LMFDB - Embedded newform 770.2.m.e.43.2

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			43.2
Root			$-1.72791i$ of defining polynomial
Character	$\chi$	$=$	770.43
Dual form			770.2.m.e.197.2

$q$-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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

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

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
$3$	−1.40684	−	1.40684i	−0.812240	−	0.812240i	0.172730	−	0.984969i	$-0.444741\pi$
$3$	−1.40684	−	1.40684i	−0.812240	−	0.812240i	−0.984969	+	0.172730i	$0.944741\pi$
$4$			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	−0.969187	−	0.246325i	$-0.920777\pi$
$13$	−2.60632	+	2.60632i	−0.722862	+	0.722862i	0.246325	+	0.969187i	$0.420777\pi$
$14$		−	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	0.510027	−	0.860158i	$-0.329635\pi$
$17$	−1.44363	−	1.44363i	−0.350132	−	0.350132i	−0.860158	+	0.510027i	$0.829635\pi$
$18$	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	−0.982664	−	0.185396i	$-0.940643\pi$
$23$	−5.60182	−	5.60182i	−1.16806	−	1.16806i	−0.185396	−	0.982664i	$-0.559357\pi$
$24$	−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	−0.873715	−	0.486438i	$-0.838296\pi$
$37$	−2.35571	+	2.35571i	−0.387277	+	0.387277i	0.486438	+	0.873715i	$0.338296\pi$
$38$	−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	$0.0366950\pi$
$41$			1.47305i			0.230051i	−0.993363	+	0.115026i	$0.963305\pi$
$42$	−1.40684	+	1.40684i	−0.217080	+	0.217080i
$43$	−1.73654	+	1.73654i	−0.264820	+	0.264820i	−0.827009	−	0.562189i	$-0.809959\pi$
$43$	−1.73654	+	1.73654i	−0.264820	+	0.264820i	0.562189	+	0.827009i	$0.309959\pi$
$44$	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	−0.826901	−	0.562348i	$-0.809898\pi$
$47$	−1.81368	+	1.81368i	−0.264553	+	0.264553i	0.562348	+	0.826901i	$0.309898\pi$
$48$	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	0.915142	−	0.403132i	$-0.132078\pi$
$53$	3.72749	+	3.72749i	0.512010	+	0.512010i	−0.403132	+	0.915142i	$0.632078\pi$
$54$	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	$0.198209\pi$
$59$			8.95966i			1.16645i	−0.812311	+	0.583224i	$0.801791\pi$
$60$	−3.38604	−	2.88561i	−0.437136	−	0.372530i
$61$			13.4479i			1.72183i	0.508752	+	0.860913i	$0.330107\pi$
$61$			13.4479i			1.72183i	−0.508752	+	0.860913i	$0.669893\pi$
$62$	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	0.211224	−	0.977438i	$-0.432255\pi$
$67$	9.72961	−	9.72961i	1.18866	−	1.18866i	0.977438	−	0.211224i	$-0.0677449\pi$
$68$	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	−0.818819	−	0.574052i	$-0.805371\pi$
$73$	−2.09129	+	2.09129i	−0.244767	+	0.244767i	0.574052	+	0.818819i	$0.305371\pi$
$74$	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	−0.0372306	+	0.999307i	$0.511854\pi$
$83$	−9.44330	+	9.44330i	−1.03654	+	1.03654i	−0.999307	+	0.0372306i	$0.988146\pi$
$84$	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	$-0.634700\pi$
$89$		−	17.2036i		−	1.82358i	0.410654	−	0.911791i	$-0.365300\pi$
$90$	−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	−0.803116	−	0.595823i	$-0.796826\pi$
$97$	−2.04160	+	2.04160i	−0.207293	+	0.207293i	0.595823	+	0.803116i	$0.296826\pi$
$98$	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	$-0.992770\pi$
$101$		−	0.456471i		−	0.0454206i	0.999742	−	0.0227103i	$-0.00722953\pi$
$102$	2.87221	−	2.87221i	0.284391	−	0.284391i
$103$	−7.10225	−	7.10225i	−0.699806	−	0.699806i	0.264563	−	0.964368i	$-0.414772\pi$
$103$	−7.10225	−	7.10225i	−0.699806	−	0.699806i	−0.964368	+	0.264563i	$0.914772\pi$
$104$			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	−0.999460	−	0.0328493i	$-0.989542\pi$
$107$	−10.6783	−	10.6783i	−1.03231	−	1.03231i	−0.0328493	−	0.999460i	$-0.510458\pi$
$108$	−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	0.797357	−	0.603507i	$-0.206231\pi$
$113$	2.06065	+	2.06065i	0.193850	+	0.193850i	−0.603507	+	0.797357i	$0.706231\pi$
$114$			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	0.300374	−	0.953821i	$-0.402889\pi$
$127$	−7.36398	−	7.36398i	−0.653447	−	0.653447i	−0.953821	+	0.300374i	$0.902889\pi$
$128$	−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	$-0.880206\pi$
$131$		−	8.41298i		−	0.735045i	0.930015	−	0.367523i	$-0.119794\pi$
$132$	−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	−0.600526	−	0.799606i	$-0.705042\pi$
$137$	2.33017	−	2.33017i	0.199080	−	0.199080i	0.799606	+	0.600526i	$0.205042\pi$
$138$	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	$-0.770448\pi$
$151$		−	16.2267i		−	1.32051i	0.751041	−	0.660256i	$-0.229552\pi$
$152$	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	−0.418482	−	0.908225i	$-0.637438\pi$
$157$	6.13645	−	6.13645i	0.489742	−	0.489742i	0.908225	+	0.418482i	$0.137438\pi$
$158$	−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	0.128823	−	0.991668i	$-0.458880\pi$
$163$	−11.0161	−	11.0161i	−0.862844	−	0.862844i	−0.991668	+	0.128823i	$0.958880\pi$
$164$	−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	0.971890	−	0.235434i	$-0.0756512\pi$
$167$	9.51711	+	9.51711i	0.736456	+	0.736456i	−0.235434	+	0.971890i	$0.575651\pi$
$168$	−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	−0.994846	−	0.101396i	$-0.967669\pi$
$173$	−11.7515	+	11.7515i	−0.893451	+	0.893451i	0.101396	+	0.994846i	$0.467669\pi$
$174$			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	$-0.779598\pi$
$179$		−	17.0823i		−	1.27679i	0.769707	−	0.638397i	$-0.220402\pi$
$180$	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	−0.944727	−	0.327857i	$-0.893674\pi$
$193$	−8.56983	+	8.56983i	−0.616870	+	0.616870i	0.327857	+	0.944727i	$0.393674\pi$
$194$	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	0.713040	−	0.701123i	$-0.247318\pi$
$197$	0.167256	+	0.167256i	0.0119165	+	0.0119165i	−0.701123	+	0.713040i	$0.747318\pi$
$198$	−3.15631	−	0.376246i	−0.224309	−	0.0267387i
$199$		−	6.24611i		−	0.442775i	−0.975186	−	0.221387i	$-0.928941\pi$
$199$		−	6.24611i		−	0.442775i	0.975186	−	0.221387i	$-0.0710585\pi$
$200$	−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	$0.0528982\pi$
$211$			4.80575i			0.330842i	−0.986223	+	0.165421i	$0.947102\pi$
$212$	−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	0.0342233	−	0.999414i	$-0.489104\pi$
$223$	−14.4134	−	14.4134i	−0.965191	−	0.965191i	−0.999414	+	0.0342233i	$0.989104\pi$
$224$			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	0.357815	−	0.933793i	$-0.383522\pi$
$227$	−8.67798	−	8.67798i	−0.575978	−	0.575978i	−0.933793	+	0.357815i	$0.883522\pi$
$228$	4.08087	−	4.08087i	0.270262	−	0.270262i
$229$		−	24.0836i		−	1.59149i	−0.605633	−	0.795744i	$-0.707080\pi$
$229$		−	24.0836i		−	1.59149i	0.605633	−	0.795744i	$-0.292920\pi$
$230$	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	0.146630	−	0.989191i	$-0.453157\pi$
$233$	17.3376	−	17.3376i	1.13582	−	1.13582i	0.989191	−	0.146630i	$-0.0468427\pi$
$234$			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	$-0.908670\pi$
$241$		−	8.78668i		−	0.566000i	0.959120	−	0.283000i	$-0.0913296\pi$
$242$	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	−0.111496	−	0.993765i	$-0.535564\pi$
$257$	14.1439	−	14.1439i	0.882269	−	0.882269i	0.993765	+	0.111496i	$0.0355641\pi$
$258$	−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	−0.778488	−	0.627659i	$-0.784013\pi$
$263$	−2.44604	+	2.44604i	−0.150830	+	0.150830i	0.627659	+	0.778488i	$0.284013\pi$
$264$	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	$0.274884\pi$
$269$			24.9354i			1.52034i	−0.649726	+	0.760169i	$0.725116\pi$
$270$	−0.722439	−	9.05394i	−0.0439663	−	0.551005i
$271$			3.67652i			0.223333i	0.993746	+	0.111666i	$0.0356188\pi$
$271$			3.67652i			0.223333i	−0.993746	+	0.111666i	$0.964381\pi$
$272$	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	0.990267	−	0.139183i	$-0.0444478\pi$
$277$	14.1648	+	14.1648i	0.851083	+	0.851083i	−0.139183	+	0.990267i	$0.544448\pi$
$278$	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	$-0.957651\pi$
$281$		−	4.44730i		−	0.265304i	0.991163	−	0.132652i	$-0.0423493\pi$
$282$	−3.60845	−	3.60845i	−0.214880	−	0.214880i
$283$	−21.9077	+	21.9077i	−1.30228	+	1.30228i	−0.375428	+	0.926852i	$0.622504\pi$
$283$	−21.9077	+	21.9077i	−1.30228	+	1.30228i	−0.926852	+	0.375428i	$0.877496\pi$
$284$		−	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	−0.210045	−	0.977692i	$-0.567361\pi$
$293$	13.1400	−	13.1400i	0.767647	−	0.767647i	0.977692	+	0.210045i	$0.0673610\pi$
$294$	−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	0.742813	−	0.669498i	$-0.233491\pi$
$307$	1.28458	+	1.28458i	0.0733149	+	0.0733149i	−0.669498	+	0.742813i	$0.733491\pi$
$308$	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	0.742075	−	0.670317i	$-0.233842\pi$
$313$	1.26952	+	1.26952i	0.0717575	+	0.0717575i	−0.670317	+	0.742075i	$0.733842\pi$
$314$	−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	−0.999117	−	0.0420140i	$-0.986623\pi$
$317$	−17.0407	+	17.0407i	−0.957103	+	0.957103i	0.0420140	+	0.999117i	$0.486623\pi$
$318$	−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	0.587709	−	0.809073i	$-0.300030\pi$
$337$	−4.06370	−	4.06370i	−0.221364	−	0.221364i	−0.809073	+	0.587709i	$0.800030\pi$
$338$	−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	0.758794	−	0.651331i	$-0.225789\pi$
$347$	2.00182	+	2.00182i	0.107463	+	0.107463i	−0.651331	+	0.758794i	$0.725789\pi$
$348$	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	0.857723	−	0.514113i	$-0.171879\pi$
$353$	6.45584	+	6.45584i	0.343610	+	0.343610i	−0.514113	+	0.857723i	$0.671879\pi$
$354$	−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	0.00683345	−	0.999977i	$-0.497825\pi$
$367$	19.2877	−	19.2877i	1.00681	−	1.00681i	0.999977	−	0.00683345i	$-0.00217517\pi$
$368$	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	−0.943592	−	0.331109i	$-0.892577\pi$
$373$	−11.8290	+	11.8290i	−0.612483	+	0.612483i	0.331109	+	0.943592i	$0.392577\pi$
$374$	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	$0.200671\pi$
$379$			22.9523i			1.17898i	−0.807775	+	0.589490i	$0.799329\pi$
$380$	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	0.671564	−	0.740946i	$-0.265623\pi$
$383$	−1.35784	−	1.35784i	−0.0693824	−	0.0693824i	−0.740946	+	0.671564i	$0.765623\pi$
$384$	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	$-0.826920\pi$
$389$		−	20.4073i		−	1.03469i	0.855777	−	0.517345i	$-0.173080\pi$
$390$	−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	−0.691599	−	0.722282i	$-0.743093\pi$
$397$	0.611346	−	0.611346i	0.0306826	−	0.0306826i	0.722282	+	0.691599i	$0.243093\pi$
$398$	−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	$0.131881\pi$
$419$			16.4805i			0.805126i	−0.915392	+	0.402563i	$0.868119\pi$
$420$	−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	$0.0792243\pi$
$431$			10.2278i			0.492658i	−0.969186	+	0.246329i	$0.920776\pi$
$432$	2.87221	−	2.87221i	0.138189	−	0.138189i
$433$	−18.8726	−	18.8726i	−0.906959	−	0.906959i	0.0890663	−	0.996026i	$-0.471612\pi$
$433$	−18.8726	−	18.8726i	−0.906959	−	0.906959i	−0.996026	+	0.0890663i	$0.971612\pi$
$434$			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	0.732875	−	0.680363i	$-0.238178\pi$
$443$	1.10525	+	1.10525i	0.0525118	+	0.0525118i	−0.680363	+	0.732875i	$0.738178\pi$
$444$			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	$-0.879113\pi$
$449$		−	15.7106i		−	0.741427i	0.928747	−	0.370714i	$-0.120887\pi$
$450$	−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	−0.996831	−	0.0795483i	$-0.974652\pi$
$457$	−23.0104	−	23.0104i	−1.07638	−	1.07638i	−0.0795483	−	0.996831i	$-0.525348\pi$
$458$	−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	$-0.954067\pi$
$461$		−	6.17517i		−	0.287606i	0.989606	−	0.143803i	$-0.0459332\pi$
$462$	6.55228	+	0.781062i	0.304840	+	0.0363383i
$463$	7.16204	+	7.16204i	0.332848	+	0.332848i	0.853667	−	0.520819i	$-0.174373\pi$
$463$	7.16204	+	7.16204i	0.332848	+	0.332848i	−0.520819	+	0.853667i	$0.674373\pi$
$464$	−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	−0.196238	−	0.980556i	$-0.562872\pi$
$467$	16.9493	−	16.9493i	0.784319	−	0.784319i	0.980556	+	0.196238i	$0.0628724\pi$
$468$	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	−0.536906	−	0.843642i	$-0.680407\pi$
$487$	6.76909	−	6.76909i	0.306737	−	0.306737i	0.843642	+	0.536906i	$0.180407\pi$
$488$	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	$-0.874513\pi$
$491$		−	17.0220i		−	0.768192i	0.923293	−	0.384096i	$-0.125487\pi$
$492$	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	$0.102835\pi$
$499$			14.1837i			0.634951i	−0.948267	+	0.317475i	$0.897165\pi$
$500$	−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	−0.284716	−	0.958612i	$-0.591899\pi$
$503$	15.1139	−	15.1139i	0.673896	−	0.673896i	0.958612	+	0.284716i	$0.0918993\pi$
$504$			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	$0.185091\pi$
$509$			24.7838i			1.09852i	−0.835651	+	0.549261i	$0.814909\pi$
$510$	−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	−0.325842	−	0.945424i	$-0.605648\pi$
$523$	14.1694	−	14.1694i	0.619583	−	0.619583i	0.945424	+	0.325842i	$0.105648\pi$
$524$	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	$-0.702664\pi$
$541$		−	37.4044i		−	1.60814i	0.594535	−	0.804070i	$-0.297336\pi$
$542$	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	0.991886	+	0.127130i	$0.0405765\pi$
$547$	26.1716	+	26.1716i	1.11902	+	1.11902i	0.127130	+	0.991886i	$0.459424\pi$
$548$	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	0.933499	−	0.358580i	$-0.116739\pi$
$557$	13.5686	+	13.5686i	0.574918	+	0.574918i	−0.358580	+	0.933499i	$0.616739\pi$
$558$	−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	−0.0549909	−	0.998487i	$-0.517513\pi$
$563$	22.3869	−	22.3869i	0.943496	−	0.943496i	0.998487	+	0.0549909i	$0.0175130\pi$
$564$			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	$-0.869398\pi$
$571$		−	19.0631i		−	0.797766i	0.917002	−	0.398883i	$-0.130602\pi$
$572$	−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	−0.912087	−	0.409996i	$-0.865530\pi$
$577$	−12.0607	+	12.0607i	−0.502092	+	0.502092i	0.409996	+	0.912087i	$0.365530\pi$
$578$	−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	0.0609921	−	0.998138i	$-0.480574\pi$
$587$	25.6607	−	25.6607i	1.05913	−	1.05913i	0.998138	−	0.0609921i	$-0.0194264\pi$
$588$	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	−0.994214	−	0.107418i	$-0.965742\pi$
$593$	−21.5949	+	21.5949i	−0.886796	+	0.886796i	0.107418	+	0.994214i	$0.465742\pi$
$594$	−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	$-0.781192\pi$
$599$		−	31.0598i		−	1.26907i	0.772895	−	0.634534i	$-0.218808\pi$
$600$	9.82199	−	1.57749i	0.400981	−	0.0644009i
$601$			5.56491i			0.226997i	0.993538	+	0.113499i	$0.0362058\pi$
$601$			5.56491i			0.226997i	−0.993538	+	0.113499i	$0.963794\pi$
$602$	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	0.785826	−	0.618448i	$-0.212238\pi$
$607$	4.12375	+	4.12375i	0.167378	+	0.167378i	−0.618448	+	0.785826i	$0.712238\pi$
$608$	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	−0.195094	−	0.980785i	$-0.562501\pi$
$613$	19.4528	−	19.4528i	0.785691	−	0.785691i	0.980785	+	0.195094i	$0.0625011\pi$
$614$		−	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	−0.956489	−	0.291770i	$-0.905756\pi$
$617$	−16.5113	+	16.5113i	−0.664718	+	0.664718i	0.291770	+	0.956489i	$0.405756\pi$
$618$	14.1304	−	14.1304i	0.568410	−	0.568410i
$619$			22.9918i			0.924118i	0.886849	+	0.462059i	$0.152889\pi$
$619$			22.9918i			0.924118i	−0.886849	+	0.462059i	$0.847111\pi$
$620$	−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	0.355837	−	0.934548i	$-0.384196\pi$
$643$	−14.6746	−	14.6746i	−0.578711	−	0.578711i	−0.934548	+	0.355837i	$0.884196\pi$
$644$	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	−0.795516	−	0.605932i	$-0.792800\pi$
$647$	−4.82230	+	4.82230i	−0.189584	+	0.189584i	0.605932	+	0.795516i	$0.292800\pi$
$648$	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	0.756833	−	0.653608i	$-0.226746\pi$
$653$	2.63780	+	2.63780i	0.103225	+	0.103225i	−0.653608	+	0.756833i	$0.726746\pi$
$654$		−	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	−0.0743478	−	0.997232i	$-0.523688\pi$
$673$	23.9417	−	23.9417i	0.922885	−	0.922885i	0.997232	+	0.0743478i	$0.0236875\pi$
$674$			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	0.272678	−	0.962105i	$-0.412091\pi$
$677$	−17.9384	−	17.9384i	−0.689427	−	0.689427i	−0.962105	+	0.272678i	$0.912091\pi$
$678$	−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	−0.915591	−	0.402112i	$-0.868276\pi$
$683$	−34.4372	−	34.4372i	−1.31770	−	1.31770i	−0.402112	−	0.915591i	$-0.631724\pi$
$684$	−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	$-0.683456\pi$
$701$		−	44.3988i		−	1.67692i	0.544962	−	0.838460i	$-0.316544\pi$
$702$	−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	$-0.890056\pi$
$709$		−	18.0304i		−	0.677145i	0.940940	−	0.338573i	$-0.109944\pi$
$710$	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	$-0.931192\pi$
$719$		−	11.5026i		−	0.428973i	0.976727	−	0.214487i	$-0.0688078\pi$
$720$	−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	−0.202867	−	0.979206i	$-0.565026\pi$
$727$	20.9324	−	20.9324i	0.776339	−	0.776339i	0.979206	+	0.202867i	$0.0650259\pi$
$728$	−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	−0.999210	−	0.0397491i	$-0.987344\pi$
$733$	−25.9764	+	25.9764i	−0.959461	+	0.959461i	0.0397491	+	0.999210i	$0.487344\pi$
$734$	−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	−0.341385	−	0.939923i	$-0.610896\pi$
$743$	16.3150	−	16.3150i	0.598538	−	0.598538i	0.939923	+	0.341385i	$0.110896\pi$
$744$	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	−0.465806	−	0.884887i	$-0.654236\pi$
$757$	11.5304	−	11.5304i	0.419080	−	0.419080i	0.884887	+	0.465806i	$0.154236\pi$
$758$	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	$-0.798534\pi$
$761$		−	32.6347i		−	1.18301i	0.806302	−	0.591504i	$-0.201466\pi$
$762$	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	0.885434	−	0.464765i	$-0.153861\pi$
$773$	11.6958	+	11.6958i	0.420669	+	0.420669i	−0.464765	+	0.885434i	$0.653861\pi$
$774$			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	0.996406	−	0.0847112i	$-0.0269968\pi$
$787$	25.5762	+	25.5762i	0.911694	+	0.911694i	−0.0847112	+	0.996406i	$0.526997\pi$
$788$	−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	−0.233329	−	0.972398i	$-0.574962\pi$
$797$	20.8648	−	20.8648i	0.739069	−	0.739069i	0.972398	+	0.233329i	$0.0749618\pi$
$798$	−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	$0.126568\pi$
$811$			22.0551i			0.774458i	−0.921984	+	0.387229i	$0.873432\pi$
$812$	−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	$-0.977672\pi$
$821$		−	4.01649i		−	0.140176i	0.997541	−	0.0700882i	$-0.0223281\pi$
$822$	4.63605	+	4.63605i	0.161701	+	0.161701i
$823$	31.5711	+	31.5711i	1.10050	+	1.10050i	0.994350	+	0.106147i	$0.0338515\pi$
$823$	31.5711	+	31.5711i	1.10050	+	1.10050i	0.106147	+	0.994350i	$0.466149\pi$
$824$	−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	0.750275	−	0.661126i	$-0.229921\pi$
$827$	2.56371	+	2.56371i	0.0891489	+	0.0891489i	−0.661126	+	0.750275i	$0.729921\pi$
$828$	5.36878	+	5.36878i	0.186578	+	0.186578i
$829$			17.6235i			0.612090i	0.952017	+	0.306045i	$0.0990057\pi$
$829$			17.6235i			0.612090i	−0.952017	+	0.306045i	$0.900994\pi$
$830$	−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	$0.175033\pi$
$839$			30.2740i			1.04517i	−0.852586	+	0.522587i	$0.824967\pi$
$840$	−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	−0.722671	−	0.691192i	$-0.757086\pi$
$853$	−0.919367	+	0.919367i	−0.0314785	+	0.0314785i	0.691192	+	0.722671i	$0.257086\pi$
$854$	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	0.945235	−	0.326392i	$-0.105833\pi$
$857$	18.1164	+	18.1164i	0.618843	+	0.618843i	−0.326392	+	0.945235i	$0.605833\pi$
$858$	−2.87891	+	24.1510i	−0.0982843	+	0.824500i
$859$			45.0602i			1.53743i	0.639589	+	0.768717i	$0.279104\pi$
$859$			45.0602i			1.53743i	−0.639589	+	0.768717i	$0.720896\pi$
$860$	−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	0.855208	−	0.518285i	$-0.173429\pi$
$863$	9.89775	+	9.89775i	0.336923	+	0.336923i	−0.518285	+	0.855208i	$0.673429\pi$
$864$	−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	0.900060	+	0.435767i	$0.143523\pi$
$877$	39.5594	+	39.5594i	1.33583	+	1.33583i	0.435767	+	0.900060i	$0.356477\pi$
$878$	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	0.821122	−	0.570753i	$-0.193349\pi$
$883$	7.43978	+	7.43978i	0.250369	+	0.250369i	−0.570753	+	0.821122i	$0.693349\pi$
$884$			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	0.857613	−	0.514296i	$-0.171947\pi$
$887$	10.2248	+	10.2248i	0.343316	+	0.343316i	−0.514296	+	0.857613i	$0.671947\pi$
$888$	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	−0.228490	+	0.973546i	$0.573379\pi$
$907$	−36.2010	+	36.2010i	−1.20204	+	1.20204i	−0.973546	+	0.228490i	$0.926621\pi$
$908$	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	$-0.988899\pi$
$929$		−	2.12556i		−	0.0697373i	0.999392	−	0.0348687i	$-0.0111013\pi$
$930$	−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	0.829734	−	0.558159i	$-0.188492\pi$
$937$	8.31304	+	8.31304i	0.271575	+	0.271575i	−0.558159	+	0.829734i	$0.688492\pi$
$938$	−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	$-0.949733\pi$
$941$		−	9.64825i		−	0.314524i	0.987557	−	0.157262i	$-0.0502667\pi$
$942$	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	−0.902016	−	0.431702i	$-0.857913\pi$
$947$	−14.4732	+	14.4732i	−0.470315	+	0.470315i	0.431702	+	0.902016i	$0.357913\pi$
$948$	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	0.442940	−	0.896551i	$-0.353936\pi$
$953$	41.3510	−	41.3510i	1.33949	−	1.33949i	0.896551	−	0.442940i	$-0.146064\pi$
$954$	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	0.918155	−	0.396220i	$-0.129678\pi$
$967$	16.2304	+	16.2304i	0.521935	+	0.521935i	−0.396220	+	0.918155i	$0.629678\pi$
$968$	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	−0.0630196	+	0.998012i	$0.520073\pi$
$977$	−33.1647	+	33.1647i	−1.06103	+	1.06103i	−0.998012	+	0.0630196i	$0.979927\pi$
$978$	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	0.600019	−	0.799986i	$-0.295160\pi$
$983$	−6.26952	−	6.26952i	−0.199967	−	0.199967i	−0.799986	+	0.600019i	$0.795160\pi$
$984$		−	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	0.960330	−	0.278866i	$-0.0899587\pi$
$997$	21.5174	+	21.5174i	0.681464	+	0.681464i	−0.278866	+	0.960330i	$0.589959\pi$
$998$	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.43.2	✓	16
5.2	odd	4	inner	770.2.m.e.197.6	yes	16
11.10	odd	2	inner	770.2.m.e.43.6	yes	16
55.32	even	4	inner	770.2.m.e.197.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.e.43.2	✓	16	1.1	even	1	trivial
770.2.m.e.43.6	yes	16	11.10	odd	2	inner
770.2.m.e.197.2	yes	16	55.32	even	4	inner
770.2.m.e.197.6	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.40684 - 1.40684i) q^{3} +1.00000i q^{4} +(-0.177857 - 2.22898i) q^{5} +1.98957i q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.958399i q^{9} +O(q^{10})\)	\(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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