LMFDB - Embedded newform 462.2.j.e.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, 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("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
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			379.2
Root			$-1.73855 - 1.26313i$ of defining polynomial
Character	$\chi$	$=$	462.379
Dual form			462.2.j.e.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.910415 - 2.80197i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.910415 - 2.80197i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +2.94617 q^{10} +(-3.06668 - 1.26313i) q^{11} +1.00000 q^{12} +(-0.164066 - 0.504942i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-2.38350 + 1.73171i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.26700 - 6.97709i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-4.35658 - 3.16524i) q^{19} +(0.910415 + 2.80197i) q^{20} +1.00000 q^{21} +(0.253650 - 3.30691i) q^{22} -0.710097 q^{23} +(0.309017 + 0.951057i) q^{24} +(-2.97709 - 2.16298i) q^{25} +(0.429529 - 0.312071i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.309017 - 0.951057i) q^{28} +(0.0769587 - 0.0559138i) q^{29} +(-2.38350 - 1.73171i) q^{30} +(-1.55784 - 4.79455i) q^{31} +1.00000 q^{32} +(1.73855 + 2.82444i) q^{33} +7.33615 q^{34} +(0.910415 + 2.80197i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(1.85257 - 1.34597i) q^{37} +(1.66407 - 5.12147i) q^{38} +(-0.164066 + 0.504942i) q^{39} +(-2.38350 + 1.73171i) q^{40} +(1.88999 + 1.37315i) q^{41} +(0.309017 + 0.951057i) q^{42} -0.172587 q^{43} +(3.22344 - 0.780656i) q^{44} +2.94617 q^{45} +(-0.219432 - 0.675342i) q^{46} +(10.6981 + 7.77259i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(1.13715 - 3.49978i) q^{50} +(-5.93507 + 4.31208i) q^{51} +(0.429529 + 0.312071i) q^{52} +(-1.22673 - 3.77550i) q^{53} +1.00000 q^{54} +(-6.33119 + 7.44277i) q^{55} +1.00000 q^{56} +(1.66407 + 5.12147i) q^{57} +(0.0769587 + 0.0559138i) q^{58} +(7.40815 - 5.38234i) q^{59} +(0.910415 - 2.80197i) q^{60} +(-2.37263 + 7.30221i) q^{61} +(4.07849 - 2.96320i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(0.309017 + 0.951057i) q^{64} -1.56420 q^{65} +(-2.14896 + 2.52626i) q^{66} -12.9240 q^{67} +(2.26700 + 6.97709i) q^{68} +(0.574481 + 0.417385i) q^{69} +(-2.38350 + 1.73171i) q^{70} +(2.74337 - 8.44322i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-5.25919 + 3.82103i) q^{73} +(1.85257 + 1.34597i) q^{74} +(1.13715 + 3.49978i) q^{75} +5.38503 q^{76} +(3.22344 - 0.780656i) q^{77} -0.530927 q^{78} +(3.17836 + 9.78198i) q^{79} +(-2.38350 - 1.73171i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.721910 + 2.22181i) q^{82} +(-4.54522 + 13.9887i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(-17.4857 - 12.7041i) q^{85} +(-0.0533324 - 0.164140i) q^{86} -0.0951262 q^{87} +(1.73855 + 2.82444i) q^{88} +8.61947 q^{89} +(0.910415 + 2.80197i) q^{90} +(0.429529 + 0.312071i) q^{91} +(0.574481 - 0.417385i) q^{92} +(-1.55784 + 4.79455i) q^{93} +(-4.08629 + 12.5763i) q^{94} +(-12.8352 + 9.32532i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-0.280568 - 0.863499i) q^{97} +1.00000 q^{98} +(0.253650 - 3.30691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 8 * q^12 + 4 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^23 - 2 * q^24 + 4 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 - 6 * q^30 - 14 * q^31 + 8 * q^32 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 + 20 * q^43 + 4 * q^45 + 6 * q^46 + 28 * q^47 - 2 * q^48 - 2 * q^49 - 6 * q^50 + 2 * q^51 - 6 * q^52 + 2 * q^53 + 8 * q^54 + 4 * q^55 + 8 * q^56 + 8 * q^57 - 4 * q^58 + 4 * q^60 - 34 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 16 * q^65 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 6 * q^70 - 2 * q^72 + 10 * q^74 - 6 * q^75 + 8 * q^76 + 4 * q^78 + 22 * q^79 - 6 * q^80 - 2 * q^81 - 2 * q^82 - 30 * q^83 - 2 * q^84 - 28 * q^85 + 36 * q^87 - 4 * q^89 + 4 * q^90 - 6 * q^91 - 4 * q^92 - 14 * q^93 - 22 * q^94 - 30 * q^95 - 2 * q^96 - 10 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.910415	−	2.80197i	0.407150	−	1.25308i	−0.511937	−	0.859023i	$-0.671072\pi$
$5$	0.910415	−	2.80197i	0.407150	−	1.25308i	0.919087	−	0.394056i	$-0.128928\pi$
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	2.94617			0.931659
$11$	−3.06668	−	1.26313i	−0.924638	−	0.380847i
$11$	−3.06668	−	1.26313i	−0.924638	−	0.380847i
$12$	1.00000			0.288675
$13$	−0.164066	−	0.504942i	−0.0455036	−	0.140046i	0.925723	−	0.378201i	$-0.123457\pi$
$13$	−0.164066	−	0.504942i	−0.0455036	−	0.140046i	−0.971227	+	0.238155i	$0.923457\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	−2.38350	+	1.73171i	−0.615416	+	0.447126i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.26700	−	6.97709i	0.549827	−	1.69219i	−0.159400	−	0.987214i	$-0.550956\pi$
$17$	2.26700	−	6.97709i	0.549827	−	1.69219i	0.709227	−	0.704980i	$-0.249044\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	−4.35658	−	3.16524i	−0.999468	−	0.726156i	−0.0374940	−	0.999297i	$-0.511937\pi$
$19$	−4.35658	−	3.16524i	−0.999468	−	0.726156i	−0.961974	+	0.273141i	$0.911937\pi$
$20$	0.910415	+	2.80197i	0.203575	+	0.626539i
$21$	1.00000			0.218218
$22$	0.253650	−	3.30691i	0.0540785	−	0.705036i
$23$	−0.710097			−0.148065			−0.0740327	−	0.997256i	$-0.523587\pi$
$23$	−0.710097			−0.148065			−0.0740327	+	0.997256i	$0.523587\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	−2.97709	−	2.16298i	−0.595418	−	0.432597i
$26$	0.429529	−	0.312071i	0.0842376	−	0.0612022i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	0.0769587	−	0.0559138i	0.0142909	−	0.0103829i	−0.580617	−	0.814177i	$-0.697189\pi$
$29$	0.0769587	−	0.0559138i	0.0142909	−	0.0103829i	0.594908	+	0.803794i	$0.297189\pi$
$30$	−2.38350	−	1.73171i	−0.435165	−	0.316166i
$31$	−1.55784	−	4.79455i	−0.279797	−	0.861127i	−0.987910	−	0.155028i	$-0.950453\pi$
$31$	−1.55784	−	4.79455i	−0.279797	−	0.861127i	0.708113	−	0.706099i	$-0.249547\pi$
$32$	1.00000			0.176777
$33$	1.73855	+	2.82444i	0.302642	+	0.491672i
$34$	7.33615			1.25814
$35$	0.910415	+	2.80197i	0.153888	+	0.473619i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	1.85257	−	1.34597i	0.304561	−	0.221276i	−0.424998	−	0.905194i	$-0.639725\pi$
$37$	1.85257	−	1.34597i	0.304561	−	0.221276i	0.729559	+	0.683918i	$0.239725\pi$
$38$	1.66407	−	5.12147i	0.269947	−	0.830812i
$39$	−0.164066	+	0.504942i	−0.0262715	+	0.0808554i
$40$	−2.38350	+	1.73171i	−0.376864	+	0.273808i
$41$	1.88999	+	1.37315i	0.295166	+	0.214451i	0.725505	−	0.688216i	$-0.241606\pi$
$41$	1.88999	+	1.37315i	0.295166	+	0.214451i	−0.430339	+	0.902667i	$0.641606\pi$
$42$	0.309017	+	0.951057i	0.0476824	+	0.146751i
$43$	−0.172587			−0.0263193			−0.0131597	−	0.999913i	$-0.504189\pi$
$43$	−0.172587			−0.0263193			−0.0131597	+	0.999913i	$0.504189\pi$
$44$	3.22344	−	0.780656i	0.485952	−	0.117688i
$45$	2.94617			0.439188
$46$	−0.219432	−	0.675342i	−0.0323535	−	0.0995738i
$47$	10.6981	+	7.77259i	1.56047	+	1.13375i	0.935622	+	0.353004i	$0.114840\pi$
$47$	10.6981	+	7.77259i	1.56047	+	1.13375i	0.624850	+	0.780745i	$0.285160\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	1.13715	−	3.49978i	0.160817	−	0.494944i
$51$	−5.93507	+	4.31208i	−0.831076	+	0.603812i
$52$	0.429529	+	0.312071i	0.0595650	+	0.0432765i
$53$	−1.22673	−	3.77550i	−0.168505	−	0.518604i	0.830773	−	0.556612i	$-0.187899\pi$
$53$	−1.22673	−	3.77550i	−0.168505	−	0.518604i	−0.999277	+	0.0380076i	$0.987899\pi$
$54$	1.00000			0.136083
$55$	−6.33119	+	7.44277i	−0.853698	+	1.00358i
$56$	1.00000			0.133631
$57$	1.66407	+	5.12147i	0.220411	+	0.678355i
$58$	0.0769587	+	0.0559138i	0.0101052	+	0.00734184i
$59$	7.40815	−	5.38234i	0.964459	−	0.700721i	0.0102772	−	0.999947i	$-0.496729\pi$
$59$	7.40815	−	5.38234i	0.964459	−	0.700721i	0.954182	+	0.299226i	$0.0967286\pi$
$60$	0.910415	−	2.80197i	0.117534	−	0.361733i
$61$	−2.37263	+	7.30221i	−0.303784	+	0.934952i	0.676344	+	0.736586i	$0.263563\pi$
$61$	−2.37263	+	7.30221i	−0.303784	+	0.934952i	−0.980128	+	0.198366i	$0.936437\pi$
$62$	4.07849	−	2.96320i	0.517969	−	0.376326i
$63$	−0.809017	−	0.587785i	−0.101927	−	0.0740540i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.56420			−0.194015
$66$	−2.14896	+	2.52626i	−0.264519	+	0.310961i
$67$	−12.9240			−1.57891			−0.789457	−	0.613805i	$-0.789638\pi$
$67$	−12.9240			−1.57891			−0.789457	+	0.613805i	$0.789638\pi$
$68$	2.26700	+	6.97709i	0.274914	+	0.846097i
$69$	0.574481	+	0.417385i	0.0691593	+	0.0502472i
$70$	−2.38350	+	1.73171i	−0.284882	+	0.206979i
$71$	2.74337	−	8.44322i	0.325578	−	1.00203i	−0.645601	−	0.763675i	$-0.723393\pi$
$71$	2.74337	−	8.44322i	0.325578	−	1.00203i	0.971179	−	0.238351i	$-0.0766069\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	−5.25919	+	3.82103i	−0.615542	+	0.447217i	−0.851361	−	0.524580i	$-0.824223\pi$
$73$	−5.25919	+	3.82103i	−0.615542	+	0.447217i	0.235820	+	0.971797i	$0.424223\pi$
$74$	1.85257	+	1.34597i	0.215357	+	0.156466i
$75$	1.13715	+	3.49978i	0.131307	+	0.404120i
$76$	5.38503			0.617705
$77$	3.22344	−	0.780656i	0.367345	−	0.0889640i
$78$	−0.530927			−0.0601157
$79$	3.17836	+	9.78198i	0.357593	+	1.10056i	0.954491	+	0.298241i	$0.0963999\pi$
$79$	3.17836	+	9.78198i	0.357593	+	1.10056i	−0.596898	+	0.802317i	$0.703600\pi$
$80$	−2.38350	−	1.73171i	−0.266483	−	0.193611i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−0.721910	+	2.22181i	−0.0797216	+	0.245358i
$83$	−4.54522	+	13.9887i	−0.498903	+	1.53546i	0.311883	+	0.950121i	$0.399040\pi$
$83$	−4.54522	+	13.9887i	−0.498903	+	1.53546i	−0.810785	+	0.585344i	$0.800960\pi$
$84$	−0.809017	+	0.587785i	−0.0882710	+	0.0641326i
$85$	−17.4857	−	12.7041i	−1.89659	−	1.37795i
$86$	−0.0533324	−	0.164140i	−0.00575098	−	0.0176997i
$87$	−0.0951262			−0.0101986
$88$	1.73855	+	2.82444i	0.185330	+	0.301086i
$89$	8.61947			0.913662			0.456831	−	0.889553i	$-0.348984\pi$
$89$	8.61947			0.913662			0.456831	+	0.889553i	$0.348984\pi$
$90$	0.910415	+	2.80197i	0.0959662	+	0.295354i
$91$	0.429529	+	0.312071i	0.0450269	+	0.0327139i
$92$	0.574481	−	0.417385i	0.0598937	−	0.0435153i
$93$	−1.55784	+	4.79455i	−0.161541	+	0.497172i
$94$	−4.08629	+	12.5763i	−0.421469	+	1.29715i
$95$	−12.8352	+	9.32532i	−1.31686	+	0.956758i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−0.280568	−	0.863499i	−0.0284874	−	0.0876751i	0.935802	−	0.352526i	$-0.114677\pi$
$97$	−0.280568	−	0.863499i	−0.0284874	−	0.0876751i	−0.964289	+	0.264851i	$0.914677\pi$
$98$	1.00000			0.101015
$99$	0.253650	−	3.30691i	0.0254928	−	0.332357i
$100$	3.67989			0.367989
$101$	−1.05938	−	3.26042i	−0.105412	−	0.324424i	0.884415	−	0.466701i	$-0.154558\pi$
$101$	−1.05938	−	3.26042i	−0.105412	−	0.324424i	−0.989827	+	0.142277i	$0.954558\pi$
$102$	−5.93507	−	4.31208i	−0.587660	−	0.426960i
$103$	0.146267	−	0.106269i	0.0144121	−	0.0104710i	−0.580556	−	0.814220i	$-0.697165\pi$
$103$	0.146267	−	0.106269i	0.0144121	−	0.0104710i	0.594968	+	0.803749i	$0.297165\pi$
$104$	−0.164066	+	0.504942i	−0.0160879	+	0.0495136i
$105$	0.910415	−	2.80197i	0.0888474	−	0.273444i
$106$	3.21163	−	2.33338i	0.311941	−	0.226638i
$107$	−12.2107	−	8.87158i	−1.18045	−	0.857648i	−0.188229	−	0.982125i	$-0.560275\pi$
$107$	−12.2107	−	8.87158i	−1.18045	−	0.857648i	−0.992222	+	0.124477i	$0.960275\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	6.58783			0.630999			0.315500	−	0.948926i	$-0.397828\pi$
$109$	6.58783			0.630999			0.315500	+	0.948926i	$0.397828\pi$
$110$	−9.03494	−	3.72138i	−0.861447	−	0.354820i
$111$	−2.28990			−0.217348
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	10.9168	+	7.93150i	1.02696	+	0.746132i	0.967699	−	0.252110i	$-0.0811244\pi$
$113$	10.9168	+	7.93150i	1.02696	+	0.746132i	0.0592646	+	0.998242i	$0.481124\pi$
$114$	−4.35658	+	3.16524i	−0.408031	+	0.296452i
$115$	−0.646483	+	1.98967i	−0.0602849	+	0.185538i
$116$	−0.0293956	+	0.0904704i	−0.00272931	+	0.00839996i
$117$	0.429529	−	0.312071i	0.0397100	−	0.0288510i
$118$	7.40815	+	5.38234i	0.681976	+	0.495484i
$119$	2.26700	+	6.97709i	0.207815	+	0.639589i
$120$	2.94617			0.268947
$121$	7.80902	+	7.74721i	0.709911	+	0.704292i
$122$	−7.67800			−0.695133
$123$	−0.721910	−	2.22181i	−0.0650924	−	0.200334i
$124$	4.07849	+	2.96320i	0.366259	+	0.266103i
$125$	3.14648	−	2.28605i	0.281430	−	0.204471i
$126$	0.309017	−	0.951057i	0.0275294	−	0.0847268i
$127$	1.05640	−	3.25125i	0.0937399	−	0.288502i	−0.893183	−	0.449693i	$-0.851533\pi$
$127$	1.05640	−	3.25125i	0.0937399	−	0.288502i	0.986923	+	0.161191i	$0.0515335\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	0.139626	+	0.101444i	0.0122934	+	0.00893167i
$130$	−0.483364	−	1.48764i	−0.0423938	−	0.130475i
$131$	4.82272			0.421363			0.210682	−	0.977555i	$-0.432432\pi$
$131$	4.82272			0.421363			0.210682	+	0.977555i	$0.432432\pi$
$132$	−3.06668	−	1.26313i	−0.266920	−	0.109941i
$133$	5.38503			0.466941
$134$	−3.99373	−	12.2914i	−0.345006	−	1.06182i
$135$	−2.38350	−	1.73171i	−0.205139	−	0.149042i
$136$	−5.93507	+	4.31208i	−0.508928	+	0.369758i
$137$	5.33390	−	16.4161i	0.455706	−	1.40252i	−0.414599	−	0.910004i	$-0.636078\pi$
$137$	5.33390	−	16.4161i	0.455706	−	1.40252i	0.870304	−	0.492514i	$-0.163922\pi$
$138$	−0.219432	+	0.675342i	−0.0186793	+	0.0574890i
$139$	14.1186	−	10.2578i	1.19753	−	0.870053i	0.203487	−	0.979078i	$-0.434773\pi$
$139$	14.1186	−	10.2578i	1.19753	−	0.870053i	0.994039	+	0.109024i	$0.0347727\pi$
$140$	−2.38350	−	1.73171i	−0.201442	−	0.146356i
$141$	−4.08629	−	12.5763i	−0.344128	−	1.05912i
$142$	8.87773			0.745002
$143$	−0.134670	+	1.75573i	−0.0112617	+	0.146821i
$144$	1.00000			0.0833333
$145$	−0.0866043	−	0.266541i	−0.00719209	−	0.0221350i
$146$	−5.25919	−	3.82103i	−0.435254	−	0.316230i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	−0.707619	+	2.17783i	−0.0581659	+	0.179016i
$149$	−3.12227	+	9.60936i	−0.255786	+	0.787230i	0.737887	+	0.674924i	$0.235824\pi$
$149$	−3.12227	+	9.60936i	−0.255786	+	0.787230i	−0.993674	+	0.112306i	$0.964176\pi$
$150$	−2.97709	+	2.16298i	−0.243079	+	0.176607i
$151$	3.05558	+	2.22001i	0.248660	+	0.180662i	0.705133	−	0.709075i	$-0.250887\pi$
$151$	3.05558	+	2.22001i	0.248660	+	0.180662i	−0.456473	+	0.889737i	$0.650887\pi$
$152$	1.66407	+	5.12147i	0.134974	+	0.415406i
$153$	7.33615			0.593093
$154$	1.73855	+	2.82444i	0.140096	+	0.227600i
$155$	−14.8525			−1.19298
$156$	−0.164066	−	0.504942i	−0.0131358	−	0.0404277i
$157$	−17.7701	−	12.9107i	−1.41821	−	1.03039i	−0.992065	−	0.125729i	$-0.959873\pi$
$157$	−17.7701	−	12.9107i	−1.41821	−	1.03039i	−0.426140	−	0.904657i	$-0.640127\pi$
$158$	−8.32105	+	6.04559i	−0.661987	+	0.480962i
$159$	−1.22673	+	3.77550i	−0.0972863	+	0.299416i
$160$	0.910415	−	2.80197i	0.0719746	−	0.221515i
$161$	0.574481	−	0.417385i	0.0452754	−	0.0328945i
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	5.93056	+	18.2524i	0.464517	+	1.42964i	0.859589	+	0.510986i	$0.170720\pi$
$163$	5.93056	+	18.2524i	0.464517	+	1.42964i	−0.395072	+	0.918650i	$0.629280\pi$
$164$	−2.33615			−0.182423
$165$	9.49679	−	2.29994i	0.739324	−	0.179050i
$166$	−14.7086			−1.14161
$167$	4.80604	+	14.7915i	0.371902	+	1.14460i	0.945545	+	0.325492i	$0.105530\pi$
$167$	4.80604	+	14.7915i	0.371902	+	1.14460i	−0.573643	+	0.819106i	$0.694470\pi$
$168$	−0.809017	−	0.587785i	−0.0624170	−	0.0453486i
$169$	10.2892	−	7.47552i	0.791475	−	0.575040i
$170$	6.67894	−	20.5557i	0.512251	−	1.57655i
$171$	1.66407	−	5.12147i	0.127254	−	0.391648i
$172$	0.139626	−	0.101444i	0.0106464	−	0.00773506i
$173$	−18.1275	−	13.1704i	−1.37820	−	1.00132i	−0.997045	−	0.0768149i	$-0.975525\pi$
$173$	−18.1275	−	13.1704i	−1.37820	−	1.00132i	−0.381159	−	0.924509i	$-0.624475\pi$
$174$	−0.0293956	−	0.0904704i	−0.00222847	−	0.00685854i
$175$	3.67989			0.278173
$176$	−2.14896	+	2.52626i	−0.161984	+	0.190424i
$177$	−9.15698			−0.688281
$178$	2.66356	+	8.19760i	0.199642	+	0.614436i
$179$	14.8494	+	10.7887i	1.10989	+	0.806385i	0.982647	−	0.185486i	$-0.0593861\pi$
$179$	14.8494	+	10.7887i	1.10989	+	0.806385i	0.127247	+	0.991871i	$0.459386\pi$
$180$	−2.38350	+	1.73171i	−0.177655	+	0.129074i
$181$	−1.02971	+	3.16911i	−0.0765375	+	0.235558i	−0.982004	−	0.188859i	$-0.939521\pi$
$181$	−1.02971	+	3.16911i	−0.0765375	+	0.235558i	0.905467	+	0.424417i	$0.139521\pi$
$182$	−0.164066	+	0.504942i	−0.0121613	+	0.0374288i
$183$	6.21163	−	4.51301i	0.459177	−	0.333611i
$184$	0.574481	+	0.417385i	0.0423513	+	0.0307700i
$185$	−2.08476	−	6.41624i	−0.153275	−	0.471731i
$186$	−5.04129			−0.369645
$187$	−15.7651	+	18.5330i	−1.15286	+	1.35527i
$188$	−13.2235			−0.964425
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	−12.8352	−	9.32532i	−0.931164	−	0.676530i
$191$	6.80888	−	4.94694i	0.492674	−	0.357948i	−0.313538	−	0.949576i	$-0.601514\pi$
$191$	6.80888	−	4.94694i	0.492674	−	0.357948i	0.806212	+	0.591627i	$0.201514\pi$
$192$	0.309017	−	0.951057i	0.0223014	−	0.0686366i
$193$	−2.13408	+	6.56804i	−0.153615	+	0.472778i	−0.998018	−	0.0629306i	$-0.979955\pi$
$193$	−2.13408	+	6.56804i	−0.153615	+	0.472778i	0.844403	+	0.535708i	$0.179955\pi$
$194$	0.734536	−	0.533672i	0.0527366	−	0.0383154i
$195$	1.26546	+	0.919413i	0.0906217	+	0.0658405i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	10.5788			0.753708			0.376854	−	0.926273i	$-0.377006\pi$
$197$	10.5788			0.753708			0.376854	+	0.926273i	$0.377006\pi$
$198$	3.22344	−	0.780656i	0.229080	−	0.0554788i
$199$	16.7261			1.18568			0.592842	−	0.805319i	$-0.298006\pi$
$199$	16.7261			1.18568			0.592842	+	0.805319i	$0.298006\pi$
$200$	1.13715	+	3.49978i	0.0804085	+	0.247472i
$201$	10.4557	+	7.59652i	0.737489	+	0.535817i
$202$	2.77348	−	2.01505i	0.195142	−	0.141779i
$203$	−0.0293956	+	0.0904704i	−0.00206317	+	0.00634977i
$204$	2.26700	−	6.97709i	0.158721	−	0.488494i
$205$	5.56821	−	4.04554i	0.388901	−	0.282553i
$206$	0.146267	+	0.106269i	0.0101909	+	0.00740413i
$207$	−0.219432	−	0.675342i	−0.0152516	−	0.0469395i
$208$	−0.530927			−0.0368132
$209$	9.36212	+	15.2097i	0.647591	+	1.05208i
$210$	2.94617			0.203305
$211$	−3.81762	−	11.7494i	−0.262816	−	0.808864i	−0.992189	−	0.124748i	$-0.960188\pi$
$211$	−3.81762	−	11.7494i	−0.262816	−	0.808864i	0.729373	−	0.684117i	$-0.239812\pi$
$212$	3.21163	+	2.33338i	0.220576	+	0.160258i
$213$	−7.18223	+	5.21820i	−0.492118	+	0.357545i
$214$	4.66407	−	14.3545i	0.318829	−	0.981255i
$215$	−0.157126	+	0.483585i	−0.0107159	+	0.0329802i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	4.07849	+	2.96320i	0.276866	+	0.201155i
$218$	2.03575	+	6.26539i	0.137878	+	0.424346i
$219$	6.50072			0.439278
$220$	0.747296	−	9.74271i	0.0503827	−	0.656853i
$221$	−3.89496			−0.262003
$222$	−0.707619	−	2.17783i	−0.0474923	−	0.146166i
$223$	−10.7487	−	7.80938i	−0.719786	−	0.522955i	0.166530	−	0.986036i	$-0.446744\pi$
$223$	−10.7487	−	7.80938i	−0.719786	−	0.522955i	−0.886316	+	0.463081i	$0.846744\pi$
$224$	−0.809017	+	0.587785i	−0.0540547	+	0.0392731i
$225$	1.13715	−	3.49978i	0.0758099	−	0.233319i
$226$	−4.16983	+	12.8334i	−0.277373	+	0.853667i
$227$	12.1889	−	8.85578i	0.809008	−	0.587779i	−0.104535	−	0.994521i	$-0.533335\pi$
$227$	12.1889	−	8.85578i	0.809008	−	0.587779i	0.913543	+	0.406742i	$0.133335\pi$
$228$	−4.35658	−	3.16524i	−0.288522	−	0.209623i
$229$	−2.59003	−	7.97129i	−0.171154	−	0.526758i	0.828283	−	0.560310i	$-0.189318\pi$
$229$	−2.59003	−	7.97129i	−0.171154	−	0.526758i	−0.999437	+	0.0335523i	$0.989318\pi$
$230$	−2.09206			−0.137947
$231$	−3.06668	−	1.26313i	−0.201773	−	0.0831077i
$232$	−0.0951262			−0.00624534
$233$	−1.75627	−	5.40524i	−0.115057	−	0.354109i	0.876902	−	0.480669i	$-0.159606\pi$
$233$	−1.75627	−	5.40524i	−0.115057	−	0.354109i	−0.991959	+	0.126560i	$0.959606\pi$
$234$	0.429529	+	0.312071i	0.0280792	+	0.0204007i
$235$	31.5182	−	22.8993i	2.05602	−	1.49379i
$236$	−2.82966	+	8.70881i	−0.184195	+	0.566895i
$237$	3.17836	−	9.78198i	0.206456	−	0.635408i
$238$	−5.93507	+	4.31208i	−0.384713	+	0.279511i
$239$	−20.0341	−	14.5556i	−1.29590	−	0.941524i	−0.295990	−	0.955191i	$-0.595649\pi$
$239$	−20.0341	−	14.5556i	−1.29590	−	0.941524i	−0.999907	+	0.0136672i	$0.995649\pi$
$240$	0.910415	+	2.80197i	0.0587670	+	0.180866i
$241$	8.91406			0.574205			0.287103	−	0.957900i	$-0.407308\pi$
$241$	8.91406			0.574205			0.287103	+	0.957900i	$0.407308\pi$
$242$	−4.95492	+	9.82084i	−0.318514	+	0.631307i
$243$	1.00000			0.0641500
$244$	−2.37263	−	7.30221i	−0.151892	−	0.467476i
$245$	−2.38350	−	1.73171i	−0.152276	−	0.110635i
$246$	1.88999	−	1.37315i	0.120501	−	0.0875491i
$247$	−0.883498	+	2.71913i	−0.0562156	+	0.173014i
$248$	−1.55784	+	4.79455i	−0.0989232	+	0.304454i
$249$	11.8995	−	8.64552i	0.754102	−	0.547888i
$250$	3.14648	+	2.28605i	0.199001	+	0.144583i
$251$	0.339359	+	1.04444i	0.0214202	+	0.0659245i	0.961195	−	0.275869i	$-0.0889656\pi$
$251$	0.339359	+	1.04444i	0.0214202	+	0.0659245i	−0.939775	+	0.341794i	$0.888966\pi$
$252$	1.00000			0.0629941
$253$	2.17764	+	0.896943i	0.136907	+	0.0563903i
$254$	3.41857			0.214500
$255$	6.67894	+	20.5557i	0.418252	+	1.28725i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	21.7922	−	15.8330i	1.35936	−	0.987635i	0.360877	−	0.932613i	$-0.382477\pi$
$257$	21.7922	−	15.8330i	1.35936	−	0.987635i	0.998485	−	0.0550211i	$-0.0175226\pi$
$258$	−0.0533324	+	0.164140i	−0.00332033	+	0.0102189i
$259$	−0.707619	+	2.17783i	−0.0439693	+	0.135324i
$260$	1.26546	−	0.919413i	0.0784807	−	0.0570196i
$261$	0.0769587	+	0.0559138i	0.00476362	+	0.00346097i
$262$	1.49030	+	4.58668i	0.0920713	+	0.283366i
$263$	−25.0868			−1.54692			−0.773460	−	0.633846i	$-0.781475\pi$
$263$	−25.0868			−1.54692			−0.773460	+	0.633846i	$0.781475\pi$
$264$	0.253650	−	3.30691i	0.0156111	−	0.203526i
$265$	−11.6957			−0.718459
$266$	1.66407	+	5.12147i	0.102030	+	0.314017i
$267$	−6.97330	−	5.06640i	−0.426759	−	0.310059i
$268$	10.4557	−	7.59652i	0.638685	−	0.464031i
$269$	8.17565	−	25.1621i	0.498478	−	1.53416i	−0.312987	−	0.949757i	$-0.601330\pi$
$269$	8.17565	−	25.1621i	0.498478	−	1.53416i	0.811465	−	0.584401i	$-0.198670\pi$
$270$	0.910415	−	2.80197i	0.0554061	−	0.170522i
$271$	21.2668	−	15.4513i	1.29187	−	0.938598i	0.292028	−	0.956410i	$-0.405670\pi$
$271$	21.2668	−	15.4513i	1.29187	−	0.938598i	0.999841	+	0.0178120i	$0.00567004\pi$
$272$	−5.93507	−	4.31208i	−0.359866	−	0.261458i
$273$	−0.164066	−	0.504942i	−0.00992970	−	0.0305605i
$274$	17.2609			1.04277
$275$	6.39766	+	10.3936i	0.385793	+	0.626759i
$276$	−0.710097			−0.0427428
$277$	1.92101	+	5.91225i	0.115422	+	0.355233i	0.992035	−	0.125964i	$-0.0402023\pi$
$277$	1.92101	+	5.91225i	0.115422	+	0.355233i	−0.876613	+	0.481197i	$0.840202\pi$
$278$	14.1186	+	10.2578i	0.846778	+	0.615221i
$279$	4.07849	−	2.96320i	0.244173	−	0.177402i
$280$	0.910415	−	2.80197i	0.0544077	−	0.167450i
$281$	−9.51501	+	29.2842i	−0.567618	+	1.74695i	0.0924243	+	0.995720i	$0.470538\pi$
$281$	−9.51501	+	29.2842i	−0.567618	+	1.74695i	−0.660042	+	0.751229i	$0.729462\pi$
$282$	10.6981	−	7.77259i	0.637060	−	0.462851i
$283$	11.9872	+	8.70924i	0.712567	+	0.517711i	0.884001	−	0.467485i	$-0.154840\pi$
$283$	11.9872	+	8.70924i	0.712567	+	0.517711i	−0.171433	+	0.985196i	$0.554840\pi$
$284$	2.74337	+	8.44322i	0.162789	+	0.501013i
$285$	15.8652			0.939772
$286$	−1.71141	+	0.414471i	−0.101198	+	0.0245082i
$287$	−2.33615			−0.137899
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	−29.7873	−	21.6417i	−1.75219	−	1.27304i
$290$	0.226733	−	0.164731i	0.0133142	−	0.00967335i
$291$	−0.280568	+	0.863499i	−0.0164472	+	0.0506192i
$292$	2.00883	−	6.18255i	0.117558	−	0.361806i
$293$	10.0886	−	7.32982i	0.589385	−	0.428213i	−0.252711	−	0.967542i	$-0.581322\pi$
$293$	10.0886	−	7.32982i	0.589385	−	0.428213i	0.842095	+	0.539329i	$0.181322\pi$
$294$	−0.809017	−	0.587785i	−0.0471828	−	0.0342803i
$295$	−8.33665	−	25.6576i	−0.485379	−	1.49384i
$296$	−2.28990			−0.133098
$297$	−2.14896	+	2.52626i	−0.124695	+	0.146588i
$298$	−10.1039			−0.585302
$299$	0.116502	+	0.358558i	0.00673751	+	0.0207359i
$300$	−2.97709	−	2.16298i	−0.171882	−	0.124880i
$301$	0.139626	−	0.101444i	0.00804792	−	0.00584715i
$302$	−1.16713	+	3.59205i	−0.0671607	+	0.206699i
$303$	−1.05938	+	3.26042i	−0.0608596	+	0.187307i
$304$	−4.35658	+	3.16524i	−0.249867	+	0.181539i
$305$	18.3005	+	13.2961i	1.04788	+	0.761331i
$306$	2.26700	+	6.97709i	0.129595	+	0.398854i
$307$	−25.1036			−1.43274			−0.716368	−	0.697722i	$-0.754197\pi$
$307$	−25.1036			−1.43274			−0.716368	+	0.697722i	$0.754197\pi$
$308$	−2.14896	+	2.52626i	−0.122448	+	0.143947i
$309$	−0.180796			−0.0102851
$310$	−4.58967	−	14.1255i	−0.260676	−	0.802277i
$311$	−17.1120	−	12.4326i	−0.970331	−	0.704987i	−0.0148042	−	0.999890i	$-0.504712\pi$
$311$	−17.1120	−	12.4326i	−0.970331	−	0.704987i	−0.955527	+	0.294903i	$0.904712\pi$
$312$	0.429529	−	0.312071i	0.0243173	−	0.0176675i
$313$	0.671869	−	2.06780i	0.0379763	−	0.116879i	−0.930271	−	0.366873i	$-0.880429\pi$
$313$	0.671869	−	2.06780i	0.0379763	−	0.116879i	0.968247	+	0.249994i	$0.0804285\pi$
$314$	6.78756	−	20.8900i	0.383044	−	1.17889i
$315$	−2.38350	+	1.73171i	−0.134295	+	0.0975709i
$316$	−8.32105	−	6.04559i	−0.468095	−	0.340091i
$317$	0.784806	+	2.41538i	0.0440791	+	0.135661i	0.970674	−	0.240399i	$-0.0772784\pi$
$317$	0.784806	+	2.41538i	0.0440791	+	0.135661i	−0.926595	+	0.376061i	$0.877278\pi$
$318$	−3.96979			−0.222615
$319$	−0.306634	+	0.0742608i	−0.0171682	+	0.00415781i
$320$	2.94617			0.164696
$321$	4.66407	+	14.3545i	0.260323	+	0.801191i
$322$	0.574481	+	0.417385i	0.0320146	+	0.0232599i
$323$	−31.9605	+	23.2207i	−1.77833	+	1.29203i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−0.603743	+	1.85813i	−0.0334896	+	0.103070i
$326$	−15.5264	+	11.2806i	−0.859928	+	0.624774i
$327$	−5.32966	−	3.87223i	−0.294731	−	0.214135i
$328$	−0.721910	−	2.22181i	−0.0398608	−	0.122679i
$329$	−13.2235			−0.729036
$330$	5.12204	+	8.32126i	0.281959	+	0.458071i
$331$	−13.6488			−0.750205			−0.375103	−	0.926983i	$-0.622393\pi$
$331$	−13.6488			−0.750205			−0.375103	+	0.926983i	$0.622393\pi$
$332$	−4.54522	−	13.9887i	−0.249451	−	0.767732i
$333$	1.85257	+	1.34597i	0.101520	+	0.0737588i
$334$	−12.5824	+	9.14162i	−0.688476	+	0.500207i
$335$	−11.7662	+	36.2126i	−0.642855	+	1.97850i
$336$	0.309017	−	0.951057i	0.0168583	−	0.0518844i
$337$	−8.17230	+	5.93752i	−0.445174	+	0.323438i	−0.787687	−	0.616075i	$-0.788722\pi$
$337$	−8.17230	+	5.93752i	−0.445174	+	0.323438i	0.342514	+	0.939513i	$0.388722\pi$
$338$	10.2892	+	7.47552i	0.559657	+	0.406615i
$339$	−4.16983	−	12.8334i	−0.226474	−	0.697016i
$340$	21.6135			1.17216
$341$	−1.27873	+	16.6711i	−0.0692469	+	0.902791i
$342$	5.38503			0.291189
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	0.139626	+	0.101444i	0.00752814	+	0.00546951i
$345$	1.69251	−	1.22968i	0.0911219	−	0.0662040i
$346$	6.92407	−	21.3101i	0.372240	−	1.14564i
$347$	9.97952	−	30.7138i	0.535729	−	1.64880i	−0.206341	−	0.978480i	$-0.566156\pi$
$347$	9.97952	−	30.7138i	0.535729	−	1.64880i	0.742069	−	0.670323i	$-0.233844\pi$
$348$	0.0769587	−	0.0559138i	0.00412542	−	0.00299729i
$349$	5.34893	+	3.88623i	0.286322	+	0.208025i	0.721670	−	0.692237i	$-0.243375\pi$
$349$	5.34893	+	3.88623i	0.286322	+	0.208025i	−0.435348	+	0.900262i	$0.643375\pi$
$350$	1.13715	+	3.49978i	0.0607831	+	0.187071i
$351$	−0.530927			−0.0283388
$352$	−3.06668	−	1.26313i	−0.163454	−	0.0673249i
$353$	−19.4835			−1.03700			−0.518501	−	0.855077i	$-0.673510\pi$
$353$	−19.4835			−1.03700			−0.518501	+	0.855077i	$0.673510\pi$
$354$	−2.82966	−	8.70881i	−0.150395	−	0.462868i
$355$	−21.1600	−	15.3737i	−1.12306	−	0.815950i
$356$	−6.97330	+	5.06640i	−0.369584	+	0.268519i
$357$	2.26700	−	6.97709i	0.119982	−	0.369267i
$358$	−5.67195	+	17.4565i	−0.299772	+	0.922603i
$359$	−7.95052	+	5.77639i	−0.419613	+	0.304866i	−0.777482	−	0.628905i	$-0.783503\pi$
$359$	−7.95052	+	5.77639i	−0.419613	+	0.304866i	0.357869	+	0.933772i	$0.383503\pi$
$360$	−2.38350	−	1.73171i	−0.125621	−	0.0912693i
$361$	3.08972	+	9.50918i	0.162617	+	0.500483i
$362$	−3.33220			−0.175137
$363$	−1.76393	−	10.8576i	−0.0925824	−	0.569879i
$364$	−0.530927			−0.0278281
$365$	5.91835	+	18.2148i	0.309781	+	0.953407i
$366$	6.21163	+	4.51301i	0.324687	+	0.235899i
$367$	9.01168	−	6.54737i	0.470406	−	0.341770i	−0.327194	−	0.944957i	$-0.606103\pi$
$367$	9.01168	−	6.54737i	0.470406	−	0.341770i	0.797599	+	0.603187i	$0.206103\pi$
$368$	−0.219432	+	0.675342i	−0.0114387	+	0.0352047i
$369$	−0.721910	+	2.22181i	−0.0375811	+	0.115663i
$370$	5.45798	−	3.96545i	0.283747	−	0.206154i
$371$	3.21163	+	2.33338i	0.166739	+	0.121143i
$372$	−1.55784	−	4.79455i	−0.0807705	−	0.248586i
$373$	−7.65347			−0.396281			−0.198141	−	0.980174i	$-0.563490\pi$
$373$	−7.65347			−0.396281			−0.198141	+	0.980174i	$0.563490\pi$
$374$	−22.4976	−	9.26649i	−1.16332	−	0.479159i
$375$	−3.88927			−0.200841
$376$	−4.08629	−	12.5763i	−0.210735	−	0.648574i
$377$	−0.0408595	−	0.0296861i	−0.00210437	−	0.00152891i
$378$	−0.809017	+	0.587785i	−0.0416113	+	0.0302324i
$379$	−2.17034	+	6.67961i	−0.111483	+	0.343109i	−0.991197	−	0.132394i	$-0.957734\pi$
$379$	−2.17034	+	6.67961i	−0.111483	+	0.343109i	0.879714	+	0.475502i	$0.157734\pi$
$380$	4.90261	−	15.0887i	0.251499	−	0.774033i
$381$	−2.76568	+	2.00938i	−0.141690	+	0.102944i
$382$	6.80888	+	4.94694i	0.348373	+	0.253108i
$383$	−8.79062	−	27.0548i	−0.449180	−	1.38243i	−0.877834	−	0.478965i	$-0.841012\pi$
$383$	−8.79062	−	27.0548i	−0.449180	−	1.38243i	0.428654	−	0.903469i	$-0.358988\pi$
$384$	1.00000			0.0510310
$385$	0.747296	−	9.74271i	0.0380857	−	0.496534i
$386$	−6.90604			−0.351508
$387$	−0.0533324	−	0.164140i	−0.00271104	−	0.00834372i
$388$	0.734536	+	0.533672i	0.0372904	+	0.0270931i
$389$	5.18355	−	3.76607i	0.262816	−	0.190947i	−0.448571	−	0.893747i	$-0.648067\pi$
$389$	5.18355	−	3.76607i	0.262816	−	0.190947i	0.711388	+	0.702800i	$0.248067\pi$
$390$	−0.483364	+	1.48764i	−0.0244761	+	0.0753297i
$391$	−1.60979	+	4.95441i	−0.0814104	+	0.250555i
$392$	−0.809017	+	0.587785i	−0.0408615	+	0.0296876i
$393$	−3.90167	−	2.83473i	−0.196813	−	0.142993i
$394$	3.26903	+	10.0610i	0.164691	+	0.506868i
$395$	30.3024			1.52468
$396$	1.73855	+	2.82444i	0.0873652	+	0.141933i
$397$	30.7498			1.54329			0.771643	−	0.636056i	$-0.219435\pi$
$397$	30.7498			1.54329			0.771643	+	0.636056i	$0.219435\pi$
$398$	5.16866	+	15.9075i	0.259082	+	0.797371i
$399$	−4.35658	−	3.16524i	−0.218102	−	0.158460i
$400$	−2.97709	+	2.16298i	−0.148855	+	0.108149i
$401$	1.60374	−	4.93581i	0.0800871	−	0.246483i	−0.902994	−	0.429653i	$-0.858636\pi$
$401$	1.60374	−	4.93581i	0.0800871	−	0.246483i	0.983081	+	0.183170i	$0.0586359\pi$
$402$	−3.99373	+	12.2914i	−0.199189	+	0.613041i
$403$	−2.16538	+	1.57324i	−0.107865	+	0.0783687i
$404$	2.77348	+	2.01505i	0.137986	+	0.100253i
$405$	0.910415	+	2.80197i	0.0452389	+	0.139231i
$406$	−0.0951262			−0.00472103
$407$	−7.38137	+	1.78763i	−0.365881	+	0.0886093i
$408$	7.33615			0.363194
$409$	8.37043	+	25.7615i	0.413891	+	1.27383i	0.913239	+	0.407424i	$0.133573\pi$
$409$	8.37043	+	25.7615i	0.413891	+	1.27383i	−0.499348	+	0.866401i	$0.666427\pi$
$410$	5.56821	+	4.04554i	0.274994	+	0.199795i
$411$	−13.9643	+	10.1457i	−0.688810	+	0.500450i
$412$	−0.0558691	+	0.171947i	−0.00275247	+	0.00847124i
$413$	−2.82966	+	8.70881i	−0.139239	+	0.428532i
$414$	0.574481	−	0.417385i	0.0282342	−	0.0205133i
$415$	35.0580	+	25.4711i	1.72093	+	1.25033i
$416$	−0.164066	−	0.504942i	−0.00804397	−	0.0247568i
$417$	−17.4516			−0.854607
$418$	−11.5722	+	13.6040i	−0.566016	+	0.665391i
$419$	−23.5391			−1.14996			−0.574980	−	0.818167i	$-0.694990\pi$
$419$	−23.5391			−1.14996			−0.574980	+	0.818167i	$0.694990\pi$
$420$	0.910415	+	2.80197i	0.0444237	+	0.136722i
$421$	6.84088	+	4.97019i	0.333404	+	0.242232i	0.741874	−	0.670540i	$-0.233937\pi$
$421$	6.84088	+	4.97019i	0.333404	+	0.242232i	−0.408470	+	0.912772i	$0.633937\pi$
$422$	9.99466	−	7.26155i	0.486533	−	0.353487i
$423$	−4.08629	+	12.5763i	−0.198682	+	0.611482i
$424$	−1.22673	+	3.77550i	−0.0595754	+	0.183354i
$425$	−21.8404	+	15.8680i	−1.05941	+	0.769710i
$426$	−7.18223	−	5.21820i	−0.347980	−	0.252823i
$427$	−2.37263	−	7.30221i	−0.114820	−	0.353379i
$428$	15.0932			0.729559
$429$	1.14094	−	1.34126i	0.0550852	−	0.0647565i
$430$	−0.508471			−0.0245206
$431$	9.86189	+	30.3518i	0.475031	+	1.46199i	0.845916	+	0.533316i	$0.179054\pi$
$431$	9.86189	+	30.3518i	0.475031	+	1.46199i	−0.370886	+	0.928679i	$0.620946\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−32.6167	+	23.6974i	−1.56746	+	1.13883i	−0.637918	+	0.770104i	$0.720204\pi$
$433$	−32.6167	+	23.6974i	−1.56746	+	1.13883i	−0.929540	+	0.368721i	$0.879796\pi$
$434$	−1.55784	+	4.79455i	−0.0747789	+	0.230146i
$435$	−0.0866043	+	0.266541i	−0.00415236	+	0.0127796i
$436$	−5.32966	+	3.87223i	−0.255245	+	0.185446i
$437$	3.09359	+	2.24763i	0.147987	+	0.107519i
$438$	2.00883	+	6.18255i	0.0959857	+	0.295414i
$439$	30.2721			1.44481			0.722404	−	0.691471i	$-0.243037\pi$
$439$	30.2721			1.44481			0.722404	+	0.691471i	$0.243037\pi$
$440$	9.49679	−	2.29994i	0.452742	−	0.109645i
$441$	1.00000			0.0476190
$442$	−1.20361	−	3.70433i	−0.0572499	−	0.176197i
$443$	−2.55179	−	1.85398i	−0.121239	−	0.0880854i	0.525513	−	0.850785i	$-0.323873\pi$
$443$	−2.55179	−	1.85398i	−0.121239	−	0.0880854i	−0.646752	+	0.762700i	$0.723873\pi$
$444$	1.85257	−	1.34597i	0.0879191	−	0.0638770i
$445$	7.84730	−	24.1515i	0.371998	−	1.14489i
$446$	4.10564	−	12.6358i	0.194407	−	0.598325i
$447$	8.17421	−	5.93891i	0.386627	−	0.280901i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	6.01127	+	18.5008i	0.283690	+	0.873107i	0.986788	+	0.162015i	$0.0517992\pi$
$449$	6.01127	+	18.5008i	0.283690	+	0.873107i	−0.703099	+	0.711092i	$0.748201\pi$
$450$	3.67989			0.173472
$451$	−4.06151	−	6.59831i	−0.191249	−	0.310703i
$452$	−13.4939			−0.634698
$453$	−1.16713	−	3.59205i	−0.0548365	−	0.168769i
$454$	12.1889	+	8.85578i	0.572055	+	0.415622i
$455$	1.26546	−	0.919413i	0.0593258	−	0.0431028i
$456$	1.66407	−	5.12147i	0.0779270	−	0.239835i
$457$	−11.6848	+	35.9623i	−0.546594	+	1.68224i	0.170576	+	0.985345i	$0.445437\pi$
$457$	−11.6848	+	35.9623i	−0.546594	+	1.68224i	−0.717170	+	0.696899i	$0.754563\pi$
$458$	6.78078	−	4.92653i	0.316845	−	0.230202i
$459$	−5.93507	−	4.31208i	−0.277025	−	0.201271i
$460$	−0.646483	−	1.98967i	−0.0301424	−	0.0927689i
$461$	15.3852			0.716560			0.358280	−	0.933614i	$-0.383363\pi$
$461$	15.3852			0.716560			0.358280	+	0.933614i	$0.383363\pi$
$462$	0.253650	−	3.30691i	0.0118009	−	0.153851i
$463$	13.7538			0.639195			0.319597	−	0.947553i	$-0.396452\pi$
$463$	13.7538			0.639195			0.319597	+	0.947553i	$0.396452\pi$
$464$	−0.0293956	−	0.0904704i	−0.00136466	−	0.00419998i
$465$	12.0159	+	8.73007i	0.557224	+	0.404847i
$466$	4.59797	−	3.34062i	0.212997	−	0.154751i
$467$	−5.88110	+	18.1002i	−0.272145	+	0.837576i	0.717816	+	0.696233i	$0.245142\pi$
$467$	−5.88110	+	18.1002i	−0.272145	+	0.837576i	−0.989961	+	0.141343i	$0.954858\pi$
$468$	−0.164066	+	0.504942i	−0.00758393	+	0.0233409i
$469$	10.4557	−	7.59652i	0.482800	−	0.350775i
$470$	31.5182	+	22.8993i	1.45383	+	1.05627i
$471$	6.78756	+	20.8900i	0.312754	+	0.962558i
$472$	−9.15698			−0.421484
$473$	0.529270	+	0.218000i	0.0243359	+	0.0100236i
$474$	10.2854			0.472423
$475$	6.12358	+	18.8464i	0.280969	+	0.864733i
$476$	−5.93507	−	4.31208i	−0.272034	−	0.197644i
$477$	3.21163	−	2.33338i	0.147050	−	0.106838i
$478$	7.65233	−	23.5515i	0.350010	−	1.07722i
$479$	11.0503	−	34.0094i	0.504902	−	1.55393i	−0.296034	−	0.955177i	$-0.595664\pi$
$479$	11.0503	−	34.0094i	0.504902	−	1.55393i	0.800936	−	0.598751i	$-0.204336\pi$
$480$	−2.38350	+	1.73171i	−0.108791	+	0.0790415i
$481$	−0.983580	−	0.714613i	−0.0448474	−	0.0325835i
$482$	2.75460	+	8.47778i	0.125468	+	0.386152i
$483$	−0.710097			−0.0323105
$484$	−10.8713	−	1.67760i	−0.494151	−	0.0762545i
$485$	−2.67493			−0.121462
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	25.4489	+	18.4897i	1.15320	+	0.837848i	0.988903	−	0.148564i	$-0.0474650\pi$
$487$	25.4489	+	18.4897i	1.15320	+	0.837848i	0.164295	+	0.986411i	$0.447465\pi$
$488$	6.21163	−	4.51301i	0.281187	−	0.204294i
$489$	5.93056	−	18.2524i	0.268189	−	0.825401i
$490$	0.910415	−	2.80197i	0.0411284	−	0.126580i
$491$	18.8669	−	13.7076i	0.851453	−	0.618617i	−0.0740931	−	0.997251i	$-0.523606\pi$
$491$	18.8669	−	13.7076i	0.851453	−	0.618617i	0.925546	+	0.378634i	$0.123606\pi$
$492$	1.88999	+	1.37315i	0.0852071	+	0.0619066i
$493$	−0.215651	−	0.663704i	−0.00971241	−	0.0298917i
$494$	−2.85906			−0.128635
$495$	−9.03494	−	3.72138i	−0.406090	−	0.167264i
$496$	−5.04129			−0.226361
$497$	2.74337	+	8.44322i	0.123057	+	0.378730i
$498$	11.8995	+	8.64552i	0.533231	+	0.387415i
$499$	−1.85774	+	1.34973i	−0.0831640	+	0.0604222i	−0.628590	−	0.777737i	$-0.716368\pi$
$499$	−1.85774	+	1.34973i	−0.0831640	+	0.0604222i	0.545426	+	0.838159i	$0.316368\pi$
$500$	−1.20185	+	3.69891i	−0.0537483	+	0.165420i
$501$	4.80604	−	14.7915i	0.214718	−	0.660834i
$502$	−0.888454	+	0.645499i	−0.0396536	+	0.0288101i
$503$	−24.9007	−	18.0914i	−1.11027	−	0.806657i	−0.127562	−	0.991831i	$-0.540715\pi$
$503$	−24.9007	−	18.0914i	−1.11027	−	0.806657i	−0.982706	+	0.185174i	$0.940715\pi$
$504$	0.309017	+	0.951057i	0.0137647	+	0.0423634i
$505$	−10.1001			−0.449448
$506$	−0.180116	+	2.34823i	−0.00800715	+	0.104391i
$507$	−12.7181			−0.564831
$508$	1.05640	+	3.25125i	0.0468700	+	0.144251i
$509$	11.0202	+	8.00665i	0.488462	+	0.354888i	0.804592	−	0.593827i	$-0.202384\pi$
$509$	11.0202	+	8.00665i	0.488462	+	0.354888i	−0.316131	+	0.948716i	$0.602384\pi$
$510$	−17.4857	+	12.7041i	−0.774280	+	0.562547i
$511$	2.00883	−	6.18255i	0.0888655	−	0.273500i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−4.35658	+	3.16524i	−0.192348	+	0.139749i
$514$	21.7922	+	15.8330i	0.961214	+	0.698363i
$515$	−0.164600	−	0.506585i	−0.00725312	−	0.0223228i
$516$	−0.172587			−0.00759774
$517$	−22.9897	−	37.3490i	−1.01109	−	1.64261i
$518$	−2.28990			−0.100613
$519$	6.92407	+	21.3101i	0.303933	+	0.935409i
$520$	1.26546	+	0.919413i	0.0554942	+	0.0403189i
$521$	−29.9244	+	21.7414i	−1.31101	+	0.952507i	−0.311015	+	0.950405i	$0.600669\pi$
$521$	−29.9244	+	21.7414i	−1.31101	+	0.952507i	−0.999998	+	0.00210172i	$0.999331\pi$
$522$	−0.0293956	+	0.0904704i	−0.00128661	+	0.00395978i
$523$	5.09391	−	15.6774i	0.222741	−	0.685526i	−0.775772	−	0.631013i	$-0.782639\pi$
$523$	5.09391	−	15.6774i	0.222741	−	0.685526i	0.998513	−	0.0545129i	$-0.0173606\pi$
$524$	−3.90167	+	2.83473i	−0.170445	+	0.123836i
$525$	−2.97709	−	2.16298i	−0.129931	−	0.0944004i
$526$	−7.75225	−	23.8590i	−0.338014	−	1.04030i
$527$	−36.9837			−1.61103
$528$	3.22344	−	0.780656i	0.140282	−	0.0339737i
$529$	−22.4958			−0.978077
$530$	−3.61416	−	11.1232i	−0.156989	−	0.483162i
$531$	7.40815	+	5.38234i	0.321486	+	0.233574i
$532$	−4.35658	+	3.16524i	−0.188882	+	0.137231i
$533$	0.383282	−	1.17962i	0.0166018	−	0.0510950i
$534$	2.66356	−	8.19760i	0.115264	−	0.354745i
$535$	−35.9747	+	26.1371i	−1.55532	+	1.13001i
$536$	10.4557	+	7.59652i	0.451618	+	0.328120i
$537$	−5.67195	−	17.4565i	−0.244763	−	0.753302i
$538$	26.4570			1.14064
$539$	−2.14896	+	2.52626i	−0.0925623	+	0.108814i
$540$	2.94617			0.126783
$541$	−5.18878	−	15.9694i	−0.223083	−	0.686579i	−0.998481	−	0.0551056i	$-0.982450\pi$
$541$	−5.18878	−	15.9694i	−0.223083	−	0.686579i	0.775397	−	0.631473i	$-0.217550\pi$
$542$	21.2668	+	15.4513i	0.913489	+	0.663689i
$543$	2.69581	−	1.95862i	0.115688	−	0.0840523i
$544$	2.26700	−	6.97709i	0.0971966	−	0.299140i
$545$	5.99766	−	18.4589i	0.256911	−	0.790692i
$546$	0.429529	−	0.312071i	0.0183821	−	0.0133554i
$547$	20.0494	+	14.5668i	0.857252	+	0.622830i	0.927136	−	0.374725i	$-0.122263\pi$
$547$	20.0494	+	14.5668i	0.857252	+	0.622830i	−0.0698841	+	0.997555i	$0.522263\pi$
$548$	5.33390	+	16.4161i	0.227853	+	0.701259i
$549$	−7.67800			−0.327689
$550$	−7.90794	+	9.29634i	−0.337196	+	0.396397i
$551$	−0.512257			−0.0218229
$552$	−0.219432	−	0.675342i	−0.00933965	−	0.0287445i
$553$	−8.32105	−	6.04559i	−0.353847	−	0.257085i
$554$	−5.02926	+	3.65397i	−0.213673	+	0.155242i
$555$	−2.08476	+	6.41624i	−0.0884932	+	0.272354i
$556$	−5.39283	+	16.5974i	−0.228707	+	0.703888i
$557$	−32.9856	+	23.9654i	−1.39764	+	1.01545i	−0.402666	+	0.915347i	$0.631916\pi$
$557$	−32.9856	+	23.9654i	−1.39764	+	1.01545i	−0.994977	+	0.100100i	$0.968084\pi$
$558$	4.07849	+	2.96320i	0.172656	+	0.125442i
$559$	0.0283156	+	0.0871466i	0.00119762	+	0.00368591i
$560$	2.94617			0.124498
$561$	23.6477	−	5.72701i	0.998405	−	0.241794i
$562$	−30.7912			−1.29885
$563$	0.600872	+	1.84929i	0.0253237	+	0.0779384i	0.962920	−	0.269788i	$-0.0869537\pi$
$563$	0.600872	+	1.84929i	0.0253237	+	0.0779384i	−0.937596	+	0.347727i	$0.886954\pi$
$564$	10.6981	+	7.77259i	0.450469	+	0.327285i
$565$	32.1626	−	23.3675i	1.35309	−	0.983078i
$566$	−4.57872	+	14.0918i	−0.192458	+	0.592324i
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$	−7.18223	+	5.21820i	−0.301360	+	0.218951i
$569$	−16.5945	−	12.0566i	−0.695679	−	0.505440i	0.182843	−	0.983142i	$-0.441470\pi$
$569$	−16.5945	−	12.0566i	−0.695679	−	0.505440i	−0.878522	+	0.477702i	$0.841470\pi$
$570$	4.90261	+	15.0887i	0.205348	+	0.631996i
$571$	−21.1757			−0.886173			−0.443087	−	0.896479i	$-0.646117\pi$
$571$	−21.1757			−0.886173			−0.443087	+	0.896479i	$0.646117\pi$
$572$	−0.923041	−	1.49957i	−0.0385943	−	0.0627002i
$573$	−8.41624			−0.351594
$574$	−0.721910	−	2.22181i	−0.0301319	−	0.0927366i
$575$	2.11402	+	1.53593i	0.0881609	+	0.0640526i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−12.8383	+	39.5124i	−0.534467	+	1.64492i	0.210329	+	0.977631i	$0.432546\pi$
$577$	−12.8383	+	39.5124i	−0.534467	+	1.64492i	−0.744797	+	0.667291i	$0.767454\pi$
$578$	11.3777	−	35.0170i	0.473251	−	1.45652i
$579$	5.58711	−	4.05927i	0.232192	−	0.168698i
$580$	0.226733	+	0.164731i	0.00941457	+	0.00684009i
$581$	−4.54522	−	13.9887i	−0.188567	−	0.580351i
$582$	−0.907937			−0.0376352
$583$	−1.00694	+	13.1277i	−0.0417032	+	0.543696i
$584$	6.50072			0.269002
$585$	−0.483364	−	1.48764i	−0.0199846	−	0.0615064i
$586$	10.0886	+	7.32982i	0.416758	+	0.302792i
$587$	28.2965	−	20.5586i	1.16792	−	0.848543i	0.177162	−	0.984182i	$-0.443309\pi$
$587$	28.2965	−	20.5586i	1.16792	−	0.848543i	0.990758	+	0.135638i	$0.0433085\pi$
$588$	0.309017	−	0.951057i	0.0127436	−	0.0392209i
$589$	−8.38904	+	25.8188i	−0.345664	+	1.06385i
$590$	21.8256	−	15.8573i	0.898547	−	0.652833i
$591$	−8.55843	−	6.21806i	−0.352047	−	0.255777i
$592$	−0.707619	−	2.17783i	−0.0290830	−	0.0895081i
$593$	−23.3437			−0.958611			−0.479306	−	0.877648i	$-0.659111\pi$
$593$	−23.3437			−0.958611			−0.479306	+	0.877648i	$0.659111\pi$
$594$	−3.06668	−	1.26313i	−0.125827	−	0.0518268i
$595$	21.6135			0.886068
$596$	−3.12227	−	9.60936i	−0.127893	−	0.393615i
$597$	−13.5317	−	9.83138i	−0.553817	−	0.402371i
$598$	−0.305007	+	0.221601i	−0.0124727	+	0.00906193i
$599$	−2.28291	+	7.02608i	−0.0932773	+	0.287078i	−0.986801	−	0.161938i	$-0.948225\pi$
$599$	−2.28291	+	7.02608i	−0.0932773	+	0.287078i	0.893524	+	0.449016i	$0.148225\pi$
$600$	1.13715	−	3.49978i	0.0464239	−	0.142878i
$601$	18.7178	−	13.5993i	0.763517	−	0.554728i	−0.136470	−	0.990644i	$-0.543576\pi$
$601$	18.7178	−	13.5993i	0.763517	−	0.554728i	0.899987	+	0.435917i	$0.143576\pi$
$602$	0.139626	+	0.101444i	0.00569074	+	0.00413456i
$603$	−3.99373	−	12.2914i	−0.162637	−	0.500546i
$604$	−3.77691			−0.153680
$605$	28.8169	−	14.8275i	1.17157	−	0.602822i
$606$	−3.42821			−0.139262
$607$	2.36650	+	7.28334i	0.0960533	+	0.295622i	0.987527	−	0.157451i	$-0.0503277\pi$
$607$	2.36650	+	7.28334i	0.0960533	+	0.295622i	−0.891473	+	0.453073i	$0.850328\pi$
$608$	−4.35658	−	3.16524i	−0.176683	−	0.128367i
$609$	0.0769587	−	0.0559138i	0.00311852	−	0.00226574i
$610$	−6.99016	+	21.5135i	−0.283023	+	0.871056i
$611$	2.16952	−	6.67711i	0.0877696	−	0.270127i
$612$	−5.93507	+	4.31208i	−0.239911	+	0.174306i
$613$	−15.0507	−	10.9350i	−0.607892	−	0.441659i	0.240780	−	0.970580i	$-0.422597\pi$
$613$	−15.0507	−	10.9350i	−0.607892	−	0.441659i	−0.848671	+	0.528921i	$0.822597\pi$
$614$	−7.75743	−	23.8749i	−0.313064	−	0.963513i
$615$	−6.88268			−0.277537
$616$	−3.06668	−	1.26313i	−0.123560	−	0.0508929i
$617$	2.11892			0.0853044			0.0426522	−	0.999090i	$-0.486419\pi$
$617$	2.11892			0.0853044			0.0426522	+	0.999090i	$0.486419\pi$
$618$	−0.0558691	−	0.171947i	−0.00224738	−	0.00691674i
$619$	7.68317	+	5.58215i	0.308813	+	0.224365i	0.731387	−	0.681963i	$-0.238873\pi$
$619$	7.68317	+	5.58215i	0.308813	+	0.224365i	−0.422574	+	0.906328i	$0.638873\pi$
$620$	12.0159	−	8.73007i	0.482570	−	0.350608i
$621$	−0.219432	+	0.675342i	−0.00880550	+	0.0271006i
$622$	6.53619	−	20.1163i	0.262078	−	0.806592i
$623$	−6.97330	+	5.06640i	−0.279379	+	0.202981i
$624$	0.429529	+	0.312071i	0.0171949	+	0.0124928i
$625$	−9.22659	−	28.3965i	−0.369063	−	1.13586i
$626$	2.17421			0.0868991
$627$	1.36592	−	17.8078i	0.0545494	−	0.711176i
$628$	21.9650			0.876499
$629$	−5.19120	−	15.9769i	−0.206987	−	0.637039i
$630$	−2.38350	−	1.73171i	−0.0949608	−	0.0689931i
$631$	34.6162	−	25.1501i	1.37805	−	1.00121i	0.380989	−	0.924579i	$-0.375583\pi$
$631$	34.6162	−	25.1501i	1.37805	−	1.00121i	0.997059	−	0.0766316i	$-0.0244165\pi$
$632$	3.17836	−	9.78198i	0.126428	−	0.389106i
$633$	−3.81762	+	11.7494i	−0.151737	+	0.466998i
$634$	−2.05465	+	1.49279i	−0.0816005	+	0.0592862i
$635$	−8.14815	−	5.91998i	−0.323349	−	0.234927i
$636$	−1.22673	−	3.77550i	−0.0486431	−	0.149708i
$637$	−0.530927			−0.0210361
$638$	−0.165381	−	0.268678i	−0.00654750	−	0.0106371i
$639$	8.87773			0.351198
$640$	0.910415	+	2.80197i	0.0359873	+	0.110758i
$641$	17.7615	+	12.9045i	0.701539	+	0.509698i	0.880433	−	0.474171i	$-0.157252\pi$
$641$	17.7615	+	12.9045i	0.701539	+	0.509698i	−0.178894	+	0.983868i	$0.557252\pi$
$642$	−12.2107	+	8.87158i	−0.481917	+	0.350133i
$643$	−6.03449	+	18.5723i	−0.237977	+	0.732418i	0.758735	+	0.651399i	$0.225818\pi$
$643$	−6.03449	+	18.5723i	−0.237977	+	0.732418i	−0.996713	+	0.0810194i	$0.974182\pi$
$644$	−0.219432	+	0.675342i	−0.00864683	+	0.0266122i
$645$	0.411362	−	0.298872i	0.0161973	−	0.0117681i
$646$	−31.9605	−	23.2207i	−1.25747	−	0.913606i
$647$	−9.68683	−	29.8130i	−0.380828	−	1.17207i	−0.939461	−	0.342655i	$-0.888674\pi$
$647$	−9.68683	−	29.8130i	−0.380828	−	1.17207i	0.558633	−	0.829415i	$-0.311326\pi$
$648$	1.00000			0.0392837
$649$	−29.5170	+	7.14845i	−1.15864	+	0.280601i
$650$	−1.95375			−0.0766325
$651$	−1.55784	−	4.79455i	−0.0610567	−	0.187913i
$652$	−15.5264	−	11.2806i	−0.608061	−	0.441782i
$653$	16.0480	−	11.6596i	0.628007	−	0.456273i	−0.227702	−	0.973731i	$-0.573121\pi$
$653$	16.0480	−	11.6596i	0.628007	−	0.456273i	0.855709	+	0.517457i	$0.173121\pi$
$654$	2.03575	−	6.26539i	0.0796041	−	0.244996i
$655$	4.39068	−	13.5131i	0.171558	−	0.528001i
$656$	1.88999	−	1.37315i	0.0737915	−	0.0536127i
$657$	−5.25919	−	3.82103i	−0.205181	−	0.149072i
$658$	−4.08629	−	12.5763i	−0.159300	−	0.490276i
$659$	37.3020			1.45308			0.726539	−	0.687125i	$-0.241128\pi$
$659$	37.3020			1.45308			0.726539	+	0.687125i	$0.241128\pi$
$660$	−6.33119	+	7.44277i	−0.246441	+	0.289709i
$661$	5.41129			0.210475			0.105237	−	0.994447i	$-0.466440\pi$
$661$	5.41129			0.210475			0.105237	+	0.994447i	$0.466440\pi$
$662$	−4.21771	−	12.9808i	−0.163926	−	0.504512i
$663$	3.15109	+	2.28940i	0.122378	+	0.0889130i
$664$	11.8995	−	8.64552i	0.461792	−	0.335511i
$665$	4.90261	−	15.0887i	0.190115	−	0.585114i
$666$	−0.707619	+	2.17783i	−0.0274197	+	0.0843891i
$667$	−0.0546481	+	0.0397042i	−0.00211598	+	0.00153735i
$668$	−12.5824	−	9.14162i	−0.486826	−	0.353700i
$669$	4.10564	+	12.6358i	0.158733	+	0.488530i
$670$	−38.0762			−1.47101
$671$	16.4997	−	19.3966i	0.636964	−	0.748797i
$672$	1.00000			0.0385758
$673$	14.9180	+	45.9129i	0.575047	+	1.76981i	0.636019	+	0.771674i	$0.280580\pi$
$673$	14.9180	+	45.9129i	0.575047	+	1.76981i	−0.0609714	+	0.998140i	$0.519420\pi$
$674$	−8.17230	−	5.93752i	−0.314785	−	0.228705i
$675$	−2.97709	+	2.16298i	−0.114588	+	0.0832533i
$676$	−3.93011	+	12.0956i	−0.151158	+	0.465217i
$677$	9.07104	−	27.9178i	0.348629	−	1.07297i	−0.610984	−	0.791643i	$-0.709226\pi$
$677$	9.07104	−	27.9178i	0.348629	−	1.07297i	0.959612	−	0.281325i	$-0.0907740\pi$
$678$	10.9168	−	7.93150i	0.419256	−	0.304607i
$679$	0.734536	+	0.533672i	0.0281889	+	0.0204804i
$680$	6.67894	+	20.5557i	0.256126	+	0.788274i
$681$	−15.0664			−0.577344
$682$	−16.2503	+	3.93551i	−0.622256	+	0.150699i
$683$	24.9058			0.952992			0.476496	−	0.879177i	$-0.341907\pi$
$683$	24.9058			0.952992			0.476496	+	0.879177i	$0.341907\pi$
$684$	1.66407	+	5.12147i	0.0636271	+	0.195824i
$685$	−41.1412	−	29.8909i	−1.57193	−	1.14207i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	−2.59003	+	7.97129i	−0.0988158	+	0.304124i
$688$	−0.0533324	+	0.164140i	−0.00203328	+	0.00625779i
$689$	−1.70514	+	1.23886i	−0.0649607	+	0.0471967i
$690$	1.69251	+	1.22968i	0.0644329	+	0.0468133i
$691$	10.5427	+	32.4470i	0.401063	+	1.23434i	0.924139	+	0.382057i	$0.124784\pi$
$691$	10.5427	+	32.4470i	0.401063	+	1.23434i	−0.523076	+	0.852286i	$0.675216\pi$
$692$	22.4068			0.851777
$693$	1.73855	+	2.82444i	0.0660419	+	0.107292i
$694$	32.2944			1.22588
$695$	−15.8882	−	48.8988i	−0.602673	−	1.85484i
$696$	0.0769587	+	0.0559138i	0.00291711	+	0.00211941i
$697$	13.8652	−	10.0737i	0.525183	−	0.381567i
$698$	−2.04311	+	6.28804i	−0.0773328	+	0.238006i
$699$	−1.75627	+	5.40524i	−0.0664282	+	0.204445i
$700$	−2.97709	+	2.16298i	−0.112524	+	0.0817531i
$701$	11.4354	+	8.30832i	0.431910	+	0.313801i	0.782412	−	0.622761i	$-0.213989\pi$
$701$	11.4354	+	8.30832i	0.431910	+	0.313801i	−0.350502	+	0.936562i	$0.613989\pi$
$702$	−0.164066	−	0.504942i	−0.00619225	−	0.0190578i
$703$	−12.3312			−0.465080
$704$	0.253650	−	3.30691i	0.00955981	−	0.124634i
$705$	−38.9587			−1.46727
$706$	−6.02073	−	18.5299i	−0.226593	−	0.697382i
$707$	2.77348	+	2.01505i	0.104308	+	0.0757839i
$708$	7.40815	−	5.38234i	0.278415	−	0.202281i
$709$	5.58255	−	17.1813i	0.209657	−	0.645258i	−0.789833	−	0.613322i	$-0.789833\pi$
$709$	5.58255	−	17.1813i	0.209657	−	0.645258i	0.999490	−	0.0319360i	$-0.0101673\pi$
$710$	8.08242	−	24.8751i	0.303328	−	0.933547i
$711$	−8.32105	+	6.04559i	−0.312064	+	0.226727i
$712$	−6.97330	−	5.06640i	−0.261335	−	0.189871i
$713$	1.10622	+	3.40460i	0.0414283	+	0.127503i
$714$	7.33615			0.274549
$715$	4.79689	+	1.97578i	0.179394	+	0.0738901i
$716$	−18.3548			−0.685952
$717$	7.65233	+	23.5515i	0.285782	+	0.879546i
$718$	−7.95052	−	5.77639i	−0.296711	−	0.215573i
$719$	16.4996	−	11.9877i	0.615333	−	0.447065i	−0.235955	−	0.971764i	$-0.575822\pi$
$719$	16.4996	−	11.9877i	0.615333	−	0.447065i	0.851288	+	0.524699i	$0.175822\pi$
$720$	0.910415	−	2.80197i	0.0339292	−	0.104423i
$721$	−0.0558691	+	0.171947i	−0.00208067	+	0.00640365i
$722$	−8.08899	+	5.87699i	−0.301041	+	0.218719i
$723$	−7.21163	−	5.23955i	−0.268203	−	0.194861i
$724$	−1.02971	−	3.16911i	−0.0382687	−	0.117779i
$725$	−0.350054			−0.0130007
$726$	9.78115	−	5.03280i	0.363013	−	0.186785i
$727$	17.3725			0.644310			0.322155	−	0.946687i	$-0.395593\pi$
$727$	17.3725			0.644310			0.322155	+	0.946687i	$0.395593\pi$
$728$	−0.164066	−	0.504942i	−0.00608067	−	0.0187144i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−15.4944	+	11.2574i	−0.573475	+	0.416654i
$731$	−0.391255	+	1.20416i	−0.0144711	+	0.0445374i
$732$	−2.37263	+	7.30221i	−0.0876950	+	0.269897i
$733$	−18.7389	+	13.6146i	−0.692138	+	0.502867i	−0.877362	−	0.479829i	$-0.840699\pi$
$733$	−18.7389	+	13.6146i	−0.692138	+	0.502867i	0.185225	+	0.982696i	$0.440699\pi$
$734$	9.01168	+	6.54737i	0.332627	+	0.241668i
$735$	0.910415	+	2.80197i	0.0335812	+	0.103352i
$736$	−0.710097			−0.0261745
$737$	39.6337	+	16.3246i	1.45992	+	0.601326i
$738$	−2.33615			−0.0859949
$739$	−12.6532	−	38.9425i	−0.465455	−	1.43252i	−0.858409	−	0.512966i	$-0.828547\pi$
$739$	−12.6532	−	38.9425i	−0.465455	−	1.43252i	0.392953	−	0.919558i	$-0.371453\pi$
$740$	5.45798	+	3.96545i	0.200639	+	0.145773i
$741$	2.31303	−	1.68051i	0.0849712	−	0.0617352i
$742$	−1.22673	+	3.77550i	−0.0450348	+	0.138603i
$743$	2.14756	−	6.60952i	0.0787864	−	0.242480i	−0.903904	−	0.427736i	$-0.859311\pi$
$743$	2.14756	−	6.60952i	0.0787864	−	0.242480i	0.982690	+	0.185256i	$0.0593114\pi$
$744$	4.07849	−	2.96320i	0.149525	−	0.108636i
$745$	24.0826	+	17.4970i	0.882318	+	0.641041i
$746$	−2.36505	−	7.27888i	−0.0865907	−	0.266499i
$747$	−14.7086			−0.538161
$748$	1.86082	−	24.2600i	0.0680382	−	0.887033i
$749$	15.0932			0.551495
$750$	−1.20185	−	3.69891i	−0.0438853	−	0.135065i
$751$	14.0636	+	10.2178i	0.513188	+	0.372853i	0.814032	−	0.580821i	$-0.197268\pi$
$751$	14.0636	+	10.2178i	0.513188	+	0.372853i	−0.300844	+	0.953674i	$0.597268\pi$
$752$	10.6981	−	7.77259i	0.390118	−	0.283437i
$753$	0.339359	−	1.04444i	0.0123669	−	0.0380615i
$754$	0.0156069	−	0.0480332i	0.000568371	−	0.00174926i
$755$	9.00225	−	6.54052i	0.327625	−	0.238034i
$756$	−0.809017	−	0.587785i	−0.0294237	−	0.0213775i
$757$	7.10161	+	21.8565i	0.258113	+	0.794389i	0.993200	+	0.116417i	$0.0371409\pi$
$757$	7.10161	+	21.8565i	0.258113	+	0.794389i	−0.735088	+	0.677972i	$0.762859\pi$
$758$	−7.02336			−0.255100
$759$	−1.23454	−	2.00563i	−0.0448108	−	0.0727996i
$760$	15.8652			0.575491
$761$	1.88927	+	5.81457i	0.0684859	+	0.210778i	0.979442	−	0.201725i	$-0.0646547\pi$
$761$	1.88927	+	5.81457i	0.0684859	+	0.210778i	−0.910956	+	0.412503i	$0.864655\pi$
$762$	−2.76568	−	2.00938i	−0.100190	−	0.0727923i
$763$	−5.32966	+	3.87223i	−0.192947	+	0.140184i
$764$	−2.60076	+	8.00432i	−0.0940923	+	0.289586i
$765$	6.67894	−	20.5557i	0.241478	−	0.743192i
$766$	23.0141	−	16.7208i	0.831535	−	0.604145i
$767$	−3.93319	−	2.85763i	−0.142019	−	0.103183i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	−13.5706			−0.489369			−0.244684	−	0.969603i	$-0.578684\pi$
$769$	−13.5706			−0.489369			−0.244684	+	0.969603i	$0.578684\pi$
$770$	9.49679	−	2.29994i	0.342241	−	0.0828841i
$771$	−26.9367			−0.970101
$772$	−2.13408	−	6.56804i	−0.0768074	−	0.236389i
$773$	−15.3040	−	11.1190i	−0.550448	−	0.399924i	0.277502	−	0.960725i	$-0.410493\pi$
$773$	−15.3040	−	11.1190i	−0.550448	−	0.399924i	−0.827951	+	0.560801i	$0.810493\pi$
$774$	0.139626	−	0.101444i	0.00501876	−	0.00364634i
$775$	−5.73269	+	17.6434i	−0.205924	+	0.633770i
$776$	−0.280568	+	0.863499i	−0.0100718	+	0.0309978i
$777$	1.85257	−	1.34597i	0.0664606	−	0.0482864i
$778$	5.18355	+	3.76607i	0.185839	+	0.135020i
$779$	−3.88751	−	11.9645i	−0.139284	−	0.428673i
$780$	−1.56420			−0.0560073
$781$	−19.0779	+	22.4274i	−0.682661	+	0.802516i
$782$	−5.20938			−0.186287
$783$	−0.0293956	−	0.0904704i	−0.00105051	−	0.00323315i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	−52.3535	+	38.0371i	−1.86858	+	1.35760i
$786$	1.49030	−	4.58668i	0.0531574	−	0.163602i
$787$	−6.79260	+	20.9055i	−0.242130	+	0.745199i	0.753965	+	0.656914i	$0.228139\pi$
$787$	−6.79260	+	20.9055i	−0.242130	+	0.745199i	−0.996095	+	0.0882851i	$0.971861\pi$
$788$	−8.55843	+	6.21806i	−0.304881	+	0.221509i
$789$	20.2957	+	14.7457i	0.722545	+	0.524959i
$790$	9.36396	+	28.8193i	0.333155	+	1.02535i
$791$	−13.4939			−0.479787
$792$	−2.14896	+	2.52626i	−0.0763600	+	0.0897666i
$793$	4.07646			0.144759
$794$	9.50220	+	29.2448i	0.337220	+	1.03786i
$795$	9.46199	+	6.87454i	0.335582	+	0.243815i
$796$	−13.5317	+	9.83138i	−0.479619	+	0.348464i
$797$	3.73330	−	11.4899i	0.132240	−	0.406994i	−0.862910	−	0.505357i	$-0.831361\pi$
$797$	3.73330	−	11.4899i	0.132240	−	0.406994i	0.995151	+	0.0983632i	$0.0313607\pi$
$798$	1.66407	−	5.12147i	0.0589073	−	0.181298i
$799$	78.4825	−	57.0209i	2.77651	−	2.01725i
$800$	−2.97709	−	2.16298i	−0.105256	−	0.0764730i
$801$	2.66356	+	8.19760i	0.0941124	+	0.289648i
$802$	5.18982			0.183259
$803$	20.9547	−	5.07482i	0.739475	−	0.179087i
$804$	−12.9240			−0.455793
$805$	−0.646483	−	1.98967i	−0.0227855	−	0.0701267i
$806$	−2.16538	−	1.57324i	−0.0762723	−	0.0554151i
$807$	−21.4041	+	15.5510i	−0.753461	+	0.547422i
$808$	−1.05938	+	3.26042i	−0.0372687	+	0.114701i
$809$	−1.28660	+	3.95976i	−0.0452346	+	0.139218i	−0.971123	−	0.238579i	$-0.923318\pi$
$809$	−1.28660	+	3.95976i	−0.0452346	+	0.139218i	0.925888	+	0.377797i	$0.123318\pi$
$810$	−2.38350	+	1.73171i	−0.0837476	+	0.0608462i
$811$	11.4988	+	8.35439i	0.403778	+	0.293362i	0.771078	−	0.636740i	$-0.219718\pi$
$811$	11.4988	+	8.35439i	0.403778	+	0.293362i	−0.367300	+	0.930103i	$0.619718\pi$
$812$	−0.0293956	−	0.0904704i	−0.00103158	−	0.00317489i
$813$	−26.2873			−0.921935
$814$	−3.98110	−	6.46769i	−0.139538	−	0.226692i
$815$	56.5419			1.98058
$816$	2.26700	+	6.97709i	0.0793607	+	0.244247i
$817$	0.751891	+	0.546281i	0.0263053	+	0.0191119i
$818$	−21.9141	+	15.9215i	−0.766207	+	0.556682i
$819$	−0.164066	+	0.504942i	−0.00573291	+	0.0176441i
$820$	−2.12687	+	6.54582i	−0.0742734	+	0.228590i
$821$	20.6905	−	15.0325i	0.722102	−	0.524638i	−0.164953	−	0.986301i	$-0.552747\pi$
$821$	20.6905	−	15.0325i	0.722102	−	0.524638i	0.887055	+	0.461663i	$0.152747\pi$
$822$	−13.9643	−	10.1457i	−0.487062	−	0.353871i
$823$	−5.80093	−	17.8534i	−0.202208	−	0.622332i	−0.999816	−	0.0191565i	$-0.993902\pi$
$823$	−5.80093	−	17.8534i	−0.202208	−	0.622332i	0.797609	−	0.603175i	$-0.206098\pi$
$824$	−0.180796			−0.00629833
$825$	0.933405	−	12.1691i	0.0324970	−	0.423672i
$826$	−9.15698			−0.318612
$827$	−0.0920121	−	0.283184i	−0.00319957	−	0.00984728i	0.949444	−	0.313936i	$-0.101648\pi$
$827$	−0.0920121	−	0.283184i	−0.00319957	−	0.00984728i	−0.952644	+	0.304089i	$0.901648\pi$
$828$	0.574481	+	0.417385i	0.0199646	+	0.0145051i
$829$	9.47190	−	6.88174i	0.328973	−	0.239013i	−0.411022	−	0.911625i	$-0.634828\pi$
$829$	9.47190	−	6.88174i	0.328973	−	0.239013i	0.739995	+	0.672613i	$0.234828\pi$
$830$	−13.3910	+	41.2131i	−0.464807	+	1.43053i
$831$	1.92101	−	5.91225i	0.0666390	−	0.205094i
$832$	0.429529	−	0.312071i	0.0148912	−	0.0108191i
$833$	−5.93507	−	4.31208i	−0.205638	−	0.149405i
$834$	−5.39283	−	16.5974i	−0.186739	−	0.574722i
$835$	45.8207			1.58569
$836$	−16.5141	−	6.80198i	−0.571154	−	0.235251i
$837$	−5.04129			−0.174253
$838$	−7.27399	−	22.3870i	−0.251276	−	0.773347i
$839$	−37.9109	−	27.5438i	−1.30883	−	0.950919i	−0.308828	−	0.951118i	$-0.599937\pi$
$839$	−37.9109	−	27.5438i	−1.30883	−	0.950919i	−1.00000		0.000198649i	$0.999937\pi$
$840$	−2.38350	+	1.73171i	−0.0822385	+	0.0597498i
$841$	−8.95870	+	27.5720i	−0.308921	+	0.950760i
$842$	−2.61298	+	8.04193i	−0.0900493	+	0.277143i
$843$	24.9106	−	18.0986i	0.857967	−	0.623350i
$844$	9.99466	+	7.26155i	0.344030	+	0.249953i
$845$	−11.5788	−	35.6358i	−0.398322	−	1.22591i
$846$	−13.2235			−0.454634
$847$	−10.8713	−	1.67760i	−0.373543	−	0.0576430i
$848$	−3.96979			−0.136323
$849$	−4.57872	−	14.0918i	−0.157141	−	0.483631i
$850$	−21.8404	−	15.8680i	−0.749119	−	0.544267i
$851$	−1.31550	+	0.955770i	−0.0450949	+	0.0327634i
$852$	2.74337	−	8.44322i	0.0939863	−	0.289260i
$853$	−10.6555	+	32.7944i	−0.364839	+	1.12286i	0.585243	+	0.810858i	$0.300999\pi$
$853$	−10.6555	+	32.7944i	−0.364839	+	1.12286i	−0.950082	+	0.312000i	$0.899001\pi$
$854$	6.21163	−	4.51301i	0.212558	−	0.154432i
$855$	−12.8352	−	9.32532i	−0.438955	−	0.318919i
$856$	4.66407	+	14.3545i	0.159414	+	0.490627i
$857$	25.3446			0.865755			0.432878	−	0.901453i	$-0.357498\pi$
$857$	25.3446			0.865755			0.432878	+	0.901453i	$0.357498\pi$
$858$	1.62818	+	0.670629i	0.0555852	+	0.0228949i
$859$	2.18125			0.0744234			0.0372117	−	0.999307i	$-0.488152\pi$
$859$	2.18125			0.0744234			0.0372117	+	0.999307i	$0.488152\pi$
$860$	−0.157126	−	0.483585i	−0.00535796	−	0.0164901i
$861$	1.88999	+	1.37315i	0.0644105	+	0.0467970i
$862$	−25.8188	+	18.7584i	−0.879391	+	0.638915i
$863$	−10.6820	+	32.8758i	−0.363620	+	1.11911i	0.587221	+	0.809427i	$0.300222\pi$
$863$	−10.6820	+	32.8758i	−0.363620	+	1.11911i	−0.950841	+	0.309680i	$0.899778\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−53.4065	+	38.8021i	−1.81587	+	1.31931i
$866$	−32.6167	−	23.6974i	−1.10836	−	0.805271i
$867$	11.3777	+	35.0170i	0.386408	+	1.18924i
$868$	−5.04129			−0.171113
$869$	2.60889	−	34.0128i	0.0885006	−	1.15381i
$870$	−0.280257			−0.00950161
$871$	2.12038	+	6.52585i	0.0718463	+	0.221120i
$872$	−5.32966	−	3.87223i	−0.180485	−	0.131130i
$873$	0.734536	−	0.533672i	0.0248603	−	0.0180621i
$874$	−1.18165	+	3.63674i	−0.0399698	+	0.123015i
$875$	−1.20185	+	3.69891i	−0.0406299	+	0.125046i
$876$	−5.25919	+	3.82103i	−0.177692	+	0.129101i
$877$	23.6161	+	17.1581i	0.797460	+	0.579389i	0.910168	−	0.414239i	$-0.135952\pi$
$877$	23.6161	+	17.1581i	0.797460	+	0.579389i	−0.112708	+	0.993628i	$0.535952\pi$
$878$	9.35459	+	28.7905i	0.315702	+	0.971631i
$879$	−12.4702			−0.420611
$880$	5.12204	+	8.32126i	0.172664	+	0.280510i
$881$	34.0184			1.14611			0.573054	−	0.819518i	$-0.305759\pi$
$881$	34.0184			1.14611			0.573054	+	0.819518i	$0.305759\pi$
$882$	0.309017	+	0.951057i	0.0104051	+	0.0320237i
$883$	28.3721	+	20.6135i	0.954797	+	0.693701i	0.951937	−	0.306295i	$-0.0990894\pi$
$883$	28.3721	+	20.6135i	0.954797	+	0.693701i	0.00286069	+	0.999996i	$0.499089\pi$
$884$	3.15109	−	2.28940i	0.105983	−	0.0770009i
$885$	−8.33665	+	25.6576i	−0.280234	+	0.862470i
$886$	0.974697	−	2.99981i	0.0327456	−	0.100781i
$887$	7.46505	−	5.42368i	0.250652	−	0.182109i	−0.455364	−	0.890305i	$-0.650491\pi$
$887$	7.46505	−	5.42368i	0.250652	−	0.182109i	0.706016	+	0.708196i	$0.250491\pi$
$888$	1.85257	+	1.34597i	0.0621682	+	0.0451678i
$889$	1.05640	+	3.25125i	0.0354304	+	0.109043i
$890$	25.3944			0.851222
$891$	3.22344	−	0.780656i	0.107989	−	0.0261530i
$892$	13.2861			0.444852
$893$	−22.0048	−	67.7238i	−0.736363	−	2.26629i
$894$	8.17421	+	5.93891i	0.273387	+	0.198627i
$895$	43.7487	−	31.7853i	1.46236	−	1.06246i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	0.116502	−	0.358558i	0.00388990	−	0.0119719i
$898$	−15.7377	+	11.4341i	−0.525175	+	0.381562i
$899$	−0.387971	−	0.281878i	−0.0129396	−	0.00940114i
$900$	1.13715	+	3.49978i	0.0379049	+	0.116659i
$901$	−29.1230			−0.970227
$902$	5.02030	−	5.90171i	0.167158	−	0.196506i
$903$	−0.172587			−0.00574335
$904$	−4.16983	−	12.8334i	−0.138687	−	0.426834i
$905$	7.94229	+	5.77041i	0.264011	+	0.191815i
$906$	3.05558	−	2.22001i	0.101515	−	0.0737549i
$907$	−8.25897	+	25.4185i	−0.274235	+	0.844007i	0.715186	+	0.698934i	$0.246342\pi$
$907$	−8.25897	+	25.4185i	−0.274235	+	0.844007i	−0.989421	+	0.145073i	$0.953658\pi$
$908$	−4.65576	+	14.3290i	−0.154507	+	0.475523i
$909$	2.77348	−	2.01505i	0.0919906	−	0.0668351i
$910$	1.26546	+	0.919413i	0.0419497	+	0.0304782i
$911$	17.2785	+	53.1778i	0.572463	+	1.76186i	0.644659	+	0.764470i	$0.276999\pi$
$911$	17.2785	+	53.1778i	0.572463	+	1.76186i	−0.0721959	+	0.997390i	$0.523001\pi$
$912$	5.38503			0.178316
$913$	31.6083	−	37.1578i	1.04608	−	1.22974i
$914$	−37.8130			−1.25074
$915$	−6.99016	−	21.5135i	−0.231088	−	0.711215i
$916$	6.78078	+	4.92653i	0.224043	+	0.162777i
$917$	−3.90167	+	2.83473i	−0.128844	+	0.0936109i
$918$	2.26700	−	6.97709i	0.0748220	−	0.230278i
$919$	0.116888	−	0.359744i	0.00385578	−	0.0118669i	−0.949110	−	0.314944i	$-0.898014\pi$
$919$	0.116888	−	0.359744i	0.00385578	−	0.0118669i	0.952966	+	0.303078i	$0.0980141\pi$
$920$	1.69251	−	1.22968i	0.0558006	−	0.0405415i
$921$	20.3092	+	14.7555i	0.669212	+	0.486211i
$922$	4.75429	+	14.6322i	0.156574	+	0.481885i
$923$	−4.71343			−0.155144
$924$	3.22344	−	0.780656i	0.106043	−	0.0256817i
$925$	−8.42659			−0.277064
$926$	4.25017	+	13.0807i	0.139669	+	0.429857i
$927$	0.146267	+	0.106269i	0.00480404	+	0.00349034i
$928$	0.0769587	−	0.0559138i	0.00252629	−	0.00183546i
$929$	14.6478	−	45.0813i	0.480578	−	1.47907i	−0.357706	−	0.933834i	$-0.616441\pi$
$929$	14.6478	−	45.0813i	0.480578	−	1.47907i	0.838284	−	0.545234i	$-0.183559\pi$
$930$	−4.58967	+	14.1255i	−0.150501	+	0.463195i
$931$	−4.35658	+	3.16524i	−0.142781	+	0.103737i
$932$	4.59797	+	3.34062i	0.150612	+	0.109426i
$933$	6.53619	+	20.1163i	0.213985	+	0.658579i
$934$	−19.0316			−0.622734
$935$	37.5761	+	61.0460i	1.22887	+	1.99642i
$936$	−0.530927			−0.0173539
$937$	−8.65356	−	26.6329i	−0.282699	−	0.870059i	−0.987079	−	0.160236i	$-0.948775\pi$
$937$	−8.65356	−	26.6329i	−0.282699	−	0.870059i	0.704379	−	0.709824i	$-0.251225\pi$
$938$	10.4557	+	7.59652i	0.341391	+	0.248035i
$939$	−1.75898	+	1.27797i	−0.0574020	+	0.0417050i
$940$	−12.0389	+	37.0519i	−0.392665	+	1.20850i
$941$	−3.04399	+	9.36845i	−0.0992313	+	0.305403i	−0.988333	−	0.152307i	$-0.951330\pi$
$941$	−3.04399	+	9.36845i	−0.0992313	+	0.305403i	0.889102	+	0.457709i	$0.151330\pi$
$942$	−17.7701	+	12.9107i	−0.578980	+	0.420653i
$943$	−1.34207	−	0.975073i	−0.0437039	−	0.0317527i
$944$	−2.82966	−	8.70881i	−0.0920977	−	0.283447i
$945$	2.94617			0.0958388
$946$	−0.0437769	+	0.570731i	−0.00142331	+	0.0185561i
$947$	6.83921			0.222244			0.111122	−	0.993807i	$-0.464555\pi$
$947$	6.83921			0.222244			0.111122	+	0.993807i	$0.464555\pi$
$948$	3.17836	+	9.78198i	0.103228	+	0.317704i
$949$	2.79225	+	2.02869i	0.0906402	+	0.0658540i
$950$	−16.0317	+	11.6477i	−0.520138	+	0.377902i
$951$	0.784806	−	2.41538i	0.0254491	−	0.0783242i
$952$	2.26700	−	6.97709i	0.0734737	−	0.226129i
$953$	−48.9900	+	35.5933i	−1.58694	+	1.15298i	−0.678795	+	0.734328i	$0.737498\pi$
$953$	−48.9900	+	35.5933i	−1.58694	+	1.15298i	−0.908146	+	0.418653i	$0.862502\pi$
$954$	3.21163	+	2.33338i	0.103980	+	0.0755461i
$955$	−7.66227	−	23.5821i	−0.247945	−	0.763097i
$956$	24.7635			0.800908
$957$	0.291721	+	0.120156i	0.00943001	+	0.00388411i
$958$	35.7596			1.15534
$959$	5.33390	+	16.4161i	0.172241	+	0.530102i
$960$	−2.38350	−	1.73171i	−0.0769271	−	0.0558908i
$961$	4.51867	−	3.28301i	0.145764	−	0.105903i
$962$	0.375694	−	1.15627i	0.0121129	−	0.0372796i
$963$	4.66407	−	14.3545i	0.150297	−	0.462568i
$964$	−7.21163	+	5.23955i	−0.232271	+	0.168755i
$965$	16.4605	+	11.9593i	0.529883	+	0.384983i
$966$	−0.219432	−	0.675342i	−0.00706011	−	0.0217288i
$967$	−34.1168			−1.09712			−0.548560	−	0.836111i	$-0.684824\pi$
$967$	−34.1168			−1.09712			−0.548560	+	0.836111i	$0.684824\pi$
$968$	−1.76393	−	10.8576i	−0.0566949	−	0.348978i
$969$	39.5054			1.26910
$970$	−0.826599	−	2.54401i	−0.0265405	−	0.0816833i
$971$	−7.63458	−	5.54684i	−0.245005	−	0.178007i	0.458505	−	0.888692i	$-0.348385\pi$
$971$	−7.63458	−	5.54684i	−0.245005	−	0.178007i	−0.703510	+	0.710685i	$0.748385\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	−5.39283	+	16.5974i	−0.172886	+	0.532089i
$974$	−9.72060	+	29.9169i	−0.311468	+	0.958600i
$975$	1.58062	−	1.14839i	0.0506203	−	0.0367778i
$976$	6.21163	+	4.51301i	0.198829	+	0.144458i
$977$	16.9493	+	52.1646i	0.542256	+	1.66889i	0.727426	+	0.686187i	$0.240717\pi$
$977$	16.9493	+	52.1646i	0.542256	+	1.66889i	−0.185169	+	0.982707i	$0.559283\pi$
$978$	19.1917			0.613683
$979$	−26.4331	−	10.8875i	−0.844807	−	0.347966i
$980$	2.94617			0.0941118
$981$	2.03575	+	6.26539i	0.0649965	+	0.200039i
$982$	18.8669	+	13.7076i	0.602068	+	0.437428i
$983$	−21.1135	+	15.3399i	−0.673417	+	0.489266i	−0.871167	−	0.490986i	$-0.836636\pi$
$983$	−21.1135	+	15.3399i	−0.673417	+	0.489266i	0.197750	+	0.980252i	$0.436636\pi$
$984$	−0.721910	+	2.22181i	−0.0230137	+	0.0708287i
$985$	9.63110	−	29.6415i	0.306872	−	0.944456i
$986$	0.564580	−	0.410192i	0.0179799	−	0.0130632i
$987$	10.6981	+	7.77259i	0.340523	+	0.247404i
$988$	−0.883498	−	2.71913i	−0.0281078	−	0.0865069i
$989$	0.122554			0.00389698
$990$	0.747296	−	9.74271i	0.0237506	−	0.309644i
$991$	−16.8285			−0.534574			−0.267287	−	0.963617i	$-0.586127\pi$
$991$	−16.8285			−0.534574			−0.267287	+	0.963617i	$0.586127\pi$
$992$	−1.55784	−	4.79455i	−0.0494616	−	0.152227i
$993$	11.0421	+	8.02256i	0.350411	+	0.254588i
$994$	−7.18223	+	5.21820i	−0.227807	+	0.165511i
$995$	15.2277	−	46.8661i	0.482751	−	1.48576i
$996$	−4.54522	+	13.9887i	−0.144021	+	0.443250i
$997$	−11.1209	+	8.07979i	−0.352202	+	0.255890i	−0.749792	−	0.661673i	$-0.769847\pi$
$997$	−11.1209	+	8.07979i	−0.352202	+	0.255890i	0.397590	+	0.917563i	$0.369847\pi$
$998$	−1.85774	−	1.34973i	−0.0588058	−	0.0427249i
$999$	−0.707619	−	2.17783i	−0.0223881	−	0.0689034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.e.379.2	yes	8
11.3	even	5		5082.2.a.cf.1.4		4
11.8	odd	10		5082.2.a.ca.1.4		4
11.9	even	5	inner	462.2.j.e.295.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.e.295.2	✓	8	11.9	even	5	inner
462.2.j.e.379.2	yes	8	1.1	even	1	trivial
5082.2.a.ca.1.4		4	11.8	odd	10
5082.2.a.cf.1.4		4	11.3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.910415 - 2.80197i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.910415 - 2.80197i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +2.94617 q^{10} +(-3.06668 - 1.26313i) q^{11} +1.00000 q^{12} +(-0.164066 - 0.504942i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-2.38350 + 1.73171i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.26700 - 6.97709i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-4.35658 - 3.16524i) q^{19} +(0.910415 + 2.80197i) q^{20} +1.00000 q^{21} +(0.253650 - 3.30691i) q^{22} -0.710097 q^{23} +(0.309017 + 0.951057i) q^{24} +(-2.97709 - 2.16298i) q^{25} +(0.429529 - 0.312071i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.309017 - 0.951057i) q^{28} +(0.0769587 - 0.0559138i) q^{29} +(-2.38350 - 1.73171i) q^{30} +(-1.55784 - 4.79455i) q^{31} +1.00000 q^{32} +(1.73855 + 2.82444i) q^{33} +7.33615 q^{34} +(0.910415 + 2.80197i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(1.85257 - 1.34597i) q^{37} +(1.66407 - 5.12147i) q^{38} +(-0.164066 + 0.504942i) q^{39} +(-2.38350 + 1.73171i) q^{40} +(1.88999 + 1.37315i) q^{41} +(0.309017 + 0.951057i) q^{42} -0.172587 q^{43} +(3.22344 - 0.780656i) q^{44} +2.94617 q^{45} +(-0.219432 - 0.675342i) q^{46} +(10.6981 + 7.77259i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(1.13715 - 3.49978i) q^{50} +(-5.93507 + 4.31208i) q^{51} +(0.429529 + 0.312071i) q^{52} +(-1.22673 - 3.77550i) q^{53} +1.00000 q^{54} +(-6.33119 + 7.44277i) q^{55} +1.00000 q^{56} +(1.66407 + 5.12147i) q^{57} +(0.0769587 + 0.0559138i) q^{58} +(7.40815 - 5.38234i) q^{59} +(0.910415 - 2.80197i) q^{60} +(-2.37263 + 7.30221i) q^{61} +(4.07849 - 2.96320i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(0.309017 + 0.951057i) q^{64} -1.56420 q^{65} +(-2.14896 + 2.52626i) q^{66} -12.9240 q^{67} +(2.26700 + 6.97709i) q^{68} +(0.574481 + 0.417385i) q^{69} +(-2.38350 + 1.73171i) q^{70} +(2.74337 - 8.44322i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-5.25919 + 3.82103i) q^{73} +(1.85257 + 1.34597i) q^{74} +(1.13715 + 3.49978i) q^{75} +5.38503 q^{76} +(3.22344 - 0.780656i) q^{77} -0.530927 q^{78} +(3.17836 + 9.78198i) q^{79} +(-2.38350 - 1.73171i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.721910 + 2.22181i) q^{82} +(-4.54522 + 13.9887i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(-17.4857 - 12.7041i) q^{85} +(-0.0533324 - 0.164140i) q^{86} -0.0951262 q^{87} +(1.73855 + 2.82444i) q^{88} +8.61947 q^{89} +(0.910415 + 2.80197i) q^{90} +(0.429529 + 0.312071i) q^{91} +(0.574481 - 0.417385i) q^{92} +(-1.55784 + 4.79455i) q^{93} +(-4.08629 + 12.5763i) q^{94} +(-12.8352 + 9.32532i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-0.280568 - 0.863499i) q^{97} +1.00000 q^{98} +(0.253650 - 3.30691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 8 * q^12 + 4 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^23 - 2 * q^24 + 4 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 - 6 * q^30 - 14 * q^31 + 8 * q^32 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 + 20 * q^43 + 4 * q^45 + 6 * q^46 + 28 * q^47 - 2 * q^48 - 2 * q^49 - 6 * q^50 + 2 * q^51 - 6 * q^52 + 2 * q^53 + 8 * q^54 + 4 * q^55 + 8 * q^56 + 8 * q^57 - 4 * q^58 + 4 * q^60 - 34 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 16 * q^65 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 6 * q^70 - 2 * q^72 + 10 * q^74 - 6 * q^75 + 8 * q^76 + 4 * q^78 + 22 * q^79 - 6 * q^80 - 2 * q^81 - 2 * q^82 - 30 * q^83 - 2 * q^84 - 28 * q^85 + 36 * q^87 - 4 * q^89 + 4 * q^90 - 6 * q^91 - 4 * q^92 - 14 * q^93 - 22 * q^94 - 30 * q^95 - 2 * q^96 - 10 * q^97 + 8 * q^98

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