LMFDB - Embedded newform 5290.2.a.be.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.a (trivial)

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:	yes
Analytic conductor:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.252973568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 11x^{4} + 18x^{3} + 19x^{2} - 20x + 4 $ x^6 - 2x^5 - 11x^4 + 18x^3 + 19x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.31410$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.31410 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.31410 q^{6} +2.29640 q^{7} -1.00000 q^{8} +7.98324 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.31410 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.31410 q^{6} +2.29640 q^{7} -1.00000 q^{8} +7.98324 q^{9} +1.00000 q^{10} -3.33912 q^{11} -3.31410 q^{12} -5.68559 q^{13} -2.29640 q^{14} +3.31410 q^{15} +1.00000 q^{16} +2.04147 q^{17} -7.98324 q^{18} +5.60442 q^{19} -1.00000 q^{20} -7.61050 q^{21} +3.33912 q^{22} +3.31410 q^{24} +1.00000 q^{25} +5.68559 q^{26} -16.5150 q^{27} +2.29640 q^{28} -1.29765 q^{29} -3.31410 q^{30} +7.95326 q^{31} -1.00000 q^{32} +11.0662 q^{33} -2.04147 q^{34} -2.29640 q^{35} +7.98324 q^{36} +3.38919 q^{37} -5.60442 q^{38} +18.8426 q^{39} +1.00000 q^{40} -11.1070 q^{41} +7.61050 q^{42} -11.3487 q^{43} -3.33912 q^{44} -7.98324 q^{45} +0.0940387 q^{47} -3.31410 q^{48} -1.72654 q^{49} -1.00000 q^{50} -6.76563 q^{51} -5.68559 q^{52} +3.87580 q^{53} +16.5150 q^{54} +3.33912 q^{55} -2.29640 q^{56} -18.5736 q^{57} +1.29765 q^{58} +0.619407 q^{59} +3.31410 q^{60} +1.92491 q^{61} -7.95326 q^{62} +18.3327 q^{63} +1.00000 q^{64} +5.68559 q^{65} -11.0662 q^{66} -9.15534 q^{67} +2.04147 q^{68} +2.29640 q^{70} -0.366011 q^{71} -7.98324 q^{72} +7.60813 q^{73} -3.38919 q^{74} -3.31410 q^{75} +5.60442 q^{76} -7.66797 q^{77} -18.8426 q^{78} +4.44597 q^{79} -1.00000 q^{80} +30.7824 q^{81} +11.1070 q^{82} -12.9148 q^{83} -7.61050 q^{84} -2.04147 q^{85} +11.3487 q^{86} +4.30055 q^{87} +3.33912 q^{88} +12.5290 q^{89} +7.98324 q^{90} -13.0564 q^{91} -26.3579 q^{93} -0.0940387 q^{94} -5.60442 q^{95} +3.31410 q^{96} +12.1288 q^{97} +1.72654 q^{98} -26.6570 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9} + 6 q^{10} - 10 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 6 q^{16} + 10 q^{17} - 8 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{21} + 10 q^{22} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 8 q^{27} - 2 q^{28} - 2 q^{30} - 2 q^{31} - 6 q^{32} + 22 q^{33} - 10 q^{34} + 2 q^{35} + 8 q^{36} + 4 q^{37} + 2 q^{38} + 24 q^{39} + 6 q^{40} + 6 q^{41} + 12 q^{42} - 12 q^{43} - 10 q^{44} - 8 q^{45} + 8 q^{47} - 2 q^{48} + 8 q^{49} - 6 q^{50} - 34 q^{51} - 2 q^{52} - 36 q^{53} + 8 q^{54} + 10 q^{55} + 2 q^{56} - 32 q^{57} + 16 q^{59} + 2 q^{60} + 10 q^{61} + 2 q^{62} + 48 q^{63} + 6 q^{64} + 2 q^{65} - 22 q^{66} - 16 q^{67} + 10 q^{68} - 2 q^{70} - 2 q^{71} - 8 q^{72} + 4 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} - 16 q^{77} - 24 q^{78} + 20 q^{79} - 6 q^{80} + 34 q^{81} - 6 q^{82} - 8 q^{83} - 12 q^{84} - 10 q^{85} + 12 q^{86} - 12 q^{87} + 10 q^{88} - 12 q^{89} + 8 q^{90} - 38 q^{91} - 28 q^{93} - 8 q^{94} + 2 q^{95} + 2 q^{96} - 2 q^{97} - 8 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9 + 6 * q^10 - 10 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 6 * q^16 + 10 * q^17 - 8 * q^18 - 2 * q^19 - 6 * q^20 - 12 * q^21 + 10 * q^22 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 8 * q^27 - 2 * q^28 - 2 * q^30 - 2 * q^31 - 6 * q^32 + 22 * q^33 - 10 * q^34 + 2 * q^35 + 8 * q^36 + 4 * q^37 + 2 * q^38 + 24 * q^39 + 6 * q^40 + 6 * q^41 + 12 * q^42 - 12 * q^43 - 10 * q^44 - 8 * q^45 + 8 * q^47 - 2 * q^48 + 8 * q^49 - 6 * q^50 - 34 * q^51 - 2 * q^52 - 36 * q^53 + 8 * q^54 + 10 * q^55 + 2 * q^56 - 32 * q^57 + 16 * q^59 + 2 * q^60 + 10 * q^61 + 2 * q^62 + 48 * q^63 + 6 * q^64 + 2 * q^65 - 22 * q^66 - 16 * q^67 + 10 * q^68 - 2 * q^70 - 2 * q^71 - 8 * q^72 + 4 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 - 16 * q^77 - 24 * q^78 + 20 * q^79 - 6 * q^80 + 34 * q^81 - 6 * q^82 - 8 * q^83 - 12 * q^84 - 10 * q^85 + 12 * q^86 - 12 * q^87 + 10 * q^88 - 12 * q^89 + 8 * q^90 - 38 * q^91 - 28 * q^93 - 8 * q^94 + 2 * q^95 + 2 * q^96 - 2 * q^97 - 8 * q^98 - 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.31410	−1.91340	−0.956698	−	0.291084i	$-0.905984\pi$
$3$	−3.31410	−1.91340	−0.956698	+	0.291084i	$0.905984\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.31410	1.35297
$7$	2.29640	0.867958	0.433979	−	0.900923i	$-0.357109\pi$
$7$	2.29640	0.867958	0.433979	+	0.900923i	$0.357109\pi$
$8$	−1.00000	−0.353553
$9$	7.98324	2.66108
$10$	1.00000	0.316228
$11$	−3.33912	−1.00678	−0.503392	−	0.864058i	$-0.667915\pi$
$11$	−3.33912	−1.00678	−0.503392	+	0.864058i	$0.667915\pi$
$12$	−3.31410	−0.956698
$13$	−5.68559	−1.57690	−0.788449	−	0.615100i	$-0.789116\pi$
$13$	−5.68559	−1.57690	−0.788449	+	0.615100i	$0.789116\pi$
$14$	−2.29640	−0.613739
$15$	3.31410	0.855696
$16$	1.00000	0.250000
$17$	2.04147	0.495129	0.247565	−	0.968871i	$-0.420370\pi$
$17$	2.04147	0.495129	0.247565	+	0.968871i	$0.420370\pi$
$18$	−7.98324	−1.88167
$19$	5.60442	1.28574	0.642871	−	0.765974i	$-0.277743\pi$
$19$	5.60442	1.28574	0.642871	+	0.765974i	$0.277743\pi$
$20$	−1.00000	−0.223607
$21$	−7.61050	−1.66075
$22$	3.33912	0.711904
$23$	0	0
$23$	0	0
$24$	3.31410	0.676487
$25$	1.00000	0.200000
$26$	5.68559	1.11504
$27$	−16.5150	−3.17830
$28$	2.29640	0.433979
$29$	−1.29765	−0.240968	−0.120484	−	0.992715i	$-0.538445\pi$
$29$	−1.29765	−0.240968	−0.120484	+	0.992715i	$0.538445\pi$
$30$	−3.31410	−0.605069
$31$	7.95326	1.42845	0.714223	−	0.699918i	$-0.246780\pi$
$31$	7.95326	1.42845	0.714223	+	0.699918i	$0.246780\pi$
$32$	−1.00000	−0.176777
$33$	11.0662	1.92638
$34$	−2.04147	−0.350109
$35$	−2.29640	−0.388163
$36$	7.98324	1.33054
$37$	3.38919	0.557179	0.278589	−	0.960410i	$-0.410133\pi$
$37$	3.38919	0.557179	0.278589	+	0.960410i	$0.410133\pi$
$38$	−5.60442	−0.909157
$39$	18.8426	3.01723
$40$	1.00000	0.158114
$41$	−11.1070	−1.73462	−0.867308	−	0.497773i	$-0.834151\pi$
$41$	−11.1070	−1.73462	−0.867308	+	0.497773i	$0.834151\pi$
$42$	7.61050	1.17433
$43$	−11.3487	−1.73065	−0.865327	−	0.501208i	$-0.832889\pi$
$43$	−11.3487	−1.73065	−0.865327	+	0.501208i	$0.832889\pi$
$44$	−3.33912	−0.503392
$45$	−7.98324	−1.19007
$46$	0	0
$47$	0.0940387	0.0137169	0.00685847	−	0.999976i	$-0.497817\pi$
$47$	0.0940387	0.0137169	0.00685847	+	0.999976i	$0.497817\pi$
$48$	−3.31410	−0.478349
$49$	−1.72654	−0.246649
$50$	−1.00000	−0.141421
$51$	−6.76563	−0.947378
$52$	−5.68559	−0.788449
$53$	3.87580	0.532382	0.266191	−	0.963920i	$-0.414235\pi$
$53$	3.87580	0.532382	0.266191	+	0.963920i	$0.414235\pi$
$54$	16.5150	2.24740
$55$	3.33912	0.450247
$56$	−2.29640	−0.306870
$57$	−18.5736	−2.46013
$58$	1.29765	0.170390
$59$	0.619407	0.0806399	0.0403200	−	0.999187i	$-0.487162\pi$
$59$	0.619407	0.0806399	0.0403200	+	0.999187i	$0.487162\pi$
$60$	3.31410	0.427848
$61$	1.92491	0.246459	0.123230	−	0.992378i	$-0.460675\pi$
$61$	1.92491	0.246459	0.123230	+	0.992378i	$0.460675\pi$
$62$	−7.95326	−1.01006
$63$	18.3327	2.30971
$64$	1.00000	0.125000
$65$	5.68559	0.705211
$66$	−11.0662	−1.36215
$67$	−9.15534	−1.11850	−0.559251	−	0.828998i	$-0.688911\pi$
$67$	−9.15534	−1.11850	−0.559251	+	0.828998i	$0.688911\pi$
$68$	2.04147	0.247565
$69$	0	0
$70$	2.29640	0.274472
$71$	−0.366011	−0.0434375	−0.0217188	−	0.999764i	$-0.506914\pi$
$71$	−0.366011	−0.0434375	−0.0217188	+	0.999764i	$0.506914\pi$
$72$	−7.98324	−0.940834
$73$	7.60813	0.890464	0.445232	−	0.895415i	$-0.353121\pi$
$73$	7.60813	0.890464	0.445232	+	0.895415i	$0.353121\pi$
$74$	−3.38919	−0.393985
$75$	−3.31410	−0.382679
$76$	5.60442	0.642871
$77$	−7.66797	−0.873846
$78$	−18.8426	−2.13350
$79$	4.44597	0.500211	0.250106	−	0.968219i	$-0.419535\pi$
$79$	4.44597	0.500211	0.250106	+	0.968219i	$0.419535\pi$
$80$	−1.00000	−0.111803
$81$	30.7824	3.42027
$82$	11.1070	1.22656
$83$	−12.9148	−1.41759	−0.708793	−	0.705417i	$-0.750760\pi$
$83$	−12.9148	−1.41759	−0.708793	+	0.705417i	$0.750760\pi$
$84$	−7.61050	−0.830374
$85$	−2.04147	−0.221428
$86$	11.3487	1.22376
$87$	4.30055	0.461068
$88$	3.33912	0.355952
$89$	12.5290	1.32807	0.664037	−	0.747700i	$-0.268842\pi$
$89$	12.5290	1.32807	0.664037	+	0.747700i	$0.268842\pi$
$90$	7.98324	0.841508
$91$	−13.0564	−1.36868
$92$	0	0
$93$	−26.3579	−2.73318
$94$	−0.0940387	−0.00969935
$95$	−5.60442	−0.575002
$96$	3.31410	0.338244
$97$	12.1288	1.23149	0.615746	−	0.787945i	$-0.288855\pi$
$97$	12.1288	1.23149	0.615746	+	0.787945i	$0.288855\pi$
$98$	1.72654	0.174407
$99$	−26.6570	−2.67913
$100$	1.00000	0.100000
$101$	−0.584209	−0.0581309	−0.0290655	−	0.999578i	$-0.509253\pi$
$101$	−0.584209	−0.0581309	−0.0290655	+	0.999578i	$0.509253\pi$
$102$	6.76563	0.669897
$103$	14.4033	1.41920	0.709599	−	0.704606i	$-0.248876\pi$
$103$	14.4033	1.41920	0.709599	+	0.704606i	$0.248876\pi$
$104$	5.68559	0.557518
$105$	7.61050	0.742709
$106$	−3.87580	−0.376451
$107$	7.24246	0.700155	0.350078	−	0.936721i	$-0.386155\pi$
$107$	7.24246	0.700155	0.350078	+	0.936721i	$0.386155\pi$
$108$	−16.5150	−1.58915
$109$	10.9072	1.04472	0.522361	−	0.852725i	$-0.325051\pi$
$109$	10.9072	1.04472	0.522361	+	0.852725i	$0.325051\pi$
$110$	−3.33912	−0.318373
$111$	−11.2321	−1.06610
$112$	2.29640	0.216990
$113$	−6.79125	−0.638867	−0.319433	−	0.947609i	$-0.603493\pi$
$113$	−6.79125	−0.638867	−0.319433	+	0.947609i	$0.603493\pi$
$114$	18.5736	1.73958
$115$	0	0
$116$	−1.29765	−0.120484
$117$	−45.3894	−4.19626
$118$	−0.619407	−0.0570210
$119$	4.68803	0.429751
$120$	−3.31410	−0.302534
$121$	0.149747	0.0136134
$122$	−1.92491	−0.174273
$123$	36.8095	3.31900
$124$	7.95326	0.714223
$125$	−1.00000	−0.0894427
$126$	−18.3327	−1.63321
$127$	−9.96984	−0.884680	−0.442340	−	0.896847i	$-0.645852\pi$
$127$	−9.96984	−0.884680	−0.442340	+	0.896847i	$0.645852\pi$
$128$	−1.00000	−0.0883883
$129$	37.6106	3.31143
$130$	−5.68559	−0.498659
$131$	−9.14364	−0.798884	−0.399442	−	0.916759i	$-0.630796\pi$
$131$	−9.14364	−0.798884	−0.399442	+	0.916759i	$0.630796\pi$
$132$	11.0662	0.963188
$133$	12.8700	1.11597
$134$	9.15534	0.790901
$135$	16.5150	1.42138
$136$	−2.04147	−0.175055
$137$	6.61758	0.565378	0.282689	−	0.959212i	$-0.408774\pi$
$137$	6.61758	0.565378	0.282689	+	0.959212i	$0.408774\pi$
$138$	0	0
$139$	21.3048	1.80705	0.903524	−	0.428538i	$-0.140971\pi$
$139$	21.3048	1.80705	0.903524	+	0.428538i	$0.140971\pi$
$140$	−2.29640	−0.194081
$141$	−0.311653	−0.0262459
$142$	0.366011	0.0307150
$143$	18.9849	1.58760
$144$	7.98324	0.665270
$145$	1.29765	0.107764
$146$	−7.60813	−0.629653
$147$	5.72192	0.471936
$148$	3.38919	0.278589
$149$	15.7021	1.28637	0.643184	−	0.765711i	$-0.277613\pi$
$149$	15.7021	1.28637	0.643184	+	0.765711i	$0.277613\pi$
$150$	3.31410	0.270595
$151$	−4.10831	−0.334329	−0.167165	−	0.985929i	$-0.553461\pi$
$151$	−4.10831	−0.334329	−0.167165	+	0.985929i	$0.553461\pi$
$152$	−5.60442	−0.454579
$153$	16.2975	1.31758
$154$	7.66797	0.617903
$155$	−7.95326	−0.638821
$156$	18.8426	1.50862
$157$	−10.2850	−0.820836	−0.410418	−	0.911897i	$-0.634617\pi$
$157$	−10.2850	−0.820836	−0.410418	+	0.911897i	$0.634617\pi$
$158$	−4.44597	−0.353703
$159$	−12.8448	−1.01866
$160$	1.00000	0.0790569
$161$	0	0
$162$	−30.7824	−2.41850
$163$	6.85849	0.537198	0.268599	−	0.963252i	$-0.413439\pi$
$163$	6.85849	0.537198	0.268599	+	0.963252i	$0.413439\pi$
$164$	−11.1070	−0.867308
$165$	−11.0662	−0.861501
$166$	12.9148	1.00238
$167$	−13.0828	−1.01237	−0.506187	−	0.862424i	$-0.668946\pi$
$167$	−13.0828	−1.01237	−0.506187	+	0.862424i	$0.668946\pi$
$168$	7.61050	0.587163
$169$	19.3259	1.48661
$170$	2.04147	0.156574
$171$	44.7415	3.42147
$172$	−11.3487	−0.865327
$173$	15.7460	1.19714	0.598572	−	0.801069i	$-0.295735\pi$
$173$	15.7460	1.19714	0.598572	+	0.801069i	$0.295735\pi$
$174$	−4.30055	−0.326024
$175$	2.29640	0.173592
$176$	−3.33912	−0.251696
$177$	−2.05278	−0.154296
$178$	−12.5290	−0.939090
$179$	13.1135	0.980147	0.490074	−	0.871681i	$-0.336970\pi$
$179$	13.1135	0.980147	0.490074	+	0.871681i	$0.336970\pi$
$180$	−7.98324	−0.595036
$181$	9.78096	0.727013	0.363506	−	0.931592i	$-0.381579\pi$
$181$	9.78096	0.727013	0.363506	+	0.931592i	$0.381579\pi$
$182$	13.0564	0.967804
$183$	−6.37934	−0.471574
$184$	0	0
$185$	−3.38919	−0.249178
$186$	26.3579	1.93265
$187$	−6.81672	−0.498488
$188$	0.0940387	0.00685847
$189$	−37.9250	−2.75864
$190$	5.60442	0.406588
$191$	−2.21824	−0.160506	−0.0802531	−	0.996775i	$-0.525573\pi$
$191$	−2.21824	−0.160506	−0.0802531	+	0.996775i	$0.525573\pi$
$192$	−3.31410	−0.239174
$193$	0.400657	0.0288400	0.0144200	−	0.999896i	$-0.495410\pi$
$193$	0.400657	0.0288400	0.0144200	+	0.999896i	$0.495410\pi$
$194$	−12.1288	−0.870797
$195$	−18.8426	−1.34935
$196$	−1.72654	−0.123324
$197$	−16.2418	−1.15718	−0.578590	−	0.815618i	$-0.696397\pi$
$197$	−16.2418	−1.15718	−0.578590	+	0.815618i	$0.696397\pi$
$198$	26.6570	1.89443
$199$	−7.97234	−0.565144	−0.282572	−	0.959246i	$-0.591188\pi$
$199$	−7.97234	−0.565144	−0.282572	+	0.959246i	$0.591188\pi$
$200$	−1.00000	−0.0707107
$201$	30.3417	2.14014
$202$	0.584209	0.0411048
$203$	−2.97994	−0.209150
$204$	−6.76563	−0.473689
$205$	11.1070	0.775744
$206$	−14.4033	−1.00352
$207$	0	0
$208$	−5.68559	−0.394225
$209$	−18.7139	−1.29446
$210$	−7.61050	−0.525174
$211$	−9.63006	−0.662960	−0.331480	−	0.943462i	$-0.607548\pi$
$211$	−9.63006	−0.662960	−0.331480	+	0.943462i	$0.607548\pi$
$212$	3.87580	0.266191
$213$	1.21300	0.0831131
$214$	−7.24246	−0.495085
$215$	11.3487	0.773972
$216$	16.5150	1.12370
$217$	18.2639	1.23983
$218$	−10.9072	−0.738730
$219$	−25.2141	−1.70381
$220$	3.33912	0.225124
$221$	−11.6070	−0.780768
$222$	11.2321	0.753849
$223$	−6.25888	−0.419125	−0.209563	−	0.977795i	$-0.567204\pi$
$223$	−6.25888	−0.419125	−0.209563	+	0.977795i	$0.567204\pi$
$224$	−2.29640	−0.153435
$225$	7.98324	0.532216
$226$	6.79125	0.451747
$227$	−5.09565	−0.338210	−0.169105	−	0.985598i	$-0.554088\pi$
$227$	−5.09565	−0.338210	−0.169105	+	0.985598i	$0.554088\pi$
$228$	−18.5736	−1.23007
$229$	−13.6668	−0.903126	−0.451563	−	0.892239i	$-0.649133\pi$
$229$	−13.6668	−0.903126	−0.451563	+	0.892239i	$0.649133\pi$
$230$	0	0
$231$	25.4124	1.67201
$232$	1.29765	0.0851952
$233$	23.9857	1.57136	0.785679	−	0.618634i	$-0.212314\pi$
$233$	23.9857	1.57136	0.785679	+	0.618634i	$0.212314\pi$
$234$	45.3894	2.96720
$235$	−0.0940387	−0.00613441
$236$	0.619407	0.0403200
$237$	−14.7344	−0.957101
$238$	−4.68803	−0.303880
$239$	−21.7197	−1.40493	−0.702467	−	0.711717i	$-0.747918\pi$
$239$	−21.7197	−1.40493	−0.702467	+	0.711717i	$0.747918\pi$
$240$	3.31410	0.213924
$241$	15.8021	1.01790	0.508951	−	0.860795i	$-0.330033\pi$
$241$	15.8021	1.01790	0.508951	+	0.860795i	$0.330033\pi$
$242$	−0.149747	−0.00962612
$243$	−52.4712	−3.36603
$244$	1.92491	0.123230
$245$	1.72654	0.110305
$246$	−36.8095	−2.34689
$247$	−31.8644	−2.02749
$248$	−7.95326	−0.505032
$249$	42.8010	2.71240
$250$	1.00000	0.0632456
$251$	10.8687	0.686027	0.343013	−	0.939331i	$-0.388552\pi$
$251$	10.8687	0.686027	0.343013	+	0.939331i	$0.388552\pi$
$252$	18.3327	1.15485
$253$	0	0
$254$	9.96984	0.625563
$255$	6.76563	0.423680
$256$	1.00000	0.0625000
$257$	−1.12171	−0.0699706	−0.0349853	−	0.999388i	$-0.511138\pi$
$257$	−1.12171	−0.0699706	−0.0349853	+	0.999388i	$0.511138\pi$
$258$	−37.6106	−2.34153
$259$	7.78294	0.483608
$260$	5.68559	0.352605
$261$	−10.3595	−0.641236
$262$	9.14364	0.564896
$263$	−26.3435	−1.62441	−0.812204	−	0.583374i	$-0.801732\pi$
$263$	−26.3435	−1.62441	−0.812204	+	0.583374i	$0.801732\pi$
$264$	−11.0662	−0.681076
$265$	−3.87580	−0.238088
$266$	−12.8700	−0.789111
$267$	−41.5224	−2.54113
$268$	−9.15534	−0.559251
$269$	−5.99834	−0.365725	−0.182862	−	0.983138i	$-0.558536\pi$
$269$	−5.99834	−0.365725	−0.182862	+	0.983138i	$0.558536\pi$
$270$	−16.5150	−1.00507
$271$	−18.1555	−1.10287	−0.551435	−	0.834218i	$-0.685919\pi$
$271$	−18.1555	−1.10287	−0.551435	+	0.834218i	$0.685919\pi$
$272$	2.04147	0.123782
$273$	43.2702	2.61883
$274$	−6.61758	−0.399782
$275$	−3.33912	−0.201357
$276$	0	0
$277$	28.2139	1.69521	0.847605	−	0.530628i	$-0.178044\pi$
$277$	28.2139	1.69521	0.847605	+	0.530628i	$0.178044\pi$
$278$	−21.3048	−1.27778
$279$	63.4928	3.80121
$280$	2.29640	0.137236
$281$	6.19042	0.369289	0.184645	−	0.982805i	$-0.440887\pi$
$281$	6.19042	0.369289	0.184645	+	0.982805i	$0.440887\pi$
$282$	0.311653	0.0185587
$283$	−12.1951	−0.724923	−0.362462	−	0.931999i	$-0.618064\pi$
$283$	−12.1951	−0.724923	−0.362462	+	0.931999i	$0.618064\pi$
$284$	−0.366011	−0.0217188
$285$	18.5736	1.10021
$286$	−18.9849	−1.12260
$287$	−25.5060	−1.50557
$288$	−7.98324	−0.470417
$289$	−12.8324	−0.754847
$290$	−1.29765	−0.0762009
$291$	−40.1960	−2.35633
$292$	7.60813	0.445232
$293$	−10.3473	−0.604493	−0.302247	−	0.953230i	$-0.597737\pi$
$293$	−10.3473	−0.604493	−0.302247	+	0.953230i	$0.597737\pi$
$294$	−5.72192	−0.333709
$295$	−0.619407	−0.0360633
$296$	−3.38919	−0.196993
$297$	55.1455	3.19987
$298$	−15.7021	−0.909600
$299$	0	0
$300$	−3.31410	−0.191340
$301$	−26.0611	−1.50214
$302$	4.10831	0.236407
$303$	1.93612	0.111227
$304$	5.60442	0.321436
$305$	−1.92491	−0.110220
$306$	−16.2975	−0.931669
$307$	16.2713	0.928655	0.464327	−	0.885664i	$-0.346296\pi$
$307$	16.2713	0.928655	0.464327	+	0.885664i	$0.346296\pi$
$308$	−7.66797	−0.436923
$309$	−47.7339	−2.71549
$310$	7.95326	0.451715
$311$	−17.9562	−1.01820	−0.509102	−	0.860706i	$-0.670022\pi$
$311$	−17.9562	−1.01820	−0.509102	+	0.860706i	$0.670022\pi$
$312$	−18.8426	−1.06675
$313$	−31.1150	−1.75872	−0.879362	−	0.476153i	$-0.842031\pi$
$313$	−31.1150	−1.75872	−0.879362	+	0.476153i	$0.842031\pi$
$314$	10.2850	0.580419
$315$	−18.3327	−1.03293
$316$	4.44597	0.250106
$317$	25.6424	1.44022	0.720111	−	0.693859i	$-0.244091\pi$
$317$	25.6424	1.44022	0.720111	+	0.693859i	$0.244091\pi$
$318$	12.8448	0.720299
$319$	4.33303	0.242603
$320$	−1.00000	−0.0559017
$321$	−24.0022	−1.33967
$322$	0	0
$323$	11.4413	0.636609
$324$	30.7824	1.71014
$325$	−5.68559	−0.315380
$326$	−6.85849	−0.379857
$327$	−36.1476	−1.99897
$328$	11.1070	0.613279
$329$	0.215951	0.0119057
$330$	11.0662	0.609173
$331$	29.5241	1.62279	0.811394	−	0.584499i	$-0.198709\pi$
$331$	29.5241	1.62279	0.811394	+	0.584499i	$0.198709\pi$
$332$	−12.9148	−0.708793
$333$	27.0567	1.48270
$334$	13.0828	0.715857
$335$	9.15534	0.500209
$336$	−7.61050	−0.415187
$337$	1.31587	0.0716801	0.0358400	−	0.999358i	$-0.488589\pi$
$337$	1.31587	0.0716801	0.0358400	+	0.999358i	$0.488589\pi$
$338$	−19.3259	−1.05119
$339$	22.5069	1.22240
$340$	−2.04147	−0.110714
$341$	−26.5569	−1.43814
$342$	−44.7415	−2.41934
$343$	−20.0396	−1.08204
$344$	11.3487	0.611879
$345$	0	0
$346$	−15.7460	−0.846509
$347$	−21.7675	−1.16854	−0.584271	−	0.811559i	$-0.698620\pi$
$347$	−21.7675	−1.16854	−0.584271	+	0.811559i	$0.698620\pi$
$348$	4.30055	0.230534
$349$	−10.9166	−0.584353	−0.292176	−	0.956364i	$-0.594379\pi$
$349$	−10.9166	−0.584353	−0.292176	+	0.956364i	$0.594379\pi$
$350$	−2.29640	−0.122748
$351$	93.8973	5.01186
$352$	3.33912	0.177976
$353$	3.98890	0.212308	0.106154	−	0.994350i	$-0.466146\pi$
$353$	3.98890	0.212308	0.106154	+	0.994350i	$0.466146\pi$
$354$	2.05278	0.109104
$355$	0.366011	0.0194258
$356$	12.5290	0.664037
$357$	−15.5366	−0.822284
$358$	−13.1135	−0.693069
$359$	−18.6892	−0.986379	−0.493189	−	0.869922i	$-0.664169\pi$
$359$	−18.6892	−0.986379	−0.493189	+	0.869922i	$0.664169\pi$
$360$	7.98324	0.420754
$361$	12.4095	0.653134
$362$	−9.78096	−0.514076
$363$	−0.496277	−0.0260478
$364$	−13.0564	−0.684341
$365$	−7.60813	−0.398228
$366$	6.37934	0.333453
$367$	29.5946	1.54482	0.772412	−	0.635121i	$-0.219050\pi$
$367$	29.5946	1.54482	0.772412	+	0.635121i	$0.219050\pi$
$368$	0	0
$369$	−88.6695	−4.61595
$370$	3.38919	0.176195
$371$	8.90039	0.462085
$372$	−26.3579	−1.36659
$373$	−13.6233	−0.705390	−0.352695	−	0.935738i	$-0.614735\pi$
$373$	−13.6233	−0.705390	−0.352695	+	0.935738i	$0.614735\pi$
$374$	6.81672	0.352484
$375$	3.31410	0.171139
$376$	−0.0940387	−0.00484967
$377$	7.37793	0.379983
$378$	37.9250	1.95065
$379$	−17.6009	−0.904099	−0.452050	−	0.891993i	$-0.649307\pi$
$379$	−17.6009	−0.904099	−0.452050	+	0.891993i	$0.649307\pi$
$380$	−5.60442	−0.287501
$381$	33.0410	1.69274
$382$	2.21824	0.113495
$383$	−9.21661	−0.470947	−0.235473	−	0.971881i	$-0.575664\pi$
$383$	−9.21661	−0.470947	−0.235473	+	0.971881i	$0.575664\pi$
$384$	3.31410	0.169122
$385$	7.66797	0.390796
$386$	−0.400657	−0.0203929
$387$	−90.5991	−4.60541
$388$	12.1288	0.615746
$389$	−26.4574	−1.34144	−0.670721	−	0.741709i	$-0.734015\pi$
$389$	−26.4574	−1.34144	−0.670721	+	0.741709i	$0.734015\pi$
$390$	18.8426	0.954132
$391$	0	0
$392$	1.72654	0.0872034
$393$	30.3029	1.52858
$394$	16.2418	0.818250
$395$	−4.44597	−0.223701
$396$	−26.6570	−1.33957
$397$	−22.5575	−1.13213	−0.566064	−	0.824361i	$-0.691534\pi$
$397$	−22.5575	−1.13213	−0.566064	+	0.824361i	$0.691534\pi$
$398$	7.97234	0.399617
$399$	−42.6525	−2.13529
$400$	1.00000	0.0500000
$401$	−11.7338	−0.585956	−0.292978	−	0.956119i	$-0.594646\pi$
$401$	−11.7338	−0.585956	−0.292978	+	0.956119i	$0.594646\pi$
$402$	−30.3417	−1.51331
$403$	−45.2189	−2.25252
$404$	−0.584209	−0.0290655
$405$	−30.7824	−1.52959
$406$	2.97994	0.147892
$407$	−11.3169	−0.560959
$408$	6.76563	0.334949
$409$	2.10727	0.104198	0.0520989	−	0.998642i	$-0.483409\pi$
$409$	2.10727	0.104198	0.0520989	+	0.998642i	$0.483409\pi$
$410$	−11.1070	−0.548533
$411$	−21.9313	−1.08179
$412$	14.4033	0.709599
$413$	1.42241	0.0699921
$414$	0	0
$415$	12.9148	0.633964
$416$	5.68559	0.278759
$417$	−70.6061	−3.45760
$418$	18.7139	0.915325
$419$	−22.2893	−1.08891	−0.544453	−	0.838791i	$-0.683263\pi$
$419$	−22.2893	−1.08891	−0.544453	+	0.838791i	$0.683263\pi$
$420$	7.61050	0.371354
$421$	−4.93018	−0.240282	−0.120141	−	0.992757i	$-0.538335\pi$
$421$	−4.93018	−0.240282	−0.120141	+	0.992757i	$0.538335\pi$
$422$	9.63006	0.468784
$423$	0.750734	0.0365019
$424$	−3.87580	−0.188225
$425$	2.04147	0.0990258
$426$	−1.21300	−0.0587698
$427$	4.42037	0.213917
$428$	7.24246	0.350078
$429$	−62.9178	−3.03770
$430$	−11.3487	−0.547281
$431$	−30.4941	−1.46885	−0.734424	−	0.678691i	$-0.762548\pi$
$431$	−30.4941	−1.46885	−0.734424	+	0.678691i	$0.762548\pi$
$432$	−16.5150	−0.794576
$433$	−6.19805	−0.297859	−0.148930	−	0.988848i	$-0.547583\pi$
$433$	−6.19805	−0.297859	−0.148930	+	0.988848i	$0.547583\pi$
$434$	−18.2639	−0.876694
$435$	−4.30055	−0.206196
$436$	10.9072	0.522361
$437$	0	0
$438$	25.2141	1.20478
$439$	16.2836	0.777175	0.388587	−	0.921412i	$-0.372963\pi$
$439$	16.2836	0.777175	0.388587	+	0.921412i	$0.372963\pi$
$440$	−3.33912	−0.159186
$441$	−13.7834	−0.656352
$442$	11.6070	0.552087
$443$	−15.9445	−0.757545	−0.378772	−	0.925490i	$-0.623654\pi$
$443$	−15.9445	−0.757545	−0.378772	+	0.925490i	$0.623654\pi$
$444$	−11.2321	−0.533052
$445$	−12.5290	−0.593932
$446$	6.25888	0.296366
$447$	−52.0384	−2.46133
$448$	2.29640	0.108495
$449$	9.40379	0.443792	0.221896	−	0.975070i	$-0.428775\pi$
$449$	9.40379	0.443792	0.221896	+	0.975070i	$0.428775\pi$
$450$	−7.98324	−0.376334
$451$	37.0875	1.74638
$452$	−6.79125	−0.319433
$453$	13.6153	0.639704
$454$	5.09565	0.239151
$455$	13.0564	0.612093
$456$	18.5736	0.869789
$457$	4.68319	0.219070	0.109535	−	0.993983i	$-0.465064\pi$
$457$	4.68319	0.219070	0.109535	+	0.993983i	$0.465064\pi$
$458$	13.6668	0.638607
$459$	−33.7148	−1.57367
$460$	0	0
$461$	11.8574	0.552252	0.276126	−	0.961121i	$-0.410949\pi$
$461$	11.8574	0.552252	0.276126	+	0.961121i	$0.410949\pi$
$462$	−25.4124	−1.18229
$463$	−30.7034	−1.42691	−0.713454	−	0.700702i	$-0.752870\pi$
$463$	−30.7034	−1.42691	−0.713454	+	0.700702i	$0.752870\pi$
$464$	−1.29765	−0.0602421
$465$	26.3579	1.22232
$466$	−23.9857	−1.11112
$467$	2.58297	0.119526	0.0597628	−	0.998213i	$-0.480966\pi$
$467$	2.58297	0.119526	0.0597628	+	0.998213i	$0.480966\pi$
$468$	−45.3894	−2.09813
$469$	−21.0243	−0.970813
$470$	0.0940387	0.00433768
$471$	34.0857	1.57058
$472$	−0.619407	−0.0285105
$473$	37.8946	1.74239
$474$	14.7344	0.676773
$475$	5.60442	0.257149
$476$	4.68803	0.214876
$477$	30.9414	1.41671
$478$	21.7197	0.993438
$479$	−12.3429	−0.563959	−0.281980	−	0.959420i	$-0.590991\pi$
$479$	−12.3429	−0.563959	−0.281980	+	0.959420i	$0.590991\pi$
$480$	−3.31410	−0.151267
$481$	−19.2695	−0.878615
$482$	−15.8021	−0.719765
$483$	0	0
$484$	0.149747	0.00680669
$485$	−12.1288	−0.550740
$486$	52.4712	2.38014
$487$	−28.6640	−1.29889	−0.649445	−	0.760409i	$-0.724999\pi$
$487$	−28.6640	−1.29889	−0.649445	+	0.760409i	$0.724999\pi$
$488$	−1.92491	−0.0871366
$489$	−22.7297	−1.02787
$490$	−1.72654	−0.0779971
$491$	9.66866	0.436340	0.218170	−	0.975911i	$-0.429991\pi$
$491$	9.66866	0.436340	0.218170	+	0.975911i	$0.429991\pi$
$492$	36.8095	1.65950
$493$	−2.64912	−0.119310
$494$	31.8644	1.43365
$495$	26.6570	1.19814
$496$	7.95326	0.357112
$497$	−0.840508	−0.0377019
$498$	−42.8010	−1.91796
$499$	−25.9957	−1.16373	−0.581863	−	0.813287i	$-0.697676\pi$
$499$	−25.9957	−1.16373	−0.581863	+	0.813287i	$0.697676\pi$
$500$	−1.00000	−0.0447214
$501$	43.3576	1.93707
$502$	−10.8687	−0.485094
$503$	−25.1548	−1.12160	−0.560799	−	0.827952i	$-0.689506\pi$
$503$	−25.1548	−1.12160	−0.560799	+	0.827952i	$0.689506\pi$
$504$	−18.3327	−0.816605
$505$	0.584209	0.0259969
$506$	0	0
$507$	−64.0480	−2.84447
$508$	−9.96984	−0.442340
$509$	37.8278	1.67669	0.838345	−	0.545141i	$-0.183524\pi$
$509$	37.8278	1.67669	0.838345	+	0.545141i	$0.183524\pi$
$510$	−6.76563	−0.299587
$511$	17.4713	0.772886
$512$	−1.00000	−0.0441942
$513$	−92.5568	−4.08648
$514$	1.12171	0.0494767
$515$	−14.4033	−0.634684
$516$	37.6106	1.65571
$517$	−0.314007	−0.0138100
$518$	−7.78294	−0.341963
$519$	−52.1837	−2.29061
$520$	−5.68559	−0.249330
$521$	−24.6659	−1.08063	−0.540317	−	0.841462i	$-0.681696\pi$
$521$	−24.6659	−1.08063	−0.540317	+	0.841462i	$0.681696\pi$
$522$	10.3595	0.453423
$523$	26.3319	1.15141	0.575706	−	0.817657i	$-0.304727\pi$
$523$	26.3319	1.15141	0.575706	+	0.817657i	$0.304727\pi$
$524$	−9.14364	−0.399442
$525$	−7.61050	−0.332149
$526$	26.3435	1.14863
$527$	16.2363	0.707266
$528$	11.0662	0.481594
$529$	0	0
$530$	3.87580	0.168354
$531$	4.94488	0.214589
$532$	12.8700	0.557985
$533$	63.1496	2.73531
$534$	41.5224	1.79685
$535$	−7.24246	−0.313119
$536$	9.15534	0.395450
$537$	−43.4593	−1.87541
$538$	5.99834	0.258607
$539$	5.76513	0.248322
$540$	16.5150	0.710691
$541$	34.0093	1.46217	0.731087	−	0.682284i	$-0.239013\pi$
$541$	34.0093	1.46217	0.731087	+	0.682284i	$0.239013\pi$
$542$	18.1555	0.779846
$543$	−32.4150	−1.39106
$544$	−2.04147	−0.0875273
$545$	−10.9072	−0.467214
$546$	−43.2702	−1.85179
$547$	12.5226	0.535428	0.267714	−	0.963498i	$-0.413732\pi$
$547$	12.5226	0.535428	0.267714	+	0.963498i	$0.413732\pi$
$548$	6.61758	0.282689
$549$	15.3670	0.655849
$550$	3.33912	0.142381
$551$	−7.27260	−0.309823
$552$	0	0
$553$	10.2097	0.434162
$554$	−28.2139	−1.19869
$555$	11.2321	0.476776
$556$	21.3048	0.903524
$557$	6.40334	0.271318	0.135659	−	0.990756i	$-0.456685\pi$
$557$	6.40334	0.271318	0.135659	+	0.990756i	$0.456685\pi$
$558$	−63.4928	−2.68786
$559$	64.5238	2.72907
$560$	−2.29640	−0.0970407
$561$	22.5913	0.953804
$562$	−6.19042	−0.261127
$563$	1.43864	0.0606316	0.0303158	−	0.999540i	$-0.490349\pi$
$563$	1.43864	0.0606316	0.0303158	+	0.999540i	$0.490349\pi$
$564$	−0.311653	−0.0131230
$565$	6.79125	0.285710
$566$	12.1951	0.512598
$567$	70.6889	2.96865
$568$	0.366011	0.0153575
$569$	0.766874	0.0321490	0.0160745	−	0.999871i	$-0.494883\pi$
$569$	0.766874	0.0321490	0.0160745	+	0.999871i	$0.494883\pi$
$570$	−18.5736	−0.777963
$571$	25.5804	1.07051	0.535253	−	0.844692i	$-0.320216\pi$
$571$	25.5804	1.07051	0.535253	+	0.844692i	$0.320216\pi$
$572$	18.9849	0.793798
$573$	7.35147	0.307112
$574$	25.5060	1.06460
$575$	0	0
$576$	7.98324	0.332635
$577$	−16.5461	−0.688824	−0.344412	−	0.938819i	$-0.611922\pi$
$577$	−16.5461	−0.688824	−0.344412	+	0.938819i	$0.611922\pi$
$578$	12.8324	0.533758
$579$	−1.32782	−0.0551822
$580$	1.29765	0.0538822
$581$	−29.6576	−1.23041
$582$	40.1960	1.66618
$583$	−12.9418	−0.535993
$584$	−7.60813	−0.314827
$585$	45.3894	1.87662
$586$	10.3473	0.427441
$587$	9.11575	0.376247	0.188124	−	0.982145i	$-0.439759\pi$
$587$	9.11575	0.376247	0.188124	+	0.982145i	$0.439759\pi$
$588$	5.72192	0.235968
$589$	44.5734	1.83662
$590$	0.619407	0.0255006
$591$	53.8269	2.21414
$592$	3.38919	0.139295
$593$	2.09558	0.0860551	0.0430275	−	0.999074i	$-0.486300\pi$
$593$	2.09558	0.0860551	0.0430275	+	0.999074i	$0.486300\pi$
$594$	−55.1455	−2.26265
$595$	−4.68803	−0.192191
$596$	15.7021	0.643184
$597$	26.4211	1.08134
$598$	0	0
$599$	5.72754	0.234021	0.117010	−	0.993131i	$-0.462669\pi$
$599$	5.72754	0.234021	0.117010	+	0.993131i	$0.462669\pi$
$600$	3.31410	0.135297
$601$	32.9160	1.34267	0.671336	−	0.741153i	$-0.265721\pi$
$601$	32.9160	1.34267	0.671336	+	0.741153i	$0.265721\pi$
$602$	26.0611	1.06217
$603$	−73.0893	−2.97643
$604$	−4.10831	−0.167165
$605$	−0.149747	−0.00608809
$606$	−1.93612	−0.0786497
$607$	16.7402	0.679463	0.339732	−	0.940522i	$-0.389664\pi$
$607$	16.7402	0.679463	0.339732	+	0.940522i	$0.389664\pi$
$608$	−5.60442	−0.227289
$609$	9.87580	0.400188
$610$	1.92491	0.0779373
$611$	−0.534665	−0.0216302
$612$	16.2975	0.658789
$613$	22.1084	0.892951	0.446476	−	0.894796i	$-0.352679\pi$
$613$	22.1084	0.892951	0.446476	+	0.894796i	$0.352679\pi$
$614$	−16.2713	−0.656658
$615$	−36.8095	−1.48430
$616$	7.66797	0.308951
$617$	−17.9237	−0.721581	−0.360791	−	0.932647i	$-0.617493\pi$
$617$	−17.9237	−0.721581	−0.360791	+	0.932647i	$0.617493\pi$
$618$	47.7339	1.92014
$619$	−19.8446	−0.797621	−0.398811	−	0.917033i	$-0.630577\pi$
$619$	−19.8446	−0.797621	−0.398811	+	0.917033i	$0.630577\pi$
$620$	−7.95326	−0.319410
$621$	0	0
$622$	17.9562	0.719979
$623$	28.7717	1.15271
$624$	18.8426	0.754308
$625$	1.00000	0.0400000
$626$	31.1150	1.24361
$627$	62.0196	2.47682
$628$	−10.2850	−0.410418
$629$	6.91892	0.275876
$630$	18.3327	0.730394
$631$	−38.0015	−1.51282	−0.756408	−	0.654100i	$-0.773048\pi$
$631$	−38.0015	−1.51282	−0.756408	+	0.654100i	$0.773048\pi$
$632$	−4.44597	−0.176851
$633$	31.9149	1.26851
$634$	−25.6424	−1.01839
$635$	9.96984	0.395641
$636$	−12.8448	−0.509328
$637$	9.81639	0.388940
$638$	−4.33303	−0.171546
$639$	−2.92195	−0.115591
$640$	1.00000	0.0395285
$641$	−45.8173	−1.80967	−0.904837	−	0.425758i	$-0.860008\pi$
$641$	−45.8173	−1.80967	−0.904837	+	0.425758i	$0.860008\pi$
$642$	24.0022	0.947293
$643$	−11.2514	−0.443712	−0.221856	−	0.975079i	$-0.571212\pi$
$643$	−11.2514	−0.443712	−0.221856	+	0.975079i	$0.571212\pi$
$644$	0	0
$645$	−37.6106	−1.48091
$646$	−11.4413	−0.450150
$647$	−5.38024	−0.211519	−0.105760	−	0.994392i	$-0.533727\pi$
$647$	−5.38024	−0.211519	−0.105760	+	0.994392i	$0.533727\pi$
$648$	−30.7824	−1.20925
$649$	−2.06828	−0.0811869
$650$	5.68559	0.223007
$651$	−60.5282	−2.37229
$652$	6.85849	0.268599
$653$	7.59065	0.297045	0.148523	−	0.988909i	$-0.452548\pi$
$653$	7.59065	0.297045	0.148523	+	0.988909i	$0.452548\pi$
$654$	36.1476	1.41348
$655$	9.14364	0.357272
$656$	−11.1070	−0.433654
$657$	60.7376	2.36960
$658$	−0.215951	−0.00841863
$659$	−29.0453	−1.13144	−0.565722	−	0.824596i	$-0.691402\pi$
$659$	−29.0453	−1.13144	−0.565722	+	0.824596i	$0.691402\pi$
$660$	−11.0662	−0.430751
$661$	−15.1653	−0.589863	−0.294931	−	0.955518i	$-0.595297\pi$
$661$	−15.1653	−0.589863	−0.294931	+	0.955518i	$0.595297\pi$
$662$	−29.5241	−1.14749
$663$	38.4666	1.49392
$664$	12.9148	0.501192
$665$	−12.8700	−0.499077
$666$	−27.0567	−1.04843
$667$	0	0
$668$	−13.0828	−0.506187
$669$	20.7425	0.801953
$670$	−9.15534	−0.353701
$671$	−6.42751	−0.248131
$672$	7.61050	0.293581
$673$	−3.16801	−0.122118	−0.0610590	−	0.998134i	$-0.519448\pi$
$673$	−3.16801	−0.122118	−0.0610590	+	0.998134i	$0.519448\pi$
$674$	−1.31587	−0.0506855
$675$	−16.5150	−0.635661
$676$	19.3259	0.743305
$677$	20.8222	0.800263	0.400131	−	0.916458i	$-0.368964\pi$
$677$	20.8222	0.800263	0.400131	+	0.916458i	$0.368964\pi$
$678$	−22.5069	−0.864371
$679$	27.8526	1.06888
$680$	2.04147	0.0782868
$681$	16.8875	0.647130
$682$	26.5569	1.01692
$683$	10.3285	0.395208	0.197604	−	0.980282i	$-0.436684\pi$
$683$	10.3285	0.395208	0.197604	+	0.980282i	$0.436684\pi$
$684$	44.7415	1.71073
$685$	−6.61758	−0.252845
$686$	20.0396	0.765117
$687$	45.2930	1.72804
$688$	−11.3487	−0.432664
$689$	−22.0362	−0.839512
$690$	0	0
$691$	8.15492	0.310228	0.155114	−	0.987897i	$-0.450426\pi$
$691$	8.15492	0.310228	0.155114	+	0.987897i	$0.450426\pi$
$692$	15.7460	0.598572
$693$	−61.2153	−2.32538
$694$	21.7675	0.826284
$695$	−21.3048	−0.808136
$696$	−4.30055	−0.163012
$697$	−22.6745	−0.858858
$698$	10.9166	0.413200
$699$	−79.4911	−3.00663
$700$	2.29640	0.0867958
$701$	−33.9373	−1.28179	−0.640897	−	0.767627i	$-0.721437\pi$
$701$	−33.9373	−1.28179	−0.640897	+	0.767627i	$0.721437\pi$
$702$	−93.8973	−3.54392
$703$	18.9944	0.716389
$704$	−3.33912	−0.125848
$705$	0.311653	0.0117375
$706$	−3.98890	−0.150124
$707$	−1.34158	−0.0504552
$708$	−2.05278	−0.0771480
$709$	−39.1522	−1.47039	−0.735196	−	0.677855i	$-0.762910\pi$
$709$	−39.1522	−1.47039	−0.735196	+	0.677855i	$0.762910\pi$
$710$	−0.366011	−0.0137361
$711$	35.4933	1.33110
$712$	−12.5290	−0.469545
$713$	0	0
$714$	15.5366	0.581443
$715$	−18.9849	−0.709994
$716$	13.1135	0.490074
$717$	71.9814	2.68819
$718$	18.6892	0.697475
$719$	−18.5815	−0.692971	−0.346486	−	0.938055i	$-0.612625\pi$
$719$	−18.5815	−0.692971	−0.346486	+	0.938055i	$0.612625\pi$
$720$	−7.98324	−0.297518
$721$	33.0757	1.23180
$722$	−12.4095	−0.461836
$723$	−52.3697	−1.94765
$724$	9.78096	0.363506
$725$	−1.29765	−0.0481937
$726$	0.496277	0.0184186
$727$	5.86676	0.217586	0.108793	−	0.994064i	$-0.465301\pi$
$727$	5.86676	0.217586	0.108793	+	0.994064i	$0.465301\pi$
$728$	13.0564	0.483902
$729$	81.5472	3.02027
$730$	7.60813	0.281590
$731$	−23.1679	−0.856897
$732$	−6.37934	−0.235787
$733$	−8.49506	−0.313772	−0.156886	−	0.987617i	$-0.550146\pi$
$733$	−8.49506	−0.313772	−0.156886	+	0.987617i	$0.550146\pi$
$734$	−29.5946	−1.09236
$735$	−5.72192	−0.211056
$736$	0	0
$737$	30.5708	1.12609
$738$	88.6695	3.26397
$739$	−21.1883	−0.779423	−0.389712	−	0.920937i	$-0.627425\pi$
$739$	−21.1883	−0.779423	−0.389712	+	0.920937i	$0.627425\pi$
$740$	−3.38919	−0.124589
$741$	105.602	3.87938
$742$	−8.90039	−0.326744
$743$	−6.02469	−0.221024	−0.110512	−	0.993875i	$-0.535249\pi$
$743$	−6.02469	−0.221024	−0.110512	+	0.993875i	$0.535249\pi$
$744$	26.3579	0.966326
$745$	−15.7021	−0.575281
$746$	13.6233	0.498786
$747$	−103.102	−3.77231
$748$	−6.81672	−0.249244
$749$	16.6316	0.607706
$750$	−3.31410	−0.121014
$751$	−13.0642	−0.476721	−0.238361	−	0.971177i	$-0.576610\pi$
$751$	−13.0642	−0.476721	−0.238361	+	0.971177i	$0.576610\pi$
$752$	0.0940387	0.00342924
$753$	−36.0199	−1.31264
$754$	−7.37793	−0.268688
$755$	4.10831	0.149517
$756$	−37.9250	−1.37932
$757$	−17.2459	−0.626814	−0.313407	−	0.949619i	$-0.601470\pi$
$757$	−17.2459	−0.626814	−0.313407	+	0.949619i	$0.601470\pi$
$758$	17.6009	0.639295
$759$	0	0
$760$	5.60442	0.203294
$761$	32.6022	1.18183	0.590914	−	0.806734i	$-0.298767\pi$
$761$	32.6022	1.18183	0.590914	+	0.806734i	$0.298767\pi$
$762$	−33.0410	−1.19695
$763$	25.0473	0.906775
$764$	−2.21824	−0.0802531
$765$	−16.2975	−0.589239
$766$	9.21661	0.333010
$767$	−3.52169	−0.127161
$768$	−3.31410	−0.119587
$769$	24.8686	0.896785	0.448392	−	0.893837i	$-0.351997\pi$
$769$	24.8686	0.896785	0.448392	+	0.893837i	$0.351997\pi$
$770$	−7.66797	−0.276334
$771$	3.71747	0.133882
$772$	0.400657	0.0144200
$773$	53.6768	1.93062	0.965310	−	0.261105i	$-0.0840868\pi$
$773$	53.6768	1.93062	0.965310	+	0.261105i	$0.0840868\pi$
$774$	90.5991	3.25652
$775$	7.95326	0.285689
$776$	−12.1288	−0.435398
$777$	−25.7934	−0.925333
$778$	26.4574	0.948543
$779$	−62.2481	−2.23027
$780$	−18.8426	−0.674673
$781$	1.22216	0.0437322
$782$	0	0
$783$	21.4307	0.765871
$784$	−1.72654	−0.0616621
$785$	10.2850	0.367089
$786$	−30.3029	−1.08087
$787$	42.3582	1.50991	0.754953	−	0.655779i	$-0.227660\pi$
$787$	42.3582	1.50991	0.754953	+	0.655779i	$0.227660\pi$
$788$	−16.2418	−0.578590
$789$	87.3048	3.10813
$790$	4.44597	0.158181
$791$	−15.5954	−0.554510
$792$	26.6570	0.947217
$793$	−10.9442	−0.388642
$794$	22.5575	0.800535
$795$	12.8448	0.455557
$796$	−7.97234	−0.282572
$797$	−17.5025	−0.619971	−0.309985	−	0.950741i	$-0.600324\pi$
$797$	−17.5025	−0.619971	−0.309985	+	0.950741i	$0.600324\pi$
$798$	42.6525	1.50988
$799$	0.191977	0.00679166
$800$	−1.00000	−0.0353553
$801$	100.022	3.53411
$802$	11.7338	0.414334
$803$	−25.4045	−0.896505
$804$	30.3417	1.07007
$805$	0	0
$806$	45.2189	1.59277
$807$	19.8791	0.699776
$808$	0.584209	0.0205524
$809$	−20.4184	−0.717874	−0.358937	−	0.933362i	$-0.616861\pi$
$809$	−20.4184	−0.717874	−0.358937	+	0.933362i	$0.616861\pi$
$810$	30.7824	1.08158
$811$	31.3932	1.10237	0.551183	−	0.834384i	$-0.314177\pi$
$811$	31.3932	1.10237	0.551183	+	0.834384i	$0.314177\pi$
$812$	−2.97994	−0.104575
$813$	60.1692	2.11022
$814$	11.3169	0.396658
$815$	−6.85849	−0.240242
$816$	−6.76563	−0.236844
$817$	−63.6027	−2.22518
$818$	−2.10727	−0.0736790
$819$	−104.232	−3.64217
$820$	11.1070	0.387872
$821$	−49.5472	−1.72921	−0.864604	−	0.502454i	$-0.832431\pi$
$821$	−49.5472	−1.72921	−0.864604	+	0.502454i	$0.832431\pi$
$822$	21.9313	0.764942
$823$	−33.1101	−1.15415	−0.577073	−	0.816693i	$-0.695805\pi$
$823$	−33.1101	−1.15415	−0.577073	+	0.816693i	$0.695805\pi$
$824$	−14.4033	−0.501762
$825$	11.0662	0.385275
$826$	−1.42241	−0.0494919
$827$	−45.5368	−1.58347	−0.791735	−	0.610864i	$-0.790822\pi$
$827$	−45.5368	−1.58347	−0.791735	+	0.610864i	$0.790822\pi$
$828$	0	0
$829$	12.0956	0.420098	0.210049	−	0.977691i	$-0.432638\pi$
$829$	12.0956	0.420098	0.210049	+	0.977691i	$0.432638\pi$
$830$	−12.9148	−0.448280
$831$	−93.5037	−3.24361
$832$	−5.68559	−0.197112
$833$	−3.52468	−0.122123
$834$	70.6061	2.44489
$835$	13.0828	0.452748
$836$	−18.7139	−0.647232
$837$	−131.348	−4.54004
$838$	22.2893	0.769973
$839$	34.0196	1.17449	0.587244	−	0.809410i	$-0.300213\pi$
$839$	34.0196	1.17449	0.587244	+	0.809410i	$0.300213\pi$
$840$	−7.61050	−0.262587
$841$	−27.3161	−0.941934
$842$	4.93018	0.169905
$843$	−20.5156	−0.706596
$844$	−9.63006	−0.331480
$845$	−19.3259	−0.664832
$846$	−0.750734	−0.0258108
$847$	0.343880	0.0118158
$848$	3.87580	0.133095
$849$	40.4157	1.38706
$850$	−2.04147	−0.0700218
$851$	0	0
$852$	1.21300	0.0415566
$853$	−36.6327	−1.25428	−0.627140	−	0.778907i	$-0.715775\pi$
$853$	−36.6327	−1.25428	−0.627140	+	0.778907i	$0.715775\pi$
$854$	−4.42037	−0.151262
$855$	−44.7415	−1.53013
$856$	−7.24246	−0.247542
$857$	−30.3489	−1.03670	−0.518350	−	0.855169i	$-0.673454\pi$
$857$	−30.3489	−1.03670	−0.518350	+	0.855169i	$0.673454\pi$
$858$	62.9178	2.14798
$859$	0.886171	0.0302358	0.0151179	−	0.999886i	$-0.495188\pi$
$859$	0.886171	0.0302358	0.0151179	+	0.999886i	$0.495188\pi$
$860$	11.3487	0.386986
$861$	84.5295	2.88076
$862$	30.4941	1.03863
$863$	−1.60813	−0.0547414	−0.0273707	−	0.999625i	$-0.508713\pi$
$863$	−1.60813	−0.0547414	−0.0273707	+	0.999625i	$0.508713\pi$
$864$	16.5150	0.561850
$865$	−15.7460	−0.535379
$866$	6.19805	0.210618
$867$	42.5278	1.44432
$868$	18.2639	0.619916
$869$	−14.8457	−0.503604
$870$	4.30055	0.145802
$871$	52.0535	1.76376
$872$	−10.9072	−0.369365
$873$	96.8271	3.27710
$874$	0	0
$875$	−2.29640	−0.0776325
$876$	−25.2141	−0.851905
$877$	−38.1008	−1.28657	−0.643285	−	0.765626i	$-0.722429\pi$
$877$	−38.1008	−1.28657	−0.643285	+	0.765626i	$0.722429\pi$
$878$	−16.2836	−0.549546
$879$	34.2918	1.15663
$880$	3.33912	0.112562
$881$	−40.7890	−1.37421	−0.687107	−	0.726556i	$-0.741120\pi$
$881$	−40.7890	−1.37421	−0.687107	+	0.726556i	$0.741120\pi$
$882$	13.7834	0.464111
$883$	11.9598	0.402481	0.201240	−	0.979542i	$-0.435503\pi$
$883$	11.9598	0.402481	0.201240	+	0.979542i	$0.435503\pi$
$884$	−11.6070	−0.390384
$885$	2.05278	0.0690033
$886$	15.9445	0.535665
$887$	30.7194	1.03146	0.515729	−	0.856752i	$-0.327521\pi$
$887$	30.7194	1.03146	0.515729	+	0.856752i	$0.327521\pi$
$888$	11.2321	0.376925
$889$	−22.8947	−0.767865
$890$	12.5290	0.419974
$891$	−102.786	−3.44347
$892$	−6.25888	−0.209563
$893$	0.527032	0.0176365
$894$	52.0384	1.74042
$895$	−13.1135	−0.438335
$896$	−2.29640	−0.0767174
$897$	0	0
$898$	−9.40379	−0.313809
$899$	−10.3206	−0.344211
$900$	7.98324	0.266108
$901$	7.91232	0.263598
$902$	−37.0875	−1.23488
$903$	86.3690	2.87418
$904$	6.79125	0.225874
$905$	−9.78096	−0.325130
$906$	−13.6153	−0.452339
$907$	−49.1844	−1.63314	−0.816570	−	0.577246i	$-0.804127\pi$
$907$	−49.1844	−1.63314	−0.816570	+	0.577246i	$0.804127\pi$
$908$	−5.09565	−0.169105
$909$	−4.66388	−0.154691
$910$	−13.0564	−0.432815
$911$	−42.4752	−1.40727	−0.703634	−	0.710563i	$-0.748440\pi$
$911$	−42.4752	−1.40727	−0.703634	+	0.710563i	$0.748440\pi$
$912$	−18.5736	−0.615033
$913$	43.1242	1.42720
$914$	−4.68319	−0.154906
$915$	6.37934	0.210894
$916$	−13.6668	−0.451563
$917$	−20.9975	−0.693398
$918$	33.7148	1.11275
$919$	−19.8327	−0.654221	−0.327110	−	0.944986i	$-0.606075\pi$
$919$	−19.8327	−0.654221	−0.327110	+	0.944986i	$0.606075\pi$
$920$	0	0
$921$	−53.9248	−1.77688
$922$	−11.8574	−0.390501
$923$	2.08099	0.0684965
$924$	25.4124	0.836007
$925$	3.38919	0.111436
$926$	30.7034	1.00898
$927$	114.985	3.77660
$928$	1.29765	0.0425976
$929$	−31.1494	−1.02198	−0.510989	−	0.859587i	$-0.670721\pi$
$929$	−31.1494	−1.02198	−0.510989	+	0.859587i	$0.670721\pi$
$930$	−26.3579	−0.864309
$931$	−9.67626	−0.317127
$932$	23.9857	0.785679
$933$	59.5086	1.94823
$934$	−2.58297	−0.0845174
$935$	6.81672	0.222931
$936$	45.3894	1.48360
$937$	42.5276	1.38932	0.694659	−	0.719340i	$-0.255555\pi$
$937$	42.5276	1.38932	0.694659	+	0.719340i	$0.255555\pi$
$938$	21.0243	0.686469
$939$	103.118	3.36514
$940$	−0.0940387	−0.00306720
$941$	−54.8670	−1.78861	−0.894307	−	0.447454i	$-0.852331\pi$
$941$	−54.8670	−1.78861	−0.894307	+	0.447454i	$0.852331\pi$
$942$	−34.0857	−1.11057
$943$	0	0
$944$	0.619407	0.0201600
$945$	37.9250	1.23370
$946$	−37.8946	−1.23206
$947$	−4.04883	−0.131569	−0.0657847	−	0.997834i	$-0.520955\pi$
$947$	−4.04883	−0.131569	−0.0657847	+	0.997834i	$0.520955\pi$
$948$	−14.7344	−0.478551
$949$	−43.2567	−1.40417
$950$	−5.60442	−0.181831
$951$	−84.9815	−2.75571
$952$	−4.68803	−0.151940
$953$	5.56515	0.180273	0.0901365	−	0.995929i	$-0.471270\pi$
$953$	5.56515	0.180273	0.0901365	+	0.995929i	$0.471270\pi$
$954$	−30.9414	−1.00177
$955$	2.21824	0.0717806
$956$	−21.7197	−0.702467
$957$	−14.3601	−0.464195
$958$	12.3429	0.398780
$959$	15.1966	0.490724
$960$	3.31410	0.106962
$961$	32.2543	1.04046
$962$	19.2695	0.621275
$963$	57.8184	1.86317
$964$	15.8021	0.508951
$965$	−0.400657	−0.0128976
$966$	0	0
$967$	3.81156	0.122572	0.0612858	−	0.998120i	$-0.480480\pi$
$967$	3.81156	0.122572	0.0612858	+	0.998120i	$0.480480\pi$
$968$	−0.149747	−0.00481306
$969$	−37.9174	−1.21808
$970$	12.1288	0.389432
$971$	8.77304	0.281540	0.140770	−	0.990042i	$-0.455042\pi$
$971$	8.77304	0.281540	0.140770	+	0.990042i	$0.455042\pi$
$972$	−52.4712	−1.68301
$973$	48.9243	1.56844
$974$	28.6640	0.918454
$975$	18.8426	0.603446
$976$	1.92491	0.0616149
$977$	−5.11182	−0.163542	−0.0817708	−	0.996651i	$-0.526058\pi$
$977$	−5.11182	−0.163542	−0.0817708	+	0.996651i	$0.526058\pi$
$978$	22.7297	0.726816
$979$	−41.8359	−1.33708
$980$	1.72654	0.0551523
$981$	87.0749	2.78009
$982$	−9.66866	−0.308539
$983$	−56.4613	−1.80084	−0.900418	−	0.435026i	$-0.856739\pi$
$983$	−56.4613	−1.80084	−0.900418	+	0.435026i	$0.856739\pi$
$984$	−36.8095	−1.17345
$985$	16.2418	0.517507
$986$	2.64912	0.0843652
$987$	−0.715681	−0.0227804
$988$	−31.8644	−1.01374
$989$	0	0
$990$	−26.6570	−0.847216
$991$	15.1455	0.481114	0.240557	−	0.970635i	$-0.422670\pi$
$991$	15.1455	0.481114	0.240557	+	0.970635i	$0.422670\pi$
$992$	−7.95326	−0.252516
$993$	−97.8456	−3.10504
$994$	0.840508	0.0266593
$995$	7.97234	0.252740
$996$	42.8010	1.35620
$997$	11.5370	0.365380	0.182690	−	0.983171i	$-0.441520\pi$
$997$	11.5370	0.365380	0.182690	+	0.983171i	$0.441520\pi$
$998$	25.9957	0.822879
$999$	−55.9723	−1.77088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.be.1.1	✓	6
23.22	odd	2		5290.2.a.bf.1.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.be.1.1	✓	6	1.1	even	1	trivial
5290.2.a.bf.1.1	yes	6	23.22	odd	2

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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.31410 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.31410 q^{6} +2.29640 q^{7} -1.00000 q^{8} +7.98324 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.31410 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.31410 q^{6} +2.29640 q^{7} -1.00000 q^{8} +7.98324 q^{9} +1.00000 q^{10} -3.33912 q^{11} -3.31410 q^{12} -5.68559 q^{13} -2.29640 q^{14} +3.31410 q^{15} +1.00000 q^{16} +2.04147 q^{17} -7.98324 q^{18} +5.60442 q^{19} -1.00000 q^{20} -7.61050 q^{21} +3.33912 q^{22} +3.31410 q^{24} +1.00000 q^{25} +5.68559 q^{26} -16.5150 q^{27} +2.29640 q^{28} -1.29765 q^{29} -3.31410 q^{30} +7.95326 q^{31} -1.00000 q^{32} +11.0662 q^{33} -2.04147 q^{34} -2.29640 q^{35} +7.98324 q^{36} +3.38919 q^{37} -5.60442 q^{38} +18.8426 q^{39} +1.00000 q^{40} -11.1070 q^{41} +7.61050 q^{42} -11.3487 q^{43} -3.33912 q^{44} -7.98324 q^{45} +0.0940387 q^{47} -3.31410 q^{48} -1.72654 q^{49} -1.00000 q^{50} -6.76563 q^{51} -5.68559 q^{52} +3.87580 q^{53} +16.5150 q^{54} +3.33912 q^{55} -2.29640 q^{56} -18.5736 q^{57} +1.29765 q^{58} +0.619407 q^{59} +3.31410 q^{60} +1.92491 q^{61} -7.95326 q^{62} +18.3327 q^{63} +1.00000 q^{64} +5.68559 q^{65} -11.0662 q^{66} -9.15534 q^{67} +2.04147 q^{68} +2.29640 q^{70} -0.366011 q^{71} -7.98324 q^{72} +7.60813 q^{73} -3.38919 q^{74} -3.31410 q^{75} +5.60442 q^{76} -7.66797 q^{77} -18.8426 q^{78} +4.44597 q^{79} -1.00000 q^{80} +30.7824 q^{81} +11.1070 q^{82} -12.9148 q^{83} -7.61050 q^{84} -2.04147 q^{85} +11.3487 q^{86} +4.30055 q^{87} +3.33912 q^{88} +12.5290 q^{89} +7.98324 q^{90} -13.0564 q^{91} -26.3579 q^{93} -0.0940387 q^{94} -5.60442 q^{95} +3.31410 q^{96} +12.1288 q^{97} +1.72654 q^{98} -26.6570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9} + 6 q^{10} - 10 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 6 q^{16} + 10 q^{17} - 8 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{21} + 10 q^{22} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 8 q^{27} - 2 q^{28} - 2 q^{30} - 2 q^{31} - 6 q^{32} + 22 q^{33} - 10 q^{34} + 2 q^{35} + 8 q^{36} + 4 q^{37} + 2 q^{38} + 24 q^{39} + 6 q^{40} + 6 q^{41} + 12 q^{42} - 12 q^{43} - 10 q^{44} - 8 q^{45} + 8 q^{47} - 2 q^{48} + 8 q^{49} - 6 q^{50} - 34 q^{51} - 2 q^{52} - 36 q^{53} + 8 q^{54} + 10 q^{55} + 2 q^{56} - 32 q^{57} + 16 q^{59} + 2 q^{60} + 10 q^{61} + 2 q^{62} + 48 q^{63} + 6 q^{64} + 2 q^{65} - 22 q^{66} - 16 q^{67} + 10 q^{68} - 2 q^{70} - 2 q^{71} - 8 q^{72} + 4 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} - 16 q^{77} - 24 q^{78} + 20 q^{79} - 6 q^{80} + 34 q^{81} - 6 q^{82} - 8 q^{83} - 12 q^{84} - 10 q^{85} + 12 q^{86} - 12 q^{87} + 10 q^{88} - 12 q^{89} + 8 q^{90} - 38 q^{91} - 28 q^{93} - 8 q^{94} + 2 q^{95} + 2 q^{96} - 2 q^{97} - 8 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9 + 6 * q^10 - 10 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 6 * q^16 + 10 * q^17 - 8 * q^18 - 2 * q^19 - 6 * q^20 - 12 * q^21 + 10 * q^22 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 8 * q^27 - 2 * q^28 - 2 * q^30 - 2 * q^31 - 6 * q^32 + 22 * q^33 - 10 * q^34 + 2 * q^35 + 8 * q^36 + 4 * q^37 + 2 * q^38 + 24 * q^39 + 6 * q^40 + 6 * q^41 + 12 * q^42 - 12 * q^43 - 10 * q^44 - 8 * q^45 + 8 * q^47 - 2 * q^48 + 8 * q^49 - 6 * q^50 - 34 * q^51 - 2 * q^52 - 36 * q^53 + 8 * q^54 + 10 * q^55 + 2 * q^56 - 32 * q^57 + 16 * q^59 + 2 * q^60 + 10 * q^61 + 2 * q^62 + 48 * q^63 + 6 * q^64 + 2 * q^65 - 22 * q^66 - 16 * q^67 + 10 * q^68 - 2 * q^70 - 2 * q^71 - 8 * q^72 + 4 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 - 16 * q^77 - 24 * q^78 + 20 * q^79 - 6 * q^80 + 34 * q^81 - 6 * q^82 - 8 * q^83 - 12 * q^84 - 10 * q^85 + 12 * q^86 - 12 * q^87 + 10 * q^88 - 12 * q^89 + 8 * q^90 - 38 * q^91 - 28 * q^93 - 8 * q^94 + 2 * q^95 + 2 * q^96 - 2 * q^97 - 8 * q^98 - 50 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more