LMFDB - Embedded newform 670.2.k.b.241.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(81,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (of order $11$, degree $10$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			241.3
Character	$\chi$	$=$	670.241
Dual form			670.2.k.b.531.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(-0.376919 + 0.825337i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.870577 - 0.255624i) q^{6} +(-1.54779 - 1.78624i) q^{7} +(0.841254 - 0.540641i) q^{8} +(1.42547 + 1.64508i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.376919 + 0.825337i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.870577 - 0.255624i) q^{6} +(-1.54779 - 1.78624i) q^{7} +(0.841254 - 0.540641i) q^{8} +(1.42547 + 1.64508i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(-5.01552 - 1.47269i) q^{11} +(-0.763295 - 0.490540i) q^{12} +(-2.73851 - 1.75993i) q^{13} +(-0.336366 + 2.33948i) q^{14} +(-0.594175 + 0.685714i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.416255 - 2.89512i) q^{17} +(0.309784 - 2.15460i) q^{18} +(5.60023 - 6.46301i) q^{19} +(-0.415415 + 0.909632i) q^{20} +(2.05764 - 0.604178i) q^{21} +(2.17148 + 4.75489i) q^{22} +(0.117812 - 0.257972i) q^{23} +(0.129127 + 0.898095i) q^{24} +(0.841254 + 0.540641i) q^{25} +(0.463273 + 3.22214i) q^{26} +(-4.50676 + 1.32330i) q^{27} +(1.98833 - 1.27782i) q^{28} +6.53412 q^{29} +0.907330 q^{30} +(-3.16630 + 2.03486i) q^{31} +(0.415415 + 0.909632i) q^{32} +(3.10591 - 3.58441i) q^{33} +(-1.91539 + 2.21048i) q^{34} +(-0.981849 - 2.14995i) q^{35} +(-1.83120 + 1.17684i) q^{36} -0.927963 q^{37} -8.55178 q^{38} +(2.48473 - 1.59684i) q^{39} +(0.959493 - 0.281733i) q^{40} +(-0.611826 - 4.25534i) q^{41} +(-1.80408 - 1.15941i) q^{42} +(-1.32137 - 9.19036i) q^{43} +(2.17148 - 4.75489i) q^{44} +(0.904255 + 1.98004i) q^{45} +(-0.272112 + 0.0798994i) q^{46} +(2.15878 - 4.72706i) q^{47} +(0.594175 - 0.685714i) q^{48} +(0.201189 - 1.39930i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(2.54634 + 0.747673i) q^{51} +(2.13175 - 2.46017i) q^{52} +(1.33221 - 9.26570i) q^{53} +(3.95139 + 2.53940i) q^{54} +(-4.39745 - 2.82607i) q^{55} +(-2.26780 - 0.665885i) q^{56} +(3.22333 + 7.05810i) q^{57} +(-4.27894 - 4.93816i) q^{58} +(-9.49195 + 6.10011i) q^{59} +(-0.594175 - 0.685714i) q^{60} +(0.442600 - 0.129959i) q^{61} +(3.61133 + 1.06038i) q^{62} +(0.732186 - 5.09247i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-2.13175 - 2.46017i) q^{65} -4.74285 q^{66} +(-0.641349 - 8.16019i) q^{67} +2.92489 q^{68} +(0.168508 + 0.194469i) q^{69} +(-0.981849 + 2.14995i) q^{70} +(-0.903983 + 6.28734i) q^{71} +(2.08858 + 0.613262i) q^{72} +(-9.00798 + 2.64498i) q^{73} +(0.607686 + 0.701307i) q^{74} +(-0.763295 + 0.490540i) q^{75} +(5.60023 + 6.46301i) q^{76} +(5.13238 + 11.2384i) q^{77} +(-2.83396 - 0.832126i) q^{78} +(-9.38615 - 6.03211i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(-0.322842 + 2.24541i) q^{81} +(-2.81531 + 3.24904i) q^{82} +(1.17028 + 0.343626i) q^{83} +(0.305195 + 2.12268i) q^{84} +(0.416255 - 2.89512i) q^{85} +(-6.08030 + 7.01704i) q^{86} +(-2.46283 + 5.39285i) q^{87} +(-5.01552 + 1.47269i) q^{88} +(6.64727 + 14.5555i) q^{89} +(0.904255 - 1.98004i) q^{90} +(1.09496 + 7.61564i) q^{91} +(0.238580 + 0.153326i) q^{92} +(-0.486005 - 3.38024i) q^{93} +(-4.98617 + 1.46407i) q^{94} +(7.19422 - 4.62344i) q^{95} -0.907330 q^{96} -3.85643 q^{97} +(-1.18927 + 0.764299i) q^{98} +(-4.72678 - 10.3502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9} + 5 q^{10} + 30 q^{11} - 9 q^{12} + 20 q^{13} - 21 q^{14} - 2 q^{15} - 5 q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + 5 q^{20} + 23 q^{21} - 3 q^{22} - 5 q^{23} + 2 q^{24} - 5 q^{25} - 2 q^{26} + 2 q^{27} - 10 q^{28} + 26 q^{29} - 2 q^{30} + 3 q^{31} - 5 q^{32} + 38 q^{33} + 2 q^{34} - 12 q^{35} - q^{36} + 22 q^{37} - 40 q^{38} - 35 q^{39} + 5 q^{40} - 18 q^{41} - 10 q^{42} + 87 q^{43} - 3 q^{44} + 12 q^{45} + 17 q^{46} + 35 q^{47} + 2 q^{48} + 60 q^{49} - 5 q^{50} + 19 q^{51} - 24 q^{52} - 9 q^{53} + 2 q^{54} + 25 q^{55} + 12 q^{56} + 64 q^{57} + 4 q^{58} - 49 q^{59} - 2 q^{60} - 47 q^{61} - 19 q^{62} - 24 q^{63} - 5 q^{64} + 24 q^{65} - 6 q^{66} - 21 q^{67} + 2 q^{68} - 25 q^{69} - 12 q^{70} + 92 q^{71} - q^{72} + 18 q^{73} - 22 q^{74} - 9 q^{75} + 4 q^{76} - 65 q^{77} + 31 q^{78} - 58 q^{79} + 5 q^{80} - 77 q^{81} - 18 q^{82} - 49 q^{83} - 54 q^{84} - 2 q^{85} - q^{86} - 147 q^{87} + 30 q^{88} - 21 q^{89} + 12 q^{90} + 62 q^{91} + 6 q^{92} - 34 q^{93} - 9 q^{94} + 7 q^{95} + 2 q^{96} + 98 q^{97} - 39 q^{98} - 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9 + 5 * q^10 + 30 * q^11 - 9 * q^12 + 20 * q^13 - 21 * q^14 - 2 * q^15 - 5 * q^16 + 2 * q^17 - q^18 + 4 * q^19 + 5 * q^20 + 23 * q^21 - 3 * q^22 - 5 * q^23 + 2 * q^24 - 5 * q^25 - 2 * q^26 + 2 * q^27 - 10 * q^28 + 26 * q^29 - 2 * q^30 + 3 * q^31 - 5 * q^32 + 38 * q^33 + 2 * q^34 - 12 * q^35 - q^36 + 22 * q^37 - 40 * q^38 - 35 * q^39 + 5 * q^40 - 18 * q^41 - 10 * q^42 + 87 * q^43 - 3 * q^44 + 12 * q^45 + 17 * q^46 + 35 * q^47 + 2 * q^48 + 60 * q^49 - 5 * q^50 + 19 * q^51 - 24 * q^52 - 9 * q^53 + 2 * q^54 + 25 * q^55 + 12 * q^56 + 64 * q^57 + 4 * q^58 - 49 * q^59 - 2 * q^60 - 47 * q^61 - 19 * q^62 - 24 * q^63 - 5 * q^64 + 24 * q^65 - 6 * q^66 - 21 * q^67 + 2 * q^68 - 25 * q^69 - 12 * q^70 + 92 * q^71 - q^72 + 18 * q^73 - 22 * q^74 - 9 * q^75 + 4 * q^76 - 65 * q^77 + 31 * q^78 - 58 * q^79 + 5 * q^80 - 77 * q^81 - 18 * q^82 - 49 * q^83 - 54 * q^84 - 2 * q^85 - q^86 - 147 * q^87 + 30 * q^88 - 21 * q^89 + 12 * q^90 + 62 * q^91 + 6 * q^92 - 34 * q^93 - 9 * q^94 + 7 * q^95 + 2 * q^96 + 98 * q^97 - 39 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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 $

$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$3$	−0.376919	+	0.825337i	−0.217614	+	0.476508i	−0.986682	−	0.162658i	$-0.947993\pi$
$3$	−0.376919	+	0.825337i	−0.217614	+	0.476508i	0.769068	+	0.639166i	$0.220721\pi$
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$6$	0.870577	−	0.255624i	0.355412	−	0.104358i
$7$	−1.54779	−	1.78624i	−0.585009	−	0.675136i	0.383665	−	0.923472i	$-0.374662\pi$
$7$	−1.54779	−	1.78624i	−0.585009	−	0.675136i	−0.968674	+	0.248336i	$0.920116\pi$
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	1.42547	+	1.64508i	0.475156	+	0.548360i
$10$	−0.415415	−	0.909632i	−0.131366	−	0.287651i
$11$	−5.01552	−	1.47269i	−1.51224	−	0.444033i	−0.582677	−	0.812704i	$-0.697995\pi$
$11$	−5.01552	−	1.47269i	−1.51224	−	0.444033i	−0.929560	+	0.368671i	$0.879813\pi$
$12$	−0.763295	−	0.490540i	−0.220344	−	0.141607i
$13$	−2.73851	−	1.75993i	−0.759525	−	0.488117i	0.102656	−	0.994717i	$-0.467266\pi$
$13$	−2.73851	−	1.75993i	−0.759525	−	0.488117i	−0.862181	+	0.506600i	$0.830902\pi$
$14$	−0.336366	+	2.33948i	−0.0898977	+	0.625252i
$15$	−0.594175	+	0.685714i	−0.153415	+	0.177051i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	−0.416255	−	2.89512i	−0.100957	−	0.702169i	−0.975944	−	0.218023i	$-0.930039\pi$
$17$	−0.416255	−	2.89512i	−0.100957	−	0.702169i	0.874987	−	0.484146i	$-0.160870\pi$
$18$	0.309784	−	2.15460i	0.0730168	−	0.507843i
$19$	5.60023	−	6.46301i	1.28478	−	1.48272i	0.495605	−	0.868548i	$-0.334947\pi$
$19$	5.60023	−	6.46301i	1.28478	−	1.48272i	0.789176	−	0.614167i	$-0.210508\pi$
$20$	−0.415415	+	0.909632i	−0.0928896	+	0.203400i
$21$	2.05764	−	0.604178i	0.449014	−	0.131842i
$22$	2.17148	+	4.75489i	0.462962	+	1.01375i
$23$	0.117812	−	0.257972i	0.0245655	−	0.0537909i	−0.896952	−	0.442129i	$-0.854223\pi$
$23$	0.117812	−	0.257972i	0.0245655	−	0.0537909i	0.921517	+	0.388338i	$0.126951\pi$
$24$	0.129127	+	0.898095i	0.0263578	+	0.183323i
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	0.463273	+	3.22214i	0.0908553	+	0.631913i
$27$	−4.50676	+	1.32330i	−0.867327	+	0.254670i
$28$	1.98833	−	1.27782i	0.375760	−	0.241486i
$29$	6.53412			1.21336			0.606678	−	0.794948i	$-0.292502\pi$
$29$	6.53412			1.21336			0.606678	+	0.794948i	$0.292502\pi$
$30$	0.907330			0.165655
$31$	−3.16630	+	2.03486i	−0.568685	+	0.365472i	−0.793165	−	0.609007i	$-0.791568\pi$
$31$	−3.16630	+	2.03486i	−0.568685	+	0.365472i	0.224480	+	0.974479i	$0.427932\pi$
$32$	0.415415	+	0.909632i	0.0734357	+	0.160802i
$33$	3.10591	−	3.58441i	0.540669	−	0.623966i
$34$	−1.91539	+	2.21048i	−0.328487	+	0.379095i
$35$	−0.981849	−	2.14995i	−0.165963	−	0.363408i
$36$	−1.83120	+	1.17684i	−0.305200	+	0.196140i
$37$	−0.927963			−0.152556			−0.0762781	−	0.997087i	$-0.524304\pi$
$37$	−0.927963			−0.152556			−0.0762781	+	0.997087i	$0.524304\pi$
$38$	−8.55178			−1.38728
$39$	2.48473	−	1.59684i	0.397875	−	0.255699i
$40$	0.959493	−	0.281733i	0.151709	−	0.0445458i
$41$	−0.611826	−	4.25534i	−0.0955512	−	0.664573i	−0.980155	−	0.198230i	$-0.936481\pi$
$41$	−0.611826	−	4.25534i	−0.0955512	−	0.664573i	0.884604	−	0.466342i	$-0.154429\pi$
$42$	−1.80408	−	1.15941i	−0.278375	−	0.178901i
$43$	−1.32137	−	9.19036i	−0.201508	−	1.40152i	−0.799813	−	0.600249i	$-0.795068\pi$
$43$	−1.32137	−	9.19036i	−0.201508	−	1.40152i	0.598305	−	0.801268i	$-0.295841\pi$
$44$	2.17148	−	4.75489i	0.327363	−	0.716826i
$45$	0.904255	+	1.98004i	0.134798	+	0.295167i
$46$	−0.272112	+	0.0798994i	−0.0401208	+	0.0117805i
$47$	2.15878	−	4.72706i	0.314890	−	0.689513i	−0.684323	−	0.729179i	$-0.739902\pi$
$47$	2.15878	−	4.72706i	0.314890	−	0.689513i	0.999213	+	0.0396662i	$0.0126295\pi$
$48$	0.594175	−	0.685714i	0.0857618	−	0.0989743i
$49$	0.201189	−	1.39930i	0.0287413	−	0.199900i
$50$	−0.142315	−	0.989821i	−0.0201264	−	0.139982i
$51$	2.54634	+	0.747673i	0.356559	+	0.104695i
$52$	2.13175	−	2.46017i	0.295620	−	0.341164i
$53$	1.33221	−	9.26570i	0.182993	−	1.27274i	−0.666645	−	0.745375i	$-0.732270\pi$
$53$	1.33221	−	9.26570i	0.182993	−	1.27274i	0.849638	−	0.527367i	$-0.176821\pi$
$54$	3.95139	+	2.53940i	0.537716	+	0.345569i
$55$	−4.39745	−	2.82607i	−0.592953	−	0.381067i
$56$	−2.26780	−	0.665885i	−0.303047	−	0.0889827i
$57$	3.22333	+	7.05810i	0.426940	+	0.934868i
$58$	−4.27894	−	4.93816i	−0.561852	−	0.648412i
$59$	−9.49195	+	6.10011i	−1.23575	+	0.794166i	−0.984776	−	0.173828i	$-0.944386\pi$
$59$	−9.49195	+	6.10011i	−1.23575	+	0.794166i	−0.250971	+	0.967995i	$0.580750\pi$
$60$	−0.594175	−	0.685714i	−0.0767077	−	0.0885253i
$61$	0.442600	−	0.129959i	0.0566691	−	0.0166395i	−0.253275	−	0.967394i	$-0.581508\pi$
$61$	0.442600	−	0.129959i	0.0566691	−	0.0166395i	0.309944	+	0.950755i	$0.399690\pi$
$62$	3.61133	+	1.06038i	0.458640	+	0.134669i
$63$	0.732186	−	5.09247i	0.0922468	−	0.641591i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−2.13175	−	2.46017i	−0.264411	−	0.305146i
$66$	−4.74285			−0.583805
$67$	−0.641349	−	8.16019i	−0.0783533	−	0.996926i
$67$	−0.641349	−	8.16019i	−0.0783533	−	0.996926i
$68$	2.92489			0.354695
$69$	0.168508	+	0.194469i	0.0202860	+	0.0234113i
$70$	−0.981849	+	2.14995i	−0.117353	+	0.256968i
$71$	−0.903983	+	6.28734i	−0.107283	+	0.746170i	0.863176	+	0.504903i	$0.168472\pi$
$71$	−0.903983	+	6.28734i	−0.107283	+	0.746170i	−0.970459	+	0.241266i	$0.922437\pi$
$72$	2.08858	+	0.613262i	0.246141	+	0.0722736i
$73$	−9.00798	+	2.64498i	−1.05430	+	0.309572i	−0.762555	−	0.646923i	$-0.776055\pi$
$73$	−9.00798	+	2.64498i	−1.05430	+	0.309572i	−0.291749	+	0.956495i	$0.594237\pi$
$74$	0.607686	+	0.701307i	0.0706421	+	0.0815253i
$75$	−0.763295	+	0.490540i	−0.0881377	+	0.0566426i
$76$	5.60023	+	6.46301i	0.642390	+	0.741358i
$77$	5.13238	+	11.2384i	0.584889	+	1.28073i
$78$	−2.83396	−	0.832126i	−0.320883	−	0.0942198i
$79$	−9.38615	−	6.03211i	−1.05602	−	0.678666i	−0.107125	−	0.994246i	$-0.534165\pi$
$79$	−9.38615	−	6.03211i	−1.05602	−	0.678666i	−0.948899	+	0.315580i	$0.897801\pi$
$80$	−0.841254	−	0.540641i	−0.0940550	−	0.0604455i
$81$	−0.322842	+	2.24541i	−0.0358713	+	0.249491i
$82$	−2.81531	+	3.24904i	−0.310899	+	0.358797i
$83$	1.17028	+	0.343626i	0.128455	+	0.0377179i	0.345328	−	0.938482i	$-0.387768\pi$
$83$	1.17028	+	0.343626i	0.128455	+	0.0377179i	−0.216873	+	0.976200i	$0.569586\pi$
$84$	0.305195	+	2.12268i	0.0332996	+	0.231603i
$85$	0.416255	−	2.89512i	0.0451492	−	0.314019i
$86$	−6.08030	+	7.01704i	−0.655655	+	0.756666i
$87$	−2.46283	+	5.39285i	−0.264043	+	0.578174i
$88$	−5.01552	+	1.47269i	−0.534656	+	0.156989i
$89$	6.64727	+	14.5555i	0.704609	+	1.54288i	0.834292	+	0.551323i	$0.185877\pi$
$89$	6.64727	+	14.5555i	0.704609	+	1.54288i	−0.129683	+	0.991555i	$0.541396\pi$
$90$	0.904255	−	1.98004i	0.0953169	−	0.208715i
$91$	1.09496	+	7.61564i	0.114783	+	0.798336i
$92$	0.238580	+	0.153326i	0.0248737	+	0.0159853i
$93$	−0.486005	−	3.38024i	−0.0503964	−	0.350515i
$94$	−4.98617	+	1.46407i	−0.514284	+	0.151008i
$95$	7.19422	−	4.62344i	0.738111	−	0.474355i
$96$	−0.907330			−0.0926040
$97$	−3.85643			−0.391561			−0.195780	−	0.980648i	$-0.562724\pi$
$97$	−3.85643			−0.391561			−0.195780	+	0.980648i	$0.562724\pi$
$98$	−1.18927	+	0.764299i	−0.120135	+	0.0772058i
$99$	−4.72678	−	10.3502i	−0.475059	−	1.04023i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	5.25826	−	6.06835i	0.523216	−	0.603824i	−0.431217	−	0.902248i	$-0.641916\pi$
$101$	5.25826	−	6.06835i	0.523216	−	0.603824i	0.954433	+	0.298425i	$0.0964612\pi$
$102$	−1.10244	−	2.41402i	−0.109158	−	0.239023i
$103$	5.73588	−	3.68623i	0.565173	−	0.363215i	−0.226639	−	0.973979i	$-0.572774\pi$
$103$	5.73588	−	3.68623i	0.565173	−	0.363215i	0.791813	+	0.610764i	$0.209138\pi$
$104$	−3.25527			−0.319205
$105$	2.14451			0.209283
$106$	−7.87496	+	5.06093i	−0.764884	+	0.491561i
$107$	7.61250	−	2.23523i	0.735928	−	0.216088i	0.107773	−	0.994176i	$-0.465628\pi$
$107$	7.61250	−	2.23523i	0.735928	−	0.216088i	0.628156	+	0.778087i	$0.283810\pi$
$108$	−0.668456	−	4.64921i	−0.0643222	−	0.447371i
$109$	6.71958	+	4.31841i	0.643619	+	0.413629i	0.821329	−	0.570454i	$-0.193233\pi$
$109$	6.71958	+	4.31841i	0.643619	+	0.413629i	−0.177711	+	0.984083i	$0.556869\pi$
$110$	0.743917	+	5.17406i	0.0709297	+	0.493327i
$111$	0.349766	−	0.765882i	0.0331984	−	0.0726943i
$112$	0.981849	+	2.14995i	0.0927760	+	0.203151i
$113$	−6.72425	+	1.97442i	−0.632564	+	0.185738i	−0.582268	−	0.812997i	$-0.697835\pi$
$113$	−6.72425	+	1.97442i	−0.632564	+	0.185738i	−0.0502961	+	0.998734i	$0.516017\pi$
$114$	3.22333	−	7.05810i	0.301892	−	0.661052i
$115$	0.185719	−	0.214331i	0.0173184	−	0.0199865i
$116$	−0.929903	+	6.46762i	−0.0863393	+	0.600503i
$117$	−1.00843	−	7.01379i	−0.0932294	−	0.648425i
$118$	10.8261	+	3.17882i	0.996620	+	0.292634i
$119$	−4.52710	+	5.22456i	−0.414999	+	0.478934i
$120$	−0.129127	+	0.898095i	−0.0117876	+	0.0819845i
$121$	13.7329	+	8.82557i	1.24844	+	0.802325i
$122$	−0.388058	−	0.249390i	−0.0351331	−	0.0225787i
$123$	3.74270	+	1.09896i	0.337468	+	0.0990895i
$124$	−1.56354	−	3.42367i	−0.140410	−	0.307454i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	−4.32811	+	2.78151i	−0.385579	+	0.247796i
$127$	−1.79768	−	2.07464i	−0.159518	−	0.184094i	0.670364	−	0.742032i	$-0.266138\pi$
$127$	−1.79768	−	2.07464i	−0.159518	−	0.184094i	−0.829882	+	0.557938i	$0.811593\pi$
$128$	−0.959493	+	0.281733i	−0.0848080	+	0.0249019i
$129$	8.08319	+	2.37344i	0.711685	+	0.208970i
$130$	−0.463273	+	3.22214i	−0.0406317	+	0.282600i
$131$	−4.02182	+	8.80655i	−0.351388	+	0.769432i	0.648578	+	0.761148i	$0.275364\pi$
$131$	−4.02182	+	8.80655i	−0.351388	+	0.769432i	−0.999966	+	0.00828348i	$0.997363\pi$
$132$	3.10591	+	3.58441i	0.270335	+	0.311983i
$133$	−20.2125			−1.75264
$134$	−5.74706	+	5.82849i	−0.496471	+	0.503505i
$135$	−4.69702			−0.404255
$136$	−1.91539	−	2.21048i	−0.164244	−	0.189547i
$137$	−5.22379	+	11.4385i	−0.446299	+	0.977258i	0.544100	+	0.839020i	$0.316871\pi$
$137$	−5.22379	+	11.4385i	−0.446299	+	0.977258i	−0.990399	+	0.138238i	$0.955856\pi$
$138$	0.0366203	−	0.254700i	0.00311733	−	0.0216815i
$139$	16.9853	+	4.98733i	1.44067	+	0.423020i	0.906446	−	0.422321i	$-0.138785\pi$
$139$	16.9853	+	4.98733i	1.44067	+	0.423020i	0.534227	+	0.845341i	$0.320603\pi$
$140$	2.26780	−	0.665885i	0.191664	−	0.0562776i
$141$	3.08773	+	3.56343i	0.260034	+	0.300095i
$142$	5.34364	−	3.43415i	0.448428	−	0.288187i
$143$	11.1432	+	12.8599i	0.931842	+	1.07540i
$144$	−0.904255	−	1.98004i	−0.0753546	−	0.165004i
$145$	6.26945	+	1.84088i	0.520649	+	0.152876i
$146$	7.89791	+	5.07568i	0.653636	+	0.420066i
$147$	1.07906	+	0.693471i	0.0889996	+	0.0571966i
$148$	0.132063	−	0.918517i	0.0108555	−	0.0755017i
$149$	−6.85492	+	7.91100i	−0.561577	+	0.648095i	−0.963541	−	0.267561i	$-0.913782\pi$
$149$	−6.85492	+	7.91100i	−0.561577	+	0.648095i	0.401964	+	0.915656i	$0.368328\pi$
$150$	0.870577	+	0.255624i	0.0710823	+	0.0208716i
$151$	−3.18170	−	22.1292i	−0.258923	−	1.80085i	−0.540534	−	0.841322i	$-0.681778\pi$
$151$	−3.18170	−	22.1292i	−0.258923	−	1.80085i	0.281611	−	0.959529i	$-0.409131\pi$
$152$	1.21705	−	8.46474i	0.0987155	−	0.686581i
$153$	4.16934	−	4.81167i	0.337071	−	0.389001i
$154$	5.13238	−	11.2384i	0.413579	−	0.905612i
$155$	−3.61133	+	1.06038i	−0.290069	+	0.0851720i
$156$	1.22697	+	2.68669i	0.0982363	+	0.215108i
$157$	−8.47797	+	18.5642i	−0.676615	+	1.48158i	0.189575	+	0.981866i	$0.439289\pi$
$157$	−8.47797	+	18.5642i	−0.676615	+	1.48158i	−0.866190	+	0.499715i	$0.833438\pi$
$158$	1.58785	+	11.0438i	0.126323	+	0.878595i
$159$	7.14519	+	4.59193i	0.566650	+	0.364164i
$160$	0.142315	+	0.989821i	0.0112510	+	0.0782523i
$161$	−0.643148	+	0.188845i	−0.0506872	+	0.0148831i
$162$	1.90839	−	1.22645i	0.149937	−	0.0963587i
$163$	10.6735			0.836014			0.418007	−	0.908444i	$-0.362729\pi$
$163$	10.6735			0.836014			0.418007	+	0.908444i	$0.362729\pi$
$164$	4.29910			0.335703
$165$	3.98994	−	2.56418i	0.310617	−	0.199621i
$166$	−0.506677	−	1.10947i	−0.0393258	−	0.0861115i
$167$	−9.33690	+	10.7754i	−0.722511	+	0.833822i	−0.991607	−	0.129291i	$-0.958730\pi$
$167$	−9.33690	+	10.7754i	−0.722511	+	0.833822i	0.269096	+	0.963113i	$0.413275\pi$
$168$	1.40435	−	1.62071i	0.108348	−	0.125041i
$169$	−0.998335	−	2.18605i	−0.0767950	−	0.168158i
$170$	−2.46057	+	1.58131i	−0.188717	+	0.121281i
$171$	18.6151			1.42353
$172$	9.28487			0.707965
$173$	8.01244	−	5.14928i	0.609174	−	0.391492i	−0.199373	−	0.979924i	$-0.563891\pi$
$173$	8.01244	−	5.14928i	0.609174	−	0.391492i	0.808547	+	0.588431i	$0.200254\pi$
$174$	5.68846	−	1.67028i	0.431241	−	0.126624i
$175$	−0.336366	−	2.33948i	−0.0254269	−	0.176848i
$176$	4.39745	+	2.82607i	0.331471	+	0.213023i
$177$	−1.45695	−	10.1333i	−0.109511	−	0.761666i
$178$	6.64727	−	14.5555i	0.498234	−	1.09098i
$179$	5.21820	+	11.4263i	0.390027	+	0.854040i	0.998185	+	0.0602236i	$0.0191814\pi$
$179$	5.21820	+	11.4263i	0.390027	+	0.854040i	−0.608158	+	0.793816i	$0.708091\pi$
$180$	−2.08858	+	0.613262i	−0.155673	+	0.0457098i
$181$	7.13418	−	15.6217i	0.530280	−	1.16115i	−0.435119	−	0.900373i	$-0.643294\pi$
$181$	7.13418	−	15.6217i	0.530280	−	1.16115i	0.965399	−	0.260777i	$-0.0839789\pi$
$182$	5.03847	−	5.81470i	0.373476	−	0.431014i
$183$	−0.0595641	+	0.414278i	−0.00440311	+	0.0306243i
$184$	−0.0403605	−	0.280714i	−0.00297542	−	0.0206945i
$185$	−0.890374	−	0.261437i	−0.0654616	−	0.0192213i
$186$	−2.23635	+	2.58089i	−0.163977	+	0.189240i
$187$	−2.17587	+	15.1335i	−0.159116	+	1.10667i
$188$	4.37172	+	2.80953i	0.318840	+	0.204906i
$189$	9.33925	+	6.00197i	0.679331	+	0.436579i
$190$	−8.20538	−	2.40932i	−0.595281	−	0.174790i
$191$	3.49281	+	7.64820i	0.252731	+	0.553404i	0.992891	−	0.119027i	$-0.0379775\pi$
$191$	3.49281	+	7.64820i	0.252731	+	0.553404i	−0.740160	+	0.672431i	$0.765250\pi$
$192$	0.594175	+	0.685714i	0.0428809	+	0.0494872i
$193$	−1.43703	+	0.923526i	−0.103440	+	0.0664769i	−0.591338	−	0.806424i	$-0.701400\pi$
$193$	−1.43703	+	0.923526i	−0.103440	+	0.0664769i	0.487898	+	0.872901i	$0.337764\pi$
$194$	2.52542	+	2.91449i	0.181315	+	0.209248i
$195$	2.83396	−	0.832126i	0.202944	−	0.0595898i
$196$	1.35643	+	0.398283i	0.0968876	+	0.0284488i
$197$	0.218506	−	1.51974i	0.0155679	−	0.108277i	−0.980556	−	0.196240i	$-0.937127\pi$
$197$	0.218506	−	1.51974i	0.0155679	−	0.108277i	0.996124	+	0.0879633i	$0.0280358\pi$
$198$	−4.72678	+	10.3502i	−0.335918	+	0.735557i
$199$	−3.68354	−	4.25104i	−0.261119	−	0.301348i	0.610018	−	0.792388i	$-0.291162\pi$
$199$	−3.68354	−	4.25104i	−0.261119	−	0.301348i	−0.871137	+	0.491040i	$0.836617\pi$
$200$	1.00000			0.0707107
$201$	6.97664	+	2.54640i	0.492094	+	0.179609i
$202$	−8.02958			−0.564959
$203$	−10.1134	−	11.6715i	−0.709824	−	0.819181i
$204$	−1.10244	+	2.41402i	−0.0771865	+	0.169015i
$205$	0.611826	−	4.25534i	0.0427318	−	0.297206i
$206$	−6.54207	−	1.92093i	−0.455808	−	0.133837i
$207$	0.592321	−	0.173921i	0.0411692	−	0.0120884i
$208$	2.13175	+	2.46017i	0.147810	+	0.170582i
$209$	−37.6061	+	24.1680i	−2.60127	+	1.67173i
$210$	−1.40435	−	1.62071i	−0.0969097	−	0.111840i
$211$	0.378385	+	0.828548i	0.0260491	+	0.0570396i	0.922209	−	0.386691i	$-0.126382\pi$
$211$	0.378385	+	0.828548i	0.0260491	+	0.0570396i	−0.896160	+	0.443731i	$0.853655\pi$
$212$	8.98180	+	2.63729i	0.616872	+	0.181130i
$213$	−4.84844	−	3.11590i	−0.332210	−	0.213498i
$214$	−6.67441	−	4.28938i	−0.456253	−	0.293216i
$215$	1.32137	−	9.19036i	0.0901170	−	0.626778i
$216$	−3.07590	+	3.54977i	−0.209288	+	0.241531i
$217$	8.53552	+	2.50625i	0.579429	+	0.170136i
$218$	−1.13675	−	7.90627i	−0.0769905	−	0.535480i
$219$	1.21227	−	8.43155i	0.0819179	−	0.569752i
$220$	3.42313	−	3.95050i	0.230787	−	0.266343i
$221$	−3.95529	+	8.66087i	−0.266062	+	0.582593i
$222$	−0.807863	+	0.237210i	−0.0542202	+	0.0159205i
$223$	−11.1181	−	24.3452i	−0.744522	−	1.63028i	−0.775970	−	0.630770i	$-0.782739\pi$
$223$	−11.1181	−	24.3452i	−0.744522	−	1.63028i	0.0314475	−	0.999505i	$-0.489988\pi$
$224$	0.981849	−	2.14995i	0.0656025	−	0.143650i
$225$	0.309784	+	2.15460i	0.0206523	+	0.143640i
$226$	5.89561	+	3.78888i	0.392170	+	0.252033i
$227$	1.06545	+	7.41038i	0.0707166	+	0.491844i	0.994143	+	0.108070i	$0.0344670\pi$
$227$	1.06545	+	7.41038i	0.0707166	+	0.491844i	−0.923427	+	0.383775i	$0.874624\pi$
$228$	−7.44499	+	2.18605i	−0.493056	+	0.144774i
$229$	14.2303	−	9.14524i	0.940363	−	0.604334i	0.0218651	−	0.999761i	$-0.493040\pi$
$229$	14.2303	−	9.14524i	0.940363	−	0.604334i	0.918498	+	0.395426i	$0.129403\pi$
$230$	−0.283600			−0.0187000
$231$	−11.2099			−0.737558
$232$	5.49685	−	3.53261i	0.360886	−	0.231927i
$233$	2.38122	+	5.21414i	0.155999	+	0.341590i	0.971453	−	0.237232i	$-0.0762401\pi$
$233$	2.38122	+	5.21414i	0.155999	+	0.341590i	−0.815454	+	0.578821i	$0.803513\pi$
$234$	−4.64029	+	5.35518i	−0.303345	+	0.350079i
$235$	3.40310	−	3.92738i	0.221994	−	0.256194i
$236$	−4.68717	−	10.2635i	−0.305109	−	0.668095i
$237$	8.51634	−	5.47312i	0.553196	−	0.355517i
$238$	6.91308			0.448108
$239$	−24.8603			−1.60808			−0.804038	−	0.594578i	$-0.797319\pi$
$239$	−24.8603			−1.60808			−0.804038	+	0.594578i	$0.797319\pi$
$240$	0.763295	−	0.490540i	0.0492705	−	0.0316642i
$241$	−23.1196	+	6.78851i	−1.48926	+	0.437287i	−0.922306	−	0.386461i	$-0.873697\pi$
$241$	−23.1196	+	6.78851i	−1.48926	+	0.437287i	−0.566956	+	0.823748i	$0.691879\pi$
$242$	−2.32319	−	16.1581i	−0.149340	−	1.03868i
$243$	−13.5857	−	8.73100i	−0.871523	−	0.560094i
$244$	0.0656477	+	0.456590i	0.00420266	+	0.0292302i
$245$	0.587268	−	1.28594i	0.0375192	−	0.0821556i
$246$	−1.62041	−	3.54821i	−0.103314	−	0.226225i
$247$	−26.7107	+	7.84297i	−1.69956	+	0.499036i
$248$	−1.56354	+	3.42367i	−0.0992846	+	0.217403i
$249$	−0.724709	+	0.836359i	−0.0459266	+	0.0530021i
$250$	0.142315	−	0.989821i	0.00900078	−	0.0626018i
$251$	1.11585	+	7.76093i	0.0704320	+	0.489865i	0.994254	+	0.107044i	$0.0341385\pi$
$251$	1.11585	+	7.76093i	0.0704320	+	0.489865i	−0.923822	+	0.382822i	$0.874952\pi$
$252$	4.93643	+	1.44947i	0.310966	+	0.0913079i
$253$	−0.970800	+	1.12036i	−0.0610337	+	0.0704366i
$254$	−0.390674	+	2.71720i	−0.0245130	+	0.170492i
$255$	2.23255	+	1.43477i	0.139808	+	0.0898490i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	8.98817	+	2.63917i	0.560667	+	0.164627i	0.549773	−	0.835314i	$-0.314714\pi$
$257$	8.98817	+	2.63917i	0.560667	+	0.164627i	0.0108937	+	0.999941i	$0.496532\pi$
$258$	−3.49964	−	7.66314i	−0.217878	−	0.477086i
$259$	1.43629	+	1.65757i	0.0892467	+	0.102996i
$260$	2.73851	−	1.75993i	0.169835	−	0.109146i
$261$	9.31419	+	10.7492i	0.576534	+	0.665356i
$262$	9.28927	−	2.72758i	0.573893	−	0.168510i
$263$	16.2081	+	4.75914i	0.999437	+	0.293461i	0.740225	−	0.672359i	$-0.234719\pi$
$263$	16.2081	+	4.75914i	0.999437	+	0.293461i	0.259212	+	0.965820i	$0.416537\pi$
$264$	0.674978	−	4.69458i	0.0415421	−	0.288931i
$265$	3.88869	−	8.51505i	0.238881	−	0.523075i
$266$	13.2363	+	15.2756i	0.811573	+	0.936605i
$267$	−14.5187			−0.888527
$268$	8.16840	+	0.526494i	0.498965	+	0.0321608i
$269$	3.51033			0.214029			0.107014	−	0.994257i	$-0.465871\pi$
$269$	3.51033			0.214029			0.107014	+	0.994257i	$0.465871\pi$
$270$	3.07590	+	3.54977i	0.187193	+	0.216032i
$271$	7.98330	−	17.4810i	0.484951	−	1.06189i	−0.496121	−	0.868253i	$-0.665243\pi$
$271$	7.98330	−	17.4810i	0.484951	−	1.06189i	0.981072	−	0.193641i	$-0.0620298\pi$
$272$	−0.416255	+	2.89512i	−0.0252392	+	0.175542i
$273$	−6.69818	−	1.96676i	−0.405392	−	0.119034i
$274$	12.0655	−	3.54275i	0.728904	−	0.214026i
$275$	−3.42313	−	3.95050i	−0.206422	−	0.238224i
$276$	−0.216471	+	0.139117i	−0.0130300	+	0.00837387i
$277$	8.97215	+	10.3544i	0.539084	+	0.622136i	0.958305	−	0.285748i	$-0.0922421\pi$
$277$	8.97215	+	10.3544i	0.539084	+	0.622136i	−0.419221	+	0.907884i	$0.637697\pi$
$278$	−7.35382	−	16.1026i	−0.441053	−	0.965772i
$279$	−7.86097	−	2.30819i	−0.470624	−	0.138188i
$280$	−1.98833	−	1.27782i	−0.118826	−	0.0763646i
$281$	19.2956	+	12.4005i	1.15108	+	0.739752i	0.969853	−	0.243690i	$-0.0783580\pi$
$281$	19.2956	+	12.4005i	1.15108	+	0.739752i	0.181223	+	0.983442i	$0.441994\pi$
$282$	0.671029	−	4.66711i	0.0399592	−	0.277922i
$283$	8.14251	−	9.39696i	0.484022	−	0.558591i	−0.460236	−	0.887796i	$-0.652235\pi$
$283$	8.14251	−	9.39696i	0.484022	−	0.558591i	0.944258	+	0.329205i	$0.106781\pi$
$284$	−6.09469	−	1.78956i	−0.361653	−	0.106191i
$285$	1.10426	+	7.68031i	0.0654109	+	0.454943i
$286$	2.42165	−	16.8429i	0.143195	−	0.995944i
$287$	−6.65410	+	7.67924i	−0.392779	+	0.453291i
$288$	−0.904255	+	1.98004i	−0.0532838	+	0.116675i
$289$	8.10295	−	2.37924i	0.476644	−	0.139955i
$290$	−2.71437	−	5.94365i	−0.159393	−	0.349023i
$291$	1.45356	−	3.18285i	0.0852091	−	0.186582i
$292$	−1.33609	−	9.29271i	−0.0781887	−	0.543815i
$293$	−7.78867	−	5.00548i	−0.455019	−	0.292423i	0.292985	−	0.956117i	$-0.405351\pi$
$293$	−7.78867	−	5.00548i	−0.455019	−	0.292423i	−0.748004	+	0.663694i	$0.768988\pi$
$294$	−0.182545	−	1.26963i	−0.0106462	−	0.0740462i
$295$	−10.8261	+	3.17882i	−0.630318	+	0.185078i
$296$	−0.780652	+	0.501695i	−0.0453745	+	0.0291604i
$297$	24.5526			1.42468
$298$	10.4678			0.606381
$299$	−0.776641	+	0.499117i	−0.0449143	+	0.0288647i
$300$	−0.376919	−	0.825337i	−0.0217614	−	0.0476508i
$301$	−14.3710	+	16.5850i	−0.828331	+	0.955945i
$302$	−14.6406	+	16.8961i	−0.842471	+	0.972263i
$303$	3.02650	+	6.62711i	0.173868	+	0.380717i
$304$	−7.19422	+	4.62344i	−0.412617	+	0.265173i
$305$	0.461285			0.0264131
$306$	−6.36675			−0.363963
$307$	−16.3053	+	10.4788i	−0.930592	+	0.598055i	−0.915713	−	0.401834i	$-0.868373\pi$
$307$	−16.3053	+	10.4788i	−0.930592	+	0.598055i	−0.0148797	+	0.999889i	$0.504737\pi$
$308$	−11.8544	+	3.48076i	−0.675466	+	0.198335i
$309$	0.880418	+	6.12344i	0.0500852	+	0.348350i
$310$	3.16630	+	2.03486i	0.179834	+	0.115572i
$311$	−1.63694	−	11.3852i	−0.0928226	−	0.645595i	−0.982119	−	0.188263i	$-0.939714\pi$
$311$	−1.63694	−	11.3852i	−0.0928226	−	0.645595i	0.889296	−	0.457332i	$-0.151195\pi$
$312$	1.22697	−	2.68669i	0.0694636	−	0.152104i
$313$	10.5044	+	23.0015i	0.593746	+	1.30012i	0.933152	+	0.359482i	$0.117047\pi$
$313$	10.5044	+	23.0015i	0.593746	+	1.30012i	−0.339406	+	0.940640i	$0.610226\pi$
$314$	19.5817	−	5.74972i	1.10506	−	0.324475i
$315$	2.13724	−	4.67991i	0.120420	−	0.263683i
$316$	7.30650	−	8.43215i	0.411023	−	0.474346i
$317$	0.743780	−	5.17310i	0.0417748	−	0.290550i	−0.958215	−	0.286049i	$-0.907658\pi$
$317$	0.743780	−	5.17310i	0.0417748	−	0.290550i	0.999990	−	0.00450153i	$-0.00143289\pi$
$318$	−1.20875	−	8.40705i	−0.0677834	−	0.471444i
$319$	−32.7720	−	9.62274i	−1.83488	−	0.538770i
$320$	0.654861	−	0.755750i	0.0366078	−	0.0422477i
$321$	−1.02447	+	7.12538i	−0.0571806	+	0.397700i
$322$	0.563892	+	0.362392i	0.0314245	+	0.0201953i
$323$	−21.0423	−	13.5231i	−1.17082	−	0.752443i
$324$	−2.17661	−	0.639112i	−0.120923	−	0.0355062i
$325$	−1.35229	−	2.96110i	−0.0750114	−	0.164252i
$326$	−6.98966	−	8.06650i	−0.387121	−	0.446762i
$327$	−6.09688	+	3.91822i	−0.337158	+	0.216678i
$328$	−2.81531	−	3.24904i	−0.155450	−	0.179398i
$329$	−11.7850	+	3.46039i	−0.649728	+	0.190777i
$330$	−4.55073	−	1.33622i	−0.250510	−	0.0735563i
$331$	−3.02671	+	21.0512i	−0.166363	+	1.15708i	0.719961	+	0.694015i	$0.244160\pi$
$331$	−3.02671	+	21.0512i	−0.166363	+	1.15708i	−0.886324	+	0.463066i	$0.846749\pi$
$332$	−0.506677	+	1.10947i	−0.0278075	+	0.0608900i
$333$	−1.32278	−	1.52657i	−0.0724880	−	0.0836556i
$334$	14.2578			0.780154
$335$	1.68362	−	8.01033i	0.0919860	−	0.437651i
$336$	−2.14451			−0.116993
$337$	−12.6423	−	14.5900i	−0.688670	−	0.794767i	0.298505	−	0.954408i	$-0.403512\pi$
$337$	−12.6423	−	14.5900i	−0.688670	−	0.794767i	−0.987175	+	0.159641i	$0.948966\pi$
$338$	−0.998335	+	2.18605i	−0.0543023	+	0.118905i
$339$	0.904936	−	6.29397i	0.0491494	−	0.341841i
$340$	2.80641	+	0.824036i	0.152199	+	0.0446896i
$341$	18.8774	−	5.54290i	1.02227	−	0.300165i
$342$	−12.1903	−	14.0684i	−0.659176	−	0.760730i
$343$	−16.7292	+	10.7512i	−0.903293	+	0.580511i
$344$	−6.08030	−	7.01704i	−0.327828	−	0.378333i
$345$	0.106894	+	0.234066i	0.00575499	+	0.0126017i
$346$	−9.13860	−	2.68333i	−0.491294	−	0.144257i
$347$	13.2261	+	8.49990i	0.710014	+	0.456298i	0.845150	−	0.534529i	$-0.179511\pi$
$347$	13.2261	+	8.49990i	0.710014	+	0.456298i	−0.135136	+	0.990827i	$0.543147\pi$
$348$	−4.98746	−	3.20525i	−0.267356	−	0.171819i
$349$	2.71317	−	18.8705i	0.145233	−	1.01011i	−0.778656	−	0.627452i	$-0.784098\pi$
$349$	2.71317	−	18.8705i	0.145233	−	1.01011i	0.923888	−	0.382663i	$-0.124993\pi$
$350$	−1.54779	+	1.78624i	−0.0827327	+	0.0954787i
$351$	14.6707	+	4.30771i	0.783065	+	0.229929i
$352$	−0.743917	−	5.17406i	−0.0396509	−	0.275778i
$353$	3.23028	−	22.4671i	0.171930	−	1.19580i	−0.702870	−	0.711318i	$-0.748099\pi$
$353$	3.23028	−	22.4671i	0.171930	−	1.19580i	0.874800	−	0.484483i	$-0.160992\pi$
$354$	−6.70414	+	7.73699i	−0.356321	+	0.411216i
$355$	−2.63871	+	5.77798i	−0.140048	+	0.306663i
$356$	−15.3533	+	4.50815i	−0.813725	+	0.238931i
$357$	−2.60567	−	5.70562i	−0.137907	−	0.301973i
$358$	5.21820	−	11.4263i	0.275791	−	0.603897i
$359$	−1.02716	−	7.14402i	−0.0542112	−	0.377047i	−0.998808	−	0.0488139i	$-0.984456\pi$
$359$	−1.02716	−	7.14402i	−0.0542112	−	0.377047i	0.944597	−	0.328233i	$-0.106453\pi$
$360$	1.83120	+	1.17684i	0.0965127	+	0.0620250i
$361$	−7.70393	−	53.5820i	−0.405470	−	2.82011i
$362$	−16.4780	+	4.83837i	−0.866063	+	0.254299i
$363$	−12.4602	+	8.00771i	−0.653993	+	0.420296i
$364$	−7.69395			−0.403273
$365$	−9.38827			−0.491404
$366$	0.352096	−	0.226279i	0.0184044	−	0.0118278i
$367$	5.83999	+	12.7878i	0.304845	+	0.667518i	0.998611	−	0.0526825i	$-0.0167771\pi$
$367$	5.83999	+	12.7878i	0.304845	+	0.667518i	−0.693766	+	0.720200i	$0.744050\pi$
$368$	−0.185719	+	0.214331i	−0.00968126	+	0.0111728i
$369$	6.12824	−	7.07236i	0.319023	−	0.368172i
$370$	0.385490	+	0.844105i	0.0200407	+	0.0438829i
$371$	−18.6128	+	11.9617i	−0.966327	+	0.621020i
$372$	3.41500			0.177060
$373$	27.8324			1.44111			0.720553	−	0.693400i	$-0.243888\pi$
$373$	27.8324			1.44111			0.720553	+	0.693400i	$0.243888\pi$
$374$	12.8621	−	8.26594i	0.665081	−	0.427422i
$375$	−0.870577	+	0.255624i	−0.0449564	+	0.0132004i
$376$	−0.739564	−	5.14378i	−0.0381401	−	0.265270i
$377$	−17.8937	−	11.4996i	−0.921575	−	0.592260i
$378$	−1.57992	−	10.9886i	−0.0812624	−	0.565192i
$379$	−3.35658	+	7.34989i	−0.172416	+	0.377539i	−0.976038	−	0.217602i	$-0.930176\pi$
$379$	−3.35658	+	7.34989i	−0.172416	+	0.377539i	0.803621	+	0.595141i	$0.202904\pi$
$380$	3.55254	+	7.77898i	0.182241	+	0.399053i
$381$	2.38985	−	0.701724i	0.122436	−	0.0359504i
$382$	3.49281	−	7.64820i	0.178708	−	0.391316i
$383$	−13.5603	+	15.6494i	−0.692898	+	0.799647i	−0.987775	−	0.155888i	$-0.950176\pi$
$383$	−13.5603	+	15.6494i	−0.692898	+	0.799647i	0.294876	+	0.955535i	$0.404722\pi$
$384$	0.129127	−	0.898095i	0.00658946	−	0.0458307i
$385$	1.75828	+	12.2291i	0.0896100	+	0.623252i
$386$	1.63901	+	0.481257i	0.0834235	+	0.0244954i
$387$	13.2353	−	15.2743i	0.672788	−	0.776439i
$388$	0.548827	−	3.81717i	0.0278625	−	0.193788i
$389$	−4.84070	−	3.11093i	−0.245433	−	0.157730i	0.412141	−	0.911120i	$-0.364781\pi$
$389$	−4.84070	−	3.11093i	−0.245433	−	0.157730i	−0.657574	+	0.753390i	$0.728417\pi$
$390$	−2.48473	−	1.59684i	−0.125819	−	0.0808591i
$391$	−0.795898	−	0.233697i	−0.0402503	−	0.0118186i
$392$	−0.587268	−	1.28594i	−0.0296615	−	0.0649497i
$393$	−5.75247	−	6.63870i	−0.290174	−	0.334878i
$394$	−1.29163	+	0.830083i	−0.0650716	+	0.0418190i
$395$	−7.30650	−	8.43215i	−0.367630	−	0.424268i
$396$	10.9175	−	3.20568i	0.548627	−	0.161092i
$397$	−25.0137	−	7.34469i	−1.25540	−	0.368620i	−0.414621	−	0.909994i	$-0.636086\pi$
$397$	−25.0137	−	7.34469i	−1.25540	−	0.368620i	−0.840782	+	0.541374i	$0.817904\pi$
$398$	−0.800510	+	5.56767i	−0.0401260	+	0.279082i
$399$	7.61845	−	16.6821i	0.381400	−	0.835149i
$400$	−0.654861	−	0.755750i	−0.0327430	−	0.0377875i
$401$	−3.21953			−0.160776			−0.0803878	−	0.996764i	$-0.525616\pi$
$401$	−3.21953			−0.160776			−0.0803878	+	0.996764i	$0.525616\pi$
$402$	−2.64429	−	6.94013i	−0.131885	−	0.346142i
$403$	12.2522			0.610323
$404$	5.25826	+	6.06835i	0.261608	+	0.301912i
$405$	−0.942371	+	2.06350i	−0.0468268	+	0.102536i
$406$	−2.19786	+	15.2865i	−0.109078	+	0.758654i
$407$	4.65422	+	1.36660i	0.230701	+	0.0677399i
$408$	2.54634	−	0.747673i	0.126063	−	0.0370153i
$409$	−19.5572	−	22.5702i	−0.967041	−	1.11602i	−0.993206	−	0.116367i	$-0.962875\pi$
$409$	−19.5572	−	22.5702i	−0.967041	−	1.11602i	0.0261652	−	0.999658i	$-0.491670\pi$
$410$	−3.61663	+	2.32427i	−0.178613	+	0.114787i
$411$	−7.47168	−	8.62278i	−0.368551	−	0.425330i
$412$	2.83241	+	6.20210i	0.139543	+	0.305556i
$413$	25.5878	+	7.51326i	1.25909	+	0.369703i
$414$	−0.519329	−	0.333752i	−0.0255236	−	0.0164030i
$415$	1.02607	+	0.659414i	0.0503677	+	0.0323694i
$416$	0.463273	−	3.22214i	0.0227138	−	0.157978i
$417$	−10.5183	+	12.1388i	−0.515083	+	0.594438i
$418$	42.8917	+	12.5941i	2.09790	+	0.615999i
$419$	−1.28330	−	8.92558i	−0.0626935	−	0.436043i	−0.996859	−	0.0792018i	$-0.974763\pi$
$419$	−1.28330	−	8.92558i	−0.0626935	−	0.436043i	0.934165	−	0.356841i	$-0.116146\pi$
$420$	−0.305195	+	2.12268i	−0.0148920	+	0.103576i
$421$	9.35305	−	10.7940i	0.455840	−	0.526067i	−0.480579	−	0.876951i	$-0.659573\pi$
$421$	9.35305	−	10.7940i	0.455840	−	0.526067i	0.936419	+	0.350884i	$0.114119\pi$
$422$	0.378385	−	0.828548i	0.0184195	−	0.0403331i
$423$	10.8537	−	3.18692i	0.527723	−	0.154953i
$424$	−3.88869	−	8.51505i	−0.188852	−	0.413527i
$425$	1.21504	−	2.66057i	0.0589382	−	0.129057i
$426$	0.820211	+	5.70469i	0.0397393	+	0.276393i
$427$	−0.917189	−	0.589441i	−0.0443859	−	0.0285251i
$428$	1.12911	+	7.85313i	0.0545775	+	0.379595i
$429$	−14.8139	+	4.34974i	−0.715220	+	0.210008i
$430$	−7.81093	+	5.01978i	−0.376676	+	0.242075i
$431$	34.7736			1.67499			0.837493	−	0.546449i	$-0.184021\pi$
$431$	34.7736			1.67499			0.837493	+	0.546449i	$0.184021\pi$
$432$	4.69702			0.225986
$433$	6.15898	−	3.95813i	0.295981	−	0.190216i	−0.384219	−	0.923242i	$-0.625529\pi$
$433$	6.15898	−	3.95813i	0.295981	−	0.190216i	0.680200	+	0.733026i	$0.261893\pi$
$434$	−3.69548	−	8.09196i	−0.177388	−	0.388427i
$435$	−3.88241	+	4.48054i	−0.186147	+	0.214826i
$436$	−5.23075	+	6.03661i	−0.250508	+	0.289101i
$437$	−1.00750	−	2.20612i	−0.0481953	−	0.105533i
$438$	−7.16601	+	4.60532i	−0.342405	+	0.220051i
$439$	−18.6184			−0.888607			−0.444304	−	0.895876i	$-0.646549\pi$
$439$	−18.6184			−0.888607			−0.444304	+	0.895876i	$0.646549\pi$
$440$	−5.22726			−0.249200
$441$	2.58875	−	1.66369i	0.123274	−	0.0792233i
$442$	9.13561	−	2.68246i	0.434537	−	0.127592i
$443$	4.25799	+	29.6149i	0.202303	+	1.40705i	0.797427	+	0.603415i	$0.206194\pi$
$443$	4.25799	+	29.6149i	0.202303	+	1.40705i	−0.595124	+	0.803634i	$0.702897\pi$
$444$	0.708309	+	0.455203i	0.0336149	+	0.0216030i
$445$	2.27725	+	15.8386i	0.107952	+	0.750823i
$446$	−11.1181	+	24.3452i	−0.526457	+	1.15278i
$447$	−3.94549	−	8.63942i	−0.186615	−	0.408631i
$448$	−2.26780	+	0.665885i	−0.107143	+	0.0314601i
$449$	11.9993	−	26.2749i	0.566284	−	1.23999i	−0.382469	−	0.923968i	$-0.624926\pi$
$449$	11.9993	−	26.2749i	0.566284	−	1.23999i	0.948753	−	0.316020i	$-0.102347\pi$
$450$	1.42547	−	1.64508i	0.0671973	−	0.0775498i
$451$	−3.19817	+	22.2438i	−0.150596	+	1.04742i
$452$	−0.997361	−	6.93680i	−0.0469119	−	0.326280i
$453$	19.4633	+	5.71494i	0.914466	+	0.268511i
$454$	4.90267	−	5.65798i	0.230094	−	0.265542i
$455$	−1.09496	+	7.61564i	−0.0513327	+	0.357027i
$456$	6.52753	+	4.19499i	0.305680	+	0.196448i
$457$	16.2784	+	10.4615i	0.761474	+	0.489369i	0.862838	−	0.505480i	$-0.168685\pi$
$457$	16.2784	+	10.4615i	0.761474	+	0.489369i	−0.101365	+	0.994849i	$0.532321\pi$
$458$	−16.2304	−	4.76566i	−0.758395	−	0.222685i
$459$	5.70708	+	12.4968i	0.266384	+	0.583299i
$460$	0.185719	+	0.214331i	0.00865918	+	0.00999323i
$461$	10.4292	−	6.70246i	0.485738	−	0.312165i	−0.274751	−	0.961515i	$-0.588596\pi$
$461$	10.4292	−	6.70246i	0.485738	−	0.312165i	0.760489	+	0.649351i	$0.224959\pi$
$462$	7.34093	+	8.47189i	0.341531	+	0.394148i
$463$	38.2734	−	11.2381i	1.77871	−	0.522278i	0.783623	−	0.621237i	$-0.213370\pi$
$463$	38.2734	−	11.2381i	1.77871	−	0.522278i	0.995091	+	0.0989594i	$0.0315514\pi$
$464$	−6.26945	−	1.84088i	−0.291052	−	0.0854605i
$465$	0.486005	−	3.38024i	0.0225380	−	0.156755i
$466$	2.38122	−	5.21414i	0.110308	−	0.241540i
$467$	−4.29019	−	4.95114i	−0.198526	−	0.229111i	0.647754	−	0.761850i	$-0.275708\pi$
$467$	−4.29019	−	4.95114i	−0.198526	−	0.229111i	−0.846280	+	0.532738i	$0.821163\pi$
$468$	7.08591			0.327546
$469$	−13.5834	+	13.7758i	−0.627223	+	0.636109i
$470$	−5.19667			−0.239705
$471$	−12.1262	−	13.9944i	−0.558745	−	0.644826i
$472$	−4.68717	+	10.2635i	−0.215745	+	0.472415i
$473$	−6.90717	+	48.0404i	−0.317592	+	2.20890i
$474$	−9.71332	−	2.85209i	−0.446148	−	0.131001i
$475$	8.20538	−	2.40932i	0.376489	−	0.110547i
$476$	−4.52710	−	5.22456i	−0.207499	−	0.239467i
$477$	17.1418	−	11.0164i	0.784871	−	0.504406i
$478$	16.2800	+	18.7881i	0.744630	+	0.859349i
$479$	−6.87675	−	15.0580i	−0.314207	−	0.688017i	0.684971	−	0.728571i	$-0.259815\pi$
$479$	−6.87675	−	15.0580i	−0.314207	−	0.688017i	−0.999177	+	0.0405540i	$0.987088\pi$
$480$	−0.870577	−	0.255624i	−0.0397362	−	0.0116676i
$481$	2.54123	+	1.63315i	0.115870	+	0.0744653i
$482$	20.2705	+	13.0271i	0.923296	+	0.593366i
$483$	0.0865535	−	0.601993i	0.00393832	−	0.0273916i
$484$	−10.6901	+	12.3371i	−0.485915	+	0.560776i
$485$	−3.70021	−	1.08648i	−0.168018	−	0.0493346i
$486$	2.29829	+	15.9850i	0.104253	+	0.725093i
$487$	3.11017	−	21.6317i	0.140935	−	0.980226i	−0.789495	−	0.613757i	$-0.789658\pi$
$487$	3.11017	−	21.6317i	0.140935	−	0.980226i	0.930430	−	0.366469i	$-0.119433\pi$
$488$	0.302077	−	0.348616i	0.0136744	−	0.0157811i
$489$	−4.02304	+	8.80924i	−0.181928	+	0.398367i
$490$	−1.35643	+	0.398283i	−0.0612771	+	0.0179926i
$491$	−15.9199	−	34.8597i	−0.718456	−	1.57320i	−0.816056	−	0.577973i	$-0.803844\pi$
$491$	−15.9199	−	34.8597i	−0.718456	−	1.57320i	0.0976005	−	0.995226i	$-0.468883\pi$
$492$	−1.62041	+	3.54821i	−0.0730538	+	0.159965i
$493$	−2.71986	−	18.9170i	−0.122496	−	0.851981i
$494$	23.4191	+	15.0506i	1.05368	+	0.677156i
$495$	−1.61932	−	11.2626i	−0.0727832	−	0.506218i
$496$	3.61133	−	1.06038i	0.162154	−	0.0476126i
$497$	12.6299	−	8.11673i	0.566528	−	0.364085i
$498$	1.10666			0.0495907
$499$	34.9762			1.56575			0.782875	−	0.622180i	$-0.213753\pi$
$499$	34.9762			1.56575			0.782875	+	0.622180i	$0.213753\pi$
$500$	−0.841254	+	0.540641i	−0.0376220	+	0.0241782i
$501$	−5.37405	−	11.7675i	−0.240095	−	0.525734i
$502$	5.13459	−	5.92563i	0.229168	−	0.264474i
$503$	−20.9312	+	24.1559i	−0.933277	+	1.07706i	0.0635910	+	0.997976i	$0.479745\pi$
$503$	−20.9312	+	24.1559i	−0.933277	+	1.07706i	−0.996868	+	0.0790830i	$0.974801\pi$
$504$	−2.13724	−	4.67991i	−0.0952003	−	0.208460i
$505$	6.75491	−	4.34112i	0.300590	−	0.193177i
$506$	1.48245			0.0659031
$507$	2.18052			0.0968401
$508$	2.30936	−	1.48413i	0.102461	−	0.0658477i
$509$	26.6290	−	7.81898i	1.18031	−	0.346570i	0.368016	−	0.929819i	$-0.380037\pi$
$509$	26.6290	−	7.81898i	1.18031	−	0.346570i	0.812293	+	0.583249i	$0.198219\pi$
$510$	−0.377681	−	2.62683i	−0.0167240	−	0.116318i
$511$	18.6670	+	11.9966i	0.825780	+	0.530697i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	−16.6864	+	36.5380i	−0.736721	+	1.61319i
$514$	−3.89145	−	8.52109i	−0.171645	−	0.375849i
$515$	6.54207	−	1.92093i	0.288278	−	0.0846461i
$516$	−3.49964	+	7.66314i	−0.154063	+	0.337351i
$517$	−17.7889	+	20.5295i	−0.782354	+	0.902885i
$518$	0.312136	−	2.17095i	0.0137144	−	0.0953861i
$519$	1.22985	+	8.55382i	0.0539846	+	0.375471i
$520$	−3.12341	−	0.917115i	−0.136970	−	0.0402182i
$521$	16.9131	−	19.5188i	0.740977	−	0.855133i	−0.252684	−	0.967549i	$-0.581313\pi$
$521$	16.9131	−	19.5188i	0.740977	−	0.855133i	0.993661	+	0.112416i	$0.0358588\pi$
$522$	2.02417	−	14.0784i	0.0885954	−	0.616195i
$523$	10.8401	+	6.96649i	0.474003	+	0.304623i	0.755744	−	0.654867i	$-0.227276\pi$
$523$	10.8401	+	6.96649i	0.474003	+	0.304623i	−0.281741	+	0.959491i	$0.590912\pi$
$524$	−8.14455	−	5.23418i	−0.355796	−	0.228656i
$525$	2.05764	+	0.604178i	0.0898028	+	0.0263685i
$526$	−7.01736	−	15.3659i	−0.305971	−	0.669984i
$527$	7.20914	+	8.31979i	0.314035	+	0.362416i
$528$	−3.98994	+	2.56418i	−0.173640	+	0.111592i
$529$	15.0091	+	17.3215i	0.652571	+	0.753107i
$530$	−8.98180	+	2.63729i	−0.390144	+	0.114557i
$531$	−23.5657	−	6.91950i	−1.02266	−	0.300281i
$532$	2.87653	−	20.0067i	0.124714	−	0.867402i
$533$	−5.81362	+	12.7301i	−0.251816	+	0.551400i
$534$	9.50770	+	10.9725i	0.411438	+	0.474825i
$535$	7.93388			0.343012
$536$	−4.95127	−	6.51805i	−0.213862	−	0.281537i
$537$	−11.3974			−0.491832
$538$	−2.29878	−	2.65293i	−0.0991074	−	0.114376i
$539$	−3.06981	+	6.72194i	−0.132226	+	0.289534i
$540$	0.668456	−	4.64921i	0.0287658	−	0.200070i
$541$	−27.8709	−	8.18363i	−1.19826	−	0.351842i	−0.379074	−	0.925366i	$-0.623758\pi$
$541$	−27.8709	−	8.18363i	−1.19826	−	0.351842i	−0.819188	+	0.573524i	$0.805576\pi$
$542$	−18.4392	+	5.41424i	−0.792032	+	0.232561i
$543$	10.2041	+	11.7762i	0.437901	+	0.505365i
$544$	2.46057	−	1.58131i	0.105496	−	0.0677982i
$545$	5.23075	+	6.03661i	0.224061	+	0.258580i
$546$	2.89999	+	6.35010i	0.124108	+	0.271759i
$547$	4.18249	+	1.22809i	0.178830	+	0.0525094i	0.369922	−	0.929063i	$-0.379384\pi$
$547$	4.18249	+	1.22809i	0.178830	+	0.0525094i	−0.191091	+	0.981572i	$0.561203\pi$
$548$	−10.5787	−	6.79849i	−0.451898	−	0.290417i
$549$	0.844705	+	0.542859i	0.0360511	+	0.0231687i
$550$	−0.743917	+	5.17406i	−0.0317207	+	0.220623i
$551$	36.5926	−	42.2301i	1.55890	−	1.79906i
$552$	0.246896	+	0.0724952i	0.0105086	+	0.00308560i
$553$	3.75295	+	26.1024i	0.159592	+	1.10999i
$554$	1.94983	−	13.5614i	0.0828405	−	0.576168i
$555$	0.551372	−	0.636317i	0.0234044	−	0.0270102i
$556$	−7.35382	+	16.1026i	−0.311872	+	0.682904i
$557$	40.5381	−	11.9031i	1.71765	−	0.504349i	0.733204	−	0.680009i	$-0.238024\pi$
$557$	40.5381	−	11.9031i	1.71765	−	0.504349i	0.984451	+	0.175660i	$0.0562059\pi$
$558$	3.40343	+	7.45247i	0.144079	+	0.315488i
$559$	−12.5558	+	27.4934i	−0.531054	+	1.16285i
$560$	0.336366	+	2.33948i	0.0142141	+	0.0988611i
$561$	−11.6701	−	7.49994i	−0.492713	−	0.316648i
$562$	−3.26423	−	22.7032i	−0.137693	−	0.957677i
$563$	12.8660	−	3.77780i	0.542238	−	0.159215i	0.000867517	−	1.00000i	$-0.499724\pi$
$563$	12.8660	−	3.77780i	0.542238	−	0.159215i	0.541370	+	0.840784i	$0.317906\pi$
$564$	−3.96659	+	2.54918i	−0.167024	+	0.107340i
$565$	−7.00813			−0.294834
$566$	−12.4340			−0.522638
$567$	4.51055	−	2.89875i	0.189425	−	0.121736i
$568$	2.63871	+	5.77798i	0.110718	+	0.242438i
$569$	−29.2773	+	33.7878i	−1.22737	+	1.41646i	−0.349927	+	0.936777i	$0.613794\pi$
$569$	−29.2773	+	33.7878i	−1.22737	+	1.41646i	−0.877442	+	0.479683i	$0.840752\pi$
$570$	5.08126	−	5.86408i	0.212830	−	0.245619i
$571$	8.14679	+	17.8390i	0.340933	+	0.746538i	0.999985	−	0.00555913i	$-0.00176953\pi$
$571$	8.14679	+	17.8390i	0.340933	+	0.746538i	−0.659052	+	0.752097i	$0.729042\pi$
$572$	−14.3149	+	9.19962i	−0.598536	+	0.384656i
$573$	−7.62884			−0.318700
$574$	10.1611			0.424116
$575$	0.238580	−	0.153326i	0.00994946	−	0.00639413i
$576$	2.08858	−	0.613262i	0.0870241	−	0.0255526i
$577$	−1.72218	−	11.9780i	−0.0716953	−	0.498652i	−0.993753	−	0.111600i	$-0.964402\pi$
$577$	−1.72218	−	11.9780i	−0.0716953	−	0.498652i	0.922058	−	0.387052i	$-0.126507\pi$
$578$	−7.10442	−	4.56573i	−0.295505	−	0.189909i
$579$	−0.220575	−	1.53413i	−0.00916678	−	0.0637563i
$580$	−2.71437	+	5.94365i	−0.112708	+	0.246797i
$581$	−1.19755	−	2.62227i	−0.0496828	−	0.108790i
$582$	−3.35732	+	0.985797i	−0.139165	+	0.0408626i
$583$	−20.3272	+	44.5104i	−0.841868	+	1.84343i
$584$	−6.14801	+	7.09518i	−0.254406	+	0.293601i
$585$	1.00843	−	7.01379i	0.0416935	−	0.289984i
$586$	1.31761	+	9.16418i	0.0544300	+	0.378569i
$587$	−8.09887	−	2.37804i	−0.334276	−	0.0981523i	0.110287	−	0.993900i	$-0.464823\pi$
$587$	−8.09887	−	2.37804i	−0.334276	−	0.0981523i	−0.444563	+	0.895747i	$0.646641\pi$
$588$	−0.839979	+	0.969388i	−0.0346402	+	0.0399769i
$589$	−4.58071	+	31.8595i	−0.188745	+	1.31275i
$590$	9.49195	+	6.10011i	0.390778	+	0.251137i
$591$	1.17194	+	0.753159i	0.0482071	+	0.0309808i
$592$	0.890374	+	0.261437i	0.0365941	+	0.0107450i
$593$	−7.89397	−	17.2854i	−0.324166	−	0.709825i	0.675453	−	0.737403i	$-0.263948\pi$
$593$	−7.89397	−	17.2854i	−0.324166	−	0.709825i	−0.999620	+	0.0275774i	$0.991221\pi$
$594$	−16.0785	−	18.5556i	−0.659710	−	0.761345i
$595$	−5.81565	+	3.73749i	−0.238419	+	0.153222i
$596$	−6.85492	−	7.91100i	−0.280789	−	0.324047i
$597$	4.89693	−	1.43787i	0.200418	−	0.0588480i
$598$	0.885799	+	0.260094i	0.0362230	+	0.0106360i
$599$	3.60437	−	25.0689i	0.147270	−	1.02429i	−0.773392	−	0.633928i	$-0.781441\pi$
$599$	3.60437	−	25.0689i	0.147270	−	1.02429i	0.920662	−	0.390360i	$-0.127649\pi$
$600$	−0.376919	+	0.825337i	−0.0153876	+	0.0336942i
$601$	1.85395	+	2.13957i	0.0756243	+	0.0872751i	0.792301	−	0.610131i	$-0.208883\pi$
$601$	1.85395	+	2.13957i	0.0756243	+	0.0872751i	−0.716677	+	0.697406i	$0.754338\pi$
$602$	21.9451			0.894417
$603$	12.5099	−	12.6872i	0.509444	−	0.516661i
$604$	22.3568			0.909685
$605$	10.6901	+	12.3371i	0.434616	+	0.501573i
$606$	3.02650	−	6.62711i	0.122943	−	0.269208i
$607$	−5.90370	+	41.0612i	−0.239624	+	1.66662i	0.414360	+	0.910113i	$0.364005\pi$
$607$	−5.90370	+	41.0612i	−0.239624	+	1.66662i	−0.653984	+	0.756508i	$0.726904\pi$
$608$	8.20538	+	2.40932i	0.332772	+	0.0977107i
$609$	13.4449	−	3.94777i	0.544814	−	0.159972i
$610$	−0.302077	−	0.348616i	−0.0122308	−	0.0141150i
$611$	−14.2311	+	9.14579i	−0.575730	+	0.369999i
$612$	4.16934	+	4.81167i	0.168535	+	0.194500i
$613$	−5.55062	−	12.1542i	−0.224187	−	0.490902i	0.763797	−	0.645457i	$-0.223333\pi$
$613$	−5.55062	−	12.1542i	−0.224187	−	0.490902i	−0.987984	+	0.154555i	$0.950606\pi$
$614$	18.5970	+	5.46058i	0.750515	+	0.220371i
$615$	3.28148	+	2.10888i	0.132322	+	0.0850382i
$616$	10.3935	+	6.67953i	0.418768	+	0.269126i
$617$	−5.96993	+	41.5217i	−0.240340	+	1.67160i	0.410097	+	0.912042i	$0.365495\pi$
$617$	−5.96993	+	41.5217i	−0.240340	+	1.67160i	−0.650437	+	0.759560i	$0.725414\pi$
$618$	4.05124	−	4.67538i	0.162965	−	0.188071i
$619$	3.25346	+	0.955301i	0.130768	+	0.0383968i	0.346461	−	0.938064i	$-0.387383\pi$
$619$	3.25346	+	0.955301i	0.130768	+	0.0383968i	−0.215694	+	0.976461i	$0.569201\pi$
$620$	−0.535643	−	3.72548i	−0.0215120	−	0.149619i
$621$	−0.189574	+	1.31852i	−0.00760736	+	0.0529103i
$622$	−7.53238	+	8.69284i	−0.302021	+	0.348551i
$623$	15.7111	−	34.4024i	0.629451	−	1.37830i
$624$	−2.83396	+	0.832126i	−0.113449	+	0.0333117i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	10.5044	−	23.0015i	0.419842	−	0.919325i
$627$	−5.77227	−	40.1470i	−0.230522	−	1.60332i
$628$	−17.1687	−	11.0336i	−0.685104	−	0.440290i
$629$	0.386269	+	2.68656i	0.0154016	+	0.107120i
$630$	−4.93643	+	1.44947i	−0.196672	+	0.0577482i
$631$	−0.863071	+	0.554662i	−0.0343583	+	0.0220807i	−0.557707	−	0.830038i	$-0.688319\pi$
$631$	−0.863071	+	0.554662i	−0.0343583	+	0.0220807i	0.523349	+	0.852118i	$0.324682\pi$
$632$	−11.1573			−0.443815
$633$	−0.826451			−0.0328485
$634$	−4.39664	+	2.82555i	−0.174613	+	0.112217i
$635$	−1.14037	−	2.49706i	−0.0452542	−	0.0990930i
$636$	−5.56206	+	6.41896i	−0.220550	+	0.254528i
$637$	−3.01363	+	3.47792i	−0.119404	+	0.137800i
$638$	14.1887	+	31.0690i	0.561738	+	1.23003i
$639$	−11.6318	+	7.47529i	−0.460146	+	0.295718i
$640$	−1.00000			−0.0395285
$641$	−9.16329			−0.361928			−0.180964	−	0.983490i	$-0.557922\pi$
$641$	−9.16329			−0.361928			−0.180964	+	0.983490i	$0.557922\pi$
$642$	6.05589	−	3.89188i	0.239007	−	0.153600i
$643$	−47.1703	+	13.8504i	−1.86021	+	0.546208i	−0.860916	+	0.508747i	$0.830109\pi$
$643$	−47.1703	+	13.8504i	−1.86021	+	0.546208i	−0.999298	+	0.0374610i	$0.988073\pi$
$644$	−0.0953936	−	0.663477i	−0.00375904	−	0.0261447i
$645$	7.08709	+	4.55460i	0.279054	+	0.179337i
$646$	3.55972	+	24.7584i	0.140055	+	0.974106i
$647$	13.9577	−	30.5631i	0.548733	−	1.20156i	−0.408638	−	0.912697i	$-0.633996\pi$
$647$	13.9577	−	30.5631i	0.548733	−	1.20156i	0.957371	−	0.288862i	$-0.0932767\pi$
$648$	0.942371	+	2.06350i	0.0370198	+	0.0810621i
$649$	56.5907	−	16.6165i	2.22138	−	0.652256i
$650$	−1.35229	+	2.96110i	−0.0530411	+	0.116144i
$651$	−5.28570	+	6.10002i	−0.207163	+	0.239079i
$652$	−1.51900	+	10.5649i	−0.0594886	+	0.413752i
$653$	−5.39381	−	37.5148i	−0.211076	−	1.46807i	−0.769573	−	0.638559i	$-0.779531\pi$
$653$	−5.39381	−	37.5148i	−0.211076	−	1.46807i	0.558497	−	0.829507i	$-0.311378\pi$
$654$	6.95380	+	2.04182i	0.271915	+	0.0798415i
$655$	−6.34000	+	7.31674i	−0.247724	+	0.285889i
$656$	−0.611826	+	4.25534i	−0.0238878	+	0.166143i
$657$	−17.1918	−	11.0485i	−0.670716	−	0.431043i
$658$	10.3327	+	6.64044i	0.402812	+	0.258871i
$659$	21.4181	+	6.28893i	0.834331	+	0.244982i	0.670877	−	0.741569i	$-0.265918\pi$
$659$	21.4181	+	6.28893i	0.834331	+	0.244982i	0.163455	+	0.986551i	$0.447736\pi$
$660$	1.97025	+	4.31425i	0.0766920	+	0.167932i
$661$	−3.77756	−	4.35953i	−0.146930	−	0.169566i	0.677514	−	0.735510i	$-0.263057\pi$
$661$	−3.77756	−	4.35953i	−0.146930	−	0.169566i	−0.824444	+	0.565944i	$0.808512\pi$
$662$	17.8915	−	11.4982i	0.695374	−	0.446890i
$663$	−5.65731	−	6.52889i	−0.219712	−	0.253561i
$664$	1.17028	−	0.343626i	0.0454158	−	0.0133353i
$665$	−19.3937	−	5.69451i	−0.752056	−	0.220824i
$666$	−0.287468	+	1.99938i	−0.0111392	+	0.0774746i
$667$	0.769797	−	1.68562i	0.0298067	−	0.0652675i
$668$	−9.33690	−	10.7754i	−0.361256	−	0.416911i
$669$	24.2836			0.938858
$670$	−7.15634	+	3.97326i	−0.276474	+	0.153500i
$671$	−2.41126			−0.0930856
$672$	1.40435	+	1.62071i	0.0541742	+	0.0625203i
$673$	−9.18565	+	20.1138i	−0.354081	+	0.775329i	0.645849	+	0.763465i	$0.276504\pi$
$673$	−9.18565	+	20.1138i	−0.354081	+	0.775329i	−0.999930	+	0.0118635i	$0.996224\pi$
$674$	−2.74743	+	19.1088i	−0.105827	+	0.736044i
$675$	−4.50676	−	1.32330i	−0.173465	−	0.0509340i
$676$	2.30588	−	0.677066i	0.0886875	−	0.0260410i
$677$	2.98938	+	3.44993i	0.114891	+	0.132591i	0.810282	−	0.586041i	$-0.199314\pi$
$677$	2.98938	+	3.44993i	0.114891	+	0.132591i	−0.695391	+	0.718632i	$0.744769\pi$
$678$	−5.34927	+	3.43777i	−0.205437	+	0.132027i
$679$	5.96893	+	6.88851i	0.229067	+	0.264357i
$680$	−1.21504	−	2.66057i	−0.0465947	−	0.102028i
$681$	−6.51765	−	1.91375i	−0.249757	−	0.0733352i
$682$	−16.5511	−	10.6367i	−0.633774	−	0.407302i
$683$	41.0913	+	26.4078i	1.57231	+	1.01046i	0.978596	+	0.205792i	$0.0659770\pi$
$683$	41.0913	+	26.4078i	1.57231	+	1.01046i	0.593718	+	0.804673i	$0.297659\pi$
$684$	−2.64921	+	18.4256i	−0.101295	+	0.704522i
$685$	−8.23480	+	9.50346i	−0.314635	+	0.363109i
$686$	19.0805	+	5.60255i	0.728499	+	0.213907i
$687$	2.18425	+	15.1918i	0.0833342	+	0.579602i
$688$	−1.32137	+	9.19036i	−0.0503769	+	0.350379i
$689$	−19.9553	+	23.0296i	−0.760235	+	0.877358i
$690$	0.106894	−	0.234066i	0.00406939	−	0.00891073i
$691$	28.9029	−	8.48665i	1.09952	−	0.322848i	0.318857	−	0.947803i	$-0.396701\pi$
$691$	28.9029	−	8.48665i	1.09952	−	0.322848i	0.780661	+	0.624955i	$0.214883\pi$
$692$	3.95658	+	8.66370i	0.150407	+	0.329344i
$693$	−11.1719	+	24.4631i	−0.424386	+	0.929276i
$694$	−2.23746	−	15.5619i	−0.0849328	−	0.590720i
$695$	14.8922	+	9.57062i	0.564892	+	0.363034i
$696$	0.843729	+	5.86826i	0.0319815	+	0.222436i
$697$	−12.0650	+	3.54261i	−0.456996	+	0.134186i
$698$	−16.0381	+	10.3071i	−0.607052	+	0.390128i
$699$	−5.20095			−0.196718
$700$	2.36354			0.0893333
$701$	−6.20932	+	3.99049i	−0.234523	+	0.150719i	−0.652624	−	0.757682i	$-0.726332\pi$
$701$	−6.20932	+	3.99049i	−0.234523	+	0.150719i	0.418102	+	0.908400i	$0.362696\pi$
$702$	−6.35173	−	13.9083i	−0.239730	−	0.524937i
$703$	−5.19680	+	5.99743i	−0.196001	+	0.226197i
$704$	−3.42313	+	3.95050i	−0.129014	+	0.148890i
$705$	1.95872	+	4.28901i	0.0737698	+	0.161533i
$706$	−19.0949	+	12.2715i	−0.718645	+	0.461845i
$707$	−18.9782			−0.713749
$708$	10.2375			0.384749
$709$	31.0446	−	19.9512i	1.16591	−	0.749282i	0.193163	−	0.981167i	$-0.438125\pi$
$709$	31.0446	−	19.9512i	1.16591	−	0.749282i	0.972743	+	0.231884i	$0.0744891\pi$
$710$	6.09469	−	1.78956i	0.228730	−	0.0671611i
$711$	−3.45637	−	24.0396i	−0.129624	−	0.901554i
$712$	13.4613	+	8.65107i	0.504485	+	0.324213i
$713$	0.151909	+	1.05655i	0.00568902	+	0.0395680i
$714$	−2.60567	+	5.70562i	−0.0975147	+	0.213527i
$715$	7.06876	+	15.4784i	0.264357	+	0.578861i
$716$	−12.0526	+	3.53896i	−0.450427	+	0.132257i
$717$	9.37029	−	20.5181i	0.349940	−	0.766262i
$718$	−4.72645	+	5.45461i	−0.176390	+	0.203564i
$719$	5.19414	−	36.1261i	0.193709	−	1.34727i	−0.628376	−	0.777910i	$-0.716280\pi$
$719$	5.19414	−	36.1261i	0.193709	−	1.34727i	0.822085	−	0.569365i	$-0.192811\pi$
$720$	−0.309784	−	2.15460i	−0.0115450	−	0.0802970i
$721$	−15.4624	−	4.54018i	−0.575851	−	0.169085i
$722$	−35.4496	+	40.9110i	−1.31930	+	1.52255i
$723$	3.11138	−	21.6401i	0.115714	−	0.804805i
$724$	14.4474	+	9.28476i	0.536932	+	0.345065i
$725$	5.49685	+	3.53261i	0.204148	+	0.131198i
$726$	14.2115	+	4.17288i	0.527440	+	0.154870i
$727$	20.7182	+	45.3666i	0.768396	+	1.68255i	0.730153	+	0.683284i	$0.239449\pi$
$727$	20.7182	+	45.3666i	0.768396	+	1.68255i	0.0382429	+	0.999268i	$0.487824\pi$
$728$	5.03847	+	5.81470i	0.186738	+	0.215507i
$729$	6.60155	−	4.24256i	0.244502	−	0.157132i
$730$	6.14801	+	7.09518i	0.227548	+	0.262604i
$731$	−26.0571	+	7.65107i	−0.963758	+	0.282985i
$732$	−0.401584	−	0.117916i	−0.0148430	−	0.00435829i
$733$	6.40483	−	44.5466i	0.236568	−	1.64537i	−0.432115	−	0.901818i	$-0.642233\pi$
$733$	6.40483	−	44.5466i	0.236568	−	1.64537i	0.668683	−	0.743547i	$-0.266858\pi$
$734$	5.83999	−	12.7878i	0.215558	−	0.472006i
$735$	0.839979	+	0.969388i	0.0309831	+	0.0357564i
$736$	0.283600			0.0104536
$737$	−8.80073	+	41.8721i	−0.324179	+	1.54238i
$738$	−9.35808			−0.344476
$739$	−24.7853	−	28.6037i	−0.911740	−	1.05220i	−0.998432	−	0.0559694i	$-0.982175\pi$
$739$	−24.7853	−	28.6037i	−0.911740	−	1.05220i	0.0866921	−	0.996235i	$-0.472370\pi$
$740$	0.385490	−	0.844105i	0.0141709	−	0.0310299i
$741$	3.59467	−	25.0015i	0.132054	−	0.918453i
$742$	21.2288	+	6.23334i	0.779334	+	0.228833i
$743$	−12.4634	+	3.65959i	−0.457239	+	0.134257i	−0.502238	−	0.864730i	$-0.667490\pi$
$743$	−12.4634	+	3.65959i	−0.457239	+	0.134257i	0.0449989	+	0.998987i	$0.485672\pi$
$744$	−2.23635	−	2.58089i	−0.0819886	−	0.0946199i
$745$	−8.80604	+	5.65930i	−0.322628	+	0.207341i
$746$	−18.2263	−	21.0343i	−0.667313	−	0.770121i
$747$	1.10291	+	2.41504i	0.0403534	+	0.0883616i
$748$	−14.6698	−	4.30745i	−0.536382	−	0.157496i
$749$	−15.7752	−	10.1381i	−0.576414	−	0.370439i
$750$	0.763295	+	0.490540i	0.0278716	+	0.0179120i
$751$	0.239658	−	1.66686i	0.00874523	−	0.0608244i	−0.984982	−	0.172660i	$-0.944764\pi$
$751$	0.239658	−	1.66686i	0.00874523	−	0.0608244i	0.993727	+	0.111835i	$0.0356730\pi$
$752$	−3.40310	+	3.92738i	−0.124098	+	0.143217i
$753$	−6.82596	−	2.00428i	−0.248752	−	0.0730401i
$754$	3.02708	+	21.0538i	0.110240	+	0.766735i
$755$	3.18170	−	22.1292i	0.115794	−	0.805365i
$756$	−7.27000	+	8.39002i	−0.264407	+	0.305142i
$757$	12.8433	−	28.1229i	0.466797	−	1.02214i	−0.519088	−	0.854721i	$-0.673728\pi$
$757$	12.8433	−	28.1229i	0.466797	−	1.02214i	0.985885	−	0.167423i	$-0.0535445\pi$
$758$	7.75277	−	2.27642i	0.281593	−	0.0826833i
$759$	−0.558764	−	1.22352i	−0.0202819	−	0.0444111i
$760$	3.55254	−	7.77898i	0.128864	−	0.282173i
$761$	−2.77136	−	19.2753i	−0.100462	−	0.698728i	−0.976347	−	0.216208i	$-0.930631\pi$
$761$	−2.77136	−	19.2753i	−0.100462	−	0.698728i	0.875885	−	0.482519i	$-0.160278\pi$
$762$	−2.09535	−	1.34660i	−0.0759065	−	0.0487821i
$763$	−2.68675	−	18.6868i	−0.0972670	−	0.676507i
$764$	−8.06743	+	2.36881i	−0.291869	+	0.0857006i
$765$	5.35605	−	3.44213i	0.193649	−	0.124450i
$766$	20.7071			0.748179
$767$	36.7296			1.32623
$768$	−0.763295	+	0.490540i	−0.0275430	+	0.0177008i
$769$	−4.05364	−	8.87624i	−0.146178	−	0.320085i	0.822353	−	0.568977i	$-0.192661\pi$
$769$	−4.05364	−	8.87624i	−0.146178	−	0.320085i	−0.968531	+	0.248892i	$0.919934\pi$
$770$	8.09069	−	9.33716i	0.291568	−	0.336488i
$771$	−5.56601	+	6.42352i	−0.200455	+	0.231337i
$772$	−0.709615	−	1.55384i	−0.0255396	−	0.0559239i
$773$	8.90074	−	5.72016i	0.320137	−	0.205740i	−0.370695	−	0.928755i	$-0.620881\pi$
$773$	8.90074	−	5.72016i	0.320137	−	0.205740i	0.690832	+	0.723015i	$0.257244\pi$
$774$	−20.2109			−0.726464
$775$	−3.76379			−0.135199
$776$	−3.24423	+	2.08494i	−0.116461	+	0.0748450i
$777$	−1.90941	+	0.560655i	−0.0684999	+	0.0201134i
$778$	0.818900	+	5.69558i	0.0293590	+	0.204196i
$779$	−30.9287	−	19.8767i	−1.10813	−	0.712155i
$780$	0.420342	+	2.92354i	0.0150506	+	0.104680i
$781$	13.7932	−	30.2030i	0.493561	−	1.08075i
$782$	0.344586	+	0.754539i	0.0123224	+	0.0269822i
$783$	−29.4477	+	8.64663i	−1.05238	+	0.309006i
$784$	−0.587268	+	1.28594i	−0.0209739	+	0.0459264i
$785$	−13.3647	+	15.4237i	−0.477006	+	0.550494i
$786$	−1.25013	+	8.69485i	−0.0445907	+	0.310135i
$787$	−5.71852	−	39.7732i	−0.203843	−	1.41776i	−0.792743	−	0.609556i	$-0.791348\pi$
$787$	−5.71852	−	39.7732i	−0.203843	−	1.41776i	0.588900	−	0.808206i	$-0.299561\pi$
$788$	1.47317	+	0.432563i	0.0524797	+	0.0154094i
$789$	−10.0370	+	11.5834i	−0.357328	+	0.412379i
$790$	−1.58785	+	11.0438i	−0.0564933	+	0.392920i
$791$	13.9345	+	8.95516i	0.495454	+	0.318409i
$792$	−9.57217	−	6.15166i	−0.340132	−	0.218590i
$793$	−1.44078	−	0.423052i	−0.0511636	−	0.0150230i
$794$	10.8298	+	23.7139i	0.384334	+	0.841574i
$795$	5.56206	+	6.41896i	0.197266	+	0.227657i
$796$	4.73199	−	3.04106i	0.167721	−	0.107788i
$797$	8.14321	+	9.39776i	0.288447	+	0.332886i	0.881417	−	0.472339i	$-0.156590\pi$
$797$	8.14321	+	9.39776i	0.288447	+	0.332886i	−0.592970	+	0.805225i	$0.702045\pi$
$798$	−17.5965	+	5.16680i	−0.622910	+	0.182903i
$799$	−14.5840	−	4.28225i	−0.515944	−	0.151495i
$800$	−0.142315	+	0.989821i	−0.00503159	+	0.0349955i
$801$	−14.4695	+	31.6837i	−0.511253	+	1.11949i
$802$	2.10834	+	2.43316i	0.0744482	+	0.0859178i
$803$	49.0749			1.73182
$804$	−3.51336	+	6.54324i	−0.123907	+	0.230762i
$805$	−0.670300			−0.0236250
$806$	−8.02346	−	9.25956i	−0.282614	−	0.326154i
$807$	−1.32311	+	2.89721i	−0.0465757	+	0.101986i
$808$	1.14273	−	7.94785i	0.0402010	−	0.279604i
$809$	−17.6576	−	5.18475i	−0.620809	−	0.182286i	−0.0438222	−	0.999039i	$-0.513954\pi$
$809$	−17.6576	−	5.18475i	−0.620809	−	0.182286i	−0.576987	+	0.816753i	$0.695772\pi$
$810$	2.17661	−	0.639112i	0.0764784	−	0.0224561i
$811$	30.1717	+	34.8200i	1.05947	+	1.22270i	0.974045	+	0.226353i	$0.0726803\pi$
$811$	30.1717	+	34.8200i	1.05947	+	1.22270i	0.0854279	+	0.996344i	$0.472774\pi$
$812$	12.9920	−	8.34947i	0.455931	−	0.293009i
$813$	11.4186	+	13.1778i	0.400469	+	0.462166i
$814$	−2.01506	−	4.41236i	−0.0706277	−	0.154653i
$815$	10.2412	+	3.00707i	0.358732	+	0.105333i
$816$	−2.23255	−	1.43477i	−0.0781549	−	0.0502271i
$817$	−66.7974	−	42.9281i	−2.33694	−	1.50186i
$818$	−4.25018	+	29.5607i	−0.148604	+	1.03357i
$819$	−10.9675	+	12.6572i	−0.383235	+	0.442277i
$820$	4.12496	+	1.21120i	0.144050	+	0.0422968i
$821$	−0.760970	−	5.29267i	−0.0265581	−	0.184715i	0.972224	−	0.234052i	$-0.0751985\pi$
$821$	−0.760970	−	5.29267i	−0.0265581	−	0.184715i	−0.998782	+	0.0493363i	$0.984289\pi$
$822$	−1.62375	+	11.2934i	−0.0566348	+	0.393904i
$823$	7.31072	−	8.43702i	0.254836	−	0.294096i	−0.613888	−	0.789393i	$-0.710395\pi$
$823$	7.31072	−	8.43702i	0.254836	−	0.294096i	0.868724	+	0.495297i	$0.164941\pi$
$824$	2.83241	−	6.20210i	0.0986716	−	0.216061i
$825$	4.55073	−	1.33622i	0.158436	−	0.0465211i
$826$	−11.0783	−	24.2581i	−0.385464	−	0.844048i
$827$	17.8151	−	39.0095i	0.619490	−	1.35649i	−0.296399	−	0.955064i	$-0.595786\pi$
$827$	17.8151	−	39.0095i	0.619490	−	1.35649i	0.915889	−	0.401431i	$-0.131487\pi$
$828$	0.0878549	+	0.611044i	0.00305317	+	0.0212352i
$829$	−20.8699	−	13.4123i	−0.724841	−	0.465827i	0.125477	−	0.992097i	$-0.459954\pi$
$829$	−20.8699	−	13.4123i	−0.724841	−	0.465827i	−0.850318	+	0.526269i	$0.823590\pi$
$830$	−0.173580	−	1.20727i	−0.00602505	−	0.0419051i
$831$	−11.9276	+	3.50227i	−0.413765	+	0.121492i
$832$	−2.73851	+	1.75993i	−0.0949406	+	0.0610146i
$833$	−4.13488			−0.143265
$834$	16.0619			0.556177
$835$	−11.9945	+	7.70837i	−0.415085	+	0.266759i
$836$	−18.5701	−	40.6628i	−0.642259	−	1.40635i
$837$	11.5770	−	13.3606i	0.400161	−	0.461810i
$838$	−5.90511	+	6.81487i	−0.203989	+	0.235416i
$839$	20.8939	+	45.7513i	0.721338	+	1.57951i	0.812020	+	0.583630i	$0.198368\pi$
$839$	20.8939	+	45.7513i	0.721338	+	1.57951i	−0.0906821	+	0.995880i	$0.528905\pi$
$840$	1.80408	−	1.15941i	0.0622465	−	0.0400034i
$841$	13.6948			0.472233
$842$	−14.2825			−0.492208
$843$	−17.5074	+	11.2513i	−0.602988	+	0.387517i
$844$	−0.873964	+	0.256619i	−0.0300831	+	0.00883319i
$845$	−0.342014	−	2.37876i	−0.0117656	−	0.0818319i
$846$	−9.51615	−	6.11566i	−0.327172	−	0.210261i
$847$	−5.49094	−	38.1903i	−0.188671	−	1.31224i
$848$	−3.88869	+	8.51505i	−0.133538	+	0.292408i
$849$	4.68659	+	10.2622i	0.160843	+	0.352198i
$850$	−2.80641	+	0.824036i	−0.0962590	+	0.0282642i
$851$	−0.109325	+	0.239388i	−0.00374761	+	0.00820613i
$852$	3.77419	−	4.35565i	0.129302	−	0.149222i
$853$	−3.77600	+	26.2627i	−0.129288	+	0.899216i	0.817172	+	0.576394i	$0.195541\pi$
$853$	−3.77600	+	26.2627i	−0.129288	+	0.899216i	−0.946460	+	0.322822i	$0.895368\pi$
$854$	0.155161	+	1.07917i	0.00530949	+	0.0369283i
$855$	17.8611	+	5.24448i	0.610836	+	0.179358i
$856$	5.19559	−	5.99603i	0.177582	−	0.204940i
$857$	−0.233750	+	1.62577i	−0.00798474	+	0.0555351i	−0.993424	−	0.114491i	$-0.963476\pi$
$857$	−0.233750	+	1.62577i	−0.00798474	+	0.0555351i	0.985440	+	0.170026i	$0.0543853\pi$
$858$	12.9883	+	8.34710i	0.443414	+	0.284965i
$859$	−10.3152	−	6.62915i	−0.351949	−	0.226184i	0.352706	−	0.935734i	$-0.385262\pi$
$859$	−10.3152	−	6.62915i	−0.351949	−	0.226184i	−0.704655	+	0.709550i	$0.748898\pi$
$860$	8.90877	+	2.61585i	0.303786	+	0.0891997i
$861$	−3.82990	−	8.38632i	−0.130523	−	0.285805i
$862$	−22.7719	−	26.2801i	−0.775613	−	0.895105i
$863$	−20.4448	+	13.1391i	−0.695950	+	0.447260i	−0.840196	−	0.542282i	$-0.817560\pi$
$863$	−20.4448	+	13.1391i	−0.695950	+	0.447260i	0.144247	+	0.989542i	$0.453924\pi$
$864$	−3.07590	−	3.54977i	−0.104644	−	0.120766i
$865$	9.13860	−	2.68333i	0.310722	−	0.0912361i
$866$	−7.02463	−	2.06262i	−0.238707	−	0.0700906i
$867$	−1.09048	+	7.58444i	−0.0370346	+	0.257581i
$868$	−3.69548	+	8.09196i	−0.125433	+	0.274659i
$869$	38.1930	+	44.0771i	1.29561	+	1.49521i
$870$	5.92861			0.200999
$871$	−12.6050	+	23.4755i	−0.427105	+	0.795436i
$872$	7.98758			0.270493
$873$	−5.49722	−	6.34413i	−0.186053	−	0.214716i
$874$	−1.00750	+	2.20612i	−0.0340792	+	0.0746231i
$875$	0.336366	−	2.33948i	0.0113713	−	0.0790889i
$876$	8.17321	+	2.39987i	0.276147	+	0.0810841i
$877$	2.65779	−	0.780398i	0.0897472	−	0.0263522i	−0.236551	−	0.971619i	$-0.576017\pi$
$877$	2.65779	−	0.780398i	0.0897472	−	0.0263522i	0.326298	+	0.945267i	$0.394199\pi$
$878$	12.1925	+	14.0708i	0.411475	+	0.474868i
$879$	7.06690	−	4.54162i	0.238361	−	0.153185i
$880$	3.42313	+	3.95050i	0.115394	+	0.133171i
$881$	−10.7350	−	23.5064i	−0.361672	−	0.791951i	−0.999758	−	0.0219859i	$-0.993001\pi$
$881$	−10.7350	−	23.5064i	−0.361672	−	0.791951i	0.638087	−	0.769965i	$-0.279726\pi$
$882$	−2.95260	−	0.866963i	−0.0994193	−	0.0291921i
$883$	−2.93054	−	1.88334i	−0.0986205	−	0.0633795i	0.490401	−	0.871497i	$-0.336850\pi$
$883$	−2.93054	−	1.88334i	−0.0986205	−	0.0633795i	−0.589022	+	0.808117i	$0.700487\pi$
$884$	−8.00982	−	5.14760i	−0.269399	−	0.173133i
$885$	1.45695	−	10.1333i	0.0489748	−	0.340627i
$886$	19.5931	−	22.6116i	0.658243	−	0.759653i
$887$	11.2919	+	3.31561i	0.379146	+	0.111327i	0.465752	−	0.884915i	$-0.345784\pi$
$887$	11.2919	+	3.31561i	0.379146	+	0.111327i	−0.0866057	+	0.996243i	$0.527602\pi$
$888$	−0.119825	−	0.833399i	−0.00402105	−	0.0279670i
$889$	−0.923372	+	6.42219i	−0.0309689	+	0.215393i
$890$	10.4788	−	12.0931i	0.351249	−	0.405363i
$891$	4.92602	−	10.7865i	0.165028	−	0.361361i
$892$	25.6797	−	7.54023i	0.859819	−	0.252466i
$893$	−18.4614	−	40.4248i	−0.617787	−	1.35276i
$894$	−3.94549	+	8.63942i	−0.131957	+	0.288946i
$895$	1.78768	+	12.4336i	0.0597554	+	0.415608i
$896$	1.98833	+	1.27782i	0.0664256	+	0.0426891i
$897$	−0.119209	−	0.829117i	−0.00398027	−	0.0276834i
$898$	−27.7151	+	8.13789i	−0.924866	+	0.271565i
$899$	−20.6890	+	13.2960i	−0.690017	+	0.443447i
$900$	−2.17675			−0.0725584
$901$	−27.3798			−0.912154
$902$	18.9051	−	12.1496i	0.629471	−	0.404536i
$903$	−8.27153	−	18.1121i	−0.275259	−	0.602734i
$904$	−4.58935	+	5.29639i	−0.152639	+	0.176155i
$905$	11.2463	−	12.9790i	0.373841	−	0.431435i
$906$	−8.42669	−	18.4519i	−0.279958	−	0.613022i
$907$	29.7875	−	19.1432i	0.989076	−	0.635641i	0.0571794	−	0.998364i	$-0.481789\pi$
$907$	29.7875	−	19.1432i	0.989076	−	0.635641i	0.931897	+	0.362723i	$0.118153\pi$
$908$	−7.48659			−0.248451
$909$	17.4784			0.579722
$910$	6.47256	−	4.15966i	0.214563	−	0.137892i
$911$	5.18804	−	1.52335i	0.171887	−	0.0504707i	−0.194656	−	0.980871i	$-0.562359\pi$
$911$	5.18804	−	1.52335i	0.171887	−	0.0504707i	0.366544	+	0.930401i	$0.380541\pi$
$912$	−1.10426	−	7.68031i	−0.0365658	−	0.254321i
$913$	−5.36353	−	3.44693i	−0.177507	−	0.114077i
$914$	−2.75382	−	19.1533i	−0.0910884	−	0.633534i
$915$	−0.173867	+	0.380715i	−0.00574786	+	0.0125861i
$916$	7.02698	+	15.3869i	0.232178	+	0.508398i
$917$	21.9555	−	6.44673i	0.725036	−	0.212890i
$918$	5.70708	−	12.4968i	0.188362	−	0.412455i
$919$	4.94109	−	5.70232i	0.162992	−	0.188102i	−0.668379	−	0.743821i	$-0.733011\pi$
$919$	4.94109	−	5.70232i	0.162992	−	0.188102i	0.831370	+	0.555719i	$0.187557\pi$
$920$	0.0403605	−	0.280714i	0.00133065	−	0.00925485i
$921$	−2.50275	−	17.4070i	−0.0824684	−	0.573580i
$922$	−11.8951	−	3.49271i	−0.391743	−	0.115026i
$923$	13.5408	−	15.6270i	0.445702	−	0.514368i
$924$	1.59534	−	11.0958i	0.0524827	−	0.365025i
$925$	−0.780652	−	0.501695i	−0.0256677	−	0.0164956i
$926$	−33.5569	−	21.5657i	−1.10275	−	0.708693i
$927$	14.2405	+	4.18138i	0.467718	+	0.137334i
$928$	2.71437	+	5.94365i	0.0891037	+	0.195110i
$929$	30.4739	+	35.1688i	0.999816	+	1.15385i	0.988084	+	0.153918i	$0.0491893\pi$
$929$	30.4739	+	35.1688i	0.999816	+	1.15385i	0.0117328	+	0.999931i	$0.496265\pi$
$930$	−2.87288	+	1.84629i	−0.0942055	+	0.0605422i
$931$	−7.91699	−	9.13669i	−0.259469	−	0.299443i
$932$	−5.49995	+	1.61493i	−0.180157	+	0.0528988i
$933$	10.0136	+	2.94026i	0.327831	+	0.0962598i
$934$	−0.932347	+	6.48461i	−0.0305073	+	0.212183i
$935$	−6.35134	+	13.9075i	−0.207711	+	0.454824i
$936$	−4.64029	−	5.35518i	−0.151673	−	0.175039i
$937$	29.3470			0.958723			0.479362	−	0.877617i	$-0.340868\pi$
$937$	29.3470			0.958723			0.479362	+	0.877617i	$0.340868\pi$
$938$	19.3063	+	1.24439i	0.630374	+	0.0406308i
$939$	−22.9433			−0.748726
$940$	3.40310	+	3.92738i	0.110997	+	0.128097i
$941$	12.1022	−	26.5001i	0.394519	−	0.863877i	−0.603277	−	0.797531i	$-0.706139\pi$
$941$	12.1022	−	26.5001i	0.394519	−	0.863877i	0.997797	−	0.0663455i	$-0.0211339\pi$
$942$	−2.63527	+	18.3287i	−0.0858617	+	0.597181i
$943$	−1.16984	−	0.343496i	−0.0380952	−	0.0111858i
$944$	10.8261	−	3.17882i	0.352358	−	0.103462i
$945$	7.27000	+	8.39002i	0.236493	+	0.272927i
$946$	40.8298	−	26.2397i	1.32749	−	0.853126i
$947$	9.81077	+	11.3222i	0.318807	+	0.367923i	0.892422	−	0.451202i	$-0.149005\pi$
$947$	9.81077	+	11.3222i	0.318807	+	0.367923i	−0.573614	+	0.819125i	$0.694459\pi$
$948$	4.20541	+	9.20856i	0.136585	+	0.299080i
$949$	29.3234	+	8.61012i	0.951877	+	0.279496i
$950$	−7.19422	−	4.62344i	−0.233411	−	0.150004i
$951$	3.98921	+	2.56371i	0.129359	+	0.0831339i
$952$	−0.983834	+	6.84271i	−0.0318862	+	0.221774i
$953$	−18.2638	+	21.0775i	−0.591621	+	0.682767i	−0.970062	−	0.242858i	$-0.921915\pi$
$953$	−18.2638	+	21.0775i	−0.591621	+	0.682767i	0.378441	+	0.925626i	$0.376460\pi$
$954$	−19.5511	−	5.74074i	−0.632992	−	0.185863i
$955$	1.19658	+	8.32243i	0.0387206	+	0.269308i
$956$	3.53798	−	24.6072i	0.114427	−	0.795854i
$957$	20.2944	−	23.4210i	0.656024	−	0.757093i
$958$	−6.87675	+	15.0580i	−0.222178	+	0.486501i
$959$	28.5173	−	8.37343i	0.920871	−	0.270392i
$960$	0.376919	+	0.825337i	0.0121650	+	0.0266376i
$961$	−6.99304	+	15.3126i	−0.225582	+	0.493956i
$962$	−0.429900	−	2.99002i	−0.0138605	−	0.0964022i
$963$	14.5285	+	9.33692i	0.468175	+	0.300878i
$964$	−3.42916	−	23.8503i	−0.110446	−	0.768168i
$965$	−1.63901	+	0.481257i	−0.0527617	+	0.0154922i
$966$	−0.511636	+	0.328809i	−0.0164616	+	0.0105792i
$967$	−0.312889			−0.0100618			−0.00503092	−	0.999987i	$-0.501601\pi$
$967$	−0.312889			−0.0100618			−0.00503092	+	0.999987i	$0.501601\pi$
$968$	16.3243			0.524682
$969$	19.0923	−	12.2699i	0.613333	−	0.394165i
$970$	1.60202	+	3.50793i	0.0514377	+	0.112633i
$971$	−19.3996	+	22.3883i	−0.622561	+	0.718474i	−0.976191	−	0.216911i	$-0.930402\pi$
$971$	−19.3996	+	22.3883i	−0.622561	+	0.718474i	0.353630	+	0.935385i	$0.384947\pi$
$972$	10.5756	−	12.2049i	0.339212	−	0.391471i
$973$	−17.3810	−	38.0592i	−0.557211	−	1.22012i
$974$	−18.3849	+	11.8152i	−0.589089	+	0.378585i
$975$	2.95360			0.0945910
$976$	−0.461285			−0.0147654
$977$	−31.2141	+	20.0601i	−0.998627	+	0.641778i	−0.934426	−	0.356159i	$-0.884086\pi$
$977$	−31.2141	+	20.0601i	−0.998627	+	0.641778i	−0.0642012	+	0.997937i	$0.520450\pi$
$978$	9.29211	−	2.72841i	0.297129	−	0.0872449i
$979$	−11.9038	−	82.7927i	−0.380447	−	2.64607i
$980$	1.18927	+	0.764299i	0.0379899	+	0.0244146i
$981$	2.47442	+	17.2100i	0.0790023	+	0.549473i
$982$	−15.9199	+	34.8597i	−0.508025	+	1.11242i
$983$	19.6279	+	42.9791i	0.626033	+	1.37082i	0.911049	+	0.412299i	$0.135274\pi$
$983$	19.6279	+	42.9791i	0.626033	+	1.37082i	−0.285016	+	0.958523i	$0.591999\pi$
$984$	3.74270	−	1.09896i	0.119313	−	0.0350334i
$985$	0.637815	−	1.39662i	0.0203225	−	0.0445000i
$986$	−12.5154	+	14.4436i	−0.398572	+	0.459977i
$987$	1.58600	−	11.0309i	0.0504830	−	0.351117i
$988$	−3.96181	−	27.5550i	−0.126042	−	0.876642i
$989$	−2.52653	−	0.741856i	−0.0803389	−	0.0235896i
$990$	−7.45130	+	8.59926i	−0.236818	+	0.273303i
$991$	−5.43751	+	37.8187i	−0.172728	+	1.20135i	0.700361	+	0.713789i	$0.253023\pi$
$991$	−5.43751	+	37.8187i	−0.172728	+	1.20135i	−0.873089	+	0.487561i	$0.837887\pi$
$992$	−3.16630	−	2.03486i	−0.100530	−	0.0646069i
$993$	−16.2335	−	10.4327i	−0.515156	−	0.331070i
$994$	−14.4050	−	4.22970i	−0.456900	−	0.134158i
$995$	−2.33668	−	5.11661i	−0.0740777	−	0.162208i
$996$	−0.724709	−	0.836359i	−0.0229633	−	0.0265010i
$997$	−28.8895	+	18.5662i	−0.914941	+	0.587997i	−0.911186	−	0.411996i	$-0.864832\pi$
$997$	−28.8895	+	18.5662i	−0.914941	+	0.587997i	−0.00375546	+	0.999993i	$0.501195\pi$
$998$	−22.9045	−	26.4332i	−0.725030	−	0.836730i
$999$	4.18211	−	1.22798i	0.132316	−	0.0388515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.b.241.3	✓	50
67.62	even	11	inner	670.2.k.b.531.3	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.b.241.3	✓	50	1.1	even	1	trivial
670.2.k.b.531.3	yes	50	67.62	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.376919 + 0.825337i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.870577 - 0.255624i) q^{6} +(-1.54779 - 1.78624i) q^{7} +(0.841254 - 0.540641i) q^{8} +(1.42547 + 1.64508i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.376919 + 0.825337i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.870577 - 0.255624i) q^{6} +(-1.54779 - 1.78624i) q^{7} +(0.841254 - 0.540641i) q^{8} +(1.42547 + 1.64508i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(-5.01552 - 1.47269i) q^{11} +(-0.763295 - 0.490540i) q^{12} +(-2.73851 - 1.75993i) q^{13} +(-0.336366 + 2.33948i) q^{14} +(-0.594175 + 0.685714i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.416255 - 2.89512i) q^{17} +(0.309784 - 2.15460i) q^{18} +(5.60023 - 6.46301i) q^{19} +(-0.415415 + 0.909632i) q^{20} +(2.05764 - 0.604178i) q^{21} +(2.17148 + 4.75489i) q^{22} +(0.117812 - 0.257972i) q^{23} +(0.129127 + 0.898095i) q^{24} +(0.841254 + 0.540641i) q^{25} +(0.463273 + 3.22214i) q^{26} +(-4.50676 + 1.32330i) q^{27} +(1.98833 - 1.27782i) q^{28} +6.53412 q^{29} +0.907330 q^{30} +(-3.16630 + 2.03486i) q^{31} +(0.415415 + 0.909632i) q^{32} +(3.10591 - 3.58441i) q^{33} +(-1.91539 + 2.21048i) q^{34} +(-0.981849 - 2.14995i) q^{35} +(-1.83120 + 1.17684i) q^{36} -0.927963 q^{37} -8.55178 q^{38} +(2.48473 - 1.59684i) q^{39} +(0.959493 - 0.281733i) q^{40} +(-0.611826 - 4.25534i) q^{41} +(-1.80408 - 1.15941i) q^{42} +(-1.32137 - 9.19036i) q^{43} +(2.17148 - 4.75489i) q^{44} +(0.904255 + 1.98004i) q^{45} +(-0.272112 + 0.0798994i) q^{46} +(2.15878 - 4.72706i) q^{47} +(0.594175 - 0.685714i) q^{48} +(0.201189 - 1.39930i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(2.54634 + 0.747673i) q^{51} +(2.13175 - 2.46017i) q^{52} +(1.33221 - 9.26570i) q^{53} +(3.95139 + 2.53940i) q^{54} +(-4.39745 - 2.82607i) q^{55} +(-2.26780 - 0.665885i) q^{56} +(3.22333 + 7.05810i) q^{57} +(-4.27894 - 4.93816i) q^{58} +(-9.49195 + 6.10011i) q^{59} +(-0.594175 - 0.685714i) q^{60} +(0.442600 - 0.129959i) q^{61} +(3.61133 + 1.06038i) q^{62} +(0.732186 - 5.09247i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-2.13175 - 2.46017i) q^{65} -4.74285 q^{66} +(-0.641349 - 8.16019i) q^{67} +2.92489 q^{68} +(0.168508 + 0.194469i) q^{69} +(-0.981849 + 2.14995i) q^{70} +(-0.903983 + 6.28734i) q^{71} +(2.08858 + 0.613262i) q^{72} +(-9.00798 + 2.64498i) q^{73} +(0.607686 + 0.701307i) q^{74} +(-0.763295 + 0.490540i) q^{75} +(5.60023 + 6.46301i) q^{76} +(5.13238 + 11.2384i) q^{77} +(-2.83396 - 0.832126i) q^{78} +(-9.38615 - 6.03211i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(-0.322842 + 2.24541i) q^{81} +(-2.81531 + 3.24904i) q^{82} +(1.17028 + 0.343626i) q^{83} +(0.305195 + 2.12268i) q^{84} +(0.416255 - 2.89512i) q^{85} +(-6.08030 + 7.01704i) q^{86} +(-2.46283 + 5.39285i) q^{87} +(-5.01552 + 1.47269i) q^{88} +(6.64727 + 14.5555i) q^{89} +(0.904255 - 1.98004i) q^{90} +(1.09496 + 7.61564i) q^{91} +(0.238580 + 0.153326i) q^{92} +(-0.486005 - 3.38024i) q^{93} +(-4.98617 + 1.46407i) q^{94} +(7.19422 - 4.62344i) q^{95} -0.907330 q^{96} -3.85643 q^{97} +(-1.18927 + 0.764299i) q^{98} +(-4.72678 - 10.3502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9} + 5 q^{10} + 30 q^{11} - 9 q^{12} + 20 q^{13} - 21 q^{14} - 2 q^{15} - 5 q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + 5 q^{20} + 23 q^{21} - 3 q^{22} - 5 q^{23} + 2 q^{24} - 5 q^{25} - 2 q^{26} + 2 q^{27} - 10 q^{28} + 26 q^{29} - 2 q^{30} + 3 q^{31} - 5 q^{32} + 38 q^{33} + 2 q^{34} - 12 q^{35} - q^{36} + 22 q^{37} - 40 q^{38} - 35 q^{39} + 5 q^{40} - 18 q^{41} - 10 q^{42} + 87 q^{43} - 3 q^{44} + 12 q^{45} + 17 q^{46} + 35 q^{47} + 2 q^{48} + 60 q^{49} - 5 q^{50} + 19 q^{51} - 24 q^{52} - 9 q^{53} + 2 q^{54} + 25 q^{55} + 12 q^{56} + 64 q^{57} + 4 q^{58} - 49 q^{59} - 2 q^{60} - 47 q^{61} - 19 q^{62} - 24 q^{63} - 5 q^{64} + 24 q^{65} - 6 q^{66} - 21 q^{67} + 2 q^{68} - 25 q^{69} - 12 q^{70} + 92 q^{71} - q^{72} + 18 q^{73} - 22 q^{74} - 9 q^{75} + 4 q^{76} - 65 q^{77} + 31 q^{78} - 58 q^{79} + 5 q^{80} - 77 q^{81} - 18 q^{82} - 49 q^{83} - 54 q^{84} - 2 q^{85} - q^{86} - 147 q^{87} + 30 q^{88} - 21 q^{89} + 12 q^{90} + 62 q^{91} + 6 q^{92} - 34 q^{93} - 9 q^{94} + 7 q^{95} + 2 q^{96} + 98 q^{97} - 39 q^{98} - 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9 + 5 * q^10 + 30 * q^11 - 9 * q^12 + 20 * q^13 - 21 * q^14 - 2 * q^15 - 5 * q^16 + 2 * q^17 - q^18 + 4 * q^19 + 5 * q^20 + 23 * q^21 - 3 * q^22 - 5 * q^23 + 2 * q^24 - 5 * q^25 - 2 * q^26 + 2 * q^27 - 10 * q^28 + 26 * q^29 - 2 * q^30 + 3 * q^31 - 5 * q^32 + 38 * q^33 + 2 * q^34 - 12 * q^35 - q^36 + 22 * q^37 - 40 * q^38 - 35 * q^39 + 5 * q^40 - 18 * q^41 - 10 * q^42 + 87 * q^43 - 3 * q^44 + 12 * q^45 + 17 * q^46 + 35 * q^47 + 2 * q^48 + 60 * q^49 - 5 * q^50 + 19 * q^51 - 24 * q^52 - 9 * q^53 + 2 * q^54 + 25 * q^55 + 12 * q^56 + 64 * q^57 + 4 * q^58 - 49 * q^59 - 2 * q^60 - 47 * q^61 - 19 * q^62 - 24 * q^63 - 5 * q^64 + 24 * q^65 - 6 * q^66 - 21 * q^67 + 2 * q^68 - 25 * q^69 - 12 * q^70 + 92 * q^71 - q^72 + 18 * q^73 - 22 * q^74 - 9 * q^75 + 4 * q^76 - 65 * q^77 + 31 * q^78 - 58 * q^79 + 5 * q^80 - 77 * q^81 - 18 * q^82 - 49 * q^83 - 54 * q^84 - 2 * q^85 - q^86 - 147 * q^87 + 30 * q^88 - 21 * q^89 + 12 * q^90 + 62 * q^91 + 6 * q^92 - 34 * q^93 - 9 * q^94 + 7 * q^95 + 2 * q^96 + 98 * q^97 - 39 * q^98 - 4 * q^99

Introduction

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