LMFDB - Embedded newform 9282.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69202 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69202 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.69202 q^{10} +2.60388 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +1.69202 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.24698 q^{19} -1.69202 q^{20} -1.00000 q^{21} -2.60388 q^{22} -4.89977 q^{23} +1.00000 q^{24} -2.13706 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +6.29590 q^{29} -1.69202 q^{30} -8.63102 q^{31} -1.00000 q^{32} -2.60388 q^{33} +1.00000 q^{34} -1.69202 q^{35} +1.00000 q^{36} -6.85086 q^{37} -1.24698 q^{38} +1.00000 q^{39} +1.69202 q^{40} -7.00969 q^{41} +1.00000 q^{42} +2.26875 q^{43} +2.60388 q^{44} -1.69202 q^{45} +4.89977 q^{46} +12.0761 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.13706 q^{50} +1.00000 q^{51} -1.00000 q^{52} +7.25667 q^{53} +1.00000 q^{54} -4.40581 q^{55} -1.00000 q^{56} -1.24698 q^{57} -6.29590 q^{58} +1.45473 q^{59} +1.69202 q^{60} +7.62565 q^{61} +8.63102 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.69202 q^{65} +2.60388 q^{66} +7.83877 q^{67} -1.00000 q^{68} +4.89977 q^{69} +1.69202 q^{70} -8.39373 q^{71} -1.00000 q^{72} +2.02715 q^{73} +6.85086 q^{74} +2.13706 q^{75} +1.24698 q^{76} +2.60388 q^{77} -1.00000 q^{78} -7.40581 q^{79} -1.69202 q^{80} +1.00000 q^{81} +7.00969 q^{82} +3.06100 q^{83} -1.00000 q^{84} +1.69202 q^{85} -2.26875 q^{86} -6.29590 q^{87} -2.60388 q^{88} +5.67994 q^{89} +1.69202 q^{90} -1.00000 q^{91} -4.89977 q^{92} +8.63102 q^{93} -12.0761 q^{94} -2.10992 q^{95} +1.00000 q^{96} -1.91723 q^{97} -1.00000 q^{98} +2.60388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{16} - 3 q^{17} - 3 q^{18} - q^{19} - 3 q^{21} + q^{22} + 8 q^{23} + 3 q^{24} - q^{25} + 3 q^{26} - 3 q^{27} + 3 q^{28} + 5 q^{29} - 11 q^{31} - 3 q^{32} + q^{33} + 3 q^{34} + 3 q^{36} - 7 q^{37} + q^{38} + 3 q^{39} + q^{41} + 3 q^{42} - q^{43} - q^{44} - 8 q^{46} + 21 q^{47} - 3 q^{48} + 3 q^{49} + q^{50} + 3 q^{51} - 3 q^{52} - 5 q^{53} + 3 q^{54} - 3 q^{56} + q^{57} - 5 q^{58} - 18 q^{59} + 11 q^{61} + 11 q^{62} + 3 q^{63} + 3 q^{64} - q^{66} - 9 q^{67} - 3 q^{68} - 8 q^{69} + 7 q^{71} - 3 q^{72} + 7 q^{74} + q^{75} - q^{76} - q^{77} - 3 q^{78} - 9 q^{79} + 3 q^{81} - q^{82} + 19 q^{83} - 3 q^{84} + q^{86} - 5 q^{87} + q^{88} - 7 q^{89} - 3 q^{91} + 8 q^{92} + 11 q^{93} - 21 q^{94} - 7 q^{95} + 3 q^{96} + q^{97} - 3 q^{98} - q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^16 - 3 * q^17 - 3 * q^18 - q^19 - 3 * q^21 + q^22 + 8 * q^23 + 3 * q^24 - q^25 + 3 * q^26 - 3 * q^27 + 3 * q^28 + 5 * q^29 - 11 * q^31 - 3 * q^32 + q^33 + 3 * q^34 + 3 * q^36 - 7 * q^37 + q^38 + 3 * q^39 + q^41 + 3 * q^42 - q^43 - q^44 - 8 * q^46 + 21 * q^47 - 3 * q^48 + 3 * q^49 + q^50 + 3 * q^51 - 3 * q^52 - 5 * q^53 + 3 * q^54 - 3 * q^56 + q^57 - 5 * q^58 - 18 * q^59 + 11 * q^61 + 11 * q^62 + 3 * q^63 + 3 * q^64 - q^66 - 9 * q^67 - 3 * q^68 - 8 * q^69 + 7 * q^71 - 3 * q^72 + 7 * q^74 + q^75 - q^76 - q^77 - 3 * q^78 - 9 * q^79 + 3 * q^81 - q^82 + 19 * q^83 - 3 * q^84 + q^86 - 5 * q^87 + q^88 - 7 * q^89 - 3 * q^91 + 8 * q^92 + 11 * q^93 - 21 * q^94 - 7 * q^95 + 3 * q^96 + q^97 - 3 * q^98 - 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.69202	−0.756695	−0.378348	−	0.925664i	$-0.623508\pi$
$5$	−1.69202	−0.756695	−0.378348	+	0.925664i	$0.623508\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.69202	0.535064
$11$	2.60388	0.785098	0.392549	−	0.919731i	$-0.371593\pi$
$11$	2.60388	0.785098	0.392549	+	0.919731i	$0.371593\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	1.69202	0.436878
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	1.24698	0.286077	0.143038	−	0.989717i	$-0.454313\pi$
$19$	1.24698	0.286077	0.143038	+	0.989717i	$0.454313\pi$
$20$	−1.69202	−0.378348
$21$	−1.00000	−0.218218
$22$	−2.60388	−0.555148
$23$	−4.89977	−1.02167	−0.510837	−	0.859678i	$-0.670664\pi$
$23$	−4.89977	−1.02167	−0.510837	+	0.859678i	$0.670664\pi$
$24$	1.00000	0.204124
$25$	−2.13706	−0.427413
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	6.29590	1.16912	0.584559	−	0.811351i	$-0.301267\pi$
$29$	6.29590	1.16912	0.584559	+	0.811351i	$0.301267\pi$
$30$	−1.69202	−0.308919
$31$	−8.63102	−1.55018	−0.775089	−	0.631852i	$-0.782295\pi$
$31$	−8.63102	−1.55018	−0.775089	+	0.631852i	$0.782295\pi$
$32$	−1.00000	−0.176777
$33$	−2.60388	−0.453277
$34$	1.00000	0.171499
$35$	−1.69202	−0.286004
$36$	1.00000	0.166667
$37$	−6.85086	−1.12627	−0.563137	−	0.826364i	$-0.690406\pi$
$37$	−6.85086	−1.12627	−0.563137	+	0.826364i	$0.690406\pi$
$38$	−1.24698	−0.202287
$39$	1.00000	0.160128
$40$	1.69202	0.267532
$41$	−7.00969	−1.09473	−0.547365	−	0.836894i	$-0.684369\pi$
$41$	−7.00969	−1.09473	−0.547365	+	0.836894i	$0.684369\pi$
$42$	1.00000	0.154303
$43$	2.26875	0.345981	0.172991	−	0.984923i	$-0.444657\pi$
$43$	2.26875	0.345981	0.172991	+	0.984923i	$0.444657\pi$
$44$	2.60388	0.392549
$45$	−1.69202	−0.252232
$46$	4.89977	0.722432
$47$	12.0761	1.76148	0.880738	−	0.473605i	$-0.157047\pi$
$47$	12.0761	1.76148	0.880738	+	0.473605i	$0.157047\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	2.13706	0.302226
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	7.25667	0.996780	0.498390	−	0.866953i	$-0.333925\pi$
$53$	7.25667	0.996780	0.498390	+	0.866953i	$0.333925\pi$
$54$	1.00000	0.136083
$55$	−4.40581	−0.594080
$56$	−1.00000	−0.133631
$57$	−1.24698	−0.165166
$58$	−6.29590	−0.826692
$59$	1.45473	0.189390	0.0946949	−	0.995506i	$-0.469812\pi$
$59$	1.45473	0.189390	0.0946949	+	0.995506i	$0.469812\pi$
$60$	1.69202	0.218439
$61$	7.62565	0.976364	0.488182	−	0.872742i	$-0.337660\pi$
$61$	7.62565	0.976364	0.488182	+	0.872742i	$0.337660\pi$
$62$	8.63102	1.09614
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	1.69202	0.209869
$66$	2.60388	0.320515
$67$	7.83877	0.957659	0.478829	−	0.877908i	$-0.341061\pi$
$67$	7.83877	0.957659	0.478829	+	0.877908i	$0.341061\pi$
$68$	−1.00000	−0.121268
$69$	4.89977	0.589863
$70$	1.69202	0.202235
$71$	−8.39373	−0.996153	−0.498076	−	0.867133i	$-0.665960\pi$
$71$	−8.39373	−0.996153	−0.498076	+	0.867133i	$0.665960\pi$
$72$	−1.00000	−0.117851
$73$	2.02715	0.237260	0.118630	−	0.992939i	$-0.462150\pi$
$73$	2.02715	0.237260	0.118630	+	0.992939i	$0.462150\pi$
$74$	6.85086	0.796396
$75$	2.13706	0.246767
$76$	1.24698	0.143038
$77$	2.60388	0.296739
$78$	−1.00000	−0.113228
$79$	−7.40581	−0.833219	−0.416610	−	0.909086i	$-0.636782\pi$
$79$	−7.40581	−0.833219	−0.416610	+	0.909086i	$0.636782\pi$
$80$	−1.69202	−0.189174
$81$	1.00000	0.111111
$82$	7.00969	0.774091
$83$	3.06100	0.335988	0.167994	−	0.985788i	$-0.446271\pi$
$83$	3.06100	0.335988	0.167994	+	0.985788i	$0.446271\pi$
$84$	−1.00000	−0.109109
$85$	1.69202	0.183525
$86$	−2.26875	−0.244646
$87$	−6.29590	−0.674991
$88$	−2.60388	−0.277574
$89$	5.67994	0.602072	0.301036	−	0.953613i	$-0.402667\pi$
$89$	5.67994	0.602072	0.301036	+	0.953613i	$0.402667\pi$
$90$	1.69202	0.178355
$91$	−1.00000	−0.104828
$92$	−4.89977	−0.510837
$93$	8.63102	0.894995
$94$	−12.0761	−1.24555
$95$	−2.10992	−0.216473
$96$	1.00000	0.102062
$97$	−1.91723	−0.194665	−0.0973326	−	0.995252i	$-0.531031\pi$
$97$	−1.91723	−0.194665	−0.0973326	+	0.995252i	$0.531031\pi$
$98$	−1.00000	−0.101015
$99$	2.60388	0.261699
$100$	−2.13706	−0.213706
$101$	15.2687	1.51930	0.759649	−	0.650334i	$-0.225371\pi$
$101$	15.2687	1.51930	0.759649	+	0.650334i	$0.225371\pi$
$102$	−1.00000	−0.0990148
$103$	7.20775	0.710201	0.355100	−	0.934828i	$-0.384447\pi$
$103$	7.20775	0.710201	0.355100	+	0.934828i	$0.384447\pi$
$104$	1.00000	0.0980581
$105$	1.69202	0.165124
$106$	−7.25667	−0.704830
$107$	1.86294	0.180097	0.0900484	−	0.995937i	$-0.471298\pi$
$107$	1.86294	0.180097	0.0900484	+	0.995937i	$0.471298\pi$
$108$	−1.00000	−0.0962250
$109$	−14.7560	−1.41337	−0.706684	−	0.707529i	$-0.749810\pi$
$109$	−14.7560	−1.41337	−0.706684	+	0.707529i	$0.749810\pi$
$110$	4.40581	0.420078
$111$	6.85086	0.650254
$112$	1.00000	0.0944911
$113$	−7.54288	−0.709574	−0.354787	−	0.934947i	$-0.615447\pi$
$113$	−7.54288	−0.709574	−0.354787	+	0.934947i	$0.615447\pi$
$114$	1.24698	0.116790
$115$	8.29052	0.773095
$116$	6.29590	0.584559
$117$	−1.00000	−0.0924500
$118$	−1.45473	−0.133919
$119$	−1.00000	−0.0916698
$120$	−1.69202	−0.154460
$121$	−4.21983	−0.383621
$122$	−7.62565	−0.690394
$123$	7.00969	0.632042
$124$	−8.63102	−0.775089
$125$	12.0761	1.08012
$126$	−1.00000	−0.0890871
$127$	−12.1032	−1.07399	−0.536993	−	0.843587i	$-0.680440\pi$
$127$	−12.1032	−1.07399	−0.536993	+	0.843587i	$0.680440\pi$
$128$	−1.00000	−0.0883883
$129$	−2.26875	−0.199752
$130$	−1.69202	−0.148400
$131$	7.66487	0.669683	0.334842	−	0.942274i	$-0.391317\pi$
$131$	7.66487	0.669683	0.334842	+	0.942274i	$0.391317\pi$
$132$	−2.60388	−0.226638
$133$	1.24698	0.108127
$134$	−7.83877	−0.677167
$135$	1.69202	0.145626
$136$	1.00000	0.0857493
$137$	2.45712	0.209926	0.104963	−	0.994476i	$-0.466528\pi$
$137$	2.45712	0.209926	0.104963	+	0.994476i	$0.466528\pi$
$138$	−4.89977	−0.417096
$139$	−6.08575	−0.516187	−0.258093	−	0.966120i	$-0.583094\pi$
$139$	−6.08575	−0.516187	−0.258093	+	0.966120i	$0.583094\pi$
$140$	−1.69202	−0.143002
$141$	−12.0761	−1.01699
$142$	8.39373	0.704386
$143$	−2.60388	−0.217747
$144$	1.00000	0.0833333
$145$	−10.6528	−0.884666
$146$	−2.02715	−0.167768
$147$	−1.00000	−0.0824786
$148$	−6.85086	−0.563137
$149$	−12.0925	−0.990653	−0.495326	−	0.868707i	$-0.664952\pi$
$149$	−12.0925	−0.990653	−0.495326	+	0.868707i	$0.664952\pi$
$150$	−2.13706	−0.174490
$151$	−10.8455	−0.882593	−0.441296	−	0.897361i	$-0.645481\pi$
$151$	−10.8455	−0.882593	−0.441296	+	0.897361i	$0.645481\pi$
$152$	−1.24698	−0.101143
$153$	−1.00000	−0.0808452
$154$	−2.60388	−0.209826
$155$	14.6039	1.17301
$156$	1.00000	0.0800641
$157$	6.91185	0.551626	0.275813	−	0.961211i	$-0.411053\pi$
$157$	6.91185	0.551626	0.275813	+	0.961211i	$0.411053\pi$
$158$	7.40581	0.589175
$159$	−7.25667	−0.575491
$160$	1.69202	0.133766
$161$	−4.89977	−0.386156
$162$	−1.00000	−0.0785674
$163$	0.818331	0.0640966	0.0320483	−	0.999486i	$-0.489797\pi$
$163$	0.818331	0.0640966	0.0320483	+	0.999486i	$0.489797\pi$
$164$	−7.00969	−0.547365
$165$	4.40581	0.342992
$166$	−3.06100	−0.237580
$167$	−1.17629	−0.0910242	−0.0455121	−	0.998964i	$-0.514492\pi$
$167$	−1.17629	−0.0910242	−0.0455121	+	0.998964i	$0.514492\pi$
$168$	1.00000	0.0771517
$169$	1.00000	0.0769231
$170$	−1.69202	−0.129772
$171$	1.24698	0.0953589
$172$	2.26875	0.172991
$173$	14.5864	1.10898	0.554492	−	0.832189i	$-0.312912\pi$
$173$	14.5864	1.10898	0.554492	+	0.832189i	$0.312912\pi$
$174$	6.29590	0.477291
$175$	−2.13706	−0.161547
$176$	2.60388	0.196274
$177$	−1.45473	−0.109344
$178$	−5.67994	−0.425729
$179$	−24.1782	−1.80716	−0.903582	−	0.428415i	$-0.859072\pi$
$179$	−24.1782	−1.80716	−0.903582	+	0.428415i	$0.859072\pi$
$180$	−1.69202	−0.126116
$181$	−13.9608	−1.03770	−0.518848	−	0.854867i	$-0.673639\pi$
$181$	−13.9608	−1.03770	−0.518848	+	0.854867i	$0.673639\pi$
$182$	1.00000	0.0741249
$183$	−7.62565	−0.563704
$184$	4.89977	0.361216
$185$	11.5918	0.852246
$186$	−8.63102	−0.632857
$187$	−2.60388	−0.190414
$188$	12.0761	0.880738
$189$	−1.00000	−0.0727393
$190$	2.10992	0.153069
$191$	−1.70171	−0.123131	−0.0615657	−	0.998103i	$-0.519609\pi$
$191$	−1.70171	−0.123131	−0.0615657	+	0.998103i	$0.519609\pi$
$192$	−1.00000	−0.0721688
$193$	−10.7235	−0.771893	−0.385947	−	0.922521i	$-0.626125\pi$
$193$	−10.7235	−0.771893	−0.385947	+	0.922521i	$0.626125\pi$
$194$	1.91723	0.137649
$195$	−1.69202	−0.121168
$196$	1.00000	0.0714286
$197$	−8.52111	−0.607104	−0.303552	−	0.952815i	$-0.598173\pi$
$197$	−8.52111	−0.607104	−0.303552	+	0.952815i	$0.598173\pi$
$198$	−2.60388	−0.185049
$199$	10.2131	0.723989	0.361995	−	0.932180i	$-0.382096\pi$
$199$	10.2131	0.723989	0.361995	+	0.932180i	$0.382096\pi$
$200$	2.13706	0.151113
$201$	−7.83877	−0.552904
$202$	−15.2687	−1.07431
$203$	6.29590	0.441885
$204$	1.00000	0.0700140
$205$	11.8605	0.828376
$206$	−7.20775	−0.502188
$207$	−4.89977	−0.340558
$208$	−1.00000	−0.0693375
$209$	3.24698	0.224598
$210$	−1.69202	−0.116761
$211$	−17.0858	−1.17623	−0.588116	−	0.808777i	$-0.700130\pi$
$211$	−17.0858	−1.17623	−0.588116	+	0.808777i	$0.700130\pi$
$212$	7.25667	0.498390
$213$	8.39373	0.575129
$214$	−1.86294	−0.127348
$215$	−3.83877	−0.261802
$216$	1.00000	0.0680414
$217$	−8.63102	−0.585912
$218$	14.7560	0.999403
$219$	−2.02715	−0.136982
$220$	−4.40581	−0.297040
$221$	1.00000	0.0672673
$222$	−6.85086	−0.459799
$223$	7.94331	0.531924	0.265962	−	0.963984i	$-0.414310\pi$
$223$	7.94331	0.531924	0.265962	+	0.963984i	$0.414310\pi$
$224$	−1.00000	−0.0668153
$225$	−2.13706	−0.142471
$226$	7.54288	0.501745
$227$	20.7114	1.37466	0.687332	−	0.726343i	$-0.258782\pi$
$227$	20.7114	1.37466	0.687332	+	0.726343i	$0.258782\pi$
$228$	−1.24698	−0.0825832
$229$	21.3817	1.41294	0.706470	−	0.707743i	$-0.250287\pi$
$229$	21.3817	1.41294	0.706470	+	0.707743i	$0.250287\pi$
$230$	−8.29052	−0.546661
$231$	−2.60388	−0.171322
$232$	−6.29590	−0.413346
$233$	4.12067	0.269954	0.134977	−	0.990849i	$-0.456904\pi$
$233$	4.12067	0.269954	0.134977	+	0.990849i	$0.456904\pi$
$234$	1.00000	0.0653720
$235$	−20.4330	−1.33290
$236$	1.45473	0.0946949
$237$	7.40581	0.481059
$238$	1.00000	0.0648204
$239$	30.5961	1.97910	0.989549	−	0.144199i	$-0.0460604\pi$
$239$	30.5961	1.97910	0.989549	+	0.144199i	$0.0460604\pi$
$240$	1.69202	0.109220
$241$	2.78687	0.179518	0.0897591	−	0.995964i	$-0.471390\pi$
$241$	2.78687	0.179518	0.0897591	+	0.995964i	$0.471390\pi$
$242$	4.21983	0.271261
$243$	−1.00000	−0.0641500
$244$	7.62565	0.488182
$245$	−1.69202	−0.108099
$246$	−7.00969	−0.446921
$247$	−1.24698	−0.0793434
$248$	8.63102	0.548070
$249$	−3.06100	−0.193983
$250$	−12.0761	−0.763757
$251$	−16.4741	−1.03984	−0.519918	−	0.854216i	$-0.674038\pi$
$251$	−16.4741	−1.03984	−0.519918	+	0.854216i	$0.674038\pi$
$252$	1.00000	0.0629941
$253$	−12.7584	−0.802114
$254$	12.1032	0.759423
$255$	−1.69202	−0.105958
$256$	1.00000	0.0625000
$257$	7.68664	0.479480	0.239740	−	0.970837i	$-0.422938\pi$
$257$	7.68664	0.479480	0.239740	+	0.970837i	$0.422938\pi$
$258$	2.26875	0.141246
$259$	−6.85086	−0.425691
$260$	1.69202	0.104935
$261$	6.29590	0.389706
$262$	−7.66487	−0.473538
$263$	11.0248	0.679815	0.339908	−	0.940459i	$-0.389604\pi$
$263$	11.0248	0.679815	0.339908	+	0.940459i	$0.389604\pi$
$264$	2.60388	0.160257
$265$	−12.2784	−0.754258
$266$	−1.24698	−0.0764572
$267$	−5.67994	−0.347607
$268$	7.83877	0.478829
$269$	2.63640	0.160744	0.0803721	−	0.996765i	$-0.474389\pi$
$269$	2.63640	0.160744	0.0803721	+	0.996765i	$0.474389\pi$
$270$	−1.69202	−0.102973
$271$	2.95108	0.179266	0.0896328	−	0.995975i	$-0.471431\pi$
$271$	2.95108	0.179266	0.0896328	+	0.995975i	$0.471431\pi$
$272$	−1.00000	−0.0606339
$273$	1.00000	0.0605228
$274$	−2.45712	−0.148440
$275$	−5.56465	−0.335561
$276$	4.89977	0.294932
$277$	25.9095	1.55675	0.778374	−	0.627800i	$-0.216045\pi$
$277$	25.9095	1.55675	0.778374	+	0.627800i	$0.216045\pi$
$278$	6.08575	0.364999
$279$	−8.63102	−0.516726
$280$	1.69202	0.101118
$281$	5.20237	0.310348	0.155174	−	0.987887i	$-0.450406\pi$
$281$	5.20237	0.310348	0.155174	+	0.987887i	$0.450406\pi$
$282$	12.0761	0.719119
$283$	1.89546	0.112673	0.0563367	−	0.998412i	$-0.482058\pi$
$283$	1.89546	0.112673	0.0563367	+	0.998412i	$0.482058\pi$
$284$	−8.39373	−0.498076
$285$	2.10992	0.124981
$286$	2.60388	0.153970
$287$	−7.00969	−0.413769
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	10.6528	0.625554
$291$	1.91723	0.112390
$292$	2.02715	0.118630
$293$	3.08038	0.179958	0.0899788	−	0.995944i	$-0.471320\pi$
$293$	3.08038	0.179958	0.0899788	+	0.995944i	$0.471320\pi$
$294$	1.00000	0.0583212
$295$	−2.46144	−0.143310
$296$	6.85086	0.398198
$297$	−2.60388	−0.151092
$298$	12.0925	0.700497
$299$	4.89977	0.283361
$300$	2.13706	0.123383
$301$	2.26875	0.130769
$302$	10.8455	0.624087
$303$	−15.2687	−0.877167
$304$	1.24698	0.0715192
$305$	−12.9028	−0.738810
$306$	1.00000	0.0571662
$307$	−4.25368	−0.242771	−0.121385	−	0.992605i	$-0.538734\pi$
$307$	−4.25368	−0.242771	−0.121385	+	0.992605i	$0.538734\pi$
$308$	2.60388	0.148370
$309$	−7.20775	−0.410035
$310$	−14.6039	−0.829444
$311$	−3.24459	−0.183984	−0.0919918	−	0.995760i	$-0.529323\pi$
$311$	−3.24459	−0.183984	−0.0919918	+	0.995760i	$0.529323\pi$
$312$	−1.00000	−0.0566139
$313$	−7.71678	−0.436178	−0.218089	−	0.975929i	$-0.569982\pi$
$313$	−7.71678	−0.436178	−0.218089	+	0.975929i	$0.569982\pi$
$314$	−6.91185	−0.390058
$315$	−1.69202	−0.0953346
$316$	−7.40581	−0.416610
$317$	2.09246	0.117524	0.0587621	−	0.998272i	$-0.481285\pi$
$317$	2.09246	0.117524	0.0587621	+	0.998272i	$0.481285\pi$
$318$	7.25667	0.406934
$319$	16.3937	0.917873
$320$	−1.69202	−0.0945869
$321$	−1.86294	−0.103979
$322$	4.89977	0.273054
$323$	−1.24698	−0.0693838
$324$	1.00000	0.0555556
$325$	2.13706	0.118543
$326$	−0.818331	−0.0453232
$327$	14.7560	0.816009
$328$	7.00969	0.387045
$329$	12.0761	0.665775
$330$	−4.40581	−0.242532
$331$	−16.0925	−0.884521	−0.442261	−	0.896887i	$-0.645823\pi$
$331$	−16.0925	−0.884521	−0.442261	+	0.896887i	$0.645823\pi$
$332$	3.06100	0.167994
$333$	−6.85086	−0.375425
$334$	1.17629	0.0643638
$335$	−13.2634	−0.724655
$336$	−1.00000	−0.0545545
$337$	18.2204	0.992530	0.496265	−	0.868171i	$-0.334704\pi$
$337$	18.2204	0.992530	0.496265	+	0.868171i	$0.334704\pi$
$338$	−1.00000	−0.0543928
$339$	7.54288	0.409673
$340$	1.69202	0.0917627
$341$	−22.4741	−1.21704
$342$	−1.24698	−0.0674289
$343$	1.00000	0.0539949
$344$	−2.26875	−0.122323
$345$	−8.29052	−0.446347
$346$	−14.5864	−0.784171
$347$	−0.883379	−0.0474223	−0.0237111	−	0.999719i	$-0.507548\pi$
$347$	−0.883379	−0.0474223	−0.0237111	+	0.999719i	$0.507548\pi$
$348$	−6.29590	−0.337496
$349$	−14.3123	−0.766119	−0.383060	−	0.923724i	$-0.625130\pi$
$349$	−14.3123	−0.766119	−0.383060	+	0.923724i	$0.625130\pi$
$350$	2.13706	0.114231
$351$	1.00000	0.0533761
$352$	−2.60388	−0.138787
$353$	28.3967	1.51140	0.755702	−	0.654915i	$-0.227296\pi$
$353$	28.3967	1.51140	0.755702	+	0.654915i	$0.227296\pi$
$354$	1.45473	0.0773181
$355$	14.2024	0.753784
$356$	5.67994	0.301036
$357$	1.00000	0.0529256
$358$	24.1782	1.27786
$359$	−11.8931	−0.627692	−0.313846	−	0.949474i	$-0.601618\pi$
$359$	−11.8931	−0.627692	−0.313846	+	0.949474i	$0.601618\pi$
$360$	1.69202	0.0891774
$361$	−17.4450	−0.918160
$362$	13.9608	0.733762
$363$	4.21983	0.221484
$364$	−1.00000	−0.0524142
$365$	−3.42998	−0.179533
$366$	7.62565	0.398599
$367$	−16.4741	−0.859941	−0.429971	−	0.902843i	$-0.641476\pi$
$367$	−16.4741	−0.859941	−0.429971	+	0.902843i	$0.641476\pi$
$368$	−4.89977	−0.255418
$369$	−7.00969	−0.364910
$370$	−11.5918	−0.602629
$371$	7.25667	0.376747
$372$	8.63102	0.447498
$373$	22.4926	1.16462	0.582312	−	0.812965i	$-0.302148\pi$
$373$	22.4926	1.16462	0.582312	+	0.812965i	$0.302148\pi$
$374$	2.60388	0.134643
$375$	−12.0761	−0.623605
$376$	−12.0761	−0.622775
$377$	−6.29590	−0.324255
$378$	1.00000	0.0514344
$379$	27.0954	1.39180	0.695900	−	0.718139i	$-0.255006\pi$
$379$	27.0954	1.39180	0.695900	+	0.718139i	$0.255006\pi$
$380$	−2.10992	−0.108236
$381$	12.1032	0.620066
$382$	1.70171	0.0870671
$383$	−15.0224	−0.767607	−0.383803	−	0.923415i	$-0.625386\pi$
$383$	−15.0224	−0.767607	−0.383803	+	0.923415i	$0.625386\pi$
$384$	1.00000	0.0510310
$385$	−4.40581	−0.224541
$386$	10.7235	0.545811
$387$	2.26875	0.115327
$388$	−1.91723	−0.0973326
$389$	13.7332	0.696299	0.348150	−	0.937439i	$-0.386810\pi$
$389$	13.7332	0.696299	0.348150	+	0.937439i	$0.386810\pi$
$390$	1.69202	0.0856788
$391$	4.89977	0.247792
$392$	−1.00000	−0.0505076
$393$	−7.66487	−0.386642
$394$	8.52111	0.429287
$395$	12.5308	0.630493
$396$	2.60388	0.130850
$397$	3.57002	0.179174	0.0895872	−	0.995979i	$-0.471445\pi$
$397$	3.57002	0.179174	0.0895872	+	0.995979i	$0.471445\pi$
$398$	−10.2131	−0.511938
$399$	−1.24698	−0.0624271
$400$	−2.13706	−0.106853
$401$	−5.89546	−0.294405	−0.147203	−	0.989106i	$-0.547027\pi$
$401$	−5.89546	−0.294405	−0.147203	+	0.989106i	$0.547027\pi$
$402$	7.83877	0.390962
$403$	8.63102	0.429942
$404$	15.2687	0.759649
$405$	−1.69202	−0.0840772
$406$	−6.29590	−0.312460
$407$	−17.8388	−0.884235
$408$	−1.00000	−0.0495074
$409$	9.67563	0.478429	0.239215	−	0.970967i	$-0.423110\pi$
$409$	9.67563	0.478429	0.239215	+	0.970967i	$0.423110\pi$
$410$	−11.8605	−0.585751
$411$	−2.45712	−0.121201
$412$	7.20775	0.355100
$413$	1.45473	0.0715826
$414$	4.89977	0.240811
$415$	−5.17928	−0.254241
$416$	1.00000	0.0490290
$417$	6.08575	0.298021
$418$	−3.24698	−0.158815
$419$	10.0556	0.491249	0.245625	−	0.969365i	$-0.421007\pi$
$419$	10.0556	0.491249	0.245625	+	0.969365i	$0.421007\pi$
$420$	1.69202	0.0825622
$421$	−3.41358	−0.166368	−0.0831839	−	0.996534i	$-0.526509\pi$
$421$	−3.41358	−0.166368	−0.0831839	+	0.996534i	$0.526509\pi$
$422$	17.0858	0.831721
$423$	12.0761	0.587158
$424$	−7.25667	−0.352415
$425$	2.13706	0.103663
$426$	−8.39373	−0.406678
$427$	7.62565	0.369031
$428$	1.86294	0.0900484
$429$	2.60388	0.125716
$430$	3.83877	0.185122
$431$	24.4228	1.17640	0.588202	−	0.808714i	$-0.299836\pi$
$431$	24.4228	1.17640	0.588202	+	0.808714i	$0.299836\pi$
$432$	−1.00000	−0.0481125
$433$	11.8436	0.569165	0.284583	−	0.958652i	$-0.408145\pi$
$433$	11.8436	0.569165	0.284583	+	0.958652i	$0.408145\pi$
$434$	8.63102	0.414302
$435$	10.6528	0.510762
$436$	−14.7560	−0.706684
$437$	−6.10992	−0.292277
$438$	2.02715	0.0968608
$439$	4.93362	0.235469	0.117735	−	0.993045i	$-0.462437\pi$
$439$	4.93362	0.235469	0.117735	+	0.993045i	$0.462437\pi$
$440$	4.40581	0.210039
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	27.1444	1.28967	0.644834	−	0.764323i	$-0.276927\pi$
$443$	27.1444	1.28967	0.644834	+	0.764323i	$0.276927\pi$
$444$	6.85086	0.325127
$445$	−9.61058	−0.455585
$446$	−7.94331	−0.376127
$447$	12.0925	0.571954
$448$	1.00000	0.0472456
$449$	−5.46548	−0.257932	−0.128966	−	0.991649i	$-0.541166\pi$
$449$	−5.46548	−0.257932	−0.128966	+	0.991649i	$0.541166\pi$
$450$	2.13706	0.100742
$451$	−18.2524	−0.859470
$452$	−7.54288	−0.354787
$453$	10.8455	0.509565
$454$	−20.7114	−0.972034
$455$	1.69202	0.0793232
$456$	1.24698	0.0583952
$457$	18.1696	0.849937	0.424969	−	0.905208i	$-0.360285\pi$
$457$	18.1696	0.849937	0.424969	+	0.905208i	$0.360285\pi$
$458$	−21.3817	−0.999099
$459$	1.00000	0.0466760
$460$	8.29052	0.386547
$461$	−28.7627	−1.33961	−0.669806	−	0.742536i	$-0.733623\pi$
$461$	−28.7627	−1.33961	−0.669806	+	0.742536i	$0.733623\pi$
$462$	2.60388	0.121143
$463$	15.0489	0.699383	0.349691	−	0.936865i	$-0.386286\pi$
$463$	15.0489	0.699383	0.349691	+	0.936865i	$0.386286\pi$
$464$	6.29590	0.292280
$465$	−14.6039	−0.677239
$466$	−4.12067	−0.190886
$467$	42.3110	1.95792	0.978959	−	0.204057i	$-0.0654129\pi$
$467$	42.3110	1.95792	0.978959	+	0.204057i	$0.0654129\pi$
$468$	−1.00000	−0.0462250
$469$	7.83877	0.361961
$470$	20.4330	0.942502
$471$	−6.91185	−0.318481
$472$	−1.45473	−0.0669594
$473$	5.90754	0.271629
$474$	−7.40581	−0.340160
$475$	−2.66487	−0.122273
$476$	−1.00000	−0.0458349
$477$	7.25667	0.332260
$478$	−30.5961	−1.39943
$479$	35.4432	1.61944	0.809721	−	0.586814i	$-0.199618\pi$
$479$	35.4432	1.61944	0.809721	+	0.586814i	$0.199618\pi$
$480$	−1.69202	−0.0772299
$481$	6.85086	0.312372
$482$	−2.78687	−0.126939
$483$	4.89977	0.222947
$484$	−4.21983	−0.191811
$485$	3.24400	0.147302
$486$	1.00000	0.0453609
$487$	16.9022	0.765910	0.382955	−	0.923767i	$-0.374906\pi$
$487$	16.9022	0.765910	0.382955	+	0.923767i	$0.374906\pi$
$488$	−7.62565	−0.345197
$489$	−0.818331	−0.0370062
$490$	1.69202	0.0764377
$491$	−37.0049	−1.67001	−0.835004	−	0.550244i	$-0.814535\pi$
$491$	−37.0049	−1.67001	−0.835004	+	0.550244i	$0.814535\pi$
$492$	7.00969	0.316021
$493$	−6.29590	−0.283553
$494$	1.24698	0.0561043
$495$	−4.40581	−0.198027
$496$	−8.63102	−0.387544
$497$	−8.39373	−0.376510
$498$	3.06100	0.137167
$499$	−24.0707	−1.07755	−0.538776	−	0.842449i	$-0.681113\pi$
$499$	−24.0707	−1.07755	−0.538776	+	0.842449i	$0.681113\pi$
$500$	12.0761	0.540058
$501$	1.17629	0.0525529
$502$	16.4741	0.735275
$503$	27.1535	1.21071	0.605356	−	0.795955i	$-0.293031\pi$
$503$	27.1535	1.21071	0.605356	+	0.795955i	$0.293031\pi$
$504$	−1.00000	−0.0445435
$505$	−25.8351	−1.14964
$506$	12.7584	0.567180
$507$	−1.00000	−0.0444116
$508$	−12.1032	−0.536993
$509$	−34.8528	−1.54482	−0.772411	−	0.635123i	$-0.780949\pi$
$509$	−34.8528	−1.54482	−0.772411	+	0.635123i	$0.780949\pi$
$510$	1.69202	0.0749240
$511$	2.02715	0.0896757
$512$	−1.00000	−0.0441942
$513$	−1.24698	−0.0550555
$514$	−7.68664	−0.339043
$515$	−12.1957	−0.537405
$516$	−2.26875	−0.0998761
$517$	31.4446	1.38293
$518$	6.85086	0.301009
$519$	−14.5864	−0.640273
$520$	−1.69202	−0.0742001
$521$	21.1105	0.924868	0.462434	−	0.886654i	$-0.346976\pi$
$521$	21.1105	0.924868	0.462434	+	0.886654i	$0.346976\pi$
$522$	−6.29590	−0.275564
$523$	−20.5448	−0.898361	−0.449181	−	0.893441i	$-0.648284\pi$
$523$	−20.5448	−0.898361	−0.449181	+	0.893441i	$0.648284\pi$
$524$	7.66487	0.334842
$525$	2.13706	0.0932691
$526$	−11.0248	−0.480702
$527$	8.63102	0.375973
$528$	−2.60388	−0.113319
$529$	1.00777	0.0438161
$530$	12.2784	0.533341
$531$	1.45473	0.0631299
$532$	1.24698	0.0540634
$533$	7.00969	0.303623
$534$	5.67994	0.245795
$535$	−3.15213	−0.136278
$536$	−7.83877	−0.338583
$537$	24.1782	1.04337
$538$	−2.63640	−0.113663
$539$	2.60388	0.112157
$540$	1.69202	0.0728130
$541$	10.4862	0.450836	0.225418	−	0.974262i	$-0.427625\pi$
$541$	10.4862	0.450836	0.225418	+	0.974262i	$0.427625\pi$
$542$	−2.95108	−0.126760
$543$	13.9608	0.599114
$544$	1.00000	0.0428746
$545$	24.9675	1.06949
$546$	−1.00000	−0.0427960
$547$	17.8562	0.763477	0.381739	−	0.924270i	$-0.375325\pi$
$547$	17.8562	0.763477	0.381739	+	0.924270i	$0.375325\pi$
$548$	2.45712	0.104963
$549$	7.62565	0.325455
$550$	5.56465	0.237277
$551$	7.85086	0.334458
$552$	−4.89977	−0.208548
$553$	−7.40581	−0.314927
$554$	−25.9095	−1.10079
$555$	−11.5918	−0.492044
$556$	−6.08575	−0.258093
$557$	40.2064	1.70360	0.851800	−	0.523866i	$-0.175511\pi$
$557$	40.2064	1.70360	0.851800	+	0.523866i	$0.175511\pi$
$558$	8.63102	0.365380
$559$	−2.26875	−0.0959579
$560$	−1.69202	−0.0715010
$561$	2.60388	0.109936
$562$	−5.20237	−0.219449
$563$	18.2107	0.767491	0.383745	−	0.923439i	$-0.374634\pi$
$563$	18.2107	0.767491	0.383745	+	0.923439i	$0.374634\pi$
$564$	−12.0761	−0.508494
$565$	12.7627	0.536931
$566$	−1.89546	−0.0796721
$567$	1.00000	0.0419961
$568$	8.39373	0.352193
$569$	8.93123	0.374417	0.187208	−	0.982320i	$-0.440056\pi$
$569$	8.93123	0.374417	0.187208	+	0.982320i	$0.440056\pi$
$570$	−2.10992	−0.0883747
$571$	30.7493	1.28682	0.643409	−	0.765523i	$-0.277519\pi$
$571$	30.7493	1.28682	0.643409	+	0.765523i	$0.277519\pi$
$572$	−2.60388	−0.108874
$573$	1.70171	0.0710900
$574$	7.00969	0.292579
$575$	10.4711	0.436676
$576$	1.00000	0.0416667
$577$	13.9729	0.581697	0.290849	−	0.956769i	$-0.406062\pi$
$577$	13.9729	0.581697	0.290849	+	0.956769i	$0.406062\pi$
$578$	−1.00000	−0.0415945
$579$	10.7235	0.445653
$580$	−10.6528	−0.442333
$581$	3.06100	0.126992
$582$	−1.91723	−0.0794718
$583$	18.8955	0.782570
$584$	−2.02715	−0.0838839
$585$	1.69202	0.0699565
$586$	−3.08038	−0.127249
$587$	−36.7241	−1.51576	−0.757882	−	0.652391i	$-0.773766\pi$
$587$	−36.7241	−1.51576	−0.757882	+	0.652391i	$0.773766\pi$
$588$	−1.00000	−0.0412393
$589$	−10.7627	−0.443470
$590$	2.46144	0.101336
$591$	8.52111	0.350511
$592$	−6.85086	−0.281568
$593$	37.8418	1.55397	0.776987	−	0.629516i	$-0.216747\pi$
$593$	37.8418	1.55397	0.776987	+	0.629516i	$0.216747\pi$
$594$	2.60388	0.106838
$595$	1.69202	0.0693661
$596$	−12.0925	−0.495326
$597$	−10.2131	−0.417995
$598$	−4.89977	−0.200367
$599$	35.0508	1.43214	0.716069	−	0.698029i	$-0.245939\pi$
$599$	35.0508	1.43214	0.716069	+	0.698029i	$0.245939\pi$
$600$	−2.13706	−0.0872452
$601$	−9.89307	−0.403547	−0.201773	−	0.979432i	$-0.564670\pi$
$601$	−9.89307	−0.403547	−0.201773	+	0.979432i	$0.564670\pi$
$602$	−2.26875	−0.0924673
$603$	7.83877	0.319220
$604$	−10.8455	−0.441296
$605$	7.14005	0.290284
$606$	15.2687	0.620251
$607$	29.1696	1.18396	0.591979	−	0.805954i	$-0.298347\pi$
$607$	29.1696	1.18396	0.591979	+	0.805954i	$0.298347\pi$
$608$	−1.24698	−0.0505717
$609$	−6.29590	−0.255123
$610$	12.9028	0.522417
$611$	−12.0761	−0.488545
$612$	−1.00000	−0.0404226
$613$	−28.2693	−1.14179	−0.570894	−	0.821024i	$-0.693403\pi$
$613$	−28.2693	−1.14179	−0.570894	+	0.821024i	$0.693403\pi$
$614$	4.25368	0.171665
$615$	−11.8605	−0.478263
$616$	−2.60388	−0.104913
$617$	−27.9724	−1.12613	−0.563063	−	0.826414i	$-0.690377\pi$
$617$	−27.9724	−1.12613	−0.563063	+	0.826414i	$0.690377\pi$
$618$	7.20775	0.289938
$619$	13.1360	0.527980	0.263990	−	0.964525i	$-0.414961\pi$
$619$	13.1360	0.527980	0.263990	+	0.964525i	$0.414961\pi$
$620$	14.6039	0.586506
$621$	4.89977	0.196621
$622$	3.24459	0.130096
$623$	5.67994	0.227562
$624$	1.00000	0.0400320
$625$	−9.74764	−0.389906
$626$	7.71678	0.308424
$627$	−3.24698	−0.129672
$628$	6.91185	0.275813
$629$	6.85086	0.273161
$630$	1.69202	0.0674117
$631$	27.1608	1.08125	0.540626	−	0.841263i	$-0.318187\pi$
$631$	27.1608	1.08125	0.540626	+	0.841263i	$0.318187\pi$
$632$	7.40581	0.294587
$633$	17.0858	0.679098
$634$	−2.09246	−0.0831021
$635$	20.4789	0.812680
$636$	−7.25667	−0.287746
$637$	−1.00000	−0.0396214
$638$	−16.3937	−0.649034
$639$	−8.39373	−0.332051
$640$	1.69202	0.0668830
$641$	−7.72109	−0.304965	−0.152482	−	0.988306i	$-0.548727\pi$
$641$	−7.72109	−0.304965	−0.152482	+	0.988306i	$0.548727\pi$
$642$	1.86294	0.0735242
$643$	−41.6209	−1.64137	−0.820683	−	0.571383i	$-0.806407\pi$
$643$	−41.6209	−1.64137	−0.820683	+	0.571383i	$0.806407\pi$
$644$	−4.89977	−0.193078
$645$	3.83877	0.151152
$646$	1.24698	0.0490618
$647$	−7.04354	−0.276910	−0.138455	−	0.990369i	$-0.544214\pi$
$647$	−7.04354	−0.276910	−0.138455	+	0.990369i	$0.544214\pi$
$648$	−1.00000	−0.0392837
$649$	3.78794	0.148690
$650$	−2.13706	−0.0838225
$651$	8.63102	0.338276
$652$	0.818331	0.0320483
$653$	16.4015	0.641840	0.320920	−	0.947106i	$-0.396008\pi$
$653$	16.4015	0.641840	0.320920	+	0.947106i	$0.396008\pi$
$654$	−14.7560	−0.577005
$655$	−12.9691	−0.506746
$656$	−7.00969	−0.273682
$657$	2.02715	0.0790865
$658$	−12.0761	−0.470774
$659$	32.6485	1.27180	0.635902	−	0.771770i	$-0.280628\pi$
$659$	32.6485	1.27180	0.635902	+	0.771770i	$0.280628\pi$
$660$	4.40581	0.171496
$661$	12.0084	0.467071	0.233536	−	0.972348i	$-0.424970\pi$
$661$	12.0084	0.467071	0.233536	+	0.972348i	$0.424970\pi$
$662$	16.0925	0.625451
$663$	−1.00000	−0.0388368
$664$	−3.06100	−0.118790
$665$	−2.10992	−0.0818190
$666$	6.85086	0.265465
$667$	−30.8485	−1.19446
$668$	−1.17629	−0.0455121
$669$	−7.94331	−0.307106
$670$	13.2634	0.512409
$671$	19.8562	0.766541
$672$	1.00000	0.0385758
$673$	−12.3636	−0.476582	−0.238291	−	0.971194i	$-0.576587\pi$
$673$	−12.3636	−0.476582	−0.238291	+	0.971194i	$0.576587\pi$
$674$	−18.2204	−0.701824
$675$	2.13706	0.0822556
$676$	1.00000	0.0384615
$677$	−30.0629	−1.15541	−0.577706	−	0.816245i	$-0.696052\pi$
$677$	−30.0629	−1.15541	−0.577706	+	0.816245i	$0.696052\pi$
$678$	−7.54288	−0.289682
$679$	−1.91723	−0.0735766
$680$	−1.69202	−0.0648861
$681$	−20.7114	−0.793663
$682$	22.4741	0.860578
$683$	23.8509	0.912628	0.456314	−	0.889819i	$-0.349169\pi$
$683$	23.8509	0.912628	0.456314	+	0.889819i	$0.349169\pi$
$684$	1.24698	0.0476795
$685$	−4.15751	−0.158850
$686$	−1.00000	−0.0381802
$687$	−21.3817	−0.815761
$688$	2.26875	0.0864953
$689$	−7.25667	−0.276457
$690$	8.29052	0.315615
$691$	37.5733	1.42935	0.714677	−	0.699454i	$-0.246574\pi$
$691$	37.5733	1.42935	0.714677	+	0.699454i	$0.246574\pi$
$692$	14.5864	0.554492
$693$	2.60388	0.0989130
$694$	0.883379	0.0335326
$695$	10.2972	0.390596
$696$	6.29590	0.238645
$697$	7.00969	0.265511
$698$	14.3123	0.541728
$699$	−4.12067	−0.155858
$700$	−2.13706	−0.0807734
$701$	−27.9590	−1.05600	−0.527998	−	0.849246i	$-0.677057\pi$
$701$	−27.9590	−1.05600	−0.527998	+	0.849246i	$0.677057\pi$
$702$	−1.00000	−0.0377426
$703$	−8.54288	−0.322201
$704$	2.60388	0.0981372
$705$	20.4330	0.769550
$706$	−28.3967	−1.06872
$707$	15.2687	0.574240
$708$	−1.45473	−0.0546721
$709$	4.70278	0.176616	0.0883082	−	0.996093i	$-0.471854\pi$
$709$	4.70278	0.176616	0.0883082	+	0.996093i	$0.471854\pi$
$710$	−14.2024	−0.533006
$711$	−7.40581	−0.277740
$712$	−5.67994	−0.212865
$713$	42.2900	1.58377
$714$	−1.00000	−0.0374241
$715$	4.40581	0.164768
$716$	−24.1782	−0.903582
$717$	−30.5961	−1.14263
$718$	11.8931	0.443845
$719$	−31.7458	−1.18392	−0.591960	−	0.805967i	$-0.701646\pi$
$719$	−31.7458	−1.18392	−0.591960	+	0.805967i	$0.701646\pi$
$720$	−1.69202	−0.0630579
$721$	7.20775	0.268431
$722$	17.4450	0.649237
$723$	−2.78687	−0.103645
$724$	−13.9608	−0.518848
$725$	−13.4547	−0.499696
$726$	−4.21983	−0.156613
$727$	20.4534	0.758575	0.379287	−	0.925279i	$-0.376169\pi$
$727$	20.4534	0.758575	0.379287	+	0.925279i	$0.376169\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	3.42998	0.126949
$731$	−2.26875	−0.0839127
$732$	−7.62565	−0.281852
$733$	−0.768086	−0.0283699	−0.0141849	−	0.999899i	$-0.504515\pi$
$733$	−0.768086	−0.0283699	−0.0141849	+	0.999899i	$0.504515\pi$
$734$	16.4741	0.608070
$735$	1.69202	0.0624112
$736$	4.89977	0.180608
$737$	20.4112	0.751856
$738$	7.00969	0.258030
$739$	−27.3672	−1.00672	−0.503359	−	0.864077i	$-0.667903\pi$
$739$	−27.3672	−1.00672	−0.503359	+	0.864077i	$0.667903\pi$
$740$	11.5918	0.426123
$741$	1.24698	0.0458089
$742$	−7.25667	−0.266401
$743$	−3.04354	−0.111657	−0.0558283	−	0.998440i	$-0.517780\pi$
$743$	−3.04354	−0.111657	−0.0558283	+	0.998440i	$0.517780\pi$
$744$	−8.63102	−0.316429
$745$	20.4607	0.749622
$746$	−22.4926	−0.823514
$747$	3.06100	0.111996
$748$	−2.60388	−0.0952071
$749$	1.86294	0.0680702
$750$	12.0761	0.440956
$751$	−17.6243	−0.643120	−0.321560	−	0.946889i	$-0.604207\pi$
$751$	−17.6243	−0.643120	−0.321560	+	0.946889i	$0.604207\pi$
$752$	12.0761	0.440369
$753$	16.4741	0.600350
$754$	6.29590	0.229283
$755$	18.3508	0.667853
$756$	−1.00000	−0.0363696
$757$	−12.6125	−0.458409	−0.229205	−	0.973378i	$-0.573612\pi$
$757$	−12.6125	−0.458409	−0.229205	+	0.973378i	$0.573612\pi$
$758$	−27.0954	−0.984151
$759$	12.7584	0.463100
$760$	2.10992	0.0765347
$761$	33.7724	1.22425	0.612124	−	0.790762i	$-0.290315\pi$
$761$	33.7724	1.22425	0.612124	+	0.790762i	$0.290315\pi$
$762$	−12.1032	−0.438453
$763$	−14.7560	−0.534203
$764$	−1.70171	−0.0615657
$765$	1.69202	0.0611752
$766$	15.0224	0.542780
$767$	−1.45473	−0.0525273
$768$	−1.00000	−0.0360844
$769$	37.7338	1.36071	0.680357	−	0.732881i	$-0.261825\pi$
$769$	37.7338	1.36071	0.680357	+	0.732881i	$0.261825\pi$
$770$	4.40581	0.158774
$771$	−7.68664	−0.276828
$772$	−10.7235	−0.385947
$773$	−2.28727	−0.0822675	−0.0411337	−	0.999154i	$-0.513097\pi$
$773$	−2.28727	−0.0822675	−0.0411337	+	0.999154i	$0.513097\pi$
$774$	−2.26875	−0.0815485
$775$	18.4450	0.662565
$776$	1.91723	0.0688246
$777$	6.85086	0.245773
$778$	−13.7332	−0.492358
$779$	−8.74094	−0.313177
$780$	−1.69202	−0.0605841
$781$	−21.8562	−0.782077
$782$	−4.89977	−0.175216
$783$	−6.29590	−0.224997
$784$	1.00000	0.0357143
$785$	−11.6950	−0.417413
$786$	7.66487	0.273397
$787$	−25.7372	−0.917433	−0.458716	−	0.888583i	$-0.651691\pi$
$787$	−25.7372	−0.917433	−0.458716	+	0.888583i	$0.651691\pi$
$788$	−8.52111	−0.303552
$789$	−11.0248	−0.392492
$790$	−12.5308	−0.445826
$791$	−7.54288	−0.268194
$792$	−2.60388	−0.0925247
$793$	−7.62565	−0.270795
$794$	−3.57002	−0.126695
$795$	12.2784	0.435471
$796$	10.2131	0.361995
$797$	−24.0315	−0.851238	−0.425619	−	0.904902i	$-0.639944\pi$
$797$	−24.0315	−0.851238	−0.425619	+	0.904902i	$0.639944\pi$
$798$	1.24698	0.0441426
$799$	−12.0761	−0.427220
$800$	2.13706	0.0755566
$801$	5.67994	0.200691
$802$	5.89546	0.208176
$803$	5.27844	0.186272
$804$	−7.83877	−0.276452
$805$	8.29052	0.292202
$806$	−8.63102	−0.304015
$807$	−2.63640	−0.0928057
$808$	−15.2687	−0.537153
$809$	10.9729	0.385785	0.192892	−	0.981220i	$-0.438213\pi$
$809$	10.9729	0.385785	0.192892	+	0.981220i	$0.438213\pi$
$810$	1.69202	0.0594516
$811$	7.71140	0.270784	0.135392	−	0.990792i	$-0.456771\pi$
$811$	7.71140	0.270784	0.135392	+	0.990792i	$0.456771\pi$
$812$	6.29590	0.220943
$813$	−2.95108	−0.103499
$814$	17.8388	0.625249
$815$	−1.38463	−0.0485016
$816$	1.00000	0.0350070
$817$	2.82908	0.0989771
$818$	−9.67563	−0.338300
$819$	−1.00000	−0.0349428
$820$	11.8605	0.414188
$821$	9.98387	0.348439	0.174220	−	0.984707i	$-0.444260\pi$
$821$	9.98387	0.348439	0.174220	+	0.984707i	$0.444260\pi$
$822$	2.45712	0.0857020
$823$	−0.366585	−0.0127783	−0.00638917	−	0.999980i	$-0.502034\pi$
$823$	−0.366585	−0.0127783	−0.00638917	+	0.999980i	$0.502034\pi$
$824$	−7.20775	−0.251094
$825$	5.56465	0.193736
$826$	−1.45473	−0.0506165
$827$	−29.7308	−1.03384	−0.516920	−	0.856034i	$-0.672922\pi$
$827$	−29.7308	−1.03384	−0.516920	+	0.856034i	$0.672922\pi$
$828$	−4.89977	−0.170279
$829$	5.25534	0.182526	0.0912628	−	0.995827i	$-0.470910\pi$
$829$	5.25534	0.182526	0.0912628	+	0.995827i	$0.470910\pi$
$830$	5.17928	0.179775
$831$	−25.9095	−0.898789
$832$	−1.00000	−0.0346688
$833$	−1.00000	−0.0346479
$834$	−6.08575	−0.210732
$835$	1.99031	0.0688776
$836$	3.24698	0.112299
$837$	8.63102	0.298332
$838$	−10.0556	−0.347366
$839$	−36.2452	−1.25132	−0.625661	−	0.780095i	$-0.715171\pi$
$839$	−36.2452	−1.25132	−0.625661	+	0.780095i	$0.715171\pi$
$840$	−1.69202	−0.0583803
$841$	10.6383	0.366839
$842$	3.41358	0.117640
$843$	−5.20237	−0.179179
$844$	−17.0858	−0.588116
$845$	−1.69202	−0.0582073
$846$	−12.0761	−0.415184
$847$	−4.21983	−0.144995
$848$	7.25667	0.249195
$849$	−1.89546	−0.0650520
$850$	−2.13706	−0.0733007
$851$	33.5676	1.15068
$852$	8.39373	0.287565
$853$	39.6098	1.35622	0.678108	−	0.734963i	$-0.262800\pi$
$853$	39.6098	1.35622	0.678108	+	0.734963i	$0.262800\pi$
$854$	−7.62565	−0.260944
$855$	−2.10992	−0.0721576
$856$	−1.86294	−0.0636739
$857$	41.4663	1.41646	0.708232	−	0.705980i	$-0.249493\pi$
$857$	41.4663	1.41646	0.708232	+	0.705980i	$0.249493\pi$
$858$	−2.60388	−0.0888948
$859$	−0.745251	−0.0254276	−0.0127138	−	0.999919i	$-0.504047\pi$
$859$	−0.745251	−0.0254276	−0.0127138	+	0.999919i	$0.504047\pi$
$860$	−3.83877	−0.130901
$861$	7.00969	0.238890
$862$	−24.4228	−0.831844
$863$	17.7313	0.603579	0.301789	−	0.953375i	$-0.402416\pi$
$863$	17.7313	0.603579	0.301789	+	0.953375i	$0.402416\pi$
$864$	1.00000	0.0340207
$865$	−24.6805	−0.839163
$866$	−11.8436	−0.402461
$867$	−1.00000	−0.0339618
$868$	−8.63102	−0.292956
$869$	−19.2838	−0.654159
$870$	−10.6528	−0.361164
$871$	−7.83877	−0.265607
$872$	14.7560	0.499701
$873$	−1.91723	−0.0648884
$874$	6.10992	0.206671
$875$	12.0761	0.408245
$876$	−2.02715	−0.0684910
$877$	55.5980	1.87741	0.938706	−	0.344719i	$-0.112026\pi$
$877$	55.5980	1.87741	0.938706	+	0.344719i	$0.112026\pi$
$878$	−4.93362	−0.166502
$879$	−3.08038	−0.103899
$880$	−4.40581	−0.148520
$881$	11.0761	0.373162	0.186581	−	0.982440i	$-0.440259\pi$
$881$	11.0761	0.373162	0.186581	+	0.982440i	$0.440259\pi$
$882$	−1.00000	−0.0336718
$883$	16.3424	0.549966	0.274983	−	0.961449i	$-0.411328\pi$
$883$	16.3424	0.549966	0.274983	+	0.961449i	$0.411328\pi$
$884$	1.00000	0.0336336
$885$	2.46144	0.0827402
$886$	−27.1444	−0.911933
$887$	−0.411190	−0.0138064	−0.00690320	−	0.999976i	$-0.502197\pi$
$887$	−0.411190	−0.0138064	−0.00690320	+	0.999976i	$0.502197\pi$
$888$	−6.85086	−0.229900
$889$	−12.1032	−0.405929
$890$	9.61058	0.322147
$891$	2.60388	0.0872331
$892$	7.94331	0.265962
$893$	15.0586	0.503917
$894$	−12.0925	−0.404432
$895$	40.9101	1.36747
$896$	−1.00000	−0.0334077
$897$	−4.89977	−0.163599
$898$	5.46548	0.182386
$899$	−54.3400	−1.81234
$900$	−2.13706	−0.0712354
$901$	−7.25667	−0.241755
$902$	18.2524	0.607737
$903$	−2.26875	−0.0754993
$904$	7.54288	0.250872
$905$	23.6219	0.785219
$906$	−10.8455	−0.360317
$907$	−42.2506	−1.40291	−0.701453	−	0.712715i	$-0.747465\pi$
$907$	−42.2506	−1.40291	−0.701453	+	0.712715i	$0.747465\pi$
$908$	20.7114	0.687332
$909$	15.2687	0.506432
$910$	−1.69202	−0.0560900
$911$	35.6021	1.17955	0.589775	−	0.807568i	$-0.299217\pi$
$911$	35.6021	1.17955	0.589775	+	0.807568i	$0.299217\pi$
$912$	−1.24698	−0.0412916
$913$	7.97046	0.263784
$914$	−18.1696	−0.600997
$915$	12.9028	0.426552
$916$	21.3817	0.706470
$917$	7.66487	0.253116
$918$	−1.00000	−0.0330049
$919$	25.2741	0.833717	0.416858	−	0.908972i	$-0.363131\pi$
$919$	25.2741	0.833717	0.416858	+	0.908972i	$0.363131\pi$
$920$	−8.29052	−0.273330
$921$	4.25368	0.140164
$922$	28.7627	0.947249
$923$	8.39373	0.276283
$924$	−2.60388	−0.0856612
$925$	14.6407	0.481384
$926$	−15.0489	−0.494538
$927$	7.20775	0.236734
$928$	−6.29590	−0.206673
$929$	26.1438	0.857749	0.428875	−	0.903364i	$-0.358910\pi$
$929$	26.1438	0.857749	0.428875	+	0.903364i	$0.358910\pi$
$930$	14.6039	0.478880
$931$	1.24698	0.0408681
$932$	4.12067	0.134977
$933$	3.24459	0.106223
$934$	−42.3110	−1.38446
$935$	4.40581	0.144085
$936$	1.00000	0.0326860
$937$	−57.2965	−1.87179	−0.935897	−	0.352273i	$-0.885409\pi$
$937$	−57.2965	−1.87179	−0.935897	+	0.352273i	$0.885409\pi$
$938$	−7.83877	−0.255945
$939$	7.71678	0.251827
$940$	−20.4330	−0.666450
$941$	−52.1377	−1.69964	−0.849819	−	0.527074i	$-0.823289\pi$
$941$	−52.1377	−1.69964	−0.849819	+	0.527074i	$0.823289\pi$
$942$	6.91185	0.225200
$943$	34.3459	1.11846
$944$	1.45473	0.0473474
$945$	1.69202	0.0550415
$946$	−5.90754	−0.192071
$947$	35.1613	1.14259	0.571295	−	0.820745i	$-0.306441\pi$
$947$	35.1613	1.14259	0.571295	+	0.820745i	$0.306441\pi$
$948$	7.40581	0.240530
$949$	−2.02715	−0.0658040
$950$	2.66487	0.0864599
$951$	−2.09246	−0.0678526
$952$	1.00000	0.0324102
$953$	21.0750	0.682686	0.341343	−	0.939939i	$-0.389118\pi$
$953$	21.0750	0.682686	0.341343	+	0.939939i	$0.389118\pi$
$954$	−7.25667	−0.234943
$955$	2.87933	0.0931729
$956$	30.5961	0.989549
$957$	−16.3937	−0.529934
$958$	−35.4432	−1.14512
$959$	2.45712	0.0793447
$960$	1.69202	0.0546098
$961$	43.4946	1.40305
$962$	−6.85086	−0.220880
$963$	1.86294	0.0600323
$964$	2.78687	0.0897591
$965$	18.1444	0.584088
$966$	−4.89977	−0.157648
$967$	−24.9560	−0.802530	−0.401265	−	0.915962i	$-0.631429\pi$
$967$	−24.9560	−0.802530	−0.401265	+	0.915962i	$0.631429\pi$
$968$	4.21983	0.135631
$969$	1.24698	0.0400588
$970$	−3.24400	−0.104158
$971$	58.0277	1.86220	0.931099	−	0.364766i	$-0.118851\pi$
$971$	58.0277	1.86220	0.931099	+	0.364766i	$0.118851\pi$
$972$	−1.00000	−0.0320750
$973$	−6.08575	−0.195100
$974$	−16.9022	−0.541580
$975$	−2.13706	−0.0684408
$976$	7.62565	0.244091
$977$	1.97631	0.0632278	0.0316139	−	0.999500i	$-0.489935\pi$
$977$	1.97631	0.0632278	0.0316139	+	0.999500i	$0.489935\pi$
$978$	0.818331	0.0261673
$979$	14.7899	0.472686
$980$	−1.69202	−0.0540496
$981$	−14.7560	−0.471123
$982$	37.0049	1.18087
$983$	−40.9560	−1.30629	−0.653147	−	0.757232i	$-0.726551\pi$
$983$	−40.9560	−1.30629	−0.653147	+	0.757232i	$0.726551\pi$
$984$	−7.00969	−0.223461
$985$	14.4179	0.459392
$986$	6.29590	0.200502
$987$	−12.0761	−0.384385
$988$	−1.24698	−0.0396717
$989$	−11.1164	−0.353480
$990$	4.40581	0.140026
$991$	45.7217	1.45240	0.726198	−	0.687485i	$-0.241285\pi$
$991$	45.7217	1.45240	0.726198	+	0.687485i	$0.241285\pi$
$992$	8.63102	0.274035
$993$	16.0925	0.510679
$994$	8.39373	0.266233
$995$	−17.2808	−0.547839
$996$	−3.06100	−0.0969915
$997$	−3.41417	−0.108128	−0.0540640	−	0.998537i	$-0.517217\pi$
$997$	−3.41417	−0.108128	−0.0540640	+	0.998537i	$0.517217\pi$
$998$	24.0707	0.761944
$999$	6.85086	0.216751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.bb.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.bb.1.1	✓	3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69202 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69202 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.69202 q^{10} +2.60388 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +1.69202 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.24698 q^{19} -1.69202 q^{20} -1.00000 q^{21} -2.60388 q^{22} -4.89977 q^{23} +1.00000 q^{24} -2.13706 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +6.29590 q^{29} -1.69202 q^{30} -8.63102 q^{31} -1.00000 q^{32} -2.60388 q^{33} +1.00000 q^{34} -1.69202 q^{35} +1.00000 q^{36} -6.85086 q^{37} -1.24698 q^{38} +1.00000 q^{39} +1.69202 q^{40} -7.00969 q^{41} +1.00000 q^{42} +2.26875 q^{43} +2.60388 q^{44} -1.69202 q^{45} +4.89977 q^{46} +12.0761 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.13706 q^{50} +1.00000 q^{51} -1.00000 q^{52} +7.25667 q^{53} +1.00000 q^{54} -4.40581 q^{55} -1.00000 q^{56} -1.24698 q^{57} -6.29590 q^{58} +1.45473 q^{59} +1.69202 q^{60} +7.62565 q^{61} +8.63102 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.69202 q^{65} +2.60388 q^{66} +7.83877 q^{67} -1.00000 q^{68} +4.89977 q^{69} +1.69202 q^{70} -8.39373 q^{71} -1.00000 q^{72} +2.02715 q^{73} +6.85086 q^{74} +2.13706 q^{75} +1.24698 q^{76} +2.60388 q^{77} -1.00000 q^{78} -7.40581 q^{79} -1.69202 q^{80} +1.00000 q^{81} +7.00969 q^{82} +3.06100 q^{83} -1.00000 q^{84} +1.69202 q^{85} -2.26875 q^{86} -6.29590 q^{87} -2.60388 q^{88} +5.67994 q^{89} +1.69202 q^{90} -1.00000 q^{91} -4.89977 q^{92} +8.63102 q^{93} -12.0761 q^{94} -2.10992 q^{95} +1.00000 q^{96} -1.91723 q^{97} -1.00000 q^{98} +2.60388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{16} - 3 q^{17} - 3 q^{18} - q^{19} - 3 q^{21} + q^{22} + 8 q^{23} + 3 q^{24} - q^{25} + 3 q^{26} - 3 q^{27} + 3 q^{28} + 5 q^{29} - 11 q^{31} - 3 q^{32} + q^{33} + 3 q^{34} + 3 q^{36} - 7 q^{37} + q^{38} + 3 q^{39} + q^{41} + 3 q^{42} - q^{43} - q^{44} - 8 q^{46} + 21 q^{47} - 3 q^{48} + 3 q^{49} + q^{50} + 3 q^{51} - 3 q^{52} - 5 q^{53} + 3 q^{54} - 3 q^{56} + q^{57} - 5 q^{58} - 18 q^{59} + 11 q^{61} + 11 q^{62} + 3 q^{63} + 3 q^{64} - q^{66} - 9 q^{67} - 3 q^{68} - 8 q^{69} + 7 q^{71} - 3 q^{72} + 7 q^{74} + q^{75} - q^{76} - q^{77} - 3 q^{78} - 9 q^{79} + 3 q^{81} - q^{82} + 19 q^{83} - 3 q^{84} + q^{86} - 5 q^{87} + q^{88} - 7 q^{89} - 3 q^{91} + 8 q^{92} + 11 q^{93} - 21 q^{94} - 7 q^{95} + 3 q^{96} + q^{97} - 3 q^{98} - q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^16 - 3 * q^17 - 3 * q^18 - q^19 - 3 * q^21 + q^22 + 8 * q^23 + 3 * q^24 - q^25 + 3 * q^26 - 3 * q^27 + 3 * q^28 + 5 * q^29 - 11 * q^31 - 3 * q^32 + q^33 + 3 * q^34 + 3 * q^36 - 7 * q^37 + q^38 + 3 * q^39 + q^41 + 3 * q^42 - q^43 - q^44 - 8 * q^46 + 21 * q^47 - 3 * q^48 + 3 * q^49 + q^50 + 3 * q^51 - 3 * q^52 - 5 * q^53 + 3 * q^54 - 3 * q^56 + q^57 - 5 * q^58 - 18 * q^59 + 11 * q^61 + 11 * q^62 + 3 * q^63 + 3 * q^64 - q^66 - 9 * q^67 - 3 * q^68 - 8 * q^69 + 7 * q^71 - 3 * q^72 + 7 * q^74 + q^75 - q^76 - q^77 - 3 * q^78 - 9 * q^79 + 3 * q^81 - q^82 + 19 * q^83 - 3 * q^84 + q^86 - 5 * q^87 + q^88 - 7 * q^89 - 3 * q^91 + 8 * q^92 + 11 * q^93 - 21 * q^94 - 7 * q^95 + 3 * q^96 + q^97 - 3 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more