LMFDB - Embedded newform 663.2.z.d.205.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [663,2,Mod(205,663)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(663, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("663.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 663 = 3 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	663.z (of order $6$, 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:	$5.29408165401$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 20x^{14} + 156x^{12} + 602x^{10} + 1212x^{8} + 1259x^{6} + 665x^{4} + 168x^{2} + 16 $ x^16 + 20x^14 + 156x^12 + 602x^10 + 1212x^8 + 1259x^6 + 665x^4 + 168*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.7
Root			$-1.64424i$ of defining polynomial
Character	$\chi$	$=$	663.205
Dual form			663.2.z.d.511.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42396 - 0.822122i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.351768 - 0.609281i) q^{4} +3.13210i q^{5} +(-1.42396 - 0.822122i) q^{6} +(-1.27469 - 0.735944i) q^{7} +2.13170i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.42396 - 0.822122i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.351768 - 0.609281i) q^{4} +3.13210i q^{5} +(-1.42396 - 0.822122i) q^{6} +(-1.27469 - 0.735944i) q^{7} +2.13170i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.57496 + 4.45997i) q^{10} +(3.71372 - 2.14412i) q^{11} -0.703537 q^{12} +(-1.94432 + 3.03638i) q^{13} -2.42014 q^{14} +(2.71247 - 1.56605i) q^{15} +(2.45605 + 4.25401i) q^{16} +(-0.500000 + 0.866025i) q^{17} +1.64424i q^{18} +(4.53099 + 2.61597i) q^{19} +(1.90833 + 1.10177i) q^{20} +1.47189i q^{21} +(3.52545 - 6.10626i) q^{22} +(2.02068 + 3.49991i) q^{23} +(1.84611 - 1.06585i) q^{24} -4.81002 q^{25} +(-0.272345 + 5.92215i) q^{26} +1.00000 q^{27} +(-0.896793 + 0.517764i) q^{28} +(3.53104 + 6.11595i) q^{29} +(2.57496 - 4.45997i) q^{30} -4.65321i q^{31} +(3.30242 + 1.90665i) q^{32} +(-3.71372 - 2.14412i) q^{33} +1.64424i q^{34} +(2.30505 - 3.99246i) q^{35} +(0.351768 + 0.609281i) q^{36} +(-6.11432 + 3.53010i) q^{37} +8.60258 q^{38} +(3.60174 + 0.165635i) q^{39} -6.67669 q^{40} +(4.81100 - 2.77763i) q^{41} +(1.21007 + 2.09590i) q^{42} +(-1.04645 + 1.81250i) q^{43} -3.01693i q^{44} +(-2.71247 - 1.56605i) q^{45} +(5.75471 + 3.32248i) q^{46} -10.5255i q^{47} +(2.45605 - 4.25401i) q^{48} +(-2.41677 - 4.18597i) q^{49} +(-6.84927 + 3.95443i) q^{50} +1.00000 q^{51} +(1.16606 + 2.25274i) q^{52} -12.4258 q^{53} +(1.42396 - 0.822122i) q^{54} +(6.71558 + 11.6317i) q^{55} +(1.56881 - 2.71726i) q^{56} -5.23194i q^{57} +(10.0561 + 5.80589i) q^{58} +(-2.69669 - 1.55694i) q^{59} -2.20354i q^{60} +(6.81083 - 11.7967i) q^{61} +(-3.82551 - 6.62597i) q^{62} +(1.27469 - 0.735944i) q^{63} -3.55422 q^{64} +(-9.51025 - 6.08979i) q^{65} -7.05090 q^{66} +(-6.64743 + 3.83789i) q^{67} +(0.351768 + 0.609281i) q^{68} +(2.02068 - 3.49991i) q^{69} -7.58012i q^{70} +(-6.50302 - 3.75452i) q^{71} +(-1.84611 - 1.06585i) q^{72} +2.27692i q^{73} +(-5.80435 + 10.0534i) q^{74} +(2.40501 + 4.16560i) q^{75} +(3.18772 - 1.84043i) q^{76} -6.31180 q^{77} +(5.26490 - 2.72522i) q^{78} +9.34938 q^{79} +(-13.3240 + 7.69260i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.56710 - 7.91045i) q^{82} -1.39891i q^{83} +(0.896793 + 0.517764i) q^{84} +(-2.71247 - 1.56605i) q^{85} +3.44123i q^{86} +(3.53104 - 6.11595i) q^{87} +(4.57062 + 7.91654i) q^{88} +(11.7375 - 6.77663i) q^{89} -5.14993 q^{90} +(4.71301 - 2.43955i) q^{91} +2.84324 q^{92} +(-4.02980 + 2.32661i) q^{93} +(-8.65321 - 14.9878i) q^{94} +(-8.19346 + 14.1915i) q^{95} -3.81330i q^{96} +(14.6705 + 8.47004i) q^{97} +(-6.88276 - 3.97376i) q^{98} +4.28824i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/663\mathbb{Z}\right)^\times$.

$n$	$443$	$547$	$613$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.42396	−	0.822122i	1.00689	−	0.581328i	0.0966100	−	0.995322i	$-0.469200\pi$
$2$	1.42396	−	0.822122i	1.00689	−	0.581328i	0.910279	+	0.413994i	$0.135867\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.351768	−	0.609281i	0.175884	−	0.304640i
$5$			3.13210i			1.40072i	0.713792	+	0.700358i	$0.246976\pi$
$5$			3.13210i			1.40072i	−0.713792	+	0.700358i	$0.753024\pi$
$6$	−1.42396	−	0.822122i	−0.581328	−	0.335630i
$7$	−1.27469	−	0.735944i	−0.481788	−	0.278161i	0.239373	−	0.970928i	$-0.423058\pi$
$7$	−1.27469	−	0.735944i	−0.481788	−	0.278161i	−0.721162	+	0.692767i	$0.756391\pi$
$8$			2.13170i			0.753670i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.57496	+	4.45997i	0.814275	+	1.41037i
$11$	3.71372	−	2.14412i	1.11973	−	0.646476i	0.178397	−	0.983959i	$-0.442909\pi$
$11$	3.71372	−	2.14412i	1.11973	−	0.646476i	0.941332	+	0.337483i	$0.109575\pi$
$12$	−0.703537			−0.203094
$13$	−1.94432	+	3.03638i	−0.539256	+	0.842142i
$13$	−1.94432	+	3.03638i	−0.539256	+	0.842142i
$14$	−2.42014			−0.646810
$15$	2.71247	−	1.56605i	0.700358	−	0.404352i
$16$	2.45605	+	4.25401i	0.614014	+	1.06350i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$			1.64424i			0.387552i
$19$	4.53099	+	2.61597i	1.03948	+	0.600144i	0.919686	−	0.392654i	$-0.128443\pi$
$19$	4.53099	+	2.61597i	1.03948	+	0.600144i	0.119794	+	0.992799i	$0.461777\pi$
$20$	1.90833	+	1.10177i	0.426715	+	0.246364i
$21$			1.47189i			0.321192i
$22$	3.52545	−	6.10626i	0.751629	−	1.30186i
$23$	2.02068	+	3.49991i	0.421340	+	0.729782i	0.996071	−	0.0885602i	$-0.0282266\pi$
$23$	2.02068	+	3.49991i	0.421340	+	0.729782i	−0.574731	+	0.818343i	$0.694893\pi$
$24$	1.84611	−	1.06585i	0.376835	−	0.217566i
$25$	−4.81002			−0.962005
$26$	−0.272345	+	5.92215i	−0.0534112	+	1.16143i
$27$	1.00000			0.192450
$28$	−0.896793	+	0.517764i	−0.169478	+	0.0978481i
$29$	3.53104	+	6.11595i	0.655698	+	1.13570i	0.981718	+	0.190340i	$0.0609590\pi$
$29$	3.53104	+	6.11595i	0.655698	+	1.13570i	−0.326020	+	0.945363i	$0.605708\pi$
$30$	2.57496	−	4.45997i	0.470122	−	0.814275i
$31$		−	4.65321i		−	0.835742i	−0.908506	−	0.417871i	$-0.862776\pi$
$31$		−	4.65321i		−	0.835742i	0.908506	−	0.417871i	$-0.137224\pi$
$32$	3.30242	+	1.90665i	0.583790	+	0.337051i
$33$	−3.71372	−	2.14412i	−0.646476	−	0.373243i
$34$			1.64424i			0.281985i
$35$	2.30505	−	3.99246i	0.389624	−	0.674849i
$36$	0.351768	+	0.609281i	0.0586281	+	0.101547i
$37$	−6.11432	+	3.53010i	−1.00519	+	0.580346i	−0.909779	−	0.415093i	$-0.863749\pi$
$37$	−6.11432	+	3.53010i	−1.00519	+	0.580346i	−0.0954089	+	0.995438i	$0.530416\pi$
$38$	8.60258			1.39552
$39$	3.60174	+	0.165635i	0.576741	+	0.0265229i
$40$	−6.67669			−1.05568
$41$	4.81100	−	2.77763i	0.751351	−	0.433793i	−0.0748305	−	0.997196i	$-0.523842\pi$
$41$	4.81100	−	2.77763i	0.751351	−	0.433793i	0.826182	+	0.563403i	$0.190508\pi$
$42$	1.21007	+	2.09590i	0.186718	+	0.323405i
$43$	−1.04645	+	1.81250i	−0.159582	+	0.276404i	−0.934718	−	0.355390i	$-0.884348\pi$
$43$	−1.04645	+	1.81250i	−0.159582	+	0.276404i	0.775136	+	0.631794i	$0.217681\pi$
$44$		−	3.01693i		−	0.454819i
$45$	−2.71247	−	1.56605i	−0.404352	−	0.233453i
$46$	5.75471	+	3.32248i	0.848486	+	0.489873i
$47$		−	10.5255i		−	1.53530i	−0.640871	−	0.767648i	$-0.721427\pi$
$47$		−	10.5255i		−	1.53530i	0.640871	−	0.767648i	$-0.278573\pi$
$48$	2.45605	−	4.25401i	0.354501	−	0.614014i
$49$	−2.41677	−	4.18597i	−0.345253	−	0.597996i
$50$	−6.84927	+	3.95443i	−0.968633	+	0.559240i
$51$	1.00000			0.140028
$52$	1.16606	+	2.25274i	0.161704	+	0.312399i
$53$	−12.4258			−1.70682			−0.853408	−	0.521243i	$-0.825468\pi$
$53$	−12.4258			−1.70682			−0.853408	+	0.521243i	$0.825468\pi$
$54$	1.42396	−	0.822122i	0.193776	−	0.111877i
$55$	6.71558	+	11.6317i	0.905529	+	1.56842i
$56$	1.56881	−	2.71726i	0.209641	−	0.363110i
$57$		−	5.23194i		−	0.692987i
$58$	10.0561	+	5.80589i	1.32043	+	0.762351i
$59$	−2.69669	−	1.55694i	−0.351080	−	0.202696i	0.314081	−	0.949396i	$-0.398304\pi$
$59$	−2.69669	−	1.55694i	−0.351080	−	0.202696i	−0.665161	+	0.746700i	$0.731637\pi$
$60$		−	2.20354i		−	0.284476i
$61$	6.81083	−	11.7967i	0.872038	−	1.51041i	0.0121522	−	0.999926i	$-0.496132\pi$
$61$	6.81083	−	11.7967i	0.872038	−	1.51041i	0.859885	−	0.510487i	$-0.170535\pi$
$62$	−3.82551	−	6.62597i	−0.485840	−	0.841499i
$63$	1.27469	−	0.735944i	0.160596	−	0.0927202i
$64$	−3.55422			−0.444278
$65$	−9.51025	−	6.08979i	−1.17960	−	0.755345i
$66$	−7.05090			−0.867906
$67$	−6.64743	+	3.83789i	−0.812112	+	0.468873i	−0.847689	−	0.530494i	$-0.822007\pi$
$67$	−6.64743	+	3.83789i	−0.812112	+	0.468873i	0.0355765	+	0.999367i	$0.488673\pi$
$68$	0.351768	+	0.609281i	0.0426582	+	0.0738861i
$69$	2.02068	−	3.49991i	0.243261	−	0.421340i
$70$		−	7.58012i		−	0.905997i
$71$	−6.50302	−	3.75452i	−0.771767	−	0.445580i	0.0617376	−	0.998092i	$-0.480336\pi$
$71$	−6.50302	−	3.75452i	−0.771767	−	0.445580i	−0.833505	+	0.552513i	$0.813669\pi$
$72$	−1.84611	−	1.06585i	−0.217566	−	0.125612i
$73$			2.27692i			0.266493i	0.991083	+	0.133246i	$0.0425402\pi$
$73$			2.27692i			0.266493i	−0.991083	+	0.133246i	$0.957460\pi$
$74$	−5.80435	+	10.0534i	−0.674742	+	1.16869i
$75$	2.40501	+	4.16560i	0.277707	+	0.481002i
$76$	3.18772	−	1.84043i	0.365656	−	0.211112i
$77$	−6.31180			−0.719297
$78$	5.26490	−	2.72522i	0.596133	−	0.308570i
$79$	9.34938			1.05189			0.525944	−	0.850519i	$-0.323712\pi$
$79$	9.34938			1.05189			0.525944	+	0.850519i	$0.323712\pi$
$80$	−13.3240	+	7.69260i	−1.48967	+	0.860059i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.56710	−	7.91045i	0.504352	−	0.873563i
$83$		−	1.39891i		−	0.153550i	−0.997048	−	0.0767752i	$-0.975538\pi$
$83$		−	1.39891i		−	0.153550i	0.997048	−	0.0767752i	$-0.0244624\pi$
$84$	0.896793	+	0.517764i	0.0978481	+	0.0564926i
$85$	−2.71247	−	1.56605i	−0.294209	−	0.169862i
$86$			3.44123i			0.371078i
$87$	3.53104	−	6.11595i	0.378568	−	0.655698i
$88$	4.57062	+	7.91654i	0.487230	+	0.843906i
$89$	11.7375	−	6.77663i	1.24417	−	0.718321i	0.274229	−	0.961665i	$-0.411577\pi$
$89$	11.7375	−	6.77663i	1.24417	−	0.718321i	0.969940	+	0.243343i	$0.0782441\pi$
$90$	−5.14993			−0.542850
$91$	4.71301	−	2.43955i	0.494058	−	0.255734i
$92$	2.84324			0.296428
$93$	−4.02980	+	2.32661i	−0.417871	+	0.241258i
$94$	−8.65321	−	14.9878i	−0.892511	−	1.54587i
$95$	−8.19346	+	14.1915i	−0.840632	+	1.45602i
$96$		−	3.81330i		−	0.389193i
$97$	14.6705	+	8.47004i	1.48957	+	0.860002i	0.999929	−	0.0119240i	$-0.00379562\pi$
$97$	14.6705	+	8.47004i	1.48957	+	0.860002i	0.489638	+	0.871926i	$0.337129\pi$
$98$	−6.88276	−	3.97376i	−0.695264	−	0.401411i
$99$			4.28824i			0.430984i
$100$	−1.69201	+	2.93065i	−0.169201	+	0.293065i
$101$	−0.844033	−	1.46191i	−0.0839844	−	0.145465i	0.820974	−	0.570966i	$-0.193431\pi$
$101$	−0.844033	−	1.46191i	−0.0839844	−	0.145465i	−0.904958	+	0.425501i	$0.860098\pi$
$102$	1.42396	−	0.822122i	0.140993	−	0.0814022i
$103$	9.94885			0.980290			0.490145	−	0.871641i	$-0.336944\pi$
$103$	9.94885			0.980290			0.490145	+	0.871641i	$0.336944\pi$
$104$	−6.47267	−	4.14470i	−0.634697	−	0.406422i
$105$	−4.61009			−0.449899
$106$	−17.6938	+	10.2155i	−1.71858	+	0.992220i
$107$	−2.06333	−	3.57378i	−0.199469	−	0.345491i	0.748887	−	0.662697i	$-0.230588\pi$
$107$	−2.06333	−	3.57378i	−0.199469	−	0.345491i	−0.948356	+	0.317207i	$0.897255\pi$
$108$	0.351768	−	0.609281i	0.0338489	−	0.0586281i
$109$			17.5512i			1.68110i	0.541737	+	0.840548i	$0.317767\pi$
$109$			17.5512i			1.68110i	−0.541737	+	0.840548i	$0.682233\pi$
$110$	19.1254	+	11.0421i	1.82353	+	1.05282i
$111$	6.11432	+	3.53010i	0.580346	+	0.335063i
$112$		−	7.23008i		−	0.683178i
$113$	7.94808	−	13.7665i	0.747693	−	1.29504i	−0.201233	−	0.979543i	$-0.564495\pi$
$113$	7.94808	−	13.7665i	0.747693	−	1.29504i	0.948926	−	0.315499i	$-0.102172\pi$
$114$	−4.30129	−	7.45005i	−0.402853	−	0.697761i
$115$	−10.9621	+	6.32895i	−1.02222	+	0.590178i
$116$	4.96844			0.461308
$117$	−1.65743	−	3.20202i	−0.153229	−	0.296027i
$118$	−5.11997			−0.471331
$119$	1.27469	−	0.735944i	0.116851	−	0.0674639i
$120$	3.33835	+	5.78219i	0.304748	+	0.527839i
$121$	3.69448	−	6.39903i	0.335862	−	0.581730i
$122$		−	22.3973i		−	2.02776i
$123$	−4.81100	−	2.77763i	−0.433793	−	0.250450i
$124$	−2.83511	−	1.63685i	−0.254601	−	0.146994i
$125$			0.595021i			0.0532203i
$126$	1.21007	−	2.09590i	0.107802	−	0.186718i
$127$	3.12513	+	5.41289i	0.277311	+	0.480316i	0.970716	−	0.240232i	$-0.0772235\pi$
$127$	3.12513	+	5.41289i	0.277311	+	0.480316i	−0.693405	+	0.720548i	$0.743890\pi$
$128$	−11.6659	+	6.73531i	−1.03113	+	0.595323i
$129$	2.09290			0.184269
$130$	−18.5487	−	0.853010i	−1.62683	−	0.0748139i
$131$	1.71562			0.149894			0.0749471	−	0.997188i	$-0.476121\pi$
$131$	1.71562			0.149894			0.0749471	+	0.997188i	$0.476121\pi$
$132$	−2.61274	+	1.50847i	−0.227410	+	0.131295i
$133$	−3.85041	−	6.66911i	−0.333873	−	0.578285i
$134$	−6.31043	+	10.9300i	−0.545138	+	0.944207i
$135$			3.13210i			0.269568i
$136$	−1.84611	−	1.06585i	−0.158302	−	0.0913959i
$137$	−10.9791	−	6.33880i	−0.938011	−	0.541561i	−0.0486744	−	0.998815i	$-0.515500\pi$
$137$	−10.9791	−	6.33880i	−0.938011	−	0.541561i	−0.889336	+	0.457254i	$0.848833\pi$
$138$		−	6.64497i		−	0.565657i
$139$	5.85317	−	10.1380i	0.496460	−	0.859894i	−0.503532	−	0.863977i	$-0.667966\pi$
$139$	5.85317	−	10.1380i	0.496460	−	0.859894i	0.999992	+	0.00408307i	$0.00129969\pi$
$140$	−1.62169	−	2.80884i	−0.137057	−	0.237390i
$141$	−9.11532	+	5.26273i	−0.767648	+	0.443202i
$142$	−12.3467			−1.03611
$143$	−0.710283	+	15.4451i	−0.0593968	+	1.29159i
$144$	−4.91211			−0.409342
$145$	−19.1557	+	11.0596i	−1.59080	+	0.918447i
$146$	1.87190	+	3.24223i	0.154920	+	0.268329i
$147$	−2.41677	+	4.18597i	−0.199332	+	0.345253i
$148$			4.96712i			0.408294i
$149$	−11.9755	−	6.91408i	−0.981074	−	0.566424i	−0.0784801	−	0.996916i	$-0.525007\pi$
$149$	−11.9755	−	6.91408i	−0.981074	−	0.566424i	−0.902594	+	0.430492i	$0.858340\pi$
$150$	6.84927	+	3.95443i	0.559240	+	0.322878i
$151$			17.4394i			1.41920i	0.704604	+	0.709601i	$0.251125\pi$
$151$			17.4394i			1.41920i	−0.704604	+	0.709601i	$0.748875\pi$
$152$	−5.57646	+	9.65872i	−0.452311	+	0.783425i
$153$	−0.500000	−	0.866025i	−0.0404226	−	0.0700140i
$154$	−8.98773	+	5.18907i	−0.724252	+	0.418147i
$155$	14.5743			1.17064
$156$	1.36790	−	2.13621i	0.109519	−	0.171034i
$157$	1.90821			0.152292			0.0761458	−	0.997097i	$-0.475739\pi$
$157$	1.90821			0.152292			0.0761458	+	0.997097i	$0.475739\pi$
$158$	13.3131	−	7.68633i	1.05913	−	0.611491i
$159$	6.21290	+	10.7611i	0.492715	+	0.853408i
$160$	−5.97181	+	10.3435i	−0.472113	+	0.817724i
$161$		−	5.94842i		−	0.468801i
$162$	−1.42396	−	0.822122i	−0.111877	−	0.0645920i
$163$	12.8605	+	7.42503i	1.00731	+	0.581573i	0.910404	−	0.413720i	$-0.135771\pi$
$163$	12.8605	+	7.42503i	1.00731	+	0.581573i	0.0969101	+	0.995293i	$0.469104\pi$
$164$		−	3.90833i		−	0.305189i
$165$	6.71558	−	11.6317i	0.522807	−	0.905529i
$166$	−1.15008	−	1.99199i	−0.0892632	−	0.154608i
$167$	6.67081	−	3.85139i	0.516203	−	0.298030i	−0.219177	−	0.975685i	$-0.570337\pi$
$167$	6.67081	−	3.85139i	0.516203	−	0.298030i	0.735380	+	0.677655i	$0.237004\pi$
$168$	−3.13763			−0.242073
$169$	−5.43927	−	11.8074i	−0.418405	−	0.908261i
$170$	−5.14993			−0.394981
$171$	−4.53099	+	2.61597i	−0.346493	+	0.200048i
$172$	0.736215	+	1.27516i	0.0561358	+	0.0972301i
$173$	0.294073	−	0.509349i	0.0223579	−	0.0387251i	−0.854630	−	0.519238i	$-0.826216\pi$
$173$	0.294073	−	0.509349i	0.0223579	−	0.0387251i	0.876988	+	0.480512i	$0.159549\pi$
$174$		−	11.6118i		−	0.880287i
$175$	6.13130	+	3.53991i	0.463483	+	0.267592i
$176$	18.2422	+	10.5321i	1.37506	+	0.793890i
$177$			3.11387i			0.234053i
$178$	11.1424	−	19.2993i	0.835160	−	1.44654i
$179$	−2.21043	−	3.82858i	−0.165216	−	0.286162i	0.771516	−	0.636210i	$-0.219499\pi$
$179$	−2.21043	−	3.82858i	−0.165216	−	0.286162i	−0.936732	+	0.350048i	$0.886165\pi$
$180$	−1.90833	+	1.10177i	−0.142238	+	0.0821212i
$181$	6.42858			0.477832			0.238916	−	0.971040i	$-0.423208\pi$
$181$	6.42858			0.477832			0.238916	+	0.971040i	$0.423208\pi$
$182$	4.70552	−	7.34848i	0.348797	−	0.544706i
$183$	−13.6217			−1.00694
$184$	−7.46077	+	4.30748i	−0.550015	+	0.317551i
$185$	−11.0566	−	19.1506i	−0.812899	−	1.40798i
$186$	−3.82551	+	6.62597i	−0.280500	+	0.485840i
$187$			4.28824i			0.313587i
$188$	−6.41296	−	3.70253i	−0.467713	−	0.270034i
$189$	−1.27469	−	0.735944i	−0.0927202	−	0.0535321i
$190$			26.9441i			1.95473i
$191$	7.35400	−	12.7375i	0.532117	−	0.921654i	−0.467180	−	0.884162i	$-0.654730\pi$
$191$	7.35400	−	12.7375i	0.532117	−	0.921654i	0.999297	−	0.0374916i	$-0.0119367\pi$
$192$	1.77711	+	3.07805i	0.128252	+	0.222139i
$193$	14.1290	−	8.15740i	1.01703	−	0.587182i	0.103787	−	0.994600i	$-0.466904\pi$
$193$	14.1290	−	8.15740i	1.01703	−	0.587182i	0.913242	+	0.407417i	$0.133571\pi$
$194$	27.8536			1.99977
$195$	−0.518785	+	11.2810i	−0.0371510	+	0.807850i
$196$	−3.40058			−0.242898
$197$	14.4785	−	8.35917i	1.03155	−	0.595566i	0.114122	−	0.993467i	$-0.463594\pi$
$197$	14.4785	−	8.35917i	1.03155	−	0.595566i	0.917429	+	0.397901i	$0.130261\pi$
$198$	3.52545	+	6.10626i	0.250543	+	0.433953i
$199$	2.45755	−	4.25660i	0.174211	−	0.301742i	−0.765677	−	0.643225i	$-0.777596\pi$
$199$	2.45755	−	4.25660i	0.174211	−	0.301742i	0.939888	+	0.341483i	$0.110929\pi$
$200$		−	10.2535i		−	0.725035i
$201$	6.64743	+	3.83789i	0.468873	+	0.270704i
$202$	−2.40373	−	1.38780i	−0.169126	−	0.0976449i
$203$		−	10.3946i		−	0.729558i
$204$	0.351768	−	0.609281i	0.0246287	−	0.0426582i
$205$	8.69980	+	15.0685i	0.607621	+	1.05243i
$206$	14.1667	−	8.17917i	0.987043	−	0.569870i
$207$	−4.04135			−0.280893
$208$	−17.6922	−	0.813618i	−1.22673	−	0.0564143i
$209$	22.4358			1.55191
$210$	−6.56457	+	3.79006i	−0.452999	+	0.261539i
$211$	−8.48546	−	14.6972i	−0.584163	−	1.01180i	−0.994979	−	0.100082i	$-0.968090\pi$
$211$	−8.48546	−	14.6972i	−0.584163	−	1.01180i	0.410816	−	0.911718i	$-0.365244\pi$
$212$	−4.37101	+	7.57080i	−0.300202	+	0.519965i
$213$			7.50904i			0.514511i
$214$	−5.87617	−	3.39261i	−0.401687	−	0.231914i
$215$	−5.67693	−	3.27758i	−0.387163	−	0.223529i
$216$			2.13170i			0.145044i
$217$	−3.42450	+	5.93141i	−0.232470	+	0.402651i
$218$	14.4292	+	24.9921i	0.977268	+	1.69268i
$219$	1.97187	−	1.13846i	0.133246	−	0.0769299i
$220$	9.44932			0.637073
$221$	−1.65743	−	3.20202i	−0.111491	−	0.215391i
$222$	11.6087			0.779125
$223$	13.5471	−	7.82145i	0.907184	−	0.523763i	0.0276599	−	0.999617i	$-0.491194\pi$
$223$	13.5471	−	7.82145i	0.907184	−	0.523763i	0.879524	+	0.475855i	$0.157861\pi$
$224$	−2.80638	−	4.86079i	−0.187509	−	0.324775i
$225$	2.40501	−	4.16560i	0.160334	−	0.277707i
$226$		−	26.1372i		−	1.73862i
$227$	−18.4280	−	10.6394i	−1.22311	−	0.706161i	−0.257528	−	0.966271i	$-0.582908\pi$
$227$	−18.4280	−	10.6394i	−1.22311	−	0.706161i	−0.965579	+	0.260109i	$0.916241\pi$
$228$	−3.18772	−	1.84043i	−0.211112	−	0.121885i
$229$		−	5.46185i		−	0.360929i	−0.983581	−	0.180465i	$-0.942240\pi$
$229$		−	5.46185i		−	0.360929i	0.983581	−	0.180465i	$-0.0577602\pi$
$230$	−10.4063	+	18.0243i	−0.686174	+	1.18849i
$231$	3.15590	+	5.46618i	0.207643	+	0.359648i
$232$	−13.0374	+	7.52713i	−0.855945	+	0.494180i
$233$	0.688077			0.0450774			0.0225387	−	0.999746i	$-0.492825\pi$
$233$	0.688077			0.0450774			0.0225387	+	0.999746i	$0.492825\pi$
$234$	−4.99256	−	3.19693i	−0.326374	−	0.208990i
$235$	32.9668			2.15051
$236$	−1.89722	+	1.09536i	−0.123499	+	0.0713020i
$237$	−4.67469	−	8.09680i	−0.303654	−	0.525944i
$238$	1.21007	−	2.09590i	0.0784373	−	0.135857i
$239$			17.2803i			1.11777i	0.829246	+	0.558884i	$0.188770\pi$
$239$			17.2803i			1.11777i	−0.829246	+	0.558884i	$0.811230\pi$
$240$	13.3240	+	7.69260i	0.860059	+	0.496555i
$241$	−20.4712	−	11.8191i	−1.31867	−	0.761334i	−0.335155	−	0.942163i	$-0.608789\pi$
$241$	−20.4712	−	11.8191i	−1.31867	−	0.761334i	−0.983515	+	0.180829i	$0.942122\pi$
$242$		−	12.1493i		−	0.780984i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−4.79167	−	8.29941i	−0.306755	−	0.531316i
$245$	13.1109	−	7.56956i	0.837623	−	0.483602i
$246$	−9.13420			−0.582375
$247$	−16.7528	+	8.67156i	−1.06595	+	0.551758i
$248$	9.91926			0.629874
$249$	−1.21149	+	0.699456i	−0.0767752	+	0.0443262i
$250$	0.489180	+	0.847284i	0.0309384	+	0.0535869i
$251$	−10.4509	+	18.1016i	−0.659658	+	1.14256i	0.321047	+	0.947063i	$0.395965\pi$
$251$	−10.4509	+	18.1016i	−0.659658	+	1.14256i	−0.980704	+	0.195497i	$0.937368\pi$
$252$		−	1.03553i		−	0.0652321i
$253$	15.0085	+	8.66513i	0.943573	+	0.544772i
$254$	8.90011	+	5.13848i	0.558443	+	0.322417i
$255$			3.13210i			0.196139i
$256$	−7.52026	+	13.0255i	−0.470016	+	0.814092i
$257$	5.95587	+	10.3159i	0.371517	+	0.643486i	0.989799	−	0.142470i	$-0.0455044\pi$
$257$	5.95587	+	10.3159i	0.371517	+	0.643486i	−0.618282	+	0.785956i	$0.712171\pi$
$258$	2.98019	−	1.72062i	0.185539	−	0.107121i
$259$	10.3918			0.645717
$260$	−7.05579	+	3.65222i	−0.437582	+	0.226501i
$261$	−7.06209			−0.437132
$262$	2.44296	−	1.41045i	0.150927	−	0.0871376i
$263$	−8.60910	−	14.9114i	−0.530860	−	0.919476i	−0.999351	−	0.0360083i	$-0.988536\pi$
$263$	−8.60910	−	14.9114i	−0.530860	−	0.919476i	0.468492	−	0.883468i	$-0.344798\pi$
$264$	4.57062	−	7.91654i	0.281302	−	0.487230i
$265$		−	38.9188i		−	2.39076i
$266$	−10.9656	−	6.33102i	−0.672347	−	0.388179i
$267$	−11.7375	−	6.77663i	−0.718321	−	0.414723i
$268$			5.40020i			0.329870i
$269$	10.9425	−	18.9529i	0.667174	−	1.15558i	−0.311517	−	0.950241i	$-0.600837\pi$
$269$	10.9425	−	18.9529i	0.667174	−	1.15558i	0.978691	−	0.205339i	$-0.0658295\pi$
$270$	2.57496	+	4.45997i	0.156707	+	0.271425i
$271$	−4.58494	+	2.64712i	−0.278515	+	0.160801i	−0.632751	−	0.774355i	$-0.718074\pi$
$271$	−4.58494	+	2.64712i	−0.278515	+	0.160801i	0.354236	+	0.935156i	$0.384741\pi$
$272$	−4.91211			−0.297840
$273$	−4.46922	−	2.86182i	−0.270489	−	0.173205i
$274$	−20.8451			−1.25930
$275$	−17.8631	+	10.3133i	−1.07718	+	0.621913i
$276$	−1.42162	−	2.46232i	−0.0855714	−	0.148214i
$277$	−8.27656	+	14.3354i	−0.497290	+	0.861332i	−0.999995	−	0.00312636i	$-0.999005\pi$
$277$	−8.27656	+	14.3354i	−0.497290	+	0.861332i	0.502705	+	0.864458i	$0.332338\pi$
$278$		−	19.2481i		−	1.15442i
$279$	4.02980	+	2.32661i	0.241258	+	0.139290i
$280$	8.51073	+	4.91367i	0.508613	+	0.293648i
$281$		−	14.9450i		−	0.891543i	−0.895147	−	0.445772i	$-0.852929\pi$
$281$		−	14.9450i		−	0.891543i	0.895147	−	0.445772i	$-0.147071\pi$
$282$	−8.65321	+	14.9878i	−0.515291	+	0.892511i
$283$	8.86328	+	15.3517i	0.526867	+	0.912561i	0.999510	+	0.0313069i	$0.00996691\pi$
$283$	8.86328	+	15.3517i	0.526867	+	0.912561i	−0.472642	+	0.881254i	$0.656700\pi$
$284$	−4.57512	+	2.64144i	−0.271483	+	0.156741i
$285$	16.3869			0.970678
$286$	11.6864	+	22.5771i	0.691029	+	1.33501i
$287$	−8.17672			−0.482657
$288$	−3.30242	+	1.90665i	−0.194597	+	0.112350i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−18.1846	+	31.4967i	−1.06784	+	1.84955i
$291$		−	16.9401i		−	0.993045i
$292$	1.38728	+	0.800947i	0.0811845	+	0.0468719i
$293$	17.4222	+	10.0587i	1.01782	+	0.587637i	0.913471	−	0.406904i	$-0.133392\pi$
$293$	17.4222	+	10.0587i	1.01782	+	0.587637i	0.104346	+	0.994541i	$0.466725\pi$
$294$			7.94753i			0.463509i
$295$	4.87648	−	8.44630i	0.283919	−	0.491763i
$296$	−7.52513	−	13.0339i	−0.437389	−	0.757580i
$297$	3.71372	−	2.14412i	0.215492	−	0.124414i
$298$	−22.7369			−1.31711
$299$	−14.5559	−	0.669390i	−0.841790	−	0.0387118i
$300$	3.38403			0.195377
$301$	2.66780	−	1.54025i	0.153769	−	0.0887788i
$302$	14.3373	+	24.8330i	0.825021	+	1.42898i
$303$	−0.844033	+	1.46191i	−0.0484884	+	0.0839844i
$304$			25.6998i			1.47399i
$305$	36.9484	+	21.3322i	2.11566	+	1.22148i
$306$	−1.42396	−	0.822122i	−0.0814022	−	0.0469976i
$307$			8.51760i			0.486125i	0.970011	+	0.243062i	$0.0781520\pi$
$307$			8.51760i			0.486125i	−0.970011	+	0.243062i	$0.921848\pi$
$308$	−2.22029	+	3.84566i	−0.126513	+	0.219127i
$309$	−4.97443	−	8.61596i	−0.282985	−	0.490145i
$310$	20.7532	−	11.9819i	1.17870	−	0.680524i
$311$	−23.0446			−1.30674			−0.653370	−	0.757038i	$-0.726646\pi$
$311$	−23.0446			−1.30674			−0.653370	+	0.757038i	$0.726646\pi$
$312$	−0.353085	+	7.67784i	−0.0199895	+	0.434672i
$313$	−16.2105			−0.916274			−0.458137	−	0.888882i	$-0.651483\pi$
$313$	−16.2105			−0.916274			−0.458137	+	0.888882i	$0.651483\pi$
$314$	2.71720	−	1.56878i	0.153341	−	0.0885313i
$315$	2.30505	+	3.99246i	0.129875	+	0.224950i
$316$	3.28881	−	5.69639i	0.185010	−	0.320447i
$317$			26.9457i			1.51342i	0.653750	+	0.756711i	$0.273195\pi$
$317$			26.9457i			1.51342i	−0.653750	+	0.756711i	$0.726805\pi$
$318$	17.6938	+	10.2155i	0.992220	+	0.572858i
$319$	26.2266	+	15.1419i	1.46841	+	0.847786i
$320$		−	11.1322i		−	0.622307i
$321$	−2.06333	+	3.57378i	−0.115164	+	0.199469i
$322$	−4.89032	−	8.47029i	−0.272527	−	0.472031i
$323$	−4.53099	+	2.61597i	−0.252111	+	0.145556i
$324$	−0.703537			−0.0390854
$325$	9.35221	−	14.6051i	0.518767	−	0.810144i
$326$	24.4171			1.35234
$327$	15.1998	−	8.77558i	0.840548	−	0.485291i
$328$	5.92108	+	10.2556i	0.326937	+	0.566271i
$329$	−7.74615	+	13.4167i	−0.427059	+	0.739688i
$330$		−	22.0841i		−	1.21569i
$331$	−13.5330	−	7.81328i	−0.743841	−	0.429457i	0.0796231	−	0.996825i	$-0.474628\pi$
$331$	−13.5330	−	7.81328i	−0.743841	−	0.429457i	−0.823464	+	0.567368i	$0.807962\pi$
$332$	−0.852330	−	0.492093i	−0.0467777	−	0.0270071i
$333$		−	7.06021i		−	0.386897i
$334$	6.33263	−	10.9684i	0.346506	−	0.600166i
$335$	−12.0207	−	20.8204i	−0.656758	−	1.13754i
$336$	−6.26143	+	3.61504i	−0.341589	+	0.197216i
$337$	−11.3886			−0.620375			−0.310188	−	0.950675i	$-0.600392\pi$
$337$	−11.3886			−0.620375			−0.310188	+	0.950675i	$0.600392\pi$
$338$	−17.4524	−	12.3415i	−0.949285	−	0.671287i
$339$	−15.8962			−0.863361
$340$	−1.90833	+	1.10177i	−0.103493	+	0.0597520i
$341$	−9.97703	−	17.2807i	−0.540287	−	0.935804i
$342$	−4.30129	+	7.45005i	−0.232587	+	0.402853i
$343$			17.4177i			0.940465i
$344$	−3.86371	−	2.23072i	−0.208317	−	0.120272i
$345$	10.9621	+	6.32895i	0.590178	+	0.340739i
$346$		−	0.967054i		−	0.0519892i
$347$	11.9073	−	20.6240i	0.639217	−	1.10716i	−0.346388	−	0.938092i	$-0.612592\pi$
$347$	11.9073	−	20.6240i	0.639217	−	1.10716i	0.985605	−	0.169065i	$-0.0540749\pi$
$348$	−2.48422	−	4.30279i	−0.133168	−	0.230654i
$349$	15.7736	−	9.10689i	0.844341	−	0.487481i	−0.0143962	−	0.999896i	$-0.504583\pi$
$349$	15.7736	−	9.10689i	0.844341	−	0.487481i	0.858738	+	0.512416i	$0.171249\pi$
$350$	11.6409			0.622235
$351$	−1.94432	+	3.03638i	−0.103780	+	0.162070i
$352$	16.3523			0.871582
$353$	−3.81680	+	2.20363i	−0.203148	+	0.117287i	−0.598123	−	0.801404i	$-0.704087\pi$
$353$	−3.81680	+	2.20363i	−0.203148	+	0.117287i	0.394975	+	0.918692i	$0.370753\pi$
$354$	2.55998	+	4.43402i	0.136062	+	0.235666i
$355$	11.7595	−	20.3681i	0.624131	−	1.08103i
$356$		−	9.53521i		−	0.505365i
$357$	−1.27469	−	0.735944i	−0.0674639	−	0.0389503i
$358$	−6.29512	−	3.63449i	−0.332708	−	0.192089i
$359$		−	16.0894i		−	0.849167i	−0.905389	−	0.424584i	$-0.860421\pi$
$359$		−	16.0894i		−	0.849167i	0.905389	−	0.424584i	$-0.139579\pi$
$360$	3.33835	−	5.78219i	0.175946	−	0.304748i
$361$	4.18658	+	7.25137i	0.220346	+	0.381651i
$362$	9.15401	−	5.28507i	0.481124	−	0.277777i
$363$	−7.38896			−0.387820
$364$	0.171520	−	3.72970i	0.00899008	−	0.195490i
$365$	−7.13152			−0.373281
$366$	−19.3967	+	11.1987i	−1.01388	+	0.585364i
$367$	−15.1052	−	26.1630i	−0.788486	−	1.36570i	−0.926894	−	0.375323i	$-0.877532\pi$
$367$	−15.1052	−	26.1630i	−0.788486	−	1.36570i	0.138408	−	0.990375i	$-0.455802\pi$
$368$	−9.92578	+	17.1920i	−0.517417	+	0.896193i
$369$			5.55526i			0.289195i
$370$	−31.4883	−	18.1798i	−1.63700	−	0.945122i
$371$	15.8391	+	9.14470i	0.822324	+	0.474769i
$372$			3.27371i			0.169734i
$373$	−14.7097	+	25.4779i	−0.761638	+	1.31920i	0.180368	+	0.983599i	$0.442271\pi$
$373$	−14.7097	+	25.4779i	−0.761638	+	1.31920i	−0.942006	+	0.335597i	$0.891062\pi$
$374$	3.52545	+	6.10626i	0.182297	+	0.315747i
$375$	0.515303	−	0.297510i	0.0266101	−	0.0153634i
$376$	22.4371			1.15711
$377$	−25.4358	−	1.16973i	−1.31001	−	0.0602442i
$378$	−2.42014			−0.124479
$379$	16.6122	−	9.59108i	0.853313	−	0.492661i	−0.00845420	−	0.999964i	$-0.502691\pi$
$379$	16.6122	−	9.59108i	0.853313	−	0.492661i	0.861767	+	0.507304i	$0.169358\pi$
$380$	5.76440	+	9.98424i	0.295708	+	0.512181i
$381$	3.12513	−	5.41289i	0.160105	−	0.277311i
$382$		−	24.1835i		−	1.23734i
$383$	20.4185	+	11.7886i	1.04334	+	0.602371i	0.920777	−	0.390090i	$-0.127556\pi$
$383$	20.4185	+	11.7886i	1.04334	+	0.602371i	0.122560	+	0.992461i	$0.460889\pi$
$384$	11.6659	+	6.73531i	0.595323	+	0.343710i
$385$		−	19.7692i		−	1.00753i
$386$	13.4127	−	23.2316i	0.682691	−	1.18246i
$387$	−1.04645	−	1.81250i	−0.0531940	−	0.0921346i
$388$	10.3213	−	5.95898i	0.523982	−	0.302521i
$389$	−10.3806			−0.526316			−0.263158	−	0.964753i	$-0.584764\pi$
$389$	−10.3806			−0.526316			−0.263158	+	0.964753i	$0.584764\pi$
$390$	8.53564	+	16.4902i	0.432219	+	0.835012i
$391$	−4.04135			−0.204380
$392$	8.92325	−	5.15184i	0.450692	−	0.260207i
$393$	−0.857808	−	1.48577i	−0.0432707	−	0.0749471i
$394$	13.7445	−	23.8062i	0.692438	−	1.19934i
$395$			29.2831i			1.47339i
$396$	2.61274	+	1.50847i	0.131295	+	0.0758032i
$397$	−1.65352	−	0.954661i	−0.0829879	−	0.0479131i	0.457932	−	0.888987i	$-0.348590\pi$
$397$	−1.65352	−	0.954661i	−0.0829879	−	0.0479131i	−0.540920	+	0.841074i	$0.681924\pi$
$398$		−	8.08162i		−	0.405095i
$399$	−3.85041	+	6.66911i	−0.192762	+	0.333873i
$400$	−11.8137	−	20.4619i	−0.590684	−	1.02310i
$401$	11.5379	−	6.66143i	0.576177	−	0.332656i	−0.183435	−	0.983032i	$-0.558722\pi$
$401$	11.5379	−	6.66143i	0.576177	−	0.332656i	0.759613	+	0.650376i	$0.225388\pi$
$402$	12.6209			0.629471
$403$	14.1289	+	9.04732i	0.703813	+	0.450679i
$404$	−1.18762			−0.0590861
$405$	2.71247	−	1.56605i	0.134784	−	0.0778175i
$406$	−8.54563	−	14.8015i	−0.424112	−	0.734584i
$407$	−15.1379	+	26.2196i	−0.750359	+	1.29966i
$408$			2.13170i			0.105535i
$409$	−1.44710	−	0.835485i	−0.0715546	−	0.0413121i	0.463796	−	0.885942i	$-0.346487\pi$
$409$	−1.44710	−	0.835485i	−0.0715546	−	0.0413121i	−0.535350	+	0.844630i	$0.679820\pi$
$410$	24.7763	+	14.3046i	1.22361	+	0.706454i
$411$			12.6776i			0.625340i
$412$	3.49969	−	6.06164i	0.172417	−	0.298636i
$413$	2.29164	+	3.96923i	0.112764	+	0.195313i
$414$	−5.75471	+	3.32248i	−0.282829	+	0.163291i
$415$	4.38152			0.215081
$416$	−12.2103	+	6.32027i	−0.598658	+	0.309877i
$417$	−11.7063			−0.573262
$418$	31.9476	−	18.4449i	1.56261	−	0.902171i
$419$	2.60633	+	4.51429i	0.127327	+	0.220537i	0.922640	−	0.385662i	$-0.126027\pi$
$419$	2.60633	+	4.51429i	0.127327	+	0.220537i	−0.795313	+	0.606199i	$0.792693\pi$
$420$	−1.62169	+	2.80884i	−0.0791301	+	0.137057i
$421$		−	2.08850i		−	0.101787i	−0.998704	−	0.0508937i	$-0.983793\pi$
$421$		−	2.08850i		−	0.101787i	0.998704	−	0.0508937i	$-0.0162070\pi$
$422$	−24.1658	−	13.9522i	−1.17637	−	0.679180i
$423$	9.11532	+	5.26273i	0.443202	+	0.255883i
$424$		−	26.4881i		−	1.28638i
$425$	2.40501	−	4.16560i	0.116660	−	0.202061i
$426$	6.17335	+	10.6926i	0.299100	+	0.518056i
$427$	−17.3634	+	10.0248i	−0.840275	+	0.485133i
$428$	−2.90325			−0.140334
$429$	13.7310	−	7.10744i	0.662940	−	0.343151i
$430$	−10.7783			−0.519774
$431$	11.4729	−	6.62386i	0.552628	−	0.319060i	−0.197553	−	0.980292i	$-0.563299\pi$
$431$	11.4729	−	6.62386i	0.552628	−	0.319060i	0.750181	+	0.661232i	$0.229966\pi$
$432$	2.45605	+	4.25401i	0.118167	+	0.204671i
$433$	−13.2063	+	22.8740i	−0.634656	+	1.09926i	0.351932	+	0.936025i	$0.385525\pi$
$433$	−13.2063	+	22.8740i	−0.634656	+	1.09926i	−0.986588	+	0.163230i	$0.947809\pi$
$434$			11.2614i			0.540566i
$435$	19.1557	+	11.0596i	0.918447	+	0.530266i
$436$	10.6936	+	6.17394i	0.512130	+	0.295678i
$437$			21.1441i			1.01146i
$438$	1.87190	−	3.24223i	0.0894430	−	0.154920i
$439$	1.92104	+	3.32734i	0.0916864	+	0.158805i	0.908221	−	0.418491i	$-0.137441\pi$
$439$	1.92104	+	3.32734i	0.0916864	+	0.158805i	−0.816534	+	0.577297i	$0.804108\pi$
$440$	−24.7954	+	14.3156i	−1.18207	+	0.682470i
$441$	4.83355			0.230169
$442$	−4.99256	−	3.19693i	−0.237472	−	0.152062i
$443$	11.1699			0.530698			0.265349	−	0.964152i	$-0.414513\pi$
$443$	11.1699			0.530698			0.265349	+	0.964152i	$0.414513\pi$
$444$	4.30165	−	2.48356i	0.204147	−	0.117864i
$445$	21.2251	+	36.7629i	1.00616	+	1.74273i
$446$	12.8604	−	22.2748i	0.608956	−	1.05474i
$447$			13.8282i			0.654050i
$448$	4.53054	+	2.61571i	0.214048	+	0.123581i
$449$	30.5264	+	17.6244i	1.44063	+	0.831747i	0.997891	−	0.0649043i	$-0.0206742\pi$
$449$	30.5264	+	17.6244i	1.44063	+	0.831747i	0.442737	+	0.896652i	$0.354008\pi$
$450$		−	7.90885i		−	0.372827i
$451$	11.9111	−	20.6307i	0.560873	−	0.971461i
$452$	−5.59177	−	9.68523i	−0.263015	−	0.455555i
$453$	15.1030	−	8.71972i	0.709601	−	0.409688i
$454$	−34.9875			−1.64205
$455$	7.64090	+	14.7616i	0.358211	+	0.692035i
$456$	11.1529			0.522284
$457$	−3.10965	+	1.79536i	−0.145463	+	0.0839832i	−0.570965	−	0.820974i	$-0.693431\pi$
$457$	−3.10965	+	1.79536i	−0.145463	+	0.0839832i	0.425502	+	0.904957i	$0.360098\pi$
$458$	−4.49031	−	7.77744i	−0.209818	−	0.363416i
$459$	−0.500000	+	0.866025i	−0.0233380	+	0.0404226i
$460$			8.90530i			0.415212i
$461$	4.01656	+	2.31896i	0.187070	+	0.108005i	0.590610	−	0.806957i	$-0.298887\pi$
$461$	4.01656	+	2.31896i	0.187070	+	0.108005i	−0.403540	+	0.914962i	$0.632220\pi$
$462$	8.98773	+	5.18907i	0.418147	+	0.241417i
$463$			36.6907i			1.70516i	0.522597	+	0.852580i	$0.324963\pi$
$463$			36.6907i			1.70516i	−0.522597	+	0.852580i	$0.675037\pi$
$464$	−17.3449	+	30.0422i	−0.805215	+	1.39467i
$465$	−7.28715	−	12.6217i	−0.337934	−	0.585318i
$466$	0.979792	−	0.565683i	0.0453880	−	0.0262048i
$467$	12.4324			0.575304			0.287652	−	0.957735i	$-0.407125\pi$
$467$	12.4324			0.575304			0.287652	+	0.957735i	$0.407125\pi$
$468$	−2.53396	−	0.116530i	−0.117132	−	0.00538662i
$469$	11.2979			0.521689
$470$	46.9432	−	27.1027i	2.16533	−	1.25015i
$471$	−0.954104	−	1.65256i	−0.0439628	−	0.0761458i
$472$	3.31892	−	5.74855i	0.152766	−	0.264598i
$473$			8.97483i			0.412663i
$474$	−13.3131	−	7.68633i	−0.611491	−	0.353045i
$475$	−21.7942	−	12.5829i	−0.999985	−	0.577342i
$476$		−	1.03553i		−	0.0474633i
$477$	6.21290	−	10.7611i	0.284469	−	0.492715i
$478$	14.2065	+	24.6064i	0.649790	+	1.12547i
$479$	−30.8911	+	17.8350i	−1.41145	+	0.814900i	−0.995525	−	0.0944993i	$-0.969875\pi$
$479$	−30.8911	+	17.8350i	−1.41145	+	0.814900i	−0.415924	+	0.909400i	$0.636542\pi$
$480$	11.9436			0.545149
$481$	1.16942	−	25.4291i	0.0533209	−	1.15947i
$482$	−38.8669			−1.77034
$483$	−5.15148	+	2.97421i	−0.234400	+	0.135331i
$484$	−2.59920	−	4.50195i	−0.118146	−	0.204634i
$485$	−26.5290	+	45.9495i	−1.20462	+	2.08646i
$486$			1.64424i			0.0745844i
$487$	−12.2528	−	7.07416i	−0.555228	−	0.320561i	0.196000	−	0.980604i	$-0.437205\pi$
$487$	−12.2528	−	7.07416i	−0.555228	−	0.320561i	−0.751228	+	0.660043i	$0.770538\pi$
$488$	25.1471	+	14.5187i	1.13835	+	0.657229i
$489$		−	14.8501i		−	0.671543i
$490$	12.4462	−	21.5575i	0.562262	−	0.973867i
$491$	10.4569	+	18.1118i	0.471911	+	0.817374i	0.999484	−	0.0321358i	$-0.0102309\pi$
$491$	10.4569	+	18.1118i	0.471911	+	0.817374i	−0.527572	+	0.849510i	$0.676898\pi$
$492$	−3.38471	+	1.95416i	−0.152595	+	0.0881006i
$493$	−7.06209			−0.318060
$494$	−16.7261	+	26.1207i	−0.752544	+	1.17523i
$495$	−13.4312			−0.603686
$496$	19.7948	−	11.4285i	0.888814	−	0.513157i
$497$	5.52624	+	9.57172i	0.247886	+	0.429350i
$498$	−1.15008	+	1.99199i	−0.0515361	+	0.0892632i
$499$		−	18.4628i		−	0.826511i	−0.910615	−	0.413255i	$-0.864392\pi$
$499$		−	18.4628i		−	0.826511i	0.910615	−	0.413255i	$-0.135608\pi$
$500$	0.362535	+	0.209309i	0.0162130	+	0.00936060i
$501$	−6.67081	−	3.85139i	−0.298030	−	0.172068i
$502$			34.3678i			1.53391i
$503$	2.47379	−	4.28473i	0.110301	−	0.191047i	−0.805591	−	0.592473i	$-0.798152\pi$
$503$	2.47379	−	4.28473i	0.110301	−	0.191047i	0.915892	+	0.401426i	$0.131485\pi$
$504$	1.56881	+	2.71726i	0.0698805	+	0.121037i
$505$	4.57883	−	2.64359i	0.203755	−	0.117638i
$506$	28.4952			1.26677
$507$	−7.50586	+	10.6142i	−0.333347	+	0.471395i
$508$	4.39729			0.195098
$509$	−26.5656	+	15.3376i	−1.17750	+	0.679829i	−0.955434	−	0.295203i	$-0.904613\pi$
$509$	−26.5656	+	15.3376i	−1.17750	+	0.679829i	−0.222064	+	0.975032i	$0.571279\pi$
$510$	2.57496	+	4.45997i	0.114021	+	0.197491i
$511$	1.67568	−	2.90237i	0.0741278	−	0.128393i
$512$		−	2.21095i		−	0.0977110i
$513$	4.53099	+	2.61597i	0.200048	+	0.115498i
$514$	16.9618	+	9.79290i	0.748153	+	0.431946i
$515$			31.1608i			1.37311i
$516$	0.736215	−	1.27516i	0.0324100	−	0.0561358i
$517$	−22.5678	−	39.0886i	−0.992532	−	1.71912i
$518$	14.7975	−	8.54336i	0.650166	−	0.375373i
$519$	−0.588146			−0.0258167
$520$	12.9816	−	20.2730i	0.569281	−	0.889030i
$521$	−3.89046			−0.170444			−0.0852221	−	0.996362i	$-0.527160\pi$
$521$	−3.89046			−0.170444			−0.0852221	+	0.996362i	$0.527160\pi$
$522$	−10.0561	+	5.80589i	−0.440144	+	0.254117i
$523$	8.51617	+	14.7504i	0.372386	+	0.644992i	0.989932	−	0.141543i	$-0.0452063\pi$
$523$	8.51617	+	14.7504i	0.372386	+	0.644992i	−0.617546	+	0.786535i	$0.711873\pi$
$524$	0.603500	−	1.04529i	0.0263640	−	0.0456638i
$525$		−	7.07982i		−	0.308989i
$526$	−24.5180	−	14.1555i	−1.06903	−	0.617207i
$527$	4.02980	+	2.32661i	0.175541	+	0.101349i
$528$		−	21.0643i		−	0.916705i
$529$	3.33374	−	5.77420i	0.144945	−	0.251052i
$530$	−31.9960	−	55.4187i	−1.38982	−	2.40724i
$531$	2.69669	−	1.55694i	0.117027	−	0.0675653i
$532$	−5.41781			−0.234892
$533$	−0.920147	+	20.0086i	−0.0398560	+	0.866670i
$534$	−22.2849			−0.964360
$535$	11.1934	−	6.46253i	0.483934	−	0.279400i
$536$	−8.18124	−	14.1703i	−0.353376	−	0.612065i
$537$	−2.21043	+	3.82858i	−0.0953873	+	0.165216i
$538$		−	35.9842i		−	1.55139i
$539$	−17.9504	−	10.3637i	−0.773180	−	0.446396i
$540$	1.90833	+	1.10177i	0.0821212	+	0.0474127i
$541$			39.7245i			1.70789i	0.520362	+	0.853946i	$0.325797\pi$
$541$			39.7245i			1.70789i	−0.520362	+	0.853946i	$0.674203\pi$
$542$	−4.35250	+	7.53875i	−0.186956	+	0.323817i
$543$	−3.21429	−	5.56731i	−0.137938	−	0.238916i
$544$	−3.30242	+	1.90665i	−0.141590	+	0.0817470i
$545$	−54.9719			−2.35474
$546$	−8.71673	−	0.400861i	−0.373042	−	0.0171553i
$547$	−1.70514			−0.0729066			−0.0364533	−	0.999335i	$-0.511606\pi$
$547$	−1.70514			−0.0729066			−0.0364533	+	0.999335i	$0.511606\pi$
$548$	−7.72422	+	4.45958i	−0.329962	+	0.190504i
$549$	6.81083	+	11.7967i	0.290679	+	0.503471i
$550$	−16.9575	+	29.3713i	−0.723071	+	1.25240i
$551$			36.9484i			1.57405i
$552$	7.46077	+	4.30748i	0.317551	+	0.183338i
$553$	−11.9176	−	6.88062i	−0.506787	−	0.292594i
$554$			27.2173i			1.15635i
$555$	−11.0566	+	19.1506i	−0.469328	+	0.812899i
$556$	−4.11792	−	7.13245i	−0.174639	−	0.302483i
$557$	3.28444	−	1.89627i	0.139166	−	0.0803477i	−0.428800	−	0.903399i	$-0.641064\pi$
$557$	3.28444	−	1.89627i	0.139166	−	0.0803477i	0.567967	+	0.823052i	$0.307730\pi$
$558$	7.65101			0.323893
$559$	−3.46883	−	6.70150i	−0.146716	−	0.283443i
$560$	22.6453			0.956938
$561$	3.71372	−	2.14412i	0.156793	−	0.0905247i
$562$	−12.2866	−	21.2810i	−0.518279	−	0.897685i
$563$	10.2219	−	17.7048i	0.430802	−	0.746170i	−0.566141	−	0.824308i	$-0.691564\pi$
$563$	10.2219	−	17.7048i	0.430802	−	0.746170i	0.996943	+	0.0781383i	$0.0248976\pi$
$564$			7.40505i			0.311809i
$565$	43.1179	+	24.8942i	1.81399	+	1.04731i
$566$	25.2419	+	14.5734i	1.06099	+	0.612565i
$567$			1.47189i			0.0618135i
$568$	8.00352	−	13.8625i	0.335820	−	0.581658i
$569$	−9.03642	−	15.6515i	−0.378826	−	0.656147i	0.612065	−	0.790807i	$-0.290339\pi$
$569$	−9.03642	−	15.6515i	−0.378826	−	0.656147i	−0.990892	+	0.134661i	$0.957006\pi$
$570$	23.3343	−	13.4720i	0.977365	−	0.564282i
$571$	−8.61524			−0.360536			−0.180268	−	0.983617i	$-0.557697\pi$
$571$	−8.61524			−0.360536			−0.180268	+	0.983617i	$0.557697\pi$
$572$	9.16056	+	5.86587i	0.383022	+	0.245264i
$573$	−14.7080			−0.614436
$574$	−11.6433	+	6.72226i	−0.485982	+	0.280582i
$575$	−9.71950	−	16.8347i	−0.405331	−	0.702054i
$576$	1.77711	−	3.07805i	0.0740463	−	0.128252i
$577$		−	28.8425i		−	1.20073i	−0.799727	−	0.600364i	$-0.795022\pi$
$577$		−	28.8425i		−	1.20073i	0.799727	−	0.600364i	$-0.204978\pi$
$578$	−1.42396	−	0.822122i	−0.0592288	−	0.0341958i
$579$	−14.1290	−	8.15740i	−0.587182	−	0.339010i
$580$			15.5616i			0.646161i
$581$	−1.02952	+	1.78318i	−0.0427117	+	0.0739788i
$582$	−13.9268	−	24.1219i	−0.577284	−	0.999886i
$583$	−46.1460	+	26.6424i	−1.91117	+	1.10342i
$584$	−4.85371			−0.200848
$585$	10.0290	−	5.19122i	0.414650	−	0.214631i
$586$	33.0780			1.36644
$587$	−17.1151	+	9.88142i	−0.706417	+	0.407850i	−0.809733	−	0.586799i	$-0.800388\pi$
$587$	−17.1151	+	9.88142i	−0.706417	+	0.407850i	0.103316	+	0.994649i	$0.467055\pi$
$588$	1.70029	+	2.94499i	0.0701187	+	0.121449i
$589$	12.1727	−	21.0837i	0.501565	−	0.868737i
$590$		−	16.0362i		−	0.660201i
$591$	−14.4785	−	8.35917i	−0.595566	−	0.343850i
$592$	−30.0342	−	17.3403i	−1.23440	−	0.712680i
$593$		−	42.6765i		−	1.75252i	−0.481843	−	0.876258i	$-0.660032\pi$
$593$		−	42.6765i		−	1.75252i	0.481843	−	0.876258i	$-0.339968\pi$
$594$	3.52545	−	6.10626i	0.144651	−	0.250543i
$595$	2.30505	+	3.99246i	0.0944977	+	0.163675i
$596$	−8.42523	+	4.86431i	−0.345111	+	0.199250i
$597$	−4.91510			−0.201162
$598$	−21.2773	+	11.0136i	−0.870094	+	0.450378i
$599$	−37.4035			−1.52827			−0.764134	−	0.645058i	$-0.776833\pi$
$599$	−37.4035			−1.52827			−0.764134	+	0.645058i	$0.776833\pi$
$600$	−8.87982	+	5.12677i	−0.362517	+	0.209299i
$601$	16.3002	+	28.2328i	0.664899	+	1.15164i	0.979313	+	0.202353i	$0.0648588\pi$
$601$	16.3002	+	28.2328i	0.664899	+	1.15164i	−0.314413	+	0.949286i	$0.601808\pi$
$602$	2.53255	−	4.38651i	0.103219	−	0.178781i
$603$		−	7.67579i		−	0.312582i
$604$	10.6255	+	6.13464i	0.432346	+	0.249615i
$605$	20.0424	+	11.5715i	0.814838	+	0.470447i
$606$			2.77559i			0.112751i
$607$	5.35413	−	9.27362i	0.217317	−	0.376405i	−0.736670	−	0.676253i	$-0.763603\pi$
$607$	5.35413	−	9.27362i	0.217317	−	0.376405i	0.953987	+	0.299848i	$0.0969360\pi$
$608$	9.97547	+	17.2780i	0.404559	+	0.700717i
$609$	−9.00199	+	5.19730i	−0.364779	+	0.210605i
$610$	70.1506			2.84031
$611$	31.9594	+	20.4648i	1.29294	+	0.827919i
$612$	−0.703537			−0.0284388
$613$	0.0727538	−	0.0420044i	0.00293850	−	0.00169654i	−0.498530	−	0.866872i	$-0.666127\pi$
$613$	0.0727538	−	0.0420044i	0.00293850	−	0.00169654i	0.501469	+	0.865176i	$0.332793\pi$
$614$	7.00250	+	12.1287i	0.282598	+	0.489474i
$615$	8.69980	−	15.0685i	0.350810	−	0.607621i
$616$		−	13.4549i		−	0.542112i
$617$	−34.2838	−	19.7938i	−1.38021	−	0.796867i	−0.388029	−	0.921647i	$-0.626844\pi$
$617$	−34.2838	−	19.7938i	−1.38021	−	0.796867i	−0.992184	+	0.124780i	$0.960177\pi$
$618$	−14.1667	−	8.17917i	−0.569870	−	0.329014i
$619$		−	28.4978i		−	1.14542i	−0.819756	−	0.572712i	$-0.805891\pi$
$619$		−	28.4978i		−	1.14542i	0.819756	−	0.572712i	$-0.194109\pi$
$620$	5.12678	−	8.87984i	0.205896	−	0.356623i
$621$	2.02068	+	3.49991i	0.0810869	+	0.140447i
$622$	−32.8145	+	18.9455i	−1.31574	+	0.759645i
$623$	−19.9489			−0.799235
$624$	8.14147	+	15.7287i	0.325920	+	0.629651i
$625$	−25.9138			−1.03655
$626$	−23.0831	+	13.3270i	−0.922587	+	0.532656i
$627$	−11.2179	−	19.4300i	−0.447999	−	0.775957i
$628$	0.671247	−	1.16263i	0.0267857	−	0.0463941i
$629$		−	7.06021i		−	0.281509i
$630$	6.56457	+	3.79006i	0.261539	+	0.151000i
$631$	20.4065	+	11.7817i	0.812368	+	0.469021i	0.847778	−	0.530352i	$-0.177940\pi$
$631$	20.4065	+	11.7817i	0.812368	+	0.469021i	−0.0354096	+	0.999373i	$0.511274\pi$
$632$			19.9301i			0.792776i
$633$	−8.48546	+	14.6972i	−0.337267	+	0.584163i
$634$	22.1527	+	38.3695i	0.879794	+	1.52385i
$635$	−16.9537	+	9.78822i	−0.672787	+	0.388434i
$636$	8.74201			0.346643
$637$	17.4092	+	0.800605i	0.689778	+	0.0317211i
$638$	49.7941			1.97137
$639$	6.50302	−	3.75452i	0.257256	−	0.148527i
$640$	−21.0956	−	36.5387i	−0.833878	−	1.44432i
$641$	12.4153	−	21.5039i	0.490373	−	0.849352i	−0.509565	−	0.860432i	$-0.670194\pi$
$641$	12.4153	−	21.5039i	0.490373	−	0.849352i	0.999939	+	0.0110804i	$0.00352706\pi$
$642$			6.78522i			0.267791i
$643$	13.1089	+	7.56842i	0.516964	+	0.298469i	0.735692	−	0.677317i	$-0.236857\pi$
$643$	13.1089	+	7.56842i	0.516964	+	0.298469i	−0.218728	+	0.975786i	$0.570191\pi$
$644$	−3.62426	−	2.09246i	−0.142816	−	0.0824547i
$645$			6.55515i			0.258109i
$646$	−4.30129	+	7.45005i	−0.169232	+	0.293118i
$647$	−16.4788	−	28.5421i	−0.647849	−	1.12211i	−0.983636	−	0.180169i	$-0.942336\pi$
$647$	−16.4788	−	28.5421i	−0.647849	−	1.12211i	0.335787	−	0.941938i	$-0.390998\pi$
$648$	1.84611	−	1.06585i	0.0725220	−	0.0418706i
$649$	−13.3530			−0.524152
$650$	1.30998	−	28.4857i	0.0513818	−	1.11730i
$651$	6.84901			0.268434
$652$	9.04785	−	5.22378i	0.354341	−	0.204579i
$653$	−10.7238	−	18.5742i	−0.419656	−	0.726865i	0.576249	−	0.817274i	$-0.304516\pi$
$653$	−10.7238	−	18.5742i	−0.419656	−	0.726865i	−0.995905	+	0.0904090i	$0.971183\pi$
$654$	14.4292	−	24.9921i	0.564226	−	0.977268i
$655$			5.37348i			0.209959i
$656$	23.6321	+	13.6440i	0.922680	+	0.532710i
$657$	−1.97187	−	1.13846i	−0.0769299	−	0.0444155i
$658$			25.4731i			0.993046i
$659$	9.34619	−	16.1881i	0.364076	−	0.630598i	−0.624552	−	0.780984i	$-0.714718\pi$
$659$	9.34619	−	16.1881i	0.364076	−	0.630598i	0.988627	+	0.150386i	$0.0480516\pi$
$660$	−4.72466	−	8.18335i	−0.183907	−	0.318536i
$661$	−34.0092	+	19.6352i	−1.32280	+	0.763722i	−0.984175	−	0.177198i	$-0.943297\pi$
$661$	−34.0092	+	19.6352i	−1.32280	+	0.763722i	−0.338629	+	0.940920i	$0.609963\pi$
$662$	−25.6939			−0.998621
$663$	−1.94432	+	3.03638i	−0.0755110	+	0.117923i
$664$	2.98206			0.115726
$665$	20.8883	−	12.0599i	0.810013	−	0.467661i
$666$	−5.80435	−	10.0534i	−0.224914	−	0.389563i
$667$	−14.2702	+	24.7167i	−0.552544	+	0.957034i
$668$		−	5.41919i		−	0.209675i
$669$	−13.5471	−	7.82145i	−0.523763	−	0.302395i
$670$	−34.2338	−	19.7649i	−1.32257	−	0.763584i
$671$		−	58.4129i		−	2.25500i
$672$	−2.80638	+	4.86079i	−0.108258	+	0.187509i
$673$	−22.0897	−	38.2604i	−0.851494	−	1.47483i	−0.879860	−	0.475233i	$-0.842364\pi$
$673$	−22.0897	−	38.2604i	−0.851494	−	1.47483i	0.0283666	−	0.999598i	$-0.490969\pi$
$674$	−16.2168	+	9.36280i	−0.624649	+	0.360642i
$675$	−4.81002			−0.185138
$676$	−9.10737	−	0.839426i	−0.350284	−	0.0322856i
$677$	18.7242			0.719630			0.359815	−	0.933024i	$-0.382840\pi$
$677$	18.7242			0.719630			0.359815	+	0.933024i	$0.382840\pi$
$678$	−22.6355	+	13.0686i	−0.869309	+	0.501896i
$679$	−12.4669	−	21.5934i	−0.478437	−	0.828678i
$680$	3.33835	−	5.78219i	0.128020	−	0.221737i
$681$			21.2788i			0.815405i
$682$	−28.4137	−	16.4047i	−1.08802	−	0.628167i
$683$	−8.05838	−	4.65251i	−0.308345	−	0.178023i	0.337841	−	0.941203i	$-0.390304\pi$
$683$	−8.05838	−	4.65251i	−0.308345	−	0.178023i	−0.646186	+	0.763180i	$0.723637\pi$
$684$			3.68086i			0.140741i
$685$	19.8537	−	34.3877i	0.758573	−	1.31389i
$686$	14.3194	+	24.8020i	0.546718	+	0.946944i
$687$	−4.73010	+	2.73093i	−0.180465	+	0.104191i
$688$	−10.2805			−0.391942
$689$	24.1597	−	37.7295i	0.920412	−	1.43738i
$690$	20.8127			0.792325
$691$	1.19985	−	0.692733i	0.0456444	−	0.0263528i	−0.477004	−	0.878901i	$-0.658277\pi$
$691$	1.19985	−	0.692733i	0.0456444	−	0.0263528i	0.522649	+	0.852548i	$0.324944\pi$
$692$	−0.206891	−	0.358346i	−0.00786481	−	0.0136223i
$693$	3.15590	−	5.46618i	0.119883	−	0.207643i
$694$		−	39.1570i		−	1.48638i
$695$	31.7532	+	18.3327i	1.20447	+	0.695399i
$696$	13.0374	+	7.52713i	0.494180	+	0.285315i
$697$			5.55526i			0.210421i
$698$	14.9739	−	25.9356i	0.566772	−	0.981678i
$699$	−0.344039	−	0.595892i	−0.0130127	−	0.0225387i
$700$	4.31360	−	2.49046i	0.163039	−	0.0941304i
$701$	−18.2004			−0.687421			−0.343710	−	0.939076i	$-0.611684\pi$
$701$	−18.2004			−0.687421			−0.343710	+	0.939076i	$0.611684\pi$
$702$	−0.272345	+	5.92215i	−0.0102790	+	0.223517i
$703$	−36.9386			−1.39316
$704$	−13.1994	+	7.62067i	−0.497471	+	0.287215i
$705$	−16.4834	−	28.5501i	−0.620800	−	1.07526i
$706$	−3.62331	+	6.27575i	−0.136365	+	0.236191i
$707$			2.48464i			0.0934446i
$708$	1.89722	+	1.09536i	0.0713020	+	0.0411662i
$709$	−17.1361	−	9.89352i	−0.643559	−	0.371559i	0.142425	−	0.989806i	$-0.454510\pi$
$709$	−17.1361	−	9.89352i	−0.643559	−	0.371559i	−0.785984	+	0.618247i	$0.787843\pi$
$710$		−	38.6710i		−	1.45130i
$711$	−4.67469	+	8.09680i	−0.175315	+	0.303654i
$712$	14.4458	+	25.0208i	0.541377	+	0.937693i
$713$	16.2858	−	9.40263i	0.609909	−	0.352131i
$714$	−2.42014			−0.0905715
$715$	−48.3756	−	2.22467i	−1.80915	−	0.0831981i
$716$	−3.11024			−0.116235
$717$	14.9652	−	8.64014i	0.558884	−	0.322672i
$718$	−13.2275	−	22.9106i	−0.493644	−	0.855017i
$719$	0.961726	−	1.66576i	0.0358663	−	0.0621223i	−0.847535	−	0.530739i	$-0.821914\pi$
$719$	0.961726	−	1.66576i	0.0358663	−	0.0621223i	0.883401	+	0.468617i	$0.155248\pi$
$720$		−	15.3852i		−	0.573372i
$721$	−12.6817	−	7.32180i	−0.472292	−	0.272678i
$722$	11.9230	+	6.88375i	0.443729	+	0.256187i
$723$			23.6382i			0.879113i
$724$	2.26137	−	3.91681i	0.0840431	−	0.145567i
$725$	−16.9844	−	29.4179i	−0.630785	−	1.09255i
$726$	−10.5216	+	6.07463i	−0.390492	+	0.225451i
$727$	12.6208			0.468078			0.234039	−	0.972227i	$-0.424806\pi$
$727$	12.6208			0.468078			0.234039	+	0.972227i	$0.424806\pi$
$728$	5.20039	+	10.0467i	0.192739	+	0.372357i
$729$	1.00000			0.0370370
$730$	−10.1550	+	5.86298i	−0.375852	+	0.216999i
$731$	−1.04645	−	1.81250i	−0.0387043	−	0.0670378i
$732$	−4.79167	+	8.29941i	−0.177105	+	0.306755i
$733$			46.9074i			1.73256i	0.499556	+	0.866282i	$0.333497\pi$
$733$			46.9074i			1.73256i	−0.499556	+	0.866282i	$0.666503\pi$
$734$	−43.0184	−	24.8367i	−1.58784	−	0.916738i
$735$	−13.1109	−	7.56956i	−0.483602	−	0.279208i
$736$			15.4109i			0.568053i
$737$	−16.4578	+	28.5057i	−0.606231	+	1.05002i
$738$	4.56710	+	7.91045i	0.168117	+	0.291188i
$739$	13.4027	−	7.73806i	0.493026	−	0.284649i	−0.232803	−	0.972524i	$-0.574790\pi$
$739$	13.4027	−	7.73806i	0.493026	−	0.284649i	0.725829	+	0.687875i	$0.241456\pi$
$740$	−15.5575			−0.571904
$741$	15.8862	+	10.1725i	0.583593	+	0.373698i
$742$	30.0722			1.10399
$743$	−11.4450	+	6.60778i	−0.419877	+	0.242416i	−0.695025	−	0.718986i	$-0.744607\pi$
$743$	−11.4450	+	6.60778i	−0.419877	+	0.242416i	0.275148	+	0.961402i	$0.411273\pi$
$744$	−4.95963	−	8.59033i	−0.181829	−	0.314937i
$745$	21.6556	−	37.5085i	0.793399	−	1.37421i
$746$			48.3726i			1.77105i
$747$	1.21149	+	0.699456i	0.0443262	+	0.0255917i
$748$	2.61274	+	1.50847i	0.0955312	+	0.0551550i
$749$			6.07397i			0.221938i
$750$	0.489180	−	0.847284i	0.0178623	−	0.0309384i
$751$	25.4439	+	44.0701i	0.928460	+	1.60814i	0.785900	+	0.618354i	$0.212200\pi$
$751$	25.4439	+	44.0701i	0.928460	+	1.60814i	0.142561	+	0.989786i	$0.454466\pi$
$752$	44.7755	−	25.8511i	1.63279	−	0.942693i
$753$	20.9019			0.761707
$754$	−37.1812	+	19.2457i	−1.35406	+	0.700887i
$755$	−54.6220			−1.98790
$756$	−0.896793	+	0.517764i	−0.0326160	+	0.0188309i
$757$	−17.6499	−	30.5705i	−0.641495	−	1.11110i	−0.985099	−	0.171987i	$-0.944981\pi$
$757$	−17.6499	−	30.5705i	−0.641495	−	1.11110i	0.343604	−	0.939115i	$-0.388352\pi$
$758$	15.7701	−	27.3146i	0.572795	−	0.992109i
$759$		−	17.3303i		−	0.629049i
$760$	−30.2520	−	17.4660i	−1.09736	−	0.633559i
$761$	33.0772	+	19.0971i	1.19905	+	0.692270i	0.960343	−	0.278822i	$-0.0899439\pi$
$761$	33.0772	+	19.0971i	1.19905	+	0.692270i	0.238705	+	0.971092i	$0.423277\pi$
$762$		−	10.2770i		−	0.372295i
$763$	12.9167	−	22.3723i	0.467615	−	0.809933i
$764$	−5.17381	−	8.96131i	−0.187182	−	0.324209i
$765$	2.71247	−	1.56605i	0.0980697	−	0.0566206i
$766$	38.7668			1.40070
$767$	9.97069	−	5.16102i	0.360021	−	0.186354i
$768$	15.0405			0.542728
$769$	−19.9286	+	11.5058i	−0.718643	+	0.414908i	−0.814253	−	0.580510i	$-0.802853\pi$
$769$	−19.9286	+	11.5058i	−0.718643	+	0.414908i	0.0956103	+	0.995419i	$0.469520\pi$
$770$	−16.2527	−	28.1504i	−0.585705	−	1.01447i
$771$	5.95587	−	10.3159i	0.214495	−	0.371517i
$772$		−	11.4781i		−	0.413104i
$773$	4.39936	+	2.53997i	0.158234	+	0.0913565i	0.577026	−	0.816726i	$-0.304213\pi$
$773$	4.39936	+	2.53997i	0.158234	+	0.0913565i	−0.418792	+	0.908082i	$0.637546\pi$
$774$	−2.98019	−	1.72062i	−0.107121	−	0.0618463i
$775$			22.3821i			0.803988i
$776$	−18.0556	+	31.2732i	−0.648158	+	1.12264i
$777$	−5.19592	−	8.99959i	−0.186403	−	0.322859i
$778$	−14.7815	+	8.53409i	−0.529942	+	0.305962i
$779$	29.0648			1.04135
$780$	6.69081	+	4.28439i	0.239569	+	0.153406i
$781$	−32.2006			−1.15223
$782$	−5.75471	+	3.32248i	−0.205788	+	0.118812i
$783$	3.53104	+	6.11595i	0.126189	+	0.218566i
$784$	11.8715	−	20.5620i	0.423980	−	0.734356i
$785$			5.97669i			0.213317i
$786$	−2.44296	−	1.41045i	−0.0871376	−	0.0503089i
$787$	2.96222	+	1.71024i	0.105592	+	0.0609633i	0.551866	−	0.833933i	$-0.313916\pi$
$787$	2.96222	+	1.71024i	0.105592	+	0.0609633i	−0.446274	+	0.894896i	$0.647249\pi$
$788$		−	11.7620i		−	0.419003i
$789$	−8.60910	+	14.9114i	−0.306492	+	0.530860i
$790$	24.0743	+	41.6979i	0.856526	+	1.48355i
$791$	−20.2627	+	11.6987i	−0.720460	+	0.415957i
$792$	−9.14124			−0.324820
$793$	22.5769	+	43.6168i	0.801730	+	1.54888i
$794$	−3.13939			−0.111413
$795$	−33.7047	+	19.4594i	−1.19538	+	0.690154i
$796$	−1.72898	−	2.99467i	−0.0612819	−	0.106143i
$797$	6.50997	−	11.2756i	0.230595	−	0.399402i	−0.727388	−	0.686226i	$-0.759266\pi$
$797$	6.50997	−	11.2756i	0.230595	−	0.399402i	0.957983	+	0.286824i	$0.0925994\pi$
$798$			12.6620i			0.448231i
$799$	9.11532	+	5.26273i	0.322477	+	0.186182i
$800$	−15.8847	−	9.17104i	−0.561609	−	0.324245i
$801$			13.5533i			0.478881i
$802$	10.9530	−	18.9712i	0.386765	−	0.669896i
$803$	4.88198	+	8.45583i	0.172281	+	0.298400i
$804$	4.67671	−	2.70010i	0.164935	−	0.0952251i
$805$	18.6310			0.656657
$806$	27.5570	+	1.26728i	0.970654	+	0.0446379i
$807$	−21.8849			−0.770386
$808$	3.11635	−	1.79923i	0.109633	−	0.0632965i
$809$	−7.39825	−	12.8142i	−0.260109	−	0.450522i	0.706162	−	0.708050i	$-0.250425\pi$
$809$	−7.39825	−	12.8142i	−0.260109	−	0.450522i	−0.966271	+	0.257529i	$0.917092\pi$
$810$	2.57496	−	4.45997i	0.0904750	−	0.156707i
$811$			19.8159i			0.695829i	0.937526	+	0.347914i	$0.113110\pi$
$811$			19.8159i			0.695829i	−0.937526	+	0.347914i	$0.886890\pi$
$812$	−6.33323	−	3.65649i	−0.222253	−	0.128318i
$813$	4.58494	+	2.64712i	0.160801	+	0.0928384i
$814$			49.7808i			1.74482i
$815$	−23.2559	+	40.2804i	−0.814619	+	1.41096i
$816$	2.45605	+	4.25401i	0.0859791	+	0.148920i
$817$	−9.48289	+	5.47495i	−0.331764	+	0.191544i
$818$	−2.74748			−0.0960634
$819$	−0.243797	+	5.30136i	−0.00851894	+	0.185245i
$820$	12.2413			0.427483
$821$	−42.8245	+	24.7248i	−1.49459	+	0.862900i	−0.999981	−	0.00621755i	$-0.998021\pi$
$821$	−42.8245	+	24.7248i	−1.49459	+	0.862900i	−0.494606	+	0.869117i	$0.664688\pi$
$822$	10.4225	+	18.0524i	0.363528	+	0.629649i
$823$	−8.38455	+	14.5225i	−0.292267	+	0.506221i	−0.974345	−	0.225058i	$-0.927743\pi$
$823$	−8.38455	+	14.5225i	−0.292267	+	0.506221i	0.682078	+	0.731279i	$0.261076\pi$
$824$			21.2080i			0.738815i
$825$	17.8631	+	10.3133i	0.621913	+	0.359062i
$826$	6.52638	+	3.76801i	0.227082	+	0.131106i
$827$			20.6549i			0.718243i	0.933291	+	0.359121i	$0.116924\pi$
$827$			20.6549i			0.718243i	−0.933291	+	0.359121i	$0.883076\pi$
$828$	−1.42162	+	2.46232i	−0.0494047	+	0.0855714i
$829$	−13.9068	−	24.0874i	−0.483005	−	0.836589i	0.516805	−	0.856103i	$-0.327121\pi$
$829$	−13.9068	−	24.0874i	−0.483005	−	0.836589i	−0.999810	+	0.0195144i	$0.993788\pi$
$830$	6.23910	−	3.60215i	0.216562	−	0.125032i
$831$	16.5531			0.574221
$832$	6.91054	−	10.7920i	0.239580	−	0.374145i
$833$	4.83355			0.167472
$834$	−16.6693	+	9.62404i	−0.577212	+	0.333253i
$835$	12.0629	+	20.8936i	0.417455	+	0.723053i
$836$	7.89219	−	13.6697i	0.272957	−	0.472776i
$837$		−	4.65321i		−	0.160839i
$838$	7.42259	+	4.28543i	0.256409	+	0.148038i
$839$	20.8886	+	12.0600i	0.721155	+	0.416359i	0.815178	−	0.579211i	$-0.196639\pi$
$839$	20.8886	+	12.0600i	0.721155	+	0.416359i	−0.0940226	+	0.995570i	$0.529973\pi$
$840$		−	9.82734i		−	0.339076i
$841$	−10.4365	+	18.0766i	−0.359880	+	0.623331i
$842$	−1.71700	−	2.97394i	−0.0591718	−	0.102489i
$843$	−12.9427	+	7.47249i	−0.445772	+	0.257366i
$844$	−11.9397			−0.410980
$845$	36.9819	−	17.0363i	1.27221	−	0.586067i
$846$	17.3064			0.595007
$847$	−9.41865	+	5.43786i	−0.323629	+	0.186847i
$848$	−30.5185	−	52.8595i	−1.04801	−	1.81520i
$849$	8.86328	−	15.3517i	0.304187	−	0.526867i
$850$		−	7.90885i		−	0.271271i
$851$	−24.7101	−	14.2664i	−0.847052	−	0.489046i
$852$	4.57512	+	2.64144i	0.156741	+	0.0904944i
$853$			14.8082i			0.507022i	0.967332	+	0.253511i	$0.0815854\pi$
$853$			14.8082i			0.507022i	−0.967332	+	0.253511i	$0.918415\pi$
$854$	−16.4832	+	28.5497i	−0.564043	+	0.976951i
$855$	−8.19346	−	14.1915i	−0.280211	−	0.485339i
$856$	7.61824	−	4.39839i	0.260386	−	0.150334i
$857$	23.4426			0.800785			0.400393	−	0.916344i	$-0.368874\pi$
$857$	23.4426			0.800785			0.400393	+	0.916344i	$0.368874\pi$
$858$	13.7092	−	21.4093i	0.468024	−	0.730900i
$859$	−37.4445			−1.27759			−0.638796	−	0.769376i	$-0.720567\pi$
$859$	−37.4445			−1.27759			−0.638796	+	0.769376i	$0.720567\pi$
$860$	−3.99393	+	2.30590i	−0.136192	+	0.0786304i
$861$	4.08836	+	7.08125i	0.139331	+	0.241328i
$862$	10.8912	−	18.8642i	0.370957	−	0.642517i
$863$			4.25735i			0.144922i	0.997371	+	0.0724609i	$0.0230852\pi$
$863$			4.25735i			0.144922i	−0.997371	+	0.0724609i	$0.976915\pi$
$864$	3.30242	+	1.90665i	0.112350	+	0.0648656i
$865$	1.59533	+	0.921064i	0.0542428	+	0.0313171i
$866$			43.4288i			1.47577i
$867$	−0.500000	+	0.866025i	−0.0169809	+	0.0294118i
$868$	2.40926	+	4.17297i	0.0817757	+	0.141640i
$869$	34.7210	−	20.0462i	1.17783	−	0.680020i
$870$	36.3692			1.23303
$871$	1.27138	−	27.6462i	0.0430791	−	0.936757i
$872$	−37.4138			−1.26699
$873$	−14.6705	+	8.47004i	−0.496522	+	0.286667i
$874$	17.3830	+	30.1083i	0.587989	+	1.01843i
$875$	0.437902	−	0.758469i	0.0148038	−	0.0256409i
$876$		−	1.60189i		−	0.0541230i
$877$	−42.0906	−	24.3010i	−1.42130	−	0.820586i	−0.424887	−	0.905246i	$-0.639686\pi$
$877$	−42.0906	−	24.3010i	−1.42130	−	0.820586i	−0.996410	+	0.0846600i	$0.973020\pi$
$878$	5.47096	+	3.15866i	0.184636	+	0.106600i
$879$		−	20.1174i		−	0.678544i
$880$	−32.9877	+	57.1363i	−1.11201	+	1.92607i
$881$	−21.3356	−	36.9543i	−0.718814	−	1.24502i	−0.961470	−	0.274910i	$-0.911352\pi$
$881$	−21.3356	−	36.9543i	−0.718814	−	1.24502i	0.242656	−	0.970112i	$-0.421981\pi$
$882$	6.88276	−	3.97376i	0.231755	−	0.133804i
$883$	12.6257			0.424887			0.212444	−	0.977173i	$-0.431858\pi$
$883$	12.6257			0.424887			0.212444	+	0.977173i	$0.431858\pi$
$884$	−2.53396	−	0.116530i	−0.0852263	−	0.00391934i
$885$	−9.75295			−0.327842
$886$	15.9055	−	9.18302i	0.534354	−	0.308510i
$887$	3.68606	+	6.38445i	0.123766	+	0.214369i	0.921250	−	0.388971i	$-0.127169\pi$
$887$	3.68606	+	6.38445i	0.123766	+	0.214369i	−0.797484	+	0.603340i	$0.793836\pi$
$888$	−7.52513	+	13.0339i	−0.252527	+	0.437389i
$889$		−	9.19969i		−	0.308548i
$890$	60.4471	+	34.8992i	2.02619	+	1.16982i
$891$	−3.71372	−	2.14412i	−0.124414	−	0.0718306i
$892$		−	11.0053i		−	0.368486i
$893$	27.5343	−	47.6908i	0.921400	−	1.59591i
$894$	11.3684	+	19.6907i	0.380217	+	0.658556i
$895$	11.9915	−	6.92329i	0.400831	−	0.231420i
$896$	19.8272			0.662381
$897$	6.69825	+	12.9405i	0.223648	+	0.432070i
$898$	57.9576			1.93407
$899$	28.4588	−	16.4307i	0.949154	−	0.547994i
$900$	−1.69201	−	2.93065i	−0.0564005	−	0.0976885i
$901$	6.21290	−	10.7611i	0.206982	−	0.358503i
$902$		−	39.1696i		−	1.30421i
$903$	−2.66780	−	1.54025i	−0.0887788	−	0.0512565i
$904$	29.3460	+	16.9429i	0.976035	+	0.563514i
$905$			20.1349i			0.669307i
$906$	14.3373	−	24.8330i	0.476326	−	0.825021i
$907$	−2.24867	−	3.89481i	−0.0746659	−	0.129325i	0.826275	−	0.563267i	$-0.190456\pi$
$907$	−2.24867	−	3.89481i	−0.0746659	−	0.129325i	−0.900941	+	0.433942i	$0.857122\pi$
$908$	−12.9648	+	7.48520i	−0.430250	+	0.248405i
$909$	1.68807			0.0559896
$910$	23.0162	+	14.7381i	0.762978	+	0.488565i
$911$	1.17141			0.0388107			0.0194053	−	0.999812i	$-0.493823\pi$
$911$	1.17141			0.0388107			0.0194053	+	0.999812i	$0.493823\pi$
$912$	22.2567	−	12.8499i	0.736994	−	0.425503i
$913$	−2.99943	−	5.19517i	−0.0992667	−	0.171935i
$914$	−2.95200	+	5.11302i	−0.0976435	+	0.169124i
$915$		−	42.6644i		−	1.41044i
$916$	−3.32780	−	1.92131i	−0.109954	−	0.0634818i
$917$	−2.18688	−	1.26260i	−0.0722173	−	0.0416947i
$918$			1.64424i			0.0542681i
$919$	−10.6625	+	18.4680i	−0.351724	+	0.609205i	−0.986552	−	0.163449i	$-0.947738\pi$
$919$	−10.6625	+	18.4680i	−0.351724	+	0.609205i	0.634827	+	0.772654i	$0.281071\pi$
$920$	−13.4914	−	23.3678i	−0.444799	−	0.770415i
$921$	7.37646	−	4.25880i	0.243062	−	0.140332i
$922$	7.62587			0.251145
$923$	24.0441	−	12.4457i	0.791422	−	0.409655i
$924$	4.44058			0.146084
$925$	29.4100	−	16.9799i	0.966996	−	0.558295i
$926$	30.1642	+	52.2459i	0.991257	+	1.71691i
$927$	−4.97443	+	8.61596i	−0.163382	+	0.282985i
$928$			26.9299i			0.884016i
$929$	20.0885	+	11.5981i	0.659083	+	0.380522i	0.791927	−	0.610615i	$-0.209078\pi$
$929$	20.0885	+	11.5981i	0.659083	+	0.380522i	−0.132845	+	0.991137i	$0.542411\pi$
$930$	−20.7532	−	11.9819i	−0.680524	−	0.392900i
$931$		−	25.2888i		−	0.828807i
$932$	0.242044	−	0.419232i	0.00792841	−	0.0137324i
$933$	11.5223	+	19.9572i	0.377224	+	0.653370i
$934$	17.7032	−	10.2210i	0.579268	−	0.334440i
$935$	−13.4312			−0.439246
$936$	6.82575	−	3.53314i	0.223107	−	0.115484i
$937$	−20.9966			−0.685928			−0.342964	−	0.939349i	$-0.611431\pi$
$937$	−20.9966			−0.685928			−0.342964	+	0.939349i	$0.611431\pi$
$938$	16.0877	−	9.28825i	0.525283	−	0.303272i
$939$	8.10527	+	14.0387i	0.264506	+	0.458137i
$940$	11.5967	−	20.0860i	0.378242	−	0.655134i
$941$		−	42.8322i		−	1.39629i	−0.715956	−	0.698146i	$-0.754009\pi$
$941$		−	42.8322i		−	1.39629i	0.715956	−	0.698146i	$-0.245991\pi$
$942$	−2.71720	−	1.56878i	−0.0885313	−	0.0511136i
$943$	19.4429	+	11.2254i	0.633149	+	0.365549i
$944$		−	15.2957i		−	0.497832i
$945$	2.30505	−	3.99246i	0.0749832	−	0.129875i
$946$	7.37841	+	12.7798i	0.239893	+	0.415506i
$947$	48.4321	−	27.9623i	1.57383	−	0.908652i	0.578139	−	0.815938i	$-0.303779\pi$
$947$	48.4321	−	27.9623i	1.57383	−	0.908652i	0.995693	−	0.0927139i	$-0.0295542\pi$
$948$	−6.57763			−0.213631
$949$	−6.91359	−	4.42705i	−0.224425	−	0.143708i
$950$	−41.3786			−1.34250
$951$	23.3357	−	13.4729i	0.756711	−	0.436887i
$952$	1.56881	+	2.71726i	0.0508455	+	0.0880670i
$953$	−4.64384	+	8.04338i	−0.150429	+	0.260550i	−0.931385	−	0.364035i	$-0.881399\pi$
$953$	−4.64384	+	8.04338i	−0.150429	+	0.260550i	0.780956	+	0.624586i	$0.214732\pi$
$954$		−	20.4311i		−	0.661480i
$955$	39.8951	+	23.0334i	1.29098	+	0.745345i
$956$	10.5285	+	6.07865i	0.340517	+	0.196598i
$957$		−	30.2839i		−	0.978939i
$958$	−29.3250	+	50.7924i	−0.947448	+	1.64103i
$959$	9.33001	+	16.1601i	0.301282	+	0.521835i
$960$	−9.64074	+	5.56608i	−0.311154	+	0.179645i
$961$	9.34762			0.301536
$962$	−19.2406	−	37.1713i	−0.620341	−	1.19845i
$963$	4.12665			0.132979
$964$	−14.4023	+	8.31516i	−0.463866	+	0.267813i
$965$	25.5497	+	44.2535i	0.822475	+	1.42457i
$966$	−4.89032	+	8.47029i	−0.157344	+	0.272527i
$967$			2.65086i			0.0852459i	0.999091	+	0.0426229i	$0.0135714\pi$
$967$			2.65086i			0.0852459i	−0.999091	+	0.0426229i	$0.986429\pi$
$968$	13.6408	+	7.87553i	0.438433	+	0.253129i
$969$	4.53099	+	2.61597i	0.145556	+	0.0840370i
$970$			87.2402i			2.80111i
$971$	−5.84413	+	10.1223i	−0.187547	+	0.324841i	−0.944432	−	0.328707i	$-0.893387\pi$
$971$	−5.84413	+	10.1223i	−0.187547	+	0.324841i	0.756885	+	0.653548i	$0.226720\pi$
$972$	0.351768	+	0.609281i	0.0112830	+	0.0195427i
$973$	−14.9220	+	8.61522i	−0.478377	+	0.276191i
$974$	−23.2633			−0.745404
$975$	−17.3245	−	0.796710i	−0.554827	−	0.0255151i
$976$	66.9111			2.14177
$977$	−14.3435	+	8.28125i	−0.458891	+	0.264941i	−0.711578	−	0.702607i	$-0.752019\pi$
$977$	−14.3435	+	8.28125i	−0.458891	+	0.264941i	0.252687	+	0.967548i	$0.418686\pi$
$978$	−12.2086	−	21.1458i	−0.390387	−	0.676169i
$979$	29.0598	−	50.3330i	0.928755	−	1.60865i
$980$		−	10.6509i		−	0.340232i
$981$	−15.1998	−	8.77558i	−0.485291	−	0.280183i
$982$	29.7802	+	17.1936i	0.950325	+	0.548670i
$983$			17.2119i			0.548974i	0.961591	+	0.274487i	$0.0885081\pi$
$983$			17.2119i			0.548974i	−0.961591	+	0.274487i	$0.911492\pi$
$984$	5.92108	−	10.2556i	0.188757	−	0.326937i
$985$	26.1817	+	45.3481i	0.834219	+	1.44491i
$986$	−10.0561	+	5.80589i	−0.320252	+	0.184897i
$987$	15.4923			0.493126
$988$	−0.609680	+	13.2575i	−0.0193965	+	0.421778i
$989$	−8.45813			−0.268953
$990$	−19.1254	+	11.0421i	−0.607845	+	0.350939i
$991$	1.85769	+	3.21761i	0.0590114	+	0.102211i	0.894022	−	0.448023i	$-0.147872\pi$
$991$	1.85769	+	3.21761i	0.0590114	+	0.102211i	−0.835010	+	0.550234i	$0.814539\pi$
$992$	8.87205	−	15.3668i	0.281688	−	0.487898i
$993$			15.6266i			0.495894i
$994$	15.7382	+	9.08648i	0.499187	+	0.288206i
$995$	13.3321	+	7.69728i	0.422655	+	0.244020i
$996$			0.984185i			0.0311851i
$997$	5.64062	−	9.76985i	0.178640	−	0.309414i	−0.762775	−	0.646664i	$-0.776163\pi$
$997$	5.64062	−	9.76985i	0.178640	−	0.309414i	0.941415	+	0.337250i	$0.109497\pi$
$998$	−15.1787	−	26.2903i	−0.480474	−	0.832205i
$999$	−6.11432	+	3.53010i	−0.193449	+	0.111688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	663.2.z.d.205.7	✓	16
13.2	odd	12		8619.2.a.bn.1.13		16
13.4	even	6	inner	663.2.z.d.511.7	yes	16
13.11	odd	12		8619.2.a.bn.1.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.z.d.205.7	✓	16	1.1	even	1	trivial
663.2.z.d.511.7	yes	16	13.4	even	6	inner
8619.2.a.bn.1.4		16	13.11	odd	12
8619.2.a.bn.1.13		16	13.2	odd	12

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:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42396 - 0.822122i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.351768 - 0.609281i) q^{4} +3.13210i q^{5} +(-1.42396 - 0.822122i) q^{6} +(-1.27469 - 0.735944i) q^{7} +2.13170i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.42396 - 0.822122i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.351768 - 0.609281i) q^{4} +3.13210i q^{5} +(-1.42396 - 0.822122i) q^{6} +(-1.27469 - 0.735944i) q^{7} +2.13170i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.57496 + 4.45997i) q^{10} +(3.71372 - 2.14412i) q^{11} -0.703537 q^{12} +(-1.94432 + 3.03638i) q^{13} -2.42014 q^{14} +(2.71247 - 1.56605i) q^{15} +(2.45605 + 4.25401i) q^{16} +(-0.500000 + 0.866025i) q^{17} +1.64424i q^{18} +(4.53099 + 2.61597i) q^{19} +(1.90833 + 1.10177i) q^{20} +1.47189i q^{21} +(3.52545 - 6.10626i) q^{22} +(2.02068 + 3.49991i) q^{23} +(1.84611 - 1.06585i) q^{24} -4.81002 q^{25} +(-0.272345 + 5.92215i) q^{26} +1.00000 q^{27} +(-0.896793 + 0.517764i) q^{28} +(3.53104 + 6.11595i) q^{29} +(2.57496 - 4.45997i) q^{30} -4.65321i q^{31} +(3.30242 + 1.90665i) q^{32} +(-3.71372 - 2.14412i) q^{33} +1.64424i q^{34} +(2.30505 - 3.99246i) q^{35} +(0.351768 + 0.609281i) q^{36} +(-6.11432 + 3.53010i) q^{37} +8.60258 q^{38} +(3.60174 + 0.165635i) q^{39} -6.67669 q^{40} +(4.81100 - 2.77763i) q^{41} +(1.21007 + 2.09590i) q^{42} +(-1.04645 + 1.81250i) q^{43} -3.01693i q^{44} +(-2.71247 - 1.56605i) q^{45} +(5.75471 + 3.32248i) q^{46} -10.5255i q^{47} +(2.45605 - 4.25401i) q^{48} +(-2.41677 - 4.18597i) q^{49} +(-6.84927 + 3.95443i) q^{50} +1.00000 q^{51} +(1.16606 + 2.25274i) q^{52} -12.4258 q^{53} +(1.42396 - 0.822122i) q^{54} +(6.71558 + 11.6317i) q^{55} +(1.56881 - 2.71726i) q^{56} -5.23194i q^{57} +(10.0561 + 5.80589i) q^{58} +(-2.69669 - 1.55694i) q^{59} -2.20354i q^{60} +(6.81083 - 11.7967i) q^{61} +(-3.82551 - 6.62597i) q^{62} +(1.27469 - 0.735944i) q^{63} -3.55422 q^{64} +(-9.51025 - 6.08979i) q^{65} -7.05090 q^{66} +(-6.64743 + 3.83789i) q^{67} +(0.351768 + 0.609281i) q^{68} +(2.02068 - 3.49991i) q^{69} -7.58012i q^{70} +(-6.50302 - 3.75452i) q^{71} +(-1.84611 - 1.06585i) q^{72} +2.27692i q^{73} +(-5.80435 + 10.0534i) q^{74} +(2.40501 + 4.16560i) q^{75} +(3.18772 - 1.84043i) q^{76} -6.31180 q^{77} +(5.26490 - 2.72522i) q^{78} +9.34938 q^{79} +(-13.3240 + 7.69260i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.56710 - 7.91045i) q^{82} -1.39891i q^{83} +(0.896793 + 0.517764i) q^{84} +(-2.71247 - 1.56605i) q^{85} +3.44123i q^{86} +(3.53104 - 6.11595i) q^{87} +(4.57062 + 7.91654i) q^{88} +(11.7375 - 6.77663i) q^{89} -5.14993 q^{90} +(4.71301 - 2.43955i) q^{91} +2.84324 q^{92} +(-4.02980 + 2.32661i) q^{93} +(-8.65321 - 14.9878i) q^{94} +(-8.19346 + 14.1915i) q^{95} -3.81330i q^{96} +(14.6705 + 8.47004i) q^{97} +(-6.88276 - 3.97376i) q^{98} +4.28824i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more