LMFDB - Embedded newform 85.2.d.a.16.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,2,Mod(16,85)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("85.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.4
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	85.16
Dual form			85.2.d.a.16.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.311108 q^{2} +2.21432i q^{3} -1.90321 q^{4} +1.00000i q^{5} -0.688892i q^{6} +1.59210i q^{7} +1.21432 q^{8} -1.90321 q^{9} -0.311108i q^{10} -1.31111i q^{11} -4.21432i q^{12} +3.52543 q^{13} -0.495316i q^{14} -2.21432 q^{15} +3.42864 q^{16} +(4.11753 - 0.214320i) q^{17} +0.592104 q^{18} -4.42864 q^{19} -1.90321i q^{20} -3.52543 q^{21} +0.407896i q^{22} -4.96989i q^{23} +2.68889i q^{24} -1.00000 q^{25} -1.09679 q^{26} +2.42864i q^{27} -3.03011i q^{28} -8.42864i q^{29} +0.688892 q^{30} +7.73975i q^{31} -3.49532 q^{32} +2.90321 q^{33} +(-1.28100 + 0.0666765i) q^{34} -1.59210 q^{35} +3.62222 q^{36} +7.05086i q^{37} +1.37778 q^{38} +7.80642i q^{39} +1.21432i q^{40} -3.67307i q^{41} +1.09679 q^{42} +2.47457 q^{43} +2.49532i q^{44} -1.90321i q^{45} +1.54617i q^{46} +3.33185 q^{47} +7.59210i q^{48} +4.46520 q^{49} +0.311108 q^{50} +(0.474572 + 9.11753i) q^{51} -6.70964 q^{52} -9.18421 q^{53} -0.755569i q^{54} +1.31111 q^{55} +1.93332i q^{56} -9.80642i q^{57} +2.62222i q^{58} +1.37778 q^{59} +4.21432 q^{60} -15.4193i q^{61} -2.40790i q^{62} -3.03011i q^{63} -5.76986 q^{64} +3.52543i q^{65} -0.903212 q^{66} -9.13828 q^{67} +(-7.83654 + 0.407896i) q^{68} +11.0049 q^{69} +0.495316 q^{70} -10.5970i q^{71} -2.31111 q^{72} +5.57136i q^{73} -2.19358i q^{74} -2.21432i q^{75} +8.42864 q^{76} +2.08742 q^{77} -2.42864i q^{78} -7.87310i q^{79} +3.42864i q^{80} -11.0874 q^{81} +1.14272i q^{82} +7.19850 q^{83} +6.70964 q^{84} +(0.214320 + 4.11753i) q^{85} -0.769859 q^{86} +18.6637 q^{87} -1.59210i q^{88} +11.6271 q^{89} +0.592104i q^{90} +5.61285i q^{91} +9.45875i q^{92} -17.1383 q^{93} -1.03657 q^{94} -4.42864i q^{95} -7.73975i q^{96} -15.4795i q^{97} -1.38916 q^{98} +2.49532i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 2 q^{4} - 6 q^{8} + 2 q^{9} + 8 q^{13} - 6 q^{16} - 2 q^{17} - 10 q^{18} - 8 q^{21} - 6 q^{25} - 20 q^{26} + 4 q^{30} + 6 q^{32} + 4 q^{33} + 6 q^{34} + 4 q^{35} + 22 q^{36} + 8 q^{38} + 20 q^{42}+ \cdots + 86 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 + 2 * q^4 - 6 * q^8 + 2 * q^9 + 8 * q^13 - 6 * q^16 - 2 * q^17 - 10 * q^18 - 8 * q^21 - 6 * q^25 - 20 * q^26 + 4 * q^30 + 6 * q^32 + 4 * q^33 + 6 * q^34 + 4 * q^35 + 22 * q^36 + 8 * q^38 + 20 * q^42 + 28 * q^43 - 20 * q^47 - 14 * q^49 + 2 * q^50 + 16 * q^51 - 28 * q^53 + 8 * q^55 + 8 * q^59 + 12 * q^60 - 22 * q^64 + 8 * q^66 + 12 * q^67 - 34 * q^68 - 24 * q^70 - 14 * q^72 + 24 * q^76 - 28 * q^77 - 26 * q^81 + 4 * q^83 - 12 * q^85 + 8 * q^86 + 32 * q^87 + 4 * q^89 - 36 * q^93 + 8 * q^94 + 86 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$-1$

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 $

$2$	−0.311108			−0.219986			−0.109993	−	0.993932i	$-0.535083\pi$
$2$	−0.311108			−0.219986			−0.109993	+	0.993932i	$0.535083\pi$
$3$			2.21432i			1.27844i	0.769025	+	0.639219i	$0.220742\pi$
$3$			2.21432i			1.27844i	−0.769025	+	0.639219i	$0.779258\pi$
$4$	−1.90321			−0.951606
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		−	0.688892i		−	0.281239i
$7$			1.59210i			0.601759i	0.953662	+	0.300879i	$0.0972802\pi$
$7$			1.59210i			0.601759i	−0.953662	+	0.300879i	$0.902720\pi$
$8$	1.21432			0.429327
$9$	−1.90321			−0.634404
$10$		−	0.311108i		−	0.0983809i
$11$		−	1.31111i		−	0.395314i	−0.980271	−	0.197657i	$-0.936667\pi$
$11$		−	1.31111i		−	0.395314i	0.980271	−	0.197657i	$-0.0633332\pi$
$12$		−	4.21432i		−	1.21657i
$13$	3.52543			0.977778			0.488889	−	0.872346i	$-0.337402\pi$
$13$	3.52543			0.977778			0.488889	+	0.872346i	$0.337402\pi$
$14$		−	0.495316i		−	0.132379i
$15$	−2.21432			−0.571735
$16$	3.42864			0.857160
$17$	4.11753	−	0.214320i	0.998648	−	0.0519802i
$17$	4.11753	−	0.214320i	0.998648	−	0.0519802i
$18$	0.592104			0.139560
$19$	−4.42864			−1.01600			−0.508000	−	0.861357i	$-0.669615\pi$
$19$	−4.42864			−1.01600			−0.508000	+	0.861357i	$0.669615\pi$
$20$		−	1.90321i		−	0.425571i
$21$	−3.52543			−0.769311
$22$			0.407896i			0.0869637i
$23$		−	4.96989i		−	1.03629i	−0.855292	−	0.518147i	$-0.826622\pi$
$23$		−	4.96989i		−	1.03629i	0.855292	−	0.518147i	$-0.173378\pi$
$24$			2.68889i			0.548868i
$25$	−1.00000			−0.200000
$26$	−1.09679			−0.215098
$27$			2.42864i			0.467392i
$28$		−	3.03011i		−	0.572637i
$29$		−	8.42864i		−	1.56516i	−0.622551	−	0.782580i	$-0.713904\pi$
$29$		−	8.42864i		−	1.56516i	0.622551	−	0.782580i	$-0.286096\pi$
$30$	0.688892			0.125774
$31$			7.73975i			1.39010i	0.718962	+	0.695050i	$0.244618\pi$
$31$			7.73975i			1.39010i	−0.718962	+	0.695050i	$0.755382\pi$
$32$	−3.49532			−0.617890
$33$	2.90321			0.505384
$34$	−1.28100	+	0.0666765i	−0.219689	+	0.0114349i
$35$	−1.59210			−0.269115
$36$	3.62222			0.603703
$37$			7.05086i			1.15915i	0.814918	+	0.579577i	$0.196782\pi$
$37$			7.05086i			1.15915i	−0.814918	+	0.579577i	$0.803218\pi$
$38$	1.37778			0.223506
$39$			7.80642i			1.25003i
$40$			1.21432i			0.192001i
$41$		−	3.67307i		−	0.573637i	−0.957985	−	0.286819i	$-0.907402\pi$
$41$		−	3.67307i		−	0.573637i	0.957985	−	0.286819i	$-0.0925977\pi$
$42$	1.09679			0.169238
$43$	2.47457			0.377369			0.188684	−	0.982038i	$-0.439578\pi$
$43$	2.47457			0.377369			0.188684	+	0.982038i	$0.439578\pi$
$44$			2.49532i			0.376183i
$45$		−	1.90321i		−	0.283714i
$46$			1.54617i			0.227970i
$47$	3.33185			0.486000			0.243000	−	0.970026i	$-0.421868\pi$
$47$	3.33185			0.486000			0.243000	+	0.970026i	$0.421868\pi$
$48$			7.59210i			1.09583i
$49$	4.46520			0.637886
$50$	0.311108			0.0439973
$51$	0.474572	+	9.11753i	0.0664534	+	1.27671i
$52$	−6.70964			−0.930459
$53$	−9.18421			−1.26155			−0.630774	−	0.775967i	$-0.717263\pi$
$53$	−9.18421			−1.26155			−0.630774	+	0.775967i	$0.717263\pi$
$54$		−	0.755569i		−	0.102820i
$55$	1.31111			0.176790
$56$			1.93332i			0.258351i
$57$		−	9.80642i		−	1.29889i
$58$			2.62222i			0.344314i
$59$	1.37778			0.179372			0.0896861	−	0.995970i	$-0.471414\pi$
$59$	1.37778			0.179372			0.0896861	+	0.995970i	$0.471414\pi$
$60$	4.21432			0.544066
$61$		−	15.4193i		−	1.97424i	−0.159996	−	0.987118i	$-0.551148\pi$
$61$		−	15.4193i		−	1.97424i	0.159996	−	0.987118i	$-0.448852\pi$
$62$		−	2.40790i		−	0.305803i
$63$		−	3.03011i		−	0.381758i
$64$	−5.76986			−0.721232
$65$			3.52543i			0.437275i
$66$	−0.903212			−0.111178
$67$	−9.13828			−1.11642			−0.558209	−	0.829700i	$-0.688511\pi$
$67$	−9.13828			−1.11642			−0.558209	+	0.829700i	$0.688511\pi$
$68$	−7.83654	+	0.407896i	−0.950320	+	0.0494646i
$69$	11.0049			1.32484
$70$	0.495316			0.0592016
$71$		−	10.5970i		−	1.25764i	−0.777553	−	0.628818i	$-0.783539\pi$
$71$		−	10.5970i		−	1.25764i	0.777553	−	0.628818i	$-0.216461\pi$
$72$	−2.31111			−0.272367
$73$			5.57136i			0.652078i	0.945356	+	0.326039i	$0.105714\pi$
$73$			5.57136i			0.652078i	−0.945356	+	0.326039i	$0.894286\pi$
$74$		−	2.19358i		−	0.254998i
$75$		−	2.21432i		−	0.255688i
$76$	8.42864			0.966831
$77$	2.08742			0.237884
$78$		−	2.42864i		−	0.274989i
$79$		−	7.87310i		−	0.885793i	−0.896573	−	0.442897i	$-0.853951\pi$
$79$		−	7.87310i		−	0.885793i	0.896573	−	0.442897i	$-0.146049\pi$
$80$			3.42864i			0.383334i
$81$	−11.0874			−1.23194
$82$			1.14272i			0.126192i
$83$	7.19850			0.790138			0.395069	−	0.918651i	$-0.370721\pi$
$83$	7.19850			0.790138			0.395069	+	0.918651i	$0.370721\pi$
$84$	6.70964			0.732081
$85$	0.214320	+	4.11753i	0.0232462	+	0.446609i
$86$	−0.769859			−0.0830160
$87$	18.6637			2.00096
$88$		−	1.59210i		−	0.169719i
$89$	11.6271			1.23247			0.616237	−	0.787561i	$-0.288656\pi$
$89$	11.6271			1.23247			0.616237	+	0.787561i	$0.288656\pi$
$90$			0.592104i			0.0624133i
$91$			5.61285i			0.588386i
$92$			9.45875i			0.986143i
$93$	−17.1383			−1.77716
$94$	−1.03657			−0.106914
$95$		−	4.42864i		−	0.454369i
$96$		−	7.73975i		−	0.789935i
$97$		−	15.4795i		−	1.57170i	−0.618414	−	0.785852i	$-0.712225\pi$
$97$		−	15.4795i		−	1.57170i	0.618414	−	0.785852i	$-0.287775\pi$
$98$	−1.38916			−0.140326
$99$			2.49532i			0.250789i
$100$	1.90321			0.190321
$101$	−14.3827			−1.43113			−0.715566	−	0.698545i	$-0.753831\pi$
$101$	−14.3827			−1.43113			−0.715566	+	0.698545i	$0.753831\pi$
$102$	−0.147643	−	2.83654i	−0.0146189	−	0.280859i
$103$	−9.39207			−0.925429			−0.462714	−	0.886507i	$-0.653124\pi$
$103$	−9.39207			−0.925429			−0.462714	+	0.886507i	$0.653124\pi$
$104$	4.28100			0.419786
$105$		−	3.52543i		−	0.344047i
$106$	2.85728			0.277523
$107$			6.77631i			0.655091i	0.944835	+	0.327545i	$0.106221\pi$
$107$			6.77631i			0.655091i	−0.944835	+	0.327545i	$0.893779\pi$
$108$		−	4.62222i		−	0.444773i
$109$			2.85728i			0.273678i	0.990593	+	0.136839i	$0.0436942\pi$
$109$			2.85728i			0.273678i	−0.990593	+	0.136839i	$0.956306\pi$
$110$	−0.407896			−0.0388913
$111$	−15.6128			−1.48191
$112$			5.45875i			0.515803i
$113$			5.86665i			0.551888i	0.961174	+	0.275944i	$0.0889904\pi$
$113$			5.86665i			0.551888i	−0.961174	+	0.275944i	$0.911010\pi$
$114$			3.05086i			0.285739i
$115$	4.96989			0.463444
$116$			16.0415i			1.48941i
$117$	−6.70964			−0.620306
$118$	−0.428639			−0.0394595
$119$	0.341219	+	6.55554i	0.0312795	+	0.600945i
$120$	−2.68889			−0.245461
$121$	9.28100			0.843727
$122$			4.79706i			0.434305i
$123$	8.13335			0.733360
$124$		−	14.7304i		−	1.32283i
$125$		−	1.00000i		−	0.0894427i
$126$			0.942691i			0.0839816i
$127$	0.280996			0.0249344			0.0124672	−	0.999922i	$-0.496031\pi$
$127$	0.280996			0.0249344			0.0124672	+	0.999922i	$0.496031\pi$
$128$	8.78568			0.776552
$129$			5.47949i			0.482443i
$130$		−	1.09679i		−	0.0961947i
$131$			13.4128i			1.17188i	0.810353	+	0.585942i	$0.199275\pi$
$131$			13.4128i			1.17188i	−0.810353	+	0.585942i	$0.800725\pi$
$132$	−5.52543			−0.480927
$133$		−	7.05086i		−	0.611387i
$134$	2.84299			0.245597
$135$	−2.42864			−0.209024
$136$	5.00000	−	0.260253i	0.428746	−	0.0223165i
$137$	10.2810			0.878365			0.439182	−	0.898398i	$-0.355268\pi$
$137$	10.2810			0.878365			0.439182	+	0.898398i	$0.355268\pi$
$138$	−3.42372			−0.291446
$139$			18.3017i			1.55233i	0.630528	+	0.776167i	$0.282838\pi$
$139$			18.3017i			1.55233i	−0.630528	+	0.776167i	$0.717162\pi$
$140$	3.03011			0.256091
$141$			7.37778i			0.621322i
$142$			3.29682i			0.276663i
$143$		−	4.62222i		−	0.386529i
$144$	−6.52543			−0.543786
$145$	8.42864			0.699960
$146$		−	1.73329i		−	0.143448i
$147$			9.88739i			0.815498i
$148$		−	13.4193i		−	1.10306i
$149$	−4.91750			−0.402857			−0.201429	−	0.979503i	$-0.564558\pi$
$149$	−4.91750			−0.402857			−0.201429	+	0.979503i	$0.564558\pi$
$150$			0.688892i			0.0562478i
$151$	12.7239			1.03546			0.517729	−	0.855545i	$-0.326777\pi$
$151$	12.7239			1.03546			0.517729	+	0.855545i	$0.326777\pi$
$152$	−5.37778			−0.436196
$153$	−7.83654	+	0.407896i	−0.633546	+	0.0329764i
$154$	−0.649413			−0.0523312
$155$	−7.73975			−0.621671
$156$		−	14.8573i		−	1.18953i
$157$	−9.18421			−0.732980			−0.366490	−	0.930422i	$-0.619441\pi$
$157$	−9.18421			−0.732980			−0.366490	+	0.930422i	$0.619441\pi$
$158$			2.44938i			0.194862i
$159$		−	20.3368i		−	1.61281i
$160$		−	3.49532i		−	0.276329i
$161$	7.91258			0.623599
$162$	3.44938			0.271009
$163$			5.07160i			0.397238i	0.980077	+	0.198619i	$0.0636457\pi$
$163$			5.07160i			0.397238i	−0.980077	+	0.198619i	$0.936354\pi$
$164$			6.99063i			0.545877i
$165$			2.90321i			0.226015i
$166$	−2.23951			−0.173820
$167$		−	19.8272i		−	1.53427i	−0.641484	−	0.767136i	$-0.721681\pi$
$167$		−	19.8272i		−	1.53427i	0.641484	−	0.767136i	$-0.278319\pi$
$168$	−4.28100			−0.330286
$169$	−0.571361			−0.0439508
$170$	−0.0666765	−	1.28100i	−0.00511386	−	0.0982479i
$171$	8.42864			0.644554
$172$	−4.70964			−0.359106
$173$		−	2.48886i		−	0.189225i	−0.995514	−	0.0946124i	$-0.969839\pi$
$173$		−	2.48886i		−	0.189225i	0.995514	−	0.0946124i	$-0.0301612\pi$
$174$	−5.80642			−0.440184
$175$		−	1.59210i		−	0.120352i
$176$		−	4.49532i		−	0.338847i
$177$			3.05086i			0.229316i
$178$	−3.61729			−0.271128
$179$	−11.6128			−0.867985			−0.433992	−	0.900916i	$-0.642896\pi$
$179$	−11.6128			−0.867985			−0.433992	+	0.900916i	$0.642896\pi$
$180$			3.62222i			0.269984i
$181$			3.86665i			0.287406i	0.989621	+	0.143703i	$0.0459009\pi$
$181$			3.86665i			0.287406i	−0.989621	+	0.143703i	$0.954099\pi$
$182$		−	1.74620i		−	0.129437i
$183$	34.1432			2.52394
$184$		−	6.03503i		−	0.444909i
$185$	−7.05086			−0.518389
$186$	5.33185			0.390950
$187$	−0.280996	−	5.39853i	−0.0205485	−	0.394779i
$188$	−6.34122			−0.462481
$189$	−3.86665			−0.281257
$190$			1.37778i			0.0999550i
$191$	−14.9175			−1.07939			−0.539696	−	0.841860i	$-0.681461\pi$
$191$	−14.9175			−1.07939			−0.539696	+	0.841860i	$0.681461\pi$
$192$		−	12.7763i		−	0.922051i
$193$			17.7462i			1.27740i	0.769456	+	0.638700i	$0.220527\pi$
$193$			17.7462i			1.27740i	−0.769456	+	0.638700i	$0.779473\pi$
$194$			4.81579i			0.345754i
$195$	−7.80642			−0.559030
$196$	−8.49823			−0.607016
$197$			9.41927i			0.671095i	0.942023	+	0.335548i	$0.108921\pi$
$197$			9.41927i			0.671095i	−0.942023	+	0.335548i	$0.891079\pi$
$198$		−	0.776312i		−	0.0551701i
$199$		−	7.21924i		−	0.511758i	−0.966709	−	0.255879i	$-0.917635\pi$
$199$		−	7.21924i		−	0.511758i	0.966709	−	0.255879i	$-0.0823649\pi$
$200$	−1.21432			−0.0858654
$201$		−	20.2351i		−	1.42727i
$202$	4.47457			0.314830
$203$	13.4193			0.941848
$204$	−0.903212	−	17.3526i	−0.0632375	−	1.21492i
$205$	3.67307			0.256538
$206$	2.92195			0.203582
$207$			9.45875i			0.657429i
$208$	12.0874			0.838112
$209$			5.80642i			0.401639i
$210$			1.09679i			0.0756856i
$211$		−	14.8825i		−	1.02455i	−0.858821	−	0.512276i	$-0.828803\pi$
$211$		−	14.8825i		−	1.02455i	0.858821	−	0.512276i	$-0.171197\pi$
$212$	17.4795			1.20050
$213$	23.4652			1.60781
$214$		−	2.10816i		−	0.144111i
$215$			2.47457i			0.168764i
$216$			2.94914i			0.200664i
$217$	−12.3225			−0.836505
$218$		−	0.888922i		−	0.0602054i
$219$	−12.3368			−0.833642
$220$	−2.49532			−0.168234
$221$	14.5161	−	0.755569i	0.976456	−	0.0508251i
$222$	4.85728			0.325999
$223$	−23.4652			−1.57135			−0.785673	−	0.618642i	$-0.787683\pi$
$223$	−23.4652			−1.57135			−0.785673	+	0.618642i	$0.787683\pi$
$224$		−	5.56491i		−	0.371821i
$225$	1.90321			0.126881
$226$		−	1.82516i		−	0.121408i
$227$		−	4.34767i		−	0.288565i	−0.989537	−	0.144283i	$-0.953913\pi$
$227$		−	4.34767i		−	0.288565i	0.989537	−	0.144283i	$-0.0460874\pi$
$228$			18.6637i			1.23603i
$229$	6.47457			0.427852			0.213926	−	0.976850i	$-0.431375\pi$
$229$	6.47457			0.427852			0.213926	+	0.976850i	$0.431375\pi$
$230$	−1.54617			−0.101952
$231$			4.62222i			0.304119i
$232$		−	10.2351i		−	0.671965i
$233$			18.5303i			1.21396i	0.794716	+	0.606982i	$0.207620\pi$
$233$			18.5303i			1.21396i	−0.794716	+	0.606982i	$0.792380\pi$
$234$	2.08742			0.136459
$235$			3.33185i			0.217346i
$236$	−2.62222			−0.170692
$237$	17.4336			1.13243
$238$	−0.106156	−	2.03948i	−0.00688107	−	0.132200i
$239$	−21.4193			−1.38550			−0.692749	−	0.721179i	$-0.743601\pi$
$239$	−21.4193			−1.38550			−0.692749	+	0.721179i	$0.743601\pi$
$240$	−7.59210			−0.490068
$241$			12.2351i			0.788130i	0.919083	+	0.394065i	$0.128931\pi$
$241$			12.2351i			0.788130i	−0.919083	+	0.394065i	$0.871069\pi$
$242$	−2.88739			−0.185608
$243$		−	17.2652i		−	1.10756i
$244$			29.3461i			1.87869i
$245$			4.46520i			0.285271i
$246$	−2.53035			−0.161329
$247$	−15.6128			−0.993422
$248$			9.39853i			0.596807i
$249$			15.9398i			1.01014i
$250$			0.311108i			0.0196762i
$251$	−4.52051			−0.285332			−0.142666	−	0.989771i	$-0.545567\pi$
$251$	−4.52051			−0.285332			−0.142666	+	0.989771i	$0.545567\pi$
$252$			5.76694i			0.363283i
$253$	−6.51606			−0.409661
$254$	−0.0874201			−0.00548523
$255$	−9.11753	+	0.474572i	−0.570962	+	0.0297189i
$256$	8.80642			0.550401
$257$	−6.18913			−0.386067			−0.193034	−	0.981192i	$-0.561833\pi$
$257$	−6.18913			−0.386067			−0.193034	+	0.981192i	$0.561833\pi$
$258$		−	1.70471i		−	0.106131i
$259$	−11.2257			−0.697531
$260$		−	6.70964i		−	0.416114i
$261$			16.0415i			0.992943i
$262$		−	4.17283i		−	0.257798i
$263$	8.18913			0.504963			0.252482	−	0.967602i	$-0.418753\pi$
$263$	8.18913			0.504963			0.252482	+	0.967602i	$0.418753\pi$
$264$	3.52543			0.216975
$265$		−	9.18421i		−	0.564181i
$266$			2.19358i			0.134497i
$267$			25.7462i			1.57564i
$268$	17.3921			1.06239
$269$		−	3.89829i		−	0.237683i	−0.992913	−	0.118841i	$-0.962082\pi$
$269$		−	3.89829i		−	0.237683i	0.992913	−	0.118841i	$-0.0379180\pi$
$270$	0.755569			0.0459824
$271$	8.85728			0.538041			0.269021	−	0.963134i	$-0.413300\pi$
$271$	8.85728			0.538041			0.269021	+	0.963134i	$0.413300\pi$
$272$	14.1175	−	0.734825i	0.856001	−	0.0445553i
$273$	−12.4286			−0.752215
$274$	−3.19850			−0.193228
$275$			1.31111i			0.0790628i
$276$	−20.9447			−1.26072
$277$			1.14272i			0.0686595i	0.999411	+	0.0343297i	$0.0109296\pi$
$277$			1.14272i			0.0686595i	−0.999411	+	0.0343297i	$0.989070\pi$
$278$		−	5.69381i		−	0.341492i
$279$		−	14.7304i		−	0.881885i
$280$	−1.93332			−0.115538
$281$	−14.6953			−0.876651			−0.438325	−	0.898816i	$-0.644428\pi$
$281$	−14.6953			−0.876651			−0.438325	+	0.898816i	$0.644428\pi$
$282$		−	2.29529i		−	0.136682i
$283$		−	1.97926i		−	0.117655i	−0.998268	−	0.0588273i	$-0.981264\pi$
$283$		−	1.97926i		−	0.117655i	0.998268	−	0.0588273i	$-0.0187361\pi$
$284$			20.1684i			1.19677i
$285$	9.80642			0.580882
$286$			1.43801i			0.0850312i
$287$	5.84791			0.345191
$288$	6.65233			0.391992
$289$	16.9081	−	1.76494i	0.994596	−	0.103820i
$290$	−2.62222			−0.153982
$291$	34.2766			2.00933
$292$		−	10.6035i		−	0.620522i
$293$	2.94914			0.172291			0.0861454	−	0.996283i	$-0.472545\pi$
$293$	2.94914			0.172291			0.0861454	+	0.996283i	$0.472545\pi$
$294$		−	3.07604i		−	0.179399i
$295$			1.37778i			0.0802177i
$296$			8.56199i			0.497656i
$297$	3.18421			0.184767
$298$	1.52987			0.0886232
$299$		−	17.5210i		−	1.01326i
$300$			4.21432i			0.243314i
$301$			3.93978i			0.227085i
$302$	−3.95851			−0.227787
$303$		−	31.8479i		−	1.82961i
$304$	−15.1842			−0.870874
$305$	15.4193			0.882905
$306$	2.43801	−	0.126900i	0.139372	−	0.00725437i
$307$	−5.68736			−0.324595			−0.162297	−	0.986742i	$-0.551890\pi$
$307$	−5.68736			−0.324595			−0.162297	+	0.986742i	$0.551890\pi$
$308$	−3.97280			−0.226371
$309$		−	20.7971i		−	1.18310i
$310$	2.40790			0.136759
$311$		−	23.7210i		−	1.34510i	−0.740054	−	0.672548i	$-0.765200\pi$
$311$		−	23.7210i		−	1.34510i	0.740054	−	0.672548i	$-0.234800\pi$
$312$			9.47949i			0.536671i
$313$		−	30.8988i		−	1.74650i	−0.487271	−	0.873251i	$-0.662008\pi$
$313$		−	30.8988i		−	1.74650i	0.487271	−	0.873251i	$-0.337992\pi$
$314$	2.85728			0.161246
$315$	3.03011			0.170727
$316$			14.9842i			0.842926i
$317$			13.7047i			0.769733i	0.922972	+	0.384867i	$0.125753\pi$
$317$			13.7047i			0.769733i	−0.922972	+	0.384867i	$0.874247\pi$
$318$			6.32693i			0.354797i
$319$	−11.0509			−0.618729
$320$		−	5.76986i		−	0.322545i
$321$	−15.0049			−0.837493
$322$	−2.46167			−0.137183
$323$	−18.2351	+	0.949145i	−1.01463	+	0.0528118i
$324$	21.1017			1.17232
$325$	−3.52543			−0.195556
$326$		−	1.57781i		−	0.0873870i
$327$	−6.32693			−0.349880
$328$		−	4.46028i		−	0.246278i
$329$			5.30465i			0.292455i
$330$		−	0.903212i		−	0.0497202i
$331$	24.8988			1.36856			0.684280	−	0.729219i	$-0.260117\pi$
$331$	24.8988			1.36856			0.684280	+	0.729219i	$0.260117\pi$
$332$	−13.7003			−0.751900
$333$		−	13.4193i		−	0.735372i
$334$			6.16839i			0.337519i
$335$		−	9.13828i		−	0.499277i
$336$	−12.0874			−0.659423
$337$			5.28592i			0.287942i	0.989582	+	0.143971i	$0.0459873\pi$
$337$			5.28592i			0.287942i	−0.989582	+	0.143971i	$0.954013\pi$
$338$	0.177755			0.00966858
$339$	−12.9906			−0.705554
$340$	−0.407896	−	7.83654i	−0.0221213	−	0.424996i
$341$	10.1476			0.549526
$342$	−2.62222			−0.141793
$343$			18.2538i			0.985613i
$344$	3.00492			0.162015
$345$			11.0049i			0.592485i
$346$			0.774305i			0.0416269i
$347$		−	31.6019i		−	1.69648i	−0.529611	−	0.848241i	$-0.677662\pi$
$347$		−	31.6019i		−	1.69648i	0.529611	−	0.848241i	$-0.322338\pi$
$348$	−35.5210			−1.90412
$349$	26.5116			1.41913			0.709567	−	0.704638i	$-0.248891\pi$
$349$	26.5116			1.41913			0.709567	+	0.704638i	$0.248891\pi$
$350$			0.495316i			0.0264758i
$351$			8.56199i			0.457005i
$352$			4.58274i			0.244261i
$353$	−3.71456			−0.197706			−0.0988530	−	0.995102i	$-0.531517\pi$
$353$	−3.71456			−0.197706			−0.0988530	+	0.995102i	$0.531517\pi$
$354$		−	0.949145i		−	0.0504465i
$355$	10.5970			0.562432
$356$	−22.1289			−1.17283
$357$	−14.5161	+	0.755569i	−0.768271	+	0.0399889i
$358$	3.61285			0.190945
$359$	10.6637			0.562809			0.281404	−	0.959589i	$-0.409200\pi$
$359$	10.6637			0.562809			0.281404	+	0.959589i	$0.409200\pi$
$360$		−	2.31111i		−	0.121806i
$361$	0.612848			0.0322551
$362$		−	1.20294i		−	0.0632253i
$363$			20.5511i			1.07865i
$364$		−	10.6824i		−	0.559912i
$365$	−5.57136			−0.291618
$366$	−10.6222			−0.555232
$367$		−	10.8780i		−	0.567828i	−0.958850	−	0.283914i	$-0.908367\pi$
$367$		−	10.8780i		−	0.567828i	0.958850	−	0.283914i	$-0.0916330\pi$
$368$		−	17.0400i		−	0.888269i
$369$			6.99063i			0.363918i
$370$	2.19358			0.114039
$371$		−	14.6222i		−	0.759148i
$372$	32.6178			1.69115
$373$	−16.5575			−0.857317			−0.428659	−	0.903467i	$-0.641014\pi$
$373$	−16.5575			−0.857317			−0.428659	+	0.903467i	$0.641014\pi$
$374$	0.0874201	+	1.67952i	0.00452039	+	0.0868461i
$375$	2.21432			0.114347
$376$	4.04593			0.208653
$377$		−	29.7146i		−	1.53038i
$378$	1.20294			0.0618728
$379$			8.16839i			0.419582i	0.977746	+	0.209791i	$0.0672783\pi$
$379$			8.16839i			0.419582i	−0.977746	+	0.209791i	$0.932722\pi$
$380$			8.42864i			0.432380i
$381$			0.622216i			0.0318771i
$382$	4.64095			0.237452
$383$	36.7926			1.88001			0.940007	−	0.341154i	$-0.110818\pi$
$383$	36.7926			1.88001			0.940007	+	0.341154i	$0.110818\pi$
$384$			19.4543i			0.992773i
$385$			2.08742i			0.106385i
$386$		−	5.52098i		−	0.281011i
$387$	−4.70964			−0.239404
$388$			29.4608i			1.49564i
$389$	12.5348			0.635539			0.317770	−	0.948168i	$-0.397066\pi$
$389$	12.5348			0.635539			0.317770	+	0.948168i	$0.397066\pi$
$390$	2.42864			0.122979
$391$	−1.06515	−	20.4637i	−0.0538667	−	1.03489i
$392$	5.42219			0.273862
$393$	−29.7003			−1.49818
$394$		−	2.93041i		−	0.147632i
$395$	7.87310			0.396139
$396$		−	4.74912i		−	0.238652i
$397$			32.1017i			1.61114i	0.592502	+	0.805569i	$0.298140\pi$
$397$			32.1017i			1.61114i	−0.592502	+	0.805569i	$0.701860\pi$
$398$			2.24596i			0.112580i
$399$	15.6128			0.781620
$400$	−3.42864			−0.171432
$401$			13.0321i			0.650793i	0.945578	+	0.325396i	$0.105498\pi$
$401$			13.0321i			0.650793i	−0.945578	+	0.325396i	$0.894502\pi$
$402$			6.29529i			0.313980i
$403$			27.2859i			1.35921i
$404$	27.3733			1.36187
$405$		−	11.0874i		−	0.550938i
$406$	−4.17484			−0.207194
$407$	9.24443			0.458229
$408$	0.576283	+	11.0716i	0.0285302	+	0.548126i
$409$	3.12399			0.154471			0.0772356	−	0.997013i	$-0.475391\pi$
$409$	3.12399			0.154471			0.0772356	+	0.997013i	$0.475391\pi$
$410$	−1.14272			−0.0564350
$411$			22.7654i			1.12294i
$412$	17.8751			0.880643
$413$			2.19358i			0.107939i
$414$		−	2.94269i		−	0.144625i
$415$			7.19850i			0.353360i
$416$	−12.3225			−0.604159
$417$	−40.5259			−1.98456
$418$		−	1.80642i		−	0.0883551i
$419$		−	13.1590i		−	0.642860i	−0.946933	−	0.321430i	$-0.895836\pi$
$419$		−	13.1590i		−	0.642860i	0.946933	−	0.321430i	$-0.104164\pi$
$420$			6.70964i			0.327397i
$421$	−27.6686			−1.34849			−0.674243	−	0.738509i	$-0.735530\pi$
$421$	−27.6686			−1.34849			−0.674243	+	0.738509i	$0.735530\pi$
$422$			4.63005i			0.225387i
$423$	−6.34122			−0.308321
$424$	−11.1526			−0.541616
$425$	−4.11753	+	0.214320i	−0.199730	+	0.0103960i
$426$	−7.30021			−0.353696
$427$	24.5491			1.18801
$428$		−	12.8968i		−	0.623388i
$429$	10.2351			0.494154
$430$		−	0.769859i		−	0.0371259i
$431$		−	17.6795i		−	0.851593i	−0.904819	−	0.425796i	$-0.859994\pi$
$431$		−	17.6795i		−	0.851593i	0.904819	−	0.425796i	$-0.140006\pi$
$432$			8.32693i			0.400630i
$433$	−24.9447			−1.19877			−0.599383	−	0.800462i	$-0.704587\pi$
$433$	−24.9447			−1.19877			−0.599383	+	0.800462i	$0.704587\pi$
$434$	3.83362			0.184020
$435$			18.6637i			0.894856i
$436$		−	5.43801i		−	0.260433i
$437$			22.0098i			1.05287i
$438$	3.83807			0.183390
$439$			11.9748i			0.571527i	0.958300	+	0.285763i	$0.0922471\pi$
$439$			11.9748i			0.571527i	−0.958300	+	0.285763i	$0.907753\pi$
$440$	1.59210			0.0759006
$441$	−8.49823			−0.404678
$442$	−4.51606	+	0.235063i	−0.214807	+	0.0111808i
$443$	−30.6909			−1.45817			−0.729084	−	0.684424i	$-0.760054\pi$
$443$	−30.6909			−1.45817			−0.729084	+	0.684424i	$0.760054\pi$
$444$	29.7146			1.41019
$445$			11.6271i			0.551179i
$446$	7.30021			0.345675
$447$		−	10.8889i		−	0.515028i
$448$		−	9.18622i		−	0.434008i
$449$			13.6543i			0.644388i	0.946674	+	0.322194i	$0.104420\pi$
$449$			13.6543i			0.644388i	−0.946674	+	0.322194i	$0.895580\pi$
$450$	−0.592104			−0.0279121
$451$	−4.81579			−0.226767
$452$		−	11.1655i		−	0.525180i
$453$			28.1748i			1.32377i
$454$			1.35260i			0.0634804i
$455$	−5.61285			−0.263134
$456$		−	11.9081i		−	0.557649i
$457$	−8.20787			−0.383948			−0.191974	−	0.981400i	$-0.561489\pi$
$457$	−8.20787			−0.383948			−0.191974	+	0.981400i	$0.561489\pi$
$458$	−2.01429			−0.0941216
$459$	0.520505	+	10.0000i	0.0242951	+	0.466760i
$460$	−9.45875			−0.441017
$461$	5.18421			0.241453			0.120726	−	0.992686i	$-0.461478\pi$
$461$	5.18421			0.241453			0.120726	+	0.992686i	$0.461478\pi$
$462$		−	1.43801i		−	0.0669022i
$463$	23.1985			1.07813			0.539063	−	0.842266i	$-0.318779\pi$
$463$	23.1985			1.07813			0.539063	+	0.842266i	$0.318779\pi$
$464$		−	28.8988i		−	1.34159i
$465$		−	17.1383i		−	0.794768i
$466$		−	5.76494i		−	0.267056i
$467$	−35.2400			−1.63071			−0.815356	−	0.578960i	$-0.803459\pi$
$467$	−35.2400			−1.63071			−0.815356	+	0.578960i	$0.803459\pi$
$468$	12.7699			0.590287
$469$		−	14.5491i		−	0.671814i
$470$		−	1.03657i		−	0.0478132i
$471$		−	20.3368i		−	0.937069i
$472$	1.67307			0.0770093
$473$		−	3.24443i		−	0.149179i
$474$	−5.42372			−0.249120
$475$	4.42864			0.203200
$476$	−0.649413	−	12.4766i	−0.0297658	−	0.571863i
$477$	17.4795			0.800331
$478$	6.66370			0.304791
$479$			11.4445i			0.522911i	0.965216	+	0.261455i	$0.0842024\pi$
$479$			11.4445i			0.522911i	−0.965216	+	0.261455i	$0.915798\pi$
$480$	7.73975			0.353270
$481$			24.8573i			1.13339i
$482$		−	3.80642i		−	0.173378i
$483$			17.5210i			0.797232i
$484$	−17.6637			−0.802896
$485$	15.4795			0.702888
$486$			5.37133i			0.243649i
$487$		−	29.7540i		−	1.34828i	−0.738602	−	0.674142i	$-0.764514\pi$
$487$		−	29.7540i		−	1.34828i	0.738602	−	0.674142i	$-0.235486\pi$
$488$		−	18.7239i		−	0.847592i
$489$	−11.2301			−0.507845
$490$		−	1.38916i		−	0.0627559i
$491$	25.4193			1.14716			0.573578	−	0.819151i	$-0.305555\pi$
$491$	25.4193			1.14716			0.573578	+	0.819151i	$0.305555\pi$
$492$	−15.4795			−0.697870
$493$	−1.80642	−	34.7052i	−0.0813572	−	1.56304i
$494$	4.85728			0.218539
$495$	−2.49532			−0.112156
$496$			26.5368i			1.19154i
$497$	16.8716			0.756793
$498$		−	4.95899i		−	0.222218i
$499$			14.8035i			0.662696i	0.943509	+	0.331348i	$0.107503\pi$
$499$			14.8035i			0.662696i	−0.943509	+	0.331348i	$0.892497\pi$
$500$			1.90321i			0.0851142i
$501$	43.9037			1.96147
$502$	1.40636			0.0627691
$503$			4.34767i			0.193853i	0.995292	+	0.0969266i	$0.0309012\pi$
$503$			4.34767i			0.193853i	−0.995292	+	0.0969266i	$0.969099\pi$
$504$		−	3.67952i		−	0.163899i
$505$		−	14.3827i		−	0.640022i
$506$	2.02720			0.0901199
$507$		−	1.26517i		−	0.0561884i
$508$	−0.534795			−0.0237277
$509$	−15.9813			−0.708357			−0.354179	−	0.935178i	$-0.615239\pi$
$509$	−15.9813			−0.708357			−0.354179	+	0.935178i	$0.615239\pi$
$510$	2.83654	−	0.147643i	0.125604	−	0.00653775i
$511$	−8.87019			−0.392394
$512$	−20.3111			−0.897633
$513$		−	10.7556i		−	0.474870i
$514$	1.92549			0.0849296
$515$		−	9.39207i		−	0.413864i
$516$		−	10.4286i		−	0.459095i
$517$		−	4.36842i		−	0.192123i
$518$	3.49240			0.153447
$519$	5.51114			0.241912
$520$			4.28100i			0.187734i
$521$			27.9081i			1.22268i	0.791369	+	0.611339i	$0.209369\pi$
$521$			27.9081i			1.22268i	−0.791369	+	0.611339i	$0.790631\pi$
$522$		−	4.99063i		−	0.218434i
$523$	15.8938			0.694989			0.347495	−	0.937682i	$-0.387032\pi$
$523$	15.8938			0.694989			0.347495	+	0.937682i	$0.387032\pi$
$524$		−	25.5274i		−	1.11517i
$525$	3.52543			0.153862
$526$	−2.54770			−0.111085
$527$	1.65878	+	31.8687i	0.0722576	+	1.38822i
$528$	9.95407			0.433195
$529$	−1.69979			−0.0739040
$530$			2.85728i			0.124112i
$531$	−2.62222			−0.113794
$532$			13.4193i			0.581799i
$533$		−	12.9491i		−	0.560890i
$534$		−	8.00984i		−	0.346620i
$535$	−6.77631			−0.292966
$536$	−11.0968			−0.479308
$537$		−	25.7146i		−	1.10967i
$538$			1.21279i			0.0522870i
$539$		−	5.85436i		−	0.252165i
$540$	4.62222			0.198908
$541$		−	24.2449i		−	1.04237i	−0.853444	−	0.521185i	$-0.825490\pi$
$541$		−	24.2449i		−	1.04237i	0.853444	−	0.521185i	$-0.174510\pi$
$542$	−2.75557			−0.118362
$543$	−8.56199			−0.367430
$544$	−14.3921	+	0.749115i	−0.617055	+	0.0321181i
$545$	−2.85728			−0.122392
$546$	3.86665			0.165477
$547$			11.7255i			0.501344i	0.968072	+	0.250672i	$0.0806516\pi$
$547$			11.7255i			0.501344i	−0.968072	+	0.250672i	$0.919348\pi$
$548$	−19.5669			−0.835857
$549$			29.3461i			1.25246i
$550$		−	0.407896i		−	0.0173927i
$551$			37.3274i			1.59020i
$552$	13.3635			0.568788
$553$	12.5348			0.533034
$554$		−	0.355509i		−	0.0151041i
$555$		−	15.6128i		−	0.662728i
$556$		−	34.8321i		−	1.47721i
$557$	−31.4336			−1.33188			−0.665941	−	0.746004i	$-0.731970\pi$
$557$	−31.4336			−1.33188			−0.665941	+	0.746004i	$0.731970\pi$
$558$			4.58274i			0.194003i
$559$	8.72393			0.368983
$560$	−5.45875			−0.230674
$561$	11.9541	−	0.622216i	0.504701	−	0.0262700i
$562$	4.57184			0.192851
$563$	11.9353			0.503014			0.251507	−	0.967855i	$-0.419074\pi$
$563$	11.9353			0.503014			0.251507	+	0.967855i	$0.419074\pi$
$564$		−	14.0415i		−	0.591253i
$565$	−5.86665			−0.246812
$566$			0.615762i			0.0258824i
$567$		−	17.6523i		−	0.741328i
$568$		−	12.8682i		−	0.539937i
$569$	1.14272			0.0479054			0.0239527	−	0.999713i	$-0.492375\pi$
$569$	1.14272			0.0479054			0.0239527	+	0.999713i	$0.492375\pi$
$570$	−3.05086			−0.127786
$571$			26.7402i			1.11904i	0.828816	+	0.559522i	$0.189015\pi$
$571$			26.7402i			1.11904i	−0.828816	+	0.559522i	$0.810985\pi$
$572$			8.79706i			0.367823i
$573$		−	33.0321i		−	1.37994i
$574$	−1.81933			−0.0759374
$575$			4.96989i			0.207259i
$576$	10.9813			0.457553
$577$	27.9956			1.16547			0.582735	−	0.812662i	$-0.301983\pi$
$577$	27.9956			1.16547			0.582735	+	0.812662i	$0.301983\pi$
$578$	−5.26025	+	0.549086i	−0.218798	+	0.0228389i
$579$	−39.2958			−1.63308
$580$	−16.0415			−0.666087
$581$			11.4608i			0.475472i
$582$	−10.6637			−0.442025
$583$			12.0415i			0.498707i
$584$			6.76541i			0.279955i
$585$		−	6.70964i		−	0.277409i
$586$	−0.917502			−0.0379017
$587$	6.60793			0.272738			0.136369	−	0.990658i	$-0.456457\pi$
$587$	6.60793			0.272738			0.136369	+	0.990658i	$0.456457\pi$
$588$		−	18.8178i		−	0.776033i
$589$		−	34.2766i		−	1.41234i
$590$		−	0.428639i		−	0.0176468i
$591$	−20.8573			−0.857954
$592$			24.1748i			0.993580i
$593$	−4.82564			−0.198165			−0.0990826	−	0.995079i	$-0.531591\pi$
$593$	−4.82564			−0.198165			−0.0990826	+	0.995079i	$0.531591\pi$
$594$	−0.990632			−0.0406461
$595$	−6.55554	+	0.341219i	−0.268751	+	0.0139886i
$596$	9.35905			0.383362
$597$	15.9857			0.654252
$598$			5.45091i			0.222904i
$599$	−39.0005			−1.59352			−0.796758	−	0.604298i	$-0.793454\pi$
$599$	−39.0005			−1.59352			−0.796758	+	0.604298i	$0.793454\pi$
$600$		−	2.68889i		−	0.109774i
$601$		−	7.19405i		−	0.293452i	−0.989177	−	0.146726i	$-0.953127\pi$
$601$		−	7.19405i		−	0.293452i	0.989177	−	0.146726i	$-0.0468735\pi$
$602$		−	1.22570i		−	0.0499556i
$603$	17.3921			0.708260
$604$	−24.2163			−0.985348
$605$			9.28100i			0.377326i
$606$			9.90813i			0.402490i
$607$			7.23353i			0.293600i	0.989166	+	0.146800i	$0.0468974\pi$
$607$			7.23353i			0.293600i	−0.989166	+	0.146800i	$0.953103\pi$
$608$	15.4795			0.627776
$609$			29.7146i			1.20409i
$610$	−4.79706			−0.194227
$611$	11.7462			0.475200
$612$	14.9146	−	0.776312i	0.602886	−	0.0313806i
$613$	14.7654			0.596369			0.298185	−	0.954508i	$-0.403619\pi$
$613$	14.7654			0.596369			0.298185	+	0.954508i	$0.403619\pi$
$614$	1.76938			0.0714065
$615$			8.13335i			0.327968i
$616$	2.53480			0.102130
$617$			10.5205i			0.423540i	0.977320	+	0.211770i	$0.0679227\pi$
$617$			10.5205i			0.423540i	−0.977320	+	0.211770i	$0.932077\pi$
$618$			6.47013i			0.260267i
$619$		−	7.94623i		−	0.319386i	−0.987167	−	0.159693i	$-0.948950\pi$
$619$		−	7.94623i		−	0.319386i	0.987167	−	0.159693i	$-0.0510504\pi$
$620$	14.7304			0.591586
$621$	12.0701			0.484355
$622$			7.37979i			0.295903i
$623$			18.5116i			0.741652i
$624$			26.7654i			1.07147i
$625$	1.00000			0.0400000
$626$			9.61285i			0.384207i
$627$	−12.8573			−0.513470
$628$	17.4795			0.697508
$629$	1.51114	+	29.0321i	0.0602530	+	1.15759i
$630$	−0.942691			−0.0375577
$631$	−14.2636			−0.567827			−0.283913	−	0.958850i	$-0.591633\pi$
$631$	−14.2636			−0.567827			−0.283913	+	0.958850i	$0.591633\pi$
$632$		−	9.56046i		−	0.380295i
$633$	32.9545			1.30983
$634$		−	4.26364i		−	0.169331i
$635$			0.280996i			0.0111510i
$636$			38.7052i			1.53476i
$637$	15.7418			0.623711
$638$	3.43801			0.136112
$639$			20.1684i			0.797849i
$640$			8.78568i			0.347285i
$641$		−	25.4509i		−	1.00525i	−0.864504	−	0.502625i	$-0.832368\pi$
$641$		−	25.4509i		−	1.00525i	0.864504	−	0.502625i	$-0.167632\pi$
$642$	4.66815			0.184237
$643$			16.1126i			0.635419i	0.948188	+	0.317710i	$0.102914\pi$
$643$			16.1126i			0.635419i	−0.948188	+	0.317710i	$0.897086\pi$
$644$	−15.0593			−0.593420
$645$	−5.47949			−0.215755
$646$	5.67307	−	0.295286i	0.223204	−	0.0116179i
$647$	40.4558			1.59048			0.795242	−	0.606293i	$-0.207344\pi$
$647$	40.4558			1.59048			0.795242	+	0.606293i	$0.207344\pi$
$648$	−13.4637			−0.528903
$649$		−	1.80642i		−	0.0709083i
$650$	1.09679			0.0430196
$651$		−	27.2859i		−	1.06942i
$652$		−	9.65233i		−	0.378014i
$653$			6.87601i			0.269079i	0.990908	+	0.134540i	$0.0429556\pi$
$653$			6.87601i			0.269079i	−0.990908	+	0.134540i	$0.957044\pi$
$654$	1.96836			0.0769689
$655$	−13.4128			−0.524082
$656$		−	12.5936i		−	0.491699i
$657$		−	10.6035i		−	0.413681i
$658$		−	1.65032i		−	0.0643361i
$659$	16.0286			0.624385			0.312192	−	0.950019i	$-0.398937\pi$
$659$	16.0286			0.624385			0.312192	+	0.950019i	$0.398937\pi$
$660$		−	5.52543i		−	0.215077i
$661$	−31.1655			−1.21220			−0.606098	−	0.795390i	$-0.707266\pi$
$661$	−31.1655			−1.21220			−0.606098	+	0.795390i	$0.707266\pi$
$662$	−7.74620			−0.301065
$663$	1.67307	+	32.1432i	0.0649767	+	1.24834i
$664$	8.74128			0.339227
$665$	7.05086			0.273420
$666$			4.17484i			0.161772i
$667$	−41.8894			−1.62196
$668$			37.7353i			1.46002i
$669$		−	51.9595i		−	2.00887i
$670$			2.84299i			0.109834i
$671$	−20.2163			−0.780443
$672$	12.3225			0.475350
$673$			19.8479i			0.765081i	0.923939	+	0.382540i	$0.124951\pi$
$673$			19.8479i			0.765081i	−0.923939	+	0.382540i	$0.875049\pi$
$674$		−	1.64449i		−	0.0633434i
$675$		−	2.42864i		−	0.0934784i
$676$	1.08742			0.0418239
$677$			28.8385i			1.10836i	0.832398	+	0.554178i	$0.186967\pi$
$677$			28.8385i			1.10836i	−0.832398	+	0.554178i	$0.813033\pi$
$678$	4.04149			0.155212
$679$	24.6450			0.945787
$680$	0.260253	+	5.00000i	0.00998024	+	0.191741i
$681$	9.62714			0.368913
$682$	−3.15701			−0.120888
$683$		−	19.2050i		−	0.734857i	−0.930052	−	0.367429i	$-0.880238\pi$
$683$		−	19.2050i		−	0.734857i	0.930052	−	0.367429i	$-0.119762\pi$
$684$	−16.0415			−0.613362
$685$			10.2810i			0.392817i
$686$		−	5.67890i		−	0.216821i
$687$			14.3368i			0.546982i
$688$	8.48442			0.323465
$689$	−32.3783			−1.23351
$690$		−	3.42372i		−	0.130339i
$691$		−	34.5555i		−	1.31455i	−0.753649	−	0.657277i	$-0.771708\pi$
$691$		−	34.5555i		−	1.31455i	0.753649	−	0.657277i	$-0.228292\pi$
$692$			4.73683i			0.180067i
$693$	−3.97280			−0.150914
$694$			9.83161i			0.373203i
$695$	−18.3017			−0.694225
$696$	22.6637			0.859065
$697$	−0.787212	−	15.1240i	−0.0298178	−	0.572862i
$698$	−8.24797			−0.312190
$699$	−41.0321			−1.55198
$700$			3.03011i			0.114527i
$701$	−20.9131			−0.789875			−0.394938	−	0.918708i	$-0.629234\pi$
$701$	−20.9131			−0.789875			−0.394938	+	0.918708i	$0.629234\pi$
$702$		−	2.66370i		−	0.100535i
$703$		−	31.2257i		−	1.17770i
$704$			7.56491i			0.285113i
$705$	−7.37778			−0.277863
$706$	1.15563			0.0434926
$707$		−	22.8988i		−	0.861197i
$708$		−	5.80642i		−	0.218219i
$709$		−	32.9906i		−	1.23899i	−0.785001	−	0.619495i	$-0.787338\pi$
$709$		−	32.9906i		−	1.23899i	0.785001	−	0.619495i	$-0.212662\pi$
$710$	−3.29682			−0.123727
$711$			14.9842i			0.561951i
$712$	14.1191			0.529134
$713$	38.4657			1.44055
$714$	4.51606	−	0.235063i	0.169009	−	0.00879702i
$715$	4.62222			0.172861
$716$	22.1017			0.825980
$717$		−	47.4291i		−	1.77127i
$718$	−3.31756			−0.123810
$719$		−	10.5141i		−	0.392108i	−0.980593	−	0.196054i	$-0.937187\pi$
$719$		−	10.5141i		−	0.392108i	0.980593	−	0.196054i	$-0.0628128\pi$
$720$		−	6.52543i		−	0.243188i
$721$		−	14.9532i		−	0.556885i
$722$	−0.190662			−0.00709569
$723$	−27.0923			−1.00758
$724$		−	7.35905i		−	0.273497i
$725$			8.42864i			0.313032i
$726$		−	6.39361i		−	0.237289i
$727$	43.2815			1.60522			0.802610	−	0.596503i	$-0.203444\pi$
$727$	43.2815			1.60522			0.802610	+	0.596503i	$0.203444\pi$
$728$			6.81579i			0.252610i
$729$	4.96836			0.184013
$730$	1.73329			0.0641521
$731$	10.1891	−	0.530350i	0.376859	−	0.0196157i
$732$	−64.9817			−2.40179
$733$	−22.8859			−0.845308			−0.422654	−	0.906291i	$-0.638902\pi$
$733$	−22.8859			−0.845308			−0.422654	+	0.906291i	$0.638902\pi$
$734$			3.38424i			0.124914i
$735$	−9.88739			−0.364702
$736$			17.3713i			0.640316i
$737$			11.9813i			0.441336i
$738$		−	2.17484i		−	0.0800570i
$739$	0.815792			0.0300094			0.0150047	−	0.999887i	$-0.495224\pi$
$739$	0.815792			0.0300094			0.0150047	+	0.999887i	$0.495224\pi$
$740$	13.4193			0.493302
$741$		−	34.5718i		−	1.27003i
$742$			4.54909i			0.167002i
$743$			30.1639i			1.10661i	0.832980	+	0.553304i	$0.186633\pi$
$743$			30.1639i			1.10661i	−0.832980	+	0.553304i	$0.813367\pi$
$744$	−20.8113			−0.762981
$745$		−	4.91750i		−	0.180163i
$746$	5.15118			0.188598
$747$	−13.7003			−0.501267
$748$	0.534795	+	10.2745i	0.0195541	+	0.375674i
$749$	−10.7886			−0.394207
$750$	−0.688892			−0.0251548
$751$			2.17728i			0.0794500i	0.999211	+	0.0397250i	$0.0126482\pi$
$751$			2.17728i			0.0794500i	−0.999211	+	0.0397250i	$0.987352\pi$
$752$	11.4237			0.416580
$753$		−	10.0098i		−	0.364779i
$754$			9.24443i			0.336662i
$755$			12.7239i			0.463071i
$756$	7.35905			0.267646
$757$	29.3230			1.06576			0.532881	−	0.846190i	$-0.321110\pi$
$757$	29.3230			1.06576			0.532881	+	0.846190i	$0.321110\pi$
$758$		−	2.54125i		−	0.0923023i
$759$		−	14.4286i		−	0.523726i
$760$		−	5.37778i		−	0.195073i
$761$	49.2212			1.78427			0.892134	−	0.451770i	$-0.149207\pi$
$761$	49.2212			1.78427			0.892134	+	0.451770i	$0.149207\pi$
$762$		−	0.193576i		−	0.00701252i
$763$	−4.54909			−0.164688
$764$	28.3912			1.02716
$765$	−0.407896	−	7.83654i	−0.0147475	−	0.283331i
$766$	−11.4465			−0.413578
$767$	4.85728			0.175386
$768$			19.5002i			0.703654i
$769$	37.0178			1.33490			0.667449	−	0.744656i	$-0.267386\pi$
$769$	37.0178			1.33490			0.667449	+	0.744656i	$0.267386\pi$
$770$		−	0.649413i		−	0.0234032i
$771$		−	13.7047i		−	0.493563i
$772$		−	33.7748i		−	1.21558i
$773$	−4.20787			−0.151346			−0.0756732	−	0.997133i	$-0.524111\pi$
$773$	−4.20787			−0.151346			−0.0756732	+	0.997133i	$0.524111\pi$
$774$	1.46520			0.0526657
$775$		−	7.73975i		−	0.278020i
$776$		−	18.7971i		−	0.674775i
$777$		−	24.8573i		−	0.891750i
$778$	−3.89967			−0.139810
$779$			16.2667i			0.582815i
$780$	14.8573			0.531976
$781$	−13.8938			−0.497161
$782$	0.331375	+	6.36641i	0.0118499	+	0.227662i
$783$	20.4701			0.731543
$784$	15.3096			0.546771
$785$		−	9.18421i		−	0.327798i
$786$	9.23999			0.329579
$787$			23.8557i			0.850366i	0.905108	+	0.425183i	$0.139790\pi$
$787$			23.8557i			0.850366i	−0.905108	+	0.425183i	$0.860210\pi$
$788$		−	17.9269i		−	0.638618i
$789$			18.1334i			0.645564i
$790$	−2.44938			−0.0871451
$791$	−9.34031			−0.332103
$792$			3.03011i			0.107670i
$793$		−	54.3595i		−	1.93036i
$794$		−	9.98709i		−	0.354429i
$795$	20.3368			0.721271
$796$			13.7397i			0.486992i
$797$	−34.4415			−1.21998			−0.609991	−	0.792408i	$-0.708827\pi$
$797$	−34.4415			−1.21998			−0.609991	+	0.792408i	$0.708827\pi$
$798$	−4.85728			−0.171946
$799$	13.7190	−	0.714082i	0.485343	−	0.0252624i
$800$	3.49532			0.123578
$801$	−22.1289			−0.781886
$802$		−	4.05439i		−	0.143166i
$803$	7.30465			0.257776
$804$			38.5116i			1.35820i
$805$			7.91258i			0.278882i
$806$		−	8.48886i		−	0.299007i
$807$	8.63206			0.303863
$808$	−17.4652			−0.614424
$809$		−	40.2578i		−	1.41539i	−0.706518	−	0.707695i	$-0.749735\pi$
$809$		−	40.2578i		−	1.41539i	0.706518	−	0.707695i	$-0.250265\pi$
$810$			3.44938i			0.121199i
$811$			20.4953i			0.719688i	0.933013	+	0.359844i	$0.117170\pi$
$811$			20.4953i			0.719688i	−0.933013	+	0.359844i	$0.882830\pi$
$812$	−25.5397			−0.896268
$813$			19.6128i			0.687853i
$814$	−2.87601			−0.100804
$815$	−5.07160			−0.177650
$816$	1.62714	+	31.2607i	0.0569612	+	1.09434i
$817$	−10.9590			−0.383407
$818$	−0.971896			−0.0339816
$819$		−	10.6824i		−	0.373275i
$820$	−6.99063			−0.244123
$821$			33.6958i			1.17599i	0.808864	+	0.587996i	$0.200083\pi$
$821$			33.6958i			1.17599i	−0.808864	+	0.587996i	$0.799917\pi$
$822$		−	7.08250i		−	0.247030i
$823$		−	16.6113i		−	0.579034i	−0.957173	−	0.289517i	$-0.906505\pi$
$823$		−	16.6113i		−	0.579034i	0.957173	−	0.289517i	$-0.0934947\pi$
$824$	−11.4050			−0.397311
$825$	−2.90321			−0.101077
$826$		−	0.682439i		−	0.0237451i
$827$			0.316030i			0.0109894i	0.999985	+	0.00549472i	$0.00174903\pi$
$827$			0.316030i			0.0109894i	−0.999985	+	0.00549472i	$0.998251\pi$
$828$		−	18.0020i		−	0.625613i
$829$	18.2034			0.632231			0.316115	−	0.948721i	$-0.397621\pi$
$829$	18.2034			0.632231			0.316115	+	0.948721i	$0.397621\pi$
$830$		−	2.23951i		−	0.0777345i
$831$	−2.53035			−0.0877769
$832$	−20.3412			−0.705205
$833$	18.3856	−	0.956981i	0.637024	−	0.0331574i
$834$	12.6079			0.436577
$835$	19.8272			0.686147
$836$		−	11.0509i		−	0.382202i
$837$	−18.7971			−0.649721
$838$			4.09387i			0.141421i
$839$			2.63851i			0.0910916i	0.998962	+	0.0455458i	$0.0145027\pi$
$839$			2.63851i			0.0910916i	−0.998962	+	0.0455458i	$0.985497\pi$
$840$		−	4.28100i		−	0.147708i
$841$	−42.0420			−1.44972
$842$	8.60793			0.296649
$843$		−	32.5402i		−	1.12074i
$844$			28.3245i			0.974969i
$845$		−	0.571361i		−	0.0196554i
$846$	1.97280			0.0678264
$847$			14.7763i			0.507720i
$848$	−31.4893			−1.08135
$849$	4.38271			0.150414
$850$	1.28100	−	0.0666765i	0.0439378	−	0.00228699i
$851$	35.0420			1.20122
$852$	−44.6593			−1.53000
$853$		−	4.68244i		−	0.160324i	−0.996782	−	0.0801618i	$-0.974456\pi$
$853$		−	4.68244i		−	0.160324i	0.996782	−	0.0801618i	$-0.0255437\pi$
$854$	−7.63741			−0.261347
$855$			8.42864i			0.288253i
$856$			8.22861i			0.281248i
$857$			47.3689i			1.61809i	0.587746	+	0.809045i	$0.300015\pi$
$857$			47.3689i			1.61809i	−0.587746	+	0.809045i	$0.699985\pi$
$858$	−3.18421			−0.108707
$859$	16.1748			0.551878			0.275939	−	0.961175i	$-0.411011\pi$
$859$	16.1748			0.551878			0.275939	+	0.961175i	$0.411011\pi$
$860$		−	4.70964i		−	0.160597i
$861$			12.9491i			0.441306i
$862$			5.50024i			0.187339i
$863$	−32.5674			−1.10861			−0.554303	−	0.832315i	$-0.687015\pi$
$863$	−32.5674			−1.10861			−0.554303	+	0.832315i	$0.687015\pi$
$864$		−	8.48886i		−	0.288797i
$865$	2.48886			0.0846239
$866$	7.76049			0.263712
$867$	3.90813	+	37.4400i	0.132727	+	1.27153i
$868$	23.4523			0.796023
$869$	−10.3225			−0.350166
$870$		−	5.80642i		−	0.196856i
$871$	−32.2163			−1.09161
$872$			3.46965i			0.117497i
$873$			29.4608i			0.997096i
$874$		−	6.84743i		−	0.231618i
$875$	1.59210			0.0538229
$876$	23.4795			0.793299
$877$			13.2543i			0.447565i	0.974639	+	0.223783i	$0.0718405\pi$
$877$			13.2543i			0.447565i	−0.974639	+	0.223783i	$0.928159\pi$
$878$		−	3.72546i		−	0.125728i
$879$			6.53035i			0.220263i
$880$	4.49532			0.151537
$881$			2.78721i			0.0939035i	0.998897	+	0.0469518i	$0.0149507\pi$
$881$			2.78721i			0.0939035i	−0.998897	+	0.0469518i	$0.985049\pi$
$882$	2.64387			0.0890236
$883$	−27.1985			−0.915302			−0.457651	−	0.889132i	$-0.651309\pi$
$883$	−27.1985			−0.915302			−0.457651	+	0.889132i	$0.651309\pi$
$884$	−27.6271	+	1.43801i	−0.929201	+	0.0483654i
$885$	−3.05086			−0.102553
$886$	9.54818			0.320777
$887$			48.2657i			1.62060i	0.586014	+	0.810301i	$0.300696\pi$
$887$			48.2657i			1.62060i	−0.586014	+	0.810301i	$0.699304\pi$
$888$	−18.9590			−0.636222
$889$			0.447375i			0.0150045i
$890$		−	3.61729i		−	0.121252i
$891$			14.5368i			0.487001i
$892$	44.6593			1.49530
$893$	−14.7556			−0.493776
$894$			3.38763i			0.113299i
$895$		−	11.6128i		−	0.388175i
$896$			13.9877i			0.467297i
$897$	38.7971			1.29540
$898$		−	4.24797i		−	0.141757i
$899$	65.2355			2.17573
$900$	−3.62222			−0.120741
$901$	−37.8163	+	1.96836i	−1.25984	+	0.0655755i
$902$	1.49823			0.0498856
$903$	−8.72393			−0.290314
$904$			7.12399i			0.236940i
$905$	−3.86665			−0.128532
$906$		−	8.76541i		−	0.291211i
$907$		−	8.93825i		−	0.296790i	−0.988928	−	0.148395i	$-0.952589\pi$
$907$		−	8.93825i		−	0.296790i	0.988928	−	0.148395i	$-0.0474106\pi$
$908$			8.27454i			0.274600i
$909$	27.3733			0.907916
$910$	1.74620			0.0578860
$911$			51.6795i			1.71222i	0.516794	+	0.856110i	$0.327125\pi$
$911$			51.6795i			1.71222i	−0.516794	+	0.856110i	$0.672875\pi$
$912$		−	33.6227i		−	1.11336i
$913$		−	9.43801i		−	0.312352i
$914$	2.55353			0.0844633
$915$			34.1432i			1.12874i
$916$	−12.3225			−0.407146
$917$	−21.3546			−0.705191
$918$	−0.161933	−	3.11108i	−0.00534460	−	0.102681i
$919$	18.9719			0.625825			0.312913	−	0.949782i	$-0.398695\pi$
$919$	18.9719			0.625825			0.312913	+	0.949782i	$0.398695\pi$
$920$	6.03503			0.198969
$921$		−	12.5936i		−	0.414974i
$922$	−1.61285			−0.0531163
$923$		−	37.3590i		−	1.22969i
$924$		−	8.79706i		−	0.289402i
$925$		−	7.05086i		−	0.231831i
$926$	−7.21723			−0.237173
$927$	17.8751			0.587096
$928$			29.4608i			0.967097i
$929$			50.3912i			1.65328i	0.562731	+	0.826640i	$0.309751\pi$
$929$			50.3912i			1.65328i	−0.562731	+	0.826640i	$0.690249\pi$
$930$			5.33185i			0.174838i
$931$	−19.7748			−0.648092
$932$		−	35.2672i		−	1.15521i
$933$	52.5259			1.71962
$934$	10.9634			0.358735
$935$	5.39853	−	0.280996i	0.176551	−	0.00918956i
$936$	−8.14764			−0.266314
$937$	58.1530			1.89978			0.949889	−	0.312589i	$-0.101196\pi$
$937$	58.1530			1.89978			0.949889	+	0.312589i	$0.101196\pi$
$938$			4.52633i			0.147790i
$939$	68.4197			2.23279
$940$		−	6.34122i		−	0.206828i
$941$		−	9.25734i		−	0.301781i	−0.988551	−	0.150890i	$-0.951786\pi$
$941$		−	9.25734i		−	0.301781i	0.988551	−	0.150890i	$-0.0482140\pi$
$942$			6.32693i			0.206142i
$943$	−18.2548			−0.594457
$944$	4.72393			0.153751
$945$		−	3.86665i		−	0.125782i
$946$			1.00937i			0.0328174i
$947$		−	43.9516i		−	1.42824i	−0.700025	−	0.714118i	$-0.746828\pi$
$947$		−	43.9516i		−	1.42824i	0.700025	−	0.714118i	$-0.253172\pi$
$948$	−33.1798			−1.07763
$949$			19.6414i			0.637588i
$950$	−1.37778			−0.0447012
$951$	−30.3466			−0.984057
$952$	0.414349	+	7.96052i	0.0134291	+	0.258002i
$953$	−38.1891			−1.23707			−0.618534	−	0.785758i	$-0.712273\pi$
$953$	−38.1891			−1.23707			−0.618534	+	0.785758i	$0.712273\pi$
$954$	−5.43801			−0.176062
$955$		−	14.9175i		−	0.482719i
$956$	40.7654			1.31845
$957$		−	24.4701i		−	0.791007i
$958$		−	3.56046i		−	0.115033i
$959$			16.3684i			0.528564i
$960$	12.7763			0.412354
$961$	−28.9037			−0.932377
$962$		−	7.73329i		−	0.249331i
$963$		−	12.8968i		−	0.415592i
$964$		−	23.2859i		−	0.749989i
$965$	−17.7462			−0.571270
$966$		−	5.45091i		−	0.175380i
$967$	−7.36043			−0.236696			−0.118348	−	0.992972i	$-0.537760\pi$
$967$	−7.36043			−0.236696			−0.118348	+	0.992972i	$0.537760\pi$
$968$	11.2701			0.362235
$969$	−2.10171	−	40.3783i	−0.0675167	−	1.29714i
$970$	−4.81579			−0.154626
$971$	−35.2257			−1.13045			−0.565223	−	0.824938i	$-0.691210\pi$
$971$	−35.2257			−1.13045			−0.565223	+	0.824938i	$0.691210\pi$
$972$			32.8593i			1.05396i
$973$	−29.1383			−0.934130
$974$			9.25671i			0.296604i
$975$		−	7.80642i		−	0.250006i
$976$		−	52.8671i		−	1.69224i
$977$	−46.9273			−1.50134			−0.750669	−	0.660678i	$-0.770269\pi$
$977$	−46.9273			−1.50134			−0.750669	+	0.660678i	$0.770269\pi$
$978$	3.49378			0.111719
$979$		−	15.2444i		−	0.487214i
$980$		−	8.49823i		−	0.271466i
$981$		−	5.43801i		−	0.173622i
$982$	−7.90813			−0.252359
$983$		−	8.21432i		−	0.261996i	−0.991383	−	0.130998i	$-0.958182\pi$
$983$		−	8.21432i		−	0.261996i	0.991383	−	0.130998i	$-0.0418182\pi$
$984$	9.87649			0.314851
$985$	−9.41927			−0.300123
$986$	0.561993	+	10.7971i	0.0178975	+	0.343848i
$987$	−11.7462			−0.373886
$988$	29.7146			0.945346
$989$		−	12.2983i		−	0.391065i
$990$	0.776312			0.0246728
$991$		−	17.7683i		−	0.564430i	−0.959351	−	0.282215i	$-0.908931\pi$
$991$		−	17.7683i		−	0.564430i	0.959351	−	0.282215i	$-0.0910691\pi$
$992$		−	27.0529i		−	0.858929i
$993$			55.1338i			1.74962i
$994$	−5.24888			−0.166484
$995$	7.21924			0.228865
$996$		−	30.3368i		−	0.961257i
$997$			11.6958i			0.370410i	0.982700	+	0.185205i	$0.0592950\pi$
$997$			11.6958i			0.370410i	−0.982700	+	0.185205i	$0.940705\pi$
$998$		−	4.60549i		−	0.145784i
$999$	−17.1240			−0.541779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.d.a.16.4	yes	6
3.2	odd	2		765.2.g.b.271.3		6
4.3	odd	2		1360.2.c.f.1121.1		6
5.2	odd	4		425.2.c.b.424.3		6
5.3	odd	4		425.2.c.a.424.4		6
5.4	even	2		425.2.d.c.101.3		6
17.4	even	4		1445.2.a.k.1.2		3
17.13	even	4		1445.2.a.j.1.2		3
17.16	even	2	inner	85.2.d.a.16.3	✓	6
51.50	odd	2		765.2.g.b.271.4		6
68.67	odd	2		1360.2.c.f.1121.6		6
85.4	even	4		7225.2.a.r.1.2		3
85.33	odd	4		425.2.c.b.424.4		6
85.64	even	4		7225.2.a.q.1.2		3
85.67	odd	4		425.2.c.a.424.3		6
85.84	even	2		425.2.d.c.101.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.d.a.16.3	✓	6	17.16	even	2	inner
85.2.d.a.16.4	yes	6	1.1	even	1	trivial
425.2.c.a.424.3		6	85.67	odd	4
425.2.c.a.424.4		6	5.3	odd	4
425.2.c.b.424.3		6	5.2	odd	4
425.2.c.b.424.4		6	85.33	odd	4
425.2.d.c.101.3		6	5.4	even	2
425.2.d.c.101.4		6	85.84	even	2
765.2.g.b.271.3		6	3.2	odd	2
765.2.g.b.271.4		6	51.50	odd	2
1360.2.c.f.1121.1		6	4.3	odd	2
1360.2.c.f.1121.6		6	68.67	odd	2
1445.2.a.j.1.2		3	17.13	even	4
1445.2.a.k.1.2		3	17.4	even	4
7225.2.a.q.1.2		3	85.64	even	4
7225.2.a.r.1.2		3	85.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.311108 q^{2} +2.21432i q^{3} -1.90321 q^{4} +1.00000i q^{5} -0.688892i q^{6} +1.59210i q^{7} +1.21432 q^{8} -1.90321 q^{9} -0.311108i q^{10} -1.31111i q^{11} -4.21432i q^{12} +3.52543 q^{13} -0.495316i q^{14} -2.21432 q^{15} +3.42864 q^{16} +(4.11753 - 0.214320i) q^{17} +0.592104 q^{18} -4.42864 q^{19} -1.90321i q^{20} -3.52543 q^{21} +0.407896i q^{22} -4.96989i q^{23} +2.68889i q^{24} -1.00000 q^{25} -1.09679 q^{26} +2.42864i q^{27} -3.03011i q^{28} -8.42864i q^{29} +0.688892 q^{30} +7.73975i q^{31} -3.49532 q^{32} +2.90321 q^{33} +(-1.28100 + 0.0666765i) q^{34} -1.59210 q^{35} +3.62222 q^{36} +7.05086i q^{37} +1.37778 q^{38} +7.80642i q^{39} +1.21432i q^{40} -3.67307i q^{41} +1.09679 q^{42} +2.47457 q^{43} +2.49532i q^{44} -1.90321i q^{45} +1.54617i q^{46} +3.33185 q^{47} +7.59210i q^{48} +4.46520 q^{49} +0.311108 q^{50} +(0.474572 + 9.11753i) q^{51} -6.70964 q^{52} -9.18421 q^{53} -0.755569i q^{54} +1.31111 q^{55} +1.93332i q^{56} -9.80642i q^{57} +2.62222i q^{58} +1.37778 q^{59} +4.21432 q^{60} -15.4193i q^{61} -2.40790i q^{62} -3.03011i q^{63} -5.76986 q^{64} +3.52543i q^{65} -0.903212 q^{66} -9.13828 q^{67} +(-7.83654 + 0.407896i) q^{68} +11.0049 q^{69} +0.495316 q^{70} -10.5970i q^{71} -2.31111 q^{72} +5.57136i q^{73} -2.19358i q^{74} -2.21432i q^{75} +8.42864 q^{76} +2.08742 q^{77} -2.42864i q^{78} -7.87310i q^{79} +3.42864i q^{80} -11.0874 q^{81} +1.14272i q^{82} +7.19850 q^{83} +6.70964 q^{84} +(0.214320 + 4.11753i) q^{85} -0.769859 q^{86} +18.6637 q^{87} -1.59210i q^{88} +11.6271 q^{89} +0.592104i q^{90} +5.61285i q^{91} +9.45875i q^{92} -17.1383 q^{93} -1.03657 q^{94} -4.42864i q^{95} -7.73975i q^{96} -15.4795i q^{97} -1.38916 q^{98} +2.49532i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 2 q^{4} - 6 q^{8} + 2 q^{9} + 8 q^{13} - 6 q^{16} - 2 q^{17} - 10 q^{18} - 8 q^{21} - 6 q^{25} - 20 q^{26} + 4 q^{30} + 6 q^{32} + 4 q^{33} + 6 q^{34} + 4 q^{35} + 22 q^{36} + 8 q^{38} + 20 q^{42}+ \cdots + 86 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 + 2 * q^4 - 6 * q^8 + 2 * q^9 + 8 * q^13 - 6 * q^16 - 2 * q^17 - 10 * q^18 - 8 * q^21 - 6 * q^25 - 20 * q^26 + 4 * q^30 + 6 * q^32 + 4 * q^33 + 6 * q^34 + 4 * q^35 + 22 * q^36 + 8 * q^38 + 20 * q^42 + 28 * q^43 - 20 * q^47 - 14 * q^49 + 2 * q^50 + 16 * q^51 - 28 * q^53 + 8 * q^55 + 8 * q^59 + 12 * q^60 - 22 * q^64 + 8 * q^66 + 12 * q^67 - 34 * q^68 - 24 * q^70 - 14 * q^72 + 24 * q^76 - 28 * q^77 - 26 * q^81 + 4 * q^83 - 12 * q^85 + 8 * q^86 + 32 * q^87 + 4 * q^89 - 36 * q^93 + 8 * q^94 + 86 * q^98

Introduction

L-functions

Modular forms

Varieties

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