LMFDB - Embedded newform 625.2.d.p.126.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			126.2
Root			$-1.20005i$ of defining polynomial
Character	$\chi$	$=$	625.126
Dual form			625.2.d.p.501.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.718805 - 2.21225i) q^{2} +(-1.86261 + 1.35327i) q^{3} +(-2.75935 + 2.00479i) q^{4} +(4.33262 + 3.14783i) q^{6} -3.59425 q^{7} +(2.65482 + 1.92884i) q^{8} +(0.710939 - 2.18805i) q^{9} +O(q^{10})$	\(q+(-0.718805 - 2.21225i) q^{2} +(-1.86261 + 1.35327i) q^{3} +(-2.75935 + 2.00479i) q^{4} +(4.33262 + 3.14783i) q^{6} -3.59425 q^{7} +(2.65482 + 1.92884i) q^{8} +(0.710939 - 2.18805i) q^{9} +(-0.153825 - 0.473424i) q^{11} +(2.42659 - 7.46828i) q^{12} +(-0.818243 + 2.51829i) q^{13} +(2.58356 + 7.95139i) q^{14} +(0.250832 - 0.771980i) q^{16} +(4.13180 + 3.00193i) q^{17} -5.35154 q^{18} +(0.798724 + 0.580307i) q^{19} +(6.69468 - 4.86397i) q^{21} +(-0.936765 + 0.680599i) q^{22} +(-1.98198 - 6.09991i) q^{23} -7.55514 q^{24} +6.15926 q^{26} +(-0.497557 - 1.53132i) q^{27} +(9.91780 - 7.20570i) q^{28} +(4.50623 - 3.27397i) q^{29} +(-4.89866 - 3.55908i) q^{31} +4.67497 q^{32} +(0.927185 + 0.673639i) q^{33} +(3.67107 - 11.2984i) q^{34} +(2.42484 + 7.46288i) q^{36} +(1.42028 - 4.37117i) q^{37} +(0.709660 - 2.18411i) q^{38} +(-1.88385 - 5.79790i) q^{39} +(-0.888346 + 2.73405i) q^{41} +(-15.5725 - 11.3141i) q^{42} +9.48858 q^{43} +(1.37357 + 0.997959i) q^{44} +(-12.0699 + 8.76929i) q^{46} +(4.34308 - 3.15543i) q^{47} +(0.577493 + 1.77734i) q^{48} +5.91861 q^{49} -11.7583 q^{51} +(-2.79082 - 8.58926i) q^{52} +(-0.248854 + 0.180803i) q^{53} +(-3.03003 + 2.20144i) q^{54} +(-9.54209 - 6.93274i) q^{56} -2.27302 q^{57} +(-10.4820 - 7.61558i) q^{58} +(-0.391355 + 1.20447i) q^{59} +(-1.92402 - 5.92152i) q^{61} +(-4.35242 + 13.3954i) q^{62} +(-2.55529 + 7.86438i) q^{63} +(-3.86206 - 11.8862i) q^{64} +(0.823796 - 2.53538i) q^{66} +(-4.27667 - 3.10718i) q^{67} -17.4193 q^{68} +(11.9465 + 8.67961i) q^{69} +(0.122941 - 0.0893215i) q^{71} +(6.10782 - 4.43759i) q^{72} +(4.59634 + 14.1461i) q^{73} -10.6910 q^{74} -3.36735 q^{76} +(0.552884 + 1.70160i) q^{77} +(-11.4723 + 8.33512i) q^{78} +(13.4205 - 9.75053i) q^{79} +(8.58283 + 6.23579i) q^{81} +6.68696 q^{82} +(11.8084 + 8.57929i) q^{83} +(-8.72176 + 26.8428i) q^{84} +(-6.82044 - 20.9912i) q^{86} +(-3.96281 + 12.1963i) q^{87} +(0.504783 - 1.55356i) q^{88} +(3.51731 + 10.8252i) q^{89} +(2.94097 - 9.05136i) q^{91} +(17.6980 + 12.8584i) q^{92} +13.9407 q^{93} +(-10.1024 - 7.33985i) q^{94} +(-8.70766 + 6.32648i) q^{96} +(0.687010 - 0.499142i) q^{97} +(-4.25432 - 13.0935i) q^{98} -1.14523 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9	$ 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9} + 2 q^{11} + 25 q^{12} + 5 q^{13} + 9 q^{14} - 14 q^{16} - 10 q^{17} + 10 q^{18} + 7 q^{21} - 40 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} + 20 q^{27} + 30 q^{28} - 10 q^{29} + 17 q^{31} - 60 q^{32} + 5 q^{33} - q^{34} - 4 q^{36} - 15 q^{37} - 15 q^{38} - 9 q^{39} + 12 q^{41} - 45 q^{42} + 49 q^{44} - 33 q^{46} + 25 q^{47} - 20 q^{48} - 8 q^{49} - 28 q^{51} + 20 q^{52} - 30 q^{54} - 35 q^{56} + 20 q^{57} + 5 q^{58} + 20 q^{59} - 23 q^{61} + 15 q^{62} + 10 q^{63} - 28 q^{64} - 26 q^{66} - 80 q^{68} + 6 q^{69} + 22 q^{71} + 5 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 40 q^{77} - 25 q^{78} + 75 q^{79} + 11 q^{81} + 90 q^{82} + 25 q^{83} - 31 q^{84} + 17 q^{86} - 20 q^{87} + 5 q^{89} + 22 q^{91} + 60 q^{92} + 80 q^{93} - 51 q^{94} - 28 q^{96} + 40 q^{97} + 15 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9 + 2 * q^11 + 25 * q^12 + 5 * q^13 + 9 * q^14 - 14 * q^16 - 10 * q^17 + 10 * q^18 + 7 * q^21 - 40 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 + 20 * q^27 + 30 * q^28 - 10 * q^29 + 17 * q^31 - 60 * q^32 + 5 * q^33 - q^34 - 4 * q^36 - 15 * q^37 - 15 * q^38 - 9 * q^39 + 12 * q^41 - 45 * q^42 + 49 * q^44 - 33 * q^46 + 25 * q^47 - 20 * q^48 - 8 * q^49 - 28 * q^51 + 20 * q^52 - 30 * q^54 - 35 * q^56 + 20 * q^57 + 5 * q^58 + 20 * q^59 - 23 * q^61 + 15 * q^62 + 10 * q^63 - 28 * q^64 - 26 * q^66 - 80 * q^68 + 6 * q^69 + 22 * q^71 + 5 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 40 * q^77 - 25 * q^78 + 75 * q^79 + 11 * q^81 + 90 * q^82 + 25 * q^83 - 31 * q^84 + 17 * q^86 - 20 * q^87 + 5 * q^89 + 22 * q^91 + 60 * q^92 + 80 * q^93 - 51 * q^94 - 28 * q^96 + 40 * q^97 + 15 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.718805	−	2.21225i	−0.508272	−	1.56430i	−0.795200	−	0.606348i	$-0.792634\pi$
$2$	−0.718805	−	2.21225i	−0.508272	−	1.56430i	0.286928	−	0.957952i	$-0.407366\pi$
$3$	−1.86261	+	1.35327i	−1.07538	+	0.781309i	−0.976871	−	0.213828i	$-0.931407\pi$
$3$	−1.86261	+	1.35327i	−1.07538	+	0.781309i	−0.0985075	+	0.995136i	$0.531407\pi$
$4$	−2.75935	+	2.00479i	−1.37968	+	1.00239i
$5$		0			0
$5$		0			0
$6$	4.33262	+	3.14783i	1.76879	+	1.28510i
$7$	−3.59425			−1.35850			−0.679249	−	0.733908i	$-0.737694\pi$
$7$	−3.59425			−1.35850			−0.679249	+	0.733908i	$0.737694\pi$
$8$	2.65482	+	1.92884i	0.938622	+	0.681949i
$9$	0.710939	−	2.18805i	0.236980	−	0.729349i
$10$		0			0
$11$	−0.153825	−	0.473424i	−0.0463799	−	0.142743i	0.925185	−	0.379517i	$-0.123910\pi$
$11$	−0.153825	−	0.473424i	−0.0463799	−	0.142743i	−0.971565	+	0.236774i	$0.923910\pi$
$12$	2.42659	−	7.46828i	0.700496	−	2.15591i
$13$	−0.818243	+	2.51829i	−0.226940	+	0.698449i	0.771149	+	0.636655i	$0.219682\pi$
$13$	−0.818243	+	2.51829i	−0.226940	+	0.698449i	−0.998089	+	0.0617942i	$0.980318\pi$
$14$	2.58356	+	7.95139i	0.690486	+	2.12510i
$15$		0			0
$16$	0.250832	−	0.771980i	0.0627079	−	0.192995i
$17$	4.13180	+	3.00193i	1.00211	+	0.728075i	0.962539	−	0.271142i	$-0.0874013\pi$
$17$	4.13180	+	3.00193i	1.00211	+	0.728075i	0.0395697	+	0.999217i	$0.487401\pi$
$18$	−5.35154			−1.26137
$19$	0.798724	+	0.580307i	0.183240	+	0.133132i	0.675624	−	0.737247i	$-0.263874\pi$
$19$	0.798724	+	0.580307i	0.183240	+	0.133132i	−0.492384	+	0.870378i	$0.663874\pi$
$20$		0			0
$21$	6.69468	−	4.86397i	1.46090	−	1.06141i
$22$	−0.936765	+	0.680599i	−0.199719	+	0.145104i
$23$	−1.98198	−	6.09991i	−0.413271	−	1.27192i	−0.913788	−	0.406192i	$-0.866857\pi$
$23$	−1.98198	−	6.09991i	−0.413271	−	1.27192i	0.500517	−	0.865727i	$-0.333143\pi$
$24$	−7.55514			−1.54219
$25$		0			0
$26$	6.15926			1.20793
$27$	−0.497557	−	1.53132i	−0.0957548	−	0.294703i
$28$	9.91780	−	7.20570i	1.87429	−	1.36175i
$29$	4.50623	−	3.27397i	0.836786	−	0.607961i	−0.0846848	−	0.996408i	$-0.526988\pi$
$29$	4.50623	−	3.27397i	0.836786	−	0.607961i	0.921471	+	0.388447i	$0.126988\pi$
$30$		0			0
$31$	−4.89866	−	3.55908i	−0.879825	−	0.639230i	0.0533803	−	0.998574i	$-0.483000\pi$
$31$	−4.89866	−	3.55908i	−0.879825	−	0.639230i	−0.933205	+	0.359344i	$0.883000\pi$
$32$	4.67497			0.826426
$33$	0.927185	+	0.673639i	0.161402	+	0.117266i
$34$	3.67107	−	11.2984i	0.629584	−	1.93766i
$35$		0			0
$36$	2.42484	+	7.46288i	0.404139	+	1.24381i
$37$	1.42028	−	4.37117i	0.233493	−	0.718616i	−0.763825	−	0.645423i	$-0.776681\pi$
$37$	1.42028	−	4.37117i	0.233493	−	0.718616i	0.997318	−	0.0731932i	$-0.0233190\pi$
$38$	0.709660	−	2.18411i	0.115122	−	0.354309i
$39$	−1.88385	−	5.79790i	−0.301658	−	0.928407i
$40$		0			0
$41$	−0.888346	+	2.73405i	−0.138736	+	0.426987i	−0.996152	−	0.0876372i	$-0.972068\pi$
$41$	−0.888346	+	2.73405i	−0.138736	+	0.426987i	0.857416	+	0.514624i	$0.172068\pi$
$42$	−15.5725	−	11.3141i	−2.40289	−	1.74580i
$43$	9.48858			1.44700			0.723498	−	0.690327i	$-0.242533\pi$
$43$	9.48858			1.44700			0.723498	+	0.690327i	$0.242533\pi$
$44$	1.37357	+	0.997959i	0.207074	+	0.150448i
$45$		0			0
$46$	−12.0699	+	8.76929i	−1.77961	+	1.29296i
$47$	4.34308	−	3.15543i	0.633503	−	0.460267i	−0.224109	−	0.974564i	$-0.571947\pi$
$47$	4.34308	−	3.15543i	0.633503	−	0.460267i	0.857612	+	0.514297i	$0.171947\pi$
$48$	0.577493	+	1.77734i	0.0833539	+	0.256537i
$49$	5.91861			0.845515
$50$		0			0
$51$	−11.7583			−1.64650
$52$	−2.79082	−	8.58926i	−0.387017	−	1.19112i
$53$	−0.248854	+	0.180803i	−0.0341827	+	0.0248352i	−0.604745	−	0.796419i	$-0.706725\pi$
$53$	−0.248854	+	0.180803i	−0.0341827	+	0.0248352i	0.570563	+	0.821254i	$0.306725\pi$
$54$	−3.03003	+	2.20144i	−0.412334	+	0.299578i
$55$		0			0
$56$	−9.54209	−	6.93274i	−1.27512	−	0.926426i
$57$	−2.27302			−0.301069
$58$	−10.4820	−	7.61558i	−1.37635	−	0.999975i
$59$	−0.391355	+	1.20447i	−0.0509500	+	0.156808i	−0.973294	−	0.229561i	$-0.926271\pi$
$59$	−0.391355	+	1.20447i	−0.0509500	+	0.156808i	0.922344	+	0.386369i	$0.126271\pi$
$60$		0			0
$61$	−1.92402	−	5.92152i	−0.246345	−	0.758173i	−0.995412	−	0.0956787i	$-0.969498\pi$
$61$	−1.92402	−	5.92152i	−0.246345	−	0.758173i	0.749067	−	0.662494i	$-0.230502\pi$
$62$	−4.35242	+	13.3954i	−0.552757	+	1.70121i
$63$	−2.55529	+	7.86438i	−0.321936	+	0.990818i
$64$	−3.86206	−	11.8862i	−0.482757	−	1.48577i
$65$		0			0
$66$	0.823796	−	2.53538i	0.101402	−	0.312084i
$67$	−4.27667	−	3.10718i	−0.522479	−	0.379603i	0.295058	−	0.955479i	$-0.404661\pi$
$67$	−4.27667	−	3.10718i	−0.522479	−	0.379603i	−0.817537	+	0.575876i	$0.804661\pi$
$68$	−17.4193			−2.11240
$69$	11.9465	+	8.67961i	1.43818	+	1.04490i
$70$		0			0
$71$	0.122941	−	0.0893215i	0.0145904	−	0.0106005i	−0.580466	−	0.814284i	$-0.697130\pi$
$71$	0.122941	−	0.0893215i	0.0145904	−	0.0106005i	0.595057	+	0.803684i	$0.297130\pi$
$72$	6.10782	−	4.43759i	0.719813	−	0.522975i
$73$	4.59634	+	14.1461i	0.537961	+	1.65567i	0.737163	+	0.675715i	$0.236165\pi$
$73$	4.59634	+	14.1461i	0.537961	+	1.65567i	−0.199202	+	0.979959i	$0.563835\pi$
$74$	−10.6910			−1.24281
$75$		0			0
$76$	−3.36735			−0.386262
$77$	0.552884	+	1.70160i	0.0630070	+	0.193916i
$78$	−11.4723	+	8.33512i	−1.29898	+	0.943766i
$79$	13.4205	−	9.75053i	1.50992	−	1.09702i	0.543706	−	0.839275i	$-0.317021\pi$
$79$	13.4205	−	9.75053i	1.50992	−	1.09702i	0.966213	−	0.257745i	$-0.0829795\pi$
$80$		0			0
$81$	8.58283	+	6.23579i	0.953648	+	0.692866i
$82$	6.68696			0.738451
$83$	11.8084	+	8.57929i	1.29614	+	0.941700i	0.999910	−	0.0134174i	$-0.00427102\pi$
$83$	11.8084	+	8.57929i	1.29614	+	0.941700i	0.296228	+	0.955117i	$0.404271\pi$
$84$	−8.72176	+	26.8428i	−0.951623	+	2.92879i
$85$		0			0
$86$	−6.82044	−	20.9912i	−0.735467	−	2.26354i
$87$	−3.96281	+	12.1963i	−0.424857	+	1.30758i
$88$	0.504783	−	1.55356i	0.0538101	−	0.165610i
$89$	3.51731	+	10.8252i	0.372834	+	1.14746i	0.944928	+	0.327277i	$0.106131\pi$
$89$	3.51731	+	10.8252i	0.372834	+	1.14746i	−0.572095	+	0.820188i	$0.693869\pi$
$90$		0			0
$91$	2.94097	−	9.05136i	0.308297	−	0.948841i
$92$	17.6980	+	12.8584i	1.84514	+	1.34058i
$93$	13.9407			1.44558
$94$	−10.1024	−	7.33985i	−1.04199	−	0.757048i
$95$		0			0
$96$	−8.70766	+	6.32648i	−0.888721	+	0.645694i
$97$	0.687010	−	0.499142i	0.0697553	−	0.0506802i	−0.552361	−	0.833605i	$-0.686273\pi$
$97$	0.687010	−	0.499142i	0.0697553	−	0.0506802i	0.622116	+	0.782925i	$0.286273\pi$
$98$	−4.25432	−	13.0935i	−0.429751	−	1.32264i
$99$	−1.14523			−0.115100
$100$		0			0
$101$	−13.2498			−1.31841			−0.659203	−	0.751965i	$-0.729106\pi$
$101$	−13.2498			−1.31841			−0.659203	+	0.751965i	$0.729106\pi$
$102$	8.45196	+	26.0125i	0.836869	+	2.57562i
$103$	0.672220	−	0.488396i	0.0662358	−	0.0481231i	−0.554175	−	0.832400i	$-0.686966\pi$
$103$	0.672220	−	0.488396i	0.0662358	−	0.0481231i	0.620410	+	0.784277i	$0.286966\pi$
$104$	−7.02968	+	5.10736i	−0.689317	+	0.500818i
$105$		0			0
$106$	0.578859	+	0.420566i	0.0562237	+	0.0408489i
$107$	0.0722844			0.00698800			0.00349400	−	0.999994i	$-0.498888\pi$
$107$	0.0722844			0.00698800			0.00349400	+	0.999994i	$0.498888\pi$
$108$	4.44291	+	3.22796i	0.427519	+	0.310611i
$109$	1.72933	−	5.32232i	0.165639	−	0.509785i	−0.833444	−	0.552605i	$-0.813634\pi$
$109$	1.72933	−	5.32232i	0.165639	−	0.509785i	0.999083	+	0.0428192i	$0.0136340\pi$
$110$		0			0
$111$	3.26993	+	10.0638i	0.310368	+	0.955215i
$112$	−0.901550	+	2.77469i	−0.0851885	+	0.262183i
$113$	0.804183	−	2.47502i	0.0756512	−	0.232830i	−0.906079	−	0.423108i	$-0.860939\pi$
$113$	0.804183	−	2.47502i	0.0756512	−	0.232830i	0.981730	+	0.190278i	$0.0609389\pi$
$114$	1.63386	+	5.02850i	0.153025	+	0.470962i
$115$		0			0
$116$	−5.87067	+	18.0681i	−0.545078	+	1.67758i
$117$	4.92842	+	3.58071i	0.455633	+	0.331036i
$118$	2.94589			0.271191
$119$	−14.8507	−	10.7897i	−1.36136	−	0.989088i
$120$		0			0
$121$	8.69872	−	6.31999i	0.790793	−	0.574544i
$122$	−11.7169	+	8.51284i	−1.06080	+	0.770716i
$123$	−2.04525	−	6.29464i	−0.184414	−	0.567568i
$124$	20.6523			1.85463
$125$		0			0
$126$	19.2348			1.71357
$127$	−1.52804	−	4.70281i	−0.135591	−	0.417307i	0.860090	−	0.510142i	$-0.170407\pi$
$127$	−1.52804	−	4.70281i	−0.135591	−	0.417307i	−0.995682	+	0.0928348i	$0.970407\pi$
$128$	−15.9549	+	11.5919i	−1.41023	+	1.02459i
$129$	−17.6735	+	12.8406i	−1.55607	+	1.13055i
$130$		0			0
$131$	−2.18711	−	1.58903i	−0.191089	−	0.138834i	0.488127	−	0.872772i	$-0.337680\pi$
$131$	−2.18711	−	1.58903i	−0.191089	−	0.138834i	−0.679216	+	0.733938i	$0.737680\pi$
$132$	−3.90893			−0.340229
$133$	−2.87081	−	2.08577i	−0.248931	−	0.180859i
$134$	−3.79979	+	11.6945i	−0.328252	+	1.01025i
$135$		0			0
$136$	5.17896	+	15.9392i	0.444092	+	1.36677i
$137$	0.694787	−	2.13833i	0.0593596	−	0.182690i	−0.916980	−	0.398933i	$-0.869380\pi$
$137$	0.694787	−	2.13833i	0.0593596	−	0.182690i	0.976340	+	0.216243i	$0.0693804\pi$
$138$	10.6143	−	32.6675i	0.903551	−	2.78085i
$139$	−3.33838	−	10.2745i	−0.283158	−	0.871469i	−0.986945	−	0.161059i	$-0.948509\pi$
$139$	−3.33838	−	10.2745i	−0.283158	−	0.871469i	0.703787	−	0.710411i	$-0.251491\pi$
$140$		0			0
$141$	−3.81933	+	11.7547i	−0.321645	+	0.989923i
$142$	−0.285972	−	0.207771i	−0.0239983	−	0.0174358i
$143$	1.31809			0.110224
$144$	−1.51080	−	1.09766i	−0.125900	−	0.0914719i
$145$		0			0
$146$	27.9909	−	20.3365i	2.31654	−	1.68306i
$147$	−11.0241	+	8.00945i	−0.909249	+	0.660608i
$148$	4.84422	+	14.9090i	0.398192	+	1.22551i
$149$	12.1878			0.998460			0.499230	−	0.866469i	$-0.333616\pi$
$149$	12.1878			0.998460			0.499230	+	0.866469i	$0.333616\pi$
$150$		0			0
$151$	17.0860			1.39044			0.695220	−	0.718797i	$-0.255307\pi$
$151$	17.0860			1.39044			0.695220	+	0.718797i	$0.255307\pi$
$152$	1.00115	+	3.08123i	0.0812041	+	0.249920i
$153$	9.50582	−	6.90638i	0.768500	−	0.558348i
$154$	3.36696	−	2.44624i	0.271318	−	0.197124i
$155$		0			0
$156$	16.8218	+	12.2217i	1.34682	+	0.978522i
$157$	7.49835			0.598433			0.299217	−	0.954185i	$-0.403275\pi$
$157$	7.49835			0.598433			0.299217	+	0.954185i	$0.403275\pi$
$158$	−31.2173	−	22.6807i	−2.48352	−	1.80438i
$159$	0.218843	−	0.673530i	0.0173554	−	0.0534144i
$160$		0			0
$161$	7.12372	+	21.9246i	0.561428	+	1.72790i
$162$	7.62577	−	23.4697i	0.599137	−	1.84396i
$163$	−0.603383	+	1.85702i	−0.0472606	+	0.145453i	−0.971902	−	0.235386i	$-0.924365\pi$
$163$	−0.603383	+	1.85702i	−0.0472606	+	0.145453i	0.924641	+	0.380839i	$0.124365\pi$
$164$	−3.02993	−	9.32515i	−0.236597	−	0.728172i
$165$		0			0
$166$	10.4917	−	32.2900i	0.814310	−	2.50619i
$167$	−0.288478	−	0.209591i	−0.0223231	−	0.0162187i	0.576568	−	0.817049i	$-0.304392\pi$
$167$	−0.288478	−	0.209591i	−0.0223231	−	0.0162187i	−0.598891	+	0.800831i	$0.704392\pi$
$168$	27.1550			2.09506
$169$	4.84494	+	3.52006i	0.372688	+	0.270774i
$170$		0			0
$171$	1.83758	−	1.33508i	0.140523	−	0.102096i
$172$	−26.1824	+	19.0226i	−1.99639	+	1.45046i
$173$	3.07482	+	9.46332i	0.233774	+	0.719483i	0.997282	+	0.0736838i	$0.0234756\pi$
$173$	3.07482	+	9.46332i	0.233774	+	0.719483i	−0.763508	+	0.645799i	$0.776524\pi$
$174$	29.8297			2.26138
$175$		0			0
$176$	−0.404058			−0.0304570
$177$	−0.901021	−	2.77306i	−0.0677249	−	0.208436i
$178$	21.4197	−	15.5624i	1.60548	−	1.16645i
$179$	−12.4446	+	9.04154i	−0.930154	+	0.675797i	−0.946031	−	0.324077i	$-0.894946\pi$
$179$	−12.4446	+	9.04154i	−0.930154	+	0.675797i	0.0158762	+	0.999874i	$0.494946\pi$
$180$		0			0
$181$	−7.21576	−	5.24256i	−0.536343	−	0.389676i	0.286382	−	0.958116i	$-0.407547\pi$
$181$	−7.21576	−	5.24256i	−0.536343	−	0.389676i	−0.822725	+	0.568439i	$0.807547\pi$
$182$	−22.1379			−1.64097
$183$	11.5971	+	8.42578i	0.857282	+	0.622852i
$184$	6.50395	−	20.0171i	0.479478	−	1.47568i
$185$		0			0
$186$	−10.0206	−	30.8403i	−0.734748	−	2.26132i
$187$	0.785612	−	2.41787i	0.0574497	−	0.176812i
$188$	−5.65812	+	17.4139i	−0.412661	+	1.27004i
$189$	1.78834	+	5.50395i	0.130083	+	0.400353i
$190$		0			0
$191$	−3.51929	+	10.8313i	−0.254647	+	0.783724i	0.739252	+	0.673429i	$0.235179\pi$
$191$	−3.51929	+	10.8313i	−0.254647	+	0.783724i	−0.993899	+	0.110294i	$0.964821\pi$
$192$	23.2787	+	16.9130i	1.67999	+	1.22059i
$193$	−17.3321			−1.24759			−0.623795	−	0.781588i	$-0.714410\pi$
$193$	−17.3321			−1.24759			−0.623795	+	0.781588i	$0.714410\pi$
$194$	−1.59806	−	1.16106i	−0.114734	−	0.0833589i
$195$		0			0
$196$	−16.3315	+	11.8655i	−1.16654	+	0.847539i
$197$	21.0028	−	15.2595i	1.49639	−	1.08719i	0.524599	−	0.851350i	$-0.324215\pi$
$197$	21.0028	−	15.2595i	1.49639	−	1.08719i	0.971792	−	0.235842i	$-0.0757847\pi$
$198$	0.823200	+	2.53355i	0.0585023	+	0.180052i
$199$	−8.38571			−0.594447			−0.297223	−	0.954808i	$-0.596061\pi$
$199$	−8.38571			−0.594447			−0.297223	+	0.954808i	$0.596061\pi$
$200$		0			0
$201$	12.1706			0.858450
$202$	9.52403	+	29.3120i	0.670109	+	2.06238i
$203$	−16.1965	+	11.7675i	−1.13677	+	0.825913i
$204$	32.4454	−	23.5730i	2.27164	−	1.65044i
$205$		0			0
$206$	−1.56365	−	1.13606i	−0.108945	−	0.0791530i
$207$	−14.7559			−1.02561
$208$	1.73883	+	1.26333i	0.120566	+	0.0875965i
$209$	0.151868	−	0.467401i	0.0105049	−	0.0323308i
$210$		0			0
$211$	4.91754	+	15.1346i	0.338537	+	1.04191i	0.964953	+	0.262422i	$0.0845212\pi$
$211$	4.91754	+	15.1346i	0.338537	+	1.04191i	−0.626416	+	0.779489i	$0.715479\pi$
$212$	0.324204	−	0.997797i	0.0222664	−	0.0685290i
$213$	−0.108115	+	0.332743i	−0.00740789	+	0.0227991i
$214$	−0.0519584	−	0.159911i	−0.00355180	−	0.0109313i
$215$		0			0
$216$	1.63275	−	5.02510i	0.111095	−	0.341915i
$217$	17.6070	+	12.7922i	1.19524	+	0.868392i
$218$	−13.0174			−0.881647
$219$	−27.7046	−	20.1286i	−1.87210	−	1.36016i
$220$		0			0
$221$	−10.9406	+	7.94878i	−0.735941	+	0.534693i
$222$	19.9133	−	14.4678i	1.33649	−	0.971017i
$223$	0.117335	+	0.361121i	0.00785736	+	0.0241825i	0.954908	−	0.296901i	$-0.0959531\pi$
$223$	0.117335	+	0.361121i	0.00785736	+	0.0241825i	−0.947051	+	0.321083i	$0.895953\pi$
$224$	−16.8030			−1.12270
$225$		0			0
$226$	−6.05343			−0.402668
$227$	−6.27333	−	19.3073i	−0.416376	−	1.28147i	−0.911015	−	0.412374i	$-0.864700\pi$
$227$	−6.27333	−	19.3073i	−0.416376	−	1.28147i	0.494639	−	0.869099i	$-0.335300\pi$
$228$	6.27207	−	4.55693i	0.415378	−	0.301790i
$229$	9.63592	−	7.00091i	0.636759	−	0.462633i	−0.221976	−	0.975052i	$-0.571251\pi$
$229$	9.63592	−	7.00091i	0.636759	−	0.462633i	0.858735	+	0.512419i	$0.171251\pi$
$230$		0			0
$231$	−3.33253	−	2.42123i	−0.219264	−	0.159305i
$232$	18.2782			1.20002
$233$	−15.4207	−	11.2038i	−1.01024	−	0.733984i	−0.0459827	−	0.998942i	$-0.514642\pi$
$233$	−15.4207	−	11.2038i	−1.01024	−	0.733984i	−0.964260	+	0.264958i	$0.914642\pi$
$234$	4.37886	−	13.4767i	0.286255	−	0.881003i
$235$		0			0
$236$	−1.33481	−	4.10813i	−0.0868889	−	0.267417i
$237$	−11.8020	+	36.3229i	−0.766624	+	2.35943i
$238$	−13.1947	+	40.6092i	−0.855288	+	2.63230i
$239$	1.27467	+	3.92304i	0.0824517	+	0.253760i	0.983781	−	0.179375i	$-0.0574074\pi$
$239$	1.27467	+	3.92304i	0.0824517	+	0.253760i	−0.901329	+	0.433135i	$0.857407\pi$
$240$		0			0
$241$	5.00169	−	15.3936i	0.322187	−	0.991590i	−0.650507	−	0.759500i	$-0.725444\pi$
$241$	5.00169	−	15.3936i	0.322187	−	0.991590i	0.972694	−	0.232090i	$-0.0745564\pi$
$242$	−20.2341	−	14.7009i	−1.30070	−	0.945012i
$243$	−19.5948			−1.25701
$244$	17.1804	+	12.4823i	1.09986	+	0.799099i
$245$		0			0
$246$	−12.4552	+	9.04923i	−0.794115	+	0.576958i
$247$	−2.11493	+	1.53659i	−0.134570	+	0.0977708i
$248$	−6.14016	−	18.8975i	−0.389901	−	1.19999i
$249$	−33.6045			−2.12960
$250$		0			0
$251$	11.8718			0.749344			0.374672	−	0.927157i	$-0.377755\pi$
$251$	11.8718			0.749344			0.374672	+	0.927157i	$0.377755\pi$
$252$	−8.71546	−	26.8234i	−0.549022	−	1.68972i
$253$	−2.58297	+	1.87663i	−0.162390	+	0.117983i
$254$	−9.30546	+	6.76081i	−0.583876	+	0.424211i
$255$		0			0
$256$	16.8908	+	12.2719i	1.05568	+	0.766993i
$257$	18.9164			1.17997			0.589986	−	0.807414i	$-0.299133\pi$
$257$	18.9164			1.17997			0.589986	+	0.807414i	$0.299133\pi$
$258$	41.1105	+	29.8685i	2.55943	+	1.85953i
$259$	−5.10484	+	15.7111i	−0.317199	+	0.976239i
$260$		0			0
$261$	−3.95994	−	12.1874i	−0.245114	−	0.754383i
$262$	−1.94323	+	5.98065i	−0.120053	+	0.369486i
$263$	2.08495	−	6.41680i	0.128563	−	0.395677i	−0.865970	−	0.500096i	$-0.833298\pi$
$263$	2.08495	−	6.41680i	0.128563	−	0.395677i	0.994533	+	0.104419i	$0.0332982\pi$
$264$	1.16217	+	3.57679i	0.0715266	+	0.220136i
$265$		0			0
$266$	−2.55069	+	7.85022i	−0.156393	+	0.481328i
$267$	−21.2007	−	15.4032i	−1.29746	−	0.942661i
$268$	18.0301			1.10136
$269$	20.4947	+	14.8903i	1.24959	+	0.907877i	0.998198	−	0.0600099i	$-0.0191132\pi$
$269$	20.4947	+	14.8903i	1.24959	+	0.907877i	0.251387	+	0.967887i	$0.419113\pi$
$270$		0			0
$271$	−7.61070	+	5.52950i	−0.462317	+	0.335893i	−0.794440	−	0.607343i	$-0.792235\pi$
$271$	−7.61070	+	5.52950i	−0.462317	+	0.335893i	0.332122	+	0.943236i	$0.392235\pi$
$272$	3.35382	−	2.43669i	0.203355	−	0.147746i
$273$	6.77103	+	20.8391i	0.409801	+	1.26124i
$274$	−5.22995			−0.315953
$275$		0			0
$276$	−50.3653			−3.03163
$277$	1.84402	+	5.67530i	0.110796	+	0.340996i	0.991047	−	0.133513i	$-0.0426258\pi$
$277$	1.84402	+	5.67530i	0.110796	+	0.340996i	−0.880251	+	0.474509i	$0.842626\pi$
$278$	−20.3301	+	14.7707i	−1.21932	+	0.885887i
$279$	−11.2701	+	8.18820i	−0.674722	+	0.490215i
$280$		0			0
$281$	−8.95766	−	6.50812i	−0.534369	−	0.388242i	0.287620	−	0.957744i	$-0.407136\pi$
$281$	−8.95766	−	6.50812i	−0.534369	−	0.388242i	−0.821990	+	0.569503i	$0.807136\pi$
$282$	28.7497			1.71202
$283$	−2.44652	−	1.77750i	−0.145431	−	0.105661i	0.512691	−	0.858573i	$-0.328649\pi$
$283$	−2.44652	−	1.77750i	−0.145431	−	0.105661i	−0.658121	+	0.752912i	$0.728649\pi$
$284$	−0.160166	+	0.492939i	−0.00950409	+	0.0292506i
$285$		0			0
$286$	−0.947447	−	2.91594i	−0.0560237	−	0.172423i
$287$	3.19293	−	9.82684i	0.188473	−	0.580060i
$288$	3.32362	−	10.2291i	0.195846	−	0.602753i
$289$	2.80691	+	8.63880i	0.165113	+	0.508164i
$290$		0			0
$291$	−0.604161	+	1.85942i	−0.0354165	+	0.109001i
$292$	−41.0428	−	29.8194i	−2.40185	−	1.74505i
$293$	−6.26426			−0.365962			−0.182981	−	0.983116i	$-0.558575\pi$
$293$	−6.26426			−0.365962			−0.182981	+	0.983116i	$0.558575\pi$
$294$	25.6431	+	18.6308i	1.49553	+	1.08657i
$295$		0			0
$296$	12.2019	−	8.86520i	0.709221	−	0.515279i
$297$	−0.648428	+	0.471111i	−0.0376256	+	0.0273366i
$298$	−8.76062	−	26.9624i	−0.507489	−	1.56189i
$299$	16.9831			0.982158
$300$		0			0
$301$	−34.1043			−1.96574
$302$	−12.2815	−	37.7986i	−0.706721	−	2.17506i
$303$	24.6793	−	17.9305i	1.41779	−	1.03008i
$304$	0.648331	−	0.471040i	0.0371843	−	0.0270160i
$305$		0			0
$306$	−22.1115	−	16.0650i	−1.26403	−	0.918372i
$307$	−25.8734			−1.47667			−0.738337	−	0.674432i	$-0.764388\pi$
$307$	−25.8734			−1.47667			−0.738337	+	0.674432i	$0.764388\pi$
$308$	−4.93696	−	3.58691i	−0.281309	−	0.204383i
$309$	−0.591154	+	1.81938i	−0.0336296	+	0.103501i
$310$		0			0
$311$	−2.78201	−	8.56214i	−0.157753	−	0.485514i	0.840676	−	0.541538i	$-0.182158\pi$
$311$	−2.78201	−	8.56214i	−0.157753	−	0.485514i	−0.998429	+	0.0560237i	$0.982158\pi$
$312$	6.18194	−	19.0261i	0.349984	−	1.07714i
$313$	10.2678	−	31.6011i	0.580372	−	1.78620i	−0.0367373	−	0.999325i	$-0.511696\pi$
$313$	10.2678	−	31.6011i	0.580372	−	1.78620i	0.617110	−	0.786877i	$-0.288304\pi$
$314$	−5.38985	−	16.5882i	−0.304167	−	0.936129i
$315$		0			0
$316$	−17.4840	+	53.8103i	−0.983554	+	3.02707i
$317$	−21.0096	−	15.2644i	−1.18002	−	0.857332i	−0.187843	−	0.982199i	$-0.560150\pi$
$317$	−21.0096	−	15.2644i	−1.18002	−	0.857332i	−0.992174	+	0.124867i	$0.960150\pi$
$318$	−1.64733			−0.0923774
$319$	−2.24315	−	1.62974i	−0.125592	−	0.0912480i
$320$		0			0
$321$	−0.134638	+	0.0978200i	−0.00751475	+	0.00545978i
$322$	43.3821	−	31.5190i	2.41759	−	1.75648i
$323$	1.55813	+	4.79543i	0.0866966	+	0.266825i
$324$	−36.1845			−2.01025
$325$		0			0
$326$	4.54192			0.251554
$327$	3.98145	+	12.2536i	0.220175	+	0.677628i
$328$	−7.63195	+	5.54494i	−0.421404	+	0.306168i
$329$	−15.6101	+	11.3414i	−0.860612	+	0.625272i
$330$		0			0
$331$	−9.81206	−	7.12888i	−0.539320	−	0.391839i	0.284513	−	0.958672i	$-0.408168\pi$
$331$	−9.81206	−	7.12888i	−0.539320	−	0.391839i	−0.823832	+	0.566834i	$0.808168\pi$
$332$	−49.7832			−2.73221
$333$	−8.55460	−	6.21528i	−0.468789	−	0.340595i
$334$	−0.256310	+	0.788841i	−0.0140247	+	0.0431635i
$335$		0			0
$336$	−2.07565	−	6.38820i	−0.113236	−	0.348505i
$337$	9.34835	−	28.7713i	0.509237	−	1.56727i	−0.284292	−	0.958738i	$-0.591759\pi$
$337$	9.34835	−	28.7713i	0.509237	−	1.56727i	0.793529	−	0.608533i	$-0.208241\pi$
$338$	4.30469	−	13.2485i	0.234144	−	0.720622i
$339$	1.85148	+	5.69828i	0.100559	+	0.309488i
$340$		0			0
$341$	−0.931421	+	2.86662i	−0.0504393	+	0.155236i
$342$	−4.27440	−	3.10554i	−0.231133	−	0.167928i
$343$	3.88680			0.209867
$344$	25.1905	+	18.3020i	1.35818	+	0.986777i
$345$		0			0
$346$	18.7251	−	13.6046i	1.00667	−	0.731386i
$347$	−10.7828	+	7.83419i	−0.578853	+	0.420561i	−0.838310	−	0.545193i	$-0.816456\pi$
$347$	−10.7828	+	7.83419i	−0.578853	+	0.420561i	0.259457	+	0.965755i	$0.416456\pi$
$348$	−13.5161	−	41.5984i	−0.724541	−	2.22991i
$349$	−27.4444			−1.46906			−0.734532	−	0.678574i	$-0.762598\pi$
$349$	−27.4444			−1.46906			−0.734532	+	0.678574i	$0.762598\pi$
$350$		0			0
$351$	4.26344			0.227566
$352$	−0.719127	−	2.21325i	−0.0383296	−	0.117966i
$353$	12.5854	−	9.14382i	0.669853	−	0.486676i	−0.200123	−	0.979771i	$-0.564134\pi$
$353$	12.5854	−	9.14382i	0.669853	−	0.486676i	0.869976	+	0.493094i	$0.164134\pi$
$354$	−5.48705	+	3.98658i	−0.291634	+	0.211884i
$355$		0			0
$356$	−31.4076	−	22.8190i	−1.66460	−	1.20940i
$357$	42.2624			2.23676
$358$	28.9474	+	21.0315i	1.52992	+	1.11155i
$359$	−6.79310	+	20.9070i	−0.358526	+	1.10343i	0.595410	+	0.803422i	$0.296989\pi$
$359$	−6.79310	+	20.9070i	−0.358526	+	1.10343i	−0.953937	+	0.300008i	$0.903011\pi$
$360$		0			0
$361$	−5.57012	−	17.1431i	−0.293164	−	0.902267i
$362$	−6.41114	+	19.7315i	−0.336962	+	1.03706i
$363$	−7.64970	+	23.5434i	−0.401505	+	1.23571i
$364$	10.0309	+	30.8719i	0.525762	+	1.61813i
$365$		0			0
$366$	10.3039	−	31.7122i	0.538594	−	1.65762i
$367$	9.79748	+	7.11829i	0.511424	+	0.371571i	0.813364	−	0.581756i	$-0.197634\pi$
$367$	9.79748	+	7.11829i	0.511424	+	0.371571i	−0.301939	+	0.953327i	$0.597634\pi$
$368$	−5.20615			−0.271389
$369$	5.35066	+	3.88749i	0.278544	+	0.202374i
$370$		0			0
$371$	0.894441	−	0.649850i	0.0464371	−	0.0337385i
$372$	−38.4673	+	27.9481i	−1.99443	+	1.44904i
$373$	−2.18971	−	6.73922i	−0.113379	−	0.348944i	0.878227	−	0.478245i	$-0.158727\pi$
$373$	−2.18971	−	6.73922i	−0.113379	−	0.348944i	−0.991605	+	0.129301i	$0.958727\pi$
$374$	−5.91364			−0.305787
$375$		0			0
$376$	17.6164			0.908499
$377$	4.55762	+	14.0269i	0.234729	+	0.722423i
$378$	10.8907	−	7.91253i	0.560155	−	0.406977i
$379$	17.3963	−	12.6391i	0.893586	−	0.649228i	−0.0432246	−	0.999065i	$-0.513763\pi$
$379$	17.3963	−	12.6391i	0.893586	−	0.649228i	0.936810	+	0.349837i	$0.113763\pi$
$380$		0			0
$381$	9.21029	+	6.69167i	0.471858	+	0.342825i
$382$	26.4912			1.35541
$383$	20.1297	+	14.6251i	1.02858	+	0.747305i	0.968023	−	0.250860i	$-0.0807132\pi$
$383$	20.1297	+	14.6251i	1.02858	+	0.747305i	0.0605541	+	0.998165i	$0.480713\pi$
$384$	14.0309	−	43.1825i	0.716009	−	2.20365i
$385$		0			0
$386$	12.4584	+	38.3429i	0.634115	+	1.95160i
$387$	6.74581	−	20.7615i	0.342909	−	1.05536i
$388$	−0.895030	+	2.75462i	−0.0454383	+	0.139845i
$389$	−10.9436	−	33.6809i	−0.554862	−	1.70769i	−0.696308	−	0.717743i	$-0.745175\pi$
$389$	−10.9436	−	33.6809i	−0.554862	−	1.70769i	0.141446	−	0.989946i	$-0.454825\pi$
$390$		0			0
$391$	10.1223	−	31.1534i	0.511909	−	1.57549i
$392$	15.7129	+	11.4161i	0.793619	+	0.576598i
$393$	6.22412			0.313965
$394$	−48.8547	−	35.4950i	−2.46127	−	1.78821i
$395$		0			0
$396$	3.16011	−	2.29595i	0.158801	−	0.115376i
$397$	4.44720	−	3.23108i	0.223199	−	0.162163i	−0.470567	−	0.882364i	$-0.655950\pi$
$397$	4.44720	−	3.23108i	0.223199	−	0.162163i	0.693765	+	0.720201i	$0.255950\pi$
$398$	6.02769	+	18.5513i	0.302141	+	0.929893i
$399$	8.16980			0.409001
$400$		0			0
$401$	24.8463			1.24077			0.620383	−	0.784299i	$-0.286977\pi$
$401$	24.8463			1.24077			0.620383	+	0.784299i	$0.286977\pi$
$402$	−8.74830	−	26.9245i	−0.436326	−	1.34287i
$403$	12.9711	−	9.42406i	0.646137	−	0.469446i
$404$	36.5609	−	26.5631i	1.81897	−	1.32156i
$405$		0			0
$406$	37.6747	+	27.3723i	1.86976	+	1.35846i
$407$	−2.28789			−0.113407
$408$	−31.2164	−	22.6800i	−1.54544	−	1.12283i
$409$	1.21492	−	3.73915i	0.0600741	−	0.184889i	−0.916516	−	0.399998i	$-0.869011\pi$
$409$	1.21492	−	3.73915i	0.0600741	−	0.184889i	0.976590	+	0.215109i	$0.0690107\pi$
$410$		0			0
$411$	1.59962	+	4.92312i	0.0789033	+	0.242839i
$412$	−0.875761	+	2.69531i	−0.0431456	+	0.132789i
$413$	1.40663	−	4.32915i	0.0692155	−	0.213023i
$414$	10.6066	+	32.6439i	0.521288	+	1.60436i
$415$		0			0
$416$	−3.82526	+	11.7730i	−0.187549	+	0.577216i
$417$	20.1222	+	14.6196i	0.985388	+	0.715926i
$418$	−1.14317			−0.0559144
$419$	3.85581	+	2.80141i	0.188369	+	0.136858i	0.677973	−	0.735087i	$-0.262859\pi$
$419$	3.85581	+	2.80141i	0.188369	+	0.136858i	−0.489604	+	0.871945i	$0.662859\pi$
$420$		0			0
$421$	−12.9913	+	9.43872i	−0.633157	+	0.460015i	−0.857492	−	0.514497i	$-0.827979\pi$
$421$	−12.9913	+	9.43872i	−0.633157	+	0.460015i	0.224336	+	0.974512i	$0.427979\pi$
$422$	29.9469	−	21.7577i	1.45779	−	1.05915i
$423$	−3.81657	−	11.7462i	−0.185568	−	0.571119i
$424$	−1.00940			−0.0490209
$425$		0			0
$426$	0.813824			0.0394299
$427$	6.91540	+	21.2834i	0.334659	+	1.02998i
$428$	−0.199458	+	0.144915i	−0.00964118	+	0.00700473i
$429$	−2.45508	+	1.78372i	−0.118533	+	0.0861189i
$430$		0			0
$431$	33.4684	+	24.3162i	1.61212	+	1.17127i	0.856277	+	0.516517i	$0.172772\pi$
$431$	33.4684	+	24.3162i	1.61212	+	1.17127i	0.755841	+	0.654755i	$0.227228\pi$
$432$	−1.30695			−0.0628808
$433$	12.2852	+	8.92574i	0.590391	+	0.428944i	0.842455	−	0.538767i	$-0.181110\pi$
$433$	12.2852	+	8.92574i	0.590391	+	0.428944i	−0.252065	+	0.967710i	$0.581110\pi$
$434$	15.6437	−	48.1462i	0.750920	−	2.31109i
$435$		0			0
$436$	5.89829	+	18.1531i	0.282477	+	0.869375i
$437$	1.95676	−	6.02230i	0.0936047	−	0.288086i
$438$	−24.6153	+	75.7582i	−1.17617	+	3.61986i
$439$	5.29018	+	16.2815i	0.252486	+	0.777074i	0.994314	+	0.106483i	$0.0339591\pi$
$439$	5.29018	+	16.2815i	0.252486	+	0.777074i	−0.741828	+	0.670590i	$0.766041\pi$
$440$		0			0
$441$	4.20777	−	12.9502i	0.200370	−	0.616675i
$442$	25.4488	+	18.4897i	1.21048	+	0.879464i
$443$	−35.3909			−1.68147			−0.840736	−	0.541445i	$-0.817877\pi$
$443$	−35.3909			−1.68147			−0.840736	+	0.541445i	$0.817877\pi$
$444$	−29.1987	−	21.2141i	−1.38571	−	1.00678i
$445$		0			0
$446$	0.714551	−	0.519152i	0.0338350	−	0.0245825i
$447$	−22.7011	+	16.4933i	−1.07372	+	0.780106i
$448$	13.8812	+	42.7219i	0.655824	+	2.01842i
$449$	20.6830			0.976090			0.488045	−	0.872818i	$-0.337710\pi$
$449$	20.6830			0.976090			0.488045	+	0.872818i	$0.337710\pi$
$450$		0			0
$451$	1.43101			0.0673838
$452$	2.74287	+	8.44168i	0.129014	+	0.397063i
$453$	−31.8246	+	23.1219i	−1.49525	+	1.08636i
$454$	−38.2034	+	27.7564i	−1.79298	+	1.30267i
$455$		0			0
$456$	−6.03447	−	4.38430i	−0.282590	−	0.205314i
$457$	−41.7664			−1.95375			−0.976876	−	0.213807i	$-0.931414\pi$
$457$	−41.7664			−1.95375			−0.976876	+	0.213807i	$0.931414\pi$
$458$	−22.4141	−	16.2848i	−1.04734	−	0.760940i
$459$	2.54112	−	7.82075i	0.118609	−	0.365041i
$460$		0			0
$461$	−3.29979	−	10.1557i	−0.153686	−	0.472998i	0.844339	−	0.535809i	$-0.179993\pi$
$461$	−3.29979	−	10.1557i	−0.153686	−	0.472998i	−0.998025	+	0.0628112i	$0.979993\pi$
$462$	−2.96093	+	9.11279i	−0.137755	+	0.423965i
$463$	2.41971	−	7.44709i	0.112453	−	0.346096i	−0.878954	−	0.476906i	$-0.841758\pi$
$463$	2.41971	−	7.44709i	0.112453	−	0.346096i	0.991407	+	0.130811i	$0.0417581\pi$
$464$	−1.39713	−	4.29994i	−0.0648603	−	0.199620i
$465$		0			0
$466$	−13.7012	+	42.1678i	−0.634694	+	1.95339i
$467$	4.02971	+	2.92776i	0.186473	+	0.135480i	0.677105	−	0.735886i	$-0.263234\pi$
$467$	4.02971	+	2.92776i	0.186473	+	0.135480i	−0.490632	+	0.871367i	$0.663234\pi$
$468$	−20.7778			−0.960455
$469$	15.3714	+	11.1680i	0.709786	+	0.515690i
$470$		0			0
$471$	−13.9665	+	10.1473i	−0.643542	+	0.467561i
$472$	−3.36220	+	2.44278i	−0.154758	+	0.112438i
$473$	−1.45958	−	4.49213i	−0.0671116	−	0.206548i
$474$	88.8388			4.08050
$475$		0			0
$476$	62.6094			2.86970
$477$	0.218685	+	0.673043i	0.0100129	+	0.0308165i
$478$	7.76252	−	5.63980i	0.355049	−	0.257958i
$479$	13.2663	−	9.63854i	0.606153	−	0.440396i	−0.241904	−	0.970300i	$-0.577772\pi$
$479$	13.2663	−	9.63854i	0.606153	−	0.440396i	0.848058	+	0.529904i	$0.177772\pi$
$480$		0			0
$481$	9.84576	+	7.15336i	0.448928	+	0.326165i
$482$	−37.6498			−1.71490
$483$	−42.9385	−	31.1966i	−1.95377	−	1.41950i
$484$	−11.3326	+	34.8782i	−0.515118	+	1.58537i
$485$		0			0
$486$	14.0848	+	43.3486i	0.638901	+	1.96633i
$487$	−0.270856	+	0.833609i	−0.0122737	+	0.0377744i	−0.957006	−	0.290069i	$-0.906322\pi$
$487$	−0.270856	+	0.833609i	−0.0122737	+	0.0377744i	0.944732	+	0.327843i	$0.106322\pi$
$488$	6.31375	−	19.4317i	0.285810	−	0.879633i
$489$	−1.38918	−	4.27545i	−0.0628208	−	0.193343i
$490$		0			0
$491$	3.77366	−	11.6141i	0.170303	−	0.524138i	−0.829085	−	0.559123i	$-0.811138\pi$
$491$	3.77366	−	11.6141i	0.170303	−	0.524138i	0.999388	+	0.0349842i	$0.0111381\pi$
$492$	18.2630	+	13.2688i	0.823359	+	0.598205i
$493$	28.4471			1.28119
$494$	4.91955	+	3.57426i	0.221341	+	0.160814i
$495$		0			0
$496$	−3.97628	+	2.88894i	−0.178540	+	0.129717i
$497$	−0.441879	+	0.321044i	−0.0198210	+	0.0144008i
$498$	24.1551	+	74.3417i	1.08241	+	3.33133i
$499$	−3.34603			−0.149789			−0.0748945	−	0.997191i	$-0.523862\pi$
$499$	−3.34603			−0.149789			−0.0748945	+	0.997191i	$0.523862\pi$
$500$		0			0
$501$	0.820954			0.0366775
$502$	−8.53353	−	26.2635i	−0.380870	−	1.17220i
$503$	9.61274	−	6.98407i	0.428611	−	0.311404i	−0.352482	−	0.935819i	$-0.614662\pi$
$503$	9.61274	−	6.98407i	0.428611	−	0.311404i	0.781093	+	0.624414i	$0.214662\pi$
$504$	−21.9530	+	15.9498i	−0.977864	+	0.710460i
$505$		0			0
$506$	6.00824	+	4.36524i	0.267099	+	0.194059i
$507$	−13.7878			−0.612339
$508$	13.6445	+	9.91333i	0.605378	+	0.439833i
$509$	11.2230	−	34.5407i	0.497449	−	1.53099i	−0.315655	−	0.948874i	$-0.602224\pi$
$509$	11.2230	−	34.5407i	0.497449	−	1.53099i	0.813105	−	0.582118i	$-0.197776\pi$
$510$		0			0
$511$	−16.5204	−	50.8445i	−0.730819	−	2.24923i
$512$	2.81886	−	8.67556i	0.124577	−	0.383409i
$513$	0.491226	−	1.51184i	0.0216882	−	0.0667493i
$514$	−13.5972	−	41.8478i	−0.599746	−	1.84583i
$515$		0			0
$516$	23.0249	−	70.8634i	1.01362	−	3.11959i
$517$	−2.16193	−	1.57074i	−0.0950816	−	0.0690809i
$518$	38.4263			1.68835
$519$	−18.5336	−	13.4654i	−0.813534	−	0.591067i
$520$		0			0
$521$	−0.165221	+	0.120040i	−0.00723845	+	0.00525904i	−0.591399	−	0.806379i	$-0.701424\pi$
$521$	−0.165221	+	0.120040i	−0.00723845	+	0.00525904i	0.584160	+	0.811638i	$0.301424\pi$
$522$	−24.1153	+	17.5208i	−1.05550	+	0.766864i
$523$	−8.66211	−	26.6592i	−0.378768	−	1.16573i	−0.940901	−	0.338681i	$-0.890019\pi$
$523$	−8.66211	−	26.6592i	−0.378768	−	1.16573i	0.562134	−	0.827046i	$-0.309981\pi$
$524$	9.22069			0.402808
$525$		0			0
$526$	−15.6943			−0.684303
$527$	−9.55616	−	29.4108i	−0.416273	−	1.28116i
$528$	0.752603	−	0.546798i	0.0327529	−	0.0237963i
$529$	−14.6732	+	10.6607i	−0.637967	+	0.463510i
$530$		0			0
$531$	2.35720	+	1.71260i	0.102294	+	0.0743207i
$532$	12.1031			0.524736
$533$	−6.15825	−	4.47423i	−0.266743	−	0.193800i
$534$	−18.8366	+	57.9732i	−0.815141	+	2.50875i
$535$		0			0
$536$	−5.36054	−	16.4981i	−0.231540	−	0.712608i
$537$	10.9439	−	33.6818i	0.472263	−	1.45348i
$538$	18.2094	−	56.0427i	0.785062	−	2.41617i
$539$	−0.910429	−	2.80201i	−0.0392149	−	0.120691i
$540$		0			0
$541$	−2.88071	+	8.86590i	−0.123851	+	0.381175i	−0.993690	−	0.112161i	$-0.964223\pi$
$541$	−2.88071	+	8.86590i	−0.123851	+	0.381175i	0.869839	+	0.493336i	$0.164223\pi$
$542$	17.7033	+	12.8622i	0.760421	+	0.552478i
$543$	20.5347			0.881230
$544$	19.3161	+	14.0339i	0.828169	+	0.601700i
$545$		0			0
$546$	41.2343	−	29.9585i	1.76466	−	1.28210i
$547$	−16.2109	+	11.7779i	−0.693129	+	0.503588i	−0.877687	−	0.479234i	$-0.840915\pi$
$547$	−16.2109	+	11.7779i	−0.693129	+	0.503588i	0.184558	+	0.982822i	$0.440915\pi$
$548$	2.36974	+	7.29332i	0.101230	+	0.311555i
$549$	−14.3244			−0.611351
$550$		0			0
$551$	5.49914			0.234271
$552$	14.9741	+	46.0857i	0.637342	+	1.96154i
$553$	−48.2364	+	35.0458i	−2.05122	+	1.49030i
$554$	11.2297	−	8.15886i	0.477105	−	0.346637i
$555$		0			0
$556$	29.8099	+	21.6582i	1.26422	+	0.918511i
$557$	28.9839			1.22809			0.614043	−	0.789272i	$-0.289542\pi$
$557$	28.9839			1.22809			0.614043	+	0.789272i	$0.289542\pi$
$558$	26.2154	+	19.0466i	1.10979	+	0.806306i
$559$	−7.76397	+	23.8950i	−0.328381	+	1.01065i
$560$		0			0
$561$	1.80873	+	5.56669i	0.0763645	+	0.235026i
$562$	−7.95880	+	24.4947i	−0.335722	+	1.03325i
$563$	−4.23431	+	13.0319i	−0.178455	+	0.549228i	−0.999774	−	0.0212408i	$-0.993238\pi$
$563$	−4.23431	+	13.0319i	−0.178455	+	0.549228i	0.821320	+	0.570468i	$0.193238\pi$
$564$	−13.0268	−	40.0923i	−0.548526	−	1.68819i
$565$		0			0
$566$	−2.17371	+	6.69000i	−0.0913680	+	0.281202i
$567$	−30.8488	−	22.4130i	−1.29553	−	0.941256i
$568$	0.498673			0.0209239
$569$	−28.0043	−	20.3463i	−1.17400	−	0.852962i	−0.182519	−	0.983202i	$-0.558425\pi$
$569$	−28.0043	−	20.3463i	−1.17400	−	0.852962i	−0.991482	+	0.130241i	$0.958425\pi$
$570$		0			0
$571$	34.3182	−	24.9337i	1.43617	−	1.04344i	0.447349	−	0.894360i	$-0.352368\pi$
$571$	34.3182	−	24.9337i	1.43617	−	1.04344i	0.988825	−	0.149082i	$-0.0476317\pi$
$572$	−3.63707	+	2.64248i	−0.152073	+	0.110488i
$573$	−8.10252	−	24.9370i	−0.338488	−	1.04176i
$574$	−24.0346			−1.00318
$575$		0			0
$576$	−28.7532			−1.19805
$577$	10.6008	+	32.6259i	0.441317	+	1.35824i	0.886472	+	0.462782i	$0.153149\pi$
$577$	10.6008	+	32.6259i	0.441317	+	1.35824i	−0.445155	+	0.895454i	$0.646851\pi$
$578$	17.0936	−	12.4192i	0.710999	−	0.516571i
$579$	32.2829	−	23.4549i	1.34163	−	0.974752i
$580$		0			0
$581$	−42.4422	−	30.8361i	−1.76080	−	1.27930i
$582$	4.54777			0.188511
$583$	0.123876	+	0.0900014i	0.00513043	+	0.00372748i
$584$	−15.0831	+	46.4210i	−0.624143	+	1.92091i
$585$		0			0
$586$	4.50278	+	13.8581i	0.186008	+	0.572474i
$587$	−9.19392	+	28.2960i	−0.379474	+	1.16790i	0.560937	+	0.827859i	$0.310441\pi$
$587$	−9.19392	+	28.2960i	−0.379474	+	1.16790i	−0.940411	+	0.340041i	$0.889559\pi$
$588$	14.3620	−	44.2018i	0.592280	−	1.82285i
$589$	−1.84731	−	5.68545i	−0.0761173	−	0.234265i
$590$		0			0
$591$	−18.4700	+	56.8449i	−0.759755	+	2.33828i
$592$	−3.01821	−	2.19286i	−0.124048	−	0.0901259i
$593$	14.8105			0.608195			0.304098	−	0.952641i	$-0.401645\pi$
$593$	14.8105			0.608195			0.304098	+	0.952641i	$0.401645\pi$
$594$	1.50831	+	1.09585i	0.0618867	+	0.0449633i
$595$		0			0
$596$	−33.6303	+	24.4339i	−1.37755	+	1.00085i
$597$	15.6193	−	11.3481i	0.639256	−	0.464446i
$598$	−12.2075	−	37.5709i	−0.499203	−	1.53639i
$599$	27.2394			1.11297			0.556486	−	0.830857i	$-0.312149\pi$
$599$	27.2394			1.11297			0.556486	+	0.830857i	$0.312149\pi$
$600$		0			0
$601$	33.1682			1.35296			0.676480	−	0.736461i	$-0.263505\pi$
$601$	33.1682			1.35296			0.676480	+	0.736461i	$0.263505\pi$
$602$	24.5143	+	75.4474i	0.999130	+	3.07501i
$603$	−9.83912	+	7.14854i	−0.400680	+	0.291111i
$604$	−47.1463	+	34.2538i	−1.91836	+	1.39377i
$605$		0			0
$606$	−57.4065	−	41.7082i	−2.33198	−	1.69428i
$607$	−5.79849			−0.235353			−0.117677	−	0.993052i	$-0.537545\pi$
$607$	−5.79849			−0.235353			−0.117677	+	0.993052i	$0.537545\pi$
$608$	3.73401	+	2.71292i	0.151434	+	0.110023i
$609$	14.2433	−	43.8364i	0.577168	−	1.77634i
$610$		0			0
$611$	4.39261	+	13.5191i	0.177706	+	0.546922i
$612$	−12.3841	+	38.1143i	−0.500597	+	1.54068i
$613$	−1.25045	+	3.84848i	−0.0505051	+	0.155439i	−0.973128	−	0.230264i	$-0.926041\pi$
$613$	−1.25045	+	3.84848i	−0.0505051	+	0.155439i	0.922623	+	0.385703i	$0.126041\pi$
$614$	18.5979	+	57.2385i	0.750551	+	2.30996i
$615$		0			0
$616$	−1.81431	+	5.58389i	−0.0731008	+	0.224981i
$617$	30.0752	+	21.8509i	1.21078	+	0.879683i	0.995301	−	0.0968252i	$-0.0308688\pi$
$617$	30.0752	+	21.8509i	1.21078	+	0.879683i	0.215479	+	0.976509i	$0.430869\pi$
$618$	4.44986			0.179000
$619$	30.5095	+	22.1664i	1.22628	+	0.890944i	0.996606	−	0.0823236i	$-0.0262341\pi$
$619$	30.5095	+	22.1664i	1.22628	+	0.890944i	0.229674	+	0.973268i	$0.426234\pi$
$620$		0			0
$621$	−8.35477	+	6.07010i	−0.335266	+	0.243585i
$622$	−16.9419	+	12.3090i	−0.679309	+	0.493547i
$623$	−12.6421	−	38.9083i	−0.506494	−	1.55883i
$624$	−4.94839			−0.198094
$625$		0			0
$626$	−77.2903			−3.08914
$627$	0.349647	+	1.07610i	0.0139636	+	0.0429754i
$628$	−20.6906	+	15.0326i	−0.825644	+	0.599866i
$629$	18.9903	−	13.7972i	0.757192	−	0.550132i
$630$		0			0
$631$	−14.9850	−	10.8872i	−0.596543	−	0.433414i	0.248107	−	0.968733i	$-0.420192\pi$
$631$	−14.9850	−	10.8872i	−0.596543	−	0.433414i	−0.844650	+	0.535319i	$0.820192\pi$
$632$	54.4362			2.16536
$633$	−29.6406	−	21.5352i	−1.17811	−	0.855947i
$634$	−18.6669	+	57.4507i	−0.741356	+	2.28166i
$635$		0			0
$636$	0.746419	+	2.29724i	0.0295975	+	0.0910916i
$637$	−4.84286	+	14.9048i	−0.191881	+	0.590549i
$638$	−1.99302	+	6.13388i	−0.0789043	+	0.242843i
$639$	−0.108036	−	0.332502i	−0.00427385	−	0.0131536i
$640$		0			0
$641$	−6.09121	+	18.7468i	−0.240588	+	0.740454i	0.755743	+	0.654869i	$0.227276\pi$
$641$	−6.09121	+	18.7468i	−0.240588	+	0.740454i	−0.996331	+	0.0855856i	$0.972724\pi$
$642$	0.313181	+	0.227539i	0.0123603	+	0.00898026i
$643$	−42.5897			−1.67957			−0.839787	−	0.542916i	$-0.817320\pi$
$643$	−42.5897			−1.67957			−0.839787	+	0.542916i	$0.817320\pi$
$644$	−63.6110	−	46.2161i	−2.50662	−	1.82117i
$645$		0			0
$646$	9.48871	−	6.89395i	0.373328	−	0.271239i
$647$	22.1685	−	16.1064i	0.871535	−	0.633207i	−0.0594633	−	0.998230i	$-0.518939\pi$
$647$	22.1685	−	16.1064i	0.871535	−	0.633207i	0.930998	+	0.365023i	$0.118939\pi$
$648$	10.7580	+	33.1099i	0.422616	+	1.30068i
$649$	0.630424			0.0247463
$650$		0			0
$651$	−50.1062			−1.96382
$652$	−2.05799	−	6.33384i	−0.0805971	−	0.248052i
$653$	17.3465	−	12.6030i	0.678820	−	0.493192i	−0.194146	−	0.980973i	$-0.562193\pi$
$653$	17.3465	−	12.6030i	0.678820	−	0.493192i	0.872966	+	0.487781i	$0.162193\pi$
$654$	24.2463	−	17.6160i	0.948105	−	0.688838i
$655$		0			0
$656$	1.88781	+	1.37157i	0.0737064	+	0.0535509i
$657$	34.2200			1.33505
$658$	36.3107	+	26.3812i	1.41554	+	1.02845i
$659$	−11.3515	+	34.9363i	−0.442191	+	1.36092i	0.443344	+	0.896351i	$0.353792\pi$
$659$	−11.3515	+	34.9363i	−0.442191	+	1.36092i	−0.885535	+	0.464572i	$0.846208\pi$
$660$		0			0
$661$	−4.86750	−	14.9806i	−0.189324	−	0.582678i	0.810672	−	0.585500i	$-0.199102\pi$
$661$	−4.86750	−	14.9806i	−0.189324	−	0.582678i	−0.999996	+	0.00282182i	$0.999102\pi$
$662$	−8.71794	+	26.8310i	−0.338832	+	1.04282i
$663$	9.62119	−	29.6110i	0.373656	−	1.14999i
$664$	14.8011	+	45.5530i	0.574393	+	1.76780i
$665$		0			0
$666$	−7.60069	+	23.3925i	−0.294521	+	0.906442i
$667$	−28.9022	−	20.9987i	−1.11910	−	0.813071i
$668$	1.21620			0.0470561
$669$	−0.707244	−	0.513843i	−0.0273436	−	0.0198663i
$670$		0			0
$671$	−2.50743	+	1.82175i	−0.0967982	+	0.0703280i
$672$	31.2975	−	22.7389i	1.20733	−	0.877173i
$673$	−9.58283	−	29.4929i	−0.369391	−	1.13687i	−0.947186	−	0.320686i	$-0.896087\pi$
$673$	−9.58283	−	29.4929i	−0.369391	−	1.13687i	0.577795	−	0.816182i	$-0.303913\pi$
$674$	−70.3690			−2.71051
$675$		0			0
$676$	−20.4259			−0.785611
$677$	2.96620	+	9.12902i	0.114000	+	0.350857i	0.991737	−	0.128286i	$-0.0409476\pi$
$677$	2.96620	+	9.12902i	0.114000	+	0.350857i	−0.877737	+	0.479143i	$0.840948\pi$
$678$	11.2752	−	8.19190i	0.433021	−	0.314608i
$679$	−2.46928	+	1.79404i	−0.0947624	+	0.0688489i
$680$		0			0
$681$	37.8127	+	27.4726i	1.44899	+	1.05275i
$682$	7.01120			0.268473
$683$	−0.702510	−	0.510403i	−0.0268808	−	0.0195300i	0.574264	−	0.818670i	$-0.305288\pi$
$683$	−0.702510	−	0.510403i	−0.0268808	−	0.0195300i	−0.601145	+	0.799140i	$0.705288\pi$
$684$	−2.39398	+	7.36793i	−0.0915363	+	0.281720i
$685$		0			0
$686$	−2.79385	−	8.59859i	−0.106670	−	0.328296i
$687$	−8.47388	+	26.0799i	−0.323299	+	0.995011i
$688$	2.38004	−	7.32500i	0.0907381	−	0.279263i
$689$	−0.251692	−	0.774627i	−0.00958868	−	0.0295109i
$690$		0			0
$691$	−4.05970	+	12.4945i	−0.154438	+	0.475312i	−0.998104	−	0.0615577i	$-0.980393\pi$
$691$	−4.05970	+	12.4945i	−0.154438	+	0.475312i	0.843665	+	0.536869i	$0.180393\pi$
$692$	−27.4565	−	19.9483i	−1.04374	−	0.758320i
$693$	4.11625			0.156364
$694$	25.0820	+	18.2231i	0.952099	+	0.691740i
$695$		0			0
$696$	−34.0452	+	24.7353i	−1.29048	+	0.937589i
$697$	−11.8779	+	8.62979i	−0.449907	+	0.326877i
$698$	19.7272	+	60.7139i	0.746684	+	2.29806i
$699$	43.8844			1.65986
$700$		0			0
$701$	7.13602			0.269524			0.134762	−	0.990878i	$-0.456973\pi$
$701$	7.13602			0.269524			0.134762	+	0.990878i	$0.456973\pi$
$702$	−3.06458	−	9.43181i	−0.115665	−	0.355981i
$703$	3.67103	−	2.66716i	0.138456	−	0.100594i
$704$	−5.03313	+	3.65678i	−0.189693	+	0.137820i
$705$		0			0
$706$	−29.2749	−	21.2695i	−1.10178	−	0.800486i
$707$	47.6231			1.79105
$708$	8.04563	+	5.84549i	0.302373	+	0.219687i
$709$	−2.47372	+	7.61333i	−0.0929025	+	0.285925i	−0.986701	−	0.162543i	$-0.948030\pi$
$709$	−2.47372	+	7.61333i	−0.0929025	+	0.285925i	0.893799	+	0.448468i	$0.148030\pi$
$710$		0			0
$711$	−11.7935	−	36.2966i	−0.442290	−	1.36123i
$712$	−11.5422	+	35.5232i	−0.432562	+	1.33129i
$713$	−12.0010	+	36.9354i	−0.449442	+	1.38324i
$714$	−30.3784	−	93.4952i	−1.13688	−	3.49897i
$715$		0			0
$716$	16.2127	−	49.8976i	0.605898	−	1.86476i
$717$	−7.68313	−	5.58212i	−0.286932	−	0.208468i
$718$	51.1345			1.90832
$719$	33.3774	+	24.2501i	1.24477	+	0.904375i	0.997906	−	0.0646763i	$-0.0206015\pi$
$719$	33.3774	+	24.2501i	1.24477	+	0.904375i	0.246859	+	0.969051i	$0.420602\pi$
$720$		0			0
$721$	−2.41612	+	1.75542i	−0.0899811	+	0.0653751i
$722$	−33.9210	+	24.6450i	−1.26241	+	0.917193i
$723$	11.5155	+	35.4409i	0.428265	+	1.31806i
$724$	30.4210			1.13059
$725$		0			0
$726$	57.5825			2.13709
$727$	−12.1321	−	37.3387i	−0.449954	−	1.38482i	−0.876959	−	0.480566i	$-0.840431\pi$
$727$	−12.1321	−	37.3387i	−0.449954	−	1.38482i	0.427005	−	0.904249i	$-0.359569\pi$
$728$	25.2664	−	18.3571i	0.936436	−	0.680360i
$729$	10.7490	−	7.80957i	0.398109	−	0.289243i
$730$		0			0
$731$	39.2050	+	28.4841i	1.45005	+	1.05352i
$732$	−48.8924			−1.80711
$733$	0.737868	+	0.536092i	0.0272538	+	0.0198010i	0.601329	−	0.799002i	$-0.294638\pi$
$733$	0.737868	+	0.536092i	0.0272538	+	0.0198010i	−0.574075	+	0.818803i	$0.694638\pi$
$734$	8.70498	−	26.7912i	0.321307	−	0.988880i
$735$		0			0
$736$	−9.26570	−	28.5169i	−0.341538	−	1.05115i
$737$	−0.813158	+	2.50264i	−0.0299531	+	0.0921860i
$738$	4.75402	−	14.6314i	0.174998	−	0.538588i
$739$	−3.61367	−	11.1217i	−0.132931	−	0.409119i	0.862331	−	0.506344i	$-0.169003\pi$
$739$	−3.61367	−	11.1217i	−0.132931	−	0.409119i	−0.995262	+	0.0972247i	$0.969003\pi$
$740$		0			0
$741$	1.85988	−	5.72413i	0.0683245	−	0.210281i
$742$	−2.08056	−	1.51162i	−0.0763798	−	0.0554932i
$743$	−11.5631			−0.424211			−0.212105	−	0.977247i	$-0.568032\pi$
$743$	−11.5631			−0.424211			−0.212105	+	0.977247i	$0.568032\pi$
$744$	37.0101	+	26.8894i	1.35685	+	0.985813i
$745$		0			0
$746$	−13.3349	+	9.68837i	−0.488225	+	0.354717i
$747$	27.1669	−	19.7379i	0.993986	−	0.722173i
$748$	2.67953	+	8.24673i	0.0979732	+	0.301530i
$749$	−0.259808			−0.00949318
$750$		0			0
$751$	−27.2430			−0.994112			−0.497056	−	0.867718i	$-0.665586\pi$
$751$	−27.2430			−0.994112			−0.497056	+	0.867718i	$0.665586\pi$
$752$	−1.34655	−	4.14425i	−0.0491036	−	0.151125i
$753$	−22.1126	+	16.0658i	−0.805828	+	0.585469i
$754$	27.7551	−	20.1652i	1.01078	−	0.734374i
$755$		0			0
$756$	−15.9689	−	11.6021i	−0.580784	−	0.421964i
$757$	−17.1080			−0.621800			−0.310900	−	0.950443i	$-0.600630\pi$
$757$	−17.1080			−0.621800			−0.310900	+	0.950443i	$0.600630\pi$
$758$	−40.4655	−	29.3999i	−1.46977	−	1.06785i
$759$	2.27147	−	6.99088i	0.0824493	−	0.253753i
$760$		0			0
$761$	11.6553	+	35.8713i	0.422504	+	1.30033i	0.905364	+	0.424635i	$0.139598\pi$
$761$	11.6553	+	35.8713i	0.422504	+	1.30033i	−0.482861	+	0.875697i	$0.660402\pi$
$762$	8.18327	−	25.1855i	0.296449	−	0.912375i
$763$	−6.21562	+	19.1297i	−0.225021	+	0.692542i
$764$	−12.0034	−	36.9428i	−0.434269	−	1.33654i
$765$		0			0
$766$	17.8850	−	55.0445i	0.646213	−	1.98884i
$767$	−2.71297	−	1.97109i	−0.0979598	−	0.0711720i
$768$	−48.0682			−1.73451
$769$	4.80028	+	3.48761i	0.173102	+	0.125766i	0.670963	−	0.741491i	$-0.265881\pi$
$769$	4.80028	+	3.48761i	0.173102	+	0.125766i	−0.497861	+	0.867257i	$0.665881\pi$
$770$		0			0
$771$	−35.2338	+	25.5989i	−1.26892	+	0.921921i
$772$	47.8253	−	34.7471i	1.72127	−	1.25058i
$773$	−7.28997	−	22.4362i	−0.262202	−	0.806975i	−0.992325	−	0.123659i	$-0.960537\pi$
$773$	−7.28997	−	22.4362i	−0.262202	−	0.806975i	0.730123	−	0.683316i	$-0.239463\pi$
$774$	−50.7786			−1.82520
$775$		0			0
$776$	2.78666			0.100035
$777$	−11.7529	−	36.1718i	−0.421634	−	1.29766i
$778$	−66.6444	+	48.4200i	−2.38932	+	1.73594i
$779$	−2.29613	+	1.66824i	−0.0822674	+	0.0597708i
$780$		0			0
$781$	−0.0611983	−	0.0444632i	−0.00218985	−	0.00159102i
$782$	−76.1952			−2.72473
$783$	−7.25561	−	5.27151i	−0.259294	−	0.188388i
$784$	1.48457	−	4.56905i	0.0530205	−	0.163180i
$785$		0			0
$786$	−4.47393	−	13.7693i	−0.159580	−	0.491136i
$787$	5.63359	−	17.3384i	0.200816	−	0.618048i	−0.799043	−	0.601273i	$-0.794660\pi$
$787$	5.63359	−	17.3384i	0.200816	−	0.618048i	0.999859	−	0.0167744i	$-0.00533970\pi$
$788$	−27.3623	+	84.2125i	−0.974741	+	2.99994i
$789$	4.80020	+	14.7735i	0.170892	+	0.525950i
$790$		0			0
$791$	−2.89043	+	8.89584i	−0.102772	+	0.316300i
$792$	−3.04040	−	2.20898i	−0.108036	−	0.0784926i
$793$	16.4864			0.585451
$794$	−10.3446	−	7.51583i	−0.367118	−	0.266727i
$795$		0			0
$796$	23.1391	−	16.8116i	0.820145	−	0.595870i
$797$	−8.76130	+	6.36546i	−0.310341	+	0.225476i	−0.732043	−	0.681259i	$-0.761433\pi$
$797$	−8.76130	+	6.36546i	−0.310341	+	0.225476i	0.421702	+	0.906735i	$0.361433\pi$
$798$	−5.87249	−	18.0737i	−0.207884	−	0.639801i
$799$	27.4171			0.969948
$800$		0			0
$801$	26.1865			0.925256
$802$	−17.8596	−	54.9663i	−0.630646	−	1.94093i
$803$	5.99007	−	4.35204i	0.211385	−	0.153580i
$804$	−33.5830	+	24.3995i	−1.18438	+	0.860505i
$805$		0			0
$806$	−30.1721	−	21.9213i	−1.06277	−	0.772145i
$807$	−58.3242			−2.05311
$808$	−35.1759	−	25.5568i	−1.23749	−	0.899086i
$809$	13.8494	−	42.6242i	0.486920	−	1.49859i	−0.342260	−	0.939605i	$-0.611192\pi$
$809$	13.8494	−	42.6242i	0.486920	−	1.49859i	0.829180	−	0.558981i	$-0.188808\pi$
$810$		0			0
$811$	−0.946507	−	2.91305i	−0.0332363	−	0.102291i	0.933062	−	0.359715i	$-0.117126\pi$
$811$	−0.946507	−	2.91305i	−0.0332363	−	0.102291i	−0.966298	+	0.257424i	$0.917126\pi$
$812$	21.1006	−	64.9411i	0.740487	−	2.27899i
$813$	6.69289	−	20.5986i	0.234730	−	0.722425i
$814$	1.64455	+	5.06140i	0.0576414	+	0.177402i
$815$		0			0
$816$	−2.94937	+	9.07721i	−0.103248	+	0.317766i
$817$	7.57876	+	5.50629i	0.265147	+	0.192641i
$818$	−9.14524			−0.319756
$819$	−17.7140	−	12.8699i	−0.618976	−	0.449712i
$820$		0			0
$821$	−16.4400	+	11.9444i	−0.573761	+	0.416862i	−0.836470	−	0.548013i	$-0.815384\pi$
$821$	−16.4400	+	11.9444i	−0.573761	+	0.416862i	0.262708	+	0.964875i	$0.415384\pi$
$822$	9.74137	−	7.07752i	0.339769	−	0.246857i
$823$	15.4623	+	47.5879i	0.538980	+	1.65881i	0.734888	+	0.678189i	$0.237235\pi$
$823$	15.4623	+	47.5879i	0.538980	+	1.65881i	−0.195907	+	0.980622i	$0.562765\pi$
$824$	2.72666			0.0949879
$825$		0			0
$826$	−10.5883			−0.368413
$827$	9.77399	+	30.0812i	0.339875	+	1.04603i	0.964271	+	0.264919i	$0.0853453\pi$
$827$	9.77399	+	30.0812i	0.339875	+	1.04603i	−0.624396	+	0.781108i	$0.714655\pi$
$828$	40.7169	−	29.5825i	1.41501	−	1.02806i
$829$	−26.8083	+	19.4774i	−0.931090	+	0.676477i	−0.946260	−	0.323408i	$-0.895171\pi$
$829$	−26.8083	+	19.4774i	−0.931090	+	0.676477i	0.0151691	+	0.999885i	$0.495171\pi$
$830$		0			0
$831$	−11.1149	−	8.07543i	−0.385571	−	0.280133i
$832$	33.0930			1.14729
$833$	24.4545	+	17.7672i	0.847298	+	0.615598i
$834$	17.8784	−	55.0241i	0.619078	−	1.90533i
$835$		0			0
$836$	0.517983	+	1.59419i	0.0179148	+	0.0551361i
$837$	−3.01274	+	9.27227i	−0.104136	+	0.320496i
$838$	3.42586	−	10.5437i	0.118344	−	0.364226i
$839$	3.20925	+	9.87707i	0.110796	+	0.340994i	0.991047	−	0.133514i	$-0.0426260\pi$
$839$	3.20925	+	9.87707i	0.110796	+	0.340994i	−0.880251	+	0.474508i	$0.842626\pi$
$840$		0			0
$841$	0.625759	−	1.92589i	0.0215779	−	0.0664099i
$842$	30.2191	+	21.9554i	1.04142	+	0.756634i
$843$	25.4918			0.877986
$844$	−43.9110	−	31.9032i	−1.51148	−	1.09815i
$845$		0			0
$846$	−23.2422	+	16.8864i	−0.799082	+	0.580567i
$847$	−31.2653	+	22.7156i	−1.07429	+	0.780517i
$848$	0.0771558	+	0.237461i	0.00264954	+	0.00815445i
$849$	6.96235			0.238947
$850$		0			0
$851$	−29.4787			−1.01052
$852$	−0.368752	−	1.13490i	−0.0126332	−	0.0388811i
$853$	−7.53563	+	5.47496i	−0.258015	+	0.187459i	−0.709272	−	0.704935i	$-0.750976\pi$
$853$	−7.53563	+	5.47496i	−0.258015	+	0.187459i	0.451256	+	0.892394i	$0.350976\pi$
$854$	42.1135	−	30.5972i	1.44109	−	1.04702i
$855$		0			0
$856$	0.191902	+	0.139425i	0.00655909	+	0.00476546i
$857$	34.0314			1.16249			0.581245	−	0.813729i	$-0.302566\pi$
$857$	34.0314			1.16249			0.581245	+	0.813729i	$0.302566\pi$
$858$	5.71077	+	4.14912i	0.194963	+	0.141649i
$859$	10.3287	−	31.7884i	0.352410	−	1.08461i	−0.605086	−	0.796160i	$-0.706861\pi$
$859$	10.3287	−	31.7884i	0.352410	−	1.08461i	0.957496	−	0.288446i	$-0.0931386\pi$
$860$		0			0
$861$	7.35114	+	22.6245i	0.250526	+	0.771040i
$862$	29.7364	−	91.5193i	1.01283	−	3.11716i
$863$	−5.12659	+	15.7780i	−0.174511	+	0.537091i	−0.999611	−	0.0278969i	$-0.991119\pi$
$863$	−5.12659	+	15.7780i	−0.174511	+	0.537091i	0.825099	+	0.564987i	$0.191119\pi$
$864$	−2.32606	−	7.15889i	−0.0791343	−	0.243550i
$865$		0			0
$866$	10.9153	−	33.5939i	0.370918	−	1.14157i
$867$	−16.9188	−	12.2922i	−0.574592	−	0.417465i
$868$	−74.2296			−2.51952
$869$	−6.68054	−	4.85370i	−0.226622	−	0.164650i
$870$		0			0
$871$	11.3242	−	8.22748i	0.383704	−	0.278778i
$872$	14.8570	−	10.7942i	0.503120	−	0.365538i
$873$	−0.603724	−	1.85807i	−0.0204330	−	0.0628862i
$874$	−14.7294			−0.498229
$875$		0			0
$876$	116.800			3.94632
$877$	10.1833	+	31.3409i	0.343865	+	1.05831i	0.962189	+	0.272383i	$0.0878118\pi$
$877$	10.1833	+	31.3409i	0.343865	+	1.05831i	−0.618324	+	0.785923i	$0.712188\pi$
$878$	32.2162	−	23.4064i	1.08724	−	0.789929i
$879$	11.6679	−	8.47721i	0.393548	−	0.285929i
$880$		0			0
$881$	40.5119	+	29.4337i	1.36488	+	0.991645i	0.998117	+	0.0613312i	$0.0195346\pi$
$881$	40.5119	+	29.4337i	1.36488	+	0.991645i	0.366765	+	0.930314i	$0.380465\pi$
$882$	−31.6737			−1.06651
$883$	10.1398	+	7.36700i	0.341232	+	0.247919i	0.745181	−	0.666862i	$-0.232363\pi$
$883$	10.1398	+	7.36700i	0.341232	+	0.247919i	−0.403950	+	0.914781i	$0.632363\pi$
$884$	14.2532	−	43.8670i	0.479389	−	1.47541i
$885$		0			0
$886$	25.4391	+	78.2936i	0.854645	+	2.63033i
$887$	−8.32361	+	25.6174i	−0.279480	+	0.860150i	0.708520	+	0.705691i	$0.249363\pi$
$887$	−8.32361	+	25.6174i	−0.279480	+	0.860150i	−0.987999	+	0.154459i	$0.950637\pi$
$888$	−10.7304	+	33.0248i	−0.360089	+	1.10824i
$889$	5.49214	+	16.9031i	0.184200	+	0.566911i
$890$		0			0
$891$	1.63192	−	5.02254i	0.0546715	−	0.168261i
$892$	−1.04774	−	0.761229i	−0.0350810	−	0.0254878i
$893$	5.30004			0.177359
$894$	52.8050	+	38.3651i	1.76606	+	1.28312i
$895$		0			0
$896$	57.3460	−	41.6643i	1.91579	−	1.39191i
$897$	−31.6329	+	22.9826i	−1.05619	+	0.767368i
$898$	−14.8670	−	45.7560i	−0.496119	−	1.52690i
$899$	−33.7268			−1.12485
$900$		0			0
$901$	−1.57097			−0.0523366
$902$	−1.02862	−	3.16577i	−0.0342493	−	0.105409i
$903$	63.5231	−	46.1522i	2.11392	−	1.53585i
$904$	6.90889	−	5.01961i	0.229786	−	0.166950i
$905$		0			0
$906$	74.0272	+	53.7839i	2.45939	+	1.78685i
$907$	28.6510			0.951342			0.475671	−	0.879623i	$-0.342205\pi$
$907$	28.6510			0.951342			0.475671	+	0.879623i	$0.342205\pi$
$908$	56.0174	+	40.6991i	1.85900	+	1.35065i
$909$	−9.41982	+	28.9912i	−0.312436	+	0.961578i
$910$		0			0
$911$	−2.75047	−	8.46508i	−0.0911271	−	0.280461i	0.895098	−	0.445870i	$-0.147106\pi$
$911$	−2.75047	−	8.46508i	−0.0911271	−	0.280461i	−0.986225	+	0.165409i	$0.947106\pi$
$912$	−0.570146	+	1.75473i	−0.0188794	+	0.0581048i
$913$	2.24522	−	6.91008i	0.0743060	−	0.228690i
$914$	30.0219	+	92.3980i	0.993037	+	3.05625i
$915$		0			0
$916$	−12.5536	+	38.6359i	−0.414782	+	1.27657i
$917$	7.86102	+	5.71137i	0.259594	+	0.188606i
$918$	−19.1280			−0.631320
$919$	−13.9071	−	10.1041i	−0.458753	−	0.333303i	0.334289	−	0.942471i	$-0.391504\pi$
$919$	−13.9071	−	10.1041i	−0.458753	−	0.333303i	−0.793042	+	0.609167i	$0.791504\pi$
$920$		0			0
$921$	48.1921	−	35.0136i	1.58798	−	1.15374i
$922$	−20.0951	+	14.5999i	−0.661796	+	0.480823i
$923$	0.124343	+	0.382687i	0.00409279	+	0.0125963i
$924$	14.0497			0.462200
$925$		0			0
$926$	−18.2141			−0.598554
$927$	−0.590726	−	1.81807i	−0.0194020	−	0.0597132i
$928$	21.0665	−	15.3057i	0.691542	−	0.502435i
$929$	−28.1367	+	20.4425i	−0.923137	+	0.670698i	−0.944303	−	0.329078i	$-0.893262\pi$
$929$	−28.1367	+	20.4425i	−0.923137	+	0.670698i	0.0211662	+	0.999776i	$0.493262\pi$
$930$		0			0
$931$	4.72733	+	3.43461i	0.154932	+	0.112565i
$932$	65.0123			2.12955
$933$	16.7686	+	12.1831i	0.548981	+	0.398858i
$934$	3.58036	−	11.0192i	0.117153	−	0.360560i
$935$		0			0
$936$	6.17747	+	19.0123i	0.201917	+	0.621437i
$937$	5.11071	−	15.7291i	0.166960	−	0.513849i	−0.832216	−	0.554452i	$-0.812928\pi$
$937$	5.11071	−	15.7291i	0.166960	−	0.513849i	0.999175	+	0.0406033i	$0.0129280\pi$
$938$	13.6574	−	42.0331i	0.445929	−	1.37243i
$939$	23.6398	+	72.7557i	0.771455	+	2.37429i
$940$		0			0
$941$	12.7310	−	39.1818i	0.415017	−	1.27729i	−0.497218	−	0.867626i	$-0.665645\pi$
$941$	12.7310	−	39.1818i	0.415017	−	1.27729i	0.912235	−	0.409666i	$-0.134355\pi$
$942$	32.4875	+	23.6036i	1.05850	+	0.769045i
$943$	18.4381			0.600428
$944$	0.831660	+	0.604236i	0.0270682	+	0.0196662i
$945$		0			0
$946$	−8.88857	+	6.45792i	−0.288992	+	0.209965i
$947$	−30.0234	+	21.8133i	−0.975629	+	0.708836i	−0.956728	−	0.290985i	$-0.906017\pi$
$947$	−30.0234	+	21.8133i	−0.975629	+	0.708836i	−0.0189019	+	0.999821i	$0.506017\pi$
$948$	−40.2537	−	123.888i	−1.30738	−	4.02370i
$949$	−39.3849			−1.27849
$950$		0			0
$951$	59.7895			1.93881
$952$	−18.6145	−	57.2894i	−0.603298	−	1.85676i
$953$	16.9054	−	12.2825i	0.547619	−	0.397869i	−0.279288	−	0.960207i	$-0.590098\pi$
$953$	16.9054	−	12.2825i	0.547619	−	0.397869i	0.826907	+	0.562339i	$0.190098\pi$
$954$	1.33175	−	0.967573i	0.0431170	−	0.0313263i
$955$		0			0
$956$	−11.3821	−	8.26960i	−0.368124	−	0.267458i
$957$	6.38358			0.206352
$958$	−30.8588	−	22.4202i	−0.997002	−	0.724364i
$959$	−2.49723	+	7.68570i	−0.0806399	+	0.248184i
$960$		0			0
$961$	1.75025	+	5.38670i	0.0564595	+	0.173765i
$962$	8.74788	−	26.9232i	0.282043	−	0.868039i
$963$	0.0513898	−	0.158162i	0.00165601	−	0.00509669i
$964$	17.0595	+	52.5038i	0.549450	+	1.69103i
$965$		0			0
$966$	−38.1505	+	117.415i	−1.22747	+	3.77777i
$967$	6.69912	+	4.86720i	0.215429	+	0.156518i	0.690267	−	0.723555i	$-0.257493\pi$
$967$	6.69912	+	4.86720i	0.215429	+	0.156518i	−0.474838	+	0.880073i	$0.657493\pi$
$968$	35.2838			1.13407
$969$	−9.39167	−	6.82345i	−0.301704	−	0.219201i
$970$		0			0
$971$	21.3643	−	15.5220i	0.685612	−	0.498126i	−0.189603	−	0.981861i	$-0.560720\pi$
$971$	21.3643	−	15.5220i	0.685612	−	0.498126i	0.875215	+	0.483735i	$0.160720\pi$
$972$	54.0689	−	39.2834i	1.73426	−	1.26001i
$973$	11.9990	+	36.9290i	0.384669	+	1.18389i
$974$	2.03885			0.0653289
$975$		0			0
$976$	−5.05390			−0.161771
$977$	−7.82677	−	24.0883i	−0.250401	−	0.770654i	−0.994701	−	0.102809i	$-0.967217\pi$
$977$	−7.82677	−	24.0883i	−0.250401	−	0.770654i	0.744300	−	0.667845i	$-0.232783\pi$
$978$	−8.45983	+	6.14643i	−0.270516	+	0.196541i
$979$	4.58384	−	3.33036i	0.146500	−	0.106439i
$980$		0			0
$981$	−10.4160	−	7.56769i	−0.332558	−	0.241618i
$982$	−28.4059			−0.906470
$983$	−4.14873	−	3.01423i	−0.132324	−	0.0961390i	0.519654	−	0.854377i	$-0.326061\pi$
$983$	−4.14873	−	3.01423i	−0.132324	−	0.0961390i	−0.651978	+	0.758238i	$0.726061\pi$
$984$	6.71158	−	20.6561i	0.213957	−	0.658493i
$985$		0			0
$986$	−20.4479	−	62.9322i	−0.651194	−	2.00417i
$987$	13.7276	−	42.2492i	0.436954	−	1.34481i
$988$	2.75531	−	8.47998i	0.0876582	−	0.269784i
$989$	−18.8062	−	57.8795i	−0.598002	−	1.84046i
$990$		0			0
$991$	−8.20120	+	25.2407i	−0.260520	+	0.801797i	0.732172	+	0.681120i	$0.238507\pi$
$991$	−8.20120	+	25.2407i	−0.260520	+	0.801797i	−0.992692	+	0.120677i	$0.961493\pi$
$992$	−22.9011	−	16.6386i	−0.727110	−	0.528277i
$993$	27.9233			0.886120
$994$	1.02785	+	0.746780i	0.0326016	+	0.0236864i
$995$		0			0
$996$	92.7267	−	67.3699i	2.93816	−	2.13470i
$997$	35.9991	−	26.1549i	1.14010	−	0.828332i	0.152968	−	0.988231i	$-0.451117\pi$
$997$	35.9991	−	26.1549i	1.14010	−	0.828332i	0.987133	+	0.159899i	$0.0511168\pi$
$998$	2.40514	+	7.40227i	0.0761335	+	0.234315i
$999$	−7.40034			−0.234136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.p.126.2		16
5.2	odd	4		625.2.e.k.499.7		32
5.3	odd	4		625.2.e.k.499.2		32
5.4	even	2		625.2.d.n.126.3		16
25.2	odd	20		625.2.b.d.624.3		16
25.3	odd	20		625.2.e.k.124.7		32
25.4	even	10		625.2.d.n.501.3		16
25.6	even	5		625.2.d.q.376.3		16
25.8	odd	20		625.2.e.j.249.7		32
25.9	even	10		625.2.d.m.251.2		16
25.11	even	5		625.2.a.e.1.3	✓	8
25.12	odd	20		625.2.e.j.374.7		32
25.13	odd	20		625.2.e.j.374.2		32
25.14	even	10		625.2.a.g.1.6	yes	8
25.16	even	5		625.2.d.q.251.3		16
25.17	odd	20		625.2.e.j.249.2		32
25.19	even	10		625.2.d.m.376.2		16
25.21	even	5	inner	625.2.d.p.501.2		16
25.22	odd	20		625.2.e.k.124.2		32
25.23	odd	20		625.2.b.d.624.14		16
75.11	odd	10		5625.2.a.be.1.6		8
75.14	odd	10		5625.2.a.s.1.3		8
100.11	odd	10		10000.2.a.bn.1.1		8
100.39	odd	10		10000.2.a.be.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.3	✓	8	25.11	even	5
625.2.a.g.1.6	yes	8	25.14	even	10
625.2.b.d.624.3		16	25.2	odd	20
625.2.b.d.624.14		16	25.23	odd	20
625.2.d.m.251.2		16	25.9	even	10
625.2.d.m.376.2		16	25.19	even	10
625.2.d.n.126.3		16	5.4	even	2
625.2.d.n.501.3		16	25.4	even	10
625.2.d.p.126.2		16	1.1	even	1	trivial
625.2.d.p.501.2		16	25.21	even	5	inner
625.2.d.q.251.3		16	25.16	even	5
625.2.d.q.376.3		16	25.6	even	5
625.2.e.j.249.2		32	25.17	odd	20
625.2.e.j.249.7		32	25.8	odd	20
625.2.e.j.374.2		32	25.13	odd	20
625.2.e.j.374.7		32	25.12	odd	20
625.2.e.k.124.2		32	25.22	odd	20
625.2.e.k.124.7		32	25.3	odd	20
625.2.e.k.499.2		32	5.3	odd	4
625.2.e.k.499.7		32	5.2	odd	4
5625.2.a.s.1.3		8	75.14	odd	10
5625.2.a.be.1.6		8	75.11	odd	10
10000.2.a.be.1.8		8	100.39	odd	10
10000.2.a.bn.1.1		8	100.11	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.718805 - 2.21225i) q^{2} +(-1.86261 + 1.35327i) q^{3} +(-2.75935 + 2.00479i) q^{4} +(4.33262 + 3.14783i) q^{6} -3.59425 q^{7} +(2.65482 + 1.92884i) q^{8} +(0.710939 - 2.18805i) q^{9} +O(q^{10})\)	\(q+(-0.718805 - 2.21225i) q^{2} +(-1.86261 + 1.35327i) q^{3} +(-2.75935 + 2.00479i) q^{4} +(4.33262 + 3.14783i) q^{6} -3.59425 q^{7} +(2.65482 + 1.92884i) q^{8} +(0.710939 - 2.18805i) q^{9} +(-0.153825 - 0.473424i) q^{11} +(2.42659 - 7.46828i) q^{12} +(-0.818243 + 2.51829i) q^{13} +(2.58356 + 7.95139i) q^{14} +(0.250832 - 0.771980i) q^{16} +(4.13180 + 3.00193i) q^{17} -5.35154 q^{18} +(0.798724 + 0.580307i) q^{19} +(6.69468 - 4.86397i) q^{21} +(-0.936765 + 0.680599i) q^{22} +(-1.98198 - 6.09991i) q^{23} -7.55514 q^{24} +6.15926 q^{26} +(-0.497557 - 1.53132i) q^{27} +(9.91780 - 7.20570i) q^{28} +(4.50623 - 3.27397i) q^{29} +(-4.89866 - 3.55908i) q^{31} +4.67497 q^{32} +(0.927185 + 0.673639i) q^{33} +(3.67107 - 11.2984i) q^{34} +(2.42484 + 7.46288i) q^{36} +(1.42028 - 4.37117i) q^{37} +(0.709660 - 2.18411i) q^{38} +(-1.88385 - 5.79790i) q^{39} +(-0.888346 + 2.73405i) q^{41} +(-15.5725 - 11.3141i) q^{42} +9.48858 q^{43} +(1.37357 + 0.997959i) q^{44} +(-12.0699 + 8.76929i) q^{46} +(4.34308 - 3.15543i) q^{47} +(0.577493 + 1.77734i) q^{48} +5.91861 q^{49} -11.7583 q^{51} +(-2.79082 - 8.58926i) q^{52} +(-0.248854 + 0.180803i) q^{53} +(-3.03003 + 2.20144i) q^{54} +(-9.54209 - 6.93274i) q^{56} -2.27302 q^{57} +(-10.4820 - 7.61558i) q^{58} +(-0.391355 + 1.20447i) q^{59} +(-1.92402 - 5.92152i) q^{61} +(-4.35242 + 13.3954i) q^{62} +(-2.55529 + 7.86438i) q^{63} +(-3.86206 - 11.8862i) q^{64} +(0.823796 - 2.53538i) q^{66} +(-4.27667 - 3.10718i) q^{67} -17.4193 q^{68} +(11.9465 + 8.67961i) q^{69} +(0.122941 - 0.0893215i) q^{71} +(6.10782 - 4.43759i) q^{72} +(4.59634 + 14.1461i) q^{73} -10.6910 q^{74} -3.36735 q^{76} +(0.552884 + 1.70160i) q^{77} +(-11.4723 + 8.33512i) q^{78} +(13.4205 - 9.75053i) q^{79} +(8.58283 + 6.23579i) q^{81} +6.68696 q^{82} +(11.8084 + 8.57929i) q^{83} +(-8.72176 + 26.8428i) q^{84} +(-6.82044 - 20.9912i) q^{86} +(-3.96281 + 12.1963i) q^{87} +(0.504783 - 1.55356i) q^{88} +(3.51731 + 10.8252i) q^{89} +(2.94097 - 9.05136i) q^{91} +(17.6980 + 12.8584i) q^{92} +13.9407 q^{93} +(-10.1024 - 7.33985i) q^{94} +(-8.70766 + 6.32648i) q^{96} +(0.687010 - 0.499142i) q^{97} +(-4.25432 - 13.0935i) q^{98} -1.14523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9	\( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9} + 2 q^{11} + 25 q^{12} + 5 q^{13} + 9 q^{14} - 14 q^{16} - 10 q^{17} + 10 q^{18} + 7 q^{21} - 40 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} + 20 q^{27} + 30 q^{28} - 10 q^{29} + 17 q^{31} - 60 q^{32} + 5 q^{33} - q^{34} - 4 q^{36} - 15 q^{37} - 15 q^{38} - 9 q^{39} + 12 q^{41} - 45 q^{42} + 49 q^{44} - 33 q^{46} + 25 q^{47} - 20 q^{48} - 8 q^{49} - 28 q^{51} + 20 q^{52} - 30 q^{54} - 35 q^{56} + 20 q^{57} + 5 q^{58} + 20 q^{59} - 23 q^{61} + 15 q^{62} + 10 q^{63} - 28 q^{64} - 26 q^{66} - 80 q^{68} + 6 q^{69} + 22 q^{71} + 5 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 40 q^{77} - 25 q^{78} + 75 q^{79} + 11 q^{81} + 90 q^{82} + 25 q^{83} - 31 q^{84} + 17 q^{86} - 20 q^{87} + 5 q^{89} + 22 q^{91} + 60 q^{92} + 80 q^{93} - 51 q^{94} - 28 q^{96} + 40 q^{97} + 15 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9 + 2 * q^11 + 25 * q^12 + 5 * q^13 + 9 * q^14 - 14 * q^16 - 10 * q^17 + 10 * q^18 + 7 * q^21 - 40 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 + 20 * q^27 + 30 * q^28 - 10 * q^29 + 17 * q^31 - 60 * q^32 + 5 * q^33 - q^34 - 4 * q^36 - 15 * q^37 - 15 * q^38 - 9 * q^39 + 12 * q^41 - 45 * q^42 + 49 * q^44 - 33 * q^46 + 25 * q^47 - 20 * q^48 - 8 * q^49 - 28 * q^51 + 20 * q^52 - 30 * q^54 - 35 * q^56 + 20 * q^57 + 5 * q^58 + 20 * q^59 - 23 * q^61 + 15 * q^62 + 10 * q^63 - 28 * q^64 - 26 * q^66 - 80 * q^68 + 6 * q^69 + 22 * q^71 + 5 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 40 * q^77 - 25 * q^78 + 75 * q^79 + 11 * q^81 + 90 * q^82 + 25 * q^83 - 31 * q^84 + 17 * q^86 - 20 * q^87 + 5 * q^89 + 22 * q^91 + 60 * q^92 + 80 * q^93 - 51 * q^94 - 28 * q^96 + 40 * q^97 + 15 * q^98 - 44 * q^99

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