LMFDB - Embedded newform 855.2.da.b.424.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(199,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("855.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.da (of order $18$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			424.2
Character	$\chi$	$=$	855.424
Dual form			855.2.da.b.244.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14717 - 1.36714i) q^{2} +(-0.205786 + 1.16707i) q^{4} +(-1.67705 + 1.47903i) q^{5} +(-3.67118 - 2.11955i) q^{7} +(-1.25953 + 0.727188i) q^{8} +(3.94589 + 0.596068i) q^{10} +(-0.245445 - 0.425123i) q^{11} +(1.42349 + 3.91099i) q^{13} +(1.31373 + 7.45051i) q^{14} +(4.66628 + 1.69839i) q^{16} +(1.30884 + 1.55982i) q^{17} +(-1.86816 - 3.93827i) q^{19} +(-1.38102 - 2.26160i) q^{20} +(-0.299637 + 0.823245i) q^{22} +(4.32847 + 0.763227i) q^{23} +(0.624964 - 4.96079i) q^{25} +(3.71391 - 6.43268i) q^{26} +(3.22915 - 3.84835i) q^{28} +(-2.49937 - 2.09722i) q^{29} +(-2.04416 + 3.54059i) q^{31} +(-2.03622 - 5.59447i) q^{32} +(0.631029 - 3.57874i) q^{34} +(9.29160 - 1.87517i) q^{35} -2.14440i q^{37} +(-3.24108 + 7.07191i) q^{38} +(1.03675 - 3.08240i) q^{40} +(4.10271 + 1.49327i) q^{41} +(10.4627 - 1.84485i) q^{43} +(0.546658 - 0.198967i) q^{44} +(-3.92205 - 6.79319i) q^{46} +(1.68502 - 2.00812i) q^{47} +(5.48502 + 9.50033i) q^{49} +(-7.49905 + 4.83645i) q^{50} +(-4.85735 + 0.856482i) q^{52} +(11.2604 + 1.98551i) q^{53} +(1.04039 + 0.349931i) q^{55} +6.16526 q^{56} +5.82287i q^{58} +(-0.415431 + 0.348588i) q^{59} +(-2.36895 + 13.4350i) q^{61} +(7.18550 - 1.26700i) q^{62} +(-0.346803 + 0.600680i) q^{64} +(-8.17171 - 4.45354i) q^{65} +(4.60042 - 5.48257i) q^{67} +(-2.08976 + 1.20652i) q^{68} +(-13.2227 - 10.5518i) q^{70} +(-1.04859 - 5.94684i) q^{71} +(-0.702575 + 1.93031i) q^{73} +(-2.93170 + 2.45999i) q^{74} +(4.98069 - 1.36984i) q^{76} +2.08093i q^{77} +(5.01823 + 1.82649i) q^{79} +(-10.3375 + 4.05327i) q^{80} +(-2.66500 - 7.32202i) q^{82} +(-7.02847 - 4.05789i) q^{83} +(-4.50199 - 0.680073i) q^{85} +(-14.5246 - 12.1876i) q^{86} +(0.618288 + 0.356969i) q^{88} +(4.07920 - 1.48471i) q^{89} +(3.06370 - 17.3751i) q^{91} +(-1.78148 + 4.89458i) q^{92} -4.67839 q^{94} +(8.95780 + 3.84160i) q^{95} +(3.62962 + 4.32562i) q^{97} +(6.69607 - 18.3973i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49}+ \cdots + 63 q^{95}+O(q^{100}) $ 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−1.14717	−	1.36714i	−0.811171	−	0.966716i	0.188712	−	0.982033i	$-0.439569\pi$
$2$	−1.14717	−	1.36714i	−0.811171	−	0.966716i	−0.999883	+	0.0153165i	$0.995124\pi$
$3$		0			0
$3$		0			0
$4$	−0.205786	+	1.16707i	−0.102893	+	0.583536i
$5$	−1.67705	+	1.47903i	−0.749998	+	0.661441i
$5$	−1.67705	+	1.47903i	−0.749998	+	0.661441i
$6$		0			0
$7$	−3.67118	−	2.11955i	−1.38757	−	0.801116i	−0.394532	−	0.918882i	$-0.629093\pi$
$7$	−3.67118	−	2.11955i	−1.38757	−	0.801116i	−0.993041	+	0.117766i	$0.962427\pi$
$8$	−1.25953	+	0.727188i	−0.445310	+	0.257100i
$9$		0			0
$10$	3.94589	+	0.596068i	1.24780	+	0.188493i
$11$	−0.245445	−	0.425123i	−0.0740043	−	0.128179i	0.826649	−	0.562719i	$-0.190245\pi$
$11$	−0.245445	−	0.425123i	−0.0740043	−	0.128179i	−0.900653	+	0.434539i	$0.856911\pi$
$12$		0			0
$13$	1.42349	+	3.91099i	0.394804	+	1.08471i	0.964781	+	0.263054i	$0.0847298\pi$
$13$	1.42349	+	3.91099i	0.394804	+	1.08471i	−0.569977	+	0.821661i	$0.693048\pi$
$14$	1.31373	+	7.45051i	0.351108	+	1.99123i
$15$		0			0
$16$	4.66628	+	1.69839i	1.16657	+	0.424596i
$17$	1.30884	+	1.55982i	0.317440	+	0.378311i	0.901044	−	0.433728i	$-0.142802\pi$
$17$	1.30884	+	1.55982i	0.317440	+	0.378311i	−0.583603	+	0.812039i	$0.698358\pi$
$18$		0			0
$19$	−1.86816	−	3.93827i	−0.428586	−	0.903501i
$19$	−1.86816	−	3.93827i	−0.428586	−	0.903501i
$20$	−1.38102	−	2.26160i	−0.308805	−	0.505709i
$21$		0			0
$22$	−0.299637	+	0.823245i	−0.0638828	+	0.175517i
$23$	4.32847	+	0.763227i	0.902549	+	0.159144i	0.605618	−	0.795755i	$-0.292926\pi$
$23$	4.32847	+	0.763227i	0.902549	+	0.159144i	0.296931	+	0.954899i	$0.404037\pi$
$24$		0			0
$25$	0.624964	−	4.96079i	0.124993	−	0.992158i
$26$	3.71391	−	6.43268i	0.728358	−	1.26155i
$27$		0			0
$28$	3.22915	−	3.84835i	0.610252	−	0.727270i
$29$	−2.49937	−	2.09722i	−0.464122	−	0.389445i	0.380523	−	0.924772i	$-0.375744\pi$
$29$	−2.49937	−	2.09722i	−0.464122	−	0.389445i	−0.844645	+	0.535327i	$0.820188\pi$
$30$		0			0
$31$	−2.04416	+	3.54059i	−0.367143	+	0.635909i	−0.989118	−	0.147128i	$-0.952997\pi$
$31$	−2.04416	+	3.54059i	−0.367143	+	0.635909i	0.621975	+	0.783037i	$0.286331\pi$
$32$	−2.03622	−	5.59447i	−0.359956	−	0.988972i
$33$		0			0
$34$	0.631029	−	3.57874i	0.108221	−	0.613750i
$35$	9.29160	−	1.87517i	1.57057	−	0.316962i
$36$		0			0
$37$		−	2.14440i		−	0.352538i	−0.984342	−	0.176269i	$-0.943597\pi$
$37$		−	2.14440i		−	0.352538i	0.984342	−	0.176269i	$-0.0564028\pi$
$38$	−3.24108	+	7.07191i	−0.525772	+	1.14721i
$39$		0			0
$40$	1.03675	−	3.08240i	0.163925	−	0.487370i
$41$	4.10271	+	1.49327i	0.640736	+	0.233209i	0.641897	−	0.766790i	$-0.278147\pi$
$41$	4.10271	+	1.49327i	0.640736	+	0.233209i	−0.00116142	+	0.999999i	$0.500370\pi$
$42$		0			0
$43$	10.4627	−	1.84485i	1.59554	−	0.281337i	0.695956	−	0.718085i	$-0.254981\pi$
$43$	10.4627	−	1.84485i	1.59554	−	0.281337i	0.899584	+	0.436748i	$0.143870\pi$
$44$	0.546658	−	0.198967i	0.0824118	−	0.0299955i
$45$		0			0
$46$	−3.92205	−	6.79319i	−0.578275	−	1.00160i
$47$	1.68502	−	2.00812i	0.245785	−	0.292915i	−0.629021	−	0.777388i	$-0.716544\pi$
$47$	1.68502	−	2.00812i	0.245785	−	0.292915i	0.874806	+	0.484473i	$0.160989\pi$
$48$		0			0
$49$	5.48502	+	9.50033i	0.783574	+	1.35719i
$50$	−7.49905	+	4.83645i	−1.06053	+	0.683977i
$51$		0			0
$52$	−4.85735	+	0.856482i	−0.673593	+	0.118773i
$53$	11.2604	+	1.98551i	1.54673	+	0.272730i	0.880874	−	0.473350i	$-0.156955\pi$
$53$	11.2604	+	1.98551i	1.54673	+	0.272730i	0.665856	+	0.746080i	$0.268066\pi$
$54$		0			0
$55$	1.04039	+	0.349931i	0.140286	+	0.0471847i
$56$	6.16526			0.823867
$57$		0			0
$58$			5.82287i			0.764581i
$59$	−0.415431	+	0.348588i	−0.0540845	+	0.0453823i	−0.669429	−	0.742876i	$-0.733461\pi$
$59$	−0.415431	+	0.348588i	−0.0540845	+	0.0453823i	0.615345	+	0.788258i	$0.289017\pi$
$60$		0			0
$61$	−2.36895	+	13.4350i	−0.303313	+	1.72018i	0.328026	+	0.944669i	$0.393617\pi$
$61$	−2.36895	+	13.4350i	−0.303313	+	1.72018i	−0.631339	+	0.775507i	$0.717494\pi$
$62$	7.18550	−	1.26700i	0.912559	−	0.160909i
$63$		0			0
$64$	−0.346803	+	0.600680i	−0.0433503	+	0.0750850i
$65$	−8.17171	−	4.45354i	−1.01358	−	0.552394i
$66$		0			0
$67$	4.60042	−	5.48257i	0.562031	−	0.669802i	−0.407944	−	0.913007i	$-0.633754\pi$
$67$	4.60042	−	5.48257i	0.562031	−	0.669802i	0.969975	+	0.243205i	$0.0781986\pi$
$68$	−2.08976	+	1.20652i	−0.253421	+	0.146312i
$69$		0			0
$70$	−13.2227	−	10.5518i	−1.58041	−	1.26118i
$71$	−1.04859	−	5.94684i	−0.124444	−	0.705760i	−0.981636	−	0.190762i	$-0.938904\pi$
$71$	−1.04859	−	5.94684i	−0.124444	−	0.705760i	0.857192	−	0.514997i	$-0.172207\pi$
$72$		0			0
$73$	−0.702575	+	1.93031i	−0.0822302	+	0.225925i	−0.973993	−	0.226577i	$-0.927246\pi$
$73$	−0.702575	+	1.93031i	−0.0822302	+	0.225925i	0.891763	+	0.452503i	$0.149469\pi$
$74$	−2.93170	+	2.45999i	−0.340804	+	0.285968i
$75$		0			0
$76$	4.98069	−	1.36984i	0.571324	−	0.157131i
$77$			2.08093i			0.237144i
$78$		0			0
$79$	5.01823	+	1.82649i	0.564595	+	0.205496i	0.608519	−	0.793539i	$-0.291764\pi$
$79$	5.01823	+	1.82649i	0.564595	+	0.205496i	−0.0439240	+	0.999035i	$0.513986\pi$
$80$	−10.3375	+	4.05327i	−1.15577	+	0.453170i
$81$		0			0
$82$	−2.66500	−	7.32202i	−0.294300	−	0.808582i
$83$	−7.02847	−	4.05789i	−0.771475	−	0.445411i	0.0619255	−	0.998081i	$-0.480276\pi$
$83$	−7.02847	−	4.05789i	−0.771475	−	0.445411i	−0.833401	+	0.552669i	$0.813609\pi$
$84$		0			0
$85$	−4.50199	−	0.680073i	−0.488310	−	0.0737642i
$86$	−14.5246	−	12.1876i	−1.56623	−	1.31422i
$87$		0			0
$88$	0.618288	+	0.356969i	0.0659097	+	0.0380530i
$89$	4.07920	−	1.48471i	0.432394	−	0.157379i	−0.116648	−	0.993173i	$-0.537215\pi$
$89$	4.07920	−	1.48471i	0.432394	−	0.157379i	0.549042	+	0.835795i	$0.314993\pi$
$90$		0			0
$91$	3.06370	−	17.3751i	0.321163	−	1.82141i
$92$	−1.78148	+	4.89458i	−0.185732	+	0.510296i
$93$		0			0
$94$	−4.67839			−0.482539
$95$	8.95780	+	3.84160i	0.919051	+	0.394140i
$96$		0			0
$97$	3.62962	+	4.32562i	0.368533	+	0.439200i	0.918160	−	0.396210i	$-0.129675\pi$
$97$	3.62962	+	4.32562i	0.368533	+	0.439200i	−0.549627	+	0.835410i	$0.685230\pi$
$98$	6.69607	−	18.3973i	0.676405	−	1.85841i
$99$		0			0
$100$	5.66099	+	1.75024i	0.566099	+	0.175024i
$101$	−3.10176	+	1.12895i	−0.308637	+	0.112335i	−0.491695	−	0.870767i	$-0.663622\pi$
$101$	−3.10176	+	1.12895i	−0.308637	+	0.112335i	0.183058	+	0.983102i	$0.441400\pi$
$102$		0			0
$103$	2.95805	−	1.70783i	0.291466	−	0.168278i	−0.347137	−	0.937814i	$-0.612846\pi$
$103$	2.95805	−	1.70783i	0.291466	−	0.168278i	0.638603	+	0.769537i	$0.279513\pi$
$104$	−4.63695	−	3.89086i	−0.454690	−	0.381530i
$105$		0			0
$106$	−10.2031	−	17.6722i	−0.991010	−	1.71648i
$107$	−1.51772	−	0.876258i	−0.146724	−	0.0847110i	0.424841	−	0.905268i	$-0.360330\pi$
$107$	−1.51772	−	0.876258i	−0.146724	−	0.0847110i	−0.571565	+	0.820557i	$0.693663\pi$
$108$		0			0
$109$	0.611108	+	3.46576i	0.0585335	+	0.331960i	0.999987	−	0.00518405i	$-0.00165014\pi$
$109$	0.611108	+	3.46576i	0.0585335	+	0.331960i	−0.941453	+	0.337144i	$0.890539\pi$
$110$	−0.715097	−	1.82379i	−0.0681818	−	0.173892i
$111$		0			0
$112$	−13.5309	−	16.1255i	−1.27855	−	1.52372i
$113$			13.2583i			1.24723i	0.781731	+	0.623616i	$0.214337\pi$
$113$			13.2583i			1.24723i	−0.781731	+	0.623616i	$0.785663\pi$
$114$		0			0
$115$	−8.38788	+	5.12196i	−0.782174	+	0.477625i
$116$	2.96195	−	2.48537i	0.275010	−	0.230761i
$117$		0			0
$118$	0.953138	+	0.168064i	0.0877435	+	0.0154715i
$119$	−1.49887	−	8.50051i	−0.137401	−	0.779241i
$120$		0			0
$121$	5.37951	−	9.31759i	0.489047	−	0.847054i
$122$	21.0852	−	12.1735i	1.90896	−	1.10214i
$123$		0			0
$124$	−3.71147	−	3.11429i	−0.333300	−	0.279672i
$125$	6.28904	+	9.24381i	0.562509	+	0.826791i
$126$		0			0
$127$	6.77480	+	18.6136i	0.601166	+	1.65169i	0.748915	+	0.662666i	$0.230575\pi$
$127$	6.77480	+	18.6136i	0.601166	+	1.65169i	−0.147749	+	0.989025i	$0.547203\pi$
$128$	−10.5071	+	1.85268i	−0.928702	+	0.163755i
$129$		0			0
$130$	3.28571	+	16.2809i	0.288175	+	1.42793i
$131$	2.62756	−	2.20479i	0.229571	−	0.192633i	−0.520745	−	0.853712i	$-0.674346\pi$
$131$	2.62756	−	2.20479i	0.229571	−	0.192633i	0.750316	+	0.661079i	$0.229901\pi$
$132$		0			0
$133$	−1.48902	+	18.4178i	−0.129115	+	1.59702i
$134$	−12.7729			−1.10341
$135$		0			0
$136$	−2.78280	−	1.01286i	−0.238623	−	0.0868517i
$137$	−0.599055	−	0.105629i	−0.0511807	−	0.00902454i	0.147999	−	0.988987i	$-0.452717\pi$
$137$	−0.599055	−	0.105629i	−0.0511807	−	0.00902454i	−0.199180	+	0.979963i	$0.563828\pi$
$138$		0			0
$139$	−7.94791	+	2.89280i	−0.674133	+	0.245364i	−0.656326	−	0.754477i	$-0.727891\pi$
$139$	−7.94791	+	2.89280i	−0.674133	+	0.245364i	−0.0178066	+	0.999841i	$0.505668\pi$
$140$	0.276379	+	11.2299i	0.0233583	+	0.949097i
$141$		0			0
$142$	−6.92727	+	8.25560i	−0.581324	+	0.692794i
$143$	1.31327	−	1.56509i	0.109821	−	0.130879i
$144$		0			0
$145$	7.29341	−	0.179499i	0.605685	−	0.0149066i
$146$	3.44498	−	1.25387i	0.285109	−	0.103771i
$147$		0			0
$148$	2.50267	+	0.441289i	0.205719	+	0.0362737i
$149$	4.35768	+	1.58607i	0.356995	+	0.129936i	0.514291	−	0.857616i	$-0.328055\pi$
$149$	4.35768	+	1.58607i	0.356995	+	0.129936i	−0.157295	+	0.987552i	$0.550277\pi$
$150$		0			0
$151$	14.2109			1.15646			0.578232	−	0.815872i	$-0.303743\pi$
$151$	14.2109			1.15646			0.578232	+	0.815872i	$0.303743\pi$
$152$	5.21686	+	3.60185i	0.423143	+	0.292149i
$153$		0			0
$154$	2.84493	−	2.38718i	0.229251	−	0.192365i
$155$	−1.80848	−	8.96111i	−0.145260	−	0.719774i
$156$		0			0
$157$	−10.5651	+	1.86291i	−0.843186	+	0.148676i	−0.578525	−	0.815665i	$-0.696371\pi$
$157$	−10.5651	+	1.86291i	−0.843186	+	0.148676i	−0.264662	+	0.964341i	$0.585260\pi$
$158$	−3.25969	−	8.95593i	−0.259327	−	0.712496i
$159$		0			0
$160$	11.6892	+	6.37056i	0.924112	+	0.503637i
$161$	−14.2729	−	11.9764i	−1.12486	−	0.943870i
$162$		0			0
$163$	14.6675	−	8.46831i	1.14885	−	0.663289i	0.200244	−	0.979746i	$-0.435827\pi$
$163$	14.6675	−	8.46831i	1.14885	−	0.663289i	0.948607	+	0.316457i	$0.102493\pi$
$164$	−2.58703	+	4.48087i	−0.202013	+	0.349897i
$165$		0			0
$166$	2.51513	+	14.2640i	0.195212	+	1.10710i
$167$	−16.0097	−	2.82295i	−1.23887	−	0.218446i	−0.484439	−	0.874825i	$-0.660976\pi$
$167$	−16.0097	−	2.82295i	−1.23887	−	0.218446i	−0.754432	+	0.656379i	$0.772087\pi$
$168$		0			0
$169$	−3.31099	+	2.77825i	−0.254692	+	0.213712i
$170$	4.23479	+	6.93503i	0.324794	+	0.531892i
$171$		0			0
$172$			12.5903i			0.960003i
$173$	5.52227	+	6.58118i	0.419850	+	0.500358i	0.933966	−	0.357363i	$-0.116324\pi$
$173$	5.52227	+	6.58118i	0.419850	+	0.500358i	−0.514115	+	0.857721i	$0.671880\pi$
$174$		0			0
$175$	−12.8090	+	16.8873i	−0.968270	+	1.27656i
$176$	−0.423290	−	2.40060i	−0.0319067	−	0.180952i
$177$		0			0
$178$	−6.70934	−	3.87364i	−0.502886	−	0.290342i
$179$	11.7638	+	20.3755i	0.879267	+	1.52293i	0.852147	+	0.523302i	$0.175300\pi$
$179$	11.7638	+	20.3755i	0.879267	+	1.52293i	0.0271196	+	0.999632i	$0.491367\pi$
$180$		0			0
$181$	−12.7266	−	10.6789i	−0.945964	−	0.793758i	0.0326493	−	0.999467i	$-0.489606\pi$
$181$	−12.7266	−	10.6789i	−0.945964	−	0.793758i	−0.978613	+	0.205709i	$0.934050\pi$
$182$	−27.2688	+	15.7437i	−2.02130	+	1.16700i
$183$		0			0
$184$	−6.00684	+	2.18631i	−0.442830	+	0.161177i
$185$	3.17163	+	3.59626i	0.233183	+	0.264402i
$186$		0			0
$187$	0.341865	−	0.939266i	0.0249996	−	0.0686859i
$188$	1.99687	+	2.37978i	0.145637	+	0.173563i
$189$		0			0
$190$	−5.02410	−	16.6536i	−0.364486	−	1.20818i
$191$	12.8109			0.926965			0.463482	−	0.886106i	$-0.346600\pi$
$191$	12.8109			0.926965			0.463482	+	0.886106i	$0.346600\pi$
$192$		0			0
$193$	−3.29702	+	9.05848i	−0.237324	+	0.652043i	0.762662	+	0.646797i	$0.223892\pi$
$193$	−3.29702	+	9.05848i	−0.237324	+	0.652043i	−0.999986	+	0.00524597i	$0.998330\pi$
$194$	1.74994	−	9.92443i	0.125639	−	0.712533i
$195$		0			0
$196$	−12.2163	+	4.44638i	−0.872594	+	0.317598i
$197$	2.68677	+	1.55121i	0.191424	+	0.110519i	0.592649	−	0.805461i	$-0.298082\pi$
$197$	2.68677	+	1.55121i	0.191424	+	0.110519i	−0.401225	+	0.915980i	$0.631415\pi$
$198$		0			0
$199$	−0.401629	−	0.337007i	−0.0284708	−	0.0238898i	0.628441	−	0.777857i	$-0.283693\pi$
$199$	−0.401629	−	0.337007i	−0.0284708	−	0.0238898i	−0.656912	+	0.753967i	$0.728138\pi$
$200$	2.82027	+	6.70271i	0.199423	+	0.473953i
$201$		0			0
$202$	5.10168	+	2.94545i	0.358953	+	0.207241i
$203$	4.73046	+	12.9968i	0.332013	+	0.912199i
$204$		0			0
$205$	−9.08901	+	3.56374i	−0.634804	+	0.248903i
$206$	−5.72824	−	2.08491i	−0.399105	−	0.145262i
$207$		0			0
$208$			20.6674i			1.43303i
$209$	−1.21572	+	1.76083i	−0.0840929	+	0.121799i
$210$		0			0
$211$	−14.6037	+	12.2539i	−1.00536	+	0.843596i	−0.987718	−	0.156249i	$-0.950060\pi$
$211$	−14.6037	+	12.2539i	−1.00536	+	0.843596i	−0.0176404	+	0.999844i	$0.505615\pi$
$212$	−4.63446	+	12.7331i	−0.318296	+	0.874512i
$213$		0			0
$214$	0.543115	+	3.08016i	0.0371266	+	0.210555i
$215$	−14.8178	+	18.5684i	−1.01056	+	1.26636i
$216$		0			0
$217$	15.0090	−	8.66543i	1.01887	−	0.588248i
$218$	4.03715	−	4.81129i	0.273430	−	0.325862i
$219$		0			0
$220$	−0.622493	+	1.14220i	−0.0419685	+	0.0770070i
$221$	−4.23731	+	7.33924i	−0.285033	+	0.493691i
$222$		0			0
$223$	−3.11478	+	0.549220i	−0.208581	+	0.0367785i	−0.276962	−	0.960881i	$-0.589328\pi$
$223$	−3.11478	+	0.549220i	−0.208581	+	0.0367785i	0.0683812	+	0.997659i	$0.478217\pi$
$224$	−4.38246	+	24.8542i	−0.292815	+	1.66064i
$225$		0			0
$226$	18.1259	−	15.2095i	1.20572	−	1.01172i
$227$			9.04654i			0.600440i	0.953870	+	0.300220i	$0.0970600\pi$
$227$			9.04654i			0.600440i	−0.953870	+	0.300220i	$0.902940\pi$
$228$		0			0
$229$	17.8920			1.18234			0.591168	−	0.806549i	$-0.298667\pi$
$229$	17.8920			1.18234			0.591168	+	0.806549i	$0.298667\pi$
$230$	16.6248	+	5.59168i	1.09620	+	0.368704i
$231$		0			0
$232$	4.67310	+	0.823994i	0.306804	+	0.0540979i
$233$	−6.34541	+	1.11887i	−0.415701	+	0.0732994i	−0.377587	−	0.925974i	$-0.623246\pi$
$233$	−6.34541	+	1.11887i	−0.415701	+	0.0732994i	−0.0381142	+	0.999273i	$0.512135\pi$
$234$		0			0
$235$	0.144219	+	5.85990i	0.00940778	+	0.382257i
$236$	−0.321337	−	0.556572i	−0.0209173	−	0.0362298i
$237$		0			0
$238$	−9.90196	+	11.8007i	−0.641849	+	0.764926i
$239$	6.73708	+	11.6690i	0.435785	+	0.754802i	0.997359	−	0.0726241i	$-0.0231374\pi$
$239$	6.73708	+	11.6690i	0.435785	+	0.754802i	−0.561574	+	0.827426i	$0.689804\pi$
$240$		0			0
$241$	16.5716	−	6.03157i	1.06747	−	0.388528i	0.252241	−	0.967664i	$-0.418832\pi$
$241$	16.5716	−	6.03157i	1.06747	−	0.388528i	0.815231	+	0.579137i	$0.196610\pi$
$242$	−18.9097	+	3.33429i	−1.21556	+	0.214336i
$243$		0			0
$244$	−15.1921	−	5.52948i	−0.972576	−	0.353989i
$245$	−23.2499	−	7.82000i	−1.48538	−	0.499602i
$246$		0			0
$247$	12.7433	−	12.9124i	0.810834	−	0.821599i
$248$		−	5.94596i		−	0.377569i
$249$		0			0
$250$	5.42301	−	19.2022i	0.342981	−	1.21446i
$251$	−3.07923	+	17.4632i	−0.194360	+	1.10227i	0.718968	+	0.695043i	$0.244615\pi$
$251$	−3.07923	+	17.4632i	−0.194360	+	1.10227i	−0.913328	+	0.407225i	$0.866496\pi$
$252$		0			0
$253$	−0.737936	−	2.02746i	−0.0463936	−	0.127465i
$254$	17.6756	−	30.6151i	1.10907	−	1.92096i
$255$		0			0
$256$	15.6489	+	13.1310i	0.978058	+	0.820688i
$257$	17.8358	−	21.2558i	1.11256	−	1.32590i	0.172459	−	0.985017i	$-0.444829\pi$
$257$	17.8358	−	21.2558i	1.11256	−	1.32590i	0.940105	−	0.340885i	$-0.110727\pi$
$258$		0			0
$259$	−4.54518	+	7.87248i	−0.282424	+	0.489172i
$260$	6.87924	−	8.62051i	0.426632	−	0.534621i
$261$		0			0
$262$	−6.02852	−	1.06299i	−0.372443	−	0.0656718i
$263$	−1.90174	+	5.22499i	−0.117266	+	0.322187i	−0.984415	−	0.175864i	$-0.943728\pi$
$263$	−1.90174	+	5.22499i	−0.117266	+	0.322187i	0.867148	+	0.498050i	$0.165950\pi$
$264$		0			0
$265$	−21.8208	+	13.3246i	−1.34044	+	0.818523i
$266$	26.8879	−	19.0926i	1.64860	−	1.17064i
$267$		0			0
$268$	5.45185	+	6.49727i	0.333025	+	0.396884i
$269$	4.34856	+	1.58275i	0.265137	+	0.0965019i	0.471168	−	0.882044i	$-0.343833\pi$
$269$	4.34856	+	1.58275i	0.265137	+	0.0965019i	−0.206031	+	0.978545i	$0.566055\pi$
$270$		0			0
$271$	−1.32118	−	7.49279i	−0.0802561	−	0.455155i	−0.998280	−	0.0586294i	$-0.981327\pi$
$271$	−1.32118	−	7.49279i	−0.0802561	−	0.455155i	0.918024	−	0.396525i	$-0.129784\pi$
$272$	3.45824	+	9.50144i	0.209687	+	0.576110i
$273$		0			0
$274$	0.542806	+	0.940168i	0.0327921	+	0.0567976i
$275$	−2.26234	+	0.951912i	−0.136424	+	0.0574025i
$276$		0			0
$277$	−6.52588	+	3.76772i	−0.392102	+	0.226380i	−0.683071	−	0.730352i	$-0.739356\pi$
$277$	−6.52588	+	3.76772i	−0.392102	+	0.226380i	0.290968	+	0.956733i	$0.406023\pi$
$278$	13.0725	+	7.54740i	0.784035	+	0.452663i
$279$		0			0
$280$	−10.3394	+	9.11857i	−0.617898	+	0.544939i
$281$	3.16993	−	17.9776i	0.189102	−	1.07245i	−0.731468	−	0.681876i	$-0.761164\pi$
$281$	3.16993	−	17.9776i	0.189102	−	1.07245i	0.920570	−	0.390577i	$-0.127724\pi$
$282$		0			0
$283$	−19.8836	−	23.6963i	−1.18196	−	1.40860i	−0.892284	−	0.451474i	$-0.850898\pi$
$283$	−19.8836	−	23.6963i	−1.18196	−	1.40860i	−0.289671	−	0.957126i	$-0.593546\pi$
$284$	7.15618			0.424641
$285$		0			0
$286$	−3.64624			−0.215607
$287$	−11.8967	−	14.1780i	−0.702241	−	0.836898i
$288$		0			0
$289$	2.23206	−	12.6586i	0.131298	−	0.744625i
$290$	−8.61218	−	9.76522i	−0.505725	−	0.573434i
$291$		0			0
$292$	−2.10823	−	1.21719i	−0.123375	−	0.0712305i
$293$	−18.9653	+	10.9496i	−1.10796	+	0.639683i	−0.938301	−	0.345820i	$-0.887601\pi$
$293$	−18.9653	+	10.9496i	−1.10796	+	0.639683i	−0.169662	+	0.985502i	$0.554268\pi$
$294$		0			0
$295$	0.181126	−	1.19903i	0.0105456	−	0.0698102i
$296$	1.55938	+	2.70093i	0.0906373	+	0.156988i
$297$		0			0
$298$	−2.83062	−	7.77706i	−0.163973	−	0.450513i
$299$	3.17654	+	18.0151i	0.183704	+	1.04184i
$300$		0			0
$301$	−42.3205	−	15.4034i	−2.43931	−	0.887837i
$302$	−16.3023	−	19.4283i	−0.938090	−	1.11797i
$303$		0			0
$304$	−2.02866	−	21.5499i	−0.116352	−	1.23597i
$305$	−15.8979	−	26.0349i	−0.910309	−	1.49075i
$306$		0			0
$307$	1.86587	−	5.12643i	0.106491	−	0.292581i	−0.874990	−	0.484141i	$-0.839132\pi$
$307$	1.86587	−	5.12643i	0.106491	−	0.292581i	0.981481	+	0.191560i	$0.0613546\pi$
$308$	−2.42860	−	0.428228i	−0.138382	−	0.0244005i
$309$		0			0
$310$	−10.1765	+	12.7524i	−0.577986	+	0.724285i
$311$	3.34861	−	5.79996i	0.189882	−	0.328885i	−0.755329	−	0.655346i	$-0.772523\pi$
$311$	3.34861	−	5.79996i	0.189882	−	0.328885i	0.945211	+	0.326461i	$0.105856\pi$
$312$		0			0
$313$	−2.94576	+	3.51062i	−0.166504	+	0.198432i	−0.842844	−	0.538157i	$-0.819121\pi$
$313$	−2.94576	+	3.51062i	−0.166504	+	0.198432i	0.676340	+	0.736590i	$0.263565\pi$
$314$	14.6668	+	12.3069i	0.827696	+	0.694520i
$315$		0			0
$316$	−3.16433	+	5.48078i	−0.178007	+	0.308318i
$317$	9.46690	+	26.0101i	0.531714	+	1.46087i	0.857030	+	0.515267i	$0.172307\pi$
$317$	9.46690	+	26.0101i	0.531714	+	1.46087i	−0.325316	+	0.945605i	$0.605471\pi$
$318$		0			0
$319$	−0.278119	+	1.57729i	−0.0155717	+	0.0883115i
$320$	−0.306817	−	1.52030i	−0.0171516	−	0.0849872i
$321$		0			0
$322$			33.2520i			1.85306i
$323$	3.69785	−	8.06856i	0.205754	−	0.448946i
$324$		0			0
$325$	20.2912	−	4.61738i	1.12556	−	0.256126i
$326$	−28.4035	−	10.3380i	−1.57313	−	0.572571i
$327$		0			0
$328$	−6.25336	+	1.10264i	−0.345284	+	0.0608829i
$329$	−10.4423	+	3.80069i	−0.575703	+	0.209539i
$330$		0			0
$331$	7.06509	+	12.2371i	0.388332	+	0.672611i	0.992225	−	0.124454i	$-0.0397179\pi$
$331$	7.06509	+	12.2371i	0.388332	+	0.672611i	−0.603893	+	0.797065i	$0.706385\pi$
$332$	6.18222	−	7.36768i	0.339293	−	0.404354i
$333$		0			0
$334$	14.5065	+	25.1260i	0.793761	+	1.37483i
$335$	0.393745	+	15.9987i	0.0215126	+	0.874100i
$336$		0			0
$337$	14.7696	−	2.60428i	0.804550	−	0.141864i	0.243775	−	0.969832i	$-0.421614\pi$
$337$	14.7696	−	2.60428i	0.804550	−	0.141864i	0.560775	+	0.827968i	$0.310503\pi$
$338$	7.59654	+	1.33947i	0.413197	+	0.0728578i
$339$		0			0
$340$	1.72014	−	5.11420i	0.0932879	−	0.277357i
$341$	2.00692			0.108681
$342$		0			0
$343$		−	16.8294i		−	0.908703i
$344$	−11.8364	+	9.93195i	−0.638178	+	0.535495i
$345$		0			0
$346$	2.66244	−	15.0995i	0.143134	−	0.811752i
$347$	20.5956	−	3.63155i	1.10563	−	0.194952i	0.409106	−	0.912487i	$-0.365841\pi$
$347$	20.5956	−	3.63155i	1.10563	−	0.194952i	0.696522	+	0.717535i	$0.254730\pi$
$348$		0			0
$349$	−1.56527	+	2.71113i	−0.0837872	+	0.145124i	−0.904874	−	0.425680i	$-0.860035\pi$
$349$	−1.56527	+	2.71113i	−0.0837872	+	0.145124i	0.821087	+	0.570804i	$0.193368\pi$
$350$	37.7814	−	1.86081i	2.01950	−	0.0994646i
$351$		0			0
$352$	−1.87856	+	2.23878i	−0.100127	+	0.119327i
$353$	−6.96750	+	4.02269i	−0.370843	+	0.214106i	−0.673827	−	0.738890i	$-0.735350\pi$
$353$	−6.96750	+	4.02269i	−0.370843	+	0.214106i	0.302984	+	0.952996i	$0.402017\pi$
$354$		0			0
$355$	10.5541	+	8.42223i	0.560151	+	0.447006i
$356$	0.893318	+	5.06626i	0.0473457	+	0.268511i
$357$		0			0
$358$	14.3611	−	39.4569i	0.759010	−	2.08536i
$359$	23.4289	−	19.6592i	1.23653	−	1.03757i	0.238742	−	0.971083i	$-0.423265\pi$
$359$	23.4289	−	19.6592i	1.23653	−	1.03757i	0.997787	−	0.0664886i	$-0.0211796\pi$
$360$		0			0
$361$	−12.0199	+	14.7147i	−0.632628	+	0.774456i
$362$			29.6497i			1.55835i
$363$		0			0
$364$	19.6475	+	7.15112i	1.02981	+	0.374821i
$365$	−1.67673	−	4.27634i	−0.0877639	−	0.223834i
$366$		0			0
$367$	−3.40370	−	9.35159i	−0.177672	−	0.488149i	0.818606	−	0.574356i	$-0.194748\pi$
$367$	−3.40370	−	9.35159i	−0.177672	−	0.488149i	−0.996277	+	0.0862072i	$0.972525\pi$
$368$	18.9016	+	10.9128i	0.985314	+	0.568871i
$369$		0			0
$370$	1.27821	−	8.46159i	0.0664510	−	0.439897i
$371$	−37.1304	−	31.1561i	−1.92771	−	1.61754i
$372$		0			0
$373$	8.03335	+	4.63806i	0.415951	+	0.240149i	0.693343	−	0.720607i	$-0.256137\pi$
$373$	8.03335	+	4.63806i	0.415951	+	0.240149i	−0.277392	+	0.960757i	$0.589470\pi$
$374$	−1.67629	+	0.610119i	−0.0866788	+	0.0315485i
$375$		0			0
$376$	−0.662039	+	3.75461i	−0.0341420	+	0.193629i
$377$	4.64441	−	12.7604i	0.239199	−	0.657195i
$378$		0			0
$379$	21.1472			1.08626			0.543129	−	0.839649i	$-0.317239\pi$
$379$	21.1472			1.08626			0.543129	+	0.839649i	$0.317239\pi$
$380$	−6.32682	+	9.66385i	−0.324559	+	0.495745i
$381$		0			0
$382$	−14.6963	−	17.5143i	−0.751927	−	0.896112i
$383$	5.18165	−	14.2365i	0.264770	−	0.727450i	−0.734060	−	0.679085i	$-0.762377\pi$
$383$	5.18165	−	14.2365i	0.264770	−	0.727450i	0.998830	−	0.0483649i	$-0.0154010\pi$
$384$		0			0
$385$	−3.07775	−	3.48982i	−0.156857	−	0.177858i
$386$	16.1665	−	5.88411i	0.822851	−	0.299493i
$387$		0			0
$388$	−5.79524	+	3.34588i	−0.294209	+	0.169861i
$389$	−24.0908	−	20.2146i	−1.22145	−	1.02492i	−0.998747	−	0.0500353i	$-0.984067\pi$
$389$	−24.0908	−	20.2146i	−1.22145	−	1.02492i	−0.222706	−	0.974886i	$-0.571489\pi$
$390$		0			0
$391$	4.47479	+	7.75056i	0.226300	+	0.391963i
$392$	−13.8171	−	7.97728i	−0.697866	−	0.402913i
$393$		0			0
$394$	−0.961457	−	5.45269i	−0.0484375	−	0.274703i
$395$	−11.1172	+	4.35900i	−0.559369	+	0.219325i
$396$		0			0
$397$	6.03294	+	7.18978i	0.302784	+	0.360844i	0.895887	−	0.444283i	$-0.146541\pi$
$397$	6.03294	+	7.18978i	0.302784	+	0.360844i	−0.593102	+	0.805127i	$0.702097\pi$
$398$			0.935689i			0.0469019i
$399$		0			0
$400$	11.3416	−	22.0870i	0.567079	−	1.10435i
$401$	−4.71921	+	3.95989i	−0.235666	+	0.197747i	−0.752971	−	0.658054i	$-0.771380\pi$
$401$	−4.71921	+	3.95989i	−0.235666	+	0.197747i	0.517305	+	0.855801i	$0.326935\pi$
$402$		0			0
$403$	−16.7571	−	2.95473i	−0.834730	−	0.147185i
$404$	−0.679265	−	3.85230i	−0.0337947	−	0.191659i
$405$		0			0
$406$	12.3419	−	21.3768i	0.612518	−	1.06091i
$407$	−0.911634	+	0.526332i	−0.0451880	+	0.0260893i
$408$		0			0
$409$	−1.75027	−	1.46865i	−0.0865454	−	0.0726202i	0.598489	−	0.801131i	$-0.295768\pi$
$409$	−1.75027	−	1.46865i	−0.0865454	−	0.0726202i	−0.685034	+	0.728511i	$0.740213\pi$
$410$	15.2988	+	8.33776i	0.755553	+	0.411773i
$411$		0			0
$412$	1.38444	+	3.80371i	0.0682064	+	0.187395i
$413$	2.26397	−	0.399199i	0.111403	−	0.0196433i
$414$		0			0
$415$	17.7888	−	3.59003i	0.873218	−	0.176227i
$416$	18.9814	−	15.9273i	0.930640	−	0.780900i
$417$		0			0
$418$	3.80193	−	0.357906i	0.185959	−	0.0175057i
$419$	−22.6494			−1.10649			−0.553247	−	0.833017i	$-0.686611\pi$
$419$	−22.6494			−1.10649			−0.553247	+	0.833017i	$0.686611\pi$
$420$		0			0
$421$	21.6100	+	7.86540i	1.05321	+	0.383336i	0.809872	−	0.586606i	$-0.199536\pi$
$421$	21.6100	+	7.86540i	1.05321	+	0.383336i	0.243335	+	0.969942i	$0.421759\pi$
$422$	33.5058	+	5.90797i	1.63103	+	0.287595i
$423$		0			0
$424$	−15.6266	+	5.68761i	−0.758893	+	0.276215i
$425$	8.55589	−	5.51805i	0.415022	−	0.267665i
$426$		0			0
$427$	37.1730	−	44.3011i	1.79893	−	2.14388i
$428$	1.33498	−	1.59097i	0.0645289	−	0.0769025i
$429$		0			0
$430$	42.3842	−	1.04312i	2.04395	−	0.0503038i
$431$	24.0861	−	8.76663i	1.16019	−	0.422274i	0.311023	−	0.950402i	$-0.399328\pi$
$431$	24.0861	−	8.76663i	1.16019	−	0.422274i	0.849164	+	0.528129i	$0.177106\pi$
$432$		0			0
$433$	−2.32740	−	0.410383i	−0.111847	−	0.0197217i	0.117444	−	0.993079i	$-0.462530\pi$
$433$	−2.32740	−	0.410383i	−0.111847	−	0.0197217i	−0.229292	+	0.973358i	$0.573641\pi$
$434$	−29.0647	−	10.5787i	−1.39515	−	0.507793i
$435$		0			0
$436$	−4.17056			−0.199734
$437$	−5.08050	−	18.4725i	−0.243033	−	0.883661i
$438$		0			0
$439$	4.83879	−	4.06022i	0.230943	−	0.193784i	−0.519972	−	0.854183i	$-0.674058\pi$
$439$	4.83879	−	4.06022i	0.230943	−	0.193784i	0.750914	+	0.660400i	$0.229613\pi$
$440$	−1.56486	+	0.315811i	−0.0746019	+	0.0150557i
$441$		0			0
$442$	14.8947	−	2.62634i	0.708469	−	0.124922i
$443$	−10.7821	−	29.6234i	−0.512271	−	1.40745i	−0.878865	−	0.477071i	$-0.841698\pi$
$443$	−10.7821	−	29.6234i	−0.512271	−	1.40745i	0.366594	−	0.930381i	$-0.380524\pi$
$444$		0			0
$445$	−4.64508	+	8.52317i	−0.220198	+	0.404037i
$446$	4.32404	+	3.62830i	0.204749	+	0.171805i
$447$		0			0
$448$	2.54635	−	1.47013i	0.120304	−	0.0694573i
$449$	7.54142	−	13.0621i	0.355902	−	0.616440i	−0.631370	−	0.775482i	$-0.717507\pi$
$449$	7.54142	−	13.0621i	0.355902	−	0.616440i	0.987272	+	0.159042i	$0.0508405\pi$
$450$		0			0
$451$	−0.372168	−	2.11067i	−0.0175247	−	0.0993876i
$452$	−15.4734	−	2.72837i	−0.727805	−	0.128332i
$453$		0			0
$454$	12.3679	−	10.3779i	0.580455	−	0.487059i
$455$	20.5603	+	33.6701i	0.963880	+	1.57848i
$456$		0			0
$457$			20.1347i			0.941861i	0.882170	+	0.470930i	$0.156082\pi$
$457$			20.1347i			0.941861i	−0.882170	+	0.470930i	$0.843918\pi$
$458$	−20.5251	−	24.4609i	−0.959076	−	1.14298i
$459$		0			0
$460$	−4.25159	−	10.8433i	−0.198231	−	0.505571i
$461$	1.29974	+	7.37118i	0.0605348	+	0.343310i	1.00000		0.000665051i	$0.000211692\pi$
$461$	1.29974	+	7.37118i	0.0605348	+	0.343310i	−0.939465	+	0.342645i	$0.888677\pi$
$462$		0			0
$463$	−18.7038	−	10.7986i	−0.869239	−	0.501855i	−0.00214362	−	0.999998i	$-0.500682\pi$
$463$	−18.7038	−	10.7986i	−0.869239	−	0.501855i	−0.867095	+	0.498142i	$0.834016\pi$
$464$	−8.10087	−	14.0311i	−0.376074	−	0.651379i
$465$		0			0
$466$	8.80891	+	7.39155i	0.408065	+	0.342407i
$467$	23.4263	−	13.5252i	1.08404	−	0.625870i	0.152056	−	0.988372i	$-0.451411\pi$
$467$	23.4263	−	13.5252i	1.08404	−	0.625870i	0.931983	+	0.362501i	$0.118077\pi$
$468$		0			0
$469$	−28.5096	+	10.3766i	−1.31645	+	0.479148i
$470$	7.84587	−	6.91946i	0.361903	−	0.319171i
$471$		0			0
$472$	0.269757	−	0.741151i	0.0124166	−	0.0341143i
$473$	−3.35229	−	3.99510i	−0.154138	−	0.183695i
$474$		0			0
$475$	−20.7045	+	6.80628i	−0.949986	+	0.312294i
$476$	10.2292			0.468853
$477$		0			0
$478$	8.22457	−	22.5968i	0.376183	−	1.03355i
$479$	−6.60791	+	37.4753i	−0.301923	+	1.71229i	0.335723	+	0.941961i	$0.391019\pi$
$479$	−6.60791	+	37.4753i	−0.301923	+	1.71229i	−0.637646	+	0.770329i	$0.720092\pi$
$480$		0			0
$481$	8.38675	−	3.05253i	0.382403	−	0.139183i
$482$	−27.2565	−	15.7365i	−1.24150	−	0.716779i
$483$		0			0
$484$	9.76728	+	8.19572i	0.443967	+	0.372533i
$485$	−12.4847	−	1.88595i	−0.566903	−	0.0856366i
$486$		0			0
$487$	15.8788	+	9.16764i	0.719538	+	0.415426i	0.814583	−	0.580047i	$-0.196966\pi$
$487$	15.8788	+	9.16764i	0.719538	+	0.415426i	−0.0950445	+	0.995473i	$0.530299\pi$
$488$	−6.78601	−	18.6444i	−0.307188	−	0.843993i
$489$		0			0
$490$	15.9805	+	40.7568i	0.721924	+	1.84120i
$491$	−14.1588	−	5.15338i	−0.638978	−	0.232569i	0.00215650	−	0.999998i	$-0.499314\pi$
$491$	−14.1588	−	5.15338i	−0.638978	−	0.232569i	−0.641134	+	0.767429i	$0.721536\pi$
$492$		0			0
$493$		−	6.64350i		−	0.299208i
$494$	−32.2718	−	2.60909i	−1.45198	−	0.117388i
$495$		0			0
$496$	−15.5519	+	13.0496i	−0.698302	+	0.585945i
$497$	−8.75509	+	24.0544i	−0.392720	+	1.07899i
$498$		0			0
$499$	−5.99606	−	34.0053i	−0.268420	−	1.52229i	−0.759115	−	0.650956i	$-0.774368\pi$
$499$	−5.99606	−	34.0053i	−0.268420	−	1.52229i	0.490695	−	0.871332i	$-0.336743\pi$
$500$	−12.0824	+	5.43752i	−0.540341	+	0.243173i
$501$		0			0
$502$	27.4071	−	15.8235i	1.22324	−	0.706237i
$503$	19.8431	−	23.6481i	0.884760	−	1.05442i	−0.113386	−	0.993551i	$-0.536170\pi$
$503$	19.8431	−	23.6481i	0.884760	−	1.05442i	0.998146	−	0.0608649i	$-0.0193859\pi$
$504$		0			0
$505$	3.53205	−	6.48088i	0.157174	−	0.288395i
$506$	−1.92529	+	3.33471i	−0.0855897	+	0.148246i
$507$		0			0
$508$	−23.1176	+	4.07626i	−1.02568	+	0.180855i
$509$	1.76734	−	10.0231i	0.0783358	−	0.444264i	−0.920261	−	0.391305i	$-0.872024\pi$
$509$	1.76734	−	10.0231i	0.0783358	−	0.444264i	0.998597	−	0.0529589i	$-0.0168652\pi$
$510$		0			0
$511$	6.67067	−	5.59735i	0.295093	−	0.247612i
$512$		−	15.1195i		−	0.668194i
$513$		0			0
$514$	−49.5204			−2.18425
$515$	−2.43486	+	7.23915i	−0.107293	+	0.318995i
$516$		0			0
$517$	−1.26728	−	0.223455i	−0.0557348	−	0.00982754i
$518$	15.9769	−	2.81716i	0.701984	−	0.123779i
$519$		0			0
$520$	13.5311	−	0.333014i	0.593376	−	0.0146036i
$521$	8.27116	+	14.3261i	0.362366	+	0.627636i	0.988350	−	0.152200i	$-0.0486357\pi$
$521$	8.27116	+	14.3261i	0.362366	+	0.627636i	−0.625984	+	0.779836i	$0.715302\pi$
$522$		0			0
$523$	−5.14102	+	6.12683i	−0.224801	+	0.267908i	−0.866642	−	0.498930i	$-0.833726\pi$
$523$	−5.14102	+	6.12683i	−0.224801	+	0.267908i	0.641841	+	0.766838i	$0.278171\pi$
$524$	2.03243	+	3.52027i	0.0887871	+	0.153784i
$525$		0			0
$526$	9.32492	−	3.39399i	0.406586	−	0.147985i
$527$	−8.19816	+	1.44556i	−0.357117	+	0.0629694i
$528$		0			0
$529$	−3.45976	−	1.25925i	−0.150424	−	0.0547500i
$530$	43.2487	+	14.5465i	1.87860	+	0.631862i
$531$		0			0
$532$	−21.1884	−	5.52792i	−0.918635	−	0.239666i
$533$			18.1713i			0.787088i
$534$		0			0
$535$	3.84130	−	0.775227i	0.166074	−	0.0335160i
$536$	−1.80749	+	10.2508i	−0.0780719	+	0.442768i
$537$		0			0
$538$	−2.82470	−	7.76079i	−0.121781	−	0.334591i
$539$	2.69254	−	4.66361i	0.115976	−	0.200876i
$540$		0			0
$541$	3.98380	+	3.34280i	0.171277	+	0.143718i	0.724397	−	0.689383i	$-0.242118\pi$
$541$	3.98380	+	3.34280i	0.171277	+	0.143718i	−0.553120	+	0.833102i	$0.686563\pi$
$542$	−8.72810	+	10.4017i	−0.374904	+	0.446793i
$543$		0			0
$544$	6.06125	−	10.4984i	0.259874	−	0.450115i
$545$	−6.15081	−	4.90840i	−0.263472	−	0.210253i
$546$		0			0
$547$	10.8663	+	1.91602i	0.464610	+	0.0819233i	0.401053	−	0.916055i	$-0.368644\pi$
$547$	10.8663	+	1.91602i	0.464610	+	0.0819233i	0.0635572	+	0.997978i	$0.479755\pi$
$548$	0.246555	−	0.677403i	0.0105323	−	0.0289372i
$549$		0			0
$550$	3.89668	+	2.00093i	0.166155	+	0.0853201i
$551$	−3.59020	+	13.7612i	−0.152948	+	0.586245i
$552$		0			0
$553$	−14.5515	−	17.3418i	−0.618792	−	0.737447i
$554$	12.6373	+	4.59960i	0.536907	+	0.195418i
$555$		0			0
$556$	−1.74054	−	9.87109i	−0.0738153	−	0.418628i
$557$	−7.27877	−	19.9983i	−0.308411	−	0.847353i	−0.992967	−	0.118393i	$-0.962226\pi$
$557$	−7.27877	−	19.9983i	−0.308411	−	0.847353i	0.684555	−	0.728961i	$-0.259996\pi$
$558$		0			0
$559$	22.1086	+	38.2933i	0.935095	+	1.61963i
$560$	46.5420	+	7.03064i	1.96676	+	0.297099i
$561$		0			0
$562$	−28.2144	+	16.2896i	−1.19015	+	0.687134i
$563$	−12.7368	−	7.35358i	−0.536791	−	0.309917i	0.206986	−	0.978344i	$-0.433634\pi$
$563$	−12.7368	−	7.35358i	−0.536791	−	0.309917i	−0.743778	+	0.668427i	$0.766968\pi$
$564$		0			0
$565$	−19.6093	−	22.2347i	−0.824970	−	0.935421i
$566$	−9.58644	+	54.3674i	−0.402948	+	2.28523i
$567$		0			0
$568$	5.64519	+	6.72768i	0.236867	+	0.282287i
$569$	40.6551			1.70435			0.852174	−	0.523258i	$-0.175284\pi$
$569$	40.6551			1.70435			0.852174	+	0.523258i	$0.175284\pi$
$570$		0			0
$571$	−24.3240			−1.01793			−0.508964	−	0.860788i	$-0.669972\pi$
$571$	−24.3240			−1.01793			−0.508964	+	0.860788i	$0.669972\pi$
$572$	1.55632	+	1.85475i	0.0650730	+	0.0775510i
$573$		0			0
$574$	−5.73575	+	32.5290i	−0.239405	+	1.35774i
$575$	6.49135	−	20.9957i	0.270708	−	0.875579i
$576$		0			0
$577$	−29.1743	−	16.8438i	−1.21454	−	0.701216i	−0.250796	−	0.968040i	$-0.580692\pi$
$577$	−29.1743	−	16.8438i	−1.21454	−	0.701216i	−0.963745	+	0.266824i	$0.914026\pi$
$578$	−19.8667	+	11.4700i	−0.826346	+	0.477091i
$579$		0			0
$580$	−1.29140	+	8.54888i	−0.0536224	+	0.354973i
$581$	17.2018	+	29.7945i	0.713652	+	1.23608i
$582$		0			0
$583$	−1.91971	−	5.27437i	−0.0795064	−	0.218442i
$584$	−0.518785	−	2.94218i	−0.0214675	−	0.121748i
$585$		0			0
$586$	36.7261	+	13.3672i	1.51714	+	0.552194i
$587$	1.44613	+	1.72343i	0.0596880	+	0.0711334i	0.795062	−	0.606528i	$-0.207438\pi$
$587$	1.44613	+	1.72343i	0.0596880	+	0.0711334i	−0.735374	+	0.677661i	$0.762994\pi$
$588$		0			0
$589$	17.7626	+	1.43606i	0.731897	+	0.0591718i
$590$	−1.84703	+	1.12787i	−0.0760409	+	0.0464335i
$591$		0			0
$592$	3.64202	−	10.0064i	0.149686	−	0.411259i
$593$	−30.9103	−	5.45032i	−1.26933	−	0.223818i	−0.501888	−	0.864932i	$-0.667361\pi$
$593$	−30.9103	−	5.45032i	−1.26933	−	0.223818i	−0.767445	+	0.641115i	$0.778472\pi$
$594$		0			0
$595$	15.0862	+	12.0389i	0.618472	+	0.493546i
$596$	−2.74781	+	4.75934i	−0.112555	+	0.194950i
$597$		0			0
$598$	20.9852	−	25.0091i	0.858147	−	1.02270i
$599$	7.97210	+	6.68939i	0.325731	+	0.273321i	0.790958	−	0.611871i	$-0.209583\pi$
$599$	7.97210	+	6.68939i	0.325731	+	0.273321i	−0.465227	+	0.885192i	$0.654027\pi$
$600$		0			0
$601$	0.647959	−	1.12230i	0.0264308	−	0.0457795i	−0.852507	−	0.522715i	$-0.824919\pi$
$601$	0.647959	−	1.12230i	0.0264308	−	0.0457795i	0.878938	+	0.476936i	$0.158253\pi$
$602$	27.4901	+	75.5285i	1.12041	+	3.07831i
$603$		0			0
$604$	−2.92440	+	16.5851i	−0.118992	+	0.674839i
$605$	4.75927	+	23.5825i	0.193492	+	0.958764i
$606$		0			0
$607$			5.50902i			0.223604i	0.993730	+	0.111802i	$0.0356623\pi$
$607$			5.50902i			0.223604i	−0.993730	+	0.111802i	$0.964338\pi$
$608$	−18.2285	+	18.4706i	−0.739265	+	0.749080i
$609$		0			0
$610$	−17.3558	+	51.6010i	−0.702716	+	2.08927i
$611$	10.2524	+	3.73155i	0.414766	+	0.150962i
$612$		0			0
$613$	−40.0547	+	7.06273i	−1.61780	+	0.285261i	−0.907945	−	0.419090i	$-0.862349\pi$
$613$	−40.0547	+	7.06273i	−1.61780	+	0.285261i	−0.709851	+	0.704351i	$0.751238\pi$
$614$	−9.14903	+	3.32997i	−0.369225	+	0.134387i
$615$		0			0
$616$	−1.51323	−	2.62099i	−0.0609697	−	0.105603i
$617$	19.6085	−	23.3684i	0.789407	−	0.940778i	−0.209911	−	0.977721i	$-0.567317\pi$
$617$	19.6085	−	23.3684i	0.789407	−	0.940778i	0.999317	+	0.0369423i	$0.0117618\pi$
$618$		0			0
$619$	2.90205	+	5.02651i	0.116643	+	0.202032i	0.918436	−	0.395571i	$-0.129453\pi$
$619$	2.90205	+	5.02651i	0.116643	+	0.202032i	−0.801792	+	0.597603i	$0.796120\pi$
$620$	10.8304	−	0.266549i	0.434960	−	0.0107049i
$621$		0			0
$622$	−11.7708	+	2.07551i	−0.471966	+	0.0832203i
$623$	−18.1224	−	3.19546i	−0.726058	−	0.128024i
$624$		0			0
$625$	−24.2188	−	6.20063i	−0.968754	−	0.248025i
$626$	8.17881			0.326891
$627$		0			0
$628$		−	12.7136i		−	0.507328i
$629$	3.34487	−	2.80668i	0.133369	−	0.111910i
$630$		0			0
$631$	−4.05716	+	23.0093i	−0.161513	+	0.915985i	0.791074	+	0.611720i	$0.209522\pi$
$631$	−4.05716	+	23.0093i	−0.161513	+	0.915985i	−0.952587	+	0.304265i	$0.901589\pi$
$632$	−7.64880	+	1.34869i	−0.304253	+	0.0536480i
$633$		0			0
$634$	24.6994	−	42.7806i	0.980937	−	1.69903i
$635$	−38.8917	−	21.1958i	−1.54337	−	0.841129i
$636$		0			0
$637$	−29.3479	+	34.9755i	−1.16281	+	1.38578i
$638$	2.47544	−	1.42919i	0.0980034	−	0.0565823i
$639$		0			0
$640$	14.8807	−	18.6473i	0.588210	−	0.737097i
$641$	−3.18574	−	18.0672i	−0.125829	−	0.713612i	−0.980812	−	0.194956i	$-0.937544\pi$
$641$	−3.18574	−	18.0672i	−0.125829	−	0.713612i	0.854983	−	0.518656i	$-0.173568\pi$
$642$		0			0
$643$	−5.39128	+	14.8124i	−0.212611	+	0.584144i	−0.999455	−	0.0330077i	$-0.989491\pi$
$643$	−5.39128	+	14.8124i	−0.212611	+	0.584144i	0.786844	+	0.617152i	$0.211714\pi$
$644$	16.9145	−	14.1929i	0.666523	−	0.559279i
$645$		0			0
$646$	−15.2729	+	4.20051i	−0.600905	+	0.165267i
$647$			25.0443i			0.984592i	0.870428	+	0.492296i	$0.163842\pi$
$647$			25.0443i			0.984592i	−0.870428	+	0.492296i	$0.836158\pi$
$648$		0			0
$649$	0.250158	+	0.0910500i	0.00981955	+	0.00357402i
$650$	−29.5901	−	22.4441i	−1.16062	−	0.880331i
$651$		0			0
$652$	6.86475	+	18.8608i	0.268844	+	0.738644i
$653$	−2.58813	−	1.49426i	−0.101282	−	0.0584749i	0.448504	−	0.893781i	$-0.351957\pi$
$653$	−2.58813	−	1.49426i	−0.101282	−	0.0584749i	−0.549785	+	0.835306i	$0.685290\pi$
$654$		0			0
$655$	−1.14561	+	7.58376i	−0.0447625	+	0.296322i
$656$	16.6082	+	13.9360i	0.648443	+	0.544108i
$657$		0			0
$658$	17.1752	+	9.91610i	0.669559	+	0.386570i
$659$	33.6123	−	12.2339i	1.30935	−	0.476564i	0.409320	−	0.912391i	$-0.365766\pi$
$659$	33.6123	−	12.2339i	1.30935	−	0.476564i	0.900031	+	0.435827i	$0.143544\pi$
$660$		0			0
$661$	0.559402	−	3.17253i	0.0217582	−	0.123397i	−0.971994	−	0.235006i	$-0.924489\pi$
$661$	0.559402	−	3.17253i	0.0217582	−	0.123397i	0.993752	+	0.111609i	$0.0356003\pi$
$662$	8.62500	−	23.6970i	0.335220	−	0.921010i
$663$		0			0
$664$	11.8034			0.458061
$665$	−24.7432	−	33.0897i	−0.959499	−	1.28316i
$666$		0			0
$667$	−9.21782	−	10.9854i	−0.356915	−	0.425355i
$668$	6.58918	−	18.1036i	0.254943	−	0.700450i
$669$		0			0
$670$	21.4208	−	18.8915i	0.827556	−	0.729841i
$671$	6.29297	−	2.29045i	0.242937	−	0.0884220i
$672$		0			0
$673$	0.554001	−	0.319853i	0.0213552	−	0.0123294i	−0.489284	−	0.872124i	$-0.662742\pi$
$673$	0.554001	−	0.319853i	0.0213552	−	0.0123294i	0.510640	+	0.859795i	$0.329409\pi$
$674$	−20.5036	−	17.2046i	−0.789770	−	0.662696i
$675$		0			0
$676$	−2.56107	−	4.43590i	−0.0985025	−	0.170611i
$677$	22.3439	+	12.9002i	0.858744	+	0.495796i	0.863592	−	0.504192i	$-0.168210\pi$
$677$	22.3439	+	12.9002i	0.858744	+	0.495796i	−0.00484733	+	0.999988i	$0.501543\pi$
$678$		0			0
$679$	−4.15661	−	23.5733i	−0.159516	−	0.904660i
$680$	6.16492	−	2.41723i	0.236414	−	0.0926964i
$681$		0			0
$682$	−2.30227	−	2.74374i	−0.0881585	−	0.105063i
$683$			5.33696i			0.204213i	0.994773	+	0.102107i	$0.0325583\pi$
$683$			5.33696i			0.204213i	−0.994773	+	0.102107i	$0.967442\pi$
$684$		0			0
$685$	1.16087	−	0.708872i	0.0443546	−	0.0270846i
$686$	−23.0082	+	19.3062i	−0.878458	+	0.737114i
$687$		0			0
$688$	51.9549	+	9.16105i	1.98076	+	0.349262i
$689$	8.26367	+	46.8656i	0.314821	+	1.78544i
$690$		0			0
$691$	−6.62534	+	11.4754i	−0.252040	+	0.436545i	−0.964087	−	0.265586i	$-0.914435\pi$
$691$	−6.62534	+	11.4754i	−0.252040	+	0.436545i	0.712048	+	0.702131i	$0.247768\pi$
$692$	−8.81712	+	5.09057i	−0.335177	+	0.193514i
$693$		0			0
$694$	−28.5915	−	23.9911i	−1.08532	−	0.910689i
$695$	9.05048	−	16.6065i	0.343304	−	0.629922i
$696$		0			0
$697$	3.04058	+	8.35392i	0.115170	+	0.316427i
$698$	5.50214	−	0.970176i	0.208259	−	0.0367217i
$699$		0			0
$700$	−17.0728	−	18.4242i	−0.645290	−	0.696370i
$701$	−31.3081	+	26.2706i	−1.18249	+	0.992228i	−0.182533	+	0.983200i	$0.558429\pi$
$701$	−31.3081	+	26.2706i	−1.18249	+	0.992228i	−0.999959	+	0.00902862i	$0.997126\pi$
$702$		0			0
$703$	−8.44523	+	4.00609i	−0.318518	+	0.151093i
$704$	0.340484			0.0128325
$705$		0			0
$706$	13.4925	+	4.91087i	0.507797	+	0.184823i
$707$	13.7800	+	2.42978i	0.518249	+	0.0913813i
$708$		0			0
$709$	6.91375	−	2.51640i	0.259651	−	0.0945053i	−0.208915	−	0.977934i	$-0.566993\pi$
$709$	6.91375	−	2.51640i	0.259651	−	0.0945053i	0.468566	+	0.883429i	$0.344771\pi$
$710$	−0.592897	−	24.0906i	−0.0222510	−	0.904105i
$711$		0			0
$712$	−4.05820	+	4.83637i	−0.152087	+	0.181251i
$713$	−11.5504	+	13.7652i	−0.432565	+	0.515511i
$714$		0			0
$715$	0.112401	+	4.56708i	0.00420355	+	0.170799i
$716$	−26.2005	+	9.53620i	−0.979158	+	0.356384i
$717$		0			0
$718$	−53.7538	−	9.47825i	−2.00607	−	0.353725i
$719$	30.0323	+	10.9309i	1.12002	+	0.407653i	0.834658	−	0.550768i	$-0.185665\pi$
$719$	30.0323	+	10.9309i	1.12002	+	0.407653i	0.285358	+	0.958421i	$0.407887\pi$
$720$		0			0
$721$	−14.4794			−0.539240
$722$	33.9059	−	0.447227i	1.26185	−	0.0166441i
$723$		0			0
$724$	15.0820	−	12.6553i	0.560520	−	0.470332i
$725$	−11.9659	+	11.0882i	−0.444403	+	0.411805i
$726$		0			0
$727$	28.9418	−	5.10323i	1.07339	−	0.189268i	0.391101	−	0.920348i	$-0.372094\pi$
$727$	28.9418	−	5.10323i	1.07339	−	0.189268i	0.682292	+	0.731079i	$0.260983\pi$
$728$	8.77615	+	24.1123i	0.325266	+	0.893661i
$729$		0			0
$730$	−3.92288	+	7.19801i	−0.145192	+	0.266410i
$731$	16.5716	+	13.9052i	0.612922	+	0.514302i
$732$		0			0
$733$	44.0187	−	25.4142i	1.62587	−	0.938696i	0.640562	−	0.767906i	$-0.278701\pi$
$733$	44.0187	−	25.4142i	1.62587	−	0.938696i	0.985307	−	0.170790i	$-0.0546319\pi$
$734$	−8.88034	+	15.3812i	−0.327779	+	0.567730i
$735$		0			0
$736$	−4.54388	−	25.7696i	−0.167490	−	0.949880i
$737$	−3.45991	−	0.610076i	−0.127448	−	0.0224724i
$738$		0			0
$739$	−11.2796	+	9.46473i	−0.414928	+	0.348166i	−0.826230	−	0.563334i	$-0.809519\pi$
$739$	−11.2796	+	9.46473i	−0.414928	+	0.348166i	0.411302	+	0.911499i	$0.365074\pi$
$740$	−4.84978	+	2.96146i	−0.178281	+	0.108865i
$741$		0			0
$742$			86.5039i			3.17566i
$743$	22.2770	+	26.5487i	0.817263	+	0.973976i	0.999958	−	0.00919385i	$-0.00292653\pi$
$743$	22.2770	+	26.5487i	0.817263	+	0.973976i	−0.182695	+	0.983170i	$0.558482\pi$
$744$		0			0
$745$	−9.65387	+	3.78522i	−0.353690	+	0.138680i
$746$	−2.87472	−	16.3034i	−0.105251	−	0.596909i
$747$		0			0
$748$	1.02584	+	0.592270i	0.0375085	+	0.0216555i
$749$	3.71455	+	6.43379i	0.135727	+	0.235086i
$750$		0			0
$751$	−6.40060	−	5.37074i	−0.233561	−	0.195981i	0.518494	−	0.855081i	$-0.326493\pi$
$751$	−6.40060	−	5.37074i	−0.233561	−	0.195981i	−0.752055	+	0.659100i	$0.770937\pi$
$752$	11.2733	−	6.50865i	0.411095	−	0.237346i
$753$		0			0
$754$	−22.7732	+	8.28878i	−0.829352	+	0.301859i
$755$	−23.8323	+	21.0182i	−0.867345	+	0.764932i
$756$		0			0
$757$	4.74412	−	13.0344i	0.172428	−	0.473742i	−0.823134	−	0.567847i	$-0.807777\pi$
$757$	4.74412	−	13.0344i	0.172428	−	0.473742i	0.995562	+	0.0941046i	$0.0299988\pi$
$758$	−24.2594	−	28.9112i	−0.881142	−	1.05010i
$759$		0			0
$760$	−14.0761	+	1.67541i	−0.510595	+	0.0607735i
$761$	−44.3970			−1.60939			−0.804696	−	0.593687i	$-0.797672\pi$
$761$	−44.3970			−1.60939			−0.804696	+	0.593687i	$0.797672\pi$
$762$		0			0
$763$	5.10239	−	14.0187i	0.184719	−	0.507511i
$764$	−2.63631	+	14.9513i	−0.0953784	+	0.540918i
$765$		0			0
$766$	−25.4075	+	9.24758i	−0.918011	+	0.334129i
$767$	−1.95468	−	1.12854i	−0.0705796	−	0.0407491i
$768$		0			0
$769$	−14.5549	−	12.2130i	−0.524863	−	0.440412i	0.341460	−	0.939896i	$-0.389079\pi$
$769$	−14.5549	−	12.2130i	−0.524863	−	0.440412i	−0.866323	+	0.499484i	$0.833523\pi$
$770$	−1.24038	+	8.21114i	−0.0447001	+	0.295909i
$771$		0			0
$772$	−9.89342	−	5.71197i	−0.356072	−	0.205578i
$773$	0.638682	+	1.75476i	0.0229718	+	0.0631144i	0.950648	−	0.310270i	$-0.100419\pi$
$773$	0.638682	+	1.75476i	0.0229718	+	0.0631144i	−0.927677	+	0.373384i	$0.878197\pi$
$774$		0			0
$775$	16.2866	+	12.3534i	0.585032	+	0.443747i
$776$	−7.71714	−	2.80881i	−0.277029	−	0.100830i
$777$		0			0
$778$			56.1252i			2.01218i
$779$	−1.78365	−	18.9473i	−0.0639060	−	0.678856i
$780$		0			0
$781$	−2.27077	+	1.90540i	−0.0812544	+	0.0681805i
$782$	5.46279	−	15.0089i	0.195349	−	0.536717i
$783$		0			0
$784$	9.45938	+	53.6468i	0.337835	+	1.91596i
$785$	14.9629	−	18.7502i	0.534047	−	0.669225i
$786$		0			0
$787$	11.2314	−	6.48445i	0.400356	−	0.231146i	−0.286282	−	0.958146i	$-0.592419\pi$
$787$	11.2314	−	6.48445i	0.400356	−	0.231146i	0.686638	+	0.727000i	$0.259086\pi$
$788$	−2.36327	+	2.81644i	−0.0841881	+	0.100331i
$789$		0			0
$790$	18.7127	+	10.1983i	0.665769	+	0.362841i
$791$	28.1016	−	48.6734i	0.999178	−	1.73063i
$792$		0			0
$793$	−55.9164	+	9.85957i	−1.98565	+	0.350124i
$794$	2.90865	−	16.4958i	0.103224	−	0.585413i
$795$		0			0
$796$	0.475962	−	0.399379i	0.0168700	−	0.0141556i
$797$			29.9226i			1.05991i	0.848025	+	0.529956i	$0.177791\pi$
$797$			29.9226i			1.05991i	−0.848025	+	0.529956i	$0.822209\pi$
$798$		0			0
$799$	5.33772			0.188835
$800$	−29.0255	+	6.60491i	−1.02621	+	0.233519i
$801$		0			0
$802$	10.8275	+	1.90918i	0.382331	+	0.0674153i
$803$	0.993061	−	0.175103i	0.0350444	−	0.00617927i
$804$		0			0
$805$	41.6496	−	1.02504i	1.46796	−	0.0361281i
$806$	15.1837	+	26.2989i	0.534822	+	0.926339i
$807$		0			0
$808$	3.08579	−	3.67750i	0.108558	−	0.129374i
$809$	−21.2289	−	36.7696i	−0.746369	−	1.29275i	−0.949552	−	0.313608i	$-0.898462\pi$
$809$	−21.2289	−	36.7696i	−0.746369	−	1.29275i	0.203183	−	0.979141i	$-0.434871\pi$
$810$		0			0
$811$	29.2727	−	10.6544i	1.02790	−	0.374126i	0.227621	−	0.973750i	$-0.426905\pi$
$811$	29.2727	−	10.6544i	1.02790	−	0.374126i	0.800282	+	0.599623i	$0.204683\pi$
$812$	−16.1417	+	2.84622i	−0.566463	+	0.0998828i
$813$		0			0
$814$	1.76537	+	0.642542i	0.0618762	+	0.0225211i
$815$	−12.0733	+	35.8954i	−0.422909	+	1.25736i
$816$		0			0
$817$	−26.8114	−	37.7583i	−0.938014	−	1.32099i
$818$			4.07767i			0.142572i
$819$		0			0
$820$	−2.28875	−	11.3409i	−0.0799267	−	0.396042i
$821$	1.07790	−	6.11310i	0.0376191	−	0.213349i	−0.960204	−	0.279301i	$-0.909897\pi$
$821$	1.07790	−	6.11310i	0.0376191	−	0.213349i	0.997823	+	0.0659521i	$0.0210085\pi$
$822$		0			0
$823$	12.3025	+	33.8009i	0.428839	+	1.17823i	0.946518	+	0.322651i	$0.104574\pi$
$823$	12.3025	+	33.8009i	0.428839	+	1.17823i	−0.517679	+	0.855575i	$0.673204\pi$
$824$	−2.48383	+	4.30212i	−0.0865283	+	0.149871i
$825$		0			0
$826$	−3.14292	−	2.63722i	−0.109356	−	0.0917606i
$827$	−9.88848	+	11.7846i	−0.343856	+	0.409792i	−0.910062	−	0.414472i	$-0.863966\pi$
$827$	−9.88848	+	11.7846i	−0.343856	+	0.409792i	0.566206	+	0.824264i	$0.308411\pi$
$828$		0			0
$829$	−12.0970	+	20.9527i	−0.420148	+	0.727717i	−0.995954	−	0.0898693i	$-0.971355\pi$
$829$	−12.0970	+	20.9527i	−0.420148	+	0.727717i	0.575806	+	0.817586i	$0.304688\pi$
$830$	−25.3148	−	20.2015i	−0.878691	−	0.701203i
$831$		0			0
$832$	−2.84293	−	0.501284i	−0.0985607	−	0.0173789i
$833$	−7.63975	+	20.9900i	−0.264702	+	0.727262i
$834$		0			0
$835$	31.0243	−	18.9446i	1.07364	−	0.655605i
$836$	−1.80483	−	1.78118i	−0.0624215	−	0.0616035i
$837$		0			0
$838$	25.9827	+	30.9649i	0.897556	+	1.06967i
$839$	−11.6771	−	4.25013i	−0.403139	−	0.146731i	0.132489	−	0.991184i	$-0.457703\pi$
$839$	−11.6771	−	4.25013i	−0.403139	−	0.146731i	−0.535628	+	0.844454i	$0.679925\pi$
$840$		0			0
$841$	−3.18727	−	18.0759i	−0.109906	−	0.623308i
$842$	−14.0372	−	38.5669i	−0.483754	−	1.32910i
$843$		0			0
$844$	−11.2960	−	19.5652i	−0.388824	−	0.673463i
$845$	1.44358	−	9.55630i	0.0496606	−	0.328747i
$846$		0			0
$847$	−39.4983	+	22.8043i	−1.35718	+	0.783566i
$848$	49.1718	+	28.3894i	1.68857	+	0.974895i
$849$		0			0
$850$	−17.3590	−	5.36699i	−0.595410	−	0.184086i
$851$	1.63667	−	9.28199i	0.0561042	−	0.318182i
$852$		0			0
$853$	14.8823	+	17.7360i	0.509560	+	0.607270i	0.958079	−	0.286503i	$-0.0924930\pi$
$853$	14.8823	+	17.7360i	0.509560	+	0.607270i	−0.448519	+	0.893773i	$0.648049\pi$
$854$	−103.210			−3.53176
$855$		0			0
$856$	2.54882			0.0871167
$857$	−1.82726	−	2.17765i	−0.0624181	−	0.0743870i	0.733932	−	0.679223i	$-0.237683\pi$
$857$	−1.82726	−	2.17765i	−0.0624181	−	0.0743870i	−0.796350	+	0.604836i	$0.793239\pi$
$858$		0			0
$859$	4.49254	−	25.4785i	0.153284	−	0.869314i	−0.807055	−	0.590477i	$-0.798940\pi$
$859$	4.49254	−	25.4785i	0.153284	−	0.869314i	0.960338	−	0.278838i	$-0.0899492\pi$
$860$	−18.6214	−	21.1145i	−0.634985	−	0.720000i
$861$		0			0
$862$	−39.6161	−	22.8724i	−1.34933	−	0.779036i
$863$	32.9118	−	19.0016i	1.12033	−	0.646823i	0.178844	−	0.983877i	$-0.442764\pi$
$863$	32.9118	−	19.0016i	1.12033	−	0.646823i	0.941485	+	0.337055i	$0.109431\pi$
$864$		0			0
$865$	−18.9948	−	2.86936i	−0.645843	−	0.0975613i
$866$	2.10886	+	3.65266i	0.0716621	+	0.124122i
$867$		0			0
$868$	7.02455	+	19.2998i	0.238429	+	0.655077i
$869$	−0.455217	−	2.58167i	−0.0154422	−	0.0875770i
$870$		0			0
$871$	27.9909	+	10.1879i	0.948437	+	0.345203i
$872$	−3.28997	−	3.92083i	−0.111412	−	0.132776i
$873$		0			0
$874$	−19.4264	+	28.1369i	−0.657108	+	0.951744i
$875$	−3.49542	−	47.2656i	−0.118167	−	1.59787i
$876$		0			0
$877$	−16.7912	+	46.1335i	−0.567000	+	1.55782i	0.242164	+	0.970235i	$0.422143\pi$
$877$	−16.7912	+	46.1335i	−0.567000	+	1.55782i	−0.809164	+	0.587583i	$0.800079\pi$
$878$	−11.1018	−	1.95755i	−0.374668	−	0.0660641i
$879$		0			0
$880$	4.26043	+	3.39986i	0.143619	+	0.114609i
$881$	−27.8747	+	48.2804i	−0.939123	+	1.62661i	−0.172011	+	0.985095i	$0.555027\pi$
$881$	−27.8747	+	48.2804i	−0.939123	+	1.62661i	−0.767112	+	0.641514i	$0.778307\pi$
$882$		0			0
$883$	10.6931	−	12.7435i	0.359851	−	0.428853i	−0.555496	−	0.831519i	$-0.687472\pi$
$883$	10.6931	−	12.7435i	0.359851	−	0.428853i	0.915347	+	0.402666i	$0.131916\pi$
$884$	−7.69345	−	6.45557i	−0.258759	−	0.217124i
$885$		0			0
$886$	−28.1307	+	48.7237i	−0.945068	+	1.63691i
$887$	−14.8397	−	40.7717i	−0.498267	−	1.36898i	−0.892948	−	0.450160i	$-0.851367\pi$
$887$	−14.8397	−	40.7717i	−0.498267	−	1.36898i	0.394680	−	0.918818i	$-0.370855\pi$
$888$		0			0
$889$	14.5811	−	82.6934i	0.489034	−	2.77345i
$890$	16.9811	−	3.42702i	0.569207	−	0.114874i
$891$		0			0
$892$		−	3.74820i		−	0.125499i
$893$	−11.0564	−	2.88455i	−0.369989	−	0.0965276i
$894$		0			0
$895$	−49.8643	−	16.7717i	−1.66678	−	0.560615i
$896$	42.5001	+	15.4688i	1.41983	+	0.516776i
$897$		0			0
$898$	−26.5091	+	4.67426i	−0.884619	+	0.155982i
$899$	12.5345	−	4.56220i	0.418051	−	0.152158i
$900$		0			0
$901$	11.6410	+	20.1628i	0.387818	+	0.671721i
$902$	−2.45865	+	2.93010i	−0.0818640	+	0.0975617i
$903$		0			0
$904$	−9.64125	−	16.6991i	−0.320663	−	0.555405i
$905$	37.1376	−	0.913997i	1.23449	−	0.0303823i
$906$		0			0
$907$	19.5350	−	3.44455i	0.648649	−	0.114374i	0.160363	−	0.987058i	$-0.448733\pi$
$907$	19.5350	−	3.44455i	0.648649	−	0.114374i	0.488286	+	0.872684i	$0.337622\pi$
$908$	−10.5580	−	1.86165i	−0.350378	−	0.0617812i
$909$		0			0
$910$	22.4458	−	66.7342i	0.744070	−	2.21222i
$911$	−15.4076			−0.510478			−0.255239	−	0.966878i	$-0.582154\pi$
$911$	−15.4076			−0.510478			−0.255239	+	0.966878i	$0.582154\pi$
$912$		0			0
$913$			3.98395i			0.131849i
$914$	27.5270	−	23.0979i	0.910512	−	0.764010i
$915$		0			0
$916$	−3.68193	+	20.8812i	−0.121654	+	0.689936i
$917$	−14.3194	+	2.52490i	−0.472869	+	0.0833795i
$918$		0			0
$919$	−6.62805	+	11.4801i	−0.218639	+	0.378694i	−0.954392	−	0.298556i	$-0.903495\pi$
$919$	−6.62805	+	11.4801i	−0.218639	+	0.378694i	0.735753	+	0.677250i	$0.236828\pi$
$920$	6.84013	−	12.5508i	0.225512	−	0.413788i
$921$		0			0
$922$	8.58644	−	10.2329i	0.282779	−	0.337003i
$923$	21.7654	−	12.5663i	0.716417	−	0.413624i
$924$		0			0
$925$	−10.6379	−	1.34017i	−0.349773	−	0.0440647i
$926$	6.69313	+	37.9586i	0.219950	+	1.24740i
$927$		0			0
$928$	−6.64358	+	18.2531i	−0.218086	+	0.599187i
$929$	23.9018	−	20.0560i	0.784193	−	0.658016i	−0.160108	−	0.987100i	$-0.551184\pi$
$929$	23.9018	−	20.0560i	0.784193	−	0.658016i	0.944301	+	0.329083i	$0.106740\pi$
$930$		0			0
$931$	27.1680	−	39.3496i	0.890394	−	1.28963i
$932$		−	7.63580i		−	0.250119i
$933$		0			0
$934$	−45.3648	−	16.5114i	−1.48438	−	0.540270i
$935$	0.815876	+	2.08082i	0.0266820	+	0.0680501i
$936$		0			0
$937$	−5.54711	−	15.2405i	−0.181216	−	0.497887i	0.815510	−	0.578743i	$-0.196457\pi$
$937$	−5.54711	−	15.2405i	−0.181216	−	0.497887i	−0.996726	+	0.0808564i	$0.974234\pi$
$938$	46.8916	+	27.0729i	1.53107	+	0.883961i
$939$		0			0
$940$	−6.86860	−	1.03757i	−0.224029	−	0.0338419i
$941$	−26.9454	−	22.6099i	−0.878396	−	0.737062i	0.0874525	−	0.996169i	$-0.472127\pi$
$941$	−26.9454	−	22.6099i	−0.878396	−	0.737062i	−0.965849	+	0.259107i	$0.916572\pi$
$942$		0			0
$943$	16.6188	+	9.59486i	0.541182	+	0.312452i
$944$	−2.53055	+	0.921045i	−0.0823624	+	0.0299775i
$945$		0			0
$946$	−1.61623	+	9.16612i	−0.0525483	+	0.298016i
$947$	−7.61965	+	20.9348i	−0.247605	+	0.680290i	0.752167	+	0.658972i	$0.229009\pi$
$947$	−7.61965	+	20.9348i	−0.247605	+	0.680290i	−0.999773	+	0.0213182i	$0.993214\pi$
$948$		0			0
$949$	−8.54953			−0.277530
$950$	33.0567	+	20.4980i	1.07250	+	0.665043i
$951$		0			0
$952$	8.06934	+	9.61666i	0.261529	+	0.311678i
$953$	1.45699	−	4.00305i	0.0471966	−	0.129672i	−0.913855	−	0.406041i	$-0.866909\pi$
$953$	1.45699	−	4.00305i	0.0471966	−	0.129672i	0.961052	+	0.276369i	$0.0891313\pi$
$954$		0			0
$955$	−21.4845	+	18.9477i	−0.695222	+	0.613132i
$956$	−15.0049	+	5.46135i	−0.485294	+	0.176633i
$957$		0			0
$958$	58.8145	−	33.9566i	1.90021	−	1.09709i
$959$	1.97535	+	1.65751i	0.0637873	+	0.0535239i
$960$		0			0
$961$	7.14280	+	12.3717i	0.230413	+	0.399087i
$962$	−13.7943	−	7.96412i	−0.444745	−	0.256773i
$963$		0			0
$964$	3.62907	+	20.5815i	0.116885	+	0.662885i
$965$	−7.86848	−	20.0678i	−0.253295	−	0.646007i
$966$		0			0
$967$	0.783596	+	0.933854i	0.0251988	+	0.0300307i	0.778497	−	0.627649i	$-0.215983\pi$
$967$	0.783596	+	0.933854i	0.0251988	+	0.0300307i	−0.753298	+	0.657679i	$0.771538\pi$
$968$			15.6477i			0.502935i
$969$		0			0
$970$	11.7438	+	19.2319i	0.377069	+	0.617500i
$971$	3.32466	−	2.78972i	0.106693	−	0.0895264i	−0.587880	−	0.808948i	$-0.700037\pi$
$971$	3.32466	−	2.78972i	0.106693	−	0.0895264i	0.694574	+	0.719421i	$0.255593\pi$
$972$		0			0
$973$	35.3096	+	6.22604i	1.13197	+	0.199598i
$974$	−5.68222	−	32.2255i	−0.182070	−	1.03257i
$975$		0			0
$976$	−33.8720	+	58.6680i	−1.08422	+	1.87792i
$977$	18.6429	−	10.7635i	0.596440	−	0.344355i	−0.171200	−	0.985236i	$-0.554764\pi$
$977$	18.6429	−	10.7635i	0.596440	−	0.344355i	0.767640	+	0.640882i	$0.221431\pi$
$978$		0			0
$979$	−1.63240	−	1.36975i	−0.0521718	−	0.0437773i
$980$	13.9110	−	25.5250i	0.444371	−	0.815367i
$981$		0			0
$982$	9.19713	+	25.2689i	0.293492	+	0.806363i
$983$	14.3780	−	2.53522i	0.458586	−	0.0808611i	0.0604172	−	0.998173i	$-0.480757\pi$
$983$	14.3780	−	2.53522i	0.458586	−	0.0808611i	0.398169	+	0.917312i	$0.369646\pi$
$984$		0			0
$985$	−6.80011	+	1.37236i	−0.216669	+	0.0437269i
$986$	−9.08261	+	7.62121i	−0.289249	+	0.242709i
$987$		0			0
$988$	12.4474	+	17.5295i	0.396004	+	0.557688i
$989$	46.6954			1.48483
$990$		0			0
$991$	−30.0031	−	10.9202i	−0.953080	−	0.346893i	−0.181762	−	0.983343i	$-0.558180\pi$
$991$	−30.0031	−	10.9202i	−0.953080	−	0.346893i	−0.771318	+	0.636450i	$0.780402\pi$
$992$	23.9701	+	4.22658i	0.761052	+	0.134194i
$993$		0			0
$994$	42.9294	−	15.6250i	1.36164	−	0.495596i
$995$	1.17199	−	0.0288441i	0.0371547	−	0.000914418i
$996$		0			0
$997$	35.4698	−	42.2712i	1.12334	−	1.33874i	0.189157	−	0.981947i	$-0.439424\pi$
$997$	35.4698	−	42.2712i	1.12334	−	1.33874i	0.934182	−	0.356797i	$-0.116131\pi$
$998$	−39.6117	+	47.2073i	−1.25389	+	1.49432i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.424.2		48
3.2	odd	2		95.2.p.a.44.7	yes	48
5.4	even	2	inner	855.2.da.b.424.7		48
15.2	even	4		475.2.l.f.101.2		48
15.8	even	4		475.2.l.f.101.7		48
15.14	odd	2		95.2.p.a.44.2	✓	48
19.16	even	9	inner	855.2.da.b.244.7		48
57.23	odd	18		1805.2.b.k.1084.20		24
57.35	odd	18		95.2.p.a.54.2	yes	48
57.53	even	18		1805.2.b.l.1084.5		24
95.54	even	18	inner	855.2.da.b.244.2		48
285.23	even	36		9025.2.a.cu.1.20		24
285.53	odd	36		9025.2.a.ct.1.5		24
285.92	even	36		475.2.l.f.301.2		48
285.137	even	36		9025.2.a.cu.1.5		24
285.149	odd	18		95.2.p.a.54.7	yes	48
285.167	odd	36		9025.2.a.ct.1.20		24
285.194	odd	18		1805.2.b.k.1084.5		24
285.224	even	18		1805.2.b.l.1084.20		24
285.263	even	36		475.2.l.f.301.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.2	✓	48	15.14	odd	2
95.2.p.a.44.7	yes	48	3.2	odd	2
95.2.p.a.54.2	yes	48	57.35	odd	18
95.2.p.a.54.7	yes	48	285.149	odd	18
475.2.l.f.101.2		48	15.2	even	4
475.2.l.f.101.7		48	15.8	even	4
475.2.l.f.301.2		48	285.92	even	36
475.2.l.f.301.7		48	285.263	even	36
855.2.da.b.244.2		48	95.54	even	18	inner
855.2.da.b.244.7		48	19.16	even	9	inner
855.2.da.b.424.2		48	1.1	even	1	trivial
855.2.da.b.424.7		48	5.4	even	2	inner
1805.2.b.k.1084.5		24	285.194	odd	18
1805.2.b.k.1084.20		24	57.23	odd	18
1805.2.b.l.1084.5		24	57.53	even	18
1805.2.b.l.1084.20		24	285.224	even	18
9025.2.a.ct.1.5		24	285.53	odd	36
9025.2.a.ct.1.20		24	285.167	odd	36
9025.2.a.cu.1.5		24	285.137	even	36
9025.2.a.cu.1.20		24	285.23	even	36

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.da (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14717 - 1.36714i) q^{2} +(-0.205786 + 1.16707i) q^{4} +(-1.67705 + 1.47903i) q^{5} +(-3.67118 - 2.11955i) q^{7} +(-1.25953 + 0.727188i) q^{8} +(3.94589 + 0.596068i) q^{10} +(-0.245445 - 0.425123i) q^{11} +(1.42349 + 3.91099i) q^{13} +(1.31373 + 7.45051i) q^{14} +(4.66628 + 1.69839i) q^{16} +(1.30884 + 1.55982i) q^{17} +(-1.86816 - 3.93827i) q^{19} +(-1.38102 - 2.26160i) q^{20} +(-0.299637 + 0.823245i) q^{22} +(4.32847 + 0.763227i) q^{23} +(0.624964 - 4.96079i) q^{25} +(3.71391 - 6.43268i) q^{26} +(3.22915 - 3.84835i) q^{28} +(-2.49937 - 2.09722i) q^{29} +(-2.04416 + 3.54059i) q^{31} +(-2.03622 - 5.59447i) q^{32} +(0.631029 - 3.57874i) q^{34} +(9.29160 - 1.87517i) q^{35} -2.14440i q^{37} +(-3.24108 + 7.07191i) q^{38} +(1.03675 - 3.08240i) q^{40} +(4.10271 + 1.49327i) q^{41} +(10.4627 - 1.84485i) q^{43} +(0.546658 - 0.198967i) q^{44} +(-3.92205 - 6.79319i) q^{46} +(1.68502 - 2.00812i) q^{47} +(5.48502 + 9.50033i) q^{49} +(-7.49905 + 4.83645i) q^{50} +(-4.85735 + 0.856482i) q^{52} +(11.2604 + 1.98551i) q^{53} +(1.04039 + 0.349931i) q^{55} +6.16526 q^{56} +5.82287i q^{58} +(-0.415431 + 0.348588i) q^{59} +(-2.36895 + 13.4350i) q^{61} +(7.18550 - 1.26700i) q^{62} +(-0.346803 + 0.600680i) q^{64} +(-8.17171 - 4.45354i) q^{65} +(4.60042 - 5.48257i) q^{67} +(-2.08976 + 1.20652i) q^{68} +(-13.2227 - 10.5518i) q^{70} +(-1.04859 - 5.94684i) q^{71} +(-0.702575 + 1.93031i) q^{73} +(-2.93170 + 2.45999i) q^{74} +(4.98069 - 1.36984i) q^{76} +2.08093i q^{77} +(5.01823 + 1.82649i) q^{79} +(-10.3375 + 4.05327i) q^{80} +(-2.66500 - 7.32202i) q^{82} +(-7.02847 - 4.05789i) q^{83} +(-4.50199 - 0.680073i) q^{85} +(-14.5246 - 12.1876i) q^{86} +(0.618288 + 0.356969i) q^{88} +(4.07920 - 1.48471i) q^{89} +(3.06370 - 17.3751i) q^{91} +(-1.78148 + 4.89458i) q^{92} -4.67839 q^{94} +(8.95780 + 3.84160i) q^{95} +(3.62962 + 4.32562i) q^{97} +(6.69607 - 18.3973i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49}+ \cdots + 63 q^{95}+O(q^{100}) \) 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Introduction

L-functions

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