LMFDB - Embedded newform 6422.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, 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("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 16x^{5} + 29x^{4} + 60x^{3} - 79x^{2} - 47x - 2 $ x^7 - 2x^6 - 16x^5 + 29x^4 + 60x^3 - 79x^2 - 47x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.95679$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.95679 q^{3} +1.00000 q^{4} -0.613661 q^{5} +1.95679 q^{6} -0.465830 q^{7} -1.00000 q^{8} +0.829012 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.95679 q^{3} +1.00000 q^{4} -0.613661 q^{5} +1.95679 q^{6} -0.465830 q^{7} -1.00000 q^{8} +0.829012 q^{9} +0.613661 q^{10} -4.22291 q^{11} -1.95679 q^{12} +0.465830 q^{14} +1.20080 q^{15} +1.00000 q^{16} +5.33414 q^{17} -0.829012 q^{18} -1.00000 q^{19} -0.613661 q^{20} +0.911529 q^{21} +4.22291 q^{22} -6.57915 q^{23} +1.95679 q^{24} -4.62342 q^{25} +4.24816 q^{27} -0.465830 q^{28} +8.11549 q^{29} -1.20080 q^{30} +4.04042 q^{31} -1.00000 q^{32} +8.26332 q^{33} -5.33414 q^{34} +0.285862 q^{35} +0.829012 q^{36} -1.69618 q^{37} +1.00000 q^{38} +0.613661 q^{40} -4.71828 q^{41} -0.911529 q^{42} +2.48682 q^{43} -4.22291 q^{44} -0.508733 q^{45} +6.57915 q^{46} -12.8042 q^{47} -1.95679 q^{48} -6.78300 q^{49} +4.62342 q^{50} -10.4378 q^{51} -3.74778 q^{53} -4.24816 q^{54} +2.59143 q^{55} +0.465830 q^{56} +1.95679 q^{57} -8.11549 q^{58} -12.6011 q^{59} +1.20080 q^{60} -4.02624 q^{61} -4.04042 q^{62} -0.386178 q^{63} +1.00000 q^{64} -8.26332 q^{66} -9.47090 q^{67} +5.33414 q^{68} +12.8740 q^{69} -0.285862 q^{70} +16.6857 q^{71} -0.829012 q^{72} +14.0690 q^{73} +1.69618 q^{74} +9.04704 q^{75} -1.00000 q^{76} +1.96715 q^{77} -6.66829 q^{79} -0.613661 q^{80} -10.7998 q^{81} +4.71828 q^{82} -6.70032 q^{83} +0.911529 q^{84} -3.27336 q^{85} -2.48682 q^{86} -15.8803 q^{87} +4.22291 q^{88} -11.0322 q^{89} +0.508733 q^{90} -6.57915 q^{92} -7.90623 q^{93} +12.8042 q^{94} +0.613661 q^{95} +1.95679 q^{96} +11.9535 q^{97} +6.78300 q^{98} -3.50084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 2 q^{3} + 7 q^{4} - 2 q^{5} - 2 q^{6} - q^{7} - 7 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 2 * q^3 + 7 * q^4 - 2 * q^5 - 2 * q^6 - q^7 - 7 * q^8 + 15 * q^9	\( 7 q - 7 q^{2} + 2 q^{3} + 7 q^{4} - 2 q^{5} - 2 q^{6} - q^{7} - 7 q^{8} + 15 q^{9} + 2 q^{10} - 5 q^{11} + 2 q^{12} + q^{14} - 13 q^{15} + 7 q^{16} + 16 q^{17} - 15 q^{18} - 7 q^{19} - 2 q^{20} + 3 q^{21} + 5 q^{22} + 3 q^{23} - 2 q^{24} + 7 q^{25} + 5 q^{27} - q^{28} - 7 q^{29} + 13 q^{30} - 11 q^{31} - 7 q^{32} - 6 q^{33} - 16 q^{34} + q^{35} + 15 q^{36} + 3 q^{37} + 7 q^{38} + 2 q^{40} - 15 q^{41} - 3 q^{42} + 23 q^{43} - 5 q^{44} + 38 q^{45} - 3 q^{46} + q^{47} + 2 q^{48} + 14 q^{49} - 7 q^{50} - 16 q^{51} + 21 q^{53} - 5 q^{54} + 8 q^{55} + q^{56} - 2 q^{57} + 7 q^{58} - 8 q^{59} - 13 q^{60} - 6 q^{61} + 11 q^{62} + 22 q^{63} + 7 q^{64} + 6 q^{66} - 28 q^{67} + 16 q^{68} + 48 q^{69} - q^{70} - 4 q^{71} - 15 q^{72} - 12 q^{73} - 3 q^{74} + 5 q^{75} - 7 q^{76} - 26 q^{77} - 4 q^{79} - 2 q^{80} + 51 q^{81} + 15 q^{82} - 13 q^{83} + 3 q^{84} + 39 q^{85} - 23 q^{86} - 16 q^{87} + 5 q^{88} + 15 q^{89} - 38 q^{90} + 3 q^{92} - 6 q^{93} - q^{94} + 2 q^{95} - 2 q^{96} + 37 q^{97} - 14 q^{98} + 15 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 2 * q^3 + 7 * q^4 - 2 * q^5 - 2 * q^6 - q^7 - 7 * q^8 + 15 * q^9 + 2 * q^10 - 5 * q^11 + 2 * q^12 + q^14 - 13 * q^15 + 7 * q^16 + 16 * q^17 - 15 * q^18 - 7 * q^19 - 2 * q^20 + 3 * q^21 + 5 * q^22 + 3 * q^23 - 2 * q^24 + 7 * q^25 + 5 * q^27 - q^28 - 7 * q^29 + 13 * q^30 - 11 * q^31 - 7 * q^32 - 6 * q^33 - 16 * q^34 + q^35 + 15 * q^36 + 3 * q^37 + 7 * q^38 + 2 * q^40 - 15 * q^41 - 3 * q^42 + 23 * q^43 - 5 * q^44 + 38 * q^45 - 3 * q^46 + q^47 + 2 * q^48 + 14 * q^49 - 7 * q^50 - 16 * q^51 + 21 * q^53 - 5 * q^54 + 8 * q^55 + q^56 - 2 * q^57 + 7 * q^58 - 8 * q^59 - 13 * q^60 - 6 * q^61 + 11 * q^62 + 22 * q^63 + 7 * q^64 + 6 * q^66 - 28 * q^67 + 16 * q^68 + 48 * q^69 - q^70 - 4 * q^71 - 15 * q^72 - 12 * q^73 - 3 * q^74 + 5 * q^75 - 7 * q^76 - 26 * q^77 - 4 * q^79 - 2 * q^80 + 51 * q^81 + 15 * q^82 - 13 * q^83 + 3 * q^84 + 39 * q^85 - 23 * q^86 - 16 * q^87 + 5 * q^88 + 15 * q^89 - 38 * q^90 + 3 * q^92 - 6 * q^93 - q^94 + 2 * q^95 - 2 * q^96 + 37 * q^97 - 14 * q^98 + 15 * 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
$3$	−1.95679	−1.12975	−0.564876	−	0.825176i	$-0.691076\pi$
$3$	−1.95679	−1.12975	−0.564876	+	0.825176i	$0.691076\pi$
$4$	1.00000	0.500000
$5$	−0.613661	−0.274438	−0.137219	−	0.990541i	$-0.543816\pi$
$5$	−0.613661	−0.274438	−0.137219	+	0.990541i	$0.543816\pi$
$6$	1.95679	0.798855
$7$	−0.465830	−0.176067	−0.0880335	−	0.996118i	$-0.528058\pi$
$7$	−0.465830	−0.176067	−0.0880335	+	0.996118i	$0.528058\pi$
$8$	−1.00000	−0.353553
$9$	0.829012	0.276337
$10$	0.613661	0.194057
$11$	−4.22291	−1.27325	−0.636627	−	0.771172i	$-0.719671\pi$
$11$	−4.22291	−1.27325	−0.636627	+	0.771172i	$0.719671\pi$
$12$	−1.95679	−0.564876
$13$	0	0
$13$	0	0
$14$	0.465830	0.124498
$15$	1.20080	0.310046
$16$	1.00000	0.250000
$17$	5.33414	1.29372	0.646860	−	0.762609i	$-0.276082\pi$
$17$	5.33414	1.29372	0.646860	+	0.762609i	$0.276082\pi$
$18$	−0.829012	−0.195400
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.613661	−0.137219
$21$	0.911529	0.198912
$22$	4.22291	0.900327
$23$	−6.57915	−1.37185	−0.685924	−	0.727673i	$-0.740602\pi$
$23$	−6.57915	−1.37185	−0.685924	+	0.727673i	$0.740602\pi$
$24$	1.95679	0.399427
$25$	−4.62342	−0.924684
$26$	0	0
$27$	4.24816	0.817559
$28$	−0.465830	−0.0880335
$29$	8.11549	1.50701	0.753504	−	0.657443i	$-0.228362\pi$
$29$	8.11549	1.50701	0.753504	+	0.657443i	$0.228362\pi$
$30$	−1.20080	−0.219236
$31$	4.04042	0.725680	0.362840	−	0.931851i	$-0.381807\pi$
$31$	4.04042	0.725680	0.362840	+	0.931851i	$0.381807\pi$
$32$	−1.00000	−0.176777
$33$	8.26332	1.43846
$34$	−5.33414	−0.914798
$35$	0.285862	0.0483194
$36$	0.829012	0.138169
$37$	−1.69618	−0.278850	−0.139425	−	0.990233i	$-0.544525\pi$
$37$	−1.69618	−0.278850	−0.139425	+	0.990233i	$0.544525\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	0.613661	0.0970284
$41$	−4.71828	−0.736871	−0.368436	−	0.929653i	$-0.620107\pi$
$41$	−4.71828	−0.736871	−0.368436	+	0.929653i	$0.620107\pi$
$42$	−0.911529	−0.140652
$43$	2.48682	0.379236	0.189618	−	0.981858i	$-0.439275\pi$
$43$	2.48682	0.379236	0.189618	+	0.981858i	$0.439275\pi$
$44$	−4.22291	−0.636627
$45$	−0.508733	−0.0758374
$46$	6.57915	0.970043
$47$	−12.8042	−1.86769	−0.933844	−	0.357680i	$-0.883568\pi$
$47$	−12.8042	−1.86769	−0.933844	+	0.357680i	$0.883568\pi$
$48$	−1.95679	−0.282438
$49$	−6.78300	−0.969000
$50$	4.62342	0.653850
$51$	−10.4378	−1.46158
$52$	0	0
$53$	−3.74778	−0.514797	−0.257399	−	0.966305i	$-0.582865\pi$
$53$	−3.74778	−0.514797	−0.257399	+	0.966305i	$0.582865\pi$
$54$	−4.24816	−0.578101
$55$	2.59143	0.349429
$56$	0.465830	0.0622491
$57$	1.95679	0.259183
$58$	−8.11549	−1.06562
$59$	−12.6011	−1.64052	−0.820262	−	0.571988i	$-0.806172\pi$
$59$	−12.6011	−1.64052	−0.820262	+	0.571988i	$0.806172\pi$
$60$	1.20080	0.155023
$61$	−4.02624	−0.515508	−0.257754	−	0.966211i	$-0.582982\pi$
$61$	−4.02624	−0.515508	−0.257754	+	0.966211i	$0.582982\pi$
$62$	−4.04042	−0.513134
$63$	−0.386178	−0.0486539
$64$	1.00000	0.125000
$65$	0	0
$66$	−8.26332	−1.01714
$67$	−9.47090	−1.15705	−0.578527	−	0.815663i	$-0.696372\pi$
$67$	−9.47090	−1.15705	−0.578527	+	0.815663i	$0.696372\pi$
$68$	5.33414	0.646860
$69$	12.8740	1.54985
$70$	−0.285862	−0.0341670
$71$	16.6857	1.98022	0.990112	−	0.140279i	$-0.0448001\pi$
$71$	16.6857	1.98022	0.990112	+	0.140279i	$0.0448001\pi$
$72$	−0.829012	−0.0977000
$73$	14.0690	1.64665	0.823325	−	0.567571i	$-0.192117\pi$
$73$	14.0690	1.64665	0.823325	+	0.567571i	$0.192117\pi$
$74$	1.69618	0.197177
$75$	9.04704	1.04466
$76$	−1.00000	−0.114708
$77$	1.96715	0.224178
$78$	0	0
$79$	−6.66829	−0.750241	−0.375121	−	0.926976i	$-0.622399\pi$
$79$	−6.66829	−0.750241	−0.375121	+	0.926976i	$0.622399\pi$
$80$	−0.613661	−0.0686094
$81$	−10.7998	−1.19998
$82$	4.71828	0.521047
$83$	−6.70032	−0.735456	−0.367728	−	0.929933i	$-0.619864\pi$
$83$	−6.70032	−0.735456	−0.367728	+	0.929933i	$0.619864\pi$
$84$	0.911529	0.0994559
$85$	−3.27336	−0.355046
$86$	−2.48682	−0.268160
$87$	−15.8803	−1.70255
$88$	4.22291	0.450163
$89$	−11.0322	−1.16941	−0.584706	−	0.811245i	$-0.698790\pi$
$89$	−11.0322	−1.16941	−0.584706	+	0.811245i	$0.698790\pi$
$90$	0.508733	0.0536251
$91$	0	0
$92$	−6.57915	−0.685924
$93$	−7.90623	−0.819838
$94$	12.8042	1.32066
$95$	0.613661	0.0629603
$96$	1.95679	0.199714
$97$	11.9535	1.21369	0.606846	−	0.794819i	$-0.292434\pi$
$97$	11.9535	1.21369	0.606846	+	0.794819i	$0.292434\pi$
$98$	6.78300	0.685187
$99$	−3.50084	−0.351848
$100$	−4.62342	−0.462342
$101$	12.2449	1.21841	0.609204	−	0.793013i	$-0.291489\pi$
$101$	12.2449	1.21841	0.609204	+	0.793013i	$0.291489\pi$
$102$	10.4378	1.03349
$103$	−10.6048	−1.04492	−0.522461	−	0.852663i	$-0.674986\pi$
$103$	−10.6048	−1.04492	−0.522461	+	0.852663i	$0.674986\pi$
$104$	0	0
$105$	−0.559370	−0.0545889
$106$	3.74778	0.364017
$107$	13.9570	1.34928	0.674638	−	0.738149i	$-0.264300\pi$
$107$	13.9570	1.34928	0.674638	+	0.738149i	$0.264300\pi$
$108$	4.24816	0.408779
$109$	2.18305	0.209099	0.104549	−	0.994520i	$-0.466660\pi$
$109$	2.18305	0.209099	0.104549	+	0.994520i	$0.466660\pi$
$110$	−2.59143	−0.247084
$111$	3.31906	0.315031
$112$	−0.465830	−0.0440168
$113$	2.84523	0.267657	0.133828	−	0.991005i	$-0.457273\pi$
$113$	2.84523	0.267657	0.133828	+	0.991005i	$0.457273\pi$
$114$	−1.95679	−0.183270
$115$	4.03737	0.376487
$116$	8.11549	0.753504
$117$	0	0
$118$	12.6011	1.16003
$119$	−2.48480	−0.227781
$120$	−1.20080	−0.109618
$121$	6.83293	0.621176
$122$	4.02624	0.364519
$123$	9.23266	0.832481
$124$	4.04042	0.362840
$125$	5.90552	0.528206
$126$	0.386178	0.0344035
$127$	−4.34142	−0.385239	−0.192619	−	0.981274i	$-0.561698\pi$
$127$	−4.34142	−0.385239	−0.192619	+	0.981274i	$0.561698\pi$
$128$	−1.00000	−0.0883883
$129$	−4.86617	−0.428442
$130$	0	0
$131$	−22.2320	−1.94241	−0.971207	−	0.238236i	$-0.923431\pi$
$131$	−22.2320	−1.94241	−0.971207	+	0.238236i	$0.923431\pi$
$132$	8.26332	0.719230
$133$	0.465830	0.0403925
$134$	9.47090	0.818161
$135$	−2.60693	−0.224369
$136$	−5.33414	−0.457399
$137$	−10.4930	−0.896481	−0.448240	−	0.893913i	$-0.647949\pi$
$137$	−10.4930	−0.896481	−0.448240	+	0.893913i	$0.647949\pi$
$138$	−12.8740	−1.09591
$139$	14.1682	1.20173	0.600867	−	0.799349i	$-0.294822\pi$
$139$	14.1682	1.20173	0.600867	+	0.799349i	$0.294822\pi$
$140$	0.285862	0.0241597
$141$	25.0551	2.11002
$142$	−16.6857	−1.40023
$143$	0	0
$144$	0.829012	0.0690844
$145$	−4.98016	−0.413580
$146$	−14.0690	−1.16436
$147$	13.2729	1.09473
$148$	−1.69618	−0.139425
$149$	−20.7814	−1.70248	−0.851241	−	0.524775i	$-0.824150\pi$
$149$	−20.7814	−1.70248	−0.851241	+	0.524775i	$0.824150\pi$
$150$	−9.04704	−0.738688
$151$	−16.5451	−1.34643	−0.673213	−	0.739449i	$-0.735086\pi$
$151$	−16.5451	−1.34643	−0.673213	+	0.739449i	$0.735086\pi$
$152$	1.00000	0.0811107
$153$	4.42207	0.357503
$154$	−1.96715	−0.158518
$155$	−2.47945	−0.199154
$156$	0	0
$157$	7.20936	0.575370	0.287685	−	0.957725i	$-0.407114\pi$
$157$	7.20936	0.575370	0.287685	+	0.957725i	$0.407114\pi$
$158$	6.66829	0.530501
$159$	7.33360	0.581593
$160$	0.613661	0.0485142
$161$	3.06476	0.241537
$162$	10.7998	0.848511
$163$	1.57738	0.123550	0.0617751	−	0.998090i	$-0.480324\pi$
$163$	1.57738	0.123550	0.0617751	+	0.998090i	$0.480324\pi$
$164$	−4.71828	−0.368436
$165$	−5.07088	−0.394768
$166$	6.70032	0.520046
$167$	5.83293	0.451366	0.225683	−	0.974201i	$-0.427539\pi$
$167$	5.83293	0.451366	0.225683	+	0.974201i	$0.427539\pi$
$168$	−0.911529	−0.0703260
$169$	0	0
$170$	3.27336	0.251055
$171$	−0.829012	−0.0633962
$172$	2.48682	0.189618
$173$	−5.59479	−0.425364	−0.212682	−	0.977121i	$-0.568220\pi$
$173$	−5.59479	−0.425364	−0.212682	+	0.977121i	$0.568220\pi$
$174$	15.8803	1.20388
$175$	2.15373	0.162806
$176$	−4.22291	−0.318313
$177$	24.6577	1.85338
$178$	11.0322	0.826900
$179$	−1.65521	−0.123716	−0.0618580	−	0.998085i	$-0.519703\pi$
$179$	−1.65521	−0.123716	−0.0618580	+	0.998085i	$0.519703\pi$
$180$	−0.508733	−0.0379187
$181$	−10.8505	−0.806509	−0.403254	−	0.915088i	$-0.632121\pi$
$181$	−10.8505	−0.806509	−0.403254	+	0.915088i	$0.632121\pi$
$182$	0	0
$183$	7.87850	0.582395
$184$	6.57915	0.485022
$185$	1.04088	0.0765269
$186$	7.90623	0.579713
$187$	−22.5256	−1.64723
$188$	−12.8042	−0.933844
$189$	−1.97892	−0.143945
$190$	−0.613661	−0.0445197
$191$	−11.6513	−0.843060	−0.421530	−	0.906814i	$-0.638507\pi$
$191$	−11.6513	−0.843060	−0.421530	+	0.906814i	$0.638507\pi$
$192$	−1.95679	−0.141219
$193$	−6.22352	−0.447979	−0.223989	−	0.974592i	$-0.571908\pi$
$193$	−6.22352	−0.447979	−0.223989	+	0.974592i	$0.571908\pi$
$194$	−11.9535	−0.858210
$195$	0	0
$196$	−6.78300	−0.484500
$197$	−9.70754	−0.691633	−0.345817	−	0.938302i	$-0.612398\pi$
$197$	−9.70754	−0.691633	−0.345817	+	0.938302i	$0.612398\pi$
$198$	3.50084	0.248794
$199$	16.4151	1.16364	0.581819	−	0.813318i	$-0.302341\pi$
$199$	16.4151	1.16364	0.581819	+	0.813318i	$0.302341\pi$
$200$	4.62342	0.326925
$201$	18.5325	1.30718
$202$	−12.2449	−0.861545
$203$	−3.78044	−0.265335
$204$	−10.4378	−0.730791
$205$	2.89543	0.202225
$206$	10.6048	0.738871
$207$	−5.45420	−0.379093
$208$	0	0
$209$	4.22291	0.292104
$210$	0.559370	0.0386002
$211$	11.0380	0.759886	0.379943	−	0.925010i	$-0.375944\pi$
$211$	11.0380	0.759886	0.379943	+	0.925010i	$0.375944\pi$
$212$	−3.74778	−0.257399
$213$	−32.6503	−2.23716
$214$	−13.9570	−0.954082
$215$	−1.52606	−0.104077
$216$	−4.24816	−0.289051
$217$	−1.88215	−0.127768
$218$	−2.18305	−0.147855
$219$	−27.5300	−1.86030
$220$	2.59143	0.174714
$221$	0	0
$222$	−3.31906	−0.222761
$223$	−22.0677	−1.47776	−0.738882	−	0.673834i	$-0.764646\pi$
$223$	−22.0677	−1.47776	−0.738882	+	0.673834i	$0.764646\pi$
$224$	0.465830	0.0311245
$225$	−3.83287	−0.255525
$226$	−2.84523	−0.189262
$227$	−25.6025	−1.69930	−0.849650	−	0.527347i	$-0.823187\pi$
$227$	−25.6025	−1.69930	−0.849650	+	0.527347i	$0.823187\pi$
$228$	1.95679	0.129591
$229$	15.8683	1.04861	0.524303	−	0.851532i	$-0.324326\pi$
$229$	15.8683	1.04861	0.524303	+	0.851532i	$0.324326\pi$
$230$	−4.03737	−0.266216
$231$	−3.84930	−0.253265
$232$	−8.11549	−0.532808
$233$	2.90658	0.190417	0.0952084	−	0.995457i	$-0.469648\pi$
$233$	2.90658	0.190417	0.0952084	+	0.995457i	$0.469648\pi$
$234$	0	0
$235$	7.85746	0.512564
$236$	−12.6011	−0.820262
$237$	13.0484	0.847586
$238$	2.48480	0.161066
$239$	4.13013	0.267156	0.133578	−	0.991038i	$-0.457353\pi$
$239$	4.13013	0.267156	0.133578	+	0.991038i	$0.457353\pi$
$240$	1.20080	0.0775116
$241$	23.5902	1.51958	0.759789	−	0.650170i	$-0.225302\pi$
$241$	23.5902	1.51958	0.759789	+	0.650170i	$0.225302\pi$
$242$	−6.83293	−0.439238
$243$	8.38838	0.538115
$244$	−4.02624	−0.257754
$245$	4.16247	0.265930
$246$	−9.23266	−0.588653
$247$	0	0
$248$	−4.04042	−0.256567
$249$	13.1111	0.830882
$250$	−5.90552	−0.373498
$251$	25.0428	1.58069	0.790343	−	0.612664i	$-0.209902\pi$
$251$	25.0428	1.58069	0.790343	+	0.612664i	$0.209902\pi$
$252$	−0.386178	−0.0243270
$253$	27.7831	1.74671
$254$	4.34142	0.272405
$255$	6.40526	0.401113
$256$	1.00000	0.0625000
$257$	10.2457	0.639112	0.319556	−	0.947567i	$-0.396466\pi$
$257$	10.2457	0.639112	0.319556	+	0.947567i	$0.396466\pi$
$258$	4.86617	0.302954
$259$	0.790130	0.0490963
$260$	0	0
$261$	6.72784	0.416443
$262$	22.2320	1.37349
$263$	29.1596	1.79806	0.899029	−	0.437889i	$-0.144274\pi$
$263$	29.1596	1.79806	0.899029	+	0.437889i	$0.144274\pi$
$264$	−8.26332	−0.508572
$265$	2.29987	0.141280
$266$	−0.465830	−0.0285618
$267$	21.5877	1.32115
$268$	−9.47090	−0.578527
$269$	13.5732	0.827570	0.413785	−	0.910375i	$-0.364207\pi$
$269$	13.5732	0.827570	0.413785	+	0.910375i	$0.364207\pi$
$270$	2.60693	0.158653
$271$	−3.79910	−0.230779	−0.115389	−	0.993320i	$-0.536812\pi$
$271$	−3.79910	−0.230779	−0.115389	+	0.993320i	$0.536812\pi$
$272$	5.33414	0.323430
$273$	0	0
$274$	10.4930	0.633908
$275$	19.5243	1.17736
$276$	12.8740	0.774923
$277$	−9.78766	−0.588084	−0.294042	−	0.955793i	$-0.595000\pi$
$277$	−9.78766	−0.588084	−0.294042	+	0.955793i	$0.595000\pi$
$278$	−14.1682	−0.849754
$279$	3.34956	0.200533
$280$	−0.285862	−0.0170835
$281$	−16.2314	−0.968285	−0.484142	−	0.874989i	$-0.660868\pi$
$281$	−16.2314	−0.968285	−0.484142	+	0.874989i	$0.660868\pi$
$282$	−25.0551	−1.49201
$283$	22.1491	1.31662	0.658312	−	0.752745i	$-0.271271\pi$
$283$	22.1491	1.31662	0.658312	+	0.752745i	$0.271271\pi$
$284$	16.6857	0.990112
$285$	−1.20080	−0.0711295
$286$	0	0
$287$	2.19791	0.129739
$288$	−0.829012	−0.0488500
$289$	11.4531	0.673712
$290$	4.98016	0.292445
$291$	−23.3904	−1.37117
$292$	14.0690	0.823325
$293$	−4.79987	−0.280411	−0.140206	−	0.990122i	$-0.544776\pi$
$293$	−4.79987	−0.280411	−0.140206	+	0.990122i	$0.544776\pi$
$294$	−13.2729	−0.774090
$295$	7.73281	0.450222
$296$	1.69618	0.0985883
$297$	−17.9396	−1.04096
$298$	20.7814	1.20384
$299$	0	0
$300$	9.04704	0.522331
$301$	−1.15843	−0.0667709
$302$	16.5451	0.952066
$303$	−23.9606	−1.37650
$304$	−1.00000	−0.0573539
$305$	2.47075	0.141475
$306$	−4.42207	−0.252793
$307$	21.2921	1.21520	0.607601	−	0.794243i	$-0.292132\pi$
$307$	21.2921	1.21520	0.607601	+	0.794243i	$0.292132\pi$
$308$	1.96715	0.112089
$309$	20.7513	1.18050
$310$	2.47945	0.140823
$311$	3.78811	0.214804	0.107402	−	0.994216i	$-0.465747\pi$
$311$	3.78811	0.214804	0.107402	+	0.994216i	$0.465747\pi$
$312$	0	0
$313$	21.1236	1.19398	0.596988	−	0.802250i	$-0.296364\pi$
$313$	21.1236	1.19398	0.596988	+	0.802250i	$0.296364\pi$
$314$	−7.20936	−0.406848
$315$	0.236983	0.0133525
$316$	−6.66829	−0.375121
$317$	−1.72135	−0.0966805	−0.0483402	−	0.998831i	$-0.515393\pi$
$317$	−1.72135	−0.0966805	−0.0483402	+	0.998831i	$0.515393\pi$
$318$	−7.33360	−0.411248
$319$	−34.2710	−1.91881
$320$	−0.613661	−0.0343047
$321$	−27.3109	−1.52435
$322$	−3.06476	−0.170793
$323$	−5.33414	−0.296800
$324$	−10.7998	−0.599988
$325$	0	0
$326$	−1.57738	−0.0873632
$327$	−4.27177	−0.236229
$328$	4.71828	0.260523
$329$	5.96459	0.328838
$330$	5.07088	0.279143
$331$	−7.09167	−0.389793	−0.194897	−	0.980824i	$-0.562437\pi$
$331$	−7.09167	−0.389793	−0.194897	+	0.980824i	$0.562437\pi$
$332$	−6.70032	−0.367728
$333$	−1.40615	−0.0770567
$334$	−5.83293	−0.319164
$335$	5.81192	0.317539
$336$	0.911529	0.0497280
$337$	8.82879	0.480935	0.240467	−	0.970657i	$-0.422699\pi$
$337$	8.82879	0.480935	0.240467	+	0.970657i	$0.422699\pi$
$338$	0	0
$339$	−5.56751	−0.302386
$340$	−3.27336	−0.177523
$341$	−17.0623	−0.923976
$342$	0.829012	0.0448279
$343$	6.42053	0.346676
$344$	−2.48682	−0.134080
$345$	−7.90027	−0.425336
$346$	5.59479	0.300778
$347$	−26.7555	−1.43631	−0.718156	−	0.695882i	$-0.755014\pi$
$347$	−26.7555	−1.43631	−0.718156	+	0.695882i	$0.755014\pi$
$348$	−15.8803	−0.851273
$349$	−4.80791	−0.257361	−0.128681	−	0.991686i	$-0.541074\pi$
$349$	−4.80791	−0.257361	−0.128681	+	0.991686i	$0.541074\pi$
$350$	−2.15373	−0.115121
$351$	0	0
$352$	4.22291	0.225082
$353$	31.8519	1.69531	0.847653	−	0.530551i	$-0.178015\pi$
$353$	31.8519	1.69531	0.847653	+	0.530551i	$0.178015\pi$
$354$	−24.6577	−1.31054
$355$	−10.2393	−0.543448
$356$	−11.0322	−0.584706
$357$	4.86223	0.257336
$358$	1.65521	0.0874804
$359$	−2.93468	−0.154887	−0.0774434	−	0.996997i	$-0.524676\pi$
$359$	−2.93468	−0.154887	−0.0774434	+	0.996997i	$0.524676\pi$
$360$	0.508733	0.0268126
$361$	1.00000	0.0526316
$362$	10.8505	0.570288
$363$	−13.3706	−0.701774
$364$	0	0
$365$	−8.63359	−0.451903
$366$	−7.87850	−0.411816
$367$	2.48889	0.129919	0.0649595	−	0.997888i	$-0.479308\pi$
$367$	2.48889	0.129919	0.0649595	+	0.997888i	$0.479308\pi$
$368$	−6.57915	−0.342962
$369$	−3.91151	−0.203625
$370$	−1.04088	−0.0541127
$371$	1.74583	0.0906388
$372$	−7.90623	−0.409919
$373$	10.6864	0.553318	0.276659	−	0.960968i	$-0.410773\pi$
$373$	10.6864	0.553318	0.276659	+	0.960968i	$0.410773\pi$
$374$	22.5256	1.16477
$375$	−11.5558	−0.596741
$376$	12.8042	0.660328
$377$	0	0
$378$	1.97892	0.101785
$379$	−11.7057	−0.601284	−0.300642	−	0.953737i	$-0.597201\pi$
$379$	−11.7057	−0.601284	−0.300642	+	0.953737i	$0.597201\pi$
$380$	0.613661	0.0314802
$381$	8.49524	0.435224
$382$	11.6513	0.596134
$383$	7.81394	0.399274	0.199637	−	0.979870i	$-0.436024\pi$
$383$	7.81394	0.399274	0.199637	+	0.979870i	$0.436024\pi$
$384$	1.95679	0.0998568
$385$	−1.20717	−0.0615229
$386$	6.22352	0.316769
$387$	2.06160	0.104797
$388$	11.9535	0.606846
$389$	3.45288	0.175068	0.0875339	−	0.996162i	$-0.472101\pi$
$389$	3.45288	0.175068	0.0875339	+	0.996162i	$0.472101\pi$
$390$	0	0
$391$	−35.0941	−1.77479
$392$	6.78300	0.342593
$393$	43.5032	2.19444
$394$	9.70754	0.489059
$395$	4.09207	0.205894
$396$	−3.50084	−0.175924
$397$	22.5431	1.13141	0.565703	−	0.824609i	$-0.308605\pi$
$397$	22.5431	1.13141	0.565703	+	0.824609i	$0.308605\pi$
$398$	−16.4151	−0.822816
$399$	−0.911529	−0.0456335
$400$	−4.62342	−0.231171
$401$	−29.5703	−1.47667	−0.738336	−	0.674433i	$-0.764388\pi$
$401$	−29.5703	−1.47667	−0.738336	+	0.674433i	$0.764388\pi$
$402$	−18.5325	−0.924318
$403$	0	0
$404$	12.2449	0.609204
$405$	6.62740	0.329318
$406$	3.78044	0.187620
$407$	7.16280	0.355047
$408$	10.4378	0.516747
$409$	2.74046	0.135507	0.0677536	−	0.997702i	$-0.478417\pi$
$409$	2.74046	0.135507	0.0677536	+	0.997702i	$0.478417\pi$
$410$	−2.89543	−0.142995
$411$	20.5326	1.01280
$412$	−10.6048	−0.522461
$413$	5.86997	0.288842
$414$	5.45420	0.268059
$415$	4.11173	0.201837
$416$	0	0
$417$	−27.7242	−1.35766
$418$	−4.22291	−0.206549
$419$	−32.2035	−1.57324	−0.786622	−	0.617435i	$-0.788172\pi$
$419$	−32.2035	−1.57324	−0.786622	+	0.617435i	$0.788172\pi$
$420$	−0.559370	−0.0272945
$421$	13.3021	0.648305	0.324153	−	0.946005i	$-0.394921\pi$
$421$	13.3021	0.648305	0.324153	+	0.946005i	$0.394921\pi$
$422$	−11.0380	−0.537320
$423$	−10.6149	−0.516112
$424$	3.74778	0.182008
$425$	−24.6620	−1.19628
$426$	32.6503	1.58191
$427$	1.87554	0.0907639
$428$	13.9570	0.674638
$429$	0	0
$430$	1.52606	0.0735933
$431$	−25.9693	−1.25090	−0.625449	−	0.780265i	$-0.715084\pi$
$431$	−25.9693	−1.25090	−0.625449	+	0.780265i	$0.715084\pi$
$432$	4.24816	0.204390
$433$	8.35232	0.401387	0.200693	−	0.979654i	$-0.435680\pi$
$433$	8.35232	0.401387	0.200693	+	0.979654i	$0.435680\pi$
$434$	1.88215	0.0903459
$435$	9.74512	0.467243
$436$	2.18305	0.104549
$437$	6.57915	0.314724
$438$	27.5300	1.31543
$439$	1.50999	0.0720677	0.0360338	−	0.999351i	$-0.488528\pi$
$439$	1.50999	0.0720677	0.0360338	+	0.999351i	$0.488528\pi$
$440$	−2.59143	−0.123542
$441$	−5.62319	−0.267771
$442$	0	0
$443$	35.9799	1.70946	0.854729	−	0.519074i	$-0.173723\pi$
$443$	35.9799	1.70946	0.854729	+	0.519074i	$0.173723\pi$
$444$	3.31906	0.157515
$445$	6.77004	0.320931
$446$	22.0677	1.04494
$447$	40.6649	1.92338
$448$	−0.465830	−0.0220084
$449$	8.07052	0.380871	0.190436	−	0.981700i	$-0.439010\pi$
$449$	8.07052	0.380871	0.190436	+	0.981700i	$0.439010\pi$
$450$	3.83287	0.180683
$451$	19.9248	0.938224
$452$	2.84523	0.133828
$453$	32.3753	1.52113
$454$	25.6025	1.20159
$455$	0	0
$456$	−1.95679	−0.0916349
$457$	−18.3167	−0.856818	−0.428409	−	0.903585i	$-0.640926\pi$
$457$	−18.3167	−0.856818	−0.428409	+	0.903585i	$0.640926\pi$
$458$	−15.8683	−0.741476
$459$	22.6603	1.05769
$460$	4.03737	0.188243
$461$	4.10208	0.191053	0.0955264	−	0.995427i	$-0.469547\pi$
$461$	4.10208	0.191053	0.0955264	+	0.995427i	$0.469547\pi$
$462$	3.84930	0.179086
$463$	4.75527	0.220996	0.110498	−	0.993876i	$-0.464755\pi$
$463$	4.75527	0.220996	0.110498	+	0.993876i	$0.464755\pi$
$464$	8.11549	0.376752
$465$	4.85175	0.224995
$466$	−2.90658	−0.134645
$467$	5.92185	0.274031	0.137015	−	0.990569i	$-0.456249\pi$
$467$	5.92185	0.274031	0.137015	+	0.990569i	$0.456249\pi$
$468$	0	0
$469$	4.41182	0.203719
$470$	−7.85746	−0.362438
$471$	−14.1072	−0.650025
$472$	12.6011	0.580013
$473$	−10.5016	−0.482864
$474$	−13.0484	−0.599334
$475$	4.62342	0.212137
$476$	−2.48480	−0.113891
$477$	−3.10696	−0.142258
$478$	−4.13013	−0.188908
$479$	1.18632	0.0542043	0.0271021	−	0.999633i	$-0.491372\pi$
$479$	1.18632	0.0542043	0.0271021	+	0.999633i	$0.491372\pi$
$480$	−1.20080	−0.0548090
$481$	0	0
$482$	−23.5902	−1.07450
$483$	−5.99709	−0.272877
$484$	6.83293	0.310588
$485$	−7.33539	−0.333083
$486$	−8.38838	−0.380504
$487$	−2.65959	−0.120518	−0.0602588	−	0.998183i	$-0.519193\pi$
$487$	−2.65959	−0.120518	−0.0602588	+	0.998183i	$0.519193\pi$
$488$	4.02624	0.182259
$489$	−3.08660	−0.139581
$490$	−4.16247	−0.188041
$491$	7.52332	0.339523	0.169761	−	0.985485i	$-0.445700\pi$
$491$	7.52332	0.339523	0.169761	+	0.985485i	$0.445700\pi$
$492$	9.23266	0.416241
$493$	43.2892	1.94965
$494$	0	0
$495$	2.14833	0.0965603
$496$	4.04042	0.181420
$497$	−7.77267	−0.348652
$498$	−13.1111	−0.587522
$499$	31.1291	1.39353	0.696766	−	0.717299i	$-0.254622\pi$
$499$	31.1291	1.39353	0.696766	+	0.717299i	$0.254622\pi$
$500$	5.90552	0.264103
$501$	−11.4138	−0.509931
$502$	−25.0428	−1.11771
$503$	−4.32945	−0.193041	−0.0965203	−	0.995331i	$-0.530771\pi$
$503$	−4.32945	−0.193041	−0.0965203	+	0.995331i	$0.530771\pi$
$504$	0.386178	0.0172018
$505$	−7.51420	−0.334377
$506$	−27.7831	−1.23511
$507$	0	0
$508$	−4.34142	−0.192619
$509$	40.2171	1.78259	0.891296	−	0.453422i	$-0.149797\pi$
$509$	40.2171	1.78259	0.891296	+	0.453422i	$0.149797\pi$
$510$	−6.40526	−0.283630
$511$	−6.55374	−0.289921
$512$	−1.00000	−0.0441942
$513$	−4.24816	−0.187561
$514$	−10.2457	−0.451920
$515$	6.50775	0.286766
$516$	−4.86617	−0.214221
$517$	54.0710	2.37804
$518$	−0.790130	−0.0347163
$519$	10.9478	0.480556
$520$	0	0
$521$	6.16600	0.270137	0.135069	−	0.990836i	$-0.456874\pi$
$521$	6.16600	0.270137	0.135069	+	0.990836i	$0.456874\pi$
$522$	−6.72784	−0.294470
$523$	−5.11015	−0.223451	−0.111726	−	0.993739i	$-0.535638\pi$
$523$	−5.11015	−0.223451	−0.111726	+	0.993739i	$0.535638\pi$
$524$	−22.2320	−0.971207
$525$	−4.21438	−0.183931
$526$	−29.1596	−1.27142
$527$	21.5522	0.938827
$528$	8.26332	0.359615
$529$	20.2852	0.881967
$530$	−2.29987	−0.0998999
$531$	−10.4465	−0.453338
$532$	0.465830	0.0201963
$533$	0	0
$534$	−21.5877	−0.934191
$535$	−8.56488	−0.370292
$536$	9.47090	0.409081
$537$	3.23889	0.139768
$538$	−13.5732	−0.585180
$539$	28.6440	1.23378
$540$	−2.60693	−0.112184
$541$	−1.78112	−0.0765763	−0.0382882	−	0.999267i	$-0.512190\pi$
$541$	−1.78112	−0.0765763	−0.0382882	+	0.999267i	$0.512190\pi$
$542$	3.79910	0.163185
$543$	21.2320	0.911154
$544$	−5.33414	−0.228700
$545$	−1.33966	−0.0573846
$546$	0	0
$547$	30.0616	1.28534	0.642670	−	0.766143i	$-0.277827\pi$
$547$	30.0616	1.28534	0.642670	+	0.766143i	$0.277827\pi$
$548$	−10.4930	−0.448240
$549$	−3.33780	−0.142454
$550$	−19.5243	−0.832517
$551$	−8.11549	−0.345732
$552$	−12.8740	−0.547954
$553$	3.10629	0.132093
$554$	9.78766	0.415838
$555$	−2.03678	−0.0864564
$556$	14.1682	0.600867
$557$	11.7171	0.496470	0.248235	−	0.968700i	$-0.420149\pi$
$557$	11.7171	0.496470	0.248235	+	0.968700i	$0.420149\pi$
$558$	−3.34956	−0.141798
$559$	0	0
$560$	0.285862	0.0120799
$561$	44.0778	1.86096
$562$	16.2314	0.684681
$563$	26.1397	1.10166	0.550828	−	0.834619i	$-0.314312\pi$
$563$	26.1397	1.10166	0.550828	+	0.834619i	$0.314312\pi$
$564$	25.0551	1.05501
$565$	−1.74601	−0.0734551
$566$	−22.1491	−0.930994
$567$	5.03085	0.211276
$568$	−16.6857	−0.700115
$569$	−29.2732	−1.22720	−0.613598	−	0.789618i	$-0.710279\pi$
$569$	−29.2732	−1.22720	−0.613598	+	0.789618i	$0.710279\pi$
$570$	1.20080	0.0502961
$571$	9.21263	0.385537	0.192768	−	0.981244i	$-0.438253\pi$
$571$	9.21263	0.385537	0.192768	+	0.981244i	$0.438253\pi$
$572$	0	0
$573$	22.7992	0.952448
$574$	−2.19791	−0.0917392
$575$	30.4182	1.26853
$576$	0.829012	0.0345422
$577$	26.1726	1.08958	0.544790	−	0.838572i	$-0.316609\pi$
$577$	26.1726	1.08958	0.544790	+	0.838572i	$0.316609\pi$
$578$	−11.4531	−0.476386
$579$	12.1781	0.506104
$580$	−4.98016	−0.206790
$581$	3.12121	0.129489
$582$	23.3904	0.969564
$583$	15.8265	0.655468
$584$	−14.0690	−0.582178
$585$	0	0
$586$	4.79987	0.198281
$587$	−27.2063	−1.12292	−0.561462	−	0.827503i	$-0.689761\pi$
$587$	−27.2063	−1.12292	−0.561462	+	0.827503i	$0.689761\pi$
$588$	13.2729	0.547365
$589$	−4.04042	−0.166483
$590$	−7.73281	−0.318355
$591$	18.9956	0.781373
$592$	−1.69618	−0.0697125
$593$	40.3463	1.65682	0.828412	−	0.560120i	$-0.189245\pi$
$593$	40.3463	1.65682	0.828412	+	0.560120i	$0.189245\pi$
$594$	17.9396	0.736070
$595$	1.52483	0.0625118
$596$	−20.7814	−0.851241
$597$	−32.1209	−1.31462
$598$	0	0
$599$	1.71500	0.0700732	0.0350366	−	0.999386i	$-0.488845\pi$
$599$	1.71500	0.0700732	0.0350366	+	0.999386i	$0.488845\pi$
$600$	−9.04704	−0.369344
$601$	−20.6190	−0.841067	−0.420533	−	0.907277i	$-0.638157\pi$
$601$	−20.6190	−0.841067	−0.420533	+	0.907277i	$0.638157\pi$
$602$	1.15843	0.0472142
$603$	−7.85149	−0.319737
$604$	−16.5451	−0.673213
$605$	−4.19311	−0.170474
$606$	23.9606	0.973332
$607$	−6.28705	−0.255184	−0.127592	−	0.991827i	$-0.540725\pi$
$607$	−6.28705	−0.255184	−0.127592	+	0.991827i	$0.540725\pi$
$608$	1.00000	0.0405554
$609$	7.39750	0.299762
$610$	−2.47075	−0.100038
$611$	0	0
$612$	4.42207	0.178752
$613$	34.1026	1.37739	0.688695	−	0.725051i	$-0.258184\pi$
$613$	34.1026	1.37739	0.688695	+	0.725051i	$0.258184\pi$
$614$	−21.2921	−0.859277
$615$	−5.66573	−0.228464
$616$	−1.96715	−0.0792589
$617$	−32.7088	−1.31680	−0.658402	−	0.752666i	$-0.728768\pi$
$617$	−32.7088	−1.31680	−0.658402	+	0.752666i	$0.728768\pi$
$618$	−20.7513	−0.834740
$619$	31.3560	1.26030	0.630152	−	0.776472i	$-0.282992\pi$
$619$	31.3560	1.26030	0.630152	+	0.776472i	$0.282992\pi$
$620$	−2.47945	−0.0995770
$621$	−27.9493	−1.12157
$622$	−3.78811	−0.151890
$623$	5.13913	0.205895
$624$	0	0
$625$	19.4931	0.779724
$626$	−21.1236	−0.844268
$627$	−8.26332	−0.330005
$628$	7.20936	0.287685
$629$	−9.04766	−0.360754
$630$	−0.236983	−0.00944162
$631$	34.2884	1.36500	0.682500	−	0.730886i	$-0.260893\pi$
$631$	34.2884	1.36500	0.682500	+	0.730886i	$0.260893\pi$
$632$	6.66829	0.265250
$633$	−21.5990	−0.858482
$634$	1.72135	0.0683634
$635$	2.66416	0.105724
$636$	7.33360	0.290796
$637$	0	0
$638$	34.2710	1.35680
$639$	13.8326	0.547210
$640$	0.613661	0.0242571
$641$	16.0556	0.634158	0.317079	−	0.948399i	$-0.397298\pi$
$641$	16.0556	0.634158	0.317079	+	0.948399i	$0.397298\pi$
$642$	27.3109	1.07788
$643$	23.7368	0.936089	0.468045	−	0.883705i	$-0.344959\pi$
$643$	23.7368	0.936089	0.468045	+	0.883705i	$0.344959\pi$
$644$	3.06476	0.120769
$645$	2.98618	0.117581
$646$	5.33414	0.209869
$647$	−0.927777	−0.0364747	−0.0182373	−	0.999834i	$-0.505805\pi$
$647$	−0.927777	−0.0364747	−0.0182373	+	0.999834i	$0.505805\pi$
$648$	10.7998	0.424255
$649$	53.2133	2.08880
$650$	0	0
$651$	3.68296	0.144346
$652$	1.57738	0.0617751
$653$	14.4520	0.565551	0.282775	−	0.959186i	$-0.408745\pi$
$653$	14.4520	0.565551	0.282775	+	0.959186i	$0.408745\pi$
$654$	4.27177	0.167039
$655$	13.6429	0.533072
$656$	−4.71828	−0.184218
$657$	11.6634	0.455031
$658$	−5.96459	−0.232524
$659$	13.3107	0.518510	0.259255	−	0.965809i	$-0.416523\pi$
$659$	13.3107	0.518510	0.259255	+	0.965809i	$0.416523\pi$
$660$	−5.07088	−0.197384
$661$	24.5314	0.954162	0.477081	−	0.878859i	$-0.341695\pi$
$661$	24.5314	0.954162	0.477081	+	0.878859i	$0.341695\pi$
$662$	7.09167	0.275626
$663$	0	0
$664$	6.70032	0.260023
$665$	−0.285862	−0.0110852
$666$	1.40615	0.0544873
$667$	−53.3931	−2.06739
$668$	5.83293	0.225683
$669$	43.1818	1.66951
$670$	−5.81192	−0.224534
$671$	17.0024	0.656372
$672$	−0.911529	−0.0351630
$673$	14.5625	0.561342	0.280671	−	0.959804i	$-0.409443\pi$
$673$	14.5625	0.561342	0.280671	+	0.959804i	$0.409443\pi$
$674$	−8.82879	−0.340072
$675$	−19.6410	−0.755983
$676$	0	0
$677$	36.1083	1.38776	0.693878	−	0.720093i	$-0.255901\pi$
$677$	36.1083	1.38776	0.693878	+	0.720093i	$0.255901\pi$
$678$	5.56751	0.213819
$679$	−5.56829	−0.213691
$680$	3.27336	0.125528
$681$	50.0987	1.91979
$682$	17.0623	0.653349
$683$	15.7902	0.604196	0.302098	−	0.953277i	$-0.402313\pi$
$683$	15.7902	0.604196	0.302098	+	0.953277i	$0.402313\pi$
$684$	−0.829012	−0.0316981
$685$	6.43917	0.246028
$686$	−6.42053	−0.245137
$687$	−31.0508	−1.18466
$688$	2.48682	0.0948090
$689$	0	0
$690$	7.90027	0.300758
$691$	4.36561	0.166075	0.0830377	−	0.996546i	$-0.473538\pi$
$691$	4.36561	0.166075	0.0830377	+	0.996546i	$0.473538\pi$
$692$	−5.59479	−0.212682
$693$	1.63080	0.0619488
$694$	26.7555	1.01563
$695$	−8.69450	−0.329801
$696$	15.8803	0.601941
$697$	−25.1680	−0.953305
$698$	4.80791	0.181982
$699$	−5.68757	−0.215123
$700$	2.15373	0.0814032
$701$	−43.4925	−1.64269	−0.821344	−	0.570433i	$-0.806776\pi$
$701$	−43.4925	−1.64269	−0.821344	+	0.570433i	$0.806776\pi$
$702$	0	0
$703$	1.69618	0.0639726
$704$	−4.22291	−0.159157
$705$	−15.3754	−0.579070
$706$	−31.8519	−1.19876
$707$	−5.70402	−0.214522
$708$	24.6577	0.926692
$709$	42.2279	1.58590	0.792952	−	0.609284i	$-0.208543\pi$
$709$	42.2279	1.58590	0.792952	+	0.609284i	$0.208543\pi$
$710$	10.2393	0.384276
$711$	−5.52809	−0.207320
$712$	11.0322	0.413450
$713$	−26.5825	−0.995523
$714$	−4.86223	−0.181964
$715$	0	0
$716$	−1.65521	−0.0618580
$717$	−8.08178	−0.301820
$718$	2.93468	0.109521
$719$	−13.2090	−0.492612	−0.246306	−	0.969192i	$-0.579217\pi$
$719$	−13.2090	−0.492612	−0.246306	+	0.969192i	$0.579217\pi$
$720$	−0.508733	−0.0189594
$721$	4.94003	0.183976
$722$	−1.00000	−0.0372161
$723$	−46.1610	−1.71674
$724$	−10.8505	−0.403254
$725$	−37.5213	−1.39351
$726$	13.3706	0.496229
$727$	−15.7688	−0.584831	−0.292415	−	0.956291i	$-0.594459\pi$
$727$	−15.7688	−0.584831	−0.292415	+	0.956291i	$0.594459\pi$
$728$	0	0
$729$	15.9851	0.592040
$730$	8.63359	0.319543
$731$	13.2650	0.490625
$732$	7.87850	0.291198
$733$	10.4745	0.386884	0.193442	−	0.981112i	$-0.438035\pi$
$733$	10.4745	0.386884	0.193442	+	0.981112i	$0.438035\pi$
$734$	−2.48889	−0.0918666
$735$	−8.14506	−0.300435
$736$	6.57915	0.242511
$737$	39.9947	1.47322
$738$	3.91151	0.143985
$739$	−31.4004	−1.15508	−0.577542	−	0.816361i	$-0.695988\pi$
$739$	−31.4004	−1.15508	−0.577542	+	0.816361i	$0.695988\pi$
$740$	1.04088	0.0382635
$741$	0	0
$742$	−1.74583	−0.0640913
$743$	−7.82445	−0.287051	−0.143526	−	0.989647i	$-0.545844\pi$
$743$	−7.82445	−0.287051	−0.143526	+	0.989647i	$0.545844\pi$
$744$	7.90623	0.289857
$745$	12.7528	0.467225
$746$	−10.6864	−0.391255
$747$	−5.55465	−0.203234
$748$	−22.5256	−0.823617
$749$	−6.50159	−0.237563
$750$	11.5558	0.421960
$751$	49.9634	1.82319	0.911596	−	0.411088i	$-0.134851\pi$
$751$	49.9634	1.82319	0.911596	+	0.411088i	$0.134851\pi$
$752$	−12.8042	−0.466922
$753$	−49.0034	−1.78578
$754$	0	0
$755$	10.1531	0.369510
$756$	−1.97892	−0.0719725
$757$	−32.1991	−1.17030	−0.585149	−	0.810926i	$-0.698964\pi$
$757$	−32.1991	−1.17030	−0.585149	+	0.810926i	$0.698964\pi$
$758$	11.7057	0.425172
$759$	−54.3657	−1.97335
$760$	−0.613661	−0.0222598
$761$	−44.5923	−1.61647	−0.808235	−	0.588860i	$-0.799577\pi$
$761$	−44.5923	−1.61647	−0.808235	+	0.588860i	$0.799577\pi$
$762$	−8.49524	−0.307750
$763$	−1.01693	−0.0368154
$764$	−11.6513	−0.421530
$765$	−2.71365	−0.0981124
$766$	−7.81394	−0.282329
$767$	0	0
$768$	−1.95679	−0.0706094
$769$	29.5367	1.06512	0.532561	−	0.846392i	$-0.321230\pi$
$769$	29.5367	1.06512	0.532561	+	0.846392i	$0.321230\pi$
$770$	1.20717	0.0435033
$771$	−20.0487	−0.722038
$772$	−6.22352	−0.223989
$773$	−36.0063	−1.29506	−0.647528	−	0.762042i	$-0.724197\pi$
$773$	−36.0063	−1.29506	−0.647528	+	0.762042i	$0.724197\pi$
$774$	−2.06160	−0.0741027
$775$	−18.6805	−0.671025
$776$	−11.9535	−0.429105
$777$	−1.54611	−0.0554666
$778$	−3.45288	−0.123792
$779$	4.71828	0.169050
$780$	0	0
$781$	−70.4620	−2.52133
$782$	35.0941	1.25496
$783$	34.4759	1.23207
$784$	−6.78300	−0.242250
$785$	−4.42411	−0.157903
$786$	−43.5032	−1.55171
$787$	−9.65981	−0.344335	−0.172168	−	0.985068i	$-0.555077\pi$
$787$	−9.65981	−0.344335	−0.172168	+	0.985068i	$0.555077\pi$
$788$	−9.70754	−0.345817
$789$	−57.0591	−2.03136
$790$	−4.09207	−0.145589
$791$	−1.32539	−0.0471255
$792$	3.50084	0.124397
$793$	0	0
$794$	−22.5431	−0.800025
$795$	−4.50035	−0.159611
$796$	16.4151	0.581819
$797$	54.4760	1.92964	0.964819	−	0.262913i	$-0.0846833\pi$
$797$	54.4760	1.92964	0.964819	+	0.262913i	$0.0846833\pi$
$798$	0.911529	0.0322678
$799$	−68.2996	−2.41627
$800$	4.62342	0.163463
$801$	−9.14584	−0.323152
$802$	29.5703	1.04416
$803$	−59.4120	−2.09660
$804$	18.5325	0.653592
$805$	−1.88073	−0.0662869
$806$	0	0
$807$	−26.5598	−0.934948
$808$	−12.2449	−0.430773
$809$	−16.9543	−0.596082	−0.298041	−	0.954553i	$-0.596333\pi$
$809$	−16.9543	−0.596082	−0.298041	+	0.954553i	$0.596333\pi$
$810$	−6.62740	−0.232863
$811$	−30.8121	−1.08196	−0.540980	−	0.841036i	$-0.681947\pi$
$811$	−30.8121	−1.08196	−0.540980	+	0.841036i	$0.681947\pi$
$812$	−3.78044	−0.132667
$813$	7.43402	0.260722
$814$	−7.16280	−0.251056
$815$	−0.967980	−0.0339068
$816$	−10.4378	−0.365395
$817$	−2.48682	−0.0870027
$818$	−2.74046	−0.0958180
$819$	0	0
$820$	2.89543	0.101113
$821$	21.2566	0.741862	0.370931	−	0.928661i	$-0.379039\pi$
$821$	21.2566	0.741862	0.370931	+	0.928661i	$0.379039\pi$
$822$	−20.5326	−0.716158
$823$	12.3494	0.430474	0.215237	−	0.976562i	$-0.430948\pi$
$823$	12.3494	0.430474	0.215237	+	0.976562i	$0.430948\pi$
$824$	10.6048	0.369435
$825$	−38.2048	−1.33012
$826$	−5.86997	−0.204242
$827$	9.26600	0.322210	0.161105	−	0.986937i	$-0.448494\pi$
$827$	9.26600	0.322210	0.161105	+	0.986937i	$0.448494\pi$
$828$	−5.45420	−0.189546
$829$	−44.5534	−1.54740	−0.773701	−	0.633551i	$-0.781597\pi$
$829$	−44.5534	−1.54740	−0.773701	+	0.633551i	$0.781597\pi$
$830$	−4.11173	−0.142720
$831$	19.1524	0.664388
$832$	0	0
$833$	−36.1815	−1.25362
$834$	27.7242	0.960011
$835$	−3.57944	−0.123872
$836$	4.22291	0.146052
$837$	17.1643	0.593286
$838$	32.2035	1.11245
$839$	40.9342	1.41321	0.706603	−	0.707610i	$-0.250227\pi$
$839$	40.9342	1.41321	0.706603	+	0.707610i	$0.250227\pi$
$840$	0.559370	0.0193001
$841$	36.8612	1.27108
$842$	−13.3021	−0.458421
$843$	31.7614	1.09392
$844$	11.0380	0.379943
$845$	0	0
$846$	10.6149	0.364946
$847$	−3.18298	−0.109369
$848$	−3.74778	−0.128699
$849$	−43.3410	−1.48746
$850$	24.6620	0.845899
$851$	11.1594	0.382540
$852$	−32.6503	−1.11858
$853$	53.3185	1.82559	0.912795	−	0.408418i	$-0.133919\pi$
$853$	53.3185	1.82559	0.912795	+	0.408418i	$0.133919\pi$
$854$	−1.87554	−0.0641797
$855$	0.508733	0.0173983
$856$	−13.9570	−0.477041
$857$	−5.51407	−0.188357	−0.0941786	−	0.995555i	$-0.530022\pi$
$857$	−5.51407	−0.188357	−0.0941786	+	0.995555i	$0.530022\pi$
$858$	0	0
$859$	21.7316	0.741472	0.370736	−	0.928738i	$-0.379105\pi$
$859$	21.7316	0.741472	0.370736	+	0.928738i	$0.379105\pi$
$860$	−1.52606	−0.0520383
$861$	−4.30085	−0.146572
$862$	25.9693	0.884519
$863$	11.5532	0.393277	0.196638	−	0.980476i	$-0.436997\pi$
$863$	11.5532	0.393277	0.196638	+	0.980476i	$0.436997\pi$
$864$	−4.24816	−0.144525
$865$	3.43331	0.116736
$866$	−8.35232	−0.283823
$867$	−22.4113	−0.761126
$868$	−1.88215	−0.0638842
$869$	28.1596	0.955248
$870$	−9.74512	−0.330390
$871$	0	0
$872$	−2.18305	−0.0739276
$873$	9.90959	0.335389
$874$	−6.57915	−0.222543
$875$	−2.75097	−0.0929996
$876$	−27.5300	−0.930152
$877$	26.4528	0.893247	0.446623	−	0.894722i	$-0.352626\pi$
$877$	26.4528	0.893247	0.446623	+	0.894722i	$0.352626\pi$
$878$	−1.50999	−0.0509595
$879$	9.39232	0.316795
$880$	2.59143	0.0873572
$881$	−36.6167	−1.23365	−0.616823	−	0.787102i	$-0.711581\pi$
$881$	−36.6167	−1.23365	−0.616823	+	0.787102i	$0.711581\pi$
$882$	5.62319	0.189343
$883$	38.0108	1.27917	0.639583	−	0.768722i	$-0.279107\pi$
$883$	38.0108	1.27917	0.639583	+	0.768722i	$0.279107\pi$
$884$	0	0
$885$	−15.1315	−0.508638
$886$	−35.9799	−1.20877
$887$	−33.2559	−1.11662	−0.558312	−	0.829631i	$-0.688551\pi$
$887$	−33.2559	−1.11662	−0.558312	+	0.829631i	$0.688551\pi$
$888$	−3.31906	−0.111380
$889$	2.02236	0.0678279
$890$	−6.77004	−0.226932
$891$	45.6064	1.52787
$892$	−22.0677	−0.738882
$893$	12.8042	0.428477
$894$	−40.6649	−1.36004
$895$	1.01574	0.0339523
$896$	0.465830	0.0155623
$897$	0	0
$898$	−8.07052	−0.269317
$899$	32.7900	1.09361
$900$	−3.83287	−0.127762
$901$	−19.9912	−0.666003
$902$	−19.9248	−0.663425
$903$	2.26680	0.0754345
$904$	−2.84523	−0.0946310
$905$	6.65851	0.221336
$906$	−32.3753	−1.07560
$907$	6.68987	0.222134	0.111067	−	0.993813i	$-0.464573\pi$
$907$	6.68987	0.222134	0.111067	+	0.993813i	$0.464573\pi$
$908$	−25.6025	−0.849650
$909$	10.1511	0.336692
$910$	0	0
$911$	−0.562558	−0.0186384	−0.00931919	−	0.999957i	$-0.502966\pi$
$911$	−0.562558	−0.0186384	−0.00931919	+	0.999957i	$0.502966\pi$
$912$	1.95679	0.0647957
$913$	28.2948	0.936422
$914$	18.3167	0.605862
$915$	−4.83473	−0.159831
$916$	15.8683	0.524303
$917$	10.3563	0.341995
$918$	−22.6603	−0.747901
$919$	10.5952	0.349505	0.174752	−	0.984612i	$-0.444088\pi$
$919$	10.5952	0.349505	0.174752	+	0.984612i	$0.444088\pi$
$920$	−4.03737	−0.133108
$921$	−41.6640	−1.37288
$922$	−4.10208	−0.135095
$923$	0	0
$924$	−3.84930	−0.126633
$925$	7.84214	0.257848
$926$	−4.75527	−0.156268
$927$	−8.79150	−0.288751
$928$	−8.11549	−0.266404
$929$	7.72458	0.253435	0.126718	−	0.991939i	$-0.459556\pi$
$929$	7.72458	0.253435	0.126718	+	0.991939i	$0.459556\pi$
$930$	−4.85175	−0.159095
$931$	6.78300	0.222304
$932$	2.90658	0.0952084
$933$	−7.41253	−0.242675
$934$	−5.92185	−0.193769
$935$	13.8231	0.452063
$936$	0	0
$937$	−35.1091	−1.14696	−0.573482	−	0.819218i	$-0.694408\pi$
$937$	−35.1091	−1.14696	−0.573482	+	0.819218i	$0.694408\pi$
$938$	−4.41182	−0.144051
$939$	−41.3344	−1.34890
$940$	7.85746	0.256282
$941$	−30.6568	−0.999383	−0.499692	−	0.866203i	$-0.666553\pi$
$941$	−30.6568	−0.999383	−0.499692	+	0.866203i	$0.666553\pi$
$942$	14.1072	0.459637
$943$	31.0423	1.01088
$944$	−12.6011	−0.410131
$945$	1.21439	0.0395040
$946$	10.5016	0.341436
$947$	11.5703	0.375983	0.187991	−	0.982171i	$-0.439802\pi$
$947$	11.5703	0.375983	0.187991	+	0.982171i	$0.439802\pi$
$948$	13.0484	0.423793
$949$	0	0
$950$	−4.62342	−0.150004
$951$	3.36831	0.109225
$952$	2.48480	0.0805329
$953$	−3.39587	−0.110003	−0.0550016	−	0.998486i	$-0.517516\pi$
$953$	−3.39587	−0.110003	−0.0550016	+	0.998486i	$0.517516\pi$
$954$	3.10696	0.100591
$955$	7.14997	0.231368
$956$	4.13013	0.133578
$957$	67.0609	2.16777
$958$	−1.18632	−0.0383282
$959$	4.88797	0.157841
$960$	1.20080	0.0387558
$961$	−14.6750	−0.473388
$962$	0	0
$963$	11.5705	0.372855
$964$	23.5902	0.759789
$965$	3.81913	0.122942
$966$	5.99709	0.192953
$967$	−49.2494	−1.58375	−0.791877	−	0.610681i	$-0.790896\pi$
$967$	−49.2494	−1.58375	−0.791877	+	0.610681i	$0.790896\pi$
$968$	−6.83293	−0.219619
$969$	10.4378	0.335310
$970$	7.33539	0.235525
$971$	43.4284	1.39368	0.696841	−	0.717225i	$-0.254588\pi$
$971$	43.4284	1.39368	0.696841	+	0.717225i	$0.254588\pi$
$972$	8.38838	0.269057
$973$	−6.59998	−0.211586
$974$	2.65959	0.0852188
$975$	0	0
$976$	−4.02624	−0.128877
$977$	−4.07927	−0.130508	−0.0652538	−	0.997869i	$-0.520786\pi$
$977$	−4.07927	−0.130508	−0.0652538	+	0.997869i	$0.520786\pi$
$978$	3.08660	0.0986987
$979$	46.5880	1.48896
$980$	4.16247	0.132965
$981$	1.80978	0.0577818
$982$	−7.52332	−0.240079
$983$	−9.77783	−0.311864	−0.155932	−	0.987768i	$-0.549838\pi$
$983$	−9.77783	−0.311864	−0.155932	+	0.987768i	$0.549838\pi$
$984$	−9.23266	−0.294327
$985$	5.95714	0.189810
$986$	−43.2892	−1.37861
$987$	−11.6714	−0.371505
$988$	0	0
$989$	−16.3611	−0.520254
$990$	−2.14833	−0.0682784
$991$	−38.9014	−1.23574	−0.617871	−	0.786279i	$-0.712005\pi$
$991$	−38.9014	−1.23574	−0.617871	+	0.786279i	$0.712005\pi$
$992$	−4.04042	−0.128283
$993$	13.8769	0.440370
$994$	7.77267	0.246534
$995$	−10.0733	−0.319346
$996$	13.1111	0.415441
$997$	35.3972	1.12104	0.560521	−	0.828140i	$-0.310601\pi$
$997$	35.3972	1.12104	0.560521	+	0.828140i	$0.310601\pi$
$998$	−31.1291	−0.985376
$999$	−7.20563	−0.227976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.be.1.2		7
13.5	odd	4		494.2.d.c.77.9	yes	14
13.8	odd	4		494.2.d.c.77.2	✓	14
13.12	even	2		6422.2.a.bf.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.d.c.77.2	✓	14	13.8	odd	4
494.2.d.c.77.9	yes	14	13.5	odd	4
6422.2.a.be.1.2		7	1.1	even	1	trivial
6422.2.a.bf.1.2		7	13.12	even	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:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.95679 q^{3} +1.00000 q^{4} -0.613661 q^{5} +1.95679 q^{6} -0.465830 q^{7} -1.00000 q^{8} +0.829012 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.95679 q^{3} +1.00000 q^{4} -0.613661 q^{5} +1.95679 q^{6} -0.465830 q^{7} -1.00000 q^{8} +0.829012 q^{9} +0.613661 q^{10} -4.22291 q^{11} -1.95679 q^{12} +0.465830 q^{14} +1.20080 q^{15} +1.00000 q^{16} +5.33414 q^{17} -0.829012 q^{18} -1.00000 q^{19} -0.613661 q^{20} +0.911529 q^{21} +4.22291 q^{22} -6.57915 q^{23} +1.95679 q^{24} -4.62342 q^{25} +4.24816 q^{27} -0.465830 q^{28} +8.11549 q^{29} -1.20080 q^{30} +4.04042 q^{31} -1.00000 q^{32} +8.26332 q^{33} -5.33414 q^{34} +0.285862 q^{35} +0.829012 q^{36} -1.69618 q^{37} +1.00000 q^{38} +0.613661 q^{40} -4.71828 q^{41} -0.911529 q^{42} +2.48682 q^{43} -4.22291 q^{44} -0.508733 q^{45} +6.57915 q^{46} -12.8042 q^{47} -1.95679 q^{48} -6.78300 q^{49} +4.62342 q^{50} -10.4378 q^{51} -3.74778 q^{53} -4.24816 q^{54} +2.59143 q^{55} +0.465830 q^{56} +1.95679 q^{57} -8.11549 q^{58} -12.6011 q^{59} +1.20080 q^{60} -4.02624 q^{61} -4.04042 q^{62} -0.386178 q^{63} +1.00000 q^{64} -8.26332 q^{66} -9.47090 q^{67} +5.33414 q^{68} +12.8740 q^{69} -0.285862 q^{70} +16.6857 q^{71} -0.829012 q^{72} +14.0690 q^{73} +1.69618 q^{74} +9.04704 q^{75} -1.00000 q^{76} +1.96715 q^{77} -6.66829 q^{79} -0.613661 q^{80} -10.7998 q^{81} +4.71828 q^{82} -6.70032 q^{83} +0.911529 q^{84} -3.27336 q^{85} -2.48682 q^{86} -15.8803 q^{87} +4.22291 q^{88} -11.0322 q^{89} +0.508733 q^{90} -6.57915 q^{92} -7.90623 q^{93} +12.8042 q^{94} +0.613661 q^{95} +1.95679 q^{96} +11.9535 q^{97} +6.78300 q^{98} -3.50084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 2 q^{3} + 7 q^{4} - 2 q^{5} - 2 q^{6} - q^{7} - 7 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 2 * q^3 + 7 * q^4 - 2 * q^5 - 2 * q^6 - q^7 - 7 * q^8 + 15 * q^9	\( 7 q - 7 q^{2} + 2 q^{3} + 7 q^{4} - 2 q^{5} - 2 q^{6} - q^{7} - 7 q^{8} + 15 q^{9} + 2 q^{10} - 5 q^{11} + 2 q^{12} + q^{14} - 13 q^{15} + 7 q^{16} + 16 q^{17} - 15 q^{18} - 7 q^{19} - 2 q^{20} + 3 q^{21} + 5 q^{22} + 3 q^{23} - 2 q^{24} + 7 q^{25} + 5 q^{27} - q^{28} - 7 q^{29} + 13 q^{30} - 11 q^{31} - 7 q^{32} - 6 q^{33} - 16 q^{34} + q^{35} + 15 q^{36} + 3 q^{37} + 7 q^{38} + 2 q^{40} - 15 q^{41} - 3 q^{42} + 23 q^{43} - 5 q^{44} + 38 q^{45} - 3 q^{46} + q^{47} + 2 q^{48} + 14 q^{49} - 7 q^{50} - 16 q^{51} + 21 q^{53} - 5 q^{54} + 8 q^{55} + q^{56} - 2 q^{57} + 7 q^{58} - 8 q^{59} - 13 q^{60} - 6 q^{61} + 11 q^{62} + 22 q^{63} + 7 q^{64} + 6 q^{66} - 28 q^{67} + 16 q^{68} + 48 q^{69} - q^{70} - 4 q^{71} - 15 q^{72} - 12 q^{73} - 3 q^{74} + 5 q^{75} - 7 q^{76} - 26 q^{77} - 4 q^{79} - 2 q^{80} + 51 q^{81} + 15 q^{82} - 13 q^{83} + 3 q^{84} + 39 q^{85} - 23 q^{86} - 16 q^{87} + 5 q^{88} + 15 q^{89} - 38 q^{90} + 3 q^{92} - 6 q^{93} - q^{94} + 2 q^{95} - 2 q^{96} + 37 q^{97} - 14 q^{98} + 15 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 2 * q^3 + 7 * q^4 - 2 * q^5 - 2 * q^6 - q^7 - 7 * q^8 + 15 * q^9 + 2 * q^10 - 5 * q^11 + 2 * q^12 + q^14 - 13 * q^15 + 7 * q^16 + 16 * q^17 - 15 * q^18 - 7 * q^19 - 2 * q^20 + 3 * q^21 + 5 * q^22 + 3 * q^23 - 2 * q^24 + 7 * q^25 + 5 * q^27 - q^28 - 7 * q^29 + 13 * q^30 - 11 * q^31 - 7 * q^32 - 6 * q^33 - 16 * q^34 + q^35 + 15 * q^36 + 3 * q^37 + 7 * q^38 + 2 * q^40 - 15 * q^41 - 3 * q^42 + 23 * q^43 - 5 * q^44 + 38 * q^45 - 3 * q^46 + q^47 + 2 * q^48 + 14 * q^49 - 7 * q^50 - 16 * q^51 + 21 * q^53 - 5 * q^54 + 8 * q^55 + q^56 - 2 * q^57 + 7 * q^58 - 8 * q^59 - 13 * q^60 - 6 * q^61 + 11 * q^62 + 22 * q^63 + 7 * q^64 + 6 * q^66 - 28 * q^67 + 16 * q^68 + 48 * q^69 - q^70 - 4 * q^71 - 15 * q^72 - 12 * q^73 - 3 * q^74 + 5 * q^75 - 7 * q^76 - 26 * q^77 - 4 * q^79 - 2 * q^80 + 51 * q^81 + 15 * q^82 - 13 * q^83 + 3 * q^84 + 39 * q^85 - 23 * q^86 - 16 * q^87 + 5 * q^88 + 15 * q^89 - 38 * q^90 + 3 * q^92 - 6 * q^93 - q^94 + 2 * q^95 - 2 * q^96 + 37 * q^97 - 14 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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