LMFDB - Embedded newform 770.2.m.e.197.2

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			197.2
Root			$1.72791i$ of defining polynomial
Character	$\chi$	$=$	770.197
Dual form			770.2.m.e.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.40684 + 1.40684i) q^{3} -1.00000i q^{4} +(-0.177857 + 2.22898i) q^{5} -1.98957i q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -0.958399i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.40684 + 1.40684i) q^{3} -1.00000i q^{4} +(-0.177857 + 2.22898i) q^{5} -1.98957i q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -0.958399i q^{9} +(-1.45037 - 1.70189i) q^{10} +(-2.05113 + 2.60632i) q^{11} +(1.40684 + 1.40684i) q^{12} +(-2.60632 - 2.60632i) q^{13} +1.00000i q^{14} +(-2.88561 - 3.38604i) q^{15} -1.00000 q^{16} +(-1.44363 + 1.44363i) q^{17} +(0.677691 + 0.677691i) q^{18} +2.90073 q^{19} +(2.22898 + 0.177857i) q^{20} +1.98957i q^{21} +(-0.392578 - 3.29331i) q^{22} +(-5.60182 + 5.60182i) q^{23} -1.98957 q^{24} +(-4.93673 - 0.792880i) q^{25} +3.68589 q^{26} +(-2.87221 - 2.87221i) q^{27} +(-0.707107 - 0.707107i) q^{28} +7.01101 q^{29} +(4.43472 + 0.353859i) q^{30} -2.04160 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.781062 - 6.55228i) q^{33} -2.04160i q^{34} +(1.45037 + 1.70189i) q^{35} -0.958399 q^{36} +(-2.35571 - 2.35571i) q^{37} +(-2.05113 + 2.05113i) q^{38} +7.33334 q^{39} +(-1.70189 + 1.45037i) q^{40} -1.47305i q^{41} +(-1.40684 - 1.40684i) q^{42} +(-1.73654 - 1.73654i) q^{43} +(2.60632 + 2.05113i) q^{44} +(2.13626 + 0.170458i) q^{45} -7.92217i q^{46} +(-1.81368 - 1.81368i) q^{47} +(1.40684 - 1.40684i) q^{48} -1.00000i q^{49} +(4.05145 - 2.93015i) q^{50} -4.06191i q^{51} +(-2.60632 + 2.60632i) q^{52} +(3.72749 - 3.72749i) q^{53} +4.06191 q^{54} +(-5.44463 - 5.03548i) q^{55} +1.00000 q^{56} +(-4.08087 + 4.08087i) q^{57} +(-4.95753 + 4.95753i) q^{58} -8.95966i q^{59} +(-3.38604 + 2.88561i) q^{60} -13.4479i q^{61} +(1.44363 - 1.44363i) q^{62} +(-0.677691 - 0.677691i) q^{63} +1.00000i q^{64} +(6.27299 - 5.34588i) q^{65} +(5.18545 + 4.08087i) q^{66} +(9.72961 + 9.72961i) q^{67} +(1.44363 + 1.44363i) q^{68} -15.7617i q^{69} +(-2.22898 - 0.177857i) q^{70} -9.43243 q^{71} +(0.677691 - 0.677691i) q^{72} +(-2.09129 - 2.09129i) q^{73} +3.33148 q^{74} +(8.06065 - 5.82974i) q^{75} -2.90073i q^{76} +(0.392578 + 3.29331i) q^{77} +(-5.18545 + 5.18545i) q^{78} +11.1360 q^{79} +(0.177857 - 2.22898i) q^{80} +10.9567 q^{81} +(1.04160 + 1.04160i) q^{82} +(-9.44330 - 9.44330i) q^{83} +1.98957 q^{84} +(-2.96107 - 3.47459i) q^{85} +2.45584 q^{86} +(-9.86337 + 9.86337i) q^{87} +(-3.29331 + 0.392578i) q^{88} +17.2036i q^{89} +(-1.63109 + 1.39003i) q^{90} -3.68589 q^{91} +(5.60182 + 5.60182i) q^{92} +(2.87221 - 2.87221i) q^{93} +2.56493 q^{94} +(-0.515915 + 6.46568i) q^{95} +1.98957i q^{96} +(-2.04160 - 2.04160i) q^{97} +(0.707107 + 0.707107i) q^{98} +(2.49789 + 1.96580i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

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

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
$3$	−1.40684	+	1.40684i	−0.812240	+	0.812240i	−0.984969	−	0.172730i	$-0.944741\pi$
$3$	−1.40684	+	1.40684i	−0.812240	+	0.812240i	0.172730	+	0.984969i	$0.444741\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.177857	+	2.22898i	−0.0795400	+	0.996832i
$5$	−0.177857	+	2.22898i	−0.0795400	+	0.996832i
$6$		−	1.98957i		−	0.812240i
$7$	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
$9$		−	0.958399i		−	0.319466i
$10$	−1.45037	−	1.70189i	−0.458646	−	0.538186i
$11$	−2.05113	+	2.60632i	−0.618438	+	0.785834i
$11$	−2.05113	+	2.60632i	−0.618438	+	0.785834i
$12$	1.40684	+	1.40684i	0.406120	+	0.406120i
$13$	−2.60632	−	2.60632i	−0.722862	−	0.722862i	0.246325	−	0.969187i	$-0.420777\pi$
$13$	−2.60632	−	2.60632i	−0.722862	−	0.722862i	−0.969187	+	0.246325i	$0.920777\pi$
$14$			1.00000i			0.267261i
$15$	−2.88561	−	3.38604i	−0.745061	−	0.874272i
$16$	−1.00000			−0.250000
$17$	−1.44363	+	1.44363i	−0.350132	+	0.350132i	−0.860158	−	0.510027i	$-0.829635\pi$
$17$	−1.44363	+	1.44363i	−0.350132	+	0.350132i	0.510027	+	0.860158i	$0.329635\pi$
$18$	0.677691	+	0.677691i	0.159733	+	0.159733i
$19$	2.90073			0.665473			0.332737	−	0.943020i	$-0.392028\pi$
$19$	2.90073			0.665473			0.332737	+	0.943020i	$0.392028\pi$
$20$	2.22898	+	0.177857i	0.498416	+	0.0397700i
$21$			1.98957i			0.434160i
$22$	−0.392578	−	3.29331i	−0.0836979	−	0.702136i
$23$	−5.60182	+	5.60182i	−1.16806	+	1.16806i	−0.185396	+	0.982664i	$0.559357\pi$
$23$	−5.60182	+	5.60182i	−1.16806	+	1.16806i	−0.982664	+	0.185396i	$0.940643\pi$
$24$	−1.98957			−0.406120
$25$	−4.93673	−	0.792880i	−0.987347	−	0.158576i
$26$	3.68589			0.722862
$27$	−2.87221	−	2.87221i	−0.552756	−	0.552756i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	7.01101			1.30191			0.650956	−	0.759115i	$-0.274368\pi$
$29$	7.01101			1.30191			0.650956	+	0.759115i	$0.274368\pi$
$30$	4.43472	+	0.353859i	0.809666	+	0.0646056i
$31$	−2.04160			−0.366682			−0.183341	−	0.983049i	$-0.558691\pi$
$31$	−2.04160			−0.366682			−0.183341	+	0.983049i	$0.558691\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.781062	−	6.55228i	−0.135966	−	1.14061i
$34$		−	2.04160i		−	0.350132i
$35$	1.45037	+	1.70189i	0.245156	+	0.287672i
$36$	−0.958399			−0.159733
$37$	−2.35571	−	2.35571i	−0.387277	−	0.387277i	0.486438	−	0.873715i	$-0.338296\pi$
$37$	−2.35571	−	2.35571i	−0.387277	−	0.387277i	−0.873715	+	0.486438i	$0.838296\pi$
$38$	−2.05113	+	2.05113i	−0.332737	+	0.332737i
$39$	7.33334			1.17427
$40$	−1.70189	+	1.45037i	−0.269093	+	0.229323i
$41$		−	1.47305i		−	0.230051i	−0.993363	−	0.115026i	$-0.963305\pi$
$41$		−	1.47305i		−	0.230051i	0.993363	−	0.115026i	$-0.0366950\pi$
$42$	−1.40684	−	1.40684i	−0.217080	−	0.217080i
$43$	−1.73654	−	1.73654i	−0.264820	−	0.264820i	0.562189	−	0.827009i	$-0.309959\pi$
$43$	−1.73654	−	1.73654i	−0.264820	−	0.264820i	−0.827009	+	0.562189i	$0.809959\pi$
$44$	2.60632	+	2.05113i	0.392917	+	0.309219i
$45$	2.13626	+	0.170458i	0.318454	+	0.0254104i
$46$		−	7.92217i		−	1.16806i
$47$	−1.81368	−	1.81368i	−0.264553	−	0.264553i	0.562348	−	0.826901i	$-0.309898\pi$
$47$	−1.81368	−	1.81368i	−0.264553	−	0.264553i	−0.826901	+	0.562348i	$0.809898\pi$
$48$	1.40684	−	1.40684i	0.203060	−	0.203060i
$49$		−	1.00000i		−	0.142857i
$50$	4.05145	−	2.93015i	0.572961	−	0.414385i
$51$		−	4.06191i		−	0.568782i
$52$	−2.60632	+	2.60632i	−0.361431	+	0.361431i
$53$	3.72749	−	3.72749i	0.512010	−	0.512010i	−0.403132	−	0.915142i	$-0.632078\pi$
$53$	3.72749	−	3.72749i	0.512010	−	0.512010i	0.915142	+	0.403132i	$0.132078\pi$
$54$	4.06191			0.552756
$55$	−5.44463	−	5.03548i	−0.734153	−	0.678984i
$56$	1.00000			0.133631
$57$	−4.08087	+	4.08087i	−0.540524	+	0.540524i
$58$	−4.95753	+	4.95753i	−0.650956	+	0.650956i
$59$		−	8.95966i		−	1.16645i	−0.812311	−	0.583224i	$-0.801791\pi$
$59$		−	8.95966i		−	1.16645i	0.812311	−	0.583224i	$-0.198209\pi$
$60$	−3.38604	+	2.88561i	−0.437136	+	0.372530i
$61$		−	13.4479i		−	1.72183i	−0.508752	−	0.860913i	$-0.669893\pi$
$61$		−	13.4479i		−	1.72183i	0.508752	−	0.860913i	$-0.330107\pi$
$62$	1.44363	−	1.44363i	0.183341	−	0.183341i
$63$	−0.677691	−	0.677691i	−0.0853810	−	0.0853810i
$64$			1.00000i			0.125000i
$65$	6.27299	−	5.34588i	0.778068	−	0.663075i
$66$	5.18545	+	4.08087i	0.638285	+	0.502320i
$67$	9.72961	+	9.72961i	1.18866	+	1.18866i	0.977438	+	0.211224i	$0.0677449\pi$
$67$	9.72961	+	9.72961i	1.18866	+	1.18866i	0.211224	+	0.977438i	$0.432255\pi$
$68$	1.44363	+	1.44363i	0.175066	+	0.175066i
$69$		−	15.7617i		−	1.89749i
$70$	−2.22898	−	0.177857i	−0.266414	−	0.0212580i
$71$	−9.43243			−1.11942			−0.559711	−	0.828688i	$-0.689088\pi$
$71$	−9.43243			−1.11942			−0.559711	+	0.828688i	$0.689088\pi$
$72$	0.677691	−	0.677691i	0.0798666	−	0.0798666i
$73$	−2.09129	−	2.09129i	−0.244767	−	0.244767i	0.574052	−	0.818819i	$-0.305371\pi$
$73$	−2.09129	−	2.09129i	−0.244767	−	0.244767i	−0.818819	+	0.574052i	$0.805371\pi$
$74$	3.33148			0.387277
$75$	8.06065	−	5.82974i	0.930764	−	0.673160i
$76$		−	2.90073i		−	0.332737i
$77$	0.392578	+	3.29331i	0.0447384	+	0.375307i
$78$	−5.18545	+	5.18545i	−0.587137	+	0.587137i
$79$	11.1360			1.25290			0.626448	−	0.779463i	$-0.284508\pi$
$79$	11.1360			1.25290			0.626448	+	0.779463i	$0.284508\pi$
$80$	0.177857	−	2.22898i	0.0198850	−	0.249208i
$81$	10.9567			1.21741
$82$	1.04160	+	1.04160i	0.115026	+	0.115026i
$83$	−9.44330	−	9.44330i	−1.03654	−	1.03654i	−0.999307	−	0.0372306i	$-0.988146\pi$
$83$	−9.44330	−	9.44330i	−1.03654	−	1.03654i	−0.0372306	−	0.999307i	$-0.511854\pi$
$84$	1.98957			0.217080
$85$	−2.96107	−	3.47459i	−0.321173	−	0.376872i
$86$	2.45584			0.264820
$87$	−9.86337	+	9.86337i	−1.05746	+	1.05746i
$88$	−3.29331	+	0.392578i	−0.351068	+	0.0418489i
$89$			17.2036i			1.82358i	0.410654	+	0.911791i	$0.365300\pi$
$89$			17.2036i			1.82358i	−0.410654	+	0.911791i	$0.634700\pi$
$90$	−1.63109	+	1.39003i	−0.171932	+	0.146522i
$91$	−3.68589			−0.386386
$92$	5.60182	+	5.60182i	0.584030	+	0.584030i
$93$	2.87221	−	2.87221i	0.297834	−	0.297834i
$94$	2.56493			0.264553
$95$	−0.515915	+	6.46568i	−0.0529318	+	0.663365i
$96$			1.98957i			0.203060i
$97$	−2.04160	−	2.04160i	−0.207293	−	0.207293i	0.595823	−	0.803116i	$-0.296826\pi$
$97$	−2.04160	−	2.04160i	−0.207293	−	0.207293i	−0.803116	+	0.595823i	$0.796826\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	2.49789	+	1.96580i	0.251048	+	0.197570i
$100$	−0.792880	+	4.93673i	−0.0792880	+	0.493673i
$101$			0.456471i			0.0454206i	0.999742	+	0.0227103i	$0.00722953\pi$
$101$			0.456471i			0.0454206i	−0.999742	+	0.0227103i	$0.992770\pi$
$102$	2.87221	+	2.87221i	0.284391	+	0.284391i
$103$	−7.10225	+	7.10225i	−0.699806	+	0.699806i	−0.964368	−	0.264563i	$-0.914772\pi$
$103$	−7.10225	+	7.10225i	−0.699806	+	0.699806i	0.264563	+	0.964368i	$0.414772\pi$
$104$		−	3.68589i		−	0.361431i
$105$	−4.43472	−	0.353859i	−0.432785	−	0.0345331i
$106$			5.27146i			0.512010i
$107$	−10.6783	+	10.6783i	−1.03231	+	1.03231i	−0.0328493	+	0.999460i	$0.510458\pi$
$107$	−10.6783	+	10.6783i	−1.03231	+	1.03231i	−0.999460	+	0.0328493i	$0.989542\pi$
$108$	−2.87221	+	2.87221i	−0.276378	+	0.276378i
$109$	−4.06191			−0.389061			−0.194530	−	0.980897i	$-0.562318\pi$
$109$	−4.06191			−0.389061			−0.194530	+	0.980897i	$0.562318\pi$
$110$	7.41055	−	0.289312i	0.706569	−	0.0275848i
$111$	6.62823			0.629123
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	2.06065	−	2.06065i	0.193850	−	0.193850i	−0.603507	−	0.797357i	$-0.706231\pi$
$113$	2.06065	−	2.06065i	0.193850	−	0.193850i	0.797357	+	0.603507i	$0.206231\pi$
$114$		−	5.77121i		−	0.540524i
$115$	−11.4900	−	13.4827i	−1.07145	−	1.25727i
$116$		−	7.01101i		−	0.650956i
$117$	−2.49789	+	2.49789i	−0.230930	+	0.230930i
$118$	6.33544	+	6.33544i	0.583224	+	0.583224i
$119$			2.04160i			0.187153i
$120$	0.353859	−	4.43472i	0.0323028	−	0.404833i
$121$	−2.58576	−	10.6918i	−0.235069	−	0.971979i
$122$	9.50909	+	9.50909i	0.860913	+	0.860913i
$123$	2.07234	+	2.07234i	0.186857	+	0.186857i
$124$			2.04160i			0.183341i
$125$	2.64535	−	10.8629i	0.236607	−	0.971605i
$126$	0.958399			0.0853810
$127$	−7.36398	+	7.36398i	−0.653447	+	0.653447i	−0.953821	−	0.300374i	$-0.902889\pi$
$127$	−7.36398	+	7.36398i	−0.653447	+	0.653447i	0.300374	+	0.953821i	$0.402889\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	4.88607			0.430195
$130$	−0.655561	+	8.21578i	−0.0574965	+	0.720572i
$131$			8.41298i			0.735045i	0.930015	+	0.367523i	$0.119794\pi$
$131$			8.41298i			0.735045i	−0.930015	+	0.367523i	$0.880206\pi$
$132$	−6.55228	+	0.781062i	−0.570303	+	0.0679828i
$133$	2.05113	−	2.05113i	0.177855	−	0.177855i
$134$	−13.7598			−1.18866
$135$	6.91294	−	5.89126i	0.594971	−	0.507039i
$136$	−2.04160			−0.175066
$137$	2.33017	+	2.33017i	0.199080	+	0.199080i	0.799606	−	0.600526i	$-0.205042\pi$
$137$	2.33017	+	2.33017i	0.199080	+	0.199080i	−0.600526	+	0.799606i	$0.705042\pi$
$138$	11.1452	+	11.1452i	0.948745	+	0.948745i
$139$	−19.2481			−1.63260			−0.816302	−	0.577625i	$-0.803980\pi$
$139$	−19.2481			−1.63260			−0.816302	+	0.577625i	$0.803980\pi$
$140$	1.70189	−	1.45037i	0.143836	−	0.122578i
$141$	5.10312			0.429760
$142$	6.66973	−	6.66973i	0.559711	−	0.559711i
$143$	12.1388	−	1.44700i	1.01509	−	0.121004i
$144$			0.958399i			0.0798666i
$145$	−1.24696	+	15.6274i	−0.103554	+	1.29779i
$146$	2.95753			0.244767
$147$	1.40684	+	1.40684i	0.116034	+	0.116034i
$148$	−2.35571	+	2.35571i	−0.193638	+	0.193638i
$149$	−1.85721			−0.152149			−0.0760744	−	0.997102i	$-0.524239\pi$
$149$	−1.85721			−0.152149			−0.0760744	+	0.997102i	$0.524239\pi$
$150$	−1.57749	+	9.82199i	−0.128802	+	0.801962i
$151$			16.2267i			1.32051i	0.751041	+	0.660256i	$0.229552\pi$
$151$			16.2267i			1.32051i	−0.751041	+	0.660256i	$0.770448\pi$
$152$	2.05113	+	2.05113i	0.166368	+	0.166368i
$153$	1.38357	+	1.38357i	0.111855	+	0.111855i
$154$	−2.60632	−	2.05113i	−0.210023	−	0.165284i
$155$	0.363113	−	4.55069i	0.0291659	−	0.365521i
$156$		−	7.33334i		−	0.587137i
$157$	6.13645	+	6.13645i	0.489742	+	0.489742i	0.908225	−	0.418482i	$-0.137438\pi$
$157$	6.13645	+	6.13645i	0.489742	+	0.489742i	−0.418482	+	0.908225i	$0.637438\pi$
$158$	−7.87433	+	7.87433i	−0.626448	+	0.626448i
$159$			10.4880i			0.831749i
$160$	1.45037	+	1.70189i	0.114661	+	0.134546i
$161$			7.92217i			0.624354i
$162$	−7.74753	+	7.74753i	−0.608704	+	0.608704i
$163$	−11.0161	+	11.0161i	−0.862844	+	0.862844i	−0.991668	−	0.128823i	$-0.958880\pi$
$163$	−11.0161	+	11.0161i	−0.862844	+	0.862844i	0.128823	+	0.991668i	$0.458880\pi$
$164$	−1.47305			−0.115026
$165$	14.7438	−	0.575607i	1.14781	−	0.0448109i
$166$	13.3548			1.03654
$167$	9.51711	−	9.51711i	0.736456	−	0.736456i	−0.235434	−	0.971890i	$-0.575651\pi$
$167$	9.51711	−	9.51711i	0.736456	−	0.736456i	0.971890	+	0.235434i	$0.0756512\pi$
$168$	−1.40684	+	1.40684i	−0.108540	+	0.108540i
$169$			0.585761i			0.0450585i
$170$	4.55069	+	0.363113i	0.349022	+	0.0278495i
$171$		−	2.78006i		−	0.212596i
$172$	−1.73654	+	1.73654i	−0.132410	+	0.132410i
$173$	−11.7515	−	11.7515i	−0.893451	−	0.893451i	0.101396	−	0.994846i	$-0.467669\pi$
$173$	−11.7515	−	11.7515i	−0.893451	−	0.893451i	−0.994846	+	0.101396i	$0.967669\pi$
$174$		−	13.9489i		−	1.05746i
$175$	−4.05145	+	2.93015i	−0.306261	+	0.221498i
$176$	2.05113	−	2.60632i	0.154609	−	0.196458i
$177$	12.6048	+	12.6048i	0.947436	+	0.947436i
$178$	−12.1648	−	12.1648i	−0.911791	−	0.911791i
$179$			17.0823i			1.27679i	0.769707	+	0.638397i	$0.220402\pi$
$179$			17.0823i			1.27679i	−0.769707	+	0.638397i	$0.779598\pi$
$180$	0.170458	−	2.13626i	0.0127052	−	0.159227i
$181$	−0.272513			−0.0202557			−0.0101279	−	0.999949i	$-0.503224\pi$
$181$	−0.272513			−0.0202557			−0.0101279	+	0.999949i	$0.503224\pi$
$182$	2.60632	−	2.60632i	0.193193	−	0.193193i
$183$	18.9190	+	18.9190i	1.39854	+	1.39854i
$184$	−7.92217			−0.584030
$185$	5.66983	−	4.83187i	0.416854	−	0.355246i
$186$			4.06191i			0.297834i
$187$	−0.801487	−	6.72362i	−0.0586106	−	0.491680i
$188$	−1.81368	+	1.81368i	−0.132276	+	0.132276i
$189$	−4.06191			−0.295461
$190$	−4.20712	−	4.93673i	−0.305217	−	0.358148i
$191$	−17.4324			−1.26137			−0.630683	−	0.776041i	$-0.717225\pi$
$191$	−17.4324			−1.26137			−0.630683	+	0.776041i	$0.717225\pi$
$192$	−1.40684	−	1.40684i	−0.101530	−	0.101530i
$193$	−8.56983	−	8.56983i	−0.616870	−	0.616870i	0.327857	−	0.944727i	$-0.393674\pi$
$193$	−8.56983	−	8.56983i	−0.616870	−	0.616870i	−0.944727	+	0.327857i	$0.893674\pi$
$194$	2.88726			0.207293
$195$	−1.30429	+	16.3459i	−0.0934018	+	1.17055i
$196$	−1.00000			−0.0714286
$197$	0.167256	−	0.167256i	0.0119165	−	0.0119165i	−0.701123	−	0.713040i	$-0.747318\pi$
$197$	0.167256	−	0.167256i	0.0119165	−	0.0119165i	0.713040	+	0.701123i	$0.247318\pi$
$198$	−3.15631	+	0.376246i	−0.224309	+	0.0267387i
$199$			6.24611i			0.442775i	0.975186	+	0.221387i	$0.0710585\pi$
$199$			6.24611i			0.442775i	−0.975186	+	0.221387i	$0.928941\pi$
$200$	−2.93015	−	4.05145i	−0.207193	−	0.286481i
$201$	−27.3760			−1.93096
$202$	−0.322774	−	0.322774i	−0.0227103	−	0.0227103i
$203$	4.95753	−	4.95753i	0.347951	−	0.347951i
$204$	−4.06191			−0.284391
$205$	3.28339	+	0.261991i	0.229322	+	0.0182983i
$206$		−	10.0441i		−	0.699806i
$207$	5.36878	+	5.36878i	0.373156	+	0.373156i
$208$	2.60632	+	2.60632i	0.180715	+	0.180715i
$209$	−5.94977	+	7.56022i	−0.411554	+	0.522951i
$210$	3.38604	−	2.88561i	0.233659	−	0.199126i
$211$		−	4.80575i		−	0.330842i	−0.986223	−	0.165421i	$-0.947102\pi$
$211$		−	4.80575i		−	0.330842i	0.986223	−	0.165421i	$-0.0528982\pi$
$212$	−3.72749	−	3.72749i	−0.256005	−	0.256005i
$213$	13.2699	−	13.2699i	0.909240	−	0.909240i
$214$		−	15.1014i		−	1.03231i
$215$	4.17958	−	3.56187i	0.285045	−	0.242917i
$216$		−	4.06191i		−	0.276378i
$217$	−1.44363	+	1.44363i	−0.0980000	+	0.0980000i
$218$	2.87221	−	2.87221i	0.194530	−	0.194530i
$219$	5.88423			0.397619
$220$	−5.03548	+	5.44463i	−0.339492	+	0.367077i
$221$	7.52511			0.506194
$222$	−4.68686	+	4.68686i	−0.314562	+	0.314562i
$223$	−14.4134	+	14.4134i	−0.965191	+	0.965191i	−0.999414	−	0.0342233i	$-0.989104\pi$
$223$	−14.4134	+	14.4134i	−0.965191	+	0.965191i	0.0342233	+	0.999414i	$0.489104\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−0.759896	+	4.73136i	−0.0506597	+	0.315424i
$226$			2.91420i			0.193850i
$227$	−8.67798	+	8.67798i	−0.575978	+	0.575978i	−0.933793	−	0.357815i	$-0.883522\pi$
$227$	−8.67798	+	8.67798i	−0.575978	+	0.575978i	0.357815	+	0.933793i	$0.383522\pi$
$228$	4.08087	+	4.08087i	0.270262	+	0.270262i
$229$			24.0836i			1.59149i	0.605633	+	0.795744i	$0.292920\pi$
$229$			24.0836i			1.59149i	−0.605633	+	0.795744i	$0.707080\pi$
$230$	17.6584	+	1.40901i	1.16436	+	0.0929076i
$231$	−5.18545	−	4.08087i	−0.341178	−	0.268501i
$232$	4.95753	+	4.95753i	0.325478	+	0.325478i
$233$	17.3376	+	17.3376i	1.13582	+	1.13582i	0.989191	+	0.146630i	$0.0468427\pi$
$233$	17.3376	+	17.3376i	1.13582	+	1.13582i	0.146630	+	0.989191i	$0.453157\pi$
$234$		−	3.53255i		−	0.230930i
$235$	4.36524	−	3.72009i	0.284757	−	0.242672i
$236$	−8.95966			−0.583224
$237$	−15.6666	+	15.6666i	−1.01765	+	1.01765i
$238$	−1.44363	−	1.44363i	−0.0935766	−	0.0935766i
$239$	18.4693			1.19468			0.597341	−	0.801988i	$-0.296224\pi$
$239$	18.4693			1.19468			0.597341	+	0.801988i	$0.296224\pi$
$240$	2.88561	+	3.38604i	0.186265	+	0.218568i
$241$			8.78668i			0.566000i	0.959120	+	0.283000i	$0.0913296\pi$
$241$			8.78668i			0.566000i	−0.959120	+	0.283000i	$0.908670\pi$
$242$	9.38863	+	5.73181i	0.603524	+	0.368455i
$243$	−6.79767	+	6.79767i	−0.436070	+	0.436070i
$244$	−13.4479			−0.860913
$245$	2.22898	+	0.177857i	0.142405	+	0.0113629i
$246$	−2.93073			−0.186857
$247$	−7.56022	−	7.56022i	−0.481045	−	0.481045i
$248$	−1.44363	−	1.44363i	−0.0916706	−	0.0916706i
$249$	26.5704			1.68383
$250$	5.81067	+	9.55176i	0.367499	+	0.604106i
$251$	−13.1261			−0.828510			−0.414255	−	0.910161i	$-0.635958\pi$
$251$	−13.1261			−0.828510			−0.414255	+	0.910161i	$0.635958\pi$
$252$	−0.677691	+	0.677691i	−0.0426905	+	0.0426905i
$253$	−3.11007	−	26.0902i	−0.195528	−	1.64027i
$254$		−	10.4142i		−	0.653447i
$255$	9.05394	+	0.722439i	0.566979	+	0.0452409i
$256$	1.00000			0.0625000
$257$	14.1439	+	14.1439i	0.882269	+	0.882269i	0.993765	−	0.111496i	$-0.0355641\pi$
$257$	14.1439	+	14.1439i	0.882269	+	0.882269i	−0.111496	+	0.993765i	$0.535564\pi$
$258$	−3.45497	+	3.45497i	−0.215097	+	0.215097i
$259$	−3.33148			−0.207008
$260$	−5.34588	−	6.27299i	−0.331538	−	0.389034i
$261$		−	6.71935i		−	0.415917i
$262$	−5.94887	−	5.94887i	−0.367523	−	0.367523i
$263$	−2.44604	−	2.44604i	−0.150830	−	0.150830i	0.627659	−	0.778488i	$-0.284013\pi$
$263$	−2.44604	−	2.44604i	−0.150830	−	0.150830i	−0.778488	+	0.627659i	$0.784013\pi$
$264$	4.08087	−	5.18545i	0.251160	−	0.319143i
$265$	7.64555	+	8.97147i	0.469662	+	0.551113i
$266$			2.90073i			0.177855i
$267$	−24.2028	−	24.2028i	−1.48119	−	1.48119i
$268$	9.72961	−	9.72961i	0.594331	−	0.594331i
$269$		−	24.9354i		−	1.52034i	−0.649726	−	0.760169i	$-0.725116\pi$
$269$		−	24.9354i		−	1.52034i	0.649726	−	0.760169i	$-0.274884\pi$
$270$	−0.722439	+	9.05394i	−0.0439663	+	0.551005i
$271$		−	3.67652i		−	0.223333i	−0.993746	−	0.111666i	$-0.964381\pi$
$271$		−	3.67652i		−	0.223333i	0.993746	−	0.111666i	$-0.0356188\pi$
$272$	1.44363	−	1.44363i	0.0875329	−	0.0875329i
$273$	5.18545	−	5.18545i	0.313838	−	0.313838i
$274$	−3.29536			−0.199080
$275$	12.1924	−	11.2404i	0.735227	−	0.677821i
$276$	−15.7617			−0.948745
$277$	14.1648	−	14.1648i	0.851083	−	0.851083i	−0.139183	−	0.990267i	$-0.544448\pi$
$277$	14.1648	−	14.1648i	0.851083	−	0.851083i	0.990267	+	0.139183i	$0.0444478\pi$
$278$	13.6105	−	13.6105i	0.816302	−	0.816302i
$279$			1.95667i			0.117143i
$280$	−0.177857	+	2.22898i	−0.0106290	+	0.133207i
$281$			4.44730i			0.265304i	0.991163	+	0.132652i	$0.0423493\pi$
$281$			4.44730i			0.265304i	−0.991163	+	0.132652i	$0.957651\pi$
$282$	−3.60845	+	3.60845i	−0.214880	+	0.214880i
$283$	−21.9077	−	21.9077i	−1.30228	−	1.30228i	−0.926852	−	0.375428i	$-0.877496\pi$
$283$	−21.9077	−	21.9077i	−1.30228	−	1.30228i	−0.375428	−	0.926852i	$-0.622504\pi$
$284$			9.43243i			0.559711i
$285$	−8.37037	−	9.82199i	−0.495818	−	0.581805i
$286$	−7.56022	+	9.60658i	−0.447045	+	0.568049i
$287$	−1.04160	−	1.04160i	−0.0614837	−	0.0614837i
$288$	−0.677691	−	0.677691i	−0.0399333	−	0.0399333i
$289$			12.8319i			0.754816i
$290$	−10.1685	−	11.9320i	−0.597117	−	0.700671i
$291$	5.74441			0.336743
$292$	−2.09129	+	2.09129i	−0.122384	+	0.122384i
$293$	13.1400	+	13.1400i	0.767647	+	0.767647i	0.977692	−	0.210045i	$-0.0673610\pi$
$293$	13.1400	+	13.1400i	0.767647	+	0.767647i	−0.210045	+	0.977692i	$0.567361\pi$
$294$	−1.98957			−0.116034
$295$	19.9709	+	1.59354i	1.16275	+	0.0927794i
$296$		−	3.33148i		−	0.193638i
$297$	13.3771	−	1.59462i	0.776220	−	0.0925291i
$298$	1.31325	−	1.31325i	0.0760744	−	0.0760744i
$299$	29.2002			1.68869
$300$	−5.82974	−	8.06065i	−0.336580	−	0.465382i
$301$	−2.45584			−0.141552
$302$	−11.4740	−	11.4740i	−0.660256	−	0.660256i
$303$	−0.642182	−	0.642182i	−0.0368924	−	0.0368924i
$304$	−2.90073			−0.166368
$305$	29.9751	+	2.39180i	1.71637	+	0.136954i
$306$	−1.95667			−0.111855
$307$	1.28458	−	1.28458i	0.0733149	−	0.0733149i	−0.669498	−	0.742813i	$-0.733491\pi$
$307$	1.28458	−	1.28458i	0.0733149	−	0.0733149i	0.742813	+	0.669498i	$0.233491\pi$
$308$	3.29331	−	0.392578i	0.187654	−	0.0223692i
$309$		−	19.9835i		−	1.13682i
$310$	2.96107	+	3.47459i	0.168177	+	0.197343i
$311$	−28.7045			−1.62768			−0.813841	−	0.581088i	$-0.802627\pi$
$311$	−28.7045			−1.62768			−0.813841	+	0.581088i	$0.802627\pi$
$312$	5.18545	+	5.18545i	0.293569	+	0.293569i
$313$	1.26952	−	1.26952i	0.0717575	−	0.0717575i	−0.670317	−	0.742075i	$-0.733842\pi$
$313$	1.26952	−	1.26952i	0.0717575	−	0.0717575i	0.742075	+	0.670317i	$0.233842\pi$
$314$	−8.67826			−0.489742
$315$	1.63109	−	1.39003i	0.0919017	−	0.0783193i
$316$		−	11.1360i		−	0.626448i
$317$	−17.0407	−	17.0407i	−0.957103	−	0.957103i	0.0420140	−	0.999117i	$-0.486623\pi$
$317$	−17.0407	−	17.0407i	−0.957103	−	0.957103i	−0.999117	+	0.0420140i	$0.986623\pi$
$318$	−7.41611	−	7.41611i	−0.415875	−	0.415875i
$319$	−14.3805	+	18.2729i	−0.805152	+	1.02309i
$320$	−2.22898	−	0.177857i	−0.124604	−	0.00994251i
$321$		−	30.0453i		−	1.67697i
$322$	−5.60182	−	5.60182i	−0.312177	−	0.312177i
$323$	−4.18758	+	4.18758i	−0.233003	+	0.233003i
$324$		−	10.9567i		−	0.608704i
$325$	10.8002	+	14.9332i	0.599087	+	0.828344i
$326$		−	15.5791i		−	0.862844i
$327$	5.71446	−	5.71446i	0.316011	−	0.316011i
$328$	1.04160	−	1.04160i	0.0575128	−	0.0575128i
$329$	−2.56493			−0.141409
$330$	−10.0184	+	10.8325i	−0.551497	+	0.596308i
$331$	30.8994			1.69838			0.849192	−	0.528084i	$-0.177089\pi$
$331$	30.8994			1.69838			0.849192	+	0.528084i	$0.177089\pi$
$332$	−9.44330	+	9.44330i	−0.518269	+	0.518269i
$333$	−2.25771	+	2.25771i	−0.123722	+	0.123722i
$334$			13.4592i			0.736456i
$335$	−23.4176	+	19.9567i	−1.27944	+	1.09035i
$336$		−	1.98957i		−	0.108540i
$337$	−4.06370	+	4.06370i	−0.221364	+	0.221364i	−0.809073	−	0.587709i	$-0.800030\pi$
$337$	−4.06370	+	4.06370i	−0.221364	+	0.221364i	0.587709	+	0.809073i	$0.300030\pi$
$338$	−0.414195	−	0.414195i	−0.0225293	−	0.0225293i
$339$			5.79802i			0.314905i
$340$	−3.47459	+	2.96107i	−0.188436	+	0.160586i
$341$	4.18758	−	5.32106i	0.226770	−	0.288151i
$342$	1.96580	+	1.96580i	0.106298	+	0.106298i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		−	2.45584i		−	0.132410i
$345$	35.1326	+	2.80333i	1.89148	+	0.150926i
$346$	16.6191			0.893451
$347$	2.00182	−	2.00182i	0.107463	−	0.107463i	−0.651331	−	0.758794i	$-0.725789\pi$
$347$	2.00182	−	2.00182i	0.107463	−	0.107463i	0.758794	+	0.651331i	$0.225789\pi$
$348$	9.86337	+	9.86337i	0.528732	+	0.528732i
$349$	−3.86771			−0.207034			−0.103517	−	0.994628i	$-0.533010\pi$
$349$	−3.86771			−0.207034			−0.103517	+	0.994628i	$0.533010\pi$
$350$	0.792880	−	4.93673i	0.0423812	−	0.263880i
$351$			14.9718i			0.799133i
$352$	0.392578	+	3.29331i	0.0209245	+	0.175534i
$353$	6.45584	−	6.45584i	0.343610	−	0.343610i	−0.514113	−	0.857723i	$-0.671879\pi$
$353$	6.45584	−	6.45584i	0.343610	−	0.343610i	0.857723	+	0.514113i	$0.171879\pi$
$354$	−17.8259			−0.947436
$355$	1.67762	−	21.0247i	0.0890390	−	1.11588i
$356$	17.2036			0.911791
$357$	−2.87221	−	2.87221i	−0.152013	−	0.152013i
$358$	−12.0790	−	12.0790i	−0.638397	−	0.638397i
$359$	−21.2978			−1.12405			−0.562026	−	0.827119i	$-0.689978\pi$
$359$	−21.2978			−1.12405			−0.562026	+	0.827119i	$0.689978\pi$
$360$	1.39003	+	1.63109i	0.0732610	+	0.0859662i
$361$	−10.5858			−0.557145
$362$	0.192696	−	0.192696i	0.0101279	−	0.0101279i
$363$	18.6794	+	11.4039i	0.980412	+	0.598547i
$364$			3.68589i			0.193193i
$365$	5.03341	−	4.28951i	0.263461	−	0.224523i
$366$	−26.7556			−1.39854
$367$	19.2877	+	19.2877i	1.00681	+	1.00681i	0.999977	+	0.00683345i	$0.00217517\pi$
$367$	19.2877	+	19.2877i	1.00681	+	1.00681i	0.00683345	+	0.999977i	$0.497825\pi$
$368$	5.60182	−	5.60182i	0.292015	−	0.292015i
$369$	−1.41177			−0.0734936
$370$	−0.592527	+	7.42582i	−0.0308040	+	0.386050i
$371$		−	5.27146i		−	0.273681i
$372$	−2.87221	−	2.87221i	−0.148917	−	0.148917i
$373$	−11.8290	−	11.8290i	−0.612483	−	0.612483i	0.331109	−	0.943592i	$-0.392577\pi$
$373$	−11.8290	−	11.8290i	−0.612483	−	0.612483i	−0.943592	+	0.331109i	$0.892577\pi$
$374$	5.32106	+	4.18758i	0.275145	+	0.216535i
$375$	11.5608	+	19.0039i	0.596995	+	0.981358i
$376$		−	2.56493i		−	0.132276i
$377$	−18.2729	−	18.2729i	−0.941103	−	0.941103i
$378$	2.87221	−	2.87221i	0.147730	−	0.147730i
$379$		−	22.9523i		−	1.17898i	−0.807775	−	0.589490i	$-0.799329\pi$
$379$		−	22.9523i		−	1.17898i	0.807775	−	0.589490i	$-0.200671\pi$
$380$	6.46568	+	0.515915i	0.331682	+	0.0264659i
$381$		−	20.7199i		−	1.06151i
$382$	12.3266	−	12.3266i	0.630683	−	0.630683i
$383$	−1.35784	+	1.35784i	−0.0693824	+	0.0693824i	−0.740946	−	0.671564i	$-0.765623\pi$
$383$	−1.35784	+	1.35784i	−0.0693824	+	0.0693824i	0.671564	+	0.740946i	$0.265623\pi$
$384$	1.98957			0.101530
$385$	−7.41055	+	0.289312i	−0.377677	+	0.0147447i
$386$	12.1196			0.616870
$387$	−1.66430	+	1.66430i	−0.0846011	+	0.0846011i
$388$	−2.04160	+	2.04160i	−0.103647	+	0.103647i
$389$			20.4073i			1.03469i	0.855777	+	0.517345i	$0.173080\pi$
$389$			20.4073i			1.03469i	−0.855777	+	0.517345i	$0.826920\pi$
$390$	−10.6360	−	12.4806i	−0.538576	−	0.631978i
$391$		−	16.1739i		−	0.817950i
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	−11.8357	−	11.8357i	−0.597033	−	0.597033i
$394$			0.236536i			0.0119165i
$395$	−1.98061	+	24.8219i	−0.0996555	+	1.24893i
$396$	1.96580	−	2.49789i	0.0987851	−	0.125524i
$397$	0.611346	+	0.611346i	0.0306826	+	0.0306826i	0.722282	−	0.691599i	$-0.243093\pi$
$397$	0.611346	+	0.611346i	0.0306826	+	0.0306826i	−0.691599	+	0.722282i	$0.743093\pi$
$398$	−4.41666	−	4.41666i	−0.221387	−	0.221387i
$399$			5.77121i			0.288922i
$400$	4.93673	+	0.792880i	0.246837	+	0.0396440i
$401$	−5.07458			−0.253413			−0.126706	−	0.991940i	$-0.540441\pi$
$401$	−5.07458			−0.253413			−0.126706	+	0.991940i	$0.540441\pi$
$402$	19.3578	−	19.3578i	0.965478	−	0.965478i
$403$	5.32106	+	5.32106i	0.265061	+	0.265061i
$404$	0.456471			0.0227103
$405$	−1.94872	+	24.4222i	−0.0968327	+	1.21355i
$406$			7.01101i			0.347951i
$407$	10.9716	−	1.30787i	0.543842	−	0.0648285i
$408$	2.87221	−	2.87221i	0.142195	−	0.142195i
$409$	11.4914			0.568215			0.284107	−	0.958792i	$-0.408303\pi$
$409$	11.4914			0.568215			0.284107	+	0.958792i	$0.408303\pi$
$410$	−2.50697	+	2.13645i	−0.123810	+	0.105512i
$411$	−6.55636			−0.323401
$412$	7.10225	+	7.10225i	0.349903	+	0.349903i
$413$	−6.33544	−	6.33544i	−0.311746	−	0.311746i
$414$	−7.59260			−0.373156
$415$	22.7285	−	19.3694i	1.11570	−	0.950807i
$416$	−3.68589			−0.180715
$417$	27.0790	−	27.0790i	1.32607	−	1.32607i
$418$	−1.13876	−	9.55300i	−0.0556987	−	0.467253i
$419$		−	16.4805i		−	0.805126i	−0.915392	−	0.402563i	$-0.868119\pi$
$419$		−	16.4805i		−	0.805126i	0.915392	−	0.402563i	$-0.131881\pi$
$420$	−0.353859	+	4.43472i	−0.0172666	+	0.216392i
$421$	10.9333			0.532854			0.266427	−	0.963855i	$-0.414157\pi$
$421$	10.9333			0.532854			0.266427	+	0.963855i	$0.414157\pi$
$422$	3.39818	+	3.39818i	0.165421	+	0.165421i
$423$	−1.73823	+	1.73823i	−0.0845157	+	0.0845157i
$424$	5.27146			0.256005
$425$	8.27144	−	5.98219i	0.401224	−	0.290179i
$426$			18.7665i			0.909240i
$427$	−9.50909	−	9.50909i	−0.460177	−	0.460177i
$428$	10.6783	+	10.6783i	0.516155	+	0.516155i
$429$	−15.0416	+	19.1130i	−0.726216	+	0.922784i
$430$	−0.436788	+	5.47403i	−0.0210638	+	0.263981i
$431$		−	10.2278i		−	0.492658i	−0.969186	−	0.246329i	$-0.920776\pi$
$431$		−	10.2278i		−	0.492658i	0.969186	−	0.246329i	$-0.0792243\pi$
$432$	2.87221	+	2.87221i	0.138189	+	0.138189i
$433$	−18.8726	+	18.8726i	−0.906959	+	0.906959i	−0.996026	−	0.0890663i	$-0.971612\pi$
$433$	−18.8726	+	18.8726i	−0.906959	+	0.906959i	0.0890663	+	0.996026i	$0.471612\pi$
$434$		−	2.04160i		−	0.0980000i
$435$	−20.2310	−	23.7396i	−0.970004	−	1.13823i
$436$			4.06191i			0.194530i
$437$	−16.2494	+	16.2494i	−0.777313	+	0.777313i
$438$	−4.16078	+	4.16078i	−0.198810	+	0.198810i
$439$	−33.7891			−1.61267			−0.806333	−	0.591461i	$-0.798551\pi$
$439$	−33.7891			−1.61267			−0.806333	+	0.591461i	$0.798551\pi$
$440$	−0.289312	−	7.41055i	−0.0137924	−	0.353284i
$441$	−0.958399			−0.0456381
$442$	−5.32106	+	5.32106i	−0.253097	+	0.253097i
$443$	1.10525	−	1.10525i	0.0525118	−	0.0525118i	−0.680363	−	0.732875i	$-0.738178\pi$
$443$	1.10525	−	1.10525i	0.0525118	−	0.0525118i	0.732875	+	0.680363i	$0.238178\pi$
$444$		−	6.62823i		−	0.314562i
$445$	−38.3466	−	3.05979i	−1.81780	−	0.145048i
$446$		−	20.3836i		−	0.965191i
$447$	2.61280	−	2.61280i	0.123581	−	0.123581i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$			15.7106i			0.741427i	0.928747	+	0.370714i	$0.120887\pi$
$449$			15.7106i			0.741427i	−0.928747	+	0.370714i	$0.879113\pi$
$450$	−2.80825	−	3.88291i	−0.132382	−	0.183042i
$451$	3.83922	+	3.02140i	0.180782	+	0.142272i
$452$	−2.06065	−	2.06065i	−0.0969249	−	0.0969249i
$453$	−22.8284	−	22.8284i	−1.07257	−	1.07257i
$454$		−	12.2725i		−	0.575978i
$455$	0.655561	−	8.21578i	0.0307332	−	0.385162i
$456$	−5.77121			−0.270262
$457$	−23.0104	+	23.0104i	−1.07638	+	1.07638i	−0.0795483	+	0.996831i	$0.525348\pi$
$457$	−23.0104	+	23.0104i	−1.07638	+	1.07638i	−0.996831	+	0.0795483i	$0.974652\pi$
$458$	−17.0297	−	17.0297i	−0.795744	−	0.795744i
$459$	8.29280			0.387075
$460$	−13.4827	+	11.4900i	−0.628634	+	0.535726i
$461$			6.17517i			0.287606i	0.989606	+	0.143803i	$0.0459332\pi$
$461$			6.17517i			0.287606i	−0.989606	+	0.143803i	$0.954067\pi$
$462$	6.55228	−	0.781062i	0.304840	−	0.0363383i
$463$	7.16204	−	7.16204i	0.332848	−	0.332848i	−0.520819	−	0.853667i	$-0.674373\pi$
$463$	7.16204	−	7.16204i	0.332848	−	0.332848i	0.853667	+	0.520819i	$0.174373\pi$
$464$	−7.01101			−0.325478
$465$	5.89126	+	6.91294i	0.273201	+	0.320580i
$466$	−24.5190			−1.13582
$467$	16.9493	+	16.9493i	0.784319	+	0.784319i	0.980556	−	0.196238i	$-0.0628724\pi$
$467$	16.9493	+	16.9493i	0.784319	+	0.784319i	−0.196238	+	0.980556i	$0.562872\pi$
$468$	2.49789	+	2.49789i	0.115465	+	0.115465i
$469$	13.7598			0.635366
$470$	−0.456191	+	5.71719i	−0.0210425	+	0.263714i
$471$	−17.2660			−0.795576
$472$	6.33544	−	6.33544i	0.291612	−	0.291612i
$473$	8.08784	−	0.964109i	0.371879	−	0.0443298i
$474$		−	22.1559i		−	1.01765i
$475$	−14.3201	−	2.29993i	−0.657053	−	0.105528i
$476$	2.04160			0.0935766
$477$	−3.57242	−	3.57242i	−0.163570	−	0.163570i
$478$	−13.0598	+	13.0598i	−0.597341	+	0.597341i
$479$	25.9276			1.18466			0.592330	−	0.805695i	$-0.298208\pi$
$479$	25.9276			1.18466			0.592330	+	0.805695i	$0.298208\pi$
$480$	−4.43472	−	0.353859i	−0.202417	−	0.0161514i
$481$			12.2795i			0.559896i
$482$	−6.21312	−	6.21312i	−0.283000	−	0.283000i
$483$	−11.1452	−	11.1452i	−0.507125	−	0.507125i
$484$	−10.6918	+	2.58576i	−0.485989	+	0.117535i
$485$	4.91381	−	4.18758i	0.223124	−	0.190148i
$486$		−	9.61335i		−	0.436070i
$487$	6.76909	+	6.76909i	0.306737	+	0.306737i	0.843642	−	0.536906i	$-0.180407\pi$
$487$	6.76909	+	6.76909i	0.306737	+	0.306737i	−0.536906	+	0.843642i	$0.680407\pi$
$488$	9.50909	−	9.50909i	0.430456	−	0.430456i
$489$		−	30.9957i		−	1.40167i
$490$	−1.70189	+	1.45037i	−0.0768837	+	0.0655208i
$491$			17.0220i			0.768192i	0.923293	+	0.384096i	$0.125487\pi$
$491$			17.0220i			0.768192i	−0.923293	+	0.384096i	$0.874513\pi$
$492$	2.07234	−	2.07234i	0.0934283	−	0.0934283i
$493$	−10.1213	+	10.1213i	−0.455841	+	0.455841i
$494$	10.6918			0.481045
$495$	−4.82600	+	5.21813i	−0.216913	+	0.234537i
$496$	2.04160			0.0916706
$497$	−6.66973	+	6.66973i	−0.299178	+	0.299178i
$498$	−18.7881	+	18.7881i	−0.841917	+	0.841917i
$499$		−	14.1837i		−	0.634951i	−0.948267	−	0.317475i	$-0.897165\pi$
$499$		−	14.1837i		−	0.634951i	0.948267	−	0.317475i	$-0.102835\pi$
$500$	−10.8629	−	2.64535i	−0.485803	−	0.118304i
$501$			26.7781i			1.19636i
$502$	9.28153	−	9.28153i	0.414255	−	0.414255i
$503$	15.1139	+	15.1139i	0.673896	+	0.673896i	0.958612	−	0.284716i	$-0.0918993\pi$
$503$	15.1139	+	15.1139i	0.673896	+	0.673896i	−0.284716	+	0.958612i	$0.591899\pi$
$504$		−	0.958399i		−	0.0426905i
$505$	−1.01747	−	0.0811866i	−0.0452767	−	0.00361275i
$506$	20.6477	+	16.2494i	0.917901	+	0.722373i
$507$	−0.824072	−	0.824072i	−0.0365983	−	0.0365983i
$508$	7.36398	+	7.36398i	0.326724	+	0.326724i
$509$		−	24.7838i		−	1.09852i	−0.835651	−	0.549261i	$-0.814909\pi$
$509$		−	24.7838i		−	1.09852i	0.835651	−	0.549261i	$-0.185091\pi$
$510$	−6.91294	+	5.89126i	−0.306110	+	0.260869i
$511$	−2.95753			−0.130834
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−8.33150	−	8.33150i	−0.367845	−	0.367845i
$514$	−20.0024			−0.882269
$515$	−14.5676	−	17.0940i	−0.641926	−	0.753251i
$516$		−	4.88607i		−	0.215097i
$517$	8.44711	−	1.00694i	0.371504	−	0.0442850i
$518$	2.35571	−	2.35571i	0.103504	−	0.103504i
$519$	33.0650			1.45139
$520$	8.21578	+	0.655561i	0.360286	+	0.0287482i
$521$	−31.7791			−1.39227			−0.696133	−	0.717913i	$-0.745098\pi$
$521$	−31.7791			−1.39227			−0.696133	+	0.717913i	$0.745098\pi$
$522$	4.75130	+	4.75130i	0.207959	+	0.207959i
$523$	14.1694	+	14.1694i	0.619583	+	0.619583i	0.945424	−	0.325842i	$-0.105648\pi$
$523$	14.1694	+	14.1694i	0.619583	+	0.619583i	−0.325842	+	0.945424i	$0.605648\pi$
$524$	8.41298			0.367523
$525$	1.57749	−	9.82199i	0.0688474	−	0.428667i
$526$	3.45923			0.150830
$527$	2.94732	−	2.94732i	0.128387	−	0.128387i
$528$	0.781062	+	6.55228i	0.0339914	+	0.285151i
$529$		−	39.7608i		−	1.72873i
$530$	−11.7500	−	0.937566i	−0.510388	−	0.0407253i
$531$	−8.58693			−0.372641
$532$	−2.05113	−	2.05113i	−0.0889276	−	0.0889276i
$533$	−3.83922	+	3.83922i	−0.166295	+	0.166295i
$534$	34.2279			1.48119
$535$	−21.9025	−	25.7009i	−0.946929	−	1.11115i
$536$			13.7598i			0.594331i
$537$	−24.0321	−	24.0321i	−1.03706	−	1.03706i
$538$	17.6320	+	17.6320i	0.760169	+	0.760169i
$539$	2.60632	+	2.05113i	0.112262	+	0.0883483i
$540$	−5.89126	−	6.91294i	−0.253519	−	0.297486i
$541$			37.4044i			1.60814i	0.594535	+	0.804070i	$0.297336\pi$
$541$			37.4044i			1.60814i	−0.594535	+	0.804070i	$0.702664\pi$
$542$	2.59969	+	2.59969i	0.111666	+	0.111666i
$543$	0.383382	−	0.383382i	0.0164525	−	0.0164525i
$544$			2.04160i			0.0875329i
$545$	0.722439	−	9.05394i	0.0309459	−	0.387828i
$546$			7.33334i			0.313838i
$547$	26.1716	−	26.1716i	1.11902	−	1.11902i	0.127130	−	0.991886i	$-0.459424\pi$
$547$	26.1716	−	26.1716i	1.11902	−	1.11902i	0.991886	−	0.127130i	$-0.0405765\pi$
$548$	2.33017	−	2.33017i	0.0995400	−	0.0995400i
$549$	−12.8884			−0.550066
$550$	−0.673147	+	16.5695i	−0.0287031	+	0.706524i
$551$	20.3371			0.866388
$552$	11.1452	−	11.1452i	0.474372	−	0.474372i
$553$	7.87433	−	7.87433i	0.334851	−	0.334851i
$554$			20.0321i			0.851083i
$555$	−1.17888	+	14.7742i	−0.0500405	+	0.627130i
$556$			19.2481i			0.816302i
$557$	13.5686	−	13.5686i	0.574918	−	0.574918i	−0.358580	−	0.933499i	$-0.616739\pi$
$557$	13.5686	−	13.5686i	0.574918	−	0.574918i	0.933499	+	0.358580i	$0.116739\pi$
$558$	−1.38357	−	1.38357i	−0.0585713	−	0.0585713i
$559$			9.05195i			0.382857i
$560$	−1.45037	−	1.70189i	−0.0612891	−	0.0719181i
$561$	10.5866	+	8.33150i	0.446968	+	0.351756i
$562$	−3.14472	−	3.14472i	−0.132652	−	0.132652i
$563$	22.3869	+	22.3869i	0.943496	+	0.943496i	0.998487	−	0.0549909i	$-0.0175130\pi$
$563$	22.3869	+	22.3869i	0.943496	+	0.943496i	−0.0549909	+	0.998487i	$0.517513\pi$
$564$		−	5.10312i		−	0.214880i
$565$	4.22666	+	4.95966i	0.177817	+	0.208655i
$566$	30.9822			1.30228
$567$	7.74753	−	7.74753i	0.325366	−	0.325366i
$568$	−6.66973	−	6.66973i	−0.279856	−	0.279856i
$569$	−38.0397			−1.59471			−0.797354	−	0.603512i	$-0.793768\pi$
$569$	−38.0397			−1.59471			−0.797354	+	0.603512i	$0.793768\pi$
$570$	12.8639	+	1.02645i	0.538811	+	0.0429933i
$571$			19.0631i			0.797766i	0.917002	+	0.398883i	$0.130602\pi$
$571$			19.0631i			0.797766i	−0.917002	+	0.398883i	$0.869398\pi$
$572$	−1.44700	−	12.1388i	−0.0605020	−	0.507547i
$573$	24.5246	−	24.5246i	1.02453	−	1.02453i
$574$	1.47305			0.0614837
$575$	32.0963	−	23.2131i	1.33851	−	0.968054i
$576$	0.958399			0.0399333
$577$	−12.0607	−	12.0607i	−0.502092	−	0.502092i	0.409996	−	0.912087i	$-0.365530\pi$
$577$	−12.0607	−	12.0607i	−0.502092	−	0.502092i	−0.912087	+	0.409996i	$0.865530\pi$
$578$	−9.07350	−	9.07350i	−0.377408	−	0.377408i
$579$	24.1128			1.00209
$580$	15.6274	+	1.24696i	0.648894	+	0.0517771i
$581$	−13.3548			−0.554052
$582$	−4.06191	+	4.06191i	−0.168372	+	0.168372i
$583$	2.06946	+	17.3606i	0.0857083	+	0.719001i
$584$		−	2.95753i		−	0.122384i
$585$	−5.12349	−	6.01203i	−0.211830	−	0.248567i
$586$	−18.5828			−0.767647
$587$	25.6607	+	25.6607i	1.05913	+	1.05913i	0.998138	+	0.0609921i	$0.0194264\pi$
$587$	25.6607	+	25.6607i	1.05913	+	1.05913i	0.0609921	+	0.998138i	$0.480574\pi$
$588$	1.40684	−	1.40684i	0.0580171	−	0.0580171i
$589$	−5.92213			−0.244017
$590$	−15.2484	+	12.9948i	−0.627766	+	0.534987i
$591$			0.470606i			0.0193581i
$592$	2.35571	+	2.35571i	0.0968192	+	0.0968192i
$593$	−21.5949	−	21.5949i	−0.886796	−	0.886796i	0.107418	−	0.994214i	$-0.465742\pi$
$593$	−21.5949	−	21.5949i	−0.886796	−	0.886796i	−0.994214	+	0.107418i	$0.965742\pi$
$594$	−8.33150	+	10.5866i	−0.341845	+	0.434375i
$595$	−4.55069	−	0.363113i	−0.186560	−	0.0148862i
$596$			1.85721i			0.0760744i
$597$	−8.78727	−	8.78727i	−0.359639	−	0.359639i
$598$	−20.6477	+	20.6477i	−0.844346	+	0.844346i
$599$			31.0598i			1.26907i	0.772895	+	0.634534i	$0.218808\pi$
$599$			31.0598i			1.26907i	−0.772895	+	0.634534i	$0.781192\pi$
$600$	9.82199	+	1.57749i	0.400981	+	0.0644009i
$601$		−	5.56491i		−	0.226997i	−0.993538	−	0.113499i	$-0.963794\pi$
$601$		−	5.56491i		−	0.226997i	0.993538	−	0.113499i	$-0.0362058\pi$
$602$	1.73654	−	1.73654i	0.0707761	−	0.0707761i
$603$	9.32486	−	9.32486i	0.379738	−	0.379738i
$604$	16.2267			0.660256
$605$	24.2917	−	3.86201i	0.987597	−	0.157013i
$606$	0.908183			0.0368924
$607$	4.12375	−	4.12375i	0.167378	−	0.167378i	−0.618448	−	0.785826i	$-0.712238\pi$
$607$	4.12375	−	4.12375i	0.167378	−	0.167378i	0.785826	+	0.618448i	$0.212238\pi$
$608$	2.05113	−	2.05113i	0.0831842	−	0.0831842i
$609$			13.9489i			0.565239i
$610$	−22.8869	+	19.5044i	−0.926662	+	0.789708i
$611$			9.45405i			0.382470i
$612$	1.38357	−	1.38357i	0.0559277	−	0.0559277i
$613$	19.4528	+	19.4528i	0.785691	+	0.785691i	0.980785	−	0.195094i	$-0.0625011\pi$
$613$	19.4528	+	19.4528i	0.785691	+	0.785691i	−0.195094	+	0.980785i	$0.562501\pi$
$614$			1.81667i			0.0733149i
$615$	−4.98779	+	4.25063i	−0.201127	+	0.171402i
$616$	−2.05113	+	2.60632i	−0.0826422	+	0.105011i
$617$	−16.5113	−	16.5113i	−0.664718	−	0.664718i	0.291770	−	0.956489i	$-0.405756\pi$
$617$	−16.5113	−	16.5113i	−0.664718	−	0.664718i	−0.956489	+	0.291770i	$0.905756\pi$
$618$	14.1304	+	14.1304i	0.568410	+	0.568410i
$619$		−	22.9918i		−	0.924118i	−0.886849	−	0.462059i	$-0.847111\pi$
$619$		−	22.9918i		−	0.924118i	0.886849	−	0.462059i	$-0.152889\pi$
$620$	−4.55069	−	0.363113i	−0.182760	−	0.0145830i
$621$	32.1792			1.29131
$622$	20.2971	−	20.2971i	0.813841	−	0.813841i
$623$	12.1648	+	12.1648i	0.487373	+	0.487373i
$624$	−7.33334			−0.293569
$625$	23.7427	+	7.82848i	0.949707	+	0.313139i
$626$			1.79537i			0.0717575i
$627$	−2.26565	−	19.0064i	−0.0904814	−	0.759042i
$628$	6.13645	−	6.13645i	0.244871	−	0.244871i
$629$	6.80156			0.271196
$630$	−0.170458	+	2.13626i	−0.00679121	+	0.0851105i
$631$	14.6318			0.582483			0.291242	−	0.956650i	$-0.405932\pi$
$631$	14.6318			0.582483			0.291242	+	0.956650i	$0.405932\pi$
$632$	7.87433	+	7.87433i	0.313224	+	0.313224i
$633$	6.76093	+	6.76093i	0.268723	+	0.268723i
$634$	24.0992			0.957103
$635$	−15.1045	−	17.7239i	−0.599402	−	0.703352i
$636$	10.4880			0.415875
$637$	−2.60632	+	2.60632i	−0.103266	+	0.103266i
$638$	−2.75237	−	23.0894i	−0.108967	−	0.914119i
$639$			9.04003i			0.357618i
$640$	1.70189	−	1.45037i	0.0672732	−	0.0573307i
$641$	−23.1578			−0.914678			−0.457339	−	0.889293i	$-0.651197\pi$
$641$	−23.1578			−0.914678			−0.457339	+	0.889293i	$0.651197\pi$
$642$	21.2452	+	21.2452i	0.838483	+	0.838483i
$643$	−14.6746	+	14.6746i	−0.578711	+	0.578711i	−0.934548	−	0.355837i	$-0.884196\pi$
$643$	−14.6746	+	14.6746i	−0.578711	+	0.578711i	0.355837	+	0.934548i	$0.384196\pi$
$644$	7.92217			0.312177
$645$	−0.869022	+	10.8910i	−0.0342177	+	0.428832i
$646$		−	5.92213i		−	0.233003i
$647$	−4.82230	−	4.82230i	−0.189584	−	0.189584i	0.605932	−	0.795516i	$-0.292800\pi$
$647$	−4.82230	−	4.82230i	−0.189584	−	0.189584i	−0.795516	+	0.605932i	$0.792800\pi$
$648$	7.74753	+	7.74753i	0.304352	+	0.304352i
$649$	23.3517	+	18.3774i	0.916635	+	0.721376i
$650$	−18.1962	−	2.92247i	−0.713715	−	0.114629i
$651$		−	4.06191i		−	0.159199i
$652$	11.0161	+	11.0161i	0.431422	+	0.431422i
$653$	2.63780	−	2.63780i	0.103225	−	0.103225i	−0.653608	−	0.756833i	$-0.726746\pi$
$653$	2.63780	−	2.63780i	0.103225	−	0.103225i	0.756833	+	0.653608i	$0.226746\pi$
$654$			8.08147i			0.316011i
$655$	−18.7524	−	1.49631i	−0.732716	−	0.0584655i
$656$			1.47305i			0.0575128i
$657$	−2.00429	+	2.00429i	−0.0781949	+	0.0781949i
$658$	1.81368	−	1.81368i	0.0707046	−	0.0707046i
$659$	20.7119			0.806822			0.403411	−	0.915019i	$-0.367824\pi$
$659$	20.7119			0.806822			0.403411	+	0.915019i	$0.367824\pi$
$660$	−0.575607	−	14.7438i	−0.0224055	−	0.573903i
$661$	−1.97882			−0.0769672			−0.0384836	−	0.999259i	$-0.512253\pi$
$661$	−1.97882			−0.0769672			−0.0384836	+	0.999259i	$0.512253\pi$
$662$	−21.8492	+	21.8492i	−0.849192	+	0.849192i
$663$	−10.5866	+	10.5866i	−0.411150	+	0.411150i
$664$		−	13.3548i		−	0.518269i
$665$	4.20712	+	4.93673i	0.163145	+	0.191438i
$666$		−	3.19289i		−	0.123722i
$667$	−39.2744	+	39.2744i	−1.52071	+	1.52071i
$668$	−9.51711	−	9.51711i	−0.368228	−	0.368228i
$669$		−	40.5546i		−	1.56793i
$670$	2.44727	−	30.6703i	0.0945462	−	1.18490i
$671$	35.0494	+	27.5833i	1.35307	+	1.06484i
$672$	1.40684	+	1.40684i	0.0542700	+	0.0542700i
$673$	23.9417	+	23.9417i	0.922885	+	0.922885i	0.997232	−	0.0743478i	$-0.0236875\pi$
$673$	23.9417	+	23.9417i	0.922885	+	0.922885i	−0.0743478	+	0.997232i	$0.523688\pi$
$674$		−	5.74694i		−	0.221364i
$675$	11.9020	+	16.4566i	0.458108	+	0.633416i
$676$	0.585761			0.0225293
$677$	−17.9384	+	17.9384i	−0.689427	+	0.689427i	−0.962105	−	0.272678i	$-0.912091\pi$
$677$	−17.9384	+	17.9384i	−0.689427	+	0.689427i	0.272678	+	0.962105i	$0.412091\pi$
$678$	−4.09982	−	4.09982i	−0.157453	−	0.157453i
$679$	−2.88726			−0.110803
$680$	0.363113	−	4.55069i	0.0139247	−	0.174511i
$681$		−	24.4171i		−	0.935664i
$682$	0.801487	+	6.72362i	0.0306905	+	0.257461i
$683$	−34.4372	+	34.4372i	−1.31770	+	1.31770i	−0.402112	+	0.915591i	$0.631724\pi$
$683$	−34.4372	+	34.4372i	−1.31770	+	1.31770i	−0.915591	+	0.402112i	$0.868276\pi$
$684$	−2.78006			−0.106298
$685$	−5.60835	+	4.77948i	−0.214284	+	0.182615i
$686$	1.00000			0.0381802
$687$	−33.8818	−	33.8818i	−1.29267	−	1.29267i
$688$	1.73654	+	1.73654i	0.0662050	+	0.0662050i
$689$	−19.4300			−0.740225
$690$	−26.8248	+	22.8603i	−1.02120	+	0.870276i
$691$	20.4658			0.778556			0.389278	−	0.921120i	$-0.372725\pi$
$691$	20.4658			0.778556			0.389278	+	0.921120i	$0.372725\pi$
$692$	−11.7515	+	11.7515i	−0.446725	+	0.446725i
$693$	3.15631	−	0.376246i	0.119898	−	0.0142924i
$694$			2.83100i			0.107463i
$695$	3.42341	−	42.9038i	0.129857	−	1.62743i
$696$	−13.9489			−0.528732
$697$	2.12653	+	2.12653i	0.0805482	+	0.0805482i
$698$	2.73489	−	2.73489i	0.103517	−	0.103517i
$699$	−48.7824			−1.84512
$700$	2.93015	+	4.05145i	0.110749	+	0.153130i
$701$			44.3988i			1.67692i	0.544962	+	0.838460i	$0.316544\pi$
$701$			44.3988i			1.67692i	−0.544962	+	0.838460i	$0.683456\pi$
$702$	−10.5866	−	10.5866i	−0.399566	−	0.399566i
$703$	−6.83329	−	6.83329i	−0.257722	−	0.257722i
$704$	−2.60632	−	2.05113i	−0.0982292	−	0.0773047i
$705$	−0.907625	+	11.3748i	−0.0341831	+	0.428398i
$706$			9.12994i			0.343610i
$707$	0.322774	+	0.322774i	0.0121392	+	0.0121392i
$708$	12.6048	−	12.6048i	0.473718	−	0.473718i
$709$			18.0304i			0.677145i	0.940940	+	0.338573i	$0.109944\pi$
$709$			18.0304i			0.677145i	−0.940940	+	0.338573i	$0.890056\pi$
$710$	13.6805	+	16.0530i	0.513419	+	0.602458i
$711$		−	10.6727i		−	0.400258i
$712$	−12.1648	+	12.1648i	−0.455896	+	0.455896i
$713$	11.4367	−	11.4367i	0.428307	−	0.428307i
$714$	4.06191			0.152013
$715$	1.06637	+	27.3145i	0.0398800	+	1.02150i
$716$	17.0823			0.638397
$717$	−25.9834	+	25.9834i	−0.970368	+	0.970368i
$718$	15.0598	−	15.0598i	0.562026	−	0.562026i
$719$			11.5026i			0.428973i	0.976727	+	0.214487i	$0.0688078\pi$
$719$			11.5026i			0.428973i	−0.976727	+	0.214487i	$0.931192\pi$
$720$	−2.13626	−	0.170458i	−0.0796136	−	0.00635259i
$721$			10.0441i			0.374062i
$722$	7.48526	−	7.48526i	0.278573	−	0.278573i
$723$	−12.3615	−	12.3615i	−0.459728	−	0.459728i
$724$			0.272513i			0.0101279i
$725$	−34.6115	−	5.55889i	−1.28544	−	0.206452i
$726$	−21.2720	+	5.14456i	−0.789480	+	0.190932i
$727$	20.9324	+	20.9324i	0.776339	+	0.776339i	0.979206	−	0.202867i	$-0.0650259\pi$
$727$	20.9324	+	20.9324i	0.776339	+	0.776339i	−0.202867	+	0.979206i	$0.565026\pi$
$728$	−2.60632	−	2.60632i	−0.0965965	−	0.0965965i
$729$			13.7435i			0.509020i
$730$	−0.526018	+	6.59229i	−0.0194688	+	0.243992i
$731$	5.01384			0.185444
$732$	18.9190	−	18.9190i	0.699268	−	0.699268i
$733$	−25.9764	−	25.9764i	−0.959461	−	0.959461i	0.0397491	−	0.999210i	$-0.487344\pi$
$733$	−25.9764	−	25.9764i	−0.959461	−	0.959461i	−0.999210	+	0.0397491i	$0.987344\pi$
$734$	−27.2769			−1.00681
$735$	−3.38604	+	2.88561i	−0.124896	+	0.106437i
$736$			7.92217i			0.292015i
$737$	−45.3151	+	5.40178i	−1.66920	+	0.198977i
$738$	0.998269	−	0.998269i	0.0367468	−	0.0367468i
$739$	−51.1611			−1.88199			−0.940996	−	0.338418i	$-0.890108\pi$
$739$	−51.1611			−1.88199			−0.940996	+	0.338418i	$0.890108\pi$
$740$	−4.83187	−	5.66983i	−0.177623	−	0.208427i
$741$	21.2720			0.781448
$742$	3.72749	+	3.72749i	0.136840	+	0.136840i
$743$	16.3150	+	16.3150i	0.598538	+	0.598538i	0.939923	−	0.341385i	$-0.110896\pi$
$743$	16.3150	+	16.3150i	0.598538	+	0.598538i	−0.341385	+	0.939923i	$0.610896\pi$
$744$	4.06191			0.148917
$745$	0.330318	−	4.13970i	0.0121019	−	0.151667i
$746$	16.7287			0.612483
$747$	−9.05046	+	9.05046i	−0.331139	+	0.331139i
$748$	−6.72362	+	0.801487i	−0.245840	+	0.0293053i
$749$			15.1014i			0.551793i
$750$	−21.6125	−	5.26312i	−0.789176	−	0.192182i
$751$	7.91932			0.288980			0.144490	−	0.989506i	$-0.453846\pi$
$751$	7.91932			0.288980			0.144490	+	0.989506i	$0.453846\pi$
$752$	1.81368	+	1.81368i	0.0661381	+	0.0661381i
$753$	18.4663	−	18.4663i	0.672948	−	0.672948i
$754$	25.8418			0.941103
$755$	−36.1691	−	2.88604i	−1.31633	−	0.105034i
$756$			4.06191i			0.147730i
$757$	11.5304	+	11.5304i	0.419080	+	0.419080i	0.884887	−	0.465806i	$-0.154236\pi$
$757$	11.5304	+	11.5304i	0.419080	+	0.419080i	−0.465806	+	0.884887i	$0.654236\pi$
$758$	16.2297	+	16.2297i	0.589490	+	0.589490i
$759$	41.0800	+	32.3293i	1.49111	+	1.17348i
$760$	−4.93673	+	4.20712i	−0.179074	+	0.152608i
$761$			32.6347i			1.18301i	0.806302	+	0.591504i	$0.201466\pi$
$761$			32.6347i			1.18301i	−0.806302	+	0.591504i	$0.798534\pi$
$762$	14.6512	+	14.6512i	0.530756	+	0.530756i
$763$	−2.87221	+	2.87221i	−0.103981	+	0.103981i
$764$			17.4324i			0.630683i
$765$	−3.33004	+	2.83788i	−0.120398	+	0.102604i
$766$		−	1.92028i		−	0.0693824i
$767$	−23.3517	+	23.3517i	−0.843181	+	0.843181i
$768$	−1.40684	+	1.40684i	−0.0507650	+	0.0507650i
$769$	−10.5368			−0.379965			−0.189983	−	0.981787i	$-0.560843\pi$
$769$	−10.5368			−0.379965			−0.189983	+	0.981787i	$0.560843\pi$
$770$	5.03548	−	5.44463i	0.181466	−	0.196211i
$771$	−39.7963			−1.43323
$772$	−8.56983	+	8.56983i	−0.308435	+	0.308435i
$773$	11.6958	−	11.6958i	0.420669	−	0.420669i	−0.464765	−	0.885434i	$-0.653861\pi$
$773$	11.6958	−	11.6958i	0.420669	−	0.420669i	0.885434	+	0.464765i	$0.153861\pi$
$774$		−	2.35368i		−	0.0846011i
$775$	10.0788	+	1.61875i	0.362043	+	0.0581470i
$776$		−	2.88726i		−	0.103647i
$777$	4.68686	−	4.68686i	0.168140	−	0.168140i
$778$	−14.4301	−	14.4301i	−0.517345	−	0.517345i
$779$		−	4.27291i		−	0.153093i
$780$	16.3459	+	1.30429i	0.585277	+	0.0467009i
$781$	19.3471	−	24.5839i	0.692294	−	0.879680i
$782$	11.4367	+	11.4367i	0.408975	+	0.408975i
$783$	−20.1371	−	20.1371i	−0.719640	−	0.719640i
$784$			1.00000i			0.0357143i
$785$	−14.7695	+	12.5866i	−0.527145	+	0.449237i
$786$	16.7382			0.597033
$787$	25.5762	−	25.5762i	0.911694	−	0.911694i	−0.0847112	−	0.996406i	$-0.526997\pi$
$787$	25.5762	−	25.5762i	0.911694	−	0.911694i	0.996406	+	0.0847112i	$0.0269968\pi$
$788$	−0.167256	−	0.167256i	−0.00595826	−	0.00595826i
$789$	6.88239			0.245019
$790$	−16.1513	−	18.9523i	−0.574636	−	0.674291i
$791$		−	2.91420i		−	0.103617i
$792$	0.376246	+	3.15631i	0.0133693	+	0.112154i
$793$	−35.0494	+	35.0494i	−1.24464	+	1.24464i
$794$	−0.864574			−0.0306826
$795$	−23.3775	−	1.86536i	−0.829114	−	0.0661574i
$796$	6.24611			0.221387
$797$	20.8648	+	20.8648i	0.739069	+	0.739069i	0.972398	−	0.233329i	$-0.0749618\pi$
$797$	20.8648	+	20.8648i	0.739069	+	0.739069i	−0.233329	+	0.972398i	$0.574962\pi$
$798$	−4.08087	−	4.08087i	−0.144461	−	0.144461i
$799$	5.23657			0.185256
$800$	−4.05145	+	2.93015i	−0.143240	+	0.103596i
$801$	16.4880			0.582573
$802$	3.58827	−	3.58827i	0.126706	−	0.126706i
$803$	9.74007	−	1.16106i	0.343720	−	0.0409730i
$804$			27.3760i			0.965478i
$805$	−17.6584	−	1.40901i	−0.622376	−	0.0496612i
$806$	−7.52511			−0.265061
$807$	35.0801	+	35.0801i	1.23488	+	1.23488i
$808$	−0.322774	+	0.322774i	−0.0113551	+	0.0113551i
$809$	−41.3229			−1.45284			−0.726418	−	0.687253i	$-0.758816\pi$
$809$	−41.3229			−1.45284			−0.726418	+	0.687253i	$0.758816\pi$
$810$	−15.8912	−	18.6471i	−0.558359	−	0.655192i
$811$		−	22.0551i		−	0.774458i	−0.921984	−	0.387229i	$-0.873432\pi$
$811$		−	22.0551i		−	0.774458i	0.921984	−	0.387229i	$-0.126568\pi$
$812$	−4.95753	−	4.95753i	−0.173975	−	0.173975i
$813$	5.17228	+	5.17228i	0.181400	+	0.181400i
$814$	−6.83329	+	8.68289i	−0.239507	+	0.304335i
$815$	−22.5953	−	26.5139i	−0.791480	−	0.928741i
$816$			4.06191i			0.142195i
$817$	−5.03724	−	5.03724i	−0.176231	−	0.176231i
$818$	−8.12567	+	8.12567i	−0.284107	+	0.284107i
$819$			3.53255i			0.123437i
$820$	0.261991	−	3.28339i	0.00914914	−	0.114661i
$821$			4.01649i			0.140176i	0.997541	+	0.0700882i	$0.0223281\pi$
$821$			4.01649i			0.140176i	−0.997541	+	0.0700882i	$0.977672\pi$
$822$	4.63605	−	4.63605i	0.161701	−	0.161701i
$823$	31.5711	−	31.5711i	1.10050	−	1.10050i	0.106147	−	0.994350i	$-0.466149\pi$
$823$	31.5711	−	31.5711i	1.10050	−	1.10050i	0.994350	−	0.106147i	$-0.0338515\pi$
$824$	−10.0441			−0.349903
$825$	−1.33927	+	32.9661i	−0.0466276	+	1.14773i
$826$	8.95966			0.311746
$827$	2.56371	−	2.56371i	0.0891489	−	0.0891489i	−0.661126	−	0.750275i	$-0.729921\pi$
$827$	2.56371	−	2.56371i	0.0891489	−	0.0891489i	0.750275	+	0.661126i	$0.229921\pi$
$828$	5.36878	−	5.36878i	0.186578	−	0.186578i
$829$		−	17.6235i		−	0.612090i	−0.952017	−	0.306045i	$-0.900994\pi$
$829$		−	17.6235i		−	0.612090i	0.952017	−	0.306045i	$-0.0990057\pi$
$830$	−2.37525	+	29.7677i	−0.0824462	+	1.03325i
$831$			39.8554i			1.38257i
$832$	2.60632	−	2.60632i	0.0903577	−	0.0903577i
$833$	1.44363	+	1.44363i	0.0500188	+	0.0500188i
$834$			38.2955i			1.32607i
$835$	19.5208	+	22.9062i	0.675545	+	0.792701i
$836$	7.56022	+	5.94977i	0.261476	+	0.205777i
$837$	5.86390	+	5.86390i	0.202686	+	0.202686i
$838$	11.6535	+	11.6535i	0.402563	+	0.402563i
$839$		−	30.2740i		−	1.04517i	−0.852586	−	0.522587i	$-0.824967\pi$
$839$		−	30.2740i		−	1.04517i	0.852586	−	0.522587i	$-0.175033\pi$
$840$	−2.88561	−	3.38604i	−0.0995629	−	0.116829i
$841$	20.1543			0.694975
$842$	−7.73098	+	7.73098i	−0.266427	+	0.266427i
$843$	−6.25665	−	6.25665i	−0.215490	−	0.215490i
$844$	−4.80575			−0.165421
$845$	−1.30565	−	0.104182i	−0.0449158	−	0.00358396i
$846$		−	2.45823i		−	0.0845157i
$847$	−9.38863	−	5.73181i	−0.322597	−	0.196947i
$848$	−3.72749	+	3.72749i	−0.128002	+	0.128002i
$849$	61.6414			2.11553
$850$	−1.61875	+	10.0788i	−0.0555225	+	0.345701i
$851$	26.3926			0.904726
$852$	−13.2699	−	13.2699i	−0.454620	−	0.454620i
$853$	−0.919367	−	0.919367i	−0.0314785	−	0.0314785i	0.691192	−	0.722671i	$-0.257086\pi$
$853$	−0.919367	−	0.919367i	−0.0314785	−	0.0314785i	−0.722671	+	0.691192i	$0.757086\pi$
$854$	13.4479			0.460177
$855$	6.19670	+	0.494453i	0.211923	+	0.0169099i
$856$	−15.1014			−0.516155
$857$	18.1164	−	18.1164i	0.618843	−	0.618843i	−0.326392	−	0.945235i	$-0.605833\pi$
$857$	18.1164	−	18.1164i	0.618843	−	0.618843i	0.945235	+	0.326392i	$0.105833\pi$
$858$	−2.87891	−	24.1510i	−0.0982843	−	0.824500i
$859$		−	45.0602i		−	1.53743i	−0.639589	−	0.768717i	$-0.720896\pi$
$859$		−	45.0602i		−	1.53743i	0.639589	−	0.768717i	$-0.279104\pi$
$860$	−3.56187	−	4.17958i	−0.121459	−	0.142522i
$861$	2.93073			0.0998791
$862$	7.23217	+	7.23217i	0.246329	+	0.246329i
$863$	9.89775	−	9.89775i	0.336923	−	0.336923i	−0.518285	−	0.855208i	$-0.673429\pi$
$863$	9.89775	−	9.89775i	0.336923	−	0.336923i	0.855208	+	0.518285i	$0.173429\pi$
$864$	−4.06191			−0.138189
$865$	28.2840	−	24.1038i	0.961685	−	0.819555i
$866$		−	26.6899i		−	0.906959i
$867$	−18.0524	−	18.0524i	−0.613091	−	0.613091i
$868$	1.44363	+	1.44363i	0.0490000	+	0.0490000i
$869$	−22.8413	+	29.0239i	−0.774839	+	0.984568i
$870$	31.0919	+	2.48091i	1.05411	+	0.0841108i
$871$		−	50.7169i		−	1.71848i
$872$	−2.87221	−	2.87221i	−0.0972652	−	0.0972652i
$873$	−1.95667	+	1.95667i	−0.0662232	+	0.0662232i
$874$		−	22.9801i		−	0.777313i
$875$	−5.81067	−	9.55176i	−0.196437	−	0.322908i
$876$		−	5.88423i		−	0.198810i
$877$	39.5594	−	39.5594i	1.33583	−	1.33583i	0.435767	−	0.900060i	$-0.356477\pi$
$877$	39.5594	−	39.5594i	1.33583	−	1.33583i	0.900060	−	0.435767i	$-0.143523\pi$
$878$	23.8925	−	23.8925i	0.806333	−	0.806333i
$879$	−36.9718			−1.24703
$880$	5.44463	+	5.03548i	0.183538	+	0.169746i
$881$	38.4566			1.29564			0.647818	−	0.761795i	$-0.275682\pi$
$881$	38.4566			1.29564			0.647818	+	0.761795i	$0.275682\pi$
$882$	0.677691	−	0.677691i	0.0228190	−	0.0228190i
$883$	7.43978	−	7.43978i	0.250369	−	0.250369i	−0.570753	−	0.821122i	$-0.693349\pi$
$883$	7.43978	−	7.43978i	0.250369	−	0.250369i	0.821122	+	0.570753i	$0.193349\pi$
$884$		−	7.52511i		−	0.253097i
$885$	−30.3378	+	25.8541i	−1.01979	+	0.869075i
$886$			1.56305i			0.0525118i
$887$	10.2248	−	10.2248i	0.343316	−	0.343316i	−0.514296	−	0.857613i	$-0.671947\pi$
$887$	10.2248	−	10.2248i	0.343316	−	0.343316i	0.857613	+	0.514296i	$0.171947\pi$
$888$	4.68686	+	4.68686i	0.157281	+	0.157281i
$889$			10.4142i			0.349282i
$890$	29.2788	−	24.9516i	0.981426	−	0.836378i
$891$	−22.4735	+	28.5565i	−0.752891	+	0.956680i
$892$	14.4134	+	14.4134i	0.482595	+	0.482595i
$893$	−5.26100	−	5.26100i	−0.176053	−	0.176053i
$894$			3.69506i			0.123581i
$895$	−38.0762	−	3.03821i	−1.27275	−	0.101556i
$896$	−1.00000			−0.0334077
$897$	−41.0800	+	41.0800i	−1.37162	+	1.37162i
$898$	−11.1090	−	11.1090i	−0.370714	−	0.370714i
$899$	−14.3137			−0.477388
$900$	4.73136	+	0.759896i	0.157712	+	0.0253299i
$901$			10.7622i			0.358542i
$902$	−4.85119	+	0.578285i	−0.161527	+	0.0192548i
$903$	3.45497	−	3.45497i	0.114974	−	0.114974i
$904$	2.91420			0.0969249
$905$	0.0484683	−	0.607426i	0.00161114	−	0.0201915i
$906$	32.2842			1.07257
$907$	−36.2010	−	36.2010i	−1.20204	−	1.20204i	−0.973546	−	0.228490i	$-0.926621\pi$
$907$	−36.2010	−	36.2010i	−1.20204	−	1.20204i	−0.228490	−	0.973546i	$-0.573379\pi$
$908$	8.67798	+	8.67798i	0.287989	+	0.287989i
$909$	0.437482			0.0145104
$910$	5.34588	+	6.27299i	0.177214	+	0.207947i
$911$	−13.2019			−0.437399			−0.218699	−	0.975792i	$-0.570181\pi$
$911$	−13.2019			−0.437399			−0.218699	+	0.975792i	$0.570181\pi$
$912$	4.08087	−	4.08087i	0.135131	−	0.135131i
$913$	43.9816	−	5.24282i	1.45558	−	0.173512i
$914$		−	32.5416i		−	1.07638i
$915$	−45.5351	+	38.8053i	−1.50534	+	1.28286i
$916$	24.0836			0.795744
$917$	5.94887	+	5.94887i	0.196449	+	0.196449i
$918$	−5.86390	+	5.86390i	−0.193537	+	0.193537i
$919$	33.9375			1.11949			0.559747	−	0.828664i	$-0.310898\pi$
$919$	33.9375			1.11949			0.559747	+	0.828664i	$0.310898\pi$
$920$	1.40901	−	17.6584i	0.0464538	−	0.582180i
$921$			3.61440i			0.119099i
$922$	−4.36650	−	4.36650i	−0.143803	−	0.143803i
$923$	24.5839	+	24.5839i	0.809188	+	0.809188i
$924$	−4.08087	+	5.18545i	−0.134251	+	0.170589i
$925$	9.76173	+	13.4973i	0.320964	+	0.443790i
$926$			10.1287i			0.332848i
$927$	6.80679	+	6.80679i	0.223564	+	0.223564i
$928$	4.95753	−	4.95753i	0.162739	−	0.162739i
$929$			2.12556i			0.0697373i	0.999392	+	0.0348687i	$0.0111013\pi$
$929$			2.12556i			0.0697373i	−0.999392	+	0.0348687i	$0.988899\pi$
$930$	−9.05394	−	0.722439i	−0.296890	−	0.0236897i
$931$		−	2.90073i		−	0.0950676i
$932$	17.3376	−	17.3376i	0.567911	−	0.567911i
$933$	40.3826	−	40.3826i	1.32207	−	1.32207i
$934$	−23.9699			−0.784319
$935$	15.1294	−	0.590659i	0.494784	−	0.0193166i
$936$	−3.53255			−0.115465
$937$	8.31304	−	8.31304i	0.271575	−	0.271575i	−0.558159	−	0.829734i	$-0.688492\pi$
$937$	8.31304	−	8.31304i	0.271575	−	0.271575i	0.829734	+	0.558159i	$0.188492\pi$
$938$	−9.72961	+	9.72961i	−0.317683	+	0.317683i
$939$			3.57203i			0.116569i
$940$	−3.72009	−	4.36524i	−0.121336	−	0.142378i
$941$			9.64825i			0.314524i	0.987557	+	0.157262i	$0.0502667\pi$
$941$			9.64825i			0.314524i	−0.987557	+	0.157262i	$0.949733\pi$
$942$	12.2089	−	12.2089i	0.397788	−	0.397788i
$943$	8.25174	+	8.25174i	0.268714	+	0.268714i
$944$			8.95966i			0.291612i
$945$	0.722439	−	9.05394i	0.0235010	−	0.294525i
$946$	−5.03724	+	6.40069i	−0.163775	+	0.208104i
$947$	−14.4732	−	14.4732i	−0.470315	−	0.470315i	0.431702	−	0.902016i	$-0.357913\pi$
$947$	−14.4732	−	14.4732i	−0.470315	−	0.470315i	−0.902016	+	0.431702i	$0.857913\pi$
$948$	15.6666	+	15.6666i	0.508826	+	0.508826i
$949$			10.9011i			0.353866i
$950$	11.7522	−	8.49957i	0.381291	−	0.275762i
$951$	47.9472			1.55479
$952$	−1.44363	+	1.44363i	−0.0467883	+	0.0467883i
$953$	41.3510	+	41.3510i	1.33949	+	1.33949i	0.896551	+	0.442940i	$0.146064\pi$
$953$	41.3510	+	41.3510i	1.33949	+	1.33949i	0.442940	+	0.896551i	$0.353936\pi$
$954$	5.05217			0.163570
$955$	3.10048	−	38.8566i	0.100329	−	1.25737i
$956$		−	18.4693i		−	0.597341i
$957$	−5.47604	−	45.9381i	−0.177015	−	1.48497i
$958$	−18.3336	+	18.3336i	−0.592330	+	0.592330i
$959$	3.29536			0.106413
$960$	3.38604	−	2.88561i	0.109284	−	0.0931326i
$961$	−26.8319			−0.865544
$962$	−8.68289	−	8.68289i	−0.279948	−	0.279948i
$963$	10.2341	+	10.2341i	0.329788	+	0.329788i
$964$	8.78668			0.283000
$965$	20.6262	−	17.5778i	0.663981	−	0.565850i
$966$	15.7617			0.507125
$967$	16.2304	−	16.2304i	0.521935	−	0.521935i	−0.396220	−	0.918155i	$-0.629678\pi$
$967$	16.2304	−	16.2304i	0.521935	−	0.521935i	0.918155	+	0.396220i	$0.129678\pi$
$968$	5.73181	−	9.38863i	0.184227	−	0.301762i
$969$		−	11.7825i		−	0.378509i
$970$	−0.513519	+	6.43565i	−0.0164881	+	0.206636i
$971$	−33.1599			−1.06415			−0.532076	−	0.846697i	$-0.678588\pi$
$971$	−33.1599			−1.06415			−0.532076	+	0.846697i	$0.678588\pi$
$972$	6.79767	+	6.79767i	0.218035	+	0.218035i
$973$	−13.6105	+	13.6105i	−0.436332	+	0.436332i
$974$	−9.57294			−0.306737
$975$	−36.2027	−	5.81446i	−1.15942	−	0.186212i
$976$			13.4479i			0.430456i
$977$	−33.1647	−	33.1647i	−1.06103	−	1.06103i	−0.998012	−	0.0630196i	$-0.979927\pi$
$977$	−33.1647	−	33.1647i	−1.06103	−	1.06103i	−0.0630196	−	0.998012i	$-0.520073\pi$
$978$	21.9173	+	21.9173i	0.700836	+	0.700836i
$979$	−44.8381	−	35.2868i	−1.43303	−	1.12777i
$980$	0.177857	−	2.22898i	0.00568143	−	0.0712023i
$981$			3.89293i			0.124292i
$982$	−12.0364	−	12.0364i	−0.384096	−	0.384096i
$983$	−6.26952	+	6.26952i	−0.199967	+	0.199967i	−0.799986	−	0.600019i	$-0.795160\pi$
$983$	−6.26952	+	6.26952i	−0.199967	+	0.199967i	0.600019	+	0.799986i	$0.295160\pi$
$984$			2.93073i			0.0934283i
$985$	0.343064	+	0.402559i	0.0109309	+	0.0128266i
$986$		−	14.3137i		−	0.455841i
$987$	3.60845	−	3.60845i	0.114858	−	0.114858i
$988$	−7.56022	+	7.56022i	−0.240523	+	0.240523i
$989$	19.4556			0.618651
$990$	−0.277276	−	7.10227i	−0.00881242	−	0.225725i
$991$	59.5675			1.89222			0.946112	−	0.323840i	$-0.104974\pi$
$991$	59.5675			1.89222			0.946112	+	0.323840i	$0.104974\pi$
$992$	−1.44363	+	1.44363i	−0.0458353	+	0.0458353i
$993$	−43.4705	+	43.4705i	−1.37950	+	1.37950i
$994$		−	9.43243i		−	0.299178i
$995$	−13.9225	−	1.11091i	−0.441372	−	0.0352183i
$996$		−	26.5704i		−	0.841917i
$997$	21.5174	−	21.5174i	0.681464	−	0.681464i	−0.278866	−	0.960330i	$-0.589959\pi$
$997$	21.5174	−	21.5174i	0.681464	−	0.681464i	0.960330	+	0.278866i	$0.0899587\pi$
$998$	10.0294	+	10.0294i	0.317475	+	0.317475i
$999$			13.5322i			0.428140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.e.197.2	yes	16
5.3	odd	4	inner	770.2.m.e.43.6	yes	16
11.10	odd	2	inner	770.2.m.e.197.6	yes	16
55.43	even	4	inner	770.2.m.e.43.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.e.43.2	✓	16	55.43	even	4	inner
770.2.m.e.43.6	yes	16	5.3	odd	4	inner
770.2.m.e.197.2	yes	16	1.1	even	1	trivial
770.2.m.e.197.6	yes	16	11.10	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.40684 + 1.40684i) q^{3} -1.00000i q^{4} +(-0.177857 + 2.22898i) q^{5} -1.98957i q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -0.958399i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.40684 + 1.40684i) q^{3} -1.00000i q^{4} +(-0.177857 + 2.22898i) q^{5} -1.98957i q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -0.958399i q^{9} +(-1.45037 - 1.70189i) q^{10} +(-2.05113 + 2.60632i) q^{11} +(1.40684 + 1.40684i) q^{12} +(-2.60632 - 2.60632i) q^{13} +1.00000i q^{14} +(-2.88561 - 3.38604i) q^{15} -1.00000 q^{16} +(-1.44363 + 1.44363i) q^{17} +(0.677691 + 0.677691i) q^{18} +2.90073 q^{19} +(2.22898 + 0.177857i) q^{20} +1.98957i q^{21} +(-0.392578 - 3.29331i) q^{22} +(-5.60182 + 5.60182i) q^{23} -1.98957 q^{24} +(-4.93673 - 0.792880i) q^{25} +3.68589 q^{26} +(-2.87221 - 2.87221i) q^{27} +(-0.707107 - 0.707107i) q^{28} +7.01101 q^{29} +(4.43472 + 0.353859i) q^{30} -2.04160 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.781062 - 6.55228i) q^{33} -2.04160i q^{34} +(1.45037 + 1.70189i) q^{35} -0.958399 q^{36} +(-2.35571 - 2.35571i) q^{37} +(-2.05113 + 2.05113i) q^{38} +7.33334 q^{39} +(-1.70189 + 1.45037i) q^{40} -1.47305i q^{41} +(-1.40684 - 1.40684i) q^{42} +(-1.73654 - 1.73654i) q^{43} +(2.60632 + 2.05113i) q^{44} +(2.13626 + 0.170458i) q^{45} -7.92217i q^{46} +(-1.81368 - 1.81368i) q^{47} +(1.40684 - 1.40684i) q^{48} -1.00000i q^{49} +(4.05145 - 2.93015i) q^{50} -4.06191i q^{51} +(-2.60632 + 2.60632i) q^{52} +(3.72749 - 3.72749i) q^{53} +4.06191 q^{54} +(-5.44463 - 5.03548i) q^{55} +1.00000 q^{56} +(-4.08087 + 4.08087i) q^{57} +(-4.95753 + 4.95753i) q^{58} -8.95966i q^{59} +(-3.38604 + 2.88561i) q^{60} -13.4479i q^{61} +(1.44363 - 1.44363i) q^{62} +(-0.677691 - 0.677691i) q^{63} +1.00000i q^{64} +(6.27299 - 5.34588i) q^{65} +(5.18545 + 4.08087i) q^{66} +(9.72961 + 9.72961i) q^{67} +(1.44363 + 1.44363i) q^{68} -15.7617i q^{69} +(-2.22898 - 0.177857i) q^{70} -9.43243 q^{71} +(0.677691 - 0.677691i) q^{72} +(-2.09129 - 2.09129i) q^{73} +3.33148 q^{74} +(8.06065 - 5.82974i) q^{75} -2.90073i q^{76} +(0.392578 + 3.29331i) q^{77} +(-5.18545 + 5.18545i) q^{78} +11.1360 q^{79} +(0.177857 - 2.22898i) q^{80} +10.9567 q^{81} +(1.04160 + 1.04160i) q^{82} +(-9.44330 - 9.44330i) q^{83} +1.98957 q^{84} +(-2.96107 - 3.47459i) q^{85} +2.45584 q^{86} +(-9.86337 + 9.86337i) q^{87} +(-3.29331 + 0.392578i) q^{88} +17.2036i q^{89} +(-1.63109 + 1.39003i) q^{90} -3.68589 q^{91} +(5.60182 + 5.60182i) q^{92} +(2.87221 - 2.87221i) q^{93} +2.56493 q^{94} +(-0.515915 + 6.46568i) q^{95} +1.98957i q^{96} +(-2.04160 - 2.04160i) q^{97} +(0.707107 + 0.707107i) q^{98} +(2.49789 + 1.96580i) 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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