e11i			1.17767i
$446$	−4.75863e11			−0.569476
$447$		−	4.44569e10i		−	0.0526690i
$448$		−	1.16273e11i		−	0.136372i
$449$		−	4.77607e10i		−	0.0554578i	−0.999615	−	0.0277289i	$-0.991172\pi$
$449$		−	4.77607e10i		−	0.0554578i	0.999615	−	0.0277289i	$-0.00882751\pi$
$450$	8.71145e10			0.100146
$451$	−1.12037e12			−1.27517
$452$			3.49408e10i			0.0393741i
$453$		−	1.42767e10i		−	0.0159289i
$454$		−	6.03470e11i		−	0.666660i
$455$	1.88603e12			2.06299
$456$			2.45246e11i			0.265620i
$457$	1.47001e12			1.57651			0.788255	−	0.615349i	$-0.210985\pi$
$457$	1.47001e12			1.57651			0.788255	+	0.615349i	$0.210985\pi$
$458$	−6.54976e11			−0.695553
$459$	4.59847e11	−	9.17567e11i	0.483567	−	0.964896i
$460$	1.37195e12			1.42866
$461$	1.65629e12			1.70797			0.853986	−	0.520295i	$-0.174178\pi$
$461$	1.65629e12			1.70797			0.853986	+	0.520295i	$0.174178\pi$
$462$		−	3.25135e11i		−	0.332029i
$463$	−1.55332e11			−0.157089			−0.0785444	−	0.996911i	$-0.525027\pi$
$463$	−1.55332e11			−0.157089			−0.0785444	+	0.996911i	$0.525027\pi$
$464$		−	1.87560e11i		−	0.187850i
$465$			1.07991e12i			1.07115i
$466$		−	1.77678e11i		−	0.174540i
$467$	−5.17128e11			−0.503120			−0.251560	−	0.967842i	$-0.580944\pi$
$467$	−5.17128e11			−0.503120			−0.251560	+	0.967842i	$0.580944\pi$
$468$	−6.66990e11			−0.642707
$469$			8.07040e11i			0.770224i
$470$			5.84369e11i			0.552392i
$471$		−	6.24570e11i		−	0.584773i
$472$	5.38130e11			0.499055
$473$		−	7.06237e11i		−	0.648747i
$474$	−1.22369e11			−0.111345
$475$	−3.01734e11			−0.271959
$476$	−3.87806e11	+	7.73818e11i	−0.346245	+	0.690888i
$477$	−3.73623e11			−0.330447
$478$	9.09515e9			0.00796865
$479$		−	4.57403e11i		−	0.396998i	−0.980101	−	0.198499i	$-0.936393\pi$
$479$		−	4.57403e11i		−	0.396998i	0.980101	−	0.198499i	$-0.0636067\pi$
$480$	−1.05532e12			−0.907399
$481$		−	3.28970e12i		−	2.80223i
$482$			6.74491e10i			0.0569200i
$483$			1.13460e12i			0.948596i
$484$	3.92146e11			0.324820
$485$	−1.22259e12			−1.00333
$486$		−	3.93777e11i		−	0.320175i
$487$		−	1.79433e11i		−	0.144552i	−0.997385	−	0.0722758i	$-0.976974\pi$
$487$		−	1.79433e11i		−	0.144552i	0.997385	−	0.0722758i	$-0.0230262\pi$
$488$			1.57478e12i			1.25698i
$489$	1.69959e12			1.34417
$490$			9.46641e10i			0.0741828i
$491$	−2.26673e12			−1.76009			−0.880043	−	0.474895i	$-0.842486\pi$
$491$	−2.26673e12			−1.76009			−0.880043	+	0.474895i	$0.842486\pi$
$492$	−8.86772e11			−0.682290
$493$	−2.06030e11	+	4.11107e11i	−0.157080	+	0.313432i
$494$	−4.52072e11			−0.341536
$495$	−8.52359e11			−0.638115
$496$			8.18165e11i			0.606978i
$497$	−3.42927e11			−0.252115
$498$		−	8.88625e10i		−	0.0647420i
$499$			1.09096e12i			0.787690i	0.919177	+	0.393845i	$0.128855\pi$
$499$			1.09096e12i			0.787690i	−0.919177	+	0.393845i	$0.871145\pi$
$500$			6.25481e11i			0.447558i
$501$	−7.75520e11			−0.549950
$502$	1.05092e12			0.738586
$503$		−	2.02678e12i		−	1.41173i	−0.708348	−	0.705863i	$-0.750559\pi$
$503$		−	2.02678e12i		−	1.41173i	0.708348	−	0.705863i	$-0.249441\pi$
$504$			4.29309e11i			0.296369i
$505$			6.72506e11i			0.460135i
$506$	9.57262e11			0.649162
$507$			2.43159e12i			1.63438i
$508$	5.73540e11			0.382100
$509$	−2.14859e11			−0.141881			−0.0709405	−	0.997481i	$-0.522600\pi$
$509$	−2.14859e11			−0.141881			−0.0709405	+	0.997481i	$0.522600\pi$
$510$	5.22475e11	+	2.61843e11i	0.341979	+	0.171386i
$511$	8.22411e11			0.533574
$512$	−1.41847e12			−0.912232
$513$			8.03030e11i			0.511922i
$514$	2.86123e11			0.180808
$515$			2.57894e12i			1.61551i
$516$		−	5.58983e11i		−	0.347116i
$517$		−	2.08365e12i		−	1.28268i
$518$	−9.64354e11			−0.588508
$519$	−1.98500e12			−1.20090
$520$		−	2.76538e12i		−	1.65859i
$521$			1.53683e12i			0.913810i	0.889515	+	0.456905i	$0.151042\pi$
$521$			1.53683e12i			0.913810i	−0.889515	+	0.456905i	$0.848958\pi$
$522$			1.03876e11i			0.0612348i
$523$	8.69337e11			0.508078			0.254039	−	0.967194i	$-0.418241\pi$
$523$	8.69337e11			0.508078			0.254039	+	0.967194i	$0.418241\pi$
$524$		−	1.46199e12i		−	0.847138i
$525$	6.95192e11			0.399381
$526$	−1.62685e11			−0.0926644
$527$	8.98733e11	−	1.79331e12i	0.507555	−	1.01276i
$528$	8.49940e11			0.475922
$529$	−1.53933e12			−0.854638
$530$		−	7.05503e11i		−	0.388380i
$531$	5.31349e11			0.290038
$532$		−	6.77225e11i		−	0.366548i
$533$		−	3.58912e12i		−	1.92626i
$534$			5.38003e11i			0.286318i
$535$	7.88962e11			0.416355
$536$	1.18332e12			0.619240
$537$			2.28340e12i			1.18494i
$538$		−	6.72679e11i		−	0.346169i
$539$		−	3.37538e11i		−	0.172255i
$540$	−2.23722e12			−1.13223
$541$			2.22560e12i			1.11702i	0.829499	+	0.558509i	$0.188626\pi$
$541$			2.22560e12i			1.11702i	−0.829499	+	0.558509i	$0.811374\pi$
$542$	−9.68209e11			−0.481917
$543$	1.20985e12			0.597218
$544$	1.75247e12	+	8.78265e11i	0.857936	+	0.429963i
$545$	5.94097e11			0.288452
$546$	1.04157e12			0.501558
$547$			1.01266e12i			0.483638i	0.970321	+	0.241819i	$0.0777441\pi$
$547$			1.01266e12i			0.483638i	−0.970321	+	0.241819i	$0.922256\pi$
$548$	2.31921e12			1.09857
$549$			1.55493e12i			0.730526i
$550$		−	5.86532e11i		−	0.273313i
$551$		−	3.59790e11i		−	0.166290i
$552$	1.66360e12			0.762647
$553$	7.41948e11			0.337373
$554$			1.42784e12i			0.644000i
$555$		−	3.32742e12i		−	1.48864i
$556$		−	1.40597e12i		−	0.623936i
$557$	−1.24117e12			−0.546364			−0.273182	−	0.961962i	$-0.588076\pi$
$557$	−1.24117e12			−0.546364			−0.273182	+	0.961962i	$0.588076\pi$
$558$		−	4.53122e11i		−	0.197862i
$559$	2.26243e12			0.979989
$560$	1.44528e12			0.621021
$561$	−1.86295e12	−	9.33636e11i	−0.794089	−	0.397965i
$562$	1.42612e11			0.0603035
$563$	1.01943e12			0.427632			0.213816	−	0.976874i	$-0.431411\pi$
$563$	1.01943e12			0.427632			0.213816	+	0.976874i	$0.431411\pi$
$564$		−	1.64920e12i		−	0.686305i
$565$	−1.43041e11			−0.0590530
$566$			1.42646e11i			0.0584233i
$567$		−	8.68351e11i		−	0.352835i
$568$			5.02815e11i			0.202694i
$569$	−1.48027e12			−0.592021			−0.296011	−	0.955185i	$-0.595656\pi$
$569$	−1.48027e12			−0.592021			−0.296011	+	0.955185i	$0.595656\pi$
$570$	−4.57256e11			−0.181436
$571$			7.76183e11i			0.305563i	0.988260	+	0.152782i	$0.0488231\pi$
$571$			7.76183e11i			0.305563i	−0.988260	+	0.152782i	$0.951177\pi$
$572$			4.49077e12i			1.75404i
$573$		−	3.04894e11i		−	0.118155i
$574$	−1.05213e12			−0.404542
$575$			2.04678e12i			0.780846i
$576$	−1.68336e11			−0.0637199
$577$	−4.47042e12			−1.67903			−0.839513	−	0.543339i	$-0.817160\pi$
$577$	−4.47042e12			−1.67903			−0.839513	+	0.543339i	$0.817160\pi$
$578$	−6.49711e11	−	8.69635e11i	−0.242128	−	0.324087i
$579$	−3.29721e12			−1.21925
$580$	1.00236e12			0.367790
$581$			5.38790e11i			0.196167i
$582$	−6.75182e11			−0.243931
$583$			2.51556e12i			0.901835i
$584$		−	1.20585e12i		−	0.428980i
$585$		−	2.73053e12i		−	0.963929i
$586$	9.20473e11			0.322457
$587$	4.82640e11			0.167784			0.0838922	−	0.996475i	$-0.473265\pi$
$587$	4.82640e11			0.167784			0.0838922	+	0.996475i	$0.473265\pi$
$588$		−	2.67160e11i		−	0.0921665i
$589$			1.56946e12i			0.537316i
$590$			1.00333e12i			0.340887i
$591$	3.26174e11			0.109978
$592$		−	2.52093e12i		−	0.843553i
$593$	2.96619e12			0.985036			0.492518	−	0.870302i	$-0.336077\pi$
$593$	2.96619e12			0.985036			0.492518	+	0.870302i	$0.336077\pi$
$594$	−1.56099e12			−0.514471
$595$	−3.16786e12	−	1.58760e12i	−1.03619	−	0.519297i
$596$	1.80001e11			0.0584343
$597$	1.32336e12			0.426375
$598$			3.06658e12i			0.980617i
$599$	−4.35994e12			−1.38376			−0.691878	−	0.722015i	$-0.743216\pi$
$599$	−4.35994e12			−1.38376			−0.691878	+	0.722015i	$0.743216\pi$
$600$		−	1.01932e12i		−	0.321092i
$601$			6.75122e11i			0.211080i	0.994415	+	0.105540i	$0.0336571\pi$
$601$			6.75122e11i			0.211080i	−0.994415	+	0.105540i	$0.966343\pi$
$602$		−	6.63215e11i		−	0.205812i
$603$	1.16840e12			0.359886
$604$	5.78048e10			0.0176725
$605$			1.60537e12i			0.487164i
$606$			3.71395e11i			0.111869i
$607$			8.01007e11i			0.239490i	0.992805	+	0.119745i	$0.0382077\pi$
$607$			8.01007e11i			0.239490i	−0.992805	+	0.119745i	$0.961792\pi$
$608$	−1.53371e12			−0.455175
$609$			8.28953e11i			0.244204i
$610$	−2.93613e12			−0.858602
$611$	6.67495e12			1.93759
$612$	1.12031e12	+	5.61453e11i	0.322817	+	0.161783i
$613$	−4.78001e12			−1.36728			−0.683639	−	0.729820i	$-0.739604\pi$
$613$	−4.78001e12			−1.36728			−0.683639	+	0.729820i	$0.739604\pi$
$614$	1.73733e12			0.493314
$615$		−	3.63027e12i		−	1.02330i
$616$	2.89049e12			0.808831
$617$		−	2.09791e12i		−	0.582778i	−0.956605	−	0.291389i	$-0.905883\pi$
$617$		−	2.09791e12i		−	0.582778i	0.956605	−	0.291389i	$-0.0941174\pi$
$618$			1.42424e12i			0.392766i
$619$			2.32970e12i			0.637812i	0.947786	+	0.318906i	$0.103315\pi$
$619$			2.32970e12i			0.637812i	−0.947786	+	0.318906i	$0.896685\pi$
$620$	−4.37246e12			−1.18840
$621$	5.44727e12			1.46983
$622$		−	1.58924e11i		−	0.0425728i
$623$		−	3.26201e12i		−	0.867540i
$624$			2.72278e12i			0.718922i
$625$	−4.74784e12			−1.24462
$626$		−	2.35091e12i		−	0.611859i
$627$	1.63041e12			0.421301
$628$	2.52882e12			0.648784
$629$	−2.76917e12	+	5.52553e12i	−0.705378	+	1.40749i
$630$	−8.00436e11			−0.202439
$631$	2.59453e12			0.651519			0.325760	−	0.945453i	$-0.394380\pi$
$631$	2.59453e12			0.651519			0.325760	+	0.945453i	$0.394380\pi$
$632$		−	1.08788e12i		−	0.271239i
$633$	2.76294e11			0.0683998
$634$		−	9.20371e11i		−	0.226236i
$635$			2.34796e12i			0.573071i
$636$			1.99106e12i			0.482533i
$637$	1.08130e12			0.260207
$638$	6.99386e11			0.167118
$639$			4.96479e11i			0.117800i
$640$		−	5.42688e12i		−	1.27862i
$641$			1.33545e12i			0.312440i	0.987722	+	0.156220i	$0.0499309\pi$
$641$			1.33545e12i			0.312440i	−0.987722	+	0.156220i	$0.950069\pi$
$642$	4.35709e11			0.101225
$643$		−	3.82970e12i		−	0.883518i	−0.897134	−	0.441759i	$-0.854355\pi$
$643$		−	3.82970e12i		−	0.883518i	0.897134	−	0.441759i	$-0.145645\pi$
$644$	−4.59389e12			−1.05243
$645$	2.28837e12			0.520604
$646$	7.59321e11	+	3.80541e11i	0.171545	+	0.0859716i
$647$	3.08395e12			0.691891			0.345945	−	0.938255i	$-0.387558\pi$
$647$	3.08395e12			0.691891			0.345945	+	0.938255i	$0.387558\pi$
$648$	−1.27321e12			−0.283670
$649$		−	3.57752e12i		−	0.791554i
$650$	1.87895e12			0.412863
$651$		−	3.61601e12i		−	0.789069i
$652$			6.88147e12i			1.49131i
$653$		−	2.77681e12i		−	0.597636i	−0.954310	−	0.298818i	$-0.903408\pi$
$653$		−	2.77681e12i		−	0.597636i	0.954310	−	0.298818i	$-0.0965924\pi$
$654$	3.28094e11			0.0701290
$655$	5.98511e12			1.27053
$656$		−	2.75037e12i		−	0.579861i
$657$		−	1.19066e12i		−	0.249312i
$658$		−	1.95672e12i		−	0.406923i
$659$	−4.83603e12			−0.998861			−0.499430	−	0.866354i	$-0.666457\pi$
$659$	−4.83603e12			−0.998861			−0.499430	+	0.866354i	$0.666457\pi$
$660$			4.54227e12i			0.931805i
$661$	−2.72225e12			−0.554653			−0.277327	−	0.960776i	$-0.589448\pi$
$661$	−2.72225e12			−0.554653			−0.277327	+	0.960776i	$0.589448\pi$
$662$	3.18633e12			0.644808
$663$	2.99090e12	−	5.96796e12i	0.601161	−	1.19954i
$664$	7.89996e11			0.157713
$665$	2.77243e12			0.549747
$666$			1.39616e12i			0.274980i
$667$	−2.44060e12			−0.477452
$668$		−	3.14000e12i		−	0.610149i
$669$			5.49787e12i			1.06115i
$670$			2.20627e12i			0.422982i
$671$	1.04692e13			1.99371
$672$	3.53366e12			0.668441
$673$		−	1.85594e12i		−	0.348735i	−0.984681	−	0.174368i	$-0.944212\pi$
$673$		−	1.85594e12i		−	0.348735i	0.984681	−	0.174368i	$-0.0557881\pi$
$674$		−	2.19848e11i		−	0.0410349i
$675$		−	3.33765e12i		−	0.618833i
$676$	−9.84525e12			−1.81329
$677$		−	6.23311e12i		−	1.14040i	−0.821507	−	0.570198i	$-0.806867\pi$
$677$		−	6.23311e12i		−	1.14040i	0.821507	−	0.570198i	$-0.193133\pi$
$678$	−7.89952e10			−0.0143571
$679$	4.09375e12			0.739108
$680$	−2.32781e12	+	4.64485e12i	−0.417501	+	0.833071i
$681$	−6.97218e12			−1.24224
$682$	−3.05082e12			−0.539992
$683$			3.80694e12i			0.669395i	0.942326	+	0.334697i	$0.108634\pi$
$683$			3.80694e12i			0.669395i	−0.942326	+	0.334697i	$0.891366\pi$
$684$	−9.80464e11			−0.171269
$685$			9.49439e12i			1.64763i
$686$		−	2.48522e12i		−	0.428456i
$687$			7.56724e12i			1.29608i
$688$	1.73372e12			0.295006
$689$	−8.05860e12			−1.36230
$690$			3.10175e12i			0.520937i
$691$			6.26370e12i			1.04515i	0.852592	+	0.522576i	$0.175029\pi$
$691$			6.26370e12i			1.04515i	−0.852592	+	0.522576i	$0.824971\pi$
$692$		−	8.03706e12i		−	1.33235i
$693$	2.85406e12			0.470072
$694$		−	8.33751e11i		−	0.136433i
$695$	5.75577e12			0.935776
$696$	1.21545e12			0.196333
$697$	−3.02121e12	+	6.02844e12i	−0.484879	+	0.967515i
$698$	−1.73907e11			−0.0277311
$699$	−2.05279e12			−0.325236
$700$			2.81476e12i			0.443099i
$701$	−8.90825e12			−1.39335			−0.696677	−	0.717385i	$-0.745339\pi$
$701$	−8.90825e12			−1.39335			−0.696677	+	0.717385i	$0.745339\pi$
$702$		−	5.00062e12i		−	0.777154i
$703$		−	4.83580e12i		−	0.746740i
$704$			1.13339e12i			0.173900i
$705$	6.75149e12			1.02932
$706$	−7.76137e11			−0.117576
$707$		−	2.25184e12i		−	0.338961i
$708$		−	2.83159e12i		−	0.423527i
$709$		−	4.27216e12i		−	0.634950i	−0.948267	−	0.317475i	$-0.897165\pi$
$709$		−	4.27216e12i		−	0.634950i	0.948267	−	0.317475i	$-0.102835\pi$
$710$	−9.37487e11			−0.138453
$711$		−	1.07417e12i		−	0.157637i
$712$	−4.78290e12			−0.697480
$713$	1.06462e13			1.54274
$714$	−1.74947e12	−	8.76763e11i	−0.251921	−	0.126253i
$715$	−1.83843e13			−2.63070
$716$	−9.24524e12			−1.31465
$717$		−	1.05081e11i		−	0.0148486i
$718$	−3.11423e12			−0.437311
$719$			3.94871e12i			0.551030i	0.961297	+	0.275515i	$0.0888484\pi$
$719$			3.94871e12i			0.551030i	−0.961297	+	0.275515i	$0.911152\pi$
$720$		−	2.09243e12i		−	0.290171i
$721$		−	8.63540e12i		−	1.19007i
$722$	2.28930e12			0.313534
$723$	7.79271e11			0.106064
$724$			4.89857e12i			0.662591i
$725$			1.49540e12i			0.201019i
$726$			8.86573e11i			0.118440i
$727$	8.36118e12			1.11010			0.555051	−	0.831817i	$-0.312699\pi$
$727$	8.36118e12			1.11010			0.555051	+	0.831817i	$0.312699\pi$
$728$			9.25966e12i			1.22181i
$729$	−7.46132e12			−0.978457
$730$	2.24829e12			0.293021
$731$	−3.80007e12	−	1.90444e12i	−0.492225	−	0.246683i
$732$	8.28631e12			1.06675
$733$	7.60099e12			0.972529			0.486264	−	0.873812i	$-0.338359\pi$
$733$	7.60099e12			0.972529			0.486264	+	0.873812i	$0.338359\pi$
$734$		−	1.26538e12i		−	0.160912i
$735$	1.09370e12			0.138231
$736$			1.04038e13i			1.30690i
$737$		−	7.86674e12i		−	0.982180i
$738$			1.52323e12i			0.189022i
$739$	−3.28352e12			−0.404986			−0.202493	−	0.979284i	$-0.564904\pi$
$739$	−3.28352e12			−0.404986			−0.202493	+	0.979284i	$0.564904\pi$
$740$	1.34724e13			1.65159
$741$			5.22300e12i			0.636412i
$742$			2.36233e12i			0.286103i
$743$			1.32835e13i			1.59905i	0.600634	+	0.799524i	$0.294915\pi$
$743$			1.32835e13i			1.59905i	−0.600634	+	0.799524i	$0.705085\pi$
$744$	−5.30195e12			−0.634391
$745$			7.36890e11i			0.0876395i
$746$	4.86310e12			0.574895
$747$	7.80041e11			0.0916589
$748$	3.78020e12	−	7.54291e12i	0.441527	−	0.881012i
$749$	−2.64178e12			−0.306711
$750$	−1.41410e12			−0.163195
$751$		−	8.12330e12i		−	0.931865i	−0.884820	−	0.465932i	$-0.845719\pi$
$751$		−	8.12330e12i		−	0.931865i	0.884820	−	0.465932i	$-0.154281\pi$
$752$	5.11508e12			0.583273
$753$		−	1.21417e13i		−	1.37627i
$754$			2.24048e12i			0.252447i
$755$			2.36641e11i			0.0265051i
$756$	7.49117e12			0.834068
$757$	−3.70809e12			−0.410410			−0.205205	−	0.978719i	$-0.565786\pi$
$757$	−3.70809e12			−0.410410			−0.205205	+	0.978719i	$0.565786\pi$
$758$		−	5.00176e12i		−	0.550315i
$759$		−	1.10597e13i		−	1.20964i
$760$		−	4.06505e12i		−	0.441982i
$761$	−4.47551e11			−0.0483739			−0.0241870	−	0.999707i	$-0.507700\pi$
$761$	−4.47551e11			−0.0483739			−0.0241870	+	0.999707i	$0.507700\pi$
$762$			1.29667e12i			0.139326i
$763$	−1.98929e12			−0.212490
$764$	1.23449e12			0.131089
$765$	−2.29848e12	+	4.58632e12i	−0.242641	+	0.484159i
$766$	3.25420e12			0.341519
$767$	1.14606e13			1.19571
$768$		−	1.92441e12i		−	0.199605i
$769$	8.98580e12			0.926592			0.463296	−	0.886204i	$-0.346667\pi$
$769$	8.98580e12			0.926592			0.463296	+	0.886204i	$0.346667\pi$
$770$			5.38925e12i			0.552484i
$771$		−	3.30571e12i		−	0.336915i
$772$		−	1.33501e13i		−	1.35271i
$773$	4.99734e12			0.503421			0.251710	−	0.967803i	$-0.419007\pi$
$773$	4.99734e12			0.503421			0.251710	+	0.967803i	$0.419007\pi$
$774$	−9.60180e11			−0.0961653
$775$		−	6.52315e12i		−	0.649530i
$776$		−	6.00244e12i		−	0.594224i
$777$			1.11416e13i			1.09662i
$778$	−6.31030e12			−0.617507
$779$		−	5.27594e12i		−	0.513311i
$780$	−1.45511e13			−1.40757
$781$	3.34274e12			0.321494
$782$	2.58136e12	−	5.15078e12i	0.246841	−	0.492541i
$783$	3.97984e12			0.378388
$784$	8.28610e11			0.0783300
$785$			1.03525e13i			0.973043i
$786$	3.30531e12			0.308895
$787$			6.77515e12i			0.629554i	0.949166	+	0.314777i	$0.101930\pi$
$787$			6.77515e12i			0.629554i	−0.949166	+	0.314777i	$0.898070\pi$
$788$			1.32065e12i			0.122017i
$789$			1.87958e12i			0.172669i
$790$	2.02832e12			0.185274
$791$	4.78962e11			0.0435018
$792$		−	4.18475e12i		−	0.377925i
$793$			3.35380e13i			3.01167i
$794$			7.87050e12i			0.702765i
$795$	−8.15100e12			−0.723701
$796$			5.35813e12i			0.473047i
$797$	−1.23826e13			−1.08705			−0.543524	−	0.839394i	$-0.682910\pi$
$797$	−1.23826e13			−1.08705			−0.543524	+	0.839394i	$0.682910\pi$
$798$	1.53109e12			0.133656
$799$	−1.12116e13	−	5.61878e12i	−0.973208	−	0.487732i
$800$	6.37459e12			0.550234
$801$	−4.72263e12			−0.405357
$802$		−	2.28077e12i		−	0.194669i
$803$	−8.01657e12			−0.680407
$804$		−	6.22649e12i		−	0.525523i
$805$		−	1.88065e13i		−	1.57843i
$806$		−	9.77330e12i		−	0.815705i
$807$	−7.77178e12			−0.645044
$808$	−3.30174e12			−0.272516
$809$			1.06631e13i			0.875219i	0.899165	+	0.437610i	$0.144175\pi$
$809$			1.06631e13i			0.875219i	−0.899165	+	0.437610i	$0.855825\pi$
$810$		−	2.37388e12i		−	0.193765i
$811$			8.22083e12i			0.667301i	0.942697	+	0.333651i	$0.108281\pi$
$811$			8.22083e12i			0.667301i	−0.942697	+	0.333651i	$0.891719\pi$
$812$	−3.35635e12			−0.270935
$813$			1.11862e13i			0.897995i
$814$	9.40018e12			0.750458
$815$	−2.81714e13			−2.23666
$816$	2.29195e12	−	4.57330e12i	0.180967	−	0.361097i
$817$	3.32573e12			0.261148
$818$	−2.25560e12			−0.176146
$819$			9.14298e12i			0.710085i
$820$	1.46986e13			1.13531
$821$		−	1.44361e13i		−	1.10894i	−0.832205	−	0.554469i	$-0.812921\pi$
$821$		−	1.44361e13i		−	1.10894i	0.832205	−	0.554469i	$-0.187079\pi$
$822$			5.24333e12i			0.400575i
$823$			7.07329e12i			0.537430i	0.963220	+	0.268715i	$0.0865990\pi$
$823$			7.07329e12i			0.537430i	−0.963220	+	0.268715i	$0.913401\pi$
$824$	−1.26616e13			−0.956789
$825$	−6.77648e12			−0.509286
$826$		−	3.35959e12i		−	0.251117i
$827$		−	7.67968e12i		−	0.570911i	−0.958392	−	0.285456i	$-0.907855\pi$
$827$		−	7.67968e12i		−	0.570911i	0.958392	−	0.285456i	$-0.0921449\pi$
$828$			6.65087e12i			0.491747i
$829$	1.96058e13			1.44174			0.720872	−	0.693068i	$-0.243741\pi$
$829$	1.96058e13			1.44174			0.720872	+	0.693068i	$0.243741\pi$
$830$			1.47293e12i			0.107729i
$831$	1.64965e13			1.20002
$832$	−3.63080e12			−0.262692
$833$	−1.81620e12	−	9.10207e11i	−0.130696	−	0.0654994i
$834$	3.17866e12			0.227508
$835$	1.28546e13			0.915099
$836$			6.60136e12i			0.467417i
$837$	−1.73606e13			−1.22265
$838$			8.17038e11i			0.0572327i
$839$			2.18456e13i			1.52207i	0.648711	+	0.761035i	$0.275308\pi$
$839$			2.18456e13i			1.52207i	−0.648711	+	0.761035i	$0.724692\pi$
$840$			9.36584e12i			0.649068i
$841$	1.27240e13			0.877086
$842$	−1.32608e12			−0.0909215
$843$		−	1.64766e12i		−	0.112368i
$844$			1.11869e12i			0.0758870i
$845$		−	4.03045e13i		−	2.71956i
$846$	−2.83287e12			−0.190134
$847$		−	5.37546e12i		−	0.358873i
$848$	−6.17538e12			−0.410093
$849$	1.64806e12			0.108865
$850$	−3.15598e12	−	1.58165e12i	−0.207371	−	0.103926i
$851$	−3.28031e13			−2.14404
$852$	2.64576e12			0.172017
$853$		−	2.71420e13i		−	1.75538i	−0.479226	−	0.877691i	$-0.659083\pi$
$853$		−	2.71420e13i		−	1.75538i	0.479226	−	0.877691i	$-0.340917\pi$
$854$	9.83144e12			0.632494
$855$		−	4.01383e12i		−	0.256869i
$856$			3.87350e12i			0.246588i
$857$			1.35044e13i			0.855188i	0.903971	+	0.427594i	$0.140639\pi$
$857$			1.35044e13i			0.855188i	−0.903971	+	0.427594i	$0.859361\pi$
$858$	−1.01529e13			−0.639581
$859$	−4.28812e12			−0.268718			−0.134359	−	0.990933i	$-0.542898\pi$
$859$	−4.28812e12			−0.268718			−0.134359	+	0.990933i	$0.542898\pi$
$860$			9.26537e12i			0.577590i
$861$			1.21557e13i			0.753817i
$862$		−	6.47511e12i		−	0.399452i
$863$	1.91319e13			1.17411			0.587057	−	0.809546i	$-0.300287\pi$
$863$	1.91319e13			1.17411			0.587057	+	0.809546i	$0.300287\pi$
$864$		−	1.69653e13i		−	1.03573i
$865$	3.29021e13			1.99826
$866$	2.14142e11			0.0129381
$867$	−1.00473e13	+	7.50641e12i	−0.603898	+	0.451177i
$868$	1.46409e13			0.875443
$869$	−7.23225e12			−0.430214
$870$			2.26617e12i			0.134108i
$871$	2.52011e13			1.48367
$872$			2.91678e12i			0.170836i
$873$		−	5.92680e12i		−	0.345347i
$874$			4.50782e12i			0.261316i
$875$	8.57398e12			0.494477
$876$	−6.34508e12			−0.364057
$877$		−	2.05194e13i		−	1.17130i	−0.810565	−	0.585649i	$-0.800840\pi$
$877$		−	2.05194e13i		−	1.17130i	0.810565	−	0.585649i	$-0.199160\pi$
$878$			1.11954e13i			0.635791i
$879$		−	1.06347e13i		−	0.600861i
$880$	−1.40881e13			−0.791918
$881$		−	2.26888e12i		−	0.126888i	−0.997985	−	0.0634439i	$-0.979792\pi$
$881$		−	2.26888e12i		−	0.126888i	0.997985	−	0.0634439i	$-0.0202084\pi$
$882$	−4.58907e11			−0.0255339
$883$	−2.33723e13			−1.29383			−0.646916	−	0.762561i	$-0.723942\pi$
$883$	−2.33723e13			−1.29383			−0.646916	+	0.762561i	$0.723942\pi$
$884$	2.41637e13	+	1.21099e13i	1.33085	+	0.666966i
$885$	1.15920e13			0.635203
$886$	−9.24888e12			−0.504240
$887$			3.36710e13i			1.82642i	0.407494	+	0.913208i	$0.366403\pi$
$887$			3.36710e13i			1.82642i	−0.407494	+	0.913208i	$0.633597\pi$
$888$	1.63363e13			0.881651
$889$		−	7.86197e12i		−	0.422157i
$890$		−	8.91762e12i		−	0.476424i
$891$			8.46438e12i			0.449931i
$892$	−2.22603e13			−1.17731
$893$	9.81206e12			0.516332
$894$			4.06952e11i			0.0213071i
$895$		−	3.78482e13i		−	1.97170i
$896$			1.81715e13i			0.941900i
$897$	3.54297e13			1.82726
$898$			4.37195e11i			0.0224353i
$899$	7.77826e12			0.397158
$900$	4.07512e12			0.207037
$901$	1.35356e13	+	6.78349e12i	0.684252	+	0.342919i
$902$	1.02558e13			0.515867
$903$	−7.66244e12			−0.383506
$904$		−	7.02275e11i		−	0.0349743i
$905$	−2.00538e13			−0.993751
$906$			1.30687e11i			0.00644398i
$907$			1.86605e13i			0.915569i	0.889063	+	0.457784i	$0.151357\pi$
$907$			1.86605e13i			0.915569i	−0.889063	+	0.457784i	$0.848643\pi$
$908$		−	2.82296e13i		−	1.37822i
$909$	−3.26014e12			−0.158379
$910$	−1.72644e13			−0.834576
$911$		−	3.60008e13i		−	1.73173i	−0.500280	−	0.865864i	$-0.666769\pi$
$911$		−	3.60008e13i		−	1.73173i	0.500280	−	0.865864i	$-0.333231\pi$
$912$			4.00243e12i			0.191579i
$913$		−	5.25193e12i		−	0.250150i
$914$	−1.34562e13			−0.637773
$915$			3.39225e13i			1.59990i
$916$	−3.06390e13			−1.43795
$917$	−2.00407e13			−0.935947
$918$	−4.20938e12	+	8.39928e12i	−0.195626	+	0.390346i
$919$	3.51601e13			1.62603			0.813017	−	0.582240i	$-0.197823\pi$
$919$	3.51601e13			1.62603			0.813017	+	0.582240i	$0.197823\pi$
$920$	−2.75748e13			−1.26902
$921$		−	2.00722e13i		−	0.919233i
$922$	−1.51614e13			−0.690956
$923$			1.07084e13i			0.485645i
$924$		−	1.52095e13i		−	0.686420i
$925$			2.00991e13i			0.902690i
$926$	1.42188e12			0.0635499
$927$	−1.25020e13			−0.556061
$928$			7.60112e12i			0.336443i
$929$		−	3.54580e13i		−	1.56187i	−0.624614	−	0.780933i	$-0.714744\pi$
$929$		−	3.54580e13i		−	1.56187i	0.624614	−	0.780933i	$-0.285256\pi$
$930$		−	9.88536e12i		−	0.433331i
$931$	1.58949e12			0.0693402
$932$		−	8.31155e12i		−	0.360837i
$933$	−1.83612e12			−0.0793295
$934$	4.73371e12			0.203536
$935$	3.08792e13	+	1.54754e13i	1.32134	+	0.662200i
$936$	1.34058e13			0.570890
$937$	2.19169e13			0.928861			0.464431	−	0.885609i	$-0.346259\pi$
$937$	2.19169e13			0.928861			0.464431	+	0.885609i	$0.346259\pi$
$938$		−	7.38753e12i		−	0.311592i
$939$	−2.71612e13			−1.14013
$940$			2.73361e13i			1.14199i
$941$			3.66369e13i			1.52323i	0.648029	+	0.761615i	$0.275593\pi$
$941$			3.66369e13i			1.52323i	−0.648029	+	0.761615i	$0.724407\pi$
$942$			5.71723e12i			0.236568i
$943$	−3.57887e13			−1.47382
$944$	8.78233e12			0.359945
$945$			3.06674e13i			1.25093i
$946$			6.46479e12i			0.262449i
$947$			2.85170e13i			1.15220i	0.817379	+	0.576100i	$0.195426\pi$
$947$			2.85170e13i			1.15220i	−0.817379	+	0.576100i	$0.804574\pi$
$948$	−5.72430e12			−0.230189
$949$		−	2.56810e13i		−	1.02781i
$950$	2.76203e12			0.110020
$951$	−1.06335e13			−0.421564
$952$	7.79451e12	−	1.55530e13i	0.307555	−	0.613687i
$953$	−1.49368e13			−0.586598			−0.293299	−	0.956021i	$-0.594753\pi$
$953$	−1.49368e13			−0.586598			−0.293299	+	0.956021i	$0.594753\pi$
$954$	3.42009e12			0.133681
$955$			5.05374e12i			0.196607i
$956$	4.25461e11			0.0164740
$957$		−	8.08034e12i		−	0.311405i
$958$			4.18700e12i			0.160605i
$959$		−	3.17913e13i		−	1.21374i
$960$	−3.67243e12			−0.139551
$961$	−7.49025e12			−0.283296
$962$			3.01135e13i			1.13363i
$963$			3.82468e12i			0.143310i
$964$			3.15519e12i			0.117674i
$965$	5.46526e13			2.02879
$966$		−	1.03860e13i		−	0.383752i
$967$	4.03685e12			0.148465			0.0742324	−	0.997241i	$-0.476349\pi$
$967$	4.03685e12			0.148465			0.0742324	+	0.997241i	$0.476349\pi$
$968$	−7.88173e12			−0.288524
$969$	4.39657e12	−	8.77280e12i	0.160198	−	0.319655i
$970$	1.11914e13			0.405893
$971$	−1.48199e13			−0.535007			−0.267504	−	0.963557i	$-0.586199\pi$
$971$	−1.48199e13			−0.535007			−0.267504	+	0.963557i	$0.586199\pi$
$972$		−	1.84204e13i		−	0.661914i
$973$	−1.92728e13			−0.689346
$974$			1.64251e12i			0.0584779i
$975$		−	2.17084e13i		−	0.769321i
$976$			2.57005e13i			0.906602i
$977$	−4.73010e13			−1.66091			−0.830453	−	0.557089i	$-0.811918\pi$
$977$	−4.73010e13			−1.66091			−0.830453	+	0.557089i	$0.811918\pi$
$978$	−1.55578e13			−0.543781
$979$			3.17970e13i			1.10628i
$980$			4.42828e12i			0.153362i
$981$			2.88003e12i			0.0992856i
$982$	2.07494e13			0.712038
$983$		−	1.71849e13i		−	0.587025i	−0.955955	−	0.293512i	$-0.905176\pi$
$983$		−	1.71849e13i		−	0.587025i	0.955955	−	0.293512i	$-0.0948242\pi$
$984$	1.78232e13			0.606049
$985$	−5.40647e12			−0.183000
$986$	1.88597e12	−	3.76322e12i	0.0635461	−	0.126798i
$987$	−2.26069e13			−0.758252
$988$	−2.11474e13			−0.706075
$989$		−	2.25597e13i		−	0.749808i
$990$	7.80237e12			0.258148
$991$		−	6.36036e12i		−	0.209484i	−0.994499	−	0.104742i	$-0.966598\pi$
$991$		−	6.36036e12i		−	0.209484i	0.994499	−	0.104742i	$-0.0334016\pi$
$992$		−	3.31572e13i		−	1.08711i
$993$		−	3.68132e13i		−	1.20152i
$994$	3.13911e12			0.101992
$995$	−2.19351e13			−0.709474
$996$		−	4.15688e12i		−	0.133845i
$997$			3.01569e13i			0.966624i	0.875448	+	0.483312i	$0.160566\pi$
$997$			3.01569e13i			0.966624i	−0.875448	+	0.483312i	$0.839434\pi$
$998$		−	9.98647e12i		−	0.318658i
$999$	5.34915e13			1.69918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.b.a.16.6	yes	12
3.2	odd	2		153.10.d.b.118.8		12
4.3	odd	2		272.10.b.c.33.4		12
17.4	even	4		289.10.a.c.1.8		12
17.13	even	4		289.10.a.c.1.7		12
17.16	even	2	inner	17.10.b.a.16.5	✓	12
51.50	odd	2		153.10.d.b.118.7		12
68.67	odd	2		272.10.b.c.33.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.5	✓	12	17.16	even	2	inner
17.10.b.a.16.6	yes	12	1.1	even	1	trivial
153.10.d.b.118.7		12	51.50	odd	2
153.10.d.b.118.8		12	3.2	odd	2
272.10.b.c.33.4		12	4.3	odd	2
272.10.b.c.33.9		12	68.67	odd	2
289.10.a.c.1.7		12	17.13	even	4
289.10.a.c.1.8		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)

\(f(q)\)	\(=\)	\(q-9.15386 q^{2} +105.759i q^{3} -428.207 q^{4} -1752.99i q^{5} -968.101i q^{6} +5869.78i q^{7} +8606.52 q^{8} +8498.07 q^{9} +O(q^{10})\)	\(q-9.15386 q^{2} +105.759i q^{3} -428.207 q^{4} -1752.99i q^{5} -968.101i q^{6} +5869.78i q^{7} +8606.52 q^{8} +8498.07 q^{9} +16046.7i q^{10} -57216.5i q^{11} -45286.7i q^{12} +183293. q^{13} -53731.1i q^{14} +185395. q^{15} +140459. q^{16} +(-307867. - 154291. i) q^{17} -77790.1 q^{18} +269437. q^{19} +750644. i q^{20} -620781. q^{21} +523752. i q^{22} -1.82770e6i q^{23} +910216. i q^{24} -1.11987e6 q^{25} -1.67784e6 q^{26} +2.98040e6i q^{27} -2.51348e6i q^{28} -1.33534e6i q^{29} -1.69708e6 q^{30} +5.82494e6i q^{31} -5.69228e6 q^{32} +6.05116e6 q^{33} +(2.81817e6 + 1.41235e6i) q^{34} +1.02897e7 q^{35} -3.63893e6 q^{36} -1.79478e7i q^{37} -2.46639e6 q^{38} +1.93849e7i q^{39} -1.50872e7i q^{40} -1.95813e7i q^{41} +5.68254e6 q^{42} +1.23432e7 q^{43} +2.45005e7i q^{44} -1.48971e7i q^{45} +1.67305e7i q^{46} +3.64169e7 q^{47} +1.48548e7i q^{48} +5.89930e6 q^{49} +1.02511e7 q^{50} +(1.63176e7 - 3.25597e7i) q^{51} -7.84873e7 q^{52} -4.39657e7 q^{53} -2.72821e7i q^{54} -1.00300e8 q^{55} +5.05184e7i q^{56} +2.84954e7i q^{57} +1.22235e7i q^{58} +6.25259e7 q^{59} -7.93873e7 q^{60} +1.82975e8i q^{61} -5.33206e7i q^{62} +4.98818e7i q^{63} -1.98087e7 q^{64} -3.21312e8i q^{65} -5.53914e7 q^{66} +1.37491e8 q^{67} +(1.31831e8 + 6.60683e7i) q^{68} +1.93295e8 q^{69} -9.41904e7 q^{70} +5.84225e7i q^{71} +7.31388e7 q^{72} -1.40109e8i q^{73} +1.64291e8i q^{74} -1.18436e8i q^{75} -1.15375e8 q^{76} +3.35848e8 q^{77} -1.77446e8i q^{78} -1.26401e8i q^{79} -2.46224e8i q^{80} -1.47936e8 q^{81} +1.79245e8i q^{82} +9.17904e7 q^{83} +2.65823e8 q^{84} +(-2.70471e8 + 5.39690e8i) q^{85} -1.12988e8 q^{86} +1.41224e8 q^{87} -4.92435e8i q^{88} -5.55730e8 q^{89} +1.36366e8i q^{90} +1.07589e9i q^{91} +7.82634e8i q^{92} -6.16038e8 q^{93} -3.33355e8 q^{94} -4.72322e8i q^{95} -6.02009e8i q^{96} -6.97429e8i q^{97} -5.40014e7 q^{98} -4.86230e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9}+O(q^{10}) \) 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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