LMFDB - Embedded newform 85.2.d.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(16,85)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

$q$-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	$-0.779258\pi$
$3$		−	2.21432i		−	1.27844i	0.769025	−	0.639219i	$-0.220742\pi$
$4$	−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	$-0.902720\pi$
$7$		−	1.59210i		−	0.601759i	0.953662	−	0.300879i	$-0.0972802\pi$
$8$	1.21432			0.429327
$9$	−1.90321			−0.634404
$10$			0.311108i			0.0983809i
$11$			1.31111i			0.395314i	0.980271	+	0.197657i	$0.0633332\pi$
$11$			1.31111i			0.395314i	−0.980271	+	0.197657i	$0.936667\pi$
$12$			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	$0.173378\pi$
$23$			4.96989i			1.03629i	−0.855292	+	0.518147i	$0.826622\pi$
$24$		−	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	$0.286096\pi$
$29$			8.42864i			1.56516i	−0.622551	+	0.782580i	$0.713904\pi$
$30$	0.688892			0.125774
$31$		−	7.73975i		−	1.39010i	−0.718962	−	0.695050i	$-0.755382\pi$
$31$		−	7.73975i		−	1.39010i	0.718962	−	0.695050i	$-0.244618\pi$
$32$	−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	$-0.803218\pi$
$37$		−	7.05086i		−	1.15915i	0.814918	−	0.579577i	$-0.196782\pi$
$38$	1.37778			0.223506
$39$		−	7.80642i		−	1.25003i
$40$		−	1.21432i		−	0.192001i
$41$			3.67307i			0.573637i	0.957985	+	0.286819i	$0.0925977\pi$
$41$			3.67307i			0.573637i	−0.957985	+	0.286819i	$0.907402\pi$
$42$	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	$0.448852\pi$
$61$			15.4193i			1.97424i	−0.159996	+	0.987118i	$0.551148\pi$
$62$			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	$0.216461\pi$
$71$			10.5970i			1.25764i	−0.777553	+	0.628818i	$0.783539\pi$
$72$	−2.31111			−0.272367
$73$		−	5.57136i		−	0.652078i	−0.945356	−	0.326039i	$-0.894286\pi$
$73$		−	5.57136i		−	0.652078i	0.945356	−	0.326039i	$-0.105714\pi$
$74$			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	$0.146049\pi$
$79$			7.87310i			0.885793i	−0.896573	+	0.442897i	$0.853951\pi$
$80$		−	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	$0.287775\pi$
$97$			15.4795i			1.57170i	−0.618414	+	0.785852i	$0.712225\pi$
$98$	−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	$-0.893779\pi$
$107$		−	6.77631i		−	0.655091i	0.944835	−	0.327545i	$-0.106221\pi$
$108$			4.62222i			0.444773i
$109$		−	2.85728i		−	0.273678i	−0.990593	−	0.136839i	$-0.956306\pi$
$109$		−	2.85728i		−	0.273678i	0.990593	−	0.136839i	$-0.0436942\pi$
$110$	−0.407896			−0.0388913
$111$	−15.6128			−1.48191
$112$		−	5.45875i		−	0.515803i
$113$		−	5.86665i		−	0.551888i	−0.961174	−	0.275944i	$-0.911010\pi$
$113$		−	5.86665i		−	0.551888i	0.961174	−	0.275944i	$-0.0889904\pi$
$114$		−	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	$-0.800725\pi$
$131$		−	13.4128i		−	1.17188i	0.810353	−	0.585942i	$-0.199275\pi$
$132$	−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	$-0.717162\pi$
$139$		−	18.3017i		−	1.55233i	0.630528	−	0.776167i	$-0.282838\pi$
$140$	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	$-0.936354\pi$
$163$		−	5.07160i		−	0.397238i	0.980077	−	0.198619i	$-0.0636457\pi$
$164$		−	6.99063i		−	0.545877i
$165$		−	2.90321i		−	0.226015i
$166$	−2.23951			−0.173820
$167$			19.8272i			1.53427i	0.641484	+	0.767136i	$0.278319\pi$
$167$			19.8272i			1.53427i	−0.641484	+	0.767136i	$0.721681\pi$
$168$	−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	$0.0301612\pi$
$173$			2.48886i			0.189225i	−0.995514	+	0.0946124i	$0.969839\pi$
$174$	−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	$-0.954099\pi$
$181$		−	3.86665i		−	0.287406i	0.989621	−	0.143703i	$-0.0459009\pi$
$182$			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	$-0.779473\pi$
$193$		−	17.7462i		−	1.27740i	0.769456	−	0.638700i	$-0.220527\pi$
$194$		−	4.81579i		−	0.345754i
$195$	−7.80642			−0.559030
$196$	−8.49823			−0.607016
$197$		−	9.41927i		−	0.671095i	−0.942023	−	0.335548i	$-0.891079\pi$
$197$		−	9.41927i		−	0.671095i	0.942023	−	0.335548i	$-0.108921\pi$
$198$			0.776312i			0.0551701i
$199$			7.21924i			0.511758i	0.966709	+	0.255879i	$0.0823649\pi$
$199$			7.21924i			0.511758i	−0.966709	+	0.255879i	$0.917635\pi$
$200$	−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	$0.171197\pi$
$211$			14.8825i			1.02455i	−0.858821	+	0.512276i	$0.828803\pi$
$212$	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	$0.0460874\pi$
$227$			4.34767i			0.288565i	−0.989537	+	0.144283i	$0.953913\pi$
$228$		−	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	$-0.792380\pi$
$233$		−	18.5303i		−	1.21396i	0.794716	−	0.606982i	$-0.207620\pi$
$234$	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	$-0.871069\pi$
$241$		−	12.2351i		−	0.788130i	0.919083	−	0.394065i	$-0.128931\pi$
$242$	−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	$0.0379180\pi$
$269$			3.89829i			0.237683i	−0.992913	+	0.118841i	$0.962082\pi$
$270$	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	$-0.989070\pi$
$277$		−	1.14272i		−	0.0686595i	0.999411	−	0.0343297i	$-0.0109296\pi$
$278$			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	$0.0187361\pi$
$283$			1.97926i			0.117655i	−0.998268	+	0.0588273i	$0.981264\pi$
$284$		−	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	$0.234800\pi$
$311$			23.7210i			1.34510i	−0.740054	+	0.672548i	$0.765200\pi$
$312$		−	9.47949i		−	0.536671i
$313$			30.8988i			1.74650i	0.487271	+	0.873251i	$0.337992\pi$
$313$			30.8988i			1.74650i	−0.487271	+	0.873251i	$0.662008\pi$
$314$	2.85728			0.161246
$315$	3.03011			0.170727
$316$		−	14.9842i		−	0.842926i
$317$		−	13.7047i		−	0.769733i	−0.922972	−	0.384867i	$-0.874247\pi$
$317$		−	13.7047i		−	0.769733i	0.922972	−	0.384867i	$-0.125753\pi$
$318$		−	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	$-0.954013\pi$
$337$		−	5.28592i		−	0.287942i	0.989582	−	0.143971i	$-0.0459873\pi$
$338$	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	$0.322338\pi$
$347$			31.6019i			1.69648i	−0.529611	+	0.848241i	$0.677662\pi$
$348$	−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	$0.0916330\pi$
$367$			10.8780i			0.567828i	−0.958850	+	0.283914i	$0.908367\pi$
$368$			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	$-0.932722\pi$
$379$		−	8.16839i		−	0.419582i	0.977746	−	0.209791i	$-0.0672783\pi$
$380$		−	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	$-0.701860\pi$
$397$		−	32.1017i		−	1.61114i	0.592502	−	0.805569i	$-0.298140\pi$
$398$		−	2.24596i		−	0.112580i
$399$	15.6128			0.781620
$400$	−3.42864			−0.171432
$401$		−	13.0321i		−	0.650793i	−0.945578	−	0.325396i	$-0.894502\pi$
$401$		−	13.0321i		−	0.650793i	0.945578	−	0.325396i	$-0.105498\pi$
$402$		−	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	$0.104164\pi$
$419$			13.1590i			0.642860i	−0.946933	+	0.321430i	$0.895836\pi$
$420$		−	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	$0.140006\pi$
$431$			17.6795i			0.851593i	−0.904819	+	0.425796i	$0.859994\pi$
$432$		−	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	$-0.907753\pi$
$439$		−	11.9748i		−	0.571527i	0.958300	−	0.285763i	$-0.0922471\pi$
$440$	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	$-0.895580\pi$
$449$		−	13.6543i		−	0.644388i	0.946674	−	0.322194i	$-0.104420\pi$
$450$	−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	$-0.915798\pi$
$479$		−	11.4445i		−	0.522911i	0.965216	−	0.261455i	$-0.0842024\pi$
$480$	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	$0.235486\pi$
$487$			29.7540i			1.34828i	−0.738602	+	0.674142i	$0.764514\pi$
$488$			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	$-0.892497\pi$
$499$		−	14.8035i		−	0.662696i	0.943509	−	0.331348i	$-0.107503\pi$
$500$		−	1.90321i		−	0.0851142i
$501$	43.9037			1.96147
$502$	1.40636			0.0627691
$503$		−	4.34767i		−	0.193853i	−0.995292	−	0.0969266i	$-0.969099\pi$
$503$		−	4.34767i		−	0.193853i	0.995292	−	0.0969266i	$-0.0309012\pi$
$504$			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	$-0.790631\pi$
$521$		−	27.9081i		−	1.22268i	0.791369	−	0.611339i	$-0.209369\pi$
$522$			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	$0.174510\pi$
$541$			24.2449i			1.04237i	−0.853444	+	0.521185i	$0.825490\pi$
$542$	−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	$-0.919348\pi$
$547$		−	11.7255i		−	0.501344i	0.968072	−	0.250672i	$-0.0806516\pi$
$548$	−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	$-0.810985\pi$
$571$		−	26.7402i		−	1.11904i	0.828816	−	0.559522i	$-0.189015\pi$
$572$		−	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	$0.0468735\pi$
$601$			7.19405i			0.293452i	−0.989177	+	0.146726i	$0.953127\pi$
$602$			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	$-0.953103\pi$
$607$		−	7.23353i		−	0.293600i	0.989166	−	0.146800i	$-0.0468974\pi$
$608$	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	$-0.932077\pi$
$617$		−	10.5205i		−	0.423540i	0.977320	−	0.211770i	$-0.0679227\pi$
$618$		−	6.47013i		−	0.260267i
$619$			7.94623i			0.319386i	0.987167	+	0.159693i	$0.0510504\pi$
$619$			7.94623i			0.319386i	−0.987167	+	0.159693i	$0.948950\pi$
$620$	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	$0.167632\pi$
$641$			25.4509i			1.00525i	−0.864504	+	0.502625i	$0.832368\pi$
$642$	4.66815			0.184237
$643$		−	16.1126i		−	0.635419i	−0.948188	−	0.317710i	$-0.897086\pi$
$643$		−	16.1126i		−	0.635419i	0.948188	−	0.317710i	$-0.102914\pi$
$644$	−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	$-0.957044\pi$
$653$		−	6.87601i		−	0.269079i	0.990908	−	0.134540i	$-0.0429556\pi$
$654$	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	$-0.875049\pi$
$673$		−	19.8479i		−	0.765081i	0.923939	−	0.382540i	$-0.124951\pi$
$674$			1.64449i			0.0633434i
$675$			2.42864i			0.0934784i
$676$	1.08742			0.0418239
$677$		−	28.8385i		−	1.10836i	−0.832398	−	0.554178i	$-0.813033\pi$
$677$		−	28.8385i		−	1.10836i	0.832398	−	0.554178i	$-0.186967\pi$
$678$	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	$0.119762\pi$
$683$			19.2050i			0.734857i	−0.930052	+	0.367429i	$0.880238\pi$
$684$	−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	$0.228292\pi$
$691$			34.5555i			1.31455i	−0.753649	+	0.657277i	$0.771708\pi$
$692$		−	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	$0.212662\pi$
$709$			32.9906i			1.23899i	−0.785001	+	0.619495i	$0.787338\pi$
$710$	−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	$0.0628128\pi$
$719$			10.5141i			0.392108i	−0.980593	+	0.196054i	$0.937187\pi$
$720$			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	$-0.813367\pi$
$743$		−	30.1639i		−	1.10661i	0.832980	−	0.553304i	$-0.186633\pi$
$744$	−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	$-0.987352\pi$
$751$		−	2.17728i		−	0.0794500i	0.999211	−	0.0397250i	$-0.0126482\pi$
$752$	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	$-0.860210\pi$
$787$		−	23.8557i		−	0.850366i	0.905108	−	0.425183i	$-0.139790\pi$
$788$			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	$0.250265\pi$
$809$			40.2578i			1.41539i	−0.706518	+	0.707695i	$0.749735\pi$
$810$		−	3.44938i		−	0.121199i
$811$		−	20.4953i		−	0.719688i	−0.933013	−	0.359844i	$-0.882830\pi$
$811$		−	20.4953i		−	0.719688i	0.933013	−	0.359844i	$-0.117170\pi$
$812$	−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	$-0.799917\pi$
$821$		−	33.6958i		−	1.17599i	0.808864	−	0.587996i	$-0.200083\pi$
$822$			7.08250i			0.247030i
$823$			16.6113i			0.579034i	0.957173	+	0.289517i	$0.0934947\pi$
$823$			16.6113i			0.579034i	−0.957173	+	0.289517i	$0.906505\pi$
$824$	−11.4050			−0.397311
$825$	−2.90321			−0.101077
$826$			0.682439i			0.0237451i
$827$		−	0.316030i		−	0.0109894i	−0.999985	−	0.00549472i	$-0.998251\pi$
$827$		−	0.316030i		−	0.0109894i	0.999985	−	0.00549472i	$-0.00174903\pi$
$828$			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	$-0.985497\pi$
$839$		−	2.63851i		−	0.0910916i	0.998962	−	0.0455458i	$-0.0145027\pi$
$840$			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	$0.0255437\pi$
$853$			4.68244i			0.160324i	−0.996782	+	0.0801618i	$0.974456\pi$
$854$	−7.63741			−0.261347
$855$		−	8.42864i		−	0.288253i
$856$		−	8.22861i		−	0.281248i
$857$		−	47.3689i		−	1.61809i	−0.587746	−	0.809045i	$-0.699985\pi$
$857$		−	47.3689i		−	1.61809i	0.587746	−	0.809045i	$-0.300015\pi$
$858$	−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	$-0.928159\pi$
$877$		−	13.2543i		−	0.447565i	0.974639	−	0.223783i	$-0.0718405\pi$
$878$			3.72546i			0.125728i
$879$		−	6.53035i		−	0.220263i
$880$	4.49532			0.151537
$881$		−	2.78721i		−	0.0939035i	−0.998897	−	0.0469518i	$-0.985049\pi$
$881$		−	2.78721i		−	0.0939035i	0.998897	−	0.0469518i	$-0.0149507\pi$
$882$	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	$-0.699304\pi$
$887$		−	48.2657i		−	1.62060i	0.586014	−	0.810301i	$-0.300696\pi$
$888$	−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	$0.0474106\pi$
$907$			8.93825i			0.296790i	−0.988928	+	0.148395i	$0.952589\pi$
$908$		−	8.27454i		−	0.274600i
$909$	27.3733			0.907916
$910$	1.74620			0.0578860
$911$		−	51.6795i		−	1.71222i	−0.516794	−	0.856110i	$-0.672875\pi$
$911$		−	51.6795i		−	1.71222i	0.516794	−	0.856110i	$-0.327125\pi$
$912$			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	$-0.690249\pi$
$929$		−	50.3912i		−	1.65328i	0.562731	−	0.826640i	$-0.309751\pi$
$930$		−	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	$0.0482140\pi$
$941$			9.25734i			0.301781i	−0.988551	+	0.150890i	$0.951786\pi$
$942$		−	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	$0.253172\pi$
$947$			43.9516i			1.42824i	−0.700025	+	0.714118i	$0.746828\pi$
$948$	−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	$0.0418182\pi$
$983$			8.21432i			0.261996i	−0.991383	+	0.130998i	$0.958182\pi$
$984$	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	$0.0910691\pi$
$991$			17.7683i			0.564430i	−0.959351	+	0.282215i	$0.908931\pi$
$992$			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	$-0.940705\pi$
$997$		−	11.6958i		−	0.370410i	0.982700	−	0.185205i	$-0.0592950\pi$
$998$			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.16.3	✓	6
3.2	odd	2		765.2.g.b.271.4		6
4.3	odd	2		1360.2.c.f.1121.6		6
5.2	odd	4		425.2.c.a.424.3		6
5.3	odd	4		425.2.c.b.424.4		6
5.4	even	2		425.2.d.c.101.4		6
17.4	even	4		1445.2.a.j.1.2		3
17.13	even	4		1445.2.a.k.1.2		3
17.16	even	2	inner	85.2.d.a.16.4	yes	6
51.50	odd	2		765.2.g.b.271.3		6
68.67	odd	2		1360.2.c.f.1121.1		6
85.4	even	4		7225.2.a.q.1.2		3
85.33	odd	4		425.2.c.a.424.4		6
85.64	even	4		7225.2.a.r.1.2		3
85.67	odd	4		425.2.c.b.424.3		6
85.84	even	2		425.2.d.c.101.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.d.a.16.3	✓	6	1.1	even	1	trivial
85.2.d.a.16.4	yes	6	17.16	even	2	inner
425.2.c.a.424.3		6	5.2	odd	4
425.2.c.a.424.4		6	85.33	odd	4
425.2.c.b.424.3		6	85.67	odd	4
425.2.c.b.424.4		6	5.3	odd	4
425.2.d.c.101.3		6	85.84	even	2
425.2.d.c.101.4		6	5.4	even	2
765.2.g.b.271.3		6	51.50	odd	2
765.2.g.b.271.4		6	3.2	odd	2
1360.2.c.f.1121.1		6	68.67	odd	2
1360.2.c.f.1121.6		6	4.3	odd	2
1445.2.a.j.1.2		3	17.4	even	4
1445.2.a.k.1.2		3	17.13	even	4
7225.2.a.q.1.2		3	85.4	even	4
7225.2.a.r.1.2		3	85.64	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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
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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Representations

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Database

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