LMFDB - Embedded newform 2100.2.s.a.1457.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1457,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("2100.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.s (of order $4$, degree $2$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{12} + 424x^{8} - 159x^{4} + 16 $ x^16 + 24x^12 + 424x^8 - 159*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.8
Root			$1.11470 + 1.82181i$ of defining polynomial
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.a.1793.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73015 - 0.0811423i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.98683 - 0.280776i) q^{9} +O(q^{10})$	$q+(1.73015 - 0.0811423i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.98683 - 0.280776i) q^{9} -2.33205i q^{11} +(-3.22550 + 3.22550i) q^{13} +(4.22402 - 4.22402i) q^{17} -7.12311i q^{19} +(-1.28078 - 1.16602i) q^{21} +(-5.87302 - 5.87302i) q^{23} +(5.14488 - 0.728143i) q^{27} -10.6378 q^{29} +8.24621 q^{31} +(-0.189228 - 4.03479i) q^{33} +(3.62258 + 3.62258i) q^{37} +(-5.31888 + 5.84233i) q^{39} -4.66410i q^{41} +(4.41674 - 4.41674i) q^{43} +(-1.64901 + 1.64901i) q^{47} +1.00000i q^{49} +(6.96543 - 7.65093i) q^{51} +(5.87302 + 5.87302i) q^{53} +(-0.577985 - 12.3240i) q^{57} +11.9473 q^{59} +3.12311 q^{61} +(-2.31055 - 1.91347i) q^{63} +(2.03427 + 2.03427i) q^{67} +(-10.6378 - 9.68466i) q^{69} -1.02248i q^{71} +(-4.24264 + 4.24264i) q^{73} +(-1.64901 + 1.64901i) q^{77} -1.43845i q^{79} +(8.84233 - 1.67726i) q^{81} +(-5.87302 - 5.87302i) q^{83} +(-18.4049 + 0.863172i) q^{87} -9.32819 q^{89} +4.56155 q^{91} +(14.2672 - 0.669116i) q^{93} +(0.397078 + 0.397078i) q^{97} +(-0.654784 - 6.96543i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{21} - 4 q^{51} - 16 q^{61} + 92 q^{81} + 40 q^{91}+O(q^{100}) $ 16 * q - 4 * q^21 - 4 * q^51 - 16 * q^61 + 92 * q^81 + 40 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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			0
$2$		0			0
$3$	1.73015	−	0.0811423i	0.998902	−	0.0468475i
$3$	1.73015	−	0.0811423i	0.998902	−	0.0468475i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$	2.98683	−	0.280776i	0.995611	−	0.0935921i
$10$		0			0
$11$		−	2.33205i		−	0.703139i	−0.936162	−	0.351569i	$-0.885648\pi$
$11$		−	2.33205i		−	0.703139i	0.936162	−	0.351569i	$-0.114352\pi$
$12$		0			0
$13$	−3.22550	+	3.22550i	−0.894594	+	0.894594i	−0.994951	−	0.100357i	$-0.968001\pi$
$13$	−3.22550	+	3.22550i	−0.894594	+	0.894594i	0.100357	+	0.994951i	$0.468001\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.22402	−	4.22402i	1.02447	−	1.02447i	0.0247820	−	0.999693i	$-0.492111\pi$
$17$	4.22402	−	4.22402i	1.02447	−	1.02447i	0.999693	−	0.0247820i	$-0.00788916\pi$
$18$		0			0
$19$		−	7.12311i		−	1.63415i	−0.576530	−	0.817076i	$-0.695593\pi$
$19$		−	7.12311i		−	1.63415i	0.576530	−	0.817076i	$-0.304407\pi$
$20$		0			0
$21$	−1.28078	−	1.16602i	−0.279488	−	0.254447i
$22$		0			0
$23$	−5.87302	−	5.87302i	−1.22461	−	1.22461i	−0.965975	−	0.258635i	$-0.916727\pi$
$23$	−5.87302	−	5.87302i	−1.22461	−	1.22461i	−0.258635	−	0.965975i	$-0.583273\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	5.14488	−	0.728143i	0.990133	−	0.140131i
$28$		0			0
$29$	−10.6378			−1.97538			−0.987691	−	0.156417i	$-0.950006\pi$
$29$	−10.6378			−1.97538			−0.987691	+	0.156417i	$0.950006\pi$
$30$		0			0
$31$	8.24621			1.48106			0.740532	−	0.672022i	$-0.234574\pi$
$31$	8.24621			1.48106			0.740532	+	0.672022i	$0.234574\pi$
$32$		0			0
$33$	−0.189228	−	4.03479i	−0.0329403	−	0.702367i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.62258	+	3.62258i	0.595549	+	0.595549i	0.939125	−	0.343576i	$-0.111638\pi$
$37$	3.62258	+	3.62258i	0.595549	+	0.595549i	−0.343576	+	0.939125i	$0.611638\pi$
$38$		0			0
$39$	−5.31888	+	5.84233i	−0.851702	+	0.935521i
$40$		0			0
$41$		−	4.66410i		−	0.728409i	−0.931319	−	0.364205i	$-0.881341\pi$
$41$		−	4.66410i		−	0.728409i	0.931319	−	0.364205i	$-0.118659\pi$
$42$		0			0
$43$	4.41674	−	4.41674i	0.673546	−	0.673546i	−0.284986	−	0.958532i	$-0.591989\pi$
$43$	4.41674	−	4.41674i	0.673546	−	0.673546i	0.958532	+	0.284986i	$0.0919888\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.64901	+	1.64901i	−0.240532	+	0.240532i	−0.817070	−	0.576538i	$-0.804403\pi$
$47$	−1.64901	+	1.64901i	−0.240532	+	0.240532i	0.576538	+	0.817070i	$0.304403\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	6.96543	−	7.65093i	0.975356	−	1.07134i
$52$		0			0
$53$	5.87302	+	5.87302i	0.806722	+	0.806722i	0.984136	−	0.177414i	$-0.0567732\pi$
$53$	5.87302	+	5.87302i	0.806722	+	0.806722i	−0.177414	+	0.984136i	$0.556773\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.577985	−	12.3240i	−0.0765560	−	1.63236i
$58$		0			0
$59$	11.9473			1.55541			0.777705	−	0.628630i	$-0.216384\pi$
$59$	11.9473			1.55541			0.777705	+	0.628630i	$0.216384\pi$
$60$		0			0
$61$	3.12311			0.399873			0.199936	−	0.979809i	$-0.435926\pi$
$61$	3.12311			0.399873			0.199936	+	0.979809i	$0.435926\pi$
$62$		0			0
$63$	−2.31055	−	1.91347i	−0.291102	−	0.241075i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.03427	+	2.03427i	0.248526	+	0.248526i	0.820365	−	0.571840i	$-0.193770\pi$
$67$	2.03427	+	2.03427i	0.248526	+	0.248526i	−0.571840	+	0.820365i	$0.693770\pi$
$68$		0			0
$69$	−10.6378	−	9.68466i	−1.28064	−	1.16590i
$70$		0			0
$71$		−	1.02248i		−	0.121346i	−0.998158	−	0.0606730i	$-0.980675\pi$
$71$		−	1.02248i		−	0.121346i	0.998158	−	0.0606730i	$-0.0193247\pi$
$72$		0			0
$73$	−4.24264	+	4.24264i	−0.496564	+	0.496564i	−0.910366	−	0.413803i	$-0.864200\pi$
$73$	−4.24264	+	4.24264i	−0.496564	+	0.496564i	0.413803	+	0.910366i	$0.364200\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.64901	+	1.64901i	−0.187922	+	0.187922i
$78$		0			0
$79$		−	1.43845i		−	0.161838i	−0.996721	−	0.0809190i	$-0.974214\pi$
$79$		−	1.43845i		−	0.161838i	0.996721	−	0.0809190i	$-0.0257855\pi$
$80$		0			0
$81$	8.84233	−	1.67726i	0.982481	−	0.186363i
$82$		0			0
$83$	−5.87302	−	5.87302i	−0.644648	−	0.644648i	0.307046	−	0.951695i	$-0.400659\pi$
$83$	−5.87302	−	5.87302i	−0.644648	−	0.644648i	−0.951695	+	0.307046i	$0.900659\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−18.4049	+	0.863172i	−1.97321	+	0.0925417i
$88$		0			0
$89$	−9.32819			−0.988786			−0.494393	−	0.869238i	$-0.664610\pi$
$89$	−9.32819			−0.988786			−0.494393	+	0.869238i	$0.664610\pi$
$90$		0			0
$91$	4.56155			0.478181
$92$		0			0
$93$	14.2672	−	0.669116i	1.47944	−	0.0693841i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.397078	+	0.397078i	0.0403171	+	0.0403171i	0.726978	−	0.686661i	$-0.240924\pi$
$97$	0.397078	+	0.397078i	0.0403171	+	0.0403171i	−0.686661	+	0.726978i	$0.740924\pi$
$98$		0			0
$99$	−0.654784	−	6.96543i	−0.0658083	−	0.700053i
$100$		0			0
$101$		−	16.6114i		−	1.65290i	−0.563011	−	0.826449i	$-0.690357\pi$
$101$		−	16.6114i		−	1.65290i	0.563011	−	0.826449i	$-0.309643\pi$
$102$		0			0
$103$	−11.8849	+	11.8849i	−1.17105	+	1.17105i	−0.189093	+	0.981959i	$0.560555\pi$
$103$	−11.8849	+	11.8849i	−1.17105	+	1.17105i	−0.981959	+	0.189093i	$0.939445\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.02102	−	4.02102i	0.388726	−	0.388726i	−0.485507	−	0.874233i	$-0.661365\pi$
$107$	4.02102	−	4.02102i	0.388726	−	0.388726i	0.874233	+	0.485507i	$0.161365\pi$
$108$		0			0
$109$		−	15.9309i		−	1.52590i	−0.646457	−	0.762950i	$-0.723750\pi$
$109$		−	15.9309i		−	1.52590i	0.646457	−	0.762950i	$-0.276250\pi$
$110$		0			0
$111$	6.56155	+	5.97366i	0.622795	+	0.566995i
$112$		0			0
$113$	5.87302	+	5.87302i	0.552488	+	0.552488i	0.927158	−	0.374670i	$-0.122244\pi$
$113$	5.87302	+	5.87302i	0.552488	+	0.552488i	−0.374670	+	0.927158i	$0.622244\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−8.72840	+	10.5397i	−0.806940	+	0.974394i
$118$		0			0
$119$	−5.97366			−0.547605
$120$		0			0
$121$	5.56155			0.505596
$122$		0			0
$123$	−0.378455	−	8.06958i	−0.0341242	−	0.727610i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	12.1079	+	12.1079i	1.07440	+	1.07440i	0.997000	+	0.0773990i	$0.0246615\pi$
$127$	12.1079	+	12.1079i	1.07440	+	1.07440i	0.0773990	+	0.997000i	$0.475338\pi$
$128$		0			0
$129$	7.28323	−	8.00000i	0.641253	−	0.704361i
$130$		0			0
$131$		−	13.9923i		−	1.22251i	−0.791433	−	0.611256i	$-0.790665\pi$
$131$		−	13.9923i		−	1.22251i	0.791433	−	0.611256i	$-0.209335\pi$
$132$		0			0
$133$	−5.03680	+	5.03680i	−0.436746	+	0.436746i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.17104	+	9.17104i	−0.783535	+	0.783535i	−0.980425	−	0.196891i	$-0.936916\pi$
$137$	−9.17104	+	9.17104i	−0.783535	+	0.783535i	0.196891	+	0.980425i	$0.436916\pi$
$138$		0			0
$139$			10.0000i			0.848189i	0.905618	+	0.424094i	$0.139408\pi$
$139$			10.0000i			0.848189i	−0.905618	+	0.424094i	$0.860592\pi$
$140$		0			0
$141$	−2.71922	+	2.98683i	−0.229000	+	0.251537i
$142$		0			0
$143$	7.52203	+	7.52203i	0.629024	+	0.629024i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.0811423	+	1.73015i	0.00669250	+	0.142700i
$148$		0			0
$149$	7.28323			0.596666			0.298333	−	0.954462i	$-0.403569\pi$
$149$	7.28323			0.596666			0.298333	+	0.954462i	$0.403569\pi$
$150$		0			0
$151$	−1.43845			−0.117059			−0.0585296	−	0.998286i	$-0.518641\pi$
$151$	−1.43845			−0.117059			−0.0585296	+	0.998286i	$0.518641\pi$
$152$		0			0
$153$	11.4304	−	13.8024i	0.924095	−	1.11586i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.174098	−	0.174098i	−0.0138945	−	0.0138945i	0.700125	−	0.714020i	$-0.253127\pi$
$157$	−0.174098	−	0.174098i	−0.0138945	−	0.0138945i	−0.714020	+	0.700125i	$0.753127\pi$
$158$		0			0
$159$	10.6378	+	9.68466i	0.843629	+	0.768043i
$160$		0			0
$161$			8.30571i			0.654582i
$162$		0			0
$163$	−4.86270	+	4.86270i	−0.380876	+	0.380876i	−0.871418	−	0.490542i	$-0.836799\pi$
$163$	−4.86270	+	4.86270i	−0.380876	+	0.380876i	0.490542	+	0.871418i	$0.336799\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.50102	+	3.50102i	−0.270917	+	0.270917i	−0.829469	−	0.558552i	$-0.811357\pi$
$167$	−3.50102	+	3.50102i	−0.270917	+	0.270917i	0.558552	+	0.829469i	$0.311357\pi$
$168$		0			0
$169$		−	7.80776i		−	0.600597i
$170$		0			0
$171$	−2.00000	−	21.2755i	−0.152944	−	1.62698i
$172$		0			0
$173$	7.52203	+	7.52203i	0.571889	+	0.571889i	0.932656	−	0.360767i	$-0.117485\pi$
$173$	7.52203	+	7.52203i	0.571889	+	0.571889i	−0.360767	+	0.932656i	$0.617485\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	20.6707	−	0.969433i	1.55370	−	0.0728671i
$178$		0			0
$179$	−15.5889			−1.16517			−0.582586	−	0.812769i	$-0.697959\pi$
$179$	−15.5889			−1.16517			−0.582586	+	0.812769i	$0.697959\pi$
$180$		0			0
$181$	4.24621			0.315618			0.157809	−	0.987470i	$-0.449557\pi$
$181$	4.24621			0.315618			0.157809	+	0.987470i	$0.449557\pi$
$182$		0			0
$183$	5.40344	−	0.253416i	0.399434	−	0.0187330i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−9.85061	−	9.85061i	−0.720348	−	0.720348i
$188$		0			0
$189$	−4.15286	−	3.12311i	−0.302076	−	0.227173i
$190$		0			0
$191$		−	14.2794i		−	1.03322i	−0.856221	−	0.516610i	$-0.827194\pi$
$191$		−	14.2794i		−	1.03322i	0.856221	−	0.516610i	$-0.172806\pi$
$192$		0			0
$193$	−8.48528	+	8.48528i	−0.610784	+	0.610784i	−0.943150	−	0.332366i	$-0.892153\pi$
$193$	−8.48528	+	8.48528i	−0.610784	+	0.610784i	0.332366	+	0.943150i	$0.392153\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.723002	−	0.723002i	0.0515118	−	0.0515118i	−0.680882	−	0.732393i	$-0.738403\pi$
$197$	0.723002	−	0.723002i	0.0515118	−	0.0515118i	0.732393	+	0.680882i	$0.238403\pi$
$198$		0			0
$199$			10.4924i			0.743788i	0.928275	+	0.371894i	$0.121292\pi$
$199$			10.4924i			0.743788i	−0.928275	+	0.371894i	$0.878708\pi$
$200$		0			0
$201$	3.68466	+	3.35453i	0.259896	+	0.236610i
$202$		0			0
$203$	7.52203	+	7.52203i	0.527943	+	0.527943i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−19.1907	−	15.8927i	−1.33385	−	1.10462i
$208$		0			0
$209$	−16.6114			−1.14904
$210$		0			0
$211$	19.6847			1.35515			0.677574	−	0.735455i	$-0.263031\pi$
$211$	19.6847			1.35515			0.677574	+	0.735455i	$0.263031\pi$
$212$		0			0
$213$	−0.0829663	−	1.76904i	−0.00568476	−	0.121213i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.83095	−	5.83095i	−0.395831	−	0.395831i
$218$		0			0
$219$	−6.99614	+	7.68466i	−0.472756	+	0.519281i
$220$		0			0
$221$			27.2492i			1.83298i
$222$		0			0
$223$	0.571175	−	0.571175i	0.0382487	−	0.0382487i	−0.687724	−	0.725972i	$-0.741390\pi$
$223$	0.571175	−	0.571175i	0.0382487	−	0.0382487i	0.725972	+	0.687724i	$0.241390\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.5430	+	11.5430i	−0.766139	+	0.766139i	−0.977424	−	0.211285i	$-0.932235\pi$
$227$	−11.5430	+	11.5430i	−0.766139	+	0.766139i	0.211285	+	0.977424i	$0.432235\pi$
$228$		0			0
$229$			8.24621i			0.544925i	0.962166	+	0.272462i	$0.0878381\pi$
$229$			8.24621i			0.544925i	−0.962166	+	0.272462i	$0.912162\pi$
$230$		0			0
$231$	−2.71922	+	2.98683i	−0.178912	+	0.196519i
$232$		0			0
$233$	−15.7671	−	15.7671i	−1.03293	−	1.03293i	−0.999439	−	0.0334960i	$-0.989336\pi$
$233$	−15.7671	−	15.7671i	−1.03293	−	1.03293i	−0.0334960	−	0.999439i	$-0.510664\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.116719	−	2.48873i	−0.00758170	−	0.161660i
$238$		0			0
$239$	−4.95118			−0.320265			−0.160133	−	0.987095i	$-0.551192\pi$
$239$	−4.95118			−0.320265			−0.160133	+	0.987095i	$0.551192\pi$
$240$		0			0
$241$	−16.2462			−1.04651			−0.523255	−	0.852176i	$-0.675283\pi$
$241$	−16.2462			−1.04651			−0.523255	+	0.852176i	$0.675283\pi$
$242$		0			0
$243$	15.1625	−	3.61940i	0.972672	−	0.232185i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	22.9756	+	22.9756i	1.46190	+	1.46190i
$248$		0			0
$249$	−10.6378	−	9.68466i	−0.674141	−	0.613740i
$250$		0			0
$251$			11.9473i			0.754109i	0.926191	+	0.377054i	$0.123063\pi$
$251$			11.9473i			0.754109i	−0.926191	+	0.377054i	$0.876937\pi$
$252$		0			0
$253$	−13.6962	+	13.6962i	−0.861071	+	0.861071i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.44600	+	1.44600i	−0.0901993	+	0.0901993i	−0.750767	−	0.660567i	$-0.770316\pi$
$257$	−1.44600	+	1.44600i	−0.0901993	+	0.0901993i	0.660567	+	0.750767i	$0.270316\pi$
$258$		0			0
$259$		−	5.12311i		−	0.318334i
$260$		0			0
$261$	−31.7732	+	2.98683i	−1.96671	+	0.184880i
$262$		0			0
$263$	−2.57501	−	2.57501i	−0.158782	−	0.158782i	0.623245	−	0.782027i	$-0.285814\pi$
$263$	−2.57501	−	2.57501i	−0.158782	−	0.158782i	−0.782027	+	0.623245i	$0.785814\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−16.1392	+	0.756911i	−0.987701	+	0.0463222i
$268$		0			0
$269$	19.2306			1.17251			0.586254	−	0.810127i	$-0.300602\pi$
$269$	19.2306			1.17251			0.586254	+	0.810127i	$0.300602\pi$
$270$		0			0
$271$	8.87689			0.539233			0.269616	−	0.962968i	$-0.413103\pi$
$271$	8.87689			0.539233			0.269616	+	0.962968i	$0.413103\pi$
$272$		0			0
$273$	7.89217	−	0.370135i	0.477656	−	0.0224016i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.86270	−	4.86270i	−0.292171	−	0.292171i	0.545766	−	0.837937i	$-0.316239\pi$
$277$	−4.86270	−	4.86270i	−0.292171	−	0.292171i	−0.837937	+	0.545766i	$0.816239\pi$
$278$		0			0
$279$	24.6300	−	2.31534i	1.47456	−	0.138616i
$280$		0			0
$281$			15.3019i			0.912832i	0.889766	+	0.456416i	$0.150867\pi$
$281$			15.3019i			0.912832i	−0.889766	+	0.456416i	$0.849133\pi$
$282$		0			0
$283$	−5.43387	+	5.43387i	−0.323010	+	0.323010i	−0.849921	−	0.526910i	$-0.823350\pi$
$283$	−5.43387	+	5.43387i	−0.323010	+	0.323010i	0.526910	+	0.849921i	$0.323350\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.29801	+	3.29801i	−0.194676	+	0.194676i
$288$		0			0
$289$		−	18.6847i		−	1.09910i
$290$		0			0
$291$	0.719224	+	0.654784i	0.0421616	+	0.0383841i
$292$		0			0
$293$	−2.37201	−	2.37201i	−0.138574	−	0.138574i	0.634417	−	0.772991i	$-0.281240\pi$
$293$	−2.37201	−	2.37201i	−0.138574	−	0.138574i	−0.772991	+	0.634417i	$0.781240\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.69807	−	11.9981i	−0.0985317	−	0.696201i
$298$		0			0
$299$	37.8869			2.19106
$300$		0			0
$301$	−6.24621			−0.360026
$302$		0			0
$303$	−1.34789	−	28.7402i	−0.0774342	−	1.65108i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	23.9927	+	23.9927i	1.36934	+	1.36934i	0.861384	+	0.507955i	$0.169598\pi$
$307$	23.9927	+	23.9927i	1.36934	+	1.36934i	0.507955	+	0.861384i	$0.330402\pi$
$308$		0			0
$309$	−19.5983	+	21.5270i	−1.11491	+	1.22463i
$310$		0			0
$311$			2.04496i			0.115959i	0.998318	+	0.0579795i	$0.0184658\pi$
$311$			2.04496i			0.115959i	−0.998318	+	0.0579795i	$0.981534\pi$
$312$		0			0
$313$	−9.32832	+	9.32832i	−0.527268	+	0.527268i	−0.919757	−	0.392489i	$-0.871614\pi$
$313$	−9.32832	+	9.32832i	−0.527268	+	0.527268i	0.392489	+	0.919757i	$0.371614\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.3631	−	22.3631i	1.25604	−	1.25604i	0.303067	−	0.952969i	$-0.401989\pi$
$317$	22.3631	−	22.3631i	1.25604	−	1.25604i	0.952969	−	0.303067i	$-0.0980107\pi$
$318$		0			0
$319$			24.8078i			1.38897i
$320$		0			0
$321$	6.63068	−	7.28323i	0.370089	−	0.406510i
$322$		0			0
$323$	−30.0881	−	30.0881i	−1.67415	−	1.67415i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.29267	−	27.5628i	−0.0714846	−	1.52423i
$328$		0			0
$329$	2.33205			0.128570
$330$		0			0
$331$	10.2462			0.563183			0.281591	−	0.959534i	$-0.409138\pi$
$331$	10.2462			0.563183			0.281591	+	0.959534i	$0.409138\pi$
$332$		0			0
$333$	11.8372	+	9.80291i	0.648674	+	0.537196i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	20.9413	+	20.9413i	1.14075	+	1.14075i	0.988314	+	0.152434i	$0.0487111\pi$
$337$	20.9413	+	20.9413i	1.14075	+	1.14075i	0.152434	+	0.988314i	$0.451289\pi$
$338$		0			0
$339$	10.6378	+	9.68466i	0.577764	+	0.525998i
$340$		0			0
$341$		−	19.2306i		−	1.04139i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.1731	−	16.1731i	0.868216	−	0.868216i	−0.124059	−	0.992275i	$-0.539591\pi$
$347$	16.1731	−	16.1731i	0.868216	−	0.868216i	0.992275	+	0.124059i	$0.0395912\pi$
$348$		0			0
$349$		−	5.36932i		−	0.287413i	−0.989620	−	0.143706i	$-0.954098\pi$
$349$		−	5.36932i		−	0.287413i	0.989620	−	0.143706i	$-0.0459021\pi$
$350$		0			0
$351$	−14.2462	+	18.9435i	−0.760407	+	1.01113i
$352$		0			0
$353$	5.67002	+	5.67002i	0.301785	+	0.301785i	0.841712	−	0.539927i	$-0.181548\pi$
$353$	5.67002	+	5.67002i	0.301785	+	0.301785i	−0.539927	+	0.841712i	$0.681548\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−10.3353	+	0.484717i	−0.547004	+	0.0256539i
$358$		0			0
$359$	26.9621			1.42300			0.711502	−	0.702684i	$-0.248015\pi$
$359$	26.9621			1.42300			0.711502	+	0.702684i	$0.248015\pi$
$360$		0			0
$361$	−31.7386			−1.67045
$362$		0			0
$363$	9.62232	−	0.451277i	0.505041	−	0.0236859i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−6.22803	−	6.22803i	−0.325101	−	0.325101i	0.525619	−	0.850720i	$-0.323834\pi$
$367$	−6.22803	−	6.22803i	−0.325101	−	0.325101i	−0.850720	+	0.525619i	$0.823834\pi$
$368$		0			0
$369$	−1.30957	−	13.9309i	−0.0681734	−	0.725212i
$370$		0			0
$371$		−	8.30571i		−	0.431211i
$372$		0			0
$373$	23.3238	−	23.3238i	1.20766	−	1.20766i	0.235878	−	0.971783i	$-0.424203\pi$
$373$	23.3238	−	23.3238i	1.20766	−	1.20766i	0.971783	−	0.235878i	$-0.0757967\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	34.3121	−	34.3121i	1.76717	−	1.76717i
$378$		0			0
$379$			16.4924i			0.847159i	0.905859	+	0.423579i	$0.139227\pi$
$379$			16.4924i			0.847159i	−0.905859	+	0.423579i	$0.860773\pi$
$380$		0			0
$381$	21.9309	+	19.9660i	1.12355	+	1.02289i
$382$		0			0
$383$	7.31903	+	7.31903i	0.373985	+	0.373985i	0.868926	−	0.494941i	$-0.164810\pi$
$383$	7.31903	+	7.31903i	0.373985	+	0.373985i	−0.494941	+	0.868926i	$0.664810\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	11.9519	−	14.4322i	0.607551	−	0.733628i
$388$		0			0
$389$	−10.6378			−0.539356			−0.269678	−	0.962951i	$-0.586917\pi$
$389$	−10.6378			−0.539356			−0.269678	+	0.962951i	$0.586917\pi$
$390$		0			0
$391$	−49.6155			−2.50917
$392$		0			0
$393$	−1.13537	−	24.2087i	−0.0572716	−	1.22117i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−17.7158	−	17.7158i	−0.889132	−	0.889132i	0.105307	−	0.994440i	$-0.466417\pi$
$397$	−17.7158	−	17.7158i	−0.889132	−	0.889132i	−0.994440	+	0.105307i	$0.966417\pi$
$398$		0			0
$399$	−8.30571	+	9.12311i	−0.415806	+	0.456727i
$400$		0			0
$401$			24.6300i			1.22997i	0.788540	+	0.614983i	$0.210837\pi$
$401$			24.6300i			1.22997i	−0.788540	+	0.614983i	$0.789163\pi$
$402$		0			0
$403$	−26.5982	+	26.5982i	−1.32495	+	1.32495i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.44804	−	8.44804i	0.418754	−	0.418754i
$408$		0			0
$409$		−	3.12311i		−	0.154428i	−0.997015	−	0.0772138i	$-0.975398\pi$
$409$		−	3.12311i		−	0.154428i	0.997015	−	0.0772138i	$-0.0246024\pi$
$410$		0			0
$411$	−15.1231	+	16.6114i	−0.745968	+	0.819381i
$412$		0			0
$413$	−8.44804	−	8.44804i	−0.415701	−	0.415701i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.811423	+	17.3015i	0.0397355	+	0.847258i
$418$		0			0
$419$	−11.9473			−0.583665			−0.291833	−	0.956469i	$-0.594265\pi$
$419$	−11.9473			−0.583665			−0.291833	+	0.956469i	$0.594265\pi$
$420$		0			0
$421$	−22.1771			−1.08084			−0.540422	−	0.841394i	$-0.681736\pi$
$421$	−22.1771			−1.08084			−0.540422	+	0.841394i	$0.681736\pi$
$422$		0			0
$423$	−4.46230	+	5.38831i	−0.216965	+	0.261989i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.20837	−	2.20837i	−0.106870	−	0.106870i
$428$		0			0
$429$	13.6246	+	12.4039i	0.657801	+	0.598865i
$430$		0			0
$431$		−	4.95118i		−	0.238490i	−0.992865	−	0.119245i	$-0.961953\pi$
$431$		−	4.95118i		−	0.238490i	0.992865	−	0.119245i	$-0.0380474\pi$
$432$		0			0
$433$	−2.65433	+	2.65433i	−0.127559	+	0.127559i	−0.768004	−	0.640445i	$-0.778750\pi$
$433$	−2.65433	+	2.65433i	−0.127559	+	0.127559i	0.640445	+	0.768004i	$0.278750\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−41.8342	+	41.8342i	−2.00120	+	2.00120i
$438$		0			0
$439$			10.4924i			0.500776i	0.968146	+	0.250388i	$0.0805582\pi$
$439$			10.4924i			0.500776i	−0.968146	+	0.250388i	$0.919442\pi$
$440$		0			0
$441$	0.280776	+	2.98683i	0.0133703	+	0.142230i
$442$		0			0
$443$	12.8751	+	12.8751i	0.611712	+	0.611712i	0.943392	−	0.331680i	$-0.107615\pi$
$443$	12.8751	+	12.8751i	0.611712	+	0.611712i	−0.331680	+	0.943392i	$0.607615\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.6011	−	0.590978i	0.596010	−	0.0279523i
$448$		0			0
$449$	−5.97366			−0.281915			−0.140957	−	0.990016i	$-0.545018\pi$
$449$	−5.97366			−0.281915			−0.140957	+	0.990016i	$0.545018\pi$
$450$		0			0
$451$	−10.8769			−0.512173
$452$		0			0
$453$	−2.48873	+	0.116719i	−0.116931	+	0.00548393i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.0444	+	14.0444i	0.656968	+	0.656968i	0.954661	−	0.297694i	$-0.0962174\pi$
$457$	14.0444	+	14.0444i	0.656968	+	0.656968i	−0.297694	+	0.954661i	$0.596217\pi$
$458$		0			0
$459$	18.6564	−	24.8078i	0.870805	−	1.15793i
$460$		0			0
$461$			18.6564i			0.868914i	0.900692	+	0.434457i	$0.143060\pi$
$461$			18.6564i			0.868914i	−0.900692	+	0.434457i	$0.856940\pi$
$462$		0			0
$463$	10.0736	−	10.0736i	0.468160	−	0.468160i	−0.433158	−	0.901318i	$-0.642601\pi$
$463$	10.0736	−	10.0736i	0.468160	−	0.468160i	0.901318	+	0.433158i	$0.142601\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−28.4391	+	28.4391i	−1.31601	+	1.31601i	−0.399097	+	0.916909i	$0.630676\pi$
$467$	−28.4391	+	28.4391i	−1.31601	+	1.31601i	−0.916909	+	0.399097i	$0.869324\pi$
$468$		0			0
$469$		−	2.87689i		−	0.132843i
$470$		0			0
$471$	−0.315342	−	0.287088i	−0.0145302	−	0.0132283i
$472$		0			0
$473$	−10.3000	−	10.3000i	−0.473597	−	0.473597i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	19.1907	+	15.8927i	0.878684	+	0.727678i
$478$		0			0
$479$	23.3205			1.06554			0.532770	−	0.846260i	$-0.321151\pi$
$479$	23.3205			1.06554			0.532770	+	0.846260i	$0.321151\pi$
$480$		0			0
$481$	−23.3693			−1.06555
$482$		0			0
$483$	0.673944	+	14.3701i	0.0306655	+	0.653863i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.97078	−	3.97078i	−0.179933	−	0.179933i	0.611394	−	0.791327i	$-0.290609\pi$
$487$	−3.97078	−	3.97078i	−0.179933	−	0.179933i	−0.791327	+	0.611394i	$0.790609\pi$
$488$		0			0
$489$	−8.01862	+	8.80776i	−0.362615	+	0.398301i
$490$		0			0
$491$		−	6.99614i		−	0.315732i	−0.987461	−	0.157866i	$-0.949539\pi$
$491$		−	6.99614i		−	0.315732i	0.987461	−	0.157866i	$-0.0504613\pi$
$492$		0			0
$493$	−44.9341	+	44.9341i	−2.02373	+	2.02373i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.723002	+	0.723002i	−0.0324311	+	0.0324311i
$498$		0			0
$499$			23.0540i			1.03204i	0.856577	+	0.516019i	$0.172587\pi$
$499$			23.0540i			1.03204i	−0.856577	+	0.516019i	$0.827413\pi$
$500$		0			0
$501$	−5.77320	+	6.34136i	−0.257928	+	0.283311i
$502$		0			0
$503$	18.5451	+	18.5451i	0.826884	+	0.826884i	0.987085	−	0.160200i	$-0.0512140\pi$
$503$	18.5451	+	18.5451i	0.826884	+	0.826884i	−0.160200	+	0.987085i	$0.551214\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.633540	−	13.5086i	−0.0281365	−	0.599938i
$508$		0			0
$509$	−28.5588			−1.26584			−0.632922	−	0.774215i	$-0.718145\pi$
$509$	−28.5588			−1.26584			−0.632922	+	0.774215i	$0.718145\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$		0			0
$513$	−5.18664	−	36.6475i	−0.228996	−	1.61803i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	3.84556	+	3.84556i	0.169128	+	0.169128i
$518$		0			0
$519$	13.6246	+	12.4039i	0.598053	+	0.544470i
$520$		0			0
$521$			25.9396i			1.13644i	0.822878	+	0.568218i	$0.192367\pi$
$521$			25.9396i			1.13644i	−0.822878	+	0.568218i	$0.807633\pi$
$522$		0			0
$523$	−6.00505	+	6.00505i	−0.262582	+	0.262582i	−0.826102	−	0.563520i	$-0.809447\pi$
$523$	−6.00505	+	6.00505i	−0.262582	+	0.262582i	0.563520	+	0.826102i	$0.309447\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	34.8321	−	34.8321i	1.51731	−	1.51731i
$528$		0			0
$529$			45.9848i			1.99934i
$530$		0			0
$531$	35.6847	−	3.35453i	1.54858	−	0.145574i
$532$		0			0
$533$	15.0441	+	15.0441i	0.651631	+	0.651631i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−26.9712	+	1.26492i	−1.16389	+	0.0545854i
$538$		0			0
$539$	2.33205			0.100448
$540$		0			0
$541$	22.3153			0.959411			0.479706	−	0.877429i	$-0.340743\pi$
$541$	22.3153			0.959411			0.479706	+	0.877429i	$0.340743\pi$
$542$		0			0
$543$	7.34658	−	0.344547i	0.315272	−	0.0147859i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−18.5589	−	18.5589i	−0.793520	−	0.793520i	0.188544	−	0.982065i	$-0.439623\pi$
$547$	−18.5589	−	18.5589i	−0.793520	−	0.793520i	−0.982065	+	0.188544i	$0.939623\pi$
$548$		0			0
$549$	9.32819	−	0.876894i	0.398118	−	0.0374249i
$550$		0			0
$551$			75.7739i			3.22808i
$552$		0			0
$553$	−1.01714	+	1.01714i	−0.0432530	+	0.0432530i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−26.0671	+	26.0671i	−1.10450	+	1.10450i	−0.110638	+	0.993861i	$0.535289\pi$
$557$	−26.0671	+	26.0671i	−1.10450	+	1.10450i	−0.993861	+	0.110638i	$0.964711\pi$
$558$		0			0
$559$			28.4924i			1.20510i
$560$		0			0
$561$	−17.8423	−	16.2437i	−0.753304	−	0.685811i
$562$		0			0
$563$	0.723002	+	0.723002i	0.0304709	+	0.0304709i	0.722178	−	0.691707i	$-0.243141\pi$
$563$	0.723002	+	0.723002i	0.0304709	+	0.0304709i	−0.691707	+	0.722178i	$0.743141\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−7.43848	−	5.06647i	−0.312387	−	0.212772i
$568$		0			0
$569$	−9.32819			−0.391058			−0.195529	−	0.980698i	$-0.562642\pi$
$569$	−9.32819			−0.391058			−0.195529	+	0.980698i	$0.562642\pi$
$570$		0			0
$571$	22.7386			0.951582			0.475791	−	0.879558i	$-0.342162\pi$
$571$	22.7386			0.951582			0.475791	+	0.879558i	$0.342162\pi$
$572$		0			0
$573$	−1.15866	−	24.7054i	−0.0484037	−	1.03208i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−26.9953	−	26.9953i	−1.12383	−	1.12383i	−0.991161	−	0.132667i	$-0.957646\pi$
$577$	−26.9953	−	26.9953i	−1.12383	−	1.12383i	−0.132667	−	0.991161i	$-0.542354\pi$
$578$		0			0
$579$	−13.9923	+	15.3693i	−0.581500	+	0.638727i
$580$		0			0
$581$			8.30571i			0.344579i
$582$		0			0
$583$	13.6962	−	13.6962i	0.567238	−	0.567238i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.31903	−	7.31903i	0.302089	−	0.302089i	−0.539742	−	0.841831i	$-0.681478\pi$
$587$	7.31903	−	7.31903i	0.302089	−	0.302089i	0.841831	+	0.539742i	$0.181478\pi$
$588$		0			0
$589$		−	58.7386i		−	2.42028i
$590$		0			0
$591$	1.19224	−	1.30957i	0.0490420	−	0.0538684i
$592$		0			0
$593$	−0.926004	−	0.926004i	−0.0380264	−	0.0380264i	0.687838	−	0.725864i	$-0.258560\pi$
$593$	−0.926004	−	0.926004i	−0.0380264	−	0.0380264i	−0.725864	+	0.687838i	$0.758560\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.851379	+	18.1535i	0.0348446	+	0.742971i
$598$		0			0
$599$	28.2717			1.15515			0.577574	−	0.816338i	$-0.303999\pi$
$599$	28.2717			1.15515			0.577574	+	0.816338i	$0.303999\pi$
$600$		0			0
$601$	−45.3693			−1.85065			−0.925327	−	0.379171i	$-0.876209\pi$
$601$	−45.3693			−1.85065			−0.925327	+	0.379171i	$0.876209\pi$
$602$		0			0
$603$	6.64720	+	5.50485i	0.270695	+	0.224175i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	25.2329	+	25.2329i	1.02417	+	1.02417i	0.999701	+	0.0244698i	$0.00778975\pi$
$607$	25.2329	+	25.2329i	1.02417	+	1.02417i	0.0244698	+	0.999701i	$0.492210\pi$
$608$		0			0
$609$	13.6246	+	12.4039i	0.552096	+	0.502631i
$610$		0			0
$611$		−	10.6378i		−	0.430358i
$612$		0			0
$613$	15.7304	−	15.7304i	0.635347	−	0.635347i	−0.314057	−	0.949404i	$-0.601688\pi$
$613$	15.7304	−	15.7304i	0.635347	−	0.635347i	0.949404	+	0.314057i	$0.101688\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.9151	−	13.9151i	0.560199	−	0.560199i	−0.369165	−	0.929364i	$-0.620356\pi$
$617$	13.9151	−	13.9151i	0.560199	−	0.560199i	0.929364	+	0.369165i	$0.120356\pi$
$618$		0			0
$619$		−	14.4924i		−	0.582500i	−0.956647	−	0.291250i	$-0.905929\pi$
$619$		−	14.4924i		−	0.582500i	0.956647	−	0.291250i	$-0.0940711\pi$
$620$		0			0
$621$	−34.4924	−	25.9396i	−1.38413	−	1.04092i
$622$		0			0
$623$	6.59603	+	6.59603i	0.264264	+	0.264264i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−28.7402	+	1.34789i	−1.14777	+	0.0538295i
$628$		0			0
$629$	30.6037			1.22025
$630$		0			0
$631$	−11.0540			−0.440052			−0.220026	−	0.975494i	$-0.570614\pi$
$631$	−11.0540			−0.440052			−0.220026	+	0.975494i	$0.570614\pi$
$632$		0			0
$633$	34.0574	−	1.59726i	1.35366	−	0.0634853i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.22550	−	3.22550i	−0.127799	−	0.127799i
$638$		0			0
$639$	−0.287088	−	3.05398i	−0.0113570	−	0.120813i
$640$		0			0
$641$		−	9.32819i		−	0.368441i	−0.982885	−	0.184221i	$-0.941024\pi$
$641$		−	9.32819i		−	0.368441i	0.982885	−	0.184221i	$-0.0589761\pi$
$642$		0			0
$643$	18.7819	−	18.7819i	0.740684	−	0.740684i	−0.232026	−	0.972710i	$-0.574535\pi$
$643$	18.7819	−	18.7819i	0.740684	−	0.740684i	0.972710	+	0.232026i	$0.0745353\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.16901	+	2.16901i	−0.0852725	+	0.0852725i	−0.748456	−	0.663184i	$-0.769205\pi$
$647$	−2.16901	+	2.16901i	−0.0852725	+	0.0852725i	0.663184	+	0.748456i	$0.269205\pi$
$648$		0			0
$649$		−	27.8617i		−	1.09367i
$650$		0			0
$651$	−10.5616	−	9.61528i	−0.413940	−	0.376853i
$652$		0			0
$653$	−5.46702	−	5.46702i	−0.213941	−	0.213941i	0.591998	−	0.805939i	$-0.298339\pi$
$653$	−5.46702	−	5.46702i	−0.213941	−	0.213941i	−0.805939	+	0.591998i	$0.798339\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−11.4808	+	13.8633i	−0.447909	+	0.540858i
$658$		0			0
$659$	26.2267			1.02165			0.510824	−	0.859686i	$-0.329341\pi$
$659$	26.2267			1.02165			0.510824	+	0.859686i	$0.329341\pi$
$660$		0			0
$661$	−5.36932			−0.208842			−0.104421	−	0.994533i	$-0.533299\pi$
$661$	−5.36932			−0.208842			−0.104421	+	0.994533i	$0.533299\pi$
$662$		0			0
$663$	2.21106	+	47.1451i	0.0858705	+	1.83097i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	62.4758	+	62.4758i	2.41907	+	2.41907i
$668$		0			0
$669$	0.941872	−	1.03457i	0.0364149	−	0.0399986i
$670$		0			0
$671$		−	7.28323i		−	0.281166i
$672$		0			0
$673$	−22.6274	+	22.6274i	−0.872223	+	0.872223i	−0.992714	−	0.120492i	$-0.961553\pi$
$673$	−22.6274	+	22.6274i	−0.872223	+	0.872223i	0.120492	+	0.992714i	$0.461553\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−17.4161	+	17.4161i	−0.669354	+	0.669354i	−0.957566	−	0.288212i	$-0.906939\pi$
$677$	−17.4161	+	17.4161i	−0.669354	+	0.669354i	0.288212	+	0.957566i	$0.406939\pi$
$678$		0			0
$679$		−	0.561553i		−	0.0215504i
$680$		0			0
$681$	−19.0346	+	20.9078i	−0.729406	+	0.801190i
$682$		0			0
$683$	26.0671	+	26.0671i	0.997430	+	0.997430i	0.999997	−	0.00256642i	$-0.000816916\pi$
$683$	26.0671	+	26.0671i	0.997430	+	0.997430i	−0.00256642	+	0.999997i	$0.500817\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	0.669116	+	14.2672i	0.0255284	+	0.544327i
$688$		0			0
$689$	−37.8869			−1.44338
$690$		0			0
$691$	37.3693			1.42160			0.710798	−	0.703396i	$-0.248334\pi$
$691$	37.3693			1.42160			0.710798	+	0.703396i	$0.248334\pi$
$692$		0			0
$693$	−4.46230	+	5.38831i	−0.169509	+	0.204685i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−19.7012	−	19.7012i	−0.746237	−	0.746237i
$698$		0			0
$699$	−28.5588	−	26.0000i	−1.08019	−	0.983410i
$700$		0			0
$701$		−	3.92870i		−	0.148385i	−0.997244	−	0.0741926i	$-0.976362\pi$
$701$		−	3.92870i		−	0.148385i	0.997244	−	0.0741926i	$-0.0236379\pi$
$702$		0			0
$703$	25.8040	−	25.8040i	0.973218	−	0.973218i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−11.7460	+	11.7460i	−0.441756	+	0.441756i
$708$		0			0
$709$			2.80776i			0.105448i	0.998609	+	0.0527239i	$0.0167903\pi$
$709$			2.80776i			0.105448i	−0.998609	+	0.0527239i	$0.983210\pi$
$710$		0			0
$711$	−0.403882	−	4.29640i	−0.0151468	−	0.161128i
$712$		0			0
$713$	−48.4302	−	48.4302i	−1.81373	−	1.81373i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−8.56629	+	0.401750i	−0.319914	+	0.0150036i
$718$		0			0
$719$	−11.9473			−0.445560			−0.222780	−	0.974869i	$-0.571513\pi$
$719$	−11.9473			−0.445560			−0.222780	+	0.974869i	$0.571513\pi$
$720$		0			0
$721$	16.8078			0.625954
$722$		0			0
$723$	−28.1084	+	1.31825i	−1.04536	+	0.0490264i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	4.76493	+	4.76493i	0.176722	+	0.176722i	0.789925	−	0.613203i	$-0.210119\pi$
$727$	4.76493	+	4.76493i	0.176722	+	0.176722i	−0.613203	+	0.789925i	$0.710119\pi$
$728$		0			0
$729$	25.9396	−	7.49242i	0.960726	−	0.277497i
$730$		0			0
$731$		−	37.3128i		−	1.38006i
$732$		0			0
$733$	5.70574	−	5.70574i	0.210746	−	0.210746i	−0.593838	−	0.804584i	$-0.702388\pi$
$733$	5.70574	−	5.70574i	0.210746	−	0.210746i	0.804584	+	0.593838i	$0.202388\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.74402	−	4.74402i	0.174748	−	0.174748i
$738$		0			0
$739$		−	8.17708i		−	0.300799i	−0.988625	−	0.150399i	$-0.951944\pi$
$739$		−	8.17708i		−	0.300799i	0.988625	−	0.150399i	$-0.0480560\pi$
$740$		0			0
$741$	41.6155	+	37.8869i	1.52878	+	1.39181i
$742$		0			0
$743$	9.57704	+	9.57704i	0.351348	+	0.351348i	0.860611	−	0.509263i	$-0.170082\pi$
$743$	9.57704	+	9.57704i	0.351348	+	0.351348i	−0.509263	+	0.860611i	$0.670082\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−19.1907	−	15.8927i	−0.702153	−	0.581485i
$748$		0			0
$749$	−5.68658			−0.207783
$750$		0			0
$751$	−22.4233			−0.818238			−0.409119	−	0.912481i	$-0.634164\pi$
$751$	−22.4233			−0.818238			−0.409119	+	0.912481i	$0.634164\pi$
$752$		0			0
$753$	0.969433	+	20.6707i	0.0353281	+	0.753281i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−15.7304	−	15.7304i	−0.571733	−	0.571733i	0.360880	−	0.932612i	$-0.382477\pi$
$757$	−15.7304	−	15.7304i	−0.571733	−	0.571733i	−0.932612	+	0.360880i	$0.882477\pi$
$758$		0			0
$759$	−22.5851	+	24.8078i	−0.819787	+	0.900465i
$760$		0			0
$761$		−	26.5138i		−	0.961124i	−0.876961	−	0.480562i	$-0.840433\pi$
$761$		−	26.5138i		−	0.961124i	0.876961	−	0.480562i	$-0.159567\pi$
$762$		0			0
$763$	−11.2648	+	11.2648i	−0.407814	+	0.407814i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−38.5362	+	38.5362i	−1.39146	+	1.39146i
$768$		0			0
$769$			8.87689i			0.320109i	0.987108	+	0.160054i	$0.0511670\pi$
$769$			8.87689i			0.320109i	−0.987108	+	0.160054i	$0.948833\pi$
$770$		0			0
$771$	−2.38447	+	2.61914i	−0.0858747	+	0.0943259i
$772$		0			0
$773$	12.2661	+	12.2661i	0.441179	+	0.441179i	0.892408	−	0.451229i	$-0.149014\pi$
$773$	12.2661	+	12.2661i	0.441179	+	0.441179i	−0.451229	+	0.892408i	$0.649014\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.415700	−	8.86374i	−0.0149132	−	0.317985i
$778$		0			0
$779$	−33.2228			−1.19033
$780$		0			0
$781$	−2.38447			−0.0853231
$782$		0			0
$783$	−54.7300	+	7.74581i	−1.95589	+	0.276813i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−21.5125	−	21.5125i	−0.766838	−	0.766838i	0.210710	−	0.977549i	$-0.432422\pi$
$787$	−21.5125	−	21.5125i	−0.766838	−	0.766838i	−0.977549	+	0.210710i	$0.932422\pi$
$788$		0			0
$789$	−4.66410	−	4.24621i	−0.166046	−	0.151169i
$790$		0			0
$791$		−	8.30571i		−	0.295317i
$792$		0			0
$793$	−10.0736	+	10.0736i	−0.357724	+	0.357724i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.4181	+	24.4181i	−0.864934	+	0.864934i	−0.991906	−	0.126973i	$-0.959474\pi$
$797$	−24.4181	+	24.4181i	−0.864934	+	0.864934i	0.126973	+	0.991906i	$0.459474\pi$
$798$		0			0
$799$			13.9309i			0.492839i
$800$		0			0
$801$	−27.8617	+	2.61914i	−0.984446	+	0.0925426i
$802$		0			0
$803$	9.89404	+	9.89404i	0.349153	+	0.349153i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	33.2717	−	1.56041i	1.17122	−	0.0549291i
$808$		0			0
$809$	41.8156			1.47016			0.735080	−	0.677980i	$-0.237145\pi$
$809$	41.8156			1.47016			0.735080	+	0.677980i	$0.237145\pi$
$810$		0			0
$811$	8.73863			0.306855			0.153427	−	0.988160i	$-0.450969\pi$
$811$	8.73863			0.306855			0.153427	+	0.988160i	$0.450969\pi$
$812$		0			0
$813$	15.3584	−	0.720291i	0.538641	−	0.0252617i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−31.4609	−	31.4609i	−1.10068	−	1.10068i
$818$		0			0
$819$	13.6246	−	1.28078i	0.476082	−	0.0447539i
$820$		0			0
$821$		−	5.39949i		−	0.188443i	−0.995551	−	0.0942217i	$-0.969964\pi$
$821$		−	5.39949i		−	0.188443i	0.995551	−	0.0942217i	$-0.0300363\pi$
$822$		0			0
$823$	10.5196	−	10.5196i	0.366689	−	0.366689i	−0.499579	−	0.866268i	$-0.666512\pi$
$823$	10.5196	−	10.5196i	0.366689	−	0.366689i	0.866268	+	0.499579i	$0.166512\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.42702	−	4.42702i	0.153943	−	0.153943i	−0.625934	−	0.779876i	$-0.715282\pi$
$827$	4.42702	−	4.42702i	0.153943	−	0.153943i	0.779876	+	0.625934i	$0.215282\pi$
$828$		0			0
$829$			36.2462i			1.25888i	0.777048	+	0.629441i	$0.216716\pi$
$829$			36.2462i			1.25888i	−0.777048	+	0.629441i	$0.783284\pi$
$830$		0			0
$831$	−8.80776	−	8.01862i	−0.305538	−	0.278163i
$832$		0			0
$833$	4.22402	+	4.22402i	0.146354	+	0.146354i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	42.4258	−	6.00442i	1.46645	−	0.207543i
$838$		0			0
$839$	43.1252			1.48885			0.744424	−	0.667707i	$-0.232724\pi$
$839$	43.1252			1.48885			0.744424	+	0.667707i	$0.232724\pi$
$840$		0			0
$841$	84.1619			2.90214
$842$		0			0
$843$	1.24163	+	26.4745i	0.0427639	+	0.911830i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−3.93261	−	3.93261i	−0.135126	−	0.135126i
$848$		0			0
$849$	−8.96050	+	9.84233i	−0.307523	+	0.337788i
$850$		0			0
$851$		−	42.5510i		−	1.45863i
$852$		0			0
$853$	20.3213	−	20.3213i	0.695787	−	0.695787i	−0.267712	−	0.963499i	$-0.586267\pi$
$853$	20.3213	−	20.3213i	0.695787	−	0.695787i	0.963499	+	0.267712i	$0.0862674\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.8961	−	16.8961i	0.577159	−	0.577159i	−0.356961	−	0.934119i	$-0.616187\pi$
$857$	16.8961	−	16.8961i	0.577159	−	0.577159i	0.934119	+	0.356961i	$0.116187\pi$
$858$		0			0
$859$		−	10.6307i		−	0.362714i	−0.983417	−	0.181357i	$-0.941951\pi$
$859$		−	10.6307i		−	0.362714i	0.983417	−	0.181357i	$-0.0580490\pi$
$860$		0			0
$861$	−5.43845	+	5.97366i	−0.185342	+	0.203582i
$862$		0			0
$863$	−24.2151	−	24.2151i	−0.824292	−	0.824292i	0.162429	−	0.986720i	$-0.448067\pi$
$863$	−24.2151	−	24.2151i	−0.824292	−	0.824292i	−0.986720	+	0.162429i	$0.948067\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.51612	−	32.3272i	−0.0514900	−	1.09789i
$868$		0			0
$869$	−3.35453			−0.113795
$870$		0			0
$871$	−13.1231			−0.444659
$872$		0			0
$873$	1.29749	+	1.07451i	0.0439135	+	0.0363668i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.6619	+	11.6619i	0.393795	+	0.393795i	0.876037	−	0.482243i	$-0.160178\pi$
$877$	11.6619	+	11.6619i	0.393795	+	0.393795i	−0.482243	+	0.876037i	$0.660178\pi$
$878$		0			0
$879$	−4.29640	−	3.91146i	−0.144914	−	0.131930i
$880$		0			0
$881$		−	51.8792i		−	1.74786i	−0.486056	−	0.873928i	$-0.661565\pi$
$881$		−	51.8792i		−	1.74786i	0.486056	−	0.873928i	$-0.338435\pi$
$882$		0			0
$883$	34.6375	−	34.6375i	1.16565	−	1.16565i	0.182426	−	0.983220i	$-0.441605\pi$
$883$	34.6375	−	34.6375i	1.16565	−	1.16565i	0.983220	−	0.182426i	$-0.0583949\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.0230	−	11.0230i	0.370118	−	0.370118i	−0.497402	−	0.867520i	$-0.665713\pi$
$887$	11.0230	−	11.0230i	0.370118	−	0.370118i	0.867520	+	0.497402i	$0.165713\pi$
$888$		0			0
$889$		−	17.1231i		−	0.574291i
$890$		0			0
$891$	−3.91146	−	20.6207i	−0.131039	−	0.690821i
$892$		0			0
$893$	11.7460	+	11.7460i	0.393067	+	0.393067i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	65.5501	−	3.07423i	2.18865	−	0.102646i
$898$		0			0
$899$	−87.7212			−2.92567
$900$		0			0
$901$	49.6155			1.65293
$902$		0			0
$903$	−10.8069	+	0.506832i	−0.359630	+	0.0168663i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−7.69113	−	7.69113i	−0.255380	−	0.255380i	0.567792	−	0.823172i	$-0.307798\pi$
$907$	−7.69113	−	7.69113i	−0.255380	−	0.255380i	−0.823172	+	0.567792i	$0.807798\pi$
$908$		0			0
$909$	−4.66410	−	49.6155i	−0.154698	−	1.64564i
$910$		0			0
$911$			43.5735i			1.44366i	0.692073	+	0.721828i	$0.256698\pi$
$911$			43.5735i			1.44366i	−0.692073	+	0.721828i	$0.743302\pi$
$912$		0			0
$913$	−13.6962	+	13.6962i	−0.453277	+	0.453277i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−9.89404	+	9.89404i	−0.326730	+	0.326730i
$918$		0			0
$919$		−	44.1771i		−	1.45727i	−0.684904	−	0.728634i	$-0.740156\pi$
$919$		−	44.1771i		−	1.45727i	0.684904	−	0.728634i	$-0.259844\pi$
$920$		0			0
$921$	43.4579	+	39.5642i	1.43199	+	1.30368i
$922$		0			0
$923$	3.29801	+	3.29801i	0.108555	+	0.108555i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−32.1612	+	38.8351i	−1.05631	+	1.27551i
$928$		0			0
$929$	6.70906			0.220117			0.110058	−	0.993925i	$-0.464896\pi$
$929$	6.70906			0.220117			0.110058	+	0.993925i	$0.464896\pi$
$930$		0			0
$931$	7.12311			0.233450
$932$		0			0
$933$	0.165933	+	3.53809i	0.00543239	+	0.115832i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.9661	+	30.9661i	1.01162	+	1.01162i	0.999932	+	0.0116851i	$0.00371955\pi$
$937$	30.9661	+	30.9661i	1.01162	+	1.01162i	0.0116851	+	0.999932i	$0.496280\pi$
$938$		0			0
$939$	−15.3825	+	16.8963i	−0.501988	+	0.551390i
$940$		0			0
$941$			38.4611i			1.25380i	0.779101	+	0.626898i	$0.215676\pi$
$941$			38.4611i			1.25380i	−0.779101	+	0.626898i	$0.784324\pi$
$942$		0			0
$943$	−27.3924	+	27.3924i	−0.892018	+	0.892018i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.6611	−	25.6611i	0.833874	−	0.833874i	−0.154170	−	0.988044i	$-0.549270\pi$
$947$	25.6611	−	25.6611i	0.833874	−	0.833874i	0.988044	+	0.154170i	$0.0492705\pi$
$948$		0			0
$949$		−	27.3693i		−	0.888446i
$950$		0			0
$951$	36.8769	−	40.5061i	1.19582	−	1.31350i
$952$		0			0
$953$	13.9151	+	13.9151i	0.450753	+	0.450753i	0.895604	−	0.444851i	$-0.146744\pi$
$953$	13.9151	+	13.9151i	0.450753	+	0.450753i	−0.444851	+	0.895604i	$0.646744\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.01296	+	42.9211i	0.0650697	+	1.38744i
$958$		0			0
$959$	12.9698			0.418817
$960$		0			0
$961$	37.0000			1.19355
$962$		0			0
$963$	10.8811	−	13.1391i	0.350638	−	0.423402i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−4.76493	−	4.76493i	−0.153230	−	0.153230i	0.626329	−	0.779559i	$-0.284557\pi$
$967$	−4.76493	−	4.76493i	−0.153230	−	0.153230i	−0.779559	+	0.626329i	$0.784557\pi$
$968$		0			0
$969$	−54.4984	−	49.6155i	−1.75074	−	1.59388i
$970$		0			0
$971$			0.574176i			0.0184262i	0.999958	+	0.00921310i	$0.00293266\pi$
$971$			0.574176i			0.0184262i	−0.999958	+	0.00921310i	$0.997067\pi$
$972$		0			0
$973$	7.07107	−	7.07107i	0.226688	−	0.226688i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	29.7711	−	29.7711i	0.952463	−	0.952463i	−0.0464575	−	0.998920i	$-0.514793\pi$
$977$	29.7711	−	29.7711i	0.952463	−	0.952463i	0.998920	+	0.0464575i	$0.0147932\pi$
$978$		0			0
$979$			21.7538i			0.695254i
$980$		0			0
$981$	−4.47301	−	47.5828i	−0.142812	−	1.51920i
$982$		0			0
$983$	−16.6931	−	16.6931i	−0.532426	−	0.532426i	0.388867	−	0.921294i	$-0.372866\pi$
$983$	−16.6931	−	16.6931i	−0.532426	−	0.532426i	−0.921294	+	0.388867i	$0.872866\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	4.03479	−	0.189228i	0.128429	−	0.00602318i
$988$		0			0
$989$	−51.8792			−1.64966
$990$		0			0
$991$	−38.2462			−1.21493			−0.607465	−	0.794346i	$-0.707814\pi$
$991$	−38.2462			−1.21493			−0.607465	+	0.794346i	$0.707814\pi$
$992$		0			0
$993$	17.7275	−	0.831401i	0.562564	−	0.0263837i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−29.1273	−	29.1273i	−0.922471	−	0.922471i	0.0747325	−	0.997204i	$-0.476190\pi$
$997$	−29.1273	−	29.1273i	−0.922471	−	0.922471i	−0.997204	+	0.0747325i	$0.976190\pi$
$998$		0			0
$999$	21.2755	+	16.0000i	0.673128	+	0.506218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.a.1457.8	yes	16
3.2	odd	2	inner	2100.2.s.a.1457.5	yes	16
5.2	odd	4	inner	2100.2.s.a.1793.4	yes	16
5.3	odd	4	inner	2100.2.s.a.1793.5	yes	16
5.4	even	2	inner	2100.2.s.a.1457.1	✓	16
15.2	even	4	inner	2100.2.s.a.1793.1	yes	16
15.8	even	4	inner	2100.2.s.a.1793.8	yes	16
15.14	odd	2	inner	2100.2.s.a.1457.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.s.a.1457.1	✓	16	5.4	even	2	inner
2100.2.s.a.1457.4	yes	16	15.14	odd	2	inner
2100.2.s.a.1457.5	yes	16	3.2	odd	2	inner
2100.2.s.a.1457.8	yes	16	1.1	even	1	trivial
2100.2.s.a.1793.1	yes	16	15.2	even	4	inner
2100.2.s.a.1793.4	yes	16	5.2	odd	4	inner
2100.2.s.a.1793.5	yes	16	5.3	odd	4	inner
2100.2.s.a.1793.8	yes	16	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73015 - 0.0811423i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.98683 - 0.280776i) q^{9} +O(q^{10})\)	\(q+(1.73015 - 0.0811423i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.98683 - 0.280776i) q^{9} -2.33205i q^{11} +(-3.22550 + 3.22550i) q^{13} +(4.22402 - 4.22402i) q^{17} -7.12311i q^{19} +(-1.28078 - 1.16602i) q^{21} +(-5.87302 - 5.87302i) q^{23} +(5.14488 - 0.728143i) q^{27} -10.6378 q^{29} +8.24621 q^{31} +(-0.189228 - 4.03479i) q^{33} +(3.62258 + 3.62258i) q^{37} +(-5.31888 + 5.84233i) q^{39} -4.66410i q^{41} +(4.41674 - 4.41674i) q^{43} +(-1.64901 + 1.64901i) q^{47} +1.00000i q^{49} +(6.96543 - 7.65093i) q^{51} +(5.87302 + 5.87302i) q^{53} +(-0.577985 - 12.3240i) q^{57} +11.9473 q^{59} +3.12311 q^{61} +(-2.31055 - 1.91347i) q^{63} +(2.03427 + 2.03427i) q^{67} +(-10.6378 - 9.68466i) q^{69} -1.02248i q^{71} +(-4.24264 + 4.24264i) q^{73} +(-1.64901 + 1.64901i) q^{77} -1.43845i q^{79} +(8.84233 - 1.67726i) q^{81} +(-5.87302 - 5.87302i) q^{83} +(-18.4049 + 0.863172i) q^{87} -9.32819 q^{89} +4.56155 q^{91} +(14.2672 - 0.669116i) q^{93} +(0.397078 + 0.397078i) q^{97} +(-0.654784 - 6.96543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{21} - 4 q^{51} - 16 q^{61} + 92 q^{81} + 40 q^{91}+O(q^{100}) \) 16 * q - 4 * q^21 - 4 * q^51 - 16 * q^61 + 92 * q^81 + 40 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more