LMFDB - Embedded newform 85.2.b.a.69.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,2,Mod(69,85)] 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("85.69"); 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([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.b (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:	$8$
Coefficient field:	8.0.619810816.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
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			69.3
Root			$-0.252709 - 0.252709i$ of defining polynomial
Character	$\chi$	$=$	85.69
Dual form			85.2.b.a.69.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.57942i q^{2} +2.87228i q^{3} -0.494582 q^{4} +(0.146426 + 2.23127i) q^{5} +4.53654 q^{6} -1.42058i q^{7} -2.37769i q^{8} -5.24997 q^{9} +(3.52412 - 0.231269i) q^{10} +0.0740063 q^{11} -1.42058i q^{12} -5.70167i q^{13} -2.24369 q^{14} +(-6.40882 + 0.420575i) q^{15} -4.74455 q^{16} +1.00000i q^{17} +8.29193i q^{18} +4.90340 q^{19} +(-0.0724196 - 1.10354i) q^{20} +4.08029 q^{21} -0.116887i q^{22} +3.88311i q^{23} +6.82940 q^{24} +(-4.95712 + 0.653431i) q^{25} -9.00536 q^{26} -6.46254i q^{27} +0.702591i q^{28} -5.91424 q^{29} +(0.664267 + 10.1222i) q^{30} +0.388531 q^{31} +2.73827i q^{32} +0.212567i q^{33} +1.57942 q^{34} +(3.16969 - 0.208009i) q^{35} +2.59654 q^{36} -9.91424i q^{37} -7.74455i q^{38} +16.3768 q^{39} +(5.30527 - 0.348156i) q^{40} -6.61055 q^{41} -6.44450i q^{42} +6.94628i q^{43} -0.0366022 q^{44} +(-0.768731 - 11.7141i) q^{45} +6.13308 q^{46} +5.70167i q^{47} -13.6277i q^{48} +4.98197 q^{49} +(1.03204 + 7.82940i) q^{50} -2.87228 q^{51} +2.81994i q^{52} -0.0216729i q^{53} -10.2071 q^{54} +(0.0108364 + 0.165128i) q^{55} -3.37769 q^{56} +14.0839i q^{57} +9.34109i q^{58} +2.00000 q^{59} +(3.16969 - 0.208009i) q^{60} -3.47337 q^{61} -0.613655i q^{62} +7.45798i q^{63} -5.16421 q^{64} +(12.7220 - 0.834872i) q^{65} +0.335733 q^{66} +6.71251i q^{67} -0.494582i q^{68} -11.1534 q^{69} +(-0.328534 - 5.00628i) q^{70} +3.84023 q^{71} +12.4828i q^{72} +13.5356i q^{73} -15.6588 q^{74} +(-1.87683 - 14.2382i) q^{75} -2.42513 q^{76} -0.105132i q^{77} -25.8659i q^{78} +1.06000 q^{79} +(-0.694725 - 10.5864i) q^{80} +2.81228 q^{81} +10.4409i q^{82} -11.8497i q^{83} -2.01803 q^{84} +(-2.23127 + 0.146426i) q^{85} +10.9711 q^{86} -16.9873i q^{87} -0.175964i q^{88} +1.99452 q^{89} +(-18.5015 + 1.21415i) q^{90} -8.09965 q^{91} -1.92052i q^{92} +1.11597i q^{93} +9.00536 q^{94} +(0.717985 + 10.9408i) q^{95} -7.86508 q^{96} -5.34109i q^{97} -7.86864i q^{98} -0.388531 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{9} + 6 q^{10} - 4 q^{11} + 12 q^{14} - 8 q^{16} - 8 q^{19} - 2 q^{20} + 24 q^{21} + 12 q^{24} - 12 q^{25} + 8 q^{29} - 16 q^{30} - 24 q^{31} + 4 q^{34} + 44 q^{39} + 22 q^{40}+ \cdots + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^9 + 6 * q^10 - 4 * q^11 + 12 * q^14 - 8 * q^16 - 8 * q^19 - 2 * q^20 + 24 * q^21 + 12 * q^24 - 12 * q^25 + 8 * q^29 - 16 * q^30 - 24 * q^31 + 4 * q^34 + 44 * q^39 + 22 * q^40 - 12 * q^41 - 32 * q^44 - 22 * q^45 - 8 * q^46 - 16 * q^49 + 44 * q^50 - 8 * q^51 - 20 * q^54 - 8 * q^55 - 8 * q^56 + 16 * q^59 + 12 * q^61 + 48 * q^64 + 20 * q^65 + 24 * q^66 - 8 * q^69 + 40 * q^70 - 20 * q^71 - 40 * q^74 + 4 * q^75 - 24 * q^76 + 24 * q^79 - 26 * q^80 - 8 * q^81 - 72 * q^84 - 2 * q^85 + 40 * q^86 - 48 * q^89 - 74 * q^90 + 36 * q^91 + 4 * q^95 + 16 * q^96 + 24 * q^99

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 $

$2$		−	1.57942i		−	1.11682i	−0.829565	−	0.558411i	$-0.811411\pi$
$2$		−	1.57942i		−	1.11682i	0.829565	−	0.558411i	$-0.188589\pi$
$3$			2.87228i			1.65831i	0.559019	+	0.829155i	$0.311178\pi$
$3$			2.87228i			1.65831i	−0.559019	+	0.829155i	$0.688822\pi$
$4$	−0.494582			−0.247291
$5$	0.146426	+	2.23127i	0.0654836	+	0.997854i
$5$	0.146426	+	2.23127i	0.0654836	+	0.997854i
$6$	4.53654			1.85204
$7$		−	1.42058i		−	0.536927i	−0.963290	−	0.268464i	$-0.913484\pi$
$7$		−	1.42058i		−	0.536927i	0.963290	−	0.268464i	$-0.0865159\pi$
$8$		−	2.37769i		−	0.840642i
$9$	−5.24997			−1.74999
$10$	3.52412	−	0.231269i	1.11442	−	0.0731335i
$11$	0.0740063			0.0223137			0.0111569	−	0.999938i	$-0.496449\pi$
$11$	0.0740063			0.0223137			0.0111569	+	0.999938i	$0.496449\pi$
$12$		−	1.42058i		−	0.410085i
$13$		−	5.70167i		−	1.58136i	−0.612230	−	0.790680i	$-0.709727\pi$
$13$		−	5.70167i		−	1.58136i	0.612230	−	0.790680i	$-0.290273\pi$
$14$	−2.24369			−0.599652
$15$	−6.40882	+	0.420575i	−1.65475	+	0.108592i
$16$	−4.74455			−1.18614
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$			8.29193i			1.95443i
$19$	4.90340			1.12492			0.562459	−	0.826825i	$-0.309856\pi$
$19$	4.90340			1.12492			0.562459	+	0.826825i	$0.309856\pi$
$20$	−0.0724196	−	1.10354i	−0.0161935	−	0.246760i
$21$	4.08029			0.890391
$22$		−	0.116887i		−	0.0249205i
$23$			3.88311i			0.809685i	0.914386	+	0.404842i	$0.132674\pi$
$23$			3.88311i			0.809685i	−0.914386	+	0.404842i	$0.867326\pi$
$24$	6.82940			1.39404
$25$	−4.95712	+	0.653431i	−0.991424	+	0.130686i
$26$	−9.00536			−1.76610
$27$		−	6.46254i		−	1.24372i
$28$			0.702591i			0.132777i
$29$	−5.91424			−1.09825			−0.549123	−	0.835741i	$-0.685038\pi$
$29$	−5.91424			−1.09825			−0.549123	+	0.835741i	$0.685038\pi$
$30$	0.664267	+	10.1222i	0.121278	+	1.84806i
$31$	0.388531			0.0697822			0.0348911	−	0.999391i	$-0.488892\pi$
$31$	0.388531			0.0697822			0.0348911	+	0.999391i	$0.488892\pi$
$32$			2.73827i			0.484063i
$33$			0.212567i			0.0370031i
$34$	1.57942			0.270869
$35$	3.16969	−	0.208009i	0.535775	−	0.0351599i
$36$	2.59654			0.432757
$37$		−	9.91424i		−	1.62989i	−0.579538	−	0.814945i	$-0.696767\pi$
$37$		−	9.91424i		−	1.62989i	0.579538	−	0.814945i	$-0.303233\pi$
$38$		−	7.74455i		−	1.25633i
$39$	16.3768			2.62238
$40$	5.30527	−	0.348156i	0.838838	−	0.0550483i
$41$	−6.61055			−1.03239			−0.516197	−	0.856470i	$-0.672653\pi$
$41$	−6.61055			−1.03239			−0.516197	+	0.856470i	$0.672653\pi$
$42$		−	6.44450i		−	0.994408i
$43$			6.94628i			1.05930i	0.848217	+	0.529649i	$0.177676\pi$
$43$			6.94628i			1.05930i	−0.848217	+	0.529649i	$0.822324\pi$
$44$	−0.0366022			−0.00551798
$45$	−0.768731	−	11.7141i	−0.114596	−	1.74623i
$46$	6.13308			0.904274
$47$			5.70167i			0.831674i	0.909439	+	0.415837i	$0.136511\pi$
$47$			5.70167i			0.831674i	−0.909439	+	0.415837i	$0.863489\pi$
$48$		−	13.6277i		−	1.96698i
$49$	4.98197			0.711709
$50$	1.03204	+	7.82940i	0.145953	+	1.10724i
$51$	−2.87228			−0.402199
$52$			2.81994i			0.391056i
$53$		−	0.0216729i		−	0.00297700i	−0.999999	−	0.00148850i	$-0.999526\pi$
$53$		−	0.0216729i		−	0.00297700i	0.999999	−	0.00148850i	$-0.000473804\pi$
$54$	−10.2071			−1.38901
$55$	0.0108364	+	0.165128i	0.00146118	+	0.0222658i
$56$	−3.37769			−0.451363
$57$			14.0839i			1.86546i
$58$			9.34109i			1.22655i
$59$	2.00000			0.260378			0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000			0.260378			0.130189	+	0.991489i	$0.458442\pi$
$60$	3.16969	−	0.208009i	0.409205	−	0.0268538i
$61$	−3.47337			−0.444720			−0.222360	−	0.974965i	$-0.571376\pi$
$61$	−3.47337			−0.444720			−0.222360	+	0.974965i	$0.571376\pi$
$62$		−	0.613655i		−	0.0779343i
$63$			7.45798i			0.939617i
$64$	−5.16421			−0.645526
$65$	12.7220	−	0.834872i	1.57796	−	0.103553i
$66$	0.335733			0.0413258
$67$			6.71251i			0.820063i	0.912071	+	0.410032i	$0.134482\pi$
$67$			6.71251i			0.820063i	−0.912071	+	0.410032i	$0.865518\pi$
$68$		−	0.494582i		−	0.0599769i
$69$	−11.1534			−1.34271
$70$	−0.328534	−	5.00628i	−0.0392674	−	0.598365i
$71$	3.84023			0.455752			0.227876	−	0.973690i	$-0.426822\pi$
$71$	3.84023			0.455752			0.227876	+	0.973690i	$0.426822\pi$
$72$			12.4828i			1.47112i
$73$			13.5356i			1.58422i	0.610375	+	0.792112i	$0.291019\pi$
$73$			13.5356i			1.58422i	−0.610375	+	0.792112i	$0.708981\pi$
$74$	−15.6588			−1.82030
$75$	−1.87683	−	14.2382i	−0.216718	−	1.64409i
$76$	−2.42513			−0.278182
$77$		−	0.105132i		−	0.0119808i
$78$		−	25.8659i		−	2.92873i
$79$	1.06000			0.119259			0.0596295	−	0.998221i	$-0.481008\pi$
$79$	1.06000			0.119259			0.0596295	+	0.998221i	$0.481008\pi$
$80$	−0.694725	−	10.5864i	−0.0776726	−	1.18359i
$81$	2.81228			0.312476
$82$			10.4409i			1.15300i
$83$		−	11.8497i		−	1.30067i	−0.759647	−	0.650336i	$-0.774628\pi$
$83$		−	11.8497i		−	1.30067i	0.759647	−	0.650336i	$-0.225372\pi$
$84$	−2.01803			−0.220186
$85$	−2.23127	+	0.146426i	−0.242015	+	0.0158821i
$86$	10.9711			1.18305
$87$		−	16.9873i		−	1.82123i
$88$		−	0.175964i		−	0.0187579i
$89$	1.99452			0.211419			0.105710	−	0.994397i	$-0.466289\pi$
$89$	1.99452			0.211419			0.105710	+	0.994397i	$0.466289\pi$
$90$	−18.5015	+	1.21415i	−1.95023	+	0.127983i
$91$	−8.09965			−0.849075
$92$		−	1.92052i		−	0.200228i
$93$			1.11597i			0.115720i
$94$	9.00536			0.928832
$95$	0.717985	+	10.9408i	0.0736637	+	1.12250i
$96$	−7.86508			−0.802726
$97$		−	5.34109i		−	0.542306i	−0.962536	−	0.271153i	$-0.912595\pi$
$97$		−	5.34109i		−	0.542306i	0.962536	−	0.271153i	$-0.0874049\pi$
$98$		−	7.86864i		−	0.794852i
$99$	−0.388531			−0.0390488
$100$	2.45170	−	0.323175i	0.245170	−	0.0323175i
$101$	11.4305			1.13738			0.568688	−	0.822553i	$-0.307451\pi$
$101$	11.4305			1.13738			0.568688	+	0.822553i	$0.307451\pi$
$102$			4.53654i			0.449185i
$103$			8.21257i			0.809208i	0.914492	+	0.404604i	$0.132591\pi$
$103$			8.21257i			0.809208i	−0.914492	+	0.404604i	$0.867409\pi$
$104$	−13.5568			−1.32936
$105$	0.597459	+	9.10421i	0.0583061	+	0.888480i
$106$	−0.0342307			−0.00332478
$107$		−	6.34882i		−	0.613764i	−0.951748	−	0.306882i	$-0.900714\pi$
$107$		−	6.34882i		−	0.613764i	0.951748	−	0.306882i	$-0.0992857\pi$
$108$			3.19625i			0.307560i
$109$	−0.292852			−0.0280501			−0.0140251	−	0.999902i	$-0.504464\pi$
$109$	−0.292852			−0.0280501			−0.0140251	+	0.999902i	$0.504464\pi$
$110$	0.260807	−	0.0171153i	0.0248670	−	0.00163188i
$111$	28.4764			2.70286
$112$			6.73999i			0.636870i
$113$			8.62311i			0.811194i	0.914052	+	0.405597i	$0.132936\pi$
$113$			8.62311i			0.811194i	−0.914052	+	0.405597i	$0.867064\pi$
$114$	22.2445			2.08339
$115$	−8.66427	+	0.568588i	−0.807947	+	0.0530211i
$116$	2.92507			0.271586
$117$			29.9336i			2.76736i
$118$		−	3.15885i		−	0.290796i
$119$	1.42058			0.130224
$120$	1.00000	+	15.2382i	0.0912871	+	1.39105i
$121$	−10.9945			−0.999502
$122$			5.48593i			0.496673i
$123$		−	18.9873i		−	1.71203i
$124$	−0.192160			−0.0172565
$125$	−2.18383	−	10.9650i	−0.195328	−	0.980738i
$126$	11.7793			1.04938
$127$		−	17.2640i		−	1.53193i	−0.642882	−	0.765965i	$-0.722261\pi$
$127$		−	17.2640i		−	1.53193i	0.642882	−	0.765965i	$-0.277739\pi$
$128$			13.6330i			1.20500i
$129$	−19.9516			−1.75664
$130$	−1.31862	−	20.0934i	−0.115650	−	1.76231i
$131$	−14.7188			−1.28599			−0.642993	−	0.765872i	$-0.722308\pi$
$131$	−14.7188			−1.28599			−0.642993	+	0.765872i	$0.722308\pi$
$132$		−	0.105132i		−	0.00915052i
$133$		−	6.96565i		−	0.603999i
$134$	10.6019			0.915865
$135$	14.4197	−	0.946283i	1.24105	−	0.0814430i
$136$	2.37769			0.203886
$137$			1.36230i			0.116389i	0.998305	+	0.0581946i	$0.0185344\pi$
$137$			1.36230i			0.116389i	−0.998305	+	0.0581946i	$0.981466\pi$
$138$			17.6159i			1.49957i
$139$	13.7454			1.16587			0.582933	−	0.812520i	$-0.301905\pi$
$139$	13.7454			1.16587			0.582933	+	0.812520i	$0.301905\pi$
$140$	−1.56767	+	0.102877i	−0.132492	+	0.00869473i
$141$	−16.3768			−1.37917
$142$		−	6.06536i		−	0.508993i
$143$		−	0.421960i		−	0.0352860i
$144$	24.9088			2.07573
$145$	−0.865997	−	13.1963i	−0.0719172	−	1.09589i
$146$	21.3785			1.76930
$147$			14.3096i			1.18023i
$148$			4.90340i			0.403057i
$149$	17.3628			1.42241			0.711207	−	0.702983i	$-0.248149\pi$
$149$	17.3628			1.42241			0.711207	+	0.702983i	$0.248149\pi$
$150$	−22.4882	+	2.96432i	−1.83615	+	0.242035i
$151$	−3.59654			−0.292682			−0.146341	−	0.989234i	$-0.546750\pi$
$151$	−3.59654			−0.292682			−0.146341	+	0.989234i	$0.546750\pi$
$152$		−	11.6588i		−	0.945653i
$153$		−	5.24997i		−	0.424435i
$154$	−0.166047			−0.0133805
$155$	0.0568910	+	0.866917i	0.00456959	+	0.0696324i
$156$	−8.09965			−0.648491
$157$		−	5.19308i		−	0.414453i	−0.978293	−	0.207226i	$-0.933556\pi$
$157$		−	5.19308i		−	0.414453i	0.978293	−	0.207226i	$-0.0664437\pi$
$158$		−	1.67418i		−	0.133191i
$159$	0.0622505			0.00493678
$160$	−6.10982	+	0.400954i	−0.483024	+	0.0316982i
$161$	5.51625			0.434742
$162$		−	4.44178i		−	0.348979i
$163$			6.56687i			0.514357i	0.966364	+	0.257178i	$0.0827928\pi$
$163$			6.56687i			0.514357i	−0.966364	+	0.257178i	$0.917207\pi$
$164$	3.26946			0.255302
$165$	−0.474293	+	0.0311252i	−0.0369237	+	0.00242310i
$166$	−18.7157			−1.45262
$167$			0.897123i			0.0694214i	0.999397	+	0.0347107i	$0.0110510\pi$
$167$			0.897123i			0.0694214i	−0.999397	+	0.0347107i	$0.988949\pi$
$168$		−	9.70167i		−	0.748500i
$169$	−19.5091			−1.50070
$170$	0.231269	+	3.52412i	0.0177375	+	0.270288i
$171$	−25.7427			−1.96859
$172$		−	3.43550i		−	0.261955i
$173$		−	3.83031i		−	0.291213i	−0.989343	−	0.145607i	$-0.953487\pi$
$173$		−	3.83031i		−	0.291213i	0.989343	−	0.145607i	$-0.0465134\pi$
$174$	−26.8302			−2.03399
$175$	0.928248	+	7.04196i	0.0701689	+	0.532322i
$176$	−0.351127			−0.0264672
$177$			5.74455i			0.431787i
$178$		−	3.15020i		−	0.236117i
$179$	−9.74455			−0.728342			−0.364171	−	0.931332i	$-0.618648\pi$
$179$	−9.74455			−0.728342			−0.364171	+	0.931332i	$0.618648\pi$
$180$	0.380201	+	5.79358i	0.0283385	+	0.431828i
$181$	22.4764			1.67066			0.835330	−	0.549749i	$-0.185277\pi$
$181$	22.4764			1.67066			0.835330	+	0.549749i	$0.185277\pi$
$182$			12.7928i			0.948265i
$183$		−	9.97649i		−	0.737483i
$184$	9.23286			0.680655
$185$	22.1213	−	1.45170i	1.62639	−	0.106731i
$186$	1.76259			0.129239
$187$			0.0740063i			0.00541188i
$188$		−	2.81994i		−	0.205665i
$189$	−9.18052			−0.667785
$190$	17.2802	−	1.13400i	1.25364	−	0.0822692i
$191$	−5.47655			−0.396269			−0.198135	−	0.980175i	$-0.563488\pi$
$191$	−5.47655			−0.396269			−0.198135	+	0.980175i	$0.563488\pi$
$192$		−	14.8330i		−	1.07048i
$193$			2.14484i			0.154389i	0.997016	+	0.0771944i	$0.0245962\pi$
$193$			2.14484i			0.154389i	−0.997016	+	0.0771944i	$0.975404\pi$
$194$	−8.43585			−0.605659
$195$	2.39798	+	36.5410i	0.171723	+	2.61675i
$196$	−2.46399			−0.175999
$197$		−	9.78513i		−	0.697162i	−0.937279	−	0.348581i	$-0.886664\pi$
$197$		−	9.78513i		−	0.697162i	0.937279	−	0.348581i	$-0.113336\pi$
$198$			0.613655i			0.0436106i
$199$	1.47257			0.104388			0.0521939	−	0.998637i	$-0.483379\pi$
$199$	1.47257			0.104388			0.0521939	+	0.998637i	$0.483379\pi$
$200$	1.55366	+	11.7865i	0.109860	+	0.833432i
$201$	−19.2802			−1.35992
$202$		−	18.0536i		−	1.27025i
$203$			8.40162i			0.589678i
$204$	1.42058			0.0994602
$205$	−0.967955	−	14.7499i	−0.0676049	−	1.03018i
$206$	12.9711			0.903741
$207$		−	20.3862i		−	1.41694i
$208$			27.0519i			1.87571i
$209$	0.362883			0.0251011
$210$	14.3794	−	0.943642i	0.992274	−	0.0651175i
$211$	−4.87591			−0.335672			−0.167836	−	0.985815i	$-0.553678\pi$
$211$	−4.87591			−0.335672			−0.167836	+	0.985815i	$0.553678\pi$
$212$			0.0107190i			0.000736184i
$213$			11.0302i			0.755777i
$214$	−10.0275			−0.685465
$215$	−15.4990	+	1.01712i	−1.05702	+	0.0693667i
$216$	−15.3659			−1.04552
$217$		−	0.551937i		−	0.0374680i
$218$			0.462537i			0.0313270i
$219$	−38.8781			−2.62714
$220$	−0.00535950	−	0.0816693i	−0.000361338	−	0.00550614i
$221$	5.70167			0.383536
$222$		−	44.9764i		−	3.01862i
$223$			20.0536i			1.34289i	0.741055	+	0.671444i	$0.234326\pi$
$223$			20.0536i			1.34289i	−0.741055	+	0.671444i	$0.765674\pi$
$224$	3.88992			0.259906
$225$	26.0247	−	3.43049i	1.73498	−	0.228700i
$226$	13.6195			0.905959
$227$			14.1308i			0.937893i	0.883227	+	0.468946i	$0.155366\pi$
$227$			14.1308i			0.937893i	−0.883227	+	0.468946i	$0.844634\pi$
$228$		−	6.96565i		−	0.461312i
$229$	−11.2156			−0.741149			−0.370575	−	0.928803i	$-0.620839\pi$
$229$	−11.2156			−0.741149			−0.370575	+	0.928803i	$0.620839\pi$
$230$	0.898042	+	13.6846i	0.0592151	+	0.902333i
$231$	0.301967			0.0198680
$232$			14.0623i			0.923232i
$233$		−	13.8285i		−	0.905934i	−0.891527	−	0.452967i	$-0.850366\pi$
$233$		−	13.8285i		−	0.905934i	0.891527	−	0.452967i	$-0.149634\pi$
$234$	47.2779			3.09065
$235$	−12.7220	+	0.834872i	−0.829889	+	0.0544610i
$236$	−0.989164			−0.0643891
$237$			3.04460i			0.197768i
$238$		−	2.24369i		−	0.145437i
$239$	16.2851			1.05339			0.526697	−	0.850053i	$-0.323430\pi$
$239$	16.2851			1.05339			0.526697	+	0.850053i	$0.323430\pi$
$240$	30.4070	−	1.99544i	1.96276	−	0.128805i
$241$	4.94081			0.318265			0.159133	−	0.987257i	$-0.449130\pi$
$241$	4.94081			0.318265			0.159133	+	0.987257i	$0.449130\pi$
$242$			17.3650i			1.11627i
$243$		−	11.3100i		−	0.725535i
$244$	1.71787			0.109975
$245$	0.729489	+	11.1161i	0.0466053	+	0.710182i
$246$	−29.9890			−1.91203
$247$		−	27.9576i		−	1.77890i
$248$		−	0.923808i		−	0.0586618i
$249$	34.0356			2.15692
$250$	−17.3184	+	3.44919i	−1.09531	+	0.218146i
$251$	12.9160			0.815248			0.407624	−	0.913150i	$-0.366357\pi$
$251$	12.9160			0.815248			0.407624	+	0.913150i	$0.366357\pi$
$252$		−	3.68858i		−	0.232359i
$253$			0.287375i			0.0180671i
$254$	−27.2672			−1.71089
$255$	−0.420575	−	6.40882i	−0.0263375	−	0.401336i
$256$	11.2039			0.700245
$257$		−	13.6159i		−	0.849337i	−0.905349	−	0.424669i	$-0.860391\pi$
$257$		−	13.6159i		−	0.849337i	0.905349	−	0.424669i	$-0.139609\pi$
$258$			31.5121i			1.96186i
$259$	−14.0839			−0.875132
$260$	−6.29205	+	0.412913i	−0.390216	+	0.0256077i
$261$	31.0496			1.92192
$262$			23.2472i			1.43622i
$263$			12.6719i			0.781385i	0.920521	+	0.390692i	$0.127764\pi$
$263$			12.6719i			0.781385i	−0.920521	+	0.390692i	$0.872236\pi$
$264$	0.505418			0.0311063
$265$	0.0483580	−	0.00317347i	0.00297061	−	0.000194945i
$266$	−11.0017			−0.674559
$267$			5.72882i			0.350598i
$268$		−	3.31988i		−	0.202794i
$269$	25.8967			1.57895			0.789474	−	0.613784i	$-0.210354\pi$
$269$	25.8967			1.57895			0.789474	+	0.613784i	$0.210354\pi$
$270$	−1.49458	−	22.7748i	−0.0909574	−	1.38603i
$271$	21.2211			1.28909			0.644545	−	0.764566i	$-0.277047\pi$
$271$	21.2211			1.28909			0.644545	+	0.764566i	$0.277047\pi$
$272$		−	4.74455i		−	0.287681i
$273$		−	23.2644i		−	1.40803i
$274$	2.15165			0.129986
$275$	−0.366858	+	0.0483580i	−0.0221224	+	0.00291610i
$276$	5.51625			0.332040
$277$			2.05908i			0.123718i	0.998085	+	0.0618590i	$0.0197029\pi$
$277$			2.05908i			0.123718i	−0.998085	+	0.0618590i	$0.980297\pi$
$278$		−	21.7097i		−	1.30206i
$279$	−2.03978			−0.122118
$280$	−0.494582	−	7.53654i	−0.0295569	−	0.450395i
$281$	−21.7336			−1.29652			−0.648259	−	0.761420i	$-0.724503\pi$
$281$	−21.7336			−1.29652			−0.648259	+	0.761420i	$0.724503\pi$
$282$			25.8659i			1.54029i
$283$			5.32226i			0.316375i	0.987409	+	0.158188i	$0.0505651\pi$
$283$			5.32226i			0.316375i	−0.987409	+	0.158188i	$0.949435\pi$
$284$	−1.89931			−0.112703
$285$	−31.4250	+	2.06225i	−1.86146	+	0.122157i
$286$	−0.666453			−0.0394082
$287$			9.39078i			0.554321i
$288$		−	14.3759i		−	0.847105i
$289$	−1.00000			−0.0588235
$290$	−20.8425	+	1.36778i	−1.22391	+	0.0803187i
$291$	15.3411			0.899311
$292$		−	6.69447i		−	0.391764i
$293$		−	23.3285i		−	1.36287i	−0.731880	−	0.681434i	$-0.761357\pi$
$293$		−	23.3285i		−	1.36287i	0.731880	−	0.681434i	$-0.238643\pi$
$294$	22.6009			1.31811
$295$	0.292852	+	4.46254i	0.0170505	+	0.259819i
$296$	−23.5730			−1.37015
$297$		−	0.478268i		−	0.0277519i
$298$		−	27.4232i		−	1.58858i
$299$	22.1402			1.28040
$300$	0.928248	+	7.04196i	0.0535924	+	0.406568i
$301$	9.86772			0.568766
$302$			5.68046i			0.326874i
$303$			32.8315i			1.88612i
$304$	−23.2644			−1.33431
$305$	−0.508592	−	7.75003i	−0.0291219	−	0.443765i
$306$	−8.29193			−0.474018
$307$			17.4588i			0.996425i	0.867055	+	0.498213i	$0.166010\pi$
$307$			17.4588i			0.996425i	−0.867055	+	0.498213i	$0.833990\pi$
$308$			0.0519961i			0.00296275i
$309$	−23.5888			−1.34192
$310$	1.36923	−	0.0898550i	0.0777670	−	0.00510342i
$311$	2.98997			0.169545			0.0847727	−	0.996400i	$-0.472984\pi$
$311$	2.98997			0.169545			0.0847727	+	0.996400i	$0.472984\pi$
$312$		−	38.9390i		−	2.20448i
$313$		−	7.76028i		−	0.438637i	−0.975653	−	0.219319i	$-0.929617\pi$
$313$		−	7.76028i		−	0.438637i	0.975653	−	0.219319i	$-0.0703834\pi$
$314$	−8.20208			−0.462870
$315$	−16.6408	+	1.09204i	−0.937600	+	0.0615295i
$316$	−0.524255			−0.0294916
$317$			6.88951i			0.386953i	0.981105	+	0.193477i	$0.0619764\pi$
$317$			6.88951i			0.386953i	−0.981105	+	0.193477i	$0.938024\pi$
$318$		−	0.0983199i		−	0.00551351i
$319$	−0.437691			−0.0245060
$320$	−0.756174	−	11.5227i	−0.0422714	−	0.644141i
$321$	18.2356			1.01781
$322$		−	8.71251i		−	0.485529i
$323$			4.90340i			0.272833i
$324$	−1.39090			−0.0772724
$325$	3.72565	+	28.2639i	0.206662	+	1.56780i
$326$	10.3719			0.574445
$327$		−	0.841151i		−	0.0465158i
$328$			15.7179i			0.867874i
$329$	8.09965			0.446548
$330$	0.0491600	+	0.749110i	0.00270617	+	0.0412371i
$331$	15.8565			0.871552			0.435776	−	0.900055i	$-0.356474\pi$
$331$	15.8565			0.871552			0.435776	+	0.900055i	$0.356474\pi$
$332$			5.86064i			0.321644i
$333$			52.0495i			2.85229i
$334$	1.41694			0.0775314
$335$	−14.9774	+	0.982885i	−0.818303	+	0.0537007i
$336$	−19.3591			−1.05613
$337$			19.1787i			1.04473i	0.852722	+	0.522365i	$0.174950\pi$
$337$			19.1787i			1.04473i	−0.852722	+	0.522365i	$0.825050\pi$
$338$			30.8131i			1.67601i
$339$	−24.7679			−1.34521
$340$	1.10354	−	0.0724196i	0.0598481	−	0.00392750i
$341$	0.0287537			0.00155710
$342$			40.6587i			2.19857i
$343$		−	17.0213i		−	0.919063i
$344$	16.5161			0.890490
$345$	−1.63314	−	24.8862i	−0.0879254	−	1.33983i
$346$	−6.04969			−0.325233
$347$		−	33.5775i		−	1.80253i	−0.433265	−	0.901266i	$-0.642639\pi$
$347$		−	33.5775i		−	1.80253i	0.433265	−	0.901266i	$-0.357361\pi$
$348$			8.40162i			0.450374i
$349$	−8.61649			−0.461230			−0.230615	−	0.973045i	$-0.574074\pi$
$349$	−8.61649			−0.461230			−0.230615	+	0.973045i	$0.574074\pi$
$350$	11.1222	−	1.46610i	0.594509	−	0.0783662i
$351$	−36.8473			−1.96676
$352$			0.202649i			0.0108013i
$353$		−	0.596657i		−	0.0317569i	−0.999874	−	0.0158784i	$-0.994946\pi$
$353$		−	0.596657i		−	0.0317569i	0.999874	−	0.0158784i	$-0.00505447\pi$
$354$	9.07309			0.482229
$355$	0.562309	+	8.56859i	0.0298443	+	0.454773i
$356$	−0.986455			−0.0522820
$357$			4.08029i			0.215952i
$358$			15.3908i			0.813428i
$359$	−31.5514			−1.66522			−0.832608	−	0.553862i	$-0.813153\pi$
$359$	−31.5514			−1.66522			−0.832608	+	0.553862i	$0.813153\pi$
$360$	−27.8525	+	1.82781i	−1.46796	+	0.0963340i
$361$	5.04335			0.265439
$362$		−	35.4998i		−	1.86583i
$363$		−	31.5793i		−	1.65748i
$364$	4.00594			0.209968
$365$	−30.2016	+	1.98197i	−1.58082	+	0.103741i
$366$	−15.7571			−0.823637
$367$		−	1.37723i		−	0.0718908i	−0.999354	−	0.0359454i	$-0.988556\pi$
$367$		−	1.37723i		−	0.0718908i	0.999354	−	0.0359454i	$-0.0114442\pi$
$368$		−	18.4236i		−	0.960398i
$369$	34.7052			1.80668
$370$	−2.29285	−	34.9390i	−0.119200	−	1.81639i
$371$	−0.0307879			−0.00159843
$372$		−	0.551937i		−	0.0286166i
$373$		−	28.5627i		−	1.47892i	−0.673201	−	0.739459i	$-0.735081\pi$
$373$		−	28.5627i		−	1.47892i	0.673201	−	0.739459i	$-0.264919\pi$
$374$	0.116887			0.00604410
$375$	31.4945	−	6.27256i	1.62637	−	0.323914i
$376$	13.5568			0.699140
$377$			33.7210i			1.73672i
$378$			14.4999i			0.745797i
$379$	24.2405			1.24515			0.622576	−	0.782559i	$-0.286086\pi$
$379$	24.2405			1.24515			0.622576	+	0.782559i	$0.286086\pi$
$380$	−0.355102	−	5.41112i	−0.0182164	−	0.277585i
$381$	49.5869			2.54041
$382$			8.64979i			0.442562i
$383$		−	24.4678i		−	1.25025i	−0.780527	−	0.625123i	$-0.785049\pi$
$383$		−	24.4678i		−	1.25025i	0.780527	−	0.625123i	$-0.214951\pi$
$384$	−39.1578			−1.99826
$385$	0.234577	−	0.0153940i	0.0119551	−	0.000784550i
$386$	3.38761			0.172425
$387$		−	36.4678i		−	1.85376i
$388$			2.64161i			0.134107i
$389$	10.9711			0.556258			0.278129	−	0.960544i	$-0.410286\pi$
$389$	10.9711			0.556258			0.278129	+	0.960544i	$0.410286\pi$
$390$	57.7137	−	3.78743i	2.92245	−	0.191784i
$391$	−3.88311			−0.196377
$392$		−	11.8456i		−	0.598293i
$393$		−	42.2764i		−	2.13256i
$394$	−15.4549			−0.778605
$395$	0.155211	+	2.36514i	0.00780951	+	0.119003i
$396$	0.192160			0.00965642
$397$			26.8550i			1.34782i	0.738815	+	0.673908i	$0.235386\pi$
$397$			26.8550i			1.34782i	−0.738815	+	0.673908i	$0.764614\pi$
$398$		−	2.32582i		−	0.116583i
$399$	20.0073			1.00162
$400$	23.5193	−	3.10024i	1.17597	−	0.155012i
$401$	−17.5080			−0.874308			−0.437154	−	0.899387i	$-0.644014\pi$
$401$	−17.5080			−0.874308			−0.437154	+	0.899387i	$0.644014\pi$
$402$			30.4516i			1.51879i
$403$		−	2.21528i		−	0.110351i
$404$	−5.65331			−0.281263
$405$	0.411790	+	6.27495i	0.0204620	+	0.311805i
$406$	13.2697			0.658565
$407$		−	0.733716i		−	0.0363690i
$408$			6.82940i			0.338105i
$409$	17.8285			0.881561			0.440781	−	0.897615i	$-0.354702\pi$
$409$	17.8285			0.881561			0.440781	+	0.897615i	$0.354702\pi$
$410$	−23.2964	+	1.52881i	−1.15053	+	0.0755027i
$411$	−3.91290			−0.193009
$412$		−	4.06179i		−	0.200110i
$413$		−	2.84115i		−	0.139804i
$414$	−32.1985			−1.58247
$415$	26.4398	−	1.73510i	1.29788	−	0.0851727i
$416$	15.6127			0.765477
$417$			39.4805i			1.93337i
$418$		−	0.573146i		−	0.0280335i
$419$	−34.7826			−1.69924			−0.849622	−	0.527393i	$-0.823170\pi$
$419$	−34.7826			−1.69924			−0.849622	+	0.527393i	$0.823170\pi$
$420$	−0.295492	−	4.50278i	−0.0144186	−	0.219713i
$421$	−17.0676			−0.831824			−0.415912	−	0.909405i	$-0.636538\pi$
$421$	−17.0676			−0.831824			−0.415912	+	0.909405i	$0.636538\pi$
$422$			7.70114i			0.374886i
$423$		−	29.9336i		−	1.45542i
$424$	−0.0515315			−0.00250259
$425$	−0.653431	−	4.95712i	−0.0316960	−	0.240456i
$426$	17.4214			0.844068
$427$			4.93419i			0.238782i
$428$			3.14001i			0.151778i
$429$	1.21198			0.0585152
$430$	1.60646	+	24.4795i	0.0774702	+	1.18051i
$431$	−22.5970			−1.08846			−0.544229	−	0.838937i	$-0.683178\pi$
$431$	−22.5970			−1.08846			−0.544229	+	0.838937i	$0.683178\pi$
$432$			30.6618i			1.47522i
$433$			13.3513i			0.641625i	0.947143	+	0.320812i	$0.103956\pi$
$433$			13.3513i			0.641625i	−0.947143	+	0.320812i	$0.896044\pi$
$434$	−0.871743			−0.0418450
$435$	37.9033	−	2.48738i	1.81732	−	0.119261i
$436$	0.144839			0.00693654
$437$			19.0405i			0.910829i
$438$			61.4049i			2.93404i
$439$	−5.73280			−0.273611			−0.136806	−	0.990598i	$-0.543684\pi$
$439$	−5.73280			−0.273611			−0.136806	+	0.990598i	$0.543684\pi$
$440$	0.392624	−	0.0257657i	0.0187176	−	0.00122833i
$441$	−26.1552			−1.24548
$442$		−	9.00536i		−	0.428341i
$443$		−	38.8153i		−	1.84417i	−0.386985	−	0.922086i	$-0.626483\pi$
$443$		−	38.8153i		−	1.84417i	0.386985	−	0.922086i	$-0.373517\pi$
$444$	−14.0839			−0.668393
$445$	0.292050	+	4.45032i	0.0138445	+	0.210965i
$446$	31.6731			1.49977
$447$			49.8707i			2.35880i
$448$			7.33615i			0.346600i
$449$	25.3848			1.19798			0.598992	−	0.800755i	$-0.295568\pi$
$449$	25.3848			1.19798			0.598992	+	0.800755i	$0.295568\pi$
$450$	−5.41820	−	41.1041i	−0.255417	−	1.93767i
$451$	−0.489222			−0.0230366
$452$		−	4.26483i		−	0.200601i
$453$		−	10.3303i		−	0.485358i
$454$	22.3185			1.04746
$455$	−1.18600	−	18.0725i	−0.0556005	−	0.847252i
$456$	33.4873			1.56818
$457$		−	8.90110i		−	0.416376i	−0.978089	−	0.208188i	$-0.933243\pi$
$457$		−	8.90110i		−	0.416376i	0.978089	−	0.208188i	$-0.0667566\pi$
$458$			17.7142i			0.827732i
$459$	6.46254			0.301645
$460$	4.28519	−	0.281213i	0.199798	−	0.0131116i
$461$	−13.9124			−0.647965			−0.323983	−	0.946063i	$-0.605022\pi$
$461$	−13.9124			−0.647965			−0.323983	+	0.946063i	$0.605022\pi$
$462$		−	0.476934i		−	0.0221890i
$463$			37.5085i			1.74317i	0.490247	+	0.871583i	$0.336906\pi$
$463$			37.5085i			1.74317i	−0.490247	+	0.871583i	$0.663094\pi$
$464$	28.0604			1.30267
$465$	−2.49002	+	0.163407i	−0.115472	+	0.00757780i
$466$	−21.8410			−1.01177
$467$			11.2108i			0.518776i	0.965773	+	0.259388i	$0.0835208\pi$
$467$			11.2108i			0.518776i	−0.965773	+	0.259388i	$0.916479\pi$
$468$		−	14.8046i		−	0.684344i
$469$	9.53562			0.440314
$470$	1.31862	+	20.0934i	0.0608233	+	0.926838i
$471$	14.9160			0.687291
$472$		−	4.75539i		−	0.218885i
$473$			0.514069i			0.0236369i
$474$	4.80872			0.220872
$475$	−24.3067	+	3.20403i	−1.11527	+	0.147011i
$476$	−0.702591			−0.0322032
$477$			0.113782i			0.00520972i
$478$		−	25.7210i		−	1.17645i
$479$	−5.16559			−0.236022			−0.118011	−	0.993012i	$-0.537652\pi$
$479$	−5.16559			−0.236022			−0.118011	+	0.993012i	$0.537652\pi$
$480$	−1.15165	−	17.5491i	−0.0525654	−	0.801003i
$481$	−56.5277			−2.57744
$482$		−	7.80363i		−	0.355446i
$483$			15.8442i			0.720936i
$484$	5.43769			0.247168
$485$	11.9174	−	0.782074i	0.541142	−	0.0355122i
$486$	−17.8632			−0.810293
$487$		−	34.0560i		−	1.54322i	−0.636094	−	0.771612i	$-0.719451\pi$
$487$		−	34.0560i		−	1.54322i	0.636094	−	0.771612i	$-0.280549\pi$
$488$			8.25862i			0.373850i
$489$	−18.8619			−0.852963
$490$	17.5570	−	1.15217i	0.793146	−	0.0520498i
$491$	−18.3051			−0.826099			−0.413050	−	0.910708i	$-0.635536\pi$
$491$	−18.3051			−0.826099			−0.413050	+	0.910708i	$0.635536\pi$
$492$			9.39078i			0.423369i
$493$		−	5.91424i		−	0.266364i
$494$	−44.1569			−1.98671
$495$	−0.0568910	−	0.866917i	−0.00255706	−	0.0389650i
$496$	−1.84341			−0.0827713
$497$		−	5.45534i		−	0.244705i
$498$		−	53.7566i		−	2.40889i
$499$	−40.7792			−1.82553			−0.912764	−	0.408488i	$-0.866056\pi$
$499$	−40.7792			−1.82553			−0.912764	+	0.408488i	$0.866056\pi$
$500$	1.08008	+	5.42308i	0.0483028	+	0.242528i
$501$	−2.57678			−0.115122
$502$		−	20.3998i		−	0.910487i
$503$			10.7274i			0.478313i	0.970981	+	0.239156i	$0.0768709\pi$
$503$			10.7274i			0.478313i	−0.970981	+	0.239156i	$0.923129\pi$
$504$	17.7328			0.789882
$505$	1.67372	+	25.5045i	0.0744795	+	1.13494i
$506$	0.453887			0.0201777
$507$		−	56.0354i		−	2.48862i
$508$			8.53845i			0.378832i
$509$	21.5278			0.954205			0.477102	−	0.878848i	$-0.341687\pi$
$509$	21.5278			0.954205			0.477102	+	0.878848i	$0.341687\pi$
$510$	−10.1222	+	0.664267i	−0.448221	+	0.0294142i
$511$	19.2284			0.850613
$512$			9.57031i			0.422952i
$513$		−	31.6884i		−	1.39908i
$514$	−21.5053			−0.948558
$515$	−18.3244	+	1.20253i	−0.807471	+	0.0529899i
$516$	9.86772			0.434402
$517$			0.421960i			0.0185578i
$518$			22.2445i			0.977367i
$519$	11.0017			0.482922
$520$	−1.98507	−	30.2489i	−0.0870511	−	1.32650i
$521$	−20.5451			−0.900098			−0.450049	−	0.893004i	$-0.648594\pi$
$521$	−20.5451			−0.900098			−0.450049	+	0.893004i	$0.648594\pi$
$522$		−	49.0405i		−	2.14644i
$523$			20.0508i			0.876762i	0.898789	+	0.438381i	$0.144448\pi$
$523$			20.0508i			0.876762i	−0.898789	+	0.438381i	$0.855552\pi$
$524$	7.27964			0.318013
$525$	−20.2265	+	2.66618i	−0.882755	+	0.116362i
$526$	20.0144			0.872667
$527$			0.388531i			0.0169247i
$528$		−	1.00853i		−	0.0438908i
$529$	7.92144			0.344410
$530$	−0.00501225	−	0.0763778i	−0.000217718	−	0.00331764i
$531$	−10.4999			−0.455659
$532$			3.44508i			0.149363i
$533$			37.6912i			1.63259i
$534$	9.04824			0.391556
$535$	14.1659	−	0.929632i	0.612447	−	0.0401915i
$536$	15.9603			0.689380
$537$		−	27.9890i		−	1.20782i
$538$		−	40.9018i		−	1.76340i
$539$	0.368697			0.0158809
$540$	−7.13170	+	0.468014i	−0.306899	+	0.0201401i
$541$	−8.55768			−0.367924			−0.183962	−	0.982933i	$-0.558892\pi$
$541$	−8.55768			−0.367924			−0.183962	+	0.982933i	$0.558892\pi$
$542$		−	33.5171i		−	1.43968i
$543$			64.5585i			2.77047i
$544$	−2.73827			−0.117403
$545$	−0.0428811	−	0.653431i	−0.00183682	−	0.0279899i
$546$	−36.7444			−1.57252
$547$		−	11.2911i		−	0.482771i	−0.970429	−	0.241385i	$-0.922398\pi$
$547$		−	11.2911i		−	0.482771i	0.970429	−	0.241385i	$-0.0776018\pi$
$548$		−	0.673769i		−	0.0287820i
$549$	18.2351			0.778256
$550$	0.0763778	+	0.579425i	0.00325676	+	0.0247067i
$551$	−28.9999			−1.23544
$552$			26.5193i			1.12874i
$553$		−	1.50580i		−	0.0640333i
$554$	3.25216			0.138171
$555$	4.16969	+	63.5386i	0.176993	+	2.69706i
$556$	−6.79820			−0.288308
$557$			22.4662i			0.951922i	0.879466	+	0.475961i	$0.157900\pi$
$557$			22.4662i			0.951922i	−0.879466	+	0.475961i	$0.842100\pi$
$558$			3.22167i			0.136384i
$559$	39.6054			1.67513
$560$	−15.0387	+	0.986909i	−0.635503	+	0.0417045i
$561$	−0.212567			−0.00897457
$562$			34.3266i			1.44798i
$563$			6.32795i			0.266691i	0.991070	+	0.133346i	$0.0425721\pi$
$563$			6.32795i			0.266691i	−0.991070	+	0.133346i	$0.957428\pi$
$564$	8.09965			0.341057
$565$	−19.2405	+	1.26265i	−0.809453	+	0.0531199i
$566$	8.40610			0.353335
$567$		−	3.99506i		−	0.167777i
$568$		−	9.13090i		−	0.383124i
$569$	16.6885			0.699620			0.349810	−	0.936821i	$-0.386246\pi$
$569$	16.6885			0.699620			0.349810	+	0.936821i	$0.386246\pi$
$570$	3.25717	+	49.6334i	0.136428	+	2.07892i
$571$	−6.20629			−0.259725			−0.129863	−	0.991532i	$-0.541454\pi$
$571$	−6.20629			−0.259725			−0.129863	+	0.991532i	$0.541454\pi$
$572$			0.208694i			0.00872591i
$573$		−	15.7302i		−	0.657137i
$574$	14.8320			0.619077
$575$	−2.53735	−	19.2491i	−0.105815	−	0.802741i
$576$	27.1119			1.12966
$577$		−	23.9273i		−	0.996105i	−0.867147	−	0.498052i	$-0.834049\pi$
$577$		−	23.9273i		−	0.996105i	0.867147	−	0.498052i	$-0.165951\pi$
$578$			1.57942i			0.0656954i
$579$	−6.16057			−0.256025
$580$	0.428306	+	6.52663i	0.0177845	+	0.271003i
$581$	−16.8334			−0.698366
$582$		−	24.2301i		−	1.00437i
$583$		−	0.00160393i		−	6.64279e-5i
$584$	32.1836			1.33177
$585$	−66.7899	+	4.38305i	−2.76142	+	0.181217i
$586$	−36.8457			−1.52208
$587$			26.1140i			1.07784i	0.842357	+	0.538920i	$0.181168\pi$
$587$			26.1140i			1.07784i	−0.842357	+	0.538920i	$0.818832\pi$
$588$		−	7.07726i		−	0.291861i
$589$	1.90512			0.0784992
$590$	7.04824	−	0.462537i	0.290171	−	0.0190424i
$591$	28.1056			1.15611
$592$			47.0386i			1.93328i
$593$			29.8969i			1.22772i	0.789415	+	0.613860i	$0.210384\pi$
$593$			29.8969i			1.22772i	−0.789415	+	0.613860i	$0.789616\pi$
$594$	−0.755389			−0.0309940
$595$	0.208009	+	3.16969i	0.00852754	+	0.129944i
$596$	−8.58731			−0.351750
$597$			4.22963i			0.173107i
$598$		−	34.9688i		−	1.42998i
$599$	−15.8194			−0.646362			−0.323181	−	0.946337i	$-0.604752\pi$
$599$	−15.8194			−0.646362			−0.323181	+	0.946337i	$0.604752\pi$
$600$	−33.8541	+	4.46254i	−1.38209	+	0.182182i
$601$	32.4048			1.32182			0.660910	−	0.750466i	$-0.270171\pi$
$601$	32.4048			1.32182			0.660910	+	0.750466i	$0.270171\pi$
$602$		−	15.5853i		−	0.635210i
$603$		−	35.2405i		−	1.43510i
$604$	1.77878			0.0723777
$605$	−1.60988	−	24.5317i	−0.0654510	−	0.997357i
$606$	51.8549			2.10646
$607$			20.4218i			0.828895i	0.910073	+	0.414447i	$0.136025\pi$
$607$			20.4218i			0.828895i	−0.910073	+	0.414447i	$0.863975\pi$
$608$			13.4269i			0.544531i
$609$	−24.1318			−0.977869
$610$	−12.2406	+	0.803282i	−0.495607	+	0.0325239i
$611$	32.5091			1.31518
$612$			2.59654i			0.104959i
$613$			12.0930i			0.488433i	0.969721	+	0.244217i	$0.0785308\pi$
$613$			12.0930i			0.488433i	−0.969721	+	0.244217i	$0.921469\pi$
$614$	27.5748			1.11283
$615$	42.3658	−	2.78024i	1.70835	−	0.112110i
$616$	−0.249971			−0.0100716
$617$			3.79742i			0.152878i	0.997074	+	0.0764392i	$0.0243551\pi$
$617$			3.79742i			0.152878i	−0.997074	+	0.0764392i	$0.975645\pi$
$618$			37.2567i			1.49868i
$619$	0.765306			0.0307602			0.0153801	−	0.999882i	$-0.495104\pi$
$619$	0.765306			0.0307602			0.0153801	+	0.999882i	$0.495104\pi$
$620$	−0.0281372	−	0.428761i	−0.00113002	−	0.0172195i
$621$	25.0948			1.00702
$622$		−	4.72242i		−	0.189352i
$623$		−	2.83337i		−	0.113517i
$624$	−77.7005			−3.11051
$625$	24.1461	−	6.47827i	0.965842	−	0.259131i
$626$	−12.2568			−0.489880
$627$			1.04230i			0.0416254i
$628$			2.56840i			0.102490i
$629$	9.91424			0.395307
$630$	1.72480	+	26.2828i	0.0687175	+	1.04713i
$631$	41.7318			1.66132			0.830658	−	0.556784i	$-0.187965\pi$
$631$	41.7318			1.66132			0.830658	+	0.556784i	$0.187965\pi$
$632$		−	2.52035i		−	0.100254i
$633$		−	14.0050i		−	0.556648i
$634$	10.8815			0.432158
$635$	38.5206	−	2.52789i	1.52864	−	0.100316i
$636$	−0.0307879			−0.00122082
$637$		−	28.4055i		−	1.12547i
$638$			0.691300i			0.0273688i
$639$	−20.1611			−0.797561
$640$	−30.4189	+	1.99623i	−1.20241	+	0.0789078i
$641$	22.6429			0.894342			0.447171	−	0.894448i	$-0.352431\pi$
$641$	22.6429			0.894342			0.447171	+	0.894448i	$0.352431\pi$
$642$		−	28.8017i		−	1.13671i
$643$		−	24.8814i		−	0.981226i	−0.871377	−	0.490613i	$-0.836773\pi$
$643$		−	24.8814i		−	0.981226i	0.871377	−	0.490613i	$-0.163227\pi$
$644$	−2.72824			−0.107508
$645$	−2.92144	−	44.5175i	−0.115031	−	1.75287i
$646$	7.74455			0.304705
$647$			35.6376i			1.40106i	0.713624	+	0.700529i	$0.247053\pi$
$647$			35.6376i			1.40106i	−0.713624	+	0.700529i	$0.752947\pi$
$648$		−	6.68674i		−	0.262680i
$649$	0.148013			0.00581000
$650$	44.6406	−	5.88438i	1.75095	−	0.230804i
$651$	1.58532			0.0621335
$652$		−	3.24785i		−	0.127196i
$653$		−	8.31930i		−	0.325559i	−0.986662	−	0.162780i	$-0.947954\pi$
$653$		−	8.31930i		−	0.325559i	0.986662	−	0.162780i	$-0.0520460\pi$
$654$	−1.32853			−0.0519498
$655$	−2.15521	−	32.8416i	−0.0842111	−	1.28323i
$656$	31.3641			1.22456
$657$		−	71.0616i		−	2.77238i
$658$		−	12.7928i		−	0.498715i
$659$	3.44669			0.134264			0.0671320	−	0.997744i	$-0.478615\pi$
$659$	3.44669			0.134264			0.0671320	+	0.997744i	$0.478615\pi$
$660$	0.234577	−	0.0153940i	0.00913088	−	0.000599210i
$661$	−36.6867			−1.42695			−0.713473	−	0.700682i	$-0.752879\pi$
$661$	−36.6867			−1.42695			−0.713473	+	0.700682i	$0.752879\pi$
$662$		−	25.0441i		−	0.973368i
$663$			16.3768i			0.636021i
$664$	−28.1749			−1.09340
$665$	15.5422	−	1.01995i	0.602702	−	0.0395520i
$666$	82.2082			3.18550
$667$		−	22.9657i		−	0.889234i
$668$		−	0.443700i		−	0.0171673i
$669$	−57.5995			−2.22692
$670$	1.55239	+	23.6557i	0.0599741	+	0.913899i
$671$	−0.257052			−0.00992336
$672$			11.1729i			0.431005i
$673$			41.5075i			1.60000i	0.600002	+	0.799998i	$0.295166\pi$
$673$			41.5075i			1.60000i	−0.600002	+	0.799998i	$0.704834\pi$
$674$	30.2913			1.16678
$675$	4.22282	+	32.0356i	0.162536	+	1.23305i
$676$	9.64882			0.371109
$677$		−	26.7378i		−	1.02762i	−0.857905	−	0.513809i	$-0.828234\pi$
$677$		−	26.7378i		−	1.02762i	0.857905	−	0.513809i	$-0.171766\pi$
$678$			39.1191i			1.50236i
$679$	−7.58742			−0.291179
$680$	0.348156	+	5.30527i	0.0133512	+	0.203448i
$681$	−40.5875			−1.55532
$682$		−	0.0454143i		−	0.00173901i
$683$			37.8270i			1.44741i	0.690110	+	0.723704i	$0.257562\pi$
$683$			37.8270i			1.44741i	−0.690110	+	0.723704i	$0.742438\pi$
$684$	12.7319			0.486815
$685$	−3.03966	+	0.199476i	−0.116139	+	0.00762159i
$686$	−26.8838			−1.02643
$687$		−	32.2144i		−	1.22905i
$688$		−	32.9570i		−	1.25647i
$689$	−0.123572			−0.00470770
$690$	−39.3058	+	2.57942i	−1.49635	+	0.0981970i
$691$	33.0739			1.25819			0.629095	−	0.777328i	$-0.283426\pi$
$691$	33.0739			1.25819			0.629095	+	0.777328i	$0.283426\pi$
$692$			1.89440i			0.0720144i
$693$			0.551937i			0.0209664i
$694$	−53.0331			−2.01311
$695$	2.01268	+	30.6696i	0.0763451	+	1.16336i
$696$	−40.3907			−1.53100
$697$		−	6.61055i		−	0.250392i
$698$			13.6091i			0.515112i
$699$	39.7192			1.50232
$700$	−0.459094	−	3.48283i	−0.0173521	−	0.131638i
$701$	−24.7292			−0.934008			−0.467004	−	0.884255i	$-0.654667\pi$
$701$	−24.7292			−0.934008			−0.467004	+	0.884255i	$0.654667\pi$
$702$			58.1975i			2.19652i
$703$		−	48.6135i		−	1.83349i
$704$	−0.382184			−0.0144041
$705$	−2.39798	−	36.5410i	−0.0903133	−	1.37621i
$706$	−0.942375			−0.0354668
$707$		−	16.2379i		−	0.610688i
$708$		−	2.84115i		−	0.106777i
$709$	−40.5902			−1.52440			−0.762199	−	0.647343i	$-0.775880\pi$
$709$	−40.5902			−1.52440			−0.762199	+	0.647343i	$0.775880\pi$
$710$	13.5334	−	0.888125i	0.507901	−	0.0333307i
$711$	−5.56495			−0.208702
$712$		−	4.74237i		−	0.177728i
$713$			1.50871i			0.0565016i
$714$	6.44450			0.241179
$715$	0.941505	−	0.0617858i	0.0352103	−	0.00231066i
$716$	4.81948			0.180112
$717$			46.7752i			1.74685i
$718$			49.8330i			1.85975i
$719$	−32.1253			−1.19807			−0.599036	−	0.800722i	$-0.704449\pi$
$719$	−32.1253			−1.19807			−0.599036	+	0.800722i	$0.704449\pi$
$720$	3.64729	+	55.5781i	0.135926	+	2.07127i
$721$	11.6666			0.434486
$722$		−	7.96558i		−	0.296448i
$723$			14.1914i			0.527782i
$724$	−11.1164			−0.413139
$725$	29.3176	−	3.86455i	1.08883	−	0.143526i
$726$	−49.8771			−1.85111
$727$			11.3089i			0.419425i	0.977763	+	0.209713i	$0.0672528\pi$
$727$			11.3089i			0.419425i	−0.977763	+	0.209713i	$0.932747\pi$
$728$			19.2585i			0.713768i
$729$	40.9222			1.51564
$730$	3.13036	+	47.7012i	0.115860	+	1.76550i
$731$	−6.94628			−0.256918
$732$			4.93419i			0.182373i
$733$		−	32.5450i		−	1.20208i	−0.799220	−	0.601039i	$-0.794754\pi$
$733$		−	32.5450i		−	1.20208i	0.799220	−	0.601039i	$-0.205246\pi$
$734$	−2.17523			−0.0802892
$735$	−31.9285	+	2.09529i	−1.17770	+	0.0772860i
$736$	−10.6330			−0.391938
$737$			0.496768i			0.0182987i
$738$		−	54.8142i		−	2.01774i
$739$	29.6821			1.09187			0.545936	−	0.837827i	$-0.316174\pi$
$739$	29.6821			1.09187			0.545936	+	0.837827i	$0.316174\pi$
$740$	−10.9408	+	0.717985i	−0.402192	+	0.0263936i
$741$	80.3019			2.94996
$742$			0.0486272i			0.00178516i
$743$		−	27.9705i		−	1.02614i	−0.858348	−	0.513069i	$-0.828509\pi$
$743$		−	27.9705i		−	1.02614i	0.858348	−	0.513069i	$-0.171491\pi$
$744$	2.65343			0.0972795
$745$	2.54236	+	38.7410i	0.0931448	+	1.41936i
$746$	−45.1126			−1.65169
$747$			62.2105i			2.27616i
$748$		−	0.0366022i		−	0.00133831i
$749$	−9.01898			−0.329546
$750$	−9.90704	−	49.7431i	−0.361754	−	1.81636i
$751$	−52.7167			−1.92366			−0.961829	−	0.273650i	$-0.911769\pi$
$751$	−52.7167			−1.92366			−0.961829	+	0.273650i	$0.911769\pi$
$752$		−	27.0519i		−	0.986481i
$753$			37.0982i			1.35193i
$754$	53.2598			1.93961
$755$	−0.526626	−	8.02485i	−0.0191659	−	0.292054i
$756$	4.54052			0.165137
$757$			7.80911i			0.283827i	0.989879	+	0.141913i	$0.0453255\pi$
$757$			7.80911i			0.283827i	−0.989879	+	0.141913i	$0.954675\pi$
$758$		−	38.2861i		−	1.39061i
$759$	−0.825420			−0.0299608
$760$	26.0139	−	1.70715i	0.943623	−	0.0619248i
$761$	19.2266			0.696963			0.348481	−	0.937316i	$-0.386697\pi$
$761$	19.2266			0.696963			0.348481	+	0.937316i	$0.386697\pi$
$762$		−	78.3188i		−	2.83719i
$763$			0.416018i			0.0150609i
$764$	2.70860			0.0979937
$765$	11.7141	−	0.768731i	0.423524	−	0.0277935i
$766$	−38.6450			−1.39630
$767$		−	11.4033i		−	0.411751i
$768$			32.1807i			1.16122i
$769$	1.45851			0.0525953			0.0262977	−	0.999654i	$-0.491628\pi$
$769$	1.45851			0.0525953			0.0262977	+	0.999654i	$0.491628\pi$
$770$	−0.0243136	−	0.370496i	−0.000876202	−	0.0133518i
$771$	39.1087			1.40846
$772$		−	1.06080i		−	0.0381790i
$773$		−	18.8055i		−	0.676388i	−0.941076	−	0.338194i	$-0.890184\pi$
$773$		−	18.8055i		−	0.676388i	0.941076	−	0.338194i	$-0.109816\pi$
$774$	−57.5981			−2.07032
$775$	−1.92599	+	0.253878i	−0.0691837	+	0.00911957i
$776$	−12.6995			−0.455885
$777$		−	40.4529i		−	1.45124i
$778$		−	17.3281i		−	0.621241i
$779$	−32.4142			−1.16136
$780$	−1.18600	−	18.0725i	−0.0424656	−	0.647099i
$781$	0.284201			0.0101695
$782$			6.13308i			0.219319i
$783$			38.2210i			1.36591i
$784$	−23.6372			−0.844186
$785$	11.5872	−	0.760401i	0.413563	−	0.0271399i
$786$	−66.7724			−2.38169
$787$		−	19.0449i		−	0.678877i	−0.940628	−	0.339439i	$-0.889763\pi$
$787$		−	19.0449i		−	0.678877i	0.940628	−	0.339439i	$-0.110237\pi$
$788$			4.83955i			0.172402i
$789$	−36.3973			−1.29578
$790$	3.73555	−	0.245144i	0.132905	−	0.00872183i
$791$	12.2498			0.435552
$792$			0.923808i			0.0328261i
$793$			19.8040i			0.703262i
$794$	42.4155			1.50527
$795$	0.00911508	+	0.138898i	0.000323278	+	0.00492619i
$796$	−0.728307			−0.0258142
$797$		−	49.6667i		−	1.75929i	−0.475634	−	0.879643i	$-0.657781\pi$
$797$		−	49.6667i		−	1.75929i	0.475634	−	0.879643i	$-0.342219\pi$
$798$		−	31.6000i		−	1.11863i
$799$	−5.70167			−0.201711
$800$	−1.78927	−	13.5739i	−0.0632603	−	0.479912i
$801$	−10.4712			−0.369981
$802$			27.6526i			0.976447i
$803$			1.00172i			0.0353500i
$804$	9.53562			0.336296
$805$	0.807722	+	12.3082i	0.0284685	+	0.433809i
$806$	−3.49886			−0.123242
$807$			74.3824i			2.61838i
$808$		−	27.1782i		−	0.956126i
$809$	−38.2625			−1.34524			−0.672619	−	0.739989i	$-0.734831\pi$
$809$	−38.2625			−1.34524			−0.672619	+	0.739989i	$0.734831\pi$
$810$	9.91081	−	0.650392i	0.348230	−	0.0228524i
$811$	−31.4356			−1.10385			−0.551927	−	0.833893i	$-0.686107\pi$
$811$	−31.4356			−1.10385			−0.551927	+	0.833893i	$0.686107\pi$
$812$		−	4.15529i		−	0.145822i
$813$			60.9529i			2.13771i
$814$	−1.15885			−0.0406176
$815$	−14.6524	+	0.961559i	−0.513253	+	0.0336819i
$816$	13.6277			0.477064
$817$			34.0604i			1.19162i
$818$		−	28.1587i		−	0.984547i
$819$	42.5229			1.48587
$820$	0.478733	+	7.29504i	0.0167181	+	0.254754i
$821$	42.9887			1.50031			0.750157	−	0.661259i	$-0.229978\pi$
$821$	42.9887			1.50031			0.750157	+	0.661259i	$0.229978\pi$
$822$			6.18014i			0.215557i
$823$			12.7450i			0.444263i	0.975017	+	0.222132i	$0.0713014\pi$
$823$			12.7450i			0.444263i	−0.975017	+	0.222132i	$0.928699\pi$
$824$	19.5270			0.680254
$825$	−0.138898	−	1.05372i	−0.00483579	−	0.0366857i
$826$	−4.48738			−0.156136
$827$			12.8443i			0.446639i	0.974745	+	0.223319i	$0.0716893\pi$
$827$			12.8443i			0.446639i	−0.974745	+	0.223319i	$0.928311\pi$
$828$			10.0827i			0.350397i
$829$	17.2491			0.599087			0.299543	−	0.954083i	$-0.403166\pi$
$829$	17.2491			0.599087			0.299543	+	0.954083i	$0.403166\pi$
$830$	−2.74046	−	41.7597i	−0.0951227	−	1.44950i
$831$	−5.91424			−0.205163
$832$			29.4446i			1.02081i
$833$			4.98197i			0.172615i
$834$	62.3564			2.15923
$835$	−2.00172	+	0.131362i	−0.0692724	+	0.00454597i
$836$	−0.179475			−0.00620728
$837$		−	2.51090i		−	0.0867892i
$838$			54.9366i			1.89775i
$839$	17.7454			0.612638			0.306319	−	0.951929i	$-0.400903\pi$
$839$	17.7454			0.612638			0.306319	+	0.951929i	$0.400903\pi$
$840$	21.6470	−	1.42058i	0.746894	−	0.0490145i
$841$	5.97821			0.206145
$842$			26.9570i			0.929000i
$843$		−	62.4249i		−	2.15003i
$844$	2.41154			0.0830086
$845$	−2.85663	−	43.5299i	−0.0982711	−	1.49748i
$846$	−47.2779			−1.62545
$847$			15.6185i			0.536660i
$848$			0.102828i			0.00353113i
$849$	−15.2870			−0.524648
$850$	−7.82940	+	1.03204i	−0.268546	+	0.0353988i
$851$	38.4981			1.31970
$852$		−	5.45534i		−	0.186897i
$853$		−	45.1570i		−	1.54615i	−0.634317	−	0.773073i	$-0.718718\pi$
$853$		−	45.1570i		−	1.54615i	0.634317	−	0.773073i	$-0.281282\pi$
$854$	7.79318			0.266677
$855$	−3.76940	−	57.4389i	−0.128911	−	1.96437i
$856$	−15.0956			−0.515956
$857$			40.5102i			1.38380i	0.721993	+	0.691900i	$0.243226\pi$
$857$			40.5102i			1.38380i	−0.721993	+	0.691900i	$0.756774\pi$
$858$		−	1.91424i		−	0.0653510i
$859$	25.4439			0.868135			0.434068	−	0.900880i	$-0.357078\pi$
$859$	25.4439			0.868135			0.434068	+	0.900880i	$0.357078\pi$
$860$	7.66553	−	0.503047i	0.261393	−	0.0171538i
$861$	−26.9729			−0.919235
$862$			35.6902i			1.21561i
$863$			21.6953i			0.738517i	0.929327	+	0.369259i	$0.120388\pi$
$863$			21.6953i			0.738517i	−0.929327	+	0.369259i	$0.879612\pi$
$864$	17.6962			0.602037
$865$	8.54646	−	0.560857i	0.290588	−	0.0190697i
$866$	21.0874			0.716581
$867$		−	2.87228i		−	0.0975476i
$868$			0.272978i			0.00926548i
$869$	0.0784464			0.00266111
$870$	−3.92863	−	59.8654i	−0.133193	−	2.02963i
$871$	38.2725			1.29681
$872$			0.696312i			0.0235801i
$873$			28.0406i			0.949030i
$874$	30.0730			1.01723
$875$	−15.5766	+	3.10230i	−0.526585	+	0.104877i
$876$	19.2284			0.649667
$877$		−	15.4643i		−	0.522191i	−0.965313	−	0.261095i	$-0.915916\pi$
$877$		−	15.4643i		−	0.522191i	0.965313	−	0.261095i	$-0.0840837\pi$
$878$			9.05452i			0.305575i
$879$	67.0060			2.26006
$880$	−0.0514140	−	0.783458i	−0.00173317	−	0.0264104i
$881$	−13.2839			−0.447544			−0.223772	−	0.974641i	$-0.571837\pi$
$881$	−13.2839			−0.447544			−0.223772	+	0.974641i	$0.571837\pi$
$882$			41.3101i			1.39098i
$883$		−	30.1936i		−	1.01609i	−0.861329	−	0.508047i	$-0.830368\pi$
$883$		−	30.1936i		−	1.01609i	0.861329	−	0.508047i	$-0.169632\pi$
$884$	−2.81994			−0.0948449
$885$	−12.8176	+	0.841151i	−0.430860	+	0.0282750i
$886$	−61.3059			−2.05961
$887$		−	39.7258i		−	1.33386i	−0.745120	−	0.666930i	$-0.767608\pi$
$887$		−	39.7258i		−	1.33386i	0.745120	−	0.666930i	$-0.232392\pi$
$888$		−	67.7082i		−	2.27214i
$889$	−24.5248			−0.822535
$890$	7.02894	−	0.461271i	0.235611	−	0.0154618i
$891$	0.208126			0.00697250
$892$		−	9.91815i		−	0.332084i
$893$			27.9576i			0.935565i
$894$	78.7669			2.63436
$895$	−1.42685	−	21.7427i	−0.0476945	−	0.726779i
$896$	19.3667			0.646997
$897$			63.5929i			2.12330i
$898$		−	40.0934i		−	1.33794i
$899$	−2.29786			−0.0766381
$900$	−12.8714	+	1.69666i	−0.429045	+	0.0565553i
$901$	0.0216729			0.000722028
$902$			0.772690i			0.0257278i
$903$			28.3428i			0.943190i
$904$	20.5031			0.681923
$905$	3.29113	+	50.1510i	0.109401	+	1.66707i
$906$	−16.3159			−0.542058
$907$			20.4051i			0.677541i	0.940869	+	0.338771i	$0.110011\pi$
$907$			20.4051i			0.677541i	−0.940869	+	0.338771i	$0.889989\pi$
$908$		−	6.98883i		−	0.231932i
$909$	−60.0098			−1.99040
$910$	−28.5442	+	1.87320i	−0.946230	+	0.0620958i
$911$	−44.1137			−1.46155			−0.730776	−	0.682618i	$-0.760841\pi$
$911$	−44.1137			−1.46155			−0.730776	+	0.682618i	$0.760841\pi$
$912$		−	66.8219i		−	2.21269i
$913$		−	0.876951i		−	0.0290228i
$914$	−14.0586			−0.465018
$915$	22.2602	−	1.46082i	0.735900	−	0.0482931i
$916$	5.54704			0.183279
$917$			20.9091i			0.690481i
$918$		−	10.2071i		−	0.336884i
$919$	−38.1261			−1.25766			−0.628832	−	0.777541i	$-0.716467\pi$
$919$	−38.1261			−1.25766			−0.628832	+	0.777541i	$0.716467\pi$
$920$	1.35193	+	20.6010i	0.0445718	+	0.679194i
$921$	−50.1464			−1.65238
$922$			21.9736i			0.723661i
$923$		−	21.8957i		−	0.720707i
$924$	−0.149347			−0.00491316
$925$	6.47827	+	49.1461i	0.213004	+	1.61591i
$926$	59.2418			1.94681
$927$		−	43.1157i		−	1.41611i
$928$		−	16.1948i		−	0.531620i
$929$	−11.6168			−0.381134			−0.190567	−	0.981674i	$-0.561033\pi$
$929$	−11.6168			−0.381134			−0.190567	+	0.981674i	$0.561033\pi$
$930$	0.258088	+	3.93281i	0.00846305	+	0.128962i
$931$	24.4286			0.800614
$932$			6.83931i			0.224029i
$933$			8.58801i			0.281159i
$934$	17.7067			0.579380
$935$	−0.165128	+	0.0108364i	−0.00540026	+	0.000354389i
$936$	71.1730			2.32636
$937$			39.8889i			1.30311i	0.758600	+	0.651557i	$0.225884\pi$
$937$			39.8889i			1.30311i	−0.758600	+	0.651557i	$0.774116\pi$
$938$		−	15.0608i		−	0.491752i
$939$	22.2897			0.727396
$940$	6.29205	−	0.412913i	0.205224	−	0.0134677i
$941$	−21.8113			−0.711028			−0.355514	−	0.934671i	$-0.615694\pi$
$941$	−21.8113			−0.711028			−0.355514	+	0.934671i	$0.615694\pi$
$942$		−	23.5586i		−	0.767582i
$943$		−	25.6695i		−	0.835914i
$944$	−9.48910			−0.308844
$945$	−1.34427	−	20.4842i	−0.0437290	−	0.666351i
$946$	0.811933			0.0263982
$947$		−	18.2678i		−	0.593625i	−0.954936	−	0.296812i	$-0.904076\pi$
$947$		−	18.2678i		−	0.593625i	0.954936	−	0.296812i	$-0.0959236\pi$
$948$		−	1.50580i		−	0.0489063i
$949$	77.1757			2.50523
$950$	5.06053	+	38.3907i	0.164185	+	1.24556i
$951$	−19.7886			−0.641688
$952$		−	3.37769i		−	0.109472i
$953$		−	27.5942i		−	0.893865i	−0.894568	−	0.446932i	$-0.852516\pi$
$953$		−	27.5942i		−	0.893865i	0.894568	−	0.446932i	$-0.147484\pi$
$954$	0.179710			0.00581832
$955$	−0.801908	−	12.2196i	−0.0259491	−	0.395419i
$956$	−8.05430			−0.260495
$957$		−	1.25717i		−	0.0406385i
$958$			8.15866i			0.263594i
$959$	1.93525			0.0624925
$960$	33.0965	−	2.17194i	1.06818	−	0.0700990i
$961$	−30.8490			−0.995130
$962$			89.2813i			2.87854i
$963$			33.3311i			1.07408i
$964$	−2.44363			−0.0787041
$965$	−4.78571	+	0.314060i	−0.154058	+	0.0101099i
$966$	25.0247			0.805157
$967$		−	36.3289i		−	1.16826i	−0.811661	−	0.584129i	$-0.801436\pi$
$967$		−	36.3289i		−	1.16826i	0.811661	−	0.584129i	$-0.198564\pi$
$968$			26.1416i			0.840223i
$969$	−14.0839			−0.452441
$970$	−1.23523	−	18.8227i	−0.0396607	−	0.604359i
$971$	45.2409			1.45185			0.725925	−	0.687774i	$-0.241412\pi$
$971$	45.2409			1.45185			0.725925	+	0.687774i	$0.241412\pi$
$972$			5.59370i			0.179418i
$973$		−	19.5263i		−	0.625985i
$974$	−53.7888			−1.72351
$975$	−81.1816	+	10.7011i	−2.59989	+	0.342709i
$976$	16.4796			0.527499
$977$		−	10.8393i		−	0.346780i	−0.984853	−	0.173390i	$-0.944528\pi$
$977$		−	10.8393i		−	0.346780i	0.984853	−	0.173390i	$-0.0554722\pi$
$978$			29.7909i			0.952607i
$979$	0.147607			0.00471755
$980$	−0.360792	−	5.49782i	−0.0115251	−	0.175621i
$981$	1.53746			0.0490874
$982$			28.9116i			0.922606i
$983$		−	3.69018i		−	0.117699i	−0.998267	−	0.0588493i	$-0.981257\pi$
$983$		−	3.69018i		−	0.117699i	0.998267	−	0.0588493i	$-0.0187431\pi$
$984$	−45.1461			−1.43920
$985$	21.8333	−	1.43280i	0.695665	−	0.0456527i
$986$	−9.34109			−0.297481
$987$			23.2644i			0.740515i
$988$			13.8273i			0.439905i
$989$	−26.9732			−0.857698
$990$	−1.36923	+	0.0898550i	−0.0435170	+	0.00285578i
$991$	36.6378			1.16384			0.581919	−	0.813247i	$-0.302302\pi$
$991$	36.6378			1.16384			0.581919	+	0.813247i	$0.302302\pi$
$992$			1.06390i			0.0337790i
$993$			45.5442i			1.44530i
$994$	−8.61630			−0.273292
$995$	0.215623	+	3.28570i	0.00683569	+	0.104164i
$996$	−16.8334			−0.533386
$997$		−	32.6021i		−	1.03252i	−0.856432	−	0.516259i	$-0.827324\pi$
$997$		−	32.6021i		−	1.03252i	0.856432	−	0.516259i	$-0.172676\pi$
$998$			64.4077i			2.03879i
$999$	−64.0711			−2.02712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.b.a.69.3	✓	8
3.2	odd	2		765.2.b.c.154.6		8
4.3	odd	2		1360.2.e.d.1089.1		8
5.2	odd	4		425.2.a.h.1.3		4
5.3	odd	4		425.2.a.g.1.2		4
5.4	even	2	inner	85.2.b.a.69.6	yes	8
15.2	even	4		3825.2.a.bh.1.2		4
15.8	even	4		3825.2.a.bj.1.3		4
15.14	odd	2		765.2.b.c.154.3		8
17.16	even	2		1445.2.b.e.579.3		8
20.3	even	4		6800.2.a.bw.1.4		4
20.7	even	4		6800.2.a.bt.1.1		4
20.19	odd	2		1360.2.e.d.1089.8		8
85.33	odd	4		7225.2.a.v.1.2		4
85.67	odd	4		7225.2.a.w.1.3		4
85.84	even	2		1445.2.b.e.579.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.b.a.69.3	✓	8	1.1	even	1	trivial
85.2.b.a.69.6	yes	8	5.4	even	2	inner
425.2.a.g.1.2		4	5.3	odd	4
425.2.a.h.1.3		4	5.2	odd	4
765.2.b.c.154.3		8	15.14	odd	2
765.2.b.c.154.6		8	3.2	odd	2
1360.2.e.d.1089.1		8	4.3	odd	2
1360.2.e.d.1089.8		8	20.19	odd	2
1445.2.b.e.579.3		8	17.16	even	2
1445.2.b.e.579.6		8	85.84	even	2
3825.2.a.bh.1.2		4	15.2	even	4
3825.2.a.bj.1.3		4	15.8	even	4
6800.2.a.bt.1.1		4	20.7	even	4
6800.2.a.bw.1.4		4	20.3	even	4
7225.2.a.v.1.2		4	85.33	odd	4
7225.2.a.w.1.3		4	85.67	odd	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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.57942i q^{2} +2.87228i q^{3} -0.494582 q^{4} +(0.146426 + 2.23127i) q^{5} +4.53654 q^{6} -1.42058i q^{7} -2.37769i q^{8} -5.24997 q^{9} +(3.52412 - 0.231269i) q^{10} +0.0740063 q^{11} -1.42058i q^{12} -5.70167i q^{13} -2.24369 q^{14} +(-6.40882 + 0.420575i) q^{15} -4.74455 q^{16} +1.00000i q^{17} +8.29193i q^{18} +4.90340 q^{19} +(-0.0724196 - 1.10354i) q^{20} +4.08029 q^{21} -0.116887i q^{22} +3.88311i q^{23} +6.82940 q^{24} +(-4.95712 + 0.653431i) q^{25} -9.00536 q^{26} -6.46254i q^{27} +0.702591i q^{28} -5.91424 q^{29} +(0.664267 + 10.1222i) q^{30} +0.388531 q^{31} +2.73827i q^{32} +0.212567i q^{33} +1.57942 q^{34} +(3.16969 - 0.208009i) q^{35} +2.59654 q^{36} -9.91424i q^{37} -7.74455i q^{38} +16.3768 q^{39} +(5.30527 - 0.348156i) q^{40} -6.61055 q^{41} -6.44450i q^{42} +6.94628i q^{43} -0.0366022 q^{44} +(-0.768731 - 11.7141i) q^{45} +6.13308 q^{46} +5.70167i q^{47} -13.6277i q^{48} +4.98197 q^{49} +(1.03204 + 7.82940i) q^{50} -2.87228 q^{51} +2.81994i q^{52} -0.0216729i q^{53} -10.2071 q^{54} +(0.0108364 + 0.165128i) q^{55} -3.37769 q^{56} +14.0839i q^{57} +9.34109i q^{58} +2.00000 q^{59} +(3.16969 - 0.208009i) q^{60} -3.47337 q^{61} -0.613655i q^{62} +7.45798i q^{63} -5.16421 q^{64} +(12.7220 - 0.834872i) q^{65} +0.335733 q^{66} +6.71251i q^{67} -0.494582i q^{68} -11.1534 q^{69} +(-0.328534 - 5.00628i) q^{70} +3.84023 q^{71} +12.4828i q^{72} +13.5356i q^{73} -15.6588 q^{74} +(-1.87683 - 14.2382i) q^{75} -2.42513 q^{76} -0.105132i q^{77} -25.8659i q^{78} +1.06000 q^{79} +(-0.694725 - 10.5864i) q^{80} +2.81228 q^{81} +10.4409i q^{82} -11.8497i q^{83} -2.01803 q^{84} +(-2.23127 + 0.146426i) q^{85} +10.9711 q^{86} -16.9873i q^{87} -0.175964i q^{88} +1.99452 q^{89} +(-18.5015 + 1.21415i) q^{90} -8.09965 q^{91} -1.92052i q^{92} +1.11597i q^{93} +9.00536 q^{94} +(0.717985 + 10.9408i) q^{95} -7.86508 q^{96} -5.34109i q^{97} -7.86864i q^{98} -0.388531 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{9} + 6 q^{10} - 4 q^{11} + 12 q^{14} - 8 q^{16} - 8 q^{19} - 2 q^{20} + 24 q^{21} + 12 q^{24} - 12 q^{25} + 8 q^{29} - 16 q^{30} - 24 q^{31} + 4 q^{34} + 44 q^{39} + 22 q^{40}+ \cdots + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^9 + 6 * q^10 - 4 * q^11 + 12 * q^14 - 8 * q^16 - 8 * q^19 - 2 * q^20 + 24 * q^21 + 12 * q^24 - 12 * q^25 + 8 * q^29 - 16 * q^30 - 24 * q^31 + 4 * q^34 + 44 * q^39 + 22 * q^40 - 12 * q^41 - 32 * q^44 - 22 * q^45 - 8 * q^46 - 16 * q^49 + 44 * q^50 - 8 * q^51 - 20 * q^54 - 8 * q^55 - 8 * q^56 + 16 * q^59 + 12 * q^61 + 48 * q^64 + 20 * q^65 + 24 * q^66 - 8 * q^69 + 40 * q^70 - 20 * q^71 - 40 * q^74 + 4 * q^75 - 24 * q^76 + 24 * q^79 - 26 * q^80 - 8 * q^81 - 72 * q^84 - 2 * q^85 + 40 * q^86 - 48 * q^89 - 74 * q^90 + 36 * q^91 + 4 * q^95 + 16 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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