LMFDB - Embedded newform 630.2.ce.c.233.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(53,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 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("630.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ce (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.1
Character	$\chi$	$=$	630.233
Dual form			630.2.ce.c.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.56834 - 1.59384i) q^{5} +(1.65758 - 2.06214i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.56834 - 1.59384i) q^{5} +(1.65758 - 2.06214i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.92741 + 1.13362i) q^{10} +(-0.565444 + 0.326459i) q^{11} +(0.771886 + 0.771886i) q^{13} +(-1.06738 + 2.42089i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.554483 - 2.06936i) q^{17} +(-4.34372 - 2.50785i) q^{19} +(-2.15514 - 0.596138i) q^{20} +(0.461683 - 0.461683i) q^{22} +(-0.242669 - 0.905652i) q^{23} +(-0.0806473 + 4.99935i) q^{25} +(-0.945363 - 0.545806i) q^{26} +(0.404442 - 2.61466i) q^{28} -9.79270 q^{29} +(-0.897620 - 1.55472i) q^{31} +(-0.258819 + 0.965926i) q^{32} +2.14236i q^{34} +(-5.88637 + 0.592200i) q^{35} +(-1.67864 - 6.26479i) q^{37} +(4.84479 + 1.29816i) q^{38} +(2.23600 + 0.0180339i) q^{40} -7.90000i q^{41} +(-0.0657249 - 0.0657249i) q^{43} +(-0.326459 + 0.565444i) q^{44} +(0.468800 + 0.811985i) q^{46} +(3.18795 - 0.854209i) q^{47} +(-1.50482 - 6.83634i) q^{49} +(-1.21603 - 4.84987i) q^{50} +(1.05442 + 0.282530i) q^{52} +(7.13943 + 1.91300i) q^{53} +(1.40713 + 0.389229i) q^{55} +(0.286062 + 2.63024i) q^{56} +(9.45902 - 2.53454i) q^{58} +(-3.39154 - 5.87431i) q^{59} +(-4.33834 + 7.51422i) q^{61} +(1.26943 + 1.26943i) q^{62} -1.00000i q^{64} +(0.0196860 - 2.44084i) q^{65} +(-6.21344 - 1.66489i) q^{67} +(-0.554483 - 2.06936i) q^{68} +(5.53252 - 2.09552i) q^{70} +7.68577i q^{71} +(2.58009 - 9.62903i) q^{73} +(3.24289 + 5.61685i) q^{74} -5.01569 q^{76} +(-0.264067 + 1.70716i) q^{77} +(-10.3402 - 5.96992i) q^{79} +(-2.16447 + 0.561299i) q^{80} +(2.04467 + 7.63081i) q^{82} +(-0.838447 + 0.838447i) q^{83} +(-4.16784 + 2.36169i) q^{85} +(0.0804962 + 0.0464745i) q^{86} +(0.168988 - 0.630670i) q^{88} +(8.65123 - 14.9844i) q^{89} +(2.87120 - 0.312269i) q^{91} +(-0.662983 - 0.662983i) q^{92} +(-2.85824 + 1.65021i) q^{94} +(2.81530 + 10.8563i) q^{95} +(-8.59970 + 8.59970i) q^{97} +(3.22292 + 6.21392i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{7}+O(q^{10}) $ 32 * q - 12 * q^7	$ 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) $ 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.56834	−	1.59384i	−0.701381	−	0.712787i
$5$	−1.56834	−	1.59384i	−0.701381	−	0.712787i
$6$		0			0
$7$	1.65758	−	2.06214i	0.626508	−	0.779415i
$7$	1.65758	−	2.06214i	0.626508	−	0.779415i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	1.92741	+	1.13362i	0.609501	+	0.358481i
$11$	−0.565444	+	0.326459i	−0.170488	+	0.0984311i	−0.582816	−	0.812604i	$-0.698049\pi$
$11$	−0.565444	+	0.326459i	−0.170488	+	0.0984311i	0.412328	+	0.911035i	$0.364716\pi$
$12$		0			0
$13$	0.771886	+	0.771886i	0.214083	+	0.214083i	0.805999	−	0.591917i	$-0.201629\pi$
$13$	0.771886	+	0.771886i	0.214083	+	0.214083i	−0.591917	+	0.805999i	$0.701629\pi$
$14$	−1.06738	+	2.42089i	−0.285270	+	0.647009i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.554483	−	2.06936i	0.134482	−	0.501894i	−0.865517	−	0.500879i	$-0.833010\pi$
$17$	0.554483	−	2.06936i	0.134482	−	0.501894i	0.999999	−	0.00101492i	$-0.000323058\pi$
$18$		0			0
$19$	−4.34372	−	2.50785i	−0.996517	−	0.575339i	−0.0893010	−	0.996005i	$-0.528463\pi$
$19$	−4.34372	−	2.50785i	−0.996517	−	0.575339i	−0.907216	+	0.420665i	$0.861797\pi$
$20$	−2.15514	−	0.596138i	−0.481904	−	0.133300i
$21$		0			0
$22$	0.461683	−	0.461683i	0.0984311	−	0.0984311i
$23$	−0.242669	−	0.905652i	−0.0505999	−	0.188841i	0.936000	−	0.352000i	$-0.114498\pi$
$23$	−0.242669	−	0.905652i	−0.0505999	−	0.188841i	−0.986600	+	0.163159i	$0.947832\pi$
$24$		0			0
$25$	−0.0806473	+	4.99935i	−0.0161295	+	0.999870i
$26$	−0.945363	−	0.545806i	−0.185401	−	0.107041i
$27$		0			0
$28$	0.404442	−	2.61466i	0.0764323	−	0.494124i
$29$	−9.79270			−1.81846			−0.909229	−	0.416296i	$-0.863328\pi$
$29$	−9.79270			−1.81846			−0.909229	+	0.416296i	$0.863328\pi$
$30$		0			0
$31$	−0.897620	−	1.55472i	−0.161217	−	0.279237i	0.774088	−	0.633078i	$-0.218209\pi$
$31$	−0.897620	−	1.55472i	−0.161217	−	0.279237i	−0.935306	+	0.353841i	$0.884875\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$			2.14236i			0.367412i
$35$	−5.88637	+	0.592200i	−0.994977	+	0.100100i
$36$		0			0
$37$	−1.67864	−	6.26479i	−0.275967	−	1.02992i	−0.955190	−	0.295993i	$-0.904350\pi$
$37$	−1.67864	−	6.26479i	−0.275967	−	1.02992i	0.679223	−	0.733932i	$-0.262317\pi$
$38$	4.84479	+	1.29816i	0.785928	+	0.210589i
$39$		0			0
$40$	2.23600	+	0.0180339i	0.353542	+	0.00285141i
$41$		−	7.90000i		−	1.23377i	−0.787052	−	0.616886i	$-0.788394\pi$
$41$		−	7.90000i		−	1.23377i	0.787052	−	0.616886i	$-0.211606\pi$
$42$		0			0
$43$	−0.0657249	−	0.0657249i	−0.0100230	−	0.0100230i	0.702078	−	0.712100i	$-0.252256\pi$
$43$	−0.0657249	−	0.0657249i	−0.0100230	−	0.0100230i	−0.712100	+	0.702078i	$0.752256\pi$
$44$	−0.326459	+	0.565444i	−0.0492155	+	0.0852438i
$45$		0			0
$46$	0.468800	+	0.811985i	0.0691208	+	0.119721i
$47$	3.18795	−	0.854209i	0.465011	−	0.124599i	−0.0187039	−	0.999825i	$-0.505954\pi$
$47$	3.18795	−	0.854209i	0.465011	−	0.124599i	0.483714	+	0.875226i	$0.339287\pi$
$48$		0			0
$49$	−1.50482	−	6.83634i	−0.214975	−	0.976620i
$50$	−1.21603	−	4.84987i	−0.171972	−	0.685876i
$51$		0			0
$52$	1.05442	+	0.282530i	0.146221	+	0.0391798i
$53$	7.13943	+	1.91300i	0.980676	+	0.262771i	0.713329	−	0.700829i	$-0.247186\pi$
$53$	7.13943	+	1.91300i	0.980676	+	0.262771i	0.267347	+	0.963600i	$0.413853\pi$
$54$		0			0
$55$	1.40713	+	0.389229i	0.189737	+	0.0524836i
$56$	0.286062	+	2.63024i	0.0382267	+	0.351481i
$57$		0			0
$58$	9.45902	−	2.53454i	1.24203	−	0.332801i
$59$	−3.39154	−	5.87431i	−0.441540	−	0.764771i	0.556264	−	0.831006i	$-0.312235\pi$
$59$	−3.39154	−	5.87431i	−0.441540	−	0.764771i	−0.997804	+	0.0662354i	$0.978901\pi$
$60$		0			0
$61$	−4.33834	+	7.51422i	−0.555467	+	0.962098i	0.442400	+	0.896818i	$0.354127\pi$
$61$	−4.33834	+	7.51422i	−0.555467	+	0.962098i	−0.997867	+	0.0652798i	$0.979206\pi$
$62$	1.26943	+	1.26943i	0.161217	+	0.161217i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.0196860	−	2.44084i	0.00244175	−	0.302749i
$66$		0			0
$67$	−6.21344	−	1.66489i	−0.759093	−	0.203398i	−0.141545	−	0.989932i	$-0.545207\pi$
$67$	−6.21344	−	1.66489i	−0.759093	−	0.203398i	−0.617548	+	0.786534i	$0.711874\pi$
$68$	−0.554483	−	2.06936i	−0.0672410	−	0.250947i
$69$		0			0
$70$	5.53252	−	2.09552i	0.661263	−	0.250463i
$71$			7.68577i			0.912134i	0.889946	+	0.456067i	$0.150742\pi$
$71$			7.68577i			0.912134i	−0.889946	+	0.456067i	$0.849258\pi$
$72$		0			0
$73$	2.58009	−	9.62903i	0.301977	−	1.12699i	−0.633540	−	0.773710i	$-0.718399\pi$
$73$	2.58009	−	9.62903i	0.301977	−	1.12699i	0.935517	−	0.353283i	$-0.114935\pi$
$74$	3.24289	+	5.61685i	0.376979	+	0.652946i
$75$		0			0
$76$	−5.01569			−0.575339
$77$	−0.264067	+	1.70716i	−0.0300933	+	0.194548i
$78$		0			0
$79$	−10.3402	−	5.96992i	−1.16336	−	0.671668i	−0.211256	−	0.977431i	$-0.567755\pi$
$79$	−10.3402	−	5.96992i	−1.16336	−	0.671668i	−0.952108	+	0.305763i	$0.901089\pi$
$80$	−2.16447	+	0.561299i	−0.241995	+	0.0627551i
$81$		0			0
$82$	2.04467	+	7.63081i	0.225796	+	0.842682i
$83$	−0.838447	+	0.838447i	−0.0920315	+	0.0920315i	−0.751624	−	0.659592i	$-0.770729\pi$
$83$	−0.838447	+	0.838447i	−0.0920315	+	0.0920315i	0.659592	+	0.751624i	$0.270729\pi$
$84$		0			0
$85$	−4.16784	+	2.36169i	−0.452066	+	0.256162i
$86$	0.0804962	+	0.0464745i	0.00868013	+	0.00501148i
$87$		0			0
$88$	0.168988	−	0.630670i	0.0180141	−	0.0672297i
$89$	8.65123	−	14.9844i	0.917028	−	1.58834i	0.113124	−	0.993581i	$-0.463914\pi$
$89$	8.65123	−	14.9844i	0.917028	−	1.58834i	0.803904	−	0.594759i	$-0.202753\pi$
$90$		0			0
$91$	2.87120	−	0.312269i	0.300984	−	0.0327347i
$92$	−0.662983	−	0.662983i	−0.0691208	−	0.0691208i
$93$		0			0
$94$	−2.85824	+	1.65021i	−0.294805	+	0.170206i
$95$	2.81530	+	10.8563i	0.288844	+	1.11384i
$96$		0			0
$97$	−8.59970	+	8.59970i	−0.873168	+	0.873168i	−0.992816	−	0.119649i	$-0.961823\pi$
$97$	−8.59970	+	8.59970i	−0.873168	+	0.873168i	0.119649	+	0.992816i	$0.461823\pi$
$98$	3.22292	+	6.21392i	0.325564	+	0.627700i
$99$		0			0
$100$	2.42983	+	4.36989i	0.242983	+	0.436989i
$101$	1.56938	−	0.906083i	0.156159	−	0.0901586i	−0.419884	−	0.907578i	$-0.637929\pi$
$101$	1.56938	−	0.906083i	0.156159	−	0.0901586i	0.576043	+	0.817419i	$0.304596\pi$
$102$		0			0
$103$	19.2321	−	5.15322i	1.89499	−	0.507762i	0.897181	−	0.441662i	$-0.145611\pi$
$103$	19.2321	−	5.15322i	1.89499	−	0.507762i	0.997813	−	0.0660998i	$-0.0210556\pi$
$104$	−1.09161			−0.107041
$105$		0			0
$106$	−7.39128			−0.717905
$107$	17.4491	−	4.67547i	1.68687	−	0.451995i	0.717289	−	0.696775i	$-0.245383\pi$
$107$	17.4491	−	4.67547i	1.68687	−	0.451995i	0.969579	+	0.244781i	$0.0787159\pi$
$108$		0			0
$109$	−9.74887	+	5.62851i	−0.933773	+	0.539114i	−0.888003	−	0.459838i	$-0.847907\pi$
$109$	−9.74887	+	5.62851i	−0.933773	+	0.539114i	−0.0457698	+	0.998952i	$0.514574\pi$
$110$	−1.45992	−	0.0117746i	−0.139198	−	0.00112267i
$111$		0			0
$112$	−0.957071	−	2.46658i	−0.0904347	−	0.233070i
$113$	−4.19672	+	4.19672i	−0.394794	+	0.394794i	−0.876392	−	0.481598i	$-0.840056\pi$
$113$	−4.19672	+	4.19672i	−0.394794	+	0.394794i	0.481598	+	0.876392i	$0.340056\pi$
$114$		0			0
$115$	−1.06288	+	1.80714i	−0.0991138	+	0.168517i
$116$	−8.48072	+	4.89635i	−0.787415	+	0.454615i
$117$		0			0
$118$	4.79636	+	4.79636i	0.441540	+	0.441540i
$119$	−3.34820	−	4.57356i	−0.306929	−	0.419258i
$120$		0			0
$121$	−5.28685	+	9.15709i	−0.480623	+	0.832463i
$122$	2.24569	−	8.38103i	0.203315	−	0.758783i
$123$		0			0
$124$	−1.55472	−	0.897620i	−0.139618	−	0.0806087i
$125$	8.09464	−	7.71212i	0.724007	−	0.689793i
$126$		0			0
$127$	0.928820	−	0.928820i	0.0824195	−	0.0824195i	−0.664695	−	0.747115i	$-0.731439\pi$
$127$	0.928820	−	0.928820i	0.0824195	−	0.0824195i	0.747115	+	0.664695i	$0.231439\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$	0.612720	+	2.36276i	0.0537391	+	0.207228i
$131$	5.19621	+	3.00003i	0.453995	+	0.262114i	0.709516	−	0.704689i	$-0.248914\pi$
$131$	5.19621	+	3.00003i	0.453995	+	0.262114i	−0.255521	+	0.966804i	$0.582247\pi$
$132$		0			0
$133$	−12.3716	+	4.80037i	−1.07275	+	0.416245i
$134$	6.43263			0.555694
$135$		0			0
$136$	1.07118	+	1.85534i	0.0918529	+	0.159094i
$137$	−2.99759	+	11.1872i	−0.256102	+	0.955784i	0.711373	+	0.702815i	$0.248074\pi$
$137$	−2.99759	+	11.1872i	−0.256102	+	0.955784i	−0.967474	+	0.252969i	$0.918593\pi$
$138$		0			0
$139$			10.4380i			0.885339i	0.896685	+	0.442669i	$0.145968\pi$
$139$			10.4380i			0.885339i	−0.896685	+	0.442669i	$0.854032\pi$
$140$	−4.80164	+	3.45604i	−0.405813	+	0.292089i
$141$		0			0
$142$	−1.98922	−	7.42389i	−0.166932	−	0.622999i
$143$	−0.688447	−	0.184469i	−0.0575708	−	0.0154261i
$144$		0			0
$145$	15.3582	+	15.6080i	1.27543	+	1.29617i
$146$			9.96871i			0.825016i
$147$		0			0
$148$	−4.58614	−	4.58614i	−0.376979	−	0.376979i
$149$	2.48624	−	4.30630i	0.203681	−	0.352786i	−0.746031	−	0.665912i	$-0.768043\pi$
$149$	2.48624	−	4.30630i	0.203681	−	0.352786i	0.949712	+	0.313126i	$0.101376\pi$
$150$		0			0
$151$	11.1035	+	19.2318i	0.903590	+	1.56506i	0.822799	+	0.568332i	$0.192411\pi$
$151$	11.1035	+	19.2318i	0.903590	+	1.56506i	0.0807906	+	0.996731i	$0.474255\pi$
$152$	4.84479	−	1.29816i	0.392964	−	0.105294i
$153$		0			0
$154$	−0.186775	−	1.71733i	−0.0150508	−	0.138387i
$155$	−1.07021	+	3.86899i	−0.0859613	+	0.310765i
$156$		0			0
$157$	−8.78399	−	2.35366i	−0.701039	−	0.187843i	−0.109343	−	0.994004i	$-0.534875\pi$
$157$	−8.78399	−	2.35366i	−0.701039	−	0.187843i	−0.591696	+	0.806161i	$0.701541\pi$
$158$	11.5330	+	3.09026i	0.917516	+	0.245848i
$159$		0			0
$160$	1.94545	−	1.10238i	0.153801	−	0.0871508i
$161$	−2.26982	−	1.00078i	−0.178887	−	0.0788724i
$162$		0			0
$163$	14.5143	−	3.88909i	1.13685	−	0.304617i	0.359164	−	0.933275i	$-0.383062\pi$
$163$	14.5143	−	3.88909i	1.13685	−	0.304617i	0.777682	+	0.628658i	$0.216395\pi$
$164$	−3.95000	−	6.84160i	−0.308443	−	0.534239i
$165$		0			0
$166$	0.592872	−	1.02688i	0.0460158	−	0.0797016i
$167$	16.2008	+	16.2008i	1.25365	+	1.25365i	0.954070	+	0.299584i	$0.0968480\pi$
$167$	16.2008	+	16.2008i	1.25365	+	1.25365i	0.299584	+	0.954070i	$0.403152\pi$
$168$		0			0
$169$		−	11.8084i		−	0.908337i
$170$	3.41458	−	3.35994i	0.261886	−	0.257696i
$171$		0			0
$172$	−0.0897819	−	0.0240570i	−0.00684581	−	0.00183433i
$173$	0.501865	+	1.87299i	0.0381561	+	0.142400i	0.982376	−	0.186915i	$-0.0598488\pi$
$173$	0.501865	+	1.87299i	0.0381561	+	0.142400i	−0.944220	+	0.329315i	$0.893182\pi$
$174$		0			0
$175$	10.1757	+	8.45315i	0.769208	+	0.638998i
$176$			0.652918i			0.0492155i
$177$		0			0
$178$	−4.47821	+	16.7129i	−0.335656	+	1.25268i
$179$	10.9132	+	18.9023i	0.815694	+	1.41282i	0.908829	+	0.417170i	$0.136978\pi$
$179$	10.9132	+	18.9023i	0.815694	+	1.41282i	−0.0931349	+	0.995653i	$0.529689\pi$
$180$		0			0
$181$	−10.6095			−0.788598			−0.394299	−	0.918982i	$-0.629013\pi$
$181$	−10.6095			−0.788598			−0.394299	+	0.918982i	$0.629013\pi$
$182$	−2.69255	+	1.04475i	−0.199585	+	0.0774420i
$183$		0			0
$184$	0.811985	+	0.468800i	0.0598603	+	0.0345604i
$185$	−7.35239	+	12.5008i	−0.540558	+	0.919076i
$186$		0			0
$187$	0.362032	+	1.35112i	0.0264744	+	0.0988039i
$188$	2.33374	−	2.33374i	0.170206	−	0.170206i
$189$		0			0
$190$	−5.52920	−	9.75776i	−0.401130	−	0.707902i
$191$	−0.576196	−	0.332667i	−0.0416921	−	0.0240709i	0.479009	−	0.877810i	$-0.340996\pi$
$191$	−0.576196	−	0.332667i	−0.0416921	−	0.0240709i	−0.520701	+	0.853739i	$0.674329\pi$
$192$		0			0
$193$	5.41238	−	20.1993i	0.389592	−	1.45398i	−0.441208	−	0.897405i	$-0.645450\pi$
$193$	5.41238	−	20.1993i	0.389592	−	1.45398i	0.830800	−	0.556572i	$-0.187884\pi$
$194$	6.08091	−	10.5324i	0.436584	−	0.756185i
$195$		0			0
$196$	−4.72139	−	5.16803i	−0.337242	−	0.369145i
$197$	−5.67368	−	5.67368i	−0.404233	−	0.404233i	0.475489	−	0.879722i	$-0.342271\pi$
$197$	−5.67368	−	5.67368i	−0.404233	−	0.404233i	−0.879722	+	0.475489i	$0.842271\pi$
$198$		0			0
$199$	12.6522	−	7.30475i	0.896890	−	0.517820i	0.0207004	−	0.999786i	$-0.493410\pi$
$199$	12.6522	−	7.30475i	0.896890	−	0.517820i	0.876190	+	0.481966i	$0.160077\pi$
$200$	−3.47805	−	3.59210i	−0.245935	−	0.254000i
$201$		0			0
$202$	−1.28139	+	1.28139i	−0.0901586	+	0.0901586i
$203$	−16.2322	+	20.1939i	−1.13928	+	1.41733i
$204$		0			0
$205$	−12.5913	+	12.3898i	−0.879417	+	0.865345i
$206$	−17.2430	+	9.95526i	−1.20138	+	0.693616i
$207$		0			0
$208$	1.05442	−	0.282530i	0.0731106	−	0.0195899i
$209$	3.27484			0.226525
$210$		0			0
$211$	21.8231			1.50237			0.751183	−	0.660093i	$-0.229483\pi$
$211$	21.8231			1.50237			0.751183	+	0.660093i	$0.229483\pi$
$212$	7.13943	−	1.91300i	0.490338	−	0.131386i
$213$		0			0
$214$	−15.6444	+	9.03232i	−1.06943	+	0.617436i
$215$	−0.00167623	+	0.207834i	−0.000114318	+	0.0141741i
$216$		0			0
$217$	−4.69394	−	0.726070i	−0.318645	−	0.0492888i
$218$	7.95992	−	7.95992i	0.539114	−	0.539114i
$219$		0			0
$220$	1.41322	−	0.366482i	0.0952795	−	0.0247082i
$221$	2.02531	−	1.16931i	0.136237	−	0.0786565i
$222$		0			0
$223$	3.35691	+	3.35691i	0.224795	+	0.224795i	0.810514	−	0.585719i	$-0.199188\pi$
$223$	3.35691	+	3.35691i	0.224795	+	0.224795i	−0.585719	+	0.810514i	$0.699188\pi$
$224$	1.56286	+	2.13482i	0.104423	+	0.142639i
$225$		0			0
$226$	2.96753	−	5.13991i	0.197397	−	0.341901i
$227$	5.48385	−	20.4660i	0.363976	−	1.35838i	−0.504828	−	0.863220i	$-0.668444\pi$
$227$	5.48385	−	20.4660i	0.363976	−	1.35838i	0.868804	−	0.495157i	$-0.164889\pi$
$228$		0			0
$229$	16.7965	+	9.69749i	1.10995	+	0.640828i	0.938816	−	0.344420i	$-0.111925\pi$
$229$	16.7965	+	9.69749i	1.10995	+	0.640828i	0.171131	+	0.985248i	$0.445258\pi$
$230$	0.558938	−	2.02066i	0.0368553	−	0.133238i
$231$		0			0
$232$	6.92448	−	6.92448i	0.454615	−	0.454615i
$233$	−1.61958	−	6.04437i	−0.106103	−	0.395980i	0.892365	−	0.451314i	$-0.149044\pi$
$233$	−1.61958	−	6.04437i	−0.106103	−	0.395980i	−0.998468	+	0.0553336i	$0.982378\pi$
$234$		0			0
$235$	−6.36125	−	3.74140i	−0.414962	−	0.244062i
$236$	−5.87431	−	3.39154i	−0.382385	−	0.220770i
$237$		0			0
$238$	4.41784	+	3.55114i	0.286366	+	0.230186i
$239$	−19.7847			−1.27976			−0.639882	−	0.768473i	$-0.721017\pi$
$239$	−19.7847			−1.27976			−0.639882	+	0.768473i	$0.721017\pi$
$240$		0			0
$241$	−1.50878	−	2.61328i	−0.0971890	−	0.168336i	0.813331	−	0.581801i	$-0.197652\pi$
$241$	−1.50878	−	2.61328i	−0.0971890	−	0.168336i	−0.910520	+	0.413465i	$0.864318\pi$
$242$	2.73667	−	10.2134i	0.175920	−	0.656543i
$243$		0			0
$244$			8.67668i			0.555467i
$245$	−8.53595	+	13.1201i	−0.545342	+	0.838214i
$246$		0			0
$247$	−1.41708	−	5.28863i	−0.0901668	−	0.336507i
$248$	1.73407	+	0.464642i	0.110113	+	0.0295048i
$249$		0			0
$250$	−5.82278	+	9.54438i	−0.368265	+	0.603640i
$251$		−	22.4148i		−	1.41481i	−0.706809	−	0.707404i	$-0.749866\pi$
$251$		−	22.4148i		−	1.41481i	0.706809	−	0.707404i	$-0.250134\pi$
$252$		0			0
$253$	0.432874	+	0.432874i	0.0272145	+	0.0272145i
$254$	−0.656775	+	1.13757i	−0.0412097	+	0.0713774i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.1504	+	2.98775i	−0.695545	+	0.186371i	−0.589234	−	0.807962i	$-0.700570\pi$
$257$	−11.1504	+	2.98775i	−0.695545	+	0.186371i	−0.106310	+	0.994333i	$0.533904\pi$
$258$		0			0
$259$	−15.7014	−	6.92282i	−0.975635	−	0.430163i
$260$	−1.20337	−	2.12367i	−0.0746299	−	0.131705i
$261$		0			0
$262$	−5.79562	−	1.55293i	−0.358055	−	0.0959404i
$263$	10.8021	+	2.89442i	0.666088	+	0.178478i	0.575992	−	0.817455i	$-0.304616\pi$
$263$	10.8021	+	2.89442i	0.666088	+	0.178478i	0.0900962	+	0.995933i	$0.471283\pi$
$264$		0			0
$265$	−8.14800	−	14.3793i	−0.500528	−	0.883315i
$266$	10.7076	−	7.83881i	0.656526	−	0.480628i
$267$		0			0
$268$	−6.21344	+	1.66489i	−0.379546	+	0.101699i
$269$	−2.72319	−	4.71670i	−0.166036	−	0.287583i	0.770987	−	0.636851i	$-0.219763\pi$
$269$	−2.72319	−	4.71670i	−0.166036	−	0.287583i	−0.937023	+	0.349269i	$0.886430\pi$
$270$		0			0
$271$	10.6364	−	18.4227i	0.646113	−	1.11910i	−0.337930	−	0.941171i	$-0.609727\pi$
$271$	10.6364	−	18.4227i	0.646113	−	1.11910i	0.984043	−	0.177929i	$-0.0569398\pi$
$272$	−1.51488	−	1.51488i	−0.0918529	−	0.0918529i
$273$		0			0
$274$		−	11.5818i		−	0.699682i
$275$	−1.58648	−	2.85318i	−0.0956684	−	0.172053i
$276$		0			0
$277$	−17.3601	−	4.65162i	−1.04307	−	0.279489i	−0.303683	−	0.952773i	$-0.598216\pi$
$277$	−17.3601	−	4.65162i	−1.04307	−	0.279489i	−0.739384	+	0.673284i	$0.764883\pi$
$278$	−2.70155	−	10.0823i	−0.162028	−	0.604698i
$279$		0			0
$280$	3.74354	−	4.58104i	0.223719	−	0.273769i
$281$		−	19.1920i		−	1.14490i	−0.819939	−	0.572450i	$-0.805993\pi$
$281$		−	19.1920i		−	1.14490i	0.819939	−	0.572450i	$-0.194007\pi$
$282$		0			0
$283$	5.59020	−	20.8629i	0.332303	−	1.24017i	−0.574460	−	0.818532i	$-0.694788\pi$
$283$	5.59020	−	20.8629i	0.332303	−	1.24017i	0.906764	−	0.421640i	$-0.138545\pi$
$284$	3.84289	+	6.65608i	0.228033	+	0.394965i
$285$		0			0
$286$	0.712733			0.0421448
$287$	−16.2909	−	13.0949i	−0.961621	−	0.772969i
$288$		0			0
$289$	10.7476	+	6.20515i	0.632214	+	0.365009i
$290$	−18.8746	−	11.1012i	−1.10835	−	0.651882i
$291$		0			0
$292$	−2.58009	−	9.62903i	−0.150988	−	0.563497i
$293$	−10.1225	+	10.1225i	−0.591361	+	0.591361i	−0.937999	−	0.346638i	$-0.887323\pi$
$293$	−10.1225	+	10.1225i	−0.591361	+	0.591361i	0.346638	+	0.937999i	$0.387323\pi$
$294$		0			0
$295$	−4.04364	+	14.6185i	−0.235430	+	0.851120i
$296$	5.61685	+	3.24289i	0.326473	+	0.188489i
$297$		0			0
$298$	−1.28697	+	4.80305i	−0.0745524	+	0.278233i
$299$	0.511747	−	0.886373i	0.0295951	−	0.0512603i
$300$		0			0
$301$	−0.244478	+	0.0265892i	−0.0140915	+	0.00153258i
$302$	−15.7027	−	15.7027i	−0.903590	−	0.903590i
$303$		0			0
$304$	−4.34372	+	2.50785i	−0.249129	+	0.143835i
$305$	18.7804	−	4.87021i	1.07536	−	0.278867i
$306$		0			0
$307$	17.6475	−	17.6475i	1.00720	−	1.00720i	0.00722381	−	0.999974i	$-0.497701\pi$
$307$	17.6475	−	17.6475i	1.00720	−	1.00720i	0.999974	−	0.00722381i	$-0.00229943\pi$
$308$	0.624889	+	1.61047i	0.0356064	+	0.0917653i
$309$		0			0
$310$	0.0323751	−	4.01415i	0.00183878	−	0.227988i
$311$	6.02853	−	3.48057i	0.341847	−	0.197365i	−0.319242	−	0.947673i	$-0.603428\pi$
$311$	6.02853	−	3.48057i	0.341847	−	0.197365i	0.661088	+	0.750308i	$0.270095\pi$
$312$		0			0
$313$	−4.48293	+	1.20120i	−0.253390	+	0.0678957i	−0.383278	−	0.923633i	$-0.625205\pi$
$313$	−4.48293	+	1.20120i	−0.253390	+	0.0678957i	0.129888	+	0.991529i	$0.458538\pi$
$314$	9.09385			0.513196
$315$		0			0
$316$	−11.9398			−0.671668
$317$	−27.9311	+	7.48412i	−1.56877	+	0.420350i	−0.935426	−	0.353523i	$-0.884984\pi$
$317$	−27.9311	+	7.48412i	−1.56877	+	0.420350i	−0.633341	+	0.773873i	$0.718317\pi$
$318$		0			0
$319$	5.53722	−	3.19691i	0.310025	−	0.178993i
$320$	−1.59384	+	1.56834i	−0.0890983	+	0.0876726i
$321$		0			0
$322$	2.45150	+	0.379204i	0.136617	+	0.0211322i
$323$	−7.59816	+	7.59816i	−0.422773	+	0.422773i
$324$		0			0
$325$	−3.92118	+	3.79668i	−0.217508	+	0.210602i
$326$	−13.0131	+	7.51314i	−0.720731	+	0.416115i
$327$		0			0
$328$	5.58614	+	5.58614i	0.308443	+	0.308443i
$329$	3.52280	−	7.98992i	0.194218	−	0.440499i
$330$		0			0
$331$	−5.41664	+	9.38189i	−0.297725	+	0.515675i	−0.975615	−	0.219488i	$-0.929561\pi$
$331$	−5.41664	+	9.38189i	−0.297725	+	0.515675i	0.677890	+	0.735163i	$0.262895\pi$
$332$	−0.306893	+	1.14534i	−0.0168429	+	0.0628587i
$333$		0			0
$334$	−19.8418	−	11.4557i	−1.08570	−	0.626827i
$335$	7.09120	+	12.5143i	0.387434	+	0.683731i
$336$		0			0
$337$	13.8548	−	13.8548i	0.754716	−	0.754716i	−0.220639	−	0.975356i	$-0.570814\pi$
$337$	13.8548	−	13.8548i	0.754716	−	0.754716i	0.975356	+	0.220639i	$0.0708143\pi$
$338$	3.05623	+	11.4060i	0.166237	+	0.620406i
$339$		0			0
$340$	−2.42861	+	4.12921i	−0.131710	+	0.223938i
$341$	1.01511	+	0.586072i	0.0549711	+	0.0317376i
$342$		0			0
$343$	−16.5918	−	8.22865i	−0.895875	−	0.444305i
$344$	0.0929491			0.00501148
$345$		0			0
$346$	−0.969529	−	1.67927i	−0.0521222	−	0.0902783i
$347$	−5.96588	+	22.2650i	−0.320265	+	1.19525i	0.598721	+	0.800958i	$0.295676\pi$
$347$	−5.96588	+	22.2650i	−0.320265	+	1.19525i	−0.918986	+	0.394289i	$0.870991\pi$
$348$		0			0
$349$			12.6496i			0.677115i	0.940946	+	0.338558i	$0.109939\pi$
$349$			12.6496i			0.677115i	−0.940946	+	0.338558i	$0.890061\pi$
$350$	−12.0168	−	5.53146i	−0.642324	−	0.295669i
$351$		0			0
$352$	−0.168988	−	0.630670i	−0.00900707	−	0.0336148i
$353$	29.3409	+	7.86188i	1.56166	+	0.418445i	0.933188	−	0.359388i	$-0.117014\pi$
$353$	29.3409	+	7.86188i	1.56166	+	0.418445i	0.628471	+	0.777833i	$0.283681\pi$
$354$		0			0
$355$	12.2499	−	12.0539i	0.650157	−	0.639753i
$356$		−	17.3025i		−	0.917028i
$357$		0			0
$358$	−15.4337	−	15.4337i	−0.815694	−	0.815694i
$359$	−4.14969	+	7.18748i	−0.219012	+	0.379341i	−0.954506	−	0.298191i	$-0.903617\pi$
$359$	−4.14969	+	7.18748i	−0.219012	+	0.379341i	0.735494	+	0.677531i	$0.236950\pi$
$360$		0			0
$361$	3.07858	+	5.33226i	0.162031	+	0.280645i
$362$	10.2480	−	2.74594i	0.538622	−	0.144323i
$363$		0			0
$364$	2.33040	−	1.70603i	0.122146	−	0.0894205i
$365$	−19.3936	+	10.9893i	−1.01511	+	0.575207i
$366$		0			0
$367$	18.5262	+	4.96408i	0.967059	+	0.259123i	0.707586	−	0.706627i	$-0.249784\pi$
$367$	18.5262	+	4.96408i	0.967059	+	0.259123i	0.259474	+	0.965750i	$0.416451\pi$
$368$	−0.905652	−	0.242669i	−0.0472104	−	0.0126500i
$369$		0			0
$370$	3.86642	−	13.9778i	0.201006	−	0.726669i
$371$	15.7791	−	11.5515i	0.819209	−	0.599725i
$372$		0			0
$373$	1.60868	−	0.431045i	0.0832944	−	0.0223187i	−0.216931	−	0.976187i	$-0.569605\pi$
$373$	1.60868	−	0.431045i	0.0832944	−	0.0223187i	0.300226	+	0.953868i	$0.402938\pi$
$374$	−0.699392	−	1.21138i	−0.0361647	−	0.0626391i
$375$		0			0
$376$	−1.65021	+	2.85824i	−0.0851028	+	0.147402i
$377$	−7.55885	−	7.55885i	−0.389300	−	0.389300i
$378$		0			0
$379$			11.3712i			0.584098i	0.956403	+	0.292049i	$0.0943370\pi$
$379$			11.3712i			0.584098i	−0.956403	+	0.292049i	$0.905663\pi$
$380$	7.86629	+	7.99421i	0.403532	+	0.410094i
$381$		0			0
$382$	0.642663	+	0.172201i	0.0328815	+	0.00881058i
$383$	−5.06539	−	18.9043i	−0.258829	−	0.965964i	−0.965920	−	0.258841i	$-0.916659\pi$
$383$	−5.06539	−	18.9043i	−0.258829	−	0.965964i	0.707091	−	0.707123i	$-0.250007\pi$
$384$		0			0
$385$	3.13508	−	2.25651i	0.159778	−	0.115003i
$386$			20.9118i			1.06438i
$387$		0			0
$388$	−3.14771	+	11.7474i	−0.159801	+	0.596385i
$389$	−6.66518	−	11.5444i	−0.337938	−	0.585326i	0.646107	−	0.763247i	$-0.276396\pi$
$389$	−6.66518	−	11.5444i	−0.337938	−	0.585326i	−0.984045	+	0.177921i	$0.943063\pi$
$390$		0			0
$391$	−2.00868			−0.101583
$392$	5.89809	+	3.76995i	0.297899	+	0.190411i
$393$		0			0
$394$	6.94881	+	4.01190i	0.350076	+	0.202117i
$395$	6.70181	+	25.8434i	0.337205	+	1.30033i
$396$		0			0
$397$	3.59227	+	13.4065i	0.180291	+	0.672854i	0.995590	+	0.0938140i	$0.0299059\pi$
$397$	3.59227	+	13.4065i	0.180291	+	0.672854i	−0.815299	+	0.579040i	$0.803427\pi$
$398$	−10.3305	+	10.3305i	−0.517820	+	0.517820i
$399$		0			0
$400$	4.28924	+	2.56952i	0.214462	+	0.128476i
$401$	−19.4231	−	11.2139i	−0.969941	−	0.559996i	−0.0707229	−	0.997496i	$-0.522531\pi$
$401$	−19.4231	−	11.2139i	−0.969941	−	0.559996i	−0.899218	+	0.437500i	$0.855864\pi$
$402$		0			0
$403$	0.507209	−	1.89293i	0.0252659	−	0.0942936i
$404$	0.906083	−	1.56938i	0.0450793	−	0.0780796i
$405$		0			0
$406$	10.4526	−	23.7070i	0.518752	−	1.17656i
$407$	2.99437	+	2.99437i	0.148426	+	0.148426i
$408$		0			0
$409$	31.7438	−	18.3273i	1.56963	−	0.906225i	0.573417	−	0.819264i	$-0.305618\pi$
$409$	31.7438	−	18.3273i	1.56963	−	0.906225i	0.996212	−	0.0869614i	$-0.0277157\pi$
$410$	8.95556	−	15.2266i	0.442284	−	0.751986i
$411$		0			0
$412$	14.0789	−	14.0789i	0.693616	−	0.693616i
$413$	−17.7354	−	2.74336i	−0.872702	−	0.134992i
$414$		0			0
$415$	2.65132	+	0.0213835i	0.130148	+	0.00104968i
$416$	−0.945363	+	0.545806i	−0.0463503	+	0.0267603i
$417$		0			0
$418$	−3.16325	+	0.847590i	−0.154720	+	0.0414570i
$419$	5.74367			0.280597			0.140298	−	0.990109i	$-0.455194\pi$
$419$	5.74367			0.280597			0.140298	+	0.990109i	$0.455194\pi$
$420$		0			0
$421$	24.6051			1.19918			0.599589	−	0.800308i	$-0.295331\pi$
$421$	24.6051			1.19918			0.599589	+	0.800308i	$0.295331\pi$
$422$	−21.0795	+	5.64824i	−1.02614	+	0.274952i
$423$		0			0
$424$	−6.40104	+	3.69564i	−0.310862	+	0.179476i
$425$	10.3007	+	2.93894i	0.499659	+	0.142560i
$426$		0			0
$427$	8.30420	+	21.4017i	0.401868	+	1.03570i
$428$	12.7736	−	12.7736i	0.617436	−	0.617436i
$429$		0			0
$430$	−0.0521722	−	0.201186i	−0.00251597	−	0.00970204i
$431$	2.17816	−	1.25756i	0.104918	−	0.0605745i	−0.446623	−	0.894722i	$-0.647373\pi$
$431$	2.17816	−	1.25756i	0.104918	−	0.0605745i	0.551541	+	0.834148i	$0.314040\pi$
$432$		0			0
$433$	−2.77846	−	2.77846i	−0.133524	−	0.133524i	0.637186	−	0.770710i	$-0.280098\pi$
$433$	−2.77846	−	2.77846i	−0.133524	−	0.133524i	−0.770710	+	0.637186i	$0.780098\pi$
$434$	4.72191	−	0.513550i	0.226659	−	0.0246512i
$435$		0			0
$436$	−5.62851	+	9.74887i	−0.269557	+	0.466886i
$437$	−1.21715	+	4.54247i	−0.0582242	+	0.217296i
$438$		0			0
$439$	−24.2061	−	13.9754i	−1.15529	−	0.667008i	−0.205121	−	0.978737i	$-0.565759\pi$
$439$	−24.2061	−	13.9754i	−1.15529	−	0.667008i	−0.950171	+	0.311729i	$0.899092\pi$
$440$	−1.27022	+	0.719764i	−0.0605552	+	0.0343134i
$441$		0			0
$442$	−1.65366	+	1.65366i	−0.0786565	+	0.0786565i
$443$	−6.07594	−	22.6757i	−0.288676	−	1.07735i	−0.946111	−	0.323843i	$-0.895025\pi$
$443$	−6.07594	−	22.6757i	−0.288676	−	1.07735i	0.657434	−	0.753512i	$-0.271642\pi$
$444$		0			0
$445$	−37.4507	+	9.71185i	−1.77533	+	0.460386i
$446$	−4.11136	−	2.37370i	−0.194679	−	0.112398i
$447$		0			0
$448$	−2.06214	−	1.65758i	−0.0974269	−	0.0783135i
$449$	−6.06770			−0.286353			−0.143176	−	0.989697i	$-0.545732\pi$
$449$	−6.06770			−0.286353			−0.143176	+	0.989697i	$0.545732\pi$
$450$		0			0
$451$	2.57903	+	4.46700i	0.121442	+	0.210343i
$452$	−1.53610	+	5.73282i	−0.0722523	+	0.269649i
$453$		0			0
$454$			21.1880i			0.994401i
$455$	−5.00071	−	4.08649i	−0.234437	−	0.191578i
$456$		0			0
$457$	1.44741	+	5.40182i	0.0677072	+	0.252687i	0.991481	−	0.130252i	$-0.0415787\pi$
$457$	1.44741	+	5.40182i	0.0677072	+	0.252687i	−0.923774	+	0.382939i	$0.874912\pi$
$458$	−18.7341	−	5.01979i	−0.875387	−	0.234559i
$459$		0			0
$460$	−0.0169086	+	2.09647i	−0.000788365	+	0.0977484i
$461$		−	14.6330i		−	0.681528i	−0.940149	−	0.340764i	$-0.889314\pi$
$461$		−	14.6330i		−	0.681528i	0.940149	−	0.340764i	$-0.110686\pi$
$462$		0			0
$463$	19.8899	+	19.8899i	0.924361	+	0.924361i	0.997334	−	0.0729729i	$-0.0232487\pi$
$463$	19.8899	+	19.8899i	0.924361	+	0.924361i	−0.0729729	+	0.997334i	$0.523249\pi$
$464$	−4.89635	+	8.48072i	−0.227307	+	0.393708i
$465$		0			0
$466$	3.12880	+	5.41924i	0.144939	+	0.251041i
$467$	−4.39462	+	1.17753i	−0.203359	+	0.0544898i	−0.359060	−	0.933314i	$-0.616903\pi$
$467$	−4.39462	+	1.17753i	−0.203359	+	0.0544898i	0.155702	+	0.987804i	$0.450236\pi$
$468$		0			0
$469$	−13.7325	+	10.0533i	−0.634109	+	0.464217i
$470$	7.11284	+	1.96750i	0.328091	+	0.0907539i
$471$		0			0
$472$	6.55195	+	1.75559i	0.301578	+	0.0808075i
$473$	0.0586202	+	0.0157072i	0.00269536	+	0.000722220i
$474$		0			0
$475$	12.8879	−	21.5135i	0.591338	−	0.987107i
$476$	−5.18641	−	2.28672i	−0.237719	−	0.104812i
$477$		0			0
$478$	19.1105	−	5.12065i	0.874095	−	0.234213i
$479$	2.21585	+	3.83796i	0.101245	+	0.175361i	0.912198	−	0.409750i	$-0.134384\pi$
$479$	2.21585	+	3.83796i	0.101245	+	0.175361i	−0.810953	+	0.585111i	$0.801051\pi$
$480$		0			0
$481$	3.53998	−	6.13142i	0.161409	−	0.279569i
$482$	2.13374	+	2.13374i	0.0971890	+	0.0971890i
$483$		0			0
$484$			10.5737i			0.480623i
$485$	27.1938	+	0.219325i	1.23481	+	0.00995902i
$486$		0			0
$487$	−12.0493	−	3.22861i	−0.546007	−	0.146302i	−0.0247373	−	0.999694i	$-0.507875\pi$
$487$	−12.0493	−	3.22861i	−0.546007	−	0.146302i	−0.521270	+	0.853392i	$0.674542\pi$
$488$	−2.24569	−	8.38103i	−0.101658	−	0.379391i
$489$		0			0
$490$	4.84936	−	14.8823i	0.219072	−	0.672315i
$491$			26.2419i			1.18428i	0.805836	+	0.592139i	$0.201716\pi$
$491$			26.2419i			1.18428i	−0.805836	+	0.592139i	$0.798284\pi$
$492$		0			0
$493$	−5.42989	+	20.2646i	−0.244550	+	0.912673i
$494$	2.73759	+	4.74165i	0.123170	+	0.213337i
$495$		0			0
$496$	−1.79524			−0.0806087
$497$	15.8491	+	12.7398i	0.710930	+	0.571459i
$498$		0			0
$499$	8.84482	+	5.10656i	0.395949	+	0.228601i	0.684734	−	0.728793i	$-0.259918\pi$
$499$	8.84482	+	5.10656i	0.395949	+	0.228601i	−0.288786	+	0.957394i	$0.593252\pi$
$500$	3.15411	−	10.7262i	0.141056	−	0.479691i
$501$		0			0
$502$	5.80137	+	21.6510i	0.258928	+	0.966332i
$503$	−18.7420	+	18.7420i	−0.835664	+	0.835664i	−0.988285	−	0.152621i	$-0.951229\pi$
$503$	−18.7420	+	18.7420i	−0.835664	+	0.835664i	0.152621	+	0.988285i	$0.451229\pi$
$504$		0			0
$505$	−3.90547	−	1.08030i	−0.173791	−	0.0480727i
$506$	−0.530160	−	0.306088i	−0.0235685	−	0.0136073i
$507$		0			0
$508$	0.339972	−	1.26879i	0.0150838	−	0.0562935i
$509$	14.8511	−	25.7228i	0.658262	−	1.14014i	−0.322804	−	0.946466i	$-0.604625\pi$
$509$	14.8511	−	25.7228i	0.658262	−	1.14014i	0.981065	−	0.193677i	$-0.0620413\pi$
$510$		0			0
$511$	−15.5797	−	21.2814i	−0.689204	−	0.941436i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	9.99720	−	5.77189i	0.440958	−	0.254587i
$515$	−38.3758	−	22.5709i	−1.69104	−	0.994592i
$516$		0			0
$517$	−1.52374	+	1.52374i	−0.0670141	+	0.0670141i
$518$	16.9581	+	2.62312i	0.745096	+	0.115253i
$519$		0			0
$520$	1.71201	+	1.73985i	0.0750768	+	0.0762976i
$521$	−7.25859	+	4.19075i	−0.318005	+	0.183600i	−0.650503	−	0.759504i	$-0.725442\pi$
$521$	−7.25859	+	4.19075i	−0.318005	+	0.183600i	0.332498	+	0.943104i	$0.392108\pi$
$522$		0			0
$523$	−36.6515	+	9.82073i	−1.60266	+	0.429430i	−0.945843	−	0.324623i	$-0.894762\pi$
$523$	−36.6515	+	9.82073i	−1.60266	+	0.429430i	−0.656813	+	0.754054i	$0.728096\pi$
$524$	6.00007			0.262114
$525$		0			0
$526$	−11.1832			−0.487610
$527$	−3.71500	+	0.995431i	−0.161828	+	0.0433617i
$528$		0			0
$529$	19.1573	−	11.0605i	0.832925	−	0.480889i
$530$	11.5920	+	11.7805i	0.503525	+	0.511713i
$531$		0			0
$532$	−8.31393	+	10.3430i	−0.360455	+	0.448428i
$533$	6.09790	−	6.09790i	0.264129	−	0.264129i
$534$		0			0
$535$	−34.8180	−	20.4783i	−1.50531	−	0.885356i
$536$	5.57082	−	3.21631i	0.240623	−	0.138924i
$537$		0			0
$538$	3.85117	+	3.85117i	0.166036	+	0.166036i
$539$	3.08268	+	3.37430i	0.132780	+	0.145341i
$540$		0			0
$541$	−2.55510	+	4.42556i	−0.109852	+	0.190270i	−0.915710	−	0.401839i	$-0.868371\pi$
$541$	−2.55510	+	4.42556i	−0.109852	+	0.190270i	0.805858	+	0.592109i	$0.201704\pi$
$542$	−5.50578	+	20.5479i	−0.236494	+	0.882607i
$543$		0			0
$544$	1.85534	+	1.07118i	0.0795469	+	0.0459265i
$545$	24.2604	+	6.71074i	1.03920	+	0.287456i
$546$		0			0
$547$	−20.5460	+	20.5460i	−0.878484	+	0.878484i	−0.993378	−	0.114894i	$-0.963347\pi$
$547$	−20.5460	+	20.5460i	−0.878484	+	0.878484i	0.114894	+	0.993378i	$0.463347\pi$
$548$	2.99759	+	11.1872i	0.128051	+	0.477892i
$549$		0			0
$550$	2.27088	+	2.34535i	0.0968306	+	0.100006i
$551$	42.5367	+	24.5586i	1.81212	+	1.04623i
$552$		0			0
$553$	−29.4505	+	11.4273i	−1.25236	+	0.485937i
$554$	17.9725			0.763578
$555$		0			0
$556$	5.21899	+	9.03956i	0.221335	+	0.383363i
$557$	9.01371	−	33.6396i	0.381923	−	1.42536i	−0.461037	−	0.887381i	$-0.652522\pi$
$557$	9.01371	−	33.6396i	0.381923	−	1.42536i	0.842960	−	0.537976i	$-0.180811\pi$
$558$		0			0
$559$		−	0.101464i		−	0.00429148i
$560$	−2.43032	+	5.39384i	−0.102700	+	0.227931i
$561$		0			0
$562$	4.96726	+	18.5381i	0.209531	+	0.781982i
$563$	7.58528	+	2.03247i	0.319681	+	0.0856584i	0.415091	−	0.909780i	$-0.363750\pi$
$563$	7.58528	+	2.03247i	0.319681	+	0.0856584i	−0.0954101	+	0.995438i	$0.530416\pi$
$564$		0			0
$565$	13.2707	+	0.107032i	0.558305	+	0.00450287i
$566$			21.5989i			0.907869i
$567$		0			0
$568$	−5.43466	−	5.43466i	−0.228033	−	0.228033i
$569$	−10.0967	+	17.4880i	−0.423277	+	0.733137i	−0.996258	−	0.0864319i	$-0.972454\pi$
$569$	−10.0967	+	17.4880i	−0.423277	+	0.733137i	0.572981	+	0.819569i	$0.305787\pi$
$570$		0			0
$571$	11.0336	+	19.1107i	0.461741	+	0.799760i	0.999048	−	0.0436275i	$-0.0138915\pi$
$571$	11.0336	+	19.1107i	0.461741	+	0.799760i	−0.537306	+	0.843387i	$0.680558\pi$
$572$	−0.688447	+	0.184469i	−0.0287854	+	0.00771303i
$573$		0			0
$574$	19.1250	+	8.43233i	0.798262	+	0.351959i
$575$	4.54724	−	1.14015i	0.189633	−	0.0475474i
$576$		0			0
$577$	24.6763	+	6.61199i	1.02729	+	0.275261i	0.732836	−	0.680406i	$-0.238196\pi$
$577$	24.6763	+	6.61199i	1.02729	+	0.275261i	0.294451	+	0.955666i	$0.404863\pi$
$578$	−11.9874	−	3.21202i	−0.498611	−	0.133602i
$579$		0			0
$580$	21.1046	+	5.83779i	0.876321	+	0.242401i
$581$	0.339196	+	3.11879i	0.0140722	+	0.129389i
$582$		0			0
$583$	−4.66146	+	1.24903i	−0.193058	+	0.0517297i
$584$	4.98435	+	8.63316i	0.206254	+	0.357243i
$585$		0			0
$586$	7.15766	−	12.3974i	0.295680	−	0.512133i
$587$	29.2059	+	29.2059i	1.20546	+	1.20546i	0.972483	+	0.232975i	$0.0748460\pi$
$587$	29.2059	+	29.2059i	1.20546	+	1.20546i	0.232975	+	0.972483i	$0.425154\pi$
$588$		0			0
$589$			9.00437i			0.371019i
$590$	0.122325	−	15.1669i	0.00503604	−	0.624412i
$591$		0			0
$592$	−6.26479	−	1.67864i	−0.257481	−	0.0689919i
$593$	2.53626	+	9.46544i	0.104152	+	0.388699i	0.998248	−	0.0591765i	$-0.0188475\pi$
$593$	2.53626	+	9.46544i	0.104152	+	0.388699i	−0.894096	+	0.447875i	$0.852181\pi$
$594$		0			0
$595$	−2.03842	+	12.5094i	−0.0835669	+	0.512834i
$596$		−	4.97249i		−	0.203681i
$597$		0			0
$598$	−0.264900	+	0.988620i	−0.0108326	+	0.0404277i
$599$	8.90006	+	15.4154i	0.363647	+	0.629854i	0.988558	−	0.150841i	$-0.0481982\pi$
$599$	8.90006	+	15.4154i	0.363647	+	0.629854i	−0.624911	+	0.780696i	$0.714865\pi$
$600$		0			0
$601$	−22.8923			−0.933798			−0.466899	−	0.884311i	$-0.654629\pi$
$601$	−22.8923			−0.933798			−0.466899	+	0.884311i	$0.654629\pi$
$602$	0.229266	−	0.0889589i	0.00934419	−	0.00362569i
$603$		0			0
$604$	19.2318	+	11.1035i	0.782532	+	0.451795i
$605$	22.8865	−	5.93500i	0.930468	−	0.241292i
$606$		0			0
$607$	−3.12100	−	11.6477i	−0.126677	−	0.472767i	0.873216	−	0.487333i	$-0.162030\pi$
$607$	−3.12100	−	11.6477i	−0.126677	−	0.472767i	−0.999894	+	0.0145659i	$0.995363\pi$
$608$	3.54663	−	3.54663i	0.143835	−	0.143835i
$609$		0			0
$610$	−16.8800	+	9.56500i	−0.683452	+	0.387275i
$611$	3.12009	+	1.80138i	0.126225	+	0.0728762i
$612$		0			0
$613$	−1.55416	+	5.80020i	−0.0627719	+	0.234268i	−0.990183	−	0.139775i	$-0.955362\pi$
$613$	−1.55416	+	5.80020i	−0.0627719	+	0.234268i	0.927411	+	0.374043i	$0.122029\pi$
$614$	−12.4787	+	21.6137i	−0.503599	+	0.872259i
$615$		0			0
$616$	−1.02042	−	1.39387i	−0.0411138	−	0.0561604i
$617$	29.7410	+	29.7410i	1.19733	+	1.19733i	0.974964	+	0.222361i	$0.0713765\pi$
$617$	29.7410	+	29.7410i	1.19733	+	1.19733i	0.222361	+	0.974964i	$0.428624\pi$
$618$		0			0
$619$	−1.14774	+	0.662650i	−0.0461317	+	0.0266341i	−0.522888	−	0.852401i	$-0.675146\pi$
$619$	−1.14774	+	0.662650i	−0.0461317	+	0.0266341i	0.476757	+	0.879035i	$0.341812\pi$
$620$	1.00767	+	3.88575i	0.0404688	+	0.156055i
$621$		0			0
$622$	−4.92227	+	4.92227i	−0.197365	+	0.197365i
$623$	−16.5597	−	42.6779i	−0.663450	−	1.70985i
$624$		0			0
$625$	−24.9870	−	0.806368i	−0.999480	−	0.0322547i
$626$	4.01929	−	2.32054i	0.160643	−	0.0927473i
$627$		0			0
$628$	−8.78399	+	2.35366i	−0.350519	+	0.0939214i
$629$	−13.8949			−0.554025
$630$		0			0
$631$	−12.2808			−0.488892			−0.244446	−	0.969663i	$-0.578606\pi$
$631$	−12.2808			−0.488892			−0.244446	+	0.969663i	$0.578606\pi$
$632$	11.5330	−	3.09026i	0.458758	−	0.122924i
$633$		0			0
$634$	25.0423	−	14.4582i	0.994558	−	0.574209i
$635$	−2.93709	−	0.0236884i	−0.116555	−	0.000940045i
$636$		0			0
$637$	4.11532	−	6.43843i	0.163055	−	0.255100i
$638$	−4.52112	+	4.52112i	−0.178993	+	0.178993i
$639$		0			0
$640$	1.13362	−	1.92741i	0.0448101	−	0.0761876i
$641$	−0.0942649	+	0.0544239i	−0.00372324	+	0.00214961i	−0.501860	−	0.864949i	$-0.667351\pi$
$641$	−0.0942649	+	0.0544239i	−0.00372324	+	0.00214961i	0.498137	+	0.867098i	$0.334018\pi$
$642$		0			0
$643$	−4.92268	−	4.92268i	−0.194132	−	0.194132i	0.603347	−	0.797479i	$-0.293833\pi$
$643$	−4.92268	−	4.92268i	−0.194132	−	0.194132i	−0.797479	+	0.603347i	$0.793833\pi$
$644$	−2.46611	+	0.268212i	−0.0971785	+	0.0105690i
$645$		0			0
$646$	5.37271	−	9.30580i	0.211386	−	0.366132i
$647$	8.01312	−	29.9054i	0.315028	−	1.17570i	−0.608935	−	0.793220i	$-0.708403\pi$
$647$	8.01312	−	29.9054i	0.315028	−	1.17570i	0.923963	−	0.382481i	$-0.124930\pi$
$648$		0			0
$649$	3.83545	+	2.21440i	0.150554	+	0.0869226i
$650$	2.80492	−	4.68218i	0.110018	−	0.183650i
$651$		0			0
$652$	10.6252	−	10.6252i	0.416115	−	0.416115i
$653$	−8.33630	−	31.1115i	−0.326224	−	1.21749i	−0.913075	−	0.407791i	$-0.866299\pi$
$653$	−8.33630	−	31.1115i	−0.326224	−	1.21749i	0.586851	−	0.809695i	$-0.300368\pi$
$654$		0			0
$655$	−3.36783	−	12.9870i	−0.131592	−	0.507444i
$656$	−6.84160	−	3.95000i	−0.267120	−	0.154222i
$657$		0			0
$658$	−1.33482	+	8.62944i	−0.0520368	+	0.336411i
$659$	10.4880			0.408556			0.204278	−	0.978913i	$-0.434515\pi$
$659$	10.4880			0.408556			0.204278	+	0.978913i	$0.434515\pi$
$660$		0			0
$661$	−12.9829	−	22.4870i	−0.504975	−	0.874643i	−0.999983	−	0.00575465i	$-0.998168\pi$
$661$	−12.9829	−	22.4870i	−0.504975	−	0.874643i	0.495008	−	0.868888i	$-0.335165\pi$
$662$	2.80386	−	10.4641i	0.108975	−	0.406700i
$663$		0			0
$664$		−	1.18574i		−	0.0460158i
$665$	27.0538	+	12.1897i	1.04910	+	0.472698i
$666$		0			0
$667$	2.37638	+	8.86877i	0.0920138	+	0.343400i
$668$	22.1307	+	5.92990i	0.856262	+	0.229435i
$669$		0			0
$670$	−10.0885	−	10.2526i	−0.389753	−	0.396091i
$671$		−	5.66516i		−	0.218701i
$672$		0			0
$673$	−10.2926	−	10.2926i	−0.396752	−	0.396752i	0.480334	−	0.877086i	$-0.340516\pi$
$673$	−10.2926	−	10.2926i	−0.396752	−	0.396752i	−0.877086	+	0.480334i	$0.840516\pi$
$674$	−9.79679	+	16.9685i	−0.377358	+	0.653604i
$675$		0			0
$676$	−5.90419	−	10.2264i	−0.227084	−	0.393322i
$677$	−34.6310	+	9.27935i	−1.33098	+	0.356634i	−0.853080	−	0.521781i	$-0.825268\pi$
$677$	−34.6310	+	9.27935i	−1.33098	+	0.356634i	−0.477898	+	0.878415i	$0.658601\pi$
$678$		0			0
$679$	3.47904	+	31.9885i	0.133513	+	1.22761i
$680$	1.27714	−	4.61708i	0.0489761	−	0.177057i
$681$		0			0
$682$	−1.13220	−	0.303373i	−0.0433544	−	0.0116168i
$683$	−14.5162	−	3.88960i	−0.555447	−	0.148831i	−0.0298330	−	0.999555i	$-0.509498\pi$
$683$	−14.5162	−	3.88960i	−0.555447	−	0.148831i	−0.525614	+	0.850723i	$0.676164\pi$
$684$		0			0
$685$	22.5318	−	12.7675i	0.860895	−	0.487823i
$686$	18.1562	+	3.65398i	0.693208	+	0.139510i
$687$		0			0
$688$	−0.0897819	+	0.0240570i	−0.00342290	+	0.000917164i
$689$	4.03420	+	6.98745i	0.153691	+	0.266200i
$690$		0			0
$691$	9.47524	−	16.4116i	0.360455	−	0.624327i	−0.627581	−	0.778552i	$-0.715955\pi$
$691$	9.47524	−	16.4116i	0.360455	−	0.624327i	0.988036	+	0.154225i	$0.0492880\pi$
$692$	1.37112	+	1.37112i	0.0521222	+	0.0521222i
$693$		0			0
$694$		−	23.0504i		−	0.874981i
$695$	16.6365	−	16.3703i	0.631057	−	0.620960i
$696$		0			0
$697$	−16.3479	−	4.38042i	−0.619223	−	0.165920i
$698$	−3.27395	−	12.2185i	−0.123921	−	0.462478i
$699$		0			0
$700$	13.0390	+	2.23281i	0.492826	+	0.0843923i
$701$			23.9293i			0.903798i	0.892069	+	0.451899i	$0.149253\pi$
$701$			23.9293i			0.903798i	−0.892069	+	0.451899i	$0.850747\pi$
$702$		0			0
$703$	−8.41956	+	31.4222i	−0.317550	+	1.18511i
$704$	0.326459	+	0.565444i	0.0123039	+	0.0213110i
$705$		0			0
$706$	−30.3760			−1.14321
$707$	0.732915	−	4.73819i	0.0275641	−	0.178198i
$708$		0			0
$709$	−1.87883	−	1.08474i	−0.0705608	−	0.0407383i	0.464305	−	0.885676i	$-0.346304\pi$
$709$	−1.87883	−	1.08474i	−0.0705608	−	0.0407383i	−0.534865	+	0.844937i	$0.679638\pi$
$710$	−8.71271	+	14.8137i	−0.326982	+	0.555946i
$711$		0			0
$712$	4.47821	+	16.7129i	0.167828	+	0.626342i
$713$	−1.19021	+	1.19021i	−0.0445739	+	0.0445739i
$714$		0			0
$715$	0.785702	+	1.38658i	0.0293836	+	0.0518553i
$716$	18.9023	+	10.9132i	0.706412	+	0.407847i
$717$		0			0
$718$	2.14804	−	8.01659i	0.0801641	−	0.299176i
$719$	−12.5298	+	21.7022i	−0.467281	+	0.809354i	−0.999301	−	0.0373772i	$-0.988100\pi$
$719$	−12.5298	+	21.7022i	−0.467281	+	0.809354i	0.532020	+	0.846732i	$0.321433\pi$
$720$		0			0
$721$	21.2522	−	48.2011i	0.791472	−	1.79510i
$722$	−4.35377	−	4.35377i	−0.162031	−	0.162031i
$723$		0			0
$724$	−9.18809	+	5.30475i	−0.341473	+	0.197149i
$725$	0.789755	−	48.9571i	0.0293307	−	1.81822i
$726$		0			0
$727$	−10.6897	+	10.6897i	−0.396460	+	0.396460i	−0.876982	−	0.480523i	$-0.840447\pi$
$727$	−10.6897	+	10.6897i	−0.396460	+	0.396460i	0.480523	+	0.876982i	$0.340447\pi$
$728$	−1.80944	+	2.25105i	−0.0670623	+	0.0834296i
$729$		0			0
$730$	15.8885	−	15.6343i	0.588061	−	0.578651i
$731$	−0.172452	+	0.0995651i	−0.00637836	+	0.00368255i
$732$		0			0
$733$	−26.1579	+	7.00900i	−0.966165	+	0.258883i	−0.707208	−	0.707006i	$-0.750046\pi$
$733$	−26.1579	+	7.00900i	−0.966165	+	0.258883i	−0.258957	+	0.965889i	$0.583379\pi$
$734$	−19.1797			−0.707937
$735$		0			0
$736$	0.937600			0.0345604
$737$	4.05687	−	1.08703i	0.149437	−	0.0400414i
$738$		0			0
$739$	40.4463	−	23.3517i	1.48784	−	0.859006i	0.487938	−	0.872878i	$-0.337749\pi$
$739$	40.4463	−	23.3517i	1.48784	−	0.859006i	0.999904	+	0.0138727i	$0.00441595\pi$
$740$	−0.116964	+	14.5022i	−0.00429968	+	0.533111i
$741$		0			0
$742$	−12.2517	+	15.2418i	−0.449773	+	0.559545i
$743$	25.2408	−	25.2408i	0.925997	−	0.925997i	−0.0714474	−	0.997444i	$-0.522762\pi$
$743$	25.2408	−	25.2408i	0.925997	−	0.925997i	0.997444	+	0.0714474i	$0.0227618\pi$
$744$		0			0
$745$	−10.7628	+	2.79105i	−0.394319	+	0.102256i
$746$	−1.44230	+	0.832715i	−0.0528065	+	0.0304879i
$747$		0			0
$748$	0.989090	+	0.989090i	0.0361647	+	0.0361647i
$749$	19.2819	−	43.7324i	0.704545	−	1.59795i
$750$		0			0
$751$	−24.7674	+	42.8984i	−0.903775	+	1.56538i	−0.0812216	+	0.996696i	$0.525882\pi$
$751$	−24.7674	+	42.8984i	−0.903775	+	1.56538i	−0.822553	+	0.568688i	$0.807451\pi$
$752$	0.854209	−	3.18795i	0.0311498	−	0.116253i
$753$		0			0
$754$	9.25766	+	5.34491i	0.337144	+	0.194650i
$755$	13.2384	−	47.8591i	0.481796	−	1.74177i
$756$		0			0
$757$	−27.1533	+	27.1533i	−0.986902	+	0.986902i	−0.999915	−	0.0130130i	$-0.995858\pi$
$757$	−27.1533	+	27.1533i	−0.986902	+	0.986902i	0.0130130	+	0.999915i	$0.495858\pi$
$758$	−2.94308	−	10.9837i	−0.106897	−	0.398946i
$759$		0			0
$760$	−9.66730	−	5.68587i	−0.350670	−	0.206248i
$761$	6.77173	+	3.90966i	0.245475	+	0.141725i	0.617691	−	0.786421i	$-0.288068\pi$
$761$	6.77173	+	3.90966i	0.245475	+	0.141725i	−0.372216	+	0.928146i	$0.621402\pi$
$762$		0			0
$763$	−4.55281	+	29.4333i	−0.164823	+	1.06556i
$764$	−0.665334			−0.0240709
$765$		0			0
$766$	9.78557	+	16.9491i	0.353567	+	0.612396i
$767$	1.91642	−	7.15218i	0.0691980	−	0.258250i
$768$		0			0
$769$		−	2.94104i		−	0.106056i	−0.998593	−	0.0530282i	$-0.983113\pi$
$769$		−	2.94104i		−	0.106056i	0.998593	−	0.0530282i	$-0.0168873\pi$
$770$	−2.44422	+	2.99104i	−0.0880837	+	0.107790i
$771$		0			0
$772$	−5.41238	−	20.1993i	−0.194796	−	0.726988i
$773$	−23.2723	−	6.23578i	−0.837045	−	0.224286i	−0.185260	−	0.982690i	$-0.559313\pi$
$773$	−23.2723	−	6.23578i	−0.837045	−	0.224286i	−0.651785	+	0.758404i	$0.725979\pi$
$774$		0			0
$775$	7.84500	−	4.36213i	0.281801	−	0.156692i
$776$		−	12.1618i		−	0.436584i
$777$		0			0
$778$	9.42599	+	9.42599i	0.337938	+	0.337938i
$779$	−19.8120	+	34.3154i	−0.709838	+	1.22948i
$780$		0			0
$781$	−2.50909	−	4.34587i	−0.0897823	−	0.155508i
$782$	1.94023	−	0.519884i	0.0693825	−	0.0185910i
$783$		0			0
$784$	−6.67285	−	2.11495i	−0.238316	−	0.0755340i
$785$	10.0249	+	17.6916i	0.357803	+	0.631440i
$786$		0			0
$787$	−21.1750	−	5.67382i	−0.754807	−	0.202250i	−0.139158	−	0.990270i	$-0.544439\pi$
$787$	−21.1750	−	5.67382i	−0.754807	−	0.202250i	−0.615649	+	0.788020i	$0.711106\pi$
$788$	−7.75039	−	2.07671i	−0.276096	−	0.0739798i
$789$		0			0
$790$	−13.1622	−	23.2283i	−0.468291	−	0.826426i
$791$	1.69779	+	15.6106i	0.0603666	+	0.555050i
$792$		0			0
$793$	−9.14883	+	2.45142i	−0.324884	+	0.0870525i
$794$	−6.93973	−	12.0200i	−0.246282	−	0.426572i
$795$		0			0
$796$	7.30475	−	12.6522i	0.258910	−	0.448445i
$797$	−1.72825	−	1.72825i	−0.0612178	−	0.0612178i	0.675835	−	0.737053i	$-0.263783\pi$
$797$	−1.72825	−	1.72825i	−0.0612178	−	0.0612178i	−0.737053	+	0.675835i	$0.763783\pi$
$798$		0			0
$799$		−	7.07067i		−	0.250142i
$800$	−4.80813	−	1.37183i	−0.169993	−	0.0485014i
$801$		0			0
$802$	21.6636	+	5.80475i	0.764969	+	0.204973i
$803$	1.68459	+	6.28697i	0.0594478	+	0.221862i
$804$		0			0
$805$	1.96476	+	5.18729i	0.0692488	+	0.182828i
$806$			1.95971i			0.0690277i
$807$		0			0
$808$	−0.469023	+	1.75042i	−0.0165002	+	0.0615795i
$809$	0.419280	+	0.726214i	0.0147411	+	0.0255323i	0.873302	−	0.487180i	$-0.161974\pi$
$809$	0.419280	+	0.726214i	0.0147411	+	0.0255323i	−0.858561	+	0.512712i	$0.828641\pi$
$810$		0			0
$811$	−25.2799			−0.887699			−0.443849	−	0.896101i	$-0.646387\pi$
$811$	−25.2799			−0.887699			−0.443849	+	0.896101i	$0.646387\pi$
$812$	−3.96057	+	25.6045i	−0.138989	+	0.898543i
$813$		0			0
$814$	−3.66735	−	2.11734i	−0.128540	−	0.0742128i
$815$	−28.9618	−	17.0340i	−1.01449	−	0.596676i
$816$		0			0
$817$	0.120662	+	0.450318i	0.00422144	+	0.0157546i
$818$	−25.9187	+	25.9187i	−0.906225	+	0.906225i
$819$		0			0
$820$	−4.70949	+	17.0256i	−0.164462	+	0.594559i
$821$	7.48620	+	4.32216i	0.261270	+	0.150844i	0.624914	−	0.780694i	$-0.285134\pi$
$821$	7.48620	+	4.32216i	0.261270	+	0.150844i	−0.363644	+	0.931538i	$0.618467\pi$
$822$		0			0
$823$	7.53721	−	28.1292i	0.262731	−	0.980524i	−0.700894	−	0.713265i	$-0.747216\pi$
$823$	7.53721	−	28.1292i	0.262731	−	0.980524i	0.963625	−	0.267259i	$-0.0861178\pi$
$824$	−9.95526	+	17.2430i	−0.346808	+	0.600689i
$825$		0			0
$826$	17.8411	−	1.94038i	0.620772	−	0.0675145i
$827$	−17.2791	−	17.2791i	−0.600853	−	0.600853i	0.339686	−	0.940539i	$-0.389679\pi$
$827$	−17.2791	−	17.2791i	−0.600853	−	0.600853i	−0.940539	+	0.339686i	$0.889679\pi$
$828$		0			0
$829$	−0.217326	+	0.125473i	−0.00754804	+	0.00435787i	−0.503769	−	0.863838i	$-0.668054\pi$
$829$	−0.217326	+	0.125473i	−0.00754804	+	0.00435787i	0.496221	+	0.868196i	$0.334720\pi$
$830$	−2.56651	+	0.665556i	−0.0890848	+	0.0231018i
$831$		0			0
$832$	0.771886	−	0.771886i	0.0267603	−	0.0267603i
$833$	−14.9812	−	0.676611i	−0.519069	−	0.0234432i
$834$		0			0
$835$	0.413181	−	51.2297i	0.0142987	−	1.77288i
$836$	2.83609	−	1.63742i	0.0980882	−	0.0566313i
$837$		0			0
$838$	−5.54796	+	1.48657i	−0.191651	+	0.0513527i
$839$	−35.4029			−1.22224			−0.611122	−	0.791537i	$-0.709281\pi$
$839$	−35.4029			−1.22224			−0.611122	+	0.791537i	$0.709281\pi$
$840$		0			0
$841$	66.8969			2.30679
$842$	−23.7667	+	6.36826i	−0.819054	+	0.219465i
$843$		0			0
$844$	18.8994	−	10.9116i	0.650544	−	0.375592i
$845$	−18.8207	+	18.5195i	−0.647451	+	0.637090i
$846$		0			0
$847$	10.1198	+	26.0809i	0.347720	+	0.896149i
$848$	5.22642	−	5.22642i	0.179476	−	0.179476i
$849$		0			0
$850$	−10.7104	−	0.172775i	−0.367364	−	0.00592615i
$851$	−5.26636	+	3.04054i	−0.180529	+	0.104228i
$852$		0			0
$853$	28.1055	+	28.1055i	0.962316	+	0.962316i	0.999315	−	0.0369997i	$-0.0117800\pi$
$853$	28.1055	+	28.1055i	0.962316	+	0.962316i	−0.0369997	+	0.999315i	$0.511780\pi$
$854$	−13.5604	−	18.5232i	−0.464028	−	0.633850i
$855$		0			0
$856$	−9.03232	+	15.6444i	−0.308718	+	0.534716i
$857$	−9.39516	+	35.0632i	−0.320932	+	1.19774i	0.597406	+	0.801939i	$0.296198\pi$
$857$	−9.39516	+	35.0632i	−0.320932	+	1.19774i	−0.918338	+	0.395797i	$0.870468\pi$
$858$		0			0
$859$	−21.6216	−	12.4833i	−0.737721	−	0.425924i	0.0835190	−	0.996506i	$-0.473384\pi$
$859$	−21.6216	−	12.4833i	−0.737721	−	0.425924i	−0.821240	+	0.570583i	$0.806717\pi$
$860$	0.102465	+	0.180827i	0.00349403	+	0.00616616i
$861$		0			0
$862$	−1.77846	+	1.77846i	−0.0605745	+	0.0605745i
$863$	−0.837748	−	3.12652i	−0.0285173	−	0.106428i	0.950200	−	0.311640i	$-0.100878\pi$
$863$	−0.837748	−	3.12652i	−0.0285173	−	0.106428i	−0.978718	+	0.205212i	$0.934212\pi$
$864$		0			0
$865$	2.19815	−	3.73736i	0.0747392	−	0.127074i
$866$	3.40290	+	1.96467i	0.115635	+	0.0667621i
$867$		0			0
$868$	−4.42810	+	1.71817i	−0.150300	+	0.0583186i
$869$	7.79573			0.264452
$870$		0			0
$871$	−3.51097	−	6.08117i	−0.118965	−	0.206053i
$872$	2.91353	−	10.8735i	0.0986647	−	0.368222i
$873$		0			0
$874$		−	4.70271i		−	0.159072i
$875$	−2.48590	−	29.4758i	−0.0840386	−	0.996462i
$876$		0			0
$877$	−6.25395	−	23.3401i	−0.211181	−	0.788138i	−0.987476	−	0.157769i	$-0.949570\pi$
$877$	−6.25395	−	23.3401i	−0.211181	−	0.788138i	0.776295	−	0.630370i	$-0.217097\pi$
$878$	26.9983	+	7.23418i	0.911150	+	0.244142i
$879$		0			0
$880$	1.04065	−	1.02399i	0.0350802	−	0.0345188i
$881$		−	18.8570i		−	0.635308i	−0.948207	−	0.317654i	$-0.897105\pi$
$881$		−	18.8570i		−	0.635308i	0.948207	−	0.317654i	$-0.102895\pi$
$882$		0			0
$883$	−6.13769	−	6.13769i	−0.206550	−	0.206550i	0.596250	−	0.802799i	$-0.296657\pi$
$883$	−6.13769	−	6.13769i	−0.206550	−	0.206550i	−0.802799	+	0.596250i	$0.796657\pi$
$884$	1.16931	−	2.02531i	0.0393282	−	0.0681185i
$885$		0			0
$886$	11.7378	+	20.3305i	0.394339	+	0.683016i
$887$	−22.5462	+	6.04124i	−0.757028	+	0.202845i	−0.616633	−	0.787251i	$-0.711504\pi$
$887$	−22.5462	+	6.04124i	−0.757028	+	0.202845i	−0.140395	+	0.990096i	$0.544837\pi$
$888$		0			0
$889$	−0.375757	−	3.45495i	−0.0126025	−	0.115875i
$890$	33.6610	−	19.0739i	1.12832	−	0.639358i
$891$		0			0
$892$	4.58563	+	1.22872i	0.153538	+	0.0411404i
$893$	−15.9898	−	4.28445i	−0.535078	−	0.143374i
$894$		0			0
$895$	13.0116	−	47.0391i	0.434929	−	1.57234i
$896$	2.42089	+	1.06738i	0.0808761	+	0.0356588i
$897$		0			0
$898$	5.86095	−	1.57044i	0.195582	−	0.0524062i
$899$	8.79012	+	15.2249i	0.293167	+	0.507780i
$900$		0			0
$901$	7.91739	−	13.7133i	0.263766	−	0.456857i
$902$	−3.64729	−	3.64729i	−0.121442	−	0.121442i
$903$		0			0
$904$		−	5.93505i		−	0.197397i
$905$	16.6393	+	16.9098i	0.553107	+	0.562102i
$906$		0			0
$907$	56.5358	+	15.1487i	1.87724	+	0.503005i	0.999725	+	0.0234563i	$0.00746705\pi$
$907$	56.5358	+	15.1487i	1.87724	+	0.503005i	0.877515	+	0.479549i	$0.159200\pi$
$908$	−5.48385	−	20.4660i	−0.181988	−	0.679189i
$909$		0			0
$910$	5.88798	+	2.65297i	0.195185	+	0.0879450i
$911$		−	48.1428i		−	1.59504i	−0.603290	−	0.797522i	$-0.706144\pi$
$911$		−	48.1428i		−	1.59504i	0.603290	−	0.797522i	$-0.293856\pi$
$912$		0			0
$913$	0.200376	−	0.747813i	0.00663148	−	0.0247490i
$914$	−2.79619	−	4.84314i	−0.0924897	−	0.160197i
$915$		0			0
$916$	19.3950			0.640828
$917$	14.7996	−	5.74249i	0.488727	−	0.189634i
$918$		0			0
$919$	−35.2708	−	20.3636i	−1.16348	−	0.671733i	−0.211341	−	0.977412i	$-0.567783\pi$
$919$	−35.2708	−	20.3636i	−1.16348	−	0.671733i	−0.952134	+	0.305680i	$0.901116\pi$
$920$	−0.526274	−	2.02941i	−0.0173507	−	0.0669077i
$921$		0			0
$922$	3.78731	+	14.1344i	0.124728	+	0.465493i
$923$	−5.93254	+	5.93254i	−0.195272	+	0.195272i
$924$		0			0
$925$	31.4552	−	7.88689i	1.03424	−	0.259319i
$926$	−24.3600	−	14.0643i	−0.800520	−	0.462181i
$927$		0			0
$928$	2.53454	−	9.45902i	0.0832002	−	0.310508i
$929$	−28.9809	+	50.1964i	−0.950833	+	1.64689i	−0.207206	+	0.978297i	$0.566437\pi$
$929$	−28.9809	+	50.1964i	−0.950833	+	1.64689i	−0.743628	+	0.668594i	$0.766896\pi$
$930$		0			0
$931$	−10.6079	+	33.4690i	−0.347661	+	1.09690i
$932$	−4.42479	−	4.42479i	−0.144939	−	0.144939i
$933$		0			0
$934$	3.94011	−	2.27482i	0.128924	−	0.0744345i
$935$	1.58568	−	2.69603i	0.0518574	−	0.0881698i
$936$		0			0
$937$	37.3931	−	37.3931i	1.22158	−	1.22158i	0.254508	−	0.967071i	$-0.418087\pi$
$937$	37.3931	−	37.3931i	1.22158	−	1.22158i	0.967071	−	0.254508i	$-0.0819135\pi$
$938$	10.6626	−	13.2650i	0.348147	−	0.433116i
$939$		0			0
$940$	−7.37970	−	0.0595192i	−0.240699	−	0.00194130i
$941$	−40.6115	+	23.4471i	−1.32390	+	0.764353i	−0.984348	−	0.176235i	$-0.943608\pi$
$941$	−40.6115	+	23.4471i	−1.32390	+	0.764353i	−0.339550	+	0.940588i	$0.610275\pi$
$942$		0			0
$943$	−7.15465	+	1.91708i	−0.232987	+	0.0624288i
$944$	−6.78307			−0.220770
$945$		0			0
$946$	−0.0606881			−0.00197314
$947$	−4.00187	+	1.07230i	−0.130043	+	0.0348450i	−0.323254	−	0.946312i	$-0.604777\pi$
$947$	−4.00187	+	1.07230i	−0.130043	+	0.0348450i	0.193210	+	0.981157i	$0.438110\pi$
$948$		0			0
$949$	9.42405	−	5.44098i	0.305918	−	0.176622i
$950$	−6.88066	+	24.1161i	−0.223238	+	0.782429i
$951$		0			0
$952$	5.60153	+	0.866459i	0.181547	+	0.0280821i
$953$	19.4496	−	19.4496i	0.630036	−	0.630036i	−0.318041	−	0.948077i	$-0.603025\pi$
$953$	19.4496	−	19.4496i	0.630036	−	0.630036i	0.948077	+	0.318041i	$0.103025\pi$
$954$		0			0
$955$	0.373451	+	1.44010i	0.0120846	+	0.0466005i
$956$	−17.1340	+	9.89233i	−0.554154	+	0.319941i
$957$		0			0
$958$	−3.13368	−	3.13368i	−0.101245	−	0.101245i
$959$	18.1007	+	24.7251i	0.584502	+	0.798416i
$960$		0			0
$961$	13.8886	−	24.0557i	0.448018	−	0.775990i
$962$	−1.83243	+	6.83872i	−0.0590799	+	0.220489i
$963$		0			0
$964$	−2.61328	−	1.50878i	−0.0841682	−	0.0485945i
$965$	−40.6829	+	23.0528i	−1.30963	+	0.742096i
$966$		0			0
$967$	−4.31421	+	4.31421i	−0.138736	+	0.138736i	−0.773064	−	0.634328i	$-0.781277\pi$
$967$	−4.31421	+	4.31421i	−0.138736	+	0.138736i	0.634328	+	0.773064i	$0.281277\pi$
$968$	−2.73667	−	10.2134i	−0.0879600	−	0.328271i
$969$		0			0
$970$	−26.3239	+	6.82641i	−0.845210	+	0.219183i
$971$	26.3375	+	15.2060i	0.845211	+	0.487983i	0.859032	−	0.511921i	$-0.171066\pi$
$971$	26.3375	+	15.2060i	0.845211	+	0.487983i	−0.0138209	+	0.999904i	$0.504399\pi$
$972$		0			0
$973$	21.5246	+	17.3019i	0.690046	+	0.554672i
$974$	12.4744			0.399705
$975$		0			0
$976$	4.33834	+	7.51422i	0.138867	+	0.240524i
$977$	−0.597152	+	2.22860i	−0.0191046	+	0.0712993i	−0.974820	−	0.222993i	$-0.928417\pi$
$977$	−0.597152	+	2.22860i	−0.0191046	+	0.0712993i	0.955715	+	0.294292i	$0.0950839\pi$
$978$		0			0
$979$			11.2971i			0.361056i
$980$	−0.832292	+	15.6303i	−0.0265866	+	0.499293i
$981$		0			0
$982$	−6.79189	−	25.3477i	−0.216738	−	0.808877i
$983$	5.68876	+	1.52430i	0.181443	+	0.0486175i	0.348397	−	0.937347i	$-0.386726\pi$
$983$	5.68876	+	1.52430i	0.181443	+	0.0486175i	−0.166953	+	0.985965i	$0.553393\pi$
$984$		0			0
$985$	−0.144700	+	17.9412i	−0.00461053	+	0.571653i
$986$		−	20.9795i		−	0.668123i
$987$		0			0
$988$	−3.87154	−	3.87154i	−0.123170	−	0.123170i
$989$	−0.0435745	+	0.0754733i	−0.00138559	+	0.00239991i
$990$		0			0
$991$	27.1283	+	46.9876i	0.861759	+	1.49261i	0.870230	+	0.492646i	$0.163970\pi$
$991$	27.1283	+	46.9876i	0.861759	+	1.49261i	−0.00847044	+	0.999964i	$0.502696\pi$
$992$	1.73407	−	0.464642i	0.0550567	−	0.0147524i
$993$		0			0
$994$	−18.6064	−	8.20367i	−0.590159	−	0.260205i
$995$	−31.4855	−	8.70927i	−0.998157	−	0.276102i
$996$		0			0
$997$	11.4153	+	3.05872i	0.361526	+	0.0968706i	0.435009	−	0.900426i	$-0.356745\pi$
$997$	11.4153	+	3.05872i	0.361526	+	0.0968706i	−0.0734837	+	0.997296i	$0.523412\pi$
$998$	−9.86512	−	2.64335i	−0.312275	−	0.0836738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.c.233.1	yes	32
3.2	odd	2	inner	630.2.ce.c.233.8	yes	32
5.2	odd	4	inner	630.2.ce.c.107.1	yes	32
7.4	even	3	inner	630.2.ce.c.53.8	yes	32
15.2	even	4	inner	630.2.ce.c.107.8	yes	32
21.11	odd	6	inner	630.2.ce.c.53.1	✓	32
35.32	odd	12	inner	630.2.ce.c.557.8	yes	32
105.32	even	12	inner	630.2.ce.c.557.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.c.53.1	✓	32	21.11	odd	6	inner
630.2.ce.c.53.8	yes	32	7.4	even	3	inner
630.2.ce.c.107.1	yes	32	5.2	odd	4	inner
630.2.ce.c.107.8	yes	32	15.2	even	4	inner
630.2.ce.c.233.1	yes	32	1.1	even	1	trivial
630.2.ce.c.233.8	yes	32	3.2	odd	2	inner
630.2.ce.c.557.1	yes	32	105.32	even	12	inner
630.2.ce.c.557.8	yes	32	35.32	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.56834 - 1.59384i) q^{5} +(1.65758 - 2.06214i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.56834 - 1.59384i) q^{5} +(1.65758 - 2.06214i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.92741 + 1.13362i) q^{10} +(-0.565444 + 0.326459i) q^{11} +(0.771886 + 0.771886i) q^{13} +(-1.06738 + 2.42089i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.554483 - 2.06936i) q^{17} +(-4.34372 - 2.50785i) q^{19} +(-2.15514 - 0.596138i) q^{20} +(0.461683 - 0.461683i) q^{22} +(-0.242669 - 0.905652i) q^{23} +(-0.0806473 + 4.99935i) q^{25} +(-0.945363 - 0.545806i) q^{26} +(0.404442 - 2.61466i) q^{28} -9.79270 q^{29} +(-0.897620 - 1.55472i) q^{31} +(-0.258819 + 0.965926i) q^{32} +2.14236i q^{34} +(-5.88637 + 0.592200i) q^{35} +(-1.67864 - 6.26479i) q^{37} +(4.84479 + 1.29816i) q^{38} +(2.23600 + 0.0180339i) q^{40} -7.90000i q^{41} +(-0.0657249 - 0.0657249i) q^{43} +(-0.326459 + 0.565444i) q^{44} +(0.468800 + 0.811985i) q^{46} +(3.18795 - 0.854209i) q^{47} +(-1.50482 - 6.83634i) q^{49} +(-1.21603 - 4.84987i) q^{50} +(1.05442 + 0.282530i) q^{52} +(7.13943 + 1.91300i) q^{53} +(1.40713 + 0.389229i) q^{55} +(0.286062 + 2.63024i) q^{56} +(9.45902 - 2.53454i) q^{58} +(-3.39154 - 5.87431i) q^{59} +(-4.33834 + 7.51422i) q^{61} +(1.26943 + 1.26943i) q^{62} -1.00000i q^{64} +(0.0196860 - 2.44084i) q^{65} +(-6.21344 - 1.66489i) q^{67} +(-0.554483 - 2.06936i) q^{68} +(5.53252 - 2.09552i) q^{70} +7.68577i q^{71} +(2.58009 - 9.62903i) q^{73} +(3.24289 + 5.61685i) q^{74} -5.01569 q^{76} +(-0.264067 + 1.70716i) q^{77} +(-10.3402 - 5.96992i) q^{79} +(-2.16447 + 0.561299i) q^{80} +(2.04467 + 7.63081i) q^{82} +(-0.838447 + 0.838447i) q^{83} +(-4.16784 + 2.36169i) q^{85} +(0.0804962 + 0.0464745i) q^{86} +(0.168988 - 0.630670i) q^{88} +(8.65123 - 14.9844i) q^{89} +(2.87120 - 0.312269i) q^{91} +(-0.662983 - 0.662983i) q^{92} +(-2.85824 + 1.65021i) q^{94} +(2.81530 + 10.8563i) q^{95} +(-8.59970 + 8.59970i) q^{97} +(3.22292 + 6.21392i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{7}+O(q^{10}) \) 32 * q - 12 * q^7	\( 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) \) 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more