LMFDB - Embedded newform 85.2.d.a.16.1

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

$q$-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	$-0.950253\pi$
$3$		−	0.539189i		−	0.311301i	0.987812	−	0.155650i	$-0.0497473\pi$
$4$	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	$-0.626462\pi$
$7$		−	4.87936i		−	1.84423i	0.386921	−	0.922113i	$-0.373538\pi$
$8$	−1.53919			−0.544185
$9$	2.70928			0.903092
$10$		−	2.17009i		−	0.686242i
$11$		−	3.17009i		−	0.955817i	−0.878410	−	0.477909i	$-0.841395\pi$
$11$		−	3.17009i		−	0.955817i	0.878410	−	0.477909i	$-0.158605\pi$
$12$		−	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	$0.183157\pi$
$23$			5.21953i			1.08835i	−0.838972	+	0.544174i	$0.816843\pi$
$24$			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	$-0.912558\pi$
$29$		−	2.92162i		−	0.542532i	0.962504	−	0.271266i	$-0.0874422\pi$
$30$	−1.17009			−0.213628
$31$			4.09171i			0.734893i	0.930045	+	0.367446i	$0.119768\pi$
$31$			4.09171i			0.734893i	−0.930045	+	0.367446i	$0.880232\pi$
$32$	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	$0.142374\pi$
$37$			5.26180i			0.865034i	−0.901626	+	0.432517i	$0.857626\pi$
$38$	−2.34017			−0.379626
$39$		−	1.41855i		−	0.227150i
$40$		−	1.53919i		−	0.243367i
$41$		−	5.60197i		−	0.874880i	−0.899247	−	0.437440i	$-0.855885\pi$
$41$		−	5.60197i		−	0.874880i	0.899247	−	0.437440i	$-0.144115\pi$
$42$	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	$0.287125\pi$
$61$			12.2557i			1.56918i	−0.620018	+	0.784588i	$0.712875\pi$
$62$		−	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	$0.0775463\pi$
$71$			4.06505i			0.482432i	−0.970471	+	0.241216i	$0.922454\pi$
$72$	−4.17009			−0.491449
$73$			11.0784i			1.29663i	0.761374	+	0.648313i	$0.224525\pi$
$73$			11.0784i			1.29663i	−0.761374	+	0.648313i	$0.775475\pi$
$74$		−	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	$0.127448\pi$
$79$			6.92881i			0.779552i	−0.920910	+	0.389776i	$0.872552\pi$
$80$		−	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	$-0.863624\pi$
$97$		−	8.18342i		−	0.830900i	0.909616	−	0.415450i	$-0.136376\pi$
$98$	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	$-0.790814\pi$
$107$		−	12.6381i		−	1.22177i	0.791719	−	0.610885i	$-0.209186\pi$
$108$		−	8.34017i		−	0.802534i
$109$		−	8.15676i		−	0.781275i	−0.920544	−	0.390638i	$-0.872255\pi$
$109$		−	8.15676i		−	0.781275i	0.920544	−	0.390638i	$-0.127745\pi$
$110$	−6.87936			−0.655921
$111$	2.83710			0.269286
$112$			10.1412i			0.958249i
$113$			17.0205i			1.60116i	0.599229	+	0.800578i	$0.295474\pi$
$113$			17.0205i			1.60116i	−0.599229	+	0.800578i	$0.704526\pi$
$114$			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	$0.170666\pi$
$131$			11.6937i			1.02168i	−0.859675	+	0.510841i	$0.829334\pi$
$132$	−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	$-0.972871\pi$
$139$		−	2.00719i		−	0.170247i	0.996370	−	0.0851237i	$-0.0271286\pi$
$140$	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	$-0.889384\pi$
$163$		−	8.69594i		−	0.681119i	0.940223	−	0.340559i	$-0.110616\pi$
$164$		−	15.1773i		−	1.18515i
$165$		−	1.70928i		−	0.133067i
$166$	−17.8660			−1.38667
$167$			1.37629i			0.106501i	0.998581	+	0.0532503i	$0.0169581\pi$
$167$			1.37629i			0.106501i	−0.998581	+	0.0532503i	$0.983042\pi$
$168$	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	$-0.770576\pi$
$173$		−	17.3607i		−	1.31991i	0.751306	−	0.659954i	$-0.229424\pi$
$174$	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	$0.188521\pi$
$181$			15.0205i			1.11647i	−0.829684	+	0.558233i	$0.811479\pi$
$182$			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	$-0.859653\pi$
$193$		−	11.8576i		−	0.853530i	0.904363	−	0.426765i	$-0.140347\pi$
$194$			17.7587i			1.27500i
$195$	1.41855			0.101585
$196$	−45.5380			−3.25271
$197$		−	18.2557i		−	1.30066i	−0.759651	−	0.650331i	$-0.774630\pi$
$197$		−	18.2557i		−	1.30066i	0.759651	−	0.650331i	$-0.225370\pi$
$198$			18.6381i			1.32455i
$199$			3.72487i			0.264049i	0.991246	+	0.132025i	$0.0421478\pi$
$199$			3.72487i			0.264049i	−0.991246	+	0.132025i	$0.957852\pi$
$200$	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	$-0.722332\pi$
$211$		−	22.2485i		−	1.53165i	0.643051	−	0.765824i	$-0.277668\pi$
$212$	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	$0.102759\pi$
$227$			9.55971i			0.634500i	−0.948342	+	0.317250i	$0.897241\pi$
$228$		−	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	$0.100124\pi$
$233$			9.44521i			0.618776i	−0.950936	+	0.309388i	$0.899876\pi$
$234$	−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	$-0.974374\pi$
$241$		−	2.49693i		−	0.160841i	0.996761	−	0.0804207i	$-0.0256264\pi$
$242$	−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	$-0.926807\pi$
$269$		−	7.47641i		−	0.455845i	0.973679	−	0.227922i	$-0.0731932\pi$
$270$	−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	$0.119004\pi$
$277$			12.1568i			0.730429i	−0.930923	+	0.365214i	$0.880996\pi$
$278$			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	$-0.863834\pi$
$283$		−	13.9577i		−	0.829701i	0.909889	−	0.414851i	$-0.136166\pi$
$284$			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	$0.241472\pi$
$311$			24.2628i			1.37582i	−0.725796	+	0.687910i	$0.758528\pi$
$312$			2.18342i			0.123612i
$313$			4.07223i			0.230176i	0.993355	+	0.115088i	$0.0367151\pi$
$313$			4.07223i			0.230176i	−0.993355	+	0.115088i	$0.963285\pi$
$314$	−8.15676			−0.460312
$315$	13.2195			0.744836
$316$			18.7721i			1.05601i
$317$			8.05786i			0.452574i	0.974061	+	0.226287i	$0.0726588\pi$
$317$			8.05786i			0.452574i	−0.974061	+	0.226287i	$0.927341\pi$
$318$			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	$-0.901006\pi$
$337$		−	11.2351i		−	0.612017i	0.952029	−	0.306008i	$-0.0989936\pi$
$338$	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	$-0.924543\pi$
$347$		−	8.74927i		−	0.469685i	0.972033	−	0.234843i	$-0.0754575\pi$
$348$	−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	$0.102402\pi$
$367$			12.1145i			0.632371i	−0.948697	+	0.316186i	$0.897598\pi$
$368$		−	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	$-0.991933\pi$
$379$		−	0.986669i		−	0.0506818i	0.999679	−	0.0253409i	$-0.00806712\pi$
$380$			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	$0.253928\pi$
$397$			28.5236i			1.43156i	−0.698327	+	0.715779i	$0.746072\pi$
$398$		−	8.08330i		−	0.405179i
$399$	−2.83710			−0.142033
$400$	2.07838			0.103919
$401$		−	33.0928i		−	1.65257i	−0.563250	−	0.826287i	$-0.690449\pi$
$401$		−	33.0928i		−	1.65257i	0.563250	−	0.826287i	$-0.309551\pi$
$402$			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	$0.146329\pi$
$419$			18.1639i			0.887367i	−0.896184	+	0.443683i	$0.853671\pi$
$420$		−	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	$0.0488518\pi$
$431$			6.34736i			0.305742i	−0.988246	+	0.152871i	$0.951148\pi$
$432$			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	$-0.951154\pi$
$439$		−	6.40522i		−	0.305704i	0.988249	−	0.152852i	$-0.0488459\pi$
$440$	−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	$-0.762648\pi$
$449$		−	28.7526i		−	1.35692i	0.734638	−	0.678459i	$-0.237352\pi$
$450$	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	$0.0156379\pi$
$479$			2.14957i			0.0982162i	−0.998793	+	0.0491081i	$0.984362\pi$
$480$	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	$-0.637477\pi$
$487$		−	40.0833i		−	1.81635i	0.418593	−	0.908174i	$-0.362523\pi$
$488$		−	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	$-0.598720\pi$
$499$		−	42.5452i		−	1.90458i	0.305190	−	0.952291i	$-0.401280\pi$
$500$		−	2.70928i		−	0.121162i
$501$	0.742080			0.0331537
$502$	25.6430			1.14450
$503$		−	9.55971i		−	0.426246i	−0.977025	−	0.213123i	$-0.931636\pi$
$503$		−	9.55971i		−	0.426246i	0.977025	−	0.213123i	$-0.0683636\pi$
$504$			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	$0.107346\pi$
$521$			15.1050i			0.661764i	−0.943672	+	0.330882i	$0.892654\pi$
$522$			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	$0.0471695\pi$
$541$			6.86830i			0.295291i	−0.989040	+	0.147646i	$0.952830\pi$
$542$	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	$-0.959744\pi$
$547$		−	5.89988i		−	0.252261i	0.992014	−	0.126130i	$-0.0402558\pi$
$548$	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	$-0.895165\pi$
$571$		−	15.4569i		−	0.646853i	0.946253	−	0.323426i	$-0.104835\pi$
$572$		−	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	$0.149058\pi$
$601$			22.1301i			0.902705i	−0.892346	+	0.451353i	$0.850942\pi$
$602$			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	$0.0668114\pi$
$607$			10.2667i			0.416713i	−0.978053	+	0.208357i	$0.933189\pi$
$608$	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	$0.116757\pi$
$617$			17.8166i			0.717269i	−0.933478	+	0.358634i	$0.883243\pi$
$618$		−	22.9939i		−	0.924949i
$619$			38.3884i			1.54296i	0.636254	+	0.771480i	$0.280483\pi$
$619$			38.3884i			1.54296i	−0.636254	+	0.771480i	$0.719517\pi$
$620$	−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	$0.0619949\pi$
$641$			9.79976i			0.387067i	−0.981094	+	0.193534i	$0.938005\pi$
$642$	14.7877			0.583622
$643$			16.9372i			0.667939i	0.942584	+	0.333969i	$0.108388\pi$
$643$			16.9372i			0.667939i	−0.942584	+	0.333969i	$0.891612\pi$
$644$	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	$0.288125\pi$
$653$			40.1978i			1.57306i	−0.617551	+	0.786531i	$0.711875\pi$
$654$	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	$-0.917268\pi$
$673$		−	13.3340i		−	0.513989i	0.966413	−	0.256995i	$-0.0827322\pi$
$674$			24.3812i			0.939129i
$675$			3.07838i			0.118487i
$676$	−16.4680			−0.633385
$677$		−	26.5113i		−	1.01891i	−0.860497	−	0.509456i	$-0.829847\pi$
$677$		−	26.5113i		−	1.01891i	0.860497	−	0.509456i	$-0.170153\pi$
$678$	−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	$0.0348824\pi$
$683$			5.71646i			0.218734i	−0.994001	+	0.109367i	$0.965118\pi$
$684$	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	$-0.686002\pi$
$691$		−	43.8504i		−	1.66815i	0.551652	−	0.834075i	$-0.313998\pi$
$692$		−	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	$-0.934857\pi$
$709$		−	10.8227i		−	0.406456i	0.979131	−	0.203228i	$-0.0651433\pi$
$710$	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	$-0.696134\pi$
$719$		−	43.7659i		−	1.63219i	0.577916	−	0.816097i	$-0.303866\pi$
$720$		−	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	$-0.945138\pi$
$743$		−	9.34963i		−	0.343005i	0.985184	−	0.171502i	$-0.0548621\pi$
$744$	−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	$0.437014\pi$
$751$			53.7392i			1.96097i	−0.196586	+	0.980487i	$0.562986\pi$
$752$	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	$0.183664\pi$
$787$			30.6069i			1.09102i	−0.838105	+	0.545509i	$0.816336\pi$
$788$		−	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	$0.270816\pi$
$809$			42.7670i			1.50361i	−0.659388	+	0.751803i	$0.729184\pi$
$810$		−	14.0361i		−	0.493179i
$811$			9.41136i			0.330478i	0.986254	+	0.165239i	$0.0528395\pi$
$811$			9.41136i			0.330478i	−0.986254	+	0.165239i	$0.947161\pi$
$812$	−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	$-0.806919\pi$
$821$		−	32.6681i		−	1.14012i	0.821602	−	0.570062i	$-0.193081\pi$
$822$			2.28231i			0.0796048i
$823$		−	15.9265i		−	0.555164i	−0.960702	−	0.277582i	$-0.910467\pi$
$823$		−	15.9265i		−	0.555164i	0.960702	−	0.277582i	$-0.0895331\pi$
$824$	30.2472			1.05371
$825$	1.70928			0.0595093
$826$		−	24.7792i		−	0.862180i
$827$		−	6.01560i		−	0.209183i	−0.994515	−	0.104591i	$-0.966647\pi$
$827$		−	6.01560i		−	0.209183i	0.994515	−	0.104591i	$-0.0333535\pi$
$828$			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	$-0.786689\pi$
$839$		−	35.9805i		−	1.24219i	0.783737	−	0.621093i	$-0.213311\pi$
$840$			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	$-0.836013\pi$
$853$		−	28.7792i		−	0.985382i	0.870204	−	0.492691i	$-0.163987\pi$
$854$	−129.771			−4.44066
$855$			2.92162i			0.0999174i
$856$			19.4524i			0.664869i
$857$		−	17.0661i		−	0.582967i	−0.956576	−	0.291483i	$-0.905851\pi$
$857$		−	17.0661i		−	0.582967i	0.956576	−	0.291483i	$-0.0941488\pi$
$858$	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	$0.0231781\pi$
$877$			4.30898i			0.145504i	−0.997350	+	0.0727519i	$0.976822\pi$
$878$			13.8999i			0.469098i
$879$		−	2.55479i		−	0.0861708i
$880$	−6.58864			−0.222103
$881$		−	12.2245i		−	0.411852i	−0.978568	−	0.205926i	$-0.933979\pi$
$881$		−	12.2245i		−	0.411852i	0.978568	−	0.205926i	$-0.0660207\pi$
$882$	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	$0.0276840\pi$
$887$			5.17396i			0.173725i	−0.996220	+	0.0868623i	$0.972316\pi$
$888$	−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	$-0.966515\pi$
$907$		−	6.32457i		−	0.210004i	0.994472	−	0.105002i	$-0.0334849\pi$
$908$			25.8999i			0.859518i
$909$	−6.70313			−0.222329
$910$	−27.8576			−0.923471
$911$			27.6526i			0.916173i	0.888908	+	0.458086i	$0.151465\pi$
$911$			27.6526i			0.916173i	−0.888908	+	0.458086i	$0.848535\pi$
$912$			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	$-0.744916\pi$
$929$		−	43.7875i		−	1.43662i	0.695723	−	0.718310i	$-0.255084\pi$
$930$		−	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	$0.194625\pi$
$941$			35.2183i			1.14808i	−0.818826	+	0.574042i	$0.805375\pi$
$942$			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	$0.294181\pi$
$947$			49.1227i			1.59627i	−0.602476	+	0.798137i	$0.705819\pi$
$948$	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	$-0.972244\pi$
$983$		−	5.46081i		−	0.174173i	0.996201	−	0.0870864i	$-0.0277556\pi$
$984$	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	$-0.767032\pi$
$991$		−	42.0749i		−	1.33655i	0.743913	−	0.668276i	$-0.232968\pi$
$992$			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	$-0.666888\pi$
$997$		−	54.6681i		−	1.73135i	0.500602	−	0.865677i	$-0.333112\pi$
$998$			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.16.1	✓	6
3.2	odd	2		765.2.g.b.271.5		6
4.3	odd	2		1360.2.c.f.1121.4		6
5.2	odd	4		425.2.c.b.424.1		6
5.3	odd	4		425.2.c.a.424.6		6
5.4	even	2		425.2.d.c.101.6		6
17.4	even	4		1445.2.a.k.1.3		3
17.13	even	4		1445.2.a.j.1.3		3
17.16	even	2	inner	85.2.d.a.16.2	yes	6
51.50	odd	2		765.2.g.b.271.6		6
68.67	odd	2		1360.2.c.f.1121.3		6
85.4	even	4		7225.2.a.r.1.1		3
85.33	odd	4		425.2.c.b.424.6		6
85.64	even	4		7225.2.a.q.1.1		3
85.67	odd	4		425.2.c.a.424.1		6
85.84	even	2		425.2.d.c.101.5		6

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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Database

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