LMFDB - Embedded newform 85.2.d.a.16.2

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			16.2
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	85.16
Dual form			85.2.d.a.16.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.17009 q^{2} +0.539189i q^{3} +2.70928 q^{4} -1.00000i q^{5} -1.17009i q^{6} +4.87936i q^{7} -1.53919 q^{8} +2.70928 q^{9} +2.17009i q^{10} +3.17009i q^{11} +1.46081i q^{12} +2.63090 q^{13} -10.5886i q^{14} +0.539189 q^{15} -2.07838 q^{16} +(-3.24846 - 2.53919i) q^{17} -5.87936 q^{18} +1.07838 q^{19} -2.70928i q^{20} -2.63090 q^{21} -6.87936i q^{22} -5.21953i q^{23} -0.829914i q^{24} -1.00000 q^{25} -5.70928 q^{26} +3.07838i q^{27} +13.2195i q^{28} +2.92162i q^{29} -1.17009 q^{30} -4.09171i q^{31} +7.58864 q^{32} -1.70928 q^{33} +(7.04945 + 5.51026i) q^{34} +4.87936 q^{35} +7.34017 q^{36} -5.26180i q^{37} -2.34017 q^{38} +1.41855i q^{39} +1.53919i q^{40} +5.60197i q^{41} +5.70928 q^{42} +3.36910 q^{43} +8.58864i q^{44} -2.70928i q^{45} +11.3268i q^{46} -6.78765 q^{47} -1.12064i q^{48} -16.8082 q^{49} +2.17009 q^{50} +(1.36910 - 1.75154i) q^{51} +7.12783 q^{52} +3.75872 q^{53} -6.68035i q^{54} +3.17009 q^{55} -7.51026i q^{56} +0.581449i q^{57} -6.34017i q^{58} -2.34017 q^{59} +1.46081 q^{60} -12.2557i q^{61} +8.87936i q^{62} +13.2195i q^{63} -12.3112 q^{64} -2.63090i q^{65} +3.70928 q^{66} +10.2062 q^{67} +(-8.80098 - 6.87936i) q^{68} +2.81432 q^{69} -10.5886 q^{70} -4.06505i q^{71} -4.17009 q^{72} -11.0784i q^{73} +11.4186i q^{74} -0.539189i q^{75} +2.92162 q^{76} -15.4680 q^{77} -3.07838i q^{78} -6.92881i q^{79} +2.07838i q^{80} +6.46800 q^{81} -12.1568i q^{82} +8.23287 q^{83} -7.12783 q^{84} +(-2.53919 + 3.24846i) q^{85} -7.31124 q^{86} -1.57531 q^{87} -4.87936i q^{88} +7.15449 q^{89} +5.87936i q^{90} +12.8371i q^{91} -14.1412i q^{92} +2.20620 q^{93} +14.7298 q^{94} -1.07838i q^{95} +4.09171i q^{96} +8.18342i q^{97} +36.4752 q^{98} +8.58864i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.17009			−1.53448			−0.767241	−	0.641358i	$-0.778371\pi$
$2$	−2.17009			−1.53448			−0.767241	+	0.641358i	$0.778371\pi$
$3$			0.539189i			0.311301i	0.987812	+	0.155650i	$0.0497473\pi$
$3$			0.539189i			0.311301i	−0.987812	+	0.155650i	$0.950253\pi$
$4$	2.70928			1.35464
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		−	1.17009i		−	0.477686i
$7$			4.87936i			1.84423i	0.386921	+	0.922113i	$0.373538\pi$
$7$			4.87936i			1.84423i	−0.386921	+	0.922113i	$0.626462\pi$
$8$	−1.53919			−0.544185
$9$	2.70928			0.903092
$10$			2.17009i			0.686242i
$11$			3.17009i			0.955817i	0.878410	+	0.477909i	$0.158605\pi$
$11$			3.17009i			0.955817i	−0.878410	+	0.477909i	$0.841395\pi$
$12$			1.46081i			0.421700i
$13$	2.63090			0.729680			0.364840	−	0.931070i	$-0.381124\pi$
$13$	2.63090			0.729680			0.364840	+	0.931070i	$0.381124\pi$
$14$		−	10.5886i		−	2.82993i
$15$	0.539189			0.139218
$16$	−2.07838			−0.519594
$17$	−3.24846	−	2.53919i	−0.787868	−	0.615844i
$17$	−3.24846	−	2.53919i	−0.787868	−	0.615844i
$18$	−5.87936			−1.38578
$19$	1.07838			0.247397			0.123698	−	0.992320i	$-0.460524\pi$
$19$	1.07838			0.247397			0.123698	+	0.992320i	$0.460524\pi$
$20$		−	2.70928i		−	0.605812i
$21$	−2.63090			−0.574109
$22$		−	6.87936i		−	1.46668i
$23$		−	5.21953i		−	1.08835i	−0.838972	−	0.544174i	$-0.816843\pi$
$23$		−	5.21953i		−	1.08835i	0.838972	−	0.544174i	$-0.183157\pi$
$24$		−	0.829914i		−	0.169405i
$25$	−1.00000			−0.200000
$26$	−5.70928			−1.11968
$27$			3.07838i			0.592434i
$28$			13.2195i			2.49826i
$29$			2.92162i			0.542532i	0.962504	+	0.271266i	$0.0874422\pi$
$29$			2.92162i			0.542532i	−0.962504	+	0.271266i	$0.912558\pi$
$30$	−1.17009			−0.213628
$31$		−	4.09171i		−	0.734893i	−0.930045	−	0.367446i	$-0.880232\pi$
$31$		−	4.09171i		−	0.734893i	0.930045	−	0.367446i	$-0.119768\pi$
$32$	7.58864			1.34149
$33$	−1.70928			−0.297547
$34$	7.04945	+	5.51026i	1.20897	+	0.945002i
$35$	4.87936			0.824763
$36$	7.34017			1.22336
$37$		−	5.26180i		−	0.865034i	−0.901626	−	0.432517i	$-0.857626\pi$
$37$		−	5.26180i		−	0.865034i	0.901626	−	0.432517i	$-0.142374\pi$
$38$	−2.34017			−0.379626
$39$			1.41855i			0.227150i
$40$			1.53919i			0.243367i
$41$			5.60197i			0.874880i	0.899247	+	0.437440i	$0.144115\pi$
$41$			5.60197i			0.874880i	−0.899247	+	0.437440i	$0.855885\pi$
$42$	5.70928			0.880960
$43$	3.36910			0.513783			0.256892	−	0.966440i	$-0.417302\pi$
$43$	3.36910			0.513783			0.256892	+	0.966440i	$0.417302\pi$
$44$			8.58864i			1.29479i
$45$		−	2.70928i		−	0.403875i
$46$			11.3268i			1.67005i
$47$	−6.78765			−0.990081			−0.495040	−	0.868870i	$-0.664847\pi$
$47$	−6.78765			−0.990081			−0.495040	+	0.868870i	$0.664847\pi$
$48$		−	1.12064i		−	0.161750i
$49$	−16.8082			−2.40117
$50$	2.17009			0.306897
$51$	1.36910	−	1.75154i	0.191713	−	0.245264i
$52$	7.12783			0.988452
$53$	3.75872			0.516300			0.258150	−	0.966105i	$-0.416887\pi$
$53$	3.75872			0.516300			0.258150	+	0.966105i	$0.416887\pi$
$54$		−	6.68035i		−	0.909080i
$55$	3.17009			0.427454
$56$		−	7.51026i		−	1.00360i
$57$			0.581449i			0.0770148i
$58$		−	6.34017i		−	0.832505i
$59$	−2.34017			−0.304665			−0.152332	−	0.988329i	$-0.548678\pi$
$59$	−2.34017			−0.304665			−0.152332	+	0.988329i	$0.548678\pi$
$60$	1.46081			0.188590
$61$		−	12.2557i		−	1.56918i	−0.620018	−	0.784588i	$-0.712875\pi$
$61$		−	12.2557i		−	1.56918i	0.620018	−	0.784588i	$-0.287125\pi$
$62$			8.87936i			1.12768i
$63$			13.2195i			1.66550i
$64$	−12.3112			−1.53891
$65$		−	2.63090i		−	0.326323i
$66$	3.70928			0.456580
$67$	10.2062			1.24689			0.623443	−	0.781869i	$-0.285733\pi$
$67$	10.2062			1.24689			0.623443	+	0.781869i	$0.285733\pi$
$68$	−8.80098	−	6.87936i	−1.06728	−	0.834245i
$69$	2.81432			0.338804
$70$	−10.5886			−1.26558
$71$		−	4.06505i		−	0.482432i	−0.970471	−	0.241216i	$-0.922454\pi$
$71$		−	4.06505i		−	0.482432i	0.970471	−	0.241216i	$-0.0775463\pi$
$72$	−4.17009			−0.491449
$73$		−	11.0784i		−	1.29663i	−0.761374	−	0.648313i	$-0.775475\pi$
$73$		−	11.0784i		−	1.29663i	0.761374	−	0.648313i	$-0.224525\pi$
$74$			11.4186i			1.32738i
$75$		−	0.539189i		−	0.0622602i
$76$	2.92162			0.335133
$77$	−15.4680			−1.76274
$78$		−	3.07838i		−	0.348558i
$79$		−	6.92881i		−	0.779552i	−0.920910	−	0.389776i	$-0.872552\pi$
$79$		−	6.92881i		−	0.779552i	0.920910	−	0.389776i	$-0.127448\pi$
$80$			2.07838i			0.232370i
$81$	6.46800			0.718667
$82$		−	12.1568i		−	1.34249i
$83$	8.23287			0.903674			0.451837	−	0.892100i	$-0.350769\pi$
$83$	8.23287			0.903674			0.451837	+	0.892100i	$0.350769\pi$
$84$	−7.12783			−0.777710
$85$	−2.53919	+	3.24846i	−0.275414	+	0.352345i
$86$	−7.31124			−0.788392
$87$	−1.57531			−0.168891
$88$		−	4.87936i		−	0.520142i
$89$	7.15449			0.758374			0.379187	−	0.925320i	$-0.376204\pi$
$89$	7.15449			0.758374			0.379187	+	0.925320i	$0.376204\pi$
$90$			5.87936i			0.619739i
$91$			12.8371i			1.34569i
$92$		−	14.1412i		−	1.47432i
$93$	2.20620			0.228773
$94$	14.7298			1.51926
$95$		−	1.07838i		−	0.110639i
$96$			4.09171i			0.417608i
$97$			8.18342i			0.830900i	0.909616	+	0.415450i	$0.136376\pi$
$97$			8.18342i			0.830900i	−0.909616	+	0.415450i	$0.863624\pi$
$98$	36.4752			3.68455
$99$			8.58864i			0.863191i
$100$	−2.70928			−0.270928
$101$	−2.47414			−0.246186			−0.123093	−	0.992395i	$-0.539281\pi$
$101$	−2.47414			−0.246186			−0.123093	+	0.992395i	$0.539281\pi$
$102$	−2.97107	+	3.80098i	−0.294180	+	0.376354i
$103$	−19.6514			−1.93631			−0.968156	−	0.250348i	$-0.919455\pi$
$103$	−19.6514			−1.93631			−0.968156	+	0.250348i	$0.919455\pi$
$104$	−4.04945			−0.397081
$105$			2.63090i			0.256749i
$106$	−8.15676			−0.792254
$107$			12.6381i			1.22177i	0.791719	+	0.610885i	$0.209186\pi$
$107$			12.6381i			1.22177i	−0.791719	+	0.610885i	$0.790814\pi$
$108$			8.34017i			0.802534i
$109$			8.15676i			0.781275i	0.920544	+	0.390638i	$0.127745\pi$
$109$			8.15676i			0.781275i	−0.920544	+	0.390638i	$0.872255\pi$
$110$	−6.87936			−0.655921
$111$	2.83710			0.269286
$112$		−	10.1412i		−	0.958249i
$113$		−	17.0205i		−	1.60116i	−0.599229	−	0.800578i	$-0.704526\pi$
$113$		−	17.0205i		−	1.60116i	0.599229	−	0.800578i	$-0.295474\pi$
$114$		−	1.26180i		−	0.118178i
$115$	−5.21953			−0.486724
$116$			7.91548i			0.734934i
$117$	7.12783			0.658968
$118$	5.07838			0.467503
$119$	12.3896	−	15.8504i	1.13575	−	1.45301i
$120$	−0.829914			−0.0757604
$121$	0.950552			0.0864138
$122$			26.5958i			2.40787i
$123$	−3.02052			−0.272351
$124$		−	11.0856i		−	0.995513i
$125$			1.00000i			0.0894427i
$126$		−	28.6875i		−	2.55569i
$127$	−8.04945			−0.714273			−0.357137	−	0.934052i	$-0.616247\pi$
$127$	−8.04945			−0.714273			−0.357137	+	0.934052i	$0.616247\pi$
$128$	11.5392			1.01993
$129$			1.81658i			0.159941i
$130$			5.70928i			0.500737i
$131$		−	11.6937i		−	1.02168i	−0.859675	−	0.510841i	$-0.829334\pi$
$131$		−	11.6937i		−	1.02168i	0.859675	−	0.510841i	$-0.170666\pi$
$132$	−4.63090			−0.403068
$133$			5.26180i			0.456256i
$134$	−22.1483			−1.91333
$135$	3.07838			0.264945
$136$	5.00000	+	3.90829i	0.428746	+	0.335133i
$137$	1.95055			0.166647			0.0833234	−	0.996523i	$-0.473447\pi$
$137$	1.95055			0.166647			0.0833234	+	0.996523i	$0.473447\pi$
$138$	−6.10731			−0.519889
$139$			2.00719i			0.170247i	0.996370	+	0.0851237i	$0.0271286\pi$
$139$			2.00719i			0.170247i	−0.996370	+	0.0851237i	$0.972871\pi$
$140$	13.2195			1.11725
$141$		−	3.65983i		−	0.308213i
$142$			8.82150i			0.740284i
$143$			8.34017i			0.697440i
$144$	−5.63090			−0.469241
$145$	2.92162			0.242628
$146$			24.0410i			1.98965i
$147$		−	9.06278i		−	0.747485i
$148$		−	14.2557i		−	1.17181i
$149$	−14.2823			−1.17005			−0.585026	−	0.811014i	$-0.698916\pi$
$149$	−14.2823			−1.17005			−0.585026	+	0.811014i	$0.698916\pi$
$150$			1.17009i			0.0955372i
$151$	12.8638			1.04684			0.523419	−	0.852075i	$-0.324656\pi$
$151$	12.8638			1.04684			0.523419	+	0.852075i	$0.324656\pi$
$152$	−1.65983			−0.134630
$153$	−8.80098	−	6.87936i	−0.711517	−	0.556163i
$154$	33.5669			2.70490
$155$	−4.09171			−0.328654
$156$			3.84324i			0.307706i
$157$	3.75872			0.299979			0.149989	−	0.988688i	$-0.452076\pi$
$157$	3.75872			0.299979			0.149989	+	0.988688i	$0.452076\pi$
$158$			15.0361i			1.19621i
$159$			2.02666i			0.160725i
$160$		−	7.58864i		−	0.599934i
$161$	25.4680			2.00716
$162$	−14.0361			−1.10278
$163$			8.69594i			0.681119i	0.940223	+	0.340559i	$0.110616\pi$
$163$			8.69594i			0.681119i	−0.940223	+	0.340559i	$0.889384\pi$
$164$			15.1773i			1.18515i
$165$			1.70928i			0.133067i
$166$	−17.8660			−1.38667
$167$		−	1.37629i		−	0.106501i	−0.998581	−	0.0532503i	$-0.983042\pi$
$167$		−	1.37629i		−	0.106501i	0.998581	−	0.0532503i	$-0.0169581\pi$
$168$	4.04945			0.312422
$169$	−6.07838			−0.467568
$170$	5.51026	−	7.04945i	0.422618	−	0.540668i
$171$	2.92162			0.223422
$172$	9.12783			0.695990
$173$			17.3607i			1.31991i	0.751306	+	0.659954i	$0.229424\pi$
$173$			17.3607i			1.31991i	−0.751306	+	0.659954i	$0.770576\pi$
$174$	3.41855			0.259160
$175$		−	4.87936i		−	0.368845i
$176$		−	6.58864i		−	0.496637i
$177$		−	1.26180i		−	0.0948423i
$178$	−15.5259			−1.16371
$179$	6.83710			0.511029			0.255514	−	0.966805i	$-0.417755\pi$
$179$	6.83710			0.511029			0.255514	+	0.966805i	$0.417755\pi$
$180$		−	7.34017i		−	0.547104i
$181$		−	15.0205i		−	1.11647i	−0.829684	−	0.558233i	$-0.811479\pi$
$181$		−	15.0205i		−	1.11647i	0.829684	−	0.558233i	$-0.188521\pi$
$182$		−	27.8576i		−	2.06494i
$183$	6.60811			0.488486
$184$			8.03385i			0.592263i
$185$	−5.26180			−0.386855
$186$	−4.78765			−0.351048
$187$	8.04945	−	10.2979i	0.588634	−	0.753058i
$188$	−18.3896			−1.34120
$189$	−15.0205			−1.09258
$190$			2.34017i			0.169774i
$191$	−24.2823			−1.75701			−0.878503	−	0.477736i	$-0.841457\pi$
$191$	−24.2823			−1.75701			−0.878503	+	0.477736i	$0.841457\pi$
$192$		−	6.63809i		−	0.479063i
$193$			11.8576i			0.853530i	0.904363	+	0.426765i	$0.140347\pi$
$193$			11.8576i			0.853530i	−0.904363	+	0.426765i	$0.859653\pi$
$194$		−	17.7587i		−	1.27500i
$195$	1.41855			0.101585
$196$	−45.5380			−3.25271
$197$			18.2557i			1.30066i	0.759651	+	0.650331i	$0.225370\pi$
$197$			18.2557i			1.30066i	−0.759651	+	0.650331i	$0.774630\pi$
$198$		−	18.6381i		−	1.32455i
$199$		−	3.72487i		−	0.264049i	−0.991246	−	0.132025i	$-0.957852\pi$
$199$		−	3.72487i		−	0.264049i	0.991246	−	0.132025i	$-0.0421478\pi$
$200$	1.53919			0.108837
$201$			5.50307i			0.388157i
$202$	5.36910			0.377769
$203$	−14.2557			−1.00055
$204$	3.70928	−	4.74539i	0.259701	−	0.332244i
$205$	5.60197			0.391258
$206$	42.6453			2.97124
$207$		−	14.1412i		−	0.982878i
$208$	−5.46800			−0.379138
$209$			3.41855i			0.236466i
$210$		−	5.70928i		−	0.393977i
$211$			22.2485i			1.53165i	0.643051	+	0.765824i	$0.277668\pi$
$211$			22.2485i			1.53165i	−0.643051	+	0.765824i	$0.722332\pi$
$212$	10.1834			0.699400
$213$	2.19183			0.150182
$214$		−	27.4257i		−	1.87478i
$215$		−	3.36910i		−	0.229771i
$216$		−	4.73820i		−	0.322394i
$217$	19.9649			1.35531
$218$		−	17.7009i		−	1.19885i
$219$	5.97334			0.403641
$220$	8.58864			0.579046
$221$	−8.54638	−	6.68035i	−0.574892	−	0.449369i
$222$	−6.15676			−0.413214
$223$	−2.19183			−0.146776			−0.0733878	−	0.997303i	$-0.523381\pi$
$223$	−2.19183			−0.146776			−0.0733878	+	0.997303i	$0.523381\pi$
$224$			37.0277i			2.47402i
$225$	−2.70928			−0.180618
$226$			36.9360i			2.45695i
$227$		−	9.55971i		−	0.634500i	−0.948342	−	0.317250i	$-0.897241\pi$
$227$		−	9.55971i		−	0.634500i	0.948342	−	0.317250i	$-0.102759\pi$
$228$			1.57531i			0.104327i
$229$	7.36910			0.486964			0.243482	−	0.969905i	$-0.421710\pi$
$229$	7.36910			0.486964			0.243482	+	0.969905i	$0.421710\pi$
$230$	11.3268			0.746870
$231$		−	8.34017i		−	0.548743i
$232$		−	4.49693i		−	0.295238i
$233$		−	9.44521i		−	0.618776i	−0.950936	−	0.309388i	$-0.899876\pi$
$233$		−	9.44521i		−	0.618776i	0.950936	−	0.309388i	$-0.100124\pi$
$234$	−15.4680			−1.01117
$235$			6.78765i			0.442778i
$236$	−6.34017			−0.412710
$237$	3.73594			0.242675
$238$	−26.8865	+	34.3968i	−1.74280	+	2.22961i
$239$	6.25565			0.404644			0.202322	−	0.979319i	$-0.435151\pi$
$239$	6.25565			0.404644			0.202322	+	0.979319i	$0.435151\pi$
$240$	−1.12064			−0.0723369
$241$			2.49693i			0.160841i	0.996761	+	0.0804207i	$0.0256264\pi$
$241$			2.49693i			0.160841i	−0.996761	+	0.0804207i	$0.974374\pi$
$242$	−2.06278			−0.132600
$243$			12.7226i			0.816156i
$244$		−	33.2039i		−	2.12566i
$245$			16.8082i			1.07383i
$246$	6.55479			0.417918
$247$	2.83710			0.180520
$248$			6.29791i			0.399918i
$249$			4.43907i			0.281315i
$250$		−	2.17009i		−	0.137248i
$251$	−11.8166			−0.745856			−0.372928	−	0.927860i	$-0.621646\pi$
$251$	−11.8166			−0.745856			−0.372928	+	0.927860i	$0.621646\pi$
$252$			35.8154i			2.25616i
$253$	16.5464			1.04026
$254$	17.4680			1.09604
$255$	−1.75154	−	1.36910i	−0.109685	−	0.0857365i
$256$	−0.418551			−0.0261594
$257$	14.9444			0.932207			0.466103	−	0.884730i	$-0.345658\pi$
$257$	14.9444			0.932207			0.466103	+	0.884730i	$0.345658\pi$
$258$		−	3.94214i		−	0.245427i
$259$	25.6742			1.59532
$260$		−	7.12783i		−	0.442049i
$261$			7.91548i			0.489956i
$262$			25.3763i			1.56775i
$263$	−12.9444			−0.798186			−0.399093	−	0.916910i	$-0.630675\pi$
$263$	−12.9444			−0.798186			−0.399093	+	0.916910i	$0.630675\pi$
$264$	2.63090			0.161921
$265$		−	3.75872i		−	0.230897i
$266$		−	11.4186i		−	0.700116i
$267$			3.85762i			0.236083i
$268$	27.6514			1.68908
$269$			7.47641i			0.455845i	0.973679	+	0.227922i	$0.0731932\pi$
$269$			7.47641i			0.455845i	−0.973679	+	0.227922i	$0.926807\pi$
$270$	−6.68035			−0.406553
$271$	−2.15676			−0.131014			−0.0655068	−	0.997852i	$-0.520866\pi$
$271$	−2.15676			−0.131014			−0.0655068	+	0.997852i	$0.520866\pi$
$272$	6.75154	+	5.27739i	0.409372	+	0.319989i
$273$	−6.92162			−0.418916
$274$	−4.23287			−0.255717
$275$		−	3.17009i		−	0.191163i
$276$	7.62475			0.458956
$277$		−	12.1568i		−	0.730429i	−0.930923	−	0.365214i	$-0.880996\pi$
$277$		−	12.1568i		−	0.730429i	0.930923	−	0.365214i	$-0.119004\pi$
$278$		−	4.35577i		−	0.261242i
$279$		−	11.0856i		−	0.663675i
$280$	−7.51026			−0.448824
$281$	13.1194			0.782639			0.391319	−	0.920255i	$-0.372019\pi$
$281$	13.1194			0.782639			0.391319	+	0.920255i	$0.372019\pi$
$282$			7.94214i			0.472948i
$283$			13.9577i			0.829701i	0.909889	+	0.414851i	$0.136166\pi$
$283$			13.9577i			0.829701i	−0.909889	+	0.414851i	$0.863834\pi$
$284$		−	11.0133i		−	0.653521i
$285$	0.581449			0.0344421
$286$		−	18.0989i		−	1.07021i
$287$	−27.3340			−1.61348
$288$	20.5597			1.21149
$289$	4.10504	+	16.4969i	0.241473	+	0.970408i
$290$	−6.34017			−0.372308
$291$	−4.41241			−0.258660
$292$		−	30.0144i		−	1.75646i
$293$	4.73820			0.276809			0.138404	−	0.990376i	$-0.455803\pi$
$293$	4.73820			0.276809			0.138404	+	0.990376i	$0.455803\pi$
$294$			19.6670i			1.14700i
$295$			2.34017i			0.136250i
$296$			8.09890i			0.470739i
$297$	−9.75872			−0.566259
$298$	30.9939			1.79543
$299$		−	13.7321i		−	0.794146i
$300$		−	1.46081i		−	0.0843400i
$301$			16.4391i			0.947532i
$302$	−27.9155			−1.60636
$303$		−	1.33403i		−	0.0766380i
$304$	−2.24128			−0.128546
$305$	−12.2557			−0.701757
$306$	19.0989	+	14.9288i	1.09181	+	0.853423i
$307$	−21.5936			−1.23241			−0.616205	−	0.787586i	$-0.711331\pi$
$307$	−21.5936			−1.23241			−0.616205	+	0.787586i	$0.711331\pi$
$308$	−41.9071			−2.38788
$309$		−	10.5958i		−	0.602775i
$310$	8.87936			0.504314
$311$		−	24.2628i		−	1.37582i	−0.725796	−	0.687910i	$-0.758528\pi$
$311$		−	24.2628i		−	1.37582i	0.725796	−	0.687910i	$-0.241472\pi$
$312$		−	2.18342i		−	0.123612i
$313$		−	4.07223i		−	0.230176i	−0.993355	−	0.115088i	$-0.963285\pi$
$313$		−	4.07223i		−	0.230176i	0.993355	−	0.115088i	$-0.0367151\pi$
$314$	−8.15676			−0.460312
$315$	13.2195			0.744836
$316$		−	18.7721i		−	1.05601i
$317$		−	8.05786i		−	0.452574i	−0.974061	−	0.226287i	$-0.927341\pi$
$317$		−	8.05786i		−	0.452574i	0.974061	−	0.226287i	$-0.0726588\pi$
$318$		−	4.39803i		−	0.246629i
$319$	−9.26180			−0.518561
$320$			12.3112i			0.688219i
$321$	−6.81432			−0.380338
$322$	−55.2678			−3.07995
$323$	−3.50307	−	2.73820i	−0.194916	−	0.152358i
$324$	17.5236			0.973533
$325$	−2.63090			−0.145936
$326$		−	18.8710i		−	1.04517i
$327$	−4.39803			−0.243212
$328$		−	8.62249i		−	0.476097i
$329$		−	33.1194i		−	1.82593i
$330$		−	3.70928i		−	0.204189i
$331$	−10.0722			−0.553620			−0.276810	−	0.960925i	$-0.589277\pi$
$331$	−10.0722			−0.553620			−0.276810	+	0.960925i	$0.589277\pi$
$332$	22.3051			1.22415
$333$		−	14.2557i		−	0.781205i
$334$			2.98667i			0.163423i
$335$		−	10.2062i		−	0.557624i
$336$	5.46800			0.298304
$337$			11.2351i			0.612017i	0.952029	+	0.306008i	$0.0989936\pi$
$337$			11.2351i			0.612017i	−0.952029	+	0.306008i	$0.901006\pi$
$338$	13.1906			0.717474
$339$	9.17727			0.498441
$340$	−6.87936	+	8.80098i	−0.373086	+	0.477300i
$341$	12.9711			0.702423
$342$	−6.34017			−0.342837
$343$		−	47.8576i		−	2.58407i
$344$	−5.18568			−0.279593
$345$		−	2.81432i		−	0.151518i
$346$		−	37.6742i		−	2.02538i
$347$			8.74927i			0.469685i	0.972033	+	0.234843i	$0.0754575\pi$
$347$			8.74927i			0.469685i	−0.972033	+	0.234843i	$0.924543\pi$
$348$	−4.26794			−0.228786
$349$	−26.9093			−1.44042			−0.720212	−	0.693754i	$-0.755955\pi$
$349$	−26.9093			−1.44042			−0.720212	+	0.693754i	$0.755955\pi$
$350$			10.5886i			0.565986i
$351$			8.09890i			0.432287i
$352$			24.0566i			1.28222i
$353$	18.3135			0.974730			0.487365	−	0.873198i	$-0.337958\pi$
$353$	18.3135			0.974730			0.487365	+	0.873198i	$0.337958\pi$
$354$			2.73820i			0.145534i
$355$	−4.06505			−0.215750
$356$	19.3835			1.02732
$357$	8.54638	+	6.68035i	0.452322	+	0.353561i
$358$	−14.8371			−0.784165
$359$	−9.57531			−0.505365			−0.252683	−	0.967549i	$-0.581313\pi$
$359$	−9.57531			−0.505365			−0.252683	+	0.967549i	$0.581313\pi$
$360$			4.17009i			0.219783i
$361$	−17.8371			−0.938795
$362$			32.5958i			1.71320i
$363$			0.512527i			0.0269007i
$364$			34.7792i			1.82293i
$365$	−11.0784			−0.579869
$366$	−14.3402			−0.749573
$367$		−	12.1145i		−	0.632371i	−0.948697	−	0.316186i	$-0.897598\pi$
$367$		−	12.1145i		−	0.632371i	0.948697	−	0.316186i	$-0.102402\pi$
$368$			10.8482i			0.565500i
$369$			15.1773i			0.790097i
$370$	11.4186			0.593622
$371$			18.3402i			0.952174i
$372$	5.97721			0.309904
$373$	30.4619			1.57726			0.788628	−	0.614871i	$-0.210792\pi$
$373$	30.4619			1.57726			0.788628	+	0.614871i	$0.210792\pi$
$374$	−17.4680	+	22.3474i	−0.903249	+	1.15555i
$375$	−0.539189			−0.0278436
$376$	10.4475			0.538788
$377$			7.68649i			0.395874i
$378$	32.5958			1.67655
$379$			0.986669i			0.0506818i	0.999679	+	0.0253409i	$0.00806712\pi$
$379$			0.986669i			0.0506818i	−0.999679	+	0.0253409i	$0.991933\pi$
$380$		−	2.92162i		−	0.149876i
$381$		−	4.34017i		−	0.222354i
$382$	52.6947			2.69610
$383$	−24.9588			−1.27533			−0.637667	−	0.770312i	$-0.720100\pi$
$383$	−24.9588			−1.27533			−0.637667	+	0.770312i	$0.720100\pi$
$384$			6.22180i			0.317505i
$385$			15.4680i			0.788322i
$386$		−	25.7321i		−	1.30973i
$387$	9.12783			0.463993
$388$			22.1711i			1.12557i
$389$	33.8082			1.71414			0.857071	−	0.515198i	$-0.172282\pi$
$389$	33.8082			1.71414			0.857071	+	0.515198i	$0.172282\pi$
$390$	−3.07838			−0.155880
$391$	−13.2534	+	16.9555i	−0.670252	+	0.857475i
$392$	25.8710			1.30668
$393$	6.30510			0.318050
$394$		−	39.6163i		−	1.99584i
$395$	−6.92881			−0.348626
$396$			23.2690i			1.16931i
$397$		−	28.5236i		−	1.43156i	−0.698327	−	0.715779i	$-0.746072\pi$
$397$		−	28.5236i		−	1.43156i	0.698327	−	0.715779i	$-0.253928\pi$
$398$			8.08330i			0.405179i
$399$	−2.83710			−0.142033
$400$	2.07838			0.103919
$401$			33.0928i			1.65257i	0.563250	+	0.826287i	$0.309551\pi$
$401$			33.0928i			1.65257i	−0.563250	+	0.826287i	$0.690449\pi$
$402$		−	11.9421i		−	0.595620i
$403$		−	10.7649i		−	0.536236i
$404$	−6.70313			−0.333493
$405$		−	6.46800i		−	0.321397i
$406$	30.9360			1.53533
$407$	16.6803			0.826814
$408$	−2.10731	+	2.69594i	−0.104327	+	0.133469i
$409$	−30.1978			−1.49318			−0.746592	−	0.665282i	$-0.768311\pi$
$409$	−30.1978			−1.49318			−0.746592	+	0.665282i	$0.768311\pi$
$410$	−12.1568			−0.600379
$411$			1.05172i			0.0518773i
$412$	−53.2411			−2.62300
$413$		−	11.4186i		−	0.561870i
$414$			30.6875i			1.50821i
$415$		−	8.23287i		−	0.404135i
$416$	19.9649			0.978861
$417$	−1.08225			−0.0529982
$418$		−	7.41855i		−	0.362853i
$419$		−	18.1639i		−	0.887367i	−0.896184	−	0.443683i	$-0.853671\pi$
$419$		−	18.1639i		−	0.887367i	0.896184	−	0.443683i	$-0.146329\pi$
$420$			7.12783i			0.347802i
$421$	0.760991			0.0370884			0.0185442	−	0.999828i	$-0.494097\pi$
$421$	0.760991			0.0370884			0.0185442	+	0.999828i	$0.494097\pi$
$422$		−	48.2811i		−	2.35029i
$423$	−18.3896			−0.894134
$424$	−5.78539			−0.280963
$425$	3.24846	+	2.53919i	0.157574	+	0.123169i
$426$	−4.75646			−0.230451
$427$	59.7998			2.89391
$428$			34.2401i			1.65506i
$429$	−4.49693			−0.217114
$430$			7.31124i			0.352579i
$431$		−	6.34736i		−	0.305742i	−0.988246	−	0.152871i	$-0.951148\pi$
$431$		−	6.34736i		−	0.305742i	0.988246	−	0.152871i	$-0.0488518\pi$
$432$		−	6.39803i		−	0.307825i
$433$	3.62475			0.174195			0.0870973	−	0.996200i	$-0.472241\pi$
$433$	3.62475			0.174195			0.0870973	+	0.996200i	$0.472241\pi$
$434$	−43.3256			−2.07970
$435$			1.57531i			0.0755302i
$436$			22.0989i			1.05835i
$437$		−	5.62863i		−	0.269254i
$438$	−12.9627			−0.619380
$439$			6.40522i			0.305704i	0.988249	+	0.152852i	$0.0488459\pi$
$439$			6.40522i			0.305704i	−0.988249	+	0.152852i	$0.951154\pi$
$440$	−4.87936			−0.232614
$441$	−45.5380			−2.16847
$442$	18.5464	+	14.4969i	0.882161	+	0.689549i
$443$	27.4824			1.30573			0.652864	−	0.757476i	$-0.273568\pi$
$443$	27.4824			1.30573			0.652864	+	0.757476i	$0.273568\pi$
$444$	7.68649			0.364785
$445$		−	7.15449i		−	0.339155i
$446$	4.75646			0.225225
$447$		−	7.70086i		−	0.364238i
$448$		−	60.0710i		−	2.83809i
$449$			28.7526i			1.35692i	0.734638	+	0.678459i	$0.237352\pi$
$449$			28.7526i			1.35692i	−0.734638	+	0.678459i	$0.762648\pi$
$450$	5.87936			0.277156
$451$	−17.7587			−0.836226
$452$		−	46.1133i		−	2.16899i
$453$			6.93600i			0.325882i
$454$			20.7454i			0.973630i
$455$	12.8371			0.601813
$456$		−	0.894960i		−	0.0419104i
$457$	−31.4101			−1.46930			−0.734652	−	0.678444i	$-0.762655\pi$
$457$	−31.4101			−1.46930			−0.734652	+	0.678444i	$0.762655\pi$
$458$	−15.9916			−0.747238
$459$	7.81658	−	10.0000i	0.364847	−	0.466760i
$460$	−14.1412			−0.659335
$461$	−7.75872			−0.361360			−0.180680	−	0.983542i	$-0.557830\pi$
$461$	−7.75872			−0.361360			−0.180680	+	0.983542i	$0.557830\pi$
$462$			18.0989i			0.842037i
$463$	24.2329			1.12620			0.563098	−	0.826390i	$-0.309609\pi$
$463$	24.2329			1.12620			0.563098	+	0.826390i	$0.309609\pi$
$464$		−	6.07223i		−	0.281896i
$465$		−	2.20620i		−	0.102310i
$466$			20.4969i			0.949502i
$467$	−12.3174			−0.569981			−0.284990	−	0.958530i	$-0.591990\pi$
$467$	−12.3174			−0.569981			−0.284990	+	0.958530i	$0.591990\pi$
$468$	19.3112			0.892663
$469$			49.7998i			2.29954i
$470$		−	14.7298i		−	0.679435i
$471$			2.02666i			0.0933837i
$472$	3.60197			0.165794
$473$			10.6803i			0.491083i
$474$	−8.10731			−0.372381
$475$	−1.07838			−0.0494794
$476$	33.5669	−	42.9432i	1.53854	−	1.96830i
$477$	10.1834			0.466267
$478$	−13.5753			−0.620920
$479$		−	2.14957i		−	0.0982162i	−0.998793	−	0.0491081i	$-0.984362\pi$
$479$		−	2.14957i		−	0.0982162i	0.998793	−	0.0491081i	$-0.0156379\pi$
$480$	4.09171			0.186760
$481$		−	13.8432i		−	0.631198i
$482$		−	5.41855i		−	0.246808i
$483$			13.7321i			0.624830i
$484$	2.57531			0.117059
$485$	8.18342			0.371590
$486$		−	27.6092i		−	1.25238i
$487$			40.0833i			1.81635i	0.418593	+	0.908174i	$0.362523\pi$
$487$			40.0833i			1.81635i	−0.418593	+	0.908174i	$0.637477\pi$
$488$			18.8638i			0.853922i
$489$	−4.68876			−0.212033
$490$		−	36.4752i		−	1.64778i
$491$	−2.25565			−0.101796			−0.0508981	−	0.998704i	$-0.516208\pi$
$491$	−2.25565			−0.101796			−0.0508981	+	0.998704i	$0.516208\pi$
$492$	−8.18342			−0.368937
$493$	7.41855	−	9.49079i	0.334115	−	0.427443i
$494$	−6.15676			−0.277006
$495$	8.58864			0.386031
$496$			8.50412i			0.381846i
$497$	19.8348			0.889714
$498$		−	9.63317i		−	0.431672i
$499$			42.5452i			1.90458i	0.305190	+	0.952291i	$0.401280\pi$
$499$			42.5452i			1.90458i	−0.305190	+	0.952291i	$0.598720\pi$
$500$			2.70928i			0.121162i
$501$	0.742080			0.0331537
$502$	25.6430			1.14450
$503$			9.55971i			0.426246i	0.977025	+	0.213123i	$0.0683636\pi$
$503$			9.55971i			0.426246i	−0.977025	+	0.213123i	$0.931636\pi$
$504$		−	20.3474i		−	0.906343i
$505$			2.47414i			0.110098i
$506$	−35.9071			−1.59626
$507$		−	3.27739i		−	0.145554i
$508$	−21.8082			−0.967581
$509$	28.3545			1.25679			0.628397	−	0.777893i	$-0.283712\pi$
$509$	28.3545			1.25679			0.628397	+	0.777893i	$0.283712\pi$
$510$	3.80098	+	2.97107i	0.168310	+	0.131561i
$511$	54.0554			2.39127
$512$	−22.1701			−0.979789
$513$			3.31965i			0.146566i
$514$	−32.4307			−1.43046
$515$			19.6514i			0.865945i
$516$			4.92162i			0.216662i
$517$		−	21.5174i		−	0.946336i
$518$	−55.7152			−2.44799
$519$	−9.36069			−0.410889
$520$			4.04945i			0.177580i
$521$		−	15.1050i		−	0.661764i	−0.943672	−	0.330882i	$-0.892654\pi$
$521$		−	15.1050i		−	0.661764i	0.943672	−	0.330882i	$-0.107346\pi$
$522$		−	17.1773i		−	0.751829i
$523$	−10.8865			−0.476036			−0.238018	−	0.971261i	$-0.576498\pi$
$523$	−10.8865			−0.476036			−0.238018	+	0.971261i	$0.576498\pi$
$524$		−	31.6814i		−	1.38401i
$525$	2.63090			0.114822
$526$	28.0905			1.22480
$527$	−10.3896	+	13.2918i	−0.452579	+	0.578999i
$528$	3.55252			0.154604
$529$	−4.24354			−0.184502
$530$			8.15676i			0.354307i
$531$	−6.34017			−0.275140
$532$			14.2557i			0.618061i
$533$			14.7382i			0.638383i
$534$		−	8.37137i		−	0.362265i
$535$	12.6381			0.546392
$536$	−15.7093			−0.678537
$537$			3.68649i			0.159084i
$538$		−	16.2245i		−	0.699486i
$539$		−	53.2834i		−	2.29508i
$540$	8.34017			0.358904
$541$		−	6.86830i		−	0.295291i	−0.989040	−	0.147646i	$-0.952830\pi$
$541$		−	6.86830i		−	0.295291i	0.989040	−	0.147646i	$-0.0471695\pi$
$542$	4.68035			0.201038
$543$	8.09890			0.347557
$544$	−24.6514	−	19.2690i	−1.05692	−	0.826151i
$545$	8.15676			0.349397
$546$	15.0205			0.642819
$547$			5.89988i			0.252261i	0.992014	+	0.126130i	$0.0402558\pi$
$547$			5.89988i			0.252261i	−0.992014	+	0.126130i	$0.959744\pi$
$548$	5.28458			0.225746
$549$		−	33.2039i		−	1.41711i
$550$			6.87936i			0.293337i
$551$			3.15061i			0.134221i
$552$	−4.33176			−0.184372
$553$	33.8082			1.43767
$554$			26.3812i			1.12083i
$555$		−	2.83710i		−	0.120428i
$556$			5.43802i			0.230624i
$557$	−17.7359			−0.751496			−0.375748	−	0.926722i	$-0.622614\pi$
$557$	−17.7359			−0.751496			−0.375748	+	0.926722i	$0.622614\pi$
$558$			24.0566i			1.01840i
$559$	8.86376			0.374897
$560$	−10.1412			−0.428542
$561$	5.55252	+	4.34017i	0.234428	+	0.183242i
$562$	−28.4703			−1.20095
$563$	−38.8020			−1.63531			−0.817655	−	0.575708i	$-0.804726\pi$
$563$	−38.8020			−1.63531			−0.817655	+	0.575708i	$0.804726\pi$
$564$		−	9.91548i		−	0.417517i
$565$	−17.0205			−0.716059
$566$		−	30.2895i		−	1.27316i
$567$			31.5597i			1.32538i
$568$			6.25687i			0.262533i
$569$	12.1568			0.509638			0.254819	−	0.966989i	$-0.417984\pi$
$569$	12.1568			0.509638			0.254819	+	0.966989i	$0.417984\pi$
$570$	−1.26180			−0.0528508
$571$			15.4569i			0.646853i	0.946253	+	0.323426i	$0.104835\pi$
$571$			15.4569i			0.646853i	−0.946253	+	0.323426i	$0.895165\pi$
$572$			22.5958i			0.944779i
$573$		−	13.0928i		−	0.546958i
$574$	59.3172			2.47585
$575$			5.21953i			0.217670i
$576$	−33.3545			−1.38977
$577$	−2.36296			−0.0983713			−0.0491856	−	0.998790i	$-0.515663\pi$
$577$	−2.36296			−0.0983713			−0.0491856	+	0.998790i	$0.515663\pi$
$578$	−8.90829	−	35.7998i	−0.370536	−	1.48907i
$579$	−6.39350			−0.265705
$580$	7.91548			0.328672
$581$			40.1711i			1.66658i
$582$	9.57531			0.396909
$583$			11.9155i			0.493489i
$584$			17.0517i			0.705605i
$585$		−	7.12783i		−	0.294699i
$586$	−10.2823			−0.424758
$587$	−3.65142			−0.150710			−0.0753550	−	0.997157i	$-0.524009\pi$
$587$	−3.65142			−0.150710			−0.0753550	+	0.997157i	$0.524009\pi$
$588$		−	24.5536i		−	1.01257i
$589$		−	4.41241i		−	0.181810i
$590$		−	5.07838i		−	0.209074i
$591$	−9.84324			−0.404897
$592$			10.9360i			0.449467i
$593$	−1.38735			−0.0569718			−0.0284859	−	0.999594i	$-0.509069\pi$
$593$	−1.38735			−0.0569718			−0.0284859	+	0.999594i	$0.509069\pi$
$594$	21.1773			0.868914
$595$	−15.8504	−	12.3896i	−0.649804	−	0.507925i
$596$	−38.6947			−1.58500
$597$	2.00841			0.0821988
$598$			29.7998i			1.21860i
$599$	−0.451356			−0.0184419			−0.00922095	−	0.999957i	$-0.502935\pi$
$599$	−0.451356			−0.0184419			−0.00922095	+	0.999957i	$0.502935\pi$
$600$			0.829914i			0.0338811i
$601$		−	22.1301i		−	0.902705i	−0.892346	−	0.451353i	$-0.850942\pi$
$601$		−	22.1301i		−	0.902705i	0.892346	−	0.451353i	$-0.149058\pi$
$602$		−	35.6742i		−	1.45397i
$603$	27.6514			1.12605
$604$	34.8515			1.41809
$605$		−	0.950552i		−	0.0386454i
$606$			2.89496i			0.117600i
$607$		−	10.2667i		−	0.416713i	−0.978053	−	0.208357i	$-0.933189\pi$
$607$		−	10.2667i		−	0.416713i	0.978053	−	0.208357i	$-0.0668114\pi$
$608$	8.18342			0.331881
$609$		−	7.68649i		−	0.311472i
$610$	26.5958			1.07683
$611$	−17.8576			−0.722442
$612$	−23.8443	−	18.6381i	−0.963848	−	0.753400i
$613$	−9.05172			−0.365595			−0.182798	−	0.983151i	$-0.558515\pi$
$613$	−9.05172			−0.365595			−0.182798	+	0.983151i	$0.558515\pi$
$614$	46.8599			1.89111
$615$			3.02052i			0.121799i
$616$	23.8082			0.959259
$617$		−	17.8166i		−	0.717269i	−0.933478	−	0.358634i	$-0.883243\pi$
$617$		−	17.8166i		−	0.717269i	0.933478	−	0.358634i	$-0.116757\pi$
$618$			22.9939i			0.924949i
$619$		−	38.3884i		−	1.54296i	−0.636254	−	0.771480i	$-0.719517\pi$
$619$		−	38.3884i		−	1.54296i	0.636254	−	0.771480i	$-0.280483\pi$
$620$	−11.0856			−0.445207
$621$	16.0677			0.644775
$622$			52.6525i			2.11117i
$623$			34.9093i			1.39861i
$624$		−	2.94828i		−	0.118026i
$625$	1.00000			0.0400000
$626$			8.83710i			0.353202i
$627$	−1.84324			−0.0736121
$628$	10.1834			0.406363
$629$	−13.3607	+	17.0928i	−0.532726	+	0.681533i
$630$	−28.6875			−1.14294
$631$	−27.4863			−1.09421			−0.547105	−	0.837064i	$-0.684270\pi$
$631$	−27.4863			−1.09421			−0.547105	+	0.837064i	$0.684270\pi$
$632$			10.6647i			0.424221i
$633$	−11.9961			−0.476803
$634$			17.4863i			0.694468i
$635$			8.04945i			0.319433i
$636$			5.49079i			0.217724i
$637$	−44.2206			−1.75208
$638$	20.0989			0.795723
$639$		−	11.0133i		−	0.435681i
$640$		−	11.5392i		−	0.456126i
$641$		−	9.79976i		−	0.387067i	−0.981094	−	0.193534i	$-0.938005\pi$
$641$		−	9.79976i		−	0.387067i	0.981094	−	0.193534i	$-0.0619949\pi$
$642$	14.7877			0.583622
$643$		−	16.9372i		−	0.667939i	−0.942584	−	0.333969i	$-0.891612\pi$
$643$		−	16.9372i		−	0.667939i	0.942584	−	0.333969i	$-0.108388\pi$
$644$	68.9998			2.71897
$645$	1.81658			0.0715279
$646$	7.60197	+	5.94214i	0.299095	+	0.233790i
$647$	−2.98545			−0.117370			−0.0586850	−	0.998277i	$-0.518691\pi$
$647$	−2.98545			−0.117370			−0.0586850	+	0.998277i	$0.518691\pi$
$648$	−9.95547			−0.391088
$649$		−	7.41855i		−	0.291204i
$650$	5.70928			0.223936
$651$			10.7649i			0.421908i
$652$			23.5597i			0.922669i
$653$		−	40.1978i		−	1.57306i	−0.617551	−	0.786531i	$-0.711875\pi$
$653$		−	40.1978i		−	1.57306i	0.617551	−	0.786531i	$-0.288125\pi$
$654$	9.54411			0.373204
$655$	−11.6937			−0.456910
$656$		−	11.6430i		−	0.454583i
$657$		−	30.0144i		−	1.17097i
$658$			71.8720i			2.80186i
$659$	43.9832			1.71334			0.856671	−	0.515864i	$-0.172529\pi$
$659$	43.9832			1.71334			0.856671	+	0.515864i	$0.172529\pi$
$660$			4.63090i			0.180257i
$661$	26.1133			1.01569			0.507844	−	0.861449i	$-0.330443\pi$
$661$	26.1133			1.01569			0.507844	+	0.861449i	$0.330443\pi$
$662$	21.8576			0.849521
$663$	3.60197	−	4.60811i	0.139889	−	0.178964i
$664$	−12.6719			−0.491766
$665$	5.26180			0.204044
$666$			30.9360i			1.19875i
$667$	15.2495			0.590463
$668$		−	3.72875i		−	0.144270i
$669$		−	1.18181i		−	0.0456914i
$670$			22.1483i			0.855665i
$671$	38.8515			1.49984
$672$	−19.9649			−0.770164
$673$			13.3340i			0.513989i	0.966413	+	0.256995i	$0.0827322\pi$
$673$			13.3340i			0.513989i	−0.966413	+	0.256995i	$0.917268\pi$
$674$		−	24.3812i		−	0.939129i
$675$		−	3.07838i		−	0.118487i
$676$	−16.4680			−0.633385
$677$			26.5113i			1.01891i	0.860497	+	0.509456i	$0.170153\pi$
$677$			26.5113i			1.01891i	−0.860497	+	0.509456i	$0.829847\pi$
$678$	−19.9155			−0.764849
$679$	−39.9299			−1.53237
$680$	3.90829	−	5.00000i	0.149876	−	0.191741i
$681$	5.15449			0.197520
$682$	−28.1483			−1.07786
$683$		−	5.71646i		−	0.218734i	−0.994001	−	0.109367i	$-0.965118\pi$
$683$		−	5.71646i		−	0.218734i	0.994001	−	0.109367i	$-0.0348824\pi$
$684$	7.91548			0.302656
$685$		−	1.95055i		−	0.0745267i
$686$			103.855i			3.96521i
$687$			3.97334i			0.151592i
$688$	−7.00227			−0.266959
$689$	9.88882			0.376734
$690$			6.10731i			0.232501i
$691$			43.8504i			1.66815i	0.551652	+	0.834075i	$0.313998\pi$
$691$			43.8504i			1.66815i	−0.551652	+	0.834075i	$0.686002\pi$
$692$			47.0349i			1.78800i
$693$	−41.9071			−1.59192
$694$		−	18.9867i		−	0.720724i
$695$	2.00719			0.0761370
$696$	2.42469			0.0919078
$697$	14.2245	−	18.1978i	0.538790	−	0.689291i
$698$	58.3956			2.21031
$699$	5.09275			0.192626
$700$		−	13.2195i		−	0.499651i
$701$	0.0806452			0.00304593			0.00152296	−	0.999999i	$-0.499515\pi$
$701$	0.0806452			0.00304593			0.00152296	+	0.999999i	$0.499515\pi$
$702$		−	17.5753i		−	0.663337i
$703$		−	5.67420i		−	0.214007i
$704$		−	39.0277i		−	1.47091i
$705$	−3.65983			−0.137837
$706$	−39.7419			−1.49571
$707$		−	12.0722i		−	0.454023i
$708$		−	3.41855i		−	0.128477i
$709$			10.8227i			0.406456i	0.979131	+	0.203228i	$0.0651433\pi$
$709$			10.8227i			0.406456i	−0.979131	+	0.203228i	$0.934857\pi$
$710$	8.82150			0.331065
$711$		−	18.7721i		−	0.704007i
$712$	−11.0121			−0.412696
$713$	−21.3568			−0.799819
$714$	−18.5464	−	14.4969i	−0.694081	−	0.542534i
$715$	8.34017			0.311905
$716$	18.5236			0.692259
$717$			3.37298i			0.125966i
$718$	20.7792			0.775474
$719$			43.7659i			1.63219i	0.577916	+	0.816097i	$0.303866\pi$
$719$			43.7659i			1.63219i	−0.577916	+	0.816097i	$0.696134\pi$
$720$			5.63090i			0.209851i
$721$		−	95.8864i		−	3.57100i
$722$	38.7081			1.44056
$723$	−1.34632			−0.0500700
$724$		−	40.6947i		−	1.51241i
$725$		−	2.92162i		−	0.108506i
$726$		−	1.11223i		−	0.0412786i
$727$	−3.59809			−0.133446			−0.0667229	−	0.997772i	$-0.521254\pi$
$727$	−3.59809			−0.133446			−0.0667229	+	0.997772i	$0.521254\pi$
$728$		−	19.7587i		−	0.732307i
$729$	12.5441			0.464597
$730$	24.0410			0.889799
$731$	−10.9444	−	8.55479i	−0.404794	−	0.316410i
$732$	17.9032			0.661721
$733$	−39.8264			−1.47102			−0.735511	−	0.677513i	$-0.763058\pi$
$733$	−39.8264			−1.47102			−0.735511	+	0.677513i	$0.763058\pi$
$734$			26.2895i			0.970363i
$735$	−9.06278			−0.334286
$736$		−	39.6092i		−	1.46001i
$737$			32.3545i			1.19180i
$738$		−	32.9360i		−	1.21239i
$739$	13.7587			0.506123			0.253061	−	0.967450i	$-0.418563\pi$
$739$	13.7587			0.506123			0.253061	+	0.967450i	$0.418563\pi$
$740$	−14.2557			−0.524048
$741$			1.52973i			0.0561962i
$742$		−	39.7998i		−	1.46110i
$743$			9.34963i			0.343005i	0.985184	+	0.171502i	$0.0548621\pi$
$743$			9.34963i			0.343005i	−0.985184	+	0.171502i	$0.945138\pi$
$744$	−3.39576			−0.124495
$745$			14.2823i			0.523264i
$746$	−66.1049			−2.42027
$747$	22.3051			0.816101
$748$	21.8082	−	27.8999i	0.797386	−	1.02012i
$749$	−61.6658			−2.25322
$750$	1.17009			0.0427255
$751$		−	53.7392i		−	1.96097i	−0.196586	−	0.980487i	$-0.562986\pi$
$751$		−	53.7392i		−	1.96097i	0.196586	−	0.980487i	$-0.437014\pi$
$752$	14.1073			0.514441
$753$		−	6.37137i		−	0.232186i
$754$		−	16.6803i		−	0.607462i
$755$		−	12.8638i		−	0.468160i
$756$	−40.6947			−1.48005
$757$	−41.5136			−1.50884			−0.754418	−	0.656394i	$-0.772081\pi$
$757$	−41.5136			−1.50884			−0.754418	+	0.656394i	$0.772081\pi$
$758$		−	2.14116i		−	0.0777703i
$759$			8.92162i			0.323834i
$760$			1.65983i			0.0602083i
$761$	−18.0372			−0.653847			−0.326923	−	0.945051i	$-0.606012\pi$
$761$	−18.0372			−0.653847			−0.326923	+	0.945051i	$0.606012\pi$
$762$			9.41855i			0.341198i
$763$	−39.7998			−1.44085
$764$	−65.7875			−2.38011
$765$	−6.87936	+	8.80098i	−0.248724	+	0.318200i
$766$	54.1627			1.95698
$767$	−6.15676			−0.222308
$768$		−	0.225678i		−	0.00814345i
$769$	−23.0843			−0.832443			−0.416221	−	0.909263i	$-0.636646\pi$
$769$	−23.0843			−0.832443			−0.416221	+	0.909263i	$0.636646\pi$
$770$		−	33.5669i		−	1.20967i
$771$			8.05786i			0.290197i
$772$			32.1256i			1.15622i
$773$	−27.4101			−0.985874			−0.492937	−	0.870065i	$-0.664077\pi$
$773$	−27.4101			−0.985874			−0.492937	+	0.870065i	$0.664077\pi$
$774$	−19.8082			−0.711990
$775$			4.09171i			0.146979i
$776$		−	12.5958i		−	0.452164i
$777$			13.8432i			0.496624i
$778$	−73.3667			−2.63032
$779$			6.04104i			0.216443i
$780$	3.84324			0.137610
$781$	12.8865			0.461117
$782$	28.7610	−	36.7948i	1.02849	−	1.31578i
$783$	−8.99386			−0.321414
$784$	34.9337			1.24763
$785$		−	3.75872i		−	0.134155i
$786$	−13.6826			−0.488043
$787$		−	30.6069i		−	1.09102i	−0.838105	−	0.545509i	$-0.816336\pi$
$787$		−	30.6069i		−	1.09102i	0.838105	−	0.545509i	$-0.183664\pi$
$788$			49.4596i			1.76192i
$789$		−	6.97948i		−	0.248476i
$790$	15.0361			0.534961
$791$	83.0493			2.95289
$792$		−	13.2195i		−	0.469736i
$793$		−	32.2434i		−	1.14500i
$794$			61.8987i			2.19670i
$795$	2.02666			0.0718783
$796$		−	10.0917i		−	0.357691i
$797$	22.9770			0.813888			0.406944	−	0.913453i	$-0.366594\pi$
$797$	22.9770			0.813888			0.406944	+	0.913453i	$0.366594\pi$
$798$	6.15676			0.217947
$799$	22.0494	+	17.2351i	0.780053	+	0.609735i
$800$	−7.58864			−0.268299
$801$	19.3835			0.684882
$802$		−	71.8141i		−	2.53585i
$803$	35.1194			1.23934
$804$			14.9093i			0.525812i
$805$		−	25.4680i		−	0.897629i
$806$			23.3607i			0.822845i
$807$	−4.03120			−0.141905
$808$	3.80817			0.133971
$809$		−	42.7670i		−	1.50361i	−0.659388	−	0.751803i	$-0.729184\pi$
$809$		−	42.7670i		−	1.50361i	0.659388	−	0.751803i	$-0.270816\pi$
$810$			14.0361i			0.493179i
$811$		−	9.41136i		−	0.330478i	−0.986254	−	0.165239i	$-0.947161\pi$
$811$		−	9.41136i		−	0.330478i	0.986254	−	0.165239i	$-0.0528395\pi$
$812$	−38.6225			−1.35538
$813$		−	1.16290i		−	0.0407846i
$814$	−36.1978			−1.26873
$815$	8.69594			0.304606
$816$	−2.84551	+	3.64035i	−0.0996128	+	0.127438i
$817$	3.63317			0.127108
$818$	65.5318			2.29127
$819$			34.7792i			1.21529i
$820$	15.1773			0.530013
$821$			32.6681i			1.14012i	0.821602	+	0.570062i	$0.193081\pi$
$821$			32.6681i			1.14012i	−0.821602	+	0.570062i	$0.806919\pi$
$822$		−	2.28231i		−	0.0796048i
$823$			15.9265i			0.555164i	0.960702	+	0.277582i	$0.0895331\pi$
$823$			15.9265i			0.555164i	−0.960702	+	0.277582i	$0.910467\pi$
$824$	30.2472			1.05371
$825$	1.70928			0.0595093
$826$			24.7792i			0.862180i
$827$			6.01560i			0.209183i	0.994515	+	0.104591i	$0.0333535\pi$
$827$			6.01560i			0.209183i	−0.994515	+	0.104591i	$0.966647\pi$
$828$		−	38.3123i		−	1.33144i
$829$	11.0472			0.383684			0.191842	−	0.981426i	$-0.438554\pi$
$829$	11.0472			0.383684			0.191842	+	0.981426i	$0.438554\pi$
$830$			17.8660i			0.620139i
$831$	6.55479			0.227383
$832$	−32.3896			−1.12291
$833$	54.6007	+	42.6791i	1.89180	+	1.47874i
$834$	2.34858			0.0813248
$835$	−1.37629			−0.0476285
$836$			9.26180i			0.320326i
$837$	12.5958			0.435375
$838$			39.4173i			1.36165i
$839$			35.9805i			1.24219i	0.783737	+	0.621093i	$0.213311\pi$
$839$			35.9805i			1.24219i	−0.783737	+	0.621093i	$0.786689\pi$
$840$		−	4.04945i		−	0.139719i
$841$	20.4641			0.705659
$842$	−1.65142			−0.0569116
$843$			7.07384i			0.243636i
$844$			60.2772i			2.07483i
$845$			6.07838i			0.209103i
$846$	39.9071			1.37203
$847$			4.63809i			0.159367i
$848$	−7.81205			−0.268267
$849$	−7.52586			−0.258287
$850$	−7.04945	−	5.51026i	−0.241794	−	0.189000i
$851$	−27.4641			−0.941458
$852$	5.93827			0.203442
$853$			28.7792i			0.985382i	0.870204	+	0.492691i	$0.163987\pi$
$853$			28.7792i			0.985382i	−0.870204	+	0.492691i	$0.836013\pi$
$854$	−129.771			−4.44066
$855$		−	2.92162i		−	0.0999174i
$856$		−	19.4524i		−	0.664869i
$857$			17.0661i			0.582967i	0.956576	+	0.291483i	$0.0941488\pi$
$857$			17.0661i			0.582967i	−0.956576	+	0.291483i	$0.905851\pi$
$858$	9.75872			0.333157
$859$	−18.9360			−0.646088			−0.323044	−	0.946384i	$-0.604706\pi$
$859$	−18.9360			−0.646088			−0.323044	+	0.946384i	$0.604706\pi$
$860$		−	9.12783i		−	0.311256i
$861$		−	14.7382i		−	0.502277i
$862$			13.7743i			0.469155i
$863$	30.8332			1.04958			0.524788	−	0.851233i	$-0.324145\pi$
$863$	30.8332			1.04958			0.524788	+	0.851233i	$0.324145\pi$
$864$			23.3607i			0.794747i
$865$	17.3607			0.590281
$866$	−7.86603			−0.267299
$867$	−8.89496	+	2.21339i	−0.302089	+	0.0751707i
$868$	54.0905			1.83595
$869$	21.9649			0.745109
$870$		−	3.41855i		−	0.115900i
$871$	26.8515			0.909828
$872$		−	12.5548i		−	0.425159i
$873$			22.1711i			0.750379i
$874$			12.2146i			0.413165i
$875$	−4.87936			−0.164953
$876$	16.1834			0.546787
$877$		−	4.30898i		−	0.145504i	−0.997350	−	0.0727519i	$-0.976822\pi$
$877$		−	4.30898i		−	0.145504i	0.997350	−	0.0727519i	$-0.0231781\pi$
$878$		−	13.8999i		−	0.469098i
$879$			2.55479i			0.0861708i
$880$	−6.58864			−0.222103
$881$			12.2245i			0.411852i	0.978568	+	0.205926i	$0.0660207\pi$
$881$			12.2245i			0.411852i	−0.978568	+	0.205926i	$0.933979\pi$
$882$	98.8213			3.32749
$883$	−28.2329			−0.950112			−0.475056	−	0.879956i	$-0.657572\pi$
$883$	−28.2329			−0.950112			−0.475056	+	0.879956i	$0.657572\pi$
$884$	−23.1545	−	18.0989i	−0.778770	−	0.608732i
$885$	−1.26180			−0.0424148
$886$	−59.6391			−2.00362
$887$		−	5.17396i		−	0.173725i	−0.996220	−	0.0868623i	$-0.972316\pi$
$887$		−	5.17396i		−	0.173725i	0.996220	−	0.0868623i	$-0.0276840\pi$
$888$	−4.36683			−0.146541
$889$		−	39.2762i		−	1.31728i
$890$			15.5259i			0.520428i
$891$			20.5041i			0.686914i
$892$	−5.93827			−0.198828
$893$	−7.31965			−0.244943
$894$			16.7115i			0.558918i
$895$		−	6.83710i		−	0.228539i
$896$			56.3039i			1.88098i
$897$	7.40417			0.247218
$898$		−	62.3956i		−	2.08217i
$899$	11.9544			0.398702
$900$	−7.34017			−0.244672
$901$	−12.2101	−	9.54411i	−0.406777	−	0.317960i
$902$	38.5380			1.28317
$903$	−8.86376			−0.294968
$904$			26.1978i			0.871326i
$905$	−15.0205			−0.499299
$906$		−	15.0517i		−	0.500060i
$907$			6.32457i			0.210004i	0.994472	+	0.105002i	$0.0334849\pi$
$907$			6.32457i			0.210004i	−0.994472	+	0.105002i	$0.966515\pi$
$908$		−	25.8999i		−	0.859518i
$909$	−6.70313			−0.222329
$910$	−27.8576			−0.923471
$911$		−	27.6526i		−	0.916173i	−0.888908	−	0.458086i	$-0.848535\pi$
$911$		−	27.6526i		−	0.916173i	0.888908	−	0.458086i	$-0.151465\pi$
$912$		−	1.20847i		−	0.0400165i
$913$			26.0989i			0.863747i
$914$	68.1627			2.25462
$915$		−	6.60811i		−	0.218457i
$916$	19.9649			0.659660
$917$	57.0577			1.88421
$918$	−16.9627	+	21.7009i	−0.559851	+	0.716235i
$919$	−47.5318			−1.56793			−0.783965	−	0.620805i	$-0.786806\pi$
$919$	−47.5318			−1.56793			−0.783965	+	0.620805i	$0.786806\pi$
$920$	8.03385			0.264868
$921$		−	11.6430i		−	0.383650i
$922$	16.8371			0.554500
$923$		−	10.6947i		−	0.352021i
$924$		−	22.5958i		−	0.743348i
$925$			5.26180i			0.173007i
$926$	−52.5874			−1.72813
$927$	−53.2411			−1.74867
$928$			22.1711i			0.727803i
$929$			43.7875i			1.43662i	0.695723	+	0.718310i	$0.255084\pi$
$929$			43.7875i			1.43662i	−0.695723	+	0.718310i	$0.744916\pi$
$930$			4.78765i			0.156993i
$931$	−18.1256			−0.594041
$932$		−	25.5897i		−	0.838218i
$933$	13.0823			0.428294
$934$	26.7298			0.874626
$935$	−10.2979	−	8.04945i	−0.336778	−	0.263245i
$936$	−10.9711			−0.358601
$937$	14.2367			0.465094			0.232547	−	0.972585i	$-0.425294\pi$
$937$	14.2367			0.465094			0.232547	+	0.972585i	$0.425294\pi$
$938$		−	108.070i		−	3.52860i
$939$	2.19570			0.0716541
$940$			18.3896i			0.599803i
$941$		−	35.2183i		−	1.14808i	−0.818826	−	0.574042i	$-0.805375\pi$
$941$		−	35.2183i		−	1.14808i	0.818826	−	0.574042i	$-0.194625\pi$
$942$		−	4.39803i		−	0.143296i
$943$	29.2397			0.952175
$944$	4.86376			0.158302
$945$			15.0205i			0.488618i
$946$		−	23.1773i		−	0.753558i
$947$		−	49.1227i		−	1.59627i	−0.602476	−	0.798137i	$-0.705819\pi$
$947$		−	49.1227i		−	1.59627i	0.602476	−	0.798137i	$-0.294181\pi$
$948$	10.1217			0.328737
$949$		−	29.1461i		−	0.946122i
$950$	2.34017			0.0759252
$951$	4.34471			0.140887
$952$	−19.0700	+	24.3968i	−0.618061	+	0.790705i
$953$	−17.0556			−0.552485			−0.276242	−	0.961088i	$-0.589089\pi$
$953$	−17.0556			−0.552485			−0.276242	+	0.961088i	$0.589089\pi$
$954$	−22.0989			−0.715478
$955$			24.2823i			0.785757i
$956$	16.9483			0.548147
$957$		−	4.99386i		−	0.161428i
$958$			4.66475i			0.150711i
$959$			9.51745i			0.307334i
$960$	−6.63809			−0.214243
$961$	14.2579			0.459933
$962$			30.0410i			0.968562i
$963$			34.2401i			1.10337i
$964$			6.76487i			0.217882i
$965$	11.8576			0.381710
$966$		−	29.7998i		−	0.958792i
$967$	−25.1955			−0.810233			−0.405117	−	0.914265i	$-0.632769\pi$
$967$	−25.1955			−0.810233			−0.405117	+	0.914265i	$0.632769\pi$
$968$	−1.46308			−0.0470251
$969$	1.47641	−	1.88882i	0.0474291	−	0.0606776i
$970$	−17.7587			−0.570198
$971$	1.67420			0.0537277			0.0268639	−	0.999639i	$-0.491448\pi$
$971$	1.67420			0.0537277			0.0268639	+	0.999639i	$0.491448\pi$
$972$			34.4690i			1.10560i
$973$	−9.79380			−0.313975
$974$		−	86.9842i		−	2.78715i
$975$		−	1.41855i		−	0.0454300i
$976$			25.4719i			0.815335i
$977$	−39.9109			−1.27686			−0.638432	−	0.769678i	$-0.720417\pi$
$977$	−39.9109			−1.27686			−0.638432	+	0.769678i	$0.720417\pi$
$978$	10.1750			0.325361
$979$			22.6803i			0.724867i
$980$			45.5380i			1.45466i
$981$			22.0989i			0.705563i
$982$	4.89496			0.156204
$983$			5.46081i			0.174173i	0.996201	+	0.0870864i	$0.0277556\pi$
$983$			5.46081i			0.174173i	−0.996201	+	0.0870864i	$0.972244\pi$
$984$	4.64915			0.148209
$985$	18.2557			0.581673
$986$	−16.0989	+	20.5958i	−0.512693	+	0.655905i
$987$	17.8576			0.568414
$988$	7.68649			0.244540
$989$		−	17.5851i		−	0.559175i
$990$	−18.6381			−0.592357
$991$			42.0749i			1.33655i	0.743913	+	0.668276i	$0.232968\pi$
$991$			42.0749i			1.33655i	−0.743913	+	0.668276i	$0.767032\pi$
$992$		−	31.0505i		−	0.985854i
$993$		−	5.43084i		−	0.172342i
$994$	−43.0433			−1.36525
$995$	−3.72487			−0.118086
$996$			12.0267i			0.381079i
$997$			54.6681i			1.73135i	0.500602	+	0.865677i	$0.333112\pi$
$997$			54.6681i			1.73135i	−0.500602	+	0.865677i	$0.666888\pi$
$998$		−	92.3267i		−	2.92255i
$999$	16.1978			0.512476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.d.a.16.2	yes	6
3.2	odd	2		765.2.g.b.271.6		6
4.3	odd	2		1360.2.c.f.1121.3		6
5.2	odd	4		425.2.c.a.424.1		6
5.3	odd	4		425.2.c.b.424.6		6
5.4	even	2		425.2.d.c.101.5		6
17.4	even	4		1445.2.a.j.1.3		3
17.13	even	4		1445.2.a.k.1.3		3
17.16	even	2	inner	85.2.d.a.16.1	✓	6
51.50	odd	2		765.2.g.b.271.5		6
68.67	odd	2		1360.2.c.f.1121.4		6
85.4	even	4		7225.2.a.q.1.1		3
85.33	odd	4		425.2.c.a.424.6		6
85.64	even	4		7225.2.a.r.1.1		3
85.67	odd	4		425.2.c.b.424.1		6
85.84	even	2		425.2.d.c.101.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.d.a.16.1	✓	6	17.16	even	2	inner
85.2.d.a.16.2	yes	6	1.1	even	1	trivial
425.2.c.a.424.1		6	5.2	odd	4
425.2.c.a.424.6		6	85.33	odd	4
425.2.c.b.424.1		6	85.67	odd	4
425.2.c.b.424.6		6	5.3	odd	4
425.2.d.c.101.5		6	5.4	even	2
425.2.d.c.101.6		6	85.84	even	2
765.2.g.b.271.5		6	51.50	odd	2
765.2.g.b.271.6		6	3.2	odd	2
1360.2.c.f.1121.3		6	4.3	odd	2
1360.2.c.f.1121.4		6	68.67	odd	2
1445.2.a.j.1.3		3	17.4	even	4
1445.2.a.k.1.3		3	17.13	even	4
7225.2.a.q.1.1		3	85.4	even	4
7225.2.a.r.1.1		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.17009 q^{2} +0.539189i q^{3} +2.70928 q^{4} -1.00000i q^{5} -1.17009i q^{6} +4.87936i q^{7} -1.53919 q^{8} +2.70928 q^{9} +2.17009i q^{10} +3.17009i q^{11} +1.46081i q^{12} +2.63090 q^{13} -10.5886i q^{14} +0.539189 q^{15} -2.07838 q^{16} +(-3.24846 - 2.53919i) q^{17} -5.87936 q^{18} +1.07838 q^{19} -2.70928i q^{20} -2.63090 q^{21} -6.87936i q^{22} -5.21953i q^{23} -0.829914i q^{24} -1.00000 q^{25} -5.70928 q^{26} +3.07838i q^{27} +13.2195i q^{28} +2.92162i q^{29} -1.17009 q^{30} -4.09171i q^{31} +7.58864 q^{32} -1.70928 q^{33} +(7.04945 + 5.51026i) q^{34} +4.87936 q^{35} +7.34017 q^{36} -5.26180i q^{37} -2.34017 q^{38} +1.41855i q^{39} +1.53919i q^{40} +5.60197i q^{41} +5.70928 q^{42} +3.36910 q^{43} +8.58864i q^{44} -2.70928i q^{45} +11.3268i q^{46} -6.78765 q^{47} -1.12064i q^{48} -16.8082 q^{49} +2.17009 q^{50} +(1.36910 - 1.75154i) q^{51} +7.12783 q^{52} +3.75872 q^{53} -6.68035i q^{54} +3.17009 q^{55} -7.51026i q^{56} +0.581449i q^{57} -6.34017i q^{58} -2.34017 q^{59} +1.46081 q^{60} -12.2557i q^{61} +8.87936i q^{62} +13.2195i q^{63} -12.3112 q^{64} -2.63090i q^{65} +3.70928 q^{66} +10.2062 q^{67} +(-8.80098 - 6.87936i) q^{68} +2.81432 q^{69} -10.5886 q^{70} -4.06505i q^{71} -4.17009 q^{72} -11.0784i q^{73} +11.4186i q^{74} -0.539189i q^{75} +2.92162 q^{76} -15.4680 q^{77} -3.07838i q^{78} -6.92881i q^{79} +2.07838i q^{80} +6.46800 q^{81} -12.1568i q^{82} +8.23287 q^{83} -7.12783 q^{84} +(-2.53919 + 3.24846i) q^{85} -7.31124 q^{86} -1.57531 q^{87} -4.87936i q^{88} +7.15449 q^{89} +5.87936i q^{90} +12.8371i q^{91} -14.1412i q^{92} +2.20620 q^{93} +14.7298 q^{94} -1.07838i q^{95} +4.09171i q^{96} +8.18342i q^{97} +36.4752 q^{98} +8.58864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 2 q^{4} - 6 q^{8} + 2 q^{9} + 8 q^{13} - 6 q^{16} - 2 q^{17} - 10 q^{18} - 8 q^{21} - 6 q^{25} - 20 q^{26} + 4 q^{30} + 6 q^{32} + 4 q^{33} + 6 q^{34} + 4 q^{35} + 22 q^{36} + 8 q^{38} + 20 q^{42}+ \cdots + 86 q^{98}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more