LMFDB - Embedded newform 770.2.m.e.197.6

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			197.6
Root			$0.313694i$ of defining polynomial
Character	$\chi$	$=$	770.197
Dual form			770.2.m.e.43.6

$q$-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} +(-3.29331 - 0.392578i) 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} +(6.55228 + 0.781062i) 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} +(6.17424 - 4.10838i) 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} +(3.29331 + 0.392578i) 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} +(-0.392578 + 3.29331i) 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	0.969187	−	0.246325i	$-0.0792232\pi$
$13$	2.60632	+	2.60632i	0.722862	+	0.722862i	−0.246325	+	0.969187i	$0.579223\pi$
$14$			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	$-0.670365\pi$
$17$	1.44363	−	1.44363i	0.350132	−	0.350132i	0.860158	+	0.510027i	$0.170365\pi$
$18$	−0.677691	−	0.677691i	−0.159733	−	0.159733i
$19$	−2.90073			−0.665473			−0.332737	−	0.943020i	$-0.607972\pi$
$19$	−2.90073			−0.665473			−0.332737	+	0.943020i	$0.607972\pi$
$20$	2.22898	+	0.177857i	0.498416	+	0.0397700i
$21$		−	1.98957i		−	0.434160i
$22$	−3.29331	−	0.392578i	−0.702136	−	0.0836979i
$23$	−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	$-0.725632\pi$
$29$	−7.01101			−1.30191			−0.650956	+	0.759115i	$0.725632\pi$
$30$	−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
$33$	6.55228	+	0.781062i	1.14061	+	0.135966i
$34$		−	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	$0.0366950\pi$
$41$			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	$-0.190041\pi$
$43$	1.73654	+	1.73654i	0.264820	+	0.264820i	−0.562189	+	0.827009i	$0.690041\pi$
$44$	−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
$55$	6.17424	−	4.10838i	0.832534	−	0.553973i
$56$	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	$0.330107\pi$
$61$			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	0.977438	+	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	0.818819	−	0.574052i	$-0.194629\pi$
$73$	2.09129	+	2.09129i	0.244767	+	0.244767i	−0.574052	+	0.818819i	$0.694629\pi$
$74$	−3.33148			−0.387277
$75$	8.06065	−	5.82974i	0.930764	−	0.673160i
$76$			2.90073i			0.332737i
$77$	3.29331	+	0.392578i	0.375307	+	0.0447384i
$78$	−5.18545	+	5.18545i	−0.587137	+	0.587137i
$79$	−11.1360			−1.25290			−0.626448	−	0.779463i	$-0.715492\pi$
$79$	−11.1360			−1.25290			−0.626448	+	0.779463i	$0.715492\pi$
$80$	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	$0.0118536\pi$
$83$	9.44330	+	9.44330i	1.03654	+	1.03654i	0.0372306	+	0.999307i	$0.488146\pi$
$84$	−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
$88$	−0.392578	+	3.29331i	−0.0418489	+	0.351068i
$89$			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	$-0.992770\pi$
$101$		−	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	−0.964368	−	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	$-0.489542\pi$
$107$	10.6783	−	10.6783i	1.03231	−	1.03231i	0.999460	−	0.0328493i	$-0.0104581\pi$
$108$	−2.87221	+	2.87221i	−0.276378	+	0.276378i
$109$	4.06191			0.389061			0.194530	−	0.980897i	$-0.437682\pi$
$109$	4.06191			0.389061			0.194530	+	0.980897i	$0.437682\pi$
$110$	1.46079	−	7.27091i	0.139281	−	0.693254i
$111$	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	−0.300374	−	0.953821i	$-0.597111\pi$
$127$	7.36398	−	7.36398i	0.653447	−	0.653447i	0.953821	+	0.300374i	$0.0971115\pi$
$128$	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	$-0.119794\pi$
$132$	0.781062	−	6.55228i	0.0679828	−	0.570303i
$133$	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	$-0.196020\pi$
$139$	19.2481			1.63260			0.816302	+	0.577625i	$0.196020\pi$
$140$	−1.70189	+	1.45037i	−0.143836	+	0.122578i
$141$	5.10312			0.429760
$142$	−6.66973	+	6.66973i	−0.559711	+	0.559711i
$143$	1.44700	−	12.1388i	0.121004	−	1.01509i
$144$			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	$-0.475761\pi$
$149$	1.85721			0.152149			0.0760744	+	0.997102i	$0.475761\pi$
$150$	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	0.908225	−	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
$165$	−2.90634	+	14.4660i	−0.226258	+	1.12618i
$166$	13.3548			1.03654
$167$	−9.51711	+	9.51711i	−0.736456	+	0.736456i	−0.971890	−	0.235434i	$-0.924349\pi$
$167$	−9.51711	+	9.51711i	−0.736456	+	0.736456i	0.235434	+	0.971890i	$0.424349\pi$
$168$	−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	$-0.0323308\pi$
$173$	11.7515	+	11.7515i	0.893451	+	0.893451i	−0.101396	+	0.994846i	$0.532331\pi$
$174$		−	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
$187$	−6.72362	−	0.801487i	−0.491680	−	0.0586106i
$188$	−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	$-0.106326\pi$
$193$	8.56983	+	8.56983i	0.616870	+	0.616870i	−0.327857	+	0.944727i	$0.606326\pi$
$194$	−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	$-0.752682\pi$
$197$	−0.167256	+	0.167256i	−0.0119165	+	0.0119165i	0.701123	+	0.713040i	$0.252682\pi$
$198$	−0.376246	+	3.15631i	−0.0267387	+	0.224309i
$199$			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	$0.0528982\pi$
$211$			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
$220$	−4.10838	−	6.17424i	−0.276987	−	0.416267i
$221$	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	−0.357815	−	0.933793i	$-0.616478\pi$
$227$	8.67798	−	8.67798i	0.575978	−	0.575978i	0.933793	+	0.357815i	$0.116478\pi$
$228$	−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	$-0.953157\pi$
$233$	−17.3376	−	17.3376i	−1.13582	−	1.13582i	−0.146630	−	0.989191i	$-0.546843\pi$
$234$		−	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	$-0.703776\pi$
$239$	−18.4693			−1.19468			−0.597341	+	0.801988i	$0.703776\pi$
$240$	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	$-0.0913296\pi$
$242$	5.73181	+	9.38863i	0.368455	+	0.603524i
$243$	−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
$253$	26.0902	+	3.11007i	1.64027	+	0.195528i
$254$		−	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	0.778488	−	0.627659i	$-0.215987\pi$
$263$	2.44604	+	2.44604i	0.150830	+	0.150830i	−0.627659	+	0.778488i	$0.715987\pi$
$264$	−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	$0.0356188\pi$
$271$			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
$275$	8.05937	+	14.4930i	0.485998	+	0.873960i
$276$	−15.7617			−0.948745
$277$	−14.1648	+	14.1648i	−0.851083	+	0.851083i	−0.990267	−	0.139183i	$-0.955552\pi$
$277$	−14.1648	+	14.1648i	−0.851083	+	0.851083i	0.139183	+	0.990267i	$0.455552\pi$
$278$	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	0.926852	+	0.375428i	$0.122504\pi$
$283$	21.9077	+	21.9077i	1.30228	+	1.30228i	0.375428	+	0.926852i	$0.377496\pi$
$284$			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	$-0.432639\pi$
$293$	−13.1400	−	13.1400i	−0.767647	−	0.767647i	−0.977692	+	0.210045i	$0.932639\pi$
$294$	1.98957			0.116034
$295$	19.9709	+	1.59354i	1.16275	+	0.0927794i
$296$			3.33148i			0.193638i
$297$	−1.59462	+	13.3771i	−0.0925291	+	0.776220i
$298$	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	$-0.766509\pi$
$307$	−1.28458	+	1.28458i	−0.0733149	+	0.0733149i	0.669498	+	0.742813i	$0.266509\pi$
$308$	0.392578	−	3.29331i	0.0223692	−	0.187654i
$309$		−	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
$330$	8.17391	+	12.2841i	0.449959	+	0.676218i
$331$	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	$-0.699970\pi$
$337$	4.06370	−	4.06370i	0.221364	−	0.221364i	0.809073	+	0.587709i	$0.199970\pi$
$338$	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	$-0.774211\pi$
$347$	−2.00182	+	2.00182i	−0.107463	+	0.107463i	0.651331	+	0.758794i	$0.274211\pi$
$348$	−9.86337	−	9.86337i	−0.528732	−	0.528732i
$349$	3.86771			0.207034			0.103517	−	0.994628i	$-0.466990\pi$
$349$	3.86771			0.207034			0.103517	+	0.994628i	$0.466990\pi$
$350$	0.792880	−	4.93673i	0.0423812	−	0.263880i
$351$		−	14.9718i		−	0.799133i
$352$	3.29331	+	0.392578i	0.175534	+	0.0209245i
$353$	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	$-0.310022\pi$
$359$	21.2978			1.12405			0.562026	+	0.827119i	$0.310022\pi$
$360$	−1.39003	−	1.63109i	−0.0732610	−	0.0859662i
$361$	−10.5858			−0.557145
$362$	−0.192696	+	0.192696i	−0.0101279	+	0.0101279i
$363$	−11.4039	−	18.6794i	−0.598547	−	0.980412i
$364$			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	0.943592	−	0.331109i	$-0.107423\pi$
$373$	11.8290	+	11.8290i	0.612483	+	0.612483i	−0.331109	+	0.943592i	$0.607423\pi$
$374$	−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
$385$	−1.46079	+	7.27091i	−0.0744486	+	0.370560i
$386$	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
$407$	−1.30787	+	10.9716i	−0.0648285	+	0.543842i
$408$	2.87221	−	2.87221i	0.142195	−	0.142195i
$409$	−11.4914			−0.568215			−0.284107	−	0.958792i	$-0.591697\pi$
$409$	−11.4914			−0.568215			−0.284107	+	0.958792i	$0.591697\pi$
$410$	−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
$418$	9.55300	+	1.13876i	0.467253	+	0.0556987i
$419$		−	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	$0.0792243\pi$
$431$			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	−0.996026	−	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	$-0.201449\pi$
$439$	33.7891			1.61267			0.806333	+	0.591461i	$0.201449\pi$
$440$	−7.27091	−	1.46079i	−0.346627	−	0.0696403i
$441$	−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	$-0.474652\pi$
$457$	23.0104	−	23.0104i	1.07638	−	1.07638i	0.996831	−	0.0795483i	$-0.0253478\pi$
$458$	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	$-0.0459332\pi$
$462$	−0.781062	+	6.55228i	−0.0363383	+	0.304840i
$463$	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
$473$	0.964109	−	8.08784i	0.0443298	−	0.371879i
$474$		−	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	$-0.701792\pi$
$479$	−25.9276			−1.18466			−0.592330	+	0.805695i	$0.701792\pi$
$480$	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	$-0.874513\pi$
$491$		−	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
$495$	−3.93746	−	5.91739i	−0.176976	−	0.265967i
$496$	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	0.284716	−	0.958612i	$-0.408101\pi$
$503$	−15.1139	−	15.1139i	−0.673896	−	0.673896i	−0.958612	+	0.284716i	$0.908101\pi$
$504$		−	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
$517$	−1.00694	+	8.44711i	−0.0442850	+	0.371504i
$518$	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	$-0.394352\pi$
$523$	−14.1694	−	14.1694i	−0.619583	−	0.619583i	−0.945424	+	0.325842i	$0.894352\pi$
$524$	−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
$528$	−6.55228	−	0.781062i	−0.285151	−	0.0339914i
$529$		−	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	−0.127130	+	0.991886i	$0.540576\pi$
$547$	−26.1716	+	26.1716i	−1.11902	+	1.11902i	−0.991886	+	0.127130i	$0.959424\pi$
$548$	2.33017	−	2.33017i	0.0995400	−	0.0995400i
$549$	12.8884			0.550066
$550$	15.9469	+	4.54925i	0.679979	+	0.193981i
$551$	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	$-0.883261\pi$
$557$	−13.5686	+	13.5686i	−0.574918	+	0.574918i	0.358580	+	0.933499i	$0.383261\pi$
$558$	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	$-0.482487\pi$
$563$	−22.3869	−	22.3869i	−0.943496	−	0.943496i	−0.998487	+	0.0549909i	$0.982487\pi$
$564$		−	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	$-0.206232\pi$
$569$	38.0397			1.59471			0.797354	+	0.603512i	$0.206232\pi$
$570$	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	$-0.130602\pi$
$572$	−12.1388	−	1.44700i	−0.507547	−	0.0605020i
$573$	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
$583$	−17.3606	−	2.06946i	−0.719001	−	0.0857083i
$584$		−	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	0.994214	−	0.107418i	$-0.0342582\pi$
$593$	21.5949	+	21.5949i	0.886796	+	0.886796i	−0.107418	+	0.994214i	$0.534258\pi$
$594$	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	$0.0362058\pi$
$601$			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
$605$	−23.3719	−	7.66522i	−0.950202	−	0.311636i
$606$	0.908183			0.0368924
$607$	−4.12375	+	4.12375i	−0.167378	+	0.167378i	−0.785826	−	0.618448i	$-0.787762\pi$
$607$	−4.12375	+	4.12375i	−0.167378	+	0.167378i	0.618448	+	0.785826i	$0.287762\pi$
$608$	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	$-0.437499\pi$
$613$	−19.4528	−	19.4528i	−0.785691	−	0.785691i	−0.980785	+	0.195094i	$0.937499\pi$
$614$			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
$627$	−19.0064	−	2.26565i	−0.759042	−	0.0904814i
$628$	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
$638$	23.0894	+	2.75237i	0.914119	+	0.108967i
$639$			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	$-0.632176\pi$
$659$	−20.7119			−0.806822			−0.403411	+	0.915019i	$0.632176\pi$
$660$	14.4660	+	2.90634i	0.563088	+	0.113129i
$661$	−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	$-0.476312\pi$
$673$	−23.9417	−	23.9417i	−0.922885	−	0.922885i	−0.997232	+	0.0743478i	$0.976312\pi$
$674$		−	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	$-0.587909\pi$
$677$	17.9384	−	17.9384i	0.689427	−	0.689427i	0.962105	+	0.272678i	$0.0879094\pi$
$678$	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
$682$	6.72362	+	0.801487i	0.257461	+	0.0306905i
$683$	−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
$693$	0.376246	−	3.15631i	0.0142924	−	0.119898i
$694$			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	$0.109944\pi$
$709$			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
$715$	26.7997	+	5.38430i	1.00225	+	0.201361i
$716$	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	0.999210	−	0.0397491i	$-0.0126559\pi$
$733$	25.9764	+	25.9764i	0.959461	+	0.959461i	−0.0397491	+	0.999210i	$0.512656\pi$
$734$	27.2769			1.00681
$735$	−3.38604	+	2.88561i	−0.124896	+	0.106437i
$736$		−	7.92217i		−	0.292015i
$737$	5.40178	−	45.3151i	0.198977	−	1.66920i
$738$	0.998269	−	0.998269i	0.0367468	−	0.0367468i
$739$	51.1611			1.88199			0.940996	−	0.338418i	$-0.109892\pi$
$739$	51.1611			1.88199			0.940996	+	0.338418i	$0.109892\pi$
$740$	−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	$-0.389104\pi$
$743$	−16.3150	−	16.3150i	−0.598538	−	0.598538i	−0.939923	+	0.341385i	$0.889104\pi$
$744$	−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
$748$	−0.801487	+	6.72362i	−0.0293053	+	0.245840i
$749$			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	$-0.798534\pi$
$761$		−	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	$-0.439157\pi$
$769$	10.5368			0.379965			0.189983	+	0.981787i	$0.439157\pi$
$770$	4.10838	+	6.17424i	0.148056	+	0.222504i
$771$	−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	−0.996406	−	0.0847112i	$-0.973003\pi$
$787$	−25.5762	+	25.5762i	−0.911694	+	0.911694i	0.0847112	+	0.996406i	$0.473003\pi$
$788$	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
$792$	3.15631	+	0.376246i	0.112154	+	0.0133693i
$793$	−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
$803$	1.16106	−	9.74007i	0.0409730	−	0.343720i
$804$			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	$-0.241184\pi$
$809$	41.3229			1.45284			0.726418	+	0.687253i	$0.241184\pi$
$810$	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	0.106147	−	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
$825$	−31.7276	−	9.05107i	−1.10461	−	0.315118i
$826$	8.95966			0.311746
$827$	−2.56371	+	2.56371i	−0.0891489	+	0.0891489i	−0.750275	−	0.661126i	$-0.770079\pi$
$827$	−2.56371	+	2.56371i	−0.0891489	+	0.0891489i	0.661126	+	0.750275i	$0.270079\pi$
$828$	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
$847$	−5.73181	−	9.38863i	−0.196947	−	0.322597i
$848$	−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	$-0.242914\pi$
$853$	0.919367	+	0.919367i	0.0314785	+	0.0314785i	−0.691192	+	0.722671i	$0.742914\pi$
$854$	−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	$-0.894167\pi$
$857$	−18.1164	+	18.1164i	−0.618843	+	0.618843i	0.326392	+	0.945235i	$0.394167\pi$
$858$	24.1510	+	2.87891i	0.824500	+	0.0982843i
$859$		−	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	$0.643523\pi$
$877$	−39.5594	+	39.5594i	−1.33583	+	1.33583i	−0.900060	+	0.435767i	$0.856477\pi$
$878$	23.8925	−	23.8925i	0.806333	−	0.806333i
$879$	36.9718			1.24703
$880$	−6.17424	+	4.10838i	−0.208134	+	0.138493i
$881$	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	−0.857613	−	0.514296i	$-0.828053\pi$
$887$	−10.2248	+	10.2248i	−0.343316	+	0.343316i	0.514296	+	0.857613i	$0.328053\pi$
$888$	−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
$902$	0.578285	−	4.85119i	0.0192548	−	0.161527i
$903$	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
$913$	5.24282	−	43.9816i	0.173512	−	1.45558i
$914$		−	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	$-0.689102\pi$
$919$	−33.9375			−1.11949			−0.559747	+	0.828664i	$0.689102\pi$
$920$	−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
$935$	2.98234	−	14.8443i	0.0975331	−	0.485460i
$936$	−3.53255			−0.115465
$937$	−8.31304	+	8.31304i	−0.271575	+	0.271575i	−0.829734	−	0.558159i	$-0.811508\pi$
$937$	−8.31304	+	8.31304i	−0.271575	+	0.271575i	0.558159	+	0.829734i	$0.311508\pi$
$938$	−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	0.431702	−	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	$-0.853936\pi$
$953$	−41.3510	−	41.3510i	−1.33949	−	1.33949i	−0.442940	−	0.896551i	$-0.646064\pi$
$954$	−5.05217			−0.163570
$955$	3.10048	−	38.8566i	0.100329	−	1.25737i
$956$			18.4693i			0.597341i
$957$	−45.9381	−	5.47604i	−1.48497	−	0.177015i
$958$	−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	$-0.870322\pi$
$967$	−16.2304	+	16.2304i	−0.521935	+	0.521935i	0.396220	+	0.918155i	$0.370322\pi$
$968$	9.38863	−	5.73181i	0.301762	−	0.184227i
$969$		−	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
$990$	−6.96843	−	1.40002i	−0.221471	−	0.0444955i
$991$	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	$-0.910041\pi$
$997$	−21.5174	+	21.5174i	−0.681464	+	0.681464i	0.278866	+	0.960330i	$0.410041\pi$
$998$	−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.197.6	yes	16
5.3	odd	4	inner	770.2.m.e.43.2	✓	16
11.10	odd	2	inner	770.2.m.e.197.2	yes	16
55.43	even	4	inner	770.2.m.e.43.6	yes	16

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

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} +(-3.29331 - 0.392578i) 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} +(6.55228 + 0.781062i) 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} +(6.17424 - 4.10838i) 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} +(3.29331 + 0.392578i) 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} +(-0.392578 + 3.29331i) 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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