LMFDB - Embedded newform 218.2.c.c.45.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [218,2,Mod(45,218)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(218, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("218.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 218 = 2 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	218.c (of order $3$, degree $2$, 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:	$1.74073876406$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 14x^{8} + 6x^{7} + 95x^{6} + 2x^{5} + 231x^{4} + 53x^{3} + 389x^{2} - 76x + 16 $ x^10 - 2x^9 + 14x^8 + 6x^7 + 95x^6 + 2x^5 + 231x^4 + 53x^3 + 389x^2 - 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.4
Root			$1.90833 + 3.30532i$ of defining polynomial
Character	$\chi$	$=$	218.45
Dual form			218.2.c.c.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.09691 - 1.89990i) q^{3} +1.00000 q^{4} +(0.908328 - 1.57327i) q^{5} +(1.09691 - 1.89990i) q^{6} +(-2.27819 + 3.94595i) q^{7} +1.00000 q^{8} +(-0.906417 - 1.56996i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.09691 - 1.89990i) q^{3} +1.00000 q^{4} +(0.908328 - 1.57327i) q^{5} +(1.09691 - 1.89990i) q^{6} +(-2.27819 + 3.94595i) q^{7} +1.00000 q^{8} +(-0.906417 - 1.56996i) q^{9} +(0.908328 - 1.57327i) q^{10} +(-0.369866 - 0.640628i) q^{11} +(1.09691 - 1.89990i) q^{12} +(0.0935834 - 0.162091i) q^{13} +(-2.27819 + 3.94595i) q^{14} +(-1.99271 - 3.45147i) q^{15} +1.00000 q^{16} -4.07692 q^{17} +(-0.906417 - 1.56996i) q^{18} -3.64790 q^{19} +(0.908328 - 1.57327i) q^{20} +(4.99794 + 8.65669i) q^{21} +(-0.369866 - 0.640628i) q^{22} -0.810006 q^{23} +(1.09691 - 1.89990i) q^{24} +(0.849881 + 1.47204i) q^{25} +(0.0935834 - 0.162091i) q^{26} +2.60443 q^{27} +(-2.27819 + 3.94595i) q^{28} +(4.03117 - 6.98219i) q^{29} +(-1.99271 - 3.45147i) q^{30} +(4.96281 + 8.59583i) q^{31} +1.00000 q^{32} -1.62284 q^{33} -4.07692 q^{34} +(4.13870 + 7.16843i) q^{35} +(-0.906417 - 1.56996i) q^{36} +(0.869866 + 1.50665i) q^{37} -3.64790 q^{38} +(-0.205305 - 0.355598i) q^{39} +(0.908328 - 1.57327i) q^{40} -8.73179 q^{41} +(4.99794 + 8.65669i) q^{42} -4.45791 q^{43} +(-0.369866 - 0.640628i) q^{44} -3.29329 q^{45} -0.810006 q^{46} +(1.09691 - 1.89990i) q^{48} +(-6.88034 - 11.9171i) q^{49} +(0.849881 + 1.47204i) q^{50} +(-4.47201 + 7.74575i) q^{51} +(0.0935834 - 0.162091i) q^{52} +(5.34520 - 9.25816i) q^{53} +2.60443 q^{54} -1.34384 q^{55} +(-2.27819 + 3.94595i) q^{56} +(-4.00141 + 6.93065i) q^{57} +(4.03117 - 6.98219i) q^{58} +(7.10009 + 12.2977i) q^{59} +(-1.99271 - 3.45147i) q^{60} +(-0.823951 + 1.42712i) q^{61} +(4.96281 + 8.59583i) q^{62} +8.25997 q^{63} +1.00000 q^{64} +(-0.170009 - 0.294464i) q^{65} -1.62284 q^{66} +(-6.69049 - 11.5883i) q^{67} -4.07692 q^{68} +(-0.888502 + 1.53893i) q^{69} +(4.13870 + 7.16843i) q^{70} +0.883106 q^{71} +(-0.906417 - 1.56996i) q^{72} +(-3.68064 - 6.37506i) q^{73} +(0.869866 + 1.50665i) q^{74} +3.72897 q^{75} -3.64790 q^{76} +3.37051 q^{77} +(-0.205305 - 0.355598i) q^{78} +(-6.92767 - 11.9991i) q^{79} +(0.908328 - 1.57327i) q^{80} +(5.57607 - 9.65803i) q^{81} -8.73179 q^{82} +(-2.02926 + 3.51477i) q^{83} +(4.99794 + 8.65669i) q^{84} +(-3.70318 + 6.41410i) q^{85} -4.45791 q^{86} +(-8.84364 - 15.3176i) q^{87} +(-0.369866 - 0.640628i) q^{88} +(-1.65727 + 2.87047i) q^{89} -3.29329 q^{90} +(0.426402 + 0.738550i) q^{91} -0.810006 q^{92} +21.7750 q^{93} +(-3.31349 + 5.73913i) q^{95} +(1.09691 - 1.89990i) q^{96} +(-1.10547 + 1.91473i) q^{97} +(-6.88034 - 11.9171i) q^{98} +(-0.670506 + 1.16135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9} - 8 q^{10} + q^{11} + q^{12} - q^{14} - q^{15} + 10 q^{16} - 16 q^{17} - 10 q^{18} - 6 q^{19} - 8 q^{20} + 4 q^{21} + q^{22} + 8 q^{23} + q^{24} - 11 q^{25} + 10 q^{27} - q^{28} + 9 q^{29} - q^{30} + 7 q^{31} + 10 q^{32} - 2 q^{33} - 16 q^{34} + 10 q^{35} - 10 q^{36} + 4 q^{37} - 6 q^{38} - 4 q^{39} - 8 q^{40} - 22 q^{41} + 4 q^{42} + 2 q^{43} + q^{44} + 38 q^{45} + 8 q^{46} + q^{48} - 10 q^{49} - 11 q^{50} - 3 q^{51} - 2 q^{53} + 10 q^{54} + 20 q^{55} - q^{56} - 49 q^{57} + 9 q^{58} - 12 q^{59} - q^{60} + 7 q^{61} + 7 q^{62} - 36 q^{63} + 10 q^{64} - 3 q^{65} - 2 q^{66} - 56 q^{67} - 16 q^{68} + 19 q^{69} + 10 q^{70} + 4 q^{71} - 10 q^{72} + 12 q^{73} + 4 q^{74} - 46 q^{75} - 6 q^{76} + 66 q^{77} - 4 q^{78} - 30 q^{79} - 8 q^{80} - 41 q^{81} - 22 q^{82} - 7 q^{83} + 4 q^{84} - 22 q^{85} + 2 q^{86} + 40 q^{87} + q^{88} + 9 q^{89} + 38 q^{90} + 20 q^{91} + 8 q^{92} + 10 q^{93} - 12 q^{95} + q^{96} + 35 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9 - 8 * q^10 + q^11 + q^12 - q^14 - q^15 + 10 * q^16 - 16 * q^17 - 10 * q^18 - 6 * q^19 - 8 * q^20 + 4 * q^21 + q^22 + 8 * q^23 + q^24 - 11 * q^25 + 10 * q^27 - q^28 + 9 * q^29 - q^30 + 7 * q^31 + 10 * q^32 - 2 * q^33 - 16 * q^34 + 10 * q^35 - 10 * q^36 + 4 * q^37 - 6 * q^38 - 4 * q^39 - 8 * q^40 - 22 * q^41 + 4 * q^42 + 2 * q^43 + q^44 + 38 * q^45 + 8 * q^46 + q^48 - 10 * q^49 - 11 * q^50 - 3 * q^51 - 2 * q^53 + 10 * q^54 + 20 * q^55 - q^56 - 49 * q^57 + 9 * q^58 - 12 * q^59 - q^60 + 7 * q^61 + 7 * q^62 - 36 * q^63 + 10 * q^64 - 3 * q^65 - 2 * q^66 - 56 * q^67 - 16 * q^68 + 19 * q^69 + 10 * q^70 + 4 * q^71 - 10 * q^72 + 12 * q^73 + 4 * q^74 - 46 * q^75 - 6 * q^76 + 66 * q^77 - 4 * q^78 - 30 * q^79 - 8 * q^80 - 41 * q^81 - 22 * q^82 - 7 * q^83 + 4 * q^84 - 22 * q^85 + 2 * q^86 + 40 * q^87 + q^88 + 9 * q^89 + 38 * q^90 + 20 * q^91 + 8 * q^92 + 10 * q^93 - 12 * q^95 + q^96 + 35 * q^97 - 10 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/218\mathbb{Z}\right)^\times$.

$n$	$115$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.09691	−	1.89990i	0.633300	−	1.09691i	−0.353572	−	0.935407i	$-0.615033\pi$
$3$	1.09691	−	1.89990i	0.633300	−	1.09691i	0.986873	−	0.161501i	$-0.0516336\pi$
$4$	1.00000			0.500000
$5$	0.908328	−	1.57327i	0.406217	−	0.703588i	−0.588246	−	0.808682i	$-0.700181\pi$
$5$	0.908328	−	1.57327i	0.406217	−	0.703588i	0.994462	+	0.105095i	$0.0335145\pi$
$6$	1.09691	−	1.89990i	0.447811	−	0.775631i
$7$	−2.27819	+	3.94595i	−0.861077	+	1.49143i	0.00981431	+	0.999952i	$0.496876\pi$
$7$	−2.27819	+	3.94595i	−0.861077	+	1.49143i	−0.870891	+	0.491476i	$0.836457\pi$
$8$	1.00000			0.353553
$9$	−0.906417	−	1.56996i	−0.302139	−	0.523320i
$10$	0.908328	−	1.57327i	0.287239	−	0.497512i
$11$	−0.369866	−	0.640628i	−0.111519	−	0.193156i	0.804864	−	0.593459i	$-0.202238\pi$
$11$	−0.369866	−	0.640628i	−0.111519	−	0.193156i	−0.916383	+	0.400303i	$0.868905\pi$
$12$	1.09691	−	1.89990i	0.316650	−	0.548454i
$13$	0.0935834	−	0.162091i	0.0259554	−	0.0449560i	−0.852756	−	0.522310i	$-0.825071\pi$
$13$	0.0935834	−	0.162091i	0.0259554	−	0.0449560i	0.878711	+	0.477354i	$0.158404\pi$
$14$	−2.27819	+	3.94595i	−0.608873	+	1.05460i
$15$	−1.99271	−	3.45147i	−0.514514	−	0.891165i
$16$	1.00000			0.250000
$17$	−4.07692			−0.988799			−0.494400	−	0.869235i	$-0.664612\pi$
$17$	−4.07692			−0.988799			−0.494400	+	0.869235i	$0.664612\pi$
$18$	−0.906417	−	1.56996i	−0.213644	−	0.370043i
$19$	−3.64790			−0.836886			−0.418443	−	0.908243i	$-0.637424\pi$
$19$	−3.64790			−0.836886			−0.418443	+	0.908243i	$0.637424\pi$
$20$	0.908328	−	1.57327i	0.203108	−	0.351794i
$21$	4.99794	+	8.65669i	1.09064	+	1.88904i
$22$	−0.369866	−	0.640628i	−0.0788558	−	0.136582i
$23$	−0.810006			−0.168898			−0.0844489	−	0.996428i	$-0.526913\pi$
$23$	−0.810006			−0.168898			−0.0844489	+	0.996428i	$0.526913\pi$
$24$	1.09691	−	1.89990i	0.223906	−	0.387816i
$25$	0.849881	+	1.47204i	0.169976	+	0.294407i
$26$	0.0935834	−	0.162091i	0.0183532	−	0.0317887i
$27$	2.60443			0.501222
$28$	−2.27819	+	3.94595i	−0.430538	+	0.745714i
$29$	4.03117	−	6.98219i	0.748569	−	1.29656i	−0.199940	−	0.979808i	$-0.564075\pi$
$29$	4.03117	−	6.98219i	0.748569	−	1.29656i	0.948509	−	0.316751i	$-0.102592\pi$
$30$	−1.99271	−	3.45147i	−0.363817	−	0.630149i
$31$	4.96281	+	8.59583i	0.891346	+	1.54386i	0.838263	+	0.545267i	$0.183572\pi$
$31$	4.96281	+	8.59583i	0.891346	+	1.54386i	0.0530836	+	0.998590i	$0.483095\pi$
$32$	1.00000			0.176777
$33$	−1.62284			−0.282500
$34$	−4.07692			−0.699187
$35$	4.13870	+	7.16843i	0.699567	+	1.21169i
$36$	−0.906417	−	1.56996i	−0.151069	−	0.261660i
$37$	0.869866	+	1.50665i	0.143005	+	0.247692i	0.928627	−	0.371015i	$-0.120990\pi$
$37$	0.869866	+	1.50665i	0.143005	+	0.247692i	−0.785622	+	0.618707i	$0.787657\pi$
$38$	−3.64790			−0.591768
$39$	−0.205305	−	0.355598i	−0.0328751	−	0.0569413i
$40$	0.908328	−	1.57327i	0.143619	−	0.248756i
$41$	−8.73179			−1.36368			−0.681839	−	0.731503i	$-0.738819\pi$
$41$	−8.73179			−1.36368			−0.681839	+	0.731503i	$0.738819\pi$
$42$	4.99794	+	8.65669i	0.771199	+	1.33576i
$43$	−4.45791			−0.679824			−0.339912	−	0.940457i	$-0.610397\pi$
$43$	−4.45791			−0.679824			−0.339912	+	0.940457i	$0.610397\pi$
$44$	−0.369866	−	0.640628i	−0.0557595	−	0.0965782i
$45$	−3.29329			−0.490935
$46$	−0.810006			−0.119429
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	1.09691	−	1.89990i	0.158325	−	0.274227i
$49$	−6.88034	−	11.9171i	−0.982906	−	1.70244i
$50$	0.849881	+	1.47204i	0.120191	+	0.208177i
$51$	−4.47201	+	7.74575i	−0.626207	+	1.08462i
$52$	0.0935834	−	0.162091i	0.0129777	−	0.0224780i
$53$	5.34520	−	9.25816i	0.734220	−	1.27171i	−0.220845	−	0.975309i	$-0.570881\pi$
$53$	5.34520	−	9.25816i	0.734220	−	1.27171i	0.955065	−	0.296398i	$-0.0957853\pi$
$54$	2.60443			0.354418
$55$	−1.34384			−0.181203
$56$	−2.27819	+	3.94595i	−0.304437	+	0.527300i
$57$	−4.00141	+	6.93065i	−0.530000	+	0.917987i
$58$	4.03117	−	6.98219i	0.529318	−	0.916806i
$59$	7.10009	+	12.2977i	0.924353	+	1.60103i	0.792599	+	0.609743i	$0.208727\pi$
$59$	7.10009	+	12.2977i	0.924353	+	1.60103i	0.131753	+	0.991283i	$0.457939\pi$
$60$	−1.99271	−	3.45147i	−0.257257	−	0.445582i
$61$	−0.823951	+	1.42712i	−0.105496	+	0.182725i	−0.913941	−	0.405848i	$-0.866976\pi$
$61$	−0.823951	+	1.42712i	−0.105496	+	0.182725i	0.808445	+	0.588572i	$0.200310\pi$
$62$	4.96281	+	8.59583i	0.630277	+	1.09167i
$63$	8.25997			1.04066
$64$	1.00000			0.125000
$65$	−0.170009	−	0.294464i	−0.0210870	−	0.0365237i
$66$	−1.62284			−0.199758
$67$	−6.69049	−	11.5883i	−0.817374	−	1.41573i	−0.907611	−	0.419812i	$-0.862096\pi$
$67$	−6.69049	−	11.5883i	−0.817374	−	1.41573i	0.0902372	−	0.995920i	$-0.471237\pi$
$68$	−4.07692			−0.494400
$69$	−0.888502	+	1.53893i	−0.106963	+	0.185265i
$70$	4.13870	+	7.16843i	0.494669	+	0.856791i
$71$	0.883106			0.104805			0.0524027	−	0.998626i	$-0.483312\pi$
$71$	0.883106			0.104805			0.0524027	+	0.998626i	$0.483312\pi$
$72$	−0.906417	−	1.56996i	−0.106822	−	0.185022i
$73$	−3.68064	−	6.37506i	−0.430786	−	0.746144i	0.566155	−	0.824299i	$-0.308430\pi$
$73$	−3.68064	−	6.37506i	−0.430786	−	0.746144i	−0.996941	+	0.0781549i	$0.975097\pi$
$74$	0.869866	+	1.50665i	0.101120	+	0.175145i
$75$	3.72897			0.430584
$76$	−3.64790			−0.418443
$77$	3.37051			0.384105
$78$	−0.205305	−	0.355598i	−0.0232462	−	0.0402636i
$79$	−6.92767	−	11.9991i	−0.779424	−	1.35000i	−0.932274	−	0.361752i	$-0.882179\pi$
$79$	−6.92767	−	11.9991i	−0.779424	−	1.35000i	0.152851	−	0.988249i	$-0.451155\pi$
$80$	0.908328	−	1.57327i	0.101554	−	0.175897i
$81$	5.57607	−	9.65803i	0.619563	−	1.07311i
$82$	−8.73179			−0.964265
$83$	−2.02926	+	3.51477i	−0.222740	+	0.385797i	−0.955639	−	0.294541i	$-0.904833\pi$
$83$	−2.02926	+	3.51477i	−0.222740	+	0.385797i	0.732899	+	0.680337i	$0.238167\pi$
$84$	4.99794	+	8.65669i	0.545320	+	0.944522i
$85$	−3.70318	+	6.41410i	−0.401667	+	0.695707i
$86$	−4.45791			−0.480708
$87$	−8.84364	−	15.3176i	−0.948138	−	1.64222i
$88$	−0.369866	−	0.640628i	−0.0394279	−	0.0682911i
$89$	−1.65727	+	2.87047i	−0.175670	+	0.304269i	−0.940393	−	0.340090i	$-0.889542\pi$
$89$	−1.65727	+	2.87047i	−0.175670	+	0.304269i	0.764723	+	0.644359i	$0.222876\pi$
$90$	−3.29329			−0.347144
$91$	0.426402	+	0.738550i	0.0446991	+	0.0774211i
$92$	−0.810006			−0.0844489
$93$	21.7750			2.25796
$94$		0			0
$95$	−3.31349	+	5.73913i	−0.339957	+	0.588823i
$96$	1.09691	−	1.89990i	0.111953	−	0.193908i
$97$	−1.10547	+	1.91473i	−0.112243	+	0.194411i	−0.916674	−	0.399635i	$-0.869137\pi$
$97$	−1.10547	+	1.91473i	−0.112243	+	0.194411i	0.804431	+	0.594046i	$0.202470\pi$
$98$	−6.88034	−	11.9171i	−0.695019	−	1.20381i
$99$	−0.670506	+	1.16135i	−0.0673884	+	0.116720i
$100$	0.849881	+	1.47204i	0.0849881	+	0.147204i
$101$	12.0690			1.20091			0.600454	−	0.799659i	$-0.294986\pi$
$101$	12.0690			1.20091			0.600454	+	0.799659i	$0.294986\pi$
$102$	−4.47201	+	7.74575i	−0.442795	+	0.766944i
$103$	−4.46472	+	7.73312i	−0.439922	+	0.761967i	−0.997683	−	0.0680348i	$-0.978327\pi$
$103$	−4.46472	+	7.73312i	−0.439922	+	0.761967i	0.557761	+	0.830001i	$0.311660\pi$
$104$	0.0935834	−	0.162091i	0.00917661	−	0.0158943i
$105$	18.1591			1.77214
$106$	5.34520	−	9.25816i	0.519172	−	0.899232i
$107$	3.02920			0.292844			0.146422	−	0.989222i	$-0.453224\pi$
$107$	3.02920			0.292844			0.146422	+	0.989222i	$0.453224\pi$
$108$	2.60443			0.250611
$109$	7.93466	−	6.78537i	0.760002	−	0.649920i
$109$	7.93466	−	6.78537i	0.760002	−	0.649920i
$110$	−1.34384			−0.128130
$111$	3.81666			0.362261
$112$	−2.27819	+	3.94595i	−0.215269	+	0.372857i
$113$	−7.84869			−0.738342			−0.369171	−	0.929361i	$-0.620358\pi$
$113$	−7.84869			−0.738342			−0.369171	+	0.929361i	$0.620358\pi$
$114$	−4.00141	+	6.93065i	−0.374767	+	0.649115i
$115$	−0.735751	+	1.27436i	−0.0686091	+	0.118834i
$116$	4.03117	−	6.98219i	0.374284	−	0.648280i
$117$	−0.339302			−0.0313685
$118$	7.10009	+	12.2977i	0.653616	+	1.13210i
$119$	9.28802	−	16.0873i	0.851432	−	1.47472i
$120$	−1.99271	−	3.45147i	−0.181908	−	0.315074i
$121$	5.22640	−	9.05239i	0.475127	−	0.822944i
$122$	−0.823951	+	1.42712i	−0.0745970	+	0.129206i
$123$	−9.57798	+	16.5895i	−0.863617	+	1.49583i
$124$	4.96281	+	8.59583i	0.445673	+	0.771928i
$125$	12.1712			1.08862
$126$	8.25997			0.735857
$127$	4.76899	+	8.26013i	0.423179	+	0.732968i	0.996248	−	0.0865390i	$-0.0275807\pi$
$127$	4.76899	+	8.26013i	0.423179	+	0.732968i	−0.573069	+	0.819507i	$0.694247\pi$
$128$	1.00000			0.0883883
$129$	−4.88992	+	8.46958i	−0.430533	+	0.745705i
$130$	−0.170009	−	0.294464i	−0.0149108	−	0.0258262i
$131$	−0.0784964	−	0.135960i	−0.00685827	−	0.0118789i	0.862576	−	0.505928i	$-0.168850\pi$
$131$	−0.0784964	−	0.135960i	−0.00685827	−	0.0118789i	−0.869434	+	0.494049i	$0.835516\pi$
$132$	−1.62284			−0.141250
$133$	8.31063	−	14.3944i	0.720623	−	1.24816i
$134$	−6.69049	−	11.5883i	−0.577970	−	1.00107i
$135$	2.36567	−	4.09747i	0.203605	−	0.352654i
$136$	−4.07692			−0.349593
$137$	4.43617	−	7.68367i	0.379008	−	0.656460i	−0.611911	−	0.790927i	$-0.709599\pi$
$137$	4.43617	−	7.68367i	0.379008	−	0.656460i	0.990918	+	0.134467i	$0.0429321\pi$
$138$	−0.888502	+	1.53893i	−0.0756343	+	0.131002i
$139$	−5.56892	−	9.64565i	−0.472350	−	0.818134i	0.527150	−	0.849772i	$-0.323261\pi$
$139$	−5.56892	−	9.64565i	−0.472350	−	0.818134i	−0.999499	+	0.0316389i	$0.989927\pi$
$140$	4.13870	+	7.16843i	0.349784	+	0.605843i
$141$		0			0
$142$	0.883106			0.0741086
$143$	−0.138453			−0.0115781
$144$	−0.906417	−	1.56996i	−0.0755347	−	0.130830i
$145$	−7.32324	−	12.6842i	−0.608162	−	1.05337i
$146$	−3.68064	−	6.37506i	−0.304612	−	0.527604i
$147$	−30.1884			−2.48990
$148$	0.869866	+	1.50665i	0.0715026	+	0.123846i
$149$	−2.92902	+	5.07321i	−0.239955	+	0.415614i	−0.960701	−	0.277585i	$-0.910466\pi$
$149$	−2.92902	+	5.07321i	−0.239955	+	0.415614i	0.720746	+	0.693199i	$0.243799\pi$
$150$	3.72897			0.304469
$151$	−4.46472	−	7.73312i	−0.363333	−	0.629312i	0.625174	−	0.780486i	$-0.285028\pi$
$151$	−4.46472	−	7.73312i	−0.363333	−	0.629312i	−0.988507	+	0.151174i	$0.951695\pi$
$152$	−3.64790			−0.295884
$153$	3.69539	+	6.40060i	0.298755	+	0.517458i
$154$	3.37051			0.271604
$155$	18.0314			1.44832
$156$	−0.205305	−	0.355598i	−0.0164375	−	0.0284707i
$157$	−10.7296	+	18.5842i	−0.856313	+	1.48318i	0.0191079	+	0.999817i	$0.493917\pi$
$157$	−10.7296	+	18.5842i	−0.856313	+	1.48318i	−0.875421	+	0.483361i	$0.839416\pi$
$158$	−6.92767	−	11.9991i	−0.551136	−	0.954595i
$159$	−11.7264	−	20.3107i	−0.929964	−	1.61074i
$160$	0.908328	−	1.57327i	0.0718096	−	0.124378i
$161$	1.84535	−	3.19624i	0.145434	−	0.251899i
$162$	5.57607	−	9.65803i	0.438097	−	0.758807i
$163$	−9.03968			−0.708042			−0.354021	−	0.935237i	$-0.615186\pi$
$163$	−9.03968			−0.708042			−0.354021	+	0.935237i	$0.615186\pi$
$164$	−8.73179			−0.681839
$165$	−1.47407	+	2.55316i	−0.114756	+	0.198764i
$166$	−2.02926	+	3.51477i	−0.157501	+	0.272799i
$167$	−10.3311	+	17.8940i	−0.799444	+	1.38468i	0.120534	+	0.992709i	$0.461539\pi$
$167$	−10.3311	+	17.8940i	−0.799444	+	1.38468i	−0.919978	+	0.391969i	$0.871794\pi$
$168$	4.99794	+	8.65669i	0.385600	+	0.667878i
$169$	6.48248	+	11.2280i	0.498653	+	0.863692i
$170$	−3.70318	+	6.41410i	−0.284021	+	0.491939i
$171$	3.30652	+	5.72706i	0.252856	+	0.437959i
$172$	−4.45791			−0.339912
$173$	2.92973			0.222743			0.111372	−	0.993779i	$-0.464476\pi$
$173$	2.92973			0.222743			0.111372	+	0.993779i	$0.464476\pi$
$174$	−8.84364	−	15.3176i	−0.670435	−	1.16123i
$175$	−7.74477			−0.585450
$176$	−0.369866	−	0.640628i	−0.0278797	−	0.0482891i
$177$	31.1526			2.34157
$178$	−1.65727	+	2.87047i	−0.124217	+	0.215151i
$179$	−8.12411	−	14.0714i	−0.607224	−	1.05174i	−0.991696	−	0.128606i	$-0.958950\pi$
$179$	−8.12411	−	14.0714i	−0.607224	−	1.05174i	0.384472	−	0.923137i	$-0.374384\pi$
$180$	−3.29329			−0.245468
$181$	−2.51062	−	4.34852i	−0.186613	−	0.323223i	0.757506	−	0.652828i	$-0.226418\pi$
$181$	−2.51062	−	4.34852i	−0.186613	−	0.323223i	−0.944119	+	0.329605i	$0.893084\pi$
$182$	0.426402	+	0.738550i	0.0316070	+	0.0547450i
$183$	1.80760	+	3.13085i	0.133621	+	0.231439i
$184$	−0.810006			−0.0597144
$185$	3.16050			0.232364
$186$	21.7750			1.59662
$187$	1.50792	+	2.61179i	0.110270	+	0.190993i
$188$		0			0
$189$	−5.93339	+	10.2769i	−0.431591	+	0.747537i
$190$	−3.31349	+	5.73913i	−0.240386	+	0.416361i
$191$	18.4219			1.33296			0.666480	−	0.745523i	$-0.267800\pi$
$191$	18.4219			1.33296			0.666480	+	0.745523i	$0.267800\pi$
$192$	1.09691	−	1.89990i	0.0791626	−	0.137114i
$193$	9.25021	+	16.0218i	0.665844	+	1.15328i	0.979056	+	0.203593i	$0.0652619\pi$
$193$	9.25021	+	16.0218i	0.665844	+	1.15328i	−0.313211	+	0.949683i	$0.601405\pi$
$194$	−1.10547	+	1.91473i	−0.0793681	+	0.137470i
$195$	−0.745936			−0.0534176
$196$	−6.88034	−	11.9171i	−0.491453	−	0.851221i
$197$	−10.1147	−	17.5192i	−0.720642	−	1.24819i	−0.960743	−	0.277440i	$-0.910514\pi$
$197$	−10.1147	−	17.5192i	−0.720642	−	1.24819i	0.240101	−	0.970748i	$-0.422819\pi$
$198$	−0.670506	+	1.16135i	−0.0476508	+	0.0825336i
$199$	23.1486			1.64096			0.820482	−	0.571673i	$-0.193705\pi$
$199$	23.1486			1.64096			0.820482	+	0.571673i	$0.193705\pi$
$200$	0.849881	+	1.47204i	0.0600956	+	0.104089i
$201$	−29.3554			−2.07057
$202$	12.0690			0.849171
$203$	18.3676	+	31.8136i	1.28915	+	2.23287i
$204$	−4.47201	+	7.74575i	−0.313103	+	0.542311i
$205$	−7.93133	+	13.7375i	−0.553948	+	0.959467i
$206$	−4.46472	+	7.73312i	−0.311072	+	0.538792i
$207$	0.734202	+	1.27168i	0.0510306	+	0.0883876i
$208$	0.0935834	−	0.162091i	0.00648884	−	0.0112390i
$209$	1.34924	+	2.33695i	0.0933286	+	0.161650i
$210$	18.1591			1.25310
$211$	−9.85638	+	17.0718i	−0.678541	+	1.17527i	0.296879	+	0.954915i	$0.404054\pi$
$211$	−9.85638	+	17.0718i	−0.678541	+	1.17527i	−0.975420	+	0.220353i	$0.929279\pi$
$212$	5.34520	−	9.25816i	0.367110	−	0.635853i
$213$	0.968686	−	1.67781i	0.0663733	−	0.114962i
$214$	3.02920			0.207072
$215$	−4.04924	+	7.01349i	−0.276156	+	0.478316i
$216$	2.60443			0.177209
$217$	−45.2249			−3.07007
$218$	7.93466	−	6.78537i	0.537403	−	0.459563i
$219$	−16.1493			−1.09127
$220$	−1.34384			−0.0906017
$221$	−0.381532	+	0.660833i	−0.0256646	+	0.0444525i
$222$	3.81666			0.256157
$223$	−6.26671	+	10.8543i	−0.419650	+	0.726855i	−0.995904	−	0.0904158i	$-0.971180\pi$
$223$	−6.26671	+	10.8543i	−0.419650	+	0.726855i	0.576254	+	0.817270i	$0.304514\pi$
$224$	−2.27819	+	3.94595i	−0.152218	+	0.263650i
$225$	1.54069	−	2.66856i	0.102713	−	0.177904i
$226$	−7.84869			−0.522087
$227$	−10.3730	−	17.9666i	−0.688483	−	1.19249i	−0.972329	−	0.233618i	$-0.924944\pi$
$227$	−10.3730	−	17.9666i	−0.688483	−	1.19249i	0.283845	−	0.958870i	$-0.408390\pi$
$228$	−4.00141	+	6.93065i	−0.265000	+	0.458994i
$229$	−11.8310	−	20.4918i	−0.781811	−	1.35414i	−0.930886	−	0.365311i	$-0.880963\pi$
$229$	−11.8310	−	20.4918i	−0.781811	−	1.35414i	0.149074	−	0.988826i	$-0.452371\pi$
$230$	−0.735751	+	1.27436i	−0.0485140	+	0.0840286i
$231$	3.69714	−	6.40364i	0.243254	−	0.421328i
$232$	4.03117	−	6.98219i	0.264659	−	0.458403i
$233$	9.34973	+	16.1942i	0.612521	+	1.06092i	0.990814	+	0.135232i	$0.0431780\pi$
$233$	9.34973	+	16.1942i	0.612521	+	1.06092i	−0.378293	+	0.925686i	$0.623489\pi$
$234$	−0.339302			−0.0221809
$235$		0			0
$236$	7.10009	+	12.2977i	0.462176	+	0.800513i
$237$	−30.3961			−1.97444
$238$	9.28802	−	16.0873i	0.602053	−	1.04279i
$239$	10.4734	+	18.1405i	0.677470	+	1.17341i	0.975740	+	0.218930i	$0.0702568\pi$
$239$	10.4734	+	18.1405i	0.677470	+	1.17341i	−0.298271	+	0.954481i	$0.596410\pi$
$240$	−1.99271	−	3.45147i	−0.128629	−	0.222791i
$241$	22.1150			1.42455			0.712276	−	0.701900i	$-0.247664\pi$
$241$	22.1150			1.42455			0.712276	+	0.701900i	$0.247664\pi$
$242$	5.22640	−	9.05239i	0.335966	−	0.581909i
$243$	−8.32623	−	14.4215i	−0.534128	−	0.925137i
$244$	−0.823951	+	1.42712i	−0.0527480	+	0.0913623i
$245$	−24.9984			−1.59709
$246$	−9.57798	+	16.5895i	−0.610670	+	1.05771i
$247$	−0.341383	+	0.591293i	−0.0217217	+	0.0376230i
$248$	4.96281	+	8.59583i	0.315138	+	0.545836i
$249$	4.45182	+	7.71077i	0.282122	+	0.488650i
$250$	12.1712			0.769772
$251$	9.23077			0.582641			0.291320	−	0.956626i	$-0.405905\pi$
$251$	9.23077			0.582641			0.291320	+	0.956626i	$0.405905\pi$
$252$	8.25997			0.520329
$253$	0.299594	+	0.518912i	0.0188353	+	0.0326237i
$254$	4.76899	+	8.26013i	0.299233	+	0.518287i
$255$	8.12411	+	14.0714i	0.508751	+	0.881183i
$256$	1.00000			0.0625000
$257$	8.95863	+	15.5168i	0.558824	+	0.967911i	0.997595	+	0.0693123i	$0.0220805\pi$
$257$	8.95863	+	15.5168i	0.558824	+	0.967911i	−0.438771	+	0.898599i	$0.644586\pi$
$258$	−4.88992	+	8.46958i	−0.304433	+	0.527293i
$259$	−7.92690			−0.492554
$260$	−0.170009	−	0.294464i	−0.0105435	−	0.0182619i
$261$	−14.6157			−0.904687
$262$	−0.0784964	−	0.135960i	−0.00484953	−	0.00839963i
$263$	−12.0847			−0.745174			−0.372587	−	0.927997i	$-0.621529\pi$
$263$	−12.0847			−0.745174			−0.372587	+	0.927997i	$0.621529\pi$
$264$	−1.62284			−0.0998788
$265$	−9.71039	−	16.8189i	−0.596505	−	1.03318i
$266$	8.31063	−	14.3944i	0.509557	−	0.882579i
$267$	3.63574	+	6.29729i	0.222504	+	0.385388i
$268$	−6.69049	−	11.5883i	−0.408687	−	0.707866i
$269$	−1.35123	+	2.34040i	−0.0823860	+	0.142697i	−0.904274	−	0.426952i	$-0.859587\pi$
$269$	−1.35123	+	2.34040i	−0.0823860	+	0.142697i	0.821888	+	0.569649i	$0.192921\pi$
$270$	2.36567	−	4.09747i	0.143970	−	0.249364i
$271$	11.1822	−	19.3682i	0.679273	−	1.17654i	−0.295927	−	0.955211i	$-0.595629\pi$
$271$	11.1822	−	19.3682i	0.679273	−	1.17654i	0.975200	−	0.221325i	$-0.0710381\pi$
$272$	−4.07692			−0.247200
$273$	1.87090			0.113232
$274$	4.43617	−	7.68367i	0.267999	−	0.464188i
$275$	0.628685	−	1.08891i	0.0379111	−	0.0656640i
$276$	−0.888502	+	1.53893i	−0.0534815	+	0.0926327i
$277$	1.86971	+	3.23843i	0.112340	+	0.194578i	0.916713	−	0.399546i	$-0.130832\pi$
$277$	1.86971	+	3.23843i	0.112340	+	0.194578i	−0.804373	+	0.594124i	$0.797499\pi$
$278$	−5.56892	−	9.64565i	−0.334002	−	0.578508i
$279$	8.99674	−	15.5828i	0.538621	−	0.932918i
$280$	4.13870	+	7.16843i	0.247334	+	0.428396i
$281$	−18.0874			−1.07900			−0.539502	−	0.841984i	$-0.681387\pi$
$281$	−18.0874			−1.07900			−0.539502	+	0.841984i	$0.681387\pi$
$282$		0			0
$283$	2.08906	+	3.61835i	0.124181	+	0.215089i	0.921413	−	0.388585i	$-0.127036\pi$
$283$	2.08906	+	3.61835i	0.124181	+	0.215089i	−0.797231	+	0.603674i	$0.793703\pi$
$284$	0.883106			0.0524027
$285$	7.26919	+	12.5906i	0.430590	+	0.745803i
$286$	−0.138453			−0.00818692
$287$	19.8927	−	34.4552i	1.17423	−	2.03383i
$288$	−0.906417	−	1.56996i	−0.0534111	−	0.0925108i
$289$	−0.378700			−0.0222765
$290$	−7.32324	−	12.6842i	−0.430036	−	0.744844i
$291$	2.42520	+	4.20057i	0.142168	+	0.246242i
$292$	−3.68064	−	6.37506i	−0.215393	−	0.373072i
$293$	−7.24950			−0.423520			−0.211760	−	0.977322i	$-0.567920\pi$
$293$	−7.24950			−0.423520			−0.211760	+	0.977322i	$0.567920\pi$
$294$	−30.1884			−1.76062
$295$	25.7968			1.50195
$296$	0.869866	+	1.50665i	0.0505600	+	0.0875724i
$297$	−0.963290	−	1.66847i	−0.0558958	−	0.0968143i
$298$	−2.92902	+	5.07321i	−0.169674	+	0.293883i
$299$	−0.0758031	+	0.131295i	−0.00438380	+	0.00759297i
$300$	3.72897			0.215292
$301$	10.1560	−	17.5907i	0.585381	−	1.01391i
$302$	−4.46472	−	7.73312i	−0.256916	−	0.444991i
$303$	13.2386	−	22.9299i	0.760536	−	1.31729i
$304$	−3.64790			−0.209221
$305$	1.49683	+	2.59259i	0.0857085	+	0.148451i
$306$	3.69539	+	6.40060i	0.211251	+	0.365898i
$307$	−12.2735	+	21.2584i	−0.700487	+	1.21328i	0.267809	+	0.963472i	$0.413700\pi$
$307$	−12.2735	+	21.2584i	−0.700487	+	1.21328i	−0.968296	+	0.249806i	$0.919633\pi$
$308$	3.37051			0.192053
$309$	9.79477	+	16.9650i	0.557205	+	0.965108i
$310$	18.0314			1.02412
$311$	18.0129			1.02142			0.510708	−	0.859754i	$-0.329383\pi$
$311$	18.0129			1.02142			0.510708	+	0.859754i	$0.329383\pi$
$312$	−0.205305	−	0.355598i	−0.0116231	−	0.0201318i
$313$	0.664077	−	1.15021i	0.0375358	−	0.0650140i	−0.846647	−	0.532155i	$-0.821382\pi$
$313$	0.664077	−	1.15021i	0.0375358	−	0.0650140i	0.884183	+	0.467141i	$0.154716\pi$
$314$	−10.7296	+	18.5842i	−0.605505	+	1.04877i
$315$	7.50276	−	12.9952i	0.422733	−	0.732195i
$316$	−6.92767	−	11.9991i	−0.389712	−	0.675001i
$317$	−2.88508	+	4.99710i	−0.162042	+	0.280665i	−0.935601	−	0.353059i	$-0.885141\pi$
$317$	−2.88508	+	4.99710i	−0.162042	+	0.280665i	0.773559	+	0.633725i	$0.218475\pi$
$318$	−11.7264	−	20.3107i	−0.657584	−	1.13897i
$319$	−5.96397			−0.333918
$320$	0.908328	−	1.57327i	0.0507771	−	0.0879485i
$321$	3.32276	−	5.75519i	0.185458	−	0.321223i
$322$	1.84535	−	3.19624i	0.102837	−	0.178119i
$323$	14.8722			0.827512
$324$	5.57607	−	9.65803i	0.309782	−	0.536557i
$325$	0.318139			0.0176472
$326$	−9.03968			−0.500661
$327$	−4.18794	−	22.5180i	−0.231593	−	1.24525i
$328$	−8.73179			−0.482133
$329$		0			0
$330$	−1.47407	+	2.55316i	−0.0811449	+	0.140547i
$331$	33.1868			1.82411			0.912057	−	0.410064i	$-0.134494\pi$
$331$	33.1868			1.82411			0.912057	+	0.410064i	$0.134494\pi$
$332$	−2.02926	+	3.51477i	−0.111370	+	0.192898i
$333$	1.57692	−	2.73131i	0.0864148	−	0.149675i
$334$	−10.3311	+	17.8940i	−0.565293	+	0.979115i
$335$	−24.3086			−1.32812
$336$	4.99794	+	8.65669i	0.272660	+	0.472261i
$337$	−0.547183	+	0.947748i	−0.0298069	+	0.0516271i	−0.880544	−	0.473964i	$-0.842823\pi$
$337$	−0.547183	+	0.947748i	−0.0298069	+	0.0516271i	0.850737	+	0.525591i	$0.176156\pi$
$338$	6.48248	+	11.2280i	0.352601	+	0.610722i
$339$	−8.60929	+	14.9117i	−0.467593	+	0.809894i
$340$	−3.70318	+	6.41410i	−0.200833	+	0.347853i
$341$	3.67115	−	6.35862i	0.198804	−	0.344339i
$342$	3.30652	+	5.72706i	0.178796	+	0.309684i
$343$	30.8043			1.66327
$344$	−4.45791			−0.240354
$345$	1.61410	+	2.79571i	0.0869003	+	0.150516i
$346$	2.92973			0.157503
$347$	16.0397	−	27.7816i	0.861058	−	1.49140i	−0.00985130	−	0.999951i	$-0.503136\pi$
$347$	16.0397	−	27.7816i	0.861058	−	1.49140i	0.870909	−	0.491444i	$-0.163531\pi$
$348$	−8.84364	−	15.3176i	−0.474069	−	0.821112i
$349$	13.4131	+	23.2321i	0.717986	+	1.24359i	0.961797	+	0.273765i	$0.0882690\pi$
$349$	13.4131	+	23.2321i	0.717986	+	1.24359i	−0.243811	+	0.969823i	$0.578398\pi$
$350$	−7.74477			−0.413976
$351$	0.243731	−	0.422155i	0.0130094	−	0.0225329i
$352$	−0.369866	−	0.640628i	−0.0197139	−	0.0341456i
$353$	7.92894	−	13.7333i	0.422015	−	0.730951i	−0.574122	−	0.818770i	$-0.694656\pi$
$353$	7.92894	−	13.7333i	0.422015	−	0.730951i	0.996136	+	0.0878191i	$0.0279897\pi$
$354$	31.1526			1.65574
$355$	0.802150	−	1.38936i	0.0425737	−	0.0737398i
$356$	−1.65727	+	2.87047i	−0.0878350	+	0.152135i
$357$	−20.3762	−	35.2927i	−1.07842	−	1.86789i
$358$	−8.12411	−	14.0714i	−0.429372	−	0.743695i
$359$	11.8615			0.626028			0.313014	−	0.949748i	$-0.398661\pi$
$359$	11.8615			0.626028			0.313014	+	0.949748i	$0.398661\pi$
$360$	−3.29329			−0.173572
$361$	−5.69282			−0.299622
$362$	−2.51062	−	4.34852i	−0.131955	−	0.228553i
$363$	−11.4658	−	19.8593i	−0.601796	−	1.04234i
$364$	0.426402	+	0.738550i	0.0223496	+	0.0387106i
$365$	−13.3729			−0.699970
$366$	1.80760	+	3.13085i	0.0944846	+	0.163652i
$367$	−10.4807	+	18.1531i	−0.547087	+	0.947582i	0.451386	+	0.892329i	$0.350930\pi$
$367$	−10.4807	+	18.1531i	−0.547087	+	0.947582i	−0.998472	+	0.0552529i	$0.982403\pi$
$368$	−0.810006			−0.0422245
$369$	7.91464	+	13.7086i	0.412020	+	0.713639i
$370$	3.16050			0.164306
$371$	24.3548	+	42.1838i	1.26444	+	2.19007i
$372$	21.7750			1.12898
$373$	23.6208			1.22304			0.611520	−	0.791229i	$-0.290558\pi$
$373$	23.6208			1.22304			0.611520	+	0.791229i	$0.290558\pi$
$374$	1.50792	+	2.61179i	0.0779725	+	0.135052i
$375$	13.3507	−	23.1240i	0.689425	−	1.19412i
$376$		0			0
$377$	−0.754500	−	1.30683i	−0.0388587	−	0.0673053i
$378$	−5.93339	+	10.2769i	−0.305181	+	0.528588i
$379$	−4.12753	+	7.14909i	−0.212017	+	0.367224i	−0.952346	−	0.305021i	$-0.901336\pi$
$379$	−4.12753	+	7.14909i	−0.212017	+	0.367224i	0.740329	+	0.672245i	$0.234670\pi$
$380$	−3.31349	+	5.73913i	−0.169978	+	0.294411i
$381$	20.9246			1.07200
$382$	18.4219			0.942545
$383$	5.50001	−	9.52630i	0.281038	−	0.486771i	−0.690603	−	0.723234i	$-0.742655\pi$
$383$	5.50001	−	9.52630i	0.281038	−	0.486771i	0.971641	+	0.236463i	$0.0759881\pi$
$384$	1.09691	−	1.89990i	0.0559764	−	0.0969539i
$385$	3.06153	−	5.30272i	0.156030	−	0.270252i
$386$	9.25021	+	16.0218i	0.470823	+	0.815489i
$387$	4.04072	+	6.99873i	0.205401	+	0.355766i
$388$	−1.10547	+	1.91473i	−0.0561217	+	0.0972057i
$389$	8.79667	+	15.2363i	0.446009	+	0.772510i	0.998122	−	0.0612592i	$-0.0195116\pi$
$389$	8.79667	+	15.2363i	0.446009	+	0.772510i	−0.552113	+	0.833769i	$0.686178\pi$
$390$	−0.745936			−0.0377720
$391$	3.30233			0.167006
$392$	−6.88034	−	11.9171i	−0.347510	−	0.601904i
$393$	−0.344414			−0.0173734
$394$	−10.1147	−	17.5192i	−0.509571	−	0.882602i
$395$	−25.1704			−1.26646
$396$	−0.670506	+	1.16135i	−0.0336942	+	0.0583601i
$397$	5.74007	+	9.94209i	0.288086	+	0.498979i	0.973353	−	0.229313i	$-0.0736478\pi$
$397$	5.74007	+	9.94209i	0.288086	+	0.498979i	−0.685267	+	0.728292i	$0.740314\pi$
$398$	23.1486			1.16034
$399$	−18.2320	−	31.5787i	−0.912741	−	1.58091i
$400$	0.849881	+	1.47204i	0.0424940	+	0.0736018i
$401$	−2.03569	−	3.52593i	−0.101658	−	0.176076i	0.810710	−	0.585448i	$-0.199081\pi$
$401$	−2.03569	−	3.52593i	−0.101658	−	0.176076i	−0.912368	+	0.409372i	$0.865748\pi$
$402$	−29.3554			−1.46412
$403$	1.85774			0.0925408
$404$	12.0690			0.600454
$405$	−10.1298	−	17.5453i	−0.503354	−	0.871834i
$406$	18.3676	+	31.8136i	0.911567	+	1.57888i
$407$	0.643469	−	1.11452i	0.0318956	−	0.0552447i
$408$	−4.47201	+	7.74575i	−0.221398	+	0.383472i
$409$	3.60651			0.178331			0.0891653	−	0.996017i	$-0.471580\pi$
$409$	3.60651			0.178331			0.0891653	+	0.996017i	$0.471580\pi$
$410$	−7.93133	+	13.7375i	−0.391701	+	0.678445i
$411$	−9.73214	−	16.8566i	−0.480051	−	0.831473i
$412$	−4.46472	+	7.73312i	−0.219961	+	0.380983i
$413$	−64.7015			−3.18375
$414$	0.734202	+	1.27168i	0.0360841	+	0.0624995i
$415$	3.68646	+	6.38513i	0.180961	+	0.313434i
$416$	0.0935834	−	0.162091i	0.00458830	−	0.00794717i
$417$	−24.4344			−1.19656
$418$	1.34924	+	2.33695i	0.0659933	+	0.114304i
$419$	−25.7552			−1.25822			−0.629111	−	0.777316i	$-0.716581\pi$
$419$	−25.7552			−1.25822			−0.629111	+	0.777316i	$0.716581\pi$
$420$	18.1591			0.886072
$421$	−0.209884	−	0.363530i	−0.0102291	−	0.0177174i	0.860866	−	0.508833i	$-0.169923\pi$
$421$	−0.209884	−	0.363530i	−0.0102291	−	0.0177174i	−0.871095	+	0.491115i	$0.836589\pi$
$422$	−9.85638	+	17.0718i	−0.479801	+	0.831040i
$423$		0			0
$424$	5.34520	−	9.25816i	0.259586	−	0.449616i
$425$	−3.46490	−	6.00138i	−0.168072	−	0.291110i
$426$	0.968686	−	1.67781i	0.0469330	−	0.0812903i
$427$	−3.75424	−	6.50253i	−0.181680	−	0.314680i
$428$	3.02920			0.146422
$429$	−0.151871	+	0.263048i	−0.00733239	+	0.0127001i
$430$	−4.04924	+	7.01349i	−0.195272	+	0.338221i
$431$	−8.80723	+	15.2546i	−0.424229	+	0.734786i	−0.996348	−	0.0853842i	$-0.972788\pi$
$431$	−8.80723	+	15.2546i	−0.424229	+	0.734786i	0.572119	+	0.820171i	$0.306122\pi$
$432$	2.60443			0.125306
$433$	2.38588	−	4.13247i	0.114658	−	0.198594i	−0.802985	−	0.595999i	$-0.796756\pi$
$433$	2.38588	−	4.13247i	0.114658	−	0.198594i	0.917643	+	0.397406i	$0.130089\pi$
$434$	−45.2249			−2.17087
$435$	−32.1317			−1.54060
$436$	7.93466	−	6.78537i	0.380001	−	0.324960i
$437$	2.95482			0.141348
$438$	−16.1493			−0.771644
$439$	−6.74066	+	11.6752i	−0.321714	+	0.557225i	−0.980842	−	0.194806i	$-0.937592\pi$
$439$	−6.74066	+	11.6752i	−0.321714	+	0.557225i	0.659128	+	0.752031i	$0.270926\pi$
$440$	−1.34384			−0.0640651
$441$	−12.4729	+	21.6037i	−0.593948	+	1.02875i
$442$	−0.381532	+	0.660833i	−0.0181476	+	0.0314326i
$443$	−5.77644	+	10.0051i	−0.274447	+	0.475356i	−0.969995	−	0.243123i	$-0.921828\pi$
$443$	−5.77644	+	10.0051i	−0.274447	+	0.475356i	0.695548	+	0.718479i	$0.255161\pi$
$444$	3.81666			0.181130
$445$	3.01068	+	5.21466i	0.142720	+	0.247198i
$446$	−6.26671	+	10.8543i	−0.296737	+	0.513964i
$447$	6.42574	+	11.1297i	0.303927	+	0.526417i
$448$	−2.27819	+	3.94595i	−0.107635	+	0.186429i
$449$	−7.00968	+	12.1411i	−0.330807	+	0.572975i	−0.982670	−	0.185362i	$-0.940654\pi$
$449$	−7.00968	+	12.1411i	−0.330807	+	0.572975i	0.651863	+	0.758337i	$0.273988\pi$
$450$	1.54069	−	2.66856i	0.0726289	−	0.125797i
$451$	3.22960	+	5.59383i	0.152076	+	0.263403i
$452$	−7.84869			−0.369171
$453$	−19.5895			−0.920397
$454$	−10.3730	−	17.9666i	−0.486831	−	0.843216i
$455$	1.54925			0.0726301
$456$	−4.00141	+	6.93065i	−0.187383	+	0.324558i
$457$	17.1130	+	29.6405i	0.800510	+	1.38652i	0.919281	+	0.393603i	$0.128771\pi$
$457$	17.1130	+	29.6405i	0.800510	+	1.38652i	−0.118770	+	0.992922i	$0.537895\pi$
$458$	−11.8310	−	20.4918i	−0.552824	−	0.957519i
$459$	−10.6180			−0.495608
$460$	−0.735751	+	1.27436i	−0.0343046	+	0.0594172i
$461$	−1.73166	−	2.99932i	−0.0806513	−	0.139692i	0.822879	−	0.568217i	$-0.192367\pi$
$461$	−1.73166	−	2.99932i	−0.0806513	−	0.139692i	−0.903530	+	0.428525i	$0.859033\pi$
$462$	3.69714	−	6.40364i	0.172007	−	0.297924i
$463$	−22.8231			−1.06068			−0.530341	−	0.847785i	$-0.677936\pi$
$463$	−22.8231			−1.06068			−0.530341	+	0.847785i	$0.677936\pi$
$464$	4.03117	−	6.98219i	0.187142	−	0.324140i
$465$	19.7788	−	34.2579i	0.917221	−	1.58867i
$466$	9.34973	+	16.1942i	0.433118	+	0.750182i
$467$	−20.1124	−	34.8357i	−0.930691	−	1.61200i	−0.782143	−	0.623099i	$-0.785873\pi$
$467$	−20.1124	−	34.8357i	−0.930691	−	1.61200i	−0.148548	−	0.988905i	$-0.547460\pi$
$468$	−0.339302			−0.0156842
$469$	60.9690			2.81529
$470$		0			0
$471$	23.5387	+	40.7703i	1.08461	+	1.87859i
$472$	7.10009	+	12.2977i	0.326808	+	0.566048i
$473$	1.64883	+	2.85586i	0.0758133	+	0.131312i
$474$	−30.3961			−1.39614
$475$	−3.10028	−	5.36984i	−0.142251	−	0.246385i
$476$	9.28802	−	16.0873i	0.425716	−	0.737361i
$477$	−19.3799			−0.887346
$478$	10.4734	+	18.1405i	0.479043	+	0.829727i
$479$	37.3552			1.70680			0.853400	−	0.521256i	$-0.174536\pi$
$479$	37.3552			1.70680			0.853400	+	0.521256i	$0.174536\pi$
$480$	−1.99271	−	3.45147i	−0.0909541	−	0.157537i
$481$	0.325620			0.0148470
$482$	22.1150			1.00731
$483$	−4.04836	−	7.01197i	−0.184207	−	0.319056i
$484$	5.22640	−	9.05239i	0.237564	−	0.411472i
$485$	2.00826	+	3.47841i	0.0911903	+	0.157946i
$486$	−8.32623	−	14.4215i	−0.377686	−	0.654171i
$487$	4.42640	−	7.66675i	0.200579	−	0.347414i	−0.748136	−	0.663546i	$-0.769051\pi$
$487$	4.42640	−	7.66675i	0.200579	−	0.347414i	0.948715	+	0.316132i	$0.102384\pi$
$488$	−0.823951	+	1.42712i	−0.0372985	+	0.0646029i
$489$	−9.91570	+	17.1745i	−0.448403	+	0.776657i
$490$	−24.9984			−1.12931
$491$	−4.42687			−0.199782			−0.0998909	−	0.994998i	$-0.531849\pi$
$491$	−4.42687			−0.199782			−0.0998909	+	0.994998i	$0.531849\pi$
$492$	−9.57798	+	16.5895i	−0.431809	+	0.747915i
$493$	−16.4348	+	28.4658i	−0.740184	+	1.28204i
$494$	−0.341383	+	0.591293i	−0.0153595	+	0.0266035i
$495$	1.21808	+	2.10977i	0.0547486	+	0.0948273i
$496$	4.96281	+	8.59583i	0.222837	+	0.385964i
$497$	−2.01189	+	3.48469i	−0.0902455	+	0.156310i
$498$	4.45182	+	7.71077i	0.199491	+	0.345528i
$499$	−10.5737			−0.473344			−0.236672	−	0.971590i	$-0.576057\pi$
$499$	−10.5737			−0.473344			−0.236672	+	0.971590i	$0.576057\pi$
$500$	12.1712			0.544311
$501$	22.6645	+	39.2561i	1.01258	+	1.75383i
$502$	9.23077			0.411989
$503$	−16.2187	−	28.0917i	−0.723158	−	1.25255i	−0.959728	−	0.280932i	$-0.909356\pi$
$503$	−16.2187	−	28.0917i	−0.723158	−	1.25255i	0.236570	−	0.971615i	$-0.423977\pi$
$504$	8.25997			0.367928
$505$	10.9626	−	18.9878i	0.487829	−	0.844945i
$506$	0.299594	+	0.518912i	0.0133186	+	0.0230684i
$507$	28.4428			1.26319
$508$	4.76899	+	8.26013i	0.211590	+	0.366484i
$509$	0.961938	+	1.66612i	0.0426371	+	0.0738497i	0.886556	−	0.462620i	$-0.153091\pi$
$509$	0.961938	+	1.66612i	0.0426371	+	0.0738497i	−0.843919	+	0.536470i	$0.819757\pi$
$510$	8.12411	+	14.0714i	0.359741	+	0.623090i
$511$	33.5409			1.48376
$512$	1.00000			0.0441942
$513$	−9.50069			−0.419466
$514$	8.95863	+	15.5168i	0.395148	+	0.684416i
$515$	8.11085	+	14.0484i	0.357407	+	0.619047i
$516$	−4.88992	+	8.46958i	−0.215267	+	0.372853i
$517$		0			0
$518$	−7.92690			−0.348288
$519$	3.21364	−	5.56619i	0.141063	−	0.244329i
$520$	−0.170009	−	0.294464i	−0.00745538	−	0.0129131i
$521$	15.7442	−	27.2697i	0.689765	−	1.19471i	−0.282149	−	0.959371i	$-0.591047\pi$
$521$	15.7442	−	27.2697i	0.689765	−	1.19471i	0.971914	−	0.235337i	$-0.0756195\pi$
$522$	−14.6157			−0.639710
$523$	−5.97494	−	10.3489i	−0.261266	−	0.452526i	0.705313	−	0.708896i	$-0.250807\pi$
$523$	−5.97494	−	10.3489i	−0.261266	−	0.452526i	−0.966579	+	0.256371i	$0.917473\pi$
$524$	−0.0784964	−	0.135960i	−0.00342913	−	0.00593943i
$525$	−8.49531	+	14.7143i	−0.370766	+	0.642185i
$526$	−12.0847			−0.526918
$527$	−20.2330	−	35.0445i	−0.881362	−	1.52656i
$528$	−1.62284			−0.0706250
$529$	−22.3439			−0.971474
$530$	−9.71039	−	16.8189i	−0.421793	−	0.730566i
$531$	12.8713	−	22.2937i	0.558566	−	0.967464i
$532$	8.31063	−	14.3944i	0.360311	−	0.624078i
$533$	−0.817151	+	1.41535i	−0.0353947	+	0.0613055i
$534$	3.63574	+	6.29729i	0.157334	+	0.272510i
$535$	2.75151	−	4.76576i	0.118958	−	0.206042i
$536$	−6.69049	−	11.5883i	−0.288985	−	0.500537i
$537$	−35.6456			−1.53822
$538$	−1.35123	+	2.34040i	−0.0582557	+	0.100902i
$539$	−5.08961	+	8.81547i	−0.219225	+	0.379709i
$540$	2.36567	−	4.09747i	0.101802	−	0.176327i
$541$	14.8696			0.639294			0.319647	−	0.947537i	$-0.396436\pi$
$541$	14.8696			0.639294			0.319647	+	0.947537i	$0.396436\pi$
$542$	11.1822	−	19.3682i	0.480319	−	0.831936i
$543$	−11.0157			−0.472728
$544$	−4.07692			−0.174797
$545$	−3.46795	−	18.6467i	−0.148550	−	0.798737i
$546$	1.87090			0.0800670
$547$	−0.574928			−0.0245822			−0.0122911	−	0.999924i	$-0.503912\pi$
$547$	−0.574928			−0.0245822			−0.0122911	+	0.999924i	$0.503912\pi$
$548$	4.43617	−	7.68367i	0.189504	−	0.328230i
$549$	2.98737			0.127498
$550$	0.628685	−	1.08891i	0.0268072	−	0.0464315i
$551$	−14.7053	+	25.4703i	−0.626467	+	1.08507i
$552$	−0.888502	+	1.53893i	−0.0378172	+	0.0655012i
$553$	63.1303			2.68457
$554$	1.86971	+	3.23843i	0.0794362	+	0.137588i
$555$	3.46678	−	6.00463i	0.147156	−	0.254882i
$556$	−5.56892	−	9.64565i	−0.236175	−	0.409067i
$557$	−9.49000	+	16.4372i	−0.402104	+	0.696465i	−0.993980	−	0.109564i	$-0.965054\pi$
$557$	−9.49000	+	16.4372i	−0.402104	+	0.696465i	0.591875	+	0.806029i	$0.298388\pi$
$558$	8.99674	−	15.5828i	0.380862	−	0.659673i
$559$	−0.417186	+	0.722587i	−0.0176451	+	0.0305622i
$560$	4.13870	+	7.16843i	0.174892	+	0.302921i
$561$	6.61619			0.279336
$562$	−18.0874			−0.762971
$563$	15.9532	+	27.6318i	0.672349	+	1.16454i	0.977236	+	0.212154i	$0.0680479\pi$
$563$	15.9532	+	27.6318i	0.672349	+	1.16454i	−0.304887	+	0.952388i	$0.598619\pi$
$564$		0			0
$565$	−7.12918	+	12.3481i	−0.299927	+	0.519489i
$566$	2.08906	+	3.61835i	0.0878095	+	0.152091i
$567$	25.4067	+	44.0058i	1.06698	+	1.84807i
$568$	0.883106			0.0370543
$569$	−23.0525	+	39.9281i	−0.966412	+	1.67387i	−0.260638	+	0.965437i	$0.583933\pi$
$569$	−23.0525	+	39.9281i	−0.966412	+	1.67387i	−0.705774	+	0.708437i	$0.749401\pi$
$570$	7.26919	+	12.5906i	0.304473	+	0.527363i
$571$	4.13891	−	7.16880i	0.173208	−	0.300005i	−0.766332	−	0.642445i	$-0.777920\pi$
$571$	4.13891	−	7.16880i	0.173208	−	0.300005i	0.939540	+	0.342440i	$0.111253\pi$
$572$	−0.138453			−0.00578903
$573$	20.2071	−	34.9998i	0.844164	−	1.46214i
$574$	19.8927	−	34.4552i	0.830306	−	1.43813i
$575$	−0.688408	−	1.19236i	−0.0287086	−	0.0497248i
$576$	−0.906417	−	1.56996i	−0.0377674	−	0.0654150i
$577$	12.2923			0.511736			0.255868	−	0.966712i	$-0.417639\pi$
$577$	12.2923			0.511736			0.255868	+	0.966712i	$0.417639\pi$
$578$	−0.378700			−0.0157518
$579$	40.5865			1.68672
$580$	−7.32324	−	12.6842i	−0.304081	−	0.526684i
$581$	−9.24608	−	16.0147i	−0.383592	−	0.664401i
$582$	2.42520	+	4.20057i	0.100528	+	0.174119i
$583$	−7.90805			−0.327518
$584$	−3.68064	−	6.37506i	−0.152306	−	0.263802i
$585$	−0.308198	+	0.533814i	−0.0127424	+	0.0220705i
$586$	−7.24950			−0.299474
$587$	−4.14152	−	7.17333i	−0.170939	−	0.296075i	0.767809	−	0.640678i	$-0.221347\pi$
$587$	−4.14152	−	7.17333i	−0.170939	−	0.296075i	−0.938748	+	0.344603i	$0.888013\pi$
$588$	−30.1884			−1.24495
$589$	−18.1038	−	31.3567i	−0.745955	−	1.29203i
$590$	25.7968			1.06204
$591$	−44.3796			−1.82553
$592$	0.869866	+	1.50665i	0.0357513	+	0.0619231i
$593$	−16.8492	+	29.1836i	−0.691912	+	1.19843i	0.279299	+	0.960204i	$0.409898\pi$
$593$	−16.8492	+	29.1836i	−0.691912	+	1.19843i	−0.971211	+	0.238222i	$0.923435\pi$
$594$	−0.963290	−	1.66847i	−0.0395243	−	0.0684580i
$595$	−16.8731	−	29.2251i	−0.691731	−	1.19811i
$596$	−2.92902	+	5.07321i	−0.119977	+	0.207807i
$597$	25.3919	−	43.9801i	1.03922	−	1.79999i
$598$	−0.0758031	+	0.131295i	−0.00309982	+	0.00536904i
$599$	11.5125			0.470388			0.235194	−	0.971948i	$-0.424427\pi$
$599$	11.5125			0.470388			0.235194	+	0.971948i	$0.424427\pi$
$600$	3.72897			0.152234
$601$	−3.09676	+	5.36375i	−0.126320	+	0.218792i	−0.922248	−	0.386599i	$-0.873650\pi$
$601$	−3.09676	+	5.36375i	−0.126320	+	0.218792i	0.795928	+	0.605391i	$0.206983\pi$
$602$	10.1560	−	17.5907i	0.413927	−	0.716942i
$603$	−12.1287	+	21.0076i	−0.493921	+	0.855496i
$604$	−4.46472	−	7.73312i	−0.181667	−	0.314656i
$605$	−9.49457	−	16.4451i	−0.386009	−	0.668587i
$606$	13.2386	−	22.9299i	0.537780	−	0.931463i
$607$	−22.2075	−	38.4645i	−0.901373	−	1.56122i	−0.825713	−	0.564091i	$-0.809227\pi$
$607$	−22.2075	−	38.4645i	−0.901373	−	1.56122i	−0.0756605	−	0.997134i	$-0.524107\pi$
$608$	−3.64790			−0.147942
$609$	80.5901			3.26568
$610$	1.49683	+	2.59259i	0.0606051	+	0.104971i
$611$		0			0
$612$	3.69539	+	6.40060i	0.149377	+	0.258729i
$613$	−8.54777			−0.345241			−0.172621	−	0.984988i	$-0.555223\pi$
$613$	−8.54777			−0.345241			−0.172621	+	0.984988i	$0.555223\pi$
$614$	−12.2735	+	21.2584i	−0.495319	+	0.857917i
$615$	17.3999	+	30.1375i	0.701631	+	1.21526i
$616$	3.37051			0.135802
$617$	6.64868	+	11.5159i	0.267666	+	0.463611i	0.968259	−	0.249950i	$-0.0804143\pi$
$617$	6.64868	+	11.5159i	0.267666	+	0.463611i	−0.700593	+	0.713561i	$0.747081\pi$
$618$	9.79477	+	16.9650i	0.394003	+	0.682434i
$619$	0.953972	+	1.65233i	0.0383434	+	0.0664127i	0.884560	−	0.466426i	$-0.154459\pi$
$619$	0.953972	+	1.65233i	0.0383434	+	0.0664127i	−0.846217	+	0.532839i	$0.821125\pi$
$620$	18.0314			0.724159
$621$	−2.10960			−0.0846553
$622$	18.0129			0.722251
$623$	−7.55115	−	13.0790i	−0.302531	−	0.523998i
$624$	−0.205305	−	0.355598i	−0.00821877	−	0.0142353i
$625$	6.80600	−	11.7883i	0.272240	−	0.471534i
$626$	0.664077	−	1.15021i	0.0265419	−	0.0459718i
$627$	5.91996			0.236420
$628$	−10.7296	+	18.5842i	−0.428157	+	0.741589i
$629$	−3.54638	−	6.14251i	−0.141403	−	0.244918i
$630$	7.50276	−	12.9952i	0.298917	−	0.517740i
$631$	−22.3869			−0.891208			−0.445604	−	0.895230i	$-0.647011\pi$
$631$	−22.3869			−0.891208			−0.445604	+	0.895230i	$0.647011\pi$
$632$	−6.92767	−	11.9991i	−0.275568	−	0.477298i
$633$	21.6231	+	37.4523i	0.859441	+	1.48860i
$634$	−2.88508	+	4.99710i	−0.114581	+	0.198460i
$635$	17.3272			0.687610
$636$	−11.7264	−	20.3107i	−0.464982	−	0.805372i
$637$	−2.57554			−0.102047
$638$	−5.96397			−0.236116
$639$	−0.800462	−	1.38644i	−0.0316658	−	0.0548467i
$640$	0.908328	−	1.57327i	0.0359048	−	0.0621890i
$641$	13.5438	−	23.4585i	0.534946	−	0.926554i	−0.464220	−	0.885720i	$-0.653665\pi$
$641$	13.5438	−	23.4585i	0.534946	−	0.926554i	0.999166	−	0.0408342i	$-0.0130015\pi$
$642$	3.32276	−	5.75519i	0.131139	−	0.227139i
$643$	−1.83870	−	3.18473i	−0.0725113	−	0.125593i	0.827490	−	0.561480i	$-0.189768\pi$
$643$	−1.83870	−	3.18473i	−0.0725113	−	0.125593i	−0.900001	+	0.435887i	$0.856435\pi$
$644$	1.84535	−	3.19624i	0.0727170	−	0.125950i
$645$	8.88329	+	15.3863i	0.349779	+	0.605836i
$646$	14.8722			0.585139
$647$	16.9055	−	29.2811i	0.664622	−	1.15116i	−0.314765	−	0.949170i	$-0.601926\pi$
$647$	16.9055	−	29.2811i	0.664622	−	1.15116i	0.979388	−	0.201990i	$-0.0647409\pi$
$648$	5.57607	−	9.65803i	0.219049	−	0.379403i
$649$	5.25217	−	9.09702i	0.206166	−	0.357089i
$650$	0.318139			0.0124784
$651$	−49.6076	+	85.9229i	−1.94428	+	3.36758i
$652$	−9.03968			−0.354021
$653$	−8.20619			−0.321133			−0.160567	−	0.987025i	$-0.551332\pi$
$653$	−8.20619			−0.321133			−0.160567	+	0.987025i	$0.551332\pi$
$654$	−4.18794	−	22.5180i	−0.163761	−	0.880523i
$655$	−0.285202			−0.0111438
$656$	−8.73179			−0.340919
$657$	−6.67239	+	11.5569i	−0.260315	+	0.450878i
$658$		0			0
$659$	−1.23419	+	2.13768i	−0.0480772	+	0.0832722i	−0.889063	−	0.457786i	$-0.848643\pi$
$659$	−1.23419	+	2.13768i	−0.0480772	+	0.0832722i	0.840985	+	0.541058i	$0.181976\pi$
$660$	−1.47407	+	2.55316i	−0.0573781	+	0.0993818i
$661$	−12.5082	+	21.6648i	−0.486513	+	0.842665i	−0.999880	−	0.0155043i	$-0.995065\pi$
$661$	−12.5082	+	21.6648i	−0.486513	+	0.842665i	0.513367	+	0.858169i	$0.328398\pi$
$662$	33.1868			1.28984
$663$	0.837012	+	1.44975i	0.0325068	+	0.0563035i
$664$	−2.02926	+	3.51477i	−0.0787504	+	0.136400i
$665$	−15.0976	−	26.1497i	−0.585458	−	1.01404i
$666$	1.57692	−	2.73131i	0.0611045	−	0.105836i
$667$	−3.26527	+	5.65561i	−0.126432	+	0.218986i
$668$	−10.3311	+	17.8940i	−0.399722	+	0.692339i
$669$	13.7480	+	23.8122i	0.531529	+	0.920635i
$670$	−24.3086			−0.939125
$671$	1.21901			0.0470592
$672$	4.99794	+	8.65669i	0.192800	+	0.333939i
$673$	−48.0836			−1.85348			−0.926742	−	0.375697i	$-0.877403\pi$
$673$	−48.0836			−1.85348			−0.926742	+	0.375697i	$0.877403\pi$
$674$	−0.547183	+	0.947748i	−0.0210767	+	0.0365059i
$675$	2.21345	+	3.83381i	0.0851958	+	0.147563i
$676$	6.48248	+	11.2280i	0.249326	+	0.431846i
$677$	−17.4257			−0.669723			−0.334862	−	0.942267i	$-0.608690\pi$
$677$	−17.4257			−0.669723			−0.334862	+	0.942267i	$0.608690\pi$
$678$	−8.60929	+	14.9117i	−0.330638	+	0.572682i
$679$	−5.03695	−	8.72426i	−0.193300	−	0.334806i
$680$	−3.70318	+	6.41410i	−0.142011	+	0.245970i
$681$	−45.5131			−1.74407
$682$	3.67115	−	6.35862i	0.140576	−	0.243484i
$683$	9.88955	−	17.1292i	0.378413	−	0.655430i	−0.612419	−	0.790534i	$-0.709803\pi$
$683$	9.88955	−	17.1292i	0.378413	−	0.655430i	0.990832	+	0.135103i	$0.0431366\pi$
$684$	3.30652	+	5.72706i	0.126428	+	0.218980i
$685$	−8.05899	−	13.9586i	−0.307918	−	0.533330i
$686$	30.8043			1.17611
$687$	−51.9099			−1.98049
$688$	−4.45791			−0.169956
$689$	−1.00044	−	1.73282i	−0.0381139	−	0.0660152i
$690$	1.61410	+	2.79571i	0.0614478	+	0.106431i
$691$	−14.6887	−	25.4416i	−0.558785	−	0.967844i	−0.997598	−	0.0692659i	$-0.977934\pi$
$691$	−14.6887	−	25.4416i	−0.558785	−	0.967844i	0.438813	−	0.898578i	$-0.355399\pi$
$692$	2.92973			0.111372
$693$	−3.05509	−	5.29157i	−0.116053	−	0.201010i
$694$	16.0397	−	27.7816i	0.608860	−	1.05458i
$695$	−20.2336			−0.767505
$696$	−8.84364	−	15.3176i	−0.335217	−	0.580614i
$697$	35.5988			1.34840
$698$	13.4131	+	23.2321i	0.507693	+	0.879349i
$699$	41.0232			1.55164
$700$	−7.74477			−0.292725
$701$	−19.0461	−	32.9888i	−0.719362	−	1.24597i	−0.961253	−	0.275667i	$-0.911101\pi$
$701$	−19.0461	−	32.9888i	−0.719362	−	1.24597i	0.241892	−	0.970303i	$-0.422232\pi$
$702$	0.243731	−	0.422155i	0.00919904	−	0.0159332i
$703$	−3.17319	−	5.49612i	−0.119679	−	0.207290i
$704$	−0.369866	−	0.640628i	−0.0139399	−	0.0241446i
$705$		0			0
$706$	7.92894	−	13.7333i	0.298409	−	0.516860i
$707$	−27.4955	+	47.6236i	−1.03407	+	1.79107i
$708$	31.1526			1.17079
$709$	12.0913			0.454100			0.227050	−	0.973883i	$-0.427092\pi$
$709$	12.0913			0.454100			0.227050	+	0.973883i	$0.427092\pi$
$710$	0.802150	−	1.38936i	0.0301041	−	0.0521419i
$711$	−12.5587	+	21.7523i	−0.470988	+	0.815776i
$712$	−1.65727	+	2.87047i	−0.0621087	+	0.107575i
$713$	−4.01990	−	6.96267i	−0.150546	−	0.260754i
$714$	−20.3762	−	35.2927i	−0.762561	−	1.32079i
$715$	−0.125761	+	0.217825i	−0.00470320	+	0.00814618i
$716$	−8.12411	−	14.0714i	−0.303612	−	0.525872i
$717$	45.9536			1.71617
$718$	11.8615			0.442669
$719$	−14.4294	−	24.9924i	−0.538125	−	0.932059i	−0.999005	−	0.0445970i	$-0.985800\pi$
$719$	−14.4294	−	24.9924i	−0.538125	−	0.932059i	0.460880	−	0.887462i	$-0.347534\pi$
$720$	−3.29329			−0.122734
$721$	−20.3430	−	35.2351i	−0.757612	−	1.31222i
$722$	−5.69282			−0.211865
$723$	24.2581	−	42.0163i	0.902169	−	1.56260i
$724$	−2.51062	−	4.34852i	−0.0933065	−	0.161612i
$725$	13.7040			0.508955
$726$	−11.4658	−	19.8593i	−0.425534	−	0.737047i
$727$	0.387073	+	0.670430i	0.0143557	+	0.0248649i	0.873114	−	0.487516i	$-0.162097\pi$
$727$	0.387073	+	0.670430i	0.0143557	+	0.0248649i	−0.858758	+	0.512381i	$0.828764\pi$
$728$	0.426402	+	0.738550i	0.0158035	+	0.0273725i
$729$	−3.07605			−0.113928
$730$	−13.3729			−0.494954
$731$	18.1745			0.672210
$732$	1.80760	+	3.13085i	0.0668107	+	0.115720i
$733$	15.7484	+	27.2770i	0.581679	+	1.00750i	0.995280	+	0.0970400i	$0.0309375\pi$
$733$	15.7484	+	27.2770i	0.581679	+	1.00750i	−0.413601	+	0.910458i	$0.635729\pi$
$734$	−10.4807	+	18.1531i	−0.386849	+	0.670042i
$735$	−27.4210	+	47.4945i	−1.01144	+	1.75186i
$736$	−0.810006			−0.0298572
$737$	−4.94918	+	8.57223i	−0.182305	+	0.315762i
$738$	7.91464	+	13.7086i	0.291342	+	0.504619i
$739$	−4.74219	+	8.21372i	−0.174444	+	0.302147i	−0.939969	−	0.341260i	$-0.889146\pi$
$739$	−4.74219	+	8.21372i	−0.174444	+	0.302147i	0.765524	+	0.643407i	$0.222480\pi$
$740$	3.16050			0.116182
$741$	0.748932	+	1.29719i	0.0275127	+	0.0476534i
$742$	24.3548	+	42.1838i	0.894094	+	1.54862i
$743$	9.17668	−	15.8945i	0.336660	−	0.583112i	−0.647142	−	0.762369i	$-0.724036\pi$
$743$	9.17668	−	15.8945i	0.336660	−	0.583112i	0.983802	+	0.179257i	$0.0573694\pi$
$744$	21.7750			0.798309
$745$	5.32102	+	9.21628i	0.194947	+	0.337659i
$746$	23.6208			0.864820
$747$	7.35740			0.269193
$748$	1.50792	+	2.61179i	0.0551349	+	0.0954965i
$749$	−6.90112	+	11.9531i	−0.252161	+	0.436756i
$750$	13.3507	−	23.1240i	0.487497	−	0.844369i
$751$	19.7074	−	34.1341i	0.719132	−	1.24557i	−0.242213	−	0.970223i	$-0.577873\pi$
$751$	19.7074	−	34.1341i	0.719132	−	1.24557i	0.961344	−	0.275349i	$-0.0887935\pi$
$752$		0			0
$753$	10.1253	−	17.5375i	0.368987	−	0.639104i
$754$	−0.754500	−	1.30683i	−0.0274773	−	0.0475921i
$755$	−16.2217			−0.590368
$756$	−5.93339	+	10.2769i	−0.215795	+	0.373768i
$757$	−7.20275	+	12.4755i	−0.261788	+	0.453431i	−0.966717	−	0.255847i	$-0.917646\pi$
$757$	−7.20275	+	12.4755i	−0.261788	+	0.453431i	0.704929	+	0.709278i	$0.250979\pi$
$758$	−4.12753	+	7.14909i	−0.149919	+	0.259667i
$759$	1.31451			0.0477136
$760$	−3.31349	+	5.73913i	−0.120193	+	0.208180i
$761$	10.8956			0.394966			0.197483	−	0.980306i	$-0.436723\pi$
$761$	10.8956			0.394966			0.197483	+	0.980306i	$0.436723\pi$
$762$	20.9246			0.758017
$763$	8.69802	+	46.7681i	0.314889	+	1.69312i
$764$	18.4219			0.666480
$765$	13.4265			0.485436
$766$	5.50001	−	9.52630i	0.198724	−	0.344199i
$767$	2.65780			0.0959676
$768$	1.09691	−	1.89990i	0.0395813	−	0.0685568i
$769$	11.9943	−	20.7748i	0.432526	−	0.749157i	−0.564564	−	0.825389i	$-0.690956\pi$
$769$	11.9943	−	20.7748i	0.432526	−	0.749157i	0.997090	+	0.0762324i	$0.0242891\pi$
$770$	3.06153	−	5.30272i	0.110330	−	0.191097i
$771$	39.3072			1.41561
$772$	9.25021	+	16.0218i	0.332922	+	0.576638i
$773$	−4.95699	+	8.58576i	−0.178290	+	0.308808i	−0.941295	−	0.337585i	$-0.890390\pi$
$773$	−4.95699	+	8.58576i	−0.178290	+	0.308808i	0.763005	+	0.646393i	$0.223723\pi$
$774$	4.04072	+	6.99873i	0.145241	+	0.251564i
$775$	−8.43559	+	14.6109i	−0.303015	+	0.524838i
$776$	−1.10547	+	1.91473i	−0.0396841	+	0.0687348i
$777$	−8.69508	+	15.0603i	−0.311934	+	0.540286i
$778$	8.79667	+	15.2363i	0.315376	+	0.546247i
$779$	31.8527			1.14124
$780$	−0.745936			−0.0267088
$781$	−0.326631	−	0.565742i	−0.0116878	−	0.0202438i
$782$	3.30233			0.118091
$783$	10.4989	−	18.1846i	0.375199	−	0.649864i
$784$	−6.88034	−	11.9171i	−0.245726	−	0.425611i
$785$	19.4919	+	33.7610i	0.695697	+	1.20498i
$786$	−0.344414			−0.0122848
$787$	0.722207	−	1.25090i	0.0257439	−	0.0445897i	−0.852866	−	0.522129i	$-0.825138\pi$
$787$	0.722207	−	1.25090i	0.0257439	−	0.0445897i	0.878610	+	0.477539i	$0.158471\pi$
$788$	−10.1147	−	17.5192i	−0.360321	−	0.624094i
$789$	−13.2558	+	22.9597i	−0.471919	+	0.817388i
$790$	−25.1704			−0.895522
$791$	17.8808	−	30.9705i	0.635769	−	1.10118i
$792$	−0.670506	+	1.16135i	−0.0238254	+	0.0412668i
$793$	0.154216	+	0.267110i	0.00547638	+	0.00948536i
$794$	5.74007	+	9.94209i	0.203707	+	0.352832i
$795$	−42.6057			−1.51107
$796$	23.1486			0.820482
$797$	−11.4030			−0.403916			−0.201958	−	0.979394i	$-0.564730\pi$
$797$	−11.4030			−0.403916			−0.201958	+	0.979394i	$0.564730\pi$
$798$	−18.2320	−	31.5787i	−0.645406	−	1.11788i
$799$		0			0
$800$	0.849881	+	1.47204i	0.0300478	+	0.0520444i
$801$	6.00870			0.212307
$802$	−2.03569	−	3.52593i	−0.0718829	−	0.124505i
$803$	−2.72269	+	4.71584i	−0.0960817	+	0.166418i
$804$	−29.3554			−1.03529
$805$	−3.35237	−	5.80647i	−0.118155	−	0.204651i
$806$	1.85774			0.0654363
$807$	2.96435	+	5.13441i	0.104350	+	0.180740i
$808$	12.0690			0.424585
$809$	5.14272			0.180809			0.0904043	−	0.995905i	$-0.471184\pi$
$809$	5.14272			0.180809			0.0904043	+	0.995905i	$0.471184\pi$
$810$	−10.1298	−	17.5453i	−0.355925	−	0.616480i
$811$	15.0837	−	26.1258i	0.529661	−	0.917401i	−0.469740	−	0.882805i	$-0.655652\pi$
$811$	15.0837	−	26.1258i	0.529661	−	0.917401i	0.999401	−	0.0345958i	$-0.0110144\pi$
$812$	18.3676	+	31.8136i	0.644575	+	1.11644i
$813$	−24.5318	−	42.4903i	−0.860368	−	1.49020i
$814$	0.643469	−	1.11452i	0.0225536	−	0.0390639i
$815$	−8.21099	+	14.2219i	−0.287618	+	0.498170i
$816$	−4.47201	+	7.74575i	−0.156552	+	0.271156i
$817$	16.2620			0.568935
$818$	3.60651			0.126099
$819$	0.772996	−	1.33887i	0.0270107	−	0.0467839i
$820$	−7.93133	+	13.7375i	−0.276974	+	0.479733i
$821$	24.1111	−	41.7617i	0.841484	−	1.45749i	−0.0471555	−	0.998888i	$-0.515016\pi$
$821$	24.1111	−	41.7617i	0.841484	−	1.45749i	0.888640	−	0.458606i	$-0.151651\pi$
$822$	−9.73214	−	16.8566i	−0.339448	−	0.587940i
$823$	14.6019	+	25.2913i	0.508991	+	0.881598i	0.999946	+	0.0104128i	$0.00331456\pi$
$823$	14.6019	+	25.2913i	0.508991	+	0.881598i	−0.490955	+	0.871185i	$0.663352\pi$
$824$	−4.46472	+	7.73312i	−0.155536	+	0.269396i
$825$	−1.37922	−	2.38888i	−0.0480183	−	0.0831701i
$826$	−64.7015			−2.25125
$827$	1.63983			0.0570226			0.0285113	−	0.999593i	$-0.490923\pi$
$827$	1.63983			0.0570226			0.0285113	+	0.999593i	$0.490923\pi$
$828$	0.734202	+	1.27168i	0.0255153	+	0.0441938i
$829$	−41.3360			−1.43566			−0.717829	−	0.696219i	$-0.754864\pi$
$829$	−41.3360			−1.43566			−0.717829	+	0.696219i	$0.754864\pi$
$830$	3.68646	+	6.38513i	0.127959	+	0.221631i
$831$	8.20359			0.284579
$832$	0.0935834	−	0.162091i	0.00324442	−	0.00561950i
$833$	28.0506	+	48.5851i	0.971896	+	1.68337i
$834$	−24.4344			−0.846093
$835$	18.7680	+	32.5072i	0.649495	+	1.12496i
$836$	1.34924	+	2.33695i	0.0466643	+	0.0808250i
$837$	12.9253	+	22.3872i	0.446762	+	0.773815i
$838$	−25.7552			−0.889697
$839$	−38.2977			−1.32218			−0.661091	−	0.750305i	$-0.729906\pi$
$839$	−38.2977			−1.32218			−0.661091	+	0.750305i	$0.729906\pi$
$840$	18.1591			0.626548
$841$	−18.0006	−	31.1780i	−0.620711	−	1.07510i
$842$	−0.209884	−	0.363530i	−0.00723308	−	0.0125281i
$843$	−19.8402	+	34.3643i	−0.683333	+	1.18357i
$844$	−9.85638	+	17.0718i	−0.339271	+	0.587634i
$845$	23.5529			0.810244
$846$		0			0
$847$	23.8135	+	41.2462i	0.818242	+	1.41724i
$848$	5.34520	−	9.25816i	0.183555	−	0.317927i
$849$	9.16601			0.314577
$850$	−3.46490	−	6.00138i	−0.118845	−	0.205846i
$851$	−0.704597	−	1.22040i	−0.0241533	−	0.0418347i
$852$	0.968686	−	1.67781i	0.0331866	−	0.0574810i
$853$	−22.6562			−0.775733			−0.387867	−	0.921716i	$-0.626788\pi$
$853$	−22.6562			−0.775733			−0.387867	+	0.921716i	$0.626788\pi$
$854$	−3.75424	−	6.50253i	−0.128467	−	0.222512i
$855$	12.0136			0.410857
$856$	3.02920			0.103536
$857$	−27.4589	−	47.5603i	−0.937979	−	1.62463i	−0.769233	−	0.638969i	$-0.779361\pi$
$857$	−27.4589	−	47.5603i	−0.937979	−	1.62463i	−0.168747	−	0.985659i	$-0.553972\pi$
$858$	−0.151871	+	0.263048i	−0.00518478	+	0.00898031i
$859$	−19.2703	+	33.3771i	−0.657493	+	1.13881i	0.323770	+	0.946136i	$0.395050\pi$
$859$	−19.2703	+	33.3771i	−0.657493	+	1.13881i	−0.981263	+	0.192675i	$0.938284\pi$
$860$	−4.04924	+	7.01349i	−0.138078	+	0.239158i
$861$	−43.6410	−	75.5884i	−1.48728	−	2.57605i
$862$	−8.80723	+	15.2546i	−0.299975	+	0.519572i
$863$	1.45489	+	2.51994i	0.0495250	+	0.0857798i	0.889725	−	0.456497i	$-0.150896\pi$
$863$	1.45489	+	2.51994i	0.0495250	+	0.0857798i	−0.840200	+	0.542276i	$0.817563\pi$
$864$	2.60443			0.0886044
$865$	2.66115	−	4.60925i	0.0904819	−	0.156719i
$866$	2.38588	−	4.13247i	0.0810756	−	0.140427i
$867$	−0.415399	+	0.719493i	−0.0141077	+	0.0244352i
$868$	−45.2249			−1.53503
$869$	−5.12463	+	8.87611i	−0.173841	+	0.301101i
$870$	−32.1317			−1.08937
$871$	−2.50448			−0.0848609
$872$	7.93466	−	6.78537i	0.268701	−	0.229782i
$873$	4.00807			0.135652
$874$	2.95482			0.0999483
$875$	−27.7283	+	48.0268i	−0.937387	+	1.62360i
$876$	−16.1493			−0.545635
$877$	−1.99276	+	3.45156i	−0.0672906	+	0.116551i	−0.897708	−	0.440591i	$-0.854769\pi$
$877$	−1.99276	+	3.45156i	−0.0672906	+	0.116551i	0.830417	+	0.557142i	$0.188102\pi$
$878$	−6.74066	+	11.6752i	−0.227486	+	0.394018i
$879$	−7.95204	+	13.7733i	−0.268216	+	0.464563i
$880$	−1.34384			−0.0453008
$881$	−22.2964	−	38.6185i	−0.751186	−	1.30109i	−0.947248	−	0.320500i	$-0.896149\pi$
$881$	−22.2964	−	38.6185i	−0.751186	−	1.30109i	0.196063	−	0.980591i	$-0.437184\pi$
$882$	−12.4729	+	21.6037i	−0.419985	+	0.727435i
$883$	−23.6273	−	40.9236i	−0.795120	−	1.37719i	−0.922763	−	0.385369i	$-0.874074\pi$
$883$	−23.6273	−	40.9236i	−0.795120	−	1.37719i	0.127642	−	0.991820i	$-0.459259\pi$
$884$	−0.381532	+	0.660833i	−0.0128323	+	0.0222262i
$885$	28.2968	−	49.0114i	0.951185	−	1.64750i
$886$	−5.77644	+	10.0051i	−0.194063	+	0.336128i
$887$	14.3803	+	24.9075i	0.482845	+	0.836311i	0.999806	−	0.0196974i	$-0.00627028\pi$
$887$	14.3803	+	24.9075i	0.482845	+	0.836311i	−0.516961	+	0.856009i	$0.672937\pi$
$888$	3.81666			0.128079
$889$	−43.4587			−1.45756
$890$	3.01068	+	5.21466i	0.100918	+	0.174796i
$891$	−8.24960			−0.276372
$892$	−6.26671	+	10.8543i	−0.209825	+	0.363427i
$893$		0			0
$894$	6.42574	+	11.1297i	0.214909	+	0.372233i
$895$	−29.5174			−0.986658
$896$	−2.27819	+	3.94595i	−0.0761091	+	0.131825i
$897$	0.166298	+	0.288037i	0.00555253	+	0.00961726i
$898$	−7.00968	+	12.1411i	−0.233916	+	0.405155i
$899$	80.0236			2.66894
$900$	1.54069	−	2.66856i	0.0513564	−	0.0889519i
$901$	−21.7920	+	37.7448i	−0.725996	+	1.25746i
$902$	3.22960	+	5.59383i	0.107534	+	0.186254i
$903$	−22.2804	−	38.5907i	−0.741444	−	1.28422i
$904$	−7.84869			−0.261043
$905$	−9.12186			−0.303221
$906$	−19.5895			−0.650819
$907$	−25.1864	−	43.6240i	−0.836299	−	1.44851i	−0.892968	−	0.450120i	$-0.851381\pi$
$907$	−25.1864	−	43.6240i	−0.836299	−	1.44851i	0.0566692	−	0.998393i	$-0.481952\pi$
$908$	−10.3730	−	17.9666i	−0.344242	−	0.596244i
$909$	−10.9395	−	18.9478i	−0.362841	−	0.628459i
$910$	1.54925			0.0513572
$911$	14.1757	+	24.5531i	0.469663	+	0.813479i	0.999398	−	0.0346833i	$-0.0110422\pi$
$911$	14.1757	+	24.5531i	0.469663	+	0.813479i	−0.529736	+	0.848163i	$0.677709\pi$
$912$	−4.00141	+	6.93065i	−0.132500	+	0.229497i
$913$	3.00221			0.0993588
$914$	17.1130	+	29.6405i	0.566046	+	0.980421i
$915$	6.56756			0.217117
$916$	−11.8310	−	20.4918i	−0.390906	−	0.677068i
$917$	0.715321			0.0236220
$918$	−10.6180			−0.350448
$919$	−1.57255	−	2.72374i	−0.0518737	−	0.0898479i	0.838923	−	0.544251i	$-0.183186\pi$
$919$	−1.57255	−	2.72374i	−0.0518737	−	0.0898479i	−0.890796	+	0.454403i	$0.849853\pi$
$920$	−0.735751	+	1.27436i	−0.0242570	+	0.0420143i
$921$	26.9258	+	46.6369i	0.887237	+	1.53674i
$922$	−1.73166	−	2.99932i	−0.0570291	−	0.0987772i
$923$	0.0826440	−	0.143144i	0.00272026	−	0.00471163i
$924$	3.69714	−	6.40364i	0.121627	−	0.210664i
$925$	−1.47857	+	2.56095i	−0.0486149	+	0.0842035i
$926$	−22.8231			−0.750015
$927$	16.1876			0.531670
$928$	4.03117	−	6.98219i	0.132330	−	0.229201i
$929$	0.652432	−	1.13005i	0.0214056	−	0.0370756i	−0.855124	−	0.518423i	$-0.826519\pi$
$929$	0.652432	−	1.13005i	0.0214056	−	0.0370756i	0.876530	+	0.481348i	$0.159853\pi$
$930$	19.7788	−	34.2579i	0.648573	−	1.12336i
$931$	25.0988	+	43.4724i	0.822580	+	1.42475i
$932$	9.34973	+	16.1942i	0.306261	+	0.530459i
$933$	19.7585	−	34.2227i	0.646864	−	1.12040i
$934$	−20.1124	−	34.8357i	−0.658098	−	1.13986i
$935$	5.47873			0.179174
$936$	−0.339302			−0.0110904
$937$	21.8111	+	37.7780i	0.712538	+	1.23415i	0.963901	+	0.266260i	$0.0857879\pi$
$937$	21.8111	+	37.7780i	0.712538	+	1.23415i	−0.251363	+	0.967893i	$0.580879\pi$
$938$	60.9690			1.99071
$939$	−1.45686	−	2.52336i	−0.0475429	−	0.0823468i
$940$		0			0
$941$	−3.74084	+	6.47933i	−0.121948	+	0.211220i	−0.920536	−	0.390658i	$-0.872247\pi$
$941$	−3.74084	+	6.47933i	−0.121948	+	0.211220i	0.798588	+	0.601878i	$0.205581\pi$
$942$	23.5387	+	40.7703i	0.766933	+	1.32837i
$943$	7.07280			0.230322
$944$	7.10009	+	12.2977i	0.231088	+	0.400256i
$945$	10.7789	+	18.6697i	0.350639	+	0.607324i
$946$	1.64883	+	2.85586i	0.0536081	+	0.0928519i
$947$	−25.3649			−0.824250			−0.412125	−	0.911127i	$-0.635213\pi$
$947$	−25.3649			−0.824250			−0.412125	+	0.911127i	$0.635213\pi$
$948$	−30.3961			−0.987219
$949$	−1.37779			−0.0447249
$950$	−3.10028	−	5.36984i	−0.100586	−	0.174221i
$951$	6.32933	+	10.9627i	0.205243	+	0.355491i
$952$	9.28802	−	16.0873i	0.301027	−	0.521393i
$953$	−0.415160	+	0.719078i	−0.0134484	+	0.0232932i	−0.872671	−	0.488308i	$-0.837614\pi$
$953$	−0.415160	+	0.719078i	−0.0134484	+	0.0232932i	0.859223	+	0.511601i	$0.170948\pi$
$954$	−19.3799			−0.627448
$955$	16.7331	−	28.9826i	0.541471	−	0.937855i
$956$	10.4734	+	18.1405i	0.338735	+	0.586706i
$957$	−6.54193	+	11.3310i	−0.211471	+	0.366278i
$958$	37.3552			1.20689
$959$	20.2129	+	35.0098i	0.652709	+	1.13053i
$960$	−1.99271	−	3.45147i	−0.0643143	−	0.111396i
$961$	−33.7589	+	58.4721i	−1.08900	+	1.88620i
$962$	0.325620			0.0104984
$963$	−2.74572	−	4.75573i	−0.0884796	−	0.153251i
$964$	22.1150			0.712276
$965$	33.6089			1.08191
$966$	−4.04836	−	7.01197i	−0.130254	−	0.225606i
$967$	17.4574	−	30.2371i	0.561392	−	0.972359i	−0.435984	−	0.899955i	$-0.643599\pi$
$967$	17.4574	−	30.2371i	0.561392	−	0.972359i	0.997375	−	0.0724044i	$-0.0230672\pi$
$968$	5.22640	−	9.05239i	0.167983	−	0.290955i
$969$	16.3135	−	28.2557i	0.524064	−	0.907705i
$970$	2.00826	+	3.47841i	0.0644813	+	0.111685i
$971$	13.6652	−	23.6688i	0.438537	−	0.759568i	−0.559040	−	0.829141i	$-0.688830\pi$
$971$	13.6652	−	23.6688i	0.438537	−	0.759568i	0.997577	+	0.0695728i	$0.0221636\pi$
$972$	−8.32623	−	14.4215i	−0.267064	−	0.462568i
$973$	50.7483			1.62692
$974$	4.42640	−	7.66675i	0.141831	−	0.245659i
$975$	0.348969	−	0.604432i	0.0111760	−	0.0193573i
$976$	−0.823951	+	1.42712i	−0.0263740	+	0.0456811i
$977$	27.3018			0.873461			0.436731	−	0.899592i	$-0.356136\pi$
$977$	27.3018			0.873461			0.436731	+	0.899592i	$0.356136\pi$
$978$	−9.91570	+	17.1745i	−0.317069	+	0.549180i
$979$	2.45187			0.0783621
$980$	−24.9984			−0.798545
$981$	−17.8449	−	6.30672i	−0.569742	−	0.201358i
$982$	−4.42687			−0.141267
$983$	−44.4347			−1.41725			−0.708623	−	0.705587i	$-0.750683\pi$
$983$	−44.4347			−1.41725			−0.708623	+	0.705587i	$0.750683\pi$
$984$	−9.57798	+	16.5895i	−0.305335	+	0.528855i
$985$	−36.7498			−1.17095
$986$	−16.4348	+	28.4658i	−0.523389	+	0.906537i
$987$		0			0
$988$	−0.341383	+	0.591293i	−0.0108608	+	0.0188115i
$989$	3.61093			0.114821
$990$	1.21808	+	2.10977i	0.0387131	+	0.0670530i
$991$	−11.0807	+	19.1923i	−0.351989	+	0.609663i	−0.986598	−	0.163171i	$-0.947828\pi$
$991$	−11.0807	+	19.1923i	−0.351989	+	0.609663i	0.634609	+	0.772833i	$0.281161\pi$
$992$	4.96281	+	8.59583i	0.157569	+	0.272918i
$993$	36.4029	−	63.0517i	1.15521	−	2.00089i
$994$	−2.01189	+	3.48469i	−0.0638132	+	0.110528i
$995$	21.0265	−	36.4191i	0.666586	−	1.15456i
$996$	4.45182	+	7.71077i	0.141061	+	0.244325i
$997$	12.2002			0.386386			0.193193	−	0.981161i	$-0.438116\pi$
$997$	12.2002			0.386386			0.193193	+	0.981161i	$0.438116\pi$
$998$	−10.5737			−0.334705
$999$	2.26550	+	3.92397i	0.0716774	+	0.124149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	218.2.c.c.45.4	✓	10
3.2	odd	2		1962.2.f.k.1135.1		10
109.63	even	3	inner	218.2.c.c.63.4	yes	10
327.281	odd	6		1962.2.f.k.1153.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
218.2.c.c.45.4	✓	10	1.1	even	1	trivial
218.2.c.c.63.4	yes	10	109.63	even	3	inner
1962.2.f.k.1135.1		10	3.2	odd	2
1962.2.f.k.1153.1		10	327.281	odd	6

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:	\( N \)	\(=\)	\( 218 = 2 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	218.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.09691 - 1.89990i) q^{3} +1.00000 q^{4} +(0.908328 - 1.57327i) q^{5} +(1.09691 - 1.89990i) q^{6} +(-2.27819 + 3.94595i) q^{7} +1.00000 q^{8} +(-0.906417 - 1.56996i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.09691 - 1.89990i) q^{3} +1.00000 q^{4} +(0.908328 - 1.57327i) q^{5} +(1.09691 - 1.89990i) q^{6} +(-2.27819 + 3.94595i) q^{7} +1.00000 q^{8} +(-0.906417 - 1.56996i) q^{9} +(0.908328 - 1.57327i) q^{10} +(-0.369866 - 0.640628i) q^{11} +(1.09691 - 1.89990i) q^{12} +(0.0935834 - 0.162091i) q^{13} +(-2.27819 + 3.94595i) q^{14} +(-1.99271 - 3.45147i) q^{15} +1.00000 q^{16} -4.07692 q^{17} +(-0.906417 - 1.56996i) q^{18} -3.64790 q^{19} +(0.908328 - 1.57327i) q^{20} +(4.99794 + 8.65669i) q^{21} +(-0.369866 - 0.640628i) q^{22} -0.810006 q^{23} +(1.09691 - 1.89990i) q^{24} +(0.849881 + 1.47204i) q^{25} +(0.0935834 - 0.162091i) q^{26} +2.60443 q^{27} +(-2.27819 + 3.94595i) q^{28} +(4.03117 - 6.98219i) q^{29} +(-1.99271 - 3.45147i) q^{30} +(4.96281 + 8.59583i) q^{31} +1.00000 q^{32} -1.62284 q^{33} -4.07692 q^{34} +(4.13870 + 7.16843i) q^{35} +(-0.906417 - 1.56996i) q^{36} +(0.869866 + 1.50665i) q^{37} -3.64790 q^{38} +(-0.205305 - 0.355598i) q^{39} +(0.908328 - 1.57327i) q^{40} -8.73179 q^{41} +(4.99794 + 8.65669i) q^{42} -4.45791 q^{43} +(-0.369866 - 0.640628i) q^{44} -3.29329 q^{45} -0.810006 q^{46} +(1.09691 - 1.89990i) q^{48} +(-6.88034 - 11.9171i) q^{49} +(0.849881 + 1.47204i) q^{50} +(-4.47201 + 7.74575i) q^{51} +(0.0935834 - 0.162091i) q^{52} +(5.34520 - 9.25816i) q^{53} +2.60443 q^{54} -1.34384 q^{55} +(-2.27819 + 3.94595i) q^{56} +(-4.00141 + 6.93065i) q^{57} +(4.03117 - 6.98219i) q^{58} +(7.10009 + 12.2977i) q^{59} +(-1.99271 - 3.45147i) q^{60} +(-0.823951 + 1.42712i) q^{61} +(4.96281 + 8.59583i) q^{62} +8.25997 q^{63} +1.00000 q^{64} +(-0.170009 - 0.294464i) q^{65} -1.62284 q^{66} +(-6.69049 - 11.5883i) q^{67} -4.07692 q^{68} +(-0.888502 + 1.53893i) q^{69} +(4.13870 + 7.16843i) q^{70} +0.883106 q^{71} +(-0.906417 - 1.56996i) q^{72} +(-3.68064 - 6.37506i) q^{73} +(0.869866 + 1.50665i) q^{74} +3.72897 q^{75} -3.64790 q^{76} +3.37051 q^{77} +(-0.205305 - 0.355598i) q^{78} +(-6.92767 - 11.9991i) q^{79} +(0.908328 - 1.57327i) q^{80} +(5.57607 - 9.65803i) q^{81} -8.73179 q^{82} +(-2.02926 + 3.51477i) q^{83} +(4.99794 + 8.65669i) q^{84} +(-3.70318 + 6.41410i) q^{85} -4.45791 q^{86} +(-8.84364 - 15.3176i) q^{87} +(-0.369866 - 0.640628i) q^{88} +(-1.65727 + 2.87047i) q^{89} -3.29329 q^{90} +(0.426402 + 0.738550i) q^{91} -0.810006 q^{92} +21.7750 q^{93} +(-3.31349 + 5.73913i) q^{95} +(1.09691 - 1.89990i) q^{96} +(-1.10547 + 1.91473i) q^{97} +(-6.88034 - 11.9171i) q^{98} +(-0.670506 + 1.16135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9} - 8 q^{10} + q^{11} + q^{12} - q^{14} - q^{15} + 10 q^{16} - 16 q^{17} - 10 q^{18} - 6 q^{19} - 8 q^{20} + 4 q^{21} + q^{22} + 8 q^{23} + q^{24} - 11 q^{25} + 10 q^{27} - q^{28} + 9 q^{29} - q^{30} + 7 q^{31} + 10 q^{32} - 2 q^{33} - 16 q^{34} + 10 q^{35} - 10 q^{36} + 4 q^{37} - 6 q^{38} - 4 q^{39} - 8 q^{40} - 22 q^{41} + 4 q^{42} + 2 q^{43} + q^{44} + 38 q^{45} + 8 q^{46} + q^{48} - 10 q^{49} - 11 q^{50} - 3 q^{51} - 2 q^{53} + 10 q^{54} + 20 q^{55} - q^{56} - 49 q^{57} + 9 q^{58} - 12 q^{59} - q^{60} + 7 q^{61} + 7 q^{62} - 36 q^{63} + 10 q^{64} - 3 q^{65} - 2 q^{66} - 56 q^{67} - 16 q^{68} + 19 q^{69} + 10 q^{70} + 4 q^{71} - 10 q^{72} + 12 q^{73} + 4 q^{74} - 46 q^{75} - 6 q^{76} + 66 q^{77} - 4 q^{78} - 30 q^{79} - 8 q^{80} - 41 q^{81} - 22 q^{82} - 7 q^{83} + 4 q^{84} - 22 q^{85} + 2 q^{86} + 40 q^{87} + q^{88} + 9 q^{89} + 38 q^{90} + 20 q^{91} + 8 q^{92} + 10 q^{93} - 12 q^{95} + q^{96} + 35 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9 - 8 * q^10 + q^11 + q^12 - q^14 - q^15 + 10 * q^16 - 16 * q^17 - 10 * q^18 - 6 * q^19 - 8 * q^20 + 4 * q^21 + q^22 + 8 * q^23 + q^24 - 11 * q^25 + 10 * q^27 - q^28 + 9 * q^29 - q^30 + 7 * q^31 + 10 * q^32 - 2 * q^33 - 16 * q^34 + 10 * q^35 - 10 * q^36 + 4 * q^37 - 6 * q^38 - 4 * q^39 - 8 * q^40 - 22 * q^41 + 4 * q^42 + 2 * q^43 + q^44 + 38 * q^45 + 8 * q^46 + q^48 - 10 * q^49 - 11 * q^50 - 3 * q^51 - 2 * q^53 + 10 * q^54 + 20 * q^55 - q^56 - 49 * q^57 + 9 * q^58 - 12 * q^59 - q^60 + 7 * q^61 + 7 * q^62 - 36 * q^63 + 10 * q^64 - 3 * q^65 - 2 * q^66 - 56 * q^67 - 16 * q^68 + 19 * q^69 + 10 * q^70 + 4 * q^71 - 10 * q^72 + 12 * q^73 + 4 * q^74 - 46 * q^75 - 6 * q^76 + 66 * q^77 - 4 * q^78 - 30 * q^79 - 8 * q^80 - 41 * q^81 - 22 * q^82 - 7 * q^83 + 4 * q^84 - 22 * q^85 + 2 * q^86 + 40 * q^87 + q^88 + 9 * q^89 + 38 * q^90 + 20 * q^91 + 8 * q^92 + 10 * q^93 - 12 * q^95 + q^96 + 35 * q^97 - 10 * q^98 + 19 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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