LMFDB - Embedded newform 6006.2.a.cf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6006,2,Mod(1,6006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6006, 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("6006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6006.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:	$47.9581514540$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.72306708.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - x^{3} + 10x^{2} - 2 $ x^6 - 11x^4 - x^3 + 10x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.508679$ of defining polynomial
Character	$\chi$	$=$	6006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.93175 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.93175 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.93175 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +3.93175 q^{15} +1.00000 q^{16} -1.01736 q^{17} +1.00000 q^{18} -1.64200 q^{19} -3.93175 q^{20} -1.00000 q^{21} +1.00000 q^{22} +5.61818 q^{23} -1.00000 q^{24} +10.4587 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -4.79931 q^{29} +3.93175 q^{30} -1.72114 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.01736 q^{34} -3.93175 q^{35} +1.00000 q^{36} -0.914393 q^{37} -1.64200 q^{38} +1.00000 q^{39} -3.93175 q^{40} -5.26018 q^{41} -1.00000 q^{42} -11.9590 q^{43} +1.00000 q^{44} -3.93175 q^{45} +5.61818 q^{46} +7.48249 q^{47} -1.00000 q^{48} +1.00000 q^{49} +10.4587 q^{50} +1.01736 q^{51} -1.00000 q^{52} +11.7928 q^{53} -1.00000 q^{54} -3.93175 q^{55} +1.00000 q^{56} +1.64200 q^{57} -4.79931 q^{58} -4.53257 q^{59} +3.93175 q^{60} -13.6333 q^{61} -1.72114 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.93175 q^{65} -1.00000 q^{66} -13.9937 q^{67} -1.01736 q^{68} -5.61818 q^{69} -3.93175 q^{70} +3.33093 q^{71} +1.00000 q^{72} +15.0530 q^{73} -0.914393 q^{74} -10.4587 q^{75} -1.64200 q^{76} +1.00000 q^{77} +1.00000 q^{78} +2.84696 q^{79} -3.93175 q^{80} +1.00000 q^{81} -5.26018 q^{82} +16.8424 q^{83} -1.00000 q^{84} +4.00000 q^{85} -11.9590 q^{86} +4.79931 q^{87} +1.00000 q^{88} -4.37809 q^{89} -3.93175 q^{90} -1.00000 q^{91} +5.61818 q^{92} +1.72114 q^{93} +7.48249 q^{94} +6.45594 q^{95} -1.00000 q^{96} +8.56729 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{11} - 6 q^{12} - 6 q^{13} + 6 q^{14} + 6 q^{16} + 6 q^{18} + 2 q^{19} - 6 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 6 q^{26} - 6 q^{27} + 6 q^{28} + 6 q^{29} + 2 q^{31} + 6 q^{32} - 6 q^{33} + 6 q^{36} + 12 q^{37} + 2 q^{38} + 6 q^{39} + 4 q^{41} - 6 q^{42} + 4 q^{43} + 6 q^{44} + 10 q^{46} + 4 q^{47} - 6 q^{48} + 6 q^{49} + 10 q^{50} - 6 q^{52} + 18 q^{53} - 6 q^{54} + 6 q^{56} - 2 q^{57} + 6 q^{58} + 14 q^{59} + 2 q^{62} + 6 q^{63} + 6 q^{64} - 6 q^{66} + 4 q^{67} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 2 q^{73} + 12 q^{74} - 10 q^{75} + 2 q^{76} + 6 q^{77} + 6 q^{78} + 6 q^{79} + 6 q^{81} + 4 q^{82} + 24 q^{83} - 6 q^{84} + 24 q^{85} + 4 q^{86} - 6 q^{87} + 6 q^{88} - 14 q^{89} - 6 q^{91} + 10 q^{92} - 2 q^{93} + 4 q^{94} + 4 q^{95} - 6 q^{96} - 2 q^{97} + 6 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^11 - 6 * q^12 - 6 * q^13 + 6 * q^14 + 6 * q^16 + 6 * q^18 + 2 * q^19 - 6 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 6 * q^26 - 6 * q^27 + 6 * q^28 + 6 * q^29 + 2 * q^31 + 6 * q^32 - 6 * q^33 + 6 * q^36 + 12 * q^37 + 2 * q^38 + 6 * q^39 + 4 * q^41 - 6 * q^42 + 4 * q^43 + 6 * q^44 + 10 * q^46 + 4 * q^47 - 6 * q^48 + 6 * q^49 + 10 * q^50 - 6 * q^52 + 18 * q^53 - 6 * q^54 + 6 * q^56 - 2 * q^57 + 6 * q^58 + 14 * q^59 + 2 * q^62 + 6 * q^63 + 6 * q^64 - 6 * q^66 + 4 * q^67 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 2 * q^73 + 12 * q^74 - 10 * q^75 + 2 * q^76 + 6 * q^77 + 6 * q^78 + 6 * q^79 + 6 * q^81 + 4 * q^82 + 24 * q^83 - 6 * q^84 + 24 * q^85 + 4 * q^86 - 6 * q^87 + 6 * q^88 - 14 * q^89 - 6 * q^91 + 10 * q^92 - 2 * q^93 + 4 * q^94 + 4 * q^95 - 6 * q^96 - 2 * q^97 + 6 * q^98 + 6 * 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
$5$	−3.93175	−1.75833	−0.879166	−	0.476515i	$-0.841900\pi$
$5$	−3.93175	−1.75833	−0.879166	+	0.476515i	$0.841900\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.93175	−1.24333
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.00000	0.267261
$15$	3.93175	1.01517
$16$	1.00000	0.250000
$17$	−1.01736	−0.246746	−0.123373	−	0.992360i	$-0.539371\pi$
$17$	−1.01736	−0.246746	−0.123373	+	0.992360i	$0.539371\pi$
$18$	1.00000	0.235702
$19$	−1.64200	−0.376701	−0.188350	−	0.982102i	$-0.560314\pi$
$19$	−1.64200	−0.376701	−0.188350	+	0.982102i	$0.560314\pi$
$20$	−3.93175	−0.879166
$21$	−1.00000	−0.218218
$22$	1.00000	0.213201
$23$	5.61818	1.17147	0.585735	−	0.810502i	$-0.300806\pi$
$23$	5.61818	1.17147	0.585735	+	0.810502i	$0.300806\pi$
$24$	−1.00000	−0.204124
$25$	10.4587	2.09173
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−4.79931	−0.891209	−0.445605	−	0.895230i	$-0.647011\pi$
$29$	−4.79931	−0.891209	−0.445605	+	0.895230i	$0.647011\pi$
$30$	3.93175	0.717836
$31$	−1.72114	−0.309126	−0.154563	−	0.987983i	$-0.549397\pi$
$31$	−1.72114	−0.309126	−0.154563	+	0.987983i	$0.549397\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.01736	−0.174476
$35$	−3.93175	−0.664587
$36$	1.00000	0.166667
$37$	−0.914393	−0.150325	−0.0751626	−	0.997171i	$-0.523948\pi$
$37$	−0.914393	−0.150325	−0.0751626	+	0.997171i	$0.523948\pi$
$38$	−1.64200	−0.266368
$39$	1.00000	0.160128
$40$	−3.93175	−0.621664
$41$	−5.26018	−0.821501	−0.410751	−	0.911748i	$-0.634733\pi$
$41$	−5.26018	−0.821501	−0.410751	+	0.911748i	$0.634733\pi$
$42$	−1.00000	−0.154303
$43$	−11.9590	−1.82373	−0.911867	−	0.410485i	$-0.865359\pi$
$43$	−11.9590	−1.82373	−0.911867	+	0.410485i	$0.865359\pi$
$44$	1.00000	0.150756
$45$	−3.93175	−0.586111
$46$	5.61818	0.828355
$47$	7.48249	1.09143	0.545717	−	0.837970i	$-0.316257\pi$
$47$	7.48249	1.09143	0.545717	+	0.837970i	$0.316257\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	10.4587	1.47908
$51$	1.01736	0.142459
$52$	−1.00000	−0.138675
$53$	11.7928	1.61987	0.809936	−	0.586519i	$-0.199502\pi$
$53$	11.7928	1.61987	0.809936	+	0.586519i	$0.199502\pi$
$54$	−1.00000	−0.136083
$55$	−3.93175	−0.530157
$56$	1.00000	0.133631
$57$	1.64200	0.217488
$58$	−4.79931	−0.630180
$59$	−4.53257	−0.590090	−0.295045	−	0.955483i	$-0.595335\pi$
$59$	−4.53257	−0.590090	−0.295045	+	0.955483i	$0.595335\pi$
$60$	3.93175	0.507587
$61$	−13.6333	−1.74557	−0.872785	−	0.488105i	$-0.837688\pi$
$61$	−13.6333	−1.74557	−0.872785	+	0.488105i	$0.837688\pi$
$62$	−1.72114	−0.218585
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	3.93175	0.487674
$66$	−1.00000	−0.123091
$67$	−13.9937	−1.70961	−0.854804	−	0.518951i	$-0.826323\pi$
$67$	−13.9937	−1.70961	−0.854804	+	0.518951i	$0.826323\pi$
$68$	−1.01736	−0.123373
$69$	−5.61818	−0.676349
$70$	−3.93175	−0.469934
$71$	3.33093	0.395309	0.197655	−	0.980272i	$-0.436668\pi$
$71$	3.33093	0.395309	0.197655	+	0.980272i	$0.436668\pi$
$72$	1.00000	0.117851
$73$	15.0530	1.76182	0.880911	−	0.473281i	$-0.156931\pi$
$73$	15.0530	1.76182	0.880911	+	0.473281i	$0.156931\pi$
$74$	−0.914393	−0.106296
$75$	−10.4587	−1.20766
$76$	−1.64200	−0.188350
$77$	1.00000	0.113961
$78$	1.00000	0.113228
$79$	2.84696	0.320308	0.160154	−	0.987092i	$-0.448801\pi$
$79$	2.84696	0.320308	0.160154	+	0.987092i	$0.448801\pi$
$80$	−3.93175	−0.439583
$81$	1.00000	0.111111
$82$	−5.26018	−0.580889
$83$	16.8424	1.84869	0.924347	−	0.381552i	$-0.124610\pi$
$83$	16.8424	1.84869	0.924347	+	0.381552i	$0.124610\pi$
$84$	−1.00000	−0.109109
$85$	4.00000	0.433861
$86$	−11.9590	−1.28958
$87$	4.79931	0.514540
$88$	1.00000	0.106600
$89$	−4.37809	−0.464076	−0.232038	−	0.972707i	$-0.574539\pi$
$89$	−4.37809	−0.464076	−0.232038	+	0.972707i	$0.574539\pi$
$90$	−3.93175	−0.414443
$91$	−1.00000	−0.104828
$92$	5.61818	0.585735
$93$	1.72114	0.178474
$94$	7.48249	0.771760
$95$	6.45594	0.662365
$96$	−1.00000	−0.102062
$97$	8.56729	0.869876	0.434938	−	0.900460i	$-0.356770\pi$
$97$	8.56729	0.869876	0.434938	+	0.900460i	$0.356770\pi$
$98$	1.00000	0.101015
$99$	1.00000	0.100504
$100$	10.4587	1.04587
$101$	−5.56205	−0.553444	−0.276722	−	0.960950i	$-0.589248\pi$
$101$	−5.56205	−0.553444	−0.276722	+	0.960950i	$0.589248\pi$
$102$	1.01736	0.100733
$103$	−7.48249	−0.737272	−0.368636	−	0.929574i	$-0.620175\pi$
$103$	−7.48249	−0.737272	−0.368636	+	0.929574i	$0.620175\pi$
$104$	−1.00000	−0.0980581
$105$	3.93175	0.383700
$106$	11.7928	1.14542
$107$	19.8439	1.91839	0.959193	−	0.282752i	$-0.0912472\pi$
$107$	19.8439	1.91839	0.959193	+	0.282752i	$0.0912472\pi$
$108$	−1.00000	−0.0962250
$109$	−1.44228	−0.138146	−0.0690728	−	0.997612i	$-0.522004\pi$
$109$	−1.44228	−0.138146	−0.0690728	+	0.997612i	$0.522004\pi$
$110$	−3.93175	−0.374878
$111$	0.914393	0.0867903
$112$	1.00000	0.0944911
$113$	13.8159	1.29969	0.649843	−	0.760068i	$-0.274835\pi$
$113$	13.8159	1.29969	0.649843	+	0.760068i	$0.274835\pi$
$114$	1.64200	0.153787
$115$	−22.0893	−2.05983
$116$	−4.79931	−0.445605
$117$	−1.00000	−0.0924500
$118$	−4.53257	−0.417257
$119$	−1.01736	−0.0932611
$120$	3.93175	0.358918
$121$	1.00000	0.0909091
$122$	−13.6333	−1.23430
$123$	5.26018	0.474294
$124$	−1.72114	−0.154563
$125$	−21.4621	−1.91963
$126$	1.00000	0.0890871
$127$	−0.206874	−0.0183571	−0.00917856	−	0.999958i	$-0.502922\pi$
$127$	−0.206874	−0.0183571	−0.00917856	+	0.999958i	$0.502922\pi$
$128$	1.00000	0.0883883
$129$	11.9590	1.05293
$130$	3.93175	0.344837
$131$	11.8044	1.03136	0.515680	−	0.856781i	$-0.327539\pi$
$131$	11.8044	1.03136	0.515680	+	0.856781i	$0.327539\pi$
$132$	−1.00000	−0.0870388
$133$	−1.64200	−0.142379
$134$	−13.9937	−1.20888
$135$	3.93175	0.338391
$136$	−1.01736	−0.0872378
$137$	15.5968	1.33252	0.666261	−	0.745719i	$-0.267894\pi$
$137$	15.5968	1.33252	0.666261	+	0.745719i	$0.267894\pi$
$138$	−5.61818	−0.478251
$139$	15.6894	1.33075	0.665377	−	0.746507i	$-0.268271\pi$
$139$	15.6894	1.33075	0.665377	+	0.746507i	$0.268271\pi$
$140$	−3.93175	−0.332294
$141$	−7.48249	−0.630139
$142$	3.33093	0.279526
$143$	−1.00000	−0.0836242
$144$	1.00000	0.0833333
$145$	18.8697	1.56704
$146$	15.0530	1.24580
$147$	−1.00000	−0.0824786
$148$	−0.914393	−0.0751626
$149$	18.1318	1.48542	0.742709	−	0.669614i	$-0.233541\pi$
$149$	18.1318	1.48542	0.742709	+	0.669614i	$0.233541\pi$
$150$	−10.4587	−0.853947
$151$	15.8799	1.29229	0.646143	−	0.763216i	$-0.276381\pi$
$151$	15.8799	1.29229	0.646143	+	0.763216i	$0.276381\pi$
$152$	−1.64200	−0.133184
$153$	−1.01736	−0.0822486
$154$	1.00000	0.0805823
$155$	6.76710	0.543547
$156$	1.00000	0.0800641
$157$	13.3460	1.06513	0.532563	−	0.846390i	$-0.321229\pi$
$157$	13.3460	1.06513	0.532563	+	0.846390i	$0.321229\pi$
$158$	2.84696	0.226492
$159$	−11.7928	−0.935233
$160$	−3.93175	−0.310832
$161$	5.61818	0.442774
$162$	1.00000	0.0785674
$163$	−7.37953	−0.578009	−0.289005	−	0.957328i	$-0.593324\pi$
$163$	−7.37953	−0.578009	−0.289005	+	0.957328i	$0.593324\pi$
$164$	−5.26018	−0.410751
$165$	3.93175	0.306086
$166$	16.8424	1.30722
$167$	12.8662	0.995619	0.497809	−	0.867286i	$-0.334138\pi$
$167$	12.8662	0.995619	0.497809	+	0.867286i	$0.334138\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	4.00000	0.306786
$171$	−1.64200	−0.125567
$172$	−11.9590	−0.911867
$173$	−21.7289	−1.65201	−0.826007	−	0.563660i	$-0.809393\pi$
$173$	−21.7289	−1.65201	−0.826007	+	0.563660i	$0.809393\pi$
$174$	4.79931	0.363835
$175$	10.4587	0.790601
$176$	1.00000	0.0753778
$177$	4.53257	0.340689
$178$	−4.37809	−0.328152
$179$	−15.2285	−1.13823	−0.569116	−	0.822257i	$-0.692714\pi$
$179$	−15.2285	−1.13823	−0.569116	+	0.822257i	$0.692714\pi$
$180$	−3.93175	−0.293055
$181$	2.60333	0.193504	0.0967519	−	0.995309i	$-0.469155\pi$
$181$	2.60333	0.193504	0.0967519	+	0.995309i	$0.469155\pi$
$182$	−1.00000	−0.0741249
$183$	13.6333	1.00780
$184$	5.61818	0.414177
$185$	3.59516	0.264322
$186$	1.72114	0.126200
$187$	−1.01736	−0.0743966
$188$	7.48249	0.545717
$189$	−1.00000	−0.0727393
$190$	6.45594	0.468363
$191$	0.0195598	0.00141530	0.000707650	−	1.00000i	$-0.499775\pi$
$191$	0.0195598	0.00141530	0.000707650		1.00000i	$0.499775\pi$
$192$	−1.00000	−0.0721688
$193$	22.7414	1.63696	0.818482	−	0.574532i	$-0.194816\pi$
$193$	22.7414	1.63696	0.818482	+	0.574532i	$0.194816\pi$
$194$	8.56729	0.615095
$195$	−3.93175	−0.281559
$196$	1.00000	0.0714286
$197$	7.51280	0.535265	0.267632	−	0.963521i	$-0.413759\pi$
$197$	7.51280	0.535265	0.267632	+	0.963521i	$0.413759\pi$
$198$	1.00000	0.0710669
$199$	−16.7778	−1.18935	−0.594673	−	0.803967i	$-0.702719\pi$
$199$	−16.7778	−1.18935	−0.594673	+	0.803967i	$0.702719\pi$
$200$	10.4587	0.739539
$201$	13.9937	0.987043
$202$	−5.56205	−0.391344
$203$	−4.79931	−0.336845
$204$	1.01736	0.0712293
$205$	20.6817	1.44447
$206$	−7.48249	−0.521330
$207$	5.61818	0.390490
$208$	−1.00000	−0.0693375
$209$	−1.64200	−0.113580
$210$	3.93175	0.271317
$211$	4.81152	0.331239	0.165620	−	0.986190i	$-0.447038\pi$
$211$	4.81152	0.331239	0.165620	+	0.986190i	$0.447038\pi$
$212$	11.7928	0.809936
$213$	−3.33093	−0.228232
$214$	19.8439	1.35650
$215$	47.0199	3.20673
$216$	−1.00000	−0.0680414
$217$	−1.72114	−0.116839
$218$	−1.44228	−0.0976837
$219$	−15.0530	−1.01719
$220$	−3.93175	−0.265079
$221$	1.01736	0.0684349
$222$	0.914393	0.0613700
$223$	−24.6385	−1.64991	−0.824957	−	0.565195i	$-0.808801\pi$
$223$	−24.6385	−1.64991	−0.824957	+	0.565195i	$0.808801\pi$
$224$	1.00000	0.0668153
$225$	10.4587	0.697244
$226$	13.8159	0.919017
$227$	−13.7971	−0.915746	−0.457873	−	0.889018i	$-0.651389\pi$
$227$	−13.7971	−0.915746	−0.457873	+	0.889018i	$0.651389\pi$
$228$	1.64200	0.108744
$229$	19.1225	1.26365	0.631824	−	0.775112i	$-0.282307\pi$
$229$	19.1225	1.26365	0.631824	+	0.775112i	$0.282307\pi$
$230$	−22.0893	−1.45652
$231$	−1.00000	−0.0657952
$232$	−4.79931	−0.315090
$233$	6.93329	0.454215	0.227107	−	0.973870i	$-0.427073\pi$
$233$	6.93329	0.454215	0.227107	+	0.973870i	$0.427073\pi$
$234$	−1.00000	−0.0653720
$235$	−29.4193	−1.91910
$236$	−4.53257	−0.295045
$237$	−2.84696	−0.184930
$238$	−1.01736	−0.0659456
$239$	−25.1891	−1.62935	−0.814674	−	0.579919i	$-0.803084\pi$
$239$	−25.1891	−1.62935	−0.814674	+	0.579919i	$0.803084\pi$
$240$	3.93175	0.253793
$241$	−19.8712	−1.28002	−0.640009	−	0.768368i	$-0.721069\pi$
$241$	−19.8712	−1.28002	−0.640009	+	0.768368i	$0.721069\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−13.6333	−0.872785
$245$	−3.93175	−0.251190
$246$	5.26018	0.335377
$247$	1.64200	0.104478
$248$	−1.72114	−0.109293
$249$	−16.8424	−1.06734
$250$	−21.4621	−1.35738
$251$	−8.46140	−0.534079	−0.267039	−	0.963686i	$-0.586045\pi$
$251$	−8.46140	−0.534079	−0.267039	+	0.963686i	$0.586045\pi$
$252$	1.00000	0.0629941
$253$	5.61818	0.353212
$254$	−0.206874	−0.0129804
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	20.8053	1.29780	0.648898	−	0.760875i	$-0.275230\pi$
$257$	20.8053	1.29780	0.648898	+	0.760875i	$0.275230\pi$
$258$	11.9590	0.744537
$259$	−0.914393	−0.0568176
$260$	3.93175	0.243837
$261$	−4.79931	−0.297070
$262$	11.8044	0.729281
$263$	2.54550	0.156962	0.0784811	−	0.996916i	$-0.474993\pi$
$263$	2.54550	0.156962	0.0784811	+	0.996916i	$0.474993\pi$
$264$	−1.00000	−0.0615457
$265$	−46.3665	−2.84827
$266$	−1.64200	−0.100677
$267$	4.37809	0.267935
$268$	−13.9937	−0.854804
$269$	18.2250	1.11120	0.555598	−	0.831451i	$-0.312490\pi$
$269$	18.2250	1.11120	0.555598	+	0.831451i	$0.312490\pi$
$270$	3.93175	0.239279
$271$	10.3437	0.628334	0.314167	−	0.949368i	$-0.398275\pi$
$271$	10.3437	0.628334	0.314167	+	0.949368i	$0.398275\pi$
$272$	−1.01736	−0.0616864
$273$	1.00000	0.0605228
$274$	15.5968	0.942235
$275$	10.4587	0.630681
$276$	−5.61818	−0.338174
$277$	−17.1250	−1.02894	−0.514471	−	0.857508i	$-0.672012\pi$
$277$	−17.1250	−1.02894	−0.514471	+	0.857508i	$0.672012\pi$
$278$	15.6894	0.940986
$279$	−1.72114	−0.103042
$280$	−3.93175	−0.234967
$281$	11.2543	0.671375	0.335688	−	0.941973i	$-0.391031\pi$
$281$	11.2543	0.671375	0.335688	+	0.941973i	$0.391031\pi$
$282$	−7.48249	−0.445576
$283$	24.2689	1.44263	0.721317	−	0.692605i	$-0.243537\pi$
$283$	24.2689	1.44263	0.721317	+	0.692605i	$0.243537\pi$
$284$	3.33093	0.197655
$285$	−6.45594	−0.382417
$286$	−1.00000	−0.0591312
$287$	−5.26018	−0.310498
$288$	1.00000	0.0589256
$289$	−15.9650	−0.939117
$290$	18.8697	1.10807
$291$	−8.56729	−0.502223
$292$	15.0530	0.880911
$293$	26.8398	1.56800	0.783999	−	0.620763i	$-0.213177\pi$
$293$	26.8398	1.56800	0.783999	+	0.620763i	$0.213177\pi$
$294$	−1.00000	−0.0583212
$295$	17.8209	1.03757
$296$	−0.914393	−0.0531480
$297$	−1.00000	−0.0580259
$298$	18.1318	1.05035
$299$	−5.61818	−0.324907
$300$	−10.4587	−0.603831
$301$	−11.9590	−0.689307
$302$	15.8799	0.913785
$303$	5.56205	0.319531
$304$	−1.64200	−0.0941752
$305$	53.6029	3.06929
$306$	−1.01736	−0.0581585
$307$	−15.1120	−0.862486	−0.431243	−	0.902236i	$-0.641925\pi$
$307$	−15.1120	−0.862486	−0.431243	+	0.902236i	$0.641925\pi$
$308$	1.00000	0.0569803
$309$	7.48249	0.425664
$310$	6.76710	0.384345
$311$	15.9451	0.904161	0.452081	−	0.891977i	$-0.350682\pi$
$311$	15.9451	0.904161	0.452081	+	0.891977i	$0.350682\pi$
$312$	1.00000	0.0566139
$313$	23.4669	1.32643	0.663215	−	0.748429i	$-0.269192\pi$
$313$	23.4669	1.32643	0.663215	+	0.748429i	$0.269192\pi$
$314$	13.3460	0.753158
$315$	−3.93175	−0.221529
$316$	2.84696	0.160154
$317$	10.3022	0.578628	0.289314	−	0.957234i	$-0.406573\pi$
$317$	10.3022	0.578628	0.289314	+	0.957234i	$0.406573\pi$
$318$	−11.7928	−0.661310
$319$	−4.79931	−0.268710
$320$	−3.93175	−0.219792
$321$	−19.8439	−1.10758
$322$	5.61818	0.313089
$323$	1.67050	0.0929493
$324$	1.00000	0.0555556
$325$	−10.4587	−0.580142
$326$	−7.37953	−0.408714
$327$	1.44228	0.0797584
$328$	−5.26018	−0.290445
$329$	7.48249	0.412523
$330$	3.93175	0.216436
$331$	32.3776	1.77963	0.889817	−	0.456318i	$-0.150832\pi$
$331$	32.3776	1.77963	0.889817	+	0.456318i	$0.150832\pi$
$332$	16.8424	0.924347
$333$	−0.914393	−0.0501084
$334$	12.8662	0.704009
$335$	55.0199	3.00606
$336$	−1.00000	−0.0545545
$337$	−24.0416	−1.30963	−0.654815	−	0.755789i	$-0.727254\pi$
$337$	−24.0416	−1.30963	−0.654815	+	0.755789i	$0.727254\pi$
$338$	1.00000	0.0543928
$339$	−13.8159	−0.750374
$340$	4.00000	0.216930
$341$	−1.72114	−0.0932050
$342$	−1.64200	−0.0887892
$343$	1.00000	0.0539949
$344$	−11.9590	−0.644788
$345$	22.0893	1.18925
$346$	−21.7289	−1.16815
$347$	−8.67201	−0.465538	−0.232769	−	0.972532i	$-0.574779\pi$
$347$	−8.67201	−0.465538	−0.232769	+	0.972532i	$0.574779\pi$
$348$	4.79931	0.257270
$349$	28.0485	1.50140	0.750700	−	0.660644i	$-0.229717\pi$
$349$	28.0485	1.50140	0.750700	+	0.660644i	$0.229717\pi$
$350$	10.4587	0.559039
$351$	1.00000	0.0533761
$352$	1.00000	0.0533002
$353$	−29.1058	−1.54915	−0.774573	−	0.632484i	$-0.782035\pi$
$353$	−29.1058	−1.54915	−0.774573	+	0.632484i	$0.782035\pi$
$354$	4.53257	0.240903
$355$	−13.0964	−0.695085
$356$	−4.37809	−0.232038
$357$	1.01736	0.0538443
$358$	−15.2285	−0.804851
$359$	31.6501	1.67043	0.835214	−	0.549925i	$-0.185344\pi$
$359$	31.6501	1.67043	0.835214	+	0.549925i	$0.185344\pi$
$360$	−3.93175	−0.207221
$361$	−16.3038	−0.858097
$362$	2.60333	0.136828
$363$	−1.00000	−0.0524864
$364$	−1.00000	−0.0524142
$365$	−59.1847	−3.09787
$366$	13.6333	0.712626
$367$	−29.8237	−1.55679	−0.778393	−	0.627778i	$-0.783965\pi$
$367$	−29.8237	−1.55679	−0.778393	+	0.627778i	$0.783965\pi$
$368$	5.61818	0.292868
$369$	−5.26018	−0.273834
$370$	3.59516	0.186904
$371$	11.7928	0.612254
$372$	1.72114	0.0892370
$373$	−11.7392	−0.607834	−0.303917	−	0.952699i	$-0.598295\pi$
$373$	−11.7392	−0.607834	−0.303917	+	0.952699i	$0.598295\pi$
$374$	−1.01736	−0.0526064
$375$	21.4621	1.10830
$376$	7.48249	0.385880
$377$	4.79931	0.247177
$378$	−1.00000	−0.0514344
$379$	8.13673	0.417955	0.208978	−	0.977920i	$-0.432986\pi$
$379$	8.13673	0.417955	0.208978	+	0.977920i	$0.432986\pi$
$380$	6.45594	0.331183
$381$	0.206874	0.0105985
$382$	0.0195598	0.00100077
$383$	31.4482	1.60693	0.803464	−	0.595354i	$-0.202988\pi$
$383$	31.4482	1.60693	0.803464	+	0.595354i	$0.202988\pi$
$384$	−1.00000	−0.0510310
$385$	−3.93175	−0.200381
$386$	22.7414	1.15751
$387$	−11.9590	−0.607912
$388$	8.56729	0.434938
$389$	14.1847	0.719195	0.359598	−	0.933107i	$-0.382914\pi$
$389$	14.1847	0.719195	0.359598	+	0.933107i	$0.382914\pi$
$390$	−3.93175	−0.199092
$391$	−5.71570	−0.289055
$392$	1.00000	0.0505076
$393$	−11.8044	−0.595456
$394$	7.51280	0.378489
$395$	−11.1935	−0.563207
$396$	1.00000	0.0502519
$397$	27.7824	1.39436	0.697179	−	0.716898i	$-0.254438\pi$
$397$	27.7824	1.39436	0.697179	+	0.716898i	$0.254438\pi$
$398$	−16.7778	−0.840995
$399$	1.64200	0.0822028
$400$	10.4587	0.522933
$401$	33.7289	1.68434	0.842169	−	0.539213i	$-0.181278\pi$
$401$	33.7289	1.68434	0.842169	+	0.539213i	$0.181278\pi$
$402$	13.9937	0.697945
$403$	1.72114	0.0857362
$404$	−5.56205	−0.276722
$405$	−3.93175	−0.195370
$406$	−4.79931	−0.238186
$407$	−0.914393	−0.0453248
$408$	1.01736	0.0503667
$409$	15.4266	0.762796	0.381398	−	0.924411i	$-0.375443\pi$
$409$	15.4266	0.762796	0.381398	+	0.924411i	$0.375443\pi$
$410$	20.6817	1.02140
$411$	−15.5968	−0.769332
$412$	−7.48249	−0.368636
$413$	−4.53257	−0.223033
$414$	5.61818	0.276118
$415$	−66.2202	−3.25062
$416$	−1.00000	−0.0490290
$417$	−15.6894	−0.768312
$418$	−1.64200	−0.0803129
$419$	23.1935	1.13308	0.566539	−	0.824035i	$-0.308282\pi$
$419$	23.1935	1.13308	0.566539	+	0.824035i	$0.308282\pi$
$420$	3.93175	0.191850
$421$	12.0805	0.588767	0.294383	−	0.955687i	$-0.404886\pi$
$421$	12.0805	0.588767	0.294383	+	0.955687i	$0.404886\pi$
$422$	4.81152	0.234221
$423$	7.48249	0.363811
$424$	11.7928	0.572711
$425$	−10.6402	−0.516126
$426$	−3.33093	−0.161384
$427$	−13.6333	−0.659763
$428$	19.8439	0.959193
$429$	1.00000	0.0482805
$430$	47.0199	2.26750
$431$	−32.7938	−1.57962	−0.789810	−	0.613351i	$-0.789821\pi$
$431$	−32.7938	−1.57962	−0.789810	+	0.613351i	$0.789821\pi$
$432$	−1.00000	−0.0481125
$433$	−28.5020	−1.36972	−0.684858	−	0.728676i	$-0.740136\pi$
$433$	−28.5020	−1.36972	−0.684858	+	0.728676i	$0.740136\pi$
$434$	−1.72114	−0.0826174
$435$	−18.8697	−0.904732
$436$	−1.44228	−0.0690728
$437$	−9.22505	−0.441294
$438$	−15.0530	−0.719261
$439$	33.9461	1.62016	0.810079	−	0.586320i	$-0.199424\pi$
$439$	33.9461	1.62016	0.810079	+	0.586320i	$0.199424\pi$
$440$	−3.93175	−0.187439
$441$	1.00000	0.0476190
$442$	1.01736	0.0483908
$443$	−16.6245	−0.789854	−0.394927	−	0.918713i	$-0.629230\pi$
$443$	−16.6245	−0.789854	−0.394927	+	0.918713i	$0.629230\pi$
$444$	0.914393	0.0433952
$445$	17.2136	0.816001
$446$	−24.6385	−1.16667
$447$	−18.1318	−0.857607
$448$	1.00000	0.0472456
$449$	−18.8634	−0.890220	−0.445110	−	0.895476i	$-0.646835\pi$
$449$	−18.8634	−0.890220	−0.445110	+	0.895476i	$0.646835\pi$
$450$	10.4587	0.493026
$451$	−5.26018	−0.247692
$452$	13.8159	0.649843
$453$	−15.8799	−0.746102
$454$	−13.7971	−0.647530
$455$	3.93175	0.184323
$456$	1.64200	0.0768937
$457$	29.1249	1.36241	0.681203	−	0.732095i	$-0.261457\pi$
$457$	29.1249	1.36241	0.681203	+	0.732095i	$0.261457\pi$
$458$	19.1225	0.893533
$459$	1.01736	0.0474862
$460$	−22.0893	−1.02992
$461$	6.81820	0.317555	0.158778	−	0.987314i	$-0.449245\pi$
$461$	6.81820	0.317555	0.158778	+	0.987314i	$0.449245\pi$
$462$	−1.00000	−0.0465242
$463$	15.2326	0.707920	0.353960	−	0.935261i	$-0.384835\pi$
$463$	15.2326	0.707920	0.353960	+	0.935261i	$0.384835\pi$
$464$	−4.79931	−0.222802
$465$	−6.76710	−0.313817
$466$	6.93329	0.321178
$467$	−29.5401	−1.36695	−0.683476	−	0.729973i	$-0.739533\pi$
$467$	−29.5401	−1.36695	−0.683476	+	0.729973i	$0.739533\pi$
$468$	−1.00000	−0.0462250
$469$	−13.9937	−0.646171
$470$	−29.4193	−1.35701
$471$	−13.3460	−0.614951
$472$	−4.53257	−0.208628
$473$	−11.9590	−0.549877
$474$	−2.84696	−0.130765
$475$	−17.1731	−0.787957
$476$	−1.01736	−0.0466305
$477$	11.7928	0.539957
$478$	−25.1891	−1.15212
$479$	28.8350	1.31750	0.658752	−	0.752360i	$-0.271085\pi$
$479$	28.8350	1.31750	0.658752	+	0.752360i	$0.271085\pi$
$480$	3.93175	0.179459
$481$	0.914393	0.0416927
$482$	−19.8712	−0.905109
$483$	−5.61818	−0.255636
$484$	1.00000	0.0454545
$485$	−33.6844	−1.52953
$486$	−1.00000	−0.0453609
$487$	−37.9030	−1.71755	−0.858775	−	0.512353i	$-0.828774\pi$
$487$	−37.9030	−1.71755	−0.858775	+	0.512353i	$0.828774\pi$
$488$	−13.6333	−0.617152
$489$	7.37953	0.333714
$490$	−3.93175	−0.177618
$491$	−1.95055	−0.0880269	−0.0440135	−	0.999031i	$-0.514014\pi$
$491$	−1.95055	−0.0880269	−0.0440135	+	0.999031i	$0.514014\pi$
$492$	5.26018	0.237147
$493$	4.88262	0.219902
$494$	1.64200	0.0738771
$495$	−3.93175	−0.176719
$496$	−1.72114	−0.0772815
$497$	3.33093	0.149413
$498$	−16.8424	−0.754726
$499$	16.9549	0.759007	0.379503	−	0.925190i	$-0.376095\pi$
$499$	16.9549	0.759007	0.379503	+	0.925190i	$0.376095\pi$
$500$	−21.4621	−0.959815
$501$	−12.8662	−0.574821
$502$	−8.46140	−0.377651
$503$	17.3089	0.771764	0.385882	−	0.922548i	$-0.373897\pi$
$503$	17.3089	0.771764	0.385882	+	0.922548i	$0.373897\pi$
$504$	1.00000	0.0445435
$505$	21.8686	0.973139
$506$	5.61818	0.249758
$507$	−1.00000	−0.0444116
$508$	−0.206874	−0.00917856
$509$	−27.4714	−1.21765	−0.608824	−	0.793305i	$-0.708359\pi$
$509$	−27.4714	−1.21765	−0.608824	+	0.793305i	$0.708359\pi$
$510$	−4.00000	−0.177123
$511$	15.0530	0.665906
$512$	1.00000	0.0441942
$513$	1.64200	0.0724961
$514$	20.8053	0.917681
$515$	29.4193	1.29637
$516$	11.9590	0.526467
$517$	7.48249	0.329080
$518$	−0.914393	−0.0401761
$519$	21.7289	0.953791
$520$	3.93175	0.172419
$521$	−21.6149	−0.946968	−0.473484	−	0.880803i	$-0.657004\pi$
$521$	−21.6149	−0.946968	−0.473484	+	0.880803i	$0.657004\pi$
$522$	−4.79931	−0.210060
$523$	30.1211	1.31710	0.658551	−	0.752536i	$-0.271170\pi$
$523$	30.1211	1.31710	0.658551	+	0.752536i	$0.271170\pi$
$524$	11.8044	0.515680
$525$	−10.4587	−0.456454
$526$	2.54550	0.110989
$527$	1.75102	0.0762755
$528$	−1.00000	−0.0435194
$529$	8.56390	0.372343
$530$	−46.3665	−2.01403
$531$	−4.53257	−0.196697
$532$	−1.64200	−0.0711897
$533$	5.26018	0.227844
$534$	4.37809	0.189458
$535$	−78.0214	−3.37316
$536$	−13.9937	−0.604438
$537$	15.2285	0.657158
$538$	18.2250	0.785734
$539$	1.00000	0.0430730
$540$	3.93175	0.169196
$541$	−26.3081	−1.13107	−0.565537	−	0.824723i	$-0.691331\pi$
$541$	−26.3081	−1.13107	−0.565537	+	0.824723i	$0.691331\pi$
$542$	10.3437	0.444299
$543$	−2.60333	−0.111719
$544$	−1.01736	−0.0436189
$545$	5.67070	0.242906
$546$	1.00000	0.0427960
$547$	9.54911	0.408291	0.204145	−	0.978941i	$-0.434558\pi$
$547$	9.54911	0.408291	0.204145	+	0.978941i	$0.434558\pi$
$548$	15.5968	0.666261
$549$	−13.6333	−0.581856
$550$	10.4587	0.445959
$551$	7.88046	0.335719
$552$	−5.61818	−0.239125
$553$	2.84696	0.121065
$554$	−17.1250	−0.727572
$555$	−3.59516	−0.152606
$556$	15.6894	0.665377
$557$	−0.190630	−0.00807726	−0.00403863	−	0.999992i	$-0.501286\pi$
$557$	−0.190630	−0.00807726	−0.00403863	+	0.999992i	$0.501286\pi$
$558$	−1.72114	−0.0728617
$559$	11.9590	0.505813
$560$	−3.93175	−0.166147
$561$	1.01736	0.0429529
$562$	11.2543	0.474734
$563$	−33.2363	−1.40074	−0.700371	−	0.713779i	$-0.746982\pi$
$563$	−33.2363	−1.40074	−0.700371	+	0.713779i	$0.746982\pi$
$564$	−7.48249	−0.315070
$565$	−54.3205	−2.28528
$566$	24.2689	1.02010
$567$	1.00000	0.0419961
$568$	3.33093	0.139763
$569$	13.5329	0.567330	0.283665	−	0.958923i	$-0.408450\pi$
$569$	13.5329	0.567330	0.283665	+	0.958923i	$0.408450\pi$
$570$	−6.45594	−0.270409
$571$	23.4441	0.981107	0.490553	−	0.871411i	$-0.336795\pi$
$571$	23.4441	0.981107	0.490553	+	0.871411i	$0.336795\pi$
$572$	−1.00000	−0.0418121
$573$	−0.0195598	−0.000817123 0
$574$	−5.26018	−0.219556
$575$	58.7586	2.45040
$576$	1.00000	0.0416667
$577$	−17.1944	−0.715814	−0.357907	−	0.933757i	$-0.616509\pi$
$577$	−17.1944	−0.715814	−0.357907	+	0.933757i	$0.616509\pi$
$578$	−15.9650	−0.664056
$579$	−22.7414	−0.945102
$580$	18.8697	0.783521
$581$	16.8424	0.698741
$582$	−8.56729	−0.355125
$583$	11.7928	0.488410
$584$	15.0530	0.622898
$585$	3.93175	0.162558
$586$	26.8398	1.10874
$587$	18.2483	0.753187	0.376593	−	0.926379i	$-0.377095\pi$
$587$	18.2483	0.753187	0.376593	+	0.926379i	$0.377095\pi$
$588$	−1.00000	−0.0412393
$589$	2.82611	0.116448
$590$	17.8209	0.733676
$591$	−7.51280	−0.309035
$592$	−0.914393	−0.0375813
$593$	−40.9531	−1.68174	−0.840871	−	0.541236i	$-0.817957\pi$
$593$	−40.9531	−1.68174	−0.840871	+	0.541236i	$0.817957\pi$
$594$	−1.00000	−0.0410305
$595$	4.00000	0.163984
$596$	18.1318	0.742709
$597$	16.7778	0.686670
$598$	−5.61818	−0.229744
$599$	20.4469	0.835436	0.417718	−	0.908577i	$-0.362830\pi$
$599$	20.4469	0.835436	0.417718	+	0.908577i	$0.362830\pi$
$600$	−10.4587	−0.426973
$601$	38.7830	1.58199	0.790995	−	0.611823i	$-0.209563\pi$
$601$	38.7830	1.58199	0.790995	+	0.611823i	$0.209563\pi$
$602$	−11.9590	−0.487414
$603$	−13.9937	−0.569869
$604$	15.8799	0.646143
$605$	−3.93175	−0.159848
$606$	5.56205	0.225943
$607$	18.0155	0.731228	0.365614	−	0.930767i	$-0.380859\pi$
$607$	18.0155	0.731228	0.365614	+	0.930767i	$0.380859\pi$
$608$	−1.64200	−0.0665919
$609$	4.79931	0.194478
$610$	53.6029	2.17032
$611$	−7.48249	−0.302709
$612$	−1.01736	−0.0411243
$613$	−15.5441	−0.627819	−0.313909	−	0.949453i	$-0.601639\pi$
$613$	−15.5441	−0.627819	−0.313909	+	0.949453i	$0.601639\pi$
$614$	−15.1120	−0.609870
$615$	−20.6817	−0.833967
$616$	1.00000	0.0402911
$617$	−1.77280	−0.0713702	−0.0356851	−	0.999363i	$-0.511361\pi$
$617$	−1.77280	−0.0713702	−0.0356851	+	0.999363i	$0.511361\pi$
$618$	7.48249	0.300990
$619$	2.80413	0.112708	0.0563538	−	0.998411i	$-0.482053\pi$
$619$	2.80413	0.112708	0.0563538	+	0.998411i	$0.482053\pi$
$620$	6.76710	0.271773
$621$	−5.61818	−0.225450
$622$	15.9451	0.639338
$623$	−4.37809	−0.175404
$624$	1.00000	0.0400320
$625$	32.0904	1.28361
$626$	23.4669	0.937928
$627$	1.64200	0.0655752
$628$	13.3460	0.532563
$629$	0.930265	0.0370921
$630$	−3.93175	−0.156645
$631$	−39.2922	−1.56420	−0.782099	−	0.623155i	$-0.785851\pi$
$631$	−39.2922	−1.56420	−0.782099	+	0.623155i	$0.785851\pi$
$632$	2.84696	0.113246
$633$	−4.81152	−0.191241
$634$	10.3022	0.409152
$635$	0.813378	0.0322779
$636$	−11.7928	−0.467617
$637$	−1.00000	−0.0396214
$638$	−4.79931	−0.190006
$639$	3.33093	0.131770
$640$	−3.93175	−0.155416
$641$	−14.8525	−0.586638	−0.293319	−	0.956015i	$-0.594760\pi$
$641$	−14.8525	−0.586638	−0.293319	+	0.956015i	$0.594760\pi$
$642$	−19.8439	−0.783178
$643$	−6.88816	−0.271642	−0.135821	−	0.990733i	$-0.543367\pi$
$643$	−6.88816	−0.271642	−0.135821	+	0.990733i	$0.543367\pi$
$644$	5.61818	0.221387
$645$	−47.0199	−1.85141
$646$	1.67050	0.0657250
$647$	−9.99816	−0.393068	−0.196534	−	0.980497i	$-0.562969\pi$
$647$	−9.99816	−0.393068	−0.196534	+	0.980497i	$0.562969\pi$
$648$	1.00000	0.0392837
$649$	−4.53257	−0.177919
$650$	−10.4587	−0.410223
$651$	1.72114	0.0674569
$652$	−7.37953	−0.289005
$653$	−13.3775	−0.523503	−0.261752	−	0.965135i	$-0.584300\pi$
$653$	−13.3775	−0.523503	−0.261752	+	0.965135i	$0.584300\pi$
$654$	1.44228	0.0563977
$655$	−46.4122	−1.81347
$656$	−5.26018	−0.205375
$657$	15.0530	0.587274
$658$	7.48249	0.291698
$659$	−14.1306	−0.550451	−0.275225	−	0.961380i	$-0.588752\pi$
$659$	−14.1306	−0.550451	−0.275225	+	0.961380i	$0.588752\pi$
$660$	3.93175	0.153043
$661$	−41.1205	−1.59940	−0.799701	−	0.600398i	$-0.795009\pi$
$661$	−41.1205	−1.59940	−0.799701	+	0.600398i	$0.795009\pi$
$662$	32.3776	1.25839
$663$	−1.01736	−0.0395109
$664$	16.8424	0.653612
$665$	6.45594	0.250350
$666$	−0.914393	−0.0354320
$667$	−26.9634	−1.04403
$668$	12.8662	0.497809
$669$	24.6385	0.952578
$670$	55.0199	2.12560
$671$	−13.6333	−0.526309
$672$	−1.00000	−0.0385758
$673$	−24.4352	−0.941908	−0.470954	−	0.882158i	$-0.656090\pi$
$673$	−24.4352	−0.941908	−0.470954	+	0.882158i	$0.656090\pi$
$674$	−24.0416	−0.926049
$675$	−10.4587	−0.402554
$676$	1.00000	0.0384615
$677$	20.4101	0.784425	0.392213	−	0.919875i	$-0.371710\pi$
$677$	20.4101	0.784425	0.392213	+	0.919875i	$0.371710\pi$
$678$	−13.8159	−0.530595
$679$	8.56729	0.328782
$680$	4.00000	0.153393
$681$	13.7971	0.528706
$682$	−1.72114	−0.0659059
$683$	3.15252	0.120628	0.0603139	−	0.998179i	$-0.480790\pi$
$683$	3.15252	0.120628	0.0603139	+	0.998179i	$0.480790\pi$
$684$	−1.64200	−0.0627834
$685$	−61.3226	−2.34302
$686$	1.00000	0.0381802
$687$	−19.1225	−0.729567
$688$	−11.9590	−0.455934
$689$	−11.7928	−0.449271
$690$	22.0893	0.840924
$691$	19.1767	0.729515	0.364758	−	0.931103i	$-0.381152\pi$
$691$	19.1767	0.729515	0.364758	+	0.931103i	$0.381152\pi$
$692$	−21.7289	−0.826007
$693$	1.00000	0.0379869
$694$	−8.67201	−0.329185
$695$	−61.6867	−2.33991
$696$	4.79931	0.181917
$697$	5.35148	0.202702
$698$	28.0485	1.06165
$699$	−6.93329	−0.262241
$700$	10.4587	0.395300
$701$	−17.2338	−0.650911	−0.325455	−	0.945557i	$-0.605518\pi$
$701$	−17.2338	−0.650911	−0.325455	+	0.945557i	$0.605518\pi$
$702$	1.00000	0.0377426
$703$	1.50143	0.0566276
$704$	1.00000	0.0376889
$705$	29.4193	1.10799
$706$	−29.1058	−1.09541
$707$	−5.56205	−0.209182
$708$	4.53257	0.170344
$709$	−14.5130	−0.545047	−0.272524	−	0.962149i	$-0.587858\pi$
$709$	−14.5130	−0.545047	−0.272524	+	0.962149i	$0.587858\pi$
$710$	−13.0964	−0.491499
$711$	2.84696	0.106769
$712$	−4.37809	−0.164076
$713$	−9.66968	−0.362132
$714$	1.01736	0.0380737
$715$	3.93175	0.147039
$716$	−15.2285	−0.569116
$717$	25.1891	0.940705
$718$	31.6501	1.18117
$719$	−3.30417	−0.123225	−0.0616124	−	0.998100i	$-0.519624\pi$
$719$	−3.30417	−0.123225	−0.0616124	+	0.998100i	$0.519624\pi$
$720$	−3.93175	−0.146528
$721$	−7.48249	−0.278663
$722$	−16.3038	−0.606766
$723$	19.8712	0.739019
$724$	2.60333	0.0967519
$725$	−50.1944	−1.86417
$726$	−1.00000	−0.0371135
$727$	8.29216	0.307539	0.153770	−	0.988107i	$-0.450859\pi$
$727$	8.29216	0.307539	0.153770	+	0.988107i	$0.450859\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	−59.1847	−2.19052
$731$	12.1666	0.449999
$732$	13.6333	0.503902
$733$	4.18597	0.154612	0.0773062	−	0.997007i	$-0.475368\pi$
$733$	4.18597	0.154612	0.0773062	+	0.997007i	$0.475368\pi$
$734$	−29.8237	−1.10081
$735$	3.93175	0.145025
$736$	5.61818	0.207089
$737$	−13.9937	−0.515466
$738$	−5.26018	−0.193630
$739$	−26.6373	−0.979869	−0.489934	−	0.871759i	$-0.662979\pi$
$739$	−26.6373	−0.979869	−0.489934	+	0.871759i	$0.662979\pi$
$740$	3.59516	0.132161
$741$	−1.64200	−0.0603204
$742$	11.7928	0.432929
$743$	−12.2456	−0.449248	−0.224624	−	0.974446i	$-0.572115\pi$
$743$	−12.2456	−0.449248	−0.224624	+	0.974446i	$0.572115\pi$
$744$	1.72114	0.0631001
$745$	−71.2899	−2.61186
$746$	−11.7392	−0.429803
$747$	16.8424	0.616231
$748$	−1.01736	−0.0371983
$749$	19.8439	0.725082
$750$	21.4621	0.783686
$751$	25.5956	0.933996	0.466998	−	0.884258i	$-0.345335\pi$
$751$	25.5956	0.933996	0.466998	+	0.884258i	$0.345335\pi$
$752$	7.48249	0.272858
$753$	8.46140	0.308350
$754$	4.79931	0.174780
$755$	−62.4358	−2.27227
$756$	−1.00000	−0.0363696
$757$	−24.1755	−0.878672	−0.439336	−	0.898323i	$-0.644786\pi$
$757$	−24.1755	−0.878672	−0.439336	+	0.898323i	$0.644786\pi$
$758$	8.13673	0.295539
$759$	−5.61818	−0.203927
$760$	6.45594	0.234181
$761$	25.5732	0.927029	0.463514	−	0.886089i	$-0.346588\pi$
$761$	25.5732	0.927029	0.463514	+	0.886089i	$0.346588\pi$
$762$	0.206874	0.00749426
$763$	−1.44228	−0.0522142
$764$	0.0195598	0.000707650 0
$765$	4.00000	0.144620
$766$	31.4482	1.13627
$767$	4.53257	0.163662
$768$	−1.00000	−0.0360844
$769$	−19.5929	−0.706540	−0.353270	−	0.935521i	$-0.614930\pi$
$769$	−19.5929	−0.706540	−0.353270	+	0.935521i	$0.614930\pi$
$770$	−3.93175	−0.141690
$771$	−20.8053	−0.749283
$772$	22.7414	0.818482
$773$	−21.8970	−0.787582	−0.393791	−	0.919200i	$-0.628837\pi$
$773$	−21.8970	−0.787582	−0.393791	+	0.919200i	$0.628837\pi$
$774$	−11.9590	−0.429858
$775$	−18.0008	−0.646609
$776$	8.56729	0.307548
$777$	0.914393	0.0328037
$778$	14.1847	0.508548
$779$	8.63721	0.309460
$780$	−3.93175	−0.140779
$781$	3.33093	0.119190
$782$	−5.71570	−0.204393
$783$	4.79931	0.171513
$784$	1.00000	0.0357143
$785$	−52.4731	−1.87285
$786$	−11.8044	−0.421051
$787$	22.5872	0.805147	0.402574	−	0.915388i	$-0.368116\pi$
$787$	22.5872	0.805147	0.402574	+	0.915388i	$0.368116\pi$
$788$	7.51280	0.267632
$789$	−2.54550	−0.0906222
$790$	−11.1935	−0.398248
$791$	13.8159	0.491235
$792$	1.00000	0.0355335
$793$	13.6333	0.484134
$794$	27.7824	0.985959
$795$	46.3665	1.64445
$796$	−16.7778	−0.594673
$797$	8.78813	0.311292	0.155646	−	0.987813i	$-0.450254\pi$
$797$	8.78813	0.311292	0.155646	+	0.987813i	$0.450254\pi$
$798$	1.64200	0.0581262
$799$	−7.61238	−0.269306
$800$	10.4587	0.369770
$801$	−4.37809	−0.154692
$802$	33.7289	1.19101
$803$	15.0530	0.531209
$804$	13.9937	0.493521
$805$	−22.0893	−0.778544
$806$	1.72114	0.0606246
$807$	−18.2250	−0.641549
$808$	−5.56205	−0.195672
$809$	−11.9608	−0.420520	−0.210260	−	0.977645i	$-0.567431\pi$
$809$	−11.9608	−0.420520	−0.210260	+	0.977645i	$0.567431\pi$
$810$	−3.93175	−0.138148
$811$	33.9590	1.19246	0.596232	−	0.802812i	$-0.296664\pi$
$811$	33.9590	1.19246	0.596232	+	0.802812i	$0.296664\pi$
$812$	−4.79931	−0.168423
$813$	−10.3437	−0.362769
$814$	−0.914393	−0.0320494
$815$	29.0145	1.01633
$816$	1.01736	0.0356147
$817$	19.6367	0.687002
$818$	15.4266	0.539378
$819$	−1.00000	−0.0349428
$820$	20.6817	0.722236
$821$	−33.1691	−1.15761	−0.578805	−	0.815466i	$-0.696481\pi$
$821$	−33.1691	−1.15761	−0.578805	+	0.815466i	$0.696481\pi$
$822$	−15.5968	−0.544000
$823$	−38.8053	−1.35267	−0.676333	−	0.736596i	$-0.736432\pi$
$823$	−38.8053	−1.35267	−0.676333	+	0.736596i	$0.736432\pi$
$824$	−7.48249	−0.260665
$825$	−10.4587	−0.364124
$826$	−4.53257	−0.157708
$827$	18.0580	0.627938	0.313969	−	0.949433i	$-0.398341\pi$
$827$	18.0580	0.627938	0.313969	+	0.949433i	$0.398341\pi$
$828$	5.61818	0.195245
$829$	−19.9204	−0.691865	−0.345932	−	0.938259i	$-0.612437\pi$
$829$	−19.9204	−0.691865	−0.345932	+	0.938259i	$0.612437\pi$
$830$	−66.2202	−2.29854
$831$	17.1250	0.594060
$832$	−1.00000	−0.0346688
$833$	−1.01736	−0.0352494
$834$	−15.6894	−0.543278
$835$	−50.5868	−1.75063
$836$	−1.64200	−0.0567898
$837$	1.72114	0.0594914
$838$	23.1935	0.801207
$839$	−35.5344	−1.22678	−0.613392	−	0.789779i	$-0.710195\pi$
$839$	−35.5344	−1.22678	−0.613392	+	0.789779i	$0.710195\pi$
$840$	3.93175	0.135658
$841$	−5.96664	−0.205746
$842$	12.0805	0.416321
$843$	−11.2543	−0.387619
$844$	4.81152	0.165620
$845$	−3.93175	−0.135256
$846$	7.48249	0.257253
$847$	1.00000	0.0343604
$848$	11.7928	0.404968
$849$	−24.2689	−0.832905
$850$	−10.6402	−0.364956
$851$	−5.13722	−0.176102
$852$	−3.33093	−0.114116
$853$	19.6174	0.671686	0.335843	−	0.941918i	$-0.390979\pi$
$853$	19.6174	0.671686	0.335843	+	0.941918i	$0.390979\pi$
$854$	−13.6333	−0.466523
$855$	6.45594	0.220788
$856$	19.8439	0.678252
$857$	−18.1812	−0.621057	−0.310529	−	0.950564i	$-0.600506\pi$
$857$	−18.1812	−0.621057	−0.310529	+	0.950564i	$0.600506\pi$
$858$	1.00000	0.0341394
$859$	1.16584	0.0397778	0.0198889	−	0.999802i	$-0.493669\pi$
$859$	1.16584	0.0397778	0.0198889	+	0.999802i	$0.493669\pi$
$860$	47.0199	1.60337
$861$	5.26018	0.179266
$862$	−32.7938	−1.11696
$863$	−41.4673	−1.41156	−0.705781	−	0.708430i	$-0.749404\pi$
$863$	−41.4673	−1.41156	−0.705781	+	0.708430i	$0.749404\pi$
$864$	−1.00000	−0.0340207
$865$	85.4325	2.90479
$866$	−28.5020	−0.968536
$867$	15.9650	0.542199
$868$	−1.72114	−0.0584193
$869$	2.84696	0.0965764
$870$	−18.8697	−0.639742
$871$	13.9937	0.474160
$872$	−1.44228	−0.0488419
$873$	8.56729	0.289959
$874$	−9.22505	−0.312042
$875$	−21.4621	−0.725552
$876$	−15.0530	−0.508594
$877$	15.1003	0.509900	0.254950	−	0.966954i	$-0.417941\pi$
$877$	15.1003	0.509900	0.254950	+	0.966954i	$0.417941\pi$
$878$	33.9461	1.14563
$879$	−26.8398	−0.905284
$880$	−3.93175	−0.132539
$881$	5.61657	0.189227	0.0946135	−	0.995514i	$-0.469838\pi$
$881$	5.61657	0.189227	0.0946135	+	0.995514i	$0.469838\pi$
$882$	1.00000	0.0336718
$883$	33.1673	1.11617	0.558085	−	0.829784i	$-0.311536\pi$
$883$	33.1673	1.11617	0.558085	+	0.829784i	$0.311536\pi$
$884$	1.01736	0.0342175
$885$	−17.8209	−0.599044
$886$	−16.6245	−0.558511
$887$	−14.8699	−0.499282	−0.249641	−	0.968338i	$-0.580313\pi$
$887$	−14.8699	−0.499282	−0.249641	+	0.968338i	$0.580313\pi$
$888$	0.914393	0.0306850
$889$	−0.206874	−0.00693834
$890$	17.2136	0.577000
$891$	1.00000	0.0335013
$892$	−24.6385	−0.824957
$893$	−12.2863	−0.411144
$894$	−18.1318	−0.606419
$895$	59.8747	2.00139
$896$	1.00000	0.0334077
$897$	5.61818	0.187585
$898$	−18.8634	−0.629481
$899$	8.26029	0.275496
$900$	10.4587	0.348622
$901$	−11.9975	−0.399696
$902$	−5.26018	−0.175145
$903$	11.9590	0.397972
$904$	13.8159	0.459508
$905$	−10.2356	−0.340244
$906$	−15.8799	−0.527574
$907$	7.75124	0.257376	0.128688	−	0.991685i	$-0.458923\pi$
$907$	7.75124	0.257376	0.128688	+	0.991685i	$0.458923\pi$
$908$	−13.7971	−0.457873
$909$	−5.56205	−0.184481
$910$	3.93175	0.130336
$911$	13.1091	0.434325	0.217162	−	0.976135i	$-0.430320\pi$
$911$	13.1091	0.434325	0.217162	+	0.976135i	$0.430320\pi$
$912$	1.64200	0.0543721
$913$	16.8424	0.557402
$914$	29.1249	0.963366
$915$	−53.6029	−1.77206
$916$	19.1225	0.631824
$917$	11.8044	0.389817
$918$	1.01736	0.0335778
$919$	20.7547	0.684635	0.342318	−	0.939584i	$-0.388788\pi$
$919$	20.7547	0.684635	0.342318	+	0.939584i	$0.388788\pi$
$920$	−22.0893	−0.728262
$921$	15.1120	0.497956
$922$	6.81820	0.224545
$923$	−3.33093	−0.109639
$924$	−1.00000	−0.0328976
$925$	−9.56333	−0.314440
$926$	15.2326	0.500575
$927$	−7.48249	−0.245757
$928$	−4.79931	−0.157545
$929$	27.6240	0.906314	0.453157	−	0.891431i	$-0.350298\pi$
$929$	27.6240	0.906314	0.453157	+	0.891431i	$0.350298\pi$
$930$	−6.76710	−0.221902
$931$	−1.64200	−0.0538144
$932$	6.93329	0.227107
$933$	−15.9451	−0.522018
$934$	−29.5401	−0.966581
$935$	4.00000	0.130814
$936$	−1.00000	−0.0326860
$937$	0.512196	0.0167327	0.00836635	−	0.999965i	$-0.497337\pi$
$937$	0.512196	0.0167327	0.00836635	+	0.999965i	$0.497337\pi$
$938$	−13.9937	−0.456912
$939$	−23.4669	−0.765815
$940$	−29.4193	−0.959551
$941$	10.2371	0.333719	0.166860	−	0.985981i	$-0.446637\pi$
$941$	10.2371	0.333719	0.166860	+	0.985981i	$0.446637\pi$
$942$	−13.3460	−0.434836
$943$	−29.5526	−0.962365
$944$	−4.53257	−0.147523
$945$	3.93175	0.127900
$946$	−11.9590	−0.388822
$947$	53.7626	1.74705	0.873525	−	0.486780i	$-0.161829\pi$
$947$	53.7626	1.74705	0.873525	+	0.486780i	$0.161829\pi$
$948$	−2.84696	−0.0924649
$949$	−15.0530	−0.488642
$950$	−17.1731	−0.557170
$951$	−10.3022	−0.334071
$952$	−1.01736	−0.0329728
$953$	43.3513	1.40429	0.702143	−	0.712036i	$-0.252227\pi$
$953$	43.3513	1.40429	0.702143	+	0.712036i	$0.252227\pi$
$954$	11.7928	0.381807
$955$	−0.0769044	−0.00248857
$956$	−25.1891	−0.814674
$957$	4.79931	0.155140
$958$	28.8350	0.931616
$959$	15.5968	0.503646
$960$	3.93175	0.126897
$961$	−28.0377	−0.904441
$962$	0.914393	0.0294812
$963$	19.8439	0.639462
$964$	−19.8712	−0.640009
$965$	−89.4137	−2.87833
$966$	−5.61818	−0.180762
$967$	−0.0763367	−0.00245482	−0.00122741	−	0.999999i	$-0.500391\pi$
$967$	−0.0763367	−0.00245482	−0.00122741	+	0.999999i	$0.500391\pi$
$968$	1.00000	0.0321412
$969$	−1.67050	−0.0536643
$970$	−33.6844	−1.08154
$971$	−11.4468	−0.367346	−0.183673	−	0.982987i	$-0.558799\pi$
$971$	−11.4468	−0.367346	−0.183673	+	0.982987i	$0.558799\pi$
$972$	−1.00000	−0.0320750
$973$	15.6894	0.502978
$974$	−37.9030	−1.21449
$975$	10.4587	0.334945
$976$	−13.6333	−0.436392
$977$	51.2895	1.64090	0.820448	−	0.571722i	$-0.193724\pi$
$977$	51.2895	1.64090	0.820448	+	0.571722i	$0.193724\pi$
$978$	7.37953	0.235971
$979$	−4.37809	−0.139924
$980$	−3.93175	−0.125595
$981$	−1.44228	−0.0460486
$982$	−1.95055	−0.0622444
$983$	−46.4554	−1.48170	−0.740849	−	0.671672i	$-0.765576\pi$
$983$	−46.4554	−1.48170	−0.740849	+	0.671672i	$0.765576\pi$
$984$	5.26018	0.167688
$985$	−29.5385	−0.941173
$986$	4.88262	0.155494
$987$	−7.48249	−0.238170
$988$	1.64200	0.0522390
$989$	−67.1879	−2.13645
$990$	−3.93175	−0.124959
$991$	1.32555	0.0421075	0.0210537	−	0.999778i	$-0.493298\pi$
$991$	1.32555	0.0421075	0.0210537	+	0.999778i	$0.493298\pi$
$992$	−1.72114	−0.0546463
$993$	−32.3776	−1.02747
$994$	3.33093	0.105651
$995$	65.9661	2.09127
$996$	−16.8424	−0.533672
$997$	43.8548	1.38890	0.694448	−	0.719543i	$-0.255649\pi$
$997$	43.8548	1.38890	0.694448	+	0.719543i	$0.255649\pi$
$998$	16.9549	0.536699
$999$	0.914393	0.0289301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6006.2.a.cf.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6006.2.a.cf.1.1	✓	6	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:	\( N \)	\(=\)	\( 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.93175 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.93175 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.93175 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +3.93175 q^{15} +1.00000 q^{16} -1.01736 q^{17} +1.00000 q^{18} -1.64200 q^{19} -3.93175 q^{20} -1.00000 q^{21} +1.00000 q^{22} +5.61818 q^{23} -1.00000 q^{24} +10.4587 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -4.79931 q^{29} +3.93175 q^{30} -1.72114 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.01736 q^{34} -3.93175 q^{35} +1.00000 q^{36} -0.914393 q^{37} -1.64200 q^{38} +1.00000 q^{39} -3.93175 q^{40} -5.26018 q^{41} -1.00000 q^{42} -11.9590 q^{43} +1.00000 q^{44} -3.93175 q^{45} +5.61818 q^{46} +7.48249 q^{47} -1.00000 q^{48} +1.00000 q^{49} +10.4587 q^{50} +1.01736 q^{51} -1.00000 q^{52} +11.7928 q^{53} -1.00000 q^{54} -3.93175 q^{55} +1.00000 q^{56} +1.64200 q^{57} -4.79931 q^{58} -4.53257 q^{59} +3.93175 q^{60} -13.6333 q^{61} -1.72114 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.93175 q^{65} -1.00000 q^{66} -13.9937 q^{67} -1.01736 q^{68} -5.61818 q^{69} -3.93175 q^{70} +3.33093 q^{71} +1.00000 q^{72} +15.0530 q^{73} -0.914393 q^{74} -10.4587 q^{75} -1.64200 q^{76} +1.00000 q^{77} +1.00000 q^{78} +2.84696 q^{79} -3.93175 q^{80} +1.00000 q^{81} -5.26018 q^{82} +16.8424 q^{83} -1.00000 q^{84} +4.00000 q^{85} -11.9590 q^{86} +4.79931 q^{87} +1.00000 q^{88} -4.37809 q^{89} -3.93175 q^{90} -1.00000 q^{91} +5.61818 q^{92} +1.72114 q^{93} +7.48249 q^{94} +6.45594 q^{95} -1.00000 q^{96} +8.56729 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{11} - 6 q^{12} - 6 q^{13} + 6 q^{14} + 6 q^{16} + 6 q^{18} + 2 q^{19} - 6 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 6 q^{26} - 6 q^{27} + 6 q^{28} + 6 q^{29} + 2 q^{31} + 6 q^{32} - 6 q^{33} + 6 q^{36} + 12 q^{37} + 2 q^{38} + 6 q^{39} + 4 q^{41} - 6 q^{42} + 4 q^{43} + 6 q^{44} + 10 q^{46} + 4 q^{47} - 6 q^{48} + 6 q^{49} + 10 q^{50} - 6 q^{52} + 18 q^{53} - 6 q^{54} + 6 q^{56} - 2 q^{57} + 6 q^{58} + 14 q^{59} + 2 q^{62} + 6 q^{63} + 6 q^{64} - 6 q^{66} + 4 q^{67} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 2 q^{73} + 12 q^{74} - 10 q^{75} + 2 q^{76} + 6 q^{77} + 6 q^{78} + 6 q^{79} + 6 q^{81} + 4 q^{82} + 24 q^{83} - 6 q^{84} + 24 q^{85} + 4 q^{86} - 6 q^{87} + 6 q^{88} - 14 q^{89} - 6 q^{91} + 10 q^{92} - 2 q^{93} + 4 q^{94} + 4 q^{95} - 6 q^{96} - 2 q^{97} + 6 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^11 - 6 * q^12 - 6 * q^13 + 6 * q^14 + 6 * q^16 + 6 * q^18 + 2 * q^19 - 6 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 6 * q^26 - 6 * q^27 + 6 * q^28 + 6 * q^29 + 2 * q^31 + 6 * q^32 - 6 * q^33 + 6 * q^36 + 12 * q^37 + 2 * q^38 + 6 * q^39 + 4 * q^41 - 6 * q^42 + 4 * q^43 + 6 * q^44 + 10 * q^46 + 4 * q^47 - 6 * q^48 + 6 * q^49 + 10 * q^50 - 6 * q^52 + 18 * q^53 - 6 * q^54 + 6 * q^56 - 2 * q^57 + 6 * q^58 + 14 * q^59 + 2 * q^62 + 6 * q^63 + 6 * q^64 - 6 * q^66 + 4 * q^67 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 2 * q^73 + 12 * q^74 - 10 * q^75 + 2 * q^76 + 6 * q^77 + 6 * q^78 + 6 * q^79 + 6 * q^81 + 4 * q^82 + 24 * q^83 - 6 * q^84 + 24 * q^85 + 4 * q^86 - 6 * q^87 + 6 * q^88 - 14 * q^89 - 6 * q^91 + 10 * q^92 - 2 * q^93 + 4 * q^94 + 4 * q^95 - 6 * q^96 - 2 * q^97 + 6 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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