LMFDB - Embedded newform 1445.2.b.e.579.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(579,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1445.579");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.b (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:	$11.5383830921$
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:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			579.3
Root			$-0.252709 - 0.252709i$ of defining polynomial
Character	$\chi$	$=$	1445.579
Dual form			1445.2.b.e.579.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$1$	$-1$

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	$-0.688822\pi$
$3$		−	2.87228i		−	1.65831i	0.559019	−	0.829155i	$-0.311178\pi$
$4$	−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	$0.0865159\pi$
$7$			1.42058i			0.536927i	−0.963290	+	0.268464i	$0.913484\pi$
$8$		−	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	$-0.503551\pi$
$11$	−0.0740063			−0.0223137			−0.0111569	+	0.999938i	$0.503551\pi$
$12$			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
$17$		0			0
$17$		0			0
$18$			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	$-0.867326\pi$
$23$		−	3.88311i		−	0.809685i	0.914386	−	0.404842i	$-0.132674\pi$
$24$	−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	$-0.314962\pi$
$29$	5.91424			1.09825			0.549123	+	0.835741i	$0.314962\pi$
$30$	0.664267	+	10.1222i	0.121278	+	1.84806i
$31$	−0.388531			−0.0697822			−0.0348911	−	0.999391i	$-0.511108\pi$
$31$	−0.388531			−0.0697822			−0.0348911	+	0.999391i	$0.511108\pi$
$32$			2.73827i			0.484063i
$33$			0.212567i			0.0370031i
$34$		0			0
$35$	3.16969	−	0.208009i	0.535775	−	0.0351599i
$36$	2.59654			0.432757
$37$			9.91424i			1.62989i	0.579538	+	0.814945i	$0.303233\pi$
$37$			9.91424i			1.62989i	−0.579538	+	0.814945i	$0.696767\pi$
$38$		−	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	$-0.327347\pi$
$41$	6.61055			1.03239			0.516197	+	0.856470i	$0.327347\pi$
$42$		−	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
$51$		0			0
$52$			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	$-0.428624\pi$
$61$	3.47337			0.444720			0.222360	+	0.974965i	$0.428624\pi$
$62$			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			0
$69$	−11.1534			−1.34271
$70$	−0.328534	−	5.00628i	−0.0392674	−	0.598365i
$71$	−3.84023			−0.455752			−0.227876	−	0.973690i	$-0.573178\pi$
$71$	−3.84023			−0.455752			−0.227876	+	0.973690i	$0.573178\pi$
$72$			12.4828i			1.47112i
$73$		−	13.5356i		−	1.58422i	−0.610375	−	0.792112i	$-0.708981\pi$
$73$		−	13.5356i		−	1.58422i	0.610375	−	0.792112i	$-0.291019\pi$
$74$	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	$-0.518992\pi$
$79$	−1.06000			−0.119259			−0.0596295	+	0.998221i	$0.518992\pi$
$80$	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
$85$		0			0
$86$	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	$0.0874049\pi$
$97$			5.34109i			0.542306i	−0.962536	+	0.271153i	$0.912595\pi$
$98$		−	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	$0.307451\pi$
$102$		0			0
$103$			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	$0.0992857\pi$
$107$			6.34882i			0.613764i	−0.951748	+	0.306882i	$0.900714\pi$
$108$		−	3.19625i		−	0.307560i
$109$	0.292852			0.0280501			0.0140251	−	0.999902i	$-0.495536\pi$
$109$	0.292852			0.0280501			0.0140251	+	0.999902i	$0.495536\pi$
$110$	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	$-0.867064\pi$
$113$		−	8.62311i		−	0.811194i	0.914052	−	0.405597i	$-0.132936\pi$
$114$	−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
$119$		0			0
$120$	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	$-0.277692\pi$
$131$	14.7188			1.28599			0.642993	+	0.765872i	$0.277692\pi$
$132$		−	0.105132i		−	0.00915052i
$133$			6.96565i			0.603999i
$134$	10.6019			0.915865
$135$	14.4197	−	0.946283i	1.24105	−	0.0814430i
$136$		0			0
$137$			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	$-0.698095\pi$
$139$	−13.7454			−1.16587			−0.582933	+	0.812520i	$0.698095\pi$
$140$	−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
$153$		0			0
$154$	−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	$-0.917207\pi$
$163$		−	6.56687i		−	0.514357i	0.966364	−	0.257178i	$-0.0827928\pi$
$164$	−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	$-0.988949\pi$
$167$		−	0.897123i		−	0.0694214i	0.999397	−	0.0347107i	$-0.0110510\pi$
$168$		−	9.70167i		−	0.748500i
$169$	−19.5091			−1.50070
$170$		0			0
$171$	−25.7427			−1.96859
$172$		−	3.43550i		−	0.261955i
$173$			3.83031i			0.291213i	0.989343	+	0.145607i	$0.0465134\pi$
$173$			3.83031i			0.291213i	−0.989343	+	0.145607i	$0.953487\pi$
$174$	−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	$-0.814723\pi$
$181$	−22.4764			−1.67066			−0.835330	+	0.549749i	$0.814723\pi$
$182$		−	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			0
$188$		−	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	$-0.975404\pi$
$193$		−	2.14484i		−	0.154389i	0.997016	−	0.0771944i	$-0.0245962\pi$
$194$	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	$0.113336\pi$
$197$			9.78513i			0.697162i	−0.937279	+	0.348581i	$0.886664\pi$
$198$		−	0.613655i		−	0.0436106i
$199$	−1.47257			−0.104388			−0.0521939	−	0.998637i	$-0.516621\pi$
$199$	−1.47257			−0.104388			−0.0521939	+	0.998637i	$0.516621\pi$
$200$	1.55366	+	11.7865i	0.109860	+	0.833432i
$201$	19.2802			1.35992
$202$		−	18.0536i		−	1.27025i
$203$			8.40162i			0.589678i
$204$		0			0
$205$	−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	$-0.446322\pi$
$211$	4.87591			0.335672			0.167836	+	0.985815i	$0.446322\pi$
$212$			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
$221$		0			0
$222$		−	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	$-0.844634\pi$
$227$		−	14.1308i		−	0.937893i	0.883227	−	0.468946i	$-0.155366\pi$
$228$			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	$0.149634\pi$
$233$			13.8285i			0.905934i	−0.891527	+	0.452967i	$0.850366\pi$
$234$	47.2779			3.09065
$235$	12.7220	−	0.834872i	0.829889	−	0.0544610i
$236$	−0.989164			−0.0643891
$237$			3.04460i			0.197768i
$238$		0			0
$239$	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	$-0.550870\pi$
$241$	−4.94081			−0.318265			−0.159133	+	0.987257i	$0.550870\pi$
$242$			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			0
$256$	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	$-0.789646\pi$
$269$	−25.8967			−1.57895			−0.789474	+	0.613784i	$0.789646\pi$
$270$	−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	$0.277047\pi$
$272$		0			0
$273$		−	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	$-0.980297\pi$
$277$		−	2.05908i		−	0.123718i	0.998085	−	0.0618590i	$-0.0197029\pi$
$278$			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	$-0.949435\pi$
$283$		−	5.32226i		−	0.316375i	0.987409	−	0.158188i	$-0.0505651\pi$
$284$	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
$289$		0			0
$290$	−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
$306$		0			0
$307$			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	$-0.527016\pi$
$311$	−2.98997			−0.169545			−0.0847727	+	0.996400i	$0.527016\pi$
$312$			38.9390i			2.20448i
$313$			7.76028i			0.438637i	0.975653	+	0.219319i	$0.0703834\pi$
$313$			7.76028i			0.438637i	−0.975653	+	0.219319i	$0.929617\pi$
$314$	−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	$-0.938024\pi$
$317$		−	6.88951i		−	0.386953i	0.981105	−	0.193477i	$-0.0619764\pi$
$318$			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
$323$		0			0
$324$	−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	$-0.825050\pi$
$337$		−	19.1787i		−	1.04473i	0.852722	−	0.522365i	$-0.174950\pi$
$338$			30.8131i			1.67601i
$339$	−24.7679			−1.34521
$340$		0			0
$341$	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	$0.357361\pi$
$347$			33.5775i			1.80253i	−0.433265	+	0.901266i	$0.642639\pi$
$348$			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
$357$		0			0
$358$			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	$0.0114442\pi$
$367$			1.37723i			0.0718908i	−0.999354	+	0.0359454i	$0.988556\pi$
$368$			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			0
$375$	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	$-0.713914\pi$
$379$	−24.2405			−1.24515			−0.622576	+	0.782559i	$0.713914\pi$
$380$	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
$391$		0			0
$392$		−	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	$-0.764614\pi$
$397$		−	26.8550i		−	1.34782i	0.738815	−	0.673908i	$-0.235386\pi$
$398$			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	$-0.355986\pi$
$401$	17.5080			0.874308			0.437154	+	0.899387i	$0.355986\pi$
$402$		−	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
$408$		0			0
$409$	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	$-0.176830\pi$
$419$	34.7826			1.69924			0.849622	+	0.527393i	$0.176830\pi$
$420$	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			0
$426$	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	$-0.316822\pi$
$431$	22.5970			1.08846			0.544229	+	0.838937i	$0.316822\pi$
$432$		−	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	$-0.456316\pi$
$439$	5.73280			0.273611			0.136806	+	0.990598i	$0.456316\pi$
$440$	0.392624	−	0.0257657i	0.0187176	−	0.00122833i
$441$	−26.1552			−1.24548
$442$		0			0
$443$		−	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	$-0.704432\pi$
$449$	−25.3848			−1.19798			−0.598992	+	0.800755i	$0.704432\pi$
$450$	−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
$459$		0			0
$460$	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			0
$477$			0.113782i			0.00520972i
$478$		−	25.7210i		−	1.17645i
$479$	5.16559			0.236022			0.118011	−	0.993012i	$-0.462348\pi$
$479$	5.16559			0.236022			0.118011	+	0.993012i	$0.462348\pi$
$480$	−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	$0.280549\pi$
$487$			34.0560i			1.54322i	−0.636094	+	0.771612i	$0.719451\pi$
$488$		−	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
$493$		0			0
$494$	−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	$-0.133944\pi$
$499$	40.7792			1.82553			0.912764	+	0.408488i	$0.133944\pi$
$500$	−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	$-0.923129\pi$
$503$		−	10.7274i		−	0.478313i	0.970981	−	0.239156i	$-0.0768709\pi$
$504$	−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	$0.341687\pi$
$510$		0			0
$511$	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	$-0.351406\pi$
$521$	20.5451			0.900098			0.450049	+	0.893004i	$0.351406\pi$
$522$			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			0
$528$		−	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	$-0.441108\pi$
$541$	8.55768			0.367924			0.183962	+	0.982933i	$0.441108\pi$
$542$		−	33.5171i		−	1.43968i
$543$			64.5585i			2.77047i
$544$		0			0
$545$	−0.0428811	−	0.653431i	−0.00183682	−	0.0279899i
$546$	−36.7444			−1.57252
$547$			11.2911i			0.482771i	0.970429	+	0.241385i	$0.0776018\pi$
$547$			11.2911i			0.482771i	−0.970429	+	0.241385i	$0.922398\pi$
$548$		−	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			0
$562$			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	$-0.458546\pi$
$571$	6.20629			0.259725			0.129863	+	0.991532i	$0.458546\pi$
$572$		−	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	$-0.165951\pi$
$578$		0			0
$579$	−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			0
$596$	−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	$-0.729829\pi$
$601$	−32.4048			−1.32182			−0.660910	+	0.750466i	$0.729829\pi$
$602$			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	$-0.863975\pi$
$607$		−	20.4218i		−	0.828895i	0.910073	−	0.414447i	$-0.136025\pi$
$608$			13.4269i			0.544531i
$609$	24.1318			0.977869
$610$	−12.2406	+	0.803282i	−0.495607	+	0.0325239i
$611$	32.5091			1.31518
$612$		0			0
$613$			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	$-0.975645\pi$
$617$		−	3.79742i		−	0.152878i	0.997074	−	0.0764392i	$-0.0243551\pi$
$618$		−	37.2567i		−	1.49868i
$619$	−0.765306			−0.0307602			−0.0153801	−	0.999882i	$-0.504896\pi$
$619$	−0.765306			−0.0307602			−0.0153801	+	0.999882i	$0.504896\pi$
$620$	−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
$629$		0			0
$630$	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	$-0.647569\pi$
$641$	−22.6429			−0.894342			−0.447171	+	0.894448i	$0.647569\pi$
$642$		−	28.8017i		−	1.13671i
$643$			24.8814i			0.981226i	0.871377	+	0.490613i	$0.163227\pi$
$643$			24.8814i			0.981226i	−0.871377	+	0.490613i	$0.836773\pi$
$644$	−2.72824			−0.107508
$645$	−2.92144	−	44.5175i	−0.115031	−	1.75287i
$646$		0			0
$647$			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	$0.0520460\pi$
$653$			8.31930i			0.325559i	−0.986662	+	0.162780i	$0.947954\pi$
$654$	−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
$663$		0			0
$664$	−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	$-0.704834\pi$
$673$		−	41.5075i		−	1.60000i	0.600002	−	0.799998i	$-0.295166\pi$
$674$	−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	$0.171766\pi$
$677$			26.7378i			1.02762i	−0.857905	+	0.513809i	$0.828234\pi$
$678$			39.1191i			1.50236i
$679$	−7.58742			−0.291179
$680$		0			0
$681$	−40.5875			−1.55532
$682$		−	0.0454143i		−	0.00173901i
$683$		−	37.8270i		−	1.44741i	−0.690110	−	0.723704i	$-0.742438\pi$
$683$		−	37.8270i		−	1.44741i	0.690110	−	0.723704i	$-0.257562\pi$
$684$	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	$-0.716574\pi$
$691$	−33.0739			−1.25819			−0.629095	+	0.777328i	$0.716574\pi$
$692$		−	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
$697$		0			0
$698$			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	$-0.224120\pi$
$709$	40.5902			1.52440			0.762199	+	0.647343i	$0.224120\pi$
$710$	13.5334	−	0.888125i	0.507901	−	0.0333307i
$711$	5.56495			0.208702
$712$		−	4.74237i		−	0.177728i
$713$			1.50871i			0.0565016i
$714$		0			0
$715$	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	$-0.295551\pi$
$719$	32.1253			1.19807			0.599036	+	0.800722i	$0.295551\pi$
$720$	−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
$731$		0			0
$732$			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	$0.171491\pi$
$743$			27.9705i			1.02614i	−0.858348	+	0.513069i	$0.828509\pi$
$744$	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			0
$749$	−9.01898			−0.329546
$750$	−9.90704	−	49.7431i	−0.361754	−	1.81636i
$751$	52.7167			1.92366			0.961829	−	0.273650i	$-0.0882309\pi$
$751$	52.7167			1.92366			0.961829	+	0.273650i	$0.0882309\pi$
$752$		−	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
$765$		0			0
$766$	−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
$782$		0			0
$783$			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	$0.110237\pi$
$787$			19.0449i			0.678877i	−0.940628	+	0.339439i	$0.889763\pi$
$788$		−	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
$799$		0			0
$800$	−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	$-0.265169\pi$
$809$	38.2625			1.34524			0.672619	+	0.739989i	$0.265169\pi$
$810$	−9.91081	+	0.650392i	−0.348230	+	0.0228524i
$811$	31.4356			1.10385			0.551927	−	0.833893i	$-0.313893\pi$
$811$	31.4356			1.10385			0.551927	+	0.833893i	$0.313893\pi$
$812$		−	4.15529i		−	0.145822i
$813$		−	60.9529i		−	2.13771i
$814$	−1.15885			−0.0406176
$815$	−14.6524	+	0.961559i	−0.513253	+	0.0336819i
$816$		0			0
$817$			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	$-0.770022\pi$
$821$	−42.9887			−1.50031			−0.750157	+	0.661259i	$0.770022\pi$
$822$		−	6.18014i		−	0.215557i
$823$		−	12.7450i		−	0.444263i	−0.975017	−	0.222132i	$-0.928699\pi$
$823$		−	12.7450i		−	0.444263i	0.975017	−	0.222132i	$-0.0713014\pi$
$824$	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	$-0.928311\pi$
$827$		−	12.8443i		−	0.446639i	0.974745	−	0.223319i	$-0.0716893\pi$
$828$		−	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
$833$		0			0
$834$	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	$-0.599097\pi$
$839$	−17.7454			−0.612638			−0.306319	+	0.951929i	$0.599097\pi$
$840$	−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
$850$		0			0
$851$	38.4981			1.31970
$852$		−	5.45534i		−	0.186897i
$853$			45.1570i			1.54615i	0.634317	+	0.773073i	$0.281282\pi$
$853$			45.1570i			1.54615i	−0.634317	+	0.773073i	$0.718718\pi$
$854$	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	$-0.756774\pi$
$857$		−	40.5102i		−	1.38380i	0.721993	−	0.691900i	$-0.243226\pi$
$858$		−	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
$867$		0			0
$868$			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	$0.0840837\pi$
$877$			15.4643i			0.522191i	−0.965313	+	0.261095i	$0.915916\pi$
$878$		−	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	$-0.428163\pi$
$881$	13.2839			0.447544			0.223772	+	0.974641i	$0.428163\pi$
$882$			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	$-0.169632\pi$
$884$		0			0
$885$	−12.8176	+	0.841151i	−0.430860	+	0.0282750i
$886$	−61.3059			−2.05961
$887$			39.7258i			1.33386i	0.745120	+	0.666930i	$0.232392\pi$
$887$			39.7258i			1.33386i	−0.745120	+	0.666930i	$0.767608\pi$
$888$		−	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			0
$902$			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	$-0.889989\pi$
$907$		−	20.4051i		−	0.677541i	0.940869	−	0.338771i	$-0.110011\pi$
$908$			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	$-0.239159\pi$
$911$	44.1137			1.46155			0.730776	+	0.682618i	$0.239159\pi$
$912$			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
$918$		0			0
$919$	−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	$-0.438967\pi$
$929$	11.6168			0.381134			0.190567	+	0.981674i	$0.438967\pi$
$930$	−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			0
$936$	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	$-0.384306\pi$
$941$	21.8113			0.711028			0.355514	+	0.934671i	$0.384306\pi$
$942$			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	$0.0959236\pi$
$947$			18.2678i			0.593625i	−0.954936	+	0.296812i	$0.904076\pi$
$948$		−	1.50580i		−	0.0489063i
$949$	−77.1757			−2.50523
$950$	5.06053	+	38.3907i	0.164185	+	1.24556i
$951$	−19.7886			−0.641688
$952$		0			0
$953$		−	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
$969$		0			0
$970$	−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	$0.0187431\pi$
$983$			3.69018i			0.117699i	−0.998267	+	0.0588493i	$0.981257\pi$
$984$	−45.1461			−1.43920
$985$	21.8333	−	1.43280i	0.695665	−	0.0456527i
$986$		0			0
$987$			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	$-0.697698\pi$
$991$	−36.6378			−1.16384			−0.581919	+	0.813247i	$0.697698\pi$
$992$		−	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	$0.172676\pi$
$997$			32.6021i			1.03252i	−0.856432	+	0.516259i	$0.827324\pi$
$998$		−	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	1445.2.b.e.579.3		8
5.2	odd	4		7225.2.a.w.1.3		4
5.3	odd	4		7225.2.a.v.1.2		4
5.4	even	2	inner	1445.2.b.e.579.6		8
17.16	even	2		85.2.b.a.69.3	✓	8
51.50	odd	2		765.2.b.c.154.6		8
68.67	odd	2		1360.2.e.d.1089.1		8
85.33	odd	4		425.2.a.g.1.2		4
85.67	odd	4		425.2.a.h.1.3		4
85.84	even	2		85.2.b.a.69.6	yes	8
255.152	even	4		3825.2.a.bh.1.2		4
255.203	even	4		3825.2.a.bj.1.3		4
255.254	odd	2		765.2.b.c.154.3		8
340.67	even	4		6800.2.a.bt.1.1		4
340.203	even	4		6800.2.a.bw.1.4		4
340.339	odd	2		1360.2.e.d.1089.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.b.a.69.3	✓	8	17.16	even	2
85.2.b.a.69.6	yes	8	85.84	even	2
425.2.a.g.1.2		4	85.33	odd	4
425.2.a.h.1.3		4	85.67	odd	4
765.2.b.c.154.3		8	255.254	odd	2
765.2.b.c.154.6		8	51.50	odd	2
1360.2.e.d.1089.1		8	68.67	odd	2
1360.2.e.d.1089.8		8	340.339	odd	2
1445.2.b.e.579.3		8	1.1	even	1	trivial
1445.2.b.e.579.6		8	5.4	even	2	inner
3825.2.a.bh.1.2		4	255.152	even	4
3825.2.a.bj.1.3		4	255.203	even	4
6800.2.a.bt.1.1		4	340.67	even	4
6800.2.a.bw.1.4		4	340.203	even	4
7225.2.a.v.1.2		4	5.3	odd	4
7225.2.a.w.1.3		4	5.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.b (of order \(2\), degree \(1\), minimal)

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

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Database

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