LMFDB - Embedded newform 207.2.i.b.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	207.127
Dual form			207.2.i.b.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.402869 - 0.258908i) q^{2} +(-0.735560 + 1.61065i) q^{4} +(-3.37102 + 0.989821i) q^{5} +(0.527646 + 0.608936i) q^{7} +(0.256983 + 1.78736i) q^{8} +(-1.10181 + 1.27155i) q^{10} +(2.98325 + 1.91722i) q^{11} +(-4.32972 + 4.99677i) q^{13} +(0.370231 + 0.108710i) q^{14} +(-1.75278 - 2.02282i) q^{16} +(-0.387956 - 0.849505i) q^{17} +(1.55773 - 3.41095i) q^{19} +(0.885331 - 6.15762i) q^{20} +1.69824 q^{22} +(4.71737 + 0.863983i) q^{23} +(6.17778 - 3.97022i) q^{25} +(-0.450608 + 3.13404i) q^{26} +(-1.36890 + 0.401945i) q^{28} +(-0.657326 - 1.43934i) q^{29} +(-0.0804100 - 0.559264i) q^{31} +(-4.69505 - 1.37859i) q^{32} +(-0.376239 - 0.241794i) q^{34} +(-2.38145 - 1.53046i) q^{35} +(7.84580 + 2.30374i) q^{37} +(-0.255563 - 1.77748i) q^{38} +(-2.63546 - 5.77086i) q^{40} +(-3.65843 + 1.07421i) q^{41} +(-0.975753 + 6.78651i) q^{43} +(-5.28234 + 3.39475i) q^{44} +(2.12417 - 0.873293i) q^{46} +5.69427 q^{47} +(0.903811 - 6.28614i) q^{49} +(1.46091 - 3.19895i) q^{50} +(-4.86328 - 10.6491i) q^{52} +(4.57100 + 5.27521i) q^{53} +(-11.9543 - 3.51011i) q^{55} +(-0.952791 + 1.09958i) q^{56} +(-0.637474 - 0.409680i) q^{58} +(0.663766 - 0.766027i) q^{59} +(1.74697 + 12.1505i) q^{61} +(-0.177193 - 0.204491i) q^{62} +(2.88789 - 0.847960i) q^{64} +(9.64969 - 21.1299i) q^{65} +(2.09309 - 1.34515i) q^{67} +1.65362 q^{68} -1.35566 q^{70} +(-11.1508 + 7.16620i) q^{71} +(2.78441 - 6.09701i) q^{73} +(3.75729 - 1.10324i) q^{74} +(4.34805 + 5.01792i) q^{76} +(0.406637 + 2.82823i) q^{77} +(-0.940694 + 1.08562i) q^{79} +(7.91090 + 5.08403i) q^{80} +(-1.19575 + 1.37997i) q^{82} +(-1.68020 - 0.493351i) q^{83} +(2.14867 + 2.47969i) q^{85} +(1.36398 + 2.98671i) q^{86} +(-2.66011 + 5.82484i) q^{88} +(-0.667422 + 4.64202i) q^{89} -5.32728 q^{91} +(-4.86148 + 6.96252i) q^{92} +(2.29404 - 1.47429i) q^{94} +(-1.87491 + 13.0403i) q^{95} +(-0.762432 + 0.223870i) q^{97} +(-1.26342 - 2.76650i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} - 5 q^{5} - 8 q^{7} + 15 q^{8} - 2 q^{10} - 7 q^{11} - 30 q^{13} - q^{14} + 12 q^{16} + 2 q^{17} + 10 q^{19} - 4 q^{20} + 6 q^{22} + q^{23} + 24 q^{25} - q^{26} + 9 q^{28} + 14 q^{29}+ \cdots - 58 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 - 5 * q^5 - 8 * q^7 + 15 * q^8 - 2 * q^10 - 7 * q^11 - 30 * q^13 - q^14 + 12 * q^16 + 2 * q^17 + 10 * q^19 - 4 * q^20 + 6 * q^22 + q^23 + 24 * q^25 - q^26 + 9 * q^28 + 14 * q^29 - 28 * q^31 - 23 * q^32 - 8 * q^34 + 4 * q^35 + 19 * q^37 + 15 * q^38 - 13 * q^40 - 19 * q^41 - 24 * q^43 - 54 * q^44 + 18 * q^46 - 26 * q^47 - 13 * q^49 + 36 * q^50 - 57 * q^52 + q^53 - 24 * q^55 + 10 * q^56 + 10 * q^58 - 2 * q^59 + 30 * q^61 + 24 * q^62 + 13 * q^64 + 4 * q^65 + 4 * q^67 + 50 * q^68 + 6 * q^70 + 14 * q^71 - 26 * q^73 + 12 * q^74 + 19 * q^76 + 43 * q^77 + 20 * q^79 + 5 * q^80 + 10 * q^82 - 18 * q^83 + 21 * q^85 - 14 * q^86 - 38 * q^88 + 5 * q^89 + 46 * q^91 - 52 * q^92 - 6 * q^94 - 5 * q^95 + 15 * q^97 - 58 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.402869	−	0.258908i	0.284871	−	0.183076i	−0.390399	−	0.920646i	$-0.627663\pi$
$2$	0.402869	−	0.258908i	0.284871	−	0.183076i	0.675271	+	0.737570i	$0.264027\pi$
$3$		0			0
$3$		0			0
$4$	−0.735560	+	1.61065i	−0.367780	+	0.805326i
$5$	−3.37102	+	0.989821i	−1.50757	+	0.442662i	−0.928099	−	0.372333i	$-0.878558\pi$
$5$	−3.37102	+	0.989821i	−1.50757	+	0.442662i	−0.579468	+	0.814995i	$0.696740\pi$
$6$		0			0
$7$	0.527646	+	0.608936i	0.199432	+	0.230156i	0.846652	−	0.532146i	$-0.178614\pi$
$7$	0.527646	+	0.608936i	0.199432	+	0.230156i	−0.647221	+	0.762302i	$0.724069\pi$
$8$	0.256983	+	1.78736i	0.0908573	+	0.631927i
$9$		0			0
$10$	−1.10181	+	1.27155i	−0.348422	+	0.402101i
$11$	2.98325	+	1.91722i	0.899485	+	0.578064i	0.906637	−	0.421911i	$-0.138640\pi$
$11$	2.98325	+	1.91722i	0.899485	+	0.578064i	−0.00715262	+	0.999974i	$0.502277\pi$
$12$		0			0
$13$	−4.32972	+	4.99677i	−1.20085	+	1.38585i	−0.298747	+	0.954332i	$0.596569\pi$
$13$	−4.32972	+	4.99677i	−1.20085	+	1.38585i	−0.902103	+	0.431522i	$0.857977\pi$
$14$	0.370231	+	0.108710i	0.0989484	+	0.0290539i
$15$		0			0
$16$	−1.75278	−	2.02282i	−0.438196	−	0.505705i
$17$	−0.387956	−	0.849505i	−0.0940931	−	0.206035i	0.856733	−	0.515760i	$-0.172490\pi$
$17$	−0.387956	−	0.849505i	−0.0940931	−	0.206035i	−0.950826	+	0.309725i	$0.899763\pi$
$18$		0			0
$19$	1.55773	−	3.41095i	0.357368	−	0.782526i	−0.642500	−	0.766285i	$-0.722103\pi$
$19$	1.55773	−	3.41095i	0.357368	−	0.782526i	0.999868	−	0.0162408i	$-0.00516984\pi$
$20$	0.885331	−	6.15762i	0.197966	−	1.37688i
$21$		0			0
$22$	1.69824			0.362067
$23$	4.71737	+	0.863983i	0.983639	+	0.180153i
$23$	4.71737	+	0.863983i	0.983639	+	0.180153i
$24$		0			0
$25$	6.17778	−	3.97022i	1.23556	−	0.794043i
$26$	−0.450608	+	3.13404i	−0.0883714	+	0.614637i
$27$		0			0
$28$	−1.36890	+	0.401945i	−0.258698	+	0.0759605i
$29$	−0.657326	−	1.43934i	−0.122062	−	0.267279i	0.838730	−	0.544547i	$-0.183298\pi$
$29$	−0.657326	−	1.43934i	−0.122062	−	0.267279i	−0.960793	+	0.277268i	$0.910571\pi$
$30$		0			0
$31$	−0.0804100	−	0.559264i	−0.0144421	−	0.100447i	0.981325	−	0.192355i	$-0.0616125\pi$
$31$	−0.0804100	−	0.559264i	−0.0144421	−	0.100447i	−0.995767	+	0.0919082i	$0.970703\pi$
$32$	−4.69505	−	1.37859i	−0.829976	−	0.243703i
$33$		0			0
$34$	−0.376239	−	0.241794i	−0.0645245	−	0.0414674i
$35$	−2.38145	−	1.53046i	−0.402538	−	0.258695i
$36$		0			0
$37$	7.84580	+	2.30374i	1.28984	+	0.378732i	0.853521	−	0.521059i	$-0.174463\pi$
$37$	7.84580	+	2.30374i	1.28984	+	0.378732i	0.436321	+	0.899791i	$0.356281\pi$
$38$	−0.255563	−	1.77748i	−0.0414577	−	0.288345i
$39$		0			0
$40$	−2.63546	−	5.77086i	−0.416703	−	0.912453i
$41$	−3.65843	+	1.07421i	−0.571351	+	0.167764i	−0.554631	−	0.832096i	$-0.687141\pi$
$41$	−3.65843	+	1.07421i	−0.571351	+	0.167764i	−0.0167200	+	0.999860i	$0.505322\pi$
$42$		0			0
$43$	−0.975753	+	6.78651i	−0.148801	+	1.03493i	0.769386	+	0.638785i	$0.220562\pi$
$43$	−0.975753	+	6.78651i	−0.148801	+	1.03493i	−0.918187	+	0.396148i	$0.870347\pi$
$44$	−5.28234	+	3.39475i	−0.796342	+	0.511778i
$45$		0			0
$46$	2.12417	−	0.873293i	0.313192	−	0.128760i
$47$	5.69427			0.830594			0.415297	−	0.909686i	$-0.363678\pi$
$47$	5.69427			0.830594			0.415297	+	0.909686i	$0.363678\pi$
$48$		0			0
$49$	0.903811	−	6.28614i	0.129116	−	0.898021i
$50$	1.46091	−	3.19895i	0.206604	−	0.452401i
$51$		0			0
$52$	−4.86328	−	10.6491i	−0.674416	−	1.47676i
$53$	4.57100	+	5.27521i	0.627875	+	0.724606i	0.977182	−	0.212402i	$-0.0681286\pi$
$53$	4.57100	+	5.27521i	0.627875	+	0.724606i	−0.349308	+	0.937008i	$0.613583\pi$
$54$		0			0
$55$	−11.9543	−	3.51011i	−1.61192	−	0.473302i
$56$	−0.952791	+	1.09958i	−0.127322	+	0.146938i
$57$		0			0
$58$	−0.637474	−	0.409680i	−0.0837044	−	0.0537936i
$59$	0.663766	−	0.766027i	0.0864150	−	0.0997282i	−0.710895	−	0.703298i	$-0.751710\pi$
$59$	0.663766	−	0.766027i	0.0864150	−	0.0997282i	0.797310	+	0.603570i	$0.206255\pi$
$60$		0			0
$61$	1.74697	+	12.1505i	0.223677	+	1.55571i	0.723958	+	0.689844i	$0.242321\pi$
$61$	1.74697	+	12.1505i	0.223677	+	1.55571i	−0.500281	+	0.865863i	$0.666770\pi$
$62$	−0.177193	−	0.204491i	−0.0225035	−	0.0259704i
$63$		0			0
$64$	2.88789	−	0.847960i	0.360986	−	0.105995i
$65$	9.64969	−	21.1299i	1.19690	−	2.62084i
$66$		0			0
$67$	2.09309	−	1.34515i	0.255712	−	0.164336i	−0.406504	−	0.913649i	$-0.633252\pi$
$67$	2.09309	−	1.34515i	0.255712	−	0.164336i	0.662216	+	0.749313i	$0.269616\pi$
$68$	1.65362			0.200531
$69$		0			0
$70$	−1.35566			−0.162032
$71$	−11.1508	+	7.16620i	−1.32336	+	0.850471i	−0.995547	−	0.0942715i	$-0.969948\pi$
$71$	−11.1508	+	7.16620i	−1.32336	+	0.850471i	−0.327813	+	0.944743i	$0.606311\pi$
$72$		0			0
$73$	2.78441	−	6.09701i	0.325891	−	0.713601i	−0.673789	−	0.738924i	$-0.735334\pi$
$73$	2.78441	−	6.09701i	0.325891	−	0.713601i	0.999679	+	0.0253229i	$0.00806139\pi$
$74$	3.75729	−	1.10324i	0.436776	−	0.128249i
$75$		0			0
$76$	4.34805	+	5.01792i	0.498756	+	0.575595i
$77$	0.406637	+	2.82823i	0.0463406	+	0.322306i
$78$		0			0
$79$	−0.940694	+	1.08562i	−0.105836	+	0.122142i	−0.806196	−	0.591648i	$-0.798477\pi$
$79$	−0.940694	+	1.08562i	−0.105836	+	0.122142i	0.700360	+	0.713790i	$0.253023\pi$
$80$	7.91090	+	5.08403i	0.884465	+	0.568411i
$81$		0			0
$82$	−1.19575	+	1.37997i	−0.132048	+	0.152392i
$83$	−1.68020	−	0.493351i	−0.184426	−	0.0541523i	0.188216	−	0.982128i	$-0.439730\pi$
$83$	−1.68020	−	0.493351i	−0.184426	−	0.0541523i	−0.372641	+	0.927975i	$0.621548\pi$
$84$		0			0
$85$	2.14867	+	2.47969i	0.233055	+	0.268960i
$86$	1.36398	+	2.98671i	0.147082	+	0.322065i
$87$		0			0
$88$	−2.66011	+	5.82484i	−0.283569	+	0.620930i
$89$	−0.667422	+	4.64202i	−0.0707466	+	0.492053i	0.923385	+	0.383875i	$0.125411\pi$
$89$	−0.667422	+	4.64202i	−0.0707466	+	0.492053i	−0.994132	+	0.108178i	$0.965498\pi$
$90$		0			0
$91$	−5.32728			−0.558450
$92$	−4.86148	+	6.96252i	−0.506844	+	0.725893i
$93$		0			0
$94$	2.29404	−	1.47429i	0.236613	−	0.152062i
$95$	−1.87491	+	13.0403i	−0.192362	+	1.33790i
$96$		0			0
$97$	−0.762432	+	0.223870i	−0.0774132	+	0.0227306i	−0.320210	−	0.947347i	$-0.603753\pi$
$97$	−0.762432	+	0.223870i	−0.0774132	+	0.0227306i	0.242797	+	0.970077i	$0.421935\pi$
$98$	−1.26342	−	2.76650i	−0.127624	−	0.279458i
$99$		0			0
$100$	1.85051	+	12.8706i	0.185051	+	1.28706i
$101$	−12.0847	−	3.54840i	−1.20248	−	0.353079i	−0.381678	−	0.924295i	$-0.624654\pi$
$101$	−12.0847	−	3.54840i	−1.20248	−	0.353079i	−0.820800	+	0.571216i	$0.806472\pi$
$102$		0			0
$103$	8.91245	+	5.72768i	0.878169	+	0.564365i	0.900241	−	0.435391i	$-0.143390\pi$
$103$	8.91245	+	5.72768i	0.878169	+	0.564365i	−0.0220720	+	0.999756i	$0.507026\pi$
$104$	−10.0437	−	6.45468i	−0.984864	−	0.632934i
$105$		0			0
$106$	3.20731	+	0.941751i	0.311521	+	0.0914709i
$107$	−0.913569	−	6.35401i	−0.0883181	−	0.614266i	−0.985124	−	0.171842i	$-0.945028\pi$
$107$	−0.913569	−	6.35401i	−0.0883181	−	0.614266i	0.896806	−	0.442423i	$-0.145881\pi$
$108$		0			0
$109$	−0.487454	−	1.06738i	−0.0466896	−	0.102236i	0.884850	−	0.465877i	$-0.154261\pi$
$109$	−0.487454	−	1.06738i	−0.0466896	−	0.102236i	−0.931539	+	0.363641i	$0.881534\pi$
$110$	−5.72482	+	1.68096i	−0.545840	+	0.160273i
$111$		0			0
$112$	0.306919	−	2.13467i	0.0290011	−	0.201707i
$113$	14.5204	−	9.33173i	1.36597	−	0.877855i	0.367334	−	0.930089i	$-0.380271\pi$
$113$	14.5204	−	9.33173i	1.36597	−	0.877855i	0.998635	+	0.0522342i	$0.0166342\pi$
$114$		0			0
$115$	−16.7575	+	1.75684i	−1.56265	+	0.163826i
$116$	2.80178			0.260139
$117$		0			0
$118$	0.0690802	−	0.480463i	0.00635934	−	0.0442302i
$119$	0.312591	−	0.684478i	0.0286552	−	0.0627460i
$120$		0			0
$121$	0.654502	+	1.43316i	0.0595002	+	0.130287i
$122$	3.84966	+	4.44274i	0.348531	+	0.402227i
$123$		0			0
$124$	0.959925	+	0.281859i	0.0862038	+	0.0253117i
$125$	−5.39189	+	6.22257i	−0.482265	+	0.556563i
$126$		0			0
$127$	7.96136	+	5.11646i	0.706457	+	0.454012i	0.843902	−	0.536497i	$-0.180253\pi$
$127$	7.96136	+	5.11646i	0.706457	+	0.454012i	−0.137445	+	0.990509i	$0.543889\pi$
$128$	7.35271	−	8.48548i	0.649894	−	0.750018i
$129$		0			0
$130$	−1.58314	−	11.0110i	−0.138850	−	0.965725i
$131$	8.83379	+	10.1947i	0.771812	+	0.890718i	0.996490	−	0.0837147i	$-0.0266784\pi$
$131$	8.83379	+	10.1947i	0.771812	+	0.890718i	−0.224678	+	0.974433i	$0.572133\pi$
$132$		0			0
$133$	2.89898	−	0.851218i	0.251374	−	0.0738100i
$134$	0.494973	−	1.08384i	0.0427591	−	0.0936294i
$135$		0			0
$136$	1.41867	−	0.911725i	0.121650	−	0.0781797i
$137$	0.768502			0.0656576			0.0328288	−	0.999461i	$-0.489548\pi$
$137$	0.768502			0.0656576			0.0328288	+	0.999461i	$0.489548\pi$
$138$		0			0
$139$	−14.8410			−1.25879			−0.629397	−	0.777084i	$-0.716698\pi$
$139$	−14.8410			−1.25879			−0.629397	+	0.777084i	$0.716698\pi$
$140$	4.21674	−	2.70993i	0.356379	−	0.229031i
$141$		0			0
$142$	−2.63693	+	5.77408i	−0.221287	+	0.484550i
$143$	−22.4966	+	6.60559i	−1.88126	+	0.552387i
$144$		0			0
$145$	3.64055	+	4.20142i	0.302331	+	0.348909i
$146$	−0.456813	−	3.17721i	−0.0378061	−	0.262947i
$147$		0			0
$148$	−9.48157	+	10.9423i	−0.779381	+	0.899453i
$149$	7.81799	+	5.02432i	0.640475	+	0.411608i	0.820175	−	0.572113i	$-0.193876\pi$
$149$	7.81799	+	5.02432i	0.640475	+	0.411608i	−0.179700	+	0.983722i	$0.557513\pi$
$150$		0			0
$151$	5.52469	−	6.37583i	0.449593	−	0.518857i	−0.485031	−	0.874497i	$-0.661192\pi$
$151$	5.52469	−	6.37583i	0.449593	−	0.518857i	0.934623	+	0.355640i	$0.115737\pi$
$152$	6.49691	+	1.90766i	0.526969	+	0.154732i
$153$		0			0
$154$	0.896073	+	1.03412i	0.0722076	+	0.0833320i
$155$	0.824635	+	1.80570i	0.0662363	+	0.145037i
$156$		0			0
$157$	3.89922	−	8.53811i	0.311192	−	0.681415i	−0.687819	−	0.725882i	$-0.741432\pi$
$157$	3.89922	−	8.53811i	0.311192	−	0.681415i	0.999011	+	0.0444670i	$0.0141590\pi$
$158$	−0.0979009	+	0.680916i	−0.00778858	+	0.0541707i
$159$		0			0
$160$	17.1917			1.35912
$161$	1.96299	+	3.32845i	0.154705	+	0.262319i
$162$		0			0
$163$	−14.3998	+	9.25418i	−1.12788	+	0.724843i	−0.965116	−	0.261822i	$-0.915677\pi$
$163$	−14.3998	+	9.25418i	−1.12788	+	0.724843i	−0.162762	+	0.986665i	$0.552040\pi$
$164$	0.960814	−	6.68261i	0.0750270	−	0.521824i
$165$		0			0
$166$	−0.804632	+	0.236261i	−0.0624516	+	0.0183374i
$167$	−4.44222	−	9.72711i	−0.343750	−	0.752707i	0.656249	−	0.754545i	$-0.272142\pi$
$167$	−4.44222	−	9.72711i	−0.343750	−	0.752707i	−0.999998	+	0.00183806i	$0.999415\pi$
$168$		0			0
$169$	−4.37109	−	30.4016i	−0.336237	−	2.33858i
$170$	1.50764	+	0.442684i	0.115631	+	0.0339523i
$171$		0			0
$172$	−10.2130	−	6.56348i	−0.778732	−	0.500461i
$173$	20.3079	+	13.0511i	1.54398	+	0.992255i	0.986815	+	0.161852i	$0.0517468\pi$
$173$	20.3079	+	13.0511i	1.54398	+	0.992255i	0.557164	+	0.830403i	$0.311890\pi$
$174$		0			0
$175$	5.67729	+	1.66700i	0.429163	+	0.126014i
$176$	−1.35080	−	9.39505i	−0.101821	−	0.708179i
$177$		0			0
$178$	0.932974	+	2.04293i	0.0699293	+	0.153124i
$179$	2.50104	−	0.734371i	0.186936	−	0.0548894i	−0.186925	−	0.982374i	$-0.559852\pi$
$179$	2.50104	−	0.734371i	0.186936	−	0.0548894i	0.373861	+	0.927485i	$0.378034\pi$
$180$		0			0
$181$	1.42736	−	9.92752i	0.106095	−	0.737907i	−0.865440	−	0.501012i	$-0.832961\pi$
$181$	1.42736	−	9.92752i	0.106095	−	0.737907i	0.971535	−	0.236895i	$-0.0761296\pi$
$182$	−2.14620	+	1.37928i	−0.159087	+	0.102239i
$183$		0			0
$184$	−0.331964	+	8.65365i	−0.0244727	+	0.637956i
$185$	−28.7287			−2.11217
$186$		0			0
$187$	0.471317	−	3.27808i	0.0344661	−	0.239717i
$188$	−4.18848	+	9.17148i	−0.305476	+	0.668899i
$189$		0			0
$190$	2.62089	+	5.73895i	0.190139	+	0.416347i
$191$	−16.4041	−	18.9313i	−1.18696	−	1.36982i	−0.912938	−	0.408097i	$-0.866192\pi$
$191$	−16.4041	−	18.9313i	−1.18696	−	1.36982i	−0.274019	−	0.961724i	$-0.588353\pi$
$192$		0			0
$193$	0.0958162	+	0.0281342i	0.00689700	+	0.00202514i	0.285179	−	0.958474i	$-0.407947\pi$
$193$	0.0958162	+	0.0281342i	0.00689700	+	0.00202514i	−0.278282	+	0.960499i	$0.589765\pi$
$194$	−0.249198	+	0.287590i	−0.0178914	+	0.0206478i
$195$		0			0
$196$	9.45998	+	6.07956i	0.675713	+	0.434254i
$197$	10.8572	−	12.5299i	0.773543	−	0.892716i	−0.223083	−	0.974800i	$-0.571612\pi$
$197$	10.8572	−	12.5299i	0.773543	−	0.892716i	0.996625	+	0.0820836i	$0.0261575\pi$
$198$		0			0
$199$	−2.85274	−	19.8412i	−0.202225	−	1.40651i	−0.797662	−	0.603104i	$-0.793930\pi$
$199$	−2.85274	−	19.8412i	−0.202225	−	1.40651i	0.595437	−	0.803402i	$-0.296979\pi$
$200$	8.68379	+	10.0216i	0.614036	+	0.708636i
$201$		0			0
$202$	−5.78728	+	1.69930i	−0.407192	+	0.119562i
$203$	0.529632	−	1.15973i	0.0371729	−	0.0813973i
$204$		0			0
$205$	11.2694	−	7.24239i	0.787087	−	0.505830i
$206$	5.07349			0.353487
$207$		0			0
$208$	17.6966			1.22704
$209$	11.1867	−	7.18922i	0.773797	−	0.497289i
$210$		0			0
$211$	−0.964715	+	2.11243i	−0.0664137	+	0.145426i	−0.939928	−	0.341373i	$-0.889108\pi$
$211$	−0.964715	+	2.11243i	−0.0664137	+	0.145426i	0.873514	+	0.486799i	$0.161835\pi$
$212$	−11.8588	+	3.48205i	−0.814464	+	0.239148i
$213$		0			0
$214$	−2.01316	−	2.32331i	−0.137616	−	0.158818i
$215$	−3.42815	−	23.8433i	−0.233798	−	1.62610i
$216$		0			0
$217$	0.298128	−	0.344058i	0.0202382	−	0.0233562i
$218$	−0.472733	−	0.303807i	−0.0320175	−	0.0205764i
$219$		0			0
$220$	14.4467	−	16.6724i	0.973995	−	1.12405i
$221$	5.92452	+	1.73960i	0.398526	+	0.117018i
$222$		0			0
$223$	3.01311	+	3.47732i	0.201773	+	0.232858i	0.847614	−	0.530614i	$-0.178038\pi$
$223$	3.01311	+	3.47732i	0.201773	+	0.232858i	−0.645841	+	0.763472i	$0.723493\pi$
$224$	−1.63785	−	3.58640i	−0.109434	−	0.239626i
$225$		0			0
$226$	3.43378	−	7.51893i	0.228412	−	0.500152i
$227$	1.24145	−	8.63450i	0.0823981	−	0.573092i	−0.906239	−	0.422767i	$-0.861059\pi$
$227$	1.24145	−	8.63450i	0.0823981	−	0.573092i	0.988637	−	0.150325i	$-0.0480320\pi$
$228$		0			0
$229$	−9.31081			−0.615276			−0.307638	−	0.951503i	$-0.599539\pi$
$229$	−9.31081			−0.615276			−0.307638	+	0.951503i	$0.599539\pi$
$230$	−6.29623	+	5.04644i	−0.415161	+	0.332752i
$231$		0			0
$232$	2.40370	−	1.54476i	0.157811	−	0.101419i
$233$	−0.419991	+	2.92111i	−0.0275146	+	0.191368i	−0.998943	−	0.0459644i	$-0.985364\pi$
$233$	−0.419991	+	2.92111i	−0.0275146	+	0.191368i	0.971429	+	0.237332i	$0.0762730\pi$
$234$		0			0
$235$	−19.1955	+	5.63631i	−1.25218	+	0.367672i
$236$	0.745563	+	1.63255i	0.0485320	+	0.106270i
$237$		0			0
$238$	−0.0512839	−	0.356688i	−0.00332424	−	0.0231206i
$239$	−15.7671	−	4.62963i	−1.01989	−	0.299466i	−0.271294	−	0.962496i	$-0.587452\pi$
$239$	−15.7671	−	4.62963i	−1.01989	−	0.299466i	−0.748592	+	0.663031i	$0.769270\pi$
$240$		0			0
$241$	−1.11201	−	0.714643i	−0.0716306	−	0.0460342i	0.504335	−	0.863508i	$-0.331738\pi$
$241$	−1.11201	−	0.714643i	−0.0716306	−	0.0460342i	−0.575966	+	0.817474i	$0.695374\pi$
$242$	0.634735	+	0.407920i	0.0408023	+	0.0262221i
$243$		0			0
$244$	−20.8552	−	6.12363i	−1.33511	−	0.392025i
$245$	3.17539	+	22.0853i	0.202868	+	1.41098i
$246$		0			0
$247$	10.2992	+	22.5521i	0.655322	+	1.43496i
$248$	0.978940	−	0.287443i	0.0621628	−	0.0182526i
$249$		0			0
$250$	−0.561150	+	3.90288i	−0.0354902	+	0.246840i
$251$	15.7308	−	10.1096i	0.992920	−	0.638111i	0.0600015	−	0.998198i	$-0.480889\pi$
$251$	15.7308	−	10.1096i	0.992920	−	0.638111i	0.932919	+	0.360087i	$0.117253\pi$
$252$		0			0
$253$	12.4166	+	11.6217i	0.780628	+	0.730651i
$254$	4.53208			0.284368
$255$		0			0
$256$	−0.0914606	+	0.636123i	−0.00571629	+	0.0397577i
$257$	−2.62732	+	5.75302i	−0.163888	+	0.358864i	−0.973703	−	0.227821i	$-0.926840\pi$
$257$	−2.62732	+	5.75302i	−0.163888	+	0.358864i	0.809816	+	0.586685i	$0.199567\pi$
$258$		0			0
$259$	2.73698	+	5.99315i	0.170068	+	0.372396i
$260$	26.9349	+	31.0846i	1.67043	+	1.92778i
$261$		0			0
$262$	6.19836	+	1.82000i	0.382936	+	0.112440i
$263$	−15.9658	+	18.4255i	−0.984491	+	1.13616i	0.00619241	+	0.999981i	$0.498029\pi$
$263$	−15.9658	+	18.4255i	−0.984491	+	1.13616i	−0.990684	+	0.136183i	$0.956517\pi$
$264$		0			0
$265$	−20.6305	−	13.2584i	−1.26732	−	0.814456i
$266$	0.947523	−	1.09350i	0.0580964	−	0.0670468i
$267$		0			0
$268$	0.626972	+	4.36068i	0.0382984	+	0.266371i
$269$	−8.87170	−	10.2385i	−0.540917	−	0.624252i	0.417825	−	0.908527i	$-0.362792\pi$
$269$	−8.87170	−	10.2385i	−0.540917	−	0.624252i	−0.958743	+	0.284276i	$0.908247\pi$
$270$		0			0
$271$	−10.6726	+	3.13375i	−0.648312	+	0.190362i	−0.589324	−	0.807897i	$-0.700606\pi$
$271$	−10.6726	+	3.13375i	−0.648312	+	0.190362i	−0.0589883	+	0.998259i	$0.518787\pi$
$272$	−1.03839	+	2.27376i	−0.0629618	+	0.137867i
$273$		0			0
$274$	0.309606	−	0.198972i	0.0187040	−	0.0120203i
$275$	26.0417			1.57037
$276$		0			0
$277$	−14.7239			−0.884673			−0.442337	−	0.896849i	$-0.645850\pi$
$277$	−14.7239			−0.884673			−0.442337	+	0.896849i	$0.645850\pi$
$278$	−5.97896	+	3.84245i	−0.358594	+	0.230455i
$279$		0			0
$280$	2.12349	−	4.64980i	0.126903	−	0.277879i
$281$	20.2215	−	5.93758i	1.20632	−	0.354206i	0.384051	−	0.923312i	$-0.374529\pi$
$281$	20.2215	−	5.93758i	1.20632	−	0.354206i	0.822264	+	0.569106i	$0.192711\pi$
$282$		0			0
$283$	3.85528	+	4.44924i	0.229173	+	0.264480i	0.858677	−	0.512518i	$-0.171287\pi$
$283$	3.85528	+	4.44924i	0.229173	+	0.264480i	−0.629504	+	0.776998i	$0.716742\pi$
$284$	−3.34015	−	23.2313i	−0.198201	−	1.37852i
$285$		0			0
$286$	−7.35293	+	8.48574i	−0.434788	+	0.501772i
$287$	−2.58449	−	1.66095i	−0.152557	−	0.0980426i
$288$		0			0
$289$	10.5615	−	12.1886i	0.621264	−	0.716977i
$290$	2.55445	+	0.750054i	0.150002	+	0.0440447i
$291$		0			0
$292$	7.77206	+	8.96944i	0.454825	+	0.524897i
$293$	0.0808672	+	0.177074i	0.00472431	+	0.0103448i	0.911979	−	0.410236i	$-0.134554\pi$
$293$	0.0808672	+	0.177074i	0.00472431	+	0.0103448i	−0.907255	+	0.420581i	$0.861826\pi$
$294$		0			0
$295$	−1.47934	+	3.23930i	−0.0861305	+	0.188600i
$296$	−2.10136	+	14.6153i	−0.122139	+	0.849496i
$297$		0			0
$298$	4.45047			0.257809
$299$	−24.7420	+	19.8308i	−1.43087	+	1.14684i
$300$		0			0
$301$	−4.64740	+	2.98671i	−0.267872	+	0.172151i
$302$	0.574971	−	3.99901i	0.0330859	−	0.230117i
$303$		0			0
$304$	−9.63010	+	2.82765i	−0.552324	+	0.162177i
$305$	−17.9159	−	39.2303i	−1.02586	−	2.24632i
$306$		0			0
$307$	1.84026	+	12.7993i	0.105029	+	0.730492i	0.972483	+	0.232975i	$0.0748459\pi$
$307$	1.84026	+	12.7993i	0.105029	+	0.730492i	−0.867454	+	0.497518i	$0.834245\pi$
$308$	−4.85439	−	1.42538i	−0.276605	−	0.0812185i
$309$		0			0
$310$	0.799730	+	0.513955i	0.0454216	+	0.0291907i
$311$	25.2289	+	16.2136i	1.43060	+	0.919391i	0.999857	+	0.0169172i	$0.00538516\pi$
$311$	25.2289	+	16.2136i	1.43060	+	0.919391i	0.430744	+	0.902474i	$0.358251\pi$
$312$		0			0
$313$	1.46922	+	0.431401i	0.0830451	+	0.0243843i	0.322991	−	0.946402i	$-0.395312\pi$
$313$	1.46922	+	0.431401i	0.0830451	+	0.0243843i	−0.239946	+	0.970786i	$0.577130\pi$
$314$	−0.639710	−	4.44928i	−0.0361009	−	0.251087i
$315$		0			0
$316$	−1.05662	−	2.31367i	−0.0594393	−	0.130154i
$317$	−20.3746	+	5.98254i	−1.14435	+	0.336013i	−0.798334	−	0.602215i	$-0.794285\pi$
$317$	−20.3746	+	5.98254i	−1.14435	+	0.336013i	−0.346020	+	0.938227i	$0.612467\pi$
$318$		0			0
$319$	0.798568	−	5.55416i	0.0447112	−	0.310973i
$320$	−8.89580	+	5.71698i	−0.497290	+	0.319589i
$321$		0			0
$322$	1.65259	+	0.832697i	0.0920953	+	0.0464044i
$323$	−3.50195			−0.194854
$324$		0			0
$325$	−6.90982	+	48.0589i	−0.383288	+	2.66583i
$326$	−3.40525	+	7.45645i	−0.188599	+	0.412974i
$327$		0			0
$328$	−2.86016	−	6.26287i	−0.157926	−	0.345809i
$329$	3.00456	+	3.46745i	0.165647	+	0.191167i
$330$		0			0
$331$	0.778568	+	0.228608i	0.0427940	+	0.0125654i	0.303059	−	0.952972i	$-0.401992\pi$
$331$	0.778568	+	0.228608i	0.0427940	+	0.0125654i	−0.260266	+	0.965537i	$0.583810\pi$
$332$	2.03050	−	2.34332i	0.111438	−	0.128607i
$333$		0			0
$334$	−4.30806	−	2.76862i	−0.235727	−	0.151492i
$335$	−5.72441	+	6.60632i	−0.312758	+	0.360942i
$336$		0			0
$337$	2.55623	+	17.7790i	0.139247	+	0.968483i	0.932906	+	0.360120i	$0.117264\pi$
$337$	2.55623	+	17.7790i	0.139247	+	0.968483i	−0.793659	+	0.608363i	$0.791827\pi$
$338$	−9.63219	−	11.1161i	−0.523922	−	0.604639i
$339$		0			0
$340$	−5.57439	+	1.63679i	−0.302314	+	0.0887674i
$341$	0.832348	−	1.82259i	0.0450742	−	0.0986987i
$342$		0			0
$343$	9.04957	−	5.81580i	0.488631	−	0.314024i
$344$	−12.3807			−0.667521
$345$		0			0
$346$	11.5604			0.621493
$347$	3.92153	−	2.52021i	0.210519	−	0.135292i	−0.431133	−	0.902288i	$-0.641886\pi$
$347$	3.92153	−	2.52021i	0.210519	−	0.135292i	0.641651	+	0.766996i	$0.278250\pi$
$348$		0			0
$349$	−6.62642	+	14.5098i	−0.354704	+	0.776694i	0.645215	+	0.764001i	$0.276768\pi$
$349$	−6.62642	+	14.5098i	−0.354704	+	0.776694i	−0.999919	+	0.0126928i	$0.995960\pi$
$350$	2.71881	−	0.798313i	0.145326	−	0.0426716i
$351$		0			0
$352$	−11.3635	−	13.1141i	−0.605675	−	0.698986i
$353$	3.97269	+	27.6307i	0.211445	+	1.47063i	0.768336	+	0.640047i	$0.221085\pi$
$353$	3.97269	+	27.6307i	0.211445	+	1.47063i	−0.556891	+	0.830586i	$0.688006\pi$
$354$		0			0
$355$	30.4964	−	35.1947i	1.61858	−	1.86794i
$356$	−6.98575	−	4.48947i	−0.370244	−	0.237941i
$357$		0			0
$358$	0.817456	−	0.943394i	0.0432039	−	0.0498599i
$359$	31.6936	+	9.30607i	1.67272	+	0.491156i	0.974436	−	0.224663i	$-0.0721282\pi$
$359$	31.6936	+	9.30607i	1.67272	+	0.491156i	0.698286	+	0.715819i	$0.253946\pi$
$360$		0			0
$361$	3.23428	+	3.73256i	0.170225	+	0.196450i
$362$	−1.99528	−	4.36905i	−0.104869	−	0.229632i
$363$		0			0
$364$	3.91853	−	8.58039i	0.205387	−	0.449734i
$365$	−3.35136	+	23.3092i	−0.175418	+	1.22006i
$366$		0			0
$367$	−13.3155			−0.695066			−0.347533	−	0.937668i	$-0.612981\pi$
$367$	−13.3155			−0.695066			−0.347533	+	0.937668i	$0.612981\pi$
$368$	−6.52083	−	11.0568i	−0.339922	−	0.576373i
$369$		0			0
$370$	−11.5739	+	7.43809i	−0.601698	+	0.386688i
$371$	−0.800398	+	5.56689i	−0.0415546	+	0.289019i
$372$		0			0
$373$	23.7335	−	6.96879i	1.22888	−	0.360830i	0.398050	−	0.917364i	$-0.369687\pi$
$373$	23.7335	−	6.96879i	1.22888	−	0.360830i	0.830825	+	0.556533i	$0.187869\pi$
$374$	−0.658844	−	1.44267i	−0.0340680	−	0.0745985i
$375$		0			0
$376$	1.46333	+	10.1777i	0.0754656	+	0.524875i
$377$	10.0381	+	2.94745i	0.516988	+	0.151801i
$378$		0			0
$379$	32.2149	+	20.7033i	1.65477	+	1.06345i	0.925152	+	0.379597i	$0.123938\pi$
$379$	32.2149	+	20.7033i	1.65477	+	1.06345i	0.729616	+	0.683857i	$0.239699\pi$
$380$	−19.6242	−	12.6117i	−1.00670	−	0.646968i
$381$		0			0
$382$	−11.5102	−	3.37969i	−0.588911	−	0.172920i
$383$	−2.38718	−	16.6032i	−0.121979	−	0.848383i	−0.955309	−	0.295608i	$-0.904478\pi$
$383$	−2.38718	−	16.6032i	−0.121979	−	0.848383i	0.833330	−	0.552775i	$-0.186431\pi$
$384$		0			0
$385$	−4.17022	−	9.13151i	−0.212534	−	0.465385i
$386$	0.0458856	−	0.0134732i	0.00233551	−	0.000685768i
$387$		0			0
$388$	0.200237	−	1.39268i	0.0101655	−	0.0707027i
$389$	−1.65871	+	1.06599i	−0.0841000	+	0.0540478i	−0.582015	−	0.813178i	$-0.697736\pi$
$389$	−1.65871	+	1.06599i	−0.0841000	+	0.0540478i	0.497915	+	0.867226i	$0.334099\pi$
$390$		0			0
$391$	−1.09617	−	4.34261i	−0.0554358	−	0.219615i
$392$	11.4679			0.579214
$393$		0			0
$394$	1.12994	−	7.85891i	0.0569256	−	0.395926i
$395$	2.09653	−	4.59076i	0.105488	−	0.230986i
$396$		0			0
$397$	−12.0830	−	26.4580i	−0.606426	−	1.32789i	−0.924992	−	0.379988i	$-0.875928\pi$
$397$	−12.0830	−	26.4580i	−0.606426	−	1.32789i	0.318565	−	0.947901i	$-0.396799\pi$
$398$	−6.28633	−	7.25481i	−0.315105	−	0.363651i
$399$		0			0
$400$	−18.8593	−	5.53760i	−0.942967	−	0.276880i
$401$	−5.76326	+	6.65116i	−0.287803	+	0.332143i	−0.881179	−	0.472783i	$-0.843249\pi$
$401$	−5.76326	+	6.65116i	−0.287803	+	0.332143i	0.593376	+	0.804926i	$0.297795\pi$
$402$		0			0
$403$	3.14266	+	2.01967i	0.156547	+	0.100607i
$404$	14.6043	−	16.8543i	0.726591	−	0.838531i
$405$		0			0
$406$	−0.0868920	−	0.604347i	−0.00431238	−	0.0299932i
$407$	18.9892	+	21.9148i	0.941262	+	1.08627i
$408$		0			0
$409$	−6.24249	+	1.83296i	−0.308671	+	0.0906340i	−0.432400	−	0.901682i	$-0.642333\pi$
$409$	−6.24249	+	1.83296i	−0.308671	+	0.0906340i	0.123729	+	0.992316i	$0.460515\pi$
$410$	2.66497	−	5.83547i	0.131613	−	0.288193i
$411$		0			0
$412$	−15.7809	+	10.1418i	−0.777471	+	0.499650i
$413$	0.816695			0.0401869
$414$		0			0
$415$	6.15231			0.302005
$416$	27.2168	−	17.4912i	1.33441	−	0.857575i
$417$		0			0
$418$	2.64541	−	5.79263i	0.129391	−	0.283327i
$419$	8.92579	−	2.62085i	0.436054	−	0.128037i	−0.0563359	−	0.998412i	$-0.517942\pi$
$419$	8.92579	−	2.62085i	0.436054	−	0.128037i	0.492389	+	0.870375i	$0.336124\pi$
$420$		0			0
$421$	3.18611	+	3.67697i	0.155282	+	0.179205i	0.828060	−	0.560640i	$-0.189445\pi$
$421$	3.18611	+	3.67697i	0.155282	+	0.179205i	−0.672778	+	0.739844i	$0.734899\pi$
$422$	0.158272	+	1.10081i	0.00770456	+	0.0535864i
$423$		0			0
$424$	−8.25402	+	9.52565i	−0.400851	+	0.462607i
$425$	−5.76942	−	3.70778i	−0.279858	−	0.179854i
$426$		0			0
$427$	−6.47707	+	7.47494i	−0.313447	+	0.361738i
$428$	10.9061	+	3.20232i	0.527166	+	0.154790i
$429$		0			0
$430$	−7.55432	−	8.71815i	−0.364302	−	0.420427i
$431$	−13.7691	−	30.1501i	−0.663234	−	1.45228i	−0.879478	−	0.475940i	$-0.842108\pi$
$431$	−13.7691	−	30.1501i	−0.663234	−	1.45228i	0.216244	−	0.976339i	$-0.430619\pi$
$432$		0			0
$433$	12.7795	−	27.9833i	0.614145	−	1.34479i	−0.305557	−	0.952174i	$-0.598843\pi$
$433$	12.7795	−	27.9833i	0.614145	−	1.34479i	0.919702	−	0.392617i	$-0.128430\pi$
$434$	0.0310271	−	0.215798i	0.00148935	−	0.0103586i
$435$		0			0
$436$	2.07772			0.0995048
$437$	10.2954	−	14.7449i	0.492495	−	0.705342i
$438$		0			0
$439$	26.1267	−	16.7906i	1.24696	−	0.801371i	0.260514	−	0.965470i	$-0.416108\pi$
$439$	26.1267	−	16.7906i	1.24696	−	0.801371i	0.986444	+	0.164099i	$0.0524716\pi$
$440$	3.20175	−	22.2687i	0.152638	−	1.06162i
$441$		0			0
$442$	2.83720	−	0.833078i	0.134952	−	0.0396255i
$443$	1.34137	+	2.93720i	0.0637305	+	0.139550i	0.938817	−	0.344416i	$-0.111923\pi$
$443$	1.34137	+	2.93720i	0.0637305	+	0.139550i	−0.875087	+	0.483966i	$0.839196\pi$
$444$		0			0
$445$	−2.34488	−	16.3090i	−0.111158	−	0.773120i
$446$	2.11420	+	0.620784i	0.100110	+	0.0293950i
$447$		0			0
$448$	2.04014	+	1.31112i	0.0963874	+	0.0619444i
$449$	−17.6082	−	11.3161i	−0.830982	−	0.534040i	0.0546076	−	0.998508i	$-0.482609\pi$
$449$	−17.6082	−	11.3161i	−0.830982	−	0.534040i	−0.885590	+	0.464468i	$0.846246\pi$
$450$		0			0
$451$	−12.9735	−	3.80937i	−0.610900	−	0.179376i
$452$	4.34950	+	30.2514i	0.204583	+	1.42291i
$453$		0			0
$454$	−1.73540	−	3.79999i	−0.0814463	−	0.178343i
$455$	17.9584	−	5.27305i	0.841901	−	0.247205i
$456$		0			0
$457$	0.0771726	−	0.536747i	0.00360998	−	0.0251080i	−0.987937	−	0.154857i	$-0.950508\pi$
$457$	0.0771726	−	0.536747i	0.00360998	−	0.0251080i	0.991547	+	0.129749i	$0.0414173\pi$
$458$	−3.75104	+	2.41065i	−0.175275	+	0.112642i
$459$		0			0
$460$	9.49651	−	28.2828i	0.442777	−	1.31869i
$461$	−2.74045			−0.127636			−0.0638178	−	0.997962i	$-0.520328\pi$
$461$	−2.74045			−0.127636			−0.0638178	+	0.997962i	$0.520328\pi$
$462$		0			0
$463$	−1.60699	+	11.1768i	−0.0746831	+	0.519432i	0.917799	+	0.397045i	$0.129964\pi$
$463$	−1.60699	+	11.1768i	−0.0746831	+	0.519432i	−0.992482	+	0.122388i	$0.960945\pi$
$464$	−1.75938	+	3.85251i	−0.0816772	+	0.178848i
$465$		0			0
$466$	0.587097	+	1.28556i	0.0271967	+	0.0595525i
$467$	−3.78682	−	4.37023i	−0.175233	−	0.202230i	0.661338	−	0.750088i	$-0.269989\pi$
$467$	−3.78682	−	4.37023i	−0.175233	−	0.202230i	−0.836571	+	0.547858i	$0.815443\pi$
$468$		0			0
$469$	1.92352	+	0.564798i	0.0888201	+	0.0260799i
$470$	−6.27399	+	7.24057i	−0.289398	+	0.333983i
$471$		0			0
$472$	1.53974	+	0.989532i	0.0708723	+	0.0455469i
$473$	−15.9222	+	18.3751i	−0.732101	+	0.844890i
$474$		0			0
$475$	−3.91891	−	27.2566i	−0.179812	−	1.25062i
$476$	0.872527	+	1.00695i	0.0399922	+	0.0461535i
$477$		0			0
$478$	−7.55071	+	2.21709i	−0.345361	+	0.101407i
$479$	−3.47182	+	7.60222i	−0.158631	+	0.347354i	−0.972214	−	0.234096i	$-0.924787\pi$
$479$	−3.47182	+	7.60222i	−0.158631	+	0.347354i	0.813582	+	0.581450i	$0.197514\pi$
$480$		0			0
$481$	−45.4814	+	29.2291i	−2.07377	+	1.33273i
$482$	−0.633020			−0.0288333
$483$		0			0
$484$	−2.78974			−0.126807
$485$	2.34858	−	1.50934i	0.106644	−	0.0685357i
$486$		0			0
$487$	−1.44084	+	3.15501i	−0.0652909	+	0.142967i	−0.939464	−	0.342647i	$-0.888677\pi$
$487$	−1.44084	+	3.15501i	−0.0652909	+	0.142967i	0.874173	+	0.485614i	$0.161404\pi$
$488$	−21.2683	+	6.24493i	−0.962770	+	0.282695i
$489$		0			0
$490$	6.99735	+	8.07537i	0.316108	+	0.364808i
$491$	0.0523189	+	0.363886i	0.00236112	+	0.0164219i	0.990968	−	0.134099i	$-0.0428140\pi$
$491$	0.0523189	+	0.363886i	0.00236112	+	0.0164219i	−0.988607	+	0.150521i	$0.951905\pi$
$492$		0			0
$493$	−0.967715	+	1.11680i	−0.0435837	+	0.0502983i
$494$	9.98815	+	6.41900i	0.449388	+	0.288804i
$495$		0			0
$496$	−0.990348	+	1.14292i	−0.0444679	+	0.0513187i
$497$	−10.2474	−	3.00892i	−0.459661	−	0.134969i
$498$		0			0
$499$	−8.88893	−	10.2584i	−0.397923	−	0.459228i	0.521063	−	0.853518i	$-0.325536\pi$
$499$	−8.88893	−	10.2584i	−0.397923	−	0.459228i	−0.918986	+	0.394291i	$0.870990\pi$
$500$	−6.05633	−	13.2615i	−0.270847	−	0.593073i
$501$		0			0
$502$	3.72001	−	8.14567i	0.166032	−	0.363559i
$503$	−2.38681	+	16.6006i	−0.106423	+	0.740186i	0.864818	+	0.502086i	$0.167434\pi$
$503$	−2.38681	+	16.6006i	−0.106423	+	0.740186i	−0.971241	+	0.238100i	$0.923475\pi$
$504$		0			0
$505$	44.2502			1.96911
$506$	8.01124	+	1.46726i	0.356143	+	0.0652275i
$507$		0			0
$508$	−14.0969	+	9.05952i	−0.625449	+	0.401951i
$509$	0.426906	−	2.96920i	0.0189223	−	0.131607i	−0.978171	−	0.207804i	$-0.933368\pi$
$509$	0.426906	−	2.96920i	0.0189223	−	0.131607i	0.997093	+	0.0761963i	$0.0242776\pi$
$510$		0			0
$511$	5.18188	−	1.52154i	0.229233	−	0.0673088i
$512$	9.45633	+	20.7065i	0.417915	+	0.915105i
$513$		0			0
$514$	0.431040	+	2.99795i	0.0190124	+	0.132234i
$515$	−35.7134	−	10.4864i	−1.57372	−	0.462086i
$516$		0			0
$517$	16.9874	+	10.9172i	0.747107	+	0.480137i
$518$	2.65432	+	1.70583i	0.116624	+	0.0749498i
$519$		0			0
$520$	40.2465	+	11.8174i	1.76492	+	0.518228i
$521$	−1.30671	−	9.08839i	−0.0572482	−	0.398170i	−0.998218	−	0.0596783i	$-0.980993\pi$
$521$	−1.30671	−	9.08839i	−0.0572482	−	0.398170i	0.940970	−	0.338491i	$-0.109917\pi$
$522$		0			0
$523$	−3.03941	−	6.65538i	−0.132904	−	0.291019i	0.831466	−	0.555575i	$-0.187502\pi$
$523$	−3.03941	−	6.65538i	−0.132904	−	0.291019i	−0.964370	+	0.264556i	$0.914775\pi$
$524$	−22.9180	+	6.72932i	−1.00118	+	0.293972i
$525$		0			0
$526$	−1.66161	+	11.5567i	−0.0724495	+	0.503897i
$527$	−0.443901	+	0.285278i	−0.0193367	+	0.0124269i
$528$		0			0
$529$	21.5071	+	8.15145i	0.935090	+	0.354411i
$530$	−11.7441			−0.510130
$531$		0			0
$532$	−0.761360	+	5.29537i	−0.0330091	+	0.229584i
$533$	10.4724	−	22.9314i	0.453610	−	0.993268i
$534$		0			0
$535$	9.36900	+	20.5153i	0.405057	+	0.886952i
$536$	2.94216	+	3.39543i	0.127082	+	0.146660i
$537$		0			0
$538$	−6.22496	−	1.82781i	−0.268377	−	0.0788027i
$539$	14.7482	−	17.0204i	0.635251	−	0.733119i
$540$		0			0
$541$	0.558457	+	0.358898i	0.0240099	+	0.0154303i	0.552591	−	0.833453i	$-0.313639\pi$
$541$	0.558457	+	0.358898i	0.0240099	+	0.0154303i	−0.528581	+	0.848883i	$0.677276\pi$
$542$	−3.48829	+	4.02570i	−0.149835	+	0.172919i
$543$		0			0
$544$	0.650353	+	4.52330i	0.0278836	+	0.193935i
$545$	2.69973	+	3.11565i	0.115644	+	0.133460i
$546$		0			0
$547$	17.4721	−	5.13026i	0.747052	−	0.219354i	0.114018	−	0.993479i	$-0.463628\pi$
$547$	17.4721	−	5.13026i	0.747052	−	0.219354i	0.633033	+	0.774124i	$0.281810\pi$
$548$	−0.565279	+	1.23779i	−0.0241475	+	0.0528757i
$549$		0			0
$550$	10.4914	−	6.74240i	0.447354	−	0.287497i
$551$	−5.93346			−0.252774
$552$		0			0
$553$	−1.15743			−0.0492188
$554$	−5.93180	+	3.81214i	−0.252018	+	0.161962i
$555$		0			0
$556$	10.9164	−	23.9036i	0.462959	−	1.01374i
$557$	−24.4462	+	7.17805i	−1.03582	+	0.304144i	−0.755075	−	0.655639i	$-0.772399\pi$
$557$	−24.4462	+	7.17805i	−1.03582	+	0.304144i	−0.280744	+	0.959783i	$0.590581\pi$
$558$		0			0
$559$	−29.6859	−	34.2593i	−1.25558	−	1.44901i
$560$	1.07831	+	7.49980i	0.0455669	+	0.316924i
$561$		0			0
$562$	6.60934	−	7.62759i	0.278798	−	0.321750i
$563$	17.8550	+	11.4747i	0.752499	+	0.483602i	0.859804	−	0.510624i	$-0.170586\pi$
$563$	17.8550	+	11.4747i	0.752499	+	0.483602i	−0.107305	+	0.994226i	$0.534222\pi$
$564$		0			0
$565$	−39.7120	+	45.8301i	−1.67070	+	1.92809i
$566$	2.70512	+	0.794295i	0.113705	+	0.0333867i
$567$		0			0
$568$	−15.6741	−	18.0889i	−0.657672	−	0.758994i
$569$	13.9743	+	30.5994i	0.585833	+	1.28279i	0.937928	+	0.346831i	$0.112742\pi$
$569$	13.9743	+	30.5994i	0.585833	+	1.28279i	−0.352095	+	0.935964i	$0.614531\pi$
$570$		0			0
$571$	−5.34091	+	11.6950i	−0.223510	+	0.489419i	−0.987853	−	0.155391i	$-0.950336\pi$
$571$	−5.34091	+	11.6950i	−0.223510	+	0.489419i	0.764343	+	0.644810i	$0.223064\pi$
$572$	5.90827	−	41.0929i	0.247037	−	1.71818i
$573$		0			0
$574$	−1.47124			−0.0614085
$575$	32.5730	−	13.3915i	1.35839	−	0.558463i
$576$		0			0
$577$	−9.24070	+	5.93864i	−0.384695	+	0.247229i	−0.718667	−	0.695354i	$-0.755247\pi$
$577$	−9.24070	+	5.93864i	−0.384695	+	0.247229i	0.333972	+	0.942583i	$0.391611\pi$
$578$	1.09917	−	7.64487i	0.0457193	−	0.317985i
$579$		0			0
$580$	−9.44487	+	2.77326i	−0.392177	+	0.115154i
$581$	−0.586131	−	1.28345i	−0.0243168	−	0.0532464i
$582$		0			0
$583$	3.52270	+	24.5009i	0.145895	+	1.01472i
$584$	11.6131	+	3.40991i	0.480553	+	0.141103i
$585$		0			0
$586$	0.0784249	+	0.0504006i	0.00323970	+	0.00208203i
$587$	11.4406	+	7.35242i	0.472204	+	0.303467i	0.755014	−	0.655709i	$-0.227630\pi$
$587$	11.4406	+	7.35242i	0.472204	+	0.303467i	−0.282810	+	0.959176i	$0.591267\pi$
$588$		0			0
$589$	−2.03288	−	0.596907i	−0.0837633	−	0.0245951i
$590$	0.242702	+	1.68803i	0.00999188	+	0.0694950i
$591$		0			0
$592$	−9.09195	−	19.9086i	−0.373677	−	0.818238i
$593$	41.1409	−	12.0800i	1.68945	−	0.496068i	0.711113	−	0.703077i	$-0.248191\pi$
$593$	41.1409	−	12.0800i	1.68945	−	0.496068i	0.978339	+	0.207009i	$0.0663731\pi$
$594$		0			0
$595$	−0.376239	+	2.61680i	−0.0154243	+	0.107278i
$596$	−13.8430	+	8.89638i	−0.567033	+	0.364410i
$597$		0			0
$598$	−4.83344	+	14.3951i	−0.197654	+	0.588660i
$599$	14.6628			0.599106			0.299553	−	0.954080i	$-0.403162\pi$
$599$	14.6628			0.599106			0.299553	+	0.954080i	$0.403162\pi$
$600$		0			0
$601$	4.44759	−	30.9337i	0.181421	−	1.26181i	−0.671985	−	0.740564i	$-0.734558\pi$
$601$	4.44759	−	30.9337i	0.181421	−	1.26181i	0.853406	−	0.521246i	$-0.174533\pi$
$602$	−1.09901	+	2.40650i	−0.0447924	+	0.0980817i
$603$		0			0
$604$	6.20550	+	13.5881i	0.252498	+	0.552894i
$605$	−3.62491	−	4.18337i	−0.147374	−	0.170078i
$606$		0			0
$607$	−3.74039	−	1.09828i	−0.151818	−	0.0445777i	0.204941	−	0.978774i	$-0.434300\pi$
$607$	−3.74039	−	1.09828i	−0.151818	−	0.0445777i	−0.356758	+	0.934197i	$0.616118\pi$
$608$	−12.0159	+	13.8671i	−0.487311	+	0.562386i
$609$		0			0
$610$	−17.3748	−	11.1661i	−0.703485	−	0.452102i
$611$	−24.6546	+	28.4529i	−0.997419	+	1.15108i
$612$		0			0
$613$	4.96719	+	34.5476i	0.200623	+	1.39536i	0.802442	+	0.596731i	$0.203534\pi$
$613$	4.96719	+	34.5476i	0.200623	+	1.39536i	−0.601819	+	0.798633i	$0.705557\pi$
$614$	4.05522	+	4.67997i	0.163655	+	0.188868i
$615$		0			0
$616$	−4.95055	+	1.45361i	−0.199464	+	0.0585678i
$617$	6.31092	−	13.8190i	0.254068	−	0.556332i	−0.739023	−	0.673681i	$-0.764712\pi$
$617$	6.31092	−	13.8190i	0.254068	−	0.556332i	0.993091	+	0.117349i	$0.0374396\pi$
$618$		0			0
$619$	−4.17467	+	2.68290i	−0.167794	+	0.107835i	−0.621843	−	0.783142i	$-0.713616\pi$
$619$	−4.17467	+	2.68290i	−0.167794	+	0.107835i	0.454048	+	0.890977i	$0.349979\pi$
$620$	−3.51492			−0.141163
$621$		0			0
$622$	14.3618			0.575856
$623$	−3.17886	+	2.04293i	−0.127358	+	0.0818482i
$624$		0			0
$625$	−3.23614	+	7.08616i	−0.129446	+	0.283447i
$626$	0.703596	−	0.206594i	0.0281214	−	0.00825718i
$627$		0			0
$628$	10.8838	+	12.5606i	0.434311	+	0.501222i
$629$	−1.08679	−	7.55879i	−0.0433332	−	0.301389i
$630$		0			0
$631$	−24.0121	+	27.7114i	−0.955905	+	1.10317i	0.0386804	+	0.999252i	$0.487685\pi$
$631$	−24.0121	+	27.7114i	−0.955905	+	1.10317i	−0.994585	+	0.103922i	$0.966861\pi$
$632$	−2.18213	−	1.40237i	−0.0868006	−	0.0557833i
$633$		0			0
$634$	−6.65939	+	7.68534i	−0.264478	+	0.305224i
$635$	−31.9023	−	9.36737i	−1.26600	−	0.371733i
$636$		0			0
$637$	27.4972	+	31.7334i	1.08948	+	1.25732i
$638$	−1.11630	−	2.44436i	−0.0441947	−	0.0967730i
$639$		0			0
$640$	−16.3870	+	35.8826i	−0.647755	+	1.41838i
$641$	1.95454	−	13.5941i	0.0771997	−	0.536936i	−0.914118	−	0.405448i	$-0.867116\pi$
$641$	1.95454	−	13.5941i	0.0771997	−	0.536936i	0.991318	−	0.131488i	$-0.0419754\pi$
$642$		0			0
$643$	−34.2265			−1.34976			−0.674880	−	0.737927i	$-0.735805\pi$
$643$	−34.2265			−1.34976			−0.674880	+	0.737927i	$0.735805\pi$
$644$	−6.80487	+	0.713416i	−0.268150	+	0.0281125i
$645$		0			0
$646$	−1.41083	+	0.906684i	−0.0555083	+	0.0356730i
$647$	−5.48316	+	38.1362i	−0.215565	+	1.49929i	0.538576	+	0.842577i	$0.318962\pi$
$647$	−5.48316	+	38.1362i	−0.215565	+	1.49929i	−0.754141	+	0.656712i	$0.771947\pi$
$648$		0			0
$649$	3.44882	−	1.01267i	0.135378	−	0.0397506i
$650$	9.65908	+	21.1504i	0.378860	+	0.829588i
$651$		0			0
$652$	−4.31336	−	30.0000i	−0.168924	−	1.17489i
$653$	19.8816	+	5.83777i	0.778027	+	0.228449i	0.646552	−	0.762870i	$-0.276210\pi$
$653$	19.8816	+	5.83777i	0.778027	+	0.228449i	0.131475	+	0.991319i	$0.458029\pi$
$654$		0			0
$655$	−39.8699	−	25.6228i	−1.55785	−	1.00117i
$656$	8.58537	+	5.51748i	0.335203	+	0.215422i
$657$		0			0
$658$	2.10819	+	0.619022i	0.0821860	+	0.0241320i
$659$	−2.25543	−	15.6869i	−0.0878592	−	0.611074i	−0.985414	−	0.170172i	$-0.945568\pi$
$659$	−2.25543	−	15.6869i	−0.0878592	−	0.611074i	0.897555	−	0.440902i	$-0.145341\pi$
$660$		0			0
$661$	−0.0565318	−	0.123787i	−0.00219883	−	0.00481477i	0.908529	−	0.417821i	$-0.137206\pi$
$661$	−0.0565318	−	0.123787i	−0.00219883	−	0.00481477i	−0.910728	+	0.413006i	$0.864479\pi$
$662$	0.372850	−	0.109479i	0.0144912	−	0.00425500i
$663$		0			0
$664$	0.450011	−	3.12990i	0.0174638	−	0.121464i
$665$	−8.92998	+	5.73895i	−0.346290	+	0.222547i
$666$		0			0
$667$	−1.85728	−	7.35782i	−0.0719141	−	0.284896i
$668$	18.9345			0.732598
$669$		0			0
$670$	−0.595757	+	4.14358i	−0.0230161	+	0.160080i
$671$	−18.0834	+	39.5972i	−0.698104	+	1.52863i
$672$		0			0
$673$	−8.57511	−	18.7769i	−0.330546	−	0.723795i	0.669269	−	0.743020i	$-0.266607\pi$
$673$	−8.57511	−	18.7769i	−0.330546	−	0.723795i	−0.999815	+	0.0192250i	$0.993880\pi$
$674$	5.63295	+	6.50077i	0.216973	+	0.250400i
$675$		0			0
$676$	52.1815	+	15.3219i	2.00698	+	0.589303i
$677$	18.5314	−	21.3864i	0.712220	−	0.821945i	−0.278129	−	0.960544i	$-0.589714\pi$
$677$	18.5314	−	21.3864i	0.712220	−	0.821945i	0.990349	+	0.138599i	$0.0442598\pi$
$678$		0			0
$679$	−0.538617	−	0.346148i	−0.0206702	−	0.0132839i
$680$	−3.87993	+	4.47767i	−0.148788	+	0.171711i
$681$		0			0
$682$	−0.136556	−	0.949767i	−0.00522899	−	0.0363684i
$683$	−12.7796	−	14.7484i	−0.488997	−	0.564332i	0.456601	−	0.889672i	$-0.349067\pi$
$683$	−12.7796	−	14.7484i	−0.488997	−	0.564332i	−0.945597	+	0.325340i	$0.894521\pi$
$684$		0			0
$685$	−2.59064	+	0.760680i	−0.0989832	+	0.0290641i
$686$	2.14003	−	4.68601i	0.0817068	−	0.178913i
$687$		0			0
$688$	15.4382	−	9.92150i	0.588574	−	0.378254i
$689$	−46.1502			−1.75818
$690$		0			0
$691$	18.2405			0.693902			0.346951	−	0.937883i	$-0.387217\pi$
$691$	18.2405			0.693902			0.346951	+	0.937883i	$0.387217\pi$
$692$	−35.9584	+	23.1091i	−1.36693	+	0.878474i
$693$		0			0
$694$	0.927358	−	2.03063i	0.0352020	−	0.0770817i
$695$	50.0292	−	14.6899i	1.89772	−	0.557220i
$696$		0			0
$697$	2.33186	+	2.69111i	0.0883254	+	0.101933i
$698$	1.08714	+	7.56120i	0.0411487	+	0.286196i
$699$		0			0
$700$	−6.86095	+	7.91796i	−0.259319	+	0.299271i
$701$	−21.0479	−	13.5267i	−0.794970	−	0.510896i	0.0790011	−	0.996875i	$-0.474827\pi$
$701$	−21.0479	−	13.5267i	−0.794970	−	0.510896i	−0.873971	+	0.485979i	$0.838463\pi$
$702$		0			0
$703$	20.0796	−	23.1731i	0.757315	−	0.873989i
$704$	10.2410	+	3.00704i	0.385973	+	0.113332i
$705$		0			0
$706$	8.75429	+	10.1030i	0.329472	+	0.380231i
$707$	−4.21572	−	9.23114i	−0.158549	−	0.347173i
$708$		0			0
$709$	−13.2237	+	28.9559i	−0.496626	+	1.08746i	0.480925	+	0.876762i	$0.340301\pi$
$709$	−13.2237	+	28.9559i	−0.496626	+	1.08746i	−0.977551	+	0.210698i	$0.932426\pi$
$710$	3.17385	−	22.0746i	0.119113	−	0.828447i
$711$		0			0
$712$	−8.46847			−0.317369
$713$	0.103871	−	2.70772i	0.00389001	−	0.101405i
$714$		0			0
$715$	69.2981	−	44.5352i	2.59160	−	1.66552i
$716$	−0.656847	+	4.56847i	−0.0245475	+	0.170732i
$717$		0			0
$718$	15.1778	−	4.45660i	0.566430	−	0.166319i
$719$	0.758817	+	1.66158i	0.0282991	+	0.0619664i	0.923254	−	0.384191i	$-0.125520\pi$
$719$	0.758817	+	1.66158i	0.0282991	+	0.0619664i	−0.894955	+	0.446157i	$0.852792\pi$
$720$		0			0
$721$	1.21483	+	8.44930i	0.0452425	+	0.314668i
$722$	2.26938	+	0.666350i	0.0844576	+	0.0247990i
$723$		0			0
$724$	14.9399	+	9.60127i	0.555236	+	0.356828i
$725$	−9.77531	−	6.28221i	−0.363046	−	0.233315i
$726$		0			0
$727$	35.9742	+	10.5630i	1.33421	+	0.391759i	0.869600	−	0.493757i	$-0.164377\pi$
$727$	35.9742	+	10.5630i	1.33421	+	0.391759i	0.464609	+	0.885516i	$0.346195\pi$
$728$	−1.36902	−	9.52175i	−0.0507393	−	0.352900i
$729$		0			0
$730$	4.68479	+	10.2583i	0.173392	+	0.379675i
$731$	6.14372	−	1.80396i	0.227234	−	0.0667218i
$732$		0			0
$733$	0.471638	−	3.28031i	0.0174203	−	0.121161i	−0.979256	−	0.202629i	$-0.935052\pi$
$733$	0.471638	−	3.28031i	0.0174203	−	0.121161i	0.996676	+	0.0814675i	$0.0259607\pi$
$734$	−5.36442	+	3.44751i	−0.198004	+	0.127250i
$735$		0			0
$736$	−20.9572	−	10.5598i	−0.772493	−	0.389238i
$737$	8.82318			0.325006
$738$		0			0
$739$	0.762673	−	5.30451i	0.0280554	−	0.195129i	−0.970974	−	0.239187i	$-0.923119\pi$
$739$	0.762673	−	5.30451i	0.0280554	−	0.195129i	0.999029	+	0.0440571i	$0.0140284\pi$
$740$	21.1317	−	46.2719i	0.776815	−	1.70099i
$741$		0			0
$742$	1.11886	+	2.44996i	0.0410746	+	0.0899408i
$743$	−16.8909	−	19.4931i	−0.619665	−	0.715132i	0.355978	−	0.934494i	$-0.384148\pi$
$743$	−16.8909	−	19.4931i	−0.619665	−	0.715132i	−0.975643	+	0.219362i	$0.929602\pi$
$744$		0			0
$745$	−31.3278	−	9.19867i	−1.14776	−	0.337013i
$746$	7.75723	−	8.95231i	0.284012	−	0.327768i
$747$		0			0
$748$	4.93317	+	3.17036i	0.180375	+	0.115920i
$749$	3.38715	−	3.90898i	0.123764	−	0.142831i
$750$		0			0
$751$	−5.51058	−	38.3269i	−0.201084	−	1.39857i	−0.801075	−	0.598564i	$-0.795738\pi$
$751$	−5.51058	−	38.3269i	−0.201084	−	1.39857i	0.599991	−	0.800007i	$-0.295171\pi$
$752$	−9.98081	−	11.5185i	−0.363963	−	0.420036i
$753$		0			0
$754$	4.80716	−	1.41151i	0.175066	−	0.0514041i
$755$	−12.3129	+	26.9615i	−0.448113	+	0.981230i
$756$		0			0
$757$	21.7825	−	13.9987i	0.791697	−	0.508793i	−0.0811996	−	0.996698i	$-0.525875\pi$
$757$	21.7825	−	13.9987i	0.791697	−	0.508793i	0.872897	+	0.487905i	$0.162239\pi$
$758$	18.3386			0.666089
$759$		0			0
$760$	−23.7895			−0.862934
$761$	−25.7260	+	16.5331i	−0.932568	+	0.599325i	−0.916278	−	0.400542i	$-0.868822\pi$
$761$	−25.7260	+	16.5331i	−0.932568	+	0.599325i	−0.0162899	+	0.999867i	$0.505185\pi$
$762$		0			0
$763$	0.392760	−	0.860025i	0.0142189	−	0.0311350i
$764$	42.5579	−	12.4961i	1.53969	−	0.452094i
$765$		0			0
$766$	−5.26042	−	6.07085i	−0.190067	−	0.219349i
$767$	0.953734	+	6.63337i	0.0344374	+	0.239517i
$768$		0			0
$769$	9.90083	−	11.4262i	0.357033	−	0.412038i	−0.548610	−	0.836078i	$-0.684843\pi$
$769$	9.90083	−	11.4262i	0.357033	−	0.412038i	0.905643	+	0.424040i	$0.139388\pi$
$770$	−4.04428	−	2.59910i	−0.145746	−	0.0936651i
$771$		0			0
$772$	−0.115793	+	0.133632i	−0.00416748	+	0.00480953i
$773$	−24.1446	−	7.08951i	−0.868423	−	0.254992i	−0.182978	−	0.983117i	$-0.558574\pi$
$773$	−24.1446	−	7.08951i	−0.868423	−	0.254992i	−0.685444	+	0.728125i	$0.740392\pi$
$774$		0			0
$775$	−2.71715	−	3.13576i	−0.0976030	−	0.112640i
$776$	−0.596068	−	1.30521i	−0.0213976	−	0.0468542i
$777$		0			0
$778$	−0.392250	+	0.858908i	−0.0140628	+	0.0307933i
$779$	−2.03476	+	14.1521i	−0.0729029	+	0.507051i
$780$		0			0
$781$	−47.0049			−1.68197
$782$	−1.56595	−	1.46570i	−0.0559983	−	0.0524132i
$783$		0			0
$784$	−14.2999	+	9.19000i	−0.510711	+	0.328214i
$785$	−4.69317	+	32.6417i	−0.167506	+	1.16503i
$786$		0			0
$787$	−21.0701	+	6.18675i	−0.751070	+	0.220534i	−0.634792	−	0.772683i	$-0.718914\pi$
$787$	−21.0701	+	6.18675i	−0.751070	+	0.220534i	−0.116277	+	0.993217i	$0.537096\pi$
$788$	12.1951	+	26.7036i	0.434434	+	0.951277i
$789$		0			0
$790$	−0.343959	−	2.39229i	−0.0122375	−	0.0851137i
$791$	13.3441	+	3.91818i	0.474461	+	0.139314i
$792$		0			0
$793$	−68.2769	−	43.8789i	−2.42458	−	1.55819i
$794$	−11.7180	−	7.53073i	−0.415858	−	0.267256i
$795$		0			0
$796$	34.0556	+	9.99964i	1.20707	+	0.354428i
$797$	−0.684007	−	4.75737i	−0.0242288	−	0.168515i	0.974114	−	0.226056i	$-0.0725831\pi$
$797$	−0.684007	−	4.75737i	−0.0242288	−	0.168515i	−0.998343	+	0.0575409i	$0.981674\pi$
$798$		0			0
$799$	−2.20912	−	4.83731i	−0.0781532	−	0.171132i
$800$	−34.4783	+	10.1237i	−1.21899	+	0.357928i
$801$		0			0
$802$	−0.599800	+	4.17170i	−0.0211797	+	0.147308i
$803$	19.9959	−	12.8506i	0.705641	−	0.453488i
$804$		0			0
$805$	−9.91185	−	9.27728i	−0.349347	−	0.326981i
$806$	1.78899			0.0630145
$807$		0			0
$808$	3.23669	−	22.5117i	0.113866	−	0.791957i
$809$	12.2663	−	26.8594i	0.431260	−	0.944327i	−0.561861	−	0.827232i	$-0.689914\pi$
$809$	12.2663	−	26.8594i	0.431260	−	0.944327i	0.993121	−	0.117095i	$-0.0373583\pi$
$810$		0			0
$811$	−9.34727	−	20.4677i	−0.328227	−	0.718717i	0.671525	−	0.740982i	$-0.265640\pi$
$811$	−9.34727	−	20.4677i	−0.328227	−	0.718717i	−0.999752	+	0.0222649i	$0.992912\pi$
$812$	1.47835	+	1.70611i	0.0518799	+	0.0598726i
$813$		0			0
$814$	13.3241	+	3.91231i	0.467009	+	0.137126i
$815$	39.3820	−	45.4493i	1.37949	−	1.59202i
$816$		0			0
$817$	21.6285	+	13.8998i	0.756685	+	0.486292i
$818$	−2.04034	+	2.35467i	−0.0713387	+	0.0823292i
$819$		0			0
$820$	3.37566	+	23.4783i	0.117883	+	0.819896i
$821$	−12.2433	−	14.1296i	−0.427296	−	0.493125i	0.500750	−	0.865592i	$-0.333058\pi$
$821$	−12.2433	−	14.1296i	−0.427296	−	0.493125i	−0.928046	+	0.372467i	$0.878512\pi$
$822$		0			0
$823$	39.1112	−	11.4841i	1.36333	−	0.400310i	0.483396	−	0.875402i	$-0.339403\pi$
$823$	39.1112	−	11.4841i	1.36333	−	0.400310i	0.879936	+	0.475092i	$0.157585\pi$
$824$	−7.94707	+	17.4017i	−0.276849	+	0.606215i
$825$		0			0
$826$	0.329021	−	0.211449i	0.0114481	−	0.00735726i
$827$	−23.5429			−0.818666			−0.409333	−	0.912385i	$-0.634239\pi$
$827$	−23.5429			−0.818666			−0.409333	+	0.912385i	$0.634239\pi$
$828$		0			0
$829$	−10.5885			−0.367752			−0.183876	−	0.982949i	$-0.558865\pi$
$829$	−10.5885			−0.367752			−0.183876	+	0.982949i	$0.558865\pi$
$830$	2.47858	−	1.59288i	0.0860327	−	0.0552898i
$831$		0			0
$832$	−8.26669	+	18.1015i	−0.286596	+	0.627558i
$833$	−5.69075	+	1.67095i	−0.197173	+	0.0578951i
$834$		0			0
$835$	24.6029	+	28.3933i	0.851420	+	0.982591i
$836$	3.35088	+	23.3059i	0.115893	+	0.806052i
$837$		0			0
$838$	2.91737	−	3.36682i	0.100779	−	0.116305i
$839$	−33.0705	−	21.2531i	−1.14172	−	0.733740i	−0.173747	−	0.984790i	$-0.555588\pi$
$839$	−33.0705	−	21.2531i	−1.14172	−	0.733740i	−0.967974	+	0.251051i	$0.919224\pi$
$840$		0			0
$841$	17.3513	−	20.0245i	0.598322	−	0.690500i
$842$	2.23558	+	0.656427i	0.0770433	+	0.0226220i
$843$		0			0
$844$	−2.69278	−	3.10764i	−0.0926894	−	0.106969i
$845$	44.8272	+	98.1578i	1.54210	+	3.37673i
$846$		0			0
$847$	−0.527357	+	1.15475i	−0.0181202	+	0.0396777i
$848$	2.65883	−	18.4926i	0.0913048	−	0.635039i
$849$		0			0
$850$	−3.28430			−0.112650
$851$	35.0211	+	17.6462i	1.20051	+	0.604904i
$852$		0			0
$853$	−34.9175	+	22.4401i	−1.19555	+	0.768335i	−0.978181	−	0.207754i	$-0.933385\pi$
$853$	−34.9175	+	22.4401i	−1.19555	+	0.768335i	−0.217372	+	0.976089i	$0.569748\pi$
$854$	−0.674089	+	4.68839i	−0.0230668	+	0.160433i
$855$		0			0
$856$	11.1221	−	3.26575i	0.380147	−	0.111621i
$857$	−4.65231	−	10.1871i	−0.158920	−	0.347986i	0.813376	−	0.581738i	$-0.197627\pi$
$857$	−4.65231	−	10.1871i	−0.158920	−	0.347986i	−0.972296	+	0.233752i	$0.924900\pi$
$858$		0			0
$859$	−0.286639	−	1.99362i	−0.00978001	−	0.0680215i	0.984347	−	0.176242i	$-0.0563940\pi$
$859$	−0.286639	−	1.99362i	−0.00978001	−	0.0680215i	−0.994127	+	0.108220i	$0.965485\pi$
$860$	40.9248	+	12.0166i	1.39553	+	0.409763i
$861$		0			0
$862$	−13.3533	−	8.58161i	−0.454814	−	0.292291i
$863$	−18.5634	−	11.9299i	−0.631904	−	0.406100i	0.185110	−	0.982718i	$-0.440736\pi$
$863$	−18.5634	−	11.9299i	−0.631904	−	0.406100i	−0.817014	+	0.576618i	$0.804372\pi$
$864$		0			0
$865$	−81.3765	−	23.8943i	−2.76688	−	0.812431i
$866$	−2.09662	−	14.5823i	−0.0712461	−	0.495528i
$867$		0			0
$868$	0.334867	+	0.733255i	0.0113661	+	0.0248883i
$869$	−4.88770	+	1.43516i	−0.165804	+	0.0486844i
$870$		0			0
$871$	−2.34112	+	16.2828i	−0.0793258	+	0.551723i
$872$	1.78252	−	1.14555i	0.0603636	−	0.0387933i
$873$		0			0
$874$	0.330128	−	8.60581i	0.0111668	−	0.291096i
$875$	−6.63416			−0.224275
$876$		0			0
$877$	7.99011	−	55.5724i	0.269807	−	1.87655i	−0.180355	−	0.983602i	$-0.557725\pi$
$877$	7.99011	−	55.5724i	0.269807	−	1.87655i	0.450162	−	0.892947i	$-0.351366\pi$
$878$	6.17841	−	13.5288i	0.208511	−	0.456576i
$879$		0			0
$880$	13.8530	+	30.3339i	0.466985	+	1.02255i
$881$	−26.6917	−	30.8039i	−0.899267	−	1.03781i	−0.999084	−	0.0428034i	$-0.986371\pi$
$881$	−26.6917	−	30.8039i	−0.899267	−	1.03781i	0.0998167	−	0.995006i	$-0.468174\pi$
$882$		0			0
$883$	7.31464	+	2.14777i	0.246157	+	0.0722783i	0.402484	−	0.915427i	$-0.368147\pi$
$883$	7.31464	+	2.14777i	0.246157	+	0.0722783i	−0.156326	+	0.987705i	$0.549965\pi$
$884$	−7.15972	+	8.26276i	−0.240808	+	0.277907i
$885$		0			0
$886$	1.30086	+	0.836013i	0.0437033	+	0.0280864i
$887$	26.3936	−	30.4598i	0.886210	−	1.02274i	−0.113364	−	0.993554i	$-0.536163\pi$
$887$	26.3936	−	30.4598i	0.886210	−	1.02274i	0.999574	−	0.0291872i	$-0.00929190\pi$
$888$		0			0
$889$	1.08519	+	7.54764i	0.0363960	+	0.253140i
$890$	−5.16721	−	5.96328i	−0.173205	−	0.199890i
$891$		0			0
$892$	−7.81707	+	2.29530i	−0.261735	+	0.0768523i
$893$	8.87013	−	19.4229i	0.296828	−	0.649962i
$894$		0			0
$895$	−7.70415	+	4.95116i	−0.257521	+	0.165499i
$896$	9.04675			0.302231
$897$		0			0
$898$	−10.0236			−0.334493
$899$	−0.752116	+	0.483356i	−0.0250845	+	0.0161208i
$900$		0			0
$901$	2.70797	−	5.92963i	0.0902156	−	0.197545i
$902$	−6.21291	+	1.82428i	−0.206867	+	0.0607417i
$903$		0			0
$904$	20.4107	+	23.5551i	0.678848	+	0.783433i
$905$	5.01480	+	34.8787i	0.166698	+	1.15941i
$906$		0			0
$907$	12.7271	−	14.6878i	0.422595	−	0.487701i	−0.504031	−	0.863686i	$-0.668150\pi$
$907$	12.7271	−	14.6878i	0.422595	−	0.487701i	0.926626	+	0.375985i	$0.122696\pi$
$908$	12.9940	+	8.35074i	0.431221	+	0.277129i
$909$		0			0
$910$	5.86963	−	6.77392i	0.194577	−	0.224553i
$911$	−45.9029	−	13.4783i	−1.52083	−	0.446556i	−0.588602	−	0.808423i	$-0.700321\pi$
$911$	−45.9029	−	13.4783i	−1.52083	−	0.446556i	−0.932230	+	0.361867i	$0.882140\pi$
$912$		0			0
$913$	−4.06659	−	4.69310i	−0.134585	−	0.155319i
$914$	−0.107878	−	0.236219i	−0.00356828	−	0.00781344i
$915$		0			0
$916$	6.84866	−	14.9965i	0.226286	−	0.495498i
$917$	−1.54683	+	10.7584i	−0.0510808	+	0.355275i
$918$		0			0
$919$	50.2660			1.65812			0.829061	−	0.559158i	$-0.188876\pi$
$919$	50.2660			1.65812			0.829061	+	0.559158i	$0.188876\pi$
$920$	−7.44651	−	29.5002i	−0.245504	−	0.972594i
$921$		0			0
$922$	−1.10404	+	0.709526i	−0.0363597	+	0.0233670i
$923$	12.4722	−	86.7457i	0.410526	−	2.85527i
$924$		0			0
$925$	57.6159	−	16.9176i	1.89440	−	0.556246i
$926$	2.24637	+	4.91887i	0.0738204	+	0.161644i
$927$		0			0
$928$	1.10191	+	7.66397i	0.0361721	+	0.251582i
$929$	45.0030	+	13.2141i	1.47650	+	0.433540i	0.918206	−	0.396103i	$-0.129638\pi$
$929$	45.0030	+	13.2141i	1.47650	+	0.433540i	0.558295	+	0.829643i	$0.311456\pi$
$930$		0			0
$931$	−20.0338	−	12.8750i	−0.656583	−	0.421960i
$932$	−4.39595	−	2.82511i	−0.143994	−	0.0925395i
$933$		0			0
$934$	−2.65708	−	0.780190i	−0.0869424	−	0.0255286i
$935$	1.65590	+	11.5170i	0.0541536	+	0.376647i
$936$		0			0
$937$	0.316944	+	0.694011i	0.0103541	+	0.0226724i	0.914738	−	0.404047i	$-0.132397\pi$
$937$	0.316944	+	0.694011i	0.0103541	+	0.0226724i	−0.904384	+	0.426719i	$0.859669\pi$
$938$	0.921159	−	0.270477i	0.0300769	−	0.00883138i
$939$		0			0
$940$	5.04131	−	35.0631i	0.164430	−	1.14363i
$941$	−27.2858	+	17.5355i	−0.889492	+	0.571642i	−0.903656	−	0.428258i	$-0.859127\pi$
$941$	−27.2858	+	17.5355i	−0.889492	+	0.571642i	0.0141648	+	0.999900i	$0.495491\pi$
$942$		0			0
$943$	−18.1863	+	1.90663i	−0.592226	+	0.0620884i
$944$	−2.71297			−0.0882997
$945$		0			0
$946$	−1.65707	+	11.5252i	−0.0538759	+	0.374715i
$947$	−13.0693	+	28.6178i	−0.424696	+	0.929954i	0.569462	+	0.822018i	$0.307152\pi$
$947$	−13.0693	+	28.6178i	−0.424696	+	0.929954i	−0.994158	+	0.107937i	$0.965576\pi$
$948$		0			0
$949$	18.4096	+	40.3114i	0.597602	+	1.30856i
$950$	−8.63577	−	9.96622i	−0.280182	−	0.323347i
$951$		0			0
$952$	1.30374	+	0.382812i	0.0422544	+	0.0124070i
$953$	−3.07721	+	3.55129i	−0.0996808	+	0.115038i	−0.803398	−	0.595442i	$-0.796977\pi$
$953$	−3.07721	+	3.55129i	−0.0996808	+	0.115038i	0.703717	+	0.710480i	$0.251522\pi$
$954$		0			0
$955$	74.0371	+	47.5808i	2.39578	+	1.53968i
$956$	19.0543	−	21.9899i	0.616261	−	0.711203i
$957$		0			0
$958$	0.569590	+	3.96158i	0.0184026	+	0.127993i
$959$	0.405497	+	0.467969i	0.0130942	+	0.0151115i
$960$		0			0
$961$	29.4380	−	8.64377i	0.949612	−	0.278831i
$962$	−10.7554	+	23.5510i	−0.346768	+	0.759315i
$963$		0			0
$964$	1.96899	−	1.26539i	0.0634168	−	0.0407555i
$965$	−0.350846			−0.0112941
$966$		0			0
$967$	−26.0335			−0.837180			−0.418590	−	0.908175i	$-0.637476\pi$
$967$	−26.0335			−0.837180			−0.418590	+	0.908175i	$0.637476\pi$
$968$	−2.39337	+	1.53813i	−0.0769259	+	0.0494373i
$969$		0			0
$970$	0.555390	−	1.21613i	0.0178325	−	0.0390477i
$971$	−1.29473	+	0.380168i	−0.0415500	+	0.0122002i	−0.302442	−	0.953168i	$-0.597802\pi$
$971$	−1.29473	+	0.380168i	−0.0415500	+	0.0122002i	0.260892	+	0.965368i	$0.415984\pi$
$972$		0			0
$973$	−7.83078	−	9.03720i	−0.251043	−	0.289719i
$974$	0.236386	+	1.64410i	0.00757430	+	0.0526804i
$975$		0			0
$976$	21.5161	−	24.8309i	0.688714	−	0.794818i
$977$	10.8844	+	6.99500i	0.348224	+	0.223790i	0.703047	−	0.711144i	$-0.251822\pi$
$977$	10.8844	+	6.99500i	0.348224	+	0.223790i	−0.354823	+	0.934934i	$0.615459\pi$
$978$		0			0
$979$	−10.8909	+	12.5687i	−0.348074	+	0.401698i
$980$	−37.9075	−	11.1306i	−1.21091	−	0.355555i
$981$		0			0
$982$	0.115291	+	0.133053i	0.00367907	+	0.00424588i
$983$	−4.04926	−	8.86663i	−0.129151	−	0.282802i	0.833999	−	0.551766i	$-0.186046\pi$
$983$	−4.04926	−	8.86663i	−0.129151	−	0.282802i	−0.963150	+	0.268964i	$0.913319\pi$
$984$		0			0
$985$	−24.1975	+	52.9851i	−0.770996	+	1.68825i
$986$	−0.100713	+	0.700475i	−0.00320736	+	0.0223077i
$987$		0			0
$988$	−43.8993			−1.39662
$989$	−10.4664	+	31.1714i	−0.332813	+	0.991193i
$990$		0			0
$991$	−17.6477	+	11.3415i	−0.560598	+	0.360274i	−0.790047	−	0.613046i	$-0.789944\pi$
$991$	−17.6477	+	11.3415i	−0.560598	+	0.360274i	0.229449	+	0.973321i	$0.426308\pi$
$992$	−0.393467	+	2.73662i	−0.0124926	+	0.0868879i
$993$		0			0
$994$	−4.90742	+	1.44095i	−0.155654	+	0.0457041i
$995$	29.2559	+	64.0615i	0.927474	+	2.03088i
$996$		0			0
$997$	1.29155	+	8.98293i	0.0409038	+	0.284492i	0.999999	+	0.00140859i	$0.000448368\pi$
$997$	1.29155	+	8.98293i	0.0409038	+	0.284492i	−0.959095	+	0.283084i	$0.908643\pi$
$998$	−6.23705	−	1.83136i	−0.197430	−	0.0579708i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.b.127.1		10
3.2	odd	2		69.2.e.a.58.1	yes	10
23.2	even	11	inner	207.2.i.b.163.1		10
23.5	odd	22		4761.2.a.bq.1.3		5
23.18	even	11		4761.2.a.br.1.3		5
69.2	odd	22		69.2.e.a.25.1	✓	10
69.5	even	22		1587.2.a.p.1.3		5
69.41	odd	22		1587.2.a.o.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.a.25.1	✓	10	69.2	odd	22
69.2.e.a.58.1	yes	10	3.2	odd	2
207.2.i.b.127.1		10	1.1	even	1	trivial
207.2.i.b.163.1		10	23.2	even	11	inner
1587.2.a.o.1.3		5	69.41	odd	22
1587.2.a.p.1.3		5	69.5	even	22
4761.2.a.bq.1.3		5	23.5	odd	22
4761.2.a.br.1.3		5	23.18	even	11

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.402869 - 0.258908i) q^{2} +(-0.735560 + 1.61065i) q^{4} +(-3.37102 + 0.989821i) q^{5} +(0.527646 + 0.608936i) q^{7} +(0.256983 + 1.78736i) q^{8} +(-1.10181 + 1.27155i) q^{10} +(2.98325 + 1.91722i) q^{11} +(-4.32972 + 4.99677i) q^{13} +(0.370231 + 0.108710i) q^{14} +(-1.75278 - 2.02282i) q^{16} +(-0.387956 - 0.849505i) q^{17} +(1.55773 - 3.41095i) q^{19} +(0.885331 - 6.15762i) q^{20} +1.69824 q^{22} +(4.71737 + 0.863983i) q^{23} +(6.17778 - 3.97022i) q^{25} +(-0.450608 + 3.13404i) q^{26} +(-1.36890 + 0.401945i) q^{28} +(-0.657326 - 1.43934i) q^{29} +(-0.0804100 - 0.559264i) q^{31} +(-4.69505 - 1.37859i) q^{32} +(-0.376239 - 0.241794i) q^{34} +(-2.38145 - 1.53046i) q^{35} +(7.84580 + 2.30374i) q^{37} +(-0.255563 - 1.77748i) q^{38} +(-2.63546 - 5.77086i) q^{40} +(-3.65843 + 1.07421i) q^{41} +(-0.975753 + 6.78651i) q^{43} +(-5.28234 + 3.39475i) q^{44} +(2.12417 - 0.873293i) q^{46} +5.69427 q^{47} +(0.903811 - 6.28614i) q^{49} +(1.46091 - 3.19895i) q^{50} +(-4.86328 - 10.6491i) q^{52} +(4.57100 + 5.27521i) q^{53} +(-11.9543 - 3.51011i) q^{55} +(-0.952791 + 1.09958i) q^{56} +(-0.637474 - 0.409680i) q^{58} +(0.663766 - 0.766027i) q^{59} +(1.74697 + 12.1505i) q^{61} +(-0.177193 - 0.204491i) q^{62} +(2.88789 - 0.847960i) q^{64} +(9.64969 - 21.1299i) q^{65} +(2.09309 - 1.34515i) q^{67} +1.65362 q^{68} -1.35566 q^{70} +(-11.1508 + 7.16620i) q^{71} +(2.78441 - 6.09701i) q^{73} +(3.75729 - 1.10324i) q^{74} +(4.34805 + 5.01792i) q^{76} +(0.406637 + 2.82823i) q^{77} +(-0.940694 + 1.08562i) q^{79} +(7.91090 + 5.08403i) q^{80} +(-1.19575 + 1.37997i) q^{82} +(-1.68020 - 0.493351i) q^{83} +(2.14867 + 2.47969i) q^{85} +(1.36398 + 2.98671i) q^{86} +(-2.66011 + 5.82484i) q^{88} +(-0.667422 + 4.64202i) q^{89} -5.32728 q^{91} +(-4.86148 + 6.96252i) q^{92} +(2.29404 - 1.47429i) q^{94} +(-1.87491 + 13.0403i) q^{95} +(-0.762432 + 0.223870i) q^{97} +(-1.26342 - 2.76650i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} - 5 q^{5} - 8 q^{7} + 15 q^{8} - 2 q^{10} - 7 q^{11} - 30 q^{13} - q^{14} + 12 q^{16} + 2 q^{17} + 10 q^{19} - 4 q^{20} + 6 q^{22} + q^{23} + 24 q^{25} - q^{26} + 9 q^{28} + 14 q^{29}+ \cdots - 58 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 - 5 * q^5 - 8 * q^7 + 15 * q^8 - 2 * q^10 - 7 * q^11 - 30 * q^13 - q^14 + 12 * q^16 + 2 * q^17 + 10 * q^19 - 4 * q^20 + 6 * q^22 + q^23 + 24 * q^25 - q^26 + 9 * q^28 + 14 * q^29 - 28 * q^31 - 23 * q^32 - 8 * q^34 + 4 * q^35 + 19 * q^37 + 15 * q^38 - 13 * q^40 - 19 * q^41 - 24 * q^43 - 54 * q^44 + 18 * q^46 - 26 * q^47 - 13 * q^49 + 36 * q^50 - 57 * q^52 + q^53 - 24 * q^55 + 10 * q^56 + 10 * q^58 - 2 * q^59 + 30 * q^61 + 24 * q^62 + 13 * q^64 + 4 * q^65 + 4 * q^67 + 50 * q^68 + 6 * q^70 + 14 * q^71 - 26 * q^73 + 12 * q^74 + 19 * q^76 + 43 * q^77 + 20 * q^79 + 5 * q^80 + 10 * q^82 - 18 * q^83 + 21 * q^85 - 14 * q^86 - 38 * q^88 + 5 * q^89 + 46 * q^91 - 52 * q^92 - 6 * q^94 - 5 * q^95 + 15 * q^97 - 58 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more