LMFDB - Embedded newform 961.2.g.s.732.2

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			732.2
Root			$-1.14660i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.s.235.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17638 + 1.58123i) q^{2} +(1.29647 + 0.577226i) q^{3} +(1.61830 + 4.98062i) q^{4} +(-0.304192 + 0.526876i) q^{5} +(1.90889 + 3.30629i) q^{6} +(-1.15551 + 1.28332i) q^{7} +(-2.69088 + 8.28167i) q^{8} +(-0.659745 - 0.732721i) q^{9} +(-1.49515 + 0.665684i) q^{10} +(1.30817 + 0.278060i) q^{11} +(-0.776863 + 7.39136i) q^{12} +(-0.383689 - 3.65056i) q^{13} +(-4.54406 + 0.965869i) q^{14} +(-0.698502 + 0.507492i) q^{15} +(-10.4781 + 7.61278i) q^{16} +(2.70245 - 0.574422i) q^{17} +(-0.277253 - 2.63789i) q^{18} +(0.268395 - 2.55361i) q^{19} +(-3.11644 - 0.662421i) q^{20} +(-2.23885 + 0.996800i) q^{21} +(2.40739 + 2.67368i) q^{22} +(-0.166641 + 0.512867i) q^{23} +(-8.26904 + 9.18370i) q^{24} +(2.31493 + 4.00958i) q^{25} +(4.93733 - 8.55171i) q^{26} +(-1.74803 - 5.37989i) q^{27} +(-8.26170 - 3.67835i) q^{28} +(6.57801 + 4.77920i) q^{29} -2.32267 q^{30} -17.4262 q^{32} +(1.53550 + 1.11560i) q^{33} +(6.78985 + 3.02304i) q^{34} +(-0.324655 - 0.999185i) q^{35} +(2.58174 - 4.47170i) q^{36} +(-3.87249 - 6.70735i) q^{37} +(4.62199 - 5.13324i) q^{38} +(1.60975 - 4.95432i) q^{39} +(-3.54487 - 3.93697i) q^{40} +(-0.0950561 + 0.0423217i) q^{41} +(-6.44876 - 1.37073i) q^{42} +(0.314077 - 2.98824i) q^{43} +(0.732101 + 6.96547i) q^{44} +(0.586742 - 0.124716i) q^{45} +(-1.17364 + 0.852697i) q^{46} +(5.44062 - 3.95284i) q^{47} +(-17.9788 + 3.82152i) q^{48} +(0.419984 + 3.99588i) q^{49} +(-1.30191 + 12.3868i) q^{50} +(3.83521 + 0.815200i) q^{51} +(17.5611 - 7.81871i) q^{52} +(1.87273 + 2.07987i) q^{53} +(4.70248 - 14.4727i) q^{54} +(-0.544437 + 0.604658i) q^{55} +(-7.51871 - 13.0228i) q^{56} +(1.82198 - 3.15576i) q^{57} +(6.75922 + 20.8027i) q^{58} +(0.425925 + 0.189634i) q^{59} +(-3.65801 - 2.65770i) q^{60} -5.11468 q^{61} +1.70266 q^{63} +(-16.9698 - 12.3293i) q^{64} +(2.04010 + 0.908313i) q^{65} +(1.57780 + 4.85596i) q^{66} +(-4.14923 + 7.18668i) q^{67} +(7.23436 + 12.5303i) q^{68} +(-0.512085 + 0.568728i) q^{69} +(0.873372 - 2.68796i) q^{70} +(3.18420 + 3.53641i) q^{71} +(7.84344 - 3.49213i) q^{72} +(-7.34216 - 1.56062i) q^{73} +(2.17787 - 20.7211i) q^{74} +(0.686809 + 6.53455i) q^{75} +(13.1529 - 2.79574i) q^{76} +(-1.86844 + 1.35750i) q^{77} +(11.3374 - 8.23708i) q^{78} +(9.48701 - 2.01653i) q^{79} +(-0.823639 - 7.83640i) q^{80} +(0.529953 - 5.04217i) q^{81} +(-0.273799 - 0.0581977i) q^{82} +(-15.2421 + 6.78623i) q^{83} +(-8.58782 - 9.53774i) q^{84} +(-0.519413 + 1.59859i) q^{85} +(5.40866 - 6.00693i) q^{86} +(5.76952 + 9.99310i) q^{87} +(-5.82292 + 10.0856i) q^{88} +(-4.73299 - 14.5666i) q^{89} +(1.47418 + 0.656347i) q^{90} +(5.12819 + 3.72585i) q^{91} -2.82407 q^{92} +18.0912 q^{94} +(1.26379 + 0.918199i) q^{95} +(-22.5925 - 10.0588i) q^{96} +(-0.395287 - 1.21657i) q^{97} +(-5.40437 + 9.36065i) q^{98} +(-0.659316 - 1.14197i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} + 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} - 2 q^{11} - 20 q^{12} - 27 q^{13} - 6 q^{14} + 4 q^{15} - 2 q^{16} - 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20}+ \cdots + 6 q^{99}+O(q^{100})$ 16 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 + 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 - 2 * q^11 - 20 * q^12 - 27 * q^13 - 6 * q^14 + 4 * q^15 - 2 * q^16 - 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 + 29 * q^21 + 4 * q^22 + 21 * q^23 - 25 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 40 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 + 28 * q^34 + 21 * q^35 + q^36 - 8 * q^37 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 - 51 * q^42 + 8 * q^43 + 4 * q^44 + 25 * q^45 - 16 * q^46 + 4 * q^47 - 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 + 24 * q^52 + 66 * q^53 + 39 * q^54 - 52 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 - 51 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 18 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 + 27 * q^73 + 28 * q^74 - 32 * q^75 + 18 * q^76 - 42 * q^77 + 15 * q^78 + 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 + 4 * q^83 - 27 * q^84 - 63 * q^85 + 34 * q^86 + 15 * q^87 - 17 * q^88 + 26 * q^89 + 57 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 - 62 * q^96 - 37 * q^97 - 10 * q^98 + 6 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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

)

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

$2$	2.17638	+	1.58123i	1.53893	+	1.11810i	0.950999	+	0.309193i	$0.100059\pi$
$2$	2.17638	+	1.58123i	1.53893	+	1.11810i	0.587935	+	0.808908i	$0.299941\pi$
$3$	1.29647	+	0.577226i	0.748518	+	0.333262i	0.745297	−	0.666733i	$-0.232308\pi$
$3$	1.29647	+	0.577226i	0.748518	+	0.333262i	0.00322140	+	0.999995i	$0.498975\pi$
$4$	1.61830	+	4.98062i	0.809151	+	2.49031i
$5$	−0.304192	+	0.526876i	−0.136039	+	0.235626i	−0.925994	−	0.377539i	$-0.876770\pi$
$5$	−0.304192	+	0.526876i	−0.136039	+	0.235626i	0.789955	+	0.613165i	$0.210104\pi$
$6$	1.90889	+	3.30629i	0.779300	+	1.34979i
$7$	−1.15551	+	1.28332i	−0.436741	+	0.485050i	−0.920827	−	0.389970i	$-0.872485\pi$
$7$	−1.15551	+	1.28332i	−0.436741	+	0.485050i	0.484087	+	0.875020i	$0.339152\pi$
$8$	−2.69088	+	8.28167i	−0.951369	+	2.92801i
$9$	−0.659745	−	0.732721i	−0.219915	−	0.244240i
$10$	−1.49515	+	0.665684i	−0.472808	+	0.210508i
$11$	1.30817	+	0.278060i	0.394427	+	0.0838381i	0.400856	−	0.916141i	$-0.368713\pi$
$11$	1.30817	+	0.278060i	0.394427	+	0.0838381i	−0.00642837	+	0.999979i	$0.502046\pi$
$12$	−0.776863	+	7.39136i	−0.224261	+	2.13370i
$13$	−0.383689	−	3.65056i	−0.106416	−	1.01248i	−0.909242	−	0.416268i	$-0.863338\pi$
$13$	−0.383689	−	3.65056i	−0.106416	−	1.01248i	0.802826	−	0.596214i	$-0.203329\pi$
$14$	−4.54406	+	0.965869i	−1.21445	+	0.258139i
$15$	−0.698502	+	0.507492i	−0.180353	+	0.131034i
$16$	−10.4781	+	7.61278i	−2.61952	+	1.90319i
$17$	2.70245	−	0.574422i	0.655439	−	0.139318i	0.131824	−	0.991273i	$-0.457916\pi$
$17$	2.70245	−	0.574422i	0.655439	−	0.139318i	0.523615	+	0.851955i	$0.324583\pi$
$18$	−0.277253	−	2.63789i	−0.0653493	−	0.621757i
$19$	0.268395	−	2.55361i	0.0615741	−	0.585839i	−0.919619	−	0.392811i	$-0.871503\pi$
$19$	0.268395	−	2.55361i	0.0615741	−	0.585839i	0.981193	−	0.193028i	$-0.0618307\pi$
$20$	−3.11644	−	0.662421i	−0.696858	−	0.148122i
$21$	−2.23885	+	0.996800i	−0.488557	+	0.217520i
$22$	2.40739	+	2.67368i	0.513258	+	0.570031i
$23$	−0.166641	+	0.512867i	−0.0347470	+	0.106940i	−0.966926	−	0.255058i	$-0.917905\pi$
$23$	−0.166641	+	0.512867i	−0.0347470	+	0.106940i	0.932179	+	0.361998i	$0.117905\pi$
$24$	−8.26904	+	9.18370i	−1.68791	+	1.87462i
$25$	2.31493	+	4.00958i	0.462987	+	0.801917i
$26$	4.93733	−	8.55171i	0.968290	−	1.67713i
$27$	−1.74803	−	5.37989i	−0.336409	−	1.03536i
$28$	−8.26170	−	3.67835i	−1.56131	−	0.695142i
$29$	6.57801	+	4.77920i	1.22151	+	0.887476i	0.996224	−	0.0868178i	$-0.0276698\pi$
$29$	6.57801	+	4.77920i	1.22151	+	0.887476i	0.225282	+	0.974294i	$0.427670\pi$
$30$	−2.32267			−0.424060
$31$		0			0
$31$		0			0
$32$	−17.4262			−3.08054
$33$	1.53550	+	1.11560i	0.267296	+	0.194202i
$34$	6.78985	+	3.02304i	1.16445	+	0.518446i
$35$	−0.324655	−	0.999185i	−0.0548767	−	0.168893i
$36$	2.58174	−	4.47170i	0.430290	−	0.745284i
$37$	−3.87249	−	6.70735i	−0.636633	−	1.10268i	−0.986167	−	0.165757i	$-0.946993\pi$
$37$	−3.87249	−	6.70735i	−0.636633	−	1.10268i	0.349533	−	0.936924i	$-0.386340\pi$
$38$	4.62199	−	5.13324i	0.749785	−	0.832721i
$39$	1.60975	−	4.95432i	0.257767	−	0.793326i
$40$	−3.54487	−	3.93697i	−0.560493	−	0.622490i
$41$	−0.0950561	+	0.0423217i	−0.0148453	+	0.00660954i	−0.414146	−	0.910211i	$-0.635920\pi$
$41$	−0.0950561	+	0.0423217i	−0.0148453	+	0.00660954i	0.399301	+	0.916820i	$0.369253\pi$
$42$	−6.44876	−	1.37073i	−0.995066	−	0.211508i
$43$	0.314077	−	2.98824i	0.0478963	−	0.455703i	−0.944121	−	0.329600i	$-0.893086\pi$
$43$	0.314077	−	2.98824i	0.0478963	−	0.455703i	0.992017	−	0.126103i	$-0.0402471\pi$
$44$	0.732101	+	6.96547i	0.110368	+	1.05008i
$45$	0.586742	−	0.124716i	0.0874663	−	0.0185915i
$46$	−1.17364	+	0.852697i	−0.173043	+	0.125723i
$47$	5.44062	−	3.95284i	0.793597	−	0.576582i	−0.115432	−	0.993315i	$-0.536825\pi$
$47$	5.44062	−	3.95284i	0.793597	−	0.576582i	0.909029	+	0.416734i	$0.136825\pi$
$48$	−17.9788	+	3.82152i	−2.59502	+	0.551589i
$49$	0.419984	+	3.99588i	0.0599977	+	0.570840i
$50$	−1.30191	+	12.3868i	−0.184118	+	1.75176i
$51$	3.83521	+	0.815200i	0.537037	+	0.114151i
$52$	17.5611	−	7.81871i	2.43529	−	1.08426i
$53$	1.87273	+	2.07987i	0.257239	+	0.285693i	0.857906	−	0.513806i	$-0.171765\pi$
$53$	1.87273	+	2.07987i	0.257239	+	0.285693i	−0.600667	+	0.799499i	$0.705098\pi$
$54$	4.70248	−	14.4727i	0.639926	−	1.96949i
$55$	−0.544437	+	0.604658i	−0.0734118	+	0.0815321i
$56$	−7.51871	−	13.0228i	−1.00473	−	1.74024i
$57$	1.82198	−	3.15576i	0.241327	−	0.417990i
$58$	6.75922	+	20.8027i	0.887529	+	2.73153i
$59$	0.425925	+	0.189634i	0.0554507	+	0.0246882i	0.434275	−	0.900781i	$-0.357005\pi$
$59$	0.425925	+	0.189634i	0.0554507	+	0.0246882i	−0.378824	+	0.925469i	$0.623671\pi$
$60$	−3.65801	−	2.65770i	−0.472247	−	0.343108i
$61$	−5.11468			−0.654867			−0.327434	−	0.944874i	$-0.606184\pi$
$61$	−5.11468			−0.654867			−0.327434	+	0.944874i	$0.606184\pi$
$62$		0			0
$63$	1.70266			0.214514
$64$	−16.9698	−	12.3293i	−2.12123	−	1.54116i
$65$	2.04010	+	0.908313i	0.253044	+	0.112662i
$66$	1.57780	+	4.85596i	0.194213	+	0.597728i
$67$	−4.14923	+	7.18668i	−0.506910	+	0.877993i	0.493058	+	0.869996i	$0.335879\pi$
$67$	−4.14923	+	7.18668i	−0.506910	+	0.877993i	−0.999968	+	0.00799701i	$0.997454\pi$
$68$	7.23436	+	12.5303i	0.877294	+	1.51952i
$69$	−0.512085	+	0.568728i	−0.0616478	+	0.0684668i
$70$	0.873372	−	2.68796i	0.104388	−	0.321273i
$71$	3.18420	+	3.53641i	0.377895	+	0.419695i	0.901849	−	0.432052i	$-0.142210\pi$
$71$	3.18420	+	3.53641i	0.377895	+	0.419695i	−0.523954	+	0.851747i	$0.675544\pi$
$72$	7.84344	−	3.49213i	0.924359	−	0.411551i
$73$	−7.34216	−	1.56062i	−0.859335	−	0.182657i	−0.242889	−	0.970054i	$-0.578095\pi$
$73$	−7.34216	−	1.56062i	−0.859335	−	0.182657i	−0.616446	+	0.787397i	$0.711428\pi$
$74$	2.17787	−	20.7211i	0.253172	−	2.40877i
$75$	0.686809	+	6.53455i	0.0793059	+	0.754545i
$76$	13.1529	−	2.79574i	1.50874	−	0.320693i
$77$	−1.86844	+	1.35750i	−0.212928	+	0.154701i
$78$	11.3374	−	8.23708i	1.28370	−	0.932666i
$79$	9.48701	−	2.01653i	1.06737	−	0.226877i	0.359448	−	0.933165i	$-0.382965\pi$
$79$	9.48701	−	2.01653i	1.06737	−	0.226877i	0.707924	+	0.706288i	$0.249632\pi$
$80$	−0.823639	−	7.83640i	−0.0920856	−	0.876136i
$81$	0.529953	−	5.04217i	0.0588837	−	0.560241i
$82$	−0.273799	−	0.0581977i	−0.0302360	−	0.00642687i
$83$	−15.2421	+	6.78623i	−1.67304	+	0.744886i	−0.673055	+	0.739592i	$0.735018\pi$
$83$	−15.2421	+	6.78623i	−1.67304	+	0.744886i	−0.999986	+	0.00529340i	$0.998315\pi$
$84$	−8.58782	−	9.53774i	−0.937008	−	1.04065i
$85$	−0.519413	+	1.59859i	−0.0563382	+	0.173391i
$86$	5.40866	−	6.00693i	0.583231	−	0.647744i
$87$	5.76952	+	9.99310i	0.618557	+	1.07137i
$88$	−5.82292	+	10.0856i	−0.620725	+	1.07513i
$89$	−4.73299	−	14.5666i	−0.501696	−	1.54406i	−0.806255	−	0.591568i	$-0.798509\pi$
$89$	−4.73299	−	14.5666i	−0.501696	−	1.54406i	0.304559	−	0.952493i	$-0.401491\pi$
$90$	1.47418	+	0.656347i	0.155392	+	0.0691850i
$91$	5.12819	+	3.72585i	0.537581	+	0.390575i
$92$	−2.82407			−0.294430
$93$		0			0
$94$	18.0912			1.86597
$95$	1.26379	+	0.918199i	0.129662	+	0.0942052i
$96$	−22.5925	−	10.0588i	−2.30584	−	1.02663i
$97$	−0.395287	−	1.21657i	−0.0401353	−	0.123524i	0.928981	−	0.370127i	$-0.120686\pi$
$97$	−0.395287	−	1.21657i	−0.0401353	−	0.123524i	−0.969117	+	0.246603i	$0.920686\pi$
$98$	−5.40437	+	9.36065i	−0.545924	+	0.945568i
$99$	−0.659316	−	1.14197i	−0.0662638	−	0.114772i
$100$	−16.2240	+	18.0185i	−1.62240	+	1.80185i
$101$	2.50929	−	7.72281i	0.249684	−	0.768448i	−0.745147	−	0.666900i	$-0.767621\pi$
$101$	2.50929	−	7.72281i	0.249684	−	0.768448i	0.994831	−	0.101547i	$-0.0323794\pi$
$102$	7.05787	+	7.83855i	0.698833	+	0.776133i
$103$	13.8425	−	6.16308i	1.36394	−	0.607266i	0.411340	−	0.911482i	$-0.365061\pi$
$103$	13.8425	−	6.16308i	1.36394	−	0.607266i	0.952603	+	0.304216i	$0.0983944\pi$
$104$	31.2652	+	6.64562i	3.06580	+	0.651656i
$105$	0.155850	−	1.48281i	0.0152094	−	0.144708i
$106$	0.787001	+	7.48782i	0.0764403	+	0.727281i
$107$	12.1052	−	2.57303i	1.17025	−	0.248745i	0.418516	−	0.908209i	$-0.362550\pi$
$107$	12.1052	−	2.57303i	1.17025	−	0.248745i	0.751735	+	0.659465i	$0.229217\pi$
$108$	23.9664	−	17.4126i	2.30616	−	1.67553i
$109$	−5.83267	+	4.23769i	−0.558669	+	0.405897i	−0.830971	−	0.556315i	$-0.812215\pi$
$109$	−5.83267	+	4.23769i	−0.558669	+	0.405897i	0.272303	+	0.962212i	$0.412215\pi$
$110$	−2.14101	+	0.455085i	−0.204137	+	0.0433907i
$111$	−1.14891	−	10.9312i	−0.109050	−	1.03754i
$112$	2.33787	−	22.2434i	0.220908	−	2.10180i
$113$	−16.3075	−	3.46626i	−1.53408	−	0.326079i	−0.638022	−	0.770018i	$-0.720247\pi$
$113$	−16.3075	−	3.46626i	−1.53408	−	0.326079i	−0.896057	+	0.443940i	$0.853580\pi$
$114$	8.95531	−	3.98716i	0.838742	−	0.373432i
$115$	−0.219527	−	0.243809i	−0.0204710	−	0.0227353i
$116$	−13.1582	+	40.4968i	−1.22171	+	3.76003i
$117$	−2.42170	+	2.68957i	−0.223886	+	0.248651i
$118$	0.627119	+	1.08620i	0.0577310	+	0.0999930i
$119$	−2.38553	+	4.13185i	−0.218681	+	0.378767i
$120$	−2.32329	−	7.15036i	−0.212087	−	0.652736i
$121$	−8.41502	−	3.74661i	−0.765001	−	0.340601i
$122$	−11.1315	−	8.08750i	−1.00780	−	0.732208i
$123$	−0.147667			−0.0133147
$124$		0			0
$125$	−5.85866			−0.524014
$126$	3.70563	+	2.69230i	0.330124	+	0.239849i
$127$	−11.7934	−	5.25074i	−1.04649	−	0.465928i	−0.189835	−	0.981816i	$-0.560795\pi$
$127$	−11.7934	−	5.25074i	−1.04649	−	0.465928i	−0.856656	+	0.515888i	$0.827462\pi$
$128$	−6.66735	−	20.5200i	−0.589316	−	1.81373i
$129$	2.13208	−	3.69288i	0.187720	−	0.325140i
$130$	3.00379	+	5.20272i	0.263450	+	0.456309i
$131$	−1.63120	+	1.81163i	−0.142518	+	0.158283i	−0.810178	−	0.586184i	$-0.800630\pi$
$131$	−1.63120	+	1.81163i	−0.142518	+	0.158283i	0.667660	+	0.744467i	$0.267296\pi$
$132$	−3.07150	+	9.45312i	−0.267340	+	0.822789i
$133$	2.96697	+	3.29515i	0.257269	+	0.285726i
$134$	−20.3941	+	9.08006i	−1.76179	+	0.784398i
$135$	3.36627	+	0.715523i	0.289722	+	0.0615824i
$136$	−2.51477	+	23.9265i	−0.215640	+	2.05168i
$137$	−0.851261	−	8.09921i	−0.0727282	−	0.691962i	−0.968765	−	0.247982i	$-0.920233\pi$
$137$	−0.851261	−	8.09921i	−0.0727282	−	0.691962i	0.896036	−	0.443980i	$-0.146434\pi$
$138$	−2.01379	+	0.428043i	−0.171425	+	0.0364375i
$139$	1.09489	−	0.795487i	0.0928677	−	0.0674723i	−0.540382	−	0.841420i	$-0.681720\pi$
$139$	1.09489	−	0.795487i	0.0928677	−	0.0674723i	0.633250	+	0.773947i	$0.281720\pi$
$140$	4.45117	−	3.23397i	0.376193	−	0.273320i
$141$	9.33530	−	1.98428i	0.786174	−	0.167106i
$142$	1.33814	+	12.7315i	0.112294	+	1.06841i
$143$	0.513143	−	4.88223i	0.0429112	−	0.408272i
$144$	12.4909	+	2.65502i	1.04091	+	0.221252i
$145$	−4.51902	+	2.01200i	−0.375285	+	0.167087i
$146$	−13.5116	−	15.0062i	−1.11823	−	1.24192i
$147$	−1.76203	+	5.42297i	−0.145330	+	0.447279i
$148$	27.1399	−	30.1419i	2.23089	−	2.47765i
$149$	4.50192	+	7.79756i	0.368812	+	0.638801i	0.989380	−	0.145351i	$-0.0464313\pi$
$149$	4.50192	+	7.79756i	0.368812	+	0.638801i	−0.620568	+	0.784153i	$0.713098\pi$
$150$	−8.83789	+	15.3077i	−0.721611	+	1.24987i
$151$	−0.991453	−	3.05138i	−0.0806833	−	0.248318i	0.902576	−	0.430531i	$-0.141674\pi$
$151$	−0.991453	−	3.05138i	−0.0806833	−	0.248318i	−0.983259	+	0.182214i	$0.941674\pi$
$152$	20.4259	+	9.09422i	1.65676	+	0.737638i
$153$	−2.20381	−	1.60117i	−0.178168	−	0.129447i
$154$	−6.21295			−0.500654
$155$		0			0
$156$	27.2807			2.18420
$157$	2.69141	+	1.95543i	0.214798	+	0.156060i	0.689982	−	0.723827i	$-0.257618\pi$
$157$	2.69141	+	1.95543i	0.214798	+	0.156060i	−0.475184	+	0.879887i	$0.657618\pi$
$158$	23.8360	+	10.6125i	1.89629	+	0.844281i
$159$	1.22738	+	3.77748i	0.0973374	+	0.299574i
$160$	5.30090	−	9.18143i	0.419073	−	0.725856i
$161$	−0.465619	−	0.806476i	−0.0366959	−	0.0635592i
$162$	9.12622	−	10.1357i	0.717024	−	0.796335i
$163$	0.537796	−	1.65517i	0.0421235	−	0.129643i	−0.927783	−	0.373120i	$-0.878288\pi$
$163$	0.537796	−	1.65517i	0.0421235	−	0.129643i	0.969907	+	0.243477i	$0.0782881\pi$
$164$	−0.364618	−	0.404949i	−0.0284719	−	0.0316212i
$165$	−1.05487	+	0.469659i	−0.0821216	+	0.0365629i
$166$	−43.9033	−	9.33194i	−3.40756	−	0.724299i
$167$	1.46512	−	13.9397i	0.113374	−	1.07869i	−0.778886	−	0.627165i	$-0.784215\pi$
$167$	1.46512	−	13.9397i	0.113374	−	1.07869i	0.892261	−	0.451521i	$-0.149118\pi$
$168$	−2.23070	−	21.2237i	−0.172102	−	1.63744i
$169$	−0.463428	+	0.0985048i	−0.0356483	+	0.00757729i
$170$	−3.65818	+	2.65782i	−0.280570	+	0.203846i
$171$	−2.04816	+	1.48807i	−0.156626	+	0.113796i
$172$	15.3916	−	3.27158i	1.17360	−	0.249456i
$173$	0.00125234	+	0.0119153i	9.52139e−5	+	0.000905900i	0.994569	−	0.104076i	$-0.0331884\pi$
$173$	0.00125234	+	0.0119153i	9.52139e−5	+	0.000905900i	−0.994474	+	0.104981i	$0.966522\pi$
$174$	−3.24475	+	30.8718i	−0.245984	+	2.34038i
$175$	−7.82051	−	1.66230i	−0.591175	−	0.125658i
$176$	−15.8239	+	7.04525i	−1.19277	+	0.531056i
$177$	0.442737	+	0.491710i	0.0332782	+	0.0369592i
$178$	12.7325	−	39.1865i	0.954339	−	2.93715i
$179$	−6.67659	+	7.41510i	−0.499032	+	0.554231i	−0.939060	−	0.343753i	$-0.888302\pi$
$179$	−6.67659	+	7.41510i	−0.499032	+	0.554231i	0.440028	+	0.897984i	$0.354968\pi$
$180$	1.57069	+	2.72051i	0.117072	+	0.202775i
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	−0.280004	−	0.959999i	$-0.590336\pi$
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	0.971385	−	0.237509i	$-0.0763308\pi$
$182$	5.26946	+	16.2177i	0.390599	+	1.20214i
$183$	−6.63103	−	2.95233i	−0.490180	−	0.218242i
$184$	−3.79899	−	2.76013i	−0.280065	−	0.203479i
$185$	4.71192			0.346427
$186$		0			0
$187$	3.69497			0.270203
$188$	28.4922	+	20.7008i	2.07801	+	1.50976i
$189$	8.92399	+	3.97322i	0.649125	+	0.289009i
$190$	1.29861	+	3.99670i	0.0942109	+	0.289951i
$191$	−0.599059	+	1.03760i	−0.0433464	+	0.0750782i	−0.886885	−	0.461991i	$-0.847135\pi$
$191$	−0.599059	+	1.03760i	−0.0433464	+	0.0750782i	0.843538	+	0.537069i	$0.180469\pi$
$192$	−14.8841	−	25.7800i	−1.07417	−	1.86051i
$193$	8.51573	−	9.45768i	0.612976	−	0.680778i	−0.354118	−	0.935201i	$-0.615219\pi$
$193$	8.51573	−	9.45768i	0.612976	−	0.680778i	0.967093	+	0.254423i	$0.0818854\pi$
$194$	1.06338	−	3.27276i	0.0763465	−	0.234971i
$195$	2.12063	+	2.35520i	0.151862	+	0.168660i
$196$	−19.2223	+	8.55832i	−1.37302	+	0.611309i
$197$	2.90372	+	0.617206i	0.206882	+	0.0439741i	0.310187	−	0.950676i	$-0.399608\pi$
$197$	2.90372	+	0.617206i	0.206882	+	0.0439741i	−0.103305	+	0.994650i	$0.532942\pi$
$198$	0.370797	−	3.52789i	0.0263514	−	0.250717i
$199$	1.37811	+	13.1118i	0.0976916	+	0.929473i	0.928103	+	0.372323i	$0.121439\pi$
$199$	1.37811	+	13.1118i	0.0976916	+	0.929473i	−0.830412	+	0.557150i	$0.811895\pi$
$200$	−39.4353	+	8.38222i	−2.78849	+	0.592713i
$201$	−9.52770	+	6.92228i	−0.672032	+	0.488260i
$202$	17.6727	−	12.8400i	1.24345	−	0.903419i
$203$	−13.7342	+	2.91929i	−0.963951	+	0.204894i
$204$	2.14633	+	20.4210i	0.150273	+	1.42976i
$205$	0.00661701	−	0.0629567i	0.000462152	−	0.00439708i
$206$	39.8718	+	8.47502i	2.77800	+	0.590483i
$207$	0.485729	−	0.216260i	0.0337605	−	0.0150311i
$208$	31.8112	+	35.3299i	2.20571	+	2.44969i
$209$	1.06116	−	3.26592i	0.0734021	−	0.225908i
$210$	2.68386	−	2.98073i	0.185204	−	0.205690i
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	−0.987343	−	0.158600i	$-0.949302\pi$
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	0.356320	−	0.934364i	$-0.384031\pi$
$212$	−7.32843	+	12.6932i	−0.503318	+	0.871773i
$213$	2.08691	+	6.42285i	0.142993	+	0.440087i
$214$	30.4141	+	13.5412i	2.07906	+	0.925658i
$215$	1.47889	+	1.07448i	0.100860	+	0.0732788i
$216$	49.2582			3.35160
$217$		0			0
$218$	−19.3949			−1.31359
$219$	−8.61807	−	6.26139i	−0.582355	−	0.423106i
$220$	−3.89264	−	1.73311i	−0.262442	−	0.116847i
$221$	−3.13386	−	9.64503i	−0.210806	−	0.648795i
$222$	14.7843	−	25.6071i	0.992256	−	1.71864i
$223$	−4.69801	−	8.13718i	−0.314602	−	0.544906i	0.664751	−	0.747065i	$-0.268538\pi$
$223$	−4.69801	−	8.13718i	−0.314602	−	0.544906i	−0.979353	+	0.202159i	$0.935204\pi$
$224$	20.1361	−	22.3634i	1.34540	−	1.49422i
$225$	1.41064	−	4.34150i	0.0940426	−	0.289433i
$226$	−30.0103	−	33.3298i	−1.99626	−	2.21707i
$227$	7.72807	−	3.44076i	0.512930	−	0.228371i	−0.133915	−	0.990993i	$-0.542755\pi$
$227$	7.72807	−	3.44076i	0.512930	−	0.228371i	0.646845	+	0.762622i	$0.276088\pi$
$228$	18.6662	+	3.96761i	1.23620	+	0.262762i
$229$	−2.38779	+	22.7183i	−0.157790	+	1.50127i	0.573503	+	0.819203i	$0.305584\pi$
$229$	−2.38779	+	22.7183i	−0.157790	+	1.50127i	−0.731293	+	0.682064i	$0.761083\pi$
$230$	−0.0922547	−	0.877744i	−0.00608309	−	0.0578768i
$231$	−3.20596	+	0.681447i	−0.210937	+	0.0448359i
$232$	−57.2804	+	41.6167i	−3.76064	+	2.73227i
$233$	−13.1493	+	9.55355i	−0.861442	+	0.625874i	−0.928277	−	0.371890i	$-0.878710\pi$
$233$	−13.1493	+	9.55355i	−0.861442	+	0.625874i	0.0668349	+	0.997764i	$0.478710\pi$
$234$	−9.52339	+	2.02426i	−0.622563	+	0.132330i
$235$	0.427664	+	4.06896i	0.0278978	+	0.265429i
$236$	−0.255220	+	2.42826i	−0.0166134	+	0.158066i
$237$	13.4636	+	2.86178i	0.874556	+	0.185893i
$238$	−11.7252	+	5.22042i	−0.760035	+	0.338389i
$239$	12.2270	+	13.5795i	0.790900	+	0.878384i	0.994929	−	0.100581i	$-0.0320703\pi$
$239$	12.2270	+	13.5795i	0.790900	+	0.878384i	−0.204029	+	0.978965i	$0.565404\pi$
$240$	3.45555	−	10.6351i	0.223055	−	0.686492i
$241$	−12.1591	+	13.5041i	−0.783239	+	0.869875i	−0.994192	−	0.107621i	$-0.965677\pi$
$241$	−12.1591	+	13.5041i	−0.783239	+	0.869875i	0.210953	+	0.977496i	$0.432343\pi$
$242$	−12.3900	−	21.4602i	−0.796461	−	1.37951i
$243$	−4.88759	+	8.46555i	−0.313539	+	0.543065i
$244$	−8.27710	−	25.4743i	−0.529887	−	1.63082i
$245$	−2.23309	−	0.994234i	−0.142667	−	0.0635193i
$246$	−0.321379	−	0.233496i	−0.0204904	−	0.0148871i
$247$	−9.42508			−0.599704
$248$		0			0
$249$	−23.6782			−1.50054
$250$	−12.7507	−	9.26390i	−0.806423	−	0.585901i
$251$	−20.9478	−	9.32656i	−1.32221	−	0.588687i	−0.380399	−	0.924822i	$-0.624213\pi$
$251$	−20.9478	−	9.32656i	−1.32221	−	0.588687i	−0.941814	+	0.336135i	$0.890880\pi$
$252$	2.75541	+	8.48029i	0.173575	+	0.534208i
$253$	−0.360602	+	0.624580i	−0.0226708	+	0.0392670i
$254$	−17.3642	−	30.0757i	−1.08953	−	1.88712i
$255$	−1.59615	+	1.77270i	−0.0999548	+	0.111011i
$256$	4.97240	−	15.3035i	0.310775	−	0.956467i
$257$	0.0710570	+	0.0789168i	0.00443241	+	0.00492270i	0.745357	−	0.666666i	$-0.232279\pi$
$257$	0.0710570	+	0.0789168i	0.00443241	+	0.00492270i	−0.740925	+	0.671588i	$0.765612\pi$
$258$	10.4795	−	4.66579i	0.652427	−	0.290479i
$259$	13.0824	+	2.78074i	0.812899	+	0.172787i
$260$	−1.22246	+	11.6309i	−0.0758137	+	0.721319i
$261$	−0.837985	−	7.97290i	−0.0518700	−	0.493510i
$262$	−6.41471	+	1.36349i	−0.396302	+	0.0842366i
$263$	5.90365	−	4.28925i	0.364034	−	0.264486i	−0.390698	−	0.920519i	$-0.627766\pi$
$263$	5.90365	−	4.28925i	0.364034	−	0.264486i	0.754733	+	0.656032i	$0.227766\pi$
$264$	−13.3709	+	9.71453i	−0.822922	+	0.597888i
$265$	−1.66550	+	0.354014i	−0.102311	+	0.0217469i
$266$	1.24685	+	11.8630i	0.0764493	+	0.727366i
$267$	2.27206	−	21.6172i	0.139048	−	1.32295i
$268$	−42.5089	−	9.03554i	−2.59664	−	0.551934i
$269$	14.8171	−	6.59701i	0.903416	−	0.402227i	0.0981714	−	0.995170i	$-0.468701\pi$
$269$	14.8171	−	6.59701i	0.903416	−	0.402227i	0.805245	+	0.592943i	$0.202034\pi$
$270$	6.19488	+	6.88011i	0.377008	+	0.418710i
$271$	−1.59009	+	4.89379i	−0.0965911	+	0.297277i	−0.987665	−	0.156581i	$-0.949953\pi$
$271$	−1.59009	+	4.89379i	−0.0965911	+	0.297277i	0.891074	+	0.453858i	$0.149953\pi$
$272$	−23.9435	+	26.5920i	−1.45179	+	1.61237i
$273$	4.49790	+	7.79058i	0.272225	+	0.471508i
$274$	10.9541	−	18.9730i	0.661760	−	1.14620i
$275$	1.91342	+	5.88890i	0.115383	+	0.355114i
$276$	−3.66133	−	1.63013i	−0.220386	−	0.0981222i
$277$	13.6909	+	9.94699i	0.822604	+	0.597657i	0.917457	−	0.397835i	$-0.130238\pi$
$277$	13.6909	+	9.94699i	0.822604	+	0.597657i	−0.0948533	+	0.995491i	$0.530238\pi$
$278$	3.64076			0.218358
$279$		0			0
$280$	9.14853			0.546729
$281$	−1.54253	−	1.12071i	−0.0920194	−	0.0668560i	0.540824	−	0.841136i	$-0.318112\pi$
$281$	−1.54253	−	1.12071i	−0.0920194	−	0.0668560i	−0.632844	+	0.774280i	$0.718112\pi$
$282$	23.4548	+	10.4427i	1.39671	+	0.621856i
$283$	−4.73099	−	14.5605i	−0.281228	−	0.865532i	−0.987504	−	0.157595i	$-0.949626\pi$
$283$	−4.73099	−	14.5605i	−0.281228	−	0.865532i	0.706276	−	0.707937i	$-0.250374\pi$
$284$	−12.4605	+	21.5823i	−0.739396	+	1.28067i
$285$	1.10846	+	1.91991i	0.0656596	+	0.113726i
$286$	8.83674	−	9.81419i	0.522527	−	0.580325i
$287$	0.0555257	−	0.170891i	0.00327758	−	0.0100874i
$288$	11.4968	+	12.7685i	0.677457	+	0.752392i
$289$	−8.55702	+	3.80983i	−0.503354	+	0.224108i
$290$	−13.0166	−	2.76676i	−0.764359	−	0.162469i
$291$	0.189757	−	1.80542i	0.0111238	−	0.105835i
$292$	−4.10896	−	39.0941i	−0.240458	−	2.28781i
$293$	−26.2082	+	5.57072i	−1.53110	+	0.325445i	−0.894965	−	0.446136i	$-0.852800\pi$
$293$	−26.2082	+	5.57072i	−1.53110	+	0.325445i	−0.636132	+	0.771580i	$0.719467\pi$
$294$	−12.4098	+	9.01626i	−0.723756	+	0.525839i
$295$	−0.229476	+	0.166724i	−0.0133606	+	0.00970706i
$296$	65.9684	−	14.0220i	3.83434	−	0.815013i
$297$	−0.790789	−	7.52385i	−0.0458862	−	0.436578i
$298$	−2.53186	+	24.0891i	−0.146667	+	1.39544i
$299$	1.93619	+	0.411550i	0.111973	+	0.0238005i
$300$	−31.4347	+	13.9956i	−1.81488	+	0.808037i
$301$	3.47196	+	3.85600i	0.200120	+	0.222256i
$302$	2.66716	−	8.20868i	0.153478	−	0.472356i
$303$	7.71103	−	8.56397i	0.442987	−	0.491987i
$304$	16.6278	+	28.8002i	0.953670	+	1.65181i
$305$	1.55584	−	2.69480i	0.0890873	−	0.154304i
$306$	−2.26453	−	6.96949i	−0.129454	−	0.398419i
$307$	8.17738	+	3.64081i	0.466708	+	0.207792i	0.626597	−	0.779343i	$-0.284447\pi$
$307$	8.17738	+	3.64081i	0.466708	+	0.207792i	−0.159889	+	0.987135i	$0.551114\pi$
$308$	−9.78489	−	7.10914i	−0.557546	−	0.405081i
$309$	21.5039			1.22331
$310$		0			0
$311$	20.6556			1.17127			0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556			1.17127			0.585637	+	0.810574i	$0.300844\pi$
$312$	36.6984	+	26.6629i	2.07764	+	1.50949i
$313$	0.412302	+	0.183569i	0.0233047	+	0.0103759i	0.418356	−	0.908283i	$-0.362606\pi$
$313$	0.412302	+	0.183569i	0.0233047	+	0.0103759i	−0.395051	+	0.918659i	$0.629273\pi$
$314$	2.76556	+	8.51151i	0.156069	+	0.480332i
$315$	−0.517934	+	0.897088i	−0.0291823	+	0.0505452i
$316$	25.3964	+	43.9879i	1.42866	+	2.47451i
$317$	−3.73431	+	4.14738i	−0.209740	+	0.232940i	−0.838831	−	0.544392i	$-0.816761\pi$
$317$	−3.73431	+	4.14738i	−0.209740	+	0.232940i	0.629091	+	0.777332i	$0.283427\pi$
$318$	−3.30184	+	10.1620i	−0.185158	+	0.569857i
$319$	7.27623	+	8.08108i	0.407391	+	0.452453i
$320$	11.6581	−	5.19052i	0.651708	−	0.290159i
$321$	17.1792	+	3.65156i	0.958851	+	0.203810i
$322$	0.261862	−	2.49145i	0.0145930	−	0.138843i
$323$	−0.741528	−	7.05517i	−0.0412597	−	0.392560i
$324$	25.9707	−	5.52025i	1.44282	−	0.306681i
$325$	13.7490	−	9.98923i	0.762657	−	0.554103i
$326$	3.78766	−	2.75189i	0.209779	−	0.152413i
$327$	−10.0080	+	2.12727i	−0.553443	+	0.117638i
$328$	−0.0947100	−	0.901106i	−0.00522949	−	0.0497552i
$329$	−1.21391	+	11.5496i	−0.0669252	+	0.636751i
$330$	−3.03844	−	0.645841i	−0.167261	−	0.0355524i
$331$	22.1128	−	9.84525i	1.21543	−	0.541144i	0.304028	−	0.952663i	$-0.401668\pi$
$331$	22.1128	−	9.84525i	1.21543	−	0.541144i	0.911401	+	0.411520i	$0.135002\pi$
$332$	−58.4660	−	64.9331i	−3.20874	−	3.56367i
$333$	−2.35976	+	7.26259i	−0.129314	+	0.397987i
$334$	25.2306	−	28.0214i	1.38056	−	1.53326i
$335$	−2.52433	−	4.37226i	−0.137919	−	0.238882i
$336$	15.8704	−	27.4884i	0.865804	−	1.49962i
$337$	3.41031	+	10.4958i	0.185771	+	0.571745i	0.999961	−	0.00885416i	$-0.00281840\pi$
$337$	3.41031	+	10.4958i	0.185771	+	0.571745i	−0.814190	+	0.580599i	$0.802818\pi$
$338$	−1.16436	−	0.518405i	−0.0633326	−	0.0281975i
$339$	−19.1414	−	13.9070i	−1.03962	−	0.755325i
$340$	−8.80253			−0.477384
$341$		0			0
$342$	−6.81056			−0.368273
$343$	−15.3928	−	11.1835i	−0.831134	−	0.603854i
$344$	23.9025	+	10.6421i	1.28874	+	0.573782i
$345$	−0.143877	−	0.442808i	−0.00774608	−	0.0238400i
$346$	−0.0161152	+	0.0279124i	−0.000866360	+	0.00150058i
$347$	9.28369	+	16.0798i	0.498375	+	0.863210i	0.999998	−	0.00187589i	$-0.000597114\pi$
$347$	9.28369	+	16.0798i	0.498375	+	0.863210i	−0.501624	+	0.865086i	$0.667264\pi$
$348$	−40.4350	+	44.9076i	−2.16755	+	2.40730i
$349$	−9.94251	+	30.5999i	−0.532210	+	1.63797i	0.217391	+	0.976085i	$0.430245\pi$
$349$	−9.94251	+	30.5999i	−0.532210	+	1.63797i	−0.749601	+	0.661890i	$0.769755\pi$
$350$	−14.3919	−	15.9839i	−0.769281	−	0.854373i
$351$	−18.9689	+	8.44549i	−1.01248	+	0.450787i
$352$	−22.7964	−	4.84552i	−1.21505	−	0.258267i
$353$	−3.36722	+	32.0369i	−0.179219	+	1.70515i	0.422433	+	0.906394i	$0.361176\pi$
$353$	−3.36722	+	32.0369i	−0.179219	+	1.70515i	−0.601652	+	0.798759i	$0.705490\pi$
$354$	0.186058	+	1.77022i	0.00988885	+	0.0940861i
$355$	−2.83186	+	0.601929i	−0.150299	+	0.0319471i
$356$	64.8915	−	47.1465i	3.43924	−	2.49876i
$357$	−5.47778	+	3.97984i	−0.289915	+	0.210636i
$358$	−26.2558	+	5.58085i	−1.38766	+	0.294957i
$359$	−2.21206	−	21.0463i	−0.116748	−	1.11078i	−0.883367	−	0.468681i	$-0.844729\pi$
$359$	−2.21206	−	21.0463i	−0.116748	−	1.11078i	0.766619	−	0.642102i	$-0.221937\pi$
$360$	−0.545995	+	5.19480i	−0.0287765	+	0.273790i
$361$	12.1359	+	2.57957i	0.638732	+	0.135767i
$362$	45.7188	−	20.3553i	2.40292	−	1.06985i
$363$	−8.74719	−	9.71473i	−0.459108	−	0.509891i
$364$	−10.2581	+	31.5711i	−0.537670	+	1.65478i
$365$	3.05568	−	3.39368i	0.159942	−	0.177633i
$366$	−9.76334	−	16.9106i	−0.510338	−	0.883931i
$367$	−6.49822	+	11.2552i	−0.339204	+	0.587519i	−0.984283	−	0.176597i	$-0.943491\pi$
$367$	−6.49822	+	11.2552i	−0.339204	+	0.587519i	0.645079	+	0.764116i	$0.276824\pi$
$368$	−2.15827	−	6.64247i	−0.112508	−	0.346263i
$369$	0.0937227	+	0.0417281i	0.00487901	+	0.00217228i
$370$	10.2549	+	7.45064i	0.533129	+	0.387341i
$371$	−4.83309			−0.250922
$372$		0			0
$373$	−4.42592			−0.229166			−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592			−0.229166			−0.114583	+	0.993414i	$0.536553\pi$
$374$	8.04167	+	5.84262i	0.415825	+	0.302115i
$375$	−7.59558	−	3.38177i	−0.392234	−	0.174634i
$376$	18.0961	+	55.6941i	0.933235	+	2.87220i
$377$	14.9228	−	25.8471i	0.768566	−	1.33119i
$378$	13.1394	+	22.7581i	0.675819	+	1.17055i
$379$	−10.0073	+	11.1143i	−0.514043	+	0.570902i	−0.943157	−	0.332348i	$-0.892159\pi$
$379$	−10.0073	+	11.1143i	−0.514043	+	0.570902i	0.429114	+	0.903250i	$0.358826\pi$
$380$	−2.52800	+	7.78040i	−0.129684	+	0.399126i
$381$	−12.2589	−	13.6149i	−0.628041	−	0.697511i
$382$	−2.94447	+	1.31096i	−0.150652	+	0.0670747i
$383$	11.3958	+	2.42224i	0.582296	+	0.123771i	0.489636	−	0.871927i	$-0.337130\pi$
$383$	11.3958	+	2.42224i	0.582296	+	0.123771i	0.0926601	+	0.995698i	$0.470463\pi$
$384$	3.20065	−	30.4521i	0.163332	−	1.55400i
$385$	−0.146870	−	1.39737i	−0.00748519	−	0.0712168i
$386$	33.4883	−	7.11815i	1.70451	−	0.362304i
$387$	−2.39676	+	1.74135i	−0.121834	+	0.0885176i
$388$	5.41958	−	3.93755i	0.275137	−	0.199899i
$389$	−14.0872	+	2.99433i	−0.714250	+	0.151819i	−0.550684	−	0.834714i	$-0.685633\pi$
$389$	−14.0872	+	2.99433i	−0.714250	+	0.151819i	−0.163566	+	0.986532i	$0.552300\pi$
$390$	0.891183	+	8.47904i	0.0451268	+	0.429353i
$391$	−0.155735	+	1.48172i	−0.00787585	+	0.0749337i
$392$	−34.2227	−	7.27425i	−1.72851	−	0.367405i
$393$	−3.16052	+	1.40715i	−0.159427	+	0.0709815i
$394$	5.34367	+	5.93474i	0.269210	+	0.298988i
$395$	−1.82341	+	5.61189i	−0.0917458	+	0.282365i
$396$	4.62075	−	5.13186i	0.232201	−	0.257886i
$397$	−7.89506	−	13.6746i	−0.396242	−	0.686311i	0.597017	−	0.802229i	$-0.296352\pi$
$397$	−7.89506	−	13.6746i	−0.396242	−	0.686311i	−0.993259	+	0.115918i	$0.963019\pi$
$398$	−17.7336	+	30.7155i	−0.888904	+	1.53963i
$399$	1.94454	+	5.98469i	0.0973489	+	0.299609i
$400$	−54.7802	−	24.3897i	−2.73901	−	1.21949i
$401$	−25.0983	−	18.2350i	−1.25335	−	0.910612i	−0.254938	−	0.966957i	$-0.582055\pi$
$401$	−25.0983	−	18.2350i	−1.25335	−	0.910612i	−0.998411	+	0.0563457i	$0.982055\pi$
$402$	−31.6817			−1.58014
$403$		0			0
$404$	42.5252			2.11571
$405$	2.49539	+	1.81301i	0.123997	+	0.0900889i
$406$	−34.5069	−	15.3635i	−1.71255	−	0.762476i
$407$	−3.20082	−	9.85111i	−0.158659	−	0.488302i
$408$	−17.0713	+	29.5684i	−0.845156	+	1.46385i
$409$	−3.29291	−	5.70349i	−0.162824	−	0.282019i	0.773056	−	0.634337i	$-0.218727\pi$
$409$	−3.29291	−	5.70349i	−0.162824	−	0.282019i	−0.935880	+	0.352318i	$0.885394\pi$
$410$	0.113950	−	0.126555i	0.00562761	−	0.00625009i
$411$	3.57144	−	10.9918i	0.176166	−	0.542184i
$412$	53.0973	+	58.9706i	2.61592	+	2.90527i
$413$	−0.735520	+	0.327475i	−0.0361926	+	0.0161140i
$414$	1.39909	+	0.297386i	0.0687615	+	0.0146157i
$415$	1.06103	−	10.0950i	0.0520839	−	0.495545i
$416$	6.68623	+	63.6153i	0.327820	+	3.11899i
$417$	1.87867	−	0.399324i	0.0919990	−	0.0195550i
$418$	7.47368	−	5.42994i	0.365550	−	0.265587i
$419$	11.8699	−	8.62397i	0.579882	−	0.421309i	−0.258800	−	0.965931i	$-0.583327\pi$
$419$	11.8699	−	8.62397i	0.579882	−	0.421309i	0.838681	+	0.544622i	$0.183327\pi$
$420$	7.63755	−	1.62341i	0.372674	−	0.0792143i
$421$	2.79257	+	26.5695i	0.136101	+	1.29492i	0.822948	+	0.568117i	$0.192328\pi$
$421$	2.79257	+	26.5695i	0.136101	+	1.29492i	−0.686847	+	0.726802i	$0.741006\pi$
$422$	5.15500	−	49.0465i	0.250941	−	2.38755i
$423$	−6.48575	−	1.37859i	−0.315348	−	0.0670293i
$424$	−22.2641	+	9.91262i	−1.08124	+	0.481399i
$425$	8.55918	+	9.50593i	0.415181	+	0.461105i
$426$	−5.61412	+	17.2785i	−0.272005	+	0.837145i
$427$	5.91005	−	6.56377i	0.286007	−	0.317643i
$428$	32.4052	+	56.1274i	1.56636	+	2.71302i
$429$	3.48342	−	6.03347i	0.168181	−	0.291299i
$430$	1.51963	+	4.67695i	0.0732832	+	0.225543i
$431$	3.64323	+	1.62207i	0.175488	+	0.0781323i	0.492600	−	0.870256i	$-0.336046\pi$
$431$	3.64323	+	1.62207i	0.175488	+	0.0781323i	−0.317112	+	0.948388i	$0.602713\pi$
$432$	59.2719	+	43.0636i	2.85172	+	2.07190i
$433$	18.0766			0.868704			0.434352	−	0.900743i	$-0.356977\pi$
$433$	18.0766			0.868704			0.434352	+	0.900743i	$0.356977\pi$
$434$		0			0
$435$	−7.02016			−0.336591
$436$	−30.5453	−	22.1925i	−1.46286	−	1.06283i
$437$	1.26494	+	0.563187i	0.0605102	+	0.0269409i
$438$	−8.85548	−	27.2544i	−0.423131	−	1.30226i
$439$	−11.4543	+	19.8394i	−0.546684	+	0.946884i	0.451815	+	0.892112i	$0.350777\pi$
$439$	−11.4543	+	19.8394i	−0.546684	+	0.946884i	−0.998499	+	0.0547723i	$0.982557\pi$
$440$	−3.54257	−	6.13591i	−0.168885	−	0.292518i
$441$	2.65078	−	2.94399i	0.126228	−	0.140190i
$442$	8.43057	−	25.9466i	0.401001	−	1.23416i
$443$	−14.3805	−	15.9712i	−0.683238	−	0.758813i	0.297376	−	0.954760i	$-0.403888\pi$
$443$	−14.3805	−	15.9712i	−0.683238	−	0.758813i	−0.980614	+	0.195948i	$0.937222\pi$
$444$	52.5848	−	23.4123i	2.49556	−	1.11110i
$445$	9.11455	+	1.93736i	0.432071	+	0.0918395i
$446$	2.64214	−	25.1383i	0.125109	−	1.19033i
$447$	1.33566	+	12.7079i	0.0631745	+	0.601065i
$448$	35.4312	−	7.53114i	1.67397	−	0.355813i
$449$	−15.2092	+	11.0501i	−0.717767	+	0.521488i	−0.885670	−	0.464315i	$-0.846300\pi$
$449$	−15.2092	+	11.0501i	−0.717767	+	0.521488i	0.167903	+	0.985804i	$0.446300\pi$
$450$	9.93502	−	7.21821i	0.468341	−	0.340270i
$451$	−0.136117	+	0.0289326i	−0.00640951	+	0.00136238i
$452$	−9.12629	−	86.8309i	−0.429265	−	4.08418i
$453$	0.475945	−	4.52831i	0.0223618	−	0.212759i
$454$	22.2599	+	4.73148i	1.04471	+	0.222059i
$455$	−3.52301	+	1.56855i	−0.165161	+	0.0735346i
$456$	21.2322	+	23.5808i	0.994290	+	1.10427i
$457$	1.26882	−	3.90503i	0.0593530	−	0.182670i	−0.916984	−	0.398924i	$-0.869384\pi$
$457$	1.26882	−	3.90503i	0.0593530	−	0.182670i	0.976337	+	0.216254i	$0.0693839\pi$
$458$	−41.1197	+	45.6680i	−1.92140	+	2.13393i
$459$	−7.81429	−	13.5347i	−0.364740	−	0.631748i
$460$	0.859060	−	1.48794i	0.0400539	−	0.0693754i
$461$	−7.06878	−	21.7555i	−0.329226	−	1.01325i	−0.969497	−	0.245104i	$-0.921178\pi$
$461$	−7.06878	−	21.7555i	−0.329226	−	1.01325i	0.640271	−	0.768149i	$-0.278822\pi$
$462$	−8.05492	−	3.58628i	−0.374749	−	0.166849i
$463$	13.4030	+	9.73782i	0.622888	+	0.452555i	0.853929	−	0.520389i	$-0.174213\pi$
$463$	13.4030	+	9.73782i	0.622888	+	0.452555i	−0.231041	+	0.972944i	$0.574213\pi$
$464$	−105.308			−4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	−30.8610	−	22.4218i	−1.42808	−	1.03756i	−0.990371	−	0.138438i	$-0.955792\pi$
$467$	−30.8610	−	22.4218i	−1.42808	−	1.03756i	−0.437704	−	0.899119i	$-0.644208\pi$
$468$	−17.3148	−	7.70904i	−0.800376	−	0.356351i
$469$	−4.42835	−	13.6291i	−0.204482	−	0.629332i
$470$	−5.50321	+	9.53184i	−0.253844	+	0.439671i
$471$	2.36062	+	4.08871i	0.108771	+	0.188398i
$472$	−2.71660	+	3.01709i	−0.125041	+	0.138873i
$473$	1.24177	−	3.82179i	0.0570969	−	0.175726i
$474$	24.7768	+	27.5175i	1.13804	+	1.26392i
$475$	10.8602	−	4.83529i	0.498302	−	0.221858i
$476$	−24.4397	−	5.19482i	−1.12019	−	0.238104i
$477$	0.288445	−	2.74437i	0.0132070	−	0.125656i
$478$	5.13833	+	48.8879i	0.235022	+	2.23608i
$479$	32.9487	−	7.00346i	1.50546	−	0.319996i	0.619961	−	0.784632i	$-0.287148\pi$
$479$	32.9487	−	7.00346i	1.50546	−	0.319996i	0.885502	+	0.464636i	$0.153815\pi$
$480$	12.1722	−	8.84364i	0.555584	−	0.403655i
$481$	−22.9997	+	16.7103i	−1.04870	+	0.761923i
$482$	−47.8161	+	10.1636i	−2.17796	+	0.462940i
$483$	−0.138143	−	1.31434i	−0.00628571	−	0.0598045i
$484$	5.04239	−	47.9752i	0.229200	−	2.18069i
$485$	0.761224	+	0.161803i	0.0345654	+	0.00734710i
$486$	−24.0233	+	10.6958i	−1.08972	+	0.485174i
$487$	−13.8354	−	15.3658i	−0.626942	−	0.696289i	0.343080	−	0.939306i	$-0.388530\pi$
$487$	−13.8354	−	15.3658i	−0.626942	−	0.696289i	−0.970022	+	0.243017i	$0.921863\pi$
$488$	13.7630	−	42.3581i	0.623020	−	1.91746i
$489$	1.65264	−	1.83545i	0.0747351	−	0.0830018i
$490$	−3.28793	−	5.69487i	−0.148534	−	0.257268i
$491$	−12.3664	+	21.4192i	−0.558087	+	0.966634i	0.439570	+	0.898209i	$0.355131\pi$
$491$	−12.3664	+	21.4192i	−0.558087	+	0.966634i	−0.997656	+	0.0684258i	$0.978202\pi$
$492$	−0.238969	−	0.735472i	−0.0107736	−	0.0331576i
$493$	20.5220	+	9.13698i	0.924264	+	0.411509i
$494$	−20.5126	−	14.9033i	−0.922905	−	0.670529i
$495$	0.802235			0.0360578
$496$		0			0
$497$	−8.21771			−0.368615
$498$	−51.5327	−	37.4407i	−2.30924	−	1.67776i
$499$	−22.4368	−	9.98952i	−1.00441	−	0.447192i	−0.162442	−	0.986718i	$-0.551937\pi$
$499$	−22.4368	−	9.98952i	−1.00441	−	0.447192i	−0.841969	+	0.539526i	$0.818604\pi$
$500$	−9.48108	−	29.1798i	−0.424007	−	1.30496i
$501$	9.94584	−	17.2267i	0.444347	−	0.769632i
$502$	−30.8429	−	53.4215i	−1.37659	−	2.38432i
$503$	9.86240	−	10.9533i	0.439743	−	0.488384i	−0.482008	−	0.876167i	$-0.660092\pi$
$503$	9.86240	−	10.9533i	0.439743	−	0.488384i	0.921751	+	0.387783i	$0.126759\pi$
$504$	−4.58164	+	14.1008i	−0.204082	+	0.628101i
$505$	3.30565	+	3.67130i	0.147100	+	0.163371i
$506$	−1.77241	+	0.789130i	−0.0787934	+	0.0350811i
$507$	−0.657681	−	0.139794i	−0.0292086	−	0.00620849i
$508$	7.06674	−	67.2355i	0.313536	−	2.98309i
$509$	−1.62085	−	15.4213i	−0.0718429	−	0.683539i	−0.969874	−	0.243607i	$-0.921669\pi$
$509$	−1.62085	−	15.4213i	−0.0718429	−	0.683539i	0.898031	−	0.439932i	$-0.144997\pi$
$510$	−6.27689	+	1.33419i	−0.277945	+	0.0590791i
$511$	10.4867	−	7.61904i	0.463905	−	0.337046i
$512$	0.109537	−	0.0795830i	0.00484088	−	0.00351710i
$513$	−14.2073	+	3.01986i	−0.627268	+	0.133330i
$514$	0.0298613	+	0.284111i	0.00131712	+	0.0125316i
$515$	−0.963600	+	9.16804i	−0.0424613	+	0.403992i
$516$	21.8432	+	4.64291i	0.961593	+	0.204393i
$517$	8.21637	−	3.65816i	0.361356	−	0.160886i
$518$	24.0752	+	26.7382i	1.05780	+	1.17481i
$519$	−0.00525417	+	0.0161707i	−0.000230632	+	0.000709813i
$520$	−13.0120	+	14.4513i	−0.570615	+	0.633732i
$521$	−14.7073	−	25.4738i	−0.644337	−	1.11603i	−0.984454	−	0.175642i	$-0.943800\pi$
$521$	−14.7073	−	25.4738i	−0.644337	−	1.11603i	0.340117	−	0.940383i	$-0.389533\pi$
$522$	10.7832	−	18.6771i	0.471970	−	0.817475i
$523$	13.9138	+	42.8222i	0.608408	+	1.87249i	0.471409	+	0.881915i	$0.343746\pi$
$523$	13.9138	+	42.8222i	0.608408	+	1.87249i	0.136999	+	0.990571i	$0.456254\pi$
$524$	−11.6628	−	5.19261i	−0.509492	−	0.226840i
$525$	−9.17954	−	6.66933i	−0.400628	−	0.291073i
$526$	19.6309			0.855947
$527$		0			0
$528$	−24.5819			−1.06979
$529$	18.3721	+	13.3481i	0.798788	+	0.580354i
$530$	−4.18455	−	1.86308i	−0.181765	−	0.0809271i
$531$	−0.142053	−	0.437194i	−0.00616457	−	0.0189726i
$532$	−11.6105	+	20.1099i	−0.503378	+	0.871876i
$533$	0.190970	+	0.330769i	0.00827182	+	0.0143272i
$534$	39.1268	−	43.4547i	1.69318	−	1.88047i
$535$	−2.32663	+	7.16062i	−0.100589	+	0.309581i
$536$	−48.3527	−	53.7011i	−2.08852	−	2.31953i
$537$	−12.9362	+	5.75956i	−0.558238	+	0.248544i
$538$	42.6791	+	9.07173i	1.84003	+	0.391110i
$539$	−0.561683	+	5.34406i	−0.0241934	+	0.230185i
$540$	1.88389	+	17.9241i	0.0810699	+	0.771329i
$541$	−36.9532	+	7.85464i	−1.58874	+	0.337697i	−0.915686	−	0.401895i	$-0.868352\pi$
$541$	−36.9532	+	7.85464i	−1.58874	+	0.337697i	−0.673055	+	0.739593i	$0.735018\pi$
$542$	−11.1989	+	8.13646i	−0.481033	+	0.349491i
$543$	21.3588	−	15.5181i	0.916595	−	0.665945i
$544$	−47.0933	+	10.0100i	−2.01911	+	0.429175i
$545$	−0.458482	−	4.36216i	−0.0196392	−	0.186855i
$546$	−2.52960	+	24.0675i	−0.108257	+	1.02999i
$547$	17.8109	+	3.78581i	0.761537	+	0.161870i	0.572281	−	0.820058i	$-0.306059\pi$
$547$	17.8109	+	3.78581i	0.761537	+	0.161870i	0.189257	+	0.981928i	$0.439392\pi$
$548$	38.9615	−	17.3468i	1.66435	−	0.741018i
$549$	3.37438	+	3.74763i	0.144015	+	0.159945i
$550$	−5.14739	+	15.8420i	−0.219486	+	0.675507i
$551$	13.9697	−	15.5150i	0.595131	−	0.660960i
$552$	−3.33206	−	5.77130i	−0.141822	−	0.245643i
$553$	−8.37446	+	14.5050i	−0.356118	+	0.616815i
$554$	14.0680	+	43.2969i	0.597693	+	1.83951i
$555$	6.10887	+	2.71984i	0.259307	+	0.115451i
$556$	5.73389	+	4.16591i	0.243171	+	0.176674i
$557$	−9.19760			−0.389715			−0.194857	−	0.980832i	$-0.562424\pi$
$557$	−9.19760			−0.389715			−0.194857	+	0.980832i	$0.562424\pi$
$558$		0			0
$559$	−11.0293			−0.466488
$560$	11.0083	+	7.99802i	0.465187	+	0.337978i
$561$	4.79043	+	2.13284i	0.202252	+	0.0900484i
$562$	−1.58502	−	4.87819i	−0.0668600	−	0.205774i
$563$	18.0809	−	31.3170i	0.762019	−	1.31986i	−0.179790	−	0.983705i	$-0.557542\pi$
$563$	18.0809	−	31.3170i	0.762019	−	1.31986i	0.941808	−	0.336150i	$-0.109125\pi$
$564$	24.9903	+	43.2844i	1.05228	+	1.82260i
$565$	6.78689	−	7.53761i	0.285527	−	0.317110i
$566$	12.7271	−	39.1700i	0.534960	−	1.64644i
$567$	5.85835	+	6.50636i	0.246028	+	0.273241i
$568$	−37.8557	+	16.8544i	−1.58839	+	0.707196i
$569$	−40.5929	−	8.62829i	−1.70174	−	0.361717i	−0.748316	−	0.663342i	$-0.769137\pi$
$569$	−40.5929	−	8.62829i	−1.70174	−	0.361717i	−0.953427	+	0.301625i	$0.902471\pi$
$570$	−0.623394	+	5.93120i	−0.0261111	+	0.248431i
$571$	3.38600	+	32.2157i	0.141700	+	1.34818i	0.802064	+	0.597238i	$0.203735\pi$
$571$	3.38600	+	32.2157i	0.141700	+	1.34818i	−0.660364	+	0.750946i	$0.729598\pi$
$572$	25.1470	−	5.34515i	1.05145	−	0.223492i
$573$	−1.37559	+	0.999427i	−0.0574662	+	0.0417517i
$574$	0.391063	−	0.284124i	0.0163227	−	0.0118591i
$575$	−2.44215	+	0.519094i	−0.101845	+	0.0216477i
$576$	2.16182	+	20.5683i	0.0900758	+	0.857014i
$577$	−4.28384	+	40.7580i	−0.178339	+	1.69678i	0.429781	+	0.902933i	$0.358591\pi$
$577$	−4.28384	+	40.7580i	−0.178339	+	1.69678i	−0.608120	+	0.793845i	$0.708076\pi$
$578$	−24.6476	−	5.23901i	−1.02520	−	0.217914i
$579$	16.4996	−	7.34610i	0.685701	−	0.305294i
$580$	−17.3342	−	19.2515i	−0.719762	−	0.799376i
$581$	8.90348	−	27.4021i	0.369379	−	1.13683i
$582$	3.26777	−	3.62923i	0.135453	−	0.150436i
$583$	1.87151	+	3.24155i	0.0775100	+	0.134251i
$584$	32.6814	−	56.6059i	1.35237	−	2.34237i
$585$	−0.680408	−	2.09408i	−0.0281314	−	0.0865796i
$586$	−65.8476	−	29.3172i	−2.72014	−	1.21108i
$587$	−20.6553	−	15.0070i	−0.852537	−	0.619404i	0.0733077	−	0.997309i	$-0.476644\pi$
$587$	−20.6553	−	15.0070i	−0.852537	−	0.619404i	−0.925844	+	0.377905i	$0.876644\pi$
$588$	−29.8612			−1.23146
$589$		0			0
$590$	−0.763058			−0.0314146
$591$	3.40833	+	2.47630i	0.140200	+	0.101861i
$592$	91.6378	+	40.7998i	3.76629	+	1.67686i
$593$	13.7611	+	42.3522i	0.565099	+	1.73920i	0.667656	+	0.744470i	$0.267298\pi$
$593$	13.7611	+	42.3522i	0.565099	+	1.73920i	−0.102557	+	0.994727i	$0.532702\pi$
$594$	10.1759	−	17.6252i	0.417523	−	0.723170i
$595$	−1.45132	−	2.51375i	−0.0594982	−	0.103054i
$596$	−31.5512	+	35.0412i	−1.29239	+	1.43534i
$597$	−5.78181	+	17.7946i	−0.236634	+	0.728284i
$598$	3.56313	+	3.95726i	0.145707	+	0.161824i
$599$	17.3390	−	7.71984i	0.708454	−	0.315424i	−0.0206883	−	0.999786i	$-0.506586\pi$
$599$	17.3390	−	7.71984i	0.708454	−	0.315424i	0.729143	+	0.684362i	$0.239919\pi$
$600$	−55.9651	−	11.8958i	−2.28477	−	0.485642i
$601$	1.34213	−	12.7695i	0.0547464	−	0.520877i	−0.932442	−	0.361319i	$-0.882326\pi$
$601$	1.34213	−	12.7695i	0.0547464	−	0.520877i	0.987189	−	0.159558i	$-0.0510069\pi$
$602$	1.45907	+	13.8821i	0.0594672	+	0.565792i
$603$	8.00327	−	1.70115i	0.325918	−	0.0692761i
$604$	13.5933	−	9.87610i	0.553103	−	0.401853i
$605$	4.53378	−	3.29398i	0.184324	−	0.133919i
$606$	30.3238	−	6.44552i	1.23182	−	0.261831i
$607$	3.98664	+	37.9304i	0.161813	+	1.53955i	0.710608	+	0.703589i	$0.248420\pi$
$607$	3.98664	+	37.9304i	0.161813	+	1.53955i	−0.548795	+	0.835957i	$0.684913\pi$
$608$	−4.67711	+	44.4997i	−0.189682	+	1.80470i
$609$	−19.4911	−	4.14296i	−0.789818	−	0.167881i
$610$	7.64722	−	3.40476i	0.309627	−	0.137855i
$611$	−16.5176	−	18.3446i	−0.668230	−	0.742145i
$612$	4.40836	−	13.5675i	0.178197	−	0.548435i
$613$	−12.4073	+	13.7797i	−0.501125	+	0.556556i	−0.939638	−	0.342169i	$-0.888838\pi$
$613$	−12.4073	+	13.7797i	−0.501125	+	0.556556i	0.438513	+	0.898725i	$0.355505\pi$
$614$	12.0401	+	20.8541i	0.485901	+	0.841605i
$615$	0.0449190	−	0.0778020i	0.00181131	−	0.00313728i
$616$	−6.21462	−	19.1266i	−0.250394	−	0.770634i
$617$	7.43219	+	3.30902i	0.299209	+	0.133216i	0.550850	−	0.834604i	$-0.314304\pi$
$617$	7.43219	+	3.30902i	0.299209	+	0.133216i	−0.251641	+	0.967821i	$0.580970\pi$
$618$	46.8007	+	34.0027i	1.88260	+	1.36779i
$619$	−5.36063			−0.215462			−0.107731	−	0.994180i	$-0.534359\pi$
$619$	−5.36063			−0.215462			−0.107731	+	0.994180i	$0.534359\pi$
$620$		0			0
$621$	3.05046			0.122411
$622$	44.9545	+	32.6614i	1.80251	+	1.30960i
$623$	24.1627	+	10.7579i	0.968058	+	0.431007i
$624$	20.8490	+	64.1665i	0.834626	+	2.56872i
$625$	−9.79252	+	16.9611i	−0.391701	+	0.678446i
$626$	0.607062	+	1.05146i	0.0242631	+	0.0420249i
$627$	3.26094	−	3.62164i	0.130229	−	0.144634i
$628$	−5.38372	+	16.5694i	−0.214834	+	0.661191i
$629$	−14.3180	−	15.9018i	−0.570898	−	0.634046i
$630$	−2.54573	+	1.13343i	−0.101424	+	0.0451570i
$631$	−28.4123	−	6.03921i	−1.13107	−	0.240417i	−0.395899	−	0.918294i	$-0.629567\pi$
$631$	−28.4123	−	6.03921i	−1.13107	−	0.240417i	−0.735176	+	0.677877i	$0.762900\pi$
$632$	−8.82818	+	83.9945i	−0.351166	+	3.34112i
$633$	−2.71947	−	25.8740i	−0.108089	−	1.02840i
$634$	−14.6853	+	3.12145i	−0.583226	+	0.123969i
$635$	6.35393	−	4.61640i	0.252148	−	0.183196i
$636$	−16.8279	+	12.2262i	−0.667271	+	0.484801i
$637$	14.4260	−	3.06635i	0.571580	−	0.121493i
$638$	3.05779	+	29.0929i	0.121059	+	1.15180i
$639$	0.490443	−	4.66625i	0.0194016	−	0.184594i
$640$	12.8396	+	2.72915i	0.507531	+	0.107879i
$641$	−25.2189	+	11.2282i	−0.996087	+	0.443487i	−0.839020	−	0.544101i	$-0.816871\pi$
$641$	−25.2189	+	11.2282i	−0.996087	+	0.443487i	−0.157068	+	0.987588i	$0.550204\pi$
$642$	31.6146	+	35.1116i	1.24773	+	1.38574i
$643$	−1.30684	+	4.02205i	−0.0515369	+	0.158614i	−0.973513	−	0.228634i	$-0.926574\pi$
$643$	−1.30684	+	4.02205i	−0.0515369	+	0.158614i	0.921976	+	0.387248i	$0.126574\pi$
$644$	3.26324	−	3.62419i	0.128590	−	0.142813i
$645$	1.29713	+	2.24669i	0.0510742	+	0.0884632i
$646$	9.54202	−	16.5273i	0.375426	−	0.650257i
$647$	−8.12124	−	24.9946i	−0.319279	−	0.982639i	−0.973957	−	0.226732i	$-0.927196\pi$
$647$	−8.12124	−	24.9946i	−0.319279	−	0.982639i	0.654679	−	0.755907i	$-0.272804\pi$
$648$	40.3315	+	17.9567i	1.58437	+	0.705408i
$649$	0.504451	+	0.366505i	0.0198014	+	0.0143866i
$650$	45.7184			1.79322
$651$		0			0
$652$	9.11408			0.356935
$653$	10.8018	+	7.84796i	0.422707	+	0.307114i	0.778726	−	0.627364i	$-0.215866\pi$
$653$	10.8018	+	7.84796i	0.422707	+	0.307114i	−0.356019	+	0.934479i	$0.615866\pi$
$654$	−25.1449	−	11.1952i	−0.983244	−	0.437768i
$655$	−0.458306	−	1.41052i	−0.0179075	−	0.0551136i
$656$	0.673821	−	1.16709i	0.0263083	−	0.0455673i
$657$	3.70045	+	6.40937i	0.144368	+	0.250053i
$658$	−20.9046	+	23.2169i	−0.814945	+	0.905088i
$659$	−4.76375	+	14.6613i	−0.185569	+	0.571124i	−0.999958	−	0.00919639i	$-0.997073\pi$
$659$	−4.76375	+	14.6613i	−0.185569	+	0.571124i	0.814388	+	0.580320i	$0.197073\pi$
$660$	−4.04629	−	4.49386i	−0.157502	−	0.174923i
$661$	−4.31473	+	1.92104i	−0.167824	+	0.0747199i	−0.488929	−	0.872324i	$-0.662612\pi$
$661$	−4.31473	+	1.92104i	−0.167824	+	0.0747199i	0.321105	+	0.947043i	$0.395946\pi$
$662$	63.6935	+	13.5385i	2.47552	+	0.526188i
$663$	1.50440	−	14.3134i	0.0584262	−	0.555888i
$664$	−15.1866	−	144.491i	−0.589356	−	5.60735i
$665$	−2.63867	+	0.560866i	−0.102323	+	0.0217494i
$666$	−16.6196	+	12.0748i	−0.643996	+	0.467890i
$667$	−3.54726	+	2.57724i	−0.137351	+	0.0997910i
$668$	71.7993	−	15.2614i	2.77800	−	0.590482i
$669$	−1.39383	−	13.2614i	−0.0538887	−	0.512717i
$670$	1.41967	−	13.5073i	0.0548466	−	0.521831i
$671$	−6.69085	−	1.42218i	−0.258298	−	0.0549028i
$672$	39.0146	−	17.3704i	1.50502	−	0.670078i
$673$	−20.7919	−	23.0917i	−0.801469	−	0.890121i	0.194400	−	0.980922i	$-0.437724\pi$
$673$	−20.7919	−	23.0917i	−0.801469	−	0.890121i	−0.995869	+	0.0908009i	$0.971057\pi$
$674$	−9.17425	+	28.2354i	−0.353379	+	1.08759i
$675$	17.5245	−	19.4630i	0.674520	−	0.749130i
$676$	−1.24058	−	2.14875i	−0.0477147	−	0.0826443i
$677$	4.51998	−	7.82883i	0.173717	−	0.300886i	−0.766000	−	0.642841i	$-0.777756\pi$
$677$	4.51998	−	7.82883i	0.173717	−	0.300886i	0.939716	+	0.341955i	$0.111089\pi$
$678$	−19.6687	−	60.5339i	−0.755371	−	2.32479i
$679$	2.01801	+	0.898474i	0.0774440	+	0.0344803i
$680$	−11.8413	−	8.60321i	−0.454093	−	0.329918i
$681$	12.0053			0.460044
$682$		0			0
$683$	7.13535			0.273027			0.136513	−	0.990638i	$-0.456410\pi$
$683$	7.13535			0.273027			0.136513	+	0.990638i	$0.456410\pi$
$684$	−10.7261	−	7.79294i	−0.410121	−	0.297971i
$685$	4.52623	+	2.01521i	0.172938	+	0.0769970i
$686$	−15.8169	−	48.6793i	−0.603890	−	1.85858i
$687$	−16.2093	+	28.0753i	−0.618423	+	1.07114i
$688$	19.4579	+	33.7021i	0.741826	+	1.28488i
$689$	6.87415	−	7.63452i	0.261884	−	0.290852i
$690$	0.387051	−	1.19122i	0.0147348	−	0.0453490i
$691$	24.4068	+	27.1065i	0.928479	+	1.03118i	0.999432	+	0.0337009i	$0.0107294\pi$
$691$	24.4068	+	27.1065i	0.928479	+	1.03118i	−0.0709528	+	0.997480i	$0.522604\pi$
$692$	−0.0573187	+	0.0255199i	−0.00217893	+	0.000970122i
$693$	2.22736	+	0.473440i	0.0846104	+	0.0179845i
$694$	−5.22111	+	49.6755i	−0.198190	+	1.88566i
$695$	0.0860650	+	0.818854i	0.00326463	+	0.0310609i
$696$	−98.2846	+	20.8910i	−3.72547	+	0.791873i
$697$	−0.232573	+	0.168974i	−0.00880934	+	0.00640036i
$698$	−70.0243	+	50.8756i	−2.65046	+	1.92567i
$699$	−22.5623	+	4.79576i	−0.853385	+	0.181392i
$700$	−4.37666	−	41.6411i	−0.165422	−	1.57389i
$701$	0.168755	−	1.60560i	0.00637379	−	0.0606425i	−0.990873	−	0.134801i	$-0.956960\pi$
$701$	0.168755	−	1.60560i	0.00637379	−	0.0606425i	0.997246	+	0.0741586i	$0.0236271\pi$
$702$	−54.6378	−	11.6136i	−2.06217	−	0.438328i
$703$	−18.1673	+	8.08861i	−0.685193	+	0.305068i
$704$	−18.7711	−	20.8474i	−0.707462	−	0.785717i
$705$	−1.79425	+	5.52214i	−0.0675755	+	0.207976i
$706$	−57.9862	+	64.4002i	−2.18234	+	2.42373i
$707$	7.01134	+	12.1440i	0.263688	+	0.456722i
$708$	−1.73254	+	3.00084i	−0.0651127	+	0.112779i
$709$	3.54997	+	10.9257i	0.133322	+	0.410323i	0.995325	−	0.0965797i	$-0.0307903\pi$
$709$	3.54997	+	10.9257i	0.133322	+	0.410323i	−0.862003	+	0.506903i	$0.830790\pi$
$710$	−7.11499	−	3.16780i	−0.267021	−	0.118885i
$711$	−7.73655	−	5.62094i	−0.290143	−	0.210802i
$712$	133.372			4.99833
$713$		0			0
$714$	−18.2148			−0.681672
$715$	2.41623	+	1.75550i	0.0903620	+	0.0656518i
$716$	−47.7366	−	21.2537i	−1.78400	−	0.794288i
$717$	8.01355	+	24.6632i	0.299271	+	0.921063i
$718$	28.4649	−	49.3026i	1.06230	−	1.83996i
$719$	7.08549	+	12.2724i	0.264244	+	0.457685i	0.967365	−	0.253386i	$-0.0815441\pi$
$719$	7.08549	+	12.2724i	0.264244	+	0.457685i	−0.703121	+	0.711070i	$0.748211\pi$
$720$	−5.19850	+	5.77352i	−0.193737	+	0.215166i
$721$	−8.08591	+	24.8859i	−0.301135	+	0.926798i
$722$	22.3335	+	24.8038i	0.831166	+	0.923103i
$723$	−23.5589	+	10.4891i	−0.876164	+	0.390094i
$724$	95.2947	+	20.2555i	3.54160	+	0.752790i
$725$	−3.93496	+	37.4386i	−0.146141	+	1.39044i
$726$	−3.67595	−	34.9743i	−0.136427	−	1.29802i
$727$	26.3589	−	5.60275i	0.977596	−	0.207794i	0.308707	−	0.951157i	$-0.400104\pi$
$727$	26.3589	−	5.60275i	0.977596	−	0.207794i	0.668889	+	0.743363i	$0.266770\pi$
$728$	−44.6556	+	32.4442i	−1.65505	+	1.20246i
$729$	−23.5282	+	17.0942i	−0.871413	+	0.633119i
$730$	12.0165	−	2.55419i	0.444752	−	0.0945349i
$731$	−0.867738	−	8.25598i	−0.0320945	−	0.305358i
$732$	3.97340	−	37.8044i	0.146861	−	1.39729i
$733$	27.8024	+	5.90959i	1.02691	+	0.218276i	0.690417	−	0.723412i	$-0.257427\pi$
$733$	27.8024	+	5.90959i	1.02691	+	0.218276i	0.336489	+	0.941687i	$0.390761\pi$
$734$	−31.9398	+	14.2205i	−1.17892	+	0.524888i
$735$	−2.32123	−	2.57799i	−0.0856200	−	0.0950907i
$736$	2.90391	−	8.93732i	0.107040	−	0.329434i
$737$	−7.42622	+	8.24765i	−0.273548	+	0.303806i
$738$	0.137995	+	0.239014i	0.00507965	+	0.00879822i
$739$	0.348653	−	0.603885i	0.0128254	−	0.0222143i	−0.859541	−	0.511066i	$-0.829251\pi$
$739$	0.348653	−	0.603885i	0.0128254	−	0.0222143i	0.872367	+	0.488852i	$0.162584\pi$
$740$	7.62531	+	23.4683i	0.280312	+	0.862711i
$741$	−12.2193	−	5.44040i	−0.448889	−	0.199858i
$742$	−10.5187	−	7.64225i	−0.386152	−	0.280556i
$743$	−18.1815			−0.667015			−0.333508	−	0.942747i	$-0.608232\pi$
$743$	−18.1815			−0.667015			−0.333508	+	0.942747i	$0.608232\pi$
$744$		0			0
$745$	−5.47779			−0.200691
$746$	−9.63250	−	6.99842i	−0.352671	−	0.256230i
$747$	15.0283	+	6.69104i	0.549858	+	0.244812i
$748$	5.97959	+	18.4033i	0.218635	+	0.672890i
$749$	−10.6856	+	18.5080i	−0.390443	+	0.676267i
$750$	−11.1835	−	19.3704i	−0.408364	−	0.707307i
$751$	−24.8020	+	27.5454i	−0.905037	+	1.00515i	0.0949159	+	0.995485i	$0.469742\pi$
$751$	−24.8020	+	27.5454i	−0.905037	+	1.00515i	−0.999953	+	0.00966064i	$0.996925\pi$
$752$	−26.9152	+	82.8365i	−0.981497	+	3.02074i
$753$	−21.7747	−	24.1832i	−0.793513	−	0.881286i
$754$	73.3482	−	32.6567i	2.67118	−	1.18929i
$755$	1.90929	+	0.405832i	0.0694861	+	0.0147697i
$756$	−5.34738	+	50.8769i	−0.194482	+	1.85037i
$757$	−0.669192	−	6.36694i	−0.0243222	−	0.231410i	−0.999929	−	0.0118865i	$-0.996216\pi$
$757$	−0.669192	−	6.36694i	−0.0243222	−	0.231410i	0.975607	−	0.219524i	$-0.0704503\pi$
$758$	−39.3541	+	8.36497i	−1.42940	+	0.303829i
$759$	−0.828034	+	0.601602i	−0.0300557	+	0.0218368i
$760$	−11.0049	+	7.99555i	−0.399191	+	0.290029i
$761$	20.8725	−	4.43659i	0.756628	−	0.160826i	0.186583	−	0.982439i	$-0.440259\pi$
$761$	20.8725	−	4.43659i	0.756628	−	0.160826i	0.570046	+	0.821613i	$0.306925\pi$
$762$	−5.15172	−	49.0153i	−0.186627	−	1.77564i
$763$	1.30139	−	12.3819i	0.0471134	−	0.448254i
$764$	−6.13736	−	1.30454i	−0.222042	−	0.0471964i
$765$	1.51400	−	0.674075i	0.0547387	−	0.0243712i
$766$	20.9714	+	23.2911i	0.757727	+	0.841541i
$767$	0.528847	−	1.62762i	0.0190955	−	0.0587700i
$768$	15.2801	−	16.9703i	0.551375	−	0.612364i
$769$	6.12828	+	10.6145i	0.220991	+	0.382768i	0.955109	−	0.296254i	$-0.0957374\pi$
$769$	6.12828	+	10.6145i	0.220991	+	0.382768i	−0.734118	+	0.679022i	$0.762404\pi$
$770$	1.88993	−	3.27346i	0.0681084	−	0.117967i
$771$	0.0465705	+	0.143329i	0.00167720	+	0.00516188i
$772$	60.8861	+	27.1083i	2.19134	+	0.975647i
$773$	28.0757	+	20.3982i	1.00981	+	0.733672i	0.964170	−	0.265286i	$-0.0854664\pi$
$773$	28.0757	+	20.3982i	1.00981	+	0.733672i	0.0456427	+	0.998958i	$0.485466\pi$
$774$	−7.96974			−0.286466
$775$		0			0
$776$	11.1389			0.399863
$777$	15.3558	+	11.1566i	0.550886	+	0.400242i
$778$	−35.3939	−	15.7584i	−1.26893	−	0.564965i
$779$	0.0825606	+	0.254095i	0.00295804	+	0.00910391i
$780$	−8.29855	+	14.3735i	−0.297136	+	0.514654i
$781$	3.18213	+	5.51161i	0.113866	+	0.197221i
$782$	−2.68188	+	2.97853i	−0.0959039	+	0.106512i
$783$	14.2130	−	43.7432i	0.507932	−	1.56325i
$784$	−34.8204	−	38.6719i	−1.24358	−	1.38114i
$785$	−1.84897	+	0.823216i	−0.0659927	+	0.0293818i
$786$	−9.10353	−	1.93501i	−0.324712	−	0.0690197i
$787$	2.10292	−	20.0080i	0.0749611	−	0.713208i	−0.890909	−	0.454181i	$-0.849932\pi$
$787$	2.10292	−	20.0080i	0.0749611	−	0.713208i	0.965870	−	0.259026i	$-0.0834016\pi$
$788$	1.62504	+	15.4612i	0.0578895	+	0.550782i
$789$	10.1298	−	2.15315i	0.360629	−	0.0766542i
$790$	−12.8421	+	9.33037i	−0.456903	+	0.331960i
$791$	23.2917	−	16.9224i	0.828159	−	0.601693i
$792$	11.2316	−	2.38734i	0.399096	−	0.0848304i
$793$	1.96245	+	18.6714i	0.0696885	+	0.663042i
$794$	4.44015	−	42.2452i	0.157575	−	1.49923i
$795$	−2.36362	−	0.502403i	−0.0838290	−	0.0178184i
$796$	−63.0749	+	28.0827i	−2.23563	+	0.995367i
$797$	17.5325	+	19.4718i	0.621034	+	0.689728i	0.968797	−	0.247854i	$-0.0797254\pi$
$797$	17.5325	+	19.4718i	0.621034	+	0.689728i	−0.347763	+	0.937582i	$0.613059\pi$
$798$	−5.23112	+	16.0997i	−0.185180	+	0.569924i
$799$	12.4324	−	13.8076i	0.439826	−	0.488476i
$800$	−40.3405	−	69.8717i	−1.42625	−	2.47034i
$801$	−7.55072	+	13.0782i	−0.266791	+	0.462096i
$802$	−25.7897	−	79.3726i	−0.910666	−	2.80274i
$803$	−9.17083	−	4.08312i	−0.323632	−	0.144090i
$804$	−49.8960	−	36.2516i	−1.75970	−	1.27849i
$805$	0.566550			0.0199683
$806$		0			0
$807$	23.0179			0.810270
$808$	57.2055	+	41.5623i	2.01248	+	1.46216i
$809$	33.2989	+	14.8256i	1.17073	+	0.521241i	0.897632	−	0.440747i	$-0.145286\pi$
$809$	33.2989	+	14.8256i	1.17073	+	0.521241i	0.273094	+	0.961987i	$0.411953\pi$
$810$	2.56413	+	7.89158i	0.0900944	+	0.277282i
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	−0.648114	−	0.761543i	$-0.724442\pi$
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	0.983573	+	0.180511i	$0.0577753\pi$
$812$	−36.7660	−	63.6805i	−1.29023	−	2.23475i
$813$	−4.88633	+	5.42682i	−0.171371	+	0.190327i
$814$	8.61071	−	26.5010i	0.301805	−	0.928861i
$815$	0.708474	+	0.786840i	0.0248168	+	0.0275618i
$816$	−46.3917	+	20.6549i	−1.62403	+	0.723066i
$817$	−7.54651	−	1.60406i	−0.264019	−	0.0561190i
$818$	1.85192	−	17.6198i	0.0647508	−	0.616063i
$819$	−0.653290	−	6.21564i	−0.0228278	−	0.217192i
$820$	0.324272	−	0.0689261i	0.0113241	−	0.00240700i
$821$	−31.9236	+	23.1939i	−1.11414	+	0.809472i	−0.983311	−	0.181933i	$-0.941765\pi$
$821$	−31.9236	+	23.1939i	−1.11414	+	0.809472i	−0.130831	+	0.991405i	$0.541765\pi$
$822$	25.1534	−	18.2750i	0.877324	−	0.637413i
$823$	30.8977	−	6.56751i	1.07703	−	0.228929i	0.364947	−	0.931028i	$-0.381087\pi$
$823$	30.8977	−	6.56751i	1.07703	−	0.228929i	0.712079	+	0.702099i	$0.247754\pi$
$824$	13.7921	+	131.223i	0.480471	+	4.57138i
$825$	−0.918533	+	8.73926i	−0.0319792	+	0.304262i
$826$	−2.11859	−	0.450320i	−0.0737151	−	0.0156686i
$827$	18.1155	−	8.06552i	0.629936	−	0.280466i	−0.0668295	−	0.997764i	$-0.521288\pi$
$827$	18.1155	−	8.06552i	0.629936	−	0.280466i	0.696766	+	0.717299i	$0.254622\pi$
$828$	1.86317	+	2.06926i	0.0647496	+	0.0719117i
$829$	2.78111	−	8.55938i	0.0965920	−	0.297280i	−0.891073	−	0.453859i	$-0.850047\pi$
$829$	2.78111	−	8.55938i	0.0965920	−	0.297280i	0.987665	+	0.156580i	$0.0500468\pi$
$830$	18.2718	−	20.2929i	0.634223	−	0.704377i
$831$	12.0081	+	20.7987i	0.416558	+	0.721499i
$832$	−38.4977	+	66.6800i	−1.33467	+	2.31171i
$833$	3.43031	+	10.5574i	0.118853	+	0.365792i
$834$	4.72014	+	2.10154i	0.163445	+	0.0727704i
$835$	6.89881	+	5.01228i	0.238743	+	0.173457i
$836$	17.9836			0.621976
$837$		0			0
$838$	39.4699			1.36347
$839$	25.7633	+	18.7181i	0.889448	+	0.646222i	0.935734	−	0.352707i	$-0.114739\pi$
$839$	25.7633	+	18.7181i	0.889448	+	0.646222i	−0.0462862	+	0.998928i	$0.514739\pi$
$840$	11.8608	+	5.28077i	0.409236	+	0.182204i
$841$	11.4679	+	35.2947i	0.395446	+	1.21706i
$842$	−35.9349	+	62.2411i	−1.23840	+	2.14497i
$843$	−1.35294	−	2.34336i	−0.0465976	−	0.0807095i
$844$	64.2399	−	71.3456i	2.21123	−	2.45582i
$845$	0.0890714	−	0.274134i	0.00306415	−	0.00943048i
$846$	−11.9356	−	13.2558i	−0.410354	−	0.455745i
$847$	14.5317	−	6.46994i	0.499316	−	0.222310i
$848$	−35.4562	−	7.53645i	−1.21757	−	0.258803i
$849$	2.27110	−	21.6081i	0.0779441	−	0.741588i
$850$	3.59694	+	34.2226i	0.123374	+	1.17383i
$851$	4.08529	−	0.868356i	0.140042	−	0.0297669i
$852$	−28.6126	+	20.7882i	−0.980250	+	0.712193i
$853$	39.7160	−	28.8554i	1.35985	−	0.987989i	0.361396	−	0.932412i	$-0.382300\pi$
$853$	39.7160	−	28.8554i	1.35985	−	0.987989i	0.998454	−	0.0555768i	$-0.0176998\pi$
$854$	23.2414	−	4.94011i	0.795304	−	0.169047i
$855$	−0.160997	−	1.53178i	−0.00550598	−	0.0523859i
$856$	−11.2645	+	107.175i	−0.385014	+	3.66316i
$857$	−18.8200	−	4.00032i	−0.642880	−	0.136648i	−0.125075	−	0.992147i	$-0.539917\pi$
$857$	−18.8200	−	4.00032i	−0.642880	−	0.136648i	−0.517804	+	0.855499i	$0.673251\pi$
$858$	17.1216	−	7.62302i	0.584521	−	0.260246i
$859$	3.10620	+	3.44979i	0.105982	+	0.117705i	0.793802	−	0.608176i	$-0.208099\pi$
$859$	3.10620	+	3.44979i	0.105982	+	0.117705i	−0.687820	+	0.725882i	$0.741432\pi$
$860$	−2.95828	+	9.10464i	−0.100876	+	0.310466i
$861$	0.170630	−	0.189504i	0.00581505	−	0.00645827i
$862$	5.36418	+	9.29104i	0.182705	+	0.316454i
$863$	19.2652	−	33.3683i	0.655795	−	1.13587i	−0.325899	−	0.945405i	$-0.605667\pi$
$863$	19.2652	−	33.3683i	0.655795	−	1.13587i	0.981694	−	0.190466i	$-0.0609999\pi$
$864$	30.4615	+	93.7509i	1.03632	+	3.18947i
$865$	−0.00665881	−	0.00296469i	−0.000226406	−	0.000100803i
$866$	39.3415	+	28.5833i	1.33688	+	0.971299i
$867$	−13.2931			−0.451456
$868$		0			0
$869$	12.9713			0.440022
$870$	−15.2786	−	11.1005i	−0.517991	−	0.376343i
$871$	27.8274	+	12.3896i	0.942896	+	0.419804i
$872$	−19.4001	−	59.7074i	−0.656970	−	2.02195i
$873$	−0.630617	+	1.09226i	−0.0213431	+	0.0369674i
$874$	1.86246	+	3.22587i	0.0629986	+	0.109117i
$875$	6.76972	−	7.51854i	0.228858	−	0.254173i
$876$	17.2390	−	53.0562i	0.582452	−	1.79260i
$877$	−6.19504	−	6.88029i	−0.209192	−	0.232331i	0.629414	−	0.777070i	$-0.283295\pi$
$877$	−6.19504	−	6.88029i	−0.209192	−	0.232331i	−0.838605	+	0.544740i	$0.816628\pi$
$878$	−56.2997	+	25.0662i	−1.90002	+	0.845944i
$879$	−37.1937	−	7.90576i	−1.25451	−	0.266655i
$880$	1.10153	−	10.4803i	0.0371325	−	0.353292i
$881$	1.86887	+	17.7811i	0.0629639	+	0.599061i	0.979825	+	0.199856i	$0.0640474\pi$
$881$	1.86887	+	17.7811i	0.0629639	+	0.599061i	−0.916861	+	0.399206i	$0.869286\pi$
$882$	10.4242	−	2.21574i	0.351003	−	0.0746079i
$883$	39.0881	−	28.3992i	1.31542	−	0.955709i	0.315443	−	0.948944i	$-0.397847\pi$
$883$	39.0881	−	28.3992i	1.31542	−	0.955709i	0.999977	−	0.00676442i	$-0.00215320\pi$
$884$	42.9667	−	31.2172i	1.44513	−	1.04995i
$885$	−0.393747	+	0.0836935i	−0.0132357	+	0.00281333i
$886$	−6.04331	−	57.4983i	−0.203029	−	1.93169i
$887$	−2.45770	+	23.3834i	−0.0825214	+	0.785138i	0.872503	+	0.488610i	$0.162496\pi$
$887$	−2.45770	+	23.3834i	−0.0825214	+	0.785138i	−0.955024	+	0.296529i	$0.904171\pi$
$888$	93.6200	+	19.8996i	3.14168	+	0.667785i
$889$	20.3657	−	9.06739i	0.683044	−	0.304111i
$890$	16.7733	+	18.6287i	0.562243	+	0.624434i
$891$	2.09529	−	6.44864i	0.0701948	−	0.216037i
$892$	32.9255	−	36.5674i	1.10243	−	1.22437i
$893$	−8.63379	−	14.9542i	−0.288919	−	0.500422i
$894$	−17.1873	+	29.7693i	−0.574830	+	0.995635i
$895$	−1.87587	−	5.77335i	−0.0627036	−	0.192982i
$896$	34.0379	+	15.1547i	1.13713	+	0.506281i
$897$	2.27266	+	1.65118i	0.0758818	+	0.0551313i
$898$	−50.5739			−1.68767
$899$		0			0
$900$	23.9062			0.796874
$901$	6.25567	+	4.54501i	0.208406	+	0.151416i
$902$	−0.341992	−	0.152265i	−0.0113871	−	0.00506986i
$903$	2.27551	+	7.00330i	0.0757242	+	0.233055i
$904$	72.5879	−	125.726i	2.41424	−	4.18158i
$905$	5.65893	+	9.80156i	0.188109	+	0.325815i
$906$	8.19616	−	9.10276i	0.272299	−	0.302419i
$907$	−3.88809	+	11.9663i	−0.129102	+	0.397335i	−0.994626	−	0.103532i	$-0.966986\pi$
$907$	−3.88809	+	11.9663i	−0.129102	+	0.397335i	0.865524	+	0.500867i	$0.166986\pi$
$908$	29.6435	+	32.9224i	0.983753	+	1.09257i
$909$	−7.31415	+	3.25647i	−0.242595	+	0.108010i
$910$	−10.1477	−	2.15695i	−0.336392	−	0.0715023i
$911$	4.94257	−	47.0255i	0.163755	−	1.55802i	−0.536358	−	0.843991i	$-0.680200\pi$
$911$	4.94257	−	47.0255i	0.163755	−	1.55802i	0.700113	−	0.714032i	$-0.253133\pi$
$912$	4.93324	+	46.9366i	0.163356	+	1.55423i
$913$	−21.8262	+	4.63931i	−0.722343	+	0.153539i
$914$	8.93621	−	6.49254i	0.295584	−	0.214754i
$915$	3.57261	−	2.59566i	0.118107	−	0.0858098i
$916$	−117.015	+	24.8724i	−3.86630	+	0.821807i
$917$	−0.440040	−	4.18670i	−0.0145314	−	0.138257i
$918$	4.39472	−	41.8130i	0.145047	−	1.38003i
$919$	22.6264	+	4.80939i	0.746376	+	0.158647i	0.565373	−	0.824836i	$-0.308732\pi$
$919$	22.6264	+	4.80939i	0.746376	+	0.158647i	0.181003	+	0.983483i	$0.442066\pi$
$920$	2.60987	−	1.16199i	0.0860447	−	0.0383096i
$921$	8.50017	+	9.44040i	0.280090	+	0.311072i
$922$	19.0161	−	58.5256i	0.626262	−	1.92744i
$923$	11.6881	−	12.9810i	0.384719	−	0.427274i
$924$	−8.58224	−	14.8649i	−0.282335	−	0.489019i
$925$	17.9291	−	31.0541i	0.589506	−	1.02105i
$926$	13.7722	+	42.3864i	0.452582	+	1.39290i
$927$	−13.6483	−	6.07663i	−0.448270	−	0.199583i
$928$	−114.630	−	83.2833i	−3.76290	−	2.73391i
$929$	1.68694			0.0553468			0.0276734	−	0.999617i	$-0.491190\pi$
$929$	1.68694			0.0553468			0.0276734	+	0.999617i	$0.491190\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	−68.8623	−	50.0314i	−2.25566	−	1.63883i
$933$	26.7794	+	11.9230i	0.876719	+	0.390341i
$934$	−31.7111	−	97.5968i	−1.03762	−	3.19346i
$935$	−1.12398	+	1.94679i	−0.0367581	+	0.0636669i
$936$	−15.7576	−	27.2930i	−0.515055	−	0.892101i
$937$	13.1997	−	14.6598i	0.431216	−	0.478913i	−0.487901	−	0.872899i	$-0.662237\pi$
$937$	13.1997	−	14.6598i	0.431216	−	0.478913i	0.919117	+	0.393985i	$0.128904\pi$
$938$	11.9130	−	36.6643i	0.388972	−	1.19713i
$939$	0.428577	+	0.475983i	0.0139861	+	0.0155331i
$940$	−19.5738	+	8.71484i	−0.638428	+	0.284247i
$941$	8.63045	+	1.83446i	0.281345	+	0.0598017i	0.346423	−	0.938079i	$-0.387396\pi$
$941$	8.63045	+	1.83446i	0.281345	+	0.0598017i	−0.0650780	+	0.997880i	$0.520730\pi$
$942$	−1.32760	+	12.6313i	−0.0432556	+	0.411549i
$943$	−0.00586520	−	0.0558037i	−0.000190997	−	0.00181722i
$944$	−5.90652	+	1.25547i	−0.192241	+	0.0408620i
$945$	−4.80800	+	3.49321i	−0.156404	+	0.113634i
$946$	8.74572	−	6.35414i	0.284348	−	0.206591i
$947$	−15.2211	+	3.23535i	−0.494620	+	0.105135i	−0.448467	−	0.893800i	$-0.648030\pi$
$947$	−15.2211	+	3.23535i	−0.494620	+	0.105135i	−0.0461536	+	0.998934i	$0.514696\pi$
$948$	7.53476	+	71.6885i	0.244718	+	2.32833i
$949$	−2.88004	+	27.4018i	−0.0934901	+	0.889499i
$950$	31.2817	+	6.64914i	1.01491	+	0.215727i
$951$	−7.23540	+	3.22141i	−0.234624	+	0.104461i
$952$	−27.7995	−	30.8745i	−0.900987	−	1.00065i
$953$	2.98255	−	9.17933i	0.0966141	−	0.297348i	−0.891057	−	0.453892i	$-0.850035\pi$
$953$	2.98255	−	9.17933i	0.0966141	−	0.297348i	0.987671	+	0.156544i	$0.0500353\pi$
$954$	4.96726	−	5.51670i	0.160821	−	0.178610i
$955$	−0.364458	−	0.631260i	−0.0117936	−	0.0204271i
$956$	−47.8473	+	82.8739i	−1.54749	+	2.68033i
$957$	4.76882	+	14.6769i	0.154154	+	0.474437i
$958$	82.7830	+	36.8574i	2.67460	+	1.19081i
$959$	11.3775	+	8.26626i	0.367400	+	0.266931i
$960$	18.1105			0.584514
$961$		0			0
$962$	−76.4790			−2.46578
$963$	−9.87164	−	7.17217i	−0.318109	−	0.231120i
$964$	−86.9360	−	38.7064i	−2.80002	−	1.24665i
$965$	2.39260	+	7.36368i	0.0770207	+	0.237045i
$966$	1.77763	−	3.07894i	0.0571942	−	0.0990633i
$967$	−14.1988	−	24.5930i	−0.456602	−	0.790858i	0.542177	−	0.840264i	$-0.317600\pi$
$967$	−14.1988	−	24.5930i	−0.456602	−	0.790858i	−0.998779	+	0.0494066i	$0.984267\pi$
$968$	53.6719	−	59.6087i	1.72508	−	1.91590i
$969$	3.11106	−	9.57485i	0.0999416	−	0.307588i
$970$	1.40087	+	1.55582i	0.0449791	+	0.0499543i
$971$	−20.2141	+	8.99989i	−0.648701	+	0.288820i	−0.704588	−	0.709617i	$-0.748868\pi$
$971$	−20.2141	+	8.99989i	−0.648701	+	0.288820i	0.0558868	+	0.998437i	$0.482201\pi$
$972$	−50.0733	−	10.6434i	−1.60610	−	0.341388i
$973$	−0.244293	+	2.32429i	−0.00783167	+	0.0745134i
$974$	−5.81424	−	55.3188i	−0.186300	−	1.77253i
$975$	23.5912	−	5.01447i	0.755524	−	0.160592i
$976$	53.5921	−	38.9369i	1.71544	−	1.24634i
$977$	16.1094	−	11.7042i	0.515385	−	0.374449i	−0.299478	−	0.954103i	$-0.596812\pi$
$977$	16.1094	−	11.7042i	0.515385	−	0.374449i	0.814862	+	0.579654i	$0.196812\pi$
$978$	6.49905	−	1.38142i	0.207817	−	0.0441728i
$979$	−2.14115	−	20.3717i	−0.0684314	−	0.651081i
$980$	1.33810	−	12.7311i	0.0427439	−	0.406681i
$981$	6.95311	+	1.47793i	0.221996	+	0.0471867i
$982$	−60.7827	+	27.0622i	−1.93965	+	0.863589i
$983$	−16.6817	−	18.5269i	−0.532063	−	0.590916i	0.415855	−	0.909431i	$-0.363482\pi$
$983$	−16.6817	−	18.5269i	−0.532063	−	0.590916i	−0.947918	+	0.318515i	$0.896816\pi$
$984$	0.397353	−	1.22293i	0.0126671	−	0.0389855i
$985$	−1.20848	+	1.34215i	−0.0385054	+	0.0427646i
$986$	30.2160	+	52.3356i	0.962273	+	1.66671i
$987$	−8.24054	+	14.2730i	−0.262299	+	0.454316i
$988$	−15.2526	−	46.9428i	−0.485251	−	1.49345i
$989$	1.48023	+	0.659043i	0.0470687	+	0.0209563i
$990$	1.74597	+	1.26852i	0.0554905	+	0.0403162i
$991$	−42.0512			−1.33580			−0.667900	−	0.744251i	$-0.732807\pi$
$991$	−42.0512			−1.33580			−0.667900	+	0.744251i	$0.732807\pi$
$992$		0			0
$993$	34.3515			1.09011
$994$	−17.8849	−	12.9941i	−0.567274	−	0.412149i
$995$	−7.32752	−	3.26242i	−0.232298	−	0.103426i
$996$	−38.3184	−	117.932i	−1.21417	−	3.73682i
$997$	−7.23233	+	12.5268i	−0.229050	+	0.396727i	−0.957527	−	0.288344i	$-0.906895\pi$
$997$	−7.23233	+	12.5268i	−0.229050	+	0.396727i	0.728477	+	0.685071i	$0.240229\pi$
$998$	−33.0353	−	57.2189i	−1.04572	−	1.81123i
$999$	−29.3155	+	32.5582i	−0.927503	+	1.03010i

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.s.732.2		16
31.2	even	5		31.2.g.a.14.1	✓	16
31.3	odd	30		961.2.d.q.388.4		16
31.4	even	5		961.2.c.j.521.1		16
31.5	even	3		961.2.g.t.816.2		16
31.6	odd	6		961.2.d.q.374.4		16
31.7	even	15		961.2.a.i.1.1		8
31.8	even	5		961.2.g.k.844.1		16
31.9	even	15		31.2.g.a.20.1	yes	16
31.10	even	15		961.2.g.k.846.1		16
31.11	odd	30		961.2.c.i.439.1		16
31.12	odd	30		961.2.d.n.628.1		16
31.13	odd	30		961.2.g.m.235.2		16
31.14	even	15		961.2.d.o.531.1		16
31.15	odd	10		961.2.g.n.338.2		16
31.16	even	5		961.2.g.t.338.2		16
31.17	odd	30		961.2.d.n.531.1		16
31.18	even	15	inner	961.2.g.s.235.2		16
31.19	even	15		961.2.d.o.628.1		16
31.20	even	15		961.2.c.j.439.1		16
31.21	odd	30		961.2.g.j.846.1		16
31.22	odd	30		961.2.g.l.547.1		16
31.23	odd	10		961.2.g.j.844.1		16
31.24	odd	30		961.2.a.j.1.1		8
31.25	even	3		961.2.d.p.374.4		16
31.26	odd	6		961.2.g.n.816.2		16
31.27	odd	10		961.2.c.i.521.1		16
31.28	even	15		961.2.d.p.388.4		16
31.29	odd	10		961.2.g.l.448.1		16
31.30	odd	2		961.2.g.m.732.2		16
93.2	odd	10		279.2.y.c.262.2		16
93.38	odd	30		8649.2.a.bf.1.8		8
93.71	odd	30		279.2.y.c.82.2		16
93.86	even	30		8649.2.a.be.1.8		8
124.71	odd	30		496.2.bg.c.113.1		16
124.95	odd	10		496.2.bg.c.417.1		16
155.2	odd	20		775.2.ck.a.324.1		32
155.9	even	30		775.2.bl.a.51.2		16
155.33	odd	20		775.2.ck.a.324.4		32
155.64	even	10		775.2.bl.a.76.2		16
155.102	odd	60		775.2.ck.a.299.4		32
155.133	odd	60		775.2.ck.a.299.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.2	even	5
31.2.g.a.20.1	yes	16	31.9	even	15
279.2.y.c.82.2		16	93.71	odd	30
279.2.y.c.262.2		16	93.2	odd	10
496.2.bg.c.113.1		16	124.71	odd	30
496.2.bg.c.417.1		16	124.95	odd	10
775.2.bl.a.51.2		16	155.9	even	30
775.2.bl.a.76.2		16	155.64	even	10
775.2.ck.a.299.1		32	155.133	odd	60
775.2.ck.a.299.4		32	155.102	odd	60
775.2.ck.a.324.1		32	155.2	odd	20
775.2.ck.a.324.4		32	155.33	odd	20
961.2.a.i.1.1		8	31.7	even	15
961.2.a.j.1.1		8	31.24	odd	30
961.2.c.i.439.1		16	31.11	odd	30
961.2.c.i.521.1		16	31.27	odd	10
961.2.c.j.439.1		16	31.20	even	15
961.2.c.j.521.1		16	31.4	even	5
961.2.d.n.531.1		16	31.17	odd	30
961.2.d.n.628.1		16	31.12	odd	30
961.2.d.o.531.1		16	31.14	even	15
961.2.d.o.628.1		16	31.19	even	15
961.2.d.p.374.4		16	31.25	even	3
961.2.d.p.388.4		16	31.28	even	15
961.2.d.q.374.4		16	31.6	odd	6
961.2.d.q.388.4		16	31.3	odd	30
961.2.g.j.844.1		16	31.23	odd	10
961.2.g.j.846.1		16	31.21	odd	30
961.2.g.k.844.1		16	31.8	even	5
961.2.g.k.846.1		16	31.10	even	15
961.2.g.l.448.1		16	31.29	odd	10
961.2.g.l.547.1		16	31.22	odd	30
961.2.g.m.235.2		16	31.13	odd	30
961.2.g.m.732.2		16	31.30	odd	2
961.2.g.n.338.2		16	31.15	odd	10
961.2.g.n.816.2		16	31.26	odd	6
961.2.g.s.235.2		16	31.18	even	15	inner
961.2.g.s.732.2		16	1.1	even	1	trivial
961.2.g.t.338.2		16	31.16	even	5
961.2.g.t.816.2		16	31.5	even	3
8649.2.a.be.1.8		8	93.86	even	30
8649.2.a.bf.1.8		8	93.38	odd	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

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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.s.732.2

Level	$961$
Weight	$2$
Character	961.732
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$