LMFDB - Embedded newform 276.2.o.a.35.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.7
Character	$\chi$	$=$	276.35
Dual form			276.2.o.a.71.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20977 + 0.732426i) q^{2} +(-0.914165 - 1.47116i) q^{3} +(0.927105 - 1.77214i) q^{4} +(0.605787 + 2.06312i) q^{5} +(2.18345 + 1.11021i) q^{6} +(0.738126 - 0.639590i) q^{7} +(0.176372 + 2.82292i) q^{8} +(-1.32861 + 2.68976i) q^{9} +O(q^{10})$	\(q+(-1.20977 + 0.732426i) q^{2} +(-0.914165 - 1.47116i) q^{3} +(0.927105 - 1.77214i) q^{4} +(0.605787 + 2.06312i) q^{5} +(2.18345 + 1.11021i) q^{6} +(0.738126 - 0.639590i) q^{7} +(0.176372 + 2.82292i) q^{8} +(-1.32861 + 2.68976i) q^{9} +(-2.24395 - 2.05222i) q^{10} +(-0.357587 - 0.229807i) q^{11} +(-3.45462 + 0.256109i) q^{12} +(2.49415 - 2.87840i) q^{13} +(-0.424514 + 1.31438i) q^{14} +(2.48139 - 2.77724i) q^{15} +(-2.28095 - 3.28592i) q^{16} +(2.23877 - 1.02241i) q^{17} +(-0.362737 - 4.22711i) q^{18} +(6.48160 + 2.96005i) q^{19} +(4.21777 + 0.839193i) q^{20} +(-1.61571 - 0.501209i) q^{21} +(0.600915 + 0.0161089i) q^{22} +(4.60907 - 1.32531i) q^{23} +(3.99173 - 2.84009i) q^{24} +(0.316772 - 0.203577i) q^{25} +(-0.909141 + 5.30899i) q^{26} +(5.17162 - 0.504297i) q^{27} +(-0.449121 - 1.90103i) q^{28} +(0.940319 - 0.429429i) q^{29} +(-0.967794 + 5.17727i) q^{30} +(-7.16183 + 1.02972i) q^{31} +(5.16613 + 2.30459i) q^{32} +(-0.0111890 + 0.736147i) q^{33} +(-1.95956 + 2.87662i) q^{34} +(1.76670 + 1.13539i) q^{35} +(3.53487 + 4.84816i) q^{36} +(3.69308 + 1.08439i) q^{37} +(-10.0093 + 1.16630i) q^{38} +(-6.51464 - 1.03795i) q^{39} +(-5.71719 + 2.07397i) q^{40} +(-3.07037 - 10.4567i) q^{41} +(2.32174 - 0.577035i) q^{42} +(5.31467 + 0.764134i) q^{43} +(-0.738770 + 0.420638i) q^{44} +(-6.35416 - 1.11165i) q^{45} +(-4.60525 + 4.97913i) q^{46} +3.75973 q^{47} +(-2.74894 + 6.35951i) q^{48} +(-0.860449 + 5.98455i) q^{49} +(-0.234117 + 0.478294i) q^{50} +(-3.55073 - 2.35893i) q^{51} +(-2.78859 - 7.08855i) q^{52} +(-6.52145 + 5.65086i) q^{53} +(-5.88713 + 4.39791i) q^{54} +(0.257498 - 0.876959i) q^{55} +(1.93570 + 1.97087i) q^{56} +(-1.57056 - 12.2414i) q^{57} +(-0.823049 + 1.20823i) q^{58} +(2.92268 - 3.37295i) q^{59} +(-2.62115 - 6.97216i) q^{60} +(0.830304 + 5.77489i) q^{61} +(7.91001 - 6.49123i) q^{62} +(0.739665 + 2.83514i) q^{63} +(-7.93779 + 0.995768i) q^{64} +(7.44941 + 3.40203i) q^{65} +(-0.525637 - 0.898767i) q^{66} +(-2.37638 - 3.69772i) q^{67} +(0.263720 - 4.91529i) q^{68} +(-6.16319 - 5.56912i) q^{69} +(-2.96889 - 0.0795877i) q^{70} +(-8.76187 + 5.63091i) q^{71} +(-7.82731 - 3.27615i) q^{72} +(-1.76386 + 3.86232i) q^{73} +(-5.26203 + 1.39305i) q^{74} +(-0.589075 - 0.279918i) q^{75} +(11.2547 - 8.74202i) q^{76} +(-0.410926 + 0.0590823i) q^{77} +(8.64146 - 3.51580i) q^{78} +(-5.26697 - 4.56386i) q^{79} +(5.39748 - 6.69645i) q^{80} +(-5.46962 - 7.14726i) q^{81} +(11.3732 + 10.4015i) q^{82} +(-6.94011 - 2.03780i) q^{83} +(-2.38614 + 2.39858i) q^{84} +(3.46557 + 3.99949i) q^{85} +(-6.98922 + 2.96817i) q^{86} +(-1.49136 - 0.990788i) q^{87} +(0.585659 - 1.04997i) q^{88} +(-14.0889 - 2.02568i) q^{89} +(8.50129 - 3.30910i) q^{90} -3.71985i q^{91} +(1.92447 - 9.39662i) q^{92} +(8.06197 + 9.59485i) q^{93} +(-4.54842 + 2.75372i) q^{94} +(-2.18047 + 15.1655i) q^{95} +(-1.33227 - 9.70696i) q^{96} +(6.11578 - 1.79575i) q^{97} +(-3.34229 - 7.87017i) q^{98} +(1.09322 - 0.656499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.20977	+	0.732426i	−0.855439	+	0.517903i
$2$	−1.20977	+	0.732426i	−0.855439	+	0.517903i
$3$	−0.914165	−	1.47116i	−0.527793	−	0.849373i
$3$	−0.914165	−	1.47116i	−0.527793	−	0.849373i
$4$	0.927105	−	1.77214i	0.463553	−	0.886069i
$5$	0.605787	+	2.06312i	0.270916	+	0.922656i	0.976769	+	0.214297i	$0.0687461\pi$
$5$	0.605787	+	2.06312i	0.270916	+	0.922656i	−0.705852	+	0.708359i	$0.749436\pi$
$6$	2.18345	+	1.11021i	0.891388	+	0.453241i
$7$	0.738126	−	0.639590i	0.278985	−	0.241742i	−0.504116	−	0.863636i	$-0.668182\pi$
$7$	0.738126	−	0.639590i	0.278985	−	0.241742i	0.783102	+	0.621893i	$0.213636\pi$
$8$	0.176372	+	2.82292i	0.0623569	+	0.998054i
$9$	−1.32861	+	2.68976i	−0.442868	+	0.896587i
$10$	−2.24395	−	2.05222i	−0.709599	−	0.648968i
$11$	−0.357587	−	0.229807i	−0.107816	−	0.0692894i	0.485621	−	0.874169i	$-0.338593\pi$
$11$	−0.357587	−	0.229807i	−0.107816	−	0.0692894i	−0.593438	+	0.804880i	$0.702230\pi$
$12$	−3.45462	+	0.256109i	−0.997263	+	0.0739324i
$13$	2.49415	−	2.87840i	0.691752	−	0.798324i	−0.295861	−	0.955231i	$-0.595607\pi$
$13$	2.49415	−	2.87840i	0.691752	−	0.798324i	0.987613	+	0.156907i	$0.0501521\pi$
$14$	−0.424514	+	1.31438i	−0.113456	+	0.351283i
$15$	2.48139	−	2.77724i	0.640691	−	0.717081i
$16$	−2.28095	−	3.28592i	−0.570238	−	0.821480i
$17$	2.23877	−	1.02241i	0.542981	−	0.247971i	−0.124991	−	0.992158i	$-0.539890\pi$
$17$	2.23877	−	1.02241i	0.542981	−	0.247971i	0.667971	+	0.744187i	$0.267163\pi$
$18$	−0.362737	−	4.22711i	−0.0854980	−	0.996338i
$19$	6.48160	+	2.96005i	1.48698	+	0.679082i	0.982827	−	0.184531i	$-0.0590767\pi$
$19$	6.48160	+	2.96005i	1.48698	+	0.679082i	0.504155	+	0.863613i	$0.331804\pi$
$20$	4.21777	+	0.839193i	0.943122	+	0.187649i
$21$	−1.61571	−	0.501209i	−0.352576	−	0.109373i
$22$	0.600915	+	0.0161089i	0.128116	+	0.00343442i
$23$	4.60907	−	1.32531i	0.961058	−	0.276346i
$23$	4.60907	−	1.32531i	0.961058	−	0.276346i
$24$	3.99173	−	2.84009i	0.814808	−	0.579730i
$25$	0.316772	−	0.203577i	0.0633544	−	0.0407154i
$26$	−0.909141	+	5.30899i	−0.178297	+	1.04118i
$27$	5.17162	−	0.504297i	0.995279	−	0.0970521i
$28$	−0.449121	−	1.90103i	−0.0848759	−	0.359261i
$29$	0.940319	−	0.429429i	0.174613	−	0.0797430i	−0.326191	−	0.945304i	$-0.605765\pi$
$29$	0.940319	−	0.429429i	0.174613	−	0.0797430i	0.500804	+	0.865561i	$0.333038\pi$
$30$	−0.967794	+	5.17727i	−0.176694	+	0.945235i
$31$	−7.16183	+	1.02972i	−1.28630	+	0.184942i	−0.751330	−	0.659927i	$-0.770587\pi$
$31$	−7.16183	+	1.02972i	−1.28630	+	0.184942i	−0.534973	+	0.844869i	$0.679678\pi$
$32$	5.16613	+	2.30459i	0.913251	+	0.407398i
$33$	−0.0111890	+	0.736147i	−0.00194775	+	0.128147i
$34$	−1.95956	+	2.87662i	−0.336062	+	0.493336i
$35$	1.76670	+	1.13539i	0.298627	+	0.191916i
$36$	3.53487	+	4.84816i	0.589145	+	0.808027i
$37$	3.69308	+	1.08439i	0.607139	+	0.178272i	0.570830	−	0.821068i	$-0.306622\pi$
$37$	3.69308	+	1.08439i	0.607139	+	0.178272i	0.0363094	+	0.999341i	$0.488440\pi$
$38$	−10.0093	+	1.16630i	−1.62372	+	0.189199i
$39$	−6.51464	−	1.03795i	−1.04318	−	0.166205i
$40$	−5.71719	+	2.07397i	−0.903967	+	0.327923i
$41$	−3.07037	−	10.4567i	−0.479512	−	1.63307i	−0.743641	−	0.668580i	$-0.766903\pi$
$41$	−3.07037	−	10.4567i	−0.479512	−	1.63307i	0.264129	−	0.964487i	$-0.414916\pi$
$42$	2.32174	−	0.577035i	0.358252	−	0.0890385i
$43$	5.31467	+	0.764134i	0.810479	+	0.116529i	0.535081	−	0.844801i	$-0.320281\pi$
$43$	5.31467	+	0.764134i	0.810479	+	0.116529i	0.275398	+	0.961330i	$0.411190\pi$
$44$	−0.738770	+	0.420638i	−0.111374	+	0.0634135i
$45$	−6.35416	−	1.11165i	−0.947222	−	0.165715i
$46$	−4.60525	+	4.97913i	−0.679007	+	0.734132i
$47$	3.75973			0.548413			0.274206	−	0.961671i	$-0.411585\pi$
$47$	3.75973			0.548413			0.274206	+	0.961671i	$0.411585\pi$
$48$	−2.74894	+	6.35951i	−0.396775	+	0.917916i
$49$	−0.860449	+	5.98455i	−0.122921	+	0.854936i
$50$	−0.234117	+	0.478294i	−0.0331092	+	0.0676410i
$51$	−3.55073	−	2.35893i	−0.497201	−	0.330316i
$52$	−2.78859	−	7.08855i	−0.386707	−	0.983006i
$53$	−6.52145	+	5.65086i	−0.895789	+	0.776206i	−0.975359	−	0.220623i	$-0.929191\pi$
$53$	−6.52145	+	5.65086i	−0.895789	+	0.776206i	0.0795697	+	0.996829i	$0.474645\pi$
$54$	−5.88713	+	4.39791i	−0.801137	+	0.598480i
$55$	0.257498	−	0.876959i	0.0347211	−	0.118249i
$56$	1.93570	+	1.97087i	0.258668	+	0.263368i
$57$	−1.57056	−	12.2414i	−0.208025	−	1.62142i
$58$	−0.823049	+	1.20823i	−0.108072	+	0.158648i
$59$	2.92268	−	3.37295i	0.380501	−	0.439121i	−0.532903	−	0.846176i	$-0.678899\pi$
$59$	2.92268	−	3.37295i	0.380501	−	0.439121i	0.913404	+	0.407055i	$0.133444\pi$
$60$	−2.62115	−	6.97216i	−0.338389	−	0.900102i
$61$	0.830304	+	5.77489i	0.106309	+	0.739399i	0.971343	+	0.237684i	$0.0763882\pi$
$61$	0.830304	+	5.77489i	0.106309	+	0.739399i	−0.865033	+	0.501715i	$0.832703\pi$
$62$	7.91001	−	6.49123i	1.00457	−	0.824387i
$63$	0.739665	+	2.83514i	0.0931890	+	0.357195i
$64$	−7.93779	+	0.995768i	−0.992223	+	0.124471i
$65$	7.44941	+	3.40203i	0.923986	+	0.421970i
$66$	−0.525637	−	0.898767i	−0.0647014	−	0.110631i
$67$	−2.37638	−	3.69772i	−0.290321	−	0.451749i	0.665202	−	0.746663i	$-0.268345\pi$
$67$	−2.37638	−	3.69772i	−0.290321	−	0.451749i	−0.955524	+	0.294914i	$0.904709\pi$
$68$	0.263720	−	4.91529i	0.0319807	−	0.596066i
$69$	−6.16319	−	5.56912i	−0.741961	−	0.670443i
$70$	−2.96889	−	0.0795877i	−0.354851	−	0.00951255i
$71$	−8.76187	+	5.63091i	−1.03984	+	0.668266i	−0.944948	−	0.327221i	$-0.893888\pi$
$71$	−8.76187	+	5.63091i	−1.03984	+	0.668266i	−0.0948946	+	0.995487i	$0.530251\pi$
$72$	−7.82731	−	3.27615i	−0.922458	−	0.386098i
$73$	−1.76386	+	3.86232i	−0.206445	+	0.452051i	−0.984326	−	0.176361i	$-0.943567\pi$
$73$	−1.76386	+	3.86232i	−0.206445	+	0.452051i	0.777881	+	0.628412i	$0.216295\pi$
$74$	−5.26203	+	1.39305i	−0.611698	+	0.161938i
$75$	−0.589075	−	0.279918i	−0.0680205	−	0.0323222i
$76$	11.2547	−	8.74202i	1.29101	−	1.00278i
$77$	−0.410926	+	0.0590823i	−0.0468294	+	0.00673305i
$78$	8.64146	−	3.51580i	0.978453	−	0.398086i
$79$	−5.26697	−	4.56386i	−0.592581	−	0.513474i	0.306145	−	0.951985i	$-0.400961\pi$
$79$	−5.26697	−	4.56386i	−0.592581	−	0.513474i	−0.898726	+	0.438511i	$0.855506\pi$
$80$	5.39748	−	6.69645i	0.603457	−	0.748686i
$81$	−5.46962	−	7.14726i	−0.607735	−	0.794140i
$82$	11.3732	+	10.4015i	1.25596	+	1.14865i
$83$	−6.94011	−	2.03780i	−0.761776	−	0.223678i	−0.122305	−	0.992493i	$-0.539028\pi$
$83$	−6.94011	−	2.03780i	−0.761776	−	0.223678i	−0.639471	+	0.768815i	$0.720847\pi$
$84$	−2.38614	+	2.39858i	−0.260349	+	0.261707i
$85$	3.46557	+	3.99949i	0.375894	+	0.433805i
$86$	−6.98922	+	2.96817i	−0.753666	+	0.320066i
$87$	−1.49136	−	0.990788i	−0.159891	−	0.106224i
$88$	0.585659	−	1.04997i	0.0624315	−	0.111927i
$89$	−14.0889	−	2.02568i	−1.49342	−	0.214722i	−0.653293	−	0.757105i	$-0.726613\pi$
$89$	−14.0889	−	2.02568i	−1.49342	−	0.214722i	−0.840131	+	0.542383i	$0.817522\pi$
$90$	8.50129	−	3.30910i	0.896115	−	0.348810i
$91$		−	3.71985i		−	0.389947i
$92$	1.92447	−	9.39662i	0.200640	−	0.979665i
$93$	8.06197	+	9.59485i	0.835987	+	0.994939i
$94$	−4.54842	+	2.75372i	−0.469134	+	0.284025i
$95$	−2.18047	+	15.1655i	−0.223711	+	1.55595i
$96$	−1.33227	−	9.70696i	−0.135975	−	0.990712i
$97$	6.11578	−	1.79575i	0.620963	−	0.182331i	0.0439068	−	0.999036i	$-0.486020\pi$
$97$	6.11578	−	1.79575i	0.620963	−	0.182331i	0.577056	+	0.816704i	$0.304201\pi$
$98$	−3.34229	−	7.87017i	−0.337622	−	0.795007i
$99$	1.09322	−	0.656499i	0.109872	−	0.0659807i
$100$	−0.0670856	−	0.750101i	−0.00670856	−	0.0750101i
$101$	−1.41441	+	4.81703i	−0.140739	+	0.479312i	−0.999450	−	0.0331467i	$-0.989447\pi$
$101$	−1.41441	+	4.81703i	−0.140739	+	0.479312i	0.858712	+	0.512459i	$0.171265\pi$
$102$	6.02332	+	0.253122i	0.596397	+	0.0250628i
$103$	2.14165	−	3.33247i	0.211023	−	0.328358i	−0.719566	−	0.694424i	$-0.755659\pi$
$103$	2.14165	−	3.33247i	0.211023	−	0.328358i	0.930589	+	0.366066i	$0.119296\pi$
$104$	8.56540	+	6.53312i	0.839906	+	0.640625i
$105$	0.0552805	−	3.63702i	0.00539482	−	0.354937i
$106$	3.75064	−	11.6127i	0.364294	−	1.12793i
$107$	0.590353	+	4.10599i	0.0570715	+	0.396941i	0.998255	+	0.0590461i	$0.0188059\pi$
$107$	0.590353	+	4.10599i	0.0570715	+	0.396941i	−0.941184	+	0.337895i	$0.890285\pi$
$108$	3.90095	−	9.63237i	0.375370	−	0.926875i
$109$	5.64268	+	12.3557i	0.540471	+	1.18347i	0.961092	+	0.276229i	$0.0890849\pi$
$109$	5.64268	+	12.3557i	0.540471	+	1.18347i	−0.420621	+	0.907236i	$0.638188\pi$
$110$	0.330792	+	1.24952i	0.0315398	+	0.119137i
$111$	−1.78078	−	6.42441i	−0.169024	−	0.609778i
$112$	−3.78527	−	0.966549i	−0.357674	−	0.0913303i
$113$	8.35781	+	13.0050i	0.786237	+	1.22341i	0.970635	+	0.240556i	$0.0773299\pi$
$113$	8.35781	+	13.0050i	0.786237	+	1.22341i	−0.184399	+	0.982852i	$0.559034\pi$
$114$	10.8660	+	13.6590i	1.01769	+	1.27929i
$115$	5.52639	+	8.70623i	0.515338	+	0.811860i
$116$	0.110767	−	2.06450i	0.0102844	−	0.191684i
$117$	4.42847	+	10.5329i	0.409412	+	0.973768i
$118$	−1.06535	+	6.22116i	−0.0980730	+	0.572704i
$119$	0.998569	−	2.18656i	0.0915386	−	0.200442i
$120$	8.27759	+	6.51494i	0.755637	+	0.594730i
$121$	−4.49451	−	9.84160i	−0.408592	−	0.894691i
$122$	−5.23416	−	6.37817i	−0.473878	−	0.577453i
$123$	−12.5767	+	14.0762i	−1.13400	+	1.26921i
$124$	−4.81497	+	13.6464i	−0.432397	+	1.22548i
$125$	8.73705	+	7.57069i	0.781465	+	0.677143i
$126$	−2.97136	−	2.88813i	−0.264710	−	0.257295i
$127$	−6.92491	+	10.7754i	−0.614486	+	0.956160i	0.384961	+	0.922933i	$0.374215\pi$
$127$	−6.92491	+	10.7754i	−0.614486	+	0.956160i	−0.999448	+	0.0332269i	$0.989422\pi$
$128$	8.87360	−	7.01849i	0.784323	−	0.620353i
$129$	−3.73432	−	8.51725i	−0.328789	−	0.749902i
$130$	−11.5038	+	1.34045i	−1.00895	+	0.117565i
$131$	4.19429	+	4.84046i	0.366456	+	0.422913i	0.908792	−	0.417248i	$-0.137005\pi$
$131$	4.19429	+	4.84046i	0.366456	+	0.422913i	−0.542336	+	0.840162i	$0.682460\pi$
$132$	1.29418	+	0.702315i	0.112644	+	0.0611286i
$133$	6.67746	−	1.96068i	0.579009	−	0.170012i
$134$	5.58319	+	2.73288i	0.482314	+	0.236085i
$135$	4.17333	+	10.3642i	0.359183	+	0.892008i
$136$	3.28104	+	6.13954i	0.281347	+	0.526461i
$137$		−	17.2248i		−	1.47161i	−0.677192	−	0.735806i	$-0.736803\pi$
$137$		−	17.2248i		−	1.47161i	0.677192	−	0.735806i	$-0.263197\pi$
$138$	11.5350	+	2.22330i	0.981927	+	0.189260i
$139$			12.8967i			1.09389i	0.837169	+	0.546944i	$0.184209\pi$
$139$			12.8967i			1.09389i	−0.837169	+	0.546944i	$0.815791\pi$
$140$	3.64998	−	2.07821i	0.308480	−	0.175641i
$141$	−3.43701	−	5.53115i	−0.289449	−	0.465807i
$142$	6.47566	−	13.2295i	0.543425	−	1.11020i
$143$	−1.55335	+	0.456105i	−0.129898	+	0.0381414i
$144$	11.8688	−	1.76952i	0.989068	−	0.147460i
$145$	1.45560	+	1.67985i	0.120881	+	0.139504i
$146$	−0.694988	−	5.96444i	−0.0575176	−	0.493620i
$147$	9.59081	−	4.20501i	0.791037	−	0.346824i
$148$	5.34556	−	5.53931i	0.439402	−	0.455329i
$149$	4.32654	−	6.73223i	0.354444	−	0.551526i	−0.617550	−	0.786532i	$-0.711875\pi$
$149$	4.32654	−	6.73223i	0.354444	−	0.551526i	0.971994	+	0.235006i	$0.0755110\pi$
$150$	0.917667	−	0.0928160i	0.0749272	−	0.00757840i
$151$	−14.8920	−	12.9040i	−1.21189	−	1.05011i	−0.997302	−	0.0734076i	$-0.976613\pi$
$151$	−14.8920	−	12.9040i	−1.21189	−	1.05011i	−0.214591	−	0.976704i	$-0.568842\pi$
$152$	−7.21282	+	18.8191i	−0.585037	+	1.52643i
$153$	−0.224398	+	7.38013i	−0.0181415	+	0.596648i
$154$	0.453854	−	0.372449i	0.0365726	−	0.0300128i
$155$	−6.46298	−	14.1519i	−0.519119	−	1.13671i
$156$	−7.87915	+	10.5826i	−0.630837	+	0.847282i
$157$	10.1676	−	22.2639i	0.811461	−	1.77685i	0.210459	−	0.977603i	$-0.432504\pi$
$157$	10.1676	−	22.2639i	0.811461	−	1.77685i	0.601001	−	0.799248i	$-0.294769\pi$
$158$	9.71453	+	1.66357i	0.772847	+	0.132347i
$159$	14.2750	+	4.42825i	1.13208	+	0.351183i
$160$	−1.62508	+	12.0544i	−0.128474	+	0.952987i
$161$	2.55442	−	3.92616i	0.201317	−	0.309425i
$162$	11.8518	+	4.64048i	0.931168	+	0.364590i
$163$	−12.6263	−	19.6469i	−0.988968	−	1.53886i	−0.834604	−	0.550851i	$-0.814303\pi$
$163$	−12.6263	−	19.6469i	−0.988968	−	1.53886i	−0.154364	−	0.988014i	$-0.549333\pi$
$164$	−21.3773	−	4.25337i	−1.66929	−	0.332132i
$165$	−1.52554	+	0.422865i	−0.118763	+	0.0329200i
$166$	9.88850	−	2.61784i	0.767496	−	0.203184i
$167$	−3.29649	−	7.21830i	−0.255090	−	0.558569i	0.738152	−	0.674635i	$-0.235699\pi$
$167$	−3.29649	−	7.21830i	−0.255090	−	0.558569i	−0.993242	+	0.116066i	$0.962972\pi$
$168$	1.12991	−	4.64941i	0.0871743	−	0.358710i
$169$	−0.214319	−	1.49062i	−0.0164861	−	0.114663i
$170$	−7.12189	−	2.30020i	−0.546224	−	0.176417i
$171$	−16.5733	+	13.5012i	−1.26739	+	1.03246i
$172$	6.28141	−	8.70989i	0.478953	−	0.664123i
$173$	2.04525	−	3.18247i	0.155497	−	0.241958i	−0.754761	−	0.656000i	$-0.772247\pi$
$173$	2.04525	−	3.18247i	0.155497	−	0.241958i	0.910258	+	0.414042i	$0.135883\pi$
$174$	2.52989	+	0.106315i	0.191791	+	0.00805975i
$175$	0.103612	−	0.352869i	0.00783232	−	0.0266744i
$176$	0.0605105	+	1.69918i	0.00456115	+	0.128080i
$177$	−7.63395	−	1.21629i	−0.573803	−	0.0914217i
$178$	18.5281	−	7.86848i	1.38874	−	0.589767i
$179$	5.16043	−	1.51524i	0.385709	−	0.113254i	−0.0831285	−	0.996539i	$-0.526491\pi$
$179$	5.16043	−	1.51524i	0.385709	−	0.113254i	0.468837	+	0.883284i	$0.344673\pi$
$180$	−7.86098	+	10.2298i	−0.585923	+	0.762486i
$181$	−3.33707	+	23.2098i	−0.248042	+	1.72517i	0.361461	+	0.932387i	$0.382278\pi$
$181$	−3.33707	+	23.2098i	−0.248042	+	1.72517i	−0.609503	+	0.792784i	$0.708631\pi$
$182$	2.72452	+	4.50018i	0.201955	+	0.333576i
$183$	7.73673	−	6.50071i	0.571916	−	0.480546i
$184$	4.55415	+	12.7773i	0.335736	+	0.941956i
$185$			8.27619i			0.608478i
$186$	−16.7807	−	5.70280i	−1.23042	−	0.418150i
$187$	−1.03551	−	0.148884i	−0.0757240	−	0.0108875i
$188$	3.48566	−	6.66276i	0.254218	−	0.485932i
$189$	3.49477	−	3.67995i	0.254207	−	0.267677i
$190$	−8.46973	−	19.9439i	−0.614459	−	1.44688i
$191$	−8.03392	−	9.27163i	−0.581314	−	0.670872i	0.386573	−	0.922259i	$-0.373659\pi$
$191$	−8.03392	−	9.27163i	−0.581314	−	0.670872i	−0.967887	+	0.251387i	$0.919113\pi$
$192$	8.72138	+	10.7674i	0.629411	+	0.777072i
$193$	−18.9984	−	5.57842i	−1.36753	−	0.401544i	−0.486120	−	0.873892i	$-0.661588\pi$
$193$	−18.9984	−	5.57842i	−1.36753	−	0.401544i	−0.881412	+	0.472348i	$0.843406\pi$
$194$	−6.08345	+	6.65181i	−0.436766	+	0.477572i
$195$	−1.80507	−	14.0693i	−0.129264	−	1.00752i
$196$	9.80773	+	7.07315i	0.700552	+	0.505225i
$197$	−1.57384	−	1.36374i	−0.112132	−	0.0971627i	0.596990	−	0.802248i	$-0.296363\pi$
$197$	−1.57384	−	1.36374i	−0.112132	−	0.0971627i	−0.709122	+	0.705086i	$0.750909\pi$
$198$	−0.841708	+	1.59492i	−0.0598176	+	0.113346i
$199$	10.6427	−	1.53019i	0.754440	−	0.108472i	0.245645	−	0.969360i	$-0.421000\pi$
$199$	10.6427	−	1.53019i	0.754440	−	0.108472i	0.508795	+	0.860888i	$0.330091\pi$
$200$	0.630551	+	0.858317i	0.0445867	+	0.0606922i
$201$	−3.26753	+	6.87636i	−0.230473	+	0.485021i
$202$	−1.81700	−	6.86346i	−0.127844	−	0.482912i
$203$	0.419415	−	0.918392i	0.0294372	−	0.0644585i
$204$	−7.47224	+	4.10541i	−0.523162	+	0.287436i
$205$	19.7135	−	12.6691i	1.37685	−	0.884849i
$206$	−0.150124	+	5.60013i	−0.0104596	+	0.390180i
$207$	−2.55888	+	14.1581i	−0.177855	+	0.984057i
$208$	−15.1472	−	1.63008i	−1.05027	−	0.113026i
$209$	−1.63749	−	2.54799i	−0.113268	−	0.176248i
$210$	2.59697	+	4.44047i	0.179208	+	0.306421i
$211$	12.3269	+	5.62949i	0.848617	+	0.387550i	0.791760	−	0.610832i	$-0.209165\pi$
$211$	12.3269	+	5.62949i	0.848617	+	0.387550i	0.0568565	+	0.998382i	$0.481892\pi$
$212$	3.96805	+	16.7959i	0.272527	+	1.15354i
$213$	16.2937	+	7.74250i	1.11643	+	0.530507i
$214$	−3.72153	−	4.53493i	−0.254398	−	0.310002i
$215$	1.64306	+	11.4277i	0.112056	+	0.779363i
$216$	2.33572	+	14.5101i	0.158926	+	0.987291i
$217$	−4.62774	+	5.34070i	−0.314151	+	0.362550i
$218$	−15.8760	−	10.8148i	−1.07526	−	0.732472i
$219$	7.29455	−	0.935880i	0.492920	−	0.0632409i
$220$	−1.31536	−	1.26936i	−0.0886819	−	0.0855800i
$221$	2.64091	−	8.99411i	0.177647	−	0.605009i
$222$	6.85975	+	6.46780i	0.460396	+	0.434090i
$223$	0.614893	−	0.532808i	0.0411763	−	0.0356795i	−0.634030	−	0.773309i	$-0.718600\pi$
$223$	0.614893	−	0.532808i	0.0411763	−	0.0356795i	0.675206	+	0.737629i	$0.264055\pi$
$224$	5.28725	−	1.60312i	0.353269	−	0.107113i
$225$	0.126708	+	1.12251i	0.00844722	+	0.0748342i
$226$	−19.6363	−	9.61164i	−1.30618	−	0.639357i
$227$	2.75708	−	19.1759i	0.182994	−	1.27275i	−0.666642	−	0.745378i	$-0.732269\pi$
$227$	2.75708	−	19.1759i	0.182994	−	1.27275i	0.849635	−	0.527371i	$-0.176822\pi$
$228$	−23.1496	−	8.56585i	−1.53312	−	0.567287i
$229$	−18.8962			−1.24869			−0.624347	−	0.781147i	$-0.714635\pi$
$229$	−18.8962			−1.24869			−0.624347	+	0.781147i	$0.714635\pi$
$230$	−13.0623	−	6.48490i	−0.861306	−	0.427602i
$231$	0.462573	+	0.550526i	0.0304351	+	0.0362219i
$232$	1.37809	+	2.57871i	0.0904762	+	0.169301i
$233$	−1.56675	−	0.225265i	−0.102641	−	0.0147576i	0.0908028	−	0.995869i	$-0.471057\pi$
$233$	−1.56675	−	0.225265i	−0.102641	−	0.0147576i	−0.193444	+	0.981111i	$0.561966\pi$
$234$	−13.0720	−	9.49892i	−0.854545	−	0.620964i
$235$	2.27760	+	7.75678i	0.148574	+	0.505997i
$236$	−3.26771	−	8.30648i	−0.212710	−	0.540706i
$237$	−1.89927	+	11.9207i	−0.123371	+	0.774330i
$238$	0.393451	+	3.37662i	0.0255036	+	0.218874i
$239$	−10.1008	−	2.96587i	−0.653367	−	0.191846i	−0.0617835	−	0.998090i	$-0.519679\pi$
$239$	−10.1008	−	2.96587i	−0.653367	−	0.191846i	−0.591584	+	0.806244i	$0.701497\pi$
$240$	−14.7857	−	1.81888i	−0.954414	−	0.117408i
$241$	−11.8045	−	7.58629i	−0.760394	−	0.488676i	0.102080	−	0.994776i	$-0.467450\pi$
$241$	−11.8045	−	7.58629i	−0.760394	−	0.488676i	−0.862474	+	0.506101i	$0.831086\pi$
$242$	12.6456	+	8.61422i	0.812889	+	0.553743i
$243$	−5.51461	+	14.5804i	−0.353762	+	0.935335i
$244$	11.0037	+	3.88252i	0.704438	+	0.248553i
$245$	−12.8681	+	1.85016i	−0.822114	+	0.118202i
$246$	4.90517	−	26.2405i	0.312742	−	1.67303i
$247$	24.6863	−	11.2738i	1.57075	−	0.717338i
$248$	−4.16995	−	20.0357i	−0.264792	−	1.27227i
$249$	3.34648	+	12.0729i	0.212075	+	0.765087i
$250$	−16.1148	−	2.75959i	−1.01919	−	0.174532i
$251$	9.91366	−	6.37112i	0.625745	−	0.402142i	−0.188987	−	0.981980i	$-0.560520\pi$
$251$	9.91366	−	6.37112i	0.625745	−	0.402142i	0.814732	+	0.579838i	$0.196884\pi$
$252$	5.71002	+	1.31769i	0.359697	+	0.0830066i
$253$	−1.95271	−	0.585285i	−0.122766	−	0.0367966i
$254$	0.485418	−	18.1077i	0.0304578	−	1.13618i
$255$	2.71577	−	8.75459i	0.170068	−	0.548234i
$256$	−5.59453	+	14.9900i	−0.349658	+	0.936877i
$257$	5.31427	+	2.42695i	0.331495	+	0.151389i	0.574208	−	0.818709i	$-0.305310\pi$
$257$	5.31427	+	2.42695i	0.331495	+	0.151389i	−0.242713	+	0.970098i	$0.578037\pi$
$258$	10.7559	+	7.56884i	0.669635	+	0.471215i
$259$	3.41952	−	1.56164i	0.212479	−	0.0970358i
$260$	12.9353	−	10.0473i	0.802211	−	0.623110i
$261$	−0.0942510	+	3.09978i	−0.00583399	+	0.191871i
$262$	−8.61942	−	2.78386i	−0.532509	−	0.171988i
$263$	−3.19764	+	3.69027i	−0.197175	+	0.227552i	−0.845724	−	0.533621i	$-0.820831\pi$
$263$	−3.19764	+	3.69027i	−0.197175	+	0.227552i	0.648549	+	0.761173i	$0.275376\pi$
$264$	−2.08006	+	0.0982501i	−0.128019	+	0.00604687i
$265$	−15.6090	−	10.0313i	−0.958855	−	0.616219i
$266$	−6.64216	+	7.26272i	−0.407257	+	0.445306i
$267$	9.89951	+	22.5788i	0.605840	+	1.38180i
$268$	−8.75603	+	0.783100i	−0.534860	+	0.0478354i
$269$	−8.84627	+	7.66533i	−0.539366	+	0.467364i	−0.881431	−	0.472313i	$-0.843419\pi$
$269$	−8.84627	+	7.66533i	−0.539366	+	0.467364i	0.342065	+	0.939676i	$0.388874\pi$
$270$	−12.6398	−	9.48168i	−0.769233	−	0.577036i
$271$	5.30499	+	18.0671i	0.322255	+	1.09750i	0.948211	+	0.317641i	$0.102891\pi$
$271$	5.30499	+	18.0671i	0.322255	+	1.09750i	−0.625956	+	0.779859i	$0.715291\pi$
$272$	−8.46608	−	5.02434i	−0.513331	−	0.304645i
$273$	−5.47249	+	3.40056i	−0.331210	+	0.205811i
$274$	12.6159	+	20.8381i	0.762153	+	1.25888i
$275$	−0.160057			−0.00965178
$276$	−15.5832	+	5.75886i	−0.937997	+	0.346643i
$277$	14.4504			0.868239			0.434119	−	0.900855i	$-0.357060\pi$
$277$	14.4504			0.868239			0.434119	+	0.900855i	$0.357060\pi$
$278$	−9.44591	−	15.6022i	−0.566528	−	0.935755i
$279$	6.74556	−	20.6317i	0.403846	−	1.23519i
$280$	−2.89352	+	5.18751i	−0.172921	+	0.310013i
$281$	−3.43351	−	11.6935i	−0.204826	−	0.697574i	−0.996267	−	0.0863281i	$-0.972487\pi$
$281$	−3.43351	−	11.6935i	−0.204826	−	0.697574i	0.791440	−	0.611246i	$-0.209332\pi$
$282$	8.20916	+	4.17409i	0.488849	+	0.248563i
$283$	−15.2641	+	13.2264i	−0.907357	+	0.786230i	−0.977418	−	0.211313i	$-0.932226\pi$
$283$	−15.2641	+	13.2264i	−0.907357	+	0.786230i	0.0700610	+	0.997543i	$0.477681\pi$
$284$	1.85558	+	20.7477i	0.110108	+	1.23115i
$285$	24.3041	−	10.6560i	1.43965	−	0.631204i
$286$	1.54514	−	1.68950i	0.0913660	−	0.0999020i
$287$	−8.95434	−	5.75461i	−0.528558	−	0.339684i
$288$	−13.0625	+	10.8337i	−0.769718	+	0.638385i
$289$	−7.16588	+	8.26987i	−0.421522	+	0.486463i
$290$	−2.99131	−	0.966122i	−0.175656	−	0.0567326i
$291$	−8.23266	−	7.35565i	−0.482607	−	0.431196i
$292$	5.20929	+	6.70659i	0.304850	+	0.392474i
$293$	−10.0113	+	4.57201i	−0.584867	+	0.267100i	−0.685796	−	0.727794i	$-0.740546\pi$
$293$	−10.0113	+	4.57201i	−0.584867	+	0.267100i	0.100929	+	0.994894i	$0.467818\pi$
$294$	−8.52285	+	12.1117i	−0.497063	+	0.706367i
$295$	8.72934	+	3.98655i	0.508242	+	0.232106i
$296$	−2.40978	+	10.6165i	−0.140066	+	0.617074i
$297$	−1.96519	−	1.00814i	−0.114032	−	0.0584985i
$298$	−0.303279	+	11.3133i	−0.0175685	+	0.655365i
$299$	7.68095	−	16.5723i	0.444201	−	0.958399i
$300$	−1.04219	+	0.784409i	−0.0601708	+	0.0452879i
$301$	4.41163	−	2.83518i	0.254282	−	0.163417i
$302$	27.4672	+	4.70363i	1.58056	+	0.270663i
$303$	8.37961	−	2.32274i	0.481396	−	0.133438i
$304$	−5.05774	−	28.0497i	−0.290081	−	1.60876i
$305$	−11.4113	+	5.21137i	−0.653410	+	0.298402i
$306$	−5.13392	−	9.09264i	−0.293487	−	0.519791i
$307$	−10.8413	+	1.55875i	−0.618748	+	0.0889626i	−0.444559	−	0.895750i	$-0.646640\pi$
$307$	−10.8413	+	1.55875i	−0.618748	+	0.0889626i	−0.174189	+	0.984712i	$0.555730\pi$
$308$	−0.276270	+	0.782994i	−0.0157419	+	0.0446152i
$309$	−6.86040	−	0.104274i	−0.390275	−	0.00593193i
$310$	18.1840	+	12.3870i	1.03278	+	0.703535i
$311$	26.6563	+	17.1310i	1.51154	+	0.971409i	0.993223	+	0.116220i	$0.0370779\pi$
$311$	26.6563	+	17.1310i	1.51154	+	0.971409i	0.518318	+	0.855188i	$0.326558\pi$
$312$	1.78105	−	18.5734i	0.100832	−	1.05151i
$313$	−16.7249	−	4.91087i	−0.945347	−	0.277579i	−0.227498	−	0.973778i	$-0.573055\pi$
$313$	−16.7249	−	4.91087i	−0.945347	−	0.277579i	−0.717848	+	0.696200i	$0.754873\pi$
$314$	4.00617	+	34.3812i	0.226081	+	1.94025i
$315$	−5.40117	+	3.24351i	−0.304321	+	0.182751i
$316$	−12.9708	+	5.10263i	−0.729666	+	0.287045i
$317$	8.47083	+	28.8490i	0.475769	+	1.62032i	0.751953	+	0.659217i	$0.229112\pi$
$317$	8.47083	+	28.8490i	0.475769	+	1.62032i	−0.276184	+	0.961105i	$0.589070\pi$
$318$	−20.5129	+	5.09819i	−1.15030	+	0.285892i
$319$	−0.434931	−	0.0625337i	−0.0243515	−	0.00350121i
$320$	−6.86300	−	15.7734i	−0.383653	−	0.881760i
$321$	5.50088	−	4.62206i	0.307029	−	0.257978i
$322$	−0.214656	+	6.62069i	−0.0119623	+	0.368957i
$323$	17.5372			0.975795
$324$	−17.7368	+	3.06666i	−0.985380	+	0.170370i
$325$	0.204100	−	1.41955i	0.0113214	−	0.0787423i
$326$	29.6649	+	14.5205i	1.64298	+	0.804215i
$327$	13.0189	−	19.5965i	0.719947	−	1.08369i
$328$	28.9770	−	10.5117i	1.59999	−	0.580411i
$329$	2.77515	−	2.40468i	0.152999	−	0.132575i
$330$	1.53584	−	1.62892i	0.0845453	−	0.0896688i
$331$	3.54350	−	12.0680i	0.194768	−	0.663320i	−0.802965	−	0.596026i	$-0.796745\pi$
$331$	3.54350	−	12.0680i	0.194768	−	0.663320i	0.997733	−	0.0672934i	$-0.0214364\pi$
$332$	−10.0455	+	10.4096i	−0.551317	+	0.571300i
$333$	−7.82339	+	8.49278i	−0.428719	+	0.465402i
$334$	9.27488	+	6.31808i	0.507499	+	0.345710i
$335$	6.18927	−	7.14280i	0.338156	−	0.390253i
$336$	2.03842	+	6.45231i	0.111205	+	0.352002i
$337$	−3.21549	−	22.3642i	−0.175159	−	1.21826i	−0.867777	−	0.496954i	$-0.834452\pi$
$337$	−3.21549	−	22.3642i	−0.175159	−	1.21826i	0.692618	−	0.721305i	$-0.256457\pi$
$338$	1.35105	+	1.64635i	0.0734874	+	0.0895494i
$339$	11.4920	−	24.1844i	0.624159	−	1.31351i
$340$	10.3006	−	2.43353i	0.558628	−	0.131977i
$341$	2.79761	+	1.27763i	0.151499	+	0.0691873i
$342$	10.1613	−	28.4721i	0.549461	−	1.53960i
$343$	6.88877	+	10.7191i	0.371959	+	0.578779i
$344$	−1.21973	+	15.1377i	−0.0657636	+	0.816168i
$345$	7.75620	−	16.0891i	0.417580	−	0.866209i
$346$	−0.143366	+	5.34806i	−0.00770743	+	0.287513i
$347$	−8.78944	+	5.64863i	−0.471842	+	0.303234i	−0.754867	−	0.655878i	$-0.772298\pi$
$347$	−8.78944	+	5.64863i	−0.471842	+	0.303234i	0.283025	+	0.959113i	$0.408662\pi$
$348$	−3.13847	+	1.72434i	−0.168239	+	0.0924344i
$349$	−5.91859	+	12.9599i	−0.316815	+	0.693728i	−0.999309	−	0.0371628i	$-0.988168\pi$
$349$	−5.91859	+	12.9599i	−0.316815	+	0.693728i	0.682494	+	0.730891i	$0.260895\pi$
$350$	0.133104	+	0.502780i	0.00711469	+	0.0268747i
$351$	11.4472	−	16.1438i	0.611007	−	0.861692i
$352$	−1.31773	−	2.01130i	−0.0702350	−	0.107203i
$353$	28.3233	−	4.07228i	1.50750	−	0.216745i	0.661505	−	0.749940i	$-0.269918\pi$
$353$	28.3233	−	4.07228i	1.50750	−	0.216745i	0.845992	+	0.533195i	$0.179009\pi$
$354$	10.1262	−	4.11987i	0.538201	−	0.218969i
$355$	−16.9251	−	14.6657i	−0.898290	−	0.778373i
$356$	−16.6517	+	23.0895i	−0.882539	+	1.22374i
$357$	−4.12963	+	0.529826i	−0.218563	+	0.0280413i
$358$	−5.13316	+	5.61273i	−0.271296	+	0.296642i
$359$	−21.1324	−	6.20504i	−1.11533	−	0.327490i	−0.328402	−	0.944538i	$-0.606510\pi$
$359$	−21.1324	−	6.20504i	−1.11533	−	0.327490i	−0.786925	+	0.617048i	$0.788328\pi$
$360$	2.01741	−	18.1334i	0.106327	−	0.955712i
$361$	20.8069	+	24.0125i	1.09510	+	1.26381i
$362$	−12.9624	−	30.5228i	−0.681287	−	1.60424i
$363$	−10.3698	+	15.6090i	−0.544274	+	0.819259i
$364$	−6.59209	−	3.44870i	−0.345520	−	0.180761i
$365$	−9.03697	−	1.29932i	−0.473017	−	0.0680096i
$366$	−4.59841	+	13.5310i	−0.240363	+	0.707275i
$367$			13.4817i			0.703741i	0.936049	+	0.351870i	$0.114454\pi$
$367$			13.4817i			0.703741i	−0.936049	+	0.351870i	$0.885546\pi$
$368$	−14.8679	−	12.1221i	−0.775044	−	0.631907i
$369$	32.2054	+	5.63430i	1.67655	+	0.293310i
$370$	−6.06169	−	10.0123i	−0.315132	−	0.520516i
$371$	−1.19941	+	8.34210i	−0.0622704	+	0.433100i
$372$	24.4777	−	5.39149i	1.26911	−	0.279536i
$373$	−18.3497	+	5.38796i	−0.950112	+	0.278978i	−0.719834	−	0.694147i	$-0.755782\pi$
$373$	−18.3497	+	5.38796i	−0.950112	+	0.278978i	−0.230279	+	0.973125i	$0.573964\pi$
$374$	1.36178	−	0.578318i	0.0704159	−	0.0299041i
$375$	3.15058	−	19.7744i	0.162695	−	1.02115i
$376$	0.663110	+	10.6134i	0.0341973	+	0.547346i
$377$	1.10923	−	3.77767i	0.0571280	−	0.194560i
$378$	−1.53258	+	7.01157i	−0.0788277	+	0.360636i
$379$	14.8863	−	23.1635i	0.764658	−	1.18983i	−0.212468	−	0.977168i	$-0.568150\pi$
$379$	14.8863	−	23.1635i	0.764658	−	1.18983i	0.977126	−	0.212663i	$-0.0682136\pi$
$380$	24.8538	+	17.9241i	1.27498	+	0.919488i
$381$	22.1828	+	0.337164i	1.13646	+	0.0172734i
$382$	16.5100	+	5.33233i	0.844725	+	0.272826i
$383$	3.93853	+	27.3931i	0.201249	+	1.39972i	0.800584	+	0.599221i	$0.204523\pi$
$383$	3.93853	+	27.3931i	0.201249	+	1.39972i	−0.599334	+	0.800499i	$0.704568\pi$
$384$	−18.4372	−	6.63840i	−0.940871	−	0.338764i
$385$	−0.370828	−	0.812000i	−0.0188991	−	0.0413833i
$386$	27.0695	−	7.16626i	1.37780	−	0.364753i
$387$	−9.11643	+	13.2799i	−0.463414	+	0.675058i
$388$	2.48764	−	12.5029i	0.126291	−	0.634736i
$389$	−4.64843	−	7.23310i	−0.235685	−	0.366733i	0.703184	−	0.711008i	$-0.251761\pi$
$389$	−4.64843	−	7.23310i	−0.235685	−	0.366733i	−0.938869	+	0.344275i	$0.888125\pi$
$390$	12.4884	+	15.6986i	0.632376	+	0.794928i
$391$	8.96363	−	7.67942i	0.453310	−	0.388365i
$392$	−17.0457	−	1.37347i	−0.860938	−	0.0693709i
$393$	3.28681	−	10.5954i	0.165798	−	0.534469i
$394$	2.90284	+	0.497098i	0.146243	+	0.0250434i
$395$	6.22513	−	13.6311i	0.313220	−	0.685857i
$396$	−0.149881	−	2.54598i	−0.00753178	−	0.127940i
$397$	0.100583	+	0.220246i	0.00504812	+	0.0110538i	0.912139	−	0.409880i	$-0.134430\pi$
$397$	0.100583	+	0.220246i	0.00504812	+	0.0110538i	−0.907091	+	0.420934i	$0.861702\pi$
$398$	−11.7545	+	9.64616i	−0.589200	+	0.483518i
$399$	−8.98876	−	8.03120i	−0.450001	−	0.402063i
$400$	−1.39148	−	0.576538i	−0.0695739	−	0.0288269i
$401$	−21.5292	−	18.6552i	−1.07512	−	0.931594i	−0.0772592	−	0.997011i	$-0.524617\pi$
$401$	−21.5292	−	18.6552i	−1.07512	−	0.931594i	−0.997858	+	0.0654167i	$0.979162\pi$
$402$	−1.08345	−	10.7121i	−0.0540378	−	0.534269i
$403$	−14.8987	+	23.1829i	−0.742159	+	1.15482i
$404$	7.22514	+	6.97242i	0.359464	+	0.346891i
$405$	11.4322	−	15.6142i	0.568073	−	0.775876i
$406$	0.165256	+	1.41824i	0.00820151	+	0.0703859i
$407$	−1.07140	−	1.23646i	−0.0531072	−	0.0612890i
$408$	6.03282	−	10.4395i	0.298669	−	0.516831i
$409$	−3.68089	+	1.08081i	−0.182008	+	0.0534424i	−0.371467	−	0.928446i	$-0.621145\pi$
$409$	−3.68089	+	1.08081i	−0.182008	+	0.0534424i	0.189458	+	0.981889i	$0.439327\pi$
$410$	−14.5697	+	29.7654i	−0.719547	+	1.47001i
$411$	−25.3404	+	15.7463i	−1.24995	+	0.776708i
$412$	−3.92006	−	6.88485i	−0.193128	−	0.339192i
$413$		−	4.35898i		−	0.214491i
$414$	−7.27409	−	19.0023i	−0.357502	−	0.933912i
$415$		−	15.5528i		−	0.763455i
$416$	19.5186	−	9.12218i	0.956979	−	0.447252i
$417$	18.9731	−	11.7898i	0.929119	−	0.577347i
$418$	3.84721	+	1.88315i	0.188173	+	0.0921079i
$419$	−28.5319	+	8.37772i	−1.39387	+	0.409279i	−0.890576	−	0.454834i	$-0.849699\pi$
$419$	−28.5319	+	8.37772i	−1.39387	+	0.409279i	−0.503299	+	0.864113i	$0.667880\pi$
$420$	−6.39406	−	3.46987i	−0.311998	−	0.169312i
$421$	−11.4455	−	13.2088i	−0.557818	−	0.643756i	0.404869	−	0.914375i	$-0.367317\pi$
$421$	−11.4455	−	13.2088i	−0.557818	−	0.643756i	−0.962687	+	0.270619i	$0.912772\pi$
$422$	−19.0359	+	2.21810i	−0.926653	+	0.107976i
$423$	−4.99519	+	10.1128i	−0.242875	+	0.491700i
$424$	−17.1022	−	17.4129i	−0.830554	−	0.845644i
$425$	0.501039	−	0.779632i	0.0243040	−	0.0378177i
$426$	−25.3826	+	2.56728i	−1.22979	+	0.124385i
$427$	4.30643	+	3.73154i	0.208403	+	0.180582i
$428$	7.82371	+	2.76050i	0.378173	+	0.133434i
$429$	2.09102	+	1.86827i	0.100955	+	0.0902007i
$430$	−10.3577	−	12.6215i	−0.499491	−	0.608664i
$431$	12.8872	+	28.2191i	0.620757	+	1.35927i	0.914968	+	0.403528i	$0.132216\pi$
$431$	12.8872	+	28.2191i	0.620757	+	1.35927i	−0.294211	+	0.955741i	$0.595057\pi$
$432$	−13.4533	−	15.8433i	−0.647272	−	0.762259i
$433$	8.75380	−	19.1681i	0.420681	−	0.921162i	−0.574067	−	0.818808i	$-0.694635\pi$
$433$	8.75380	−	19.1681i	0.420681	−	0.921162i	0.994748	−	0.102354i	$-0.0326375\pi$
$434$	1.68686	−	9.85051i	0.0809716	−	0.472840i
$435$	1.14067	−	3.67708i	0.0546908	−	0.176302i
$436$	27.1275	+	1.45547i	1.29917	+	0.0697043i
$437$	33.7972	+	5.05297i	1.61674	+	0.241716i
$438$	−8.13929	+	6.47492i	−0.388910	+	0.309383i
$439$	6.42694	+	10.0005i	0.306741	+	0.477299i	0.960064	−	0.279781i	$-0.0902619\pi$
$439$	6.42694	+	10.0005i	0.306741	+	0.477299i	−0.653323	+	0.757080i	$0.726626\pi$
$440$	2.52100	+	0.572227i	0.120184	+	0.0272799i
$441$	−14.9538	−	10.2655i	−0.712087	−	0.488834i
$442$	3.39261	+	12.8151i	0.161370	+	0.609552i
$443$	−1.37346	−	3.00747i	−0.0652552	−	0.142889i	0.874194	−	0.485576i	$-0.161390\pi$
$443$	−1.37346	−	3.00747i	−0.0652552	−	0.142889i	−0.939450	+	0.342687i	$0.888663\pi$
$444$	−13.0359	−	2.80031i	−0.618658	−	0.132897i
$445$	−4.35567	−	30.2943i	−0.206478	−	1.43609i
$446$	−0.353639	+	1.09494i	−0.0167453	+	0.0518469i
$447$	−13.8593	−	0.210653i	−0.655524	−	0.00996355i
$448$	−5.22220	+	5.81193i	−0.246726	+	0.274588i
$449$	15.8264	−	24.6264i	0.746896	−	1.16219i	−0.234857	−	0.972030i	$-0.575462\pi$
$449$	15.8264	−	24.6264i	0.746896	−	1.16219i	0.981753	−	0.190163i	$-0.0609015\pi$
$450$	−0.975446	−	1.26518i	−0.0459830	−	0.0596413i
$451$	−1.30510	+	4.44478i	−0.0614550	+	0.209296i
$452$	30.7952	−	2.75419i	1.44849	−	0.129546i
$453$	−5.37005	+	33.7048i	−0.252307	+	1.58359i
$454$	10.7095	+	25.2179i	0.502621	+	1.18353i
$455$	7.67451	−	2.25344i	0.359787	−	0.105643i
$456$	34.2796	−	6.59261i	1.60529	−	0.308727i
$457$	−5.57586	+	38.7810i	−0.260828	+	1.81410i	0.265830	+	0.964020i	$0.414354\pi$
$457$	−5.57586	+	38.7810i	−0.260828	+	1.81410i	−0.526658	+	0.850077i	$0.676555\pi$
$458$	22.8601	−	13.8400i	1.06818	−	0.646702i
$459$	11.0625	−	6.41653i	0.516351	−	0.299498i
$460$	20.5522	−	1.72193i	0.958251	−	0.0802856i
$461$			31.9989i			1.49034i	0.666876	+	0.745169i	$0.267631\pi$
$461$			31.9989i			1.49034i	−0.666876	+	0.745169i	$0.732369\pi$
$462$	−0.962829	−	0.327211i	−0.0447948	−	0.0152232i
$463$	−21.8454	−	3.14090i	−1.01524	−	0.145970i	−0.385447	−	0.922730i	$-0.625953\pi$
$463$	−21.8454	−	3.14090i	−1.01524	−	0.145970i	−0.629796	+	0.776760i	$0.716862\pi$
$464$	−3.55589	−	2.11031i	−0.165078	−	0.0979685i
$465$	−14.9115	+	22.4453i	−0.691505	+	1.04087i
$466$	2.06040	−	0.875009i	0.0954464	−	0.0405340i
$467$	3.35407	+	3.87081i	0.155208	+	0.179120i	0.828028	−	0.560686i	$-0.189463\pi$
$467$	3.35407	+	3.87081i	0.155208	+	0.179120i	−0.672820	+	0.739806i	$0.734917\pi$
$468$	22.7714	+	1.91727i	1.05261	+	0.0886256i
$469$	−4.11910	−	1.20948i	−0.190202	−	0.0558484i
$470$	−8.43664	−	7.71578i	−0.389153	−	0.355902i
$471$	−42.0485	+	5.39476i	−1.93749	+	0.248577i
$472$	10.0371	+	7.65561i	0.461993	+	0.352378i
$473$	−1.72485	−	1.49459i	−0.0793087	−	0.0687214i
$474$	−6.43331	−	15.8124i	−0.295492	−	0.726287i
$475$	2.65579	−	0.381844i	0.121856	−	0.0175202i
$476$	−2.94911	−	3.79677i	−0.135172	−	0.174025i
$477$	−6.53504	−	25.0489i	−0.299219	−	1.14691i
$478$	14.3920	−	3.81007i	0.658273	−	0.174268i
$479$	3.33370	−	7.29979i	0.152321	−	0.333536i	−0.818054	−	0.575142i	$-0.804947\pi$
$479$	3.33370	−	7.29979i	0.152321	−	0.333536i	0.970374	+	0.241606i	$0.0776741\pi$
$480$	19.2196	−	8.62900i	0.877249	−	0.393858i
$481$	12.3324	−	7.92555i	0.562309	−	0.361374i
$482$	19.8372	+	0.531778i	0.903558	+	0.0242218i
$483$	−8.11116	−	0.168802i	−0.369071	−	0.00768074i
$484$	−21.6076	−	1.15931i	−0.982162	−	0.0526959i
$485$	7.40972	+	11.5298i	0.336458	+	0.523539i
$486$	−4.00766	−	21.6781i	−0.181791	−	0.983337i
$487$	−20.7435	−	9.47326i	−0.939980	−	0.429274i	−0.114321	−	0.993444i	$-0.536469\pi$
$487$	−20.7435	−	9.47326i	−0.939980	−	0.429274i	−0.825659	+	0.564169i	$0.809196\pi$
$488$	−16.1556	+	3.36241i	−0.731331	+	0.152209i
$489$	−17.3612	+	36.5358i	−0.785099	+	1.65221i
$490$	14.2124	−	11.6632i	0.642051	−	0.526890i
$491$	2.94467	+	20.4806i	0.132891	+	0.924277i	0.941759	+	0.336287i	$0.109171\pi$
$491$	2.94467	+	20.4806i	0.132891	+	0.924277i	−0.808868	+	0.587990i	$0.799920\pi$
$492$	13.2850	+	35.3377i	0.598936	+	1.59315i
$493$	1.66610	−	1.92278i	0.0750375	−	0.0865979i
$494$	−21.6076	+	31.7197i	−0.972170	+	1.42714i
$495$	2.01670	+	1.85774i	0.0906437	+	0.0834993i
$496$	19.7194	+	21.1845i	0.885425	+	0.951211i
$497$	−2.86589	+	9.76032i	−0.128553	+	0.437810i
$498$	−12.8910	−	12.1544i	−0.577658	−	0.544652i
$499$	18.1339	−	15.7131i	0.811783	−	0.703414i	−0.146507	−	0.989210i	$-0.546803\pi$
$499$	18.1339	−	15.7131i	0.811783	−	0.703414i	0.958291	+	0.285795i	$0.0922577\pi$
$500$	21.5165	−	8.46443i	0.962246	−	0.378541i
$501$	−7.60572	+	11.4484i	−0.339799	+	0.511476i
$502$	−7.32691	+	14.9686i	−0.327016	+	0.668083i
$503$	−2.53136	+	17.6060i	−0.112868	+	0.785013i	0.852238	+	0.523154i	$0.175245\pi$
$503$	−2.53136	+	17.6060i	−0.112868	+	0.785013i	−0.965106	+	0.261859i	$0.915664\pi$
$504$	−7.87294	+	2.58806i	−0.350688	+	0.115281i
$505$	−10.7949			−0.480369
$506$	2.79101	−	0.722150i	0.124076	−	0.0321035i
$507$	−1.99702	+	1.67797i	−0.0886907	+	0.0745215i
$508$	12.6753	+	22.2618i	0.562377	+	0.987708i
$509$	−4.85977	−	0.698729i	−0.215405	−	0.0309706i	0.0337671	−	0.999430i	$-0.489250\pi$
$509$	−4.85977	−	0.698729i	−0.215405	−	0.0309706i	−0.249173	+	0.968459i	$0.580159\pi$
$510$	3.12663	+	12.5802i	0.138449	+	0.557060i
$511$	1.16835	+	3.97903i	0.0516847	+	0.176022i
$512$	−4.21098	−	22.2321i	−0.186101	−	0.982531i
$513$	35.0132	+	12.0396i	1.54587	+	0.531561i
$514$	−8.20662	+	0.956252i	−0.361979	+	0.0421785i
$515$	8.17268	+	2.39971i	0.360131	+	0.105744i
$516$	−18.5559	−	1.27866i	−0.816876	−	0.0562897i
$517$	−1.34443	−	0.864012i	−0.0591279	−	0.0379992i
$518$	−2.99306	+	4.39378i	−0.131508	+	0.193052i
$519$	−6.55160	−	0.0995802i	−0.287583	−	0.00437108i
$520$	−8.28981	+	21.6291i	−0.363532	+	0.948501i
$521$	36.7962	−	5.29049i	1.61207	−	0.231781i	0.723433	−	0.690394i	$-0.242563\pi$
$521$	36.7962	−	5.29049i	1.61207	−	0.231781i	0.888636	+	0.458614i	$0.151654\pi$
$522$	−2.15633	−	3.81906i	−0.0943801	−	0.167156i
$523$	−33.6612	+	15.3725i	−1.47190	+	0.672194i	−0.980098	−	0.198513i	$-0.936389\pi$
$523$	−33.6612	+	15.3725i	−1.47190	+	0.672194i	−0.491802	+	0.870707i	$0.663661\pi$
$524$	12.4665	−	2.94524i	0.544602	−	0.128663i
$525$	−0.613845	+	0.170152i	−0.0267904	+	0.00742602i
$526$	1.16557	−	6.80642i	0.0508213	−	0.296774i
$527$	−14.9809	+	9.62763i	−0.652577	+	0.419386i
$528$	2.44444	−	1.64235i	0.106381	−	0.0714741i
$529$	19.4871	−	12.2169i	0.847266	−	0.531168i
$530$	26.2306	+	0.703169i	1.13938	+	0.0305437i
$531$	5.18935	+	12.3426i	0.225198	+	0.535625i
$532$	2.71611	−	13.6511i	0.117758	−	0.591852i
$533$	−37.7566	−	17.2429i	−1.63542	−	0.746871i
$534$	−28.5135	−	20.0646i	−1.23390	−	0.868282i
$535$	−8.11354	+	3.70533i	−0.350779	+	0.160195i
$536$	10.0193	−	7.36052i	0.432766	−	0.317926i
$537$	−6.94664	−	6.20663i	−0.299770	−	0.267836i
$538$	5.08769	−	15.7526i	0.219346	−	0.679141i
$539$	1.68298	−	1.94226i	0.0724910	−	0.0836590i
$540$	22.2359	+	2.21298i	0.956881	+	0.0952315i
$541$	13.5297	+	8.69500i	0.581687	+	0.373827i	0.798146	−	0.602464i	$-0.205814\pi$
$541$	13.5297	+	8.69500i	0.581687	+	0.373827i	−0.216459	+	0.976292i	$0.569451\pi$
$542$	−19.6507	−	17.9716i	−0.844068	−	0.771948i
$543$	37.1959	−	16.3082i	1.59623	−	0.699854i
$544$	13.9220	−	0.122458i	0.596900	−	0.00525035i
$545$	−22.0732	+	19.1265i	−0.945510	+	0.819289i
$546$	4.12982	−	8.12210i	0.176740	−	0.347594i
$547$	−8.08653	−	27.5402i	−0.345755	−	1.17753i	−0.930492	−	0.366311i	$-0.880621\pi$
$547$	−8.08653	−	27.5402i	−0.345755	−	1.17753i	0.584737	−	0.811223i	$-0.301198\pi$
$548$	−30.5247	−	15.9692i	−1.30395	−	0.682170i
$549$	−16.6362	−	5.43923i	−0.710016	−	0.232141i
$550$	0.193632	−	0.117230i	0.00825651	−	0.00499869i
$551$	7.36591			0.313798
$552$	14.6342	−	18.3804i	0.622872	−	0.782323i
$553$	−6.80669			−0.289450
$554$	−17.4817	+	10.5838i	−0.742726	+	0.449664i
$555$	12.1756	−	7.56580i	0.516824	−	0.321150i
$556$	22.8548	+	11.9566i	0.969261	+	0.507075i
$557$	−3.97092	−	13.5237i	−0.168253	−	0.573018i	−0.999845	−	0.0176297i	$-0.994388\pi$
$557$	−3.97092	−	13.5237i	−0.168253	−	0.573018i	0.831591	−	0.555388i	$-0.187430\pi$
$558$	6.95058	+	29.9003i	0.294242	+	1.26578i
$559$	15.4550	−	13.3919i	0.653679	−	0.566416i
$560$	−0.298959	−	8.39500i	−0.0126333	−	0.354753i
$561$	0.727595	+	1.65950i	0.0307191	+	0.0700642i
$562$	12.7184	+	11.6317i	0.536492	+	0.490652i
$563$	24.0709	+	15.4694i	1.01447	+	0.651957i	0.938545	−	0.345157i	$-0.112174\pi$
$563$	24.0709	+	15.4694i	1.01447	+	0.651957i	0.0759203	+	0.997114i	$0.475811\pi$
$564$	−12.9884	+	0.962902i	−0.546912	+	0.0405455i
$565$	−21.7679	+	25.1215i	−0.915781	+	1.05687i
$566$	8.77875	−	27.1808i	0.368998	−	1.14249i
$567$	−8.60858	−	1.77727i	−0.361526	−	0.0746381i
$568$	−17.4410	−	23.7409i	−0.731807	−	0.996148i
$569$	−11.1117	+	5.07452i	−0.465825	+	0.212735i	−0.634479	−	0.772940i	$-0.718785\pi$
$569$	−11.1117	+	5.07452i	−0.465825	+	0.212735i	0.168654	+	0.985675i	$0.446058\pi$
$570$	−21.5978	+	30.6923i	−0.904633	+	1.28556i
$571$	−2.67975	−	1.22380i	−0.112144	−	0.0512144i	0.358553	−	0.933509i	$-0.383270\pi$
$571$	−2.67975	−	1.22380i	−0.112144	−	0.0512144i	−0.470697	+	0.882295i	$0.655997\pi$
$572$	−0.631838	+	3.17561i	−0.0264185	+	0.132779i
$573$	−6.29570	+	20.2950i	−0.263007	+	0.847834i
$574$	15.0475	+	0.403383i	0.628073	+	0.0168369i
$575$	1.19022	−	1.35812i	0.0496357	−	0.0566375i
$576$	7.86781	−	22.6737i	0.327825	−	0.944738i
$577$	32.5111	−	20.8936i	1.35346	−	0.869813i	0.355560	−	0.934653i	$-0.384290\pi$
$577$	32.5111	−	20.8936i	1.35346	−	0.869813i	0.997896	+	0.0648403i	$0.0206538\pi$
$578$	2.61203	−	15.2531i	0.108646	−	0.634447i
$579$	9.16090	+	33.0492i	0.380714	+	1.37348i
$580$	4.32642	−	1.02212i	0.179645	−	0.0424414i
$581$	−6.42603	+	2.93467i	−0.266597	+	0.121751i
$582$	15.3471	+	2.86886i	0.636159	+	0.118918i
$583$	3.63059	−	0.522000i	0.150364	−	0.0216190i
$584$	−11.2141	−	4.29805i	−0.464044	−	0.177854i
$585$	−19.0480	+	15.5172i	−0.787537	+	0.641556i
$586$	8.76276	−	12.8636i	0.361986	−	0.531392i
$587$	−10.6076	−	6.81712i	−0.437825	−	0.281373i	0.303103	−	0.952958i	$-0.401977\pi$
$587$	−10.6076	−	6.81712i	−0.437825	−	0.281373i	−0.740927	+	0.671585i	$0.765614\pi$
$588$	1.43983	−	20.8947i	0.0593774	−	0.861684i
$589$	−49.4682	−	14.5252i	−2.03830	−	0.598499i
$590$	−13.4804	+	1.57076i	−0.554978	+	0.0646672i
$591$	−0.567528	+	3.56206i	−0.0233450	+	0.146524i
$592$	−4.86053	−	14.6086i	−0.199767	−	0.600410i
$593$	0.749164	+	2.55142i	0.0307645	+	0.104774i	0.973444	−	0.228925i	$-0.0735211\pi$
$593$	0.749164	+	2.55142i	0.0307645	+	0.104774i	−0.942680	+	0.333699i	$0.891703\pi$
$594$	3.11583	−	0.219731i	0.127844	−	0.00901568i
$595$	5.11606	+	0.735579i	0.209738	+	0.0301558i
$596$	−7.91929	−	13.9087i	−0.324387	−	0.569723i
$597$	−11.9803	−	14.2582i	−0.490322	−	0.583550i
$598$	2.84574	+	25.6744i	0.116371	+	1.04990i
$599$	−18.2930			−0.747432			−0.373716	−	0.927543i	$-0.621916\pi$
$599$	−18.2930			−0.747432			−0.373716	+	0.927543i	$0.621916\pi$
$600$	0.686291	−	1.71228i	0.0280177	−	0.0699037i
$601$	−1.16172	+	8.07992i	−0.0473874	+	0.329587i	0.952313	+	0.305122i	$0.0986973\pi$
$601$	−1.16172	+	8.07992i	−0.0473874	+	0.329587i	−0.999701	+	0.0244649i	$0.992212\pi$
$602$	−3.26051	+	6.66111i	−0.132889	+	0.271487i
$603$	13.1033	−	1.47908i	0.533606	−	0.0602329i
$604$	−36.6741	+	14.4273i	−1.49225	+	0.587039i
$605$	17.5817	−	15.2346i	0.714798	−	0.619376i
$606$	−8.43619	+	8.94743i	−0.342697	+	0.363465i
$607$	−7.87336	+	26.8142i	−0.319570	+	1.08835i	0.630467	+	0.776216i	$0.282863\pi$
$607$	−7.87336	+	26.8142i	−0.319570	+	1.08835i	−0.950037	+	0.312139i	$0.898955\pi$
$608$	26.6631	+	30.2294i	1.08133	+	1.22597i
$609$	−1.73451	+	0.222536i	−0.0702860	+	0.00901759i
$610$	9.98817	−	14.6625i	0.404409	−	0.593668i
$611$	9.37732	−	10.8220i	0.379366	−	0.437811i
$612$	12.8706	+	7.23982i	0.520262	+	0.292652i
$613$	−1.59730	−	11.1095i	−0.0645143	−	0.448707i	−0.996317	−	0.0857424i	$-0.972674\pi$
$613$	−1.59730	−	11.1095i	−0.0645143	−	0.448707i	0.931803	−	0.362964i	$-0.118235\pi$
$614$	11.9739	−	9.82621i	0.483228	−	0.396554i
$615$	−36.6597	−	17.4200i	−1.47826	−	0.702443i
$616$	−0.239260	−	1.14959i	−0.00964008	−	0.0463184i
$617$	7.61874	+	3.47936i	0.306719	+	0.140074i	0.562828	−	0.826574i	$-0.309713\pi$
$617$	7.61874	+	3.47936i	0.306719	+	0.140074i	−0.256109	+	0.966648i	$0.582441\pi$
$618$	8.37591	−	4.89859i	0.336929	−	0.197050i
$619$	−7.53335	−	11.7221i	−0.302791	−	0.471152i	0.656201	−	0.754586i	$-0.272162\pi$
$619$	−7.53335	−	11.7221i	−0.302791	−	0.471152i	−0.958992	+	0.283435i	$0.908526\pi$
$620$	−31.0711	−	1.66705i	−1.24784	−	0.0669505i
$621$	23.1680	−	9.17833i	0.929702	−	0.368314i
$622$	−44.7953	−	1.20084i	−1.79613	−	0.0481491i
$623$	−11.6950	+	7.51593i	−0.468551	+	0.301119i
$624$	11.4490	+	23.7741i	0.458325	+	0.951725i
$625$	−9.54436	+	20.8992i	−0.381774	+	0.835969i
$626$	23.8302	−	6.30869i	0.952445	−	0.252146i
$627$	−2.25155	+	4.73829i	−0.0899184	+	0.189229i
$628$	−30.0283	−	38.6593i	−1.19826	−	1.54267i
$629$	9.37664	−	1.34816i	0.373871	−	0.0537546i
$630$	4.15856	−	7.87987i	0.165681	−	0.313942i
$631$	0.614072	+	0.532096i	0.0244458	+	0.0211824i	0.666998	−	0.745060i	$-0.267579\pi$
$631$	0.614072	+	0.532096i	0.0244458	+	0.0211824i	−0.642552	+	0.766242i	$0.722124\pi$
$632$	11.9545	−	15.6732i	0.475523	−	0.623446i
$633$	−2.98692	−	23.2810i	−0.118720	−	0.925338i
$634$	−31.3775	−	28.6965i	−1.24616	−	1.13968i
$635$	−26.4259	−	7.75935i	−1.04868	−	0.307921i
$636$	21.0819	−	21.1918i	0.835951	−	0.840310i
$637$	15.0799	+	17.4031i	0.597485	+	0.689535i
$638$	0.571970	−	0.242903i	0.0226445	−	0.00961663i
$639$	−3.50473	−	31.0486i	−0.138645	−	1.22826i
$640$	19.8555	+	14.0556i	0.784858	+	0.555597i
$641$	−21.6956	−	3.11935i	−0.856924	−	0.123207i	−0.300171	−	0.953885i	$-0.597044\pi$
$641$	−21.6956	−	3.11935i	−0.856924	−	0.123207i	−0.556753	+	0.830678i	$0.687953\pi$
$642$	−3.26951	+	9.62063i	−0.129037	+	0.379696i
$643$		−	2.57371i		−	0.101497i	−0.998711	−	0.0507486i	$-0.983839\pi$
$643$		−	2.57371i		−	0.101497i	0.998711	−	0.0507486i	$-0.0161607\pi$
$644$	−4.58948	−	8.16676i	−0.180851	−	0.321815i
$645$	15.3099	−	12.8640i	0.602828	−	0.506520i
$646$	−21.2160	+	12.8447i	−0.834733	+	0.505367i
$647$	−4.54504	+	31.6114i	−0.178684	+	1.24277i	0.681129	+	0.732164i	$0.261489\pi$
$647$	−4.54504	+	31.6114i	−0.178684	+	1.24277i	−0.859812	+	0.510610i	$0.829420\pi$
$648$	19.2115	−	16.7009i	0.754698	−	0.656073i
$649$	−1.82024	+	0.534470i	−0.0714506	+	0.0209798i
$650$	0.792797	+	1.86682i	0.0310961	+	0.0732226i
$651$	12.0875	+	1.92585i	0.473747	+	0.0754802i
$652$	−46.5230	+	4.16080i	−1.82198	+	0.162950i
$653$	10.2910	−	35.0479i	0.402718	−	1.37153i	−0.469724	−	0.882813i	$-0.655647\pi$
$653$	10.2910	−	35.0479i	0.402718	−	1.37153i	0.872442	−	0.488718i	$-0.162535\pi$
$654$	−1.39698	+	33.2427i	−0.0546262	+	1.29989i
$655$	−7.44562	+	11.5856i	−0.290925	+	0.452688i
$656$	−27.3566	+	33.9403i	−1.06810	+	1.32515i
$657$	−8.04525	−	9.87588i	−0.313875	−	0.385295i
$658$	−1.59606	+	4.94172i	−0.0622207	+	0.192648i
$659$	−5.26305	−	36.6053i	−0.205019	−	1.42594i	−0.789110	−	0.614252i	$-0.789458\pi$
$659$	−5.26305	−	36.6053i	−0.205019	−	1.42594i	0.584091	−	0.811688i	$-0.301451\pi$
$660$	−0.664962	+	3.09551i	−0.0258836	+	0.120493i
$661$	3.51908	+	7.70571i	0.136876	+	0.299717i	0.965641	−	0.259880i	$-0.0836830\pi$
$661$	3.51908	+	7.70571i	0.136876	+	0.299717i	−0.828765	+	0.559597i	$0.810956\pi$
$662$	4.55211	+	17.1949i	0.176923	+	0.668301i
$663$	−15.6460	+	4.33691i	−0.607639	+	0.168432i
$664$	4.52851	−	19.9508i	0.175740	−	0.774241i
$665$	8.09024	+	12.5887i	0.313726	+	0.488167i
$666$	3.24420	−	16.0044i	0.125710	−	0.620158i
$667$	3.76488	−	3.22548i	0.145777	−	0.124891i
$668$	−15.8480	−	0.850293i	−0.613179	−	0.0328988i
$669$	−1.34596	−	0.417530i	−0.0520377	−	0.0161426i
$670$	−2.25605	+	13.1744i	−0.0871588	+	0.508970i
$671$	1.03020	−	2.25583i	0.0397706	−	0.0870854i
$672$	−7.19186	−	6.31285i	−0.277432	−	0.243523i
$673$	6.27903	+	13.7491i	0.242039	+	0.529991i	0.991196	−	0.132401i	$-0.0422687\pi$
$673$	6.27903	+	13.7491i	0.242039	+	0.529991i	−0.749158	+	0.662392i	$0.769541\pi$
$674$	20.2702	+	24.7006i	0.780778	+	0.951430i
$675$	1.53556	−	1.21257i	0.0591038	−	0.0466718i
$676$	−2.84029	−	1.00216i	−0.109242	−	0.0385447i
$677$	−22.8977	−	19.8410i	−0.880030	−	0.762550i	0.0924059	−	0.995721i	$-0.470544\pi$
$677$	−22.8977	−	19.8410i	−0.880030	−	0.762550i	−0.972436	+	0.233171i	$0.925090\pi$
$678$	3.81054	+	37.6746i	0.146343	+	1.44689i
$679$	3.36567	−	5.23708i	0.129162	−	0.200981i
$680$	−10.6790	+	10.4884i	−0.409521	+	0.402214i
$681$	−30.7312	+	13.4738i	−1.17762	+	0.516319i
$682$	−4.32024	+	0.503403i	−0.165431	+	0.0192763i
$683$	−5.63727	−	6.50576i	−0.215704	−	0.248936i	0.637577	−	0.770386i	$-0.279937\pi$
$683$	−5.63727	−	6.50576i	−0.215704	−	0.248936i	−0.853282	+	0.521450i	$0.825391\pi$
$684$	8.56083	+	41.8873i	0.327331	+	1.60160i
$685$	35.5368	−	10.4346i	1.35779	−	0.398684i
$686$	−16.1848	−	7.92222i	−0.617940	−	0.302472i
$687$	17.2742	+	27.7992i	0.659052	+	1.06061i
$688$	−9.61161	−	19.2065i	−0.366439	−	0.732241i
$689$			32.8654i			1.25207i
$690$	2.40083	+	25.1450i	0.0913982	+	0.957255i
$691$			29.3861i			1.11790i	0.829202	+	0.558950i	$0.188795\pi$
$691$			29.3861i			1.11790i	−0.829202	+	0.558950i	$0.811205\pi$
$692$	−3.74361	−	6.57494i	−0.142311	−	0.249942i
$693$	0.387041	−	1.18379i	0.0147025	−	0.0449684i
$694$	6.49603	−	13.2712i	0.246586	−	0.503767i
$695$	−26.6076	+	7.81269i	−1.00928	+	0.296352i
$696$	2.53388	−	4.38476i	0.0960466	−	0.166204i
$697$	−17.5649	−	20.2710i	−0.665319	−	0.767819i
$698$	−2.33201	−	20.0135i	−0.0882680	−	0.757522i
$699$	1.10087	+	2.51087i	0.0416387	+	0.0949696i
$700$	−0.529274	−	0.510762i	−0.0200047	−	0.0193050i
$701$	0.926148	−	1.44111i	0.0349801	−	0.0544301i	−0.823323	−	0.567573i	$-0.807883\pi$
$701$	0.926148	−	1.44111i	0.0349801	−	0.0544301i	0.858303	+	0.513143i	$0.171519\pi$
$702$	−2.02442	+	27.9146i	−0.0764069	+	1.05357i
$703$	20.7273	+	17.9603i	0.781743	+	0.677385i
$704$	3.06728	+	1.46808i	0.115602	+	0.0553305i
$705$	9.32934	−	10.4417i	0.351363	−	0.393256i
$706$	−31.2822	+	25.6713i	−1.17732	+	0.966150i
$707$	2.03691	+	4.46021i	0.0766060	+	0.167744i
$708$	−9.23291	+	12.4008i	−0.346994	+	0.466051i
$709$	−3.59741	+	7.87723i	−0.135104	+	0.295836i	−0.965077	−	0.261968i	$-0.915629\pi$
$709$	−3.59741	+	7.87723i	−0.135104	+	0.295836i	0.829973	+	0.557804i	$0.188356\pi$
$710$	31.2170	+	5.34578i	1.17155	+	0.200623i
$711$	19.2734	−	8.10333i	0.722809	−	0.303899i
$712$	3.23345	−	40.1292i	0.121179	−	1.50391i
$713$	−31.6447	+	14.2377i	−1.18510	+	0.533205i
$714$	4.60786	−	3.66562i	0.172445	−	0.137182i
$715$	−1.88200	−	2.92845i	−0.0703828	−	0.109518i
$716$	2.09905	−	10.5498i	0.0784452	−	0.394264i
$717$	4.87055	+	17.5712i	0.181894	+	0.656207i
$718$	30.1102	−	7.97124i	1.12370	−	0.297484i
$719$	1.83098	+	4.00930i	0.0682842	+	0.149522i	0.940697	−	0.339249i	$-0.110173\pi$
$719$	1.83098	+	4.00930i	0.0682842	+	0.149522i	−0.872412	+	0.488770i	$0.837446\pi$
$720$	10.8407	+	23.4149i	0.404010	+	0.872621i
$721$	−0.550607	−	3.82956i	−0.0205057	−	0.142620i
$722$	−42.7590	−	13.8101i	−1.59133	−	0.513960i
$723$	−0.369365	+	24.3014i	−0.0137368	+	0.903778i
$724$	38.0372	+	27.4317i	1.41364	+	1.01949i
$725$	0.210445	−	0.327458i	0.00781572	−	0.0121615i
$726$	1.11272	−	26.4784i	0.0412970	−	0.982707i
$727$	9.63510	−	32.8142i	0.357346	−	1.21701i	−0.563182	−	0.826333i	$-0.690423\pi$
$727$	9.63510	−	32.8142i	0.357346	−	1.21701i	0.920528	−	0.390677i	$-0.127759\pi$
$728$	10.5009	−	0.656077i	0.389188	−	0.0243158i
$729$	26.4914	−	5.21607i	0.981162	−	0.193188i
$730$	11.8844	−	5.04703i	0.439860	−	0.186799i
$731$	12.6796	−	3.72305i	0.468970	−	0.137702i
$732$	−4.34739	−	19.7374i	−0.160684	−	0.729515i
$733$	−1.22814	+	8.54187i	−0.0453622	+	0.315501i	0.954489	+	0.298247i	$0.0964017\pi$
$733$	−1.22814	+	8.54187i	−0.0453622	+	0.315501i	−0.999851	+	0.0172548i	$0.994507\pi$
$734$	−9.87437	−	16.3099i	−0.364470	−	0.602008i
$735$	14.4855	+	17.2397i	0.534304	+	0.635895i
$736$	26.8653	+	3.77533i	0.990270	+	0.139161i
$737$			1.86836i			0.0688221i
$738$	−43.0880	+	16.7718i	−1.58609	+	0.617380i
$739$	12.5640	+	1.80643i	0.462175	+	0.0664508i	0.369470	−	0.929243i	$-0.379539\pi$
$739$	12.5640	+	1.80643i	0.462175	+	0.0664508i	0.0927056	+	0.995694i	$0.470448\pi$
$740$	14.6666	+	7.67290i	0.539153	+	0.282061i
$741$	−39.1529	−	26.0112i	−1.43832	−	0.955546i
$742$	−4.65895	−	10.9705i	−0.171035	−	0.402741i
$743$	−2.17158	−	2.50614i	−0.0796675	−	0.0919412i	0.714516	−	0.699619i	$-0.246647\pi$
$743$	−2.17158	−	2.50614i	−0.0796675	−	0.0919412i	−0.794184	+	0.607678i	$0.792101\pi$
$744$	−25.6636	+	24.4506i	−0.940874	+	0.896402i
$745$	16.5104	+	4.84789i	0.604894	+	0.177613i
$746$	18.2527	−	19.9580i	0.668280	−	0.730715i
$747$	14.7019	−	15.9598i	0.537913	−	0.583938i
$748$	−1.22387	+	1.69704i	−0.0447491	+	0.0620498i
$749$	3.06191	+	2.65316i	0.111880	+	0.0969442i
$750$	10.6718	+	26.2301i	0.389679	+	0.957790i
$751$	−9.16102	+	1.31716i	−0.334290	+	0.0480637i	−0.307416	−	0.951575i	$-0.599464\pi$
$751$	−9.16102	+	1.31716i	−0.334290	+	0.0480637i	−0.0268741	+	0.999639i	$0.508555\pi$
$752$	−8.57576	−	12.3542i	−0.312726	−	0.450510i
$753$	−18.4356	−	8.76029i	−0.671832	−	0.319243i
$754$	1.42495	+	5.38256i	0.0518938	+	0.196021i
$755$	17.6011	−	38.5411i	0.640570	−	1.40265i
$756$	−3.28137	−	9.60491i	−0.119342	−	0.349327i
$757$	25.8312	−	16.6007i	0.938852	−	0.603364i	0.0207831	−	0.999784i	$-0.493384\pi$
$757$	25.8312	−	16.6007i	0.938852	−	0.603364i	0.918069	+	0.396420i	$0.129748\pi$
$758$	−1.04349	+	38.9257i	−0.0379013	+	1.41385i
$759$	0.924050	+	3.40779i	0.0335409	+	0.123695i
$760$	−43.1956	−	3.48053i	−1.56687	−	0.126252i
$761$	9.99011	+	15.5449i	0.362141	+	0.563503i	0.973739	−	0.227666i	$-0.0731094\pi$
$761$	9.99011	+	15.5449i	0.362141	+	0.563503i	−0.611598	+	0.791169i	$0.709473\pi$
$762$	−27.0831	+	15.8393i	−0.981117	+	0.573799i
$763$	12.0676	+	5.51110i	0.436877	+	0.199515i
$764$	−23.8789	+	5.64143i	−0.863909	+	0.204100i
$765$	−15.3620	+	4.00783i	−0.555416	+	0.144903i
$766$	−24.8281	−	30.2547i	−0.897076	−	1.09315i
$767$	−2.41911	−	16.8253i	−0.0873490	−	0.607526i
$768$	27.1670	−	5.47294i	0.980305	−	0.197488i
$769$	23.6653	−	27.3112i	0.853392	−	0.984867i	−0.146598	−	0.989196i	$-0.546832\pi$
$769$	23.6653	−	27.3112i	0.853392	−	0.984867i	0.999991	+	0.00432885i	$0.00137792\pi$
$770$	1.04335	+	0.710732i	0.0375996	+	0.0256130i
$771$	−1.28770	−	10.0368i	−0.0463754	−	0.361465i
$772$	−27.4992	+	28.4959i	−0.989719	+	1.02559i
$773$	6.52494	−	22.2219i	0.234686	−	0.799267i	−0.754964	−	0.655766i	$-0.772346\pi$
$773$	6.52494	−	22.2219i	0.234686	−	0.799267i	0.989650	−	0.143501i	$-0.0458360\pi$
$774$	1.30225	−	22.7428i	0.0468083	−	0.817474i
$775$	−2.05904	+	1.78417i	−0.0739629	+	0.0640892i
$776$	6.14793	+	16.9476i	0.220698	+	0.608385i
$777$	−5.42343	−	3.60306i	−0.194565	−	0.129259i
$778$	10.9213	+	5.34579i	0.391546	+	0.191656i
$779$	11.0515	−	76.8648i	0.395961	−	2.75397i
$780$	−26.6062	−	9.84487i	−0.952655	−	0.352503i
$781$	4.42715			0.158416
$782$	−5.21937	+	15.8556i	−0.186644	+	0.566993i
$783$	4.64642	−	2.69505i	0.166049	−	0.0963131i
$784$	21.6274	−	10.8231i	0.772407	−	0.386540i
$785$	52.0925	+	7.48977i	1.85926	+	0.267321i
$786$	3.78407	+	15.2254i	0.134973	+	0.543073i
$787$	0.469208	+	1.59797i	0.0167254	+	0.0569616i	0.967433	−	0.253128i	$-0.0814592\pi$
$787$	0.469208	+	1.59797i	0.0167254	+	0.0569616i	−0.950707	+	0.310089i	$0.899641\pi$
$788$	−3.87586	+	1.52474i	−0.138072	+	0.0543165i
$789$	8.35213	+	1.33071i	0.297344	+	0.0473746i
$790$	2.45279	+	21.0500i	0.0872664	+	0.748927i
$791$	14.4870	+	4.25376i	0.515098	+	0.151246i
$792$	2.04606	+	2.97028i	0.0727036	+	0.105544i
$793$	18.6933	+	12.0135i	0.663820	+	0.426611i
$794$	−0.282997	−	0.192778i	−0.0100432	−	0.00684145i
$795$	−0.488411	+	32.1336i	−0.0173221	+	1.13966i
$796$	7.15519	−	20.2790i	0.253609	−	0.718769i
$797$	−0.993391	+	0.142828i	−0.0351877	+	0.00505923i	−0.159886	−	0.987135i	$-0.551113\pi$
$797$	−0.993391	+	0.142828i	−0.0351877	+	0.00505923i	0.124699	+	0.992195i	$0.460204\pi$
$798$	16.7566	+	3.13234i	0.593178	+	0.110884i
$799$	8.41716	−	3.84399i	0.297778	−	0.135990i
$800$	2.10564	−	0.321674i	0.0744458	−	0.0113729i
$801$	24.1672	−	35.2045i	0.853907	−	1.24389i
$802$	39.7090	+	6.79999i	1.40217	+	0.240116i
$803$	1.51832	−	0.975767i	0.0535805	−	0.0344341i
$804$	9.15652	+	12.1656i	0.322926	+	0.429048i
$805$	9.64759	+	2.89167i	0.340033	+	0.101918i
$806$	1.04436	−	38.9582i	0.0367861	−	1.37225i
$807$	19.3639	+	6.00687i	0.681640	+	0.211452i
$808$	−13.8476	−	3.14317i	−0.487156	−	0.110576i
$809$	−24.4495	−	11.1657i	−0.859599	−	0.392566i	−0.0636811	−	0.997970i	$-0.520284\pi$
$809$	−24.4495	−	11.1657i	−0.859599	−	0.392566i	−0.795918	+	0.605405i	$0.793011\pi$
$810$	−2.39418	+	27.2629i	−0.0841230	+	0.957922i
$811$	5.40026	−	2.46621i	0.189629	−	0.0866005i	−0.318338	−	0.947977i	$-0.603125\pi$
$811$	5.40026	−	2.46621i	0.189629	−	0.0866005i	0.507967	+	0.861377i	$0.330397\pi$
$812$	−1.23868	−	1.59471i	−0.0434690	−	0.0559633i
$813$	21.7299	−	24.3208i	0.762103	−	0.852968i
$814$	2.20176	+	0.711116i	0.0771717	+	0.0249246i
$815$	32.8851	−	37.9515i	1.15192	−	1.32938i
$816$	0.347800	+	17.0480i	0.0121754	+	0.596799i
$817$	32.1857	+	20.6845i	1.12603	+	0.723658i
$818$	3.66143	−	4.00351i	0.128019	−	0.139979i
$819$	10.0055	+	4.94222i	0.349621	+	0.172695i
$820$	−4.17491	−	46.6807i	−0.145794	−	1.63016i
$821$	6.30148	−	5.46027i	0.219923	−	0.190565i	−0.537930	−	0.842989i	$-0.680794\pi$
$821$	6.30148	−	5.46027i	0.219923	−	0.190565i	0.757853	+	0.652425i	$0.226248\pi$
$822$	19.1231	−	37.6094i	0.666995	−	1.31178i
$823$	2.50231	+	8.52209i	0.0872250	+	0.297061i	0.991539	−	0.129806i	$-0.0414354\pi$
$823$	2.50231	+	8.52209i	0.0872250	+	0.297061i	−0.904314	+	0.426867i	$0.859617\pi$
$824$	9.78503	+	5.45795i	0.340878	+	0.190137i
$825$	0.146318	+	0.235469i	0.00509415	+	0.00819796i
$826$	3.19263	+	5.27338i	0.111086	+	0.183484i
$827$	−32.2311			−1.12079			−0.560393	−	0.828227i	$-0.689350\pi$
$827$	−32.2311			−1.12079			−0.560393	+	0.828227i	$0.689350\pi$
$828$	22.7178	+	17.6608i	0.789498	+	0.613754i
$829$	−9.86128			−0.342496			−0.171248	−	0.985228i	$-0.554780\pi$
$829$	−9.86128			−0.342496			−0.171248	+	0.985228i	$0.554780\pi$
$830$	11.3912	+	18.8153i	0.395396	+	0.653090i
$831$	−13.2100	−	21.2588i	−0.458251	−	0.737458i
$832$	−16.9318	+	25.3317i	−0.587004	+	0.878219i
$833$	4.19233	+	14.2778i	0.145256	+	0.494695i
$834$	−14.3181	+	28.1594i	−0.495795	+	0.975079i
$835$	12.8953	−	11.1738i	0.446259	−	0.386686i
$836$	−6.03352	+	0.539611i	−0.208674	+	0.0186628i
$837$	−36.5190	+	8.93700i	−1.26228	+	0.308908i
$838$	28.3811	−	31.0326i	0.980409	−	1.07201i
$839$	38.5449	+	24.7713i	1.33072	+	0.855201i	0.996192	−	0.0871854i	$-0.0277872\pi$
$839$	38.5449	+	24.7713i	1.33072	+	0.855201i	0.334527	+	0.942386i	$0.391424\pi$
$840$	10.2768	−	0.485416i	0.354583	−	0.0167485i
$841$	−18.2912	+	21.1091i	−0.630730	+	0.727901i
$842$	23.5209	+	7.59667i	0.810582	+	0.261799i
$843$	−14.0641	+	15.7410i	−0.484395	+	0.542149i
$844$	21.4045	−	16.6258i	0.736775	−	0.572283i
$845$	2.94551	−	1.34517i	0.101329	−	0.0462752i
$846$	−1.36379	−	15.8928i	−0.0468882	−	0.546405i
$847$	−9.61210	−	4.38970i	−0.330276	−	0.150832i
$848$	33.4434	+	8.53960i	1.14845	+	0.293251i
$849$	33.4121	+	10.3648i	1.14670	+	0.355718i
$850$	−0.0351215	+	1.31015i	−0.00120466	+	0.0449379i
$851$	18.4588	+	0.103552i	0.632761	+	0.00354971i
$852$	28.8268	−	21.6967i	0.987590	−	0.743315i
$853$	0.612434	−	0.393587i	0.0209693	−	0.0134762i	−0.530114	−	0.847926i	$-0.677851\pi$
$853$	0.612434	−	0.393587i	0.0209693	−	0.0134762i	0.551083	+	0.834450i	$0.314215\pi$
$854$	−7.94288	−	1.36018i	−0.271800	−	0.0465445i
$855$	−37.8946	−	26.0139i	−1.29597	−	0.889657i
$856$	−11.4868	+	2.39070i	−0.392610	+	0.0817125i
$857$	−8.65613	+	3.95312i	−0.295688	+	0.135036i	−0.557735	−	0.830019i	$-0.688330\pi$
$857$	−8.65613	+	3.95312i	−0.295688	+	0.135036i	0.262047	+	0.965055i	$0.415602\pi$
$858$	−3.89803	−	0.728664i	−0.133076	−	0.0248762i
$859$	39.7626	−	5.71700i	1.35668	−	0.195062i	0.574702	−	0.818363i	$-0.305118\pi$
$859$	39.7626	−	5.71700i	1.35668	−	0.195062i	0.781982	+	0.623301i	$0.214209\pi$
$860$	21.7748	+	7.68297i	0.742514	+	0.261987i
$861$	−0.280184	+	18.4339i	−0.00954863	+	0.628226i
$862$	−36.2591	−	24.6998i	−1.23499	−	0.841279i
$863$	−40.8538	−	26.2552i	−1.39068	−	0.893736i	−0.391036	−	0.920376i	$-0.627883\pi$
$863$	−40.8538	−	26.2552i	−1.39068	−	0.893736i	−0.999645	+	0.0266392i	$0.991519\pi$
$864$	27.8795	+	9.31322i	0.948478	+	0.316842i
$865$	7.80480	+	2.29170i	0.265371	+	0.0779200i
$866$	3.44912	+	29.6006i	0.117206	+	1.00587i
$867$	18.7171	+	2.98211i	0.635665	+	0.101278i
$868$	5.17405	+	13.1524i	0.175619	+	0.446421i
$869$	0.834592	+	2.84236i	0.0283116	+	0.0964205i
$870$	1.31324	+	5.28388i	0.0445229	+	0.179140i
$871$	−16.5706	−	2.38249i	−0.561472	−	0.0807275i
$872$	−33.8841	+	18.1081i	−1.14746	+	0.613216i
$873$	−3.29531	+	18.8358i	−0.111529	+	0.637496i
$874$	−44.5878	+	18.6410i	−1.50821	+	0.630540i
$875$	11.2912			0.381712
$876$	5.10431	−	13.7946i	0.172459	−	0.466077i
$877$	2.56504	−	17.8403i	0.0866154	−	0.602423i	−0.899570	−	0.436777i	$-0.856120\pi$
$877$	2.56504	−	17.8403i	0.0866154	−	0.602423i	0.986185	−	0.165646i	$-0.0529710\pi$
$878$	−15.0998	−	7.39111i	−0.509593	−	0.249438i
$879$	15.8781	+	10.5486i	0.535556	+	0.355797i
$880$	−3.46896	+	1.15418i	−0.116939	+	0.0389075i
$881$	−17.6466	+	15.2908i	−0.594528	+	0.515161i	−0.899339	−	0.437252i	$-0.855952\pi$
$881$	−17.6466	+	15.2908i	−0.594528	+	0.515161i	0.304812	+	0.952413i	$0.401406\pi$
$882$	25.6095	+	1.46639i	0.862315	+	0.0493758i
$883$	4.09539	−	13.9476i	0.137821	−	0.469374i	−0.861438	−	0.507862i	$-0.830436\pi$
$883$	4.09539	−	13.9476i	0.137821	−	0.469374i	0.999259	+	0.0384880i	$0.0122541\pi$
$884$	−13.4904	−	13.0185i	−0.453731	−	0.437861i
$885$	−2.11521	−	16.4866i	−0.0711019	−	0.554191i
$886$	3.86433	+	2.63239i	0.129825	+	0.0884370i
$887$	29.8958	−	34.5016i	1.00380	−	1.15845i	0.0164587	−	0.999865i	$-0.494761\pi$
$887$	29.8958	−	34.5016i	1.00380	−	1.15845i	0.987345	−	0.158587i	$-0.0506938\pi$
$888$	17.8215	−	6.16010i	0.598052	−	0.206719i
$889$	1.78036	+	12.3827i	0.0597114	+	0.415302i
$890$	27.4577	+	33.4591i	0.920385	+	1.12155i
$891$	0.313372	+	3.81272i	0.0104984	+	0.127731i
$892$	−0.374139	−	1.58365i	−0.0125271	−	0.0530244i
$893$	24.3691	+	11.1290i	0.815480	+	0.372417i
$894$	16.9210	−	9.89609i	0.565921	−	0.330975i
$895$	6.25225	+	9.72869i	0.208990	+	0.325194i
$896$	2.06088	−	10.8560i	0.0688491	−	0.362673i
$897$	−31.4021	+	3.84991i	−1.04848	+	0.128545i
$898$	−1.10939	+	41.3841i	−0.0370209	+	1.38100i
$899$	−6.29222	+	4.04376i	−0.209857	+	0.134867i
$900$	2.10672	+	0.816144i	0.0702240	+	0.0272048i
$901$	−8.82249	+	19.3186i	−0.293920	+	0.643595i
$902$	−1.67659	−	6.33307i	−0.0558243	−	0.210868i
$903$	−8.20395	−	3.89837i	−0.273010	−	0.129730i
$904$	−35.2380	+	25.8872i	−1.17200	+	0.860994i
$905$	−49.9062	+	7.17543i	−1.65894	+	0.238519i
$906$	−18.1897	−	44.7084i	−0.604313	−	1.48534i
$907$	40.8911	+	35.4323i	1.35777	+	1.17651i	0.966630	+	0.256178i	$0.0824634\pi$
$907$	40.8911	+	35.4323i	1.35777	+	1.17651i	0.391136	+	0.920333i	$0.372082\pi$
$908$	−31.4263	−	22.6640i	−1.04292	−	0.752131i
$909$	−11.0775	−	10.2043i	−0.367416	−	0.338457i
$910$	−7.63395	+	8.34716i	−0.253063	+	0.276706i
$911$	−43.4245	−	12.7506i	−1.43872	−	0.422446i	−0.532923	−	0.846164i	$-0.678907\pi$
$911$	−43.4245	−	12.7506i	−1.43872	−	0.422446i	−0.905794	+	0.423718i	$0.860725\pi$
$912$	−36.6420	+	33.0828i	−1.21334	+	1.09548i
$913$	2.01339	+	2.32357i	0.0666334	+	0.0768991i
$914$	−21.6586	−	51.0001i	−0.716404	−	1.68693i
$915$	18.0986	+	12.0238i	0.598320	+	0.397494i
$916$	−17.5187	+	33.4866i	−0.578835	+	1.10643i
$917$	6.19182	+	0.890250i	0.204472	+	0.0293986i
$918$	−8.68345	+	15.8650i	−0.286596	+	0.523622i
$919$			49.8869i			1.64562i	0.568318	+	0.822809i	$0.307594\pi$
$919$			49.8869i			1.64562i	−0.568318	+	0.822809i	$0.692406\pi$
$920$	−23.6023	+	17.1361i	−0.778145	+	0.564961i
$921$	12.2039	+	14.5244i	0.402134	+	0.478594i
$922$	−23.4368	−	38.7114i	−0.771850	−	1.27489i
$923$	−5.64538	+	39.2645i	−0.185820	+	1.29241i
$924$	1.40446	−	0.309349i	0.0462034	−	0.0101768i
$925$	1.39062	−	0.408323i	0.0457233	−	0.0134256i
$926$	28.7285	−	12.2004i	0.944077	−	0.400929i
$927$	6.11814	+	10.1881i	0.200946	+	0.334620i
$928$	5.84747	−	0.0514344i	0.191953	−	0.00168842i
$929$	−12.6006	+	42.9138i	−0.413414	+	1.40796i	0.445245	+	0.895409i	$0.353117\pi$
$929$	−12.6006	+	42.9138i	−0.413414	+	1.40796i	−0.858658	+	0.512549i	$0.828701\pi$
$930$	1.60006	−	38.0753i	0.0524681	−	1.24854i
$931$	−23.2917	+	36.2425i	−0.763353	+	1.18780i
$932$	−1.85174	+	2.56766i	−0.0606559	+	0.0841063i
$933$	0.834083	−	54.8762i	0.0273066	−	1.79656i
$934$	−6.89275	−	2.22619i	−0.225538	−	0.0728432i
$935$	−0.320133	−	2.22658i	−0.0104695	−	0.0728168i
$936$	−28.9525	+	14.3589i	−0.946344	+	0.469336i
$937$	16.4128	+	35.9391i	0.536184	+	1.17408i	0.962941	+	0.269713i	$0.0869289\pi$
$937$	16.4128	+	35.9391i	0.536184	+	1.17408i	−0.426756	+	0.904367i	$0.640344\pi$
$938$	5.86902	−	1.55374i	0.191630	−	0.0507314i
$939$	8.06464	+	29.0943i	0.263180	+	0.949456i
$940$	15.8577	+	3.15514i	0.517220	+	0.102909i
$941$	7.62910	+	11.8711i	0.248702	+	0.386987i	0.943050	−	0.332652i	$-0.107943\pi$
$941$	7.62910	+	11.8711i	0.248702	+	0.386987i	−0.694348	+	0.719639i	$0.744307\pi$
$942$	46.9179	−	37.3238i	1.52867	−	1.21608i
$943$	−28.0100	−	44.1267i	−0.912130	−	1.43696i
$944$	−17.7497	−	1.91015i	−0.577705	−	0.0621701i
$945$	9.70928	+	4.98086i	0.315843	+	0.162027i
$946$	3.18136	+	0.544793i	0.103435	+	0.0177127i
$947$	−4.91974	+	10.7727i	−0.159870	+	0.350066i	−0.972568	−	0.232619i	$-0.925271\pi$
$947$	−4.91974	+	10.7727i	−0.159870	+	0.350066i	0.812698	+	0.582685i	$0.197998\pi$
$948$	19.3642	+	14.4175i	0.628921	+	0.468258i
$949$	6.71797	+	14.7103i	0.218075	+	0.477517i
$950$	−2.93323	+	2.40711i	−0.0951665	+	0.0780970i
$951$	34.6977	−	38.8347i	1.12515	−	1.25930i
$952$	6.34861	+	2.43323i	0.205760	+	0.0788616i
$953$	13.8634	+	12.0127i	0.449081	+	0.389131i	0.849830	−	0.527057i	$-0.176705\pi$
$953$	13.8634	+	12.0127i	0.449081	+	0.389131i	−0.400749	+	0.916188i	$0.631250\pi$
$954$	26.2524	+	25.5171i	0.849952	+	0.826145i
$955$	14.2617	−	22.1916i	0.461497	−	0.718103i
$956$	−14.6204	+	15.1504i	−0.472859	+	0.489998i
$957$	0.305602	+	0.697018i	0.00987871	+	0.0225314i
$958$	1.31353	+	11.2728i	0.0424381	+	0.364207i
$959$	−11.0168	−	12.7141i	−0.355751	−	0.410559i
$960$	−16.9312	+	24.5160i	−0.546453	+	0.791252i
$961$	20.4872	−	6.01560i	0.660879	−	0.194052i
$962$	−9.11453	+	18.6207i	−0.293864	+	0.600355i
$963$	−11.8285	−	3.86734i	−0.381167	−	0.124623i
$964$	−24.3880	+	13.8859i	−0.785483	+	0.447235i
$965$		−	42.5753i		−	1.37055i
$966$	9.93631	−	5.73661i	0.319695	−	0.184572i
$967$		−	21.3513i		−	0.686611i	−0.939224	−	0.343305i	$-0.888453\pi$
$967$		−	21.3513i		−	0.686611i	0.939224	−	0.343305i	$-0.111547\pi$
$968$	26.9894	−	14.4234i	0.867471	−	0.463587i
$969$	−16.0319	−	25.7999i	−0.515018	−	0.828814i
$970$	−17.4088	−	8.52132i	−0.558962	−	0.273603i
$971$	34.4380	−	10.1119i	1.10517	−	0.324506i	0.322264	−	0.946650i	$-0.395556\pi$
$971$	34.4380	−	10.1119i	1.10517	−	0.324506i	0.782903	+	0.622144i	$0.213738\pi$
$972$	20.7259	+	23.2902i	0.664785	+	0.747035i
$973$	8.24863	+	9.51943i	0.264439	+	0.305179i
$974$	32.0335	−	3.73260i	1.02642	−	0.119600i
$975$	−2.27496	+	0.997436i	−0.0728569	+	0.0319435i
$976$	17.0819	−	15.9005i	0.546779	−	0.508964i
$977$	15.2167	−	23.6777i	0.486826	−	0.757516i	−0.507753	−	0.861503i	$-0.669524\pi$
$977$	15.2167	−	23.6777i	0.486826	−	0.757516i	0.994579	+	0.103987i	$0.0331599\pi$
$978$	−5.75666	−	56.9158i	−0.184078	−	1.81997i
$979$	4.57250	+	3.96209i	0.146138	+	0.126629i
$980$	−8.65137	+	24.5194i	−0.276358	+	0.783243i
$981$	−40.7309	−	1.23845i	−1.30044	−	0.0395408i
$982$	−18.5629	−	22.6202i	−0.592366	−	0.721838i
$983$	19.8774	+	43.5255i	0.633991	+	1.38825i	0.904892	+	0.425640i	$0.139951\pi$
$983$	19.8774	+	43.5255i	0.633991	+	1.38825i	−0.270901	+	0.962607i	$0.587322\pi$
$984$	−41.9541	−	33.0203i	−1.33745	−	1.05265i
$985$	1.86016	−	4.07317i	0.0592695	−	0.129782i
$986$	−0.607310	+	3.54643i	−0.0193407	+	0.112941i
$987$	−6.07462	−	1.88441i	−0.193357	−	0.0599814i
$988$	2.90797	−	54.1995i	0.0925147	−	1.72432i
$989$	25.5084	−	3.52161i	0.811120	−	0.111981i
$990$	−3.80040	−	0.770367i	−0.120785	−	0.0244839i
$991$	1.99223	+	3.09996i	0.0632851	+	0.0984736i	0.871454	−	0.490477i	$-0.163178\pi$
$991$	1.99223	+	3.09996i	0.0632851	+	0.0984736i	−0.808169	+	0.588951i	$0.799541\pi$
$992$	−39.3720	−	11.1855i	−1.25006	−	0.355139i
$993$	−20.9933	+	5.81914i	−0.666203	+	0.184665i
$994$	−3.68163	−	13.9068i	−0.116774	−	0.441098i
$995$	9.60417	+	21.0302i	0.304473	+	0.666702i
$996$	24.4973	+	5.26240i	0.776228	+	0.166746i
$997$	5.66516	+	39.4021i	0.179417	+	1.24788i	0.858115	+	0.513458i	$0.171636\pi$
$997$	5.66516	+	39.4021i	0.179417	+	1.24788i	−0.678697	+	0.734418i	$0.737455\pi$
$998$	−10.4292	+	32.2910i	−0.330131	+	1.02215i
$999$	19.6461	+	3.74563i	0.621575	+	0.118506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.35.7	✓	440
3.2	odd	2	inner	276.2.o.a.35.38	yes	440
4.3	odd	2	inner	276.2.o.a.35.37	yes	440
12.11	even	2	inner	276.2.o.a.35.8	yes	440
23.2	even	11	inner	276.2.o.a.71.8	yes	440
69.2	odd	22	inner	276.2.o.a.71.37	yes	440
92.71	odd	22	inner	276.2.o.a.71.38	yes	440
276.71	even	22	inner	276.2.o.a.71.7	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.35.7	✓	440	1.1	even	1	trivial
276.2.o.a.35.8	yes	440	12.11	even	2	inner
276.2.o.a.35.37	yes	440	4.3	odd	2	inner
276.2.o.a.35.38	yes	440	3.2	odd	2	inner
276.2.o.a.71.7	yes	440	276.71	even	22	inner
276.2.o.a.71.8	yes	440	23.2	even	11	inner
276.2.o.a.71.37	yes	440	69.2	odd	22	inner
276.2.o.a.71.38	yes	440	92.71	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20977 + 0.732426i) q^{2} +(-0.914165 - 1.47116i) q^{3} +(0.927105 - 1.77214i) q^{4} +(0.605787 + 2.06312i) q^{5} +(2.18345 + 1.11021i) q^{6} +(0.738126 - 0.639590i) q^{7} +(0.176372 + 2.82292i) q^{8} +(-1.32861 + 2.68976i) q^{9} +O(q^{10})\)	\(q+(-1.20977 + 0.732426i) q^{2} +(-0.914165 - 1.47116i) q^{3} +(0.927105 - 1.77214i) q^{4} +(0.605787 + 2.06312i) q^{5} +(2.18345 + 1.11021i) q^{6} +(0.738126 - 0.639590i) q^{7} +(0.176372 + 2.82292i) q^{8} +(-1.32861 + 2.68976i) q^{9} +(-2.24395 - 2.05222i) q^{10} +(-0.357587 - 0.229807i) q^{11} +(-3.45462 + 0.256109i) q^{12} +(2.49415 - 2.87840i) q^{13} +(-0.424514 + 1.31438i) q^{14} +(2.48139 - 2.77724i) q^{15} +(-2.28095 - 3.28592i) q^{16} +(2.23877 - 1.02241i) q^{17} +(-0.362737 - 4.22711i) q^{18} +(6.48160 + 2.96005i) q^{19} +(4.21777 + 0.839193i) q^{20} +(-1.61571 - 0.501209i) q^{21} +(0.600915 + 0.0161089i) q^{22} +(4.60907 - 1.32531i) q^{23} +(3.99173 - 2.84009i) q^{24} +(0.316772 - 0.203577i) q^{25} +(-0.909141 + 5.30899i) q^{26} +(5.17162 - 0.504297i) q^{27} +(-0.449121 - 1.90103i) q^{28} +(0.940319 - 0.429429i) q^{29} +(-0.967794 + 5.17727i) q^{30} +(-7.16183 + 1.02972i) q^{31} +(5.16613 + 2.30459i) q^{32} +(-0.0111890 + 0.736147i) q^{33} +(-1.95956 + 2.87662i) q^{34} +(1.76670 + 1.13539i) q^{35} +(3.53487 + 4.84816i) q^{36} +(3.69308 + 1.08439i) q^{37} +(-10.0093 + 1.16630i) q^{38} +(-6.51464 - 1.03795i) q^{39} +(-5.71719 + 2.07397i) q^{40} +(-3.07037 - 10.4567i) q^{41} +(2.32174 - 0.577035i) q^{42} +(5.31467 + 0.764134i) q^{43} +(-0.738770 + 0.420638i) q^{44} +(-6.35416 - 1.11165i) q^{45} +(-4.60525 + 4.97913i) q^{46} +3.75973 q^{47} +(-2.74894 + 6.35951i) q^{48} +(-0.860449 + 5.98455i) q^{49} +(-0.234117 + 0.478294i) q^{50} +(-3.55073 - 2.35893i) q^{51} +(-2.78859 - 7.08855i) q^{52} +(-6.52145 + 5.65086i) q^{53} +(-5.88713 + 4.39791i) q^{54} +(0.257498 - 0.876959i) q^{55} +(1.93570 + 1.97087i) q^{56} +(-1.57056 - 12.2414i) q^{57} +(-0.823049 + 1.20823i) q^{58} +(2.92268 - 3.37295i) q^{59} +(-2.62115 - 6.97216i) q^{60} +(0.830304 + 5.77489i) q^{61} +(7.91001 - 6.49123i) q^{62} +(0.739665 + 2.83514i) q^{63} +(-7.93779 + 0.995768i) q^{64} +(7.44941 + 3.40203i) q^{65} +(-0.525637 - 0.898767i) q^{66} +(-2.37638 - 3.69772i) q^{67} +(0.263720 - 4.91529i) q^{68} +(-6.16319 - 5.56912i) q^{69} +(-2.96889 - 0.0795877i) q^{70} +(-8.76187 + 5.63091i) q^{71} +(-7.82731 - 3.27615i) q^{72} +(-1.76386 + 3.86232i) q^{73} +(-5.26203 + 1.39305i) q^{74} +(-0.589075 - 0.279918i) q^{75} +(11.2547 - 8.74202i) q^{76} +(-0.410926 + 0.0590823i) q^{77} +(8.64146 - 3.51580i) q^{78} +(-5.26697 - 4.56386i) q^{79} +(5.39748 - 6.69645i) q^{80} +(-5.46962 - 7.14726i) q^{81} +(11.3732 + 10.4015i) q^{82} +(-6.94011 - 2.03780i) q^{83} +(-2.38614 + 2.39858i) q^{84} +(3.46557 + 3.99949i) q^{85} +(-6.98922 + 2.96817i) q^{86} +(-1.49136 - 0.990788i) q^{87} +(0.585659 - 1.04997i) q^{88} +(-14.0889 - 2.02568i) q^{89} +(8.50129 - 3.30910i) q^{90} -3.71985i q^{91} +(1.92447 - 9.39662i) q^{92} +(8.06197 + 9.59485i) q^{93} +(-4.54842 + 2.75372i) q^{94} +(-2.18047 + 15.1655i) q^{95} +(-1.33227 - 9.70696i) q^{96} +(6.11578 - 1.79575i) q^{97} +(-3.34229 - 7.87017i) q^{98} +(1.09322 - 0.656499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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