LMFDB - Embedded newform 930.2.n.c.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 25x^{10} + 205x^{8} + 675x^{6} + 795x^{4} + 230x^{2} + 5 $ x^12 + 25x^10 + 205x^8 + 675x^6 + 795x^4 + 230*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.2
Root			$2.29476i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.c.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.0931451 + 0.286671i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.0931451 + 0.286671i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.593145 - 1.82551i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(1.37343 - 0.997852i) q^{13} +(0.0931451 - 0.286671i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.87343 + 5.76581i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-0.820551 - 0.596165i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(-0.243857 - 0.177173i) q^{21} +(-0.593145 + 1.82551i) q^{22} +(0.226561 - 0.697284i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} -1.69765 q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.243857 + 0.177173i) q^{28} +(-6.77812 - 4.92459i) q^{29} -1.00000 q^{30} +(3.38009 - 4.42436i) q^{31} +1.00000 q^{32} +(1.55287 + 1.12823i) q^{33} +(4.90469 - 3.56347i) q^{34} +(-0.0931451 - 0.286671i) q^{35} +1.00000 q^{36} +5.63079 q^{37} +(0.313423 + 0.964616i) q^{38} +(-0.524602 + 1.61456i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-8.62572 - 6.26696i) q^{41} +(0.0931451 + 0.286671i) q^{42} +(3.50107 + 2.54368i) q^{43} +(1.55287 - 1.12823i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-0.593145 + 0.430945i) q^{46} +(6.97623 - 5.06853i) q^{47} +(0.309017 - 0.951057i) q^{48} +(5.58961 - 4.06109i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.87343 - 5.76581i) q^{51} +(1.37343 + 0.997852i) q^{52} +(3.79288 - 11.6733i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.593145 + 1.82551i) q^{55} +0.301424 q^{56} +1.01426 q^{57} +(2.58901 + 7.96815i) q^{58} +(10.0044 - 7.26861i) q^{59} +(0.809017 + 0.587785i) q^{60} -4.04671 q^{61} +(-5.33513 + 1.59262i) q^{62} +0.301424 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.37343 + 0.997852i) q^{65} +(-0.593145 - 1.82551i) q^{66} -8.33875 q^{67} -6.06253 q^{68} +(0.226561 + 0.697284i) q^{69} +(-0.0931451 + 0.286671i) q^{70} +(-4.12375 + 12.6916i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-4.20008 - 12.9265i) q^{73} +(-4.55540 - 3.30969i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(0.313423 - 0.964616i) q^{76} +(0.468074 - 0.340075i) q^{77} +(1.37343 - 0.997852i) q^{78} +(4.36251 - 13.4264i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.29473 + 10.1401i) q^{82} +(-4.46362 - 3.24301i) q^{83} +(0.0931451 - 0.286671i) q^{84} +(1.87343 - 5.76581i) q^{85} +(-1.33729 - 4.11575i) q^{86} +8.37821 q^{87} -1.91946 q^{88} +(-1.55287 - 4.77926i) q^{89} +(0.809017 - 0.587785i) q^{90} +(0.413983 + 0.300777i) q^{91} +0.733168 q^{92} +(-0.133974 + 5.56615i) q^{93} -8.62309 q^{94} +(0.820551 + 0.596165i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(3.23821 + 9.96617i) q^{97} -6.90914 q^{98} -1.91946 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - 5 q^{11} - 3 q^{12} - 3 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} + 4 q^{21} - 5 q^{22} + 10 q^{23} - 3 q^{24} + 12 q^{25} + 2 q^{26} - 3 q^{27} + 4 q^{28} - 5 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 5 q^{33} + 2 q^{34} + q^{35} + 12 q^{36} + 2 q^{37} + 11 q^{38} + 2 q^{39} + 3 q^{40} + 13 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} + 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 4 q^{49} - 3 q^{50} - 3 q^{51} - 3 q^{52} + 3 q^{53} - 3 q^{54} + 5 q^{55} - 6 q^{56} - 14 q^{57} + 10 q^{58} + 23 q^{59} + 3 q^{60} - 46 q^{61} + 7 q^{62} - 6 q^{63} - 3 q^{64} + 3 q^{65} - 5 q^{66} - 66 q^{67} + 2 q^{68} + 10 q^{69} + q^{70} + 23 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 3 q^{75} + 11 q^{76} + 10 q^{77} - 3 q^{78} + 21 q^{79} + 3 q^{80} - 3 q^{81} + 13 q^{82} + 4 q^{83} - q^{84} + 3 q^{85} - 4 q^{86} - 10 q^{87} - 5 q^{89} + 3 q^{90} - 6 q^{91} - 10 q^{92} - 3 q^{93} + 6 q^{94} + 4 q^{95} - 3 q^{96} + 25 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 - 5 * q^11 - 3 * q^12 - 3 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 + 4 * q^21 - 5 * q^22 + 10 * q^23 - 3 * q^24 + 12 * q^25 + 2 * q^26 - 3 * q^27 + 4 * q^28 - 5 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 5 * q^33 + 2 * q^34 + q^35 + 12 * q^36 + 2 * q^37 + 11 * q^38 + 2 * q^39 + 3 * q^40 + 13 * q^41 - q^42 + 16 * q^43 + 5 * q^44 + 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 4 * q^49 - 3 * q^50 - 3 * q^51 - 3 * q^52 + 3 * q^53 - 3 * q^54 + 5 * q^55 - 6 * q^56 - 14 * q^57 + 10 * q^58 + 23 * q^59 + 3 * q^60 - 46 * q^61 + 7 * q^62 - 6 * q^63 - 3 * q^64 + 3 * q^65 - 5 * q^66 - 66 * q^67 + 2 * q^68 + 10 * q^69 + q^70 + 23 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 3 * q^75 + 11 * q^76 + 10 * q^77 - 3 * q^78 + 21 * q^79 + 3 * q^80 - 3 * q^81 + 13 * q^82 + 4 * q^83 - q^84 + 3 * q^85 - 4 * q^86 - 10 * q^87 - 5 * q^89 + 3 * q^90 - 6 * q^91 - 10 * q^92 - 3 * q^93 + 6 * q^94 + 4 * q^95 - 3 * q^96 + 25 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.00000			0.408248
$7$	0.0931451	+	0.286671i	0.0352056	+	0.108352i	0.967115	−	0.254339i	$-0.0818580\pi$
$7$	0.0931451	+	0.286671i	0.0352056	+	0.108352i	−0.931909	+	0.362691i	$0.881858\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	−0.593145	−	1.82551i	−0.178840	−	0.550413i	0.820948	−	0.571003i	$-0.193446\pi$
$11$	−0.593145	−	1.82551i	−0.178840	−	0.550413i	−0.999788	+	0.0205901i	$0.993446\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	1.37343	−	0.997852i	0.380920	−	0.276754i	−0.380805	−	0.924655i	$-0.624353\pi$
$13$	1.37343	−	0.997852i	0.380920	−	0.276754i	0.761724	+	0.647901i	$0.224353\pi$
$14$	0.0931451	−	0.286671i	0.0248941	−	0.0766161i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.87343	+	5.76581i	−0.454372	+	1.39841i	0.417498	+	0.908678i	$0.362907\pi$
$17$	−1.87343	+	5.76581i	−0.454372	+	1.39841i	−0.871870	+	0.489737i	$0.837093\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	−0.820551	−	0.596165i	−0.188247	−	0.136770i	0.489670	−	0.871908i	$-0.337117\pi$
$19$	−0.820551	−	0.596165i	−0.188247	−	0.136770i	−0.677917	+	0.735138i	$0.737117\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	−0.243857	−	0.177173i	−0.0532140	−	0.0386622i
$22$	−0.593145	+	1.82551i	−0.126459	+	0.389201i
$23$	0.226561	−	0.697284i	0.0472413	−	0.145394i	−0.924653	−	0.380810i	$-0.875645\pi$
$23$	0.226561	−	0.697284i	0.0472413	−	0.145394i	0.971895	+	0.235416i	$0.0756453\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	1.00000			0.200000
$26$	−1.69765			−0.332936
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.243857	+	0.177173i	−0.0460847	+	0.0334825i
$29$	−6.77812	−	4.92459i	−1.25866	−	0.914473i	−0.259973	−	0.965616i	$-0.583714\pi$
$29$	−6.77812	−	4.92459i	−1.25866	−	0.914473i	−0.998691	+	0.0511425i	$0.983714\pi$
$30$	−1.00000			−0.182574
$31$	3.38009	−	4.42436i	0.607082	−	0.794639i
$31$	3.38009	−	4.42436i	0.607082	−	0.794639i
$32$	1.00000			0.176777
$33$	1.55287	+	1.12823i	0.270321	+	0.196399i
$34$	4.90469	−	3.56347i	0.841148	−	0.611129i
$35$	−0.0931451	−	0.286671i	−0.0157444	−	0.0484563i
$36$	1.00000			0.166667
$37$	5.63079			0.925696			0.462848	−	0.886438i	$-0.346828\pi$
$37$	5.63079			0.925696			0.462848	+	0.886438i	$0.346828\pi$
$38$	0.313423	+	0.964616i	0.0508439	+	0.156481i
$39$	−0.524602	+	1.61456i	−0.0840035	+	0.258536i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	−8.62572	−	6.26696i	−1.34711	−	0.978734i	−0.999150	−	0.0412253i	$-0.986874\pi$
$41$	−8.62572	−	6.26696i	−1.34711	−	0.978734i	−0.347962	−	0.937509i	$-0.613126\pi$
$42$	0.0931451	+	0.286671i	0.0143726	+	0.0442343i
$43$	3.50107	+	2.54368i	0.533908	+	0.387907i	0.821818	−	0.569751i	$-0.192960\pi$
$43$	3.50107	+	2.54368i	0.533908	+	0.387907i	−0.287910	+	0.957658i	$0.592960\pi$
$44$	1.55287	−	1.12823i	0.234105	−	0.170087i
$45$	−0.309017	+	0.951057i	−0.0460655	+	0.141775i
$46$	−0.593145	+	0.430945i	−0.0874545	+	0.0635394i
$47$	6.97623	−	5.06853i	1.01759	−	0.739321i	0.0518005	−	0.998657i	$-0.483504\pi$
$47$	6.97623	−	5.06853i	1.01759	−	0.739321i	0.965787	+	0.259337i	$0.0835040\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	5.58961	−	4.06109i	0.798516	−	0.580156i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−1.87343	−	5.76581i	−0.262332	−	0.807375i
$52$	1.37343	+	0.997852i	0.190460	+	0.138377i
$53$	3.79288	−	11.6733i	0.520993	−	1.60345i	−0.251114	−	0.967957i	$-0.580797\pi$
$53$	3.79288	−	11.6733i	0.520993	−	1.60345i	0.772107	−	0.635493i	$-0.219203\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	0.593145	+	1.82551i	0.0799797	+	0.246152i
$56$	0.301424			0.0402795
$57$	1.01426			0.134342
$58$	2.58901	+	7.96815i	0.339954	+	1.04627i
$59$	10.0044	−	7.26861i	1.30246	−	0.946292i	0.302483	−	0.953155i	$-0.402184\pi$
$59$	10.0044	−	7.26861i	1.30246	−	0.946292i	0.999976	+	0.00686274i	$0.00218449\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−4.04671			−0.518128			−0.259064	−	0.965860i	$-0.583414\pi$
$61$	−4.04671			−0.518128			−0.259064	+	0.965860i	$0.583414\pi$
$62$	−5.33513	+	1.59262i	−0.677562	+	0.202263i
$63$	0.301424			0.0379759
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.37343	+	0.997852i	−0.170352	+	0.123768i
$66$	−0.593145	−	1.82551i	−0.0730111	−	0.224705i
$67$	−8.33875			−1.01874			−0.509370	−	0.860548i	$-0.670122\pi$
$67$	−8.33875			−1.01874			−0.509370	+	0.860548i	$0.670122\pi$
$68$	−6.06253			−0.735190
$69$	0.226561	+	0.697284i	0.0272748	+	0.0839431i
$70$	−0.0931451	+	0.286671i	−0.0111330	+	0.0342638i
$71$	−4.12375	+	12.6916i	−0.489399	+	1.50622i	0.336108	+	0.941824i	$0.390889\pi$
$71$	−4.12375	+	12.6916i	−0.489399	+	1.50622i	−0.825507	+	0.564392i	$0.809111\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−4.20008	−	12.9265i	−0.491583	−	1.51294i	−0.822216	−	0.569176i	$-0.807262\pi$
$73$	−4.20008	−	12.9265i	−0.491583	−	1.51294i	0.330633	−	0.943759i	$-0.392738\pi$
$74$	−4.55540	−	3.30969i	−0.529555	−	0.384744i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	0.313423	−	0.964616i	0.0359520	−	0.110649i
$77$	0.468074	−	0.340075i	0.0533419	−	0.0387552i
$78$	1.37343	−	0.997852i	0.155510	−	0.112984i
$79$	4.36251	−	13.4264i	0.490820	−	1.51059i	−0.332550	−	0.943086i	$-0.607909\pi$
$79$	4.36251	−	13.4264i	0.490820	−	1.51059i	0.823371	−	0.567504i	$-0.192091\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	3.29473	+	10.1401i	0.363842	+	1.11979i
$83$	−4.46362	−	3.24301i	−0.489946	−	0.355967i	0.315217	−	0.949020i	$-0.397923\pi$
$83$	−4.46362	−	3.24301i	−0.489946	−	0.355967i	−0.805164	+	0.593053i	$0.797923\pi$
$84$	0.0931451	−	0.286671i	0.0101630	−	0.0312784i
$85$	1.87343	−	5.76581i	0.203202	−	0.625390i
$86$	−1.33729	−	4.11575i	−0.144204	−	0.443813i
$87$	8.37821			0.898239
$88$	−1.91946			−0.204615
$89$	−1.55287	−	4.77926i	−0.164604	−	0.506600i	0.834403	−	0.551155i	$-0.185813\pi$
$89$	−1.55287	−	4.77926i	−0.164604	−	0.506600i	−0.999007	+	0.0445554i	$0.985813\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	0.413983	+	0.300777i	0.0433972	+	0.0315299i
$92$	0.733168			0.0764380
$93$	−0.133974	+	5.56615i	−0.0138924	+	0.577183i
$94$	−8.62309			−0.889404
$95$	0.820551	+	0.596165i	0.0841868	+	0.0611653i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	3.23821	+	9.96617i	0.328790	+	1.01191i	0.969701	+	0.244296i	$0.0785568\pi$
$97$	3.23821	+	9.96617i	0.328790	+	1.01191i	−0.640911	+	0.767615i	$0.721443\pi$
$98$	−6.90914			−0.697929
$99$	−1.91946			−0.192913
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	5.26846	−	16.2146i	0.524231	−	1.61342i	−0.241600	−	0.970376i	$-0.577672\pi$
$101$	5.26846	−	16.2146i	0.524231	−	1.61342i	0.765831	−	0.643042i	$-0.222328\pi$
$102$	−1.87343	+	5.76581i	−0.185497	+	0.570900i
$103$	12.2257	+	8.88246i	1.20463	+	0.875214i	0.994732	−	0.102509i	$-0.0326871\pi$
$103$	12.2257	+	8.88246i	1.20463	+	0.875214i	0.209897	+	0.977723i	$0.432687\pi$
$104$	−0.524602	−	1.61456i	−0.0514414	−	0.158320i
$105$	0.243857	+	0.177173i	0.0237980	+	0.0172903i
$106$	−9.92990	+	7.21449i	−0.964477	+	0.700733i
$107$	−2.91795	+	8.98053i	−0.282089	+	0.868181i	0.705167	+	0.709041i	$0.250872\pi$
$107$	−2.91795	+	8.98053i	−0.282089	+	0.868181i	−0.987256	+	0.159140i	$0.949128\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−2.36335	+	1.71708i	−0.226368	+	0.164466i	−0.695188	−	0.718827i	$-0.744679\pi$
$109$	−2.36335	+	1.71708i	−0.226368	+	0.164466i	0.468821	+	0.883293i	$0.344679\pi$
$110$	0.593145	−	1.82551i	0.0565542	−	0.174056i
$111$	−4.55540	+	3.30969i	−0.432380	+	0.314142i
$112$	−0.243857	−	0.177173i	−0.0230423	−	0.0167412i
$113$	−2.07035	−	6.37187i	−0.194762	−	0.599416i	−0.999979	−	0.00643577i	$-0.997951\pi$
$113$	−2.07035	−	6.37187i	−0.194762	−	0.599416i	0.805217	−	0.592980i	$-0.202049\pi$
$114$	−0.820551	−	0.596165i	−0.0768517	−	0.0558360i
$115$	−0.226561	+	0.697284i	−0.0211269	+	0.0650221i
$116$	2.58901	−	7.96815i	0.240384	−	0.739824i
$117$	−0.524602	−	1.61456i	−0.0484995	−	0.149266i
$118$	−12.3661			−1.13839
$119$	−1.82739			−0.167517
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	5.91851	−	4.30005i	0.538046	−	0.390914i
$122$	3.27386	+	2.37860i	0.296401	+	0.215348i
$123$	10.6620			0.961358
$124$	5.25233	+	1.84745i	0.471673	+	0.165906i
$125$	−1.00000			−0.0894427
$126$	−0.243857	−	0.177173i	−0.0217245	−	0.0157838i
$127$	−7.06331	+	5.13180i	−0.626768	+	0.455373i	−0.855279	−	0.518168i	$-0.826614\pi$
$127$	−7.06331	+	5.13180i	−0.626768	+	0.455373i	0.228511	+	0.973541i	$0.426614\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−4.32756			−0.381020
$130$	1.69765			0.148893
$131$	−4.53811	−	13.9669i	−0.396496	−	1.22029i	−0.927790	−	0.373102i	$-0.878294\pi$
$131$	−4.53811	−	13.9669i	−0.396496	−	1.22029i	0.531294	−	0.847188i	$-0.321706\pi$
$132$	−0.593145	+	1.82551i	−0.0516267	+	0.158891i
$133$	0.0944731	−	0.290758i	0.00819186	−	0.0252119i
$134$	6.74619	+	4.90139i	0.582782	+	0.423416i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	4.90469	+	3.56347i	0.420574	+	0.305565i
$137$	−8.84654	+	6.42739i	−0.755811	+	0.549129i	−0.897623	−	0.440765i	$-0.854707\pi$
$137$	−8.84654	+	6.42739i	−0.755811	+	0.549129i	0.141812	+	0.989894i	$0.454707\pi$
$138$	0.226561	−	0.697284i	0.0192862	−	0.0593568i
$139$	4.50876	−	3.27580i	0.382428	−	0.277850i	−0.379918	−	0.925020i	$-0.624048\pi$
$139$	4.50876	−	3.27580i	0.382428	−	0.277850i	0.762345	+	0.647170i	$0.224048\pi$
$140$	0.243857	−	0.177173i	0.0206097	−	0.0149738i
$141$	−2.66468	+	8.20105i	−0.224407	+	0.690653i
$142$	10.7961	−	7.84384i	0.905990	−	0.658240i
$143$	−2.63623	−	1.91533i	−0.220453	−	0.160168i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	6.77812	+	4.92459i	0.562892	+	0.408965i
$146$	−4.20008	+	12.9265i	−0.347601	+	1.06981i
$147$	−2.13504	+	6.57099i	−0.176095	+	0.541966i
$148$	1.74001	+	5.35520i	0.143028	+	0.440195i
$149$	−7.00394			−0.573785			−0.286893	−	0.957963i	$-0.592622\pi$
$149$	−7.00394			−0.573785			−0.286893	+	0.957963i	$0.592622\pi$
$150$	1.00000			0.0816497
$151$	0.00761175	+	0.0234266i	0.000619435	+	0.00190643i	0.951366	−	0.308064i	$-0.0996810\pi$
$151$	0.00761175	+	0.0234266i	0.000619435	+	0.00190643i	−0.950746	+	0.309970i	$0.899681\pi$
$152$	−0.820551	+	0.596165i	−0.0665555	+	0.0483554i
$153$	4.90469	+	3.56347i	0.396521	+	0.288089i
$154$	−0.578571			−0.0466226
$155$	−3.38009	+	4.42436i	−0.271495	+	0.355373i
$156$	−1.69765			−0.135921
$157$	−10.2440	−	7.44272i	−0.817562	−	0.593994i	0.0984509	−	0.995142i	$-0.468611\pi$
$157$	−10.2440	−	7.44272i	−0.817562	−	0.593994i	−0.916013	+	0.401148i	$0.868611\pi$
$158$	−11.4212	+	8.29798i	−0.908621	+	0.660152i
$159$	3.79288	+	11.6733i	0.300795	+	0.925752i
$160$	−1.00000			−0.0790569
$161$	0.220994			0.0174168
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	1.60749	−	4.94733i	0.125908	−	0.387505i	−0.868157	−	0.496289i	$-0.834696\pi$
$163$	1.60749	−	4.94733i	0.125908	−	0.387505i	0.994065	+	0.108784i	$0.0346956\pi$
$164$	3.29473	−	10.1401i	0.257275	−	0.791812i
$165$	−1.55287	−	1.12823i	−0.120891	−	0.0878325i
$166$	1.70495	+	5.24731i	0.132330	+	0.407270i
$167$	11.2920	+	8.20414i	0.873804	+	0.634856i	0.931605	−	0.363473i	$-0.118409\pi$
$167$	11.2920	+	8.20414i	0.873804	+	0.634856i	−0.0578012	+	0.998328i	$0.518409\pi$
$168$	−0.243857	+	0.177173i	−0.0188140	+	0.0136692i
$169$	−3.12663	+	9.62278i	−0.240510	+	0.740214i
$170$	−4.90469	+	3.56347i	−0.376173	+	0.273305i
$171$	−0.820551	+	0.596165i	−0.0627491	+	0.0455899i
$172$	−1.33729	+	4.11575i	−0.101967	+	0.313823i
$173$	−2.71001	+	1.96894i	−0.206038	+	0.149695i	−0.686019	−	0.727583i	$-0.740643\pi$
$173$	−2.71001	+	1.96894i	−0.206038	+	0.149695i	0.479981	+	0.877279i	$0.340643\pi$
$174$	−6.77812	−	4.92459i	−0.513848	−	0.373332i
$175$	0.0931451	+	0.286671i	0.00704111	+	0.0216703i
$176$	1.55287	+	1.12823i	0.117052	+	0.0850435i
$177$	−3.82133	+	11.7609i	−0.287229	+	0.884000i
$178$	−1.55287	+	4.77926i	−0.116393	+	0.358220i
$179$	2.49401	+	7.67579i	0.186411	+	0.573715i	0.999970	−	0.00776783i	$-0.00247260\pi$
$179$	2.49401	+	7.67579i	0.186411	+	0.573715i	−0.813558	+	0.581483i	$0.802473\pi$
$180$	−1.00000			−0.0745356
$181$	−5.83254			−0.433529			−0.216765	−	0.976224i	$-0.569550\pi$
$181$	−5.83254			−0.433529			−0.216765	+	0.976224i	$0.569550\pi$
$182$	−0.158128	−	0.486667i	−0.0117212	−	0.0360741i
$183$	3.27386	−	2.37860i	0.242011	−	0.175831i
$184$	−0.593145	−	0.430945i	−0.0437272	−	0.0317697i
$185$	−5.63079			−0.413984
$186$	3.38009	−	4.42436i	0.247840	−	0.324410i
$187$	11.6368			0.850965
$188$	6.97623	+	5.06853i	0.508794	+	0.369660i
$189$	−0.243857	+	0.177173i	−0.0177380	+	0.0128874i
$190$	−0.313423	−	0.964616i	−0.0227381	−	0.0699806i
$191$	1.89318			0.136986			0.0684928	−	0.997652i	$-0.478181\pi$
$191$	1.89318			0.136986			0.0684928	+	0.997652i	$0.478181\pi$
$192$	1.00000			0.0721688
$193$	−2.57844	−	7.93563i	−0.185600	−	0.571219i	0.814358	−	0.580363i	$-0.197089\pi$
$193$	−2.57844	−	7.93563i	−0.185600	−	0.571219i	−0.999958	+	0.00914401i	$0.997089\pi$
$194$	3.23821	−	9.96617i	0.232490	−	0.715529i
$195$	0.524602	−	1.61456i	0.0375675	−	0.115621i
$196$	5.58961	+	4.06109i	0.399258	+	0.290078i
$197$	2.57451	+	7.92354i	0.183426	+	0.564529i	0.999918	−	0.0128292i	$-0.00408377\pi$
$197$	2.57451	+	7.92354i	0.183426	+	0.564529i	−0.816491	+	0.577358i	$0.804084\pi$
$198$	1.55287	+	1.12823i	0.110358	+	0.0801798i
$199$	−3.00060	+	2.18007i	−0.212707	+	0.154541i	−0.689038	−	0.724725i	$-0.741967\pi$
$199$	−3.00060	+	2.18007i	−0.212707	+	0.154541i	0.476331	+	0.879266i	$0.341967\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	6.74619	−	4.90139i	0.475840	−	0.345718i
$202$	−13.7930	+	10.0212i	−0.970472	+	0.705089i
$203$	0.780390	−	2.40179i	0.0547726	−	0.168573i
$204$	4.90469	−	3.56347i	0.343397	−	0.249493i
$205$	8.62572	+	6.26696i	0.602447	+	0.437703i
$206$	−4.66978	−	14.3721i	−0.325359	−	1.00135i
$207$	−0.593145	−	0.430945i	−0.0412264	−	0.0299528i
$208$	−0.524602	+	1.61456i	−0.0363746	+	0.111949i
$209$	−0.601602	+	1.85154i	−0.0416137	+	0.128074i
$210$	−0.0931451	−	0.286671i	−0.00642763	−	0.0197822i
$211$	−4.81058			−0.331174			−0.165587	−	0.986195i	$-0.552952\pi$
$211$	−4.81058			−0.331174			−0.165587	+	0.986195i	$0.552952\pi$
$212$	12.2740			0.842984
$213$	−4.12375	−	12.6916i	−0.282555	−	0.869614i
$214$	7.63930	−	5.55028i	0.522212	−	0.379409i
$215$	−3.50107	−	2.54368i	−0.238771	−	0.173477i
$216$	1.00000			0.0680414
$217$	1.58318	+	0.556866i	0.107473	+	0.0378026i
$218$	2.92126			0.197853
$219$	10.9960	+	7.98903i	0.743038	+	0.539849i
$220$	−1.55287	+	1.12823i	−0.104695	+	0.0760652i
$221$	3.18041	+	9.78831i	0.213938	+	0.658433i
$222$	5.63079			0.377914
$223$	5.83323			0.390622			0.195311	−	0.980741i	$-0.437428\pi$
$223$	5.83323			0.390622			0.195311	+	0.980741i	$0.437428\pi$
$224$	0.0931451	+	0.286671i	0.00622352	+	0.0191540i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−2.07035	+	6.37187i	−0.137717	+	0.423851i
$227$	22.3073	+	16.2072i	1.48059	+	1.07571i	0.977366	+	0.211556i	$0.0678530\pi$
$227$	22.3073	+	16.2072i	1.48059	+	1.07571i	0.503224	+	0.864156i	$0.332147\pi$
$228$	0.313423	+	0.964616i	0.0207569	+	0.0638832i
$229$	4.84150	+	3.51755i	0.319935	+	0.232447i	0.736148	−	0.676821i	$-0.236643\pi$
$229$	4.84150	+	3.51755i	0.319935	+	0.232447i	−0.416213	+	0.909267i	$0.636643\pi$
$230$	0.593145	−	0.430945i	0.0391108	−	0.0284157i
$231$	−0.178788	+	0.550253i	−0.0117634	+	0.0362040i
$232$	−6.77812	+	4.92459i	−0.445005	+	0.323315i
$233$	−13.9212	+	10.1143i	−0.912007	+	0.662612i	−0.941522	−	0.336952i	$-0.890604\pi$
$233$	−13.9212	+	10.1143i	−0.912007	+	0.662612i	0.0295143	+	0.999564i	$0.490604\pi$
$234$	−0.524602	+	1.61456i	−0.0342943	+	0.105547i
$235$	−6.97623	+	5.06853i	−0.455079	+	0.330634i
$236$	10.0044	+	7.26861i	0.651230	+	0.473146i
$237$	4.36251	+	13.4264i	0.283375	+	0.872139i
$238$	1.47839	+	1.07411i	0.0958299	+	0.0696245i
$239$	−5.13678	+	15.8094i	−0.332271	+	1.02262i	0.635780	+	0.771870i	$0.280678\pi$
$239$	−5.13678	+	15.8094i	−0.332271	+	1.02262i	−0.968051	+	0.250754i	$0.919322\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	4.36415	+	13.4315i	0.281120	+	0.865197i	0.987535	+	0.157400i	$0.0503111\pi$
$241$	4.36415	+	13.4315i	0.281120	+	0.865197i	−0.706415	+	0.707797i	$0.749689\pi$
$242$	−7.31568			−0.470270
$243$	1.00000			0.0641500
$244$	−1.25050	−	3.84865i	−0.0800552	−	0.246385i
$245$	−5.58961	+	4.06109i	−0.357107	+	0.259454i
$246$	−8.62572	−	6.26696i	−0.549956	−	0.399566i
$247$	−1.72185			−0.109559
$248$	−3.16332	−	4.58186i	−0.200871	−	0.290948i
$249$	5.51734			0.349647
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	25.2280	−	18.3292i	1.59238	−	1.15693i	0.691928	−	0.721966i	$-0.256761\pi$
$251$	25.2280	−	18.3292i	1.59238	−	1.15693i	0.900448	−	0.434963i	$-0.143239\pi$
$252$	0.0931451	+	0.286671i	0.00586759	+	0.0180586i
$253$	−1.40728			−0.0884752
$254$	8.73074			0.547815
$255$	1.87343	+	5.76581i	0.117318	+	0.361069i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.20029	+	6.77179i	−0.137250	+	0.422412i	−0.995933	−	0.0900945i	$-0.971283\pi$
$257$	−2.20029	+	6.77179i	−0.137250	+	0.422412i	0.858683	+	0.512507i	$0.171283\pi$
$258$	3.50107	+	2.54368i	0.217967	+	0.158362i
$259$	0.524481	+	1.61419i	0.0325896	+	0.100301i
$260$	−1.37343	−	0.997852i	−0.0851762	−	0.0618841i
$261$	−6.77812	+	4.92459i	−0.419555	+	0.304824i
$262$	−4.53811	+	13.9669i	−0.280365	+	0.862875i
$263$	15.1342	−	10.9956i	0.933214	−	0.678020i	−0.0135636	−	0.999908i	$-0.504318\pi$
$263$	15.1342	−	10.9956i	0.933214	−	0.678020i	0.946778	+	0.321888i	$0.104318\pi$
$264$	1.55287	−	1.12823i	0.0955728	−	0.0694377i
$265$	−3.79288	+	11.6733i	−0.232995	+	0.717085i
$266$	−0.247334	+	0.179699i	−0.0151650	+	0.0110180i
$267$	4.06548	+	2.95374i	0.248803	+	0.180766i
$268$	−2.57682	−	7.93062i	−0.157404	−	0.484440i
$269$	−18.0011	−	13.0786i	−1.09755	−	0.797416i	−0.116891	−	0.993145i	$-0.537293\pi$
$269$	−18.0011	−	13.0786i	−1.09755	−	0.797416i	−0.980658	+	0.195729i	$0.937293\pi$
$270$	−0.309017	+	0.951057i	−0.0188062	+	0.0578795i
$271$	−7.32369	+	22.5400i	−0.444883	+	1.36921i	0.437729	+	0.899107i	$0.355783\pi$
$271$	−7.32369	+	22.5400i	−0.444883	+	1.36921i	−0.882612	+	0.470102i	$0.844217\pi$
$272$	−1.87343	−	5.76581i	−0.113593	−	0.349604i
$273$	−0.511712			−0.0309702
$274$	10.9349			0.660603
$275$	−0.593145	−	1.82551i	−0.0357680	−	0.110083i
$276$	−0.593145	+	0.430945i	−0.0357031	+	0.0259399i
$277$	−16.9054	−	12.2825i	−1.01575	−	0.737983i	−0.0503397	−	0.998732i	$-0.516030\pi$
$277$	−16.9054	−	12.2825i	−1.01575	−	0.737983i	−0.965407	+	0.260749i	$0.916030\pi$
$278$	−5.57313			−0.334254
$279$	−3.16332	−	4.58186i	−0.189383	−	0.274309i
$280$	−0.301424			−0.0180135
$281$	12.2074	+	8.86921i	0.728234	+	0.529093i	0.889004	−	0.457899i	$-0.151398\pi$
$281$	12.2074	+	8.86921i	0.728234	+	0.529093i	−0.160770	+	0.986992i	$0.551398\pi$
$282$	6.97623	−	5.06853i	0.415428	−	0.301826i
$283$	−3.36020	−	10.3416i	−0.199743	−	0.614746i	−0.999888	−	0.0149398i	$-0.995244\pi$
$283$	−3.36020	−	10.3416i	−0.199743	−	0.614746i	0.800145	−	0.599806i	$-0.204756\pi$
$284$	−13.3447			−0.791864
$285$	−1.01426			−0.0600794
$286$	1.00695	+	3.09908i	0.0595423	+	0.183252i
$287$	0.993112	−	3.05648i	0.0586215	−	0.180419i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−15.9816	−	11.6113i	−0.940091	−	0.683016i
$290$	−2.58901	−	7.96815i	−0.152032	−	0.467906i
$291$	−8.47773	−	6.15943i	−0.496973	−	0.361072i
$292$	10.9960	−	7.98903i	0.643490	−	0.467523i
$293$	−0.254741	+	0.784012i	−0.0148821	+	0.0458024i	−0.958222	−	0.286026i	$-0.907666\pi$
$293$	−0.254741	+	0.784012i	−0.0148821	+	0.0458024i	0.943340	+	0.331829i	$0.107666\pi$
$294$	5.58961	−	4.06109i	0.325993	−	0.236848i
$295$	−10.0044	+	7.26861i	−0.582478	+	0.423195i
$296$	1.74001	−	5.35520i	0.101136	−	0.311265i
$297$	1.55287	−	1.12823i	0.0901069	−	0.0654665i
$298$	5.66631	+	4.11681i	0.328240	+	0.238481i
$299$	−0.384621	−	1.18374i	−0.0222432	−	0.0684576i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	−0.403091	+	1.24059i	−0.0232338	+	0.0715062i
$302$	0.00761175	−	0.0234266i	0.000438007	−	0.00134805i
$303$	5.26846	+	16.2146i	0.302665	+	0.931507i
$304$	1.01426			0.0581716
$305$	4.04671			0.231714
$306$	−1.87343	−	5.76581i	−0.107097	−	0.329609i
$307$	7.67922	−	5.57928i	0.438276	−	0.318426i	−0.346673	−	0.937986i	$-0.612689\pi$
$307$	7.67922	−	5.57928i	0.438276	−	0.318426i	0.784950	+	0.619559i	$0.212689\pi$
$308$	0.468074	+	0.340075i	0.0266710	+	0.0193776i
$309$	−15.1117			−0.859677
$310$	5.33513	−	1.59262i	0.303015	−	0.0904547i
$311$	0.780955			0.0442839			0.0221419	−	0.999755i	$-0.492951\pi$
$311$	0.780955			0.0442839			0.0221419	+	0.999755i	$0.492951\pi$
$312$	1.37343	+	0.997852i	0.0777549	+	0.0564922i
$313$	6.90155	−	5.01427i	0.390099	−	0.283423i	−0.375397	−	0.926864i	$-0.622494\pi$
$313$	6.90155	−	5.01427i	0.390099	−	0.283423i	0.765496	+	0.643441i	$0.222494\pi$
$314$	3.91287	+	12.0426i	0.220816	+	0.679602i
$315$	−0.301424			−0.0169833
$316$	14.1174			0.794164
$317$	10.9028	+	33.5552i	0.612360	+	1.88465i	0.434757	+	0.900548i	$0.356834\pi$
$317$	10.9028	+	33.5552i	0.612360	+	1.88465i	0.177603	+	0.984102i	$0.443166\pi$
$318$	3.79288	−	11.6733i	0.212694	−	0.654606i
$319$	−4.96950	+	15.2945i	−0.278238	+	0.856330i
$320$	0.809017	+	0.587785i	0.0452254	+	0.0328582i
$321$	−2.91795	−	8.98053i	−0.162864	−	0.501245i
$322$	−0.178788	−	0.129897i	−0.00996348	−	0.00723889i
$323$	4.97462	−	3.61427i	0.276795	−	0.201103i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	1.37343	−	0.997852i	0.0761839	−	0.0553509i
$326$	−4.20845	+	3.05762i	−0.233085	+	0.169346i
$327$	0.902720	−	2.77829i	0.0499205	−	0.153640i
$328$	−8.62572	+	6.26696i	−0.476276	+	0.346035i
$329$	2.10280	+	1.52778i	0.115931	+	0.0842290i
$330$	0.593145	+	1.82551i	0.0326516	+	0.100491i
$331$	12.6633	+	9.20040i	0.696036	+	0.505700i	0.878639	−	0.477487i	$-0.158452\pi$
$331$	12.6633	+	9.20040i	0.696036	+	0.505700i	−0.182603	+	0.983187i	$0.558452\pi$
$332$	1.70495	−	5.24731i	0.0935714	−	0.287983i
$333$	1.74001	−	5.35520i	0.0953519	−	0.293463i
$334$	−4.31317	−	13.2746i	−0.236006	−	0.726353i
$335$	8.33875			0.455595
$336$	0.301424			0.0164440
$337$	−5.30292	−	16.3207i	−0.288868	−	0.889045i	−0.985212	−	0.171337i	$-0.945191\pi$
$337$	−5.30292	−	16.3207i	−0.288868	−	0.889045i	0.696344	−	0.717708i	$-0.254809\pi$
$338$	8.18563	−	5.94721i	0.445240	−	0.323485i
$339$	5.42024	+	3.93803i	0.294387	+	0.213885i
$340$	6.06253			0.328787
$341$	−10.0816	−	3.54611i	−0.545950	−	0.192032i
$342$	1.01426			0.0548447
$343$	3.39184	+	2.46432i	0.183142	+	0.133061i
$344$	3.50107	−	2.54368i	0.188765	−	0.137146i
$345$	−0.226561	−	0.697284i	−0.0121976	−	0.0375405i
$346$	3.34975			0.180084
$347$	−24.4307			−1.31151			−0.655754	−	0.754974i	$-0.727649\pi$
$347$	−24.4307			−1.31151			−0.655754	+	0.754974i	$0.727649\pi$
$348$	2.58901	+	7.96815i	0.138786	+	0.427138i
$349$	6.04244	−	18.5967i	0.323444	−	0.995459i	−0.648694	−	0.761050i	$-0.724684\pi$
$349$	6.04244	−	18.5967i	0.323444	−	0.995459i	0.972138	−	0.234409i	$-0.0753156\pi$
$350$	0.0931451	−	0.286671i	0.00497882	−	0.0153232i
$351$	1.37343	+	0.997852i	0.0733080	+	0.0532614i
$352$	−0.593145	−	1.82551i	−0.0316147	−	0.0973002i
$353$	−25.1595	−	18.2795i	−1.33911	−	0.972918i	−0.999476	−	0.0323583i	$-0.989698\pi$
$353$	−25.1595	−	18.2795i	−1.33911	−	0.972918i	−0.339630	−	0.940559i	$-0.610302\pi$
$354$	10.0044	−	7.26861i	0.531727	−	0.386322i
$355$	4.12375	−	12.6916i	0.218866	−	0.673600i
$356$	4.06548	−	2.95374i	0.215470	−	0.156548i
$357$	1.47839	−	1.07411i	0.0782448	−	0.0568482i
$358$	2.49401	−	7.67579i	0.131813	−	0.405678i
$359$	−9.40505	+	6.83317i	−0.496380	+	0.360641i	−0.807632	−	0.589686i	$-0.799251\pi$
$359$	−9.40505	+	6.83317i	−0.496380	+	0.360641i	0.311253	+	0.950327i	$0.399251\pi$
$360$	0.809017	+	0.587785i	0.0426389	+	0.0309790i
$361$	−5.55343	−	17.0917i	−0.292286	−	0.899563i
$362$	4.71863	+	3.42828i	0.248005	+	0.180186i
$363$	−2.26067	+	6.95763i	−0.118654	+	0.365181i
$364$	−0.158128	+	0.486667i	−0.00828814	+	0.0255083i
$365$	4.20008	+	12.9265i	0.219842	+	0.676605i
$366$	−4.04671			−0.211525
$367$	−3.17893			−0.165939			−0.0829694	−	0.996552i	$-0.526440\pi$
$367$	−3.17893			−0.165939			−0.0829694	+	0.996552i	$0.526440\pi$
$368$	0.226561	+	0.697284i	0.0118103	+	0.0363484i
$369$	−8.62572	+	6.26696i	−0.449037	+	0.326245i
$370$	4.55540	+	3.30969i	0.236824	+	0.172063i
$371$	3.69969			0.192078
$372$	−5.33513	+	1.59262i	−0.276613	+	0.0825734i
$373$	−11.1982			−0.579821			−0.289910	−	0.957054i	$-0.593626\pi$
$373$	−11.1982			−0.579821			−0.289910	+	0.957054i	$0.593626\pi$
$374$	−9.41435	−	6.83992i	−0.486804	−	0.353684i
$375$	0.809017	−	0.587785i	0.0417775	−	0.0303531i
$376$	−2.66468	−	8.20105i	−0.137420	−	0.422937i
$377$	−14.2232			−0.732535
$378$	0.301424			0.0155036
$379$	−5.36811	−	16.5213i	−0.275741	−	0.848644i	−0.989022	−	0.147766i	$-0.952792\pi$
$379$	−5.36811	−	16.5213i	−0.275741	−	0.848644i	0.713281	−	0.700878i	$-0.247208\pi$
$380$	−0.313423	+	0.964616i	−0.0160782	+	0.0494837i
$381$	2.69795	−	8.30342i	0.138220	−	0.425397i
$382$	−1.53161	−	1.11278i	−0.0783641	−	0.0569349i
$383$	−5.98349	−	18.4153i	−0.305742	−	0.940978i	−0.979399	−	0.201934i	$-0.935277\pi$
$383$	−5.98349	−	18.4153i	−0.305742	−	0.940978i	0.673657	−	0.739044i	$-0.264723\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	−0.468074	+	0.340075i	−0.0238552	+	0.0173318i
$386$	−2.57844	+	7.93563i	−0.131239	+	0.403913i
$387$	3.50107	−	2.54368i	0.177969	−	0.129302i
$388$	−8.47773	+	6.15943i	−0.430392	+	0.312698i
$389$	1.94161	−	5.97565i	0.0984433	−	0.302977i	−0.889692	−	0.456560i	$-0.849081\pi$
$389$	1.94161	−	5.97565i	0.0984433	−	0.302977i	0.988136	+	0.153583i	$0.0490812\pi$
$390$	−1.37343	+	0.997852i	−0.0695461	+	0.0505282i
$391$	3.59596	+	2.61262i	0.181856	+	0.132126i
$392$	−2.13504	−	6.57099i	−0.107836	−	0.331885i
$393$	11.8809	+	8.63199i	0.599313	+	0.435426i
$394$	2.57451	−	7.92354i	0.129702	−	0.399182i
$395$	−4.36251	+	13.4264i	−0.219502	+	0.675556i
$396$	−0.593145	−	1.82551i	−0.0298067	−	0.0917355i
$397$	−15.2426			−0.765004			−0.382502	−	0.923955i	$-0.624938\pi$
$397$	−15.2426			−0.765004			−0.382502	+	0.923955i	$0.624938\pi$
$398$	3.70895			0.185913
$399$	0.0944731	+	0.290758i	0.00472957	+	0.0145561i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	15.7850	+	11.4685i	0.788265	+	0.572708i	0.907448	−	0.420164i	$-0.138027\pi$
$401$	15.7850	+	11.4685i	0.788265	+	0.572708i	−0.119183	+	0.992872i	$0.538027\pi$
$402$	−8.33875			−0.415899
$403$	0.227440	−	9.44936i	0.0113296	−	0.470706i
$404$	17.0491			0.848224
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	−2.04309	+	1.48439i	−0.101397	+	0.0736690i
$407$	−3.33987	−	10.2791i	−0.165551	−	0.509515i
$408$	−6.06253			−0.300140
$409$	−36.4460			−1.80214			−0.901069	−	0.433675i	$-0.857216\pi$
$409$	−36.4460			−1.80214			−0.901069	+	0.433675i	$0.857216\pi$
$410$	−3.29473	−	10.1401i	−0.162715	−	0.500786i
$411$	3.37908	−	10.3997i	0.166678	−	0.512981i
$412$	−4.66978	+	14.3721i	−0.230064	+	0.708063i
$413$	3.01556	+	2.19093i	0.148386	+	0.107809i
$414$	0.226561	+	0.697284i	0.0111349	+	0.0342696i
$415$	4.46362	+	3.24301i	0.219111	+	0.159193i
$416$	1.37343	−	0.997852i	0.0673377	−	0.0489237i
$417$	−1.72219	+	5.30036i	−0.0843361	+	0.259560i
$418$	1.57501	−	1.14431i	0.0770364	−	0.0559702i
$419$	26.4835	−	19.2414i	1.29380	−	0.940003i	0.293929	−	0.955827i	$-0.405037\pi$
$419$	26.4835	−	19.2414i	1.29380	−	0.940003i	0.999875	+	0.0158240i	$0.00503716\pi$
$420$	−0.0931451	+	0.286671i	−0.00454502	+	0.0139881i
$421$	28.6747	−	20.8334i	1.39752	−	1.01536i	0.402526	−	0.915408i	$-0.368132\pi$
$421$	28.6747	−	20.8334i	1.39752	−	1.01536i	0.994993	−	0.0999486i	$-0.0318678\pi$
$422$	3.89184	+	2.82759i	0.189452	+	0.137645i
$423$	−2.66468	−	8.20105i	−0.129561	−	0.398749i
$424$	−9.92990	−	7.21449i	−0.482238	−	0.350367i
$425$	−1.87343	+	5.76581i	−0.0908745	+	0.279683i
$426$	−4.12375	+	12.6916i	−0.199796	+	0.614910i
$427$	−0.376931	−	1.16008i	−0.0182410	−	0.0561400i
$428$	−9.44269			−0.456430
$429$	3.25856			0.157325
$430$	1.33729	+	4.11575i	0.0644898	+	0.198479i
$431$	−11.1014	+	8.06565i	−0.534737	+	0.388509i	−0.822127	−	0.569305i	$-0.807212\pi$
$431$	−11.1014	+	8.06565i	−0.534737	+	0.388509i	0.287390	+	0.957814i	$0.407212\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−16.9141			−0.812842			−0.406421	−	0.913686i	$-0.633223\pi$
$433$	−16.9141			−0.812842			−0.406421	+	0.913686i	$0.633223\pi$
$434$	−0.953499	−	1.38108i	−0.0457694	−	0.0662941i
$435$	−8.37821			−0.401705
$436$	−2.36335	−	1.71708i	−0.113184	−	0.0822330i
$437$	−0.601602	+	0.437089i	−0.0287785	+	0.0209088i
$438$	−4.20008	−	12.9265i	−0.200688	−	0.617653i
$439$	−29.7817			−1.42140			−0.710702	−	0.703493i	$-0.751623\pi$
$439$	−29.7817			−1.42140			−0.710702	+	0.703493i	$0.751623\pi$
$440$	1.91946			0.0915066
$441$	−2.13504	−	6.57099i	−0.101669	−	0.312904i
$442$	3.18041	−	9.78831i	0.151277	−	0.465582i
$443$	3.53498	−	10.8795i	0.167952	−	0.516903i	−0.831290	−	0.555839i	$-0.812397\pi$
$443$	3.53498	−	10.8795i	0.167952	−	0.516903i	0.999242	+	0.0389366i	$0.0123970\pi$
$444$	−4.55540	−	3.30969i	−0.216190	−	0.157071i
$445$	1.55287	+	4.77926i	0.0736133	+	0.226558i
$446$	−4.71918	−	3.42869i	−0.223460	−	0.162353i
$447$	5.66631	−	4.11681i	0.268007	−	0.194719i
$448$	0.0931451	−	0.286671i	0.00440069	−	0.0135439i
$449$	−22.0797	+	16.0419i	−1.04201	+	0.757062i	−0.970676	−	0.240390i	$-0.922725\pi$
$449$	−22.0797	+	16.0419i	−1.04201	+	0.757062i	−0.0713307	+	0.997453i	$0.522725\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	−6.32410	+	19.4636i	−0.297790	+	0.916504i
$452$	5.42024	−	3.93803i	0.254947	−	0.185230i
$453$	−0.0199278	−	0.0144784i	−0.000936290	−	0.000680255i
$454$	−8.52065	−	26.2239i	−0.399894	−	1.23075i
$455$	−0.413983	−	0.300777i	−0.0194078	−	0.0141006i
$456$	0.313423	−	0.964616i	0.0146774	−	0.0451723i
$457$	5.18402	−	15.9548i	0.242498	−	0.746333i	−0.753539	−	0.657403i	$-0.771655\pi$
$457$	5.18402	−	15.9548i	0.242498	−	0.746333i	0.996038	−	0.0889306i	$-0.0283449\pi$
$458$	−1.84929	−	5.69152i	−0.0864116	−	0.265947i
$459$	−6.06253			−0.282975
$460$	−0.733168			−0.0341841
$461$	−1.49597	−	4.60414i	−0.0696745	−	0.214436i	0.910156	−	0.414265i	$-0.135961\pi$
$461$	−1.49597	−	4.60414i	−0.0696745	−	0.214436i	−0.979831	+	0.199829i	$0.935961\pi$
$462$	0.468074	−	0.340075i	0.0217768	−	0.0158217i
$463$	−3.41551	−	2.48152i	−0.158732	−	0.115326i	0.505584	−	0.862777i	$-0.331277\pi$
$463$	−3.41551	−	2.48152i	−0.158732	−	0.115326i	−0.664316	+	0.747452i	$0.731277\pi$
$464$	8.37821			0.388949
$465$	0.133974	−	5.56615i	0.00621289	−	0.258124i
$466$	17.2075			0.797124
$467$	16.4997	+	11.9877i	0.763515	+	0.554726i	0.899987	−	0.435918i	$-0.143576\pi$
$467$	16.4997	+	11.9877i	0.763515	+	0.554726i	−0.136471	+	0.990644i	$0.543576\pi$
$468$	1.37343	−	0.997852i	0.0634866	−	0.0461257i
$469$	−0.776714	−	2.39048i	−0.0358653	−	0.110382i
$470$	8.62309			0.397754
$471$	12.6623			0.583449
$472$	−3.82133	−	11.7609i	−0.175891	−	0.541337i
$473$	2.56687	−	7.90002i	0.118025	−	0.363243i
$474$	4.36251	−	13.4264i	0.200377	−	0.616696i
$475$	−0.820551	−	0.596165i	−0.0376495	−	0.0273539i
$476$	−0.564695	−	1.73795i	−0.0258828	−	0.0796590i
$477$	−9.92990	−	7.21449i	−0.454659	−	0.330329i
$478$	13.4483	−	9.77073i	0.615109	−	0.446903i
$479$	−7.34868	+	22.6169i	−0.335770	+	1.03339i	0.630572	+	0.776131i	$0.282821\pi$
$479$	−7.34868	+	22.6169i	−0.335770	+	1.03339i	−0.966342	+	0.257263i	$0.917179\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	7.73347	−	5.61869i	0.352616	−	0.256190i
$482$	4.36415	−	13.4315i	0.198782	−	0.611787i
$483$	−0.178788	+	0.129897i	−0.00813514	+	0.00591053i
$484$	5.91851	+	4.30005i	0.269023	+	0.195457i
$485$	−3.23821	−	9.96617i	−0.147039	−	0.452540i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	−2.97634	+	9.16022i	−0.134871	+	0.415089i	−0.995570	−	0.0940247i	$-0.970027\pi$
$487$	−2.97634	+	9.16022i	−0.134871	+	0.415089i	0.860699	+	0.509114i	$0.170027\pi$
$488$	−1.25050	+	3.84865i	−0.0566076	+	0.174220i
$489$	1.60749	+	4.94733i	0.0726930	+	0.223726i
$490$	6.90914			0.312123
$491$	0.214977			0.00970179			0.00485090	−	0.999988i	$-0.498456\pi$
$491$	0.214977			0.00970179			0.00485090	+	0.999988i	$0.498456\pi$
$492$	3.29473	+	10.1401i	0.148538	+	0.457153i
$493$	41.0925	−	29.8555i	1.85072	−	1.34462i
$494$	1.39301	+	1.01208i	0.0626743	+	0.0455356i
$495$	1.91946			0.0862732
$496$	−0.133974	+	5.56615i	−0.00601560	+	0.249928i
$497$	−4.02242			−0.180430
$498$	−4.46362	−	3.24301i	−0.200020	−	0.145323i
$499$	−0.798799	+	0.580362i	−0.0357592	+	0.0259806i	−0.605521	−	0.795829i	$-0.707035\pi$
$499$	−0.798799	+	0.580362i	−0.0357592	+	0.0259806i	0.569762	+	0.821810i	$0.307035\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−13.9577			−0.623585
$502$	−31.1835			−1.39179
$503$	10.1217	+	31.1514i	0.451305	+	1.38897i	0.875419	+	0.483364i	$0.160585\pi$
$503$	10.1217	+	31.1514i	0.451305	+	1.38897i	−0.424115	+	0.905608i	$0.639415\pi$
$504$	0.0931451	−	0.286671i	0.00414901	−	0.0127694i
$505$	−5.26846	+	16.2146i	−0.234443	+	0.721542i
$506$	1.13852	+	0.827181i	0.0506133	+	0.0367727i
$507$	−3.12663	−	9.62278i	−0.138859	−	0.427363i
$508$	−7.06331	−	5.13180i	−0.313384	−	0.227687i
$509$	23.2269	−	16.8753i	1.02951	−	0.747985i	0.0613014	−	0.998119i	$-0.480475\pi$
$509$	23.2269	−	16.8753i	1.02951	−	0.747985i	0.968211	+	0.250135i	$0.0804749\pi$
$510$	1.87343	−	5.76581i	0.0829567	−	0.255314i
$511$	3.31445	−	2.40809i	0.146622	−	0.106527i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	0.313423	−	0.964616i	0.0138379	−	0.0425888i
$514$	5.76043	−	4.18519i	0.254081	−	0.184601i
$515$	−12.2257	−	8.88246i	−0.538727	−	0.391408i
$516$	−1.33729	−	4.11575i	−0.0588709	−	0.181186i
$517$	−13.3906	−	9.72882i	−0.588917	−	0.427873i
$518$	0.524481	−	1.61419i	0.0230444	−	0.0709232i
$519$	1.03513	−	3.18580i	0.0454372	−	0.139841i
$520$	0.524602	+	1.61456i	0.0230053	+	0.0708031i
$521$	−29.6167			−1.29753			−0.648767	−	0.760987i	$-0.724715\pi$
$521$	−29.6167			−1.29753			−0.648767	+	0.760987i	$0.724715\pi$
$522$	8.37821			0.366704
$523$	−5.30259	−	16.3197i	−0.231866	−	0.713610i	−0.997522	−	0.0703593i	$-0.977585\pi$
$523$	−5.30259	−	16.3197i	−0.231866	−	0.713610i	0.765656	−	0.643250i	$-0.222415\pi$
$524$	11.8809	−	8.63199i	0.519020	−	0.377090i
$525$	−0.243857	−	0.177173i	−0.0106428	−	0.00773245i
$526$	−18.7069			−0.815659
$527$	19.1777	+	27.7777i	0.835394	+	1.21001i
$528$	−1.91946			−0.0835337
$529$	18.1725	+	13.2031i	0.790109	+	0.574048i
$530$	9.92990	−	7.21449i	0.431327	−	0.313378i
$531$	−3.82133	−	11.7609i	−0.165832	−	0.510378i
$532$	0.305721			0.0132547
$533$	−18.1003			−0.784010
$534$	−1.55287	−	4.77926i	−0.0671994	−	0.206819i
$535$	2.91795	−	8.98053i	0.126154	−	0.388262i
$536$	−2.57682	+	7.93062i	−0.111301	+	0.342551i
$537$	−6.52942	−	4.74390i	−0.281765	−	0.204714i
$538$	6.87582	+	21.1616i	0.296438	+	0.912342i
$539$	−10.7290	−	7.79510i	−0.462132	−	0.335759i
$540$	0.809017	−	0.587785i	0.0348145	−	0.0252942i
$541$	−2.34950	+	7.23102i	−0.101013	+	0.310886i	−0.988774	−	0.149419i	$-0.952260\pi$
$541$	−2.34950	+	7.23102i	−0.101013	+	0.310886i	0.887761	+	0.460305i	$0.152260\pi$
$542$	19.1737	−	13.9305i	0.823580	−	0.598366i
$543$	4.71863	−	3.42828i	0.202496	−	0.147122i
$544$	−1.87343	+	5.76581i	−0.0803224	+	0.247207i
$545$	2.36335	−	1.71708i	0.101235	−	0.0735514i
$546$	0.413983	+	0.300777i	0.0177169	+	0.0128720i
$547$	−8.71765	−	26.8302i	−0.372740	−	1.14718i	−0.944991	−	0.327097i	$-0.893930\pi$
$547$	−8.71765	−	26.8302i	−0.372740	−	1.14718i	0.572251	−	0.820079i	$-0.306070\pi$
$548$	−8.84654	−	6.42739i	−0.377905	−	0.274564i
$549$	−1.25050	+	3.84865i	−0.0533701	+	0.164256i
$550$	−0.593145	+	1.82551i	−0.0252918	+	0.0778401i
$551$	2.62592	+	8.08176i	0.111868	+	0.344294i
$552$	0.733168			0.0312057
$553$	4.25531			0.180954
$554$	6.45728	+	19.8735i	0.274344	+	0.844343i
$555$	4.55540	−	3.30969i	0.193366	−	0.140489i
$556$	4.50876	+	3.27580i	0.191214	+	0.138925i
$557$	29.7642			1.26115			0.630575	−	0.776128i	$-0.282819\pi$
$557$	29.7642			1.26115			0.630575	+	0.776128i	$0.282819\pi$
$558$	−0.133974	+	5.56615i	−0.00567156	+	0.235634i
$559$	7.34667			0.310731
$560$	0.243857	+	0.177173i	0.0103048	+	0.00748691i
$561$	−9.41435	+	6.83992i	−0.397474	+	0.288782i
$562$	−4.66282	−	14.3507i	−0.196689	−	0.605347i
$563$	24.7782			1.04428			0.522138	−	0.852861i	$-0.325135\pi$
$563$	24.7782			1.04428			0.522138	+	0.852861i	$0.325135\pi$
$564$	−8.62309			−0.363098
$565$	2.07035	+	6.37187i	0.0871002	+	0.268067i
$566$	−3.36020	+	10.3416i	−0.141240	+	0.434691i
$567$	0.0931451	−	0.286671i	0.00391173	−	0.0120391i
$568$	10.7961	+	7.84384i	0.452995	+	0.329120i
$569$	4.99091	+	15.3604i	0.209230	+	0.643943i	0.999513	+	0.0312015i	$0.00993335\pi$
$569$	4.99091	+	15.3604i	0.209230	+	0.643943i	−0.790283	+	0.612742i	$0.790067\pi$
$570$	0.820551	+	0.596165i	0.0343691	+	0.0249706i
$571$	−12.1262	+	8.81020i	−0.507466	+	0.368696i	−0.811861	−	0.583850i	$-0.801546\pi$
$571$	−12.1262	+	8.81020i	−0.507466	+	0.368696i	0.304396	+	0.952546i	$0.401546\pi$
$572$	1.00695	−	3.09908i	0.0421027	−	0.129579i
$573$	−1.53161	+	1.11278i	−0.0639840	+	0.0464871i
$574$	−2.60000	+	1.88901i	−0.108522	+	0.0788458i
$575$	0.226561	−	0.697284i	0.00944826	−	0.0290788i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−27.7142	−	20.1355i	−1.15376	−	0.838253i	−0.164781	−	0.986330i	$-0.552692\pi$
$577$	−27.7142	−	20.1355i	−1.15376	−	0.838253i	−0.988976	+	0.148077i	$0.952692\pi$
$578$	6.10441	+	18.7874i	0.253910	+	0.781455i
$579$	6.75045	+	4.90449i	0.280539	+	0.203824i
$580$	−2.58901	+	7.96815i	−0.107503	+	0.330860i
$581$	0.513914	−	1.58166i	0.0213207	−	0.0656185i
$582$	3.23821	+	9.96617i	0.134228	+	0.413111i
$583$	−23.5595			−0.975734
$584$	−13.5918			−0.562431
$585$	0.524602	+	1.61456i	0.0216896	+	0.0667538i
$586$	0.666920	−	0.484546i	0.0275502	−	0.0200164i
$587$	−33.4170	−	24.2789i	−1.37927	−	1.00210i	−0.996948	−	0.0780665i	$-0.975125\pi$
$587$	−33.4170	−	24.2789i	−1.37927	−	1.00210i	−0.382320	−	0.924030i	$-0.624875\pi$
$588$	−6.90914			−0.284928
$589$	−5.41119	+	1.61532i	−0.222964	+	0.0665583i
$590$	12.3661			0.509104
$591$	−6.74016	−	4.89702i	−0.277253	−	0.201436i
$592$	−4.55540	+	3.30969i	−0.187226	+	0.136028i
$593$	7.29433	+	22.4496i	0.299542	+	0.921896i	0.981658	+	0.190652i	$0.0610600\pi$
$593$	7.29433	+	22.4496i	0.299542	+	0.921896i	−0.682116	+	0.731244i	$0.738940\pi$
$594$	−1.91946			−0.0787563
$595$	1.82739			0.0749158
$596$	−2.16434	−	6.66115i	−0.0886547	−	0.272851i
$597$	1.14613	−	3.52742i	0.0469079	−	0.144368i
$598$	−0.384621	+	1.18374i	−0.0157283	+	0.0484068i
$599$	32.4054	+	23.5439i	1.32405	+	0.961978i	0.999872	+	0.0159816i	$0.00508732\pi$
$599$	32.4054	+	23.5439i	1.32405	+	0.961978i	0.324177	+	0.945996i	$0.394913\pi$
$600$	0.309017	+	0.951057i	0.0126156	+	0.0388267i
$601$	30.3192	+	22.0282i	1.23675	+	0.898549i	0.997377	−	0.0723797i	$-0.0230594\pi$
$601$	30.3192	+	22.0282i	1.23675	+	0.898549i	0.239369	+	0.970929i	$0.423059\pi$
$602$	1.05531	−	0.766725i	0.0430111	−	0.0312494i
$603$	−2.57682	+	7.93062i	−0.104936	+	0.322960i
$604$	−0.0199278	+	0.0144784i	−0.000810851	+	0.000589118i
$605$	−5.91851	+	4.30005i	−0.240622	+	0.174822i
$606$	5.26846	−	16.2146i	0.214017	−	0.658675i
$607$	12.8881	−	9.36373i	0.523110	−	0.380062i	−0.294664	−	0.955601i	$-0.595208\pi$
$607$	12.8881	−	9.36373i	0.523110	−	0.380062i	0.817774	+	0.575539i	$0.195208\pi$
$608$	−0.820551	−	0.596165i	−0.0332777	−	0.0241777i
$609$	0.780390	+	2.40179i	0.0316230	+	0.0973256i
$610$	−3.27386	−	2.37860i	−0.132555	−	0.0963066i
$611$	4.52369	−	13.9225i	0.183009	−	0.563243i
$612$	−1.87343	+	5.76581i	−0.0757287	+	0.233069i
$613$	5.65357	+	17.3999i	0.228345	+	0.702775i	0.997935	+	0.0642356i	$0.0204609\pi$
$613$	5.65357	+	17.3999i	0.228345	+	0.702775i	−0.769589	+	0.638539i	$0.779539\pi$
$614$	−9.49204			−0.383068
$615$	−10.6620			−0.429933
$616$	−0.178788	−	0.550253i	−0.00720358	−	0.0221703i
$617$	13.0595	−	9.48829i	0.525756	−	0.381984i	−0.293012	−	0.956109i	$-0.594657\pi$
$617$	13.0595	−	9.48829i	0.525756	−	0.381984i	0.818768	+	0.574125i	$0.194657\pi$
$618$	12.2257	+	8.88246i	0.491788	+	0.357305i
$619$	13.3098			0.534966			0.267483	−	0.963563i	$-0.413808\pi$
$619$	13.3098			0.534966			0.267483	+	0.963563i	$0.413808\pi$
$620$	−5.25233	−	1.84745i	−0.210938	−	0.0741955i
$621$	0.733168			0.0294210
$622$	−0.631805	−	0.459034i	−0.0253331	−	0.0184056i
$623$	1.22543	−	0.890329i	0.0490959	−	0.0356703i
$624$	−0.524602	−	1.61456i	−0.0210009	−	0.0646341i
$625$	1.00000			0.0400000
$626$	−8.53079			−0.340959
$627$	−0.601602	−	1.85154i	−0.0240257	−	0.0739434i
$628$	3.91287	−	12.0426i	0.156141	−	0.480551i
$629$	−10.5489	+	32.4661i	−0.420611	+	1.29451i
$630$	0.243857	+	0.177173i	0.00971550	+	0.00705872i
$631$	−9.57670	−	29.4741i	−0.381243	−	1.17334i	−0.939170	−	0.343454i	$-0.888403\pi$
$631$	−9.57670	−	29.4741i	−0.381243	−	1.17334i	0.557927	−	0.829890i	$-0.311597\pi$
$632$	−11.4212	−	8.29798i	−0.454311	−	0.330076i
$633$	3.89184	−	2.82759i	0.154687	−	0.112387i
$634$	10.9028	−	33.5552i	0.433004	−	1.33265i
$635$	7.06331	−	5.13180i	0.280299	−	0.203649i
$636$	−9.92990	+	7.21449i	−0.393746	+	0.286073i
$637$	3.62455	−	11.1552i	0.143610	−	0.441986i
$638$	13.0103	−	9.45254i	0.515083	−	0.374230i
$639$	10.7961	+	7.84384i	0.427088	+	0.310297i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	18.7966	+	13.6566i	0.742423	+	0.539402i	0.893469	−	0.449125i	$-0.148264\pi$
$641$	18.7966	+	13.6566i	0.742423	+	0.539402i	−0.151046	+	0.988527i	$0.548264\pi$
$642$	−2.91795	+	8.98053i	−0.115162	+	0.354433i
$643$	0.805716	−	2.47974i	0.0317744	−	0.0977914i	−0.933912	−	0.357504i	$-0.883628\pi$
$643$	0.805716	−	2.47974i	0.0317744	−	0.0977914i	0.965686	+	0.259713i	$0.0836278\pi$
$644$	0.0682910	+	0.210178i	0.00269104	+	0.00828218i
$645$	4.32756			0.170397
$646$	−6.14897			−0.241928
$647$	5.96242	+	18.3505i	0.234407	+	0.721431i	0.997200	+	0.0747874i	$0.0238278\pi$
$647$	5.96242	+	18.3505i	0.234407	+	0.721431i	−0.762792	+	0.646643i	$0.776172\pi$
$648$	−0.809017	+	0.587785i	−0.0317812	+	0.0230904i
$649$	−19.2030	−	13.9518i	−0.753783	−	0.547656i
$650$	−1.69765			−0.0665872
$651$	−1.60813	+	0.480054i	−0.0630278	+	0.0188148i
$652$	5.20194			0.203724
$653$	11.6485	+	8.46312i	0.455840	+	0.331187i	0.791897	−	0.610654i	$-0.209093\pi$
$653$	11.6485	+	8.46312i	0.455840	+	0.331187i	−0.336057	+	0.941842i	$0.609093\pi$
$654$	−2.36335	+	1.71708i	−0.0924143	+	0.0671429i
$655$	4.53811	+	13.9669i	0.177319	+	0.545730i
$656$	10.6620			0.416280
$657$	−13.5918			−0.530265
$658$	−0.803199	−	2.47199i	−0.0313120	−	0.0963683i
$659$	11.2919	−	34.7530i	0.439872	−	1.35379i	−0.448139	−	0.893964i	$-0.647913\pi$
$659$	11.2919	−	34.7530i	0.439872	−	1.35379i	0.888011	−	0.459822i	$-0.152087\pi$
$660$	0.593145	−	1.82551i	0.0230881	−	0.0710580i
$661$	23.0838	+	16.7714i	0.897856	+	0.652331i	0.937915	−	0.346866i	$-0.112754\pi$
$661$	23.0838	+	16.7714i	0.897856	+	0.652331i	−0.0400581	+	0.999197i	$0.512754\pi$
$662$	−4.83693	−	14.8866i	−0.187993	−	0.578582i
$663$	−8.32643	−	6.04951i	−0.323372	−	0.234943i
$664$	−4.46362	+	3.24301i	−0.173222	+	0.125853i
$665$	−0.0944731	+	0.290758i	−0.00366351	+	0.0112751i
$666$	−4.55540	+	3.30969i	−0.176518	+	0.128248i
$667$	−4.96950	+	3.61055i	−0.192420	+	0.139801i
$668$	−4.31317	+	13.2746i	−0.166882	+	0.513609i
$669$	−4.71918	+	3.42869i	−0.182454	+	0.132561i
$670$	−6.74619	−	4.90139i	−0.260628	−	0.189357i
$671$	2.40029	+	7.38732i	0.0926620	+	0.285184i
$672$	−0.243857	−	0.177173i	−0.00940699	−	0.00683458i
$673$	−3.57193	+	10.9933i	−0.137688	+	0.423759i	−0.995998	−	0.0893712i	$-0.971514\pi$
$673$	−3.57193	+	10.9933i	−0.137688	+	0.423759i	0.858311	+	0.513130i	$0.171514\pi$
$674$	−5.30292	+	16.3207i	−0.204261	+	0.628650i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	−10.1180			−0.389154
$677$	−3.65262			−0.140381			−0.0701907	−	0.997534i	$-0.522361\pi$
$677$	−3.65262			−0.140381			−0.0701907	+	0.997534i	$0.522361\pi$
$678$	−2.07035	−	6.37187i	−0.0795112	−	0.244710i
$679$	−2.55539	+	1.85660i	−0.0980669	+	0.0712498i
$680$	−4.90469	−	3.56347i	−0.188086	−	0.136653i
$681$	−27.5734			−1.05661
$682$	6.07185	+	8.79469i	0.232503	+	0.336766i
$683$	43.1871			1.65251			0.826255	−	0.563297i	$-0.190467\pi$
$683$	43.1871			1.65251			0.826255	+	0.563297i	$0.190467\pi$
$684$	−0.820551	−	0.596165i	−0.0313746	−	0.0227949i
$685$	8.84654	−	6.42739i	0.338009	−	0.245578i
$686$	−1.29557	−	3.98735i	−0.0494651	−	0.152238i
$687$	−5.98442			−0.228320
$688$	−4.32756			−0.164987
$689$	−6.43898	−	19.8171i	−0.245305	−	0.754973i
$690$	−0.226561	+	0.697284i	−0.00862504	+	0.0265451i
$691$	2.64432	−	8.13838i	0.100595	−	0.309599i	−0.888077	−	0.459695i	$-0.847959\pi$
$691$	2.64432	−	8.13838i	0.100595	−	0.309599i	0.988671	+	0.150097i	$0.0479586\pi$
$692$	−2.71001	−	1.96894i	−0.103019	−	0.0748477i
$693$	−0.178788	−	0.550253i	−0.00679160	−	0.0209024i
$694$	19.7649	+	14.3600i	0.750264	+	0.545098i
$695$	−4.50876	+	3.27580i	−0.171027	+	0.124258i
$696$	2.58901	−	7.96815i	0.0981362	−	0.302032i
$697$	52.2937	−	37.9936i	1.98077	−	1.43911i
$698$	−15.8193	+	11.4934i	−0.598770	+	0.435032i
$699$	5.31742	−	16.3653i	0.201123	−	0.618994i
$700$	−0.243857	+	0.177173i	−0.00921693	+	0.00669649i
$701$	6.79451	+	4.93650i	0.256625	+	0.186449i	0.708658	−	0.705552i	$-0.249301\pi$
$701$	6.79451	+	4.93650i	0.256625	+	0.186449i	−0.452033	+	0.892001i	$0.649301\pi$
$702$	−0.524602	−	1.61456i	−0.0197998	−	0.0609376i
$703$	−4.62035	−	3.35688i	−0.174260	−	0.126607i
$704$	−0.593145	+	1.82551i	−0.0223550	+	0.0688016i
$705$	2.66468	−	8.20105i	0.100358	−	0.308869i
$706$	9.61008	+	29.5768i	0.361680	+	1.11314i
$707$	5.13901			0.193272
$708$	−12.3661			−0.464746
$709$	0.400983	+	1.23410i	0.0150592	+	0.0463476i	0.958304	−	0.285751i	$-0.0922432\pi$
$709$	0.400983	+	1.23410i	0.0150592	+	0.0463476i	−0.943245	+	0.332099i	$0.892243\pi$
$710$	−10.7961	+	7.84384i	−0.405171	+	0.294374i
$711$	−11.4212	−	8.29798i	−0.428328	−	0.311199i
$712$	−5.02521			−0.188328
$713$	−2.31924	−	3.35927i	−0.0868562	−	0.125806i
$714$	−1.82739			−0.0683884
$715$	2.63623	+	1.91533i	0.0985895	+	0.0716295i
$716$	−6.52942	+	4.74390i	−0.244016	+	0.177288i
$717$	−5.13678	−	15.8094i	−0.191837	−	0.590412i
$718$	11.6253			0.433852
$719$	18.0319			0.672476			0.336238	−	0.941777i	$-0.390845\pi$
$719$	18.0319			0.672476			0.336238	+	0.941777i	$0.390845\pi$
$720$	−0.309017	−	0.951057i	−0.0115164	−	0.0354438i
$721$	−1.40758	+	4.33210i	−0.0524212	+	0.161336i
$722$	−5.55343	+	17.0917i	−0.206677	+	0.636087i
$723$	−11.4255	−	8.30111i	−0.424919	−	0.308721i
$724$	−1.80235	−	5.54708i	−0.0669840	−	0.206155i
$725$	−6.77812	−	4.92459i	−0.251733	−	0.182895i
$726$	5.91851	−	4.30005i	0.219657	−	0.159590i
$727$	0.686422	−	2.11259i	0.0254580	−	0.0783516i	−0.937520	−	0.347931i	$-0.886885\pi$
$727$	0.686422	−	2.11259i	0.0254580	−	0.0783516i	0.962978	+	0.269579i	$0.0868845\pi$
$728$	0.413983	−	0.300777i	0.0153432	−	0.0111475i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	4.20008	−	12.9265i	0.155452	−	0.478432i
$731$	−21.2253	+	15.4211i	−0.785048	+	0.570370i
$732$	3.27386	+	2.37860i	0.121005	+	0.0879155i
$733$	12.5632	+	38.6655i	0.464032	+	1.42814i	0.860196	+	0.509964i	$0.170341\pi$
$733$	12.5632	+	38.6655i	0.464032	+	1.42814i	−0.396164	+	0.918180i	$0.629659\pi$
$734$	2.57181	+	1.86853i	0.0949271	+	0.0689686i
$735$	2.13504	−	6.57099i	0.0787522	−	0.242374i
$736$	0.226561	−	0.697284i	0.00835116	−	0.0257022i
$737$	4.94609	+	15.2225i	0.182192	+	0.560728i
$738$	10.6620			0.392473
$739$	−33.5249			−1.23323			−0.616616	−	0.787264i	$-0.711497\pi$
$739$	−33.5249			−1.23323			−0.616616	+	0.787264i	$0.711497\pi$
$740$	−1.74001	−	5.35520i	−0.0639640	−	0.196861i
$741$	1.39301	−	1.01208i	0.0511734	−	0.0371796i
$742$	−2.99311	−	2.17462i	−0.109881	−	0.0798329i
$743$	−35.9338			−1.31828			−0.659141	−	0.752019i	$-0.729080\pi$
$743$	−35.9338			−1.31828			−0.659141	+	0.752019i	$0.729080\pi$
$744$	5.25233	+	1.84745i	0.192560	+	0.0677309i
$745$	7.00394			0.256605
$746$	9.05954	+	6.58214i	0.331693	+	0.240989i
$747$	−4.46362	+	3.24301i	−0.163315	+	0.118656i
$748$	3.59596	+	11.0672i	0.131481	+	0.404658i
$749$	−2.84625			−0.104000
$750$	−1.00000			−0.0365148
$751$	13.0765	+	40.2453i	0.477168	+	1.46857i	0.843012	+	0.537896i	$0.180781\pi$
$751$	13.0765	+	40.2453i	0.477168	+	1.46857i	−0.365844	+	0.930676i	$0.619219\pi$
$752$	−2.66468	+	8.20105i	−0.0971710	+	0.299061i
$753$	−9.63623	+	29.6573i	−0.351164	+	1.08077i
$754$	11.5068	+	8.36022i	0.419055	+	0.304461i
$755$	−0.00761175	−	0.0234266i	−0.000277020	−	0.000852579i
$756$	−0.243857	−	0.177173i	−0.00886900	−	0.00644370i
$757$	−23.9301	+	17.3863i	−0.869756	+	0.631914i	−0.930521	−	0.366238i	$-0.880646\pi$
$757$	−23.9301	+	17.3863i	−0.869756	+	0.631914i	0.0607657	+	0.998152i	$0.480646\pi$
$758$	−5.36811	+	16.5213i	−0.194978	+	0.600082i
$759$	1.13852	−	0.827181i	0.0413256	−	0.0300248i
$760$	0.820551	−	0.596165i	0.0297645	−	0.0216252i
$761$	13.6876	−	42.1261i	0.496176	−	1.52707i	−0.318941	−	0.947775i	$-0.603327\pi$
$761$	13.6876	−	42.1261i	0.496176	−	1.52707i	0.815117	−	0.579297i	$-0.196673\pi$
$762$	−7.06331	+	5.13180i	−0.255877	+	0.185905i
$763$	−0.712371	−	0.517568i	−0.0257896	−	0.0187372i
$764$	0.585024	+	1.80052i	0.0211654	+	0.0651405i
$765$	−4.90469	−	3.56347i	−0.177329	−	0.128837i
$766$	−5.98349	+	18.4153i	−0.216192	+	0.665372i
$767$	6.48727	−	19.9658i	0.234242	−	0.720922i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	10.7428			0.387394			0.193697	−	0.981061i	$-0.437952\pi$
$769$	10.7428			0.387394			0.193697	+	0.981061i	$0.437952\pi$
$770$	0.578571			0.0208502
$771$	−2.20029	−	6.77179i	−0.0792414	−	0.243880i
$772$	6.75045	−	4.90449i	0.242954	−	0.176516i
$773$	−30.5443	−	22.1917i	−1.09860	−	0.798181i	−0.117770	−	0.993041i	$-0.537575\pi$
$773$	−30.5443	−	22.1917i	−1.09860	−	0.798181i	−0.980831	+	0.194860i	$0.937575\pi$
$774$	−4.32756			−0.155551
$775$	3.38009	−	4.42436i	0.121416	−	0.158928i
$776$	10.4791			0.376176
$777$	−1.37311	−	0.997621i	−0.0492600	−	0.0357895i
$778$	−5.08319	+	3.69315i	−0.182241	+	0.132406i
$779$	3.34171	+	10.2847i	0.119729	+	0.368488i
$780$	1.69765			0.0607855
$781$	25.6147			0.916565
$782$	−1.37353	−	4.22731i	−0.0491175	−	0.151168i
$783$	2.58901	−	7.96815i	0.0925237	−	0.284759i
$784$	−2.13504	+	6.57099i	−0.0762515	+	0.234678i
$785$	10.2440	+	7.44272i	0.365625	+	0.265642i
$786$	−4.53811	−	13.9669i	−0.161869	−	0.498181i
$787$	−41.0698	−	29.8389i	−1.46398	−	1.06364i	−0.982304	−	0.187293i	$-0.940029\pi$
$787$	−41.0698	−	29.8389i	−1.46398	−	1.06364i	−0.481675	−	0.876350i	$-0.659971\pi$
$788$	−6.74016	+	4.89702i	−0.240108	+	0.174449i
$789$	−5.78075	+	17.7913i	−0.205800	+	0.633387i
$790$	11.4212	−	8.29798i	0.406348	−	0.295229i
$791$	1.63379	−	1.18702i	0.0580909	−	0.0422055i
$792$	−0.593145	+	1.82551i	−0.0210765	+	0.0648668i
$793$	−5.55785	+	4.03802i	−0.197365	+	0.143394i
$794$	12.3315	+	8.95937i	0.437629	+	0.317956i
$795$	−3.79288	−	11.6733i	−0.134520	−	0.414009i
$796$	−3.00060	−	2.18007i	−0.106354	−	0.0772704i
$797$	−2.33463	+	7.18525i	−0.0826968	+	0.254515i	−0.983853	−	0.178981i	$-0.942720\pi$
$797$	−2.33463	+	7.18525i	−0.0826968	+	0.254515i	0.901156	+	0.433495i	$0.142720\pi$
$798$	0.0944731	−	0.290758i	0.00334431	−	0.0102927i
$799$	16.1547	+	49.7191i	0.571513	+	1.75894i
$800$	1.00000			0.0353553
$801$	−5.02521			−0.177557
$802$	−6.02933	−	18.5564i	−0.212903	−	0.655249i
$803$	−21.1063	+	15.3346i	−0.744825	+	0.541147i
$804$	6.74619	+	4.90139i	0.237920	+	0.172859i
$805$	−0.220994			−0.00778903
$806$	−5.73820	+	7.51101i	−0.202119	+	0.264564i
$807$	22.2506			0.783259
$808$	−13.7930	−	10.0212i	−0.485236	−	0.352545i
$809$	23.5745	−	17.1279i	0.828837	−	0.602185i	−0.0903931	−	0.995906i	$-0.528812\pi$
$809$	23.5745	−	17.1279i	0.828837	−	0.602185i	0.919230	+	0.393721i	$0.128812\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−0.929803			−0.0326498			−0.0163249	−	0.999867i	$-0.505197\pi$
$811$	−0.929803			−0.0326498			−0.0163249	+	0.999867i	$0.505197\pi$
$812$	2.52539			0.0886240
$813$	−7.32369	−	22.5400i	−0.256853	−	0.790513i
$814$	−3.33987	+	10.2791i	−0.117063	+	0.360281i
$815$	−1.60749	+	4.94733i	−0.0563078	+	0.173298i
$816$	4.90469	+	3.56347i	0.171699	+	0.124746i
$817$	−1.35636	−	4.17443i	−0.0474529	−	0.146045i
$818$	29.4854	+	21.4224i	1.03093	+	0.749017i
$819$	0.413983	−	0.300777i	0.0144657	−	0.0105100i
$820$	−3.29473	+	10.1401i	−0.115057	+	0.354109i
$821$	19.6620	−	14.2853i	0.686209	−	0.498560i	−0.189202	−	0.981938i	$-0.560590\pi$
$821$	19.6620	−	14.2853i	0.686209	−	0.498560i	0.875412	+	0.483378i	$0.160590\pi$
$822$	−8.84654	+	6.42739i	−0.308558	+	0.224181i
$823$	−0.767845	+	2.36318i	−0.0267654	+	0.0823754i	−0.963547	−	0.267539i	$-0.913789\pi$
$823$	−0.767845	+	2.36318i	−0.0267654	+	0.0823754i	0.936782	+	0.349915i	$0.113789\pi$
$824$	12.2257	−	8.88246i	0.425901	−	0.309435i
$825$	1.55287	+	1.12823i	0.0540641	+	0.0392799i
$826$	−1.15184	−	3.54500i	−0.0400777	−	0.123346i
$827$	11.0198	+	8.00636i	0.383196	+	0.278408i	0.762662	−	0.646798i	$-0.223892\pi$
$827$	11.0198	+	8.00636i	0.383196	+	0.278408i	−0.379466	+	0.925206i	$0.623892\pi$
$828$	0.226561	−	0.697284i	0.00787355	−	0.0242323i
$829$	−6.34237	+	19.5198i	−0.220280	+	0.677951i	0.778457	+	0.627698i	$0.216003\pi$
$829$	−6.34237	+	19.5198i	−0.220280	+	0.677951i	−0.998737	+	0.0502528i	$0.983997\pi$
$830$	−1.70495	−	5.24731i	−0.0591798	−	0.182137i
$831$	20.8962			0.724881
$832$	−1.69765			−0.0588553
$833$	12.9438	+	39.8368i	0.448475	+	1.38026i
$834$	4.50876	−	3.27580i	0.156125	−	0.113432i
$835$	−11.2920	−	8.20414i	−0.390777	−	0.283916i
$836$	−1.94682			−0.0673323
$837$	5.25233	+	1.84745i	0.181547	+	0.0638573i
$838$	−32.7354			−1.13083
$839$	28.1049	+	20.4194i	0.970287	+	0.704955i	0.955517	−	0.294936i	$-0.0952983\pi$
$839$	28.1049	+	20.4194i	0.970287	+	0.704955i	0.0147703	+	0.999891i	$0.495298\pi$
$840$	0.243857	−	0.177173i	0.00841387	−	0.00611304i
$841$	12.7298	+	39.1782i	0.438958	+	1.35097i
$842$	−35.4439			−1.22148
$843$	−15.0892			−0.519700
$844$	−1.48655	−	4.57514i	−0.0511692	−	0.157483i
$845$	3.12663	−	9.62278i	0.107559	−	0.331034i
$846$	−2.66468	+	8.20105i	−0.0916137	+	0.281958i
$847$	1.78398	+	1.29614i	0.0612983	+	0.0445358i
$848$	3.79288	+	11.6733i	0.130248	+	0.400863i
$849$	8.79712	+	6.39148i	0.301916	+	0.219355i
$850$	4.90469	−	3.56347i	0.168230	−	0.122226i
$851$	1.27572	−	3.92626i	0.0437311	−	0.134590i
$852$	10.7961	−	7.84384i	0.369869	−	0.268725i
$853$	45.7299	−	33.2247i	1.56576	−	1.13759i	0.634686	−	0.772770i	$-0.281130\pi$
$853$	45.7299	−	33.2247i	1.56576	−	1.13759i	0.931077	−	0.364823i	$-0.118870\pi$
$854$	−0.376931	+	1.16008i	−0.0128983	+	0.0396970i
$855$	0.820551	−	0.596165i	0.0280623	−	0.0203884i
$856$	7.63930	+	5.55028i	0.261106	+	0.189705i
$857$	−3.90634	−	12.0225i	−0.133438	−	0.410680i	0.861906	−	0.507068i	$-0.169271\pi$
$857$	−3.90634	−	12.0225i	−0.133438	−	0.410680i	−0.995344	+	0.0963885i	$0.969271\pi$
$858$	−2.63623	−	1.91533i	−0.0899995	−	0.0653885i
$859$	−9.47310	+	29.1552i	−0.323218	+	0.994763i	0.649020	+	0.760771i	$0.275179\pi$
$859$	−9.47310	+	29.1552i	−0.323218	+	0.994763i	−0.972239	+	0.233992i	$0.924821\pi$
$860$	1.33729	−	4.11575i	0.0456012	−	0.140346i
$861$	0.993112	+	3.05648i	0.0338452	+	0.104165i
$862$	13.7221			0.467377
$863$	1.02759			0.0349796			0.0174898	−	0.999847i	$-0.494433\pi$
$863$	1.02759			0.0349796			0.0174898	+	0.999847i	$0.494433\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	2.71001	−	1.96894i	0.0921430	−	0.0669458i
$866$	13.6838	+	9.94188i	0.464995	+	0.337839i
$867$	19.7543			0.670891
$868$	−0.0403829	+	1.67777i	−0.00137069	+	0.0569473i
$869$	−27.0977			−0.919226
$870$	6.77812	+	4.92459i	0.229800	+	0.166959i
$871$	−11.4526	+	8.32084i	−0.388058	+	0.281941i
$872$	0.902720	+	2.77829i	0.0305699	+	0.0940846i
$873$	10.4791			0.354662
$874$	0.743620			0.0251533
$875$	−0.0931451	−	0.286671i	−0.00314888	−	0.00969126i
$876$	−4.20008	+	12.9265i	−0.141908	+	0.436747i
$877$	−4.57402	+	14.0774i	−0.154454	+	0.475359i	−0.998105	−	0.0615318i	$-0.980401\pi$
$877$	−4.57402	+	14.0774i	−0.154454	+	0.475359i	0.843652	+	0.536891i	$0.180401\pi$
$878$	24.0939	+	17.5053i	0.813131	+	0.590774i
$879$	−0.254741	−	0.784012i	−0.00859219	−	0.0264441i
$880$	−1.55287	−	1.12823i	−0.0523474	−	0.0380326i
$881$	−12.0154	+	8.72968i	−0.404808	+	0.294110i	−0.771497	−	0.636234i	$-0.780491\pi$
$881$	−12.0154	+	8.72968i	−0.404808	+	0.294110i	0.366689	+	0.930344i	$0.380491\pi$
$882$	−2.13504	+	6.57099i	−0.0718906	+	0.221257i
$883$	−12.3555	+	8.97677i	−0.415795	+	0.302092i	−0.775944	−	0.630802i	$-0.782726\pi$
$883$	−12.3555	+	8.97677i	−0.415795	+	0.302092i	0.360149	+	0.932895i	$0.382726\pi$
$884$	−8.32643	+	6.04951i	−0.280048	+	0.203467i
$885$	3.82133	−	11.7609i	0.128453	−	0.395337i
$886$	−9.25469	+	6.72393i	−0.310917	+	0.225895i
$887$	40.6309	+	29.5201i	1.36425	+	0.991187i	0.998162	+	0.0606075i	$0.0193038\pi$
$887$	40.6309	+	29.5201i	1.36425	+	0.991187i	0.366090	+	0.930579i	$0.380696\pi$
$888$	1.74001	+	5.35520i	0.0583909	+	0.179709i
$889$	−2.12905	−	1.54685i	−0.0714061	−	0.0518796i
$890$	1.55287	−	4.77926i	0.0520525	−	0.160201i
$891$	−0.593145	+	1.82551i	−0.0198711	+	0.0611570i
$892$	1.80257	+	5.54773i	0.0603544	+	0.185752i
$893$	−8.74603			−0.292675
$894$	−7.00394			−0.234247
$895$	−2.49401	−	7.67579i	−0.0833657	−	0.256573i
$896$	−0.243857	+	0.177173i	−0.00814670	+	0.00591892i
$897$	1.00695	+	0.731593i	0.0336211	+	0.0244272i
$898$	27.2920			0.910747
$899$	−44.6988	+	13.3433i	−1.49079	+	0.445024i
$900$	1.00000			0.0333333
$901$	60.2003	+	43.7381i	2.00556	+	1.45713i
$902$	16.5567	−	12.0292i	0.551278	−	0.400527i
$903$	−0.403091	−	1.24059i	−0.0134140	−	0.0412841i
$904$	−6.69978			−0.222832
$905$	5.83254			0.193880
$906$	0.00761175	+	0.0234266i	0.000252883	+	0.000778295i
$907$	8.61028	−	26.4997i	0.285900	−	0.879909i	−0.700228	−	0.713919i	$-0.746918\pi$
$907$	8.61028	−	26.4997i	0.285900	−	0.879909i	0.986128	−	0.165989i	$-0.0530818\pi$
$908$	−8.52065	+	26.2239i	−0.282768	+	0.870269i
$909$	−13.7930	−	10.0212i	−0.457485	−	0.332382i
$910$	0.158128	+	0.486667i	0.00524188	+	0.0161328i
$911$	−43.2410	−	31.4164i	−1.43264	−	1.04087i	−0.989518	−	0.144411i	$-0.953871\pi$
$911$	−43.2410	−	31.4164i	−1.43264	−	1.04087i	−0.443121	−	0.896462i	$-0.646129\pi$
$912$	−0.820551	+	0.596165i	−0.0271712	+	0.0197410i
$913$	−3.27259	+	10.0720i	−0.108307	+	0.333334i
$914$	−13.5719	+	9.86060i	−0.448920	+	0.326160i
$915$	−3.27386	+	2.37860i	−0.108230	+	0.0786340i
$916$	−1.84929	+	5.69152i	−0.0611022	+	0.188053i
$917$	3.58119	−	2.60189i	0.118261	−	0.0859220i
$918$	4.90469	+	3.56347i	0.161879	+	0.117612i
$919$	8.68136	+	26.7185i	0.286372	+	0.881361i	0.985984	+	0.166839i	$0.0533560\pi$
$919$	8.68136	+	26.7185i	0.286372	+	0.881361i	−0.699613	+	0.714522i	$0.746644\pi$
$920$	0.593145	+	0.430945i	0.0195554	+	0.0142078i
$921$	−2.93320	+	9.02747i	−0.0966523	+	0.297465i
$922$	−1.49597	+	4.60414i	−0.0492673	+	0.151629i
$923$	7.00067	+	21.5459i	0.230430	+	0.709190i
$924$	−0.578571			−0.0190336
$925$	5.63079			0.185139
$926$	1.30461	+	4.01518i	0.0428721	+	0.131947i
$927$	12.2257	−	8.88246i	0.401543	−	0.291738i
$928$	−6.77812	−	4.92459i	−0.222503	−	0.161658i
$929$	−11.2536			−0.369219			−0.184610	−	0.982812i	$-0.559102\pi$
$929$	−11.2536			−0.369219			−0.184610	+	0.982812i	$0.559102\pi$
$930$	−3.38009	+	4.42436i	−0.110837	+	0.145081i
$931$	−7.00765			−0.229666
$932$	−13.9212	−	10.1143i	−0.456004	−	0.331306i
$933$	−0.631805	+	0.459034i	−0.0206844	+	0.0150281i
$934$	−6.30233	−	19.3966i	−0.206218	−	0.634675i
$935$	−11.6368			−0.380563
$936$	−1.69765			−0.0554893
$937$	−2.06420	−	6.35294i	−0.0674343	−	0.207541i	0.911661	−	0.410943i	$-0.134800\pi$
$937$	−2.06420	−	6.35294i	−0.0674343	−	0.207541i	−0.979095	+	0.203401i	$0.934800\pi$
$938$	−0.776714	+	2.39048i	−0.0253606	+	0.0780519i
$939$	−2.63616	+	8.11326i	−0.0860278	+	0.264766i
$940$	−6.97623	−	5.06853i	−0.227539	−	0.165317i
$941$	1.48922	+	4.58334i	0.0485471	+	0.149413i	0.972391	−	0.233356i	$-0.0749707\pi$
$941$	1.48922	+	4.58334i	0.0485471	+	0.149413i	−0.923844	+	0.382769i	$0.874971\pi$
$942$	−10.2440	−	7.44272i	−0.333768	−	0.242497i
$943$	−6.32410	+	4.59473i	−0.205941	+	0.149625i
$944$	−3.82133	+	11.7609i	−0.124374	+	0.382783i
$945$	0.243857	−	0.177173i	0.00793267	−	0.00576342i
$946$	−6.72015	+	4.88248i	−0.218491	+	0.158743i
$947$	5.69908	−	17.5399i	0.185195	−	0.569972i	−0.814757	−	0.579803i	$-0.803129\pi$
$947$	5.69908	−	17.5399i	0.185195	−	0.569972i	0.999952	+	0.00983134i	$0.00312946\pi$
$948$	−11.4212	+	8.29798i	−0.370943	+	0.269506i
$949$	−18.6673	−	13.5626i	−0.605965	−	0.440259i
$950$	0.313423	+	0.964616i	0.0101688	+	0.0312963i
$951$	−28.5438	−	20.7383i	−0.925596	−	0.672485i
$952$	−0.564695	+	1.73795i	−0.0183019	+	0.0563274i
$953$	−7.15490	+	22.0205i	−0.231770	+	0.713315i	0.765763	+	0.643122i	$0.222361\pi$
$953$	−7.15490	+	22.0205i	−0.231770	+	0.713315i	−0.997533	+	0.0701924i	$0.977639\pi$
$954$	3.79288	+	11.6733i	0.122799	+	0.377937i
$955$	−1.89318			−0.0612618
$956$	−16.6230			−0.537625
$957$	−4.96950	−	15.2945i	−0.160641	−	0.494402i
$958$	19.2391	−	13.9780i	0.621587	−	0.451610i
$959$	−2.66656	−	1.93737i	−0.0861077	−	0.0625609i
$960$	−1.00000			−0.0322749
$961$	−8.14999	−	29.9095i	−0.262903	−	0.964822i
$962$	−9.55909			−0.308197
$963$	7.63930	+	5.55028i	0.246173	+	0.178855i
$964$	−11.4255	+	8.30111i	−0.367990	+	0.267361i
$965$	2.57844	+	7.93563i	0.0830030	+	0.255457i
$966$	0.220994			0.00711038
$967$	13.6179			0.437922			0.218961	−	0.975734i	$-0.429733\pi$
$967$	13.6179			0.437922			0.218961	+	0.975734i	$0.429733\pi$
$968$	−2.26067	−	6.95763i	−0.0726607	−	0.223627i
$969$	−1.90013	+	5.84801i	−0.0610411	+	0.187865i
$970$	−3.23821	+	9.96617i	−0.103972	+	0.319994i
$971$	−11.4346	−	8.30773i	−0.366954	−	0.266608i	0.388993	−	0.921241i	$-0.372823\pi$
$971$	−11.4346	−	8.30773i	−0.366954	−	0.266608i	−0.755947	+	0.654633i	$0.772823\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	1.35905	+	0.987405i	0.0435690	+	0.0316548i
$974$	7.79215	−	5.66133i	0.249676	−	0.181401i
$975$	−0.524602	+	1.61456i	−0.0168007	+	0.0517072i
$976$	3.27386	−	2.37860i	0.104794	−	0.0761370i
$977$	−22.8617	+	16.6100i	−0.731411	+	0.531401i	−0.890009	−	0.455942i	$-0.849302\pi$
$977$	−22.8617	+	16.6100i	−0.731411	+	0.531401i	0.158599	+	0.987343i	$0.449302\pi$
$978$	1.60749	−	4.94733i	0.0514017	−	0.158198i
$979$	−7.80351	+	5.66958i	−0.249401	+	0.181201i
$980$	−5.58961	−	4.06109i	−0.178554	−	0.129727i
$981$	0.902720	+	2.77829i	0.0288216	+	0.0887038i
$982$	−0.173920	−	0.126360i	−0.00555002	−	0.00403233i
$983$	6.18082	−	19.0226i	0.197138	−	0.606727i	−0.802807	−	0.596238i	$-0.796661\pi$
$983$	6.18082	−	19.0226i	0.197138	−	0.606727i	0.999945	−	0.0104887i	$-0.00333872\pi$
$984$	3.29473	−	10.1401i	0.105032	−	0.323256i
$985$	−2.57451	−	7.92354i	−0.0820308	−	0.252465i
$986$	−50.7932			−1.61758
$987$	−2.59921			−0.0827337
$988$	−0.532081	−	1.63758i	−0.0169278	−	0.0520983i
$989$	2.56687	−	1.86494i	0.0816217	−	0.0593017i
$990$	−1.55287	−	1.12823i	−0.0493536	−	0.0358575i
$991$	8.49416			0.269826			0.134913	−	0.990857i	$-0.456925\pi$
$991$	8.49416			0.269826			0.134913	+	0.990857i	$0.456925\pi$
$992$	3.38009	−	4.42436i	0.107318	−	0.140474i
$993$	−15.6526			−0.496722
$994$	3.25421	+	2.36432i	0.103217	+	0.0749917i
$995$	3.00060	−	2.18007i	0.0951256	−	0.0691128i
$996$	1.70495	+	5.24731i	0.0540235	+	0.166267i
$997$	−10.8277			−0.342917			−0.171459	−	0.985191i	$-0.554848\pi$
$997$	−10.8277			−0.342917			−0.171459	+	0.985191i	$0.554848\pi$
$998$	0.987370			0.0312547
$999$	1.74001	+	5.35520i	0.0550515	+	0.169431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.c.901.2	yes	12
31.16	even	5	inner	930.2.n.c.481.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.c.481.2	✓	12	31.16	even	5	inner
930.2.n.c.901.2	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.0931451 + 0.286671i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.0931451 + 0.286671i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.593145 - 1.82551i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(1.37343 - 0.997852i) q^{13} +(0.0931451 - 0.286671i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.87343 + 5.76581i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-0.820551 - 0.596165i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(-0.243857 - 0.177173i) q^{21} +(-0.593145 + 1.82551i) q^{22} +(0.226561 - 0.697284i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} -1.69765 q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.243857 + 0.177173i) q^{28} +(-6.77812 - 4.92459i) q^{29} -1.00000 q^{30} +(3.38009 - 4.42436i) q^{31} +1.00000 q^{32} +(1.55287 + 1.12823i) q^{33} +(4.90469 - 3.56347i) q^{34} +(-0.0931451 - 0.286671i) q^{35} +1.00000 q^{36} +5.63079 q^{37} +(0.313423 + 0.964616i) q^{38} +(-0.524602 + 1.61456i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-8.62572 - 6.26696i) q^{41} +(0.0931451 + 0.286671i) q^{42} +(3.50107 + 2.54368i) q^{43} +(1.55287 - 1.12823i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-0.593145 + 0.430945i) q^{46} +(6.97623 - 5.06853i) q^{47} +(0.309017 - 0.951057i) q^{48} +(5.58961 - 4.06109i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.87343 - 5.76581i) q^{51} +(1.37343 + 0.997852i) q^{52} +(3.79288 - 11.6733i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.593145 + 1.82551i) q^{55} +0.301424 q^{56} +1.01426 q^{57} +(2.58901 + 7.96815i) q^{58} +(10.0044 - 7.26861i) q^{59} +(0.809017 + 0.587785i) q^{60} -4.04671 q^{61} +(-5.33513 + 1.59262i) q^{62} +0.301424 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.37343 + 0.997852i) q^{65} +(-0.593145 - 1.82551i) q^{66} -8.33875 q^{67} -6.06253 q^{68} +(0.226561 + 0.697284i) q^{69} +(-0.0931451 + 0.286671i) q^{70} +(-4.12375 + 12.6916i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-4.20008 - 12.9265i) q^{73} +(-4.55540 - 3.30969i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(0.313423 - 0.964616i) q^{76} +(0.468074 - 0.340075i) q^{77} +(1.37343 - 0.997852i) q^{78} +(4.36251 - 13.4264i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.29473 + 10.1401i) q^{82} +(-4.46362 - 3.24301i) q^{83} +(0.0931451 - 0.286671i) q^{84} +(1.87343 - 5.76581i) q^{85} +(-1.33729 - 4.11575i) q^{86} +8.37821 q^{87} -1.91946 q^{88} +(-1.55287 - 4.77926i) q^{89} +(0.809017 - 0.587785i) q^{90} +(0.413983 + 0.300777i) q^{91} +0.733168 q^{92} +(-0.133974 + 5.56615i) q^{93} -8.62309 q^{94} +(0.820551 + 0.596165i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(3.23821 + 9.96617i) q^{97} -6.90914 q^{98} -1.91946 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - 5 q^{11} - 3 q^{12} - 3 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} + 4 q^{21} - 5 q^{22} + 10 q^{23} - 3 q^{24} + 12 q^{25} + 2 q^{26} - 3 q^{27} + 4 q^{28} - 5 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 5 q^{33} + 2 q^{34} + q^{35} + 12 q^{36} + 2 q^{37} + 11 q^{38} + 2 q^{39} + 3 q^{40} + 13 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} + 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 4 q^{49} - 3 q^{50} - 3 q^{51} - 3 q^{52} + 3 q^{53} - 3 q^{54} + 5 q^{55} - 6 q^{56} - 14 q^{57} + 10 q^{58} + 23 q^{59} + 3 q^{60} - 46 q^{61} + 7 q^{62} - 6 q^{63} - 3 q^{64} + 3 q^{65} - 5 q^{66} - 66 q^{67} + 2 q^{68} + 10 q^{69} + q^{70} + 23 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 3 q^{75} + 11 q^{76} + 10 q^{77} - 3 q^{78} + 21 q^{79} + 3 q^{80} - 3 q^{81} + 13 q^{82} + 4 q^{83} - q^{84} + 3 q^{85} - 4 q^{86} - 10 q^{87} - 5 q^{89} + 3 q^{90} - 6 q^{91} - 10 q^{92} - 3 q^{93} + 6 q^{94} + 4 q^{95} - 3 q^{96} + 25 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 - 5 * q^11 - 3 * q^12 - 3 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 + 4 * q^21 - 5 * q^22 + 10 * q^23 - 3 * q^24 + 12 * q^25 + 2 * q^26 - 3 * q^27 + 4 * q^28 - 5 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 5 * q^33 + 2 * q^34 + q^35 + 12 * q^36 + 2 * q^37 + 11 * q^38 + 2 * q^39 + 3 * q^40 + 13 * q^41 - q^42 + 16 * q^43 + 5 * q^44 + 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 4 * q^49 - 3 * q^50 - 3 * q^51 - 3 * q^52 + 3 * q^53 - 3 * q^54 + 5 * q^55 - 6 * q^56 - 14 * q^57 + 10 * q^58 + 23 * q^59 + 3 * q^60 - 46 * q^61 + 7 * q^62 - 6 * q^63 - 3 * q^64 + 3 * q^65 - 5 * q^66 - 66 * q^67 + 2 * q^68 + 10 * q^69 + q^70 + 23 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 3 * q^75 + 11 * q^76 + 10 * q^77 - 3 * q^78 + 21 * q^79 + 3 * q^80 - 3 * q^81 + 13 * q^82 + 4 * q^83 - q^84 + 3 * q^85 - 4 * q^86 - 10 * q^87 - 5 * q^89 + 3 * q^90 - 6 * q^91 - 10 * q^92 - 3 * q^93 + 6 * q^94 + 4 * q^95 - 3 * q^96 + 25 * q^97 - 6 * q^98

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