LMFDB - Embedded newform 637.2.e.k.508.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.1
Root			$1.43310 - 2.48220i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.k.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933099 - 1.61618i) q^{2} +(-1.67445 + 2.90023i) q^{3} +(-0.741348 + 1.28405i) q^{4} +(0.433099 + 0.750150i) q^{5} +6.24970 q^{6} -0.965392 q^{8} +(-4.10755 - 7.11448i) q^{9} +O(q^{10})$	\(q+(-0.933099 - 1.61618i) q^{2} +(-1.67445 + 2.90023i) q^{3} +(-0.741348 + 1.28405i) q^{4} +(0.433099 + 0.750150i) q^{5} +6.24970 q^{6} -0.965392 q^{8} +(-4.10755 - 7.11448i) q^{9} +(0.808249 - 1.39993i) q^{10} +(1.93310 - 3.34823i) q^{11} +(-2.48270 - 4.30016i) q^{12} -1.00000 q^{13} -2.90081 q^{15} +(2.38350 + 4.12835i) q^{16} +(-1.67445 + 2.90023i) q^{17} +(-7.66550 + 13.2770i) q^{18} +(-2.69175 - 4.66225i) q^{19} -1.28431 q^{20} -7.21509 q^{22} +(2.62485 + 4.54637i) q^{23} +(1.61650 - 2.79986i) q^{24} +(2.12485 - 3.68035i) q^{25} +(0.933099 + 1.61618i) q^{26} +17.4648 q^{27} +1.69779 q^{29} +(2.70674 + 4.68821i) q^{30} +(3.78199 - 6.55060i) q^{31} +(3.48270 - 6.03221i) q^{32} +(6.47374 + 11.2129i) q^{33} +6.24970 q^{34} +12.1805 q^{36} +(2.41580 + 4.18428i) q^{37} +(-5.02334 + 8.70068i) q^{38} +(1.67445 - 2.90023i) q^{39} +(-0.418110 - 0.724188i) q^{40} +4.06922 q^{41} +4.03461 q^{43} +(2.86620 + 4.96440i) q^{44} +(3.55795 - 6.16255i) q^{45} +(4.89849 - 8.48444i) q^{46} +(-1.82555 - 3.16195i) q^{47} -15.9642 q^{48} -7.93078 q^{50} +(-5.60755 - 9.71255i) q^{51} +(0.741348 - 1.28405i) q^{52} +(0.107546 - 0.186276i) q^{53} +(-16.2964 - 28.2262i) q^{54} +3.34889 q^{55} +18.0288 q^{57} +(-1.58420 - 2.74392i) q^{58} +(-1.39245 + 2.41180i) q^{59} +(2.15051 - 3.72479i) q^{60} +(4.51730 + 7.82420i) q^{61} -14.1159 q^{62} -3.46479 q^{64} +(-0.433099 - 0.750150i) q^{65} +(12.0813 - 20.9254i) q^{66} +(3.83159 - 6.63651i) q^{67} +(-2.48270 - 4.30016i) q^{68} -17.5807 q^{69} +4.90081 q^{71} +(3.96539 + 6.86826i) q^{72} +(7.77304 - 13.4633i) q^{73} +(4.50835 - 7.80870i) q^{74} +(7.11590 + 12.3251i) q^{75} +7.98210 q^{76} -6.24970 q^{78} +(-4.71509 - 8.16678i) q^{79} +(-2.06459 + 3.57597i) q^{80} +(-16.9212 + 29.3084i) q^{81} +(-3.79698 - 6.57657i) q^{82} +4.09919 q^{83} -2.90081 q^{85} +(-3.76469 - 6.52063i) q^{86} +(-2.84286 + 4.92397i) q^{87} +(-1.86620 + 3.23235i) q^{88} +(-0.209055 - 0.362094i) q^{89} -13.2797 q^{90} -7.78371 q^{92} +(12.6655 + 21.9373i) q^{93} +(-3.40684 + 5.90083i) q^{94} +(2.33159 - 4.03843i) q^{95} +(11.6632 + 20.2012i) q^{96} +7.11590 q^{97} -31.7612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 5 * q^5 + 4 * q^6 - 12 * q^8 - 11 * q^9	$ 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9} + 14 q^{10} + 4 q^{11} - 18 q^{12} - 6 q^{13} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 7 q^{19} + 32 q^{20} - 16 q^{22} - q^{23} + 28 q^{24} - 4 q^{25} - 2 q^{26} + 44 q^{27} - 14 q^{29} + 24 q^{30} + 3 q^{31} + 24 q^{32} + 10 q^{33} + 4 q^{34} + 52 q^{36} + 10 q^{37} - 12 q^{38} + 4 q^{39} + 22 q^{40} + 12 q^{41} + 18 q^{43} + 2 q^{44} - 3 q^{45} + 28 q^{46} - 17 q^{47} + 32 q^{48} - 60 q^{50} - 20 q^{51} + 6 q^{52} - 13 q^{53} - 28 q^{54} + 8 q^{55} + 8 q^{57} - 14 q^{58} - 22 q^{59} - 42 q^{60} + 24 q^{61} - 36 q^{62} + 40 q^{64} + 5 q^{65} + 30 q^{66} + 14 q^{67} - 18 q^{68} + 4 q^{69} + 8 q^{71} + 30 q^{72} - 5 q^{73} - 8 q^{74} - 6 q^{75} - 16 q^{76} - 4 q^{78} - q^{79} - 40 q^{80} - 15 q^{81} - 20 q^{82} + 46 q^{83} + 4 q^{85} - 6 q^{86} - 20 q^{87} + 4 q^{88} + 11 q^{89} - 80 q^{90} + 60 q^{92} + 38 q^{93} + 16 q^{94} + 5 q^{95} + 52 q^{96} - 6 q^{97} - 60 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 5 * q^5 + 4 * q^6 - 12 * q^8 - 11 * q^9 + 14 * q^10 + 4 * q^11 - 18 * q^12 - 6 * q^13 + 4 * q^15 - 4 * q^16 - 4 * q^17 - 8 * q^18 - 7 * q^19 + 32 * q^20 - 16 * q^22 - q^23 + 28 * q^24 - 4 * q^25 - 2 * q^26 + 44 * q^27 - 14 * q^29 + 24 * q^30 + 3 * q^31 + 24 * q^32 + 10 * q^33 + 4 * q^34 + 52 * q^36 + 10 * q^37 - 12 * q^38 + 4 * q^39 + 22 * q^40 + 12 * q^41 + 18 * q^43 + 2 * q^44 - 3 * q^45 + 28 * q^46 - 17 * q^47 + 32 * q^48 - 60 * q^50 - 20 * q^51 + 6 * q^52 - 13 * q^53 - 28 * q^54 + 8 * q^55 + 8 * q^57 - 14 * q^58 - 22 * q^59 - 42 * q^60 + 24 * q^61 - 36 * q^62 + 40 * q^64 + 5 * q^65 + 30 * q^66 + 14 * q^67 - 18 * q^68 + 4 * q^69 + 8 * q^71 + 30 * q^72 - 5 * q^73 - 8 * q^74 - 6 * q^75 - 16 * q^76 - 4 * q^78 - q^79 - 40 * q^80 - 15 * q^81 - 20 * q^82 + 46 * q^83 + 4 * q^85 - 6 * q^86 - 20 * q^87 + 4 * q^88 + 11 * q^89 - 80 * q^90 + 60 * q^92 + 38 * q^93 + 16 * q^94 + 5 * q^95 + 52 * q^96 - 6 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.933099	−	1.61618i	−0.659801	−	1.14281i	−0.980667	−	0.195684i	$-0.937307\pi$
$2$	−0.933099	−	1.61618i	−0.659801	−	1.14281i	0.320866	−	0.947124i	$-0.396026\pi$
$3$	−1.67445	+	2.90023i	−0.966742	+	1.67445i	−0.261884	+	0.965099i	$0.584344\pi$
$3$	−1.67445	+	2.90023i	−0.966742	+	1.67445i	−0.704859	+	0.709348i	$0.748990\pi$
$4$	−0.741348	+	1.28405i	−0.370674	+	0.642026i
$5$	0.433099	+	0.750150i	0.193688	+	0.335477i	0.946470	−	0.322793i	$-0.104622\pi$
$5$	0.433099	+	0.750150i	0.193688	+	0.335477i	−0.752782	+	0.658270i	$0.771288\pi$
$6$	6.24970			2.55143
$7$		0			0
$7$		0			0
$8$	−0.965392			−0.341318
$9$	−4.10755	−	7.11448i	−1.36918	−	2.37149i
$10$	0.808249	−	1.39993i	0.255591	−	0.442696i
$11$	1.93310	−	3.34823i	0.582851	−	1.00953i	−0.412288	−	0.911053i	$-0.635270\pi$
$11$	1.93310	−	3.34823i	0.582851	−	1.00953i	0.995140	−	0.0984746i	$-0.0313963\pi$
$12$	−2.48270	−	4.30016i	−0.716693	−	1.24135i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−2.90081			−0.748985
$16$	2.38350	+	4.12835i	0.595876	+	1.03209i
$17$	−1.67445	+	2.90023i	−0.406113	+	0.703408i	−0.994450	−	0.105207i	$-0.966449\pi$
$17$	−1.67445	+	2.90023i	−0.406113	+	0.703408i	0.588337	+	0.808616i	$0.299783\pi$
$18$	−7.66550	+	13.2770i	−1.80677	+	3.12943i
$19$	−2.69175	−	4.66225i	−0.617530	−	1.06959i	−0.989935	−	0.141523i	$-0.954800\pi$
$19$	−2.69175	−	4.66225i	−0.617530	−	1.06959i	0.372405	−	0.928070i	$-0.378533\pi$
$20$	−1.28431			−0.287180
$21$		0			0
$22$	−7.21509			−1.53826
$23$	2.62485	+	4.54637i	0.547319	+	0.947985i	0.998457	+	0.0555303i	$0.0176849\pi$
$23$	2.62485	+	4.54637i	0.547319	+	0.947985i	−0.451138	+	0.892454i	$0.648982\pi$
$24$	1.61650	−	2.79986i	0.329966	−	0.571518i
$25$	2.12485	−	3.68035i	0.424970	−	0.736070i
$26$	0.933099	+	1.61618i	0.182996	+	0.316958i
$27$	17.4648			3.36110
$28$		0			0
$29$	1.69779			0.315271			0.157636	−	0.987497i	$-0.449613\pi$
$29$	1.69779			0.315271			0.157636	+	0.987497i	$0.449613\pi$
$30$	2.70674	+	4.68821i	0.494181	+	0.855946i
$31$	3.78199	−	6.55060i	0.679266	−	1.17652i	−0.295936	−	0.955208i	$-0.595632\pi$
$31$	3.78199	−	6.55060i	0.679266	−	1.17652i	0.975202	−	0.221316i	$-0.0710351\pi$
$32$	3.48270	−	6.03221i	0.615659	−	1.06635i
$33$	6.47374	+	11.2129i	1.12693	+	1.95191i
$34$	6.24970			1.07181
$35$		0			0
$36$	12.1805			2.03008
$37$	2.41580	+	4.18428i	0.397154	+	0.687891i	0.993374	−	0.114930i	$-0.0366645\pi$
$37$	2.41580	+	4.18428i	0.397154	+	0.687891i	−0.596219	+	0.802822i	$0.703331\pi$
$38$	−5.02334	+	8.70068i	−0.814894	+	1.41144i
$39$	1.67445	−	2.90023i	0.268126	−	0.464408i
$40$	−0.418110	−	0.724188i	−0.0661091	−	0.114504i
$41$	4.06922			0.635505			0.317752	−	0.948174i	$-0.397072\pi$
$41$	4.06922			0.635505			0.317752	+	0.948174i	$0.397072\pi$
$42$		0			0
$43$	4.03461			0.615272			0.307636	−	0.951504i	$-0.400462\pi$
$43$	4.03461			0.615272			0.307636	+	0.951504i	$0.400462\pi$
$44$	2.86620	+	4.96440i	0.432096	+	0.748412i
$45$	3.55795	−	6.16255i	0.530388	−	0.918659i
$46$	4.89849	−	8.48444i	0.722243	−	1.25096i
$47$	−1.82555	−	3.16195i	−0.266284	−	0.461218i	0.701615	−	0.712556i	$-0.252463\pi$
$47$	−1.82555	−	3.16195i	−0.266284	−	0.461218i	−0.967899	+	0.251338i	$0.919129\pi$
$48$	−15.9642			−2.30423
$49$		0			0
$50$	−7.93078			−1.12158
$51$	−5.60755	−	9.71255i	−0.785214	−	1.36003i
$52$	0.741348	−	1.28405i	0.102806	−	0.178066i
$53$	0.107546	−	0.186276i	0.0147726	−	0.0255869i	−0.858545	−	0.512739i	$-0.828631\pi$
$53$	0.107546	−	0.186276i	0.0147726	−	0.0255869i	0.873317	+	0.487152i	$0.161964\pi$
$54$	−16.2964	−	28.2262i	−2.21766	−	3.84109i
$55$	3.34889			0.451565
$56$		0			0
$57$	18.0288			2.38797
$58$	−1.58420	−	2.74392i	−0.208016	−	0.360295i
$59$	−1.39245	+	2.41180i	−0.181282	+	0.313990i	−0.942317	−	0.334721i	$-0.891358\pi$
$59$	−1.39245	+	2.41180i	−0.181282	+	0.313990i	0.761035	+	0.648710i	$0.224691\pi$
$60$	2.15051	−	3.72479i	0.277629	−	0.480868i
$61$	4.51730	+	7.82420i	0.578382	+	1.00179i	0.995665	+	0.0930099i	$0.0296488\pi$
$61$	4.51730	+	7.82420i	0.578382	+	1.00179i	−0.417284	+	0.908776i	$0.637018\pi$
$62$	−14.1159			−1.79272
$63$		0			0
$64$	−3.46479			−0.433099
$65$	−0.433099	−	0.750150i	−0.0537193	−	0.0930446i
$66$	12.0813	−	20.9254i	1.48710	−	2.57574i
$67$	3.83159	−	6.63651i	0.468103	−	0.810779i	−0.531232	−	0.847226i	$-0.678271\pi$
$67$	3.83159	−	6.63651i	0.468103	−	0.810779i	0.999336	+	0.0364476i	$0.0116042\pi$
$68$	−2.48270	−	4.30016i	−0.301071	−	0.521470i
$69$	−17.5807			−2.11647
$70$		0			0
$71$	4.90081			0.581619			0.290809	−	0.956781i	$-0.406075\pi$
$71$	4.90081			0.581619			0.290809	+	0.956781i	$0.406075\pi$
$72$	3.96539	+	6.86826i	0.467326	+	0.809432i
$73$	7.77304	−	13.4633i	0.909766	−	1.57576i	0.0953766	−	0.995441i	$-0.469594\pi$
$73$	7.77304	−	13.4633i	0.909766	−	1.57576i	0.814389	−	0.580319i	$-0.197072\pi$
$74$	4.50835	−	7.80870i	0.524085	−	0.907742i
$75$	7.11590	+	12.3251i	0.821673	+	1.42318i
$76$	7.98210			0.915609
$77$		0			0
$78$	−6.24970			−0.707639
$79$	−4.71509	−	8.16678i	−0.530489	−	0.918835i	−0.999367	−	0.0355715i	$-0.988675\pi$
$79$	−4.71509	−	8.16678i	−0.530489	−	0.918835i	0.468878	−	0.883263i	$-0.344658\pi$
$80$	−2.06459	+	3.57597i	−0.230828	+	0.399805i
$81$	−16.9212	+	29.3084i	−1.88014	+	3.25649i
$82$	−3.79698	−	6.57657i	−0.419307	−	0.726260i
$83$	4.09919			0.449945			0.224972	−	0.974365i	$-0.427771\pi$
$83$	4.09919			0.449945			0.224972	+	0.974365i	$0.427771\pi$
$84$		0			0
$85$	−2.90081			−0.314637
$86$	−3.76469	−	6.52063i	−0.405957	−	0.703138i
$87$	−2.84286	+	4.92397i	−0.304786	+	0.527905i
$88$	−1.86620	+	3.23235i	−0.198937	+	0.344570i
$89$	−0.209055	−	0.362094i	−0.0221598	−	0.0383819i	0.854733	−	0.519068i	$-0.173721\pi$
$89$	−0.209055	−	0.362094i	−0.0221598	−	0.0383819i	−0.876893	+	0.480686i	$0.840388\pi$
$90$	−13.2797			−1.39980
$91$		0			0
$92$	−7.78371			−0.811508
$93$	12.6655	+	21.9373i	1.31335	+	2.27479i
$94$	−3.40684	+	5.90083i	−0.351389	+	0.608624i
$95$	2.33159	−	4.03843i	0.239216	−	0.414334i
$96$	11.6632	+	20.2012i	1.19037	+	2.06178i
$97$	7.11590			0.722510			0.361255	−	0.932467i	$-0.382348\pi$
$97$	7.11590			0.722510			0.361255	+	0.932467i	$0.382348\pi$
$98$		0			0
$99$	−31.7612			−3.19212
$100$	3.15051	+	5.45684i	0.315051	+	0.545684i
$101$	−7.05795	+	12.2247i	−0.702292	+	1.21641i	0.265368	+	0.964147i	$0.414507\pi$
$101$	−7.05795	+	12.2247i	−0.702292	+	1.21641i	−0.967660	+	0.252259i	$0.918827\pi$
$102$	−10.4648	+	18.1256i	−1.03617	+	1.79470i
$103$	−8.43018	−	14.6015i	−0.830651	−	1.43873i	−0.897523	−	0.440968i	$-0.854635\pi$
$103$	−8.43018	−	14.6015i	−0.830651	−	1.43873i	0.0668721	−	0.997762i	$-0.478698\pi$
$104$	0.965392			0.0946645
$105$		0			0
$106$	−0.401405			−0.0389879
$107$	−5.09024	−	8.81656i	−0.492092	−	0.852329i	0.507866	−	0.861436i	$-0.330434\pi$
$107$	−5.09024	−	8.81656i	−0.492092	−	0.852329i	−0.999959	+	0.00910710i	$0.997101\pi$
$108$	−12.9475	+	22.4257i	−1.24587	+	2.15791i
$109$	3.10151	−	5.37197i	0.297071	−	0.514542i	−0.678394	−	0.734699i	$-0.737324\pi$
$109$	3.10151	−	5.37197i	0.297071	−	0.514542i	0.975464	+	0.220157i	$0.0706570\pi$
$110$	−3.12485	−	5.41240i	−0.297943	−	0.516052i
$111$	−16.1805			−1.53578
$112$		0			0
$113$	10.2843			0.967466			0.483733	−	0.875216i	$-0.339281\pi$
$113$	10.2843			0.967466			0.483733	+	0.875216i	$0.339281\pi$
$114$	−16.8226	−	29.1377i	−1.57558	−	2.72899i
$115$	−2.27364	+	3.93806i	−0.212018	+	0.367226i
$116$	−1.25865	+	2.18005i	−0.116863	+	0.202412i
$117$	4.10755	+	7.11448i	0.379743	+	0.657734i
$118$	5.19719			0.478440
$119$		0			0
$120$	2.80041			0.255642
$121$	−1.97374	−	3.41863i	−0.179431	−	0.310784i
$122$	8.43018	−	14.6015i	0.763233	−	1.32196i
$123$	−6.81369	+	11.8017i	−0.614369	+	1.06412i
$124$	5.60755	+	9.71255i	0.503573	+	0.872213i
$125$	8.01207			0.716622
$126$		0			0
$127$	−1.91288			−0.169741			−0.0848704	−	0.996392i	$-0.527048\pi$
$127$	−1.91288			−0.169741			−0.0848704	+	0.996392i	$0.527048\pi$
$128$	−3.73240	−	6.46470i	−0.329900	−	0.571404i
$129$	−6.75574	+	11.7013i	−0.594810	+	1.03024i
$130$	−0.808249	+	1.39993i	−0.0708881	+	0.122782i
$131$	5.08129	+	8.80105i	0.443954	+	0.768952i	0.997979	−	0.0635489i	$-0.0202419\pi$
$131$	5.08129	+	8.80105i	0.443954	+	0.768952i	−0.554024	+	0.832500i	$0.686909\pi$
$132$	−19.1972			−1.67090
$133$		0			0
$134$	−14.3010			−1.23542
$135$	7.56399	+	13.1012i	0.651004	+	1.12757i
$136$	1.61650	−	2.79986i	0.138614	−	0.240086i
$137$	−3.89849	+	6.75238i	−0.333071	+	0.576895i	−0.983112	−	0.183003i	$-0.941418\pi$
$137$	−3.89849	+	6.75238i	−0.333071	+	0.576895i	0.650042	+	0.759899i	$0.274751\pi$
$138$	16.4045	+	28.4135i	1.39645	+	2.41872i
$139$	5.08129			0.430989			0.215495	−	0.976505i	$-0.430864\pi$
$139$	5.08129			0.430989			0.215495	+	0.976505i	$0.430864\pi$
$140$		0			0
$141$	12.2272			1.02971
$142$	−4.57294	−	7.92056i	−0.383752	−	0.664679i
$143$	−1.93310	+	3.34823i	−0.161654	+	0.279993i
$144$	19.5807	−	33.9148i	1.63172	−	2.82623i
$145$	0.735311	+	1.27360i	0.0610642	+	0.105766i
$146$	−29.0121			−2.40106
$147$		0			0
$148$	−7.16378			−0.588859
$149$	1.24739	+	2.16053i	0.102190	+	0.176998i	0.912587	−	0.408884i	$-0.134082\pi$
$149$	1.24739	+	2.16053i	0.102190	+	0.176998i	−0.810397	+	0.585881i	$0.800748\pi$
$150$	13.2797	−	23.0011i	1.08428	−	1.87803i
$151$	1.63089	−	2.82478i	0.132720	−	0.229877i	−0.792004	−	0.610515i	$-0.790962\pi$
$151$	1.63089	−	2.82478i	0.132720	−	0.229877i	0.924724	+	0.380638i	$0.124296\pi$
$152$	2.59859	+	4.50090i	0.210774	+	0.365071i
$153$	27.5115			2.22417
$154$		0			0
$155$	6.55191			0.526262
$156$	2.48270	+	4.30016i	0.198775	+	0.344288i
$157$	−0.360161	+	0.623817i	−0.0287440	+	0.0497860i	−0.880040	−	0.474900i	$-0.842484\pi$
$157$	−0.360161	+	0.623817i	−0.0287440	+	0.0497860i	0.851296	+	0.524686i	$0.175817\pi$
$158$	−8.79930	+	15.2408i	−0.700035	+	1.21250i
$159$	0.360161	+	0.623817i	0.0285626	+	0.0494719i
$160$	6.03341			0.476983
$161$		0			0
$162$	63.1568			4.96206
$163$	−0.651106	−	1.12775i	−0.0509985	−	0.0883321i	0.839399	−	0.543515i	$-0.182907\pi$
$163$	−0.651106	−	1.12775i	−0.0509985	−	0.0883321i	−0.890398	+	0.455183i	$0.849574\pi$
$164$	−3.01671	+	5.22509i	−0.235565	+	0.408011i
$165$	−5.60755	+	9.71255i	−0.436547	+	0.756121i
$166$	−3.82495	−	6.62501i	−0.296874	−	0.514201i
$167$	−16.1505			−1.24976			−0.624882	−	0.780719i	$-0.714853\pi$
$167$	−16.1505			−1.24976			−0.624882	+	0.780719i	$0.714853\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	2.70674	+	4.68821i	0.207597	+	0.359569i
$171$	−22.1130	+	38.3008i	−1.69102	+	2.92894i
$172$	−2.99105	+	5.18065i	−0.228065	+	0.395021i
$173$	−7.92415	−	13.7250i	−0.602462	−	1.04349i	−0.992447	−	0.122673i	$-0.960853\pi$
$173$	−7.92415	−	13.7250i	−0.602462	−	1.04349i	0.389985	−	0.920821i	$-0.372480\pi$
$174$	10.6107			0.804393
$175$		0			0
$176$	18.4302			1.38923
$177$	−4.66318	−	8.07687i	−0.350506	−	0.607094i
$178$	−0.390138	+	0.675740i	−0.0292421	+	0.0506488i
$179$	10.2324	−	17.7230i	0.764805	−	1.32468i	−0.175544	−	0.984472i	$-0.556169\pi$
$179$	10.2324	−	17.7230i	0.764805	−	1.32468i	0.940349	−	0.340210i	$-0.110498\pi$
$180$	5.27536	+	9.13719i	0.393202	+	0.681046i
$181$	6.58189			0.489228			0.244614	−	0.969621i	$-0.421339\pi$
$181$	6.58189			0.489228			0.244614	+	0.969621i	$0.421339\pi$
$182$		0			0
$183$	−30.2559			−2.23658
$184$	−2.53401	−	4.38903i	−0.186810	−	0.323564i
$185$	−2.09256	+	3.62442i	−0.153848	+	0.266472i
$186$	23.6363	−	40.9393i	1.73310	−	3.00182i
$187$	6.47374	+	11.2129i	0.473407	+	0.819965i
$188$	5.41348			0.394819
$189$		0			0
$190$	−8.70242			−0.631340
$191$	−6.37455	−	11.0410i	−0.461246	−	0.798902i	0.537777	−	0.843087i	$-0.319264\pi$
$191$	−6.37455	−	11.0410i	−0.461246	−	0.798902i	−0.999023	+	0.0441850i	$0.985931\pi$
$192$	5.80161	−	10.0487i	0.418695	−	0.725202i
$193$	−1.13380	+	1.96380i	−0.0816128	+	0.141358i	−0.903943	−	0.427653i	$-0.859340\pi$
$193$	−1.13380	+	1.96380i	−0.0816128	+	0.141358i	0.822330	+	0.569011i	$0.192674\pi$
$194$	−6.63984	−	11.5005i	−0.476713	−	0.825691i
$195$	2.90081			0.207731
$196$		0			0
$197$	−18.6978			−1.33216			−0.666081	−	0.745879i	$-0.732030\pi$
$197$	−18.6978			−1.33216			−0.666081	+	0.745879i	$0.732030\pi$
$198$	29.6363	+	51.3316i	2.10616	+	3.64798i
$199$	9.95876	−	17.2491i	0.705957	−	1.22275i	−0.260387	−	0.965504i	$-0.583850\pi$
$199$	9.95876	−	17.2491i	0.705957	−	1.22275i	0.966345	−	0.257250i	$-0.0828164\pi$
$200$	−2.05131	+	3.55298i	−0.145050	+	0.251234i
$201$	12.8316	+	22.2250i	0.905071	+	1.56763i
$202$	26.3431			1.85349
$203$		0			0
$204$	16.6286			1.16423
$205$	1.76237	+	3.05252i	0.123090	+	0.213197i
$206$	−15.7324	+	27.2493i	−1.09613	+	1.89855i
$207$	21.5634	−	37.3489i	1.49876	−	2.59593i
$208$	−2.38350	−	4.12835i	−0.165266	−	0.286249i
$209$	−20.8137			−1.43971
$210$		0			0
$211$	0.645277			0.0444227			0.0222114	−	0.999753i	$-0.492929\pi$
$211$	0.645277			0.0444227			0.0222114	+	0.999753i	$0.492929\pi$
$212$	0.159458	+	0.276190i	0.0109516	+	0.0189688i
$213$	−8.20614	+	14.2135i	−0.562276	+	0.973890i
$214$	−9.49940	+	16.4534i	−0.649366	+	1.12473i
$215$	1.74739	+	3.02656i	0.119171	+	0.206410i
$216$	−16.8604			−1.14720
$217$		0			0
$218$	−11.5761			−0.784030
$219$	26.0311	+	45.0872i	1.75902	+	3.04671i
$220$	−2.48270	+	4.30016i	−0.167383	+	0.289916i
$221$	1.67445	−	2.90023i	0.112636	−	0.195090i
$222$	15.0980	+	26.1505i	1.01331	+	1.75511i
$223$	−5.83159			−0.390512			−0.195256	−	0.980752i	$-0.562554\pi$
$223$	−5.83159			−0.390512			−0.195256	+	0.980752i	$0.562554\pi$
$224$		0			0
$225$	−34.9117			−2.32745
$226$	−9.59628	−	16.6212i	−0.638335	−	1.10563i
$227$	−7.86620	+	13.6247i	−0.522098	+	0.904300i	0.477572	+	0.878593i	$0.341517\pi$
$227$	−7.86620	+	13.6247i	−0.522098	+	0.904300i	−0.999670	+	0.0257073i	$0.991816\pi$
$228$	−13.3656	+	23.1499i	−0.885158	+	1.53314i
$229$	−4.43914	−	7.68881i	−0.293346	−	0.508091i	0.681252	−	0.732049i	$-0.261436\pi$
$229$	−4.43914	−	7.68881i	−0.293346	−	0.508091i	−0.974599	+	0.223958i	$0.928102\pi$
$230$	8.48613			0.559559
$231$		0			0
$232$	−1.63903			−0.107608
$233$	5.89558	+	10.2114i	0.386232	+	0.668974i	0.991939	−	0.126714i	$-0.0404431\pi$
$233$	5.89558	+	10.2114i	0.386232	+	0.668974i	−0.605707	+	0.795688i	$0.707110\pi$
$234$	7.66550	−	13.2770i	0.501109	−	0.867946i
$235$	1.58129	−	2.73888i	0.103152	−	0.178665i
$236$	−2.06459	−	3.57597i	−0.134393	−	0.232776i
$237$	31.5807			2.05139
$238$		0			0
$239$	−16.0692			−1.03943			−0.519716	−	0.854339i	$-0.673962\pi$
$239$	−16.0692			−1.03943			−0.519716	+	0.854339i	$0.673962\pi$
$240$	−6.91408	−	11.9755i	−0.446302	−	0.773017i
$241$	2.46771	−	4.27419i	0.158959	−	0.275325i	−0.775535	−	0.631305i	$-0.782520\pi$
$241$	2.46771	−	4.27419i	0.158959	−	0.275325i	0.934494	+	0.355980i	$0.115853\pi$
$242$	−3.68340	+	6.37983i	−0.236778	+	0.410111i
$243$	−30.4702	−	52.7760i	−1.95467	−	3.38558i
$244$	−13.3956			−0.857564
$245$		0			0
$246$	25.4314			1.62145
$247$	2.69175	+	4.66225i	0.171272	+	0.296652i
$248$	−3.65111	+	6.32390i	−0.231845	+	0.401568i
$249$	−6.86388	+	11.8886i	−0.434981	+	0.753409i
$250$	−7.47606	−	12.9489i	−0.472828	−	0.818961i
$251$	−15.2439			−0.962185			−0.481092	−	0.876670i	$-0.659760\pi$
$251$	−15.2439			−0.962185			−0.481092	+	0.876670i	$0.659760\pi$
$252$		0			0
$253$	20.2964			1.27602
$254$	1.78491	+	3.09155i	0.111995	+	0.193981i
$255$	4.85725	−	8.41300i	0.304173	−	0.526842i
$256$	−10.4302	+	18.0656i	−0.651887	+	1.12910i
$257$	−7.80825	−	13.5243i	−0.487065	−	0.843622i	0.512824	−	0.858494i	$-0.328599\pi$
$257$	−7.80825	−	13.5243i	−0.487065	−	0.843622i	−0.999889	+	0.0148720i	$0.995266\pi$
$258$	25.2151			1.56982
$259$		0			0
$260$	1.28431			0.0796494
$261$	−6.97374	−	12.0789i	−0.431664	−	0.747664i
$262$	9.48270	−	16.4245i	0.585843	−	1.01471i
$263$	−8.54668	+	14.8033i	−0.527011	+	0.912810i	0.472493	+	0.881334i	$0.343354\pi$
$263$	−8.54668	+	14.8033i	−0.527011	+	0.912810i	−0.999505	+	0.0314757i	$0.989979\pi$
$264$	−6.24970	−	10.8248i	−0.384642	−	0.666220i
$265$	0.186313			0.0114451
$266$		0			0
$267$	1.40021			0.0856913
$268$	5.68108	+	9.83992i	0.347027	+	0.601069i
$269$	8.16841	−	14.1481i	0.498037	−	0.862625i	−0.501961	−	0.864890i	$-0.667388\pi$
$269$	8.16841	−	14.1481i	0.498037	−	0.862625i	0.999997	+	0.00226550i	$0.000721131\pi$
$270$	14.1159	−	24.4495i	0.859066	−	1.48795i
$271$	−6.24970	−	10.8248i	−0.379642	−	0.657560i	0.611368	−	0.791347i	$-0.290620\pi$
$271$	−6.24970	−	10.8248i	−0.379642	−	0.657560i	−0.991010	+	0.133787i	$0.957286\pi$
$272$	−15.9642			−0.967971
$273$		0			0
$274$	14.5507			0.879041
$275$	−8.21509	−	14.2290i	−0.495389	−	0.858038i
$276$	13.0334	−	22.5745i	0.784519	−	1.35883i
$277$	1.50000	−	2.59808i	0.0901263	−	0.156103i	−0.817438	−	0.576017i	$-0.804606\pi$
$277$	1.50000	−	2.59808i	0.0901263	−	0.156103i	0.907564	+	0.419914i	$0.137940\pi$
$278$	−4.74135	−	8.21226i	−0.284367	−	0.492538i
$279$	−62.1389			−3.72016
$280$		0			0
$281$	0.831590			0.0496085			0.0248043	−	0.999692i	$-0.492104\pi$
$281$	0.831590			0.0496085			0.0248043	+	0.999692i	$0.492104\pi$
$282$	−11.4092	−	19.7612i	−0.679406	−	1.17676i
$283$	5.52938	−	9.57716i	0.328687	−	0.569303i	−0.653564	−	0.756871i	$-0.726727\pi$
$283$	5.52938	−	9.57716i	0.328687	−	0.569303i	0.982252	+	0.187568i	$0.0600604\pi$
$284$	−3.63320	+	6.29289i	−0.215591	+	0.373414i
$285$	7.80825	+	13.5243i	0.462521	+	0.801109i
$286$	7.21509			0.426637
$287$		0			0
$288$	−57.2213			−3.37180
$289$	2.89245	+	5.00988i	0.170144	+	0.294699i
$290$	1.37224	−	2.37678i	0.0805804	−	0.139569i
$291$	−11.9152	+	20.6377i	−0.698481	+	1.20980i
$292$	11.5251	+	19.9620i	0.674453	+	1.16819i
$293$	26.9175			1.57254			0.786269	−	0.617884i	$-0.212010\pi$
$293$	26.9175			1.57254			0.786269	+	0.617884i	$0.212010\pi$
$294$		0			0
$295$	−2.41228			−0.140448
$296$	−2.33219	−	4.03947i	−0.135556	−	0.234789i
$297$	33.7612	−	58.4761i	1.95902	−	3.39313i
$298$	2.32787	−	4.03199i	0.134850	−	0.233567i
$299$	−2.62485	−	4.54637i	−0.151799	−	0.262924i
$300$	−21.1014			−1.21829
$301$		0			0
$302$	−6.08712			−0.350274
$303$	−23.6363	−	40.9393i	−1.35787	−	2.35190i
$304$	12.8316	−	22.2250i	0.735942	−	1.27469i
$305$	−3.91288	+	6.77731i	−0.224051	+	0.388068i
$306$	−25.6709	−	44.4634i	−1.46751	−	2.54180i
$307$	15.1580			0.865110			0.432555	−	0.901608i	$-0.357612\pi$
$307$	15.1580			0.865110			0.432555	+	0.901608i	$0.357612\pi$
$308$		0			0
$309$	56.4636			3.21210
$310$	−6.11358	−	10.5890i	−0.347228	−	0.601417i
$311$	2.12253	−	3.67634i	0.120358	−	0.208466i	−0.799551	−	0.600598i	$-0.794929\pi$
$311$	2.12253	−	3.67634i	0.120358	−	0.208466i	0.919909	+	0.392132i	$0.128262\pi$
$312$	−1.61650	+	2.79986i	−0.0915162	+	0.158511i
$313$	8.97666	+	15.5480i	0.507391	+	0.878827i	0.999963	+	0.00855523i	$0.00272325\pi$
$313$	8.97666	+	15.5480i	0.507391	+	0.878827i	−0.492573	+	0.870271i	$0.663943\pi$
$314$	1.34426			0.0758612
$315$		0			0
$316$	13.9821			0.786554
$317$	7.63320	+	13.2211i	0.428723	+	0.742571i	0.996760	−	0.0804326i	$-0.0256302\pi$
$317$	7.63320	+	13.2211i	0.428723	+	0.742571i	−0.568037	+	0.823003i	$0.692297\pi$
$318$	0.672132	−	1.16417i	0.0376913	−	0.0652832i
$319$	3.28199	−	5.68458i	0.183756	−	0.318275i
$320$	−1.50060	−	2.59911i	−0.0838860	−	0.145295i
$321$	34.0934			1.90291
$322$		0			0
$323$	18.0288			1.00315
$324$	−25.0890	−	43.4555i	−1.39384	−	2.41419i
$325$	−2.12485	+	3.68035i	−0.117865	+	0.204149i
$326$	−1.21509	+	2.10460i	−0.0672977	+	0.116563i
$327$	10.3866	+	17.9902i	0.574382	+	0.994858i
$328$	−3.92839			−0.216909
$329$		0			0
$330$	20.9296			1.15214
$331$	−8.63320	−	14.9531i	−0.474524	−	0.821899i	0.525051	−	0.851071i	$-0.324046\pi$
$331$	−8.63320	−	14.9531i	−0.474524	−	0.821899i	−0.999574	+	0.0291717i	$0.990713\pi$
$332$	−3.03893	+	5.26358i	−0.166783	+	0.288876i
$333$	19.8460	−	34.3742i	1.08755	−	1.88370i
$334$	15.0700	+	26.1020i	0.824595	+	1.42824i
$335$	6.63783			0.362664
$336$		0			0
$337$	−25.5415			−1.39133			−0.695666	−	0.718366i	$-0.744891\pi$
$337$	−25.5415			−1.39133			−0.695666	+	0.718366i	$0.744891\pi$
$338$	−0.933099	−	1.61618i	−0.0507539	−	0.0879083i
$339$	−17.2205	+	29.8268i	−0.935291	+	1.61997i
$340$	2.15051	−	3.72479i	0.116628	−	0.202005i
$341$	−14.6219	−	25.3259i	−0.791822	−	1.37148i
$342$	82.5344			4.46295
$343$		0			0
$344$	−3.89498			−0.210003
$345$	−7.61418	−	13.1882i	−0.409934	−	0.710026i
$346$	−14.7880	+	25.6136i	−0.795009	+	1.37700i
$347$	6.31429	−	10.9367i	0.338969	−	0.587111i	−0.645270	−	0.763954i	$-0.723255\pi$
$347$	6.31429	−	10.9367i	0.338969	−	0.587111i	0.984239	+	0.176843i	$0.0565886\pi$
$348$	−4.21509	−	7.30075i	−0.225953	−	0.391362i
$349$	−35.6394			−1.90774			−0.953868	−	0.300226i	$-0.902938\pi$
$349$	−35.6394			−1.90774			−0.953868	+	0.300226i	$0.902938\pi$
$350$		0			0
$351$	−17.4648			−0.932202
$352$	−13.4648	−	23.3217i	−0.717676	−	1.24305i
$353$	2.70674	−	4.68821i	0.144065	−	0.249528i	−0.784959	−	0.619548i	$-0.787316\pi$
$353$	2.70674	−	4.68821i	0.144065	−	0.249528i	0.929024	+	0.370020i	$0.120649\pi$
$354$	−8.70242	+	15.0730i	−0.462528	+	0.801123i
$355$	2.12253	+	3.67634i	0.112652	+	0.195120i
$356$	0.619931			0.0328563
$357$		0			0
$358$	−38.1914			−2.01848
$359$	9.41580	+	16.3086i	0.496947	+	0.860737i	0.999994	−	0.00352211i	$-0.00112113\pi$
$359$	9.41580	+	16.3086i	0.496947	+	0.860737i	−0.503047	+	0.864259i	$0.667788\pi$
$360$	−3.43482	+	5.94928i	−0.181031	+	0.313554i
$361$	−4.99105	+	8.64475i	−0.262687	+	0.454987i
$362$	−6.14156	−	10.6375i	−0.322793	−	0.559094i
$363$	13.2197			0.693856
$364$		0			0
$365$	13.4660			0.704842
$366$	28.2318	+	48.8989i	1.47570	+	2.55599i
$367$	−11.5753	+	20.0489i	−0.604223	+	1.04655i	0.387950	+	0.921680i	$0.373183\pi$
$367$	−11.5753	+	20.0489i	−0.604223	+	1.04655i	−0.992174	+	0.124865i	$0.960150\pi$
$368$	−12.5127	+	21.6726i	−0.652268	+	1.12976i
$369$	−16.7145	−	28.9504i	−0.870122	−	1.50710i
$370$	7.81025			0.406036
$371$		0			0
$372$	−37.5582			−1.94730
$373$	16.5896	+	28.7341i	0.858979	+	1.48780i	0.872904	+	0.487893i	$0.162234\pi$
$373$	16.5896	+	28.7341i	0.858979	+	1.48780i	−0.0139245	+	0.999903i	$0.504432\pi$
$374$	12.0813	−	20.9254i	0.624709	−	1.08203i
$375$	−13.4158	+	23.2368i	−0.692789	+	1.19995i
$376$	1.76237	+	3.05252i	0.0908875	+	0.157422i
$377$	−1.69779			−0.0874406
$378$		0			0
$379$	37.7853			1.94090			0.970451	−	0.241299i	$-0.0775733\pi$
$379$	37.7853			1.94090			0.970451	+	0.241299i	$0.0775733\pi$
$380$	3.45704	+	5.98777i	0.177342	+	0.307166i
$381$	3.20302	−	5.54779i	0.164096	−	0.284222i
$382$	−11.8962	+	20.6048i	−0.608661	+	1.05423i
$383$	0.115899	+	0.200743i	0.00592215	+	0.0102575i	0.868971	−	0.494862i	$-0.164782\pi$
$383$	0.115899	+	0.200743i	0.00592215	+	0.0102575i	−0.863049	+	0.505120i	$0.831448\pi$
$384$	24.9988			1.27571
$385$		0			0
$386$	4.23180			0.215393
$387$	−16.5723	−	28.7041i	−0.842419	−	1.45911i
$388$	−5.27536	+	9.13719i	−0.267816	+	0.463870i
$389$	−4.67676	+	8.10039i	−0.237121	+	0.410706i	−0.959887	−	0.280387i	$-0.909537\pi$
$389$	−4.67676	+	8.10039i	−0.237121	+	0.410706i	0.722766	+	0.691093i	$0.242871\pi$
$390$	−2.70674	−	4.68821i	−0.137061	−	0.237397i
$391$	−17.5807			−0.889094
$392$		0			0
$393$	−34.0334			−1.71676
$394$	17.4469	+	30.2189i	0.878962	+	1.52241i
$395$	4.08420	−	7.07405i	0.205499	−	0.355934i
$396$	23.5461	−	40.7830i	1.18324	−	2.04942i
$397$	4.87224	+	8.43896i	0.244530	+	0.423539i	0.962000	−	0.273051i	$-0.0880328\pi$
$397$	4.87224	+	8.43896i	0.244530	+	0.423539i	−0.717469	+	0.696590i	$0.754700\pi$
$398$	−37.1700			−1.86317
$399$		0			0
$400$	20.2583			1.01292
$401$	−4.86620	−	8.42850i	−0.243006	−	0.420899i	0.718563	−	0.695462i	$-0.244800\pi$
$401$	−4.86620	−	8.42850i	−0.243006	−	0.420899i	−0.961569	+	0.274563i	$0.911467\pi$
$402$	23.9463	−	41.4762i	1.19433	−	2.06864i
$403$	−3.78199	+	6.55060i	−0.188395	+	0.326309i
$404$	−10.4648	−	18.1256i	−0.520643	−	0.901780i
$405$	−29.3143			−1.45664
$406$		0			0
$407$	18.6799			0.925928
$408$	5.41348	+	9.37642i	0.268007	+	0.464202i
$409$	−6.18652	+	10.7154i	−0.305904	+	0.529841i	−0.977462	−	0.211111i	$-0.932292\pi$
$409$	−6.18652	+	10.7154i	−0.305904	+	0.529841i	0.671558	+	0.740952i	$0.265625\pi$
$410$	3.28894	−	5.69661i	0.162429	−	0.281336i
$411$	−13.0556	−	22.6130i	−0.643987	−	1.11542i
$412$	24.9988			1.23160
$413$		0			0
$414$	−80.4831			−3.95553
$415$	1.77536	+	3.07501i	0.0871489	+	0.150946i
$416$	−3.48270	+	6.03221i	−0.170753	+	0.295753i
$417$	−8.50835	+	14.7369i	−0.416656	+	0.721669i
$418$	19.4212	+	33.6386i	0.949924	+	1.64532i
$419$	21.1054			1.03107			0.515534	−	0.856869i	$-0.327594\pi$
$419$	21.1054			1.03107			0.515534	+	0.856869i	$0.327594\pi$
$420$		0			0
$421$	23.2618			1.13371			0.566855	−	0.823818i	$-0.308160\pi$
$421$	23.2618			1.13371			0.566855	+	0.823818i	$0.308160\pi$
$422$	−0.602108	−	1.04288i	−0.0293102	−	0.0507667i
$423$	−14.9971	+	25.9757i	−0.729183	+	1.26298i
$424$	−0.103824	+	0.179829i	−0.00504215	+	0.00873326i
$425$	7.11590	+	12.3251i	0.345172	+	0.597855i
$426$	30.6286			1.48396
$427$		0			0
$428$	15.0946			0.729623
$429$	−6.47374	−	11.2129i	−0.312555	−	0.541362i
$430$	3.26097	−	5.64816i	0.157258	−	0.272379i
$431$	8.49477	−	14.7134i	0.409179	−	0.708718i	−0.585619	−	0.810586i	$-0.699149\pi$
$431$	8.49477	−	14.7134i	0.409179	−	0.708718i	0.994798	+	0.101868i	$0.0324819\pi$
$432$	41.6274	+	72.1007i	2.00280	+	3.46895i
$433$	−30.8604			−1.48305			−0.741527	−	0.670923i	$-0.765898\pi$
$433$	−30.8604			−1.48305			−0.741527	+	0.670923i	$0.765898\pi$
$434$		0			0
$435$	−4.92496			−0.236134
$436$	4.59859	+	7.96500i	0.220233	+	0.381454i
$437$	14.1309	−	24.4754i	0.675972	−	1.17082i
$438$	48.5792	−	84.1416i	2.32120	−	4.02044i
$439$	−9.59859	−	16.6253i	−0.458116	−	0.793480i	0.540745	−	0.841186i	$-0.318142\pi$
$439$	−9.59859	−	16.6253i	−0.458116	−	0.793480i	−0.998861	+	0.0477062i	$0.984809\pi$
$440$	−3.23300			−0.154127
$441$		0			0
$442$	−6.24970			−0.297268
$443$	17.1888	+	29.7719i	0.816666	+	1.41451i	0.908125	+	0.418699i	$0.137514\pi$
$443$	17.1888	+	29.7719i	0.816666	+	1.41451i	−0.0914589	+	0.995809i	$0.529153\pi$
$444$	11.9954	−	20.7766i	0.569275	−	0.986013i
$445$	0.181083	−	0.313645i	0.00858417	−	0.0148682i
$446$	5.44145	+	9.42487i	0.257660	+	0.446281i
$447$	−8.35472			−0.395165
$448$		0			0
$449$	29.6274			1.39820			0.699101	−	0.715023i	$-0.253584\pi$
$449$	29.6274			1.39820			0.699101	+	0.715023i	$0.253584\pi$
$450$	32.5761	+	56.4234i	1.53565	+	2.65982i
$451$	7.86620	−	13.6247i	0.370405	−	0.641560i
$452$	−7.62425	+	13.2056i	−0.358615	+	0.621139i
$453$	5.46167	+	9.45989i	0.256612	+	0.444464i
$454$	29.3598			1.37792
$455$		0			0
$456$	−17.4048			−0.815056
$457$	8.51962	+	14.7564i	0.398531	+	0.690276i	0.993545	−	0.113439i	$-0.0361868\pi$
$457$	8.51962	+	14.7564i	0.398531	+	0.690276i	−0.595014	+	0.803715i	$0.702853\pi$
$458$	−8.28431	+	14.3488i	−0.387100	+	0.670477i
$459$	−29.2439	+	50.6519i	−1.36499	+	2.36423i
$460$	−3.37112	−	5.83895i	−0.157179	−	0.272242i
$461$	15.1280			0.704580			0.352290	−	0.935891i	$-0.385403\pi$
$461$	15.1280			0.704580			0.352290	+	0.935891i	$0.385403\pi$
$462$		0			0
$463$	26.1221			1.21400			0.607000	−	0.794702i	$-0.292373\pi$
$463$	26.1221			1.21400			0.607000	+	0.794702i	$0.292373\pi$
$464$	4.04668	+	7.00906i	0.187863	+	0.325387i
$465$	−10.9708	+	19.0020i	−0.508760	+	0.881198i
$466$	11.0023	−	19.0566i	0.509672	−	0.882779i
$467$	−11.4594	−	19.8482i	−0.530276	−	0.918464i	−0.999376	−	0.0353196i	$-0.988755\pi$
$467$	−11.4594	−	19.8482i	−0.530276	−	0.918464i	0.469100	−	0.883145i	$-0.344578\pi$
$468$	−12.1805			−0.563043
$469$		0			0
$470$	−5.90200			−0.272239
$471$	−1.20614	−	2.08910i	−0.0555760	−	0.0962605i
$472$	1.34426	−	2.32833i	0.0618747	−	0.107170i
$473$	7.79930	−	13.5088i	0.358612	−	0.621134i
$474$	−29.4679	−	51.0399i	−1.35351	−	2.34434i
$475$	−22.8783			−1.04973
$476$		0			0
$477$	−1.76700			−0.0809056
$478$	14.9942	+	25.9707i	0.685817	+	1.18787i
$479$	−17.5957	+	30.4766i	−0.803967	+	1.39251i	0.113019	+	0.993593i	$0.463948\pi$
$479$	−17.5957	+	30.4766i	−0.803967	+	1.39251i	−0.916986	+	0.398919i	$0.869385\pi$
$480$	−10.1026	+	17.4983i	−0.461120	+	0.798683i
$481$	−2.41580	−	4.18428i	−0.110151	−	0.190787i
$482$	−9.21046			−0.419525
$483$		0			0
$484$	5.85293			0.266042
$485$	3.08189	+	5.33799i	0.139941	+	0.242386i
$486$	−56.8635	+	98.4905i	−2.57938	+	4.46762i
$487$	14.1505	−	24.5094i	0.641221	−	1.11063i	−0.343940	−	0.938992i	$-0.611762\pi$
$487$	14.1505	−	24.5094i	0.641221	−	1.11063i	0.985161	−	0.171635i	$-0.0549050\pi$
$488$	−4.36097	−	7.55342i	−0.197412	−	0.341927i
$489$	4.36097			0.197210
$490$		0			0
$491$	8.24970			0.372304			0.186152	−	0.982521i	$-0.440398\pi$
$491$	8.24970			0.372304			0.186152	+	0.982521i	$0.440398\pi$
$492$	−10.1026	−	17.4983i	−0.455462	−	0.788883i
$493$	−2.84286	+	4.92397i	−0.128036	+	0.221765i
$494$	5.02334	−	8.70068i	0.226011	−	0.391462i
$495$	−13.7557	−	23.8256i	−0.618274	−	1.07088i
$496$	36.0576			1.61903
$497$		0			0
$498$	25.6187			1.14800
$499$	8.36328	+	14.4856i	0.374392	+	0.648466i	0.990236	−	0.139402i	$-0.0445181\pi$
$499$	8.36328	+	14.4856i	0.374392	+	0.648466i	−0.615844	+	0.787868i	$0.711185\pi$
$500$	−5.93974	+	10.2879i	−0.265633	+	0.460090i
$501$	27.0432	−	46.8401i	1.20820	−	2.09266i
$502$	14.2240	+	24.6368i	0.634850	+	1.09959i
$503$	21.2213			0.946213			0.473106	−	0.881005i	$-0.343133\pi$
$503$	21.2213			0.946213			0.473106	+	0.881005i	$0.343133\pi$
$504$		0			0
$505$	−12.2272			−0.544102
$506$	−18.9385	−	32.8025i	−0.841921	−	1.45825i
$507$	−1.67445	+	2.90023i	−0.0743648	+	0.128804i
$508$	1.41811	−	2.45624i	0.0629185	−	0.108978i
$509$	20.3024	+	35.1648i	0.899889	+	1.55865i	0.827635	+	0.561267i	$0.189686\pi$
$509$	20.3024	+	35.1648i	0.899889	+	1.55865i	0.0722543	+	0.997386i	$0.476981\pi$
$510$	−18.1292			−0.802773
$511$		0			0
$512$	24.0000			1.06066
$513$	−47.0109	−	81.4252i	−2.07558	−	3.59501i
$514$	−14.5717	+	25.2390i	−0.642732	+	1.11324i
$515$	7.30221	−	12.6478i	0.321774	−	0.557329i
$516$	−10.0167	−	17.3494i	−0.440961	−	0.763767i
$517$	−14.1159			−0.620817
$518$		0			0
$519$	53.0743			2.32970
$520$	0.418110	+	0.724188i	0.0183354	+	0.0317578i
$521$	−1.73240	+	3.00060i	−0.0758977	+	0.131459i	−0.901476	−	0.432828i	$-0.857516\pi$
$521$	−1.73240	+	3.00060i	−0.0758977	+	0.131459i	0.825579	+	0.564287i	$0.190849\pi$
$522$	−13.0144	+	22.5416i	−0.569624	+	0.986618i
$523$	−2.78491	−	4.82360i	−0.121776	−	0.210921i	0.798692	−	0.601740i	$-0.205525\pi$
$523$	−2.78491	−	4.82360i	−0.121776	−	0.210921i	−0.920468	+	0.390818i	$0.872192\pi$
$524$	−15.0680			−0.658249
$525$		0			0
$526$	31.8996			1.39089
$527$	12.6655	+	21.9373i	0.551718	+	0.955603i
$528$	−30.8604	+	53.4517i	−1.34303	+	2.32619i
$529$	−2.27968	+	3.94852i	−0.0991164	+	0.171675i
$530$	−0.173848	−	0.301114i	−0.00755149	−	0.0130796i
$531$	22.8783			0.992832
$532$		0			0
$533$	−4.06922			−0.176257
$534$	−1.30653	−	2.26298i	−0.0565392	−	0.0979287i
$535$	4.40916	−	7.63689i	0.190625	−	0.330171i
$536$	−3.69899	+	6.40683i	−0.159772	+	0.276733i
$537$	34.2672	+	59.3526i	1.47874	+	2.56125i
$538$	−30.4877			−1.31442
$539$		0			0
$540$	−22.4302			−0.965241
$541$	−12.1182	−	20.9894i	−0.521003	−	0.902403i	−0.999702	−	0.0244241i	$-0.992225\pi$
$541$	−12.1182	−	20.9894i	−0.521003	−	0.902403i	0.478699	−	0.877979i	$-0.341109\pi$
$542$	−11.6632	+	20.2012i	−0.500976	+	0.867717i
$543$	−11.0210	+	19.0890i	−0.472957	+	0.819186i
$544$	11.6632	+	20.2012i	0.500055	+	0.866120i
$545$	5.37304			0.230156
$546$		0			0
$547$	15.7733			0.674416			0.337208	−	0.941430i	$-0.390518\pi$
$547$	15.7733			0.674416			0.337208	+	0.941430i	$0.390518\pi$
$548$	−5.78028	−	10.0117i	−0.246921	−	0.427680i
$549$	37.1101	−	64.2765i	1.58382	−	2.74326i
$550$	−15.3310	+	26.5541i	−0.653716	+	1.13227i
$551$	−4.57002	−	7.91551i	−0.194690	−	0.337212i
$552$	16.9723			0.722387
$553$		0			0
$554$	−5.59859			−0.237861
$555$	−7.00775	−	12.1378i	−0.297463	−	0.515220i
$556$	−3.76700	+	6.52464i	−0.159757	+	0.276707i
$557$	8.61067	−	14.9141i	0.364846	−	0.631931i	−0.623906	−	0.781500i	$-0.714455\pi$
$557$	8.61067	−	14.9141i	0.364846	−	0.631931i	0.988751	+	0.149568i	$0.0477884\pi$
$558$	57.9817	+	100.427i	2.45456	+	4.25143i
$559$	−4.03461			−0.170646
$560$		0			0
$561$	−43.3598			−1.83065
$562$	−0.775956	−	1.34400i	−0.0327317	−	0.0566930i
$563$	7.67989	−	13.3020i	0.323669	−	0.560610i	−0.657573	−	0.753390i	$-0.728417\pi$
$563$	7.67989	−	13.3020i	0.323669	−	0.560610i	0.981242	+	0.192780i	$0.0617504\pi$
$564$	−9.06459	+	15.7003i	−0.381688	+	0.661103i
$565$	4.45413	+	7.71477i	0.187386	+	0.324563i
$566$	−20.6378			−0.867473
$567$		0			0
$568$	−4.73120			−0.198517
$569$	−11.8610	−	20.5438i	−0.497238	−	0.861241i	0.502757	−	0.864428i	$-0.332319\pi$
$569$	−11.8610	−	20.5438i	−0.497238	−	0.861241i	−0.999995	+	0.00318672i	$0.998986\pi$
$570$	14.5717	−	25.2390i	0.610343	−	1.05715i
$571$	13.6595	−	23.6589i	0.571631	−	0.990093i	−0.424768	−	0.905302i	$-0.639644\pi$
$571$	13.6595	−	23.6589i	0.571631	−	0.990093i	0.996399	−	0.0847910i	$-0.0270223\pi$
$572$	−2.86620	−	4.96440i	−0.119842	−	0.207572i
$573$	42.6954			1.78363
$574$		0			0
$575$	22.3097			0.930377
$576$	14.2318	+	24.6502i	0.592992	+	1.02709i
$577$	11.6332	−	20.1493i	0.484297	−	0.838826i	−0.515541	−	0.856865i	$-0.672409\pi$
$577$	11.6332	−	20.1493i	0.484297	−	0.838826i	0.999837	+	0.0180388i	$0.00574224\pi$
$578$	5.39789	−	9.34942i	0.224523	−	0.388885i
$579$	−3.79698	−	6.57657i	−0.157797	−	0.273313i
$580$	−2.18048			−0.0905397
$581$		0			0
$582$	44.4722			1.84343
$583$	−0.415795	−	0.720178i	−0.0172205	−	0.0298267i
$584$	−7.50403	+	12.9974i	−0.310519	+	0.537835i
$585$	−3.55795	+	6.16255i	−0.147103	+	0.254790i
$586$	−25.1167	−	43.5034i	−1.03756	−	1.79711i
$587$	45.7266			1.88734			0.943669	−	0.330892i	$-0.107349\pi$
$587$	45.7266			1.88734			0.943669	+	0.330892i	$0.107349\pi$
$588$		0			0
$589$	−40.7207			−1.67787
$590$	2.25090	+	3.89867i	0.0926680	+	0.160506i
$591$	31.3085	−	54.2278i	1.28786	−	2.23064i
$592$	−11.5161	+	19.9465i	−0.473309	+	0.819795i
$593$	−14.6949	−	25.4523i	−0.603446	−	1.04520i	−0.992295	−	0.123898i	$-0.960460\pi$
$593$	−14.6949	−	25.4523i	−0.603446	−	1.04520i	0.388849	−	0.921302i	$-0.372873\pi$
$594$	−126.010			−5.17026
$595$		0			0
$596$	−3.69899			−0.151516
$597$	33.3508	+	57.7653i	1.36496	+	2.36418i
$598$	−4.89849	+	8.48444i	−0.200314	+	0.346954i
$599$	−11.0294	+	19.1034i	−0.450648	+	0.780546i	−0.998426	−	0.0560780i	$-0.982140\pi$
$599$	−11.0294	+	19.1034i	−0.450648	+	0.780546i	0.547778	+	0.836624i	$0.315474\pi$
$600$	−6.86963	−	11.8986i	−0.280452	−	0.485756i
$601$	−30.8604			−1.25882			−0.629410	−	0.777073i	$-0.716704\pi$
$601$	−30.8604			−1.25882			−0.629410	+	0.777073i	$0.716704\pi$
$602$		0			0
$603$	−62.9537			−2.56367
$604$	2.41811	+	4.18829i	0.0983915	+	0.170419i
$605$	1.70965	−	2.96121i	0.0695073	−	0.120390i
$606$	−44.1101	+	76.4009i	−1.79185	+	3.10357i
$607$	18.2431	+	31.5979i	0.740463	+	1.28252i	0.952285	+	0.305211i	$0.0987271\pi$
$607$	18.2431	+	31.5979i	0.740463	+	1.28252i	−0.211821	+	0.977308i	$0.567940\pi$
$608$	−37.4982			−1.52075
$609$		0			0
$610$	14.6044			0.591316
$611$	1.82555	+	3.16195i	0.0738540	+	0.127919i
$612$	−20.3956	+	35.3262i	−0.824442	+	1.42798i
$613$	−14.4994	+	25.1137i	−0.585625	+	1.01433i	0.409172	+	0.912457i	$0.365818\pi$
$613$	−14.4994	+	25.1137i	−0.585625	+	1.01433i	−0.994797	+	0.101875i	$0.967516\pi$
$614$	−14.1439	−	24.4979i	−0.570800	−	0.988655i
$615$	−11.8040			−0.475984
$616$		0			0
$617$	−41.6515			−1.67683			−0.838414	−	0.545035i	$-0.816517\pi$
$617$	−41.6515			−1.67683			−0.838414	+	0.545035i	$0.816517\pi$
$618$	−52.6861	−	91.2551i	−2.11935	−	3.67082i
$619$	6.24970	−	10.8248i	0.251197	−	0.435085i	−0.712659	−	0.701511i	$-0.752509\pi$
$619$	6.24970	−	10.8248i	0.251197	−	0.435085i	0.963856	+	0.266425i	$0.0858426\pi$
$620$	−4.85725	+	8.41300i	−0.195072	+	0.337874i
$621$	45.8425	+	79.4015i	1.83959	+	3.18627i
$622$	−7.92214			−0.317649
$623$		0			0
$624$	15.9642			0.639079
$625$	−7.15423	−	12.3915i	−0.286169	−	0.495660i
$626$	16.7522	−	29.0157i	0.669554	−	1.15970i
$627$	34.8514	−	60.3644i	1.39183	−	2.41072i
$628$	−0.534009	−	0.924931i	−0.0213093	−	0.0369088i
$629$	−16.1805			−0.645158
$630$		0			0
$631$	−35.5582			−1.41555			−0.707774	−	0.706439i	$-0.750300\pi$
$631$	−35.5582			−1.41555			−0.707774	+	0.706439i	$0.750300\pi$
$632$	4.55191	+	7.88414i	0.181065	+	0.313614i
$633$	−1.08048	+	1.87145i	−0.0429453	+	0.0743835i
$634$	14.2451	−	24.6732i	0.565744	−	0.979897i
$635$	−0.828467	−	1.43495i	−0.0328767	−	0.0569441i
$636$	−1.06802			−0.0423497
$637$		0			0
$638$	−12.2497			−0.484970
$639$	−20.1303	−	34.8667i	−0.796342	−	1.37930i
$640$	3.23300	−	5.59971i	0.127795	−	0.221348i
$641$	−0.680484	+	1.17863i	−0.0268775	+	0.0465532i	−0.879151	−	0.476543i	$-0.841890\pi$
$641$	−0.680484	+	1.17863i	−0.0268775	+	0.0465532i	0.852274	+	0.523096i	$0.175223\pi$
$642$	−31.8125	−	55.1008i	−1.25554	−	2.17466i
$643$	−12.1867			−0.480598			−0.240299	−	0.970699i	$-0.577245\pi$
$643$	−12.1867			−0.480598			−0.240299	+	0.970699i	$0.577245\pi$
$644$		0			0
$645$	−11.7036			−0.460829
$646$	−16.8226	−	29.1377i	−0.661878	−	1.14641i
$647$	−1.86076	+	3.22293i	−0.0731540	+	0.126706i	−0.900282	−	0.435307i	$-0.856640\pi$
$647$	−1.86076	+	3.22293i	−0.0731540	+	0.126706i	0.827128	+	0.562014i	$0.189973\pi$
$648$	16.3356	−	28.2941i	0.641724	−	1.11150i
$649$	5.38350	+	9.32450i	0.211321	+	0.366019i
$650$	7.93078			0.311071
$651$		0			0
$652$	1.93078			0.0756153
$653$	22.5294	+	39.0220i	0.881643	+	1.52705i	0.849514	+	0.527566i	$0.176895\pi$
$653$	22.5294	+	39.0220i	0.881643	+	1.52705i	0.0321288	+	0.999484i	$0.489771\pi$
$654$	19.3835	−	33.5732i	0.757955	−	1.31282i
$655$	−4.40141	+	7.62346i	−0.171977	+	0.297873i
$656$	9.69899	+	16.7991i	0.378682	+	0.655896i
$657$	−127.713			−4.98254
$658$		0			0
$659$	5.37887			0.209531			0.104766	−	0.994497i	$-0.466591\pi$
$659$	5.37887			0.209531			0.104766	+	0.994497i	$0.466591\pi$
$660$	−8.31429	−	14.4008i	−0.323633	−	0.560549i
$661$	−21.2468	+	36.8005i	−0.826404	+	1.43137i	0.0744372	+	0.997226i	$0.476284\pi$
$661$	−21.2468	+	36.8005i	−0.826404	+	1.43137i	−0.900841	+	0.434148i	$0.857049\pi$
$662$	−16.1113	+	27.9055i	−0.626182	+	1.08458i
$663$	5.60755	+	9.71255i	0.217779	+	0.377204i
$664$	−3.95733			−0.153574
$665$		0			0
$666$	−74.0731			−2.87027
$667$	4.45644	+	7.71878i	0.172554	+	0.298872i
$668$	11.9731	−	20.7381i	0.463255	−	0.802381i
$669$	9.76469	−	16.9129i	0.377525	−	0.653892i
$670$	−6.19376	−	10.7279i	−0.239286	−	0.414455i
$671$	34.9296			1.34844
$672$		0			0
$673$	−37.3765			−1.44076			−0.720379	−	0.693581i	$-0.756032\pi$
$673$	−37.3765			−1.44076			−0.720379	+	0.693581i	$0.756032\pi$
$674$	23.8327	+	41.2795i	0.918002	+	1.59003i
$675$	37.1101	−	64.2765i	1.42837	−	2.47400i
$676$	−0.741348	+	1.28405i	−0.0285134	+	0.0493866i
$677$	−21.7378	−	37.6510i	−0.835453	−	1.44705i	−0.893661	−	0.448742i	$-0.851872\pi$
$677$	−21.7378	−	37.6510i	−0.835453	−	1.44705i	0.0582083	−	0.998304i	$-0.481461\pi$
$678$	64.2738			2.46842
$679$		0			0
$680$	2.80041			0.107391
$681$	−26.3431	−	45.6275i	−1.00947	−	1.74845i
$682$	−27.2874	+	47.2632i	−1.04489	+	1.80980i
$683$	−15.6978	+	27.1894i	−0.600659	+	1.04037i	0.392062	+	0.919939i	$0.371762\pi$
$683$	−15.6978	+	27.1894i	−0.600659	+	1.04037i	−0.992721	+	0.120434i	$0.961572\pi$
$684$	−32.7868	−	56.7885i	−1.25364	−	2.17136i
$685$	−6.75373			−0.258047
$686$		0			0
$687$	29.7324			1.13436
$688$	9.61650	+	16.6563i	0.366626	+	0.635014i
$689$	−0.107546	+	0.186276i	−0.00409719	+	0.00709653i
$690$	−14.2096	+	24.6117i	−0.540949	+	0.936952i
$691$	6.72053	+	11.6403i	0.255661	+	0.442818i	0.965075	−	0.261974i	$-0.0843736\pi$
$691$	6.72053	+	11.6403i	0.255661	+	0.442818i	−0.709414	+	0.704792i	$0.751040\pi$
$692$	23.4982			0.893268
$693$		0			0
$694$	−23.5674			−0.894607
$695$	2.20070	+	3.81173i	0.0834774	+	0.144587i
$696$	2.74447	−	4.75356i	0.104029	−	0.180183i
$697$	−6.81369	+	11.8017i	−0.258087	+	0.447019i
$698$	33.2551	+	57.5996i	1.25873	+	2.18018i
$699$	−39.4873			−1.49355
$700$		0			0
$701$	−28.0346			−1.05885			−0.529426	−	0.848356i	$-0.677593\pi$
$701$	−28.0346			−1.05885			−0.529426	+	0.848356i	$0.677593\pi$
$702$	16.2964	+	28.2262i	0.615067	+	1.06533i
$703$	13.0054	−	22.5261i	0.490509	−	0.849587i
$704$	−6.69779	+	11.6009i	−0.252432	+	0.437226i
$705$	5.29558	+	9.17221i	0.199443	+	0.345445i
$706$	−10.1026			−0.380217
$707$		0			0
$708$	13.8282			0.519694
$709$	20.1424	+	34.8876i	0.756462	+	1.31023i	0.944644	+	0.328097i	$0.106407\pi$
$709$	20.1424	+	34.8876i	0.756462	+	1.31023i	−0.188182	+	0.982134i	$0.560259\pi$
$710$	3.96107	−	6.86078i	0.148656	−	0.257480i
$711$	−38.7349	+	67.0909i	−1.45267	+	2.51610i
$712$	0.201820	+	0.349563i	0.00756353	+	0.0131004i
$713$	39.7087			1.48710
$714$		0			0
$715$	−3.34889			−0.125242
$716$	15.1715	+	26.2779i	0.566987	+	0.982050i
$717$	26.9071	−	46.6044i	1.00486	−	1.74047i
$718$	17.5717	−	30.4351i	0.655772	−	1.13583i
$719$	8.37224	+	14.5011i	0.312232	+	0.540801i	0.978845	−	0.204602i	$-0.0655901\pi$
$719$	8.37224	+	14.5011i	0.312232	+	0.540801i	−0.666613	+	0.745404i	$0.732257\pi$
$720$	33.9215			1.26418
$721$		0			0
$722$	18.6286			0.693284
$723$	8.26409	+	14.3138i	0.307345	+	0.532337i
$724$	−4.87947	+	8.45149i	−0.181344	+	0.314097i
$725$	3.60755	−	6.24845i	0.133981	−	0.232062i
$726$	−12.3353	−	21.3654i	−0.457806	−	0.792944i
$727$	−51.4982			−1.90996			−0.954981	−	0.296666i	$-0.904125\pi$
$727$	−51.4982			−1.90996			−0.954981	+	0.296666i	$0.904125\pi$
$728$		0			0
$729$	102.556			3.79836
$730$	−12.5651	−	21.7634i	−0.465055	−	0.805500i
$731$	−6.75574	+	11.7013i	−0.249870	+	0.432788i
$732$	22.4302	−	38.8502i	0.829043	−	1.43595i
$733$	16.9158	+	29.2990i	0.624799	+	1.08218i	0.988580	+	0.150699i	$0.0481525\pi$
$733$	16.9158	+	29.2990i	0.624799	+	1.08218i	−0.363781	+	0.931485i	$0.618514\pi$
$734$	43.2034			1.59467
$735$		0			0
$736$	36.5662			1.34785
$737$	−14.8137	−	25.6581i	−0.545669	−	0.945127i
$738$	−31.1926	+	54.0271i	−1.14821	+	1.98876i
$739$	−10.3345	+	17.8999i	−0.380161	+	0.658458i	−0.991085	−	0.133231i	$-0.957465\pi$
$739$	−10.3345	+	17.8999i	−0.380161	+	0.658458i	0.610924	+	0.791689i	$0.290798\pi$
$740$	−3.10263	−	5.37391i	−0.114055	−	0.197549i
$741$	−18.0288			−0.662304
$742$		0			0
$743$	−29.6966			−1.08946			−0.544731	−	0.838611i	$-0.683368\pi$
$743$	−29.6966			−1.08946			−0.544731	+	0.838611i	$0.683368\pi$
$744$	−12.2272	−	21.1781i	−0.448270	−	0.776426i
$745$	−1.08048	+	1.87145i	−0.0395858	+	0.0685647i
$746$	30.9596	−	53.6235i	1.13351	−	1.96330i
$747$	−16.8376	−	29.1636i	−0.616057	−	1.06704i
$748$	−19.1972			−0.701919
$749$		0			0
$750$	50.0731			1.82841
$751$	6.01148	+	10.4122i	0.219362	+	0.379946i	0.954613	−	0.297849i	$-0.0962691\pi$
$751$	6.01148	+	10.4122i	0.219362	+	0.379946i	−0.735251	+	0.677795i	$0.762936\pi$
$752$	8.70242	−	15.0730i	0.317345	−	0.549657i
$753$	25.5251	−	44.2107i	0.930185	−	1.61113i
$754$	1.58420	+	2.74392i	0.0576933	+	0.0999278i
$755$	2.82534			0.102825
$756$		0			0
$757$	−30.2906			−1.10093			−0.550464	−	0.834859i	$-0.685549\pi$
$757$	−30.2906			−1.10093			−0.550464	+	0.834859i	$0.685549\pi$
$758$	−35.2575	−	61.0677i	−1.28061	−	2.21808i
$759$	−33.9852	+	58.8641i	−1.23359	+	2.13663i
$760$	−2.25090	+	3.89867i	−0.0816487	+	0.141420i
$761$	22.9792	+	39.8011i	0.832995	+	1.44279i	0.895653	+	0.444754i	$0.146709\pi$
$761$	22.9792	+	39.8011i	0.832995	+	1.44279i	−0.0626580	+	0.998035i	$0.519958\pi$
$762$	−11.9549			−0.433082
$763$		0			0
$764$	18.9030			0.683888
$765$	11.9152	+	20.6377i	0.430795	+	0.746159i
$766$	0.216290	−	0.374626i	0.00781488	−	0.0135358i
$767$	1.39245	−	2.41180i	0.0502786	−	0.0870851i
$768$	−34.9296	−	60.4998i	−1.26041	−	2.18310i
$769$	4.03924			0.145659			0.0728293	−	0.997344i	$-0.476797\pi$
$769$	4.03924			0.145659			0.0728293	+	0.997344i	$0.476797\pi$
$770$		0			0
$771$	52.2980			1.88347
$772$	−1.68108	−	2.91172i	−0.0605035	−	0.104795i
$773$	−18.0588	+	31.2787i	−0.649528	+	1.12502i	0.333707	+	0.942677i	$0.391700\pi$
$773$	−18.0588	+	31.2787i	−0.649528	+	1.12502i	−0.983236	+	0.182339i	$0.941633\pi$
$774$	−30.9273	+	53.5676i	−1.11166	+	1.92545i
$775$	−16.0723	−	27.8381i	−0.577335	−	0.999974i
$776$	−6.86963			−0.246605
$777$		0			0
$778$	17.4555			0.625811
$779$	−10.9533	−	18.9717i	−0.392443	−	0.679732i
$780$	−2.15051	+	3.72479i	−0.0770005	+	0.133369i
$781$	9.47374	−	16.4090i	0.338997	−	0.587160i
$782$	16.4045	+	28.4135i	0.586625	+	1.01606i
$783$	29.6515			1.05966
$784$		0			0
$785$	−0.623942			−0.0222694
$786$	31.7565	+	55.0040i	1.13272	+	1.96193i
$787$	12.9325	−	22.3997i	0.460994	−	0.798465i	−0.538017	−	0.842934i	$-0.680826\pi$
$787$	12.9325	−	22.3997i	0.460994	−	0.798465i	0.999011	+	0.0444693i	$0.0141597\pi$
$788$	13.8616	−	24.0089i	0.493798	−	0.855283i
$789$	−28.6219	−	49.5746i	−1.01897	−	1.76490i
$790$	−15.2439			−0.542353
$791$		0			0
$792$	30.6620			1.08953
$793$	−4.51730	−	7.82420i	−0.160414	−	0.277845i
$794$	9.09256	−	15.7488i	0.322683	−	0.558903i
$795$	−0.311971	+	0.540349i	−0.0110645	+	0.0191642i
$796$	14.7658	+	25.5751i	0.523360	+	0.906486i
$797$	−0.291753			−0.0103344			−0.00516720	−	0.999987i	$-0.501645\pi$
$797$	−0.291753			−0.0103344			−0.00516720	+	0.999987i	$0.501645\pi$
$798$		0			0
$799$	12.2272			0.432566
$800$	−14.8004	−	25.6351i	−0.523274	−	0.906337i
$801$	−1.71741	+	2.97464i	−0.0606816	+	0.105104i
$802$	−9.08129	+	15.7293i	−0.320672	+	0.555419i
$803$	−30.0521	−	52.0518i	−1.06052	−	1.83687i
$804$	−38.0507			−1.34194
$805$		0			0
$806$	14.1159			0.497211
$807$	27.3551	+	47.3805i	0.962947	+	1.66787i
$808$	6.81369	−	11.8017i	0.239705	−	0.415181i
$809$	2.62797	−	4.55178i	0.0923946	−	0.160032i	−0.816124	−	0.577877i	$-0.803881\pi$
$809$	2.62797	−	4.55178i	0.0923946	−	0.160032i	0.908518	+	0.417845i	$0.137215\pi$
$810$	27.3531	+	47.3770i	0.961091	+	1.66466i
$811$	−37.8499			−1.32909			−0.664545	−	0.747248i	$-0.731375\pi$
$811$	−37.8499			−1.32909			−0.664545	+	0.747248i	$0.731375\pi$
$812$		0			0
$813$	41.8592			1.46807
$814$	−17.4302	−	30.1900i	−0.610928	−	1.05816i
$815$	0.563987	−	0.976854i	0.0197556	−	0.0342177i
$816$	26.7312	−	46.2998i	0.935779	−	1.62082i
$817$	−10.8602	−	18.8104i	−0.379949	−	0.658091i
$818$	23.0906			0.807342
$819$		0			0
$820$	−5.22613			−0.182504
$821$	12.8604	+	22.2748i	0.448830	+	0.777396i	0.998310	−	0.0581104i	$-0.0185075\pi$
$821$	12.8604	+	22.2748i	0.448830	+	0.777396i	−0.549480	+	0.835507i	$0.685174\pi$
$822$	−24.3644	+	42.2004i	−0.849806	+	1.47191i
$823$	9.74135	−	16.8725i	0.339562	−	0.588139i	−0.644788	−	0.764361i	$-0.723054\pi$
$823$	9.74135	−	16.8725i	0.339562	−	0.588139i	0.984350	+	0.176222i	$0.0563878\pi$
$824$	8.13843	+	14.0962i	0.283516	+	0.491064i
$825$	55.0230			1.91565
$826$		0			0
$827$	−32.0934			−1.11600			−0.557998	−	0.829842i	$-0.688430\pi$
$827$	−32.0934			−1.11600			−0.557998	+	0.829842i	$0.688430\pi$
$828$	31.9719	+	55.3770i	1.11110	+	1.92449i
$829$	1.94668	−	3.37175i	0.0676110	−	0.117106i	−0.830238	−	0.557409i	$-0.811796\pi$
$829$	1.94668	−	3.37175i	0.0676110	−	0.117106i	0.897849	+	0.440303i	$0.145129\pi$
$830$	3.31317	−	5.73858i	0.115002	−	0.199189i
$831$	5.02334	+	8.70068i	0.174258	+	0.301823i
$832$	3.46479			0.120120
$833$		0			0
$834$	31.7565			1.09964
$835$	−6.99477	−	12.1153i	−0.242064	−	0.419267i
$836$	15.4302	−	26.7259i	0.533664	−	0.924333i
$837$	66.0517	−	114.405i	2.28308	−	3.95441i
$838$	−19.6935	−	34.1101i	−0.680300	−	1.17831i
$839$	41.8592			1.44514			0.722570	−	0.691298i	$-0.242961\pi$
$839$	41.8592			1.44514			0.722570	+	0.691298i	$0.242961\pi$
$840$		0			0
$841$	−26.1175			−0.900604
$842$	−21.7055	−	37.5951i	−0.748022	−	1.29561i
$843$	−1.39245	+	2.41180i	−0.0479587	+	0.0830668i
$844$	−0.478375	+	0.828570i	−0.0164664	+	0.0285206i
$845$	0.433099	+	0.750150i	0.0148991	+	0.0258059i
$846$	55.9751			1.92446
$847$		0			0
$848$	1.02535			0.0352106
$849$	18.5173	+	32.0729i	0.635512	+	1.10074i
$850$	13.2797	−	23.0011i	0.455489	−	0.788930i
$851$	−12.6822	+	21.9662i	−0.434740	+	0.752992i
$852$	−12.1672	−	21.0742i	−0.416842	−	0.721991i
$853$	1.70242			0.0582897			0.0291449	−	0.999575i	$-0.490722\pi$
$853$	1.70242			0.0582897			0.0291449	+	0.999575i	$0.490722\pi$
$854$		0			0
$855$	−38.3085			−1.31012
$856$	4.91408	+	8.51143i	0.167960	+	0.290915i
$857$	4.78954	−	8.29572i	0.163608	−	0.283377i	−0.772552	−	0.634951i	$-0.781020\pi$
$857$	4.78954	−	8.29572i	0.163608	−	0.283377i	0.936160	+	0.351574i	$0.114354\pi$
$858$	−12.0813	+	20.9254i	−0.412448	+	0.714382i
$859$	−3.08712	−	5.34705i	−0.105331	−	0.182439i	0.808542	−	0.588438i	$-0.200257\pi$
$859$	−3.08712	−	5.34705i	−0.105331	−	0.182439i	−0.913873	+	0.405999i	$0.866924\pi$
$860$	−5.18168			−0.176694
$861$		0			0
$862$	−31.7059			−1.07991
$863$	−12.4302	−	21.5297i	−0.423128	−	0.732880i	0.573115	−	0.819475i	$-0.305735\pi$
$863$	−12.4302	−	21.5297i	−0.423128	−	0.732880i	−0.996244	+	0.0865949i	$0.972401\pi$
$864$	60.8246	−	105.351i	2.06929	−	3.58412i
$865$	6.86388	−	11.8886i	0.233379	−	0.404224i
$866$	28.7958	+	49.8758i	0.978521	+	1.69485i
$867$	−19.3730			−0.657943
$868$		0			0
$869$	−36.4590			−1.23679
$870$	4.59547	+	7.95959i	0.155801	+	0.269855i
$871$	−3.83159	+	6.63651i	−0.129828	+	0.224870i
$872$	−2.99417	+	5.18606i	−0.101395	+	0.175622i
$873$	−29.2289	−	50.6259i	−0.989248	−	1.71343i
$874$	−52.7421			−1.78403
$875$		0			0
$876$	−77.1924			−2.60809
$877$	−12.8281	−	22.2189i	−0.433173	−	0.750278i	0.563971	−	0.825794i	$-0.309273\pi$
$877$	−12.8281	−	22.2189i	−0.433173	−	0.750278i	−0.997145	+	0.0755161i	$0.975940\pi$
$878$	−17.9129	+	31.0260i	−0.604530	+	1.04708i
$879$	−45.0719	+	78.0669i	−1.52024	+	2.63313i
$880$	7.98210	+	13.8254i	0.269076	+	0.466054i
$881$	25.6632			0.864615			0.432307	−	0.901726i	$-0.357700\pi$
$881$	25.6632			0.864615			0.432307	+	0.901726i	$0.357700\pi$
$882$		0			0
$883$	48.6682			1.63782			0.818908	−	0.573925i	$-0.194580\pi$
$883$	48.6682			1.63782			0.818908	+	0.573925i	$0.194580\pi$
$884$	2.48270	+	4.30016i	0.0835021	+	0.144630i
$885$	4.03924	−	6.99617i	0.135778	−	0.235174i
$886$	32.0778	−	55.5603i	1.07767	−	1.86659i
$887$	8.76237	+	15.1769i	0.294212	+	0.509590i	0.974801	−	0.223075i	$-0.0716096\pi$
$887$	8.76237	+	15.1769i	0.294212	+	0.509590i	−0.680589	+	0.732665i	$0.738276\pi$
$888$	15.6205			0.524190
$889$		0			0
$890$	−0.675874			−0.0226554
$891$	65.4208	+	113.312i	2.19168	+	3.79610i
$892$	4.32324	−	7.48807i	0.144753	−	0.250719i
$893$	−9.82787	+	17.0224i	−0.328877	+	0.569632i
$894$	7.79578	+	13.5027i	0.260730	+	0.451598i
$895$	17.7266			0.592534
$896$		0			0
$897$	17.5807			0.587002
$898$	−27.6453	−	47.8830i	−0.922535	−	1.59788i
$899$	6.42102	−	11.1215i	0.214153	−	0.370924i
$900$	25.8817	−	44.8284i	0.862724	−	1.49428i
$901$	0.360161	+	0.623817i	0.0119987	+	0.0207824i
$902$	−29.3598			−0.977573
$903$		0			0
$904$	−9.92839			−0.330213
$905$	2.85061	+	4.93740i	0.0947575	+	0.164125i
$906$	10.1926	−	17.6540i	0.338625	−	0.586516i
$907$	−28.6882	+	49.6895i	−0.952577	+	1.64991i	−0.212760	+	0.977104i	$0.568245\pi$
$907$	−28.6882	+	49.6895i	−0.952577	+	1.64991i	−0.739817	+	0.672808i	$0.765088\pi$
$908$	−11.6632	−	20.2012i	−0.387056	−	0.670401i
$909$	115.963			3.84626
$910$		0			0
$911$	7.87203			0.260812			0.130406	−	0.991461i	$-0.458372\pi$
$911$	7.87203			0.260812			0.130406	+	0.991461i	$0.458372\pi$
$912$	42.9716	+	74.4291i	1.42293	+	2.46459i
$913$	7.92415	−	13.7250i	0.262251	−	0.454232i
$914$	15.8993	−	27.5384i	0.525902	−	0.910889i
$915$	−13.1038	−	22.6965i	−0.433199	−	0.750323i
$916$	13.1638			0.434944
$917$		0			0
$918$	109.150			3.60248
$919$	23.5115	+	40.7231i	0.775572	+	1.34333i	0.934472	+	0.356036i	$0.115872\pi$
$919$	23.5115	+	40.7231i	0.775572	+	1.34333i	−0.158900	+	0.987295i	$0.550795\pi$
$920$	2.19495	−	3.80177i	0.0723655	−	0.125341i
$921$	−25.3812	+	43.9615i	−0.836339	+	1.44858i
$922$	−14.1159	−	24.4495i	−0.464882	−	0.805200i
$923$	−4.90081			−0.161312
$924$		0			0
$925$	20.5328			0.675115
$926$	−24.3746	−	42.2180i	−0.800997	−	1.38737i
$927$	−69.2547	+	119.953i	−2.27462	+	3.93977i
$928$	5.91288	−	10.2414i	0.194100	−	0.336191i
$929$	−14.1309	−	24.4754i	−0.463619	−	0.803012i	0.535519	−	0.844523i	$-0.320116\pi$
$929$	−14.1309	−	24.4754i	−0.463619	−	0.803012i	−0.999138	+	0.0415111i	$0.986783\pi$
$930$	40.9475			1.34272
$931$		0			0
$932$	−17.4827			−0.572665
$933$	7.10815	+	12.3117i	0.232710	+	0.403066i
$934$	−21.3854	+	37.0406i	−0.699753	+	1.21201i
$935$	−5.60755	+	9.71255i	−0.183386	+	0.317635i
$936$	−3.96539	−	6.86826i	−0.129613	−	0.224496i
$937$	8.83784			0.288720			0.144360	−	0.989525i	$-0.453888\pi$
$937$	8.83784			0.288720			0.144360	+	0.989525i	$0.453888\pi$
$938$		0			0
$939$	−60.1238			−1.96206
$940$	2.34457	+	4.06092i	0.0764716	+	0.132453i
$941$	21.3927	−	37.0532i	0.697381	−	1.20790i	−0.271991	−	0.962300i	$-0.587682\pi$
$941$	21.3927	−	37.0532i	0.697381	−	1.20790i	0.969371	−	0.245599i	$-0.0789847\pi$
$942$	−2.25090	+	3.89867i	−0.0733382	+	0.127026i
$943$	10.6811	+	18.5002i	0.347824	+	0.602449i
$944$	−13.2757			−0.432086
$945$		0			0
$946$	−29.1101			−0.946450
$947$	−14.6107	−	25.3064i	−0.474783	−	0.822348i	0.524800	−	0.851226i	$-0.324140\pi$
$947$	−14.6107	−	25.3064i	−0.474783	−	0.822348i	−0.999583	+	0.0288774i	$0.990807\pi$
$948$	−23.4123	+	40.5513i	−0.760396	+	1.31704i
$949$	−7.77304	+	13.4633i	−0.252324	+	0.437037i
$950$	21.3477	+	36.9753i	0.692611	+	1.19964i
$951$	−51.1256			−1.65786
$952$		0			0
$953$	3.66198			0.118623			0.0593116	−	0.998240i	$-0.481109\pi$
$953$	3.66198			0.118623			0.0593116	+	0.998240i	$0.481109\pi$
$954$	1.64879	+	2.85579i	0.0533816	+	0.0924596i
$955$	5.52162	−	9.56373i	0.178676	−	0.309475i
$956$	11.9129	−	20.6337i	0.385290	−	0.667342i
$957$	10.9910	+	19.0371i	0.355290	+	0.615381i
$958$	65.6741			2.12183
$959$		0			0
$960$	10.0507			0.324385
$961$	−13.1069	−	22.7019i	−0.422805	−	0.732319i
$962$	−4.50835	+	7.80870i	−0.145355	+	0.251762i
$963$	−41.8168	+	72.4288i	−1.34753	+	2.33399i
$964$	3.65886	+	6.33733i	0.117844	+	0.204112i
$965$	−1.96419			−0.0632296
$966$		0			0
$967$	−30.0288			−0.965660			−0.482830	−	0.875714i	$-0.660391\pi$
$967$	−30.0288			−0.965660			−0.482830	+	0.875714i	$0.660391\pi$
$968$	1.90544	+	3.30031i	0.0612431	+	0.106076i
$969$	−30.1882	+	52.2876i	−0.969786	+	1.67972i
$970$	5.75142	−	9.96175i	0.184667	−	0.319852i
$971$	2.45272	+	4.24823i	0.0787115	+	0.136332i	0.902694	−	0.430283i	$-0.141586\pi$
$971$	2.45272	+	4.24823i	0.0787115	+	0.136332i	−0.823983	+	0.566615i	$0.808253\pi$
$972$	90.3562			2.89818
$973$		0			0
$974$	−52.8153			−1.69231
$975$	−7.11590	−	12.3251i	−0.227891	−	0.394719i
$976$	−21.5340	+	37.2980i	−0.689287	+	1.19388i
$977$	−11.3166	+	19.6009i	−0.362050	+	0.627089i	−0.988298	−	0.152535i	$-0.951256\pi$
$977$	−11.3166	+	19.6009i	−0.362050	+	0.627089i	0.626248	+	0.779624i	$0.284590\pi$
$978$	−4.06922	−	7.04809i	−0.130119	−	0.225373i
$979$	−1.61650			−0.0516635
$980$		0			0
$981$	−50.9584			−1.62698
$982$	−7.69779	−	13.3330i	−0.245646	−	0.425472i
$983$	−28.7026	+	49.7144i	−0.915472	+	1.58564i	−0.109262	+	0.994013i	$0.534849\pi$
$983$	−28.7026	+	49.7144i	−0.915472	+	1.58564i	−0.806209	+	0.591630i	$0.798484\pi$
$984$	6.57788	−	11.3932i	0.209695	−	0.363203i
$985$	−8.09800	−	14.0261i	−0.258024	−	0.446910i
$986$	10.6107			0.337913
$987$		0			0
$988$	−7.98210			−0.253944
$989$	10.5902	+	18.3428i	0.336750	+	0.583268i
$990$	−25.6709	+	44.4634i	−0.815876	+	1.41314i
$991$	−15.5896	+	27.0021i	−0.495221	+	0.857749i	−0.999985	−	0.00550916i	$-0.998246\pi$
$991$	−15.5896	+	27.0021i	−0.495221	+	0.857749i	0.504763	+	0.863258i	$0.331580\pi$
$992$	−26.3431	−	45.6275i	−0.836393	−	1.44868i
$993$	57.8234			1.83497
$994$		0			0
$995$	17.2525			0.546941
$996$	−10.1771	−	17.6272i	−0.322472	−	0.558538i
$997$	−18.0288	+	31.2268i	−0.570977	+	0.988961i	0.425489	+	0.904964i	$0.360102\pi$
$997$	−18.0288	+	31.2268i	−0.570977	+	0.988961i	−0.996466	+	0.0839978i	$0.973231\pi$
$998$	15.6075	−	27.0331i	0.494048	−	0.855717i
$999$	42.1914	+	73.0776i	1.33488	+	2.31207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.k.508.1		6
7.2	even	3	inner	637.2.e.k.79.1		6
7.3	odd	6		637.2.a.h.1.3	✓	3
7.4	even	3		637.2.a.i.1.3	yes	3
7.5	odd	6		637.2.e.l.79.1		6
7.6	odd	2		637.2.e.l.508.1		6
21.11	odd	6		5733.2.a.bd.1.1		3
21.17	even	6		5733.2.a.be.1.1		3
91.25	even	6		8281.2.a.bk.1.1		3
91.38	odd	6		8281.2.a.bh.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.h.1.3	✓	3	7.3	odd	6
637.2.a.i.1.3	yes	3	7.4	even	3
637.2.e.k.79.1		6	7.2	even	3	inner
637.2.e.k.508.1		6	1.1	even	1	trivial
637.2.e.l.79.1		6	7.5	odd	6
637.2.e.l.508.1		6	7.6	odd	2
5733.2.a.bd.1.1		3	21.11	odd	6
5733.2.a.be.1.1		3	21.17	even	6
8281.2.a.bh.1.1		3	91.38	odd	6
8281.2.a.bk.1.1		3	91.25	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.933099 - 1.61618i) q^{2} +(-1.67445 + 2.90023i) q^{3} +(-0.741348 + 1.28405i) q^{4} +(0.433099 + 0.750150i) q^{5} +6.24970 q^{6} -0.965392 q^{8} +(-4.10755 - 7.11448i) q^{9} +O(q^{10})\)	\(q+(-0.933099 - 1.61618i) q^{2} +(-1.67445 + 2.90023i) q^{3} +(-0.741348 + 1.28405i) q^{4} +(0.433099 + 0.750150i) q^{5} +6.24970 q^{6} -0.965392 q^{8} +(-4.10755 - 7.11448i) q^{9} +(0.808249 - 1.39993i) q^{10} +(1.93310 - 3.34823i) q^{11} +(-2.48270 - 4.30016i) q^{12} -1.00000 q^{13} -2.90081 q^{15} +(2.38350 + 4.12835i) q^{16} +(-1.67445 + 2.90023i) q^{17} +(-7.66550 + 13.2770i) q^{18} +(-2.69175 - 4.66225i) q^{19} -1.28431 q^{20} -7.21509 q^{22} +(2.62485 + 4.54637i) q^{23} +(1.61650 - 2.79986i) q^{24} +(2.12485 - 3.68035i) q^{25} +(0.933099 + 1.61618i) q^{26} +17.4648 q^{27} +1.69779 q^{29} +(2.70674 + 4.68821i) q^{30} +(3.78199 - 6.55060i) q^{31} +(3.48270 - 6.03221i) q^{32} +(6.47374 + 11.2129i) q^{33} +6.24970 q^{34} +12.1805 q^{36} +(2.41580 + 4.18428i) q^{37} +(-5.02334 + 8.70068i) q^{38} +(1.67445 - 2.90023i) q^{39} +(-0.418110 - 0.724188i) q^{40} +4.06922 q^{41} +4.03461 q^{43} +(2.86620 + 4.96440i) q^{44} +(3.55795 - 6.16255i) q^{45} +(4.89849 - 8.48444i) q^{46} +(-1.82555 - 3.16195i) q^{47} -15.9642 q^{48} -7.93078 q^{50} +(-5.60755 - 9.71255i) q^{51} +(0.741348 - 1.28405i) q^{52} +(0.107546 - 0.186276i) q^{53} +(-16.2964 - 28.2262i) q^{54} +3.34889 q^{55} +18.0288 q^{57} +(-1.58420 - 2.74392i) q^{58} +(-1.39245 + 2.41180i) q^{59} +(2.15051 - 3.72479i) q^{60} +(4.51730 + 7.82420i) q^{61} -14.1159 q^{62} -3.46479 q^{64} +(-0.433099 - 0.750150i) q^{65} +(12.0813 - 20.9254i) q^{66} +(3.83159 - 6.63651i) q^{67} +(-2.48270 - 4.30016i) q^{68} -17.5807 q^{69} +4.90081 q^{71} +(3.96539 + 6.86826i) q^{72} +(7.77304 - 13.4633i) q^{73} +(4.50835 - 7.80870i) q^{74} +(7.11590 + 12.3251i) q^{75} +7.98210 q^{76} -6.24970 q^{78} +(-4.71509 - 8.16678i) q^{79} +(-2.06459 + 3.57597i) q^{80} +(-16.9212 + 29.3084i) q^{81} +(-3.79698 - 6.57657i) q^{82} +4.09919 q^{83} -2.90081 q^{85} +(-3.76469 - 6.52063i) q^{86} +(-2.84286 + 4.92397i) q^{87} +(-1.86620 + 3.23235i) q^{88} +(-0.209055 - 0.362094i) q^{89} -13.2797 q^{90} -7.78371 q^{92} +(12.6655 + 21.9373i) q^{93} +(-3.40684 + 5.90083i) q^{94} +(2.33159 - 4.03843i) q^{95} +(11.6632 + 20.2012i) q^{96} +7.11590 q^{97} -31.7612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 5 * q^5 + 4 * q^6 - 12 * q^8 - 11 * q^9	\( 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9} + 14 q^{10} + 4 q^{11} - 18 q^{12} - 6 q^{13} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 7 q^{19} + 32 q^{20} - 16 q^{22} - q^{23} + 28 q^{24} - 4 q^{25} - 2 q^{26} + 44 q^{27} - 14 q^{29} + 24 q^{30} + 3 q^{31} + 24 q^{32} + 10 q^{33} + 4 q^{34} + 52 q^{36} + 10 q^{37} - 12 q^{38} + 4 q^{39} + 22 q^{40} + 12 q^{41} + 18 q^{43} + 2 q^{44} - 3 q^{45} + 28 q^{46} - 17 q^{47} + 32 q^{48} - 60 q^{50} - 20 q^{51} + 6 q^{52} - 13 q^{53} - 28 q^{54} + 8 q^{55} + 8 q^{57} - 14 q^{58} - 22 q^{59} - 42 q^{60} + 24 q^{61} - 36 q^{62} + 40 q^{64} + 5 q^{65} + 30 q^{66} + 14 q^{67} - 18 q^{68} + 4 q^{69} + 8 q^{71} + 30 q^{72} - 5 q^{73} - 8 q^{74} - 6 q^{75} - 16 q^{76} - 4 q^{78} - q^{79} - 40 q^{80} - 15 q^{81} - 20 q^{82} + 46 q^{83} + 4 q^{85} - 6 q^{86} - 20 q^{87} + 4 q^{88} + 11 q^{89} - 80 q^{90} + 60 q^{92} + 38 q^{93} + 16 q^{94} + 5 q^{95} + 52 q^{96} - 6 q^{97} - 60 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 5 * q^5 + 4 * q^6 - 12 * q^8 - 11 * q^9 + 14 * q^10 + 4 * q^11 - 18 * q^12 - 6 * q^13 + 4 * q^15 - 4 * q^16 - 4 * q^17 - 8 * q^18 - 7 * q^19 + 32 * q^20 - 16 * q^22 - q^23 + 28 * q^24 - 4 * q^25 - 2 * q^26 + 44 * q^27 - 14 * q^29 + 24 * q^30 + 3 * q^31 + 24 * q^32 + 10 * q^33 + 4 * q^34 + 52 * q^36 + 10 * q^37 - 12 * q^38 + 4 * q^39 + 22 * q^40 + 12 * q^41 + 18 * q^43 + 2 * q^44 - 3 * q^45 + 28 * q^46 - 17 * q^47 + 32 * q^48 - 60 * q^50 - 20 * q^51 + 6 * q^52 - 13 * q^53 - 28 * q^54 + 8 * q^55 + 8 * q^57 - 14 * q^58 - 22 * q^59 - 42 * q^60 + 24 * q^61 - 36 * q^62 + 40 * q^64 + 5 * q^65 + 30 * q^66 + 14 * q^67 - 18 * q^68 + 4 * q^69 + 8 * q^71 + 30 * q^72 - 5 * q^73 - 8 * q^74 - 6 * q^75 - 16 * q^76 - 4 * q^78 - q^79 - 40 * q^80 - 15 * q^81 - 20 * q^82 + 46 * q^83 + 4 * q^85 - 6 * q^86 - 20 * q^87 + 4 * q^88 + 11 * q^89 - 80 * q^90 + 60 * q^92 + 38 * q^93 + 16 * q^94 + 5 * q^95 + 52 * q^96 - 6 * q^97 - 60 * q^99

Introduction

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