LMFDB - Embedded newform 961.2.g.j.338.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$961 = 31^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	961.g (of order $15$ , degree $8$ , not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1$ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			338.2
Root			$1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.338
Dual form			961.2.g.j.816.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.557811 - 0.405274i) q^{2} +(-0.0943266 + 0.897457i) q^{3} +(-0.471127 + 1.44998i) q^{4} +(-1.85376 + 3.21080i) q^{5} +(0.311099 + 0.538840i) q^{6} +(-0.746712 + 0.158719i) q^{7} +(0.750969 + 2.31124i) q^{8} +(2.13791 + 0.454427i) q^{9} +(0.267207 + 2.54230i) q^{10} +(2.75389 + 3.05850i) q^{11} +(-1.25686 - 0.559588i) q^{12} +(2.65819 - 1.18350i) q^{13} +(-0.352200 + 0.391158i) q^{14} +(-2.70670 - 1.96653i) q^{15} +(-1.11127 - 0.807384i) q^{16} +(-0.875573 + 0.972423i) q^{17} +(1.37672 - 0.612954i) q^{18} +(-3.47105 - 1.54541i) q^{19} +(-3.78225 - 4.20061i) q^{20} +(-0.0720083 - 0.685114i) q^{21} +(2.77568 + 0.589989i) q^{22} +(1.01449 + 3.12228i) q^{23} +(-2.14508 + 0.455951i) q^{24} +(-4.37284 - 7.57398i) q^{25} +(1.00313 - 1.73747i) q^{26} +(-1.44606 + 4.45052i) q^{27} +(0.121658 - 1.15749i) q^{28} +(3.96065 - 2.87758i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(-3.00464 + 2.18300i) q^{33} +(-0.0943074 + 0.897275i) q^{34} +(0.874609 - 2.69177i) q^{35} +(-1.66614 + 2.88584i) q^{36} +(-5.20639 - 9.01773i) q^{37} +(-2.56251 + 0.544678i) q^{38} +(0.811405 + 2.49725i) q^{39} +(-8.81306 - 1.87327i) q^{40} +(-0.0790179 - 0.751805i) q^{41} +(-0.317826 - 0.352981i) q^{42} +(6.53814 + 2.91097i) q^{43} +(-5.73220 + 2.55214i) q^{44} +(-5.42224 + 6.02201i) q^{45} +(1.83127 + 1.33050i) q^{46} +(0.708753 + 0.514939i) q^{47} +(0.829415 - 0.921159i) q^{48} +(-5.86243 + 2.61012i) q^{49} +(-5.50875 - 2.45265i) q^{50} +(-0.790118 - 0.877515i) q^{51} +(0.463710 + 4.41190i) q^{52} +(3.49757 + 0.743431i) q^{53} +(0.997049 + 3.06860i) q^{54} +(-14.9253 + 3.17247i) q^{55} +(-0.927595 - 1.60664i) q^{56} +(1.71435 - 2.96935i) q^{57} +(1.04309 - 3.21029i) q^{58} +(-0.0969261 + 0.922190i) q^{59} +(4.12664 - 2.99818i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(-1.01693 + 0.738843i) q^{64} +(-1.12765 + 10.7289i) q^{65} +(-0.791311 + 2.43540i) q^{66} +(1.04345 - 1.80731i) q^{67} +(-0.997488 - 1.72770i) q^{68} +(-2.89781 + 0.615948i) q^{69} +(-0.603037 - 1.85596i) q^{70} +(7.56703 + 1.60842i) q^{71} +(0.555212 + 5.28249i) q^{72} +(3.78559 + 4.20433i) q^{73} +(-6.55883 - 2.92018i) q^{74} +(7.20980 - 3.21001i) q^{75} +(3.87613 - 4.30487i) q^{76} +(-2.54180 - 1.84673i) q^{77} +(1.46468 + 1.06415i) q^{78} +(9.43121 - 10.4744i) q^{79} +(4.65238 - 2.07137i) q^{80} +(2.13238 + 0.949398i) q^{81} +(-0.348764 - 0.387341i) q^{82} +(-1.47466 - 14.0304i) q^{83} +(1.02733 + 0.218365i) q^{84} +(-1.49916 - 4.61393i) q^{85} +(4.82679 - 1.02597i) q^{86} +(2.20891 + 3.82595i) q^{87} +(-5.00086 + 8.66175i) q^{88} +(1.37043 - 4.21776i) q^{89} +(-0.584026 + 5.55664i) q^{90} +(-1.79706 + 1.30564i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(11.3965 - 8.28005i) q^{95} +(0.547798 - 5.21195i) q^{96} +(-1.63088 + 5.01933i) q^{97} +(-2.21232 + 3.83184i) q^{98} +(4.49770 + 7.79025i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} + 7 q^{11} + 10 q^{12} - 8 q^{13} - 21 q^{14} - 14 q^{15} - 2 q^{16} - 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots - 6 q^{99}+O(q^{100})$ 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 + 7 * q^11 + 10 * q^12 - 8 * q^13 - 21 * q^14 - 14 * q^15 - 2 * q^16 - 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 + 6 * q^21 + 21 * q^22 - q^23 + 5 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 45 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 17 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 51 * q^42 + 37 * q^43 + 6 * q^44 - 70 * q^45 - 34 * q^46 + 14 * q^47 - 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 + 46 * q^52 + 9 * q^53 + 46 * q^54 - 8 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 - 11 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 - 18 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 + 13 * q^73 - 43 * q^74 + 17 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 + 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 - 44 * q^83 - 23 * q^84 - 37 * q^85 - 19 * q^86 + 15 * q^87 + 17 * q^88 - q^89 + 7 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$ .

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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

)

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

$2$	0.557811	−	0.405274i	0.394432	−	0.286572i	−0.372837	−	0.927897i	$-0.621615\pi$
$2$	0.557811	−	0.405274i	0.394432	−	0.286572i	0.767269	+	0.641325i	$0.221615\pi$
$3$	−0.0943266	+	0.897457i	−0.0544595	+	0.518147i	0.932955	+	0.359993i	$0.117221\pi$
$3$	−0.0943266	+	0.897457i	−0.0544595	+	0.518147i	−0.987414	+	0.158154i	$0.949446\pi$
$4$	−0.471127	+	1.44998i	−0.235564	+	0.724990i
$5$	−1.85376	+	3.21080i	−0.829026	+	1.43591i	0.0697774	+	0.997563i	$0.477771\pi$
$5$	−1.85376	+	3.21080i	−0.829026	+	1.43591i	−0.898803	+	0.438352i	$0.855562\pi$
$6$	0.311099	+	0.538840i	0.127006	+	0.219981i
$7$	−0.746712	+	0.158719i	−0.282231	+	0.0599900i	−0.346852	−	0.937920i	$-0.612749\pi$
$7$	−0.746712	+	0.158719i	−0.282231	+	0.0599900i	0.0646214	+	0.997910i	$0.479416\pi$
$8$	0.750969	+	2.31124i	0.265508	+	0.817148i
$9$	2.13791	+	0.454427i	0.712637	+	0.151476i
$10$	0.267207	+	2.54230i	0.0844982	+	0.803946i
$11$	2.75389	+	3.05850i	0.830329	+	0.922174i	0.997971	−	0.0636744i	$-0.0202819\pi$
$11$	2.75389	+	3.05850i	0.830329	+	0.922174i	−0.167642	+	0.985848i	$0.553615\pi$
$12$	−1.25686	−	0.559588i	−0.362823	−	0.161539i
$13$	2.65819	−	1.18350i	0.737249	−	0.328245i	−0.00352937	−	0.999994i	$-0.501123\pi$
$13$	2.65819	−	1.18350i	0.737249	−	0.328245i	0.740779	+	0.671749i	$0.234457\pi$
$14$	−0.352200	+	0.391158i	−0.0941294	+	0.104541i
$15$	−2.70670	−	1.96653i	−0.698867	−	0.507757i
$16$	−1.11127	−	0.807384i	−0.277817	−	0.201846i
$17$	−0.875573	+	0.972423i	−0.212358	+	0.235847i	−0.839908	−	0.542729i	$-0.817391\pi$
$17$	−0.875573	+	0.972423i	−0.212358	+	0.235847i	0.627550	+	0.778576i	$0.284058\pi$
$18$	1.37672	−	0.612954i	0.324496	−	0.144475i
$19$	−3.47105	−	1.54541i	−0.796314	−	0.354542i	−0.0320839	−	0.999485i	$-0.510214\pi$
$19$	−3.47105	−	1.54541i	−0.796314	−	0.354542i	−0.764231	+	0.644943i	$0.776881\pi$
$20$	−3.78225	−	4.20061i	−0.845736	−	0.939285i
$21$	−0.0720083	−	0.685114i	−0.0157135	−	0.149504i
$22$	2.77568	+	0.589989i	0.591777	+	0.125786i
$23$	1.01449	+	3.12228i	0.211536	+	0.651040i	0.999381	+	0.0351674i	$0.0111964\pi$
$23$	1.01449	+	3.12228i	0.211536	+	0.651040i	−0.787846	+	0.615873i	$0.788804\pi$
$24$	−2.14508	+	0.455951i	−0.437863	+	0.0930706i
$25$	−4.37284	−	7.57398i	−0.874568	−	1.51480i
$26$	1.00313	−	1.73747i	0.196729	−	0.340745i
$27$	−1.44606	+	4.45052i	−0.278295	+	0.856503i
$28$	0.121658	−	1.15749i	0.0229911	−	0.218746i
$29$	3.96065	−	2.87758i	0.735474	−	0.534353i	−0.155816	−	0.987786i	$-0.549801\pi$
$29$	3.96065	−	2.87758i	0.735474	−	0.534353i	0.891290	+	0.453433i	$0.149801\pi$
$30$	−2.30681			−0.421164
$31$		0			0
$31$		0			0
$32$	−5.80746			−1.02662
$33$	−3.00464	+	2.18300i	−0.523041	+	0.380012i
$34$	−0.0943074	+	0.897275i	−0.0161736	+	0.153881i
$35$	0.874609	−	2.69177i	0.147836	−	0.454992i
$36$	−1.66614	+	2.88584i	−0.277690	+	0.480973i
$37$	−5.20639	−	9.01773i	−0.855925	−	1.48251i	−0.875784	−	0.482704i	$-0.839655\pi$
$37$	−5.20639	−	9.01773i	−0.855925	−	1.48251i	0.0198583	−	0.999803i	$-0.493679\pi$
$38$	−2.56251	+	0.544678i	−0.415694	+	0.0883584i
$39$	0.811405	+	2.49725i	0.129929	+	0.399880i
$40$	−8.81306	−	1.87327i	−1.39347	−	0.296191i
$41$	−0.0790179	−	0.751805i	−0.0123405	−	0.117412i	0.986617	−	0.163052i	$-0.0521339\pi$
$41$	−0.0790179	−	0.751805i	−0.0123405	−	0.117412i	−0.998958	+	0.0456401i	$0.985467\pi$
$42$	−0.317826	−	0.352981i	−0.0490415	−	0.0544662i
$43$	6.53814	+	2.91097i	0.997058	+	0.443919i	0.839364	−	0.543569i	$-0.182928\pi$
$43$	6.53814	+	2.91097i	0.997058	+	0.443919i	0.157693	+	0.987488i	$0.449594\pi$
$44$	−5.73220	+	2.55214i	−0.864162	+	0.384750i
$45$	−5.42224	+	6.02201i	−0.808300	+	0.897709i
$46$	1.83127	+	1.33050i	0.270006	+	0.196171i
$47$	0.708753	+	0.514939i	0.103382	+	0.0751116i	0.638275	−	0.769808i	$-0.279648\pi$
$47$	0.708753	+	0.514939i	0.103382	+	0.0751116i	−0.534893	+	0.844920i	$0.679648\pi$
$48$	0.829415	−	0.921159i	0.119716	−	0.132958i
$49$	−5.86243	+	2.61012i	−0.837490	+	0.372875i
$50$	−5.50875	−	2.45265i	−0.779055	−	0.346858i
$51$	−0.790118	−	0.877515i	−0.110639	−	0.122877i
$52$	0.463710	+	4.41190i	0.0643050	+	0.611821i
$53$	3.49757	+	0.743431i	0.480428	+	0.102118i	0.441759	−	0.897134i	$-0.354355\pi$
$53$	3.49757	+	0.743431i	0.480428	+	0.102118i	0.0386692	+	0.999252i	$0.487688\pi$
$54$	0.997049	+	3.06860i	0.135681	+	0.417584i
$55$	−14.9253	+	3.17247i	−2.01253	+	0.427776i
$56$	−0.927595	−	1.60664i	−0.123955	−	0.214696i
$57$	1.71435	−	2.96935i	0.227072	−	0.393300i
$58$	1.04309	−	3.21029i	0.136964	−	0.421532i
$59$	−0.0969261	+	0.922190i	−0.0126187	+	0.120059i	−0.999018	−	0.0443084i	$-0.985892\pi$
$59$	−0.0969261	+	0.922190i	−0.0126187	+	0.120059i	0.986399	+	0.164367i	$0.0525582\pi$
$60$	4.12664	−	2.99818i	0.532746	−	0.387063i
$61$	−2.31704			−0.296666			−0.148333	−	0.988937i	$-0.547391\pi$
$61$	−2.31704			−0.296666			−0.148333	+	0.988937i	$0.547391\pi$
$62$		0			0
$63$	−1.66853			−0.210215
$64$	−1.01693	+	0.738843i	−0.127116	+	0.0923554i
$65$	−1.12765	+	10.7289i	−0.139867	+	1.33075i
$66$	−0.791311	+	2.43540i	−0.0974036	+	0.299778i
$67$	1.04345	−	1.80731i	0.127478	−	0.220798i	−0.795221	−	0.606320i	$-0.792645\pi$
$67$	1.04345	−	1.80731i	0.127478	−	0.220798i	0.922699	+	0.385522i	$0.125979\pi$
$68$	−0.997488	−	1.72770i	−0.120963	−	0.209514i
$69$	−2.89781	+	0.615948i	−0.348855	+	0.0741514i
$70$	−0.603037	−	1.85596i	−0.0720767	−	0.221829i
$71$	7.56703	+	1.60842i	0.898042	+	0.190885i	0.633731	−	0.773553i	$-0.281522\pi$
$71$	7.56703	+	1.60842i	0.898042	+	0.190885i	0.264310	+	0.964438i	$0.414856\pi$
$72$	0.555212	+	5.28249i	0.0654324	+	0.622548i
$73$	3.78559	+	4.20433i	0.443070	+	0.492079i	0.922769	−	0.385354i	$-0.125921\pi$
$73$	3.78559	+	4.20433i	0.443070	+	0.492079i	−0.479699	+	0.877433i	$0.659254\pi$
$74$	−6.55883	−	2.92018i	−0.762449	−	0.339464i
$75$	7.20980	−	3.21001i	0.832516	−	0.370660i
$76$	3.87613	−	4.30487i	0.444622	−	0.493803i
$77$	−2.54180	−	1.84673i	−0.289665	−	0.210454i
$78$	1.46468	+	1.06415i	0.165842	+	0.120492i
$79$	9.43121	−	10.4744i	1.06109	−	1.17846i	0.0777003	−	0.996977i	$-0.475242\pi$
$79$	9.43121	−	10.4744i	1.06109	−	1.17846i	0.983393	−	0.181487i	$-0.0580911\pi$
$80$	4.65238	−	2.07137i	0.520151	−	0.231586i
$81$	2.13238	+	0.949398i	0.236931	+	0.105489i
$82$	−0.348764	−	0.387341i	−0.0385145	−	0.0427747i
$83$	−1.47466	−	14.0304i	−0.161865	−	1.54004i	−0.710331	−	0.703867i	$-0.751455\pi$
$83$	−1.47466	−	14.0304i	−0.161865	−	1.54004i	0.548467	−	0.836172i	$-0.315212\pi$
$84$	1.02733	+	0.218365i	0.112090	+	0.0238256i
$85$	−1.49916	−	4.61393i	−0.162606	−	0.500451i
$86$	4.82679	−	1.02597i	0.520486	−	0.110633i
$87$	2.20891	+	3.82595i	0.236820	+	0.410184i
$88$	−5.00086	+	8.66175i	−0.533094	+	0.923346i
$89$	1.37043	−	4.21776i	0.145266	−	0.447081i	−0.851780	−	0.523900i	$-0.824476\pi$
$89$	1.37043	−	4.21776i	0.145266	−	0.447081i	0.997045	+	0.0768191i	$0.0244764\pi$
$90$	−0.584026	+	5.55664i	−0.0615618	+	0.585721i
$91$	−1.79706	+	1.30564i	−0.188383	+	0.136868i
$92$	−5.00520			−0.521828
$93$		0			0
$94$	0.604042			0.0623021
$95$	11.3965	−	8.28005i	1.16926	−	0.849515i
$96$	0.547798	−	5.21195i	0.0559094	−	0.531942i
$97$	−1.63088	+	5.01933i	−0.165591	+	0.509636i	−0.999079	−	0.0429007i	$-0.986340\pi$
$97$	−1.63088	+	5.01933i	−0.165591	+	0.509636i	0.833489	+	0.552537i	$0.186340\pi$
$98$	−2.21232	+	3.83184i	−0.223478	+	0.387075i
$99$	4.49770	+	7.79025i	0.452036	+	0.782949i
$100$	13.0423	−	2.77222i	1.30423	−	0.277222i
$101$	1.17656	+	3.62108i	0.117072	+	0.360311i	0.992374	−	0.123267i	$-0.0393371\pi$
$101$	1.17656	+	3.62108i	0.117072	+	0.360311i	−0.875301	+	0.483578i	$0.839337\pi$
$102$	−0.796371	−	0.169274i	−0.0788525	−	0.0167606i
$103$	0.652853	+	6.21148i	0.0643275	+	0.612035i	0.978434	+	0.206561i	$0.0662271\pi$
$103$	0.652853	+	6.21148i	0.0643275	+	0.612035i	−0.914106	+	0.405475i	$0.867106\pi$
$104$	4.73158	+	5.25495i	0.463970	+	0.515290i
$105$	2.33325	+	1.03883i	0.227702	+	0.101379i
$106$	2.25228	−	1.00278i	0.218760	−	0.0973984i
$107$	1.55732	−	1.72958i	0.150552	−	0.167205i	−0.663151	−	0.748485i	$-0.730781\pi$
$107$	1.55732	−	1.72958i	0.150552	−	0.167205i	0.813703	+	0.581280i	$0.197448\pi$
$108$	−5.77189	−	4.19352i	−0.555400	−	0.403522i
$109$	−1.19478	−	0.868057i	−0.114439	−	0.0831448i	0.529094	−	0.848563i	$-0.322532\pi$
$109$	−1.19478	−	0.868057i	−0.114439	−	0.0831448i	−0.643533	+	0.765419i	$0.722532\pi$
$110$	−7.03978	+	7.81847i	−0.671217	+	0.745462i
$111$	8.58413	−	3.82190i	0.814770	−	0.362759i
$112$	0.957945	+	0.426504i	0.0905173	+	0.0403009i
$113$	4.26942	+	4.74167i	0.401633	+	0.446059i	0.909705	−	0.415256i	$-0.136308\pi$
$113$	4.26942	+	4.74167i	0.401633	+	0.446059i	−0.508071	+	0.861315i	$0.669641\pi$
$114$	−0.247113	−	2.35112i	−0.0231442	−	0.220203i
$115$	−11.9056	−	2.53062i	−1.11021	−	0.235982i
$116$	2.30647	+	7.09857i	0.214150	+	0.659086i
$117$	6.22079	−	1.32227i	0.575112	−	0.122244i
$118$	0.319673	+	0.553690i	0.0294283	+	0.0509713i
$119$	0.499460	−	0.865089i	0.0457854	−	0.0793026i
$120$	2.51249	−	7.73265i	0.229358	−	0.705891i
$121$	−0.620727	+	5.90582i	−0.0564297	+	0.536893i
$122$	−1.29247	+	0.939035i	−0.117015	+	0.0850162i
$123$	0.682166			0.0615089
$124$		0			0
$125$	13.8872			1.24211
$126$	−0.930724	+	0.676211i	−0.0829155	+	0.0602417i
$127$	−0.149686	+	1.42417i	−0.0132825	+	0.126375i	−0.999154	−	0.0411300i	$-0.986904\pi$
$127$	−0.149686	+	1.42417i	−0.0132825	+	0.126375i	0.985871	+	0.167505i	$0.0535709\pi$
$128$	3.32139	−	10.2222i	0.293572	−	0.903521i
$129$	−3.22919	+	5.59312i	−0.284314	+	0.492447i
$130$	3.71911	+	6.44168i	0.326187	+	0.564973i
$131$	−6.15538	+	1.30837i	−0.537798	+	0.114313i	−0.468800	−	0.883304i	$-0.655314\pi$
$131$	−6.15538	+	1.30837i	−0.537798	+	0.114313i	−0.0689982	+	0.997617i	$0.521980\pi$
$132$	−1.74974	−	5.38514i	−0.152295	−	0.468717i
$133$	2.83716	+	0.603058i	0.246013	+	0.0522917i
$134$	−0.150406	−	1.43102i	−0.0129931	−	0.123621i
$135$	−11.6091	−	12.8932i	−0.999152	−	1.10967i
$136$	−2.90503	−	1.29340i	−0.249105	−	0.110909i
$137$	−11.6476	+	5.18585i	−0.995123	+	0.443057i	−0.838677	−	0.544629i	$-0.816670\pi$
$137$	−11.6476	+	5.18585i	−0.995123	+	0.443057i	−0.156446	+	0.987686i	$0.550004\pi$
$138$	−1.36680	+	1.51799i	−0.116350	+	0.129220i
$139$	15.1397	+	10.9997i	1.28414	+	0.932979i	0.999670	−	0.0257067i	$-0.00818361\pi$
$139$	15.1397	+	10.9997i	1.28414	+	0.932979i	0.284466	+	0.958686i	$0.408184\pi$
$140$	3.49096	+	2.53633i	0.295040	+	0.214359i
$141$	−0.528990	+	0.587503i	−0.0445490	+	0.0494767i
$142$	4.87283	−	2.16952i	0.408919	−	0.182062i
$143$	10.9401	+	4.87085i	0.914858	+	0.407321i
$144$	−2.00890	−	2.23111i	−0.167408	−	0.185925i
$145$	1.89726	+	18.0512i	0.157559	+	1.49907i
$146$	3.81555	+	0.811020i	0.315777	+	0.0671205i
$147$	−1.78949	−	5.50749i	−0.147595	−	0.454250i
$148$	15.5284	−	3.30067i	1.27643	−	0.271313i
$149$	10.0677	+	17.4377i	0.824774	+	1.42855i	0.902092	+	0.431545i	$0.142031\pi$
$149$	10.0677	+	17.4377i	0.824774	+	1.42855i	−0.0773172	+	0.997007i	$0.524635\pi$
$150$	2.72078	−	4.71252i	0.222150	−	0.384776i
$151$	−4.75035	+	14.6201i	−0.386578	+	1.18977i	0.548751	+	0.835986i	$0.315104\pi$
$151$	−4.75035	+	14.6201i	−0.386578	+	1.18977i	−0.935329	+	0.353779i	$0.884896\pi$
$152$	0.965173	−	9.18301i	0.0782859	−	0.744840i
$153$	−2.31379	+	1.68107i	−0.187059	+	0.135906i
$154$	−2.16628			−0.174564
$155$		0			0
$156$	−4.00324			−0.320515
$157$	−12.2544	+	8.90334i	−0.978008	+	0.710564i	−0.957262	−	0.289221i	$-0.906604\pi$
$157$	−12.2544	+	8.90334i	−0.978008	+	0.710564i	−0.0207452	+	0.999785i	$0.506604\pi$
$158$	1.01583	−	9.66497i	0.0808150	−	0.768904i
$159$	−0.997111	+	3.06879i	−0.0790760	+	0.243371i
$160$	10.7656	−	18.6466i	0.851098	−	1.47414i
$161$	−1.25310	−	2.17042i	−0.0987577	−	0.171053i
$162$	1.57423	−	0.334614i	0.123683	−	0.0262897i
$163$	−0.322882	−	0.993730i	−0.0252901	−	0.0778349i	0.937615	−	0.347676i	$-0.113029\pi$
$163$	−0.322882	−	0.993730i	−0.0252901	−	0.0778349i	−0.962905	+	0.269841i	$0.913029\pi$
$164$	1.12733	+	0.239621i	0.0880297	+	0.0187113i
$165$	−1.43930	−	13.6941i	−0.112050	−	1.06608i
$166$	−6.50874	−	7.22869i	−0.505177	−	0.561055i
$167$	10.3134	+	4.59181i	0.798074	+	0.355325i	0.764920	−	0.644125i	$-0.222778\pi$
$167$	10.3134	+	4.59181i	0.798074	+	0.355325i	0.0331533	+	0.999450i	$0.489445\pi$
$168$	1.52939	−	0.680928i	0.117995	−	0.0525347i
$169$	−3.03340	+	3.36893i	−0.233339	+	0.259149i
$170$	−2.70615	−	1.96613i	−0.207552	−	0.150796i
$171$	−6.71853	−	4.88129i	−0.513778	−	0.373282i
$172$	−7.30115	+	8.10874i	−0.556707	+	0.618286i
$173$	−18.8672	+	8.40020i	−1.43444	+	0.638656i	−0.969143	−	0.246497i	$-0.920720\pi$
$173$	−18.8672	+	8.40020i	−1.43444	+	0.638656i	−0.465300	+	0.885153i	$0.654054\pi$
$174$	2.78271	+	1.23894i	0.210957	+	0.0939240i
$175$	4.46738	+	4.96153i	0.337702	+	0.375056i
$176$	−0.590924	−	5.62227i	−0.0445426	−	0.423794i
$177$	−0.818484	−	0.173974i	−0.0615210	−	0.0130767i
$178$	−0.944903	−	2.90811i	−0.0708235	−	0.217972i
$179$	−0.128785	+	0.0273741i	−0.00962586	+	0.00204604i	−0.212722	−	0.977113i	$-0.568233\pi$
$179$	−0.128785	+	0.0273741i	−0.00962586	+	0.00204604i	0.203096	+	0.979159i	$0.434900\pi$
$180$	−6.17723	−	10.6993i	−0.460424	−	0.797477i
$181$	3.86599	−	6.69610i	0.287357	−	0.497717i	−0.685821	−	0.727770i	$-0.740557\pi$
$181$	3.86599	−	6.69610i	0.287357	−	0.497717i	0.973178	+	0.230053i	$0.0738901\pi$
$182$	−0.473278	+	1.45660i	−0.0350817	+	0.107970i
$183$	0.218558	−	2.07944i	0.0161563	−	0.153717i
$184$	−6.45450	+	4.68947i	−0.475832	+	0.345712i
$185$	38.6056			2.83834
$186$		0			0
$187$	−5.38539			−0.393819
$188$	−1.08056	+	0.785076i	−0.0788083	+	0.0572576i
$189$	0.373412	−	3.55277i	0.0271617	−	0.258426i
$190$	3.00142	−	9.23741i	0.217746	−	0.670152i
$191$	10.5513	−	18.2755i	0.763468	−	1.32237i	−0.177585	−	0.984106i	$-0.556828\pi$
$191$	10.5513	−	18.2755i	0.763468	−	1.32237i	0.941053	−	0.338260i	$-0.109838\pi$
$192$	−0.567157	−	0.982344i	−0.0409310	−	0.0708946i
$193$	−5.53948	+	1.17745i	−0.398740	+	0.0847549i	−0.402917	−	0.915236i	$-0.632004\pi$
$193$	−5.53948	+	1.17745i	−0.398740	+	0.0847549i	0.00417685	+	0.999991i	$0.498670\pi$
$194$	1.12448	+	3.46079i	0.0807330	+	0.248471i
$195$	−9.52232	−	2.02403i	−0.681908	−	0.144944i
$196$	−1.02268	−	9.73011i	−0.0730483	−	0.695008i
$197$	−10.6491	−	11.8270i	−0.758716	−	0.842639i	0.232814	−	0.972521i	$-0.425207\pi$
$197$	−10.6491	−	11.8270i	−0.758716	−	0.842639i	−0.991529	+	0.129882i	$0.958540\pi$
$198$	5.66605	+	2.52269i	0.402669	+	0.179280i
$199$	3.89303	−	1.73329i	0.275970	−	0.122870i	−0.264085	−	0.964499i	$-0.585070\pi$
$199$	3.89303	−	1.73329i	0.275970	−	0.122870i	0.540055	+	0.841630i	$0.318403\pi$
$200$	14.2214	−	15.7945i	1.00561	−	1.11684i
$201$	1.52356	+	1.10693i	0.107463	+	0.0780767i
$202$	2.12383	+	1.54305i	0.149432	+	0.108569i
$203$	−2.50074	+	2.77735i	−0.175517	+	0.194932i
$204$	1.64463	−	0.732235i	0.115147	−	0.0512667i
$205$	2.56038	+	1.13995i	0.178824	+	0.0796178i
$206$	2.88152	+	3.20025i	0.200765	+	0.222972i
$207$	0.750041	+	7.13616i	0.0521315	+	0.495998i
$208$	−3.90950	−	0.830991i	−0.271075	−	0.0576189i
$209$	−4.83225	−	14.8721i	−0.334254	−	1.02873i
$210$	1.72252	−	0.366134i	0.118865	−	0.0252656i
$211$	5.75414	+	9.96646i	0.396131	+	0.686120i	0.993245	−	0.116037i	$-0.0370191\pi$
$211$	5.75414	+	9.96646i	0.396131	+	0.686120i	−0.597113	+	0.802157i	$0.703686\pi$
$212$	−2.72576	+	4.72115i	−0.187206	+	0.324250i
$213$	−2.15726	+	6.63937i	−0.147813	+	0.454922i
$214$	0.167738	−	1.59592i	0.0114664	−	0.109095i
$215$	−21.4667	+	15.5965i	−1.46402	+	1.06367i
$216$	−11.3722			−0.773780
$217$		0			0
$218$	−1.01826			−0.0689654
$219$	−4.13028	+	3.00083i	−0.279099	+	0.202777i
$220$	2.43169	−	23.1360i	0.163945	−	1.55983i
$221$	−1.17658	+	3.62113i	−0.0791450	+	0.243583i
$222$	3.23941	−	5.61082i	0.217415	−	0.376574i
$223$	4.71196	+	8.16135i	0.315536	+	0.546524i	0.979551	−	0.201195i	$-0.0644824\pi$
$223$	4.71196	+	8.16135i	0.315536	+	0.546524i	−0.664015	+	0.747719i	$0.731149\pi$
$224$	4.33650	−	0.921752i	0.289745	−	0.0615871i
$225$	−5.90692	−	18.1796i	−0.393795	−	1.21197i
$226$	4.30320	+	0.914674i	0.286245	+	0.0608432i
$227$	−2.27486	−	21.6438i	−0.150987	−	1.43655i	−0.763356	−	0.645978i	$-0.776450\pi$
$227$	−2.27486	−	21.6438i	−0.150987	−	1.43655i	0.612369	−	0.790572i	$-0.290217\pi$
$228$	3.49782	+	3.88472i	0.231649	+	0.257272i
$229$	−15.4900	−	6.89658i	−1.02361	−	0.455739i	−0.174891	−	0.984588i	$-0.555957\pi$
$229$	−15.4900	−	6.89658i	−1.02361	−	0.455739i	−0.848716	+	0.528849i	$0.822624\pi$
$230$	−7.66670	+	3.41343i	−0.505527	+	0.225075i
$231$	1.89712	−	2.10696i	0.124821	−	0.138628i
$232$	9.62511	+	6.99305i	0.631920	+	0.459117i
$233$	7.95758	+	5.78152i	0.521318	+	0.378760i	0.817100	−	0.576496i	$-0.195580\pi$
$233$	7.95758	+	5.78152i	0.521318	+	0.378760i	−0.295782	+	0.955255i	$0.595580\pi$
$234$	2.93414	−	3.25870i	0.191811	−	0.213028i
$235$	−2.96722	+	1.32109i	−0.193560	+	0.0861786i
$236$	−1.29149	−	0.575010i	−0.0840691	−	0.0374300i
$237$	8.51073	+	9.45212i	0.552831	+	0.613981i
$238$	−0.0719937	−	0.684975i	−0.00466666	−	0.0444003i
$239$	0.577728	+	0.122800i	0.0373701	+	0.00794327i	0.226559	−	0.973997i	$-0.427252\pi$
$239$	0.577728	+	0.122800i	0.0373701	+	0.00794327i	−0.189189	+	0.981941i	$0.560586\pi$
$240$	1.42012	+	4.37069i	0.0916687	+	0.282127i
$241$	15.0346	−	3.19570i	0.968461	−	0.205853i	0.303583	−	0.952805i	$-0.401817\pi$
$241$	15.0346	−	3.19570i	0.968461	−	0.205853i	0.664878	+	0.746952i	$0.268484\pi$
$242$	2.04722	+	3.54590i	0.131601	+	0.227939i
$243$	−8.07252	+	13.9820i	−0.517852	+	0.896946i
$244$	1.09162	−	3.35966i	0.0698838	−	0.215080i
$245$	2.48694	−	23.6616i	0.158885	−	1.51169i
$246$	0.380520	−	0.276464i	0.0242611	−	0.0176267i
$247$	−11.0557			−0.703459
$248$		0			0
$249$	12.7308			0.806783
$250$	7.74642	−	5.62810i	0.489926	−	0.355952i
$251$	−0.632554	+	6.01835i	−0.0399265	+	0.379875i	0.956253	+	0.292542i	$0.0945011\pi$
$251$	−0.632554	+	6.01835i	−0.0399265	+	0.379875i	−0.996179	+	0.0873331i	$0.972166\pi$
$252$	0.786090	−	2.41933i	0.0495190	−	0.152404i
$253$	−6.75571	+	11.7012i	−0.424728	+	0.735650i
$254$	0.493682	+	0.855082i	0.0309763	+	0.0536526i
$255$	4.28222	−	0.910213i	0.268163	−	0.0569998i
$256$	−3.06694	−	9.43906i	−0.191684	−	0.589942i
$257$	4.42890	+	0.941391i	0.276267	+	0.0587223i	0.343962	−	0.938984i	$-0.388231\pi$
$257$	4.42890	+	0.941391i	0.276267	+	0.0587223i	−0.0676946	+	0.997706i	$0.521564\pi$
$258$	0.465466	+	4.42861i	0.0289787	+	0.275713i
$259$	5.31896	+	5.90730i	0.330504	+	0.367062i
$260$	−15.0254	−	6.68972i	−0.931833	−	0.414879i
$261$	9.77516	−	4.35218i	0.605067	−	0.269393i
$262$	−2.90330	+	3.22444i	−0.179366	+	0.199206i
$263$	−2.02971	−	1.47467i	−0.125157	−	0.0909322i	0.523445	−	0.852059i	$-0.324646\pi$
$263$	−2.02971	−	1.47467i	−0.125157	−	0.0909322i	−0.648603	+	0.761127i	$0.724646\pi$
$264$	−7.30184	−	5.30510i	−0.449397	−	0.326506i
$265$	−8.87065	+	9.85186i	−0.544920	+	0.605195i
$266$	1.82701	−	0.813435i	0.112021	−	0.0498749i
$267$	3.65599	+	1.62775i	0.223743	+	0.0996167i
$268$	2.12896	+	2.36445i	0.130047	+	0.144432i
$269$	1.39439	+	13.2667i	0.0850172	+	0.808885i	0.951079	+	0.308948i	$0.0999768\pi$
$269$	1.39439	+	13.2667i	0.0850172	+	0.808885i	−0.866062	+	0.499937i	$0.833357\pi$
$270$	−11.7010	−	2.48712i	−0.712098	−	0.151361i
$271$	−4.27190	−	13.1476i	−0.259500	−	0.798658i	−0.992910	−	0.118871i	$-0.962072\pi$
$271$	−4.27190	−	13.1476i	−0.259500	−	0.798658i	0.733410	−	0.679787i	$-0.237928\pi$
$272$	1.75812	−	0.373699i	0.106601	−	0.0226588i
$273$	−1.00225	−	1.73594i	−0.0606586	−	0.105064i
$274$	−4.39548	+	7.61320i	−0.265541	+	0.459930i
$275$	11.1227	−	34.2322i	0.670726	−	2.06428i
$276$	0.472123	−	4.49195i	0.0284185	−	0.270384i
$277$	9.36093	−	6.80111i	0.562444	−	0.408639i	−0.269909	−	0.962886i	$-0.586994\pi$
$277$	9.36093	−	6.80111i	0.562444	−	0.408639i	0.832353	+	0.554247i	$0.186994\pi$
$278$	12.9030			0.773870
$279$		0			0
$280$	6.87814			0.411048
$281$	12.4583	−	9.05151i	0.743202	−	0.539968i	−0.150510	−	0.988608i	$-0.548092\pi$
$281$	12.4583	−	9.05151i	0.743202	−	0.539968i	0.893712	+	0.448641i	$0.148092\pi$
$282$	−0.0569772	+	0.542102i	−0.00339294	+	0.0322817i
$283$	−7.01336	+	21.5849i	−0.416901	+	1.28309i	0.493638	+	0.869667i	$0.335667\pi$
$283$	−7.01336	+	21.5849i	−0.416901	+	1.28309i	−0.910539	+	0.413422i	$0.864333\pi$
$284$	−5.89722	+	10.2143i	−0.349935	+	0.606106i
$285$	6.35600	+	11.0089i	0.376497	+	0.652112i
$286$	8.07654	−	1.71672i	0.477576	−	0.101512i
$287$	0.178329	+	0.548840i	0.0105264	+	0.0323970i
$288$	−12.4158	−	2.63907i	−0.731610	−	0.155509i
$289$	1.59801	+	15.2040i	0.0940004	+	0.894354i
$290$	8.37399	+	9.30026i	0.491738	+	0.546130i
$291$	−4.35080	−	1.93710i	−0.255049	−	0.113555i
$292$	−7.87969	+	3.50826i	−0.461124	+	0.205305i
$293$	8.29780	−	9.21564i	0.484762	−	0.538383i	−0.450295	−	0.892880i	$-0.648681\pi$
$293$	8.29780	−	9.21564i	0.484762	−	0.538383i	0.935057	+	0.354497i	$0.115348\pi$
$294$	−3.23024	−	2.34690i	−0.188391	−	0.136874i
$295$	−2.78129	−	2.02073i	−0.161933	−	0.117651i
$296$	16.9323	−	18.8053i	0.984173	−	1.09303i
$297$	−17.5942	+	7.83346i	−1.02092	+	0.454543i
$298$	12.6829	+	5.64679i	0.734700	+	0.327110i
$299$	6.39193	+	7.09896i	0.369655	+	0.410543i
$300$	1.25772	+	11.9664i	0.0726144	+	0.690880i
$301$	−5.34413	−	1.13593i	−0.308031	−	0.0654740i
$302$	3.27533	+	10.0804i	0.188474	+	0.580064i
$303$	−3.36075	+	0.714349i	−0.193070	+	0.0410383i
$304$	2.60953	+	4.51984i	0.149667	+	0.259231i
$305$	4.29523	−	7.43956i	0.245944	−	0.425988i
$306$	−0.609367	+	1.87544i	−0.0348352	+	0.107212i
$307$	−3.21111	+	30.5517i	−0.183268	+	1.74368i	0.386875	+	0.922132i	$0.373554\pi$
$307$	−3.21111	+	30.5517i	−0.183268	+	1.74368i	−0.570143	+	0.821546i	$0.693112\pi$
$308$	3.87523	−	2.81552i	0.220812	−	0.160429i
$309$	−5.63612			−0.320628
$310$		0			0
$311$	2.38141			0.135037			0.0675187	−	0.997718i	$-0.478492\pi$
$311$	2.38141			0.135037			0.0675187	+	0.997718i	$0.478492\pi$
$312$	−5.16241	+	3.75071i	−0.292264	+	0.212342i
$313$	1.12322	−	10.6867i	0.0634882	−	0.604049i	−0.915808	−	0.401616i	$-0.868449\pi$
$313$	1.12322	−	10.6867i	0.0634882	−	0.604049i	0.979296	−	0.202433i	$-0.0648848\pi$
$314$	−3.22735	+	9.93277i	−0.182130	+	0.560539i
$315$	3.09305	−	5.35732i	0.174274	−	0.301851i
$316$	10.7444	+	18.6098i	0.604420	+	1.04689i
$317$	−8.55522	+	1.81847i	−0.480509	+	0.102135i	−0.441797	−	0.897115i	$-0.645659\pi$
$317$	−8.55522	+	1.81847i	−0.480509	+	0.102135i	−0.0387120	+	0.999250i	$0.512326\pi$
$318$	0.687501	+	2.11591i	0.0385531	+	0.118654i
$319$	19.7083	+	4.18912i	1.10345	+	0.234546i
$320$	−0.487137	−	4.63480i	−0.0272318	−	0.259093i
$321$	1.40533	+	1.56078i	0.0784379	+	0.0871141i
$322$	−1.57861	−	0.702841i	−0.0879723	−	0.0391678i
$323$	4.54196	−	2.02221i	0.252721	−	0.112519i
$324$	−2.38123	+	2.64463i	−0.132291	+	0.146924i
$325$	−20.5877	−	14.9578i	−1.14200	−	0.829710i
$326$	−0.582840	−	0.423458i	−0.0322805	−	0.0234532i
$327$	0.891744	−	0.990382i	0.0493135	−	0.0547682i
$328$	1.67826	−	0.747211i	0.0926666	−	0.0412578i
$329$	−0.610965	−	0.272019i	−0.0336836	−	0.0149969i
$330$	−6.35271	−	7.05539i	−0.349705	−	0.388387i
$331$	−3.38349	−	32.1918i	−0.185974	−	1.76942i	−0.547257	−	0.836964i	$-0.684328\pi$
$331$	−3.38349	−	32.1918i	−0.185974	−	1.76942i	0.361284	−	0.932456i	$-0.382339\pi$
$332$	21.0386	+	4.47189i	1.15464	+	0.245427i
$333$	−7.03290	−	21.6450i	−0.385400	−	1.18614i
$334$	7.61386	−	1.61838i	0.416612	−	0.0885536i
$335$	3.86860	+	6.70062i	0.211364	+	0.366094i
$336$	−0.473129	+	0.819484i	−0.0258113	+	0.0447065i
$337$	−8.57021	+	26.3764i	−0.466849	+	1.43681i	0.389792	+	0.920903i	$0.372547\pi$
$337$	−8.57021	+	26.3764i	−0.466849	+	1.43681i	−0.856642	+	0.515912i	$0.827453\pi$
$338$	−0.326726	+	3.10859i	−0.0177715	+	0.169085i
$339$	−4.65817	+	3.38436i	−0.252997	+	0.183813i
$340$	7.39640			0.401126
$341$		0			0
$342$	−5.72593			−0.309623
$343$	8.28646	−	6.02047i	0.447427	−	0.325075i
$344$	−1.81802	+	17.2973i	−0.0980210	+	0.932608i
$345$	3.39414	−	10.4461i	0.182735	−	0.562399i
$346$	−7.11994	+	12.3321i	−0.382770	+	0.662977i
$347$	−12.9580	−	22.4440i	−0.695624	−	1.20486i	−0.969970	−	0.243224i	$-0.921795\pi$
$347$	−12.9580	−	22.4440i	−0.695624	−	1.20486i	0.274347	−	0.961631i	$-0.411538\pi$
$348$	−6.58823	+	1.40037i	−0.353166	+	0.0750677i
$349$	1.72862	+	5.32015i	0.0925309	+	0.284781i	0.986602	−	0.163144i	$-0.0521634\pi$
$349$	1.72862	+	5.32015i	0.0925309	+	0.284781i	−0.894071	+	0.447924i	$0.852163\pi$
$350$	4.50273	+	0.957086i	0.240681	+	0.0511584i
$351$	1.42330	+	13.5418i	0.0759699	+	0.722805i
$352$	−15.9931	−	17.7621i	−0.852435	−	0.946725i
$353$	−10.6601	−	4.74620i	−0.567382	−	0.252615i	0.102937	−	0.994688i	$-0.467176\pi$
$353$	−10.6601	−	4.74620i	−0.567382	−	0.252615i	−0.670319	+	0.742073i	$0.733843\pi$
$354$	−0.527067	+	0.234665i	−0.0280133	+	0.0124723i
$355$	−19.1918	+	21.3146i	−1.01859	+	1.13126i
$356$	5.47002	+	3.97420i	0.289910	+	0.210632i
$357$	0.729269	+	0.529845i	0.0385970	+	0.0280424i
$358$	−0.0607438	+	0.0674629i	−0.00321041	+	0.00356552i
$359$	23.9348	−	10.6564i	1.26323	−	0.562425i	0.337753	−	0.941235i	$-0.390333\pi$
$359$	23.9348	−	10.6564i	1.26323	−	0.562425i	0.925475	+	0.378809i	$0.123666\pi$
$360$	−17.9903	−	8.00979i	−0.948171	−	0.422153i
$361$	−3.05357	−	3.39133i	−0.160714	−	0.178491i
$362$	−0.557257	−	5.30194i	−0.0292888	−	0.278664i
$363$	−5.24167	−	1.11415i	−0.275116	−	0.0584778i
$364$	−1.04651	−	3.22082i	−0.0548519	−	0.168817i
$365$	−20.5168	+	4.36099i	−1.07390	+	0.228265i
$366$	−0.720830	−	1.24851i	−0.0376784	−	0.0652608i
$367$	13.5073	−	23.3953i	0.705076	−	1.22123i	−0.261589	−	0.965179i	$-0.584246\pi$
$367$	13.5073	−	23.3953i	0.705076	−	1.22123i	0.966664	−	0.256047i	$-0.0824203\pi$
$368$	1.39351	−	4.28877i	0.0726416	−	0.223568i
$369$	0.172707	−	1.64320i	0.00899078	−	0.0855415i
$370$	21.5346	−	15.6458i	1.11953	−	0.813387i
$371$	−2.72967			−0.141717
$372$		0			0
$373$	−12.4058			−0.642351			−0.321175	−	0.947020i	$-0.604078\pi$
$373$	−12.4058			−0.642351			−0.321175	+	0.947020i	$0.604078\pi$
$374$	−3.00403	+	2.18256i	−0.155335	+	0.112857i
$375$	−1.30993	+	12.4631i	−0.0676444	+	0.643594i
$376$	−0.657899	+	2.02480i	−0.0339285	+	0.104421i
$377$	7.12253	−	12.3366i	0.366829	−	0.635367i
$378$	−1.23155	−	2.13311i	−0.0633442	−	0.109715i
$379$	4.53764	−	0.964505i	0.233083	−	0.0495433i	−0.0898893	−	0.995952i	$-0.528651\pi$
$379$	4.53764	−	0.964505i	0.233083	−	0.0495433i	0.322972	+	0.946408i	$0.395318\pi$
$380$	6.63670	+	20.4257i	0.340456	+	1.04782i
$381$	−1.26401	−	0.268674i	−0.0647573	−	0.0137646i
$382$	−1.52090	−	14.4704i	−0.0778162	−	0.740372i
$383$	3.35993	+	3.73158i	0.171684	+	0.190675i	0.822846	−	0.568264i	$-0.192385\pi$
$383$	3.35993	+	3.73158i	0.171684	+	0.190675i	−0.651162	+	0.758939i	$0.725718\pi$
$384$	8.86068	+	3.94503i	0.452169	+	0.201319i
$385$	10.6414	−	4.73784i	0.542334	−	0.241463i
$386$	−2.61279	+	2.90180i	−0.132988	+	0.147698i
$387$	12.6551	+	9.19450i	0.643297	+	0.467383i
$388$	−6.50958	−	4.72949i	−0.330474	−	0.240103i
$389$	−12.4471	+	13.8239i	−0.631091	+	0.700897i	−0.970870	−	0.239608i	$-0.922981\pi$
$389$	−12.4471	+	13.8239i	−0.631091	+	0.700897i	0.339779	+	0.940505i	$0.389648\pi$
$390$	−6.13195	+	2.73012i	−0.310503	+	0.138245i
$391$	−3.92444	−	1.74727i	−0.198467	−	0.0883633i
$392$	−10.4351	−	11.5894i	−0.527054	−	0.585353i
$393$	−0.593588	−	5.64761i	−0.0299425	−	0.284884i
$394$	−10.7333	−	2.28144i	−0.540738	−	0.114937i
$395$	16.1481	+	49.6988i	0.812500	+	2.50062i
$396$	−13.4147	+	2.85138i	−0.674114	+	0.143287i
$397$	−16.2794	−	28.1968i	−0.817040	−	1.41515i	−0.907854	−	0.419287i	$-0.862280\pi$
$397$	−16.2794	−	28.1968i	−0.817040	−	1.41515i	0.0908142	−	0.995868i	$-0.471053\pi$
$398$	1.46912	−	2.54459i	0.0736404	−	0.127549i
$399$	−0.808838	+	2.48935i	−0.0404926	+	0.124623i
$400$	−1.25571	+	11.9473i	−0.0627855	+	0.597364i
$401$	−10.0239	+	7.28282i	−0.500572	+	0.363687i	−0.809235	−	0.587485i	$-0.800118\pi$
$401$	−10.0239	+	7.28282i	−0.500572	+	0.363687i	0.308664	+	0.951171i	$0.400118\pi$
$402$	1.29847			0.0647616
$403$		0			0
$404$	−5.80481			−0.288800
$405$	−7.00125	+	5.08671i	−0.347895	+	0.252760i
$406$	−0.269353	+	2.56272i	−0.0133678	+	0.127186i
$407$	13.2429	−	40.7576i	0.656429	−	2.02028i
$408$	1.43480	−	2.48514i	0.0710331	−	0.123033i
$409$	−1.72404	−	2.98613i	−0.0852484	−	0.147654i	0.820249	−	0.572007i	$-0.193835\pi$
$409$	−1.72404	−	2.98613i	−0.0852484	−	0.147654i	−0.905497	+	0.424353i	$0.860502\pi$
$410$	1.89020	−	0.401774i	0.0933503	−	0.0198422i
$411$	−3.55540	−	10.9424i	−0.175375	−	0.539749i
$412$	−9.31410	−	1.97977i	−0.458873	−	0.0975364i
$413$	−0.0739928	−	0.703994i	−0.00364095	−	0.0346413i
$414$	3.31048	+	3.67666i	0.162701	+	0.180698i
$415$	47.7826	+	21.2742i	2.34556	+	1.04431i
$416$	−15.4373	+	6.87314i	−0.756878	+	0.336984i
$417$	−11.2998	+	12.5497i	−0.553354	+	0.614562i
$418$	−8.72276	−	6.33746i	−0.426644	−	0.309975i
$419$	32.3988	+	23.5391i	1.58279	+	1.14996i	0.913412	+	0.407035i	$0.133437\pi$
$419$	32.3988	+	23.5391i	1.58279	+	1.14996i	0.669374	+	0.742926i	$0.266563\pi$
$420$	−2.60554	+	2.89375i	−0.127137	+	0.141200i
$421$	19.8097	−	8.81985i	0.965466	−	0.429853i	0.137420	−	0.990513i	$-0.456119\pi$
$421$	19.8097	−	8.81985i	0.965466	−	0.429853i	0.828046	+	0.560660i	$0.189452\pi$
$422$	7.24887	+	3.22741i	0.352870	+	0.157108i
$423$	1.28125	+	1.42297i	0.0622964	+	0.0691872i
$424$	0.908313	+	8.64202i	0.0441116	+	0.419694i
$425$	11.1939	+	2.37933i	0.542982	+	0.115414i
$426$	1.48742	+	4.57780i	0.0720656	+	0.221795i
$427$	1.73016	−	0.367757i	0.0837284	−	0.0177970i
$428$	1.77417	+	3.07294i	0.0857575	+	0.148536i
$429$	−5.40332	+	9.35883i	−0.260875	+	0.451849i
$430$	−5.65353	+	17.3998i	−0.272637	+	0.839091i
$431$	1.21469	−	11.5570i	0.0585096	−	0.556682i	−0.925523	−	0.378692i	$-0.876374\pi$
$431$	1.21469	−	11.5570i	0.0585096	−	0.556682i	0.984032	−	0.177990i	$-0.0569593\pi$
$432$	5.20024	−	3.77820i	0.250197	−	0.181779i
$433$	−24.5964			−1.18203			−0.591015	−	0.806661i	$-0.701272\pi$
$433$	−24.5964			−1.18203			−0.591015	+	0.806661i	$0.701272\pi$
$434$		0			0
$435$	−16.3791			−0.785320
$436$	1.82156	−	1.32344i	0.0872368	−	0.0633813i
$437$	1.30386	−	12.4054i	0.0623721	−	0.593431i
$438$	−1.08776	+	3.34779i	−0.0519753	+	0.159964i
$439$	−9.09662	+	15.7558i	−0.434158	+	0.751984i	−0.997227	−	0.0744265i	$-0.976287\pi$
$439$	−9.09662	+	15.7558i	−0.434158	+	0.751984i	0.563068	+	0.826410i	$0.309621\pi$
$440$	−18.5408	−	32.1136i	−0.883897	−	1.53096i
$441$	−13.7195	+	2.91616i	−0.653308	+	0.138865i
$442$	0.811240	+	2.49674i	0.0385868	+	0.118758i
$443$	−17.3722	−	3.69258i	−0.825380	−	0.175440i	−0.224189	−	0.974546i	$-0.571973\pi$
$443$	−17.3722	−	3.69258i	−0.825380	−	0.175440i	−0.601190	+	0.799106i	$0.705307\pi$
$444$	1.49747	+	14.2474i	0.0710666	+	0.676153i
$445$	11.0019	+	12.2189i	0.521542	+	0.579231i
$446$	5.93596	+	2.64286i	0.281076	+	0.125143i
$447$	−16.5992	+	7.39045i	−0.785117	+	0.349556i
$448$	0.642086	−	0.713109i	0.0303357	−	0.0336912i
$449$	−7.44180	−	5.40679i	−0.351200	−	0.255162i	0.398172	−	0.917311i	$-0.369645\pi$
$449$	−7.44180	−	5.40679i	−0.351200	−	0.255162i	−0.749372	+	0.662149i	$0.769645\pi$
$450$	−10.6627	−	7.74688i	−0.502643	−	0.365192i
$451$	2.08179	−	2.31206i	0.0980277	−	0.108871i
$452$	−8.88677	+	3.95664i	−0.417998	+	0.186105i
$453$	−12.6728	−	5.64230i	−0.595421	−	0.265098i
$454$	−10.0406	−	11.1512i	−0.471229	−	0.523353i
$455$	−0.860839	−	8.19034i	−0.0403568	−	0.383969i
$456$	8.15032	+	1.73240i	0.381674	+	0.0811272i
$457$	9.64130	+	29.6729i	0.451001	+	1.38804i	0.875767	+	0.482735i	$0.160356\pi$
$457$	9.64130	+	29.6729i	0.451001	+	1.38804i	−0.424766	+	0.905303i	$0.639644\pi$
$458$	−11.4355	+	2.43069i	−0.534345	+	0.113579i
$459$	−3.06166	−	5.30294i	−0.142906	−	0.247520i
$460$	9.27842	−	16.0707i	0.432609	−	0.749300i
$461$	2.06067	−	6.34209i	0.0959750	−	0.295381i	−0.891532	−	0.452959i	$-0.850369\pi$
$461$	2.06067	−	6.34209i	0.0959750	−	0.295381i	0.987507	+	0.157578i	$0.0503685\pi$
$462$	0.204337	−	1.94414i	0.00950664	−	0.0904496i
$463$	28.5732	−	20.7597i	1.32791	−	0.964784i	0.328114	−	0.944638i	$-0.393587\pi$
$463$	28.5732	−	20.7597i	1.32791	−	0.964784i	0.999797	−	0.0201457i	$-0.00641301\pi$
$464$	−6.72466			−0.312184
$465$		0			0
$466$	6.78192			0.314167
$467$	−29.0789	+	21.1270i	−1.34561	+	0.977642i	−0.346391	+	0.938090i	$0.612593\pi$
$467$	−29.0789	+	21.1270i	−1.34561	+	0.977642i	−0.999218	+	0.0395520i	$0.987407\pi$
$468$	−1.01352	+	9.64298i	−0.0468499	+	0.445747i
$469$	−0.492303	+	1.51515i	−0.0227324	+	0.0699632i
$470$	−1.11975	+	1.93946i	−0.0516501	+	0.0894606i
$471$	−6.83446	−	11.8376i	−0.314915	−	0.545449i
$472$	−2.20420	+	0.468516i	−0.101456	+	0.0215652i
$473$	9.10211	+	28.0134i	0.418516	+	1.28806i
$474$	8.57808	+	1.82333i	0.394004	+	0.0837482i
$475$	3.47344	+	33.0475i	0.159372	+	1.51632i
$476$	1.01905	+	1.13177i	0.0467083	+	0.0518748i
$477$	7.13965	+	3.17878i	0.326902	+	0.145546i
$478$	0.372031	−	0.165639i	0.0170163	−	0.00757614i
$479$	22.2449	−	24.7054i	1.01639	−	1.12882i	0.0247649	−	0.999693i	$-0.492116\pi$
$479$	22.2449	−	24.7054i	1.01639	−	1.12882i	0.991628	−	0.129126i	$-0.0412171\pi$
$480$	15.7191	+	11.4206i	0.717474	+	0.521275i
$481$	−24.5121	−	17.8091i	−1.11765	−	0.812024i
$482$	7.09132	−	7.87571i	0.323001	−	0.358729i
$483$	2.06606	−	0.919871i	0.0940092	−	0.0418556i
$484$	−8.27088	−	3.68243i	−0.375949	−	0.167383i
$485$	−13.0928	−	14.5411i	−0.594515	−	0.660276i
$486$	1.16360	+	11.0709i	0.0527819	+	0.502186i
$487$	27.8922	+	5.92868i	1.26392	+	0.268654i	0.790652	−	0.612266i	$-0.209742\pi$
$487$	27.8922	+	5.92868i	1.26392	+	0.268654i	0.473266	+	0.880920i	$0.343075\pi$
$488$	−1.74002	−	5.35524i	−0.0787672	−	0.242420i
$489$	0.922287	−	0.196038i	0.0417072	−	0.00886515i
$490$	−8.20220	−	14.2066i	−0.370538	−	0.641790i
$491$	−13.9818	+	24.2172i	−0.630991	+	1.09291i	0.356359	+	0.934349i	$0.384018\pi$
$491$	−13.9818	+	24.2172i	−0.630991	+	1.09291i	−0.987350	+	0.158559i	$0.949315\pi$
$492$	−0.321387	+	0.989128i	−0.0144892	+	0.0445933i
$493$	−0.669615	+	6.37096i	−0.0301579	+	0.286934i
$494$	−6.16701	+	4.48059i	−0.277467	+	0.201591i
$495$	−33.3506			−1.49900
$496$		0			0
$497$	−5.90568			−0.264906
$498$	7.10139	−	5.15946i	0.318221	−	0.231201i
$499$	−4.31754	+	41.0787i	−0.193280	+	1.83893i	0.282377	+	0.959304i	$0.408877\pi$
$499$	−4.31754	+	41.0787i	−0.193280	+	1.83893i	−0.475657	+	0.879631i	$0.657789\pi$
$500$	−6.54262	+	20.1361i	−0.292595	+	0.900514i
$501$	−5.09378	+	8.82269i	−0.227573	+	0.394169i
$502$	2.08623	+	3.61346i	0.0931132	+	0.161277i
$503$	25.0269	−	5.31964i	1.11590	−	0.237191i	0.387178	−	0.922005i	$-0.373450\pi$
$503$	25.0269	−	5.31964i	1.11590	−	0.237191i	0.728718	+	0.684814i	$0.240117\pi$
$504$	−1.25301	−	3.85638i	−0.0558136	−	0.171777i
$505$	−13.8076	−	2.93490i	−0.614432	−	0.130602i
$506$	0.973790	+	9.26499i	0.0432902	+	0.411879i
$507$	−2.73734	−	3.04013i	−0.121570	−	0.135017i
$508$	−1.99450	−	0.888007i	−0.0884915	−	0.0393989i
$509$	22.3524	−	9.95195i	0.990754	−	0.441112i	0.153632	−	0.988128i	$-0.450903\pi$
$509$	22.3524	−	9.95195i	0.990754	−	0.441112i	0.837122	+	0.547016i	$0.184236\pi$
$510$	2.01978	−	2.24320i	0.0894375	−	0.0993304i
$511$	−3.49405	−	2.53858i	−0.154568	−	0.112300i
$512$	11.8548	+	8.61304i	0.523915	+	0.380646i
$513$	11.8973	−	13.2132i	0.525277	−	0.583379i
$514$	2.85201	−	1.26980i	0.125797	−	0.0560083i
$515$	−21.1541	−	9.41840i	−0.932160	−	0.415024i
$516$	−6.58856	−	7.31734i	−0.290045	−	0.322128i
$517$	0.376884	+	3.58581i	0.0165753	+	0.157704i
$518$	5.36105	+	1.13953i	0.235551	+	0.0500679i
$519$	−5.75915	−	17.7248i	−0.252799	−	0.778034i
$520$	−25.6438	+	5.45076i	−1.12456	+	0.239032i
$521$	−7.48279	−	12.9606i	−0.327827	−	0.567813i	0.654253	−	0.756275i	$-0.272983\pi$
$521$	−7.48279	−	12.9606i	−0.327827	−	0.567813i	−0.982080	+	0.188462i	$0.939650\pi$
$522$	3.68887	−	6.38931i	0.161458	−	0.279653i
$523$	6.47873	−	19.9395i	0.283295	−	0.871893i	−0.703609	−	0.710587i	$-0.748429\pi$
$523$	6.47873	−	19.9395i	0.283295	−	0.871893i	0.986904	−	0.161306i	$-0.0515706\pi$
$524$	1.00286	−	9.54160i	0.0438102	−	0.416827i
$525$	−4.87415	+	3.54128i	−0.212726	+	0.154554i
$526$	−1.72984			−0.0754247
$527$		0			0
$528$	5.10148			0.222014
$529$	9.88796	−	7.18402i	0.429911	−	0.312349i
$530$	−0.955452	+	9.09052i	−0.0415022	+	0.394867i
$531$	−0.626287	+	1.92751i	−0.0271786	+	0.0836470i
$532$	−2.21109	+	3.82971i	−0.0958628	+	0.166039i
$533$	−1.09981	−	1.90492i	−0.0476379	−	0.0825113i
$534$	2.69904	−	0.573698i	0.116799	−	0.0248263i
$535$	2.66645	+	8.20649i	0.115281	+	0.354798i
$536$	4.96072	+	1.05443i	0.214271	+	0.0455446i
$537$	−0.0124193	−	0.118161i	−0.000535931	−	0.00509904i
$538$	6.15445	+	6.83521i	0.265337	+	0.294687i
$539$	−24.1276	−	10.7423i	−1.03925	−	0.462703i
$540$	24.1643	−	10.7586i	1.03986	−	0.462978i
$541$	1.15847	−	1.28661i	0.0498064	−	0.0553156i	−0.717727	−	0.696325i	$-0.754817\pi$
$541$	1.15847	−	1.28661i	0.0498064	−	0.0553156i	0.767533	+	0.641009i	$0.221484\pi$
$542$	−7.71128	−	5.60257i	−0.331228	−	0.240651i
$543$	5.64480	+	4.10118i	0.242241	+	0.175999i
$544$	5.08486	−	5.64731i	0.218012	−	0.242126i
$545$	5.00199	−	2.22703i	0.214262	−	0.0953955i
$546$	−1.26259	−	0.562143i	−0.0540341	−	0.0240575i
$547$	−8.77995	−	9.75112i	−0.375404	−	0.416928i	0.525605	−	0.850729i	$-0.323839\pi$
$547$	−8.77995	−	9.75112i	−0.375404	−	0.416928i	−0.901009	+	0.433801i	$0.857172\pi$
$548$	−2.03188	−	19.3320i	−0.0867975	−	0.825823i
$549$	−4.95362	−	1.05293i	−0.211415	−	0.0449377i
$550$	−7.66904	−	23.6029i	−0.327009	−	1.00643i
$551$	−18.1947	+	3.86740i	−0.775119	+	0.164757i
$552$	−3.59977	−	6.23498i	−0.153216	−	0.265378i
$553$	−5.37991	+	9.31828i	−0.228777	+	0.396254i
$554$	2.46532	−	7.58748i	0.104741	−	0.322361i
$555$	−3.64153	+	34.6469i	−0.154574	+	1.47068i
$556$	−23.0820	+	16.7701i	−0.978897	+	0.711210i
$557$	28.0246			1.18744			0.593721	−	0.804671i	$-0.297658\pi$
$557$	28.0246			1.18744			0.593721	+	0.804671i	$0.297658\pi$
$558$		0			0
$559$	20.8248			0.880794
$560$	−3.14522	+	2.28514i	−0.132910	+	0.0965646i
$561$	0.507986	−	4.83316i	0.0214472	−	0.204056i
$562$	3.28106	−	10.0981i	0.138403	−	0.425961i
$563$	−11.3259	+	19.6171i	−0.477331	+	0.826762i	−0.999662	−	0.0259808i	$-0.991729\pi$
$563$	−11.3259	+	19.6171i	−0.477331	+	0.826762i	0.522331	+	0.852743i	$0.325062\pi$
$564$	−0.602646	−	1.04381i	−0.0253760	−	0.0439525i
$565$	−23.1390	+	4.91835i	−0.973467	+	0.206917i
$566$	4.83566	+	14.8826i	0.203258	+	0.625564i
$567$	−1.74296	−	0.370478i	−0.0731975	−	0.0155586i
$568$	1.96515	+	18.6971i	0.0824558	+	0.784514i
$569$	31.0758	+	34.5131i	1.30276	+	1.44687i	0.821408	+	0.570342i	$0.193189\pi$
$569$	31.0758	+	34.5131i	1.30276	+	1.44687i	0.481357	+	0.876525i	$0.340144\pi$
$570$	8.00707	+	3.56498i	0.335379	+	0.149320i
$571$	11.4178	−	5.08354i	0.477821	−	0.212740i	−0.153671	−	0.988122i	$-0.549110\pi$
$571$	11.4178	−	5.08354i	0.477821	−	0.212740i	0.631492	+	0.775383i	$0.282443\pi$
$572$	−12.2168	+	13.5682i	−0.510811	+	0.567313i
$573$	15.4062	+	11.1932i	0.643602	+	0.467604i
$574$	0.321904	+	0.233877i	0.0134360	+	0.00976184i
$575$	19.2119	−	21.3369i	0.801190	−	0.889812i
$576$	−2.50986	+	1.11746i	−0.104577	+	0.0465608i
$577$	−27.8488	−	12.3991i	−1.15936	−	0.516180i	−0.265317	−	0.964161i	$-0.585477\pi$
$577$	−27.8488	−	12.3991i	−1.15936	−	0.516180i	−0.894043	+	0.447981i	$0.852143\pi$
$578$	7.05317	+	7.83334i	0.293373	+	0.325824i
$579$	−0.534194	−	5.08251i	−0.0222003	−	0.211222i
$580$	−27.0677	−	5.75343i	−1.12393	−	0.238898i
$581$	3.32803	+	10.2426i	0.138070	+	0.424936i
$582$	−3.21198	+	0.682728i	−0.133141	+	0.0283000i
$583$	7.35812	+	12.7446i	0.304742	+	0.527829i
$584$	−6.87436	+	11.9067i	−0.284463	+	0.492705i
$585$	−7.28629	+	22.4249i	−0.301251	+	0.927155i
$586$	0.893750	−	8.50346i	0.0369205	−	0.351275i
$587$	27.2300	−	19.7837i	1.12390	−	0.816562i	0.139105	−	0.990278i	$-0.455577\pi$
$587$	27.2300	−	19.7837i	1.12390	−	0.816562i	0.984796	+	0.173716i	$0.0555774\pi$
$588$	8.82883			0.364095
$589$		0			0
$590$	−2.37039			−0.0975872
$591$	11.6187	−	8.44150i	0.477930	−	0.347237i
$592$	−1.49507	+	14.2247i	−0.0614472	+	0.584631i
$593$	−13.8711	+	42.6909i	−0.569619	+	1.75311i	0.0841933	+	0.996449i	$0.473169\pi$
$593$	−13.8711	+	42.6909i	−0.569619	+	1.75311i	−0.653812	+	0.756657i	$0.726831\pi$
$594$	−6.63957	+	11.5001i	−0.272425	+	0.471854i
$595$	1.85175	+	3.20733i	0.0759145	+	0.131488i
$596$	−30.0275	+	6.38253i	−1.22997	+	0.261439i
$597$	1.18834	+	3.65733i	0.0486354	+	0.149684i
$598$	6.44251	+	1.36940i	0.263454	+	0.0559989i
$599$	2.04715	+	19.4773i	0.0836443	+	0.795822i	0.953272	+	0.302114i	$0.0976923\pi$
$599$	2.04715	+	19.4773i	0.0836443	+	0.795822i	−0.869628	+	0.493708i	$0.835641\pi$
$600$	12.8334	+	14.2530i	0.523923	+	0.581876i
$601$	−27.8261	−	12.3890i	−1.13505	−	0.505357i	−0.248796	−	0.968556i	$-0.580035\pi$
$601$	−27.8261	−	12.3890i	−1.13505	−	0.505357i	−0.886254	+	0.463199i	$0.846702\pi$
$602$	−3.44138	+	1.53220i	−0.140260	+	0.0624479i
$603$	3.05209	−	3.38969i	0.124291	−	0.138039i
$604$	−18.9608	−	13.7758i	−0.771504	−	0.560531i
$605$	−17.8117	−	12.9410i	−0.724150	−	0.526126i
$606$	−1.58516	+	1.76049i	−0.0643926	+	0.0715152i
$607$	−12.2183	+	5.43993i	−0.495924	+	0.220800i	−0.639429	−	0.768850i	$-0.720829\pi$
$607$	−12.2183	+	5.43993i	−0.495924	+	0.220800i	0.143505	+	0.989650i	$0.454163\pi$
$608$	20.1580	+	8.97493i	0.817515	+	0.363981i
$609$	−2.25667	−	2.50628i	−0.0914448	−	0.101560i
$610$	−0.619128	−	5.89061i	−0.0250678	−	0.238504i
$611$	2.49343	+	0.529995i	0.100873	+	0.0214413i
$612$	−1.34743	−	4.14695i	−0.0544665	−	0.167631i
$613$	−5.08168	+	1.08014i	−0.205247	+	0.0436266i	−0.309388	−	0.950936i	$-0.600124\pi$
$613$	−5.08168	+	1.08014i	−0.205247	+	0.0436266i	0.104141	+	0.994563i	$0.466791\pi$
$614$	10.5906	+	18.3435i	0.427402	+	0.740282i
$615$	−1.26457	+	2.19030i	−0.0509924	+	0.0883215i
$616$	2.35942	−	7.26156i	0.0950639	−	0.292577i
$617$	3.13722	−	29.8487i	0.126300	−	1.20166i	−0.729363	−	0.684127i	$-0.760183\pi$
$617$	3.13722	−	29.8487i	0.126300	−	1.20166i	0.855662	−	0.517534i	$-0.173150\pi$
$618$	−3.14389	+	2.28417i	−0.126466	+	0.0918828i
$619$	−18.3260			−0.736584			−0.368292	−	0.929710i	$-0.620057\pi$
$619$	−18.3260			−0.736584			−0.368292	+	0.929710i	$0.620057\pi$
$620$		0			0
$621$	−15.3628			−0.616487
$622$	1.32838	−	0.965124i	0.0532631	−	0.0386979i
$623$	−0.353882	+	3.36696i	−0.0141780	+	0.134894i
$624$	1.11455	−	3.43023i	0.0446177	−	0.137319i
$625$	−3.87924	+	6.71905i	−0.155170	+	0.268762i
$626$	−3.70450	−	6.41639i	−0.148062	−	0.256450i
$627$	13.8029	−	2.93390i	0.551235	−	0.117169i
$628$	−7.13629	−	21.9632i	−0.284769	−	0.876429i
$629$	13.3276	+	2.83288i	0.531407	+	0.112954i
$630$	−0.445842	−	4.24190i	−0.0177628	−	0.169002i
$631$	−6.91561	−	7.68056i	−0.275306	−	0.305758i	0.589597	−	0.807698i	$-0.299287\pi$
$631$	−6.91561	−	7.68056i	−0.275306	−	0.305758i	−0.864903	+	0.501940i	$0.832620\pi$
$632$	31.2915	+	13.9319i	1.24471	+	0.554180i
$633$	−9.48725	+	4.22399i	−0.377084	+	0.167889i
$634$	−4.03522	+	4.48157i	−0.160259	+	0.177986i
$635$	−4.29525	−	3.12068i	−0.170452	−	0.123840i
$636$	−3.97992	−	2.89158i	−0.157814	−	0.114659i
$637$	−12.4944	+	13.8764i	−0.495045	+	0.549803i
$638$	12.6912	−	5.65050i	0.502451	−	0.223706i
$639$	15.4467	+	6.87733i	0.611063	+	0.272063i
$640$	26.6644	+	29.6138i	1.05400	+	1.17059i
$641$	0.0105837	+	0.100697i	0.000418031	+	0.00397730i	0.994729	−	0.102540i	$-0.0326968\pi$
$641$	0.0105837	+	0.100697i	0.000418031	+	0.00397730i	−0.994311	+	0.106517i	$0.966030\pi$
$642$	1.41645	+	0.301076i	0.0559029	+	0.0118825i
$643$	4.23719	+	13.0407i	0.167098	+	0.514276i	0.999185	−	0.0403701i	$-0.0128537\pi$
$643$	4.23719	+	13.0407i	0.167098	+	0.514276i	−0.832086	+	0.554646i	$0.812854\pi$
$644$	3.73744	−	0.794417i	0.147276	−	0.0313044i
$645$	−11.9723	−	20.7366i	−0.471408	−	0.816503i
$646$	1.71401	−	2.96875i	0.0674367	−	0.116804i
$647$	3.34800	−	10.3041i	0.131624	−	0.405096i	−0.863426	−	0.504476i	$-0.831686\pi$
$647$	3.34800	−	10.3041i	0.131624	−	0.405096i	0.995050	+	0.0993798i	$0.0316859\pi$
$648$	−0.592938	+	5.64142i	−0.0232928	+	0.221616i
$649$	−3.08745	+	2.24316i	−0.121193	+	0.0880518i
$650$	−17.5460			−0.688212
$651$		0			0
$652$	1.59301			0.0623870
$653$	19.6204	−	14.2551i	0.767807	−	0.557844i	−0.133488	−	0.991050i	$-0.542618\pi$
$653$	19.6204	−	14.2551i	0.767807	−	0.557844i	0.901295	+	0.433206i	$0.142618\pi$
$654$	0.0960491	−	0.913846i	0.00375582	−	0.0357342i
$655$	7.20968	−	22.1891i	0.281706	−	0.867001i
$656$	−0.519185	+	0.899255i	−0.0202708	+	0.0351100i
$657$	6.18270	+	10.7087i	0.241210	+	0.417788i
$658$	−0.451045	+	0.0958726i	−0.0175836	+	0.00373750i
$659$	−2.63699	−	8.11583i	−0.102723	−	0.316148i	0.886467	−	0.462793i	$-0.153153\pi$
$659$	−2.63699	−	8.11583i	−0.102723	−	0.316148i	−0.989189	+	0.146645i	$0.953153\pi$
$660$	20.5342	+	4.36468i	0.799294	+	0.169895i
$661$	−3.95998	−	37.6767i	−0.154025	−	1.46545i	−0.749460	−	0.662049i	$-0.769687\pi$
$661$	−3.95998	−	37.6767i	−0.154025	−	1.46545i	0.595435	−	0.803403i	$-0.296980\pi$
$662$	−14.9338	−	16.5857i	−0.580420	−	0.644622i
$663$	−3.13883	−	1.39750i	−0.121902	−	0.0542742i
$664$	31.3203	−	13.9447i	1.21546	−	0.541160i
$665$	−7.19571	+	7.99165i	−0.279038	+	0.309903i
$666$	−12.6952	−	9.22360i	−0.491929	−	0.357407i
$667$	13.0026	+	9.44697i	0.503464	+	0.365788i
$668$	−11.5170	+	12.7909i	−0.445604	+	0.494894i
$669$	−7.76892	+	3.45895i	−0.300364	+	0.133731i
$670$	4.87353	+	2.16984i	0.188281	+	0.0838281i
$671$	−6.38087	−	7.08667i	−0.246331	−	0.273578i
$672$	0.418186	+	3.97877i	0.0161319	+	0.153484i
$673$	6.96451	+	1.48035i	0.268462	+	0.0570634i	0.340176	−	0.940362i	$-0.389513\pi$
$673$	6.96451	+	1.48035i	0.268462	+	0.0570634i	−0.0717135	+	0.997425i	$0.522847\pi$
$674$	5.90910	+	18.1863i	0.227610	+	0.700512i
$675$	40.0316	−	8.50897i	1.54082	−	0.327510i
$676$	−3.45577	−	5.98557i	−0.132914	−	0.230214i
$677$	24.0305	−	41.6220i	0.923567	−	1.59966i	0.129716	−	0.991551i	$-0.458593\pi$
$677$	24.0305	−	41.6220i	0.923567	−	1.59966i	0.793850	−	0.608113i	$-0.208073\pi$
$678$	−1.22679	+	3.77566i	−0.0471145	+	0.145004i
$679$	0.421137	−	4.00685i	0.0161617	−	0.153769i
$680$	9.53810	−	6.92984i	0.365769	−	0.265747i
$681$	19.6390			0.752567
$682$		0			0
$683$	32.5731			1.24638			0.623188	−	0.782072i	$-0.285837\pi$
$683$	32.5731			1.24638			0.623188	+	0.782072i	$0.285837\pi$
$684$	10.2431	−	7.44202i	0.391653	−	0.284553i
$685$	4.94111	−	47.0115i	0.188790	−	1.79622i
$686$	2.18235	−	6.71657i	0.0833224	−	0.256440i
$687$	7.65051	−	13.2511i	0.291885	−	0.505560i
$688$	−4.91537	−	8.51366i	−0.187397	−	0.324580i
$689$	10.1770	−	2.16320i	0.387715	−	0.0824113i
$690$	−2.34024	−	7.20251i	−0.0890913	−	0.274195i
$691$	−26.6575	−	5.66623i	−1.01410	−	0.215554i	−0.329254	−	0.944241i	$-0.606797\pi$
$691$	−26.6575	−	5.66623i	−1.01410	−	0.215554i	−0.684846	+	0.728688i	$0.740131\pi$
$692$	−3.29130	−	31.3146i	−0.125116	−	1.19040i
$693$	−4.59494	−	5.10320i	−0.174547	−	0.193855i
$694$	−16.3241	−	7.26795i	−0.619654	−	0.275888i
$695$	−63.3832	+	28.2200i	−2.40426	+	1.07045i
$696$	−7.18387	+	7.97850i	−0.272304	+	0.302424i
$697$	0.800258	+	0.581421i	0.0303119	+	0.0220229i
$698$	3.12036	+	2.26707i	0.118107	+	0.0858100i
$699$	−5.93928	+	6.59624i	−0.224644	+	0.249493i
$700$	−9.29883	+	4.14010i	−0.351463	+	0.156481i
$701$	7.75523	+	3.45285i	0.292911	+	0.130412i	0.547931	−	0.836523i	$-0.315416\pi$
$701$	7.75523	+	3.45285i	0.292911	+	0.130412i	−0.255020	+	0.966936i	$0.582082\pi$
$702$	6.28205	+	6.97692i	0.237101	+	0.263327i
$703$	4.13554	+	39.3471i	0.155975	+	1.48400i
$704$	−5.06027	−	1.07559i	−0.190716	−	0.0405379i
$705$	−0.905737	−	2.78757i	−0.0341120	−	0.104986i
$706$	−7.86986	+	1.67279i	−0.296186	+	0.0629563i
$707$	−1.45328	−	2.51716i	−0.0546564	−	0.0946676i
$708$	0.637869	−	1.10482i	0.0239726	−	0.0415217i
$709$	7.22670	−	22.2415i	0.271404	−	0.835297i	−0.718744	−	0.695275i	$-0.755283\pi$
$709$	7.22670	−	22.2415i	0.271404	−	0.835297i	0.990148	−	0.140022i	$-0.0447174\pi$
$710$	−2.06713	+	19.6675i	−0.0775781	+	0.738107i
$711$	24.9229	−	18.1076i	0.934683	−	0.679087i
$712$	10.7774			0.403901
$713$		0			0
$714$	0.621526			0.0232600
$715$	−35.9197	+	26.0972i	−1.34332	+	0.975978i
$716$	0.0209823	−	0.199633i	0.000784144	−	0.00746063i
$717$	−0.164703	+	0.506903i	−0.00615094	+	0.0189306i
$718$	9.03230	−	15.6444i	0.337083	−	0.583844i
$719$	6.48843	+	11.2383i	0.241978	+	0.419118i	0.961278	−	0.275582i	$-0.0888706\pi$
$719$	6.48843	+	11.2383i	0.241978	+	0.419118i	−0.719300	+	0.694700i	$0.755537\pi$
$720$	10.8876	−	2.31424i	0.405759	−	0.0862467i
$721$	−1.47337	−	4.53457i	−0.0548712	−	0.168876i
$722$	−3.07773	−	0.654192i	−0.114541	−	0.0243465i
$723$	1.44984	+	13.7943i	0.0539202	+	0.513016i
$724$	7.88783	+	8.76033i	0.293149	+	0.325575i
$725$	−39.1140	−	17.4147i	−1.45266	−	0.646765i
$726$	−3.37540	+	1.50282i	−0.125273	+	0.0557751i
$727$	−8.31262	+	9.23210i	−0.308298	+	0.342400i	−0.877305	−	0.479933i	$-0.840661\pi$
$727$	−8.31262	+	9.23210i	−0.308298	+	0.342400i	0.569007	+	0.822333i	$0.307328\pi$
$728$	−4.36719	−	3.17295i	−0.161859	−	0.117597i
$729$	−6.12163	−	4.44762i	−0.226727	−	0.164727i
$730$	−9.67713	+	10.7475i	−0.358167	+	0.397784i
$731$	−8.55532	+	3.80907i	−0.316430	+	0.140884i
$732$	2.91218	+	1.29659i	0.107637	+	0.0479233i
$733$	−22.8557	−	25.3839i	−0.844195	−	0.937574i	0.154533	−	0.987988i	$-0.450613\pi$
$733$	−22.8557	−	25.3839i	−0.844195	−	0.937574i	−0.998728	+	0.0504137i	$0.983946\pi$
$734$	−1.94699	−	18.5243i	−0.0718646	−	0.683746i
$735$	21.0007	+	4.46384i	0.774624	+	0.164651i
$736$	−5.89161	−	18.1325i	−0.217168	−	0.668373i
$737$	8.40119	−	1.78573i	0.309462	−	0.0657782i
$738$	−0.569607	−	0.986589i	−0.0209675	−	0.0363168i
$739$	−6.18747	+	10.7170i	−0.227610	+	0.394231i	−0.957099	−	0.289761i	$-0.906424\pi$
$739$	−6.18747	+	10.7170i	−0.227610	+	0.394231i	0.729490	+	0.683992i	$0.239758\pi$
$740$	−18.1881	+	55.9773i	−0.668609	+	2.05777i
$741$	1.04285	−	9.92204i	0.0383100	−	0.364495i
$742$	−1.52264	+	1.10626i	−0.0558979	+	0.0406122i
$743$	16.2455			0.595990			0.297995	−	0.954567i	$-0.403682\pi$
$743$	16.2455			0.595990			0.297995	+	0.954567i	$0.403682\pi$
$744$		0			0
$745$	−74.6520			−2.73504
$746$	−6.92012	+	5.02776i	−0.253364	+	0.184080i
$747$	3.22312	−	30.6659i	0.117928	−	1.12201i
$748$	2.53720	−	7.80871i	0.0927694	−	0.285515i
$749$	−0.888356	+	1.53868i	−0.0324598	+	0.0562220i
$750$	4.32029	+	7.48296i	0.157755	+	0.273239i
$751$	10.5525	−	2.24301i	0.385067	−	0.0818485i	−0.0113107	−	0.999936i	$-0.503600\pi$
$751$	10.5525	−	2.24301i	0.385067	−	0.0818485i	0.396378	+	0.918088i	$0.370267\pi$
$752$	−0.371861	−	1.14447i	−0.0135604	−	0.0417346i
$753$	−5.34155	−	1.13538i	−0.194657	−	0.0413756i
$754$	−1.02667	−	9.76807i	−0.0373889	−	0.355732i
$755$	−38.1362	−	42.3545i	−1.38792	−	1.54144i
$756$	4.97553	+	2.21525i	0.180958	+	0.0805678i
$757$	−37.5482	+	16.7176i	−1.36471	+	0.607610i	−0.952796	−	0.303611i	$-0.901808\pi$
$757$	−37.5482	+	16.7176i	−1.36471	+	0.607610i	−0.411918	+	0.911221i	$0.635141\pi$
$758$	2.14026	−	2.37700i	0.0777377	−	0.0863364i
$759$	−9.86411	−	7.16670i	−0.358045	−	0.260135i
$760$	27.6956	+	20.1221i	1.00463	+	0.729904i
$761$	−13.1555	+	14.6106i	−0.476885	+	0.529634i	−0.932803	−	0.360388i	$-0.882644\pi$
$761$	−13.1555	+	14.6106i	−0.476885	+	0.529634i	0.455918	+	0.890022i	$0.349311\pi$
$762$	−0.813967	+	0.362401i	−0.0294869	+	0.0131284i
$763$	1.02993	+	0.458555i	0.0372860	+	0.0166008i
$764$	21.5280	+	23.9093i	0.778857	+	0.865008i
$765$	−1.10837	−	10.5454i	−0.0400732	−	0.381271i
$766$	3.38652	+	0.719826i	0.122360	+	0.0260084i
$767$	0.833766	+	2.56607i	0.0301056	+	0.0926554i
$768$	8.76045	−	1.86209i	0.316116	−	0.0671924i
$769$	−1.89417	−	3.28080i	−0.0683055	−	0.118309i	0.829850	−	0.557986i	$-0.188426\pi$
$769$	−1.89417	−	3.28080i	−0.0683055	−	0.118309i	−0.898155	+	0.439678i	$0.855093\pi$
$770$	4.01575	−	6.95549i	0.144718	−	0.250658i
$771$	−1.26262	+	3.88595i	−0.0454722	+	0.139949i
$772$	0.902516	−	8.58687i	0.0324823	−	0.309048i
$773$	−20.5244	+	14.9119i	−0.738212	+	0.536342i	−0.892151	−	0.451738i	$-0.850804\pi$
$773$	−20.5244	+	14.9119i	−0.738212	+	0.536342i	0.153939	+	0.988080i	$0.450804\pi$
$774$	10.7855			0.387676
$775$		0			0
$776$	−12.8256			−0.460414
$777$	−5.80327	+	4.21632i	−0.208191	+	0.151260i
$778$	−1.34066	+	12.7556i	−0.0480651	+	0.457309i
$779$	−0.887573	+	2.73167i	−0.0318006	+	0.0978722i
$780$	7.42103	−	12.8536i	0.265716	−	0.460233i
$781$	15.9194	+	27.5732i	0.569641	+	0.986647i
$782$	−2.89722	+	0.615823i	−0.103604	+	0.0220218i
$783$	7.07939	+	21.7881i	0.252997	+	0.778644i
$784$	8.62211	+	1.83269i	0.307932	+	0.0654531i
$785$	−5.87019	−	55.8511i	−0.209516	−	1.99341i
$786$	−2.61994	−	2.90974i	−0.0934501	−	0.103787i
$787$	23.7034	+	10.5534i	0.844935	+	0.376189i	0.783099	−	0.621897i	$-0.213638\pi$
$787$	23.7034	+	10.5534i	0.844935	+	0.376189i	0.0618357	+	0.998086i	$0.480305\pi$
$788$	22.1660	−	9.86894i	0.789631	−	0.351566i
$789$	1.51491	−	1.68248i	0.0539323	−	0.0598979i
$790$	29.1492	+	21.1781i	1.03708	+	0.753484i
$791$	−3.94062	−	2.86303i	−0.140112	−	0.101797i
$792$	−14.6275	+	16.2455i	−0.519767	+	0.577259i
$793$	−6.15913	+	2.74222i	−0.218717	+	0.0973791i
$794$	−20.5082	−	9.13086i	−0.727810	−	0.324042i
$795$	−8.00488	−	8.89032i	−0.283904	−	0.315307i
$796$	0.679123	+	6.46142i	0.0240709	+	0.229019i
$797$	−18.0983	−	3.84691i	−0.641074	−	0.136265i	−0.124106	−	0.992269i	$-0.539606\pi$
$797$	−18.0983	−	3.84691i	−0.641074	−	0.136265i	−0.516968	+	0.856004i	$0.672940\pi$
$798$	0.557688	+	1.71639i	0.0197419	+	0.0607595i
$799$	−1.12130	+	0.238340i	−0.0396689	+	0.00843188i
$800$	25.3951	+	43.9856i	0.897852	+	1.55513i
$801$	4.84652	−	8.39442i	0.171243	−	0.296602i
$802$	−2.63993	+	8.12488i	−0.0932192	+	0.286899i
$803$	−2.43385	+	23.1565i	−0.0858885	+	0.817175i
$804$	−2.32281	+	1.68762i	−0.0819193	+	0.0595178i
$805$	9.29174			0.327491
$806$		0			0
$807$	−12.0378			−0.423751
$808$	−7.48564	+	5.43864i	−0.263344	+	0.191331i
$809$	3.84119	−	36.5465i	0.135049	−	1.28491i	−0.691637	−	0.722245i	$-0.743110\pi$
$809$	3.84119	−	36.5465i	0.135049	−	1.28491i	0.826687	−	0.562663i	$-0.190223\pi$
$810$	−1.84387	+	5.67484i	−0.0647869	+	0.199394i
$811$	19.7151	−	34.1475i	0.692289	−	1.19908i	−0.278797	−	0.960350i	$-0.589936\pi$
$811$	19.7151	−	34.1475i	0.692289	−	1.19908i	0.971086	−	0.238730i	$-0.0767310\pi$
$812$	−2.84894	−	4.93451i	−0.0999782	−	0.173167i
$813$	12.2023	−	2.59369i	0.427955	−	0.0909646i
$814$	−9.13092	−	28.1021i	−0.320039	−	0.984977i
$815$	3.78922	+	0.805423i	0.132730	+	0.0282127i
$816$	0.169542	+	1.61308i	0.00593516	+	0.0564692i
$817$	−18.1956	−	20.2083i	−0.636584	−	0.706998i
$818$	−2.17189	−	0.966987i	−0.0759383	−	0.0338099i
$819$	−4.43527	+	1.97471i	−0.154981	+	0.0690019i
$820$	−2.85917	+	3.17543i	−0.0998467	+	0.110891i
$821$	1.19782	+	0.870264i	0.0418041	+	0.0303724i	0.608491	−	0.793561i	$-0.291775\pi$
$821$	1.19782	+	0.870264i	0.0418041	+	0.0303724i	−0.566687	+	0.823933i	$0.691775\pi$
$822$	−6.41791	−	4.66289i	−0.223850	−	0.162637i
$823$	26.0059	−	28.8825i	0.906509	−	1.00678i	−0.0934289	−	0.995626i	$-0.529783\pi$
$823$	26.0059	−	28.8825i	0.906509	−	1.00678i	0.999938	−	0.0111542i	$-0.00355056\pi$
$824$	−13.8660	+	6.17353i	−0.483044	+	0.215065i
$825$	29.6728	+	13.2112i	1.03307	+	0.459954i
$826$	−0.326584	−	0.362709i	−0.0113633	−	0.0126203i
$827$	3.54731	+	33.7504i	0.123352	+	1.17362i	0.864627	+	0.502414i	$0.167555\pi$
$827$	3.54731	+	33.7504i	0.123352	+	1.17362i	−0.741275	+	0.671201i	$0.765779\pi$
$828$	−10.7007	−	2.27450i	−0.371874	−	0.0790442i
$829$	−5.10827	−	15.7216i	−0.177417	−	0.546035i	0.822318	−	0.569028i	$-0.192680\pi$
$829$	−5.10827	−	15.7216i	−0.177417	−	0.546035i	−0.999736	+	0.0229933i	$0.992680\pi$
$830$	35.2756	−	7.49805i	1.22443	−	0.260261i
$831$	5.22073	+	9.04256i	0.181105	+	0.313683i
$832$	−1.82877	+	3.16752i	−0.0634012	+	0.109814i
$833$	2.59485	−	7.98612i	0.0899061	−	0.276703i
$834$	−1.21710	+	11.5799i	−0.0421446	+	0.400979i
$835$	−33.8619	+	24.6021i	−1.17184	+	0.851392i
$836$	23.8409			0.824555
$837$		0			0
$838$	27.6122			0.953848
$839$	43.7501	−	31.7863i	1.51042	−	1.09738i	0.544430	−	0.838806i	$-0.316746\pi$
$839$	43.7501	−	31.7863i	1.51042	−	1.09738i	0.965990	−	0.258579i	$-0.0832542\pi$
$840$	−0.648792	+	6.17284i	−0.0223854	+	0.212983i
$841$	−1.55522	+	4.78647i	−0.0536282	+	0.165051i
$842$	7.47562	−	12.9482i	0.257627	−	0.446223i
$843$	6.94819	+	12.0346i	0.239308	+	0.414494i
$844$	−17.1621	+	3.64792i	−0.590744	+	0.125567i
$845$	−5.19379	−	15.9848i	−0.178672	−	0.549896i
$846$	1.29139	+	0.274493i	0.0443988	+	0.00943726i
$847$	−0.473859	−	4.50847i	−0.0162820	−	0.154913i
$848$	−3.28650	−	3.65003i	−0.112859	−	0.125343i
$849$	−18.7100	−	8.33022i	−0.642125	−	0.285893i
$850$	7.20834	−	3.20936i	0.247244	−	0.110080i
$851$	22.8740	−	25.4042i	0.784112	−	0.870845i
$852$	−8.61062	−	6.25598i	−0.294995	−	0.214326i
$853$	−32.0178	−	23.2623i	−1.09627	−	0.796487i	−0.115823	−	0.993270i	$-0.536950\pi$
$853$	−32.0178	−	23.2623i	−1.09627	−	0.796487i	−0.980447	+	0.196783i	$0.936950\pi$
$854$	0.816061	−	0.906328i	0.0279250	−	0.0310139i
$855$	28.1274	−	12.5231i	0.961937	−	0.428282i
$856$	5.16699	+	2.30049i	0.176604	+	0.0786292i
$857$	8.51472	+	9.45655i	0.290857	+	0.323030i	0.870809	−	0.491621i	$-0.163595\pi$
$857$	8.51472	+	9.45655i	0.290857	+	0.323030i	−0.579952	+	0.814651i	$0.696929\pi$
$858$	0.778852	+	7.41029i	0.0265896	+	0.252983i
$859$	−20.6921	−	4.39823i	−0.706004	−	0.150066i	−0.159102	−	0.987262i	$-0.550860\pi$
$859$	−20.6921	−	4.39823i	−0.706004	−	0.150066i	−0.546902	+	0.837196i	$0.684193\pi$
$860$	−12.5010	−	38.4742i	−0.426281	−	1.31196i
$861$	−0.509382	+	0.108272i	−0.0173597	+	0.00368991i
$862$	−4.00618	−	6.93891i	−0.136451	−	0.236340i
$863$	4.66987	−	8.08845i	0.158964	−	0.275334i	−0.775531	−	0.631309i	$-0.782518\pi$
$863$	4.66987	−	8.08845i	0.158964	−	0.275334i	0.934495	+	0.355975i	$0.115851\pi$
$864$	8.39795	−	25.8462i	0.285704	−	0.879307i
$865$	8.00376	−	76.1507i	0.272136	−	2.58920i
$866$	−13.7202	+	9.96829i	−0.466230	+	0.338736i
$867$	−13.7957			−0.468526
$868$		0			0
$869$	58.0085			1.96780
$870$	−9.13647	+	6.63804i	−0.309755	+	0.225051i
$871$	0.634734	−	6.03909i	0.0215071	−	0.204627i
$872$	1.10905	−	3.41331i	0.0375572	−	0.115589i
$873$	−5.76760	+	9.98977i	−0.195204	+	0.338102i
$874$	−4.30028	−	7.44830i	−0.145459	−	0.251942i
$875$	−10.3697	+	2.20415i	−0.350560	+	0.0745139i
$876$	−2.40525	−	7.40260i	−0.0812659	−	0.250111i
$877$	−21.9450	−	4.66455i	−0.741030	−	0.157511i	−0.178096	−	0.984013i	$-0.556994\pi$
$877$	−21.9450	−	4.66455i	−0.741030	−	0.157511i	−0.562933	+	0.826502i	$0.690327\pi$
$878$	1.31122	+	12.4754i	0.0442514	+	0.421024i
$879$	7.48794	+	8.31620i	0.252562	+	0.280498i
$880$	19.1474	+	8.52498i	0.645459	+	0.287377i
$881$	42.4173	−	18.8854i	1.42907	−	0.636265i	0.461107	−	0.887344i	$-0.347452\pi$
$881$	42.4173	−	18.8854i	1.42907	−	0.636265i	0.967966	+	0.251080i	$0.0807856\pi$
$882$	−6.47103	+	7.18680i	−0.217891	+	0.241992i
$883$	29.5611	+	21.4774i	0.994811	+	0.722773i	0.960969	−	0.276654i	$-0.0892257\pi$
$883$	29.5611	+	21.4774i	0.994811	+	0.722773i	0.0338419	+	0.999427i	$0.489226\pi$
$884$	−4.69625	−	3.41202i	−0.157952	−	0.114759i
$885$	2.07587	−	2.30548i	0.0697795	−	0.0774980i
$886$	−11.1869	+	4.98074i	−0.375832	+	0.167331i
$887$	26.2051	+	11.6673i	0.879881	+	0.391748i	0.796406	−	0.604762i	$-0.206732\pi$
$887$	26.2051	+	11.6673i	0.879881	+	0.391748i	0.0834744	+	0.996510i	$0.473398\pi$
$888$	15.2798	+	16.9699i	0.512755	+	0.569473i
$889$	−0.114270	−	1.08720i	−0.00383248	−	0.0364636i
$890$	11.0890	+	2.35704i	0.371704	+	0.0790081i
$891$	2.96861	+	9.13643i	0.0994521	+	0.306082i
$892$	−14.0537	+	2.98721i	−0.470553	+	0.100019i
$893$	−1.66433	−	2.88270i	−0.0556945	−	0.0964658i
$894$	−6.26408	+	10.8497i	−0.209502	+	0.362869i
$895$	0.150844	−	0.464249i	0.00504215	−	0.0155181i
$896$	−0.857670	+	8.16019i	−0.0286528	+	0.272613i
$897$	−6.97394	+	5.06687i	−0.232853	+	0.169178i
$898$	−6.34235			−0.211647
$899$		0			0
$900$	29.1430			0.971434
$901$	−3.78531	+	2.75019i	−0.126107	+	0.0916220i
$902$	0.224228	−	2.13339i	0.00746599	−	0.0710341i
$903$	1.52354	−	4.68898i	0.0507004	−	0.156040i
$904$	−7.75296	+	13.4285i	−0.257860	+	0.446626i
$905$	14.3332	+	24.8259i	0.476453	+	0.825240i
$906$	−9.35571	+	1.98862i	−0.310823	+	0.0660674i
$907$	−6.85697	−	21.1036i	−0.227682	−	0.700733i	−0.998008	−	0.0630831i	$-0.979907\pi$
$907$	−6.85697	−	21.1036i	−0.227682	−	0.700733i	0.770326	−	0.637650i	$-0.220093\pi$
$908$	32.4548	+	6.89849i	1.07705	+	0.228934i
$909$	0.869864	+	8.27621i	0.0288516	+	0.274504i
$910$	−3.79952	−	4.21979i	−0.125953	−	0.139885i
$911$	26.3397	+	11.7272i	0.872674	+	0.388540i	0.793680	−	0.608335i	$-0.208162\pi$
$911$	26.3397	+	11.7272i	0.872674	+	0.388540i	0.0789944	+	0.996875i	$0.474829\pi$
$912$	−4.30252	+	1.91560i	−0.142471	+	0.0634320i
$913$	38.8511	−	43.1485i	1.28578	−	1.42801i
$914$	17.4037	+	12.6445i	0.575662	+	0.418243i
$915$	6.27153	+	4.55653i	0.207330	+	0.150634i
$916$	17.2977	−	19.2110i	0.571531	−	0.634749i
$917$	4.38864	−	1.95395i	0.144926	−	0.0645250i
$918$	−3.85697	−	1.71723i	−0.127299	−	0.0566771i
$919$	32.1600	+	35.7173i	1.06086	+	1.17820i	0.983445	+	0.181205i	$0.0579999\pi$
$919$	32.1600	+	35.7173i	1.06086	+	1.17820i	0.0774146	+	0.996999i	$0.475333\pi$
$920$	−3.09188	−	29.4173i	−0.101936	−	0.969858i
$921$	−27.1160	−	5.76367i	−0.893501	−	0.189920i
$922$	−1.42082	−	4.37283i	−0.0467921	−	0.144011i
$923$	22.0182	−	4.68011i	0.724737	−	0.154048i
$924$	2.16127	+	3.74343i	0.0711007	+	0.123150i
$925$	−45.5334	+	78.8662i	−1.49713	+	2.59310i
$926$	7.52513	−	23.1600i	0.247291	−	0.761084i
$927$	−1.42692	+	13.5763i	−0.0468663	+	0.445903i
$928$	−23.0013	+	16.7114i	−0.755055	+	0.548580i
$929$	−7.01617			−0.230193			−0.115097	−	0.993354i	$-0.536718\pi$
$929$	−7.01617			−0.230193			−0.115097	+	0.993354i	$0.536718\pi$
$930$		0			0
$931$	24.3825			0.799105
$932$	−12.1321	+	8.81450i	−0.397401	+	0.288729i
$933$	−0.224630	+	2.13722i	−0.00735407	+	0.0699693i
$934$	−7.65829	+	23.5698i	−0.250587	+	0.771227i
$935$	9.98321	−	17.2914i	0.326486	−	0.565490i
$936$	7.72770	+	13.3848i	0.252588	+	0.437495i
$937$	12.5992	−	2.67804i	0.411597	−	0.0874877i	0.00254077	−	0.999997i	$-0.499191\pi$
$937$	12.5992	−	2.67804i	0.411597	−	0.0874877i	0.409056	+	0.912509i	$0.365858\pi$
$938$	0.339439	+	1.04469i	0.0110831	+	0.0341102i
$939$	9.48493	+	2.01608i	0.309529	+	0.0657924i
$940$	−0.517620	−	4.92482i	−0.0168829	−	0.160630i
$941$	33.4828	+	37.1864i	1.09151	+	1.21224i	0.975732	+	0.218967i	$0.0702686\pi$
$941$	33.4828	+	37.1864i	1.09151	+	1.21224i	0.115775	+	0.993275i	$0.463065\pi$
$942$	−8.60981	−	3.83334i	−0.280523	−	0.124897i
$943$	2.26718	−	1.00941i	0.0738296	−	0.0328710i
$944$	0.852273	−	0.946545i	0.0277391	−	0.0308074i
$945$	10.7150	+	7.78494i	0.348560	+	0.253244i
$946$	16.4304	+	11.9374i	0.534197	+	0.388117i
$947$	−34.7064	+	38.5454i	−1.12781	+	1.25256i	−0.163854	+	0.986485i	$0.552393\pi$
$947$	−34.7064	+	38.5454i	−1.12781	+	1.25256i	−0.963953	+	0.266072i	$0.914274\pi$
$948$	−17.7150	+	7.88724i	−0.575357	+	0.256166i
$949$	15.0387	+	6.69564i	0.488175	+	0.217350i
$950$	15.3308	+	17.0266i	0.497397	+	0.552416i
$951$	−0.825013	−	7.84948i	−0.0267529	−	0.254537i
$952$	2.37451	+	0.504718i	0.0769584	+	0.0163580i
$953$	−5.78950	−	17.8183i	−0.187540	−	0.577190i	0.812443	−	0.583041i	$-0.198137\pi$
$953$	−5.78950	−	17.8183i	−0.187540	−	0.577190i	−0.999983	+	0.00585146i	$0.998137\pi$
$954$	5.27085	−	1.12035i	0.170650	−	0.0362728i
$955$	39.1193	+	67.7565i	1.26587	+	2.19255i
$956$	−0.450241	+	0.779840i	−0.0145618	+	0.0252218i
$957$	−5.61857	+	17.2922i	−0.181623	+	0.558977i
$958$	2.39598	−	22.7962i	0.0774105	−	0.736512i
$959$	7.87432	−	5.72103i	0.254275	−	0.184742i
$960$	4.20549			0.135731
$961$		0			0
$962$	−20.8907			−0.673542
$963$	4.11539	−	2.99001i	0.132617	−	0.0963516i
$964$	−2.44950	+	23.3054i	−0.0788930	+	0.750616i
$965$	6.48829	−	19.9689i	0.208865	−	0.642821i
$966$	0.779674	−	1.35044i	0.0250856	−	0.0434496i
$967$	−23.8923	−	41.3827i	−0.768324	−	1.33078i	−0.938471	−	0.345358i	$-0.887757\pi$
$967$	−23.8923	−	41.3827i	−0.768324	−	1.33078i	0.170146	−	0.985419i	$-0.445576\pi$
$968$	−14.1159	+	3.00043i	−0.453703	+	0.0964376i
$969$	1.38642	+	4.26696i	0.0445382	+	0.137075i
$970$	−13.1964	−	2.80499i	−0.423712	−	0.0900628i
$971$	3.25090	+	30.9303i	0.104326	+	0.992600i	0.913999	+	0.405718i	$0.132978\pi$
$971$	3.25090	+	30.9303i	0.104326	+	0.992600i	−0.809672	+	0.586883i	$0.800355\pi$
$972$	−16.4705	−	18.2923i	−0.528290	−	0.586726i
$973$	−13.0509	−	5.81062i	−0.418392	−	0.186280i
$974$	17.9613	−	7.99690i	0.575518	−	0.256237i
$975$	15.3660	−	17.0656i	0.492105	−	0.546537i
$976$	2.57485	+	1.87074i	0.0824191	+	0.0598810i
$977$	17.8624	+	12.9778i	0.571469	+	0.415197i	0.835639	−	0.549280i	$-0.185098\pi$
$977$	17.8624	+	12.9778i	0.571469	+	0.415197i	−0.264170	+	0.964476i	$0.585098\pi$
$978$	0.435013	−	0.483131i	0.0139102	−	0.0154488i
$979$	16.6740	−	7.42376i	0.532905	−	0.237264i
$980$	33.1373	+	14.7537i	1.05853	+	0.471288i
$981$	−2.15986	−	2.39877i	−0.0689590	−	0.0765867i
$982$	2.01538	+	19.1751i	0.0643135	+	0.611902i
$983$	−36.7557	−	7.81267i	−1.17233	−	0.249185i	−0.419718	−	0.907655i	$-0.637871\pi$
$983$	−36.7557	−	7.81267i	−1.17233	−	0.249185i	−0.752608	+	0.658469i	$0.771204\pi$
$984$	0.512285	+	1.57665i	0.0163311	+	0.0502618i
$985$	57.7150	−	12.2677i	1.83895	−	0.390881i
$986$	2.20846	+	3.82517i	0.0703318	+	0.121818i
$987$	0.301756	−	0.522656i	0.00960499	−	0.0166363i
$988$	5.20865	−	16.0306i	0.165709	−	0.510001i
$989$	−2.45598	+	23.3671i	−0.0780955	+	0.743029i
$990$	−18.6033	+	13.5161i	−0.591253	+	0.429571i
$991$	6.77397			0.215182			0.107591	−	0.994195i	$-0.465686\pi$
$991$	6.77397			0.215182			0.107591	+	0.994195i	$0.465686\pi$
$992$		0			0
$993$	29.2099			0.926948
$994$	−3.29426	+	2.39342i	−0.104487	+	0.0759146i
$995$	−1.65149	+	15.7129i	−0.0523557	+	0.498131i
$996$	−5.99783	+	18.4594i	−0.190049	+	0.584909i
$997$	14.7866	−	25.6112i	0.468298	−	0.811115i	−0.531046	−	0.847343i	$-0.678201\pi$
$997$	14.7866	−	25.6112i	0.468298	−	0.811115i	0.999344	+	0.0362278i	$0.0115342\pi$
$998$	14.2397	+	24.6639i	0.450751	+	0.780724i
$999$	47.6624	−	10.1310i	1.50797	−	0.320529i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.j.338.2		16
31.2	even	5		961.2.g.l.732.2		16
31.3	odd	30		961.2.d.p.531.1		16
31.4	even	5		961.2.g.n.448.1		16
31.5	even	3		961.2.g.l.235.2		16
31.6	odd	6		961.2.d.o.388.4		16
31.7	even	15		961.2.d.q.628.1		16
31.8	even	5		961.2.c.i.521.3		16
31.9	even	15		961.2.c.i.439.3		16
31.10	even	15	inner	961.2.g.j.816.2		16
31.11	odd	30		961.2.g.s.846.1		16
31.12	odd	30		961.2.d.o.374.4		16
31.13	odd	30		961.2.g.t.547.1		16
31.14	even	15		961.2.a.j.1.3		8
31.15	odd	10		961.2.g.s.844.1		16
31.16	even	5		961.2.g.m.844.1		16
31.17	odd	30		961.2.a.i.1.3		8
31.18	even	15		961.2.g.n.547.1		16
31.19	even	15		961.2.d.n.374.4		16
31.20	even	15		961.2.g.m.846.1		16
31.21	odd	30		961.2.g.k.816.2		16
31.22	odd	30		961.2.c.j.439.3		16
31.23	odd	10		961.2.c.j.521.3		16
31.24	odd	30		961.2.d.p.628.1		16
31.25	even	3		961.2.d.n.388.4		16
31.26	odd	6		31.2.g.a.18.2	✓	16
31.27	odd	10		961.2.g.t.448.1		16
31.28	even	15		961.2.d.q.531.1		16
31.29	odd	10		31.2.g.a.19.2	yes	16
31.30	odd	2		961.2.g.k.338.2		16
93.14	odd	30		8649.2.a.be.1.6		8
93.17	even	30		8649.2.a.bf.1.6		8
93.26	even	6		279.2.y.c.235.1		16
93.29	even	10		279.2.y.c.19.1		16
124.91	even	10		496.2.bg.c.81.1		16
124.119	even	6		496.2.bg.c.49.1		16
155.29	odd	10		775.2.bl.a.701.1		16
155.57	even	12		775.2.ck.a.49.3		32
155.88	even	12		775.2.ck.a.49.2		32
155.119	odd	6		775.2.bl.a.576.1		16
155.122	even	20		775.2.ck.a.174.2		32
155.153	even	20		775.2.ck.a.174.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.26	odd	6
31.2.g.a.19.2	yes	16	31.29	odd	10
279.2.y.c.19.1		16	93.29	even	10
279.2.y.c.235.1		16	93.26	even	6
496.2.bg.c.49.1		16	124.119	even	6
496.2.bg.c.81.1		16	124.91	even	10
775.2.bl.a.576.1		16	155.119	odd	6
775.2.bl.a.701.1		16	155.29	odd	10
775.2.ck.a.49.2		32	155.88	even	12
775.2.ck.a.49.3		32	155.57	even	12
775.2.ck.a.174.2		32	155.122	even	20
775.2.ck.a.174.3		32	155.153	even	20
961.2.a.i.1.3		8	31.17	odd	30
961.2.a.j.1.3		8	31.14	even	15
961.2.c.i.439.3		16	31.9	even	15
961.2.c.i.521.3		16	31.8	even	5
961.2.c.j.439.3		16	31.22	odd	30
961.2.c.j.521.3		16	31.23	odd	10
961.2.d.n.374.4		16	31.19	even	15
961.2.d.n.388.4		16	31.25	even	3
961.2.d.o.374.4		16	31.12	odd	30
961.2.d.o.388.4		16	31.6	odd	6
961.2.d.p.531.1		16	31.3	odd	30
961.2.d.p.628.1		16	31.24	odd	30
961.2.d.q.531.1		16	31.28	even	15
961.2.d.q.628.1		16	31.7	even	15
961.2.g.j.338.2		16	1.1	even	1	trivial
961.2.g.j.816.2		16	31.10	even	15	inner
961.2.g.k.338.2		16	31.30	odd	2
961.2.g.k.816.2		16	31.21	odd	30
961.2.g.l.235.2		16	31.5	even	3
961.2.g.l.732.2		16	31.2	even	5
961.2.g.m.844.1		16	31.16	even	5
961.2.g.m.846.1		16	31.20	even	15
961.2.g.n.448.1		16	31.4	even	5
961.2.g.n.547.1		16	31.18	even	15
961.2.g.s.844.1		16	31.15	odd	10
961.2.g.s.846.1		16	31.11	odd	30
961.2.g.t.448.1		16	31.27	odd	10
961.2.g.t.547.1		16	31.13	odd	30
8649.2.a.be.1.6		8	93.14	odd	30
8649.2.a.bf.1.6		8	93.17	even	30

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	961.2.g.j.338.2

Level	$961$
Weight	$2$
Character	961.338
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$