LMFDB - Embedded newform 819.2.fm.g.496.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			496.1
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.g.748.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61897 - 0.433802i) q^{2} +(0.700831 + 0.404625i) q^{4} +(-1.42145 - 1.42145i) q^{5} +(-1.11484 - 2.39940i) q^{7} +(1.41124 + 1.41124i) q^{8} +O(q^{10})$	\(q+(-1.61897 - 0.433802i) q^{2} +(0.700831 + 0.404625i) q^{4} +(-1.42145 - 1.42145i) q^{5} +(-1.11484 - 2.39940i) q^{7} +(1.41124 + 1.41124i) q^{8} +(1.68466 + 2.91792i) q^{10} +(-0.254101 + 0.948318i) q^{11} +(1.60977 - 3.22624i) q^{13} +(0.764036 + 4.36818i) q^{14} +(-2.48181 - 4.29862i) q^{16} +(2.99281 - 5.18370i) q^{17} +(-2.71200 + 0.726678i) q^{19} +(-0.421043 - 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 + 1.49448i) q^{23} -0.958941i q^{25} +(-4.00573 + 4.52487i) q^{26} +(0.189540 - 2.13267i) q^{28} +(-3.65708 - 6.33425i) q^{29} +(6.11048 + 6.11048i) q^{31} +(1.12013 + 4.18037i) q^{32} +(-7.09397 + 7.09397i) q^{34} +(-1.82594 + 4.99533i) q^{35} +(-1.24143 + 4.63309i) q^{37} +4.70588 q^{38} -4.01202i q^{40} +(-0.886060 + 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.561795 + 0.561795i) q^{44} +(4.83903 - 1.29661i) q^{46} +(-2.17001 + 2.17001i) q^{47} +(-4.51424 + 5.34992i) q^{49} +(-0.415990 + 1.55250i) q^{50} +(2.43360 - 1.60970i) q^{52} -6.32446 q^{53} +(1.70918 - 0.986797i) q^{55} +(1.81282 - 4.95944i) q^{56} +(3.17290 + 11.8414i) q^{58} +(-0.131692 - 0.491481i) q^{59} +(-11.2829 - 6.51419i) q^{61} +(-7.24196 - 12.5434i) q^{62} +2.67342i q^{64} +(-6.87417 + 2.29773i) q^{65} +(-0.827827 - 0.221815i) q^{67} +(4.19491 - 2.42193i) q^{68} +(5.12312 - 7.29521i) q^{70} +(3.01121 + 11.2380i) q^{71} +(1.03002 - 1.03002i) q^{73} +(4.01968 - 6.96230i) q^{74} +(-2.19469 - 0.588064i) q^{76} +(2.55868 - 0.447537i) q^{77} -11.6027 q^{79} +(-2.58251 + 9.63806i) q^{80} +(2.86901 - 4.96927i) q^{82} +(-1.23779 - 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(1.02452 + 1.02452i) q^{86} +(-1.69690 + 0.979707i) q^{88} +(-7.75255 - 2.07729i) q^{89} +(-9.53569 - 0.265737i) q^{91} -2.41881 q^{92} +(4.45454 - 2.57183i) q^{94} +(4.88792 + 2.82204i) q^{95} +(12.0756 - 3.23566i) q^{97} +(9.62923 - 6.70307i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.61897	−	0.433802i	−1.14479	−	0.306744i	−0.363912	−	0.931433i	$-0.618559\pi$
$2$	−1.61897	−	0.433802i	−1.14479	−	0.306744i	−0.780873	+	0.624689i	$0.785226\pi$
$3$		0			0
$3$		0			0
$4$	0.700831	+	0.404625i	0.350416	+	0.202313i
$5$	−1.42145	−	1.42145i	−0.635693	−	0.635693i	0.313797	−	0.949490i	$-0.398399\pi$
$5$	−1.42145	−	1.42145i	−0.635693	−	0.635693i	−0.949490	+	0.313797i	$0.898399\pi$
$6$		0			0
$7$	−1.11484	−	2.39940i	−0.421372	−	0.906888i
$7$	−1.11484	−	2.39940i	−0.421372	−	0.906888i
$8$	1.41124	+	1.41124i	0.498948	+	0.498948i
$9$		0			0
$10$	1.68466	+	2.91792i	0.532737	+	0.922727i
$11$	−0.254101	+	0.948318i	−0.0766144	+	0.285929i	−0.993595	−	0.113004i	$-0.963953\pi$
$11$	−0.254101	+	0.948318i	−0.0766144	+	0.285929i	0.916980	+	0.398933i	$0.130619\pi$
$12$		0			0
$13$	1.60977	−	3.22624i	0.446471	−	0.894798i
$13$	1.60977	−	3.22624i	0.446471	−	0.894798i
$14$	0.764036	+	4.36818i	0.204197	+	1.16745i
$15$		0			0
$16$	−2.48181	−	4.29862i	−0.620452	−	1.07465i
$17$	2.99281	−	5.18370i	0.725863	−	1.25723i	−0.232755	−	0.972535i	$-0.574774\pi$
$17$	2.99281	−	5.18370i	0.725863	−	1.25723i	0.958618	−	0.284696i	$-0.0918925\pi$
$18$		0			0
$19$	−2.71200	+	0.726678i	−0.622175	+	0.166711i	−0.556116	−	0.831104i	$-0.687709\pi$
$19$	−2.71200	+	0.726678i	−0.622175	+	0.166711i	−0.0660587	+	0.997816i	$0.521042\pi$
$20$	−0.421043	−	1.57135i	−0.0941481	−	0.351366i
$21$		0			0
$22$	0.822765	−	1.42507i	0.175414	−	0.303826i
$23$	−2.58851	+	1.49448i	−0.539742	+	0.311620i	−0.744974	−	0.667093i	$-0.767538\pi$
$23$	−2.58851	+	1.49448i	−0.539742	+	0.311620i	0.205233	+	0.978713i	$0.434205\pi$
$24$		0			0
$25$		−	0.958941i		−	0.191788i
$26$	−4.00573	+	4.52487i	−0.785588	+	0.887399i
$27$		0			0
$28$	0.189540	−	2.13267i	0.0358196	−	0.403037i
$29$	−3.65708	−	6.33425i	−0.679103	−	1.17624i	−0.975251	−	0.221099i	$-0.929036\pi$
$29$	−3.65708	−	6.33425i	−0.679103	−	1.17624i	0.296148	−	0.955142i	$-0.404298\pi$
$30$		0			0
$31$	6.11048	+	6.11048i	1.09748	+	1.09748i	0.994705	+	0.102770i	$0.0327707\pi$
$31$	6.11048	+	6.11048i	1.09748	+	1.09748i	0.102770	+	0.994705i	$0.467229\pi$
$32$	1.12013	+	4.18037i	0.198012	+	0.738992i
$33$		0			0
$34$	−7.09397	+	7.09397i	−1.21661	+	1.21661i
$35$	−1.82594	+	4.99533i	−0.308639	+	0.844366i
$36$		0			0
$37$	−1.24143	+	4.63309i	−0.204090	+	0.761675i	0.785635	+	0.618690i	$0.212336\pi$
$37$	−1.24143	+	4.63309i	−0.204090	+	0.761675i	−0.989725	+	0.142984i	$0.954330\pi$
$38$	4.70588			0.763395
$39$		0			0
$40$		−	4.01202i		−	0.634356i
$41$	−0.886060	+	3.30682i	−0.138379	+	0.516439i	0.861582	+	0.507619i	$0.169474\pi$
$41$	−0.886060	+	3.30682i	−0.138379	+	0.516439i	−0.999961	+	0.00881984i	$0.997193\pi$
$42$		0			0
$43$	−0.748633	−	0.432224i	−0.114165	−	0.0659135i	0.441830	−	0.897099i	$-0.354329\pi$
$43$	−0.748633	−	0.432224i	−0.114165	−	0.0659135i	−0.555995	+	0.831185i	$0.687663\pi$
$44$	−0.561795	+	0.561795i	−0.0846939	+	0.0846939i
$45$		0			0
$46$	4.83903	−	1.29661i	0.713476	−	0.191175i
$47$	−2.17001	+	2.17001i	−0.316529	+	0.316529i	−0.847432	−	0.530903i	$-0.821853\pi$
$47$	−2.17001	+	2.17001i	−0.316529	+	0.316529i	0.530903	+	0.847432i	$0.321853\pi$
$48$		0			0
$49$	−4.51424	+	5.34992i	−0.644892	+	0.764274i
$50$	−0.415990	+	1.55250i	−0.0588299	+	0.219556i
$51$		0			0
$52$	2.43360	−	1.60970i	0.337479	−	0.223225i
$53$	−6.32446			−0.868732			−0.434366	−	0.900737i	$-0.643028\pi$
$53$	−6.32446			−0.868732			−0.434366	+	0.900737i	$0.643028\pi$
$54$		0			0
$55$	1.70918	−	0.986797i	0.230466	−	0.133060i
$56$	1.81282	−	4.95944i	0.242248	−	0.662733i
$57$		0			0
$58$	3.17290	+	11.8414i	0.416622	+	1.55485i
$59$	−0.131692	−	0.491481i	−0.0171448	−	0.0639854i	0.956823	−	0.290670i	$-0.0938781\pi$
$59$	−0.131692	−	0.491481i	−0.0171448	−	0.0639854i	−0.973968	+	0.226684i	$0.927211\pi$
$60$		0			0
$61$	−11.2829	−	6.51419i	−1.44463	−	0.834057i	−0.446475	−	0.894796i	$-0.647321\pi$
$61$	−11.2829	−	6.51419i	−1.44463	−	0.834057i	−0.998154	+	0.0607392i	$0.980654\pi$
$62$	−7.24196	−	12.5434i	−0.919729	−	1.59302i
$63$		0			0
$64$			2.67342i			0.334178i
$65$	−6.87417	+	2.29773i	−0.852636	+	0.284998i
$66$		0			0
$67$	−0.827827	−	0.221815i	−0.101135	−	0.0270991i	0.207897	−	0.978151i	$-0.433338\pi$
$67$	−0.827827	−	0.221815i	−0.101135	−	0.0270991i	−0.309032	+	0.951052i	$0.600005\pi$
$68$	4.19491	−	2.42193i	0.508707	−	0.293702i
$69$		0			0
$70$	5.12312	−	7.29521i	0.612330	−	0.871944i
$71$	3.01121	+	11.2380i	0.357365	+	1.33370i	0.877482	+	0.479609i	$0.159222\pi$
$71$	3.01121	+	11.2380i	0.357365	+	1.33370i	−0.520117	+	0.854095i	$0.674112\pi$
$72$		0			0
$73$	1.03002	−	1.03002i	0.120555	−	0.120555i	−0.644255	−	0.764810i	$-0.722833\pi$
$73$	1.03002	−	1.03002i	0.120555	−	0.120555i	0.764810	+	0.644255i	$0.222833\pi$
$74$	4.01968	−	6.96230i	0.467279	−	0.809350i
$75$		0			0
$76$	−2.19469	−	0.588064i	−0.251748	−	0.0674556i
$77$	2.55868	−	0.447537i	0.291588	−	0.0510016i
$78$		0			0
$79$	−11.6027			−1.30541			−0.652705	−	0.757612i	$-0.726366\pi$
$79$	−11.6027			−1.30541			−0.652705	+	0.757612i	$0.726366\pi$
$80$	−2.58251	+	9.63806i	−0.288733	+	1.07757i
$81$		0			0
$82$	2.86901	−	4.96927i	0.316829	−	0.548764i
$83$	−1.23779	−	1.23779i	−0.135865	−	0.135865i	0.635904	−	0.771768i	$-0.280628\pi$
$83$	−1.23779	−	1.23779i	−0.135865	−	0.135865i	−0.771768	+	0.635904i	$0.780628\pi$
$84$		0			0
$85$	−11.6225	+	3.11424i	−1.26064	+	0.337787i
$86$	1.02452	+	1.02452i	0.110476	+	0.110476i
$87$		0			0
$88$	−1.69690	+	0.979707i	−0.180890	+	0.104437i
$89$	−7.75255	−	2.07729i	−0.821769	−	0.220192i	−0.176649	−	0.984274i	$-0.556526\pi$
$89$	−7.75255	−	2.07729i	−0.821769	−	0.220192i	−0.645120	+	0.764082i	$0.723193\pi$
$90$		0			0
$91$	−9.53569	−	0.265737i	−0.999612	−	0.0278568i
$92$	−2.41881			−0.252179
$93$		0			0
$94$	4.45454	−	2.57183i	0.459451	−	0.265264i
$95$	4.88792	+	2.82204i	0.501490	+	0.289535i
$96$		0			0
$97$	12.0756	−	3.23566i	1.22609	−	0.328531i	0.413037	−	0.910714i	$-0.364468\pi$
$97$	12.0756	−	3.23566i	1.22609	−	0.328531i	0.813058	+	0.582183i	$0.197801\pi$
$98$	9.62923	−	6.70307i	0.972699	−	0.677112i
$99$		0			0
$100$	0.388012	−	0.672056i	0.0388012	−	0.0672056i
$101$	3.99818	+	6.92504i	0.397833	+	0.689068i	0.993458	−	0.114195i	$-0.0364289\pi$
$101$	3.99818	+	6.92504i	0.397833	+	0.689068i	−0.595625	+	0.803263i	$0.703096\pi$
$102$		0			0
$103$	−10.3386			−1.01869			−0.509344	−	0.860563i	$-0.670112\pi$
$103$	−10.3386			−1.01869			−0.509344	+	0.860563i	$0.670112\pi$
$104$	6.82477	−	2.28122i	0.669224	−	0.223692i
$105$		0			0
$106$	10.2391	+	2.74356i	0.994511	+	0.266479i
$107$	6.52593	+	11.3032i	0.630885	+	1.09273i	0.987371	+	0.158425i	$0.0506415\pi$
$107$	6.52593	+	11.3032i	0.630885	+	1.09273i	−0.356486	+	0.934301i	$0.616025\pi$
$108$		0			0
$109$	−8.28013	+	8.28013i	−0.793093	+	0.793093i	−0.981996	−	0.188903i	$-0.939507\pi$
$109$	−8.28013	+	8.28013i	−0.793093	+	0.793093i	0.188903	+	0.981996i	$0.439507\pi$
$110$	−3.19519	+	0.856149i	−0.304650	+	0.0816306i
$111$		0			0
$112$	−7.54727	+	10.7471i	−0.713150	+	1.01551i
$113$	−4.05748	+	7.02777i	−0.381696	+	0.661117i	−0.991305	−	0.131586i	$-0.957993\pi$
$113$	−4.05748	+	7.02777i	−0.381696	+	0.661117i	0.609609	+	0.792702i	$0.291326\pi$
$114$		0			0
$115$	5.80377	+	1.55512i	0.541205	+	0.145015i
$116$		−	5.91899i		−	0.549565i
$117$		0			0
$118$			0.852822i			0.0785086i
$119$	−15.7743	−	1.40193i	−1.44603	−	0.128515i
$120$		0			0
$121$	8.69154	+	5.01806i	0.790140	+	0.456188i
$122$	15.4408	+	15.4408i	1.39795	+	1.39795i
$123$		0			0
$124$	1.80996	+	6.75488i	0.162540	+	0.606606i
$125$	−8.47036	+	8.47036i	−0.757612	+	0.757612i
$126$		0			0
$127$	6.81853	−	3.93668i	0.605047	−	0.349324i	−0.165977	−	0.986130i	$-0.553078\pi$
$127$	6.81853	−	3.93668i	0.605047	−	0.349324i	0.771024	+	0.636805i	$0.219745\pi$
$128$	3.39999	−	12.6889i	0.300519	−	1.12155i
$129$		0			0
$130$	12.1258	−	0.737931i	1.06351	−	0.0647208i
$131$		−	19.9597i		−	1.74389i	−0.489604	−	0.871945i	$-0.662859\pi$
$131$		−	19.9597i		−	1.74389i	0.489604	−	0.871945i	$-0.337141\pi$
$132$		0			0
$133$	4.76705	+	5.69704i	0.413355	+	0.493996i
$134$	1.24400	+	0.718226i	0.107466	+	0.0620452i
$135$		0			0
$136$	11.5390	−	3.09187i	0.989461	−	0.265125i
$137$	−10.3872	+	2.78324i	−0.887437	+	0.237788i	−0.673613	−	0.739084i	$-0.735259\pi$
$137$	−10.3872	+	2.78324i	−0.887437	+	0.237788i	−0.213824	+	0.976872i	$0.568592\pi$
$138$		0			0
$139$	−14.1096	−	8.14616i	−1.19676	−	0.690949i	−0.236927	−	0.971527i	$-0.576140\pi$
$139$	−14.1096	−	8.14616i	−1.19676	−	0.690949i	−0.959831	+	0.280579i	$0.909474\pi$
$140$	−3.30091	+	2.76207i	−0.278978	+	0.233437i
$141$		0			0
$142$		−	19.5002i		−	1.63642i
$143$	2.65046	+	2.34637i	0.221642	+	0.196213i
$144$		0			0
$145$	−3.80547	+	14.2022i	−0.316027	+	1.17943i
$146$	−2.11440	+	1.22075i	−0.174989	+	0.101030i
$147$		0			0
$148$	−2.74470	+	2.74470i	−0.225613	+	0.225613i
$149$	−4.84157	−	18.0690i	−0.396637	−	1.48027i	−0.818975	−	0.573829i	$-0.805457\pi$
$149$	−4.84157	−	18.0690i	−0.396637	−	1.48027i	0.422338	−	0.906438i	$-0.361209\pi$
$150$		0			0
$151$	−0.0257634	−	0.0257634i	−0.00209659	−	0.00209659i	0.706058	−	0.708154i	$-0.250472\pi$
$151$	−0.0257634	−	0.0257634i	−0.00209659	−	0.00209659i	−0.708154	+	0.706058i	$0.750472\pi$
$152$	−4.85280	−	2.80176i	−0.393614	−	0.227253i
$153$		0			0
$154$	−4.33657	−	0.385410i	−0.349451	−	0.0310572i
$155$		−	17.3715i		−	1.39532i
$156$		0			0
$157$			7.18863i			0.573716i	0.957973	+	0.286858i	$0.0926107\pi$
$157$			7.18863i			0.573716i	−0.957973	+	0.286858i	$0.907389\pi$
$158$	18.7845	+	5.03329i	1.49442	+	0.400427i
$159$		0			0
$160$	4.34999	−	7.53441i	0.343897	−	0.595647i
$161$	6.47163	+	4.54476i	0.510036	+	0.358177i
$162$		0			0
$163$	15.8950	−	4.25905i	1.24499	−	0.333594i	0.424592	−	0.905385i	$-0.360418\pi$
$163$	15.8950	−	4.25905i	1.24499	−	0.333594i	0.820400	+	0.571791i	$0.193751\pi$
$164$	−1.95900	+	1.95900i	−0.152972	+	0.152972i
$165$		0			0
$166$	1.46699	+	2.54090i	0.113860	+	0.197212i
$167$	−6.49344	−	1.73991i	−0.502478	−	0.134638i	−0.00132801	−	0.999999i	$-0.500423\pi$
$167$	−6.49344	−	1.73991i	−0.502478	−	0.134638i	−0.501150	+	0.865361i	$0.667089\pi$
$168$		0			0
$169$	−7.81725	−	10.3870i	−0.601327	−	0.799003i
$170$	20.1675			1.54678
$171$		0			0
$172$	−0.349777	−	0.605832i	−0.0266702	−	0.0461942i
$173$	4.75865	−	8.24223i	0.361794	−	0.626645i	−0.626462	−	0.779452i	$-0.715498\pi$
$173$	4.75865	−	8.24223i	0.361794	−	0.626645i	0.988256	+	0.152807i	$0.0488312\pi$
$174$		0			0
$175$	−2.30088	+	1.06907i	−0.173930	+	0.0808141i
$176$	4.70709	−	1.26126i	0.354810	−	0.0950711i
$177$		0			0
$178$	11.6500	+	6.72614i	0.873206	+	0.504146i
$179$	5.20227	−	3.00353i	0.388836	−	0.224495i	−0.292820	−	0.956168i	$-0.594594\pi$
$179$	5.20227	−	3.00353i	0.388836	−	0.224495i	0.681656	+	0.731673i	$0.261260\pi$
$180$		0			0
$181$	6.05960			0.450407			0.225203	−	0.974312i	$-0.427695\pi$
$181$	6.05960			0.450407			0.225203	+	0.974312i	$0.427695\pi$
$182$	15.3227	+	4.56682i	1.13580	+	0.338515i
$183$		0			0
$184$	−5.76207	−	1.54394i	−0.424786	−	0.113821i
$185$	8.35035	−	4.82108i	0.613930	−	0.354453i
$186$		0			0
$187$	4.15532	+	4.15532i	0.303867	+	0.303867i
$188$	−2.39886	+	0.642771i	−0.174955	+	0.0468789i
$189$		0			0
$190$	−6.68919	−	6.68919i	−0.485285	−	0.485285i
$191$	10.8137	−	18.7298i	0.782449	−	1.35524i	−0.148062	−	0.988978i	$-0.547304\pi$
$191$	10.8137	−	18.7298i	0.782449	−	1.35524i	0.930511	−	0.366263i	$-0.119363\pi$
$192$		0			0
$193$	2.50822	−	9.36080i	0.180546	−	0.673805i	−0.814995	−	0.579468i	$-0.803260\pi$
$193$	2.50822	−	9.36080i	0.180546	−	0.673805i	0.995540	−	0.0943368i	$-0.0300731\pi$
$194$	−20.9537			−1.50439
$195$		0			0
$196$	−5.32843	+	1.92281i	−0.380602	+	0.137344i
$197$	4.47322	+	1.19859i	0.318704	+	0.0853964i	0.414624	−	0.909993i	$-0.363913\pi$
$197$	4.47322	+	1.19859i	0.318704	+	0.0853964i	−0.0959210	+	0.995389i	$0.530580\pi$
$198$		0			0
$199$	10.7801	−	18.6717i	0.764182	−	1.32360i	−0.176496	−	0.984301i	$-0.556476\pi$
$199$	10.7801	−	18.6717i	0.764182	−	1.32360i	0.940678	−	0.339300i	$-0.110190\pi$
$200$	1.35330	−	1.35330i	0.0956924	−	0.0956924i
$201$		0			0
$202$	−3.46883	−	12.9459i	−0.244066	−	0.910868i
$203$	−11.1213	+	15.8365i	−0.780564	+	1.11151i
$204$		0			0
$205$	5.95998	−	3.44100i	0.416263	−	0.240330i
$206$	16.7378	+	4.48489i	1.16618	+	0.312477i
$207$		0			0
$208$	−17.8635	+	1.08710i	−1.23861	+	0.0753771i
$209$		−	2.75649i		−	0.190670i
$210$		0			0
$211$	7.39505	+	12.8086i	0.509096	+	0.881780i	0.999945	+	0.0105352i	$0.00335353\pi$
$211$	7.39505	+	12.8086i	0.509096	+	0.881780i	−0.490848	+	0.871245i	$0.663313\pi$
$212$	−4.43238	−	2.55904i	−0.304417	−	0.175755i
$213$		0			0
$214$	−5.66192	−	21.1306i	−0.387041	−	1.44446i
$215$	0.449761	+	1.67853i	0.0306735	+	0.114475i
$216$		0			0
$217$	7.84926	−	21.4737i	0.532842	−	1.45773i
$218$	16.9972	−	9.81336i	1.15120	−	0.664644i
$219$		0			0
$220$	1.59713			0.107679
$221$	−11.9061	−	18.0001i	−0.800891	−	1.21082i
$222$		0			0
$223$	−5.52568	+	20.6221i	−0.370027	+	1.38096i	0.490450	+	0.871469i	$0.336832\pi$
$223$	−5.52568	+	20.6221i	−0.370027	+	1.38096i	−0.860477	+	0.509490i	$0.829834\pi$
$224$	8.78161	−	7.34809i	0.586746	−	0.490965i
$225$		0			0
$226$	9.61760	−	9.61760i	0.639753	−	0.639753i
$227$	13.0566	−	3.49849i	0.866594	−	0.232203i	0.201980	−	0.979390i	$-0.435262\pi$
$227$	13.0566	−	3.49849i	0.866594	−	0.232203i	0.664615	+	0.747186i	$0.268596\pi$
$228$		0			0
$229$	5.08550	−	5.08550i	0.336059	−	0.336059i	−0.518823	−	0.854882i	$-0.673629\pi$
$229$	5.08550	−	5.08550i	0.336059	−	0.336059i	0.854882	+	0.518823i	$0.173629\pi$
$230$	−8.72153	−	5.03538i	−0.575081	−	0.332023i
$231$		0			0
$232$	3.77813	−	14.1002i	0.248046	−	0.925721i
$233$			23.2048i			1.52019i	0.649809	+	0.760097i	$0.274849\pi$
$233$			23.2048i			1.52019i	−0.649809	+	0.760097i	$0.725151\pi$
$234$		0			0
$235$	6.16915			0.402431
$236$	0.106572	−	0.397731i	0.00693723	−	0.0258901i
$237$		0			0
$238$	24.9299	+	9.11259i	1.61597	+	0.590682i
$239$	2.77302	−	2.77302i	0.179372	−	0.179372i	−0.611710	−	0.791082i	$-0.709518\pi$
$239$	2.77302	−	2.77302i	0.179372	−	0.179372i	0.791082	+	0.611710i	$0.209518\pi$
$240$		0			0
$241$	−0.825382	−	3.08037i	−0.0531675	−	0.198424i	0.934233	−	0.356662i	$-0.116085\pi$
$241$	−0.825382	−	3.08037i	−0.0531675	−	0.198424i	−0.987401	+	0.158238i	$0.949419\pi$
$242$	−11.8945	−	11.8945i	−0.764608	−	0.764608i
$243$		0			0
$244$	−5.27161	−	9.13070i	−0.337480	−	0.584533i
$245$	14.0214	−	1.18787i	0.895797	−	0.0758903i
$246$		0			0
$247$	−2.02127	+	9.91935i	−0.128610	+	0.631153i
$248$			17.2467i			1.09517i
$249$		0			0
$250$	17.3877	−	10.0388i	1.09970	−	0.634910i
$251$	5.89697	−	10.2138i	0.372213	−	0.644692i	−0.617692	−	0.786420i	$-0.711932\pi$
$251$	5.89697	−	10.2138i	0.372213	−	0.644692i	0.989906	+	0.141727i	$0.0452656\pi$
$252$		0			0
$253$	−0.759496	−	2.83448i	−0.0477491	−	0.178202i
$254$	−12.7467	+	3.41548i	−0.799802	+	0.214306i
$255$		0			0
$256$	−8.33554	+	14.4376i	−0.520971	+	0.902349i
$257$	8.34519	+	14.4543i	0.520559	+	0.901634i	0.999714	+	0.0239041i	$0.00760964\pi$
$257$	8.34519	+	14.4543i	0.520559	+	0.901634i	−0.479156	+	0.877730i	$0.659057\pi$
$258$		0			0
$259$	12.5006	−	2.18648i	0.776751	−	0.135861i
$260$	−5.74735	−	1.17114i	−0.356436	−	0.0726310i
$261$		0			0
$262$	−8.65857	+	32.3142i	−0.534928	+	1.99638i
$263$	4.75769	+	8.24055i	0.293371	+	0.508134i	0.974605	−	0.223932i	$-0.0718894\pi$
$263$	4.75769	+	8.24055i	0.293371	+	0.508134i	−0.681233	+	0.732066i	$0.738556\pi$
$264$		0			0
$265$	8.98993	+	8.98993i	0.552247	+	0.552247i
$266$	−5.24633	−	11.2913i	−0.321673	−	0.692313i
$267$		0			0
$268$	−0.490415	−	0.490415i	−0.0299569	−	0.0299569i
$269$	0.275945	+	0.159317i	0.0168247	+	0.00971373i	0.508389	−	0.861128i	$-0.330241\pi$
$269$	0.275945	+	0.159317i	0.0168247	+	0.00971373i	−0.491564	+	0.870841i	$0.663575\pi$
$270$		0			0
$271$	−25.9248	−	6.94654i	−1.57482	−	0.421972i	−0.637504	−	0.770447i	$-0.720033\pi$
$271$	−25.9248	−	6.94654i	−1.57482	−	0.421972i	−0.937318	+	0.348475i	$0.886700\pi$
$272$	−29.7103			−1.80145
$273$		0			0
$274$	18.0239			1.08886
$275$	0.909381	+	0.243668i	0.0548378	+	0.0146937i
$276$		0			0
$277$	−13.1218	−	7.57587i	−0.788412	−	0.455190i	0.0509909	−	0.998699i	$-0.483762\pi$
$277$	−13.1218	−	7.57587i	−0.788412	−	0.455190i	−0.839403	+	0.543509i	$0.817095\pi$
$278$	19.3092	+	19.3092i	1.15809	+	1.15809i
$279$		0			0
$280$	−9.62645	+	4.47278i	−0.575290	+	0.267300i
$281$	−5.40600	−	5.40600i	−0.322495	−	0.322495i	0.527228	−	0.849724i	$-0.323231\pi$
$281$	−5.40600	−	5.40600i	−0.322495	−	0.322495i	−0.849724	+	0.527228i	$0.823231\pi$
$282$		0			0
$283$	0.896218	+	1.55229i	0.0532746	+	0.0922743i	0.891433	−	0.453153i	$-0.149701\pi$
$283$	0.896218	+	1.55229i	0.0532746	+	0.0922743i	−0.838158	+	0.545427i	$0.816367\pi$
$284$	−2.43682	+	9.09435i	−0.144599	+	0.539650i
$285$		0			0
$286$	−3.27315	−	4.94848i	−0.193546	−	0.292610i
$287$	8.92220	−	1.56058i	0.526661	−	0.0921180i
$288$		0			0
$289$	−9.41380	−	16.3052i	−0.553753	−	0.959128i
$290$	12.3219	−	21.3422i	0.723567	−	1.25325i
$291$		0			0
$292$	1.13864	−	0.305099i	0.0666341	−	0.0178546i
$293$	−6.85691	−	25.5903i	−0.400585	−	1.49500i	−0.812055	−	0.583580i	$-0.801651\pi$
$293$	−6.85691	−	25.5903i	−0.400585	−	1.49500i	0.411471	−	0.911423i	$-0.365015\pi$
$294$		0			0
$295$	−0.511424	+	0.885812i	−0.0297762	+	0.0515739i
$296$	−8.29035	+	4.78644i	−0.481867	+	0.278206i
$297$		0			0
$298$			31.3534i			1.81625i
$299$	0.654624	+	10.7569i	0.0378579	+	0.622089i
$300$		0			0
$301$	−0.202468	+	2.27813i	−0.0116700	+	0.131309i
$302$	0.0305339	+	0.0528863i	0.00175703	+	0.00304327i
$303$		0			0
$304$	9.85437	+	9.85437i	0.565187	+	0.565187i
$305$	6.77851	+	25.2978i	0.388136	+	1.44855i
$306$		0			0
$307$	−1.54710	+	1.54710i	−0.0882978	+	0.0882978i	−0.749876	−	0.661578i	$-0.769887\pi$
$307$	−1.54710	+	1.54710i	−0.0882978	+	0.0882978i	0.661578	+	0.749876i	$0.269887\pi$
$308$	1.97429	+	0.721658i	0.112495	+	0.0411203i
$309$		0			0
$310$	−7.53581	+	28.1240i	−0.428005	+	1.59734i
$311$	−29.3344			−1.66340			−0.831699	−	0.555226i	$-0.812632\pi$
$311$	−29.3344			−1.66340			−0.831699	+	0.555226i	$0.812632\pi$
$312$		0			0
$313$		−	27.9847i		−	1.58179i	−0.611954	−	0.790893i	$-0.709616\pi$
$313$		−	27.9847i		−	1.58179i	0.611954	−	0.790893i	$-0.290384\pi$
$314$	3.11844	−	11.6382i	0.175984	−	0.656781i
$315$		0			0
$316$	−8.13157	−	4.69476i	−0.457436	−	0.264101i
$317$	−5.56105	+	5.56105i	−0.312340	+	0.312340i	−0.845815	−	0.533476i	$-0.820886\pi$
$317$	−5.56105	+	5.56105i	−0.312340	+	0.312340i	0.533476	+	0.845815i	$0.320886\pi$
$318$		0			0
$319$	6.93616	−	1.85854i	0.388350	−	0.104058i
$320$	3.80014	−	3.80014i	0.212434	−	0.212434i
$321$		0			0
$322$	−8.50586	−	10.1652i	−0.474013	−	0.566487i
$323$	−4.34961	+	16.2330i	−0.242019	+	0.903227i
$324$		0			0
$325$	−3.09377	−	1.54368i	−0.171612	−	0.0856279i
$326$	−27.5811			−1.52758
$327$		0			0
$328$	−5.91716	+	3.41627i	−0.326720	+	0.188632i
$329$	7.62596	+	2.78750i	0.420433	+	0.153680i
$330$		0			0
$331$	4.21415	+	15.7274i	0.231630	+	0.864457i	0.979639	+	0.200767i	$0.0643436\pi$
$331$	4.21415	+	15.7274i	0.231630	+	0.864457i	−0.748008	+	0.663689i	$0.768990\pi$
$332$	−0.366640	−	1.36832i	−0.0201220	−	0.0750963i
$333$		0			0
$334$	9.75792	+	5.63374i	0.533929	+	0.308264i
$335$	0.861417	+	1.49202i	0.0470642	+	0.0815176i
$336$		0			0
$337$			11.0114i			0.599827i	0.953966	+	0.299913i	$0.0969578\pi$
$337$			11.0114i			0.599827i	−0.953966	+	0.299913i	$0.903042\pi$
$338$	8.14999	+	20.2075i	0.443301	+	1.09914i
$339$		0			0
$340$	−9.40553	−	2.52020i	−0.510086	−	0.136677i
$341$	−7.34737	+	4.24200i	−0.397882	+	0.229717i
$342$		0			0
$343$	17.8693	+	4.86715i	0.964850	+	0.262801i
$344$	−0.446530	−	1.66647i	−0.0240753	−	0.0898501i
$345$		0			0
$346$	−11.2796	+	11.2796i	−0.606396	+	0.606396i
$347$	2.36362	−	4.09391i	0.126886	−	0.219772i	−0.795583	−	0.605845i	$-0.792835\pi$
$347$	2.36362	−	4.09391i	0.126886	−	0.219772i	0.922468	+	0.386073i	$0.126169\pi$
$348$		0			0
$349$	−22.4353	−	6.01151i	−1.20093	−	0.321789i	−0.397734	−	0.917501i	$-0.630203\pi$
$349$	−22.4353	−	6.01151i	−1.20093	−	0.321789i	−0.803198	+	0.595712i	$0.796870\pi$
$350$	4.18883	−	0.732666i	0.223902	−	0.0391626i
$351$		0			0
$352$	−4.24895			−0.226470
$353$	3.40370	−	12.7028i	0.181161	−	0.676101i	−0.814259	−	0.580501i	$-0.802857\pi$
$353$	3.40370	−	12.7028i	0.181161	−	0.676101i	0.995420	−	0.0955993i	$-0.0304767\pi$
$354$		0			0
$355$	11.6940	−	20.2546i	0.620652	−	1.07500i
$356$	−4.59271	−	4.59271i	−0.243413	−	0.243413i
$357$		0			0
$358$	−9.72526	+	2.60588i	−0.513996	+	0.137725i
$359$	−6.64709	−	6.64709i	−0.350820	−	0.350820i	0.509594	−	0.860415i	$-0.329795\pi$
$359$	−6.64709	−	6.64709i	−0.350820	−	0.350820i	−0.860415	+	0.509594i	$0.829795\pi$
$360$		0			0
$361$	−9.62761	+	5.55850i	−0.506716	+	0.292553i
$362$	−9.81032	−	2.62867i	−0.515619	−	0.138160i
$363$		0			0
$364$	−6.57539	−	4.04462i	−0.344644	−	0.211996i
$365$	−2.92826			−0.153272
$366$		0			0
$367$	−6.33897	+	3.65981i	−0.330892	+	0.191040i	−0.656237	−	0.754555i	$-0.727853\pi$
$367$	−6.33897	+	3.65981i	−0.330892	+	0.191040i	0.325345	+	0.945595i	$0.394519\pi$
$368$	12.8484	+	7.41801i	0.669767	+	0.386690i
$369$		0			0
$370$	−15.6104	+	4.18279i	−0.811544	+	0.217453i
$371$	7.05079	+	15.1749i	0.366059	+	0.787843i
$372$		0			0
$373$	0.542562	−	0.939745i	0.0280928	−	0.0486582i	−0.851637	−	0.524132i	$-0.824390\pi$
$373$	0.542562	−	0.939745i	0.0280928	−	0.0486582i	0.879730	+	0.475474i	$0.157723\pi$
$374$	−4.92475	−	8.52992i	−0.254653	−	0.441072i
$375$		0			0
$376$	−6.12482			−0.315863
$377$	−26.3229	+	1.60191i	−1.35570	+	0.0825025i
$378$		0			0
$379$	−25.1695	−	6.74414i	−1.29287	−	0.346423i	−0.454119	−	0.890941i	$-0.650046\pi$
$379$	−25.1695	−	6.74414i	−1.29287	−	0.346423i	−0.838749	+	0.544518i	$0.816713\pi$
$380$	2.28374	+	3.95555i	0.117153	+	0.202915i
$381$		0			0
$382$	−25.6320	+	25.6320i	−1.31145	+	1.31145i
$383$	5.14879	−	1.37961i	0.263091	−	0.0704950i	−0.124862	−	0.992174i	$-0.539849\pi$
$383$	5.14879	−	1.37961i	0.263091	−	0.0704950i	0.387953	+	0.921679i	$0.373182\pi$
$384$		0			0
$385$	−4.27320	−	3.00089i	−0.217782	−	0.152939i
$386$	−8.12146	+	14.0668i	−0.413372	+	0.715981i
$387$		0			0
$388$	9.77221	+	2.61846i	0.496109	+	0.132932i
$389$		−	3.43917i		−	0.174373i	−0.996192	−	0.0871864i	$-0.972212\pi$
$389$		−	3.43917i		−	0.174373i	0.996192	−	0.0871864i	$-0.0277876\pi$
$390$		0			0
$391$			17.8907i			0.904773i
$392$	−13.9207	+	1.17934i	−0.703101	+	0.0595654i
$393$		0			0
$394$	−6.72205	−	3.88098i	−0.338652	−	0.195521i
$395$	16.4928	+	16.4928i	0.829841	+	0.829841i
$396$		0			0
$397$	0.155514	+	0.580386i	0.00780502	+	0.0291287i	0.969719	−	0.244225i	$-0.0785336\pi$
$397$	0.155514	+	0.580386i	0.00780502	+	0.0291287i	−0.961914	+	0.273354i	$0.911867\pi$
$398$	−25.5525	+	25.5525i	−1.28083	+	1.28083i
$399$		0			0
$400$	−4.12212	+	2.37991i	−0.206106	+	0.118995i
$401$	−3.10377	+	11.5834i	−0.154995	+	0.578448i	0.844111	+	0.536168i	$0.180129\pi$
$401$	−3.10377	+	11.5834i	−0.154995	+	0.578448i	−0.999106	+	0.0422800i	$0.986538\pi$
$402$		0			0
$403$	29.5504	−	9.87739i	1.47201	−	0.492028i
$404$			6.47105i			0.321947i
$405$		0			0
$406$	24.8750	−	20.8144i	1.23453	−	1.03300i
$407$	−4.07819	−	2.35454i	−0.202148	−	0.116710i
$408$		0			0
$409$	11.2120	−	3.00424i	0.554396	−	0.148550i	0.0292657	−	0.999572i	$-0.490683\pi$
$409$	11.2120	−	3.00424i	0.554396	−	0.148550i	0.525131	+	0.851022i	$0.324016\pi$
$410$	−11.1418	+	2.98542i	−0.550252	+	0.147440i
$411$		0			0
$412$	−7.24558	−	4.18324i	−0.356964	−	0.206093i
$413$	−1.03244	+	0.863907i	−0.0508033	+	0.0425101i
$414$		0			0
$415$			3.51891i			0.172737i
$416$	15.2900	+	3.11565i	0.749655	+	0.152758i
$417$		0			0
$418$	−1.19577	+	4.46267i	−0.0584870	+	0.218276i
$419$	30.9881	−	17.8910i	1.51387	−	0.874032i	0.513999	−	0.857791i	$-0.328164\pi$
$419$	30.9881	−	17.8910i	1.51387	−	0.874032i	0.999868	−	0.0162408i	$-0.00516982\pi$
$420$		0			0
$421$	−3.47255	+	3.47255i	−0.169242	+	0.169242i	−0.786646	−	0.617404i	$-0.788184\pi$
$421$	−3.47255	+	3.47255i	−0.169242	+	0.169242i	0.617404	+	0.786646i	$0.288184\pi$
$422$	−6.41597	−	23.9447i	−0.312325	−	1.16561i
$423$		0			0
$424$	−8.92533	−	8.92533i	−0.433452	−	0.433452i
$425$	−4.97086	−	2.86993i	−0.241122	−	0.139212i
$426$		0			0
$427$	−3.05146	+	34.3345i	−0.147671	+	1.66156i
$428$			10.5622i			0.510544i
$429$		0			0
$430$		−	2.91260i		−	0.140458i
$431$	0.474207	+	0.127063i	0.0228418	+	0.00612043i	0.270222	−	0.962798i	$-0.412903\pi$
$431$	0.474207	+	0.127063i	0.0228418	+	0.00612043i	−0.247380	+	0.968919i	$0.579570\pi$
$432$		0			0
$433$	8.89347	−	15.4039i	0.427393	−	0.740266i	−0.569248	−	0.822166i	$-0.692765\pi$
$433$	8.89347	−	15.4039i	0.427393	−	0.740266i	0.996641	+	0.0818999i	$0.0260988\pi$
$434$	−22.0231	+	31.3603i	−1.05714	+	1.50534i
$435$		0			0
$436$	−9.15333	+	2.45263i	−0.438365	+	0.117460i
$437$	5.93403	−	5.93403i	0.283863	−	0.283863i
$438$		0			0
$439$	14.3012	+	24.7704i	0.682559	+	1.18223i	0.974197	+	0.225698i	$0.0724662\pi$
$439$	14.3012	+	24.7704i	0.682559	+	1.18223i	−0.291639	+	0.956529i	$0.594200\pi$
$440$	3.80467	+	1.01946i	0.181381	+	0.0486008i
$441$		0			0
$442$	11.4672	+	34.3065i	0.545437	+	1.63179i
$443$	7.37150			0.350231			0.175115	−	0.984548i	$-0.443970\pi$
$443$	7.37150			0.350231			0.175115	+	0.984548i	$0.443970\pi$
$444$		0			0
$445$	8.06712	+	13.9727i	0.382418	+	0.662368i
$446$	17.8918	−	30.9896i	0.847203	−	1.46740i
$447$		0			0
$448$	6.41461	−	2.98045i	0.303062	−	0.140813i
$449$	−22.5220	+	6.03476i	−1.06288	+	0.284798i	−0.747565	−	0.664189i	$-0.768777\pi$
$449$	−22.5220	+	6.03476i	−1.06288	+	0.284798i	−0.315315	+	0.948987i	$0.602110\pi$
$450$		0			0
$451$	−2.91077	−	1.68053i	−0.137063	−	0.0791332i
$452$	−5.68722	+	3.28352i	−0.267504	+	0.154444i
$453$		0			0
$454$	−22.6558			−1.06329
$455$	13.1768	+	13.9323i	0.617738	+	0.653155i
$456$		0			0
$457$	4.35841	+	1.16783i	0.203878	+	0.0546289i	0.359313	−	0.933217i	$-0.383011\pi$
$457$	4.35841	+	1.16783i	0.203878	+	0.0546289i	−0.155435	+	0.987846i	$0.549678\pi$
$458$	−10.4394	+	6.02718i	−0.487800	+	0.281631i
$459$		0			0
$460$	3.43823	+	3.43823i	0.160308	+	0.160308i
$461$	−32.1809	+	8.62285i	−1.49882	+	0.401606i	−0.912703	−	0.408623i	$-0.866009\pi$
$461$	−32.1809	+	8.62285i	−1.49882	+	0.401606i	−0.586112	+	0.810230i	$0.699342\pi$
$462$		0			0
$463$	29.0991	+	29.0991i	1.35235	+	1.35235i	0.883028	+	0.469321i	$0.155501\pi$
$463$	29.0991	+	29.0991i	1.35235	+	1.35235i	0.469321	+	0.883028i	$0.344499\pi$
$464$	−18.1524	+	31.4408i	−0.842702	+	1.45960i
$465$		0			0
$466$	10.0663	−	37.5678i	0.466311	−	1.74030i
$467$	−5.71733			−0.264566			−0.132283	−	0.991212i	$-0.542231\pi$
$467$	−5.71733			−0.264566			−0.132283	+	0.991212i	$0.542231\pi$
$468$		0			0
$469$	0.390674	+	2.23358i	0.0180396	+	0.103137i
$470$	−9.98767	−	2.67619i	−0.460697	−	0.123443i
$471$		0			0
$472$	0.507749	−	0.879447i	0.0233710	−	0.0404798i
$473$	0.600114	−	0.600114i	0.0275933	−	0.0275933i
$474$		0			0
$475$	0.696841	+	2.60065i	0.0319733	+	0.119326i
$476$	−10.4879	−	7.36519i	−0.480710	−	0.337583i
$477$		0			0
$478$	−5.69239	+	3.28650i	−0.260364	+	0.150321i
$479$	−32.1894	−	8.62513i	−1.47077	−	0.394092i	−0.567576	−	0.823321i	$-0.692119\pi$
$479$	−32.1894	−	8.62513i	−1.47077	−	0.394092i	−0.903196	+	0.429229i	$0.858785\pi$
$480$		0			0
$481$	12.9490	+	11.4634i	0.590425	+	0.522685i
$482$			5.34507i			0.243461i
$483$		0			0
$484$	4.06087	+	7.03363i	0.184585	+	0.319711i
$485$	−21.7643	−	12.5656i	−0.988265	−	0.570575i
$486$		0			0
$487$	−3.91309	−	14.6038i	−0.177319	−	0.661763i	−0.996145	−	0.0877214i	$-0.972041\pi$
$487$	−3.91309	−	14.6038i	−0.177319	−	0.661763i	0.818826	−	0.574041i	$-0.194625\pi$
$488$	−6.72980	−	25.1160i	−0.304644	−	1.13695i
$489$		0			0
$490$	−23.2156	−	4.15940i	−1.04877	−	0.187903i
$491$	3.79911	−	2.19342i	0.171451	−	0.0989875i	−0.411819	−	0.911266i	$-0.635106\pi$
$491$	3.79911	−	2.19342i	0.171451	−	0.0989875i	0.583270	+	0.812278i	$0.301773\pi$
$492$		0			0
$493$	−43.7798			−1.97174
$494$	7.57541	−	15.1823i	0.340834	−	0.683084i
$495$		0			0
$496$	11.1016	−	41.4317i	0.498476	−	1.86034i
$497$	23.6074	−	19.7537i	1.05894	−	0.886075i
$498$		0			0
$499$	14.1707	−	14.1707i	0.634366	−	0.634366i	−0.314794	−	0.949160i	$-0.601936\pi$
$499$	14.1707	−	14.1707i	0.634366	−	0.634366i	0.949160	+	0.314794i	$0.101936\pi$
$500$	−9.36361	+	2.50897i	−0.418753	+	0.112205i
$501$		0			0
$502$	−13.9778	+	13.9778i	−0.623860	+	0.623860i
$503$	0.917016	+	0.529439i	0.0408877	+	0.0236065i	0.520305	−	0.853981i	$-0.325818\pi$
$503$	0.917016	+	0.529439i	0.0408877	+	0.0236065i	−0.479417	+	0.877587i	$0.659152\pi$
$504$		0			0
$505$	4.16041	−	15.5268i	0.185136	−	0.690936i
$506$			4.91841i			0.218650i
$507$		0			0
$508$	6.37152			0.282691
$509$	−2.91008	+	10.8606i	−0.128987	+	0.481387i	−0.999950	−	0.00996149i	$-0.996829\pi$
$509$	−2.91008	+	10.8606i	−0.128987	+	0.481387i	0.870963	+	0.491348i	$0.163496\pi$
$510$		0			0
$511$	−3.61975	−	1.32312i	−0.160128	−	0.0585314i
$512$	1.18017	−	1.18017i	0.0521565	−	0.0521565i
$513$		0			0
$514$	−7.24032	−	27.0212i	−0.319357	−	1.19186i
$515$	14.6958	+	14.6958i	0.647573	+	0.647573i
$516$		0			0
$517$	−1.50646	−	2.60927i	−0.0662541	−	0.114755i
$518$	−21.1867	−	1.88295i	−0.930888	−	0.0827321i
$519$		0			0
$520$	−12.9437	−	6.45845i	−0.567621	−	0.283222i
$521$		−	16.9175i		−	0.741168i	−0.928799	−	0.370584i	$-0.879157\pi$
$521$		−	16.9175i		−	0.741168i	0.928799	−	0.370584i	$-0.120843\pi$
$522$		0			0
$523$	−0.268849	+	0.155220i	−0.0117560	+	0.00678731i	−0.505866	−	0.862612i	$-0.668827\pi$
$523$	−0.268849	+	0.155220i	−0.0117560	+	0.00678731i	0.494111	+	0.869399i	$0.335494\pi$
$524$	8.07621	−	13.9884i	0.352811	−	0.611086i
$525$		0			0
$526$	−4.12779	−	15.4051i	−0.179980	−	0.671695i
$527$	49.9624	−	13.3874i	2.17640	−	0.583164i
$528$		0			0
$529$	−7.03308	+	12.1816i	−0.305786	+	0.529637i
$530$	−10.6546	−	18.4543i	−0.462806	−	0.801603i
$531$		0			0
$532$	1.03573	+	5.92153i	0.0449047	+	0.256731i
$533$	9.24224	+	8.18188i	0.400326	+	0.354396i
$534$		0			0
$535$	6.79073	−	25.3433i	0.293589	−	1.09569i
$536$	−0.855227	−	1.48130i	−0.0369402	−	0.0639823i
$537$		0			0
$538$	−0.377635	−	0.377635i	−0.0162810	−	0.0162810i
$539$	−3.92635	−	5.64036i	−0.169120	−	0.242947i
$540$		0			0
$541$	−22.0115	−	22.0115i	−0.946347	−	0.946347i	0.0522854	−	0.998632i	$-0.483349\pi$
$541$	−22.0115	−	22.0115i	−0.946347	−	0.946347i	−0.998632	+	0.0522854i	$0.983349\pi$
$542$	38.9581	+	22.4925i	1.67340	+	0.966135i
$543$		0			0
$544$	25.0221	+	6.70465i	1.07281	+	0.287459i
$545$	23.5396			1.00833
$546$		0			0
$547$	−13.8672			−0.592920			−0.296460	−	0.955045i	$-0.595806\pi$
$547$	−13.8672			−0.592920			−0.296460	+	0.955045i	$0.595806\pi$
$548$	−8.40583	−	2.25234i	−0.359079	−	0.0962150i
$549$		0			0
$550$	−1.36656	−	0.788983i	−0.0582702	−	0.0336423i
$551$	14.5210	+	14.5210i	0.618614	+	0.618614i
$552$		0			0
$553$	12.9353	+	27.8396i	0.550063	+	1.18386i
$554$	17.9574	+	17.9574i	0.762936	+	0.762936i
$555$		0			0
$556$	−6.59229	−	11.4182i	−0.279575	−	0.484238i
$557$	5.87298	−	21.9183i	0.248846	−	0.928706i	−0.722565	−	0.691303i	$-0.757037\pi$
$557$	5.87298	−	21.9183i	0.248846	−	0.928706i	0.971411	−	0.237403i	$-0.0762963\pi$
$558$		0			0
$559$	−2.59959	+	1.71949i	−0.109951	+	0.0727266i
$560$	26.0046	−	4.54846i	1.09890	−	0.192208i
$561$		0			0
$562$	6.40703	+	11.0973i	0.270264	+	0.468111i
$563$	−11.2217	+	19.4366i	−0.472940	+	0.819156i	−0.999520	−	0.0309690i	$-0.990141\pi$
$563$	−11.2217	+	19.4366i	−0.472940	+	0.819156i	0.526580	+	0.850125i	$0.323474\pi$
$564$		0			0
$565$	15.7572	−	4.22212i	0.662909	−	0.177626i
$566$	−0.777562	−	2.90190i	−0.0326834	−	0.121976i
$567$		0			0
$568$	−11.6100	+	20.1090i	−0.487143	+	0.843756i
$569$	11.1921	−	6.46175i	0.469196	−	0.270891i	−0.246707	−	0.969090i	$-0.579349\pi$
$569$	11.1921	−	6.46175i	0.469196	−	0.270891i	0.715903	+	0.698200i	$0.246015\pi$
$570$		0			0
$571$		−	17.4421i		−	0.729930i	−0.931021	−	0.364965i	$-0.881081\pi$
$571$		−	17.4421i		−	0.729930i	0.931021	−	0.364965i	$-0.118919\pi$
$572$	0.908123	+	2.71685i	0.0379705	+	0.113597i
$573$		0			0
$574$	−15.1218	−	1.34394i	−0.631171	−	0.0560949i
$575$	1.43312	+	2.48223i	0.0597650	+	0.103516i
$576$		0			0
$577$	−10.2002	−	10.2002i	−0.424642	−	0.424642i	0.462157	−	0.886798i	$-0.347076\pi$
$577$	−10.2002	−	10.2002i	−0.424642	−	0.424642i	−0.886798	+	0.462157i	$0.847076\pi$
$578$	8.16745	+	30.4813i	0.339721	+	1.26786i
$579$		0			0
$580$	−8.41357	+	8.41357i	−0.349354	+	0.349354i
$581$	−1.59001	+	4.34989i	−0.0659646	+	0.180464i
$582$		0			0
$583$	1.60705	−	5.99760i	0.0665573	−	0.248395i
$584$	2.90721			0.120301
$585$		0			0
$586$			44.4045i			1.83433i
$587$	−4.97130	+	18.5532i	−0.205188	+	0.765771i	0.784205	+	0.620502i	$0.213071\pi$
$587$	−4.97130	+	18.5532i	−0.205188	+	0.765771i	−0.989392	+	0.145268i	$0.953595\pi$
$588$		0			0
$589$	−21.0120	−	12.1313i	−0.865783	−	0.499860i
$590$	1.21225	−	1.21225i	0.0499074	−	0.0499074i
$591$		0			0
$592$	22.9969	−	6.16199i	0.945165	−	0.253256i
$593$	−1.84156	+	1.84156i	−0.0756236	+	0.0756236i	−0.743907	−	0.668283i	$-0.767029\pi$
$593$	−1.84156	+	1.84156i	−0.0756236	+	0.0756236i	0.668283	+	0.743907i	$0.267029\pi$
$594$		0			0
$595$	20.4296	+	24.4152i	0.837533	+	1.00092i
$596$	3.91804	−	14.6223i	0.160489	−	0.598954i
$597$		0			0
$598$	3.60656	−	17.6991i	0.147483	−	0.723771i
$599$	−24.8100			−1.01371			−0.506855	−	0.862031i	$-0.669192\pi$
$599$	−24.8100			−1.01371			−0.506855	+	0.862031i	$0.669192\pi$
$600$		0			0
$601$	15.2889	−	8.82708i	0.623649	−	0.360064i	−0.154639	−	0.987971i	$-0.549422\pi$
$601$	15.2889	−	8.82708i	0.623649	−	0.360064i	0.778288	+	0.627907i	$0.216088\pi$
$602$	1.31605	−	3.60040i	0.0536381	−	0.146741i
$603$		0			0
$604$	−0.00763126	−	0.0284803i	−0.000310512	−	0.00115885i
$605$	−5.22168	−	19.4876i	−0.212291	−	0.792282i
$606$		0			0
$607$	−13.0545	−	7.53700i	−0.529864	−	0.305917i	0.211097	−	0.977465i	$-0.432296\pi$
$607$	−13.0545	−	7.53700i	−0.529864	−	0.305917i	−0.740961	+	0.671548i	$0.765630\pi$
$608$	−6.07556	−	10.5232i	−0.246397	−	0.426771i
$609$		0			0
$610$		−	43.8969i		−	1.77733i
$611$	3.50775	+	10.4942i	0.141908	+	0.424551i
$612$		0			0
$613$	33.8842	+	9.07924i	1.36857	+	0.366707i	0.866956	−	0.498384i	$-0.166073\pi$
$613$	33.8842	+	9.07924i	1.36857	+	0.366707i	0.501614	+	0.865092i	$0.332740\pi$
$614$	3.17585	−	1.83358i	0.128167	−	0.0739972i
$615$		0			0
$616$	4.24249	+	2.97933i	0.170935	+	0.120040i
$617$	−9.01921	−	33.6601i	−0.363100	−	1.35511i	−0.869979	−	0.493089i	$-0.835868\pi$
$617$	−9.01921	−	33.6601i	−0.363100	−	1.35511i	0.506879	−	0.862017i	$-0.330799\pi$
$618$		0			0
$619$	−5.61860	+	5.61860i	−0.225830	+	0.225830i	−0.810948	−	0.585118i	$-0.801048\pi$
$619$	−5.61860	+	5.61860i	−0.225830	+	0.225830i	0.585118	+	0.810948i	$0.301048\pi$
$620$	7.02896	−	12.1745i	0.282290	−	0.488940i
$621$		0			0
$622$	47.4915	+	12.7253i	1.90423	+	0.510238i
$623$	3.65864	+	20.9173i	0.146580	+	0.838035i
$624$		0			0
$625$	19.2857			0.771429
$626$	−12.1398	+	45.3063i	−0.485204	+	1.81081i
$627$		0			0
$628$	−2.90870	+	5.03802i	−0.116070	+	0.201039i
$629$	20.3011	+	20.3011i	0.809460	+	0.809460i
$630$		0			0
$631$	40.9973	−	10.9852i	1.63208	−	0.437314i	0.677559	−	0.735469i	$-0.263038\pi$
$631$	40.9973	−	10.9852i	1.63208	−	0.437314i	0.954517	+	0.298155i	$0.0963713\pi$
$632$	−16.3743	−	16.3743i	−0.651333	−	0.651333i
$633$		0			0
$634$	11.4156	−	6.59079i	0.453370	−	0.261754i
$635$	−15.2880	−	4.09642i	−0.606687	−	0.162561i
$636$		0			0
$637$	9.99320	+	23.1762i	0.395945	+	0.918274i
$638$	−12.0357			−0.476497
$639$		0			0
$640$	−22.8696	+	13.2038i	−0.904002	+	0.521926i
$641$	17.7415	+	10.2431i	0.700748	+	0.404577i	0.807626	−	0.589695i	$-0.200752\pi$
$641$	17.7415	+	10.2431i	0.700748	+	0.404577i	−0.106878	+	0.994272i	$0.534085\pi$
$642$		0			0
$643$	−20.9593	+	5.61604i	−0.826556	+	0.221475i	−0.647211	−	0.762311i	$-0.724065\pi$
$643$	−20.9593	+	5.61604i	−0.826556	+	0.221475i	−0.179345	+	0.983786i	$0.557398\pi$
$644$	2.69660	+	5.80370i	0.106261	+	0.228698i
$645$		0			0
$646$	14.0838	−	24.3939i	0.554120	−	0.959763i
$647$	−19.5669	−	33.8908i	−0.769252	−	1.33238i	−0.937969	−	0.346720i	$-0.887296\pi$
$647$	−19.5669	−	33.8908i	−0.769252	−	1.33238i	0.168716	−	0.985665i	$-0.446038\pi$
$648$		0			0
$649$	0.499544			0.0196088
$650$	4.33908	+	3.84126i	0.170193	+	0.150666i
$651$		0			0
$652$	12.8630	+	3.44664i	0.503755	+	0.134981i
$653$	−14.8092	−	25.6503i	−0.579528	−	1.00377i	−0.995533	−	0.0944103i	$-0.969903\pi$
$653$	−14.8092	−	25.6503i	−0.579528	−	1.00377i	0.416005	−	0.909362i	$-0.363430\pi$
$654$		0			0
$655$	−28.3718	+	28.3718i	−1.10858	+	1.10858i
$656$	16.4138	−	4.39806i	0.640851	−	0.171715i
$657$		0			0
$658$	−11.1370	−	7.82104i	−0.434165	−	0.304896i
$659$	−1.87682	+	3.25074i	−0.0731104	+	0.126631i	−0.900263	−	0.435346i	$-0.856626\pi$
$659$	−1.87682	+	3.25074i	−0.0731104	+	0.126631i	0.827153	+	0.561977i	$0.189959\pi$
$660$		0			0
$661$	−41.9725	−	11.2465i	−1.63254	−	0.437438i	−0.677889	−	0.735164i	$-0.737105\pi$
$661$	−41.9725	−	11.2465i	−1.63254	−	0.437438i	−0.954651	+	0.297726i	$0.903772\pi$
$662$		−	27.2903i		−	1.06067i
$663$		0			0
$664$		−	3.49363i		−	0.135579i
$665$	1.32194	−	14.8742i	0.0512625	−	0.576797i
$666$		0			0
$667$	18.9328	+	10.9309i	0.733081	+	0.423244i
$668$	−3.84680	−	3.84680i	−0.148837	−	0.148837i
$669$		0			0
$670$	−0.747368	−	2.78922i	−0.0288734	−	0.107757i
$671$	9.04453	−	9.04453i	0.349160	−	0.349160i
$672$		0			0
$673$	23.1880	−	13.3876i	0.893833	−	0.516055i	0.0186390	−	0.999826i	$-0.494067\pi$
$673$	23.1880	−	13.3876i	0.893833	−	0.516055i	0.875194	+	0.483771i	$0.160733\pi$
$674$	4.77675	−	17.8271i	0.183993	−	0.686673i
$675$		0			0
$676$	−1.27572	−	10.4426i	−0.0490661	−	0.401639i
$677$			20.8667i			0.801971i	0.916084	+	0.400985i	$0.131332\pi$
$677$			20.8667i			0.801971i	−0.916084	+	0.400985i	$0.868668\pi$
$678$		0			0
$679$	−21.2261	−	25.3670i	−0.814582	−	0.973497i
$680$	−20.7971	−	12.0072i	−0.797532	−	0.460456i
$681$		0			0
$682$	13.7354	−	3.68038i	0.525954	−	0.140929i
$683$	31.6796	−	8.48852i	1.21219	−	0.324804i	0.404567	−	0.914509i	$-0.367422\pi$
$683$	31.6796	−	8.48852i	1.21219	−	0.324804i	0.807619	+	0.589704i	$0.200756\pi$
$684$		0			0
$685$	18.7211	+	10.8087i	0.715298	+	0.412977i
$686$	−26.8184	−	15.6315i	−1.02393	−	0.596813i
$687$		0			0
$688$			4.29078i			0.163585i
$689$	−10.1810	+	20.4042i	−0.387864	+	0.777340i
$690$		0			0
$691$	11.6421	−	43.4491i	0.442888	−	1.65288i	−0.278564	−	0.960418i	$-0.589859\pi$
$691$	11.6421	−	43.4491i	0.442888	−	1.65288i	0.721453	−	0.692464i	$-0.243475\pi$
$692$	6.67003	−	3.85094i	0.253556	−	0.146391i
$693$		0			0
$694$	−5.60257	+	5.60257i	−0.212671	+	0.212671i
$695$	8.47670	+	31.6355i	0.321540	+	1.20000i
$696$		0			0
$697$	14.4897	+	14.4897i	0.548838	+	0.548838i
$698$	33.7142	+	19.4649i	1.27610	+	0.736758i
$699$		0			0
$700$	−2.04510	−	0.181757i	−0.0772977	−	0.00686978i
$701$		−	38.7293i		−	1.46279i	−0.681956	−	0.731393i	$-0.738871\pi$
$701$		−	38.7293i		−	1.46279i	0.681956	−	0.731393i	$-0.261129\pi$
$702$		0			0
$703$		−	13.4670i		−	0.507919i
$704$	−2.53525	−	0.679319i	−0.0955510	−	0.0256028i
$705$		0			0
$706$	−11.0210	+	19.0889i	−0.414780	+	0.718420i
$707$	12.1586	−	17.3136i	0.457272	−	0.651144i
$708$		0			0
$709$	−28.4986	+	7.63617i	−1.07029	+	0.286782i	−0.750611	−	0.660745i	$-0.770241\pi$
$709$	−28.4986	+	7.63617i	−1.07029	+	0.286782i	−0.319675	+	0.947527i	$0.603574\pi$
$710$	−27.7187	+	27.7187i	−1.04026	+	1.04026i
$711$		0			0
$712$	−8.00915	−	13.8723i	−0.300156	−	0.519885i
$713$	−24.9490	−	6.68507i	−0.934348	−	0.250358i
$714$		0			0
$715$	−0.432246	−	7.10276i	−0.0161651	−	0.265628i
$716$	4.86122			0.181672
$717$		0			0
$718$	7.87793	+	13.6450i	0.294002	+	0.509226i
$719$	−4.23114	+	7.32855i	−0.157795	+	0.273309i	−0.934073	−	0.357082i	$-0.883772\pi$
$719$	−4.23114	+	7.32855i	−0.157795	+	0.273309i	0.776278	+	0.630390i	$0.217105\pi$
$720$		0			0
$721$	11.5259	+	24.8063i	0.429246	+	0.923836i
$722$	17.9981	−	4.82258i	0.669820	−	0.179478i
$723$		0			0
$724$	4.24676	+	2.45187i	0.157830	+	0.0911229i
$725$	−6.07418	+	3.50693i	−0.225589	+	0.130244i
$726$		0			0
$727$	3.27056			0.121299			0.0606493	−	0.998159i	$-0.480683\pi$
$727$	3.27056			0.121299			0.0606493	+	0.998159i	$0.480683\pi$
$728$	−13.0821	−	13.8322i	−0.484856	−	0.512654i
$729$		0			0
$730$	4.74076	+	1.27028i	0.175463	+	0.0470153i
$731$	−4.48103	+	2.58712i	−0.165737	+	0.0956882i
$732$		0			0
$733$	9.76212	+	9.76212i	0.360572	+	0.360572i	0.864023	−	0.503451i	$-0.167937\pi$
$733$	9.76212	+	9.76212i	0.360572	+	0.360572i	−0.503451	+	0.864023i	$0.667937\pi$
$734$	11.8502	−	3.17526i	0.437400	−	0.117201i
$735$		0			0
$736$	−9.14692	−	9.14692i	−0.337160	−	0.337160i
$737$	0.420703	−	0.728680i	0.0154968	−	0.0268413i
$738$		0			0
$739$	11.0030	−	41.0638i	0.404753	−	1.51056i	−0.399759	−	0.916620i	$-0.630906\pi$
$739$	11.0030	−	41.0638i	0.404753	−	1.51056i	0.804512	−	0.593937i	$-0.202427\pi$
$740$	7.80292			0.286841
$741$		0			0
$742$	−4.83212	−	27.6264i	−0.177393	−	1.01420i
$743$	47.1919	+	12.6450i	1.73130	+	0.463901i	0.980482	−	0.196606i	$-0.0629921\pi$
$743$	47.1919	+	12.6450i	1.73130	+	0.463901i	0.750820	+	0.660507i	$0.229659\pi$
$744$		0			0
$745$	−18.8021	+	32.5663i	−0.688857	+	1.19314i
$746$	−1.28606	+	1.28606i	−0.0470858	+	0.0470858i
$747$		0			0
$748$	1.23083	+	4.59352i	0.0450036	+	0.167956i
$749$	19.8456	−	28.2597i	0.725142	−	1.03259i
$750$		0			0
$751$	−9.96838	+	5.75525i	−0.363751	+	0.210012i	−0.670725	−	0.741706i	$-0.734017\pi$
$751$	−9.96838	+	5.75525i	−0.363751	+	0.210012i	0.306974	+	0.951718i	$0.400684\pi$
$752$	14.7136	+	3.94250i	0.536550	+	0.143768i
$753$		0			0
$754$	43.3109	+	8.82548i	1.57729	+	0.321405i
$755$			0.0732428i			0.00266558i
$756$		0			0
$757$	−8.97468	−	15.5446i	−0.326190	−	0.564978i	0.655562	−	0.755141i	$-0.272432\pi$
$757$	−8.97468	−	15.5446i	−0.326190	−	0.564978i	−0.981753	+	0.190163i	$0.939098\pi$
$758$	37.8230	+	21.8371i	1.37379	+	0.793160i
$759$		0			0
$760$	2.91545	+	10.8806i	0.105754	+	0.394681i
$761$	2.86608	+	10.6964i	0.103895	+	0.387743i	0.998218	−	0.0596806i	$-0.0190082\pi$
$761$	2.86608	+	10.6964i	0.103895	+	0.387743i	−0.894322	+	0.447424i	$0.852342\pi$
$762$		0			0
$763$	29.0984	+	10.6363i	1.05343	+	0.385060i
$764$	15.1571	−	8.75096i	0.548365	−	0.316599i
$765$		0			0
$766$	−8.93422			−0.322806
$767$	−1.79763	−	0.366304i	−0.0649087	−	0.0132265i
$768$		0			0
$769$	−2.87361	+	10.7245i	−0.103625	+	0.386734i	−0.998186	−	0.0602130i	$-0.980822\pi$
$769$	−2.87361	+	10.7245i	−0.103625	+	0.386734i	0.894561	+	0.446947i	$0.147489\pi$
$770$	5.61639	+	6.71207i	0.202401	+	0.241886i
$771$		0			0
$772$	5.54545	−	5.54545i	0.199585	−	0.199585i
$773$	−2.67962	+	0.718001i	−0.0963792	+	0.0258247i	−0.306686	−	0.951811i	$-0.599220\pi$
$773$	−2.67962	+	0.718001i	−0.0963792	+	0.0258247i	0.210307	+	0.977635i	$0.432554\pi$
$774$		0			0
$775$	5.85959	−	5.85959i	0.210483	−	0.210483i
$776$	21.6079	+	12.4753i	0.775678	+	0.447838i
$777$		0			0
$778$	−1.49192	+	5.56791i	−0.0534879	+	0.199619i
$779$		−	9.61197i		−	0.344385i
$780$		0			0
$781$	−11.4223			−0.408724
$782$	7.76103	−	28.9646i	0.277534	−	1.03577i
$783$		0			0
$784$	34.2007	+	6.12754i	1.22145	+	0.218841i
$785$	10.2183	−	10.2183i	0.364707	−	0.364707i
$786$		0			0
$787$	−10.0968	−	37.6817i	−0.359912	−	1.34321i	−0.874189	−	0.485585i	$-0.838607\pi$
$787$	−10.0968	−	37.6817i	−0.359912	−	1.34321i	0.514278	−	0.857624i	$-0.328060\pi$
$788$	2.64999	+	2.64999i	0.0944020	+	0.0944020i
$789$		0			0
$790$	−19.5467	−	33.8559i	−0.695441	−	1.20454i
$791$	21.3859	+	1.90066i	0.760395	+	0.0675796i
$792$		0			0
$793$	−39.1793	+	25.9150i	−1.39130	+	0.920269i
$794$		−	1.00709i		−	0.0357403i
$795$		0			0
$796$	15.1101	−	8.72381i	0.535563	−	0.309207i
$797$	16.0998	−	27.8857i	0.570285	−	0.987763i	−0.426251	−	0.904605i	$-0.640166\pi$
$797$	16.0998	−	27.8857i	0.570285	−	0.987763i	0.996536	−	0.0831583i	$-0.0265007\pi$
$798$		0			0
$799$	4.75426	+	17.7431i	0.168193	+	0.627707i
$800$	4.00873	−	1.07414i	0.141730	−	0.0379764i
$801$		0			0
$802$	10.0498	−	17.4068i	0.354871	−	0.614655i
$803$	0.715059	+	1.23852i	0.0252339	+	0.0437064i
$804$		0			0
$805$	−2.73896	−	15.6593i	−0.0965356	−	0.551917i
$806$	−52.1261	+	3.17219i	−1.83606	+	0.111736i
$807$		0			0
$808$	−4.13051	+	15.4153i	−0.145311	+	0.542308i
$809$	5.89662	+	10.2133i	0.207314	+	0.359079i	0.950868	−	0.309598i	$-0.100194\pi$
$809$	5.89662	+	10.2133i	0.207314	+	0.359079i	−0.743553	+	0.668677i	$0.766861\pi$
$810$		0			0
$811$	14.4330	+	14.4330i	0.506811	+	0.506811i	0.913546	−	0.406735i	$-0.133333\pi$
$811$	14.4330	+	14.4330i	0.506811	+	0.506811i	−0.406735	+	0.913546i	$0.633333\pi$
$812$	−14.2020	+	6.59876i	−0.498394	+	0.231571i
$813$		0			0
$814$	5.58107	+	5.58107i	0.195616	+	0.195616i
$815$	−28.6480	−	16.5399i	−1.00350	−	0.579369i
$816$		0			0
$817$	2.34438	+	0.628174i	0.0820194	+	0.0219770i
$818$	−19.4551			−0.680232
$819$		0			0
$820$	5.56926			0.194487
$821$	−8.75856	−	2.34685i	−0.305676	−	0.0819056i	0.102721	−	0.994710i	$-0.467245\pi$
$821$	−8.75856	−	2.34685i	−0.305676	−	0.0819056i	−0.408396	+	0.912805i	$0.633912\pi$
$822$		0			0
$823$	−14.1019	−	8.14175i	−0.491562	−	0.283804i	0.233660	−	0.972318i	$-0.424930\pi$
$823$	−14.1019	−	8.14175i	−0.491562	−	0.283804i	−0.725222	+	0.688515i	$0.758263\pi$
$824$	−14.5902	−	14.5902i	−0.508273	−	0.508273i
$825$		0			0
$826$	2.04626	−	0.950764i	0.0711985	−	0.0330813i
$827$	27.1227	+	27.1227i	0.943148	+	0.943148i	0.998469	−	0.0553203i	$-0.0176180\pi$
$827$	27.1227	+	27.1227i	0.943148	+	0.943148i	−0.0553203	+	0.998469i	$0.517618\pi$
$828$		0			0
$829$	−1.40529	−	2.43404i	−0.0488079	−	0.0845377i	0.840589	−	0.541673i	$-0.182209\pi$
$829$	−1.40529	−	2.43404i	−0.0488079	−	0.0845377i	−0.889397	+	0.457135i	$0.848876\pi$
$830$	1.52651	−	5.69702i	0.0529860	−	0.197746i
$831$		0			0
$832$	8.62510	+	4.30360i	0.299021	+	0.149201i
$833$	14.2221	+	39.4117i	0.492766	+	1.36554i
$834$		0			0
$835$	6.75692	+	11.7033i	0.233833	+	0.405010i
$836$	1.11534	−	1.93183i	0.0385750	−	0.0668138i
$837$		0			0
$838$	−57.9299	+	15.5223i	−2.00116	+	0.536208i
$839$	9.79321	+	36.5488i	0.338099	+	1.26180i	0.900470	+	0.434918i	$0.143223\pi$
$839$	9.79321	+	36.5488i	0.338099	+	1.26180i	−0.562371	+	0.826885i	$0.690111\pi$
$840$		0			0
$841$	−12.2485	+	21.2150i	−0.422363	+	0.731553i
$842$	7.12836	−	4.11556i	0.245660	−	0.141832i
$843$		0			0
$844$			11.9689i			0.411986i
$845$	−3.65283	+	25.8765i	−0.125661	+	0.890180i
$846$		0			0
$847$	2.35062	−	26.4488i	0.0807684	−	0.908793i
$848$	15.6961	+	27.1864i	0.539006	+	0.933586i
$849$		0			0
$850$	6.80270	+	6.80270i	0.233331	+	0.233331i
$851$	−3.71058	−	13.8481i	−0.127197	−	0.474706i
$852$		0			0
$853$	7.88711	−	7.88711i	0.270050	−	0.270050i	−0.559070	−	0.829120i	$-0.688842\pi$
$853$	7.88711	−	7.88711i	0.270050	−	0.270050i	0.829120	+	0.559070i	$0.188842\pi$
$854$	19.8346	−	54.2629i	0.678726	−	1.85684i
$855$		0			0
$856$	−6.74193	+	25.1612i	−0.230434	+	0.859993i
$857$	−17.7293			−0.605621			−0.302811	−	0.953051i	$-0.597925\pi$
$857$	−17.7293			−0.605621			−0.302811	+	0.953051i	$0.597925\pi$
$858$		0			0
$859$		−	3.70465i		−	0.126401i	−0.998001	−	0.0632005i	$-0.979869\pi$
$859$		−	3.70465i		−	0.126401i	0.998001	−	0.0632005i	$-0.0201308\pi$
$860$	−0.363970	+	1.35835i	−0.0124113	+	0.0463195i
$861$		0			0
$862$	−0.712607	−	0.411424i	−0.0242715	−	0.0140132i
$863$	−27.8842	+	27.8842i	−0.949191	+	0.949191i	−0.998770	−	0.0495793i	$-0.984212\pi$
$863$	−27.8842	+	27.8842i	−0.949191	+	0.949191i	0.0495793	+	0.998770i	$0.484212\pi$
$864$		0			0
$865$	−18.4801	+	4.95174i	−0.628344	+	0.168364i
$866$	−21.0805	+	21.0805i	−0.716345	+	0.716345i
$867$		0			0
$868$	14.1898	−	11.8735i	0.481634	−	0.403012i
$869$	2.94827	−	11.0031i	0.100013	−	0.373254i
$870$		0			0
$871$	−2.04824	+	2.31369i	−0.0694021	+	0.0783966i
$872$	−23.3705			−0.791425
$873$		0			0
$874$	−12.1812	+	7.03283i	−0.412036	+	0.237889i
$875$	29.7669	+	10.8806i	1.00631	+	0.367833i
$876$		0			0
$877$	−10.3037	−	38.4541i	−0.347933	−	1.29850i	−0.889148	−	0.457619i	$-0.848702\pi$
$877$	−10.3037	−	38.4541i	−0.347933	−	1.29850i	0.541215	−	0.840884i	$-0.317964\pi$
$878$	−12.4078	−	46.3064i	−0.418742	−	1.56277i
$879$		0			0
$880$	−8.48373	−	4.89808i	−0.285986	−	0.165114i
$881$	1.49665	+	2.59227i	0.0504233	+	0.0873357i	0.890135	−	0.455696i	$-0.150610\pi$
$881$	1.49665	+	2.59227i	0.0504233	+	0.0873357i	−0.839712	+	0.543032i	$0.817276\pi$
$882$		0			0
$883$			1.38623i			0.0466504i	0.999728	+	0.0233252i	$0.00742531\pi$
$883$			1.38623i			0.0466504i	−0.999728	+	0.0233252i	$0.992575\pi$
$884$	−1.06088	−	17.4325i	−0.0356811	−	0.586320i
$885$		0			0
$886$	−11.9342	−	3.19777i	−0.400939	−	0.107431i
$887$	30.8094	−	17.7878i	1.03448	−	0.597256i	0.116214	−	0.993224i	$-0.462924\pi$
$887$	30.8094	−	17.7878i	1.03448	−	0.597256i	0.918264	+	0.395968i	$0.129591\pi$
$888$		0			0
$889$	−17.0473	−	11.9716i	−0.571747	−	0.401515i
$890$	−6.99906	−	26.1209i	−0.234609	−	0.875573i
$891$		0			0
$892$	−12.2168	+	12.2168i	−0.409049	+	0.409049i
$893$	4.30817	−	7.46197i	0.144168	−	0.249705i
$894$		0			0
$895$	−11.6642	−	3.12540i	−0.389890	−	0.104471i
$896$	−34.2363	+	5.98825i	−1.14375	+	0.200053i
$897$		0			0
$898$	39.0804			1.30413
$899$	16.3588	−	61.0519i	0.545597	−	2.03620i
$900$		0			0
$901$	−18.9279	+	32.7841i	−0.630580	+	1.09220i
$902$	3.98343	+	3.98343i	0.132634	+	0.132634i
$903$		0			0
$904$	−15.6439	+	4.19178i	−0.520310	+	0.139417i
$905$	−8.61344	−	8.61344i	−0.286320	−	0.286320i
$906$		0			0
$907$	−43.1379	+	24.9057i	−1.43237	+	0.826979i	−0.997301	−	0.0734190i	$-0.976609\pi$
$907$	−43.1379	+	24.9057i	−1.43237	+	0.826979i	−0.435068	+	0.900398i	$0.643276\pi$
$908$	10.5660	+	2.83116i	0.350646	+	0.0939553i
$909$		0			0
$910$	−15.2890	−	28.2721i	−0.506826	−	0.937210i
$911$	55.7036			1.84554			0.922772	−	0.385347i	$-0.125918\pi$
$911$	55.7036			1.84554			0.922772	+	0.385347i	$0.125918\pi$
$912$		0			0
$913$	1.48834	−	0.859293i	0.0492568	−	0.0284385i
$914$	−6.54953	−	3.78137i	−0.216639	−	0.125077i
$915$		0			0
$916$	5.62180	−	1.50636i	0.185749	−	0.0497714i
$917$	−47.8914	+	22.2520i	−1.58151	+	0.734826i
$918$		0			0
$919$	10.0323	−	17.3764i	0.330934	−	0.573194i	−0.651762	−	0.758424i	$-0.725970\pi$
$919$	10.0323	−	17.3764i	0.330934	−	0.573194i	0.982695	+	0.185230i	$0.0593030\pi$
$920$	5.99587	+	10.3852i	0.197678	+	0.342388i
$921$		0			0
$922$	55.8406			1.83901
$923$	41.1038	+	8.37574i	1.35295	+	0.275691i
$924$		0			0
$925$	4.44286	+	1.19046i	0.146080	+	0.0391421i
$926$	−34.4873	−	59.7338i	−1.13332	−	1.96297i
$927$		0			0
$928$	22.3831	−	22.3831i	0.734762	−	0.734762i
$929$	−30.5947	+	8.19783i	−1.00378	+	0.268962i	−0.723029	−	0.690818i	$-0.757251\pi$
$929$	−30.5947	+	8.19783i	−1.00378	+	0.268962i	−0.280752	+	0.959780i	$0.590584\pi$
$930$		0			0
$931$	8.35495	−	17.7894i	0.273823	−	0.583023i
$932$	−9.38923	+	16.2626i	−0.307555	+	0.532700i
$933$		0			0
$934$	9.25619	+	2.48019i	0.302872	+	0.0811542i
$935$		−	11.8132i		−	0.386332i
$936$		0			0
$937$		−	43.3600i		−	1.41651i	−0.705957	−	0.708255i	$-0.749483\pi$
$937$		−	43.3600i		−	1.41651i	0.705957	−	0.708255i	$-0.250517\pi$
$938$	0.336440	−	3.78557i	0.0109852	−	0.123603i
$939$		0			0
$940$	4.32353	+	2.49619i	0.141018	+	0.0814168i
$941$	−27.4469	−	27.4469i	−0.894743	−	0.894743i	0.100222	−	0.994965i	$-0.468045\pi$
$941$	−27.4469	−	27.4469i	−0.894743	−	0.894743i	−0.994965	+	0.100222i	$0.968045\pi$
$942$		0			0
$943$	−2.64839	−	9.88393i	−0.0862435	−	0.321865i
$944$	−1.78586	+	1.78586i	−0.0581246	+	0.0581246i
$945$		0			0
$946$	−1.23190	+	0.711236i	−0.0400524	+	0.0231243i
$947$	−10.6763	+	39.8444i	−0.346932	+	1.29477i	0.543406	+	0.839470i	$0.317134\pi$
$947$	−10.6763	+	39.8444i	−0.346932	+	1.29477i	−0.890339	+	0.455299i	$0.849532\pi$
$948$		0			0
$949$	−1.66499	−	4.98120i	−0.0540480	−	0.161697i
$950$		−	4.51266i		−	0.146410i
$951$		0			0
$952$	−20.2828	−	24.2397i	−0.657370	−	0.785614i
$953$	9.00364	+	5.19825i	0.291656	+	0.168388i	0.638689	−	0.769465i	$-0.279477\pi$
$953$	9.00364	+	5.19825i	0.291656	+	0.168388i	−0.347032	+	0.937853i	$0.612811\pi$
$954$		0			0
$955$	−41.9947	+	11.2524i	−1.35892	+	0.364120i
$956$	3.06546	−	0.821387i	0.0991439	−	0.0265655i
$957$		0			0
$958$	48.3721	+	27.9277i	1.56283	+	0.902301i
$959$	18.2582	+	21.8201i	0.589588	+	0.704609i
$960$		0			0
$961$			43.6760i			1.40890i
$962$	−15.9913	−	24.1762i	−0.515579	−	0.779472i
$963$		0			0
$964$	0.667940	−	2.49279i	0.0215129	−	0.0802873i
$965$	−16.8713	+	9.74062i	−0.543105	+	0.313562i
$966$		0			0
$967$	15.1251	−	15.1251i	0.486390	−	0.486390i	−0.420775	−	0.907165i	$-0.638242\pi$
$967$	15.1251	−	15.1251i	0.486390	−	0.486390i	0.907165	+	0.420775i	$0.138242\pi$
$968$	5.18415	+	19.3475i	0.166625	+	0.621853i
$969$		0			0
$970$	29.7847	+	29.7847i	0.956331	+	0.956331i
$971$	−15.1229	−	8.73122i	−0.485318	−	0.280198i	0.237312	−	0.971433i	$-0.423734\pi$
$971$	−15.1229	−	8.73122i	−0.485318	−	0.280198i	−0.722630	+	0.691235i	$0.757067\pi$
$972$		0			0
$973$	−3.81593	+	42.9362i	−0.122333	+	1.37647i
$974$			25.3407i			0.811968i
$975$		0			0
$976$			64.6679i			2.06997i
$977$	−11.5532	−	3.09568i	−0.369621	−	0.0990396i	0.0692272	−	0.997601i	$-0.477947\pi$
$977$	−11.5532	−	3.09568i	−0.369621	−	0.0990396i	−0.438848	+	0.898561i	$0.644613\pi$
$978$		0			0
$979$	3.93986	−	6.82405i	0.125919	−	0.218097i
$980$	10.3073	+	4.84093i	0.329255	+	0.154638i
$981$		0			0
$982$	−7.10215	+	1.90302i	−0.226639	+	0.0607277i
$983$	8.69175	−	8.69175i	0.277224	−	0.277224i	−0.554776	−	0.832000i	$-0.687196\pi$
$983$	8.69175	−	8.69175i	0.277224	−	0.277224i	0.832000	+	0.554776i	$0.187196\pi$
$984$		0			0
$985$	−4.65472	−	8.06222i	−0.148312	−	0.256884i
$986$	70.8782	+	18.9918i	2.25722	+	0.604821i
$987$		0			0
$988$	−5.43019	+	6.13393i	−0.172757	+	0.195146i
$989$	2.58379			0.0821598
$990$		0			0
$991$	19.1774	+	33.2162i	0.609189	+	1.05515i	0.991374	+	0.131060i	$0.0418382\pi$
$991$	19.1774	+	33.2162i	0.609189	+	1.05515i	−0.382186	+	0.924086i	$0.624829\pi$
$992$	−18.6996	+	32.3886i	−0.593712	+	1.02834i
$993$		0			0
$994$	−46.7889	+	21.7397i	−1.48405	+	0.689543i
$995$	−41.8644	+	11.2175i	−1.32719	+	0.355619i
$996$		0			0
$997$	33.1334	+	19.1296i	1.04935	+	0.605840i	0.922466	−	0.386078i	$-0.126171\pi$
$997$	33.1334	+	19.1296i	1.04935	+	0.605840i	0.126879	+	0.991918i	$0.459504\pi$
$998$	−29.0891	+	16.7946i	−0.920800	+	0.531624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.g.496.1		32
3.2	odd	2		91.2.bc.a.41.7	yes	32
7.6	odd	2	inner	819.2.fm.g.496.2		32
13.7	odd	12	inner	819.2.fm.g.748.2		32
21.2	odd	6		637.2.x.b.80.1		32
21.5	even	6		637.2.x.b.80.2		32
21.11	odd	6		637.2.bb.b.509.2		32
21.17	even	6		637.2.bb.b.509.1		32
21.20	even	2		91.2.bc.a.41.8	yes	32
39.20	even	12		91.2.bc.a.20.8	yes	32
91.20	even	12	inner	819.2.fm.g.748.1		32
273.20	odd	12		91.2.bc.a.20.7	✓	32
273.59	odd	12		637.2.x.b.215.2		32
273.137	even	12		637.2.x.b.215.1		32
273.215	odd	12		637.2.bb.b.423.2		32
273.254	even	12		637.2.bb.b.423.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.7	✓	32	273.20	odd	12
91.2.bc.a.20.8	yes	32	39.20	even	12
91.2.bc.a.41.7	yes	32	3.2	odd	2
91.2.bc.a.41.8	yes	32	21.20	even	2
637.2.x.b.80.1		32	21.2	odd	6
637.2.x.b.80.2		32	21.5	even	6
637.2.x.b.215.1		32	273.137	even	12
637.2.x.b.215.2		32	273.59	odd	12
637.2.bb.b.423.1		32	273.254	even	12
637.2.bb.b.423.2		32	273.215	odd	12
637.2.bb.b.509.1		32	21.17	even	6
637.2.bb.b.509.2		32	21.11	odd	6
819.2.fm.g.496.1		32	1.1	even	1	trivial
819.2.fm.g.496.2		32	7.6	odd	2	inner
819.2.fm.g.748.1		32	91.20	even	12	inner
819.2.fm.g.748.2		32	13.7	odd	12	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61897 - 0.433802i) q^{2} +(0.700831 + 0.404625i) q^{4} +(-1.42145 - 1.42145i) q^{5} +(-1.11484 - 2.39940i) q^{7} +(1.41124 + 1.41124i) q^{8} +O(q^{10})\)	\(q+(-1.61897 - 0.433802i) q^{2} +(0.700831 + 0.404625i) q^{4} +(-1.42145 - 1.42145i) q^{5} +(-1.11484 - 2.39940i) q^{7} +(1.41124 + 1.41124i) q^{8} +(1.68466 + 2.91792i) q^{10} +(-0.254101 + 0.948318i) q^{11} +(1.60977 - 3.22624i) q^{13} +(0.764036 + 4.36818i) q^{14} +(-2.48181 - 4.29862i) q^{16} +(2.99281 - 5.18370i) q^{17} +(-2.71200 + 0.726678i) q^{19} +(-0.421043 - 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 + 1.49448i) q^{23} -0.958941i q^{25} +(-4.00573 + 4.52487i) q^{26} +(0.189540 - 2.13267i) q^{28} +(-3.65708 - 6.33425i) q^{29} +(6.11048 + 6.11048i) q^{31} +(1.12013 + 4.18037i) q^{32} +(-7.09397 + 7.09397i) q^{34} +(-1.82594 + 4.99533i) q^{35} +(-1.24143 + 4.63309i) q^{37} +4.70588 q^{38} -4.01202i q^{40} +(-0.886060 + 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.561795 + 0.561795i) q^{44} +(4.83903 - 1.29661i) q^{46} +(-2.17001 + 2.17001i) q^{47} +(-4.51424 + 5.34992i) q^{49} +(-0.415990 + 1.55250i) q^{50} +(2.43360 - 1.60970i) q^{52} -6.32446 q^{53} +(1.70918 - 0.986797i) q^{55} +(1.81282 - 4.95944i) q^{56} +(3.17290 + 11.8414i) q^{58} +(-0.131692 - 0.491481i) q^{59} +(-11.2829 - 6.51419i) q^{61} +(-7.24196 - 12.5434i) q^{62} +2.67342i q^{64} +(-6.87417 + 2.29773i) q^{65} +(-0.827827 - 0.221815i) q^{67} +(4.19491 - 2.42193i) q^{68} +(5.12312 - 7.29521i) q^{70} +(3.01121 + 11.2380i) q^{71} +(1.03002 - 1.03002i) q^{73} +(4.01968 - 6.96230i) q^{74} +(-2.19469 - 0.588064i) q^{76} +(2.55868 - 0.447537i) q^{77} -11.6027 q^{79} +(-2.58251 + 9.63806i) q^{80} +(2.86901 - 4.96927i) q^{82} +(-1.23779 - 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(1.02452 + 1.02452i) q^{86} +(-1.69690 + 0.979707i) q^{88} +(-7.75255 - 2.07729i) q^{89} +(-9.53569 - 0.265737i) q^{91} -2.41881 q^{92} +(4.45454 - 2.57183i) q^{94} +(4.88792 + 2.82204i) q^{95} +(12.0756 - 3.23566i) q^{97} +(9.62923 - 6.70307i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more