LMFDB - Embedded newform 770.2.m.e.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 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("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (of order $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 32x^{14} + 404x^{12} + 2600x^{10} + 9170x^{8} + 17648x^{6} + 17180x^{4} + 6904x^{2} + 529 $ x^16 + 32x^14 + 404x^12 + 2600x^10 + 9170x^8 + 17648x^6 + 17180x^4 + 6904*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$-3.26007i$ of defining polynomial
Character	$\chi$	$=$	770.43
Dual form			770.2.m.e.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.668611 - 0.668611i) q^{3} +1.00000i q^{4} +(-2.17741 + 0.508801i) q^{5} +0.945559i q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.10592i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.668611 - 0.668611i) q^{3} +1.00000i q^{4} +(-2.17741 + 0.508801i) q^{5} +0.945559i q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.10592i q^{9} +(1.89944 + 1.17989i) q^{10} +(2.68621 - 1.94532i) q^{11} +(0.668611 - 0.668611i) q^{12} +(-1.94532 + 1.94532i) q^{13} -1.00000i q^{14} +(1.79603 + 1.11565i) q^{15} -1.00000 q^{16} +(-3.61043 - 3.61043i) q^{17} +(-1.48911 + 1.48911i) q^{18} -3.79888 q^{19} +(-0.508801 - 2.17741i) q^{20} -0.945559i q^{21} +(-3.27499 - 0.523891i) q^{22} +(6.28411 + 6.28411i) q^{23} -0.945559 q^{24} +(4.48224 - 2.21574i) q^{25} +2.75110 q^{26} +(-3.41387 + 3.41387i) q^{27} +(-0.707107 + 0.707107i) q^{28} -4.14263 q^{29} +(-0.481101 - 2.05887i) q^{30} -5.10592 q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.09669 - 0.495370i) q^{33} +5.10592i q^{34} +(-1.89944 - 1.17989i) q^{35} +2.10592 q^{36} +(-6.35482 + 6.35482i) q^{37} +(2.68621 + 2.68621i) q^{38} +2.60132 q^{39} +(-1.17989 + 1.89944i) q^{40} +5.80665i q^{41} +(-0.668611 + 0.668611i) q^{42} +(-8.15817 + 8.15817i) q^{43} +(1.94532 + 2.68621i) q^{44} +(1.07149 + 4.58545i) q^{45} -8.88707i q^{46} +(-0.337222 + 0.337222i) q^{47} +(0.668611 + 0.668611i) q^{48} +1.00000i q^{49} +(-4.73619 - 1.60266i) q^{50} +4.82795i q^{51} +(-1.94532 - 1.94532i) q^{52} +(5.85701 + 5.85701i) q^{53} +4.82795 q^{54} +(-4.85921 + 5.60251i) q^{55} +1.00000 q^{56} +(2.53997 + 2.53997i) q^{57} +(2.92928 + 2.92928i) q^{58} -13.4843i q^{59} +(-1.11565 + 1.79603i) q^{60} -0.995343i q^{61} +(3.61043 + 3.61043i) q^{62} +(1.48911 - 1.48911i) q^{63} -1.00000i q^{64} +(3.24598 - 5.22554i) q^{65} +(1.83941 + 2.53997i) q^{66} +(-2.69798 + 2.69798i) q^{67} +(3.61043 - 3.61043i) q^{68} -8.40325i q^{69} +(0.508801 + 2.17741i) q^{70} +4.97615 q^{71} +(-1.48911 - 1.48911i) q^{72} +(3.48553 - 3.48553i) q^{73} +8.98708 q^{74} +(-4.47834 - 1.51541i) q^{75} -3.79888i q^{76} +(3.27499 + 0.523891i) q^{77} +(-1.83941 - 1.83941i) q^{78} -8.68486 q^{79} +(2.17741 - 0.508801i) q^{80} -1.75265 q^{81} +(4.10592 - 4.10592i) q^{82} +(-8.86108 + 8.86108i) q^{83} +0.945559 q^{84} +(9.69838 + 6.02440i) q^{85} +11.5374 q^{86} +(2.76981 + 2.76981i) q^{87} +(0.523891 - 3.27499i) q^{88} +6.56822i q^{89} +(2.48474 - 4.00006i) q^{90} -2.75110 q^{91} +(-6.28411 + 6.28411i) q^{92} +(3.41387 + 3.41387i) q^{93} +0.476904 q^{94} +(8.27172 - 1.93287i) q^{95} -0.945559i q^{96} +(-5.10592 + 5.10592i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-4.09668 - 5.65695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 8 q^{5}+O(q^{10}) $ 16 * q - 8 * q^3 - 8 * q^5	$ 16 q - 8 q^{3} - 8 q^{5} - 8 q^{11} + 8 q^{12} + 24 q^{15} - 16 q^{16} + 16 q^{20} - 8 q^{22} + 32 q^{23} + 16 q^{25} + 16 q^{26} - 32 q^{27} - 24 q^{33} - 48 q^{36} - 48 q^{37} - 8 q^{38} - 8 q^{42} + 72 q^{45} + 8 q^{48} - 16 q^{53} - 48 q^{55} + 16 q^{56} + 32 q^{58} - 56 q^{60} - 32 q^{66} + 48 q^{67} - 16 q^{70} - 48 q^{71} + 112 q^{75} + 8 q^{77} + 32 q^{78} + 8 q^{80} - 80 q^{81} - 16 q^{82} + 32 q^{86} - 8 q^{88} - 16 q^{91} - 32 q^{92} + 32 q^{93}+O(q^{100}) $ 16 * q - 8 * q^3 - 8 * q^5 - 8 * q^11 + 8 * q^12 + 24 * q^15 - 16 * q^16 + 16 * q^20 - 8 * q^22 + 32 * q^23 + 16 * q^25 + 16 * q^26 - 32 * q^27 - 24 * q^33 - 48 * q^36 - 48 * q^37 - 8 * q^38 - 8 * q^42 + 72 * q^45 + 8 * q^48 - 16 * q^53 - 48 * q^55 + 16 * q^56 + 32 * q^58 - 56 * q^60 - 32 * q^66 + 48 * q^67 - 16 * q^70 - 48 * q^71 + 112 * q^75 + 8 * q^77 + 32 * q^78 + 8 * q^80 - 80 * q^81 - 16 * q^82 + 32 * q^86 - 8 * q^88 - 16 * q^91 - 32 * q^92 + 32 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.668611	−	0.668611i	−0.386023	−	0.386023i	0.487243	−	0.873266i	$-0.338002\pi$
$3$	−0.668611	−	0.668611i	−0.386023	−	0.386023i	−0.873266	+	0.487243i	$0.838002\pi$
$4$			1.00000i			0.500000i
$5$	−2.17741	+	0.508801i	−0.973768	+	0.227543i
$5$	−2.17741	+	0.508801i	−0.973768	+	0.227543i
$6$			0.945559i			0.386023i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	2.10592i		−	0.701973i
$10$	1.89944	+	1.17989i	0.600655	+	0.373113i
$11$	2.68621	−	1.94532i	0.809924	−	0.586535i
$11$	2.68621	−	1.94532i	0.809924	−	0.586535i
$12$	0.668611	−	0.668611i	0.193011	−	0.193011i
$13$	−1.94532	+	1.94532i	−0.539534	+	0.539534i	−0.923392	−	0.383858i	$-0.874595\pi$
$13$	−1.94532	+	1.94532i	−0.539534	+	0.539534i	0.383858	+	0.923392i	$0.374595\pi$
$14$		−	1.00000i		−	0.267261i
$15$	1.79603	+	1.11565i	0.463733	+	0.288060i
$16$	−1.00000			−0.250000
$17$	−3.61043	−	3.61043i	−0.875658	−	0.875658i	0.117424	−	0.993082i	$-0.462536\pi$
$17$	−3.61043	−	3.61043i	−0.875658	−	0.875658i	−0.993082	+	0.117424i	$0.962536\pi$
$18$	−1.48911	+	1.48911i	−0.350986	+	0.350986i
$19$	−3.79888			−0.871522			−0.435761	−	0.900062i	$-0.643521\pi$
$19$	−3.79888			−0.871522			−0.435761	+	0.900062i	$0.643521\pi$
$20$	−0.508801	−	2.17741i	−0.113771	−	0.486884i
$21$		−	0.945559i		−	0.206338i
$22$	−3.27499	−	0.523891i	−0.698230	−	0.111694i
$23$	6.28411	+	6.28411i	1.31033	+	1.31033i	0.921172	+	0.389155i	$0.127233\pi$
$23$	6.28411	+	6.28411i	1.31033	+	1.31033i	0.389155	+	0.921172i	$0.372767\pi$
$24$	−0.945559			−0.193011
$25$	4.48224	−	2.21574i	0.896449	−	0.443147i
$26$	2.75110			0.539534
$27$	−3.41387	+	3.41387i	−0.657000	+	0.657000i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−4.14263			−0.769268			−0.384634	−	0.923069i	$-0.625672\pi$
$29$	−4.14263			−0.769268			−0.384634	+	0.923069i	$0.625672\pi$
$30$	−0.481101	−	2.05887i	−0.0878366	−	0.375897i
$31$	−5.10592			−0.917050			−0.458525	−	0.888681i	$-0.651622\pi$
$31$	−5.10592			−0.917050			−0.458525	+	0.888681i	$0.651622\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−3.09669	−	0.495370i	−0.539065	−	0.0862329i
$34$			5.10592i			0.875658i
$35$	−1.89944	−	1.17989i	−0.321064	−	0.199437i
$36$	2.10592			0.350986
$37$	−6.35482	+	6.35482i	−1.04473	+	1.04473i	−0.0457748	+	0.998952i	$0.514576\pi$
$37$	−6.35482	+	6.35482i	−1.04473	+	1.04473i	−0.998952	+	0.0457748i	$0.985424\pi$
$38$	2.68621	+	2.68621i	0.435761	+	0.435761i
$39$	2.60132			0.416545
$40$	−1.17989	+	1.89944i	−0.186556	+	0.300328i
$41$			5.80665i			0.906846i	0.891296	+	0.453423i	$0.149797\pi$
$41$			5.80665i			0.906846i	−0.891296	+	0.453423i	$0.850203\pi$
$42$	−0.668611	+	0.668611i	−0.103169	+	0.103169i
$43$	−8.15817	+	8.15817i	−1.24411	+	1.24411i	−0.285828	+	0.958281i	$0.592269\pi$
$43$	−8.15817	+	8.15817i	−1.24411	+	1.24411i	−0.958281	+	0.285828i	$0.907731\pi$
$44$	1.94532	+	2.68621i	0.293268	+	0.404962i
$45$	1.07149	+	4.58545i	0.159729	+	0.683559i
$46$		−	8.88707i		−	1.31033i
$47$	−0.337222	+	0.337222i	−0.0491889	+	0.0491889i	−0.731273	−	0.682084i	$-0.761074\pi$
$47$	−0.337222	+	0.337222i	−0.0491889	+	0.0491889i	0.682084	+	0.731273i	$0.261074\pi$
$48$	0.668611	+	0.668611i	0.0965057	+	0.0965057i
$49$			1.00000i			0.142857i
$50$	−4.73619	−	1.60266i	−0.669798	−	0.226651i
$51$			4.82795i			0.676048i
$52$	−1.94532	−	1.94532i	−0.269767	−	0.269767i
$53$	5.85701	+	5.85701i	0.804523	+	0.804523i	0.983799	−	0.179276i	$-0.0573755\pi$
$53$	5.85701	+	5.85701i	0.804523	+	0.804523i	−0.179276	+	0.983799i	$0.557376\pi$
$54$	4.82795			0.657000
$55$	−4.85921	+	5.60251i	−0.655216	+	0.755442i
$56$	1.00000			0.133631
$57$	2.53997	+	2.53997i	0.336427	+	0.336427i
$58$	2.92928	+	2.92928i	0.384634	+	0.384634i
$59$		−	13.4843i		−	1.75550i	−0.479116	−	0.877752i	$-0.659043\pi$
$59$		−	13.4843i		−	1.75550i	0.479116	−	0.877752i	$-0.340957\pi$
$60$	−1.11565	+	1.79603i	−0.144030	+	0.231867i
$61$		−	0.995343i		−	0.127441i	−0.997968	−	0.0637203i	$-0.979703\pi$
$61$		−	0.995343i		−	0.127441i	0.997968	−	0.0637203i	$-0.0202966\pi$
$62$	3.61043	+	3.61043i	0.458525	+	0.458525i
$63$	1.48911	−	1.48911i	0.187610	−	0.187610i
$64$		−	1.00000i		−	0.125000i
$65$	3.24598	−	5.22554i	0.402614	−	0.648148i
$66$	1.83941	+	2.53997i	0.226416	+	0.312649i
$67$	−2.69798	+	2.69798i	−0.329611	+	0.329611i	−0.852438	−	0.522828i	$-0.824877\pi$
$67$	−2.69798	+	2.69798i	−0.329611	+	0.329611i	0.522828	+	0.852438i	$0.324877\pi$
$68$	3.61043	−	3.61043i	0.437829	−	0.437829i
$69$		−	8.40325i		−	1.01163i
$70$	0.508801	+	2.17741i	0.0608133	+	0.260250i
$71$	4.97615			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$71$	4.97615			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$72$	−1.48911	−	1.48911i	−0.175493	−	0.175493i
$73$	3.48553	−	3.48553i	0.407950	−	0.407950i	−0.473073	−	0.881023i	$-0.656855\pi$
$73$	3.48553	−	3.48553i	0.407950	−	0.407950i	0.881023	+	0.473073i	$0.156855\pi$
$74$	8.98708			1.04473
$75$	−4.47834	−	1.51541i	−0.517115	−	0.174985i
$76$		−	3.79888i		−	0.435761i
$77$	3.27499	+	0.523891i	0.373219	+	0.0597030i
$78$	−1.83941	−	1.83941i	−0.208272	−	0.208272i
$79$	−8.68486			−0.977123			−0.488561	−	0.872530i	$-0.662478\pi$
$79$	−8.68486			−0.977123			−0.488561	+	0.872530i	$0.662478\pi$
$80$	2.17741	−	0.508801i	0.243442	−	0.0568857i
$81$	−1.75265			−0.194739
$82$	4.10592	−	4.10592i	0.453423	−	0.453423i
$83$	−8.86108	+	8.86108i	−0.972630	+	0.972630i	−0.999635	−	0.0270055i	$-0.991403\pi$
$83$	−8.86108	+	8.86108i	−0.972630	+	0.972630i	0.0270055	+	0.999635i	$0.491403\pi$
$84$	0.945559			0.103169
$85$	9.69838	+	6.02440i	1.05194	+	0.653438i
$86$	11.5374			1.24411
$87$	2.76981	+	2.76981i	0.296955	+	0.296955i
$88$	0.523891	−	3.27499i	0.0558470	−	0.349115i
$89$			6.56822i			0.696229i	0.937452	+	0.348115i	$0.113178\pi$
$89$			6.56822i			0.696229i	−0.937452	+	0.348115i	$0.886822\pi$
$90$	2.48474	−	4.00006i	0.261915	−	0.421644i
$91$	−2.75110			−0.288393
$92$	−6.28411	+	6.28411i	−0.655164	+	0.655164i
$93$	3.41387	+	3.41387i	0.354002	+	0.354002i
$94$	0.476904			0.0491889
$95$	8.27172	−	1.93287i	0.848661	−	0.198308i
$96$		−	0.945559i		−	0.0965057i
$97$	−5.10592	+	5.10592i	−0.518427	+	0.518427i	−0.917095	−	0.398668i	$-0.869473\pi$
$97$	−5.10592	+	5.10592i	−0.518427	+	0.518427i	0.398668	+	0.917095i	$0.369473\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	−4.09668	−	5.65695i	−0.411732	−	0.568544i
$100$	2.21574	+	4.48224i	0.221574	+	0.448224i
$101$			16.0748i			1.59950i	0.600332	+	0.799751i	$0.295035\pi$
$101$			16.0748i			1.59950i	−0.600332	+	0.799751i	$0.704965\pi$
$102$	3.41387	−	3.41387i	0.338024	−	0.338024i
$103$	2.37242	+	2.37242i	0.233762	+	0.233762i	0.814261	−	0.580499i	$-0.197142\pi$
$103$	2.37242	+	2.37242i	0.233762	+	0.233762i	−0.580499	+	0.814261i	$0.697142\pi$
$104$			2.75110i			0.269767i
$105$	0.481101	+	2.05887i	0.0469506	+	0.200925i
$106$		−	8.28307i		−	0.804523i
$107$	−0.568662	−	0.568662i	−0.0549746	−	0.0549746i	0.679085	−	0.734060i	$-0.262377\pi$
$107$	−0.568662	−	0.568662i	−0.0549746	−	0.0549746i	−0.734060	+	0.679085i	$0.762377\pi$
$108$	−3.41387	−	3.41387i	−0.328500	−	0.328500i
$109$	−4.82795			−0.462433			−0.231217	−	0.972902i	$-0.574271\pi$
$109$	−4.82795			−0.462433			−0.231217	+	0.972902i	$0.574271\pi$
$110$	7.39755	−	0.525588i	0.705329	−	0.0501129i
$111$	8.49781			0.806576
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−10.4783	−	10.4783i	−0.985720	−	0.985720i	0.0141798	−	0.999899i	$-0.495486\pi$
$113$	−10.4783	−	10.4783i	−0.985720	−	0.985720i	−0.999899	+	0.0141798i	$0.995486\pi$
$114$		−	3.59206i		−	0.336427i
$115$	−16.8804	−	10.4857i	−1.57411	−	0.977799i
$116$		−	4.14263i		−	0.384634i
$117$	4.09668	+	4.09668i	0.378738	+	0.378738i
$118$	−9.53483	+	9.53483i	−0.877752	+	0.877752i
$119$		−	5.10592i		−	0.468059i
$120$	2.05887	−	0.481101i	0.187948	−	0.0439183i
$121$	3.43147	−	10.4511i	0.311952	−	0.950098i
$122$	−0.703814	+	0.703814i	−0.0637203	+	0.0637203i
$123$	3.88239	−	3.88239i	0.350063	−	0.350063i
$124$		−	5.10592i		−	0.458525i
$125$	−8.63232	+	7.10514i	−0.772098	+	0.635503i
$126$	−2.10592			−0.187610
$127$	−11.6188	−	11.6188i	−1.03100	−	1.03100i	−0.999504	−	0.0314986i	$-0.989972\pi$
$127$	−11.6188	−	11.6188i	−1.03100	−	1.03100i	−0.0314986	−	0.999504i	$-0.510028\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	10.9093			0.960509
$130$	−5.99027	+	1.39976i	−0.525381	+	0.122767i
$131$		−	15.1126i		−	1.32039i	−0.751093	−	0.660196i	$-0.770473\pi$
$131$		−	15.1126i		−	1.32039i	0.751093	−	0.660196i	$-0.229527\pi$
$132$	0.495370	−	3.09669i	0.0431164	−	0.269532i
$133$	−2.68621	−	2.68621i	−0.232924	−	0.232924i
$134$	3.81552			0.329611
$135$	5.69643	−	9.17039i	0.490270	−	0.789261i
$136$	−5.10592			−0.437829
$137$	−2.60373	+	2.60373i	−0.222452	+	0.222452i	−0.809530	−	0.587078i	$-0.800278\pi$
$137$	−2.60373	+	2.60373i	−0.222452	+	0.222452i	0.587078	+	0.809530i	$0.300278\pi$
$138$	−5.94199	+	5.94199i	−0.505816	+	0.505816i
$139$	15.4144			1.30743			0.653715	−	0.756741i	$-0.273210\pi$
$139$	15.4144			1.30743			0.653715	+	0.756741i	$0.273210\pi$
$140$	1.17989	−	1.89944i	0.0997186	−	0.160532i
$141$	0.450941			0.0379760
$142$	−3.51867	−	3.51867i	−0.295280	−	0.295280i
$143$	−1.44128	+	9.00980i	−0.120525	+	0.753437i
$144$			2.10592i			0.175493i
$145$	9.02022	−	2.10778i	0.749088	−	0.175041i
$146$	−4.92928			−0.407950
$147$	0.668611	−	0.668611i	0.0551461	−	0.0551461i
$148$	−6.35482	−	6.35482i	−0.522363	−	0.522363i
$149$	3.64084			0.298269			0.149135	−	0.988817i	$-0.452351\pi$
$149$	3.64084			0.298269			0.149135	+	0.988817i	$0.452351\pi$
$150$	2.09511	+	4.23822i	0.171065	+	0.346050i
$151$		−	0.183516i		−	0.0149343i	−0.999972	−	0.00746717i	$-0.997623\pi$
$151$		−	0.183516i		−	0.0149343i	0.999972	−	0.00746717i	$-0.00237690\pi$
$152$	−2.68621	+	2.68621i	−0.217881	+	0.217881i
$153$	−7.60327	+	7.60327i	−0.614688	+	0.614688i
$154$	−1.94532	−	2.68621i	−0.156758	−	0.216461i
$155$	11.1177	−	2.59790i	0.892994	−	0.208668i
$156$			2.60132i			0.208272i
$157$	−7.02937	+	7.02937i	−0.561005	+	0.561005i	−0.929593	−	0.368588i	$-0.879841\pi$
$157$	−7.02937	+	7.02937i	−0.561005	+	0.561005i	0.368588	+	0.929593i	$0.379841\pi$
$158$	6.14112	+	6.14112i	0.488561	+	0.488561i
$159$		−	7.83213i		−	0.621128i
$160$	−1.89944	−	1.17989i	−0.150164	−	0.0932782i
$161$			8.88707i			0.700399i
$162$	1.23931	+	1.23931i	0.0973694	+	0.0973694i
$163$	−5.14737	−	5.14737i	−0.403173	−	0.403173i	0.476177	−	0.879350i	$-0.342022\pi$
$163$	−5.14737	−	5.14737i	−0.403173	−	0.403173i	−0.879350	+	0.476177i	$0.842022\pi$
$164$	−5.80665			−0.453423
$165$	6.99482	−	0.496975i	0.544546	−	0.0386894i
$166$	12.5315			0.972630
$167$	−8.05816	−	8.05816i	−0.623559	−	0.623559i	0.322880	−	0.946440i	$-0.395349\pi$
$167$	−8.05816	−	8.05816i	−0.623559	−	0.623559i	−0.946440	+	0.322880i	$0.895349\pi$
$168$	−0.668611	−	0.668611i	−0.0515845	−	0.0515845i
$169$			5.43147i			0.417806i
$170$	−2.59790	−	11.1177i	−0.199249	−	0.852688i
$171$			8.00013i			0.611785i
$172$	−8.15817	−	8.15817i	−0.622055	−	0.622055i
$173$	14.5064	−	14.5064i	1.10290	−	1.10290i	0.108839	−	0.994059i	$-0.465287\pi$
$173$	14.5064	−	14.5064i	1.10290	−	1.10290i	0.994059	−	0.108839i	$-0.0347134\pi$
$174$		−	3.91710i		−	0.296955i
$175$	4.73619	+	1.60266i	0.358022	+	0.121150i
$176$	−2.68621	+	1.94532i	−0.202481	+	0.146634i
$177$	−9.01574	+	9.01574i	−0.677664	+	0.677664i
$178$	4.64443	−	4.64443i	0.348115	−	0.348115i
$179$		−	18.3885i		−	1.37442i	−0.726459	−	0.687209i	$-0.758835\pi$
$179$		−	18.3885i		−	1.37442i	0.726459	−	0.687209i	$-0.241165\pi$
$180$	−4.58545	+	1.07149i	−0.341779	+	0.0798644i
$181$	1.85701			0.138031			0.0690154	−	0.997616i	$-0.478014\pi$
$181$	1.85701			0.138031			0.0690154	+	0.997616i	$0.478014\pi$
$182$	1.94532	+	1.94532i	0.144197	+	0.144197i
$183$	−0.665497	+	0.665497i	−0.0491950	+	0.0491950i
$184$	8.88707			0.655164
$185$	10.6037	−	17.0704i	0.779602	−	1.25504i
$186$		−	4.82795i		−	0.354002i
$187$	−16.7218	−	2.67495i	−1.22282	−	0.195611i
$188$	−0.337222	−	0.337222i	−0.0245944	−	0.0245944i
$189$	−4.82795			−0.351181
$190$	−7.21574	−	4.48224i	−0.523485	−	0.325176i
$191$	−3.02385			−0.218798			−0.109399	−	0.993998i	$-0.534893\pi$
$191$	−3.02385			−0.218798			−0.109399	+	0.993998i	$0.534893\pi$
$192$	−0.668611	+	0.668611i	−0.0482528	+	0.0482528i
$193$	15.9830	−	15.9830i	1.15048	−	1.15048i	0.164028	−	0.986456i	$-0.447551\pi$
$193$	15.9830	−	15.9830i	1.15048	−	1.15048i	0.986456	−	0.164028i	$-0.0524488\pi$
$194$	7.22086			0.518427
$195$	−5.66415	+	1.32355i	−0.405618	+	0.0947817i
$196$	−1.00000			−0.0714286
$197$	10.4344	+	10.4344i	0.743423	+	0.743423i	0.973235	−	0.229812i	$-0.0738113\pi$
$197$	10.4344	+	10.4344i	0.743423	+	0.743423i	−0.229812	+	0.973235i	$0.573811\pi$
$198$	−1.10327	+	6.89686i	−0.0784062	+	0.490138i
$199$			9.63893i			0.683286i	0.939830	+	0.341643i	$0.110983\pi$
$199$			9.63893i			0.683286i	−0.939830	+	0.341643i	$0.889017\pi$
$200$	1.60266	−	4.73619i	0.113325	−	0.334899i
$201$	3.60780			0.254475
$202$	11.3666	−	11.3666i	0.799751	−	0.799751i
$203$	−2.92928	−	2.92928i	−0.205595	−	0.205595i
$204$	−4.82795			−0.338024
$205$	−2.95443	−	12.6435i	−0.206346	−	0.883057i
$206$		−	3.35512i		−	0.233762i
$207$	13.2338	−	13.2338i	0.919814	−	0.919814i
$208$	1.94532	−	1.94532i	0.134884	−	0.134884i
$209$	−10.2046	+	7.39003i	−0.705867	+	0.511179i
$210$	1.11565	−	1.79603i	0.0769873	−	0.123938i
$211$			21.6150i			1.48804i	0.668159	+	0.744019i	$0.267083\pi$
$211$			21.6150i			1.48804i	−0.668159	+	0.744019i	$0.732917\pi$
$212$	−5.85701	+	5.85701i	−0.402261	+	0.402261i
$213$	−3.32711	−	3.32711i	−0.227970	−	0.227970i
$214$			0.804210i			0.0549746i
$215$	13.6128	−	21.9146i	0.928386	−	1.49456i
$216$			4.82795i			0.328500i
$217$	−3.61043	−	3.61043i	−0.245092	−	0.245092i
$218$	3.41387	+	3.41387i	0.231217	+	0.231217i
$219$	−4.66093			−0.314956
$220$	−5.60251	−	4.85921i	−0.377721	−	0.327608i
$221$	14.0469			0.944895
$222$	−6.00886	−	6.00886i	−0.403288	−	0.403288i
$223$	−15.6081	−	15.6081i	−1.04520	−	1.04520i	−0.998929	−	0.0462672i	$-0.985267\pi$
$223$	−15.6081	−	15.6081i	−1.04520	−	1.04520i	−0.0462672	−	0.998929i	$-0.514733\pi$
$224$			1.00000i			0.0668153i
$225$	−4.66616	−	9.43924i	−0.311078	−	0.629283i
$226$			14.8186i			0.985720i
$227$	−7.17217	−	7.17217i	−0.476034	−	0.476034i	0.427827	−	0.903861i	$-0.359279\pi$
$227$	−7.17217	−	7.17217i	−0.476034	−	0.476034i	−0.903861	+	0.427827i	$0.859279\pi$
$228$	−2.53997	+	2.53997i	−0.168214	+	0.168214i
$229$		−	6.01011i		−	0.397159i	−0.980085	−	0.198580i	$-0.936367\pi$
$229$		−	6.01011i		−	0.397159i	0.980085	−	0.198580i	$-0.0636329\pi$
$230$	4.52175	+	19.3508i	0.298155	+	1.27595i
$231$	−1.83941	−	2.53997i	−0.121024	−	0.167118i
$232$	−2.92928	+	2.92928i	−0.192317	+	0.192317i
$233$	−12.5141	+	12.5141i	−0.819829	+	0.819829i	−0.986083	−	0.166254i	$-0.946833\pi$
$233$	−12.5141	+	12.5141i	−0.819829	+	0.819829i	0.166254	+	0.986083i	$0.446833\pi$
$234$		−	5.79358i		−	0.378738i
$235$	0.562692	−	0.905850i	0.0367060	−	0.0590911i
$236$	13.4843			0.877752
$237$	5.80679	+	5.80679i	0.377192	+	0.377192i
$238$	−3.61043	+	3.61043i	−0.234029	+	0.234029i
$239$	−6.08354			−0.393511			−0.196756	−	0.980453i	$-0.563041\pi$
$239$	−6.08354			−0.393511			−0.196756	+	0.980453i	$0.563041\pi$
$240$	−1.79603	−	1.11565i	−0.115933	−	0.0720150i
$241$			3.89903i			0.251159i	0.992084	+	0.125579i	$0.0400790\pi$
$241$			3.89903i			0.251159i	−0.992084	+	0.125579i	$0.959921\pi$
$242$	−9.81645	+	4.96361i	−0.631025	+	0.319073i
$243$	11.4135	+	11.4135i	0.732174	+	0.732174i
$244$	0.995343			0.0637203
$245$	−0.508801	−	2.17741i	−0.0325061	−	0.139110i
$246$	−5.49052			−0.350063
$247$	7.39003	−	7.39003i	0.470216	−	0.470216i
$248$	−3.61043	+	3.61043i	−0.229263	+	0.229263i
$249$	11.8492			0.750914
$250$	11.1281	+	1.07988i	0.703801	+	0.0682975i
$251$	−2.93940			−0.185533			−0.0927665	−	0.995688i	$-0.529571\pi$
$251$	−2.93940			−0.185533			−0.0927665	+	0.995688i	$0.529571\pi$
$252$	1.48911	+	1.48911i	0.0938051	+	0.0938051i
$253$	29.1050	+	4.65586i	1.82982	+	0.292711i
$254$			16.4315i			1.03100i
$255$	−2.45646	−	10.5124i	−0.153830	−	0.658314i
$256$	1.00000			0.0625000
$257$	7.73349	−	7.73349i	0.482402	−	0.482402i	−0.423496	−	0.905898i	$-0.639197\pi$
$257$	7.73349	−	7.73349i	0.482402	−	0.482402i	0.905898	+	0.423496i	$0.139197\pi$
$258$	−7.71403	−	7.71403i	−0.480254	−	0.480254i
$259$	−8.98708			−0.558430
$260$	5.22554	+	3.24598i	0.324074	+	0.201307i
$261$			8.72405i			0.540005i
$262$	−10.6862	+	10.6862i	−0.660196	+	0.660196i
$263$	15.1292	−	15.1292i	0.932908	−	0.932908i	−0.0649784	−	0.997887i	$-0.520698\pi$
$263$	15.1292	−	15.1292i	0.932908	−	0.932908i	0.997887	+	0.0649784i	$0.0206978\pi$
$264$	−2.53997	+	1.83941i	−0.156324	+	0.113208i
$265$	−15.7332	−	9.77308i	−0.966482	−	0.600355i
$266$			3.79888i			0.232924i
$267$	4.39158	−	4.39158i	0.268760	−	0.268760i
$268$	−2.69798	−	2.69798i	−0.164805	−	0.164805i
$269$		−	25.8212i		−	1.57435i	−0.616732	−	0.787173i	$-0.711544\pi$
$269$		−	25.8212i		−	1.57435i	0.616732	−	0.787173i	$-0.288456\pi$
$270$	−10.5124	+	2.45646i	−0.639766	+	0.149496i
$271$			7.45416i			0.452808i	0.974033	+	0.226404i	$0.0726970\pi$
$271$			7.45416i			0.452808i	−0.974033	+	0.226404i	$0.927303\pi$
$272$	3.61043	+	3.61043i	0.218914	+	0.218914i
$273$	1.83941	+	1.83941i	0.111326	+	0.111326i
$274$	3.68223			0.222452
$275$	7.72994	−	14.6713i	0.466133	−	0.884715i
$276$	8.40325			0.505816
$277$	5.86526	+	5.86526i	0.352409	+	0.352409i	0.861005	−	0.508596i	$-0.169835\pi$
$277$	5.86526	+	5.86526i	0.352409	+	0.352409i	−0.508596	+	0.861005i	$0.669835\pi$
$278$	−10.8996	−	10.8996i	−0.653715	−	0.653715i
$279$			10.7526i			0.643744i
$280$	−2.17741	+	0.508801i	−0.130125	+	0.0304067i
$281$		−	2.20173i		−	0.131344i	−0.997841	−	0.0656721i	$-0.979081\pi$
$281$		−	2.20173i		−	0.131344i	0.997841	−	0.0656721i	$-0.0209191\pi$
$282$	−0.318863	−	0.318863i	−0.0189880	−	0.0189880i
$283$	−19.2375	+	19.2375i	−1.14355	+	1.14355i	−0.155753	+	0.987796i	$0.549781\pi$
$283$	−19.2375	+	19.2375i	−1.14355	+	1.14355i	−0.987796	+	0.155753i	$0.950219\pi$
$284$			4.97615i			0.295280i
$285$	−6.82290	−	4.23822i	−0.404154	−	0.251051i
$286$	7.39003	−	5.35176i	0.436981	−	0.316456i
$287$	−4.10592	+	4.10592i	−0.242365	+	0.242365i
$288$	1.48911	−	1.48911i	0.0877466	−	0.0877466i
$289$			9.07041i			0.533553i
$290$	−7.86868	−	4.88784i	−0.462065	−	0.287024i
$291$	6.82775			0.400250
$292$	3.48553	+	3.48553i	0.203975	+	0.203975i
$293$	15.7686	−	15.7686i	0.921211	−	0.921211i	−0.0759042	−	0.997115i	$-0.524184\pi$
$293$	15.7686	−	15.7686i	0.921211	−	0.921211i	0.997115	+	0.0759042i	$0.0241843\pi$
$294$	−0.945559			−0.0551461
$295$	6.86081	+	29.3608i	0.399452	+	1.70945i
$296$			8.98708i			0.522363i
$297$	−2.52932	+	15.8115i	−0.146766	+	0.917474i
$298$	−2.57446	−	2.57446i	−0.149135	−	0.149135i
$299$	−24.4492			−1.41393
$300$	1.51541	−	4.47834i	0.0874923	−	0.258557i
$301$	−11.5374			−0.665004
$302$	−0.129766	+	0.129766i	−0.00746717	+	0.00746717i
$303$	10.7478	−	10.7478i	0.617444	−	0.617444i
$304$	3.79888			0.217881
$305$	0.506431	+	2.16727i	0.0289982	+	0.124098i
$306$	10.7526			0.614688
$307$	−6.64285	−	6.64285i	−0.379127	−	0.379127i	0.491660	−	0.870787i	$-0.336390\pi$
$307$	−6.64285	−	6.64285i	−0.379127	−	0.379127i	−0.870787	+	0.491660i	$0.836390\pi$
$308$	−0.523891	+	3.27499i	−0.0298515	+	0.186610i
$309$		−	3.17246i		−	0.180475i
$310$	−9.69838	−	6.02440i	−0.550831	−	0.342163i
$311$	16.8583			0.955944			0.477972	−	0.878375i	$-0.341372\pi$
$311$	16.8583			0.955944			0.477972	+	0.878375i	$0.341372\pi$
$312$	1.83941	−	1.83941i	0.104136	−	0.104136i
$313$	8.87462	+	8.87462i	0.501623	+	0.501623i	0.911942	−	0.410319i	$-0.134583\pi$
$313$	8.87462	+	8.87462i	0.501623	+	0.501623i	−0.410319	+	0.911942i	$0.634583\pi$
$314$	9.94103			0.561005
$315$	−2.48474	+	4.00006i	−0.139999	+	0.225378i
$316$		−	8.68486i		−	0.488561i
$317$	−15.2826	+	15.2826i	−0.858354	+	0.858354i	−0.991144	−	0.132790i	$-0.957606\pi$
$317$	−15.2826	+	15.2826i	−0.858354	+	0.858354i	0.132790	+	0.991144i	$0.457606\pi$
$318$	−5.53815	+	5.53815i	−0.310564	+	0.310564i
$319$	−11.1280	+	8.05874i	−0.623048	+	0.451203i
$320$	0.508801	+	2.17741i	0.0284428	+	0.121721i
$321$			0.760427i			0.0424429i
$322$	6.28411	−	6.28411i	0.350200	−	0.350200i
$323$	13.7156	+	13.7156i	0.763155	+	0.763155i
$324$		−	1.75265i		−	0.0973694i
$325$	−4.40908	+	13.0297i	−0.244572	+	0.722758i
$326$			7.27948i			0.403173i
$327$	3.22802	+	3.22802i	0.178510	+	0.178510i
$328$	4.10592	+	4.10592i	0.226711	+	0.226711i
$329$	−0.476904			−0.0262926
$330$	−5.29750	−	4.59467i	−0.291618	−	0.252928i
$331$	−3.20766			−0.176309			−0.0881545	−	0.996107i	$-0.528097\pi$
$331$	−3.20766			−0.176309			−0.0881545	+	0.996107i	$0.528097\pi$
$332$	−8.86108	−	8.86108i	−0.486315	−	0.486315i
$333$	13.3827	+	13.3827i	0.733370	+	0.733370i
$334$			11.3960i			0.623559i
$335$	4.50188	−	7.24735i	0.245964	−	0.395965i
$336$			0.945559i			0.0515845i
$337$	22.5772	+	22.5772i	1.22986	+	1.22986i	0.964017	+	0.265841i	$0.0856497\pi$
$337$	22.5772	+	22.5772i	1.22986	+	1.22986i	0.265841	+	0.964017i	$0.414350\pi$
$338$	3.84063	−	3.84063i	0.208903	−	0.208903i
$339$			14.0119i			0.761020i
$340$	−6.02440	+	9.69838i	−0.326719	+	0.525969i
$341$	−13.7156	+	9.93264i	−0.742740	+	0.537882i
$342$	5.65695	−	5.65695i	0.305893	−	0.305893i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$			11.5374i			0.622055i
$345$	4.27558	+	18.2973i	0.230189	+	0.985095i
$346$	−20.5151			−1.10290
$347$	−16.8954	−	16.8954i	−0.906995	−	0.906995i	0.0890335	−	0.996029i	$-0.471622\pi$
$347$	−16.8954	−	16.8954i	−0.906995	−	0.906995i	−0.996029	+	0.0890335i	$0.971622\pi$
$348$	−2.76981	+	2.76981i	−0.148477	+	0.148477i
$349$	−16.4330			−0.879638			−0.439819	−	0.898087i	$-0.644957\pi$
$349$	−16.4330			−0.879638			−0.439819	+	0.898087i	$0.644957\pi$
$350$	−2.21574	−	4.48224i	−0.118436	−	0.239586i
$351$		−	13.2821i		−	0.708948i
$352$	3.27499	+	0.523891i	0.174557	+	0.0279235i
$353$	15.5374	+	15.5374i	0.826972	+	0.826972i	0.987097	−	0.160125i	$-0.0511897\pi$
$353$	15.5374	+	15.5374i	0.826972	+	0.826972i	−0.160125	+	0.987097i	$0.551190\pi$
$354$	12.7502			0.677664
$355$	−10.8351	+	2.53187i	−0.575069	+	0.134378i
$356$	−6.56822			−0.348115
$357$	−3.41387	+	3.41387i	−0.180681	+	0.180681i
$358$	−13.0026	+	13.0026i	−0.687209	+	0.687209i
$359$	3.25511			0.171798			0.0858990	−	0.996304i	$-0.472624\pi$
$359$	3.25511			0.171798			0.0858990	+	0.996304i	$0.472624\pi$
$360$	4.00006	+	2.48474i	0.210822	+	0.130958i
$361$	−4.56853			−0.240449
$362$	−1.31311	−	1.31311i	−0.0690154	−	0.0690154i
$363$	−9.28203	+	4.69338i	−0.487180	+	0.246339i
$364$		−	2.75110i		−	0.144197i
$365$	−5.81599	+	9.36287i	−0.304423	+	0.490075i
$366$	0.941155			0.0491950
$367$	6.46699	−	6.46699i	0.337574	−	0.337574i	−0.517880	−	0.855454i	$-0.673278\pi$
$367$	6.46699	−	6.46699i	0.337574	−	0.337574i	0.855454	+	0.517880i	$0.173278\pi$
$368$	−6.28411	−	6.28411i	−0.327582	−	0.327582i
$369$	12.2283			0.636581
$370$	−19.5686	+	4.57263i	−1.01732	+	0.237720i
$371$			8.28307i			0.430035i
$372$	−3.41387	+	3.41387i	−0.177001	+	0.177001i
$373$	0.368648	−	0.368648i	0.0190879	−	0.0190879i	−0.697498	−	0.716586i	$-0.745704\pi$
$373$	0.368648	−	0.368648i	0.0190879	−	0.0190879i	0.716586	+	0.697498i	$0.245704\pi$
$374$	9.93264	+	13.7156i	0.513604	+	0.709216i
$375$	10.5222	+	1.02109i	0.543366	+	0.0527288i
$376$			0.476904i			0.0245944i
$377$	8.05874	−	8.05874i	0.415046	−	0.415046i
$378$	3.41387	+	3.41387i	0.175591	+	0.175591i
$379$		−	28.8505i		−	1.48195i	−0.671533	−	0.740974i	$-0.734364\pi$
$379$		−	28.8505i		−	1.48195i	0.671533	−	0.740974i	$-0.265636\pi$
$380$	1.93287	+	8.27172i	0.0991542	+	0.424330i
$381$			15.5369i			0.795981i
$382$	2.13818	+	2.13818i	0.109399	+	0.109399i
$383$	9.20017	+	9.20017i	0.470107	+	0.470107i	0.901949	−	0.431842i	$-0.142136\pi$
$383$	9.20017	+	9.20017i	0.470107	+	0.470107i	−0.431842	+	0.901949i	$0.642136\pi$
$384$	0.945559			0.0482528
$385$	−7.39755	+	0.525588i	−0.377014	+	0.0267865i
$386$	−22.6034			−1.15048
$387$	17.1804	+	17.1804i	0.873331	+	0.873331i
$388$	−5.10592	−	5.10592i	−0.259214	−	0.259214i
$389$			27.1364i			1.37587i	0.725772	+	0.687936i	$0.241483\pi$
$389$			27.1364i			1.37587i	−0.725772	+	0.687936i	$0.758517\pi$
$390$	4.94105	+	3.06926i	0.250200	+	0.155418i
$391$		−	45.3767i		−	2.29480i
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	−10.1044	+	10.1044i	−0.509702	+	0.509702i
$394$		−	14.7565i		−	0.743423i
$395$	18.9105	−	4.41886i	0.951491	−	0.222337i
$396$	5.65695	−	4.09668i	0.284272	−	0.205866i
$397$	−19.0762	+	19.0762i	−0.957409	+	0.957409i	−0.999129	−	0.0417203i	$-0.986716\pi$
$397$	−19.0762	+	19.0762i	−0.957409	+	0.957409i	0.0417203	+	0.999129i	$0.486716\pi$
$398$	6.81575	−	6.81575i	0.341643	−	0.341643i
$399$			3.59206i			0.179828i
$400$	−4.48224	+	2.21574i	−0.224112	+	0.110787i
$401$	−1.22402			−0.0611246			−0.0305623	−	0.999533i	$-0.509730\pi$
$401$	−1.22402			−0.0611246			−0.0305623	+	0.999533i	$0.509730\pi$
$402$	−2.55110	−	2.55110i	−0.127237	−	0.127237i
$403$	9.93264	−	9.93264i	0.494780	−	0.494780i
$404$	−16.0748			−0.799751
$405$	3.81624	−	0.891750i	0.189630	−	0.0443114i
$406$			4.14263i			0.205595i
$407$	−4.70825	+	29.4326i	−0.233379	+	1.45892i
$408$	3.41387	+	3.41387i	0.169012	+	0.169012i
$409$	31.3123			1.54829			0.774146	−	0.633007i	$-0.218180\pi$
$409$	31.3123			1.54829			0.774146	+	0.633007i	$0.218180\pi$
$410$	−6.85118	+	11.0294i	−0.338356	+	0.544702i
$411$	3.48176			0.171743
$412$	−2.37242	+	2.37242i	−0.116881	+	0.116881i
$413$	9.53483	−	9.53483i	0.469178	−	0.469178i
$414$	−18.7154			−0.919814
$415$	14.7857	−	23.8027i	0.725801	−	1.16843i
$416$	−2.75110			−0.134884
$417$	−10.3062	−	10.3062i	−0.504698	−	0.504698i
$418$	12.4413	+	1.99020i	0.608523	+	0.0973438i
$419$			29.6726i			1.44960i	0.688959	+	0.724800i	$0.258068\pi$
$419$			29.6726i			1.44960i	−0.688959	+	0.724800i	$0.741932\pi$
$420$	−2.05887	+	0.481101i	−0.100463	+	0.0234753i
$421$	−25.2662			−1.23140			−0.615700	−	0.787981i	$-0.711126\pi$
$421$	−25.2662			−1.23140			−0.615700	+	0.787981i	$0.711126\pi$
$422$	15.2841	−	15.2841i	0.744019	−	0.744019i
$423$	0.710162	+	0.710162i	0.0345293	+	0.0345293i
$424$	8.28307			0.402261
$425$	−24.1826	−	8.18306i	−1.17303	−	0.396937i
$426$			4.70524i			0.227970i
$427$	0.703814	−	0.703814i	0.0340599	−	0.0340599i
$428$	0.568662	−	0.568662i	0.0274873	−	0.0274873i
$429$	6.98770	−	5.06040i	0.337370	−	0.244318i
$430$	−25.1217	+	5.87023i	−1.21147	+	0.283088i
$431$		−	24.5243i		−	1.18129i	−0.806930	−	0.590647i	$-0.798873\pi$
$431$		−	24.5243i		−	1.18129i	0.806930	−	0.590647i	$-0.201127\pi$
$432$	3.41387	−	3.41387i	0.164250	−	0.164250i
$433$	4.78785	+	4.78785i	0.230090	+	0.230090i	0.812730	−	0.582640i	$-0.197980\pi$
$433$	4.78785	+	4.78785i	0.230090	+	0.230090i	−0.582640	+	0.812730i	$0.697980\pi$
$434$			5.10592i			0.245092i
$435$	−7.44030	−	4.62174i	−0.356735	−	0.221595i
$436$		−	4.82795i		−	0.231217i
$437$	−23.8726	−	23.8726i	−1.14198	−	1.14198i
$438$	3.29577	+	3.29577i	0.157478	+	0.157478i
$439$	14.9182			0.712006			0.356003	−	0.934485i	$-0.384139\pi$
$439$	14.9182			0.712006			0.356003	+	0.934485i	$0.384139\pi$
$440$	0.525588	+	7.39755i	0.0250564	+	0.352664i
$441$	2.10592			0.100282
$442$	−9.93264	−	9.93264i	−0.472447	−	0.472447i
$443$	−18.1041	−	18.1041i	−0.860150	−	0.860150i	0.131206	−	0.991355i	$-0.458115\pi$
$443$	−18.1041	−	18.1041i	−0.860150	−	0.860150i	−0.991355	+	0.131206i	$0.958115\pi$
$444$			8.49781i			0.403288i
$445$	−3.34191	−	14.3017i	−0.158422	−	0.677966i
$446$			22.0732i			1.04520i
$447$	−2.43430	−	2.43430i	−0.115139	−	0.115139i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$		−	18.8863i		−	0.891299i	−0.895208	−	0.445649i	$-0.852973\pi$
$449$		−	18.8863i		−	0.891299i	0.895208	−	0.445649i	$-0.147027\pi$
$450$	−3.37508	+	9.97403i	−0.159103	+	0.470180i
$451$	11.2958	+	15.5979i	0.531897	+	0.734476i
$452$	10.4783	−	10.4783i	0.492860	−	0.492860i
$453$	−0.122701	+	0.122701i	−0.00576500	+	0.00576500i
$454$			10.1430i			0.476034i
$455$	5.99027	−	1.39976i	0.280828	−	0.0656217i
$456$	3.59206			0.168214
$457$	−6.35866	−	6.35866i	−0.297446	−	0.297446i	0.542567	−	0.840013i	$-0.317453\pi$
$457$	−6.35866	−	6.35866i	−0.297446	−	0.297446i	−0.840013	+	0.542567i	$0.817453\pi$
$458$	−4.24979	+	4.24979i	−0.198580	+	0.198580i
$459$	24.6511			1.15061
$460$	10.4857	−	16.8804i	0.488900	−	0.787055i
$461$			26.6094i			1.23932i	0.784870	+	0.619661i	$0.212730\pi$
$461$			26.6094i			1.23932i	−0.784870	+	0.619661i	$0.787270\pi$
$462$	−0.495370	+	3.09669i	−0.0230467	+	0.144071i
$463$	−19.6741	−	19.6741i	−0.914335	−	0.914335i	0.0822751	−	0.996610i	$-0.473781\pi$
$463$	−19.6741	−	19.6741i	−0.914335	−	0.914335i	−0.996610	+	0.0822751i	$0.973781\pi$
$464$	4.14263			0.192317
$465$	−9.17039	−	5.69643i	−0.425267	−	0.264165i
$466$	17.6977			0.819829
$467$	−2.51551	+	2.51551i	−0.116404	+	0.116404i	−0.762909	−	0.646505i	$-0.776230\pi$
$467$	−2.51551	+	2.51551i	−0.116404	+	0.116404i	0.646505	+	0.762909i	$0.276230\pi$
$468$	−4.09668	+	4.09668i	−0.189369	+	0.189369i
$469$	−3.81552			−0.176184
$470$	−1.03842	+	0.242649i	−0.0478986	+	0.0111926i
$471$	9.39983			0.433121
$472$	−9.53483	−	9.53483i	−0.438876	−	0.438876i
$473$	−6.04434	+	37.7848i	−0.277919	+	1.73735i
$474$		−	8.21204i		−	0.377192i
$475$	−17.0275	+	8.41732i	−0.781275	+	0.386213i
$476$	5.10592			0.234029
$477$	12.3344	−	12.3344i	0.564753	−	0.564753i
$478$	4.30171	+	4.30171i	0.196756	+	0.196756i
$479$	−29.0438			−1.32705			−0.663523	−	0.748156i	$-0.730940\pi$
$479$	−29.0438			−1.32705			−0.663523	+	0.748156i	$0.730940\pi$
$480$	0.481101	+	2.05887i	0.0219592	+	0.0939742i
$481$		−	24.7243i		−	1.12733i
$482$	2.75703	−	2.75703i	0.125579	−	0.125579i
$483$	5.94199	−	5.94199i	0.270370	−	0.270370i
$484$	10.4511	+	3.43147i	0.475049	+	0.155976i
$485$	8.51979	−	13.7156i	0.386864	−	0.622793i
$486$		−	16.1411i		−	0.732174i
$487$	11.9629	−	11.9629i	0.542092	−	0.542092i	−0.382050	−	0.924142i	$-0.624782\pi$
$487$	11.9629	−	11.9629i	0.542092	−	0.542092i	0.924142	+	0.382050i	$0.124782\pi$
$488$	−0.703814	−	0.703814i	−0.0318602	−	0.0318602i
$489$			6.88317i			0.311268i
$490$	−1.17989	+	1.89944i	−0.0533018	+	0.0858079i
$491$			40.7509i			1.83906i	0.393016	+	0.919532i	$0.371432\pi$
$491$			40.7509i			1.83906i	−0.393016	+	0.919532i	$0.628568\pi$
$492$	3.88239	+	3.88239i	0.175032	+	0.175032i
$493$	14.9567	+	14.9567i	0.673615	+	0.673615i
$494$	−10.4511			−0.470216
$495$	11.7984	+	10.2331i	0.530300	+	0.459944i
$496$	5.10592			0.229263
$497$	3.51867	+	3.51867i	0.157834	+	0.157834i
$498$	−8.37867	−	8.37867i	−0.375457	−	0.375457i
$499$			1.19268i			0.0533918i	0.999644	+	0.0266959i	$0.00849857\pi$
$499$			1.19268i			0.0533918i	−0.999644	+	0.0266959i	$0.991501\pi$
$500$	−7.10514	−	8.63232i	−0.317752	−	0.386049i
$501$			10.7756i			0.481416i
$502$	2.07847	+	2.07847i	0.0927665	+	0.0927665i
$503$	−13.6150	+	13.6150i	−0.607063	+	0.607063i	−0.942177	−	0.335114i	$-0.891225\pi$
$503$	−13.6150	+	13.6150i	−0.607063	+	0.607063i	0.335114	+	0.942177i	$0.391225\pi$
$504$		−	2.10592i		−	0.0938051i
$505$	−8.17886	−	35.0014i	−0.363955	−	1.55754i
$506$	−17.2882	−	23.8726i	−0.768553	−	1.06126i
$507$	3.63154	−	3.63154i	0.161283	−	0.161283i
$508$	11.6188	−	11.6188i	0.515501	−	0.515501i
$509$		−	24.7191i		−	1.09566i	−0.836591	−	0.547828i	$-0.815455\pi$
$509$		−	24.7191i		−	1.09566i	0.836591	−	0.547828i	$-0.184545\pi$
$510$	−5.69643	+	9.17039i	−0.252242	+	0.406072i
$511$	4.92928			0.218059
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	12.9689	−	12.9689i	0.572590	−	0.572590i
$514$	−10.9368			−0.482402
$515$	−6.37284	−	3.95865i	−0.280821	−	0.174439i
$516$			10.9093i			0.480254i
$517$	−0.249846	+	1.56185i	−0.0109882	+	0.0686903i
$518$	6.35482	+	6.35482i	0.279215	+	0.279215i
$519$	−19.3982			−0.851488
$520$	−1.39976	−	5.99027i	−0.0613835	−	0.262691i
$521$	17.6342			0.772570			0.386285	−	0.922379i	$-0.373758\pi$
$521$	17.6342			0.772570			0.386285	+	0.922379i	$0.373758\pi$
$522$	6.16883	−	6.16883i	0.270003	−	0.270003i
$523$	−25.0105	+	25.0105i	−1.09363	+	1.09363i	−0.0984974	+	0.995137i	$0.531404\pi$
$523$	−25.0105	+	25.0105i	−1.09363	+	1.09363i	−0.995137	+	0.0984974i	$0.968596\pi$
$524$	15.1126			0.660196
$525$	−2.09511	−	4.23822i	−0.0914381	−	0.184971i
$526$	−21.3960			−0.932908
$527$	18.4346	+	18.4346i	0.803022	+	0.803022i
$528$	3.09669	+	0.495370i	0.134766	+	0.0215582i
$529$			55.9800i			2.43391i
$530$	4.21443	+	18.0357i	0.183063	+	0.783419i
$531$	−28.3968			−1.23232
$532$	2.68621	−	2.68621i	0.116462	−	0.116462i
$533$	−11.2958	−	11.2958i	−0.489274	−	0.489274i
$534$	−6.21063			−0.268760
$535$	1.52755	+	0.948876i	0.0660416	+	0.0410235i
$536$			3.81552i			0.164805i
$537$	−12.2947	+	12.2947i	−0.530557	+	0.530557i
$538$	−18.2583	+	18.2583i	−0.787173	+	0.787173i
$539$	1.94532	+	2.68621i	0.0837908	+	0.115703i
$540$	9.17039	+	5.69643i	0.394631	+	0.245135i
$541$			25.4990i			1.09629i	0.836384	+	0.548144i	$0.184665\pi$
$541$			25.4990i			1.09629i	−0.836384	+	0.548144i	$0.815335\pi$
$542$	5.27089	−	5.27089i	0.226404	−	0.226404i
$543$	−1.24162	−	1.24162i	−0.0532830	−	0.0532830i
$544$		−	5.10592i		−	0.218914i
$545$	10.5124	−	2.45646i	0.450303	−	0.105223i
$546$		−	2.60132i		−	0.111326i
$547$	25.4952	+	25.4952i	1.09010	+	1.09010i	0.995517	+	0.0945778i	$0.0301501\pi$
$547$	25.4952	+	25.4952i	1.09010	+	1.09010i	0.0945778	+	0.995517i	$0.469850\pi$
$548$	−2.60373	−	2.60373i	−0.111226	−	0.111226i
$549$	−2.09611			−0.0894599
$550$	−15.8401	+	4.90830i	−0.675424	+	0.209291i
$551$	15.7374			0.670434
$552$	−5.94199	−	5.94199i	−0.252908	−	0.252908i
$553$	−6.14112	−	6.14112i	−0.261147	−	0.261147i
$554$		−	8.29473i		−	0.352409i
$555$	−18.5032	+	4.32369i	−0.785418	+	0.183530i
$556$			15.4144i			0.653715i
$557$	−12.7943	−	12.7943i	−0.542114	−	0.542114i	0.382034	−	0.924148i	$-0.375224\pi$
$557$	−12.7943	−	12.7943i	−0.542114	−	0.542114i	−0.924148	+	0.382034i	$0.875224\pi$
$558$	7.60327	−	7.60327i	0.321872	−	0.321872i
$559$		−	31.7405i		−	1.34248i
$560$	1.89944	+	1.17989i	0.0802659	+	0.0498593i
$561$	9.39189	+	12.9689i	0.396526	+	0.547547i
$562$	−1.55686	+	1.55686i	−0.0656721	+	0.0656721i
$563$	−5.11418	+	5.11418i	−0.215537	+	0.215537i	−0.806615	−	0.591078i	$-0.798703\pi$
$563$	−5.11418	+	5.11418i	−0.215537	+	0.215537i	0.591078	+	0.806615i	$0.298703\pi$
$564$			0.450941i			0.0189880i
$565$	28.1471	+	17.4843i	1.18416	+	0.735569i
$566$	27.2059			1.14355
$567$	−1.23931	−	1.23931i	−0.0520462	−	0.0520462i
$568$	3.51867	−	3.51867i	0.147640	−	0.147640i
$569$	−17.2120			−0.721563			−0.360782	−	0.932650i	$-0.617490\pi$
$569$	−17.2120			−0.721563			−0.360782	+	0.932650i	$0.617490\pi$
$570$	1.82764	+	7.82140i	0.0765516	+	0.327602i
$571$		−	30.8995i		−	1.29310i	−0.762871	−	0.646551i	$-0.776211\pi$
$571$		−	30.8995i		−	1.29310i	0.762871	−	0.646551i	$-0.223789\pi$
$572$	−9.00980	−	1.44128i	−0.376719	−	0.0602627i
$573$	2.02178	+	2.02178i	0.0844610	+	0.0844610i
$574$	5.80665			0.242365
$575$	42.0908	+	14.2430i	1.75531	+	0.593973i
$576$	−2.10592			−0.0877466
$577$	0.478344	−	0.478344i	0.0199137	−	0.0199137i	−0.697080	−	0.716994i	$-0.745518\pi$
$577$	0.478344	−	0.478344i	0.0199137	−	0.0199137i	0.716994	+	0.697080i	$0.245518\pi$
$578$	6.41375	−	6.41375i	0.266777	−	0.266777i
$579$	−21.3729			−0.888226
$580$	2.10778	+	9.02022i	0.0875206	+	0.374544i
$581$	−12.5315			−0.519892
$582$	−4.82795	−	4.82795i	−0.200125	−	0.200125i
$583$	27.1269	+	4.33943i	1.12348	+	0.179721i
$584$		−	4.92928i		−	0.203975i
$585$	−11.0046	−	6.83577i	−0.454982	−	0.282624i
$586$	−22.3002			−0.921211
$587$	14.1941	−	14.1941i	0.585855	−	0.585855i	−0.350651	−	0.936506i	$-0.614040\pi$
$587$	14.1941	−	14.1941i	0.585855	−	0.585855i	0.936506	+	0.350651i	$0.114040\pi$
$588$	0.668611	+	0.668611i	0.0275731	+	0.0275731i
$589$	19.3968			0.799230
$590$	15.9099	−	25.6126i	0.655001	−	1.05445i
$591$		−	13.9532i		−	0.573956i
$592$	6.35482	−	6.35482i	0.261182	−	0.261182i
$593$	12.4700	−	12.4700i	0.512080	−	0.512080i	−0.403083	−	0.915163i	$-0.632061\pi$
$593$	12.4700	−	12.4700i	0.512080	−	0.512080i	0.915163	+	0.403083i	$0.132061\pi$
$594$	12.9689	−	9.39189i	0.532120	−	0.385354i
$595$	2.59790	+	11.1177i	0.106503	+	0.455781i
$596$			3.64084i			0.149135i
$597$	6.44470	−	6.44470i	0.263764	−	0.263764i
$598$	17.2882	+	17.2882i	0.706966	+	0.706966i
$599$		−	13.6983i		−	0.559697i	−0.960044	−	0.279848i	$-0.909716\pi$
$599$		−	13.6983i		−	0.559697i	0.960044	−	0.279848i	$-0.0902842\pi$
$600$	−4.23822	+	2.09511i	−0.173025	+	0.0855325i
$601$		−	31.9888i		−	1.30485i	−0.757854	−	0.652424i	$-0.773752\pi$
$601$		−	31.9888i		−	1.30485i	0.757854	−	0.652424i	$-0.226248\pi$
$602$	8.15817	+	8.15817i	0.332502	+	0.332502i
$603$	5.68173	+	5.68173i	0.231378	+	0.231378i
$604$	0.183516			0.00746717
$605$	−2.15422	+	24.5022i	−0.0875814	+	0.996157i
$606$	−15.1997			−0.617444
$607$	−11.3635	−	11.3635i	−0.461230	−	0.461230i	0.437829	−	0.899058i	$-0.355748\pi$
$607$	−11.3635	−	11.3635i	−0.461230	−	0.461230i	−0.899058	+	0.437829i	$0.855748\pi$
$608$	−2.68621	−	2.68621i	−0.108940	−	0.108940i
$609$			3.91710i			0.158729i
$610$	1.17439	−	1.89059i	0.0475497	−	0.0765479i
$611$		−	1.31201i		−	0.0530782i
$612$	−7.60327	−	7.60327i	−0.307344	−	0.307344i
$613$	−17.4553	+	17.4553i	−0.705012	+	0.705012i	−0.965482	−	0.260470i	$-0.916123\pi$
$613$	−17.4553	+	17.4553i	−0.705012	+	0.705012i	0.260470	+	0.965482i	$0.416123\pi$
$614$			9.39441i			0.379127i
$615$	−6.47819	+	10.4289i	−0.261226	+	0.420535i
$616$	2.68621	−	1.94532i	0.108231	−	0.0783791i
$617$	30.8621	−	30.8621i	1.24246	−	1.24246i	0.283486	−	0.958976i	$-0.408509\pi$
$617$	30.8621	−	30.8621i	1.24246	−	1.24246i	0.958976	−	0.283486i	$-0.0914909\pi$
$618$	−2.24327	+	2.24327i	−0.0902374	+	0.0902374i
$619$		−	11.1895i		−	0.449746i	−0.974388	−	0.224873i	$-0.927803\pi$
$619$		−	11.1895i		−	0.449746i	0.974388	−	0.224873i	$-0.0721967\pi$
$620$	2.59790	+	11.1177i	0.104334	+	0.446497i
$621$	−42.9063			−1.72177
$622$	−11.9206	−	11.9206i	−0.477972	−	0.477972i
$623$	−4.64443	+	4.64443i	−0.186075	+	0.186075i
$624$	−2.60132			−0.104136
$625$	15.1810	−	19.8629i	0.607241	−	0.794518i
$626$		−	12.5506i		−	0.501623i
$627$	11.7640	+	1.88185i	0.469807	+	0.0751539i
$628$	−7.02937	−	7.02937i	−0.280502	−	0.280502i
$629$	45.8873			1.82965
$630$	4.58545	−	1.07149i	0.182689	−	0.0426893i
$631$	5.56562			0.221564			0.110782	−	0.993845i	$-0.464664\pi$
$631$	5.56562			0.221564			0.110782	+	0.993845i	$0.464664\pi$
$632$	−6.14112	+	6.14112i	−0.244281	+	0.244281i
$633$	14.4520	−	14.4520i	0.574416	−	0.574416i
$634$	21.6128			0.858354
$635$	31.2106	+	19.3873i	1.23855	+	0.769360i
$636$	7.83213			0.310564
$637$	−1.94532	−	1.94532i	−0.0770763	−	0.0770763i
$638$	13.5671	+	2.17029i	0.537125	+	0.0859226i
$639$		−	10.4794i		−	0.414558i
$640$	1.17989	−	1.89944i	0.0466391	−	0.0750819i
$641$	−25.4359			−1.00466			−0.502328	−	0.864677i	$-0.667523\pi$
$641$	−25.4359			−1.00466			−0.502328	+	0.864677i	$0.667523\pi$
$642$	0.537703	−	0.537703i	0.0212215	−	0.0212215i
$643$	−11.8965	−	11.8965i	−0.469152	−	0.469152i	0.432488	−	0.901640i	$-0.357636\pi$
$643$	−11.8965	−	11.8965i	−0.469152	−	0.469152i	−0.901640	+	0.432488i	$0.857636\pi$
$644$	−8.88707			−0.350200
$645$	−23.7540	+	5.55065i	−0.935313	+	0.218557i
$646$		−	19.3968i		−	0.763155i
$647$	−13.3250	+	13.3250i	−0.523861	+	0.523861i	−0.918735	−	0.394874i	$-0.870788\pi$
$647$	−13.3250	+	13.3250i	−0.523861	+	0.523861i	0.394874	+	0.918735i	$0.370788\pi$
$648$	−1.23931	+	1.23931i	−0.0486847	+	0.0486847i
$649$	−26.2312	−	36.2216i	−1.02967	−	1.42182i
$650$	12.3311	−	6.09570i	0.483665	−	0.239093i
$651$			4.82795i			0.189222i
$652$	5.14737	−	5.14737i	0.201586	−	0.201586i
$653$	−25.8976	−	25.8976i	−1.01345	−	1.01345i	−0.999908	−	0.0135446i	$-0.995688\pi$
$653$	−25.8976	−	25.8976i	−1.01345	−	1.01345i	−0.0135446	−	0.999908i	$-0.504312\pi$
$654$		−	4.56511i		−	0.178510i
$655$	7.68930	+	32.9063i	0.300446	+	1.28576i
$656$		−	5.80665i		−	0.226711i
$657$	−7.34024	−	7.34024i	−0.286370	−	0.286370i
$658$	0.337222	+	0.337222i	0.0131463	+	0.0131463i
$659$	−12.3506			−0.481111			−0.240555	−	0.970635i	$-0.577330\pi$
$659$	−12.3506			−0.481111			−0.240555	+	0.970635i	$0.577330\pi$
$660$	0.496975	+	6.99482i	0.0193447	+	0.272273i
$661$	−32.1393			−1.25007			−0.625036	−	0.780596i	$-0.714916\pi$
$661$	−32.1393			−1.25007			−0.625036	+	0.780596i	$0.714916\pi$
$662$	2.26816	+	2.26816i	0.0881545	+	0.0881545i
$663$	−9.39189	−	9.39189i	−0.364751	−	0.364751i
$664$			12.5315i			0.486315i
$665$	7.21574	+	4.48224i	0.279814	+	0.173814i
$666$		−	18.9261i		−	0.733370i
$667$	−26.0328	−	26.0328i	−1.00799	−	1.00799i
$668$	8.05816	−	8.05816i	0.311780	−	0.311780i
$669$			20.8715i			0.806939i
$670$	−8.30796	+	1.94134i	−0.320965	+	0.0750005i
$671$	−1.93626	−	2.67370i	−0.0747485	−	0.103217i
$672$	0.668611	−	0.668611i	0.0257922	−	0.0257922i
$673$	1.06758	−	1.06758i	0.0411522	−	0.0411522i	−0.686231	−	0.727383i	$-0.740736\pi$
$673$	1.06758	−	1.06758i	0.0411522	−	0.0411522i	0.727383	+	0.686231i	$0.240736\pi$
$674$		−	31.9290i		−	1.22986i
$675$	−7.73757	+	22.8661i	−0.297819	+	0.880115i
$676$	−5.43147			−0.208903
$677$	24.7303	+	24.7303i	0.950464	+	0.950464i	0.998830	−	0.0483656i	$-0.0154013\pi$
$677$	24.7303	+	24.7303i	0.950464	+	0.950464i	−0.0483656	+	0.998830i	$0.515401\pi$
$678$	9.90789	−	9.90789i	0.380510	−	0.380510i
$679$	−7.22086			−0.277111
$680$	11.1177	−	2.59790i	0.426344	−	0.0996247i
$681$			9.59079i			0.367520i
$682$	16.7218	+	2.67495i	0.640311	+	0.102429i
$683$	−34.9199	−	34.9199i	−1.33617	−	1.33617i	−0.899733	−	0.436441i	$-0.856239\pi$
$683$	−34.9199	−	34.9199i	−1.33617	−	1.33617i	−0.436441	−	0.899733i	$-0.643761\pi$
$684$	−8.00013			−0.305893
$685$	4.34461	−	6.99417i	0.165999	−	0.267233i
$686$	1.00000			0.0381802
$687$	−4.01843	+	4.01843i	−0.153313	+	0.153313i
$688$	8.15817	−	8.15817i	0.311027	−	0.311027i
$689$	−22.7875			−0.868135
$690$	9.91487	−	15.9615i	0.377453	−	0.607642i
$691$	−25.0598			−0.953319			−0.476659	−	0.879088i	$-0.658153\pi$
$691$	−25.0598			−0.953319			−0.476659	+	0.879088i	$0.658153\pi$
$692$	14.5064	+	14.5064i	0.551449	+	0.551449i
$693$	1.10327	−	6.89686i	0.0419099	−	0.261990i
$694$			23.8938i			0.906995i
$695$	−33.5634	+	7.84284i	−1.27313	+	0.297496i
$696$	3.91710			0.148477
$697$	20.9645	−	20.9645i	0.794087	−	0.794087i
$698$	11.6199	+	11.6199i	0.439819	+	0.439819i
$699$	16.7342			0.632945
$700$	−1.60266	+	4.73619i	−0.0605749	+	0.179011i
$701$		−	33.9279i		−	1.28144i	−0.767775	−	0.640719i	$-0.778636\pi$
$701$		−	33.9279i		−	1.28144i	0.767775	−	0.640719i	$-0.221364\pi$
$702$	−9.39189	+	9.39189i	−0.354474	+	0.354474i
$703$	24.1412	−	24.1412i	0.910503	−	0.910503i
$704$	−1.94532	−	2.68621i	−0.0733169	−	0.101240i
$705$	−0.981883	+	0.229439i	−0.0369799	+	0.00864117i
$706$		−	21.9732i		−	0.826972i
$707$	−11.3666	+	11.3666i	−0.427485	+	0.427485i
$708$	−9.01574	−	9.01574i	−0.338832	−	0.338832i
$709$			3.35200i			0.125887i	0.998017	+	0.0629434i	$0.0200488\pi$
$709$			3.35200i			0.125887i	−0.998017	+	0.0629434i	$0.979951\pi$
$710$	9.45190	+	5.87129i	0.354723	+	0.220346i
$711$			18.2896i			0.685914i
$712$	4.64443	+	4.64443i	0.174057	+	0.174057i
$713$	−32.0861	−	32.0861i	−1.20164	−	1.20164i
$714$	4.82795			0.180681
$715$	−1.44594	−	20.3514i	−0.0540752	−	0.761098i
$716$	18.3885			0.687209
$717$	4.06752	+	4.06752i	0.151904	+	0.151904i
$718$	−2.30171	−	2.30171i	−0.0858990	−	0.0858990i
$719$			0.643312i			0.0239915i	0.999928	+	0.0119957i	$0.00381846\pi$
$719$			0.643312i			0.0239915i	−0.999928	+	0.0119957i	$0.996182\pi$
$720$	−1.07149	−	4.58545i	−0.0399322	−	0.170890i
$721$			3.35512i			0.124951i
$722$	3.23044	+	3.23044i	0.120224	+	0.120224i
$723$	2.60693	−	2.60693i	0.0969529	−	0.0969529i
$724$			1.85701i			0.0690154i
$725$	−18.5683	+	9.17899i	−0.689609	+	0.340899i
$726$	9.88211	+	3.24466i	0.366759	+	0.120421i
$727$	−20.0896	+	20.0896i	−0.745081	+	0.745081i	−0.973551	−	0.228470i	$-0.926628\pi$
$727$	−20.0896	+	20.0896i	−0.745081	+	0.745081i	0.228470	+	0.973551i	$0.426628\pi$
$728$	−1.94532	+	1.94532i	−0.0720983	+	0.0720983i
$729$		−	10.0044i		−	0.370533i
$730$	10.7331	−	2.50802i	0.397249	−	0.0928261i
$731$	58.9090			2.17883
$732$	−0.665497	−	0.665497i	−0.0245975	−	0.0245975i
$733$	−2.57260	+	2.57260i	−0.0950210	+	0.0950210i	−0.753019	−	0.657998i	$-0.771403\pi$
$733$	−2.57260	+	2.57260i	−0.0950210	+	0.0950210i	0.657998	+	0.753019i	$0.271403\pi$
$734$	−9.14570			−0.337574
$735$	−1.11565	+	1.79603i	−0.0411514	+	0.0662476i
$736$			8.88707i			0.327582i
$737$	−1.99892	+	12.4958i	−0.0736311	+	0.460288i
$738$	−8.64673	−	8.64673i	−0.318291	−	0.318291i
$739$	8.73064			0.321162			0.160581	−	0.987023i	$-0.448663\pi$
$739$	8.73064			0.321162			0.160581	+	0.987023i	$0.448663\pi$
$740$	17.0704	+	10.6037i	0.627521	+	0.389801i
$741$	−9.88211			−0.363028
$742$	5.85701	−	5.85701i	0.215018	−	0.215018i
$743$	6.77216	−	6.77216i	0.248447	−	0.248447i	−0.571886	−	0.820333i	$-0.693788\pi$
$743$	6.77216	−	6.77216i	0.248447	−	0.248447i	0.820333	+	0.571886i	$0.193788\pi$
$744$	4.82795			0.177001
$745$	−7.92760	+	1.85246i	−0.290445	+	0.0678689i
$746$	−0.521347			−0.0190879
$747$	18.6607	+	18.6607i	0.682760	+	0.682760i
$748$	2.67495	−	16.7218i	0.0978057	−	0.611410i
$749$		−	0.804210i		−	0.0293852i
$750$	−6.71833	−	8.16237i	−0.245319	−	0.298047i
$751$	−36.9686			−1.34900			−0.674501	−	0.738274i	$-0.735641\pi$
$751$	−36.9686			−1.34900			−0.674501	+	0.738274i	$0.735641\pi$
$752$	0.337222	−	0.337222i	0.0122972	−	0.0122972i
$753$	1.96531	+	1.96531i	0.0716200	+	0.0716200i
$754$	−11.3968			−0.415046
$755$	0.0933732	+	0.399591i	0.00339820	+	0.0145426i
$756$		−	4.82795i		−	0.175591i
$757$	16.7614	−	16.7614i	0.609204	−	0.609204i	−0.333534	−	0.942738i	$-0.608241\pi$
$757$	16.7614	−	16.7614i	0.609204	−	0.609204i	0.942738	+	0.333534i	$0.108241\pi$
$758$	−20.4004	+	20.4004i	−0.740974	+	0.740974i
$759$	−16.3470	−	22.5729i	−0.593358	−	0.819345i
$760$	4.48224	−	7.21574i	0.162588	−	0.261742i
$761$			34.4447i			1.24862i	0.781177	+	0.624309i	$0.214620\pi$
$761$			34.4447i			1.24862i	−0.781177	+	0.624309i	$0.785380\pi$
$762$	10.9863	−	10.9863i	0.397990	−	0.397990i
$763$	−3.41387	−	3.41387i	−0.123591	−	0.123591i
$764$		−	3.02385i		−	0.109399i
$765$	12.6869	−	20.4240i	0.458696	−	0.738431i
$766$		−	13.0110i		−	0.470107i
$767$	26.2312	+	26.2312i	0.947154	+	0.947154i
$768$	−0.668611	−	0.668611i	−0.0241264	−	0.0241264i
$769$	38.7265			1.39651			0.698257	−	0.715847i	$-0.253959\pi$
$769$	38.7265			1.39651			0.698257	+	0.715847i	$0.253959\pi$
$770$	5.60251	+	4.85921i	0.201900	+	0.175114i
$771$	−10.3414			−0.372436
$772$	15.9830	+	15.9830i	0.575242	+	0.575242i
$773$	−21.2428	−	21.2428i	−0.764049	−	0.764049i	0.213003	−	0.977052i	$-0.431676\pi$
$773$	−21.2428	−	21.2428i	−0.764049	−	0.764049i	−0.977052	+	0.213003i	$0.931676\pi$
$774$		−	24.2968i		−	0.873331i
$775$	−22.8860	+	11.3134i	−0.822088	+	0.406388i
$776$			7.22086i			0.259214i
$777$	6.00886	+	6.00886i	0.215567	+	0.215567i
$778$	19.1884	−	19.1884i	0.687936	−	0.687936i
$779$		−	22.0587i		−	0.790336i
$780$	−1.32355	−	5.66415i	−0.0473909	−	0.202809i
$781$	13.3670	−	9.68020i	0.478309	−	0.346385i
$782$	−32.0861	+	32.0861i	−1.14740	+	1.14740i
$783$	14.1424	−	14.1424i	0.505409	−	0.505409i
$784$		−	1.00000i		−	0.0357143i
$785$	11.7293	−	18.8824i	0.418636	−	0.673941i
$786$	14.2898			0.509702
$787$	30.7700	+	30.7700i	1.09683	+	1.09683i	0.994779	+	0.102055i	$0.0325417\pi$
$787$	30.7700	+	30.7700i	1.09683	+	1.09683i	0.102055	+	0.994779i	$0.467458\pi$
$788$	−10.4344	+	10.4344i	−0.371711	+	0.371711i
$789$	−20.2311			−0.720248
$790$	−16.4964	−	10.2471i	−0.586914	−	0.364577i
$791$		−	14.8186i		−	0.526889i
$792$	−6.89686	−	1.10327i	−0.245069	−	0.0392031i
$793$	1.93626	+	1.93626i	0.0687586	+	0.0687586i
$794$	26.9779			0.957409
$795$	3.98499	+	17.0538i	0.141333	+	0.604835i
$796$	−9.63893			−0.341643
$797$	14.6510	−	14.6510i	0.518965	−	0.518965i	−0.398293	−	0.917258i	$-0.630397\pi$
$797$	14.6510	−	14.6510i	0.518965	−	0.518965i	0.917258	+	0.398293i	$0.130397\pi$
$798$	2.53997	−	2.53997i	0.0899140	−	0.0899140i
$799$	2.43503			0.0861453
$800$	4.73619	+	1.60266i	0.167450	+	0.0566627i
$801$	13.8321			0.488734
$802$	0.865512	+	0.865512i	0.0305623	+	0.0305623i
$803$	2.58241	−	16.1433i	0.0911313	−	0.569686i
$804$			3.60780i			0.127237i
$805$	−4.52175	−	19.3508i	−0.159371	−	0.682026i
$806$	−14.0469			−0.494780
$807$	−17.2643	+	17.2643i	−0.607733	+	0.607733i
$808$	11.3666	+	11.3666i	0.399875	+	0.399875i
$809$	0.595169			0.0209250			0.0104625	−	0.999945i	$-0.496670\pi$
$809$	0.595169			0.0209250			0.0104625	+	0.999945i	$0.496670\pi$
$810$	−3.32905	−	2.06793i	−0.116971	−	0.0726596i
$811$			2.51220i			0.0882153i	0.999027	+	0.0441076i	$0.0140445\pi$
$811$			2.51220i			0.0882153i	−0.999027	+	0.0441076i	$0.985956\pi$
$812$	2.92928	−	2.92928i	0.102798	−	0.102798i
$813$	4.98393	−	4.98393i	0.174794	−	0.174794i
$814$	24.1412	−	17.4827i	0.846149	−	0.612769i
$815$	13.8269	+	8.58895i	0.484336	+	0.300858i
$816$		−	4.82795i		−	0.169012i
$817$	30.9919	−	30.9919i	1.08427	−	1.08427i
$818$	−22.1411	−	22.1411i	−0.774146	−	0.774146i
$819$			5.79358i			0.202444i
$820$	12.6435	−	2.95443i	0.441529	−	0.103173i
$821$		−	21.3817i		−	0.746226i	−0.927786	−	0.373113i	$-0.878290\pi$
$821$		−	21.3817i		−	0.746226i	0.927786	−	0.373113i	$-0.121710\pi$
$822$	−2.46198	−	2.46198i	−0.0858713	−	0.0858713i
$823$	−33.1638	−	33.1638i	−1.15602	−	1.15602i	−0.985324	−	0.170695i	$-0.945399\pi$
$823$	−33.1638	−	33.1638i	−1.15602	−	1.15602i	−0.170695	−	0.985324i	$-0.554601\pi$
$824$	3.35512			0.116881
$825$	−14.9777	+	4.64109i	−0.521458	+	0.161582i
$826$	−13.4843			−0.469178
$827$	−6.34437	−	6.34437i	−0.220615	−	0.220615i	0.588142	−	0.808757i	$-0.299860\pi$
$827$	−6.34437	−	6.34437i	−0.220615	−	0.220615i	−0.808757	+	0.588142i	$0.799860\pi$
$828$	13.2338	+	13.2338i	0.459907	+	0.459907i
$829$			19.5827i			0.680136i	0.940401	+	0.340068i	$0.110450\pi$
$829$			19.5827i			0.680136i	−0.940401	+	0.340068i	$0.889550\pi$
$830$	−27.2861	+	6.37602i	−0.947116	+	0.221315i
$831$		−	7.84316i		−	0.272076i
$832$	1.94532	+	1.94532i	0.0674418	+	0.0674418i
$833$	3.61043	−	3.61043i	0.125094	−	0.125094i
$834$			14.5752i			0.504698i
$835$	21.6459	+	13.4459i	0.749088	+	0.465316i
$836$	−7.39003	−	10.2046i	−0.255589	−	0.352933i
$837$	17.4310	−	17.4310i	0.602502	−	0.602502i
$838$	20.9817	−	20.9817i	0.724800	−	0.724800i
$839$			31.7658i			1.09668i	0.836256	+	0.548338i	$0.184739\pi$
$839$			31.7658i			1.09668i	−0.836256	+	0.548338i	$0.815261\pi$
$840$	1.79603	+	1.11565i	0.0619690	+	0.0384936i
$841$	−11.8386			−0.408227
$842$	17.8659	+	17.8659i	0.615700	+	0.615700i
$843$	−1.47210	+	1.47210i	−0.0507019	+	0.0507019i
$844$	−21.6150			−0.744019
$845$	−2.76354	−	11.8266i	−0.0950686	−	0.406846i
$846$		−	1.00432i		−	0.0345293i
$847$	9.81645	−	4.96361i	0.337297	−	0.170552i
$848$	−5.85701	−	5.85701i	−0.201131	−	0.201131i
$849$	25.7248			0.882872
$850$	11.3134	+	22.8860i	0.388046	+	0.784982i
$851$	−79.8688			−2.73787
$852$	3.32711	−	3.32711i	0.113985	−	0.113985i
$853$	4.56328	−	4.56328i	0.156244	−	0.156244i	−0.624656	−	0.780900i	$-0.714761\pi$
$853$	4.56328	−	4.56328i	0.156244	−	0.156244i	0.780900	+	0.624656i	$0.214761\pi$
$854$	−0.995343			−0.0340599
$855$	−4.07047	−	17.4196i	−0.139207	−	0.595737i
$856$	−0.804210			−0.0274873
$857$	−21.8450	−	21.8450i	−0.746210	−	0.746210i	0.227555	−	0.973765i	$-0.426927\pi$
$857$	−21.8450	−	21.8450i	−0.746210	−	0.746210i	−0.973765	+	0.227555i	$0.926927\pi$
$858$	−8.51930	−	1.36281i	−0.290844	−	0.0465256i
$859$			3.49656i			0.119301i	0.998219	+	0.0596506i	$0.0189987\pi$
$859$			3.49656i			0.119301i	−0.998219	+	0.0596506i	$0.981001\pi$
$860$	21.9146	+	13.6128i	0.747281	+	0.464193i
$861$	5.49052			0.187117
$862$	−17.3413	+	17.3413i	−0.590647	+	0.590647i
$863$	19.3724	+	19.3724i	0.659445	+	0.659445i	0.955249	−	0.295804i	$-0.0955874\pi$
$863$	19.3724	+	19.3724i	0.659445	+	0.659445i	−0.295804	+	0.955249i	$0.595587\pi$
$864$	−4.82795			−0.164250
$865$	−24.2055	+	38.9672i	−0.823011	+	1.32492i
$866$		−	6.77105i		−	0.230090i
$867$	6.06457	−	6.06457i	0.205964	−	0.205964i
$868$	3.61043	−	3.61043i	0.122546	−	0.122546i
$869$	−23.3294	+	16.8948i	−0.791395	+	0.573117i
$870$	1.99303	+	8.52915i	0.0675699	+	0.289165i
$871$		−	10.4969i		−	0.355673i
$872$	−3.41387	+	3.41387i	−0.115608	+	0.115608i
$873$	10.7526	+	10.7526i	0.363922	+	0.363922i
$874$			33.7609i			1.14198i
$875$	−11.1281	−	1.07988i	−0.376197	−	0.0365066i
$876$		−	4.66093i		−	0.157478i
$877$	13.2861	+	13.2861i	0.448641	+	0.448641i	0.894903	−	0.446262i	$-0.147245\pi$
$877$	13.2861	+	13.2861i	0.448641	+	0.448641i	−0.446262	+	0.894903i	$0.647245\pi$
$878$	−10.5487	−	10.5487i	−0.356003	−	0.356003i
$879$	−21.0861			−0.711217
$880$	4.85921	−	5.60251i	0.163804	−	0.188860i
$881$	−0.866059			−0.0291783			−0.0145891	−	0.999894i	$-0.504644\pi$
$881$	−0.866059			−0.0291783			−0.0145891	+	0.999894i	$0.504644\pi$
$882$	−1.48911	−	1.48911i	−0.0501409	−	0.0501409i
$883$	22.3900	+	22.3900i	0.753484	+	0.753484i	0.975128	−	0.221643i	$-0.0711421\pi$
$883$	22.3900	+	22.3900i	0.753484	+	0.753484i	−0.221643	+	0.975128i	$0.571142\pi$
$884$			14.0469i			0.472447i
$885$	15.0438	−	24.2182i	0.505690	−	0.814085i
$886$			25.6030i			0.860150i
$887$	−3.94042	−	3.94042i	−0.132306	−	0.132306i	0.637852	−	0.770159i	$-0.279823\pi$
$887$	−3.94042	−	3.94042i	−0.132306	−	0.132306i	−0.770159	+	0.637852i	$0.779823\pi$
$888$	6.00886	−	6.00886i	0.201644	−	0.201644i
$889$		−	16.4315i		−	0.551094i
$890$	−7.74975	+	12.4759i	−0.259772	+	0.418194i
$891$	−4.70799	+	3.40946i	−0.157724	+	0.114221i
$892$	15.6081	−	15.6081i	0.522598	−	0.522598i
$893$	1.28107	−	1.28107i	0.0428692	−	0.0428692i
$894$			3.44263i			0.115139i
$895$	9.35607	+	40.0393i	0.312739	+	1.33837i
$896$	−1.00000			−0.0334077
$897$	16.3470	+	16.3470i	0.545810	+	0.545810i
$898$	−13.3546	+	13.3546i	−0.445649	+	0.445649i
$899$	21.1520			0.705457
$900$	9.43924	−	4.66616i	0.314641	−	0.155539i
$901$		−	42.2927i		−	1.40897i
$902$	3.04205	−	19.0167i	0.101289	−	0.633186i
$903$	7.71403	+	7.71403i	0.256707	+	0.256707i
$904$	−14.8186			−0.492860
$905$	−4.04348	+	0.944850i	−0.134410	+	0.0314079i
$906$	0.173525			0.00576500
$907$	2.03831	−	2.03831i	0.0676810	−	0.0676810i	−0.672456	−	0.740137i	$-0.734761\pi$
$907$	2.03831	−	2.03831i	0.0676810	−	0.0676810i	0.740137	+	0.672456i	$0.234761\pi$
$908$	7.17217	−	7.17217i	0.238017	−	0.238017i
$909$	33.8522			1.12281
$910$	−5.22554	−	3.24598i	−0.173225	−	0.107603i
$911$	20.2149			0.669751			0.334876	−	0.942262i	$-0.391306\pi$
$911$	20.2149			0.669751			0.334876	+	0.942262i	$0.391306\pi$
$912$	−2.53997	−	2.53997i	−0.0841069	−	0.0841069i
$913$	−6.56512	+	41.0404i	−0.217274	+	1.35824i
$914$			8.99251i			0.297446i
$915$	1.11046	−	1.78767i	0.0367106	−	0.0590985i
$916$	6.01011			0.198580
$917$	10.6862	−	10.6862i	0.352890	−	0.352890i
$918$	−17.4310	−	17.4310i	−0.575307	−	0.575307i
$919$	13.4773			0.444576			0.222288	−	0.974981i	$-0.428648\pi$
$919$	13.4773			0.444576			0.222288	+	0.974981i	$0.428648\pi$
$920$	−19.3508	+	4.52175i	−0.637977	+	0.149078i
$921$			8.88296i			0.292704i
$922$	18.8157	−	18.8157i	0.619661	−	0.619661i
$923$	−9.68020	+	9.68020i	−0.318628	+	0.318628i
$924$	2.53997	−	1.83941i	0.0835589	−	0.0605122i
$925$	−14.4032	+	42.5645i	−0.473576	+	1.39951i
$926$			27.8234i			0.914335i
$927$	4.99613	−	4.99613i	0.164095	−	0.164095i
$928$	−2.92928	−	2.92928i	−0.0961585	−	0.0961585i
$929$			52.0667i			1.70825i	0.520066	+	0.854126i	$0.325907\pi$
$929$			52.0667i			1.70825i	−0.520066	+	0.854126i	$0.674093\pi$
$930$	2.45646	+	10.5124i	0.0805506	+	0.344716i
$931$		−	3.79888i		−	0.124503i
$932$	−12.5141	−	12.5141i	−0.409914	−	0.409914i
$933$	−11.2716	−	11.2716i	−0.369016	−	0.369016i
$934$	3.55747			0.116404
$935$	37.7713	−	2.68361i	1.23525	−	0.0877635i
$936$	5.79358			0.189369
$937$	−7.86146	−	7.86146i	−0.256823	−	0.256823i	0.566938	−	0.823761i	$-0.308128\pi$
$937$	−7.86146	−	7.86146i	−0.256823	−	0.256823i	−0.823761	+	0.566938i	$0.808128\pi$
$938$	2.69798	+	2.69798i	0.0880922	+	0.0880922i
$939$		−	11.8673i		−	0.387276i
$940$	0.905850	+	0.562692i	0.0295456	+	0.0183530i
$941$			10.2930i			0.335543i	0.985826	+	0.167772i	$0.0536571\pi$
$941$			10.2930i			0.335543i	−0.985826	+	0.167772i	$0.946343\pi$
$942$	−6.64668	−	6.64668i	−0.216561	−	0.216561i
$943$	−36.4896	+	36.4896i	−1.18826	+	1.18826i
$944$			13.4843i			0.438876i
$945$	10.5124	−	2.45646i	0.341969	−	0.0799087i
$946$	30.9919	−	22.4439i	1.00763	−	0.729714i
$947$	1.69360	−	1.69360i	0.0550346	−	0.0550346i	−0.679054	−	0.734088i	$-0.737610\pi$
$947$	1.69360	−	1.69360i	0.0550346	−	0.0550346i	0.734088	+	0.679054i	$0.237610\pi$
$948$	−5.80679	+	5.80679i	−0.188596	+	0.188596i
$949$			13.5609i			0.440206i
$950$	17.9922	+	6.08832i	0.583744	+	0.197531i
$951$	20.4362			0.662688
$952$	−3.61043	−	3.61043i	−0.117015	−	0.117015i
$953$	26.7457	−	26.7457i	0.866378	−	0.866378i	−0.125691	−	0.992069i	$-0.540115\pi$
$953$	26.7457	−	26.7457i	0.866378	−	0.866378i	0.992069	+	0.125691i	$0.0401149\pi$
$954$	−17.4435			−0.564753
$955$	6.58416	−	1.53854i	0.213058	−	0.0497858i
$956$		−	6.08354i		−	0.196756i
$957$	12.8285	+	2.05214i	0.414685	+	0.0663362i
$958$	20.5371	+	20.5371i	0.663523	+	0.663523i
$959$	−3.68223			−0.118905
$960$	1.11565	−	1.79603i	0.0360075	−	0.0579667i
$961$	−4.92959			−0.159019
$962$	−17.4827	+	17.4827i	−0.563666	+	0.563666i
$963$	−1.19756	+	1.19756i	−0.0385907	+	0.0385907i
$964$	−3.89903			−0.125579
$965$	−26.6695	+	42.9338i	−0.858520	+	1.38209i
$966$	−8.40325			−0.270370
$967$	31.2405	+	31.2405i	1.00463	+	1.00463i	0.999989	+	0.00463675i	$0.00147593\pi$
$967$	31.2405	+	31.2405i	1.00463	+	1.00463i	0.00463675	+	0.999989i	$0.498524\pi$
$968$	−4.96361	−	9.81645i	−0.159536	−	0.315513i
$969$		−	18.3408i		−	0.589191i
$970$	−15.7228	+	3.67398i	−0.504828	+	0.117964i
$971$	−20.8809			−0.670099			−0.335049	−	0.942201i	$-0.608753\pi$
$971$	−20.8809			−0.670099			−0.335049	+	0.942201i	$0.608753\pi$
$972$	−11.4135	+	11.4135i	−0.366087	+	0.366087i
$973$	10.8996	+	10.8996i	0.349425	+	0.349425i
$974$	−16.9181			−0.542092
$975$	11.6598	−	5.76385i	0.373411	−	0.184591i
$976$			0.995343i			0.0318602i
$977$	−35.7769	+	35.7769i	−1.14461	+	1.14461i	−0.157009	+	0.987597i	$0.550185\pi$
$977$	−35.7769	+	35.7769i	−1.14461	+	1.14461i	−0.987597	+	0.157009i	$0.949815\pi$
$978$	4.86714	−	4.86714i	0.155634	−	0.155634i
$979$	12.7773	+	17.6436i	0.408363	+	0.563893i
$980$	2.17741	−	0.508801i	0.0695549	−	0.0162530i
$981$			10.1673i			0.324616i
$982$	28.8153	−	28.8153i	0.919532	−	0.919532i
$983$	−13.8746	−	13.8746i	−0.442532	−	0.442532i	0.450330	−	0.892862i	$-0.351306\pi$
$983$	−13.8746	−	13.8746i	−0.442532	−	0.442532i	−0.892862	+	0.450330i	$0.851306\pi$
$984$		−	5.49052i		−	0.175032i
$985$	−28.0291	−	17.4110i	−0.893081	−	0.554761i
$986$		−	21.1520i		−	0.673615i
$987$	0.318863	+	0.318863i	0.0101495	+	0.0101495i
$988$	7.39003	+	7.39003i	0.235108	+	0.235108i
$989$	−102.534			−3.26038
$990$	−1.10685	−	15.5786i	−0.0351779	−	0.495122i
$991$	20.7493			0.659124			0.329562	−	0.944134i	$-0.393099\pi$
$991$	20.7493			0.659124			0.329562	+	0.944134i	$0.393099\pi$
$992$	−3.61043	−	3.61043i	−0.114631	−	0.114631i
$993$	2.14468	+	2.14468i	0.0680593	+	0.0680593i
$994$		−	4.97615i		−	0.157834i
$995$	−4.90430	−	20.9879i	−0.155477	−	0.665362i
$996$			11.8492i			0.375457i
$997$	−16.0145	−	16.0145i	−0.507185	−	0.507185i	0.406476	−	0.913661i	$-0.366757\pi$
$997$	−16.0145	−	16.0145i	−0.507185	−	0.507185i	−0.913661	+	0.406476i	$0.866757\pi$
$998$	0.843353	−	0.843353i	0.0266959	−	0.0266959i
$999$		−	43.3891i		−	1.37277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.e.43.3	✓	16
5.2	odd	4	inner	770.2.m.e.197.7	yes	16
11.10	odd	2	inner	770.2.m.e.43.7	yes	16
55.32	even	4	inner	770.2.m.e.197.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.e.43.3	✓	16	1.1	even	1	trivial
770.2.m.e.43.7	yes	16	11.10	odd	2	inner
770.2.m.e.197.3	yes	16	55.32	even	4	inner
770.2.m.e.197.7	yes	16	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.668611 - 0.668611i) q^{3} +1.00000i q^{4} +(-2.17741 + 0.508801i) q^{5} +0.945559i q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.10592i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.668611 - 0.668611i) q^{3} +1.00000i q^{4} +(-2.17741 + 0.508801i) q^{5} +0.945559i q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.10592i q^{9} +(1.89944 + 1.17989i) q^{10} +(2.68621 - 1.94532i) q^{11} +(0.668611 - 0.668611i) q^{12} +(-1.94532 + 1.94532i) q^{13} -1.00000i q^{14} +(1.79603 + 1.11565i) q^{15} -1.00000 q^{16} +(-3.61043 - 3.61043i) q^{17} +(-1.48911 + 1.48911i) q^{18} -3.79888 q^{19} +(-0.508801 - 2.17741i) q^{20} -0.945559i q^{21} +(-3.27499 - 0.523891i) q^{22} +(6.28411 + 6.28411i) q^{23} -0.945559 q^{24} +(4.48224 - 2.21574i) q^{25} +2.75110 q^{26} +(-3.41387 + 3.41387i) q^{27} +(-0.707107 + 0.707107i) q^{28} -4.14263 q^{29} +(-0.481101 - 2.05887i) q^{30} -5.10592 q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.09669 - 0.495370i) q^{33} +5.10592i q^{34} +(-1.89944 - 1.17989i) q^{35} +2.10592 q^{36} +(-6.35482 + 6.35482i) q^{37} +(2.68621 + 2.68621i) q^{38} +2.60132 q^{39} +(-1.17989 + 1.89944i) q^{40} +5.80665i q^{41} +(-0.668611 + 0.668611i) q^{42} +(-8.15817 + 8.15817i) q^{43} +(1.94532 + 2.68621i) q^{44} +(1.07149 + 4.58545i) q^{45} -8.88707i q^{46} +(-0.337222 + 0.337222i) q^{47} +(0.668611 + 0.668611i) q^{48} +1.00000i q^{49} +(-4.73619 - 1.60266i) q^{50} +4.82795i q^{51} +(-1.94532 - 1.94532i) q^{52} +(5.85701 + 5.85701i) q^{53} +4.82795 q^{54} +(-4.85921 + 5.60251i) q^{55} +1.00000 q^{56} +(2.53997 + 2.53997i) q^{57} +(2.92928 + 2.92928i) q^{58} -13.4843i q^{59} +(-1.11565 + 1.79603i) q^{60} -0.995343i q^{61} +(3.61043 + 3.61043i) q^{62} +(1.48911 - 1.48911i) q^{63} -1.00000i q^{64} +(3.24598 - 5.22554i) q^{65} +(1.83941 + 2.53997i) q^{66} +(-2.69798 + 2.69798i) q^{67} +(3.61043 - 3.61043i) q^{68} -8.40325i q^{69} +(0.508801 + 2.17741i) q^{70} +4.97615 q^{71} +(-1.48911 - 1.48911i) q^{72} +(3.48553 - 3.48553i) q^{73} +8.98708 q^{74} +(-4.47834 - 1.51541i) q^{75} -3.79888i q^{76} +(3.27499 + 0.523891i) q^{77} +(-1.83941 - 1.83941i) q^{78} -8.68486 q^{79} +(2.17741 - 0.508801i) q^{80} -1.75265 q^{81} +(4.10592 - 4.10592i) q^{82} +(-8.86108 + 8.86108i) q^{83} +0.945559 q^{84} +(9.69838 + 6.02440i) q^{85} +11.5374 q^{86} +(2.76981 + 2.76981i) q^{87} +(0.523891 - 3.27499i) q^{88} +6.56822i q^{89} +(2.48474 - 4.00006i) q^{90} -2.75110 q^{91} +(-6.28411 + 6.28411i) q^{92} +(3.41387 + 3.41387i) q^{93} +0.476904 q^{94} +(8.27172 - 1.93287i) q^{95} -0.945559i q^{96} +(-5.10592 + 5.10592i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-4.09668 - 5.65695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 8 q^{5}+O(q^{10}) \) 16 * q - 8 * q^3 - 8 * q^5	\( 16 q - 8 q^{3} - 8 q^{5} - 8 q^{11} + 8 q^{12} + 24 q^{15} - 16 q^{16} + 16 q^{20} - 8 q^{22} + 32 q^{23} + 16 q^{25} + 16 q^{26} - 32 q^{27} - 24 q^{33} - 48 q^{36} - 48 q^{37} - 8 q^{38} - 8 q^{42} + 72 q^{45} + 8 q^{48} - 16 q^{53} - 48 q^{55} + 16 q^{56} + 32 q^{58} - 56 q^{60} - 32 q^{66} + 48 q^{67} - 16 q^{70} - 48 q^{71} + 112 q^{75} + 8 q^{77} + 32 q^{78} + 8 q^{80} - 80 q^{81} - 16 q^{82} + 32 q^{86} - 8 q^{88} - 16 q^{91} - 32 q^{92} + 32 q^{93}+O(q^{100}) \) 16 * q - 8 * q^3 - 8 * q^5 - 8 * q^11 + 8 * q^12 + 24 * q^15 - 16 * q^16 + 16 * q^20 - 8 * q^22 + 32 * q^23 + 16 * q^25 + 16 * q^26 - 32 * q^27 - 24 * q^33 - 48 * q^36 - 48 * q^37 - 8 * q^38 - 8 * q^42 + 72 * q^45 + 8 * q^48 - 16 * q^53 - 48 * q^55 + 16 * q^56 + 32 * q^58 - 56 * q^60 - 32 * q^66 + 48 * q^67 - 16 * q^70 - 48 * q^71 + 112 * q^75 + 8 * q^77 + 32 * q^78 + 8 * q^80 - 80 * q^81 - 16 * q^82 + 32 * q^86 - 8 * q^88 - 16 * q^91 - 32 * q^92 + 32 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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