LMFDB - Embedded newform 418.2.f.f.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, degree $4$, 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:	$3.33774680449$
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} - 6 x^{15} + 24 x^{14} - 62 x^{13} + 148 x^{12} - 232 x^{11} + 432 x^{10} - 356 x^{9} + 424 x^{8} + \cdots + 16 $ x^16 - 6x^15 + 24x^14 - 62x^13 + 148x^12 - 232x^11 + 432x^10 - 356x^9 + 424x^8 - 320x^7 + 712x^6 - 936x^5 + 968x^4 - 336x^3 + 208x^2 - 80*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.4
Root			$-0.972875 - 0.706835i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.f.267.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.931534 - 2.86697i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.62603 - 1.18138i) q^{5} +(-2.43879 + 1.77188i) q^{6} +(0.750517 + 2.30985i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.92469 - 3.57799i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.931534 - 2.86697i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.62603 - 1.18138i) q^{5} +(-2.43879 + 1.77188i) q^{6} +(0.750517 + 2.30985i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.92469 - 3.57799i) q^{9} -2.00989 q^{10} +(2.41358 - 2.27479i) q^{11} +3.01451 q^{12} +(-2.45583 - 1.78426i) q^{13} +(0.750517 - 2.30985i) q^{14} +(-1.87228 - 5.76227i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.49232 - 2.53732i) q^{17} +(1.88106 + 5.78932i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(1.62603 + 1.18138i) q^{20} +7.32140 q^{21} +(-3.28971 + 0.421676i) q^{22} -2.27832 q^{23} +(-2.43879 - 1.77188i) q^{24} +(-0.296768 + 0.913359i) q^{25} +(0.938042 + 2.88700i) q^{26} +(-7.52914 + 5.47024i) q^{27} +(-1.96488 + 1.42757i) q^{28} +(2.72288 + 8.38017i) q^{29} +(-1.87228 + 5.76227i) q^{30} +(-7.51972 - 5.46339i) q^{31} +1.00000 q^{32} +(-4.27340 - 9.03868i) q^{33} -4.31675 q^{34} +(3.94918 + 2.86925i) q^{35} +(1.88106 - 5.78932i) q^{36} +(0.330046 + 1.01578i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-7.40310 + 5.37867i) q^{39} +(-0.621089 - 1.91151i) q^{40} +(-1.59330 + 4.90367i) q^{41} +(-5.92314 - 4.30341i) q^{42} +11.9841 q^{43} +(2.90929 + 1.59250i) q^{44} -12.2347 q^{45} +(1.84320 + 1.33917i) q^{46} +(-2.78119 + 8.55962i) q^{47} +(0.931534 + 2.86697i) q^{48} +(0.890976 - 0.647332i) q^{49} +(0.776949 - 0.564487i) q^{50} +(-4.02120 - 12.3760i) q^{51} +(0.938042 - 2.88700i) q^{52} +(-4.12220 - 2.99495i) q^{53} +9.30653 q^{54} +(1.23716 - 6.55022i) q^{55} +2.42872 q^{56} +(2.43879 + 1.77188i) q^{57} +(2.72288 - 8.38017i) q^{58} +(-1.48041 - 4.55624i) q^{59} +(4.90168 - 3.56128i) q^{60} +(-7.49309 + 5.44405i) q^{61} +(2.87228 + 8.83996i) q^{62} +(4.56858 - 14.0606i) q^{63} +(-0.809017 - 0.587785i) q^{64} -6.10114 q^{65} +(-1.85555 + 9.82429i) q^{66} +9.19479 q^{67} +(3.49232 + 2.53732i) q^{68} +(-2.12234 + 6.53188i) q^{69} +(-1.50845 - 4.64254i) q^{70} +(8.70566 - 6.32503i) q^{71} +(-4.92469 + 3.57799i) q^{72} +(2.76254 + 8.50223i) q^{73} +(0.330046 - 1.01578i) q^{74} +(2.34212 + 1.70165i) q^{75} -1.00000 q^{76} +(7.06585 + 3.86774i) q^{77} +9.15074 q^{78} +(-5.27562 - 3.83296i) q^{79} +(-0.621089 + 1.91151i) q^{80} +(3.02616 + 9.31355i) q^{81} +(4.17131 - 3.03064i) q^{82} +(3.30975 - 2.40468i) q^{83} +(2.26244 + 6.96306i) q^{84} +(2.68108 - 8.25153i) q^{85} +(-9.69534 - 7.04408i) q^{86} +26.5621 q^{87} +(-1.41761 - 2.99839i) q^{88} +6.04832 q^{89} +(9.89806 + 7.19136i) q^{90} +(2.27824 - 7.01171i) q^{91} +(-0.704041 - 2.16682i) q^{92} +(-22.6682 + 16.4694i) q^{93} +(7.28125 - 5.29014i) q^{94} +(0.621089 + 1.91151i) q^{95} +(0.931534 - 2.86697i) q^{96} +(7.62654 + 5.54101i) q^{97} -1.10131 q^{98} +(-20.0253 + 2.56684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9	$ 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9 + 4 * q^10 + 2 * q^11 - 14 * q^13 + 6 * q^14 - 10 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^19 + 4 * q^20 + 28 * q^21 + 2 * q^22 + 24 * q^23 - 4 * q^26 - 18 * q^27 - 14 * q^28 - 22 * q^29 - 10 * q^30 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 8 * q^34 - 20 * q^35 + 6 * q^37 + 4 * q^38 + 72 * q^39 - 6 * q^40 - 14 * q^41 - 22 * q^42 + 56 * q^43 + 12 * q^44 - 56 * q^45 + 4 * q^46 - 38 * q^47 - 36 * q^49 + 56 * q^51 - 4 * q^52 + 22 * q^53 - 48 * q^54 - 6 * q^55 + 16 * q^56 - 22 * q^58 - 28 * q^59 + 12 * q^61 + 26 * q^62 - 20 * q^63 - 4 * q^64 - 32 * q^65 + 12 * q^66 - 44 * q^67 + 8 * q^68 + 64 * q^69 - 20 * q^70 + 16 * q^71 - 20 * q^72 + 12 * q^73 + 6 * q^74 + 32 * q^75 - 16 * q^76 - 12 * q^77 - 8 * q^78 + 48 * q^79 - 6 * q^80 - 64 * q^81 + 6 * q^82 + 14 * q^83 + 8 * q^84 + 6 * q^85 - 14 * q^86 + 84 * q^87 - 8 * q^88 - 56 * q^89 + 34 * q^90 + 26 * q^91 - 16 * q^92 - 46 * q^93 + 32 * q^94 + 6 * q^95 - 24 * q^97 + 64 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.931534	−	2.86697i	0.537821	−	1.65524i	−0.199652	−	0.979867i	$-0.563981\pi$
$3$	0.931534	−	2.86697i	0.537821	−	1.65524i	0.737473	−	0.675377i	$-0.236019\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.62603	−	1.18138i	0.727183	−	0.528330i	−0.161488	−	0.986875i	$-0.551629\pi$
$5$	1.62603	−	1.18138i	0.727183	−	0.528330i	0.888671	+	0.458545i	$0.151629\pi$
$6$	−2.43879	+	1.77188i	−0.995631	+	0.723368i
$7$	0.750517	+	2.30985i	0.283669	+	0.873042i	0.986795	+	0.161977i	$0.0517870\pi$
$7$	0.750517	+	2.30985i	0.283669	+	0.873042i	−0.703126	+	0.711065i	$0.748213\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−4.92469	−	3.57799i	−1.64156	−	1.19266i
$10$	−2.00989			−0.635581
$11$	2.41358	−	2.27479i	0.727721	−	0.685874i
$11$	2.41358	−	2.27479i	0.727721	−	0.685874i
$12$	3.01451			0.870213
$13$	−2.45583	−	1.78426i	−0.681123	−	0.494865i	0.192607	−	0.981276i	$-0.438306\pi$
$13$	−2.45583	−	1.78426i	−0.681123	−	0.494865i	−0.873730	+	0.486411i	$0.838306\pi$
$14$	0.750517	−	2.30985i	0.200584	−	0.617334i
$15$	−1.87228	−	5.76227i	−0.483419	−	1.48781i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.49232	−	2.53732i	0.847013	−	0.615391i	−0.0773081	−	0.997007i	$-0.524632\pi$
$17$	3.49232	−	2.53732i	0.847013	−	0.615391i	0.924321	+	0.381617i	$0.124632\pi$
$18$	1.88106	+	5.78932i	0.443371	+	1.36456i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$20$	1.62603	+	1.18138i	0.363592	+	0.264165i
$21$	7.32140			1.59766
$22$	−3.28971	+	0.421676i	−0.701368	+	0.0899015i
$23$	−2.27832			−0.475064			−0.237532	−	0.971380i	$-0.576338\pi$
$23$	−2.27832			−0.475064			−0.237532	+	0.971380i	$0.576338\pi$
$24$	−2.43879	−	1.77188i	−0.497815	−	0.361684i
$25$	−0.296768	+	0.913359i	−0.0593537	+	0.182672i
$26$	0.938042	+	2.88700i	0.183965	+	0.566187i
$27$	−7.52914	+	5.47024i	−1.44898	+	1.05275i
$28$	−1.96488	+	1.42757i	−0.371327	+	0.269785i
$29$	2.72288	+	8.38017i	0.505627	+	1.55616i	0.799714	+	0.600381i	$0.204984\pi$
$29$	2.72288	+	8.38017i	0.505627	+	1.55616i	−0.294088	+	0.955778i	$0.595016\pi$
$30$	−1.87228	+	5.76227i	−0.341829	+	1.05204i
$31$	−7.51972	−	5.46339i	−1.35058	−	0.981254i	−0.998982	−	0.0451034i	$-0.985638\pi$
$31$	−7.51972	−	5.46339i	−1.35058	−	0.981254i	−0.351598	−	0.936151i	$-0.614362\pi$
$32$	1.00000			0.176777
$33$	−4.27340	−	9.03868i	−0.743904	−	1.57343i
$34$	−4.31675			−0.740316
$35$	3.94918	+	2.86925i	0.667533	+	0.484991i
$36$	1.88106	−	5.78932i	0.313511	−	0.964886i
$37$	0.330046	+	1.01578i	0.0542592	+	0.166993i	0.974514	−	0.224327i	$-0.0720185\pi$
$37$	0.330046	+	1.01578i	0.0542592	+	0.166993i	−0.920255	+	0.391320i	$0.872018\pi$
$38$	0.809017	−	0.587785i	0.131240	−	0.0953514i
$39$	−7.40310	+	5.37867i	−1.18544	+	0.861276i
$40$	−0.621089	−	1.91151i	−0.0982027	−	0.302237i
$41$	−1.59330	+	4.90367i	−0.248832	+	0.765825i	0.746151	+	0.665777i	$0.231900\pi$
$41$	−1.59330	+	4.90367i	−0.248832	+	0.765825i	−0.994983	+	0.100048i	$0.968100\pi$
$42$	−5.92314	−	4.30341i	−0.913960	−	0.664031i
$43$	11.9841			1.82756			0.913779	−	0.406212i	$-0.133151\pi$
$43$	11.9841			1.82756			0.913779	+	0.406212i	$0.133151\pi$
$44$	2.90929	+	1.59250i	0.438591	+	0.240078i
$45$	−12.2347			−1.82384
$46$	1.84320	+	1.33917i	0.271766	+	0.197449i
$47$	−2.78119	+	8.55962i	−0.405678	+	1.24855i	0.514650	+	0.857401i	$0.327922\pi$
$47$	−2.78119	+	8.55962i	−0.405678	+	1.24855i	−0.920328	+	0.391148i	$0.872078\pi$
$48$	0.931534	+	2.86697i	0.134455	+	0.413811i
$49$	0.890976	−	0.647332i	0.127282	−	0.0924760i
$50$	0.776949	−	0.564487i	0.109877	−	0.0798305i
$51$	−4.02120	−	12.3760i	−0.563080	−	1.73298i
$52$	0.938042	−	2.88700i	0.130083	−	0.400354i
$53$	−4.12220	−	2.99495i	−0.566227	−	0.411388i	0.267505	−	0.963556i	$-0.413801\pi$
$53$	−4.12220	−	2.99495i	−0.566227	−	0.411388i	−0.833733	+	0.552168i	$0.813801\pi$
$54$	9.30653			1.26646
$55$	1.23716	−	6.55022i	0.166819	−	0.883232i
$56$	2.42872			0.324552
$57$	2.43879	+	1.77188i	0.323025	+	0.234692i
$58$	2.72288	−	8.38017i	0.357532	−	1.10037i
$59$	−1.48041	−	4.55624i	−0.192733	−	0.593172i	−0.999996	−	0.00297914i	$-0.999052\pi$
$59$	−1.48041	−	4.55624i	−0.192733	−	0.593172i	0.807262	−	0.590193i	$-0.200948\pi$
$60$	4.90168	−	3.56128i	0.632804	−	0.459759i
$61$	−7.49309	+	5.44405i	−0.959392	+	0.697039i	−0.953010	−	0.302940i	$-0.902032\pi$
$61$	−7.49309	+	5.44405i	−0.959392	+	0.697039i	−0.00638270	+	0.999980i	$0.502032\pi$
$62$	2.87228	+	8.83996i	0.364779	+	1.12268i
$63$	4.56858	−	14.0606i	0.575587	−	1.77147i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−6.10114			−0.756753
$66$	−1.85555	+	9.82429i	−0.228402	+	1.20929i
$67$	9.19479			1.12332			0.561661	−	0.827367i	$-0.310162\pi$
$67$	9.19479			1.12332			0.561661	+	0.827367i	$0.310162\pi$
$68$	3.49232	+	2.53732i	0.423506	+	0.307695i
$69$	−2.12234	+	6.53188i	−0.255499	+	0.786346i
$70$	−1.50845	−	4.64254i	−0.180294	−	0.554889i
$71$	8.70566	−	6.32503i	1.03317	−	0.750643i	0.0642307	−	0.997935i	$-0.479541\pi$
$71$	8.70566	−	6.32503i	1.03317	−	0.750643i	0.968941	+	0.247292i	$0.0795406\pi$
$72$	−4.92469	+	3.57799i	−0.580380	+	0.421671i
$73$	2.76254	+	8.50223i	0.323331	+	0.995110i	0.972188	+	0.234200i	$0.0752472\pi$
$73$	2.76254	+	8.50223i	0.323331	+	0.995110i	−0.648857	+	0.760910i	$0.724753\pi$
$74$	0.330046	−	1.01578i	0.0383671	−	0.118082i
$75$	2.34212	+	1.70165i	0.270445	+	0.196489i
$76$	−1.00000			−0.114708
$77$	7.06585	+	3.86774i	0.805228	+	0.440770i
$78$	9.15074			1.03612
$79$	−5.27562	−	3.83296i	−0.593554	−	0.431242i	0.250031	−	0.968238i	$-0.419559\pi$
$79$	−5.27562	−	3.83296i	−0.593554	−	0.431242i	−0.843585	+	0.536996i	$0.819559\pi$
$80$	−0.621089	+	1.91151i	−0.0694398	+	0.213714i
$81$	3.02616	+	9.31355i	0.336240	+	1.03484i
$82$	4.17131	−	3.03064i	0.460645	−	0.334678i
$83$	3.30975	−	2.40468i	0.363293	−	0.263948i	−0.391132	−	0.920335i	$-0.627916\pi$
$83$	3.30975	−	2.40468i	0.363293	−	0.263948i	0.754424	+	0.656387i	$0.227916\pi$
$84$	2.26244	+	6.96306i	0.246852	+	0.759733i
$85$	2.68108	−	8.25153i	0.290804	−	0.895004i
$86$	−9.69534	−	7.04408i	−1.04548	−	0.759582i
$87$	26.5621			2.84776
$88$	−1.41761	−	2.99839i	−0.151118	−	0.319630i
$89$	6.04832			0.641121			0.320560	−	0.947228i	$-0.396129\pi$
$89$	6.04832			0.641121			0.320560	+	0.947228i	$0.396129\pi$
$90$	9.89806	+	7.19136i	1.04335	+	0.758036i
$91$	2.27824	−	7.01171i	0.238825	−	0.735027i
$92$	−0.704041	−	2.16682i	−0.0734014	−	0.225906i
$93$	−22.6682	+	16.4694i	−2.35059	+	1.70780i
$94$	7.28125	−	5.29014i	0.751003	−	0.545636i
$95$	0.621089	+	1.91151i	0.0637223	+	0.196117i
$96$	0.931534	−	2.86697i	0.0950743	−	0.292608i
$97$	7.62654	+	5.54101i	0.774358	+	0.562604i	0.903280	−	0.429051i	$-0.141152\pi$
$97$	7.62654	+	5.54101i	0.774358	+	0.562604i	−0.128922	+	0.991655i	$0.541152\pi$
$98$	−1.10131			−0.111249
$99$	−20.0253	+	2.56684i	−2.01262	+	0.257977i
$100$	−0.960362			−0.0960362
$101$	7.10793	+	5.16422i	0.707266	+	0.513859i	0.882290	−	0.470705i	$-0.156001\pi$
$101$	7.10793	+	5.16422i	0.707266	+	0.513859i	−0.175025	+	0.984564i	$0.556001\pi$
$102$	−4.02120	+	12.3760i	−0.398158	+	1.22540i
$103$	−3.25866	−	10.0291i	−0.321086	−	0.988200i	−0.973177	−	0.230060i	$-0.926108\pi$
$103$	−3.25866	−	10.0291i	−0.321086	−	0.988200i	0.652091	−	0.758141i	$-0.273892\pi$
$104$	−2.45583	+	1.78426i	−0.240814	+	0.174961i
$105$	11.9048	−	8.64936i	1.16179	−	0.844091i
$106$	1.57454	+	4.84593i	0.152933	+	0.470679i
$107$	−2.37801	+	7.31878i	−0.229891	+	0.707533i	0.767867	+	0.640610i	$0.221318\pi$
$107$	−2.37801	+	7.31878i	−0.229891	+	0.707533i	−0.997758	+	0.0669233i	$0.978682\pi$
$108$	−7.52914	−	5.47024i	−0.724492	−	0.526374i
$109$	−14.2327			−1.36324			−0.681622	−	0.731705i	$-0.738725\pi$
$109$	−14.2327			−1.36324			−0.681622	+	0.731705i	$0.738725\pi$
$110$	−4.85101	+	4.57206i	−0.462526	+	0.435929i
$111$	3.21965			0.305596
$112$	−1.96488	−	1.42757i	−0.185663	−	0.134892i
$113$	−2.93737	+	9.04030i	−0.276325	+	0.850440i	0.712541	+	0.701630i	$0.247544\pi$
$113$	−2.93737	+	9.04030i	−0.276325	+	0.850440i	−0.988866	+	0.148809i	$0.952456\pi$
$114$	−0.931534	−	2.86697i	−0.0872461	−	0.268516i
$115$	−3.70463	+	2.69157i	−0.345458	+	0.250990i
$116$	−7.12860	+	5.17923i	−0.661874	+	0.480880i
$117$	5.71009	+	17.5739i	0.527898	+	1.62470i
$118$	−1.48041	+	4.55624i	−0.136283	+	0.419436i
$119$	8.48188	+	6.16245i	0.777533	+	0.564911i
$120$	−6.05881			−0.553091
$121$	0.650702	−	10.9807i	0.0591547	−	0.998249i
$122$	9.26197			0.838540
$123$	12.5745	+	9.13587i	1.13380	+	0.823754i
$124$	2.87228	−	8.83996i	0.257938	−	0.793851i
$125$	3.70191	+	11.3933i	0.331109	+	1.01905i
$126$	−11.9607	+	8.68996i	−1.06554	+	0.774163i
$127$	8.13791	−	5.91254i	0.722123	−	0.524653i	−0.164939	−	0.986304i	$-0.552743\pi$
$127$	8.13791	−	5.91254i	0.722123	−	0.524653i	0.887062	+	0.461651i	$0.152743\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	11.1636	−	34.3580i	0.982899	−	3.02505i
$130$	4.93593	+	3.58616i	0.432909	+	0.314527i
$131$	8.33735			0.728437			0.364219	−	0.931313i	$-0.381336\pi$
$131$	8.33735			0.728437			0.364219	+	0.931313i	$0.381336\pi$
$132$	7.27574	−	6.85736i	0.633272	−	0.596856i
$133$	−2.42872			−0.210597
$134$	−7.43874	−	5.40456i	−0.642610	−	0.466883i
$135$	−5.78018	+	17.7896i	−0.497479	+	1.53108i
$136$	−1.33395	−	4.10547i	−0.114385	−	0.352041i
$137$	15.2539	−	11.0826i	1.30323	−	0.946852i	0.303248	−	0.952912i	$-0.401929\pi$
$137$	15.2539	−	11.0826i	1.30323	−	0.946852i	0.999982	+	0.00605974i	$0.00192889\pi$
$138$	5.55635	−	4.03692i	0.472988	−	0.343646i
$139$	1.12031	+	3.44797i	0.0950237	+	0.292453i	0.987260	−	0.159116i	$-0.0508645\pi$
$139$	1.12031	+	3.44797i	0.0950237	+	0.292453i	−0.892236	+	0.451569i	$0.850864\pi$
$140$	−1.50845	+	4.64254i	−0.127487	+	0.392366i
$141$	21.9494	+	15.9471i	1.84847	+	1.34299i
$142$	−10.7608			−0.903025
$143$	−9.98614	+	1.28002i	−0.835083	+	0.107041i
$144$	6.08725			0.507271
$145$	14.3277	+	10.4097i	1.18985	+	0.864475i
$146$	2.76254	−	8.50223i	0.228630	−	0.703649i
$147$	−1.02590	−	3.15741i	−0.0846152	−	0.260419i
$148$	−0.864072	+	0.627785i	−0.0710263	+	0.0516036i
$149$	−4.38605	+	3.18665i	−0.359319	+	0.261061i	−0.752768	−	0.658286i	$-0.771282\pi$
$149$	−4.38605	+	3.18665i	−0.359319	+	0.261061i	0.393449	+	0.919346i	$0.371282\pi$
$150$	−0.894610	−	2.75333i	−0.0730446	−	0.224808i
$151$	2.37160	−	7.29902i	0.192998	−	0.593986i	−0.806996	−	0.590556i	$-0.798908\pi$
$151$	2.37160	−	7.29902i	0.192998	−	0.593986i	0.999994	−	0.00342969i	$-0.00109171\pi$
$152$	0.809017	+	0.587785i	0.0656199	+	0.0476757i
$153$	−26.2771			−2.12438
$154$	−3.44299	−	7.28227i	−0.277444	−	0.586822i
$155$	−18.6816			−1.50055
$156$	−7.40310	−	5.37867i	−0.592722	−	0.430638i
$157$	−7.41723	+	22.8279i	−0.591959	+	1.82186i	−0.0226447	+	0.999744i	$0.507209\pi$
$157$	−7.41723	+	22.8279i	−0.591959	+	1.82186i	−0.569315	+	0.822120i	$0.692791\pi$
$158$	2.01511	+	6.20187i	0.160313	+	0.493394i
$159$	−12.4264	+	9.02830i	−0.985477	+	0.715991i
$160$	1.62603	−	1.18138i	0.128549	−	0.0933964i
$161$	−1.70992	−	5.26259i	−0.134761	−	0.414751i
$162$	3.02616	−	9.31355i	0.237757	−	0.731742i
$163$	−0.120269	−	0.0873802i	−0.00942016	−	0.00684415i	0.583065	−	0.812425i	$-0.301853\pi$
$163$	−0.120269	−	0.0873802i	−0.00942016	−	0.00684415i	−0.592485	+	0.805581i	$0.701853\pi$
$164$	−5.15603			−0.402618
$165$	−17.6268	−	9.64866i	−1.37225	−	0.751147i
$166$	−4.09108			−0.317529
$167$	−0.405980	−	0.294961i	−0.0314156	−	0.0228248i	0.571967	−	0.820277i	$-0.306181\pi$
$167$	−0.405980	−	0.294961i	−0.0314156	−	0.0228248i	−0.603382	+	0.797452i	$0.706181\pi$
$168$	2.26244	−	6.96306i	0.174551	−	0.537212i
$169$	−1.16973	−	3.60006i	−0.0899794	−	0.276928i
$170$	−7.01917	+	5.09972i	−0.538346	+	0.391131i
$171$	4.92469	−	3.57799i	0.376600	−	0.273616i
$172$	3.70329	+	11.3976i	0.282373	+	0.869055i
$173$	0.762254	−	2.34598i	0.0579531	−	0.178361i	−0.917889	−	0.396836i	$-0.870108\pi$
$173$	0.762254	−	2.34598i	0.0579531	−	0.178361i	0.975843	+	0.218475i	$0.0701081\pi$
$174$	−21.4892	−	15.6128i	−1.62909	−	1.18361i
$175$	−2.33245			−0.176317
$176$	−0.615539	+	3.25900i	−0.0463980	+	0.245657i
$177$	−14.4416			−1.08550
$178$	−4.89319	−	3.55511i	−0.366760	−	0.266467i
$179$	5.96105	−	18.3462i	0.445550	−	1.37126i	−0.436329	−	0.899787i	$-0.643722\pi$
$179$	5.96105	−	18.3462i	0.445550	−	1.37126i	0.881879	−	0.471475i	$-0.156278\pi$
$180$	−3.78072	−	11.6359i	−0.281798	−	0.867286i
$181$	6.91560	−	5.02448i	0.514033	−	0.373466i	−0.300319	−	0.953839i	$-0.597093\pi$
$181$	6.91560	−	5.02448i	0.514033	−	0.373466i	0.814351	+	0.580372i	$0.197093\pi$
$182$	−5.96452	+	4.33348i	−0.442120	+	0.321219i
$183$	8.62784	+	26.5538i	0.637788	+	1.96291i
$184$	−0.704041	+	2.16682i	−0.0519026	+	0.159740i
$185$	1.73669	+	1.26178i	0.127684	+	0.0927676i
$186$	28.0195			2.05449
$187$	2.65713	−	14.0683i	0.194308	−	1.02878i
$188$	−9.00012			−0.656401
$189$	−18.2862	−	13.2857i	−1.33012	−	0.966392i
$190$	0.621089	−	1.91151i	0.0450585	−	0.138676i
$191$	−0.308916	−	0.950746i	−0.0223524	−	0.0687936i	0.939258	−	0.343212i	$-0.111515\pi$
$191$	−0.308916	−	0.950746i	−0.0223524	−	0.0687936i	−0.961610	+	0.274418i	$0.911515\pi$
$192$	−2.43879	+	1.77188i	−0.176004	+	0.127875i
$193$	−4.06224	+	2.95139i	−0.292406	+	0.212446i	−0.724311	−	0.689474i	$-0.757842\pi$
$193$	−4.06224	+	2.95139i	−0.292406	+	0.212446i	0.431904	+	0.901919i	$0.357842\pi$
$194$	−2.91308	−	8.96554i	−0.209147	−	0.643688i
$195$	−5.68342	+	17.4918i	−0.406998	+	1.25261i
$196$	0.890976	+	0.647332i	0.0636412	+	0.0462380i
$197$	−11.0791			−0.789355			−0.394677	−	0.918820i	$-0.629144\pi$
$197$	−11.0791			−0.789355			−0.394677	+	0.918820i	$0.629144\pi$
$198$	17.7095	+	9.69394i	1.25856	+	0.688919i
$199$	−10.4170			−0.738442			−0.369221	−	0.929342i	$-0.620375\pi$
$199$	−10.4170			−0.738442			−0.369221	+	0.929342i	$0.620375\pi$
$200$	0.776949	+	0.564487i	0.0549386	+	0.0399152i
$201$	8.56526	−	26.3612i	0.604147	−	1.85937i
$202$	−2.71499	−	8.35588i	−0.191026	−	0.587917i
$203$	−17.3134	+	12.5789i	−1.21516	+	0.882867i
$204$	10.5276	−	7.64877i	0.737081	−	0.535521i
$205$	3.20235	+	9.85582i	0.223662	+	0.688360i
$206$	−3.25866	+	10.0291i	−0.227042	+	0.698763i
$207$	11.2200	+	8.15183i	0.779847	+	0.566592i
$208$	3.03557			0.210479
$209$	1.41761	+	2.99839i	0.0980584	+	0.207403i
$210$	−14.7152			−1.01544
$211$	−17.1784	−	12.4808i	−1.18261	−	0.859217i	−0.190147	−	0.981756i	$-0.560896\pi$
$211$	−17.1784	−	12.4808i	−1.18261	−	0.859217i	−0.992464	+	0.122539i	$0.960896\pi$
$212$	1.57454	−	4.84593i	0.108140	−	0.332820i
$213$	−10.0240	−	30.8508i	−0.686836	−	2.11386i
$214$	6.22572	−	4.52325i	0.425582	−	0.309203i
$215$	19.4865	−	14.1578i	1.32897	−	0.965553i
$216$	2.87588	+	8.85104i	0.195679	+	0.602237i
$217$	6.97596	−	21.4698i	0.473559	−	1.45746i
$218$	11.5145	+	8.36576i	0.779859	+	0.566601i
$219$	26.9490			1.82104
$220$	6.61194	−	0.847519i	0.445777	−	0.0571397i
$221$	−13.1038			−0.881456
$222$	−2.60475	−	1.89246i	−0.174819	−	0.127014i
$223$	−1.85028	+	5.69459i	−0.123904	+	0.381338i	−0.993700	−	0.112074i	$-0.964251\pi$
$223$	−1.85028	+	5.69459i	−0.123904	+	0.381338i	0.869796	+	0.493412i	$0.164251\pi$
$224$	0.750517	+	2.30985i	0.0501460	+	0.154334i
$225$	4.72948	−	3.43617i	0.315299	−	0.229078i
$226$	7.69014	−	5.58721i	0.511540	−	0.371656i
$227$	4.21804	+	12.9818i	0.279961	+	0.861632i	0.987864	+	0.155322i	$0.0496415\pi$
$227$	4.21804	+	12.9818i	0.279961	+	0.861632i	−0.707903	+	0.706310i	$0.750359\pi$
$228$	−0.931534	+	2.86697i	−0.0616923	+	0.189869i
$229$	9.16175	+	6.65640i	0.605425	+	0.439867i	0.847800	−	0.530315i	$-0.177926\pi$
$229$	9.16175	+	6.65640i	0.605425	+	0.439867i	−0.242375	+	0.970183i	$0.577926\pi$
$230$	4.57917			0.301942
$231$	17.6708	−	16.6546i	1.16265	−	1.09579i
$232$	8.81144			0.578499
$233$	−6.08452	−	4.42067i	−0.398610	−	0.289607i	0.370364	−	0.928887i	$-0.379233\pi$
$233$	−6.08452	−	4.42067i	−0.398610	−	0.289607i	−0.768975	+	0.639279i	$0.779233\pi$
$234$	5.71009	−	17.5739i	0.373281	−	1.14884i
$235$	5.58987	+	17.2038i	0.364643	+	1.12226i
$236$	3.87577	−	2.81591i	0.252291	−	0.183300i
$237$	−15.9034	+	11.5545i	−1.03304	+	0.750545i
$238$	−3.23979	−	9.97105i	−0.210004	−	0.646327i
$239$	−0.157844	+	0.485794i	−0.0102101	+	0.0314234i	−0.956032	−	0.293263i	$-0.905259\pi$
$239$	−0.157844	+	0.485794i	−0.0102101	+	0.0314234i	0.945822	+	0.324687i	$0.105259\pi$
$240$	4.90168	+	3.56128i	0.316402	+	0.229880i
$241$	−22.6208			−1.45713			−0.728566	−	0.684975i	$-0.759813\pi$
$241$	−22.6208			−1.45713			−0.728566	+	0.684975i	$0.759813\pi$
$242$	−6.98074	+	8.50113i	−0.448739	+	0.546473i
$243$	1.60101			0.102705
$244$	−7.49309	−	5.44405i	−0.479696	−	0.348520i
$245$	0.684009	−	2.10516i	0.0436998	−	0.134494i
$246$	−4.80301	−	14.7822i	−0.306229	−	0.942476i
$247$	2.45583	−	1.78426i	0.156260	−	0.113530i
$248$	−7.51972	+	5.46339i	−0.477502	+	0.346926i
$249$	−3.81098	−	11.7290i	−0.241511	−	0.743294i
$250$	3.70191	−	11.3933i	0.234130	−	0.720577i
$251$	10.2196	+	7.42498i	0.645056	+	0.468661i	0.861583	−	0.507616i	$-0.169473\pi$
$251$	10.2196	+	7.42498i	0.645056	+	0.468661i	−0.216527	+	0.976277i	$0.569473\pi$
$252$	14.7842			0.931319
$253$	−5.49891	+	5.18270i	−0.345714	+	0.325834i
$254$	−10.0590			−0.631158
$255$	−21.1593	−	15.3731i	−1.32505	−	0.962704i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	7.74078	+	23.8237i	0.482857	+	1.48608i	0.835061	+	0.550157i	$0.185432\pi$
$257$	7.74078	+	23.8237i	0.482857	+	1.48608i	−0.352205	+	0.935923i	$0.614568\pi$
$258$	−29.2267	+	21.2344i	−1.81957	+	1.32200i
$259$	−2.09859	+	1.52472i	−0.130400	+	0.0947412i
$260$	−1.88536	−	5.80253i	−0.116925	−	0.359858i
$261$	16.5749	−	51.0122i	1.02596	−	3.15758i
$262$	−6.74506	−	4.90057i	−0.416711	−	0.302758i
$263$	−1.50368			−0.0927212			−0.0463606	−	0.998925i	$-0.514762\pi$
$263$	−1.50368			−0.0927212			−0.0463606	+	0.998925i	$0.514762\pi$
$264$	−9.91685	+	1.27114i	−0.610340	+	0.0782335i
$265$	−10.2410			−0.629100
$266$	1.96488	+	1.42757i	0.120474	+	0.0875298i
$267$	5.63422	−	17.3403i	0.344808	−	1.06121i
$268$	2.84135	+	8.74477i	0.173563	+	0.534172i
$269$	8.53455	−	6.20071i	0.520361	−	0.378064i	−0.296379	−	0.955070i	$-0.595779\pi$
$269$	8.53455	−	6.20071i	0.520361	−	0.378064i	0.816740	+	0.577006i	$0.195779\pi$
$270$	15.1327	−	10.9946i	0.920947	−	0.669107i
$271$	0.603383	+	1.85702i	0.0366529	+	0.112806i	0.967709	−	0.252070i	$-0.0811114\pi$
$271$	0.603383	+	1.85702i	0.0366529	+	0.112806i	−0.931056	+	0.364876i	$0.881111\pi$
$272$	−1.33395	+	4.10547i	−0.0808825	+	0.248931i
$273$	−17.9801	−	13.0633i	−1.08820	−	0.790626i
$274$	−18.8549			−1.13906
$275$	1.36142	+	2.87955i	0.0820969	+	0.173643i
$276$	−6.86802			−0.413407
$277$	−26.3089	−	19.1146i	−1.58075	−	1.14848i	−0.915829	−	0.401569i	$-0.868465\pi$
$277$	−26.3089	−	19.1146i	−1.58075	−	1.14848i	−0.664922	−	0.746913i	$-0.731535\pi$
$278$	1.12031	−	3.44797i	0.0671919	−	0.206795i
$279$	17.4843	+	53.8110i	1.04675	+	3.22158i
$280$	3.94918	−	2.86925i	0.236009	−	0.171470i
$281$	−11.2894	+	8.20224i	−0.673470	+	0.489304i	−0.871185	−	0.490955i	$-0.836648\pi$
$281$	−11.2894	+	8.20224i	−0.673470	+	0.489304i	0.197715	+	0.980260i	$0.436648\pi$
$282$	−8.38391	−	25.8030i	−0.499255	−	1.53655i
$283$	−6.97848	+	21.4775i	−0.414827	+	1.27671i	0.497578	+	0.867419i	$0.334223\pi$
$283$	−6.97848	+	21.4775i	−0.414827	+	1.27671i	−0.912405	+	0.409288i	$0.865777\pi$
$284$	8.70566	+	6.32503i	0.516586	+	0.375322i
$285$	6.05881			0.358893
$286$	8.83133	+	4.83414i	0.522208	+	0.285849i
$287$	−12.5226			−0.739183
$288$	−4.92469	−	3.57799i	−0.290190	−	0.210835i
$289$	0.505031	−	1.55433i	0.0297077	−	0.0914310i
$290$	−5.47268	−	16.8432i	−0.321367	−	0.989066i
$291$	22.9903	−	16.7034i	1.34771	−	0.979171i
$292$	−7.23243	+	5.25467i	−0.423246	+	0.307506i
$293$	8.07242	+	24.8443i	0.471596	+	1.45142i	0.850494	+	0.525984i	$0.176303\pi$
$293$	8.07242	+	24.8443i	0.471596	+	1.45142i	−0.378899	+	0.925438i	$0.623697\pi$
$294$	−1.02590	+	3.15741i	−0.0598320	+	0.184144i
$295$	−7.78985	−	5.65966i	−0.453543	−	0.329518i
$296$	1.06805			0.0620792
$297$	−5.72853	+	30.3300i	−0.332403	+	1.75993i
$298$	5.42145			0.314056
$299$	5.59517	+	4.06513i	0.323577	+	0.235092i
$300$	−0.894610	+	2.75333i	−0.0516503	+	0.158963i
$301$	8.99426	+	27.6815i	0.518421	+	1.59553i
$302$	−6.20892	+	4.51105i	−0.357283	+	0.259581i
$303$	21.4269	−	15.5676i	1.23094	−	0.894333i
$304$	−0.309017	−	0.951057i	−0.0177233	−	0.0545468i
$305$	−5.75251	+	17.7044i	−0.329387	+	1.01375i
$306$	21.2586	+	15.4453i	1.21528	+	0.882949i
$307$	−17.6119			−1.00516			−0.502581	−	0.864530i	$-0.667616\pi$
$307$	−17.6119			−1.00516			−0.502581	+	0.864530i	$0.667616\pi$
$308$	−1.49497	+	7.91522i	−0.0851840	+	0.451011i
$309$	−31.7888			−1.80840
$310$	15.1138	+	10.9808i	0.858404	+	0.623667i
$311$	−2.71489	+	8.35559i	−0.153948	+	0.473802i	−0.998053	−	0.0623758i	$-0.980132\pi$
$311$	−2.71489	+	8.35559i	−0.153948	+	0.473802i	0.844105	+	0.536178i	$0.180132\pi$
$312$	2.82773	+	8.70287i	0.160089	+	0.492703i
$313$	−26.0750	+	18.9446i	−1.47385	+	1.07081i	−0.494369	+	0.869252i	$0.664601\pi$
$313$	−26.0750	+	18.9446i	−1.47385	+	1.07081i	−0.979476	+	0.201559i	$0.935399\pi$
$314$	19.4186	−	14.1084i	1.09585	−	0.796183i
$315$	−9.18232	−	28.2603i	−0.517365	−	1.59229i
$316$	2.01511	−	6.20187i	0.113359	−	0.348882i
$317$	−0.610047	−	0.443225i	−0.0342637	−	0.0248940i	0.570522	−	0.821283i	$-0.306741\pi$
$317$	−0.610047	−	0.443225i	−0.0342637	−	0.0248940i	−0.604785	+	0.796389i	$0.706741\pi$
$318$	15.3599			0.861339
$319$	25.6350	+	14.0322i	1.43528	+	0.785653i
$320$	−2.00989			−0.112356
$321$	18.7675	+	13.6354i	1.04750	+	0.761052i
$322$	−1.70992	+	5.26259i	−0.0952901	+	0.293273i
$323$	1.33395	+	4.10547i	0.0742229	+	0.228435i
$324$	−7.92258	+	5.75609i	−0.440143	+	0.319783i
$325$	2.35848	−	1.71354i	0.130825	−	0.0950500i
$326$	0.0459385	+	0.141384i	0.00254430	+	0.00783054i
$327$	−13.2582	+	40.8046i	−0.733181	+	2.25650i
$328$	4.17131	+	3.03064i	0.230322	+	0.167339i
$329$	−21.8588			−1.20511
$330$	8.58905	+	18.1667i	0.472812	+	1.00004i
$331$	6.33131			0.348000			0.174000	−	0.984746i	$-0.444331\pi$
$331$	6.33131			0.348000			0.174000	+	0.984746i	$0.444331\pi$
$332$	3.30975	+	2.40468i	0.181646	+	0.131974i
$333$	2.00907	−	6.18329i	0.110097	−	0.338842i
$334$	0.155070	+	0.477258i	0.00848507	+	0.0261144i
$335$	14.9510	−	10.8626i	0.816862	−	0.593485i
$336$	−5.92314	+	4.30341i	−0.323134	+	0.234770i
$337$	2.81490	+	8.66338i	0.153338	+	0.471924i	0.997989	−	0.0633927i	$-0.0201921\pi$
$337$	2.81490	+	8.66338i	0.153338	+	0.471924i	−0.844651	+	0.535317i	$0.820192\pi$
$338$	−1.16973	+	3.60006i	−0.0636250	+	0.195818i
$339$	23.1820	+	16.8427i	1.25907	+	0.914769i
$340$	8.67617			0.470531
$341$	−30.5775	+	3.91942i	−1.65586	+	0.212249i
$342$	−6.08725			−0.329161
$343$	15.9181	+	11.5652i	0.859495	+	0.624460i
$344$	3.70329	−	11.3976i	0.199668	−	0.614515i
$345$	4.26565	+	13.1283i	0.229655	+	0.706805i
$346$	−1.99561	+	1.44989i	−0.107285	+	0.0779468i
$347$	0.655926	−	0.476558i	0.0352119	−	0.0255830i	−0.570040	−	0.821617i	$-0.693072\pi$
$347$	0.655926	−	0.476558i	0.0352119	−	0.0255830i	0.605252	+	0.796034i	$0.293072\pi$
$348$	8.20815	+	25.2621i	0.440003	+	1.35419i
$349$	−8.00589	+	24.6396i	−0.428545	+	1.31893i	0.471013	+	0.882126i	$0.343889\pi$
$349$	−8.00589	+	24.6396i	−0.428545	+	1.31893i	−0.899558	+	0.436801i	$0.856111\pi$
$350$	1.88699	+	1.37098i	0.100864	+	0.0732821i
$351$	28.2506			1.50791
$352$	2.41358	−	2.27479i	0.128644	−	0.121246i
$353$	30.9371			1.64662			0.823309	−	0.567594i	$-0.192125\pi$
$353$	30.9371			1.64662			0.823309	+	0.567594i	$0.192125\pi$
$354$	11.6835	+	8.48858i	0.620973	+	0.451163i
$355$	6.68340	−	20.5694i	0.354718	−	1.09171i
$356$	1.86903	+	5.75230i	0.0990586	+	0.304871i
$357$	25.5687	−	18.5767i	1.35324	−	0.983185i
$358$	−15.6062	+	11.3386i	−0.824815	+	0.599263i
$359$	−10.4707	−	32.2254i	−0.552620	−	1.70079i	−0.702146	−	0.712033i	$-0.747775\pi$
$359$	−10.4707	−	32.2254i	−0.552620	−	1.70079i	0.149526	−	0.988758i	$-0.452225\pi$
$360$	−3.78072	+	11.6359i	−0.199261	+	0.613264i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−8.54815			−0.449281
$363$	−30.8752	−	12.0945i	−1.62053	−	0.634795i
$364$	7.37255			0.386427
$365$	14.5363	+	10.5613i	0.760867	+	0.552802i
$366$	8.62784	−	26.5538i	0.450984	−	1.38799i
$367$	−7.94432	−	24.4501i	−0.414690	−	1.27629i	−0.912528	−	0.409015i	$-0.865872\pi$
$367$	−7.94432	−	24.4501i	−0.414690	−	1.27629i	0.497838	−	0.867270i	$-0.334128\pi$
$368$	1.84320	−	1.33917i	0.0960836	−	0.0698088i
$369$	25.3918	−	18.4482i	1.32185	−	0.960377i
$370$	−0.663355	−	2.04160i	−0.0344862	−	0.106138i
$371$	3.82412	−	11.7694i	0.198538	−	0.611038i
$372$	−22.6682	−	16.4694i	−1.17529	−	0.853900i
$373$	12.1401			0.628589			0.314294	−	0.949326i	$-0.398232\pi$
$373$	12.1401			0.628589			0.314294	+	0.949326i	$0.398232\pi$
$374$	−10.4188	+	9.81968i	−0.538743	+	0.507763i
$375$	36.1127			1.86485
$376$	7.28125	+	5.29014i	0.375502	+	0.272818i
$377$	8.26550	−	25.4386i	0.425695	−	1.31015i
$378$	6.98470	+	21.4967i	0.359254	+	1.10567i
$379$	−25.8874	+	18.8083i	−1.32975	+	0.966118i	−0.329992	+	0.943984i	$0.607046\pi$
$379$	−25.8874	+	18.8083i	−1.32975	+	0.966118i	−0.999755	+	0.0221344i	$0.992954\pi$
$380$	−1.62603	+	1.18138i	−0.0834136	+	0.0606036i
$381$	−9.37031	−	28.8388i	−0.480055	−	1.47746i
$382$	−0.308916	+	0.950746i	−0.0158055	+	0.0486444i
$383$	15.8487	+	11.5148i	0.809833	+	0.588378i	0.913782	−	0.406205i	$-0.133148\pi$
$383$	15.8487	+	11.5148i	0.809833	+	0.588378i	−0.103949	+	0.994583i	$0.533148\pi$
$384$	3.01451			0.153833
$385$	16.0586	−	2.05839i	0.818420	−	0.104905i
$386$	5.02121			0.255573
$387$	−59.0179	−	42.8790i	−3.00005	−	2.17966i
$388$	−2.91308	+	8.96554i	−0.147889	+	0.455156i
$389$	−3.38152	−	10.4073i	−0.171450	−	0.527669i	0.828004	−	0.560723i	$-0.189477\pi$
$389$	−3.38152	−	10.4073i	−0.171450	−	0.527669i	−0.999454	+	0.0330539i	$0.989477\pi$
$390$	14.8794	−	10.8105i	0.753447	−	0.547411i
$391$	−7.95665	+	5.78084i	−0.402385	+	0.292350i
$392$	−0.340323	−	1.04741i	−0.0171889	−	0.0529020i
$393$	7.76652	−	23.9029i	0.391769	−	1.20574i
$394$	8.96320	+	6.51214i	0.451559	+	0.328077i
$395$	−13.1065			−0.659460
$396$	−8.62936	−	18.2520i	−0.433642	−	0.917196i
$397$	17.4801			0.877303			0.438651	−	0.898657i	$-0.355456\pi$
$397$	17.4801			0.877303			0.438651	+	0.898657i	$0.355456\pi$
$398$	8.42754	+	6.12296i	0.422434	+	0.306916i
$399$	−2.26244	+	6.96306i	−0.113264	+	0.348589i
$400$	−0.296768	−	0.913359i	−0.0148384	−	0.0456679i
$401$	−13.5839	+	9.86930i	−0.678349	+	0.492849i	−0.872809	−	0.488061i	$-0.837704\pi$
$401$	−13.5839	+	9.86930i	−0.678349	+	0.492849i	0.194461	+	0.980910i	$0.437704\pi$
$402$	−22.4241	+	16.2921i	−1.11841	+	0.812576i
$403$	8.71899	+	26.8343i	0.434324	+	1.33671i
$404$	−2.71499	+	8.35588i	−0.135076	+	0.415720i
$405$	15.9235	+	11.5691i	0.791244	+	0.574872i
$406$	21.4005			1.06209
$407$	3.10727	+	1.70087i	0.154022	+	0.0843091i
$408$	−13.0129			−0.644233
$409$	5.67252	+	4.12133i	0.280488	+	0.203787i	0.719130	−	0.694875i	$-0.244540\pi$
$409$	5.67252	+	4.12133i	0.280488	+	0.203787i	−0.438642	+	0.898662i	$0.644540\pi$
$410$	3.20235	−	9.85582i	0.158153	−	0.486744i
$411$	−17.5640	−	54.0563i	−0.866366	−	2.66640i
$412$	8.53130	−	6.19835i	0.420307	−	0.305371i
$413$	9.41317	−	6.83907i	0.463192	−	0.336528i
$414$	−4.28567	−	13.1899i	−0.210629	−	0.648250i
$415$	2.54092	−	7.82016i	0.124729	−	0.383876i
$416$	−2.45583	−	1.78426i	−0.120407	−	0.0874806i
$417$	10.9288			0.535186
$418$	0.615539	−	3.25900i	0.0301070	−	0.159403i
$419$	−22.9541			−1.12138			−0.560690	−	0.828026i	$-0.689464\pi$
$419$	−22.9541			−1.12138			−0.560690	+	0.828026i	$0.689464\pi$
$420$	11.9048	+	8.64936i	0.580896	+	0.422046i
$421$	1.58632	−	4.88218i	0.0773123	−	0.237943i	−0.904930	−	0.425561i	$-0.860077\pi$
$421$	1.58632	−	4.88218i	0.0773123	−	0.237943i	0.982242	+	0.187618i	$0.0600768\pi$
$422$	6.56157	+	20.1944i	0.319412	+	0.983050i
$423$	44.3228	−	32.2024i	2.15505	−	1.56573i
$424$	−4.12220	+	2.99495i	−0.200192	+	0.145448i
$425$	1.28107	+	3.94274i	0.0621412	+	0.191251i
$426$	−10.0240	+	30.8508i	−0.485666	+	1.49473i
$427$	−18.1986	−	13.2221i	−0.880694	−	0.639862i
$428$	−7.69542			−0.371972
$429$	−5.63263	+	29.8223i	−0.271946	+	1.43983i
$430$	−24.0867			−1.16156
$431$	31.7617	+	23.0763i	1.52991	+	1.11154i	0.956289	+	0.292422i	$0.0944612\pi$
$431$	31.7617	+	23.0763i	1.52991	+	1.11154i	0.573620	+	0.819122i	$0.305539\pi$
$432$	2.87588	−	8.85104i	0.138366	−	0.425846i
$433$	−7.36715	−	22.6738i	−0.354043	−	1.08963i	−0.956562	−	0.291528i	$-0.905837\pi$
$433$	−7.36715	−	22.6738i	−0.354043	−	1.08963i	0.602520	−	0.798104i	$-0.294163\pi$
$434$	−18.2633	+	13.2691i	−0.876666	+	0.636935i
$435$	43.1909	−	31.3800i	2.07084	−	1.50456i
$436$	−4.39814	−	13.5361i	−0.210633	−	0.648261i
$437$	0.704041	−	2.16682i	0.0336789	−	0.103653i
$438$	−21.8022	−	15.8402i	−1.04175	−	0.756875i
$439$	−20.4659			−0.976783			−0.488391	−	0.872625i	$-0.662416\pi$
$439$	−20.4659			−0.976783			−0.488391	+	0.872625i	$0.662416\pi$
$440$	−5.84733	−	3.20074i	−0.278761	−	0.152589i
$441$	−6.70393			−0.319235
$442$	10.6012	+	7.70221i	0.504247	+	0.366357i
$443$	6.33344	−	19.4923i	0.300911	−	0.926108i	−0.680261	−	0.732970i	$-0.738133\pi$
$443$	6.33344	−	19.4923i	0.300911	−	0.926108i	0.981172	−	0.193138i	$-0.0618665\pi$
$444$	0.994926	+	3.06207i	0.0472171	+	0.145319i
$445$	9.83476	−	7.14537i	0.466212	−	0.338723i
$446$	4.84410	−	3.51945i	0.229375	−	0.166651i
$447$	5.05027	+	15.5431i	0.238869	+	0.735165i
$448$	0.750517	−	2.30985i	0.0354586	−	0.109130i
$449$	−24.2361	−	17.6086i	−1.14377	−	0.831000i	−0.156133	−	0.987736i	$-0.549903\pi$
$449$	−24.2361	−	17.6086i	−1.14377	−	0.831000i	−0.987641	+	0.156736i	$0.949903\pi$
$450$	−5.84596			−0.275581
$451$	7.30925	+	15.4598i	0.344179	+	0.727974i
$452$	−9.50553			−0.447103
$453$	−18.7168	−	13.5986i	−0.879393	−	0.638917i
$454$	4.21804	−	12.9818i	0.197962	−	0.609266i
$455$	−4.57901	−	14.0927i	−0.214667	−	0.660678i
$456$	2.43879	−	1.77188i	0.114207	−	0.0829760i
$457$	23.8249	−	17.3098i	1.11448	−	0.809717i	0.131116	−	0.991367i	$-0.458144\pi$
$457$	23.8249	−	17.3098i	1.11448	−	0.809717i	0.983363	+	0.181650i	$0.0581438\pi$
$458$	−3.49948	−	10.7703i	−0.163520	−	0.503262i
$459$	−12.4144	+	38.2077i	−0.579456	+	1.78338i
$460$	−3.70463	−	2.69157i	−0.172729	−	0.125495i
$461$	−12.7886			−0.595624			−0.297812	−	0.954624i	$-0.596257\pi$
$461$	−12.7886			−0.595624			−0.297812	+	0.954624i	$0.596257\pi$
$462$	−24.0853	+	3.08725i	−1.12055	+	0.143632i
$463$	−22.8327			−1.06112			−0.530562	−	0.847646i	$-0.678019\pi$
$463$	−22.8327			−1.06112			−0.530562	+	0.847646i	$0.678019\pi$
$464$	−7.12860	−	5.17923i	−0.330937	−	0.240440i
$465$	−17.4026	+	53.5596i	−0.807025	+	2.48377i
$466$	2.32408	+	7.15279i	0.107661	+	0.331346i
$467$	−18.8165	+	13.6710i	−0.870724	+	0.632618i	−0.930781	−	0.365577i	$-0.880872\pi$
$467$	−18.8165	+	13.6710i	−0.870724	+	0.632618i	0.0600571	+	0.998195i	$0.480872\pi$
$468$	−14.9492	+	10.8612i	−0.691028	+	0.502061i
$469$	6.90084	+	21.2386i	0.318651	+	0.980708i
$470$	5.58987	−	17.2038i	0.257841	−	0.793554i
$471$	58.5374	+	42.5299i	2.69726	+	1.95967i
$472$	−4.79071			−0.220511
$473$	28.9245	−	27.2612i	1.32995	−	1.25347i
$474$	19.6577			0.902907
$475$	−0.776949	−	0.564487i	−0.0356489	−	0.0259004i
$476$	−3.23979	+	9.97105i	−0.148496	+	0.457022i
$477$	9.58461	+	29.4984i	0.438849	+	1.35064i
$478$	0.413241	−	0.300237i	0.0189012	−	0.0137325i
$479$	10.1706	−	7.38938i	0.464707	−	0.337629i	−0.330668	−	0.943747i	$-0.607274\pi$
$479$	10.1706	−	7.38938i	0.464707	−	0.337629i	0.795375	+	0.606118i	$0.207274\pi$
$480$	−1.87228	−	5.76227i	−0.0854573	−	0.263011i
$481$	1.00188	−	3.08346i	0.0456817	−	0.140594i
$482$	18.3006	+	13.2962i	0.833569	+	0.605624i
$483$	−16.6805			−0.758990
$484$	10.6444	−	2.77438i	0.483835	−	0.126108i
$485$	18.9470			0.860341
$486$	−1.29524	−	0.941049i	−0.0587534	−	0.0426869i
$487$	−6.37848	+	19.6309i	−0.289037	+	0.889563i	0.696123	+	0.717923i	$0.254907\pi$
$487$	−6.37848	+	19.6309i	−0.289037	+	0.889563i	−0.985160	+	0.171641i	$0.945093\pi$
$488$	2.86211	+	8.80866i	0.129561	+	0.398749i
$489$	−0.362550	+	0.263408i	−0.0163951	+	0.0119117i
$490$	−1.79076	+	1.30106i	−0.0808983	+	0.0587760i
$491$	−9.35239	−	28.7837i	−0.422067	−	1.29899i	−0.905775	−	0.423760i	$-0.860710\pi$
$491$	−9.35239	−	28.7837i	−0.422067	−	1.29899i	0.483707	−	0.875230i	$-0.339290\pi$
$492$	−4.80301	+	14.7822i	−0.216537	+	0.666431i
$493$	30.7724	+	22.3574i	1.38592	+	1.00693i
$494$	−3.03557			−0.136577
$495$	−29.5293	+	27.8312i	−1.32724	+	1.25092i
$496$	9.29488			0.417352
$497$	21.1436	+	15.3617i	0.948422	+	0.689069i
$498$	−3.81098	+	11.7290i	−0.170774	+	0.525588i
$499$	−11.2020	−	34.4761i	−0.501469	−	1.54336i	−0.806626	−	0.591062i	$-0.798709\pi$
$499$	−11.2020	−	34.4761i	−0.501469	−	1.54336i	0.305157	−	0.952302i	$-0.401291\pi$
$500$	−9.69173	+	7.04146i	−0.433428	+	0.314904i
$501$	−1.22383	+	0.889163i	−0.0546766	+	0.0397249i
$502$	−3.90354	−	12.0139i	−0.174224	−	0.536205i
$503$	4.45084	−	13.6983i	0.198453	−	0.610776i	−0.801466	−	0.598041i	$-0.795946\pi$
$503$	4.45084	−	13.6983i	0.198453	−	0.610776i	0.999919	−	0.0127355i	$-0.00405396\pi$
$504$	−11.9607	−	8.68996i	−0.532772	−	0.387081i
$505$	17.6586			0.785799
$506$	7.49503	−	0.960714i	0.333195	−	0.0427089i
$507$	−11.4109			−0.506776
$508$	8.13791	+	5.91254i	0.361061	+	0.262326i
$509$	11.1185	−	34.2193i	0.492820	−	1.51675i	−0.327506	−	0.944849i	$-0.606208\pi$
$509$	11.1185	−	34.2193i	0.492820	−	1.51675i	0.820326	−	0.571896i	$-0.193792\pi$
$510$	8.08214	+	24.8743i	0.357883	+	1.10145i
$511$	−17.5656	+	12.7621i	−0.777055	+	0.564563i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−2.87588	−	8.85104i	−0.126973	−	0.390783i
$514$	7.74078	−	23.8237i	0.341431	−	1.05082i
$515$	−17.1469	−	12.4580i	−0.755584	−	0.548964i
$516$	36.1261			1.59036
$517$	12.7587	+	26.9859i	0.561126	+	1.18684i
$518$	2.59400			0.113974
$519$	−6.01577	−	4.37072i	−0.264063	−	0.191853i
$520$	−1.88536	+	5.80253i	−0.0826783	+	0.254458i
$521$	−7.43088	−	22.8699i	−0.325553	−	1.00195i	−0.971190	−	0.238305i	$-0.923408\pi$
$521$	−7.43088	−	22.8699i	−0.325553	−	1.00195i	0.645637	−	0.763644i	$-0.276592\pi$
$522$	−43.3936	+	31.5273i	−1.89928	+	1.37991i
$523$	−27.3141	+	19.8449i	−1.19436	+	0.867756i	−0.993719	−	0.111908i	$-0.964304\pi$
$523$	−27.3141	+	19.8449i	−1.19436	+	0.867756i	−0.200645	+	0.979664i	$0.564304\pi$
$524$	2.57638	+	7.92929i	0.112550	+	0.346393i
$525$	−2.17276	+	6.68706i	−0.0948270	+	0.291847i
$526$	1.21651	+	0.883844i	0.0530422	+	0.0385374i
$527$	−40.1237			−1.74781
$528$	8.77006	+	4.80060i	0.381668	+	0.208919i
$529$	−17.8092			−0.774315
$530$	8.28514	+	6.01951i	0.359884	+	0.261471i
$531$	−9.01164	+	27.7350i	−0.391072	+	1.20359i
$532$	−0.750517	−	2.30985i	−0.0325390	−	0.100145i
$533$	12.6623	−	9.19970i	0.548465	−	0.398483i
$534$	−14.7506	+	10.7169i	−0.638319	+	0.463766i
$535$	4.77954	+	14.7099i	0.206637	+	0.635964i
$536$	2.84135	−	8.74477i	0.122728	−	0.377716i
$537$	−47.0451	−	34.1803i	−2.03015	−	1.47499i
$538$	−10.5493			−0.454812
$539$	0.677897	−	3.58917i	0.0291991	−	0.154596i
$540$	−18.7051			−0.804937
$541$	6.98942	+	5.07811i	0.300499	+	0.218325i	0.727809	−	0.685780i	$-0.240539\pi$
$541$	6.98942	+	5.07811i	0.300499	+	0.218325i	−0.427310	+	0.904105i	$0.640539\pi$
$542$	0.603383	−	1.85702i	0.0259175	−	0.0797659i
$543$	−7.96289	−	24.5073i	−0.341720	−	1.05171i
$544$	3.49232	−	2.53732i	0.149732	−	0.108787i
$545$	−23.1428	+	16.8142i	−0.991328	+	0.720242i
$546$	6.86778	+	21.1369i	0.293914	+	0.904574i
$547$	−6.06770	+	18.6744i	−0.259436	+	0.798462i	0.733487	+	0.679703i	$0.237891\pi$
$547$	−6.06770	+	18.6744i	−0.259436	+	0.798462i	−0.992923	+	0.118759i	$0.962109\pi$
$548$	15.2539	+	11.0826i	0.651615	+	0.473426i
$549$	56.3799			2.40624
$550$	0.591140	−	3.12983i	0.0252063	−	0.133456i
$551$	−8.81144			−0.375380
$552$	5.55635	+	4.03692i	0.236494	+	0.171823i
$553$	4.89414	−	15.0626i	0.208120	−	0.640527i
$554$	10.0491	+	30.9280i	0.426946	+	1.31400i
$555$	5.23525	−	3.80363i	0.222224	−	0.161455i
$556$	−2.93302	+	2.13096i	−0.124388	+	0.0903729i
$557$	−13.0643	−	40.2079i	−0.553554	−	1.70366i	−0.699732	−	0.714405i	$-0.746697\pi$
$557$	−13.0643	−	40.2079i	−0.553554	−	1.70366i	0.146179	−	0.989258i	$-0.453303\pi$
$558$	17.4843	−	53.8110i	0.740168	−	2.27800i
$559$	−29.4309	−	21.3828i	−1.24479	−	0.904395i
$560$	−4.88145			−0.206279
$561$	−37.8581	−	20.7230i	−1.59837	−	0.874925i
$562$	13.9545			0.588634
$563$	−12.8937	−	9.36786i	−0.543407	−	0.394808i	0.281942	−	0.959431i	$-0.409021\pi$
$563$	−12.8937	−	9.36786i	−0.543407	−	0.394808i	−0.825349	+	0.564623i	$0.809021\pi$
$564$	−8.38391	+	25.8030i	−0.353026	+	1.08650i
$565$	5.90378	+	18.1700i	0.248374	+	0.764416i
$566$	18.2699	−	13.2739i	0.767941	−	0.557942i
$567$	−19.2417	+	13.9799i	−0.808077	+	0.587103i
$568$	−3.32527	−	10.2341i	−0.139525	−	0.429414i
$569$	−6.62219	+	20.3810i	−0.277617	+	0.854416i	0.710898	+	0.703295i	$0.248289\pi$
$569$	−6.62219	+	20.3810i	−0.277617	+	0.854416i	−0.988515	+	0.151122i	$0.951711\pi$
$570$	−4.90168	−	3.56128i	−0.205309	−	0.149166i
$571$	21.2358			0.888691			0.444346	−	0.895855i	$-0.353436\pi$
$571$	21.2358			0.888691			0.444346	+	0.895855i	$0.353436\pi$
$572$	−4.30326	−	9.10183i	−0.179928	−	0.380567i
$573$	−3.01352			−0.125892
$574$	10.1310	+	7.36058i	0.422858	+	0.307225i
$575$	0.676135	−	2.08093i	0.0281968	−	0.0867807i
$576$	1.88106	+	5.78932i	0.0783776	+	0.241222i
$577$	−4.74740	+	3.44919i	−0.197637	+	0.143592i	−0.682202	−	0.731163i	$-0.738978\pi$
$577$	−4.74740	+	3.44919i	−0.197637	+	0.143592i	0.484566	+	0.874755i	$0.338978\pi$
$578$	−1.32219	+	0.960627i	−0.0549958	+	0.0399568i
$579$	4.67742	+	14.3956i	0.194387	+	0.598262i
$580$	−5.47268	+	16.8432i	−0.227241	+	0.699375i
$581$	8.03847	+	5.84029i	0.333492	+	0.242296i
$582$	−28.4175			−1.17794
$583$	−16.7621	+	2.14857i	−0.694216	+	0.0889847i
$584$	8.93977			0.369930
$585$	30.0462	+	21.8299i	1.24226	+	0.902553i
$586$	8.07242	−	24.8443i	0.333468	−	1.02631i
$587$	−12.8626	−	39.5869i	−0.530895	−	1.63393i	−0.752356	−	0.658757i	$-0.771083\pi$
$587$	−12.8626	−	39.5869i	−0.530895	−	1.63393i	0.221461	−	0.975169i	$-0.428917\pi$
$588$	2.68585	−	1.95139i	0.110763	−	0.0804738i
$589$	7.51972	−	5.46339i	0.309844	−	0.225115i
$590$	2.97546	+	9.15752i	0.122498	+	0.377009i
$591$	−10.3206	+	31.7635i	−0.424532	+	1.30657i
$592$	−0.864072	−	0.627785i	−0.0355131	−	0.0258018i
$593$	−13.4779			−0.553469			−0.276735	−	0.960946i	$-0.589252\pi$
$593$	−13.4779			−0.553469			−0.276735	+	0.960946i	$0.589252\pi$
$594$	22.4620	−	21.1704i	0.921628	−	0.868630i
$595$	21.0720			0.863868
$596$	−4.38605	−	3.18665i	−0.179660	−	0.130530i
$597$	−9.70379	+	29.8652i	−0.397150	+	1.22230i
$598$	−2.13716	−	6.57751i	−0.0873951	−	0.268975i
$599$	−6.95155	+	5.05060i	−0.284033	+	0.206362i	−0.720674	−	0.693274i	$-0.756168\pi$
$599$	−6.95155	+	5.05060i	−0.284033	+	0.206362i	0.436642	+	0.899635i	$0.356168\pi$
$600$	2.34212	−	1.70165i	0.0956166	−	0.0694695i
$601$	2.62327	+	8.07359i	0.107005	+	0.329329i	0.990196	−	0.139686i	$-0.0446092\pi$
$601$	2.62327	+	8.07359i	0.107005	+	0.329329i	−0.883191	+	0.469014i	$0.844609\pi$
$602$	8.99426	−	27.6815i	0.366579	−	1.12821i
$603$	−45.2815	−	32.8989i	−1.84400	−	1.33975i
$604$	7.67465			0.312277
$605$	−11.9144	−	18.6237i	−0.484388	−	0.757163i
$606$	−26.4851			−1.07588
$607$	3.84472	+	2.79335i	0.156052	+	0.113379i	0.663071	−	0.748556i	$-0.269253\pi$
$607$	3.84472	+	2.79335i	0.156052	+	0.113379i	−0.507019	+	0.861935i	$0.669253\pi$
$608$	−0.309017	+	0.951057i	−0.0125323	+	0.0385704i
$609$	19.9353	+	61.3546i	0.807820	+	2.48621i
$610$	15.0603	−	10.9419i	0.609772	−	0.443025i
$611$	22.1027	−	16.0586i	0.894180	−	0.649660i
$612$	−8.12008	−	24.9910i	−0.328235	−	1.01020i
$613$	9.07861	−	27.9411i	0.366682	−	1.12853i	−0.582239	−	0.813017i	$-0.697823\pi$
$613$	9.07861	−	27.9411i	0.366682	−	1.12853i	0.948921	−	0.315513i	$-0.102177\pi$
$614$	14.2483	+	10.3520i	0.575015	+	0.417773i
$615$	31.2394			1.25969
$616$	5.86191	−	5.52482i	0.236183	−	0.222601i
$617$	14.0808			0.566870			0.283435	−	0.958991i	$-0.408526\pi$
$617$	14.0808			0.566870			0.283435	+	0.958991i	$0.408526\pi$
$618$	25.7176	+	18.6850i	1.03452	+	0.751619i
$619$	−6.91200	+	21.2729i	−0.277817	+	0.855032i	0.710644	+	0.703552i	$0.248404\pi$
$619$	−6.91200	+	21.2729i	−0.277817	+	0.855032i	−0.988460	+	0.151480i	$0.951596\pi$
$620$	−5.77294	−	17.7673i	−0.231847	−	0.713552i
$621$	17.1538	−	12.4630i	0.688359	−	0.500122i
$622$	7.10769	−	5.16404i	0.284992	−	0.207059i
$623$	4.53937	+	13.9707i	0.181866	+	0.559725i
$624$	2.82773	−	8.70287i	0.113200	−	0.348394i
$625$	15.5945	+	11.3301i	0.623781	+	0.453203i
$626$	32.2305			1.28819
$627$	9.91685	−	1.27114i	0.396041	−	0.0507646i
$628$	−24.0027			−0.957810
$629$	3.72998	+	2.70999i	0.148724	+	0.108054i
$630$	−9.18232	+	28.2603i	−0.365832	+	1.12592i
$631$	−11.2617	−	34.6600i	−0.448321	−	1.37979i	−0.878800	−	0.477190i	$-0.841655\pi$
$631$	−11.2617	−	34.6600i	−0.448321	−	1.37979i	0.430479	−	0.902601i	$-0.358345\pi$
$632$	−5.27562	+	3.83296i	−0.209853	+	0.152467i
$633$	−51.7844	+	37.6236i	−2.05825	+	1.49540i
$634$	0.233017	+	0.717154i	0.00925430	+	0.0284818i
$635$	6.24754	−	19.2279i	0.247926	−	0.763038i
$636$	−12.4264	−	9.02830i	−0.492739	−	0.357995i
$637$	−3.34309			−0.132458
$638$	−12.4912	−	26.4202i	−0.494532	−	1.04598i
$639$	−65.5036			−2.59128
$640$	1.62603	+	1.18138i	0.0642745	+	0.0466982i
$641$	−4.74087	+	14.5909i	−0.187253	+	0.576306i	−0.999980	−	0.00633915i	$-0.997982\pi$
$641$	−4.74087	+	14.5909i	−0.187253	+	0.576306i	0.812727	+	0.582645i	$0.197982\pi$
$642$	−7.16854	−	22.0625i	−0.282920	−	0.870737i
$643$	23.6238	−	17.1637i	0.931634	−	0.676871i	−0.0147586	−	0.999891i	$-0.504698\pi$
$643$	23.6238	−	17.1637i	0.931634	−	0.676871i	0.946392	+	0.323020i	$0.104698\pi$
$644$	4.47663	−	3.25246i	0.176404	−	0.128165i
$645$	−22.4375	−	69.0556i	−0.883477	−	2.71906i
$646$	1.33395	−	4.10547i	0.0524835	−	0.161528i
$647$	−16.1200	−	11.7119i	−0.633744	−	0.460442i	0.223951	−	0.974600i	$-0.428104\pi$
$647$	−16.1200	−	11.7119i	−0.633744	−	0.460442i	−0.857695	+	0.514158i	$0.828104\pi$
$648$	9.79285			0.384699
$649$	−13.9376	−	7.62921i	−0.547097	−	0.299473i
$650$	−2.91524			−0.114345
$651$	−55.0548	−	39.9997i	−2.15777	−	1.56771i
$652$	0.0459385	−	0.141384i	0.00179909	−	0.00553703i
$653$	−1.07215	−	3.29974i	−0.0419565	−	0.129129i	0.927884	−	0.372868i	$-0.121626\pi$
$653$	−1.07215	−	3.29974i	−0.0419565	−	0.129129i	−0.969841	+	0.243740i	$0.921626\pi$
$654$	34.7105	−	25.2186i	1.35729	−	0.986127i
$655$	13.5568	−	9.84958i	0.529707	−	0.384855i
$656$	−1.59330	−	4.90367i	−0.0622079	−	0.191456i
$657$	16.8163	−	51.7552i	0.656065	−	2.01916i
$658$	17.6841	+	12.8483i	0.689399	+	0.500878i
$659$	−3.67907			−0.143316			−0.0716582	−	0.997429i	$-0.522829\pi$
$659$	−3.67907			−0.143316			−0.0716582	+	0.997429i	$0.522829\pi$
$660$	3.72943	−	19.7457i	0.145168	−	0.768600i
$661$	45.8391			1.78294			0.891468	−	0.453084i	$-0.149676\pi$
$661$	45.8391			1.78294			0.891468	+	0.453084i	$0.149676\pi$
$662$	−5.12214	−	3.72145i	−0.199078	−	0.144638i
$663$	−12.2066	+	37.5681i	−0.474066	+	1.45902i
$664$	−1.26421	−	3.89085i	−0.0490610	−	0.150994i
$665$	−3.94918	+	2.86925i	−0.153143	+	0.111265i
$666$	−5.25982	+	3.82148i	−0.203814	+	0.148079i
$667$	−6.20361	−	19.0928i	−0.240205	−	0.739275i
$668$	0.155070	−	0.477258i	0.00599985	−	0.0184657i
$669$	14.6026	+	10.6094i	0.564568	+	0.410183i
$670$	−18.4805			−0.713963
$671$	−5.70110	+	30.1848i	−0.220089	+	1.16527i
$672$	7.32140			0.282429
$673$	−11.2947	−	8.20605i	−0.435377	−	0.316320i	0.348418	−	0.937339i	$-0.386719\pi$
$673$	−11.2947	−	8.20605i	−0.435377	−	0.316320i	−0.783795	+	0.621019i	$0.786719\pi$
$674$	2.81490	−	8.66338i	0.108426	−	0.333701i
$675$	−2.76188	−	8.50020i	−0.106305	−	0.327173i
$676$	3.06240	−	2.22496i	0.117785	−	0.0855755i
$677$	7.62517	−	5.54001i	0.293059	−	0.212920i	−0.431534	−	0.902097i	$-0.642028\pi$
$677$	7.62517	−	5.54001i	0.293059	−	0.212920i	0.724593	+	0.689177i	$0.242028\pi$
$678$	−8.85472	−	27.2520i	−0.340064	−	1.04661i
$679$	−7.07506	+	21.7748i	−0.271516	+	0.835640i
$680$	−7.01917	−	5.09972i	−0.269173	−	0.195565i
$681$	41.1476			1.57678
$682$	27.0415	+	14.8021i	1.03547	+	0.566802i
$683$	45.4023			1.73727			0.868635	−	0.495453i	$-0.164998\pi$
$683$	45.4023			1.73727			0.868635	+	0.495453i	$0.164998\pi$
$684$	4.92469	+	3.57799i	0.188300	+	0.136808i
$685$	11.7105	−	36.0414i	0.447437	−	1.37707i
$686$	−6.08016	−	18.7128i	−0.232142	−	0.714459i
$687$	27.6181	−	20.0658i	1.05370	−	0.765556i
$688$	−9.69534	+	7.04408i	−0.369631	+	0.268553i
$689$	4.77962	+	14.7102i	0.182089	+	0.560413i
$690$	4.26565	−	13.1283i	0.162391	−	0.499787i
$691$	34.2495	+	24.8837i	1.30291	+	0.946621i	0.999980	−	0.00639117i	$-0.00203439\pi$
$691$	34.2495	+	24.8837i	1.30291	+	0.946621i	0.302932	+	0.953012i	$0.402034\pi$
$692$	2.46671			0.0937701
$693$	−20.9583	−	44.3290i	−0.796141	−	1.68392i
$694$	−0.810769			−0.0307764
$695$	5.89503	+	4.28299i	0.223611	+	0.162463i
$696$	8.20815	−	25.2621i	0.311129	−	0.957557i
$697$	6.87788	+	21.1679i	0.260518	+	0.801792i
$698$	20.9597	−	15.2281i	0.793336	−	0.576392i
$699$	−18.3418	+	13.3261i	−0.693752	+	0.504040i
$700$	−0.720768	−	2.21829i	−0.0272425	−	0.0838437i
$701$	−9.54839	+	29.3869i	−0.360638	+	1.10993i	0.592030	+	0.805916i	$0.298327\pi$
$701$	−9.54839	+	29.3869i	−0.360638	+	1.10993i	−0.952668	+	0.304013i	$0.901673\pi$
$702$	−22.8552	−	16.6053i	−0.862614	−	0.626726i
$703$	−1.06805			−0.0402823
$704$	−3.28971	+	0.421676i	−0.123986	+	0.0158925i
$705$	54.5300			2.05372
$706$	−25.0287	−	18.1844i	−0.941966	−	0.684379i
$707$	−6.59395	+	20.2941i	−0.247991	+	0.763238i
$708$	−4.46271	−	13.7348i	−0.167719	−	0.516186i
$709$	−10.8528	+	7.88503i	−0.407586	+	0.296129i	−0.772624	−	0.634864i	$-0.781056\pi$
$709$	−10.8528	+	7.88503i	−0.407586	+	0.296129i	0.365038	+	0.930993i	$0.381056\pi$
$710$	−17.4974	+	12.7126i	−0.656665	+	0.477095i
$711$	12.2665	+	37.7523i	0.460028	+	1.41582i
$712$	1.86903	−	5.75230i	0.0700450	−	0.215576i
$713$	17.1324	+	12.4474i	0.641612	+	0.466158i
$714$	−31.6046			−1.18277
$715$	−14.7256	+	13.8788i	−0.550705	+	0.519037i
$716$	19.2904			0.720915
$717$	1.24572	+	0.905067i	0.0465222	+	0.0338003i
$718$	−10.4707	+	32.2254i	−0.390762	+	1.20264i
$719$	12.5651	+	38.6713i	0.468597	+	1.44219i	0.854401	+	0.519614i	$0.173924\pi$
$719$	12.5651	+	38.6713i	0.468597	+	1.44219i	−0.385804	+	0.922581i	$0.626076\pi$
$720$	9.89806	−	7.19136i	0.368879	−	0.268006i
$721$	20.7201	−	15.0541i	0.771659	−	0.560643i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$	−21.0720	+	64.8530i	−0.783677	+	2.41191i
$724$	6.91560	+	5.02448i	0.257016	+	0.186733i
$725$	−8.46217			−0.314277
$726$	17.8697	+	27.9326i	0.663205	+	1.03668i
$727$	−21.0063			−0.779080			−0.389540	−	0.921010i	$-0.627366\pi$
$727$	−21.0063			−0.779080			−0.389540	+	0.921010i	$0.627366\pi$
$728$	−5.96452	−	4.33348i	−0.221060	−	0.160609i
$729$	−7.58707	+	23.3506i	−0.281003	+	0.864838i
$730$	−5.55239	−	17.0885i	−0.205503	−	0.632474i
$731$	41.8523	−	30.4075i	1.54796	−	1.12466i
$732$	−22.5880	+	16.4111i	−0.834876	+	0.606573i
$733$	11.0078	+	33.8787i	0.406584	+	1.25134i	0.919565	+	0.392937i	$0.128541\pi$
$733$	11.0078	+	33.8787i	0.406584	+	1.25134i	−0.512981	+	0.858400i	$0.671459\pi$
$734$	−7.94432	+	24.4501i	−0.293230	+	0.902470i
$735$	−5.39826	−	3.92206i	−0.199118	−	0.144667i
$736$	−2.27832			−0.0839802
$737$	22.1923	−	20.9162i	0.817465	−	0.770458i
$738$	−31.3860			−1.15534
$739$	−31.3990	−	22.8127i	−1.15503	−	0.839179i	−0.165889	−	0.986144i	$-0.553049\pi$
$739$	−31.3990	−	22.8127i	−1.15503	−	0.839179i	−0.989142	+	0.146965i	$0.953049\pi$
$740$	−0.663355	+	2.04160i	−0.0243854	+	0.0750506i
$741$	−2.82773	−	8.70287i	−0.103879	−	0.319708i
$742$	−10.0117	+	7.27391i	−0.367540	+	0.267034i
$743$	16.5844	−	12.0493i	0.608422	−	0.442044i	−0.240436	−	0.970665i	$-0.577291\pi$
$743$	16.5844	−	12.0493i	0.608422	−	0.442044i	0.848858	+	0.528620i	$0.177291\pi$
$744$	8.65849	+	26.6481i	0.317436	+	0.976967i
$745$	−3.36720	+	10.3632i	−0.123365	+	0.379678i
$746$	−9.82152	−	7.13575i	−0.359591	−	0.261258i
$747$	−24.9034			−0.911168
$748$	14.2008	−	1.82027i	0.519234	−	0.0665556i
$749$	−18.6900			−0.682919
$750$	−29.2158	−	21.2265i	−1.06681	−	0.775083i
$751$	11.4589	−	35.2670i	0.418142	−	1.28691i	−0.491268	−	0.871009i	$-0.663466\pi$
$751$	11.4589	−	35.2670i	0.418142	−	1.28691i	0.909410	−	0.415901i	$-0.136534\pi$
$752$	−2.78119	−	8.55962i	−0.101420	−	0.312137i
$753$	30.8071	−	22.3827i	1.12267	−	0.815669i
$754$	−21.6394	+	15.7219i	−0.788059	+	0.572558i
$755$	−4.76664	−	14.6702i	−0.173476	−	0.533903i
$756$	6.98470	−	21.4967i	0.254031	−	0.781828i
$757$	−1.61500	−	1.17337i	−0.0586981	−	0.0426467i	0.558049	−	0.829808i	$-0.311550\pi$
$757$	−1.61500	−	1.17337i	−0.0586981	−	0.0426467i	−0.616747	+	0.787161i	$0.711550\pi$
$758$	31.9986			1.16224
$759$	9.73620	+	20.5931i	0.353402	+	0.747480i
$760$	2.00989			0.0729062
$761$	−12.1946	−	8.85993i	−0.442056	−	0.321172i	0.344396	−	0.938825i	$-0.388084\pi$
$761$	−12.1946	−	8.85993i	−0.442056	−	0.321172i	−0.786451	+	0.617652i	$0.788084\pi$
$762$	−9.37031	+	28.8388i	−0.339450	+	1.04472i
$763$	−10.6819	−	32.8754i	−0.386709	−	1.19017i
$764$	0.808753	−	0.587594i	0.0292597	−	0.0212584i
$765$	−42.7274	+	31.0433i	−1.54481	+	1.12237i
$766$	−6.05368	−	18.6313i	−0.218728	−	0.673177i
$767$	−4.49389	+	13.8308i	−0.162265	+	0.499400i
$768$	−2.43879	−	1.77188i	−0.0880021	−	0.0639373i
$769$	−30.4602			−1.09842			−0.549212	−	0.835683i	$-0.685072\pi$
$769$	−30.4602			−1.09842			−0.549212	+	0.835683i	$0.685072\pi$
$770$	−14.2015	−	7.77371i	−0.511788	−	0.280145i
$771$	75.5125			2.71951
$772$	−4.06224	−	2.95139i	−0.146203	−	0.106223i
$773$	−7.22422	+	22.2339i	−0.259837	+	0.799697i	0.733001	+	0.680228i	$0.238119\pi$
$773$	−7.22422	+	22.2339i	−0.259837	+	0.799697i	−0.992838	+	0.119469i	$0.961881\pi$
$774$	22.5428	+	69.3797i	0.810286	+	2.49380i
$775$	7.22165	−	5.24684i	0.259409	−	0.188472i
$776$	7.62654	−	5.54101i	0.273777	−	0.198911i
$777$	2.41640	+	7.43691i	0.0866878	+	0.266798i
$778$	−3.38152	+	10.4073i	−0.121233	+	0.373118i
$779$	−4.17131	−	3.03064i	−0.149453	−	0.108584i
$780$	−18.3919			−0.658537
$781$	6.62368	−	35.0695i	0.237014	−	1.25488i
$782$	9.83496			0.351697
$783$	−66.3425	−	48.2007i	−2.37089	−	1.72255i
$784$	−0.340323	+	1.04741i	−0.0121544	+	0.0374073i
$785$	14.9078	+	45.8814i	0.532081	+	1.63758i
$786$	−20.3330	+	14.7728i	−0.725255	+	0.526928i
$787$	4.94446	−	3.59236i	0.176251	−	0.128054i	−0.496162	−	0.868230i	$-0.665258\pi$
$787$	4.94446	−	3.59236i	0.176251	−	0.128054i	0.672413	+	0.740176i	$0.265258\pi$
$788$	−3.42364	−	10.5369i	−0.121962	−	0.375360i
$789$	−1.40073	+	4.31101i	−0.0498674	+	0.153476i
$790$	10.6034	+	7.70382i	0.377252	+	0.274090i
$791$	−23.0863			−0.820854
$792$	−3.74694	+	19.8384i	−0.133142	+	0.704926i
$793$	28.1153			0.998405
$794$	−14.1417	−	10.2746i	−0.501871	−	0.364631i
$795$	−9.53984	+	29.3606i	−0.338343	+	1.04131i
$796$	−3.21903	−	9.90716i	−0.114096	−	0.351150i
$797$	1.03054	−	0.748732i	0.0365036	−	0.0265215i	−0.569384	−	0.822072i	$-0.692818\pi$
$797$	1.03054	−	0.748732i	0.0365036	−	0.0265215i	0.605887	+	0.795550i	$0.292818\pi$
$798$	5.92314	−	4.30341i	0.209677	−	0.152339i
$799$	12.0057	+	36.9497i	0.424731	+	1.30719i
$800$	−0.296768	+	0.913359i	−0.0104923	+	0.0322921i
$801$	−29.7861	−	21.6409i	−1.05244	−	0.764642i
$802$	16.7907			0.592899
$803$	26.0083	+	14.2366i	0.917815	+	0.502398i
$804$	27.7178			0.977530
$805$	−8.99751	−	6.53707i	−0.317121	−	0.230402i
$806$	8.71899	−	26.8343i	0.307113	−	0.945197i
$807$	−9.82701	−	30.2444i	−0.345927	−	1.06465i
$808$	7.10793	−	5.16422i	0.250056	−	0.181676i
$809$	31.9389	−	23.2050i	1.12291	−	0.815845i	0.138265	−	0.990395i	$-0.455847\pi$
$809$	31.9389	−	23.2050i	1.12291	−	0.815845i	0.984648	+	0.174551i	$0.0558473\pi$
$810$	−6.08223	−	18.7192i	−0.213708	−	0.657724i
$811$	1.25337	−	3.85747i	0.0440117	−	0.135454i	−0.926636	−	0.375960i	$-0.877313\pi$
$811$	1.25337	−	3.85747i	0.0440117	−	0.135454i	0.970648	+	0.240505i	$0.0773132\pi$
$812$	−17.3134	−	12.5789i	−0.607581	−	0.441433i
$813$	5.88609			0.206434
$814$	−1.51408	−	3.20244i	−0.0530686	−	0.112245i
$815$	−0.298790			−0.0104661
$816$	10.5276	+	7.64877i	0.368541	+	0.267761i
$817$	−3.70329	+	11.3976i	−0.129562	+	0.398750i
$818$	−2.16671	−	6.66845i	−0.0757573	−	0.233157i
$819$	−36.3075	+	26.3789i	−1.26869	+	0.921755i
$820$	−8.38386	+	6.09123i	−0.292777	+	0.212715i
$821$	1.58076	+	4.86507i	0.0551688	+	0.169792i	0.974844	−	0.222887i	$-0.0715482\pi$
$821$	1.58076	+	4.86507i	0.0551688	+	0.169792i	−0.919675	+	0.392679i	$0.871548\pi$
$822$	−17.5640	+	54.0563i	−0.612613	+	1.88543i
$823$	29.6181	+	21.5188i	1.03242	+	0.750099i	0.968792	−	0.247874i	$-0.0797320\pi$
$823$	29.6181	+	21.5188i	1.03242	+	0.750099i	0.0636307	+	0.997974i	$0.479732\pi$
$824$	−10.5453			−0.367362
$825$	9.52377	−	1.22076i	0.331575	−	0.0425013i
$826$	−11.6353			−0.404844
$827$	−20.9342	−	15.2096i	−0.727954	−	0.528889i	0.160962	−	0.986961i	$-0.448540\pi$
$827$	−20.9342	−	15.2096i	−0.727954	−	0.528889i	−0.888915	+	0.458071i	$0.848540\pi$
$828$	−4.28567	+	13.1899i	−0.148937	+	0.458382i
$829$	−9.99678	−	30.7669i	−0.347203	−	1.06858i	−0.960394	−	0.278645i	$-0.910115\pi$
$829$	−9.99678	−	30.7669i	−0.347203	−	1.06858i	0.613192	−	0.789934i	$-0.289885\pi$
$830$	−6.65222	+	4.83312i	−0.230902	+	0.167760i
$831$	−79.3084	+	57.6210i	−2.75118	+	1.99885i
$832$	0.938042	+	2.88700i	0.0325208	+	0.100089i
$833$	1.46909	−	4.52139i	0.0509009	−	0.156657i
$834$	−8.84160	−	6.42380i	−0.306159	−	0.222438i
$835$	−1.00860			−0.0349039
$836$	−2.41358	+	2.27479i	−0.0834753	+	0.0786751i
$837$	86.5031			2.98998
$838$	18.5702	+	13.4921i	0.641498	+	0.466075i
$839$	9.07419	−	27.9275i	0.313276	−	0.964164i	−0.663182	−	0.748458i	$-0.730795\pi$
$839$	9.07419	−	27.9275i	0.313276	−	0.964164i	0.976458	−	0.215706i	$-0.0692054\pi$
$840$	−4.54724	−	13.9950i	−0.156895	−	0.482872i
$841$	−39.3517	+	28.5907i	−1.35696	+	0.985886i
$842$	−4.15303	+	3.01735i	−0.143123	+	0.103985i
$843$	12.9991	+	40.0070i	0.447712	+	1.37791i
$844$	6.56157	−	20.1944i	0.225859	−	0.695121i
$845$	−6.15507	−	4.47192i	−0.211741	−	0.153839i
$846$	−54.7859			−1.88358
$847$	25.8522	−	6.73820i	0.888294	−	0.231527i
$848$	5.09532			0.174974
$849$	55.0747	+	40.0141i	1.89016	+	1.37328i
$850$	1.28107	−	3.94274i	0.0439405	−	0.135235i
$851$	−0.751952	−	2.31427i	−0.0257766	−	0.0793322i
$852$	26.2433	−	19.0668i	0.899080	−	0.653219i
$853$	−26.5379	+	19.2809i	−0.908640	+	0.660165i	−0.940670	−	0.339322i	$-0.889803\pi$
$853$	−26.5379	+	19.2809i	−0.908640	+	0.660165i	0.0320309	+	0.999487i	$0.489803\pi$
$854$	6.95126	+	21.3938i	0.237867	+	0.732080i
$855$	3.78072	−	11.6359i	0.129298	−	0.397938i
$856$	6.22572	+	4.52325i	0.212791	+	0.154602i
$857$	−10.5746			−0.361222			−0.180611	−	0.983555i	$-0.557807\pi$
$857$	−10.5746			−0.361222			−0.180611	+	0.983555i	$0.557807\pi$
$858$	22.0860	−	20.8160i	0.754004	−	0.710645i
$859$	31.7422			1.08303			0.541514	−	0.840692i	$-0.317851\pi$
$859$	31.7422			1.08303			0.541514	+	0.840692i	$0.317851\pi$
$860$	19.4865	+	14.1578i	0.664485	+	0.482776i
$861$	−11.6652	+	35.9018i	−0.397548	+	1.22353i
$862$	−12.1319	−	37.3382i	−0.413214	−	1.27174i
$863$	23.6504	−	17.1830i	0.805069	−	0.584917i	−0.107328	−	0.994224i	$-0.534229\pi$
$863$	23.6504	−	17.1830i	0.805069	−	0.584917i	0.912397	+	0.409307i	$0.134229\pi$
$864$	−7.52914	+	5.47024i	−0.256147	+	0.186101i
$865$	−1.53204	−	4.71515i	−0.0520911	−	0.160320i
$866$	−7.36715	+	22.6738i	−0.250346	+	0.770486i
$867$	−3.98575	−	2.89582i	−0.135363	−	0.0983470i
$868$	22.5747			0.766235
$869$	−21.4523	+	2.74976i	−0.727719	+	0.0932792i
$870$	−53.3868			−1.80998
$871$	−22.5808	−	16.4059i	−0.765122	−	0.555893i
$872$	−4.39814	+	13.5361i	−0.148940	+	0.458390i
$873$	−17.7326	−	54.5755i	−0.600159	−	1.84710i
$874$	−1.84320	+	1.33917i	−0.0623473	+	0.0452980i
$875$	−23.5385	+	17.1017i	−0.795748	+	0.578145i
$876$	8.32770	+	25.6300i	0.281367	+	0.865958i
$877$	0.0871577	−	0.268244i	0.00294311	−	0.00905795i	−0.949574	−	0.313542i	$-0.898484\pi$
$877$	0.0871577	−	0.268244i	0.00294311	−	0.00905795i	0.952517	+	0.304485i	$0.0984842\pi$
$878$	16.5572	+	12.0295i	0.558780	+	0.405977i
$879$	78.7476			2.65609
$880$	2.84924	+	6.02643i	0.0960479	+	0.203151i
$881$	−16.1017			−0.542480			−0.271240	−	0.962512i	$-0.587434\pi$
$881$	−16.1017			−0.542480			−0.271240	+	0.962512i	$0.587434\pi$
$882$	5.42359	+	3.94047i	0.182622	+	0.132683i
$883$	−6.99091	+	21.5158i	−0.235263	+	0.724064i	0.761824	+	0.647784i	$0.224304\pi$
$883$	−6.99091	+	21.5158i	−0.235263	+	0.724064i	−0.997086	+	0.0762798i	$0.975696\pi$
$884$	−4.04929	−	12.4624i	−0.136192	−	0.419157i
$885$	−23.4826	+	17.0611i	−0.789357	+	0.573502i
$886$	−16.5812	+	12.0469i	−0.557055	+	0.404724i
$887$	2.99177	+	9.20773i	0.100454	+	0.309165i	0.988637	−	0.150325i	$-0.0480321\pi$
$887$	2.99177	+	9.20773i	0.100454	+	0.309165i	−0.888183	+	0.459490i	$0.848032\pi$
$888$	0.994926	−	3.06207i	0.0333875	−	0.102756i
$889$	19.7647	+	14.3599i	0.662888	+	0.481616i
$890$	−12.1564			−0.407484
$891$	28.4902	+	15.5951i	0.954457	+	0.522456i
$892$	−5.98764			−0.200481
$893$	−7.28125	−	5.29014i	−0.243658	−	0.177028i
$894$	5.05027	−	15.5431i	0.168906	−	0.519840i
$895$	−11.9810	−	36.8738i	−0.400482	−	1.23256i
$896$	−1.96488	+	1.42757i	−0.0656420	+	0.0476917i
$897$	16.8667	−	12.2544i	0.563162	−	0.409161i
$898$	9.25738	+	28.4913i	0.308923	+	0.950766i
$899$	25.3089	−	77.8927i	0.844098	−	2.59787i
$900$	4.72948	+	3.43617i	0.157649	+	0.114539i
$901$	−21.9952			−0.732766
$902$	3.17374	−	16.8035i	0.105674	−	0.559496i
$903$	87.7404			2.91982
$904$	7.69014	+	5.58721i	0.255770	+	0.185828i
$905$	5.30916	−	16.3399i	0.176482	−	0.543157i
$906$	7.14919	+	22.0030i	0.237516	+	0.730999i
$907$	−39.8507	+	28.9533i	−1.32322	+	0.961377i	−0.323336	+	0.946284i	$0.604804\pi$
$907$	−39.8507	+	28.9533i	−1.32322	+	0.961377i	−0.999886	+	0.0150930i	$0.995196\pi$
$908$	−11.0430	+	8.02319i	−0.366474	+	0.266259i
$909$	−16.5268	−	50.8643i	−0.548160	−	1.68706i
$910$	−4.57901	+	14.0927i	−0.151793	+	0.467170i
$911$	−37.5813	−	27.3044i	−1.24512	−	0.904636i	−0.247196	−	0.968966i	$-0.579509\pi$
$911$	−37.5813	−	27.3044i	−1.24512	−	0.904636i	−0.997929	+	0.0643298i	$0.979509\pi$
$912$	−3.01451			−0.0998203
$913$	2.51822	−	13.3328i	0.0833409	−	0.441253i
$914$	−29.4491			−0.974091
$915$	45.3992	+	32.9845i	1.50085	+	1.09043i
$916$	−3.49948	+	10.7703i	−0.115626	+	0.355860i
$917$	6.25732	+	19.2580i	0.206635	+	0.635957i
$918$	32.5014	−	23.6137i	1.07271	−	0.779367i
$919$	−4.77663	+	3.47042i	−0.157566	+	0.114479i	−0.663775	−	0.747932i	$-0.731047\pi$
$919$	−4.77663	+	3.47042i	−0.157566	+	0.114479i	0.506208	+	0.862411i	$0.331047\pi$
$920$	1.41504	+	4.35505i	0.0466525	+	0.143582i
$921$	−16.4061	+	50.4927i	−0.540598	+	1.66379i
$922$	10.3462	+	7.51695i	0.340734	+	0.247558i
$923$	−32.6651			−1.07518
$924$	21.3000	+	11.6593i	0.700720	+	0.383564i
$925$	−1.02572			−0.0337254
$926$	18.4720	+	13.4207i	0.607028	+	0.441031i
$927$	−19.8363	+	61.0499i	−0.651510	+	2.00514i
$928$	2.72288	+	8.38017i	0.0893830	+	0.275093i
$929$	−22.4589	+	16.3173i	−0.736852	+	0.535354i	−0.891724	−	0.452580i	$-0.850504\pi$
$929$	−22.4589	+	16.3173i	−0.736852	+	0.535354i	0.154872	+	0.987935i	$0.450504\pi$
$930$	45.5605	−	33.1017i	1.49399	−	1.08545i
$931$	0.340323	+	1.04741i	0.0111536	+	0.0343273i
$932$	2.32408	−	7.15279i	0.0761278	−	0.234297i
$933$	21.4262	+	15.5670i	0.701461	+	0.509641i
$934$	23.2585			0.761041
$935$	−12.2995	−	26.0146i	−0.402235	−	0.850768i
$936$	18.4783			0.603981
$937$	−11.5669	−	8.40383i	−0.377873	−	0.274541i	0.382595	−	0.923916i	$-0.375031\pi$
$937$	−11.5669	−	8.40383i	−0.377873	−	0.274541i	−0.760468	+	0.649375i	$0.775031\pi$
$938$	6.90084	−	21.2386i	0.225321	−	0.693465i
$939$	30.0238	+	92.4036i	0.979788	+	3.01548i
$940$	−14.6345	+	10.6326i	−0.477324	+	0.346796i
$941$	−33.9419	+	24.6602i	−1.10647	+	0.803901i	−0.982105	−	0.188335i	$-0.939691\pi$
$941$	−33.9419	+	24.6602i	−1.10647	+	0.803901i	−0.124370	+	0.992236i	$0.539691\pi$
$942$	−22.3593	−	68.8148i	−0.728505	−	2.24211i
$943$	3.63006	−	11.1722i	0.118211	−	0.363816i
$944$	3.87577	+	2.81591i	0.126146	+	0.0916501i
$945$	−45.4294			−1.47782
$946$	−39.4242	+	5.05340i	−1.28179	+	0.164300i
$947$	20.2850			0.659174			0.329587	−	0.944125i	$-0.393090\pi$
$947$	20.2850			0.659174			0.329587	+	0.944125i	$0.393090\pi$
$948$	−15.9034	−	11.5545i	−0.516518	−	0.375273i
$949$	8.38588	−	25.8091i	0.272217	−	0.837798i
$950$	0.296768	+	0.913359i	0.00962843	+	0.0296333i
$951$	−1.83899	+	1.33611i	−0.0596334	+	0.0433262i
$952$	8.48188	−	6.16245i	0.274899	−	0.199726i
$953$	10.3201	+	31.7621i	0.334302	+	1.02888i	0.967065	+	0.254530i	$0.0819208\pi$
$953$	10.3201	+	31.7621i	0.334302	+	1.02888i	−0.632763	+	0.774346i	$0.718079\pi$
$954$	9.58461	−	29.4984i	0.310313	−	0.955046i
$955$	−1.62550	−	1.18100i	−0.0526000	−	0.0382161i
$956$	−0.510794			−0.0165203
$957$	64.1097	−	60.4231i	2.07237	−	1.95320i
$958$	−12.5716			−0.406169
$959$	37.0475	+	26.9166i	1.19633	+	0.869182i
$960$	−1.87228	+	5.76227i	−0.0604274	+	0.185977i
$961$	17.1179	+	52.6836i	0.552191	+	1.69947i
$962$	−2.62295	+	1.90568i	−0.0845673	+	0.0614417i
$963$	37.8975	−	27.5342i	1.22123	−	0.887276i
$964$	−6.99021	−	21.5136i	−0.225139	−	0.692908i
$965$	−3.11861	+	9.59811i	−0.100392	+	0.308974i
$966$	13.4948	+	9.80457i	0.434189	+	0.315457i
$967$	27.7370			0.891963			0.445981	−	0.895042i	$-0.352855\pi$
$967$	27.7370			0.891963			0.445981	+	0.895042i	$0.352855\pi$
$968$	−10.2422	−	4.01209i	−0.329198	−	0.128953i
$969$	13.0129			0.418033
$970$	−15.3285	−	11.1368i	−0.492168	−	0.357581i
$971$	−1.92301	+	5.91840i	−0.0617122	+	0.189931i	−0.977159	−	0.212507i	$-0.931837\pi$
$971$	−1.92301	+	5.91840i	−0.0617122	+	0.189931i	0.915447	+	0.402438i	$0.131837\pi$
$972$	0.494739	+	1.52265i	0.0158688	+	0.0488390i
$973$	−7.12348	+	5.17551i	−0.228368	+	0.165919i
$974$	16.6991	−	12.1326i	0.535073	−	0.388753i
$975$	−2.71565	−	8.35791i	−0.0869703	−	0.267667i
$976$	2.86211	−	8.80866i	0.0916138	−	0.281958i
$977$	−21.2073	−	15.4080i	−0.678482	−	0.492946i	0.194372	−	0.980928i	$-0.437733\pi$
$977$	−21.2073	−	15.4080i	−0.678482	−	0.492946i	−0.872854	+	0.487982i	$0.837733\pi$
$978$	0.448137			0.0143298
$979$	14.5981	−	13.7586i	0.466557	−	0.439728i
$980$	2.21350			0.0707077
$981$	70.0915	+	50.9245i	2.23785	+	1.62589i
$982$	−9.35239	+	28.7837i	−0.298447	+	0.918524i
$983$	5.03185	+	15.4864i	0.160491	+	0.493941i	0.998676	−	0.0514458i	$-0.0163829\pi$
$983$	5.03185	+	15.4864i	0.160491	+	0.493941i	−0.838185	+	0.545386i	$0.816383\pi$
$984$	12.5745	−	9.13587i	0.400859	−	0.291241i
$985$	−18.0150	+	13.0887i	−0.574005	+	0.417039i
$986$	−11.7540	−	36.1751i	−0.374324	−	1.15205i
$987$	−20.3622	+	62.6684i	−0.648136	+	1.99476i
$988$	2.45583	+	1.78426i	0.0781302	+	0.0567649i
$989$	−27.3037			−0.868206
$990$	40.2485	−	5.15906i	1.27918	−	0.163966i
$991$	22.4663			0.713664			0.356832	−	0.934169i	$-0.383857\pi$
$991$	22.4663			0.713664			0.356832	+	0.934169i	$0.383857\pi$
$992$	−7.51972	−	5.46339i	−0.238751	−	0.173463i
$993$	5.89783	−	18.1516i	0.187162	−	0.576025i
$994$	−8.07615	−	24.8558i	−0.256160	−	0.788379i
$995$	−16.9384	+	12.3065i	−0.536983	+	0.390141i
$996$	9.97727	−	7.24891i	0.316142	−	0.229691i
$997$	−5.97042	−	18.3751i	−0.189085	−	0.581944i	0.810910	−	0.585171i	$-0.198973\pi$
$997$	−5.97042	−	18.3751i	−0.189085	−	0.581944i	−0.999995	+	0.00322730i	$0.998973\pi$
$998$	−11.2020	+	34.4761i	−0.354592	+	1.09132i
$999$	−8.04151	−	5.84250i	−0.254422	−	0.184849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.f.191.4	✓	16
11.3	even	5	inner	418.2.f.f.267.4	yes	16
11.5	even	5		4598.2.a.ca.1.8		8
11.6	odd	10		4598.2.a.bx.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.191.4	✓	16	1.1	even	1	trivial
418.2.f.f.267.4	yes	16	11.3	even	5	inner
4598.2.a.bx.1.8		8	11.6	odd	10
4598.2.a.ca.1.8		8	11.5	even	5

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.931534 - 2.86697i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.62603 - 1.18138i) q^{5} +(-2.43879 + 1.77188i) q^{6} +(0.750517 + 2.30985i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.92469 - 3.57799i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.931534 - 2.86697i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.62603 - 1.18138i) q^{5} +(-2.43879 + 1.77188i) q^{6} +(0.750517 + 2.30985i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.92469 - 3.57799i) q^{9} -2.00989 q^{10} +(2.41358 - 2.27479i) q^{11} +3.01451 q^{12} +(-2.45583 - 1.78426i) q^{13} +(0.750517 - 2.30985i) q^{14} +(-1.87228 - 5.76227i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.49232 - 2.53732i) q^{17} +(1.88106 + 5.78932i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(1.62603 + 1.18138i) q^{20} +7.32140 q^{21} +(-3.28971 + 0.421676i) q^{22} -2.27832 q^{23} +(-2.43879 - 1.77188i) q^{24} +(-0.296768 + 0.913359i) q^{25} +(0.938042 + 2.88700i) q^{26} +(-7.52914 + 5.47024i) q^{27} +(-1.96488 + 1.42757i) q^{28} +(2.72288 + 8.38017i) q^{29} +(-1.87228 + 5.76227i) q^{30} +(-7.51972 - 5.46339i) q^{31} +1.00000 q^{32} +(-4.27340 - 9.03868i) q^{33} -4.31675 q^{34} +(3.94918 + 2.86925i) q^{35} +(1.88106 - 5.78932i) q^{36} +(0.330046 + 1.01578i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-7.40310 + 5.37867i) q^{39} +(-0.621089 - 1.91151i) q^{40} +(-1.59330 + 4.90367i) q^{41} +(-5.92314 - 4.30341i) q^{42} +11.9841 q^{43} +(2.90929 + 1.59250i) q^{44} -12.2347 q^{45} +(1.84320 + 1.33917i) q^{46} +(-2.78119 + 8.55962i) q^{47} +(0.931534 + 2.86697i) q^{48} +(0.890976 - 0.647332i) q^{49} +(0.776949 - 0.564487i) q^{50} +(-4.02120 - 12.3760i) q^{51} +(0.938042 - 2.88700i) q^{52} +(-4.12220 - 2.99495i) q^{53} +9.30653 q^{54} +(1.23716 - 6.55022i) q^{55} +2.42872 q^{56} +(2.43879 + 1.77188i) q^{57} +(2.72288 - 8.38017i) q^{58} +(-1.48041 - 4.55624i) q^{59} +(4.90168 - 3.56128i) q^{60} +(-7.49309 + 5.44405i) q^{61} +(2.87228 + 8.83996i) q^{62} +(4.56858 - 14.0606i) q^{63} +(-0.809017 - 0.587785i) q^{64} -6.10114 q^{65} +(-1.85555 + 9.82429i) q^{66} +9.19479 q^{67} +(3.49232 + 2.53732i) q^{68} +(-2.12234 + 6.53188i) q^{69} +(-1.50845 - 4.64254i) q^{70} +(8.70566 - 6.32503i) q^{71} +(-4.92469 + 3.57799i) q^{72} +(2.76254 + 8.50223i) q^{73} +(0.330046 - 1.01578i) q^{74} +(2.34212 + 1.70165i) q^{75} -1.00000 q^{76} +(7.06585 + 3.86774i) q^{77} +9.15074 q^{78} +(-5.27562 - 3.83296i) q^{79} +(-0.621089 + 1.91151i) q^{80} +(3.02616 + 9.31355i) q^{81} +(4.17131 - 3.03064i) q^{82} +(3.30975 - 2.40468i) q^{83} +(2.26244 + 6.96306i) q^{84} +(2.68108 - 8.25153i) q^{85} +(-9.69534 - 7.04408i) q^{86} +26.5621 q^{87} +(-1.41761 - 2.99839i) q^{88} +6.04832 q^{89} +(9.89806 + 7.19136i) q^{90} +(2.27824 - 7.01171i) q^{91} +(-0.704041 - 2.16682i) q^{92} +(-22.6682 + 16.4694i) q^{93} +(7.28125 - 5.29014i) q^{94} +(0.621089 + 1.91151i) q^{95} +(0.931534 - 2.86697i) q^{96} +(7.62654 + 5.54101i) q^{97} -1.10131 q^{98} +(-20.0253 + 2.56684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9	\( 16 q - 4 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{7} - 4 q^{8} - 20 q^{9} + 4 q^{10} + 2 q^{11} - 14 q^{13} + 6 q^{14} - 10 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{19} + 4 q^{20} + 28 q^{21} + 2 q^{22} + 24 q^{23} - 4 q^{26} - 18 q^{27} - 14 q^{28} - 22 q^{29} - 10 q^{30} - 24 q^{31} + 16 q^{32} + 2 q^{33} + 8 q^{34} - 20 q^{35} + 6 q^{37} + 4 q^{38} + 72 q^{39} - 6 q^{40} - 14 q^{41} - 22 q^{42} + 56 q^{43} + 12 q^{44} - 56 q^{45} + 4 q^{46} - 38 q^{47} - 36 q^{49} + 56 q^{51} - 4 q^{52} + 22 q^{53} - 48 q^{54} - 6 q^{55} + 16 q^{56} - 22 q^{58} - 28 q^{59} + 12 q^{61} + 26 q^{62} - 20 q^{63} - 4 q^{64} - 32 q^{65} + 12 q^{66} - 44 q^{67} + 8 q^{68} + 64 q^{69} - 20 q^{70} + 16 q^{71} - 20 q^{72} + 12 q^{73} + 6 q^{74} + 32 q^{75} - 16 q^{76} - 12 q^{77} - 8 q^{78} + 48 q^{79} - 6 q^{80} - 64 q^{81} + 6 q^{82} + 14 q^{83} + 8 q^{84} + 6 q^{85} - 14 q^{86} + 84 q^{87} - 8 q^{88} - 56 q^{89} + 34 q^{90} + 26 q^{91} - 16 q^{92} - 46 q^{93} + 32 q^{94} + 6 q^{95} - 24 q^{97} + 64 q^{98} - 56 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^7 - 4 * q^8 - 20 * q^9 + 4 * q^10 + 2 * q^11 - 14 * q^13 + 6 * q^14 - 10 * q^15 - 4 * q^16 + 8 * q^17 + 4 * q^19 + 4 * q^20 + 28 * q^21 + 2 * q^22 + 24 * q^23 - 4 * q^26 - 18 * q^27 - 14 * q^28 - 22 * q^29 - 10 * q^30 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 8 * q^34 - 20 * q^35 + 6 * q^37 + 4 * q^38 + 72 * q^39 - 6 * q^40 - 14 * q^41 - 22 * q^42 + 56 * q^43 + 12 * q^44 - 56 * q^45 + 4 * q^46 - 38 * q^47 - 36 * q^49 + 56 * q^51 - 4 * q^52 + 22 * q^53 - 48 * q^54 - 6 * q^55 + 16 * q^56 - 22 * q^58 - 28 * q^59 + 12 * q^61 + 26 * q^62 - 20 * q^63 - 4 * q^64 - 32 * q^65 + 12 * q^66 - 44 * q^67 + 8 * q^68 + 64 * q^69 - 20 * q^70 + 16 * q^71 - 20 * q^72 + 12 * q^73 + 6 * q^74 + 32 * q^75 - 16 * q^76 - 12 * q^77 - 8 * q^78 + 48 * q^79 - 6 * q^80 - 64 * q^81 + 6 * q^82 + 14 * q^83 + 8 * q^84 + 6 * q^85 - 14 * q^86 + 84 * q^87 - 8 * q^88 - 56 * q^89 + 34 * q^90 + 26 * q^91 - 16 * q^92 - 46 * q^93 + 32 * q^94 + 6 * q^95 - 24 * q^97 + 64 * q^98 - 56 * q^99

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