LMFDB - Embedded newform 6006.2.a.cf.1.6

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			1.6
Root			$0.597364$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.34804 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.34804 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.34804 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} -3.34804 q^{15} +1.00000 q^{16} +1.19473 q^{17} +1.00000 q^{18} -5.08058 q^{19} +3.34804 q^{20} -1.00000 q^{21} +1.00000 q^{22} +5.00365 q^{23} -1.00000 q^{24} +6.20938 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +0.676479 q^{29} -3.34804 q^{30} -3.96223 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.19473 q^{34} +3.34804 q^{35} +1.00000 q^{36} +4.15331 q^{37} -5.08058 q^{38} +1.00000 q^{39} +3.34804 q^{40} -8.08423 q^{41} -1.00000 q^{42} +12.5295 q^{43} +1.00000 q^{44} +3.34804 q^{45} +5.00365 q^{46} +7.28631 q^{47} -1.00000 q^{48} +1.00000 q^{49} +6.20938 q^{50} -1.19473 q^{51} -1.00000 q^{52} +0.0518562 q^{53} -1.00000 q^{54} +3.34804 q^{55} +1.00000 q^{56} +5.08058 q^{57} +0.676479 q^{58} +1.14966 q^{59} -3.34804 q^{60} +1.74242 q^{61} -3.96223 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.34804 q^{65} -1.00000 q^{66} +14.9190 q^{67} +1.19473 q^{68} -5.00365 q^{69} +3.34804 q^{70} -5.54642 q^{71} +1.00000 q^{72} +6.13609 q^{73} +4.15331 q^{74} -6.20938 q^{75} -5.08058 q^{76} +1.00000 q^{77} +1.00000 q^{78} +5.47739 q^{79} +3.34804 q^{80} +1.00000 q^{81} -8.08423 q^{82} +17.4464 q^{83} -1.00000 q^{84} +4.00000 q^{85} +12.5295 q^{86} -0.676479 q^{87} +1.00000 q^{88} -17.9441 q^{89} +3.34804 q^{90} -1.00000 q^{91} +5.00365 q^{92} +3.96223 q^{93} +7.28631 q^{94} -17.0100 q^{95} -1.00000 q^{96} -1.53912 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.34804	1.49729	0.748645	−	0.662971i	$-0.230705\pi$
$5$	3.34804	1.49729	0.748645	+	0.662971i	$0.230705\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.34804	1.05874
$11$	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
$15$	−3.34804	−0.864460
$16$	1.00000	0.250000
$17$	1.19473	0.289764	0.144882	−	0.989449i	$-0.453720\pi$
$17$	1.19473	0.289764	0.144882	+	0.989449i	$0.453720\pi$
$18$	1.00000	0.235702
$19$	−5.08058	−1.16557	−0.582783	−	0.812628i	$-0.698036\pi$
$19$	−5.08058	−1.16557	−0.582783	+	0.812628i	$0.698036\pi$
$20$	3.34804	0.748645
$21$	−1.00000	−0.218218
$22$	1.00000	0.213201
$23$	5.00365	1.04333	0.521666	−	0.853150i	$-0.325311\pi$
$23$	5.00365	1.04333	0.521666	+	0.853150i	$0.325311\pi$
$24$	−1.00000	−0.204124
$25$	6.20938	1.24188
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	0.676479	0.125619	0.0628095	−	0.998026i	$-0.479994\pi$
$29$	0.676479	0.125619	0.0628095	+	0.998026i	$0.479994\pi$
$30$	−3.34804	−0.611266
$31$	−3.96223	−0.711638	−0.355819	−	0.934555i	$-0.615798\pi$
$31$	−3.96223	−0.711638	−0.355819	+	0.934555i	$0.615798\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.19473	0.204894
$35$	3.34804	0.565922
$36$	1.00000	0.166667
$37$	4.15331	0.682800	0.341400	−	0.939918i	$-0.389099\pi$
$37$	4.15331	0.682800	0.341400	+	0.939918i	$0.389099\pi$
$38$	−5.08058	−0.824180
$39$	1.00000	0.160128
$40$	3.34804	0.529372
$41$	−8.08423	−1.26255	−0.631273	−	0.775561i	$-0.717467\pi$
$41$	−8.08423	−1.26255	−0.631273	+	0.775561i	$0.717467\pi$
$42$	−1.00000	−0.154303
$43$	12.5295	1.91073	0.955367	−	0.295421i	$-0.0954601\pi$
$43$	12.5295	1.91073	0.955367	+	0.295421i	$0.0954601\pi$
$44$	1.00000	0.150756
$45$	3.34804	0.499096
$46$	5.00365	0.737748
$47$	7.28631	1.06282	0.531409	−	0.847115i	$-0.321663\pi$
$47$	7.28631	1.06282	0.531409	+	0.847115i	$0.321663\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	6.20938	0.878138
$51$	−1.19473	−0.167295
$52$	−1.00000	−0.138675
$53$	0.0518562	0.00712300	0.00356150	−	0.999994i	$-0.498866\pi$
$53$	0.0518562	0.00712300	0.00356150	+	0.999994i	$0.498866\pi$
$54$	−1.00000	−0.136083
$55$	3.34804	0.451450
$56$	1.00000	0.133631
$57$	5.08058	0.672940
$58$	0.676479	0.0888261
$59$	1.14966	0.149673	0.0748367	−	0.997196i	$-0.476156\pi$
$59$	1.14966	0.149673	0.0748367	+	0.997196i	$0.476156\pi$
$60$	−3.34804	−0.432230
$61$	1.74242	0.223094	0.111547	−	0.993759i	$-0.464420\pi$
$61$	1.74242	0.223094	0.111547	+	0.993759i	$0.464420\pi$
$62$	−3.96223	−0.503204
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−3.34804	−0.415273
$66$	−1.00000	−0.123091
$67$	14.9190	1.82264	0.911322	−	0.411695i	$-0.135063\pi$
$67$	14.9190	1.82264	0.911322	+	0.411695i	$0.135063\pi$
$68$	1.19473	0.144882
$69$	−5.00365	−0.602368
$70$	3.34804	0.400167
$71$	−5.54642	−0.658239	−0.329119	−	0.944288i	$-0.606752\pi$
$71$	−5.54642	−0.658239	−0.329119	+	0.944288i	$0.606752\pi$
$72$	1.00000	0.117851
$73$	6.13609	0.718175	0.359087	−	0.933304i	$-0.383088\pi$
$73$	6.13609	0.718175	0.359087	+	0.933304i	$0.383088\pi$
$74$	4.15331	0.482813
$75$	−6.20938	−0.716997
$76$	−5.08058	−0.582783
$77$	1.00000	0.113961
$78$	1.00000	0.113228
$79$	5.47739	0.616255	0.308127	−	0.951345i	$-0.400298\pi$
$79$	5.47739	0.616255	0.308127	+	0.951345i	$0.400298\pi$
$80$	3.34804	0.374322
$81$	1.00000	0.111111
$82$	−8.08423	−0.892754
$83$	17.4464	1.91499	0.957493	−	0.288455i	$-0.0931415\pi$
$83$	17.4464	1.91499	0.957493	+	0.288455i	$0.0931415\pi$
$84$	−1.00000	−0.109109
$85$	4.00000	0.433861
$86$	12.5295	1.35109
$87$	−0.676479	−0.0725262
$88$	1.00000	0.106600
$89$	−17.9441	−1.90207	−0.951034	−	0.309088i	$-0.899976\pi$
$89$	−17.9441	−1.90207	−0.951034	+	0.309088i	$0.899976\pi$
$90$	3.34804	0.352914
$91$	−1.00000	−0.104828
$92$	5.00365	0.521666
$93$	3.96223	0.410864
$94$	7.28631	0.751526
$95$	−17.0100	−1.74519
$96$	−1.00000	−0.102062
$97$	−1.53912	−0.156274	−0.0781370	−	0.996943i	$-0.524897\pi$
$97$	−1.53912	−0.156274	−0.0781370	+	0.996943i	$0.524897\pi$
$98$	1.00000	0.101015
$99$	1.00000	0.100504
$100$	6.20938	0.620938
$101$	4.77981	0.475609	0.237804	−	0.971313i	$-0.423572\pi$
$101$	4.77981	0.475609	0.237804	+	0.971313i	$0.423572\pi$
$102$	−1.19473	−0.118296
$103$	−7.28631	−0.717942	−0.358971	−	0.933349i	$-0.616872\pi$
$103$	−7.28631	−0.717942	−0.358971	+	0.933349i	$0.616872\pi$
$104$	−1.00000	−0.0980581
$105$	−3.34804	−0.326735
$106$	0.0518562	0.00503672
$107$	−5.05269	−0.488462	−0.244231	−	0.969717i	$-0.578535\pi$
$107$	−5.05269	−0.488462	−0.244231	+	0.969717i	$0.578535\pi$
$108$	−1.00000	−0.0962250
$109$	−5.92446	−0.567461	−0.283730	−	0.958904i	$-0.591572\pi$
$109$	−5.92446	−0.567461	−0.283730	+	0.958904i	$0.591572\pi$
$110$	3.34804	0.319223
$111$	−4.15331	−0.394215
$112$	1.00000	0.0944911
$113$	−8.84995	−0.832534	−0.416267	−	0.909243i	$-0.636662\pi$
$113$	−8.84995	−0.832534	−0.416267	+	0.909243i	$0.636662\pi$
$114$	5.08058	0.475840
$115$	16.7524	1.56217
$116$	0.676479	0.0628095
$117$	−1.00000	−0.0924500
$118$	1.14966	0.105835
$119$	1.19473	0.109521
$120$	−3.34804	−0.305633
$121$	1.00000	0.0909091
$122$	1.74242	0.157751
$123$	8.08423	0.728931
$124$	−3.96223	−0.355819
$125$	4.04904	0.362157
$126$	1.00000	0.0890871
$127$	−3.63744	−0.322771	−0.161385	−	0.986891i	$-0.551596\pi$
$127$	−3.63744	−0.322771	−0.161385	+	0.986891i	$0.551596\pi$
$128$	1.00000	0.0883883
$129$	−12.5295	−1.10316
$130$	−3.34804	−0.293643
$131$	15.4469	1.34960	0.674802	−	0.737999i	$-0.264229\pi$
$131$	15.4469	1.34960	0.674802	+	0.737999i	$0.264229\pi$
$132$	−1.00000	−0.0870388
$133$	−5.08058	−0.440543
$134$	14.9190	1.28880
$135$	−3.34804	−0.288153
$136$	1.19473	0.102447
$137$	0.830735	0.0709745	0.0354872	−	0.999370i	$-0.488702\pi$
$137$	0.830735	0.0709745	0.0354872	+	0.999370i	$0.488702\pi$
$138$	−5.00365	−0.425939
$139$	18.9238	1.60509	0.802546	−	0.596590i	$-0.203478\pi$
$139$	18.9238	1.60509	0.802546	+	0.596590i	$0.203478\pi$
$140$	3.34804	0.282961
$141$	−7.28631	−0.613618
$142$	−5.54642	−0.465445
$143$	−1.00000	−0.0836242
$144$	1.00000	0.0833333
$145$	2.26488	0.188088
$146$	6.13609	0.507826
$147$	−1.00000	−0.0824786
$148$	4.15331	0.341400
$149$	−21.2976	−1.74477	−0.872385	−	0.488820i	$-0.837427\pi$
$149$	−21.2976	−1.74477	−0.872385	+	0.488820i	$0.837427\pi$
$150$	−6.20938	−0.506993
$151$	−7.41117	−0.603112	−0.301556	−	0.953448i	$-0.597506\pi$
$151$	−7.41117	−0.603112	−0.301556	+	0.953448i	$0.597506\pi$
$152$	−5.08058	−0.412090
$153$	1.19473	0.0965881
$154$	1.00000	0.0805823
$155$	−13.2657	−1.06553
$156$	1.00000	0.0800641
$157$	−1.40977	−0.112512	−0.0562559	−	0.998416i	$-0.517916\pi$
$157$	−1.40977	−0.112512	−0.0562559	+	0.998416i	$0.517916\pi$
$158$	5.47739	0.435758
$159$	−0.0518562	−0.00411247
$160$	3.34804	0.264686
$161$	5.00365	0.394343
$162$	1.00000	0.0785674
$163$	−4.32773	−0.338974	−0.169487	−	0.985532i	$-0.554211\pi$
$163$	−4.32773	−0.338974	−0.169487	+	0.985532i	$0.554211\pi$
$164$	−8.08423	−0.631273
$165$	−3.34804	−0.260645
$166$	17.4464	1.35410
$167$	17.5233	1.35599	0.677997	−	0.735065i	$-0.262848\pi$
$167$	17.5233	1.35599	0.677997	+	0.735065i	$0.262848\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	4.00000	0.306786
$171$	−5.08058	−0.388522
$172$	12.5295	0.955367
$173$	3.57586	0.271867	0.135934	−	0.990718i	$-0.456597\pi$
$173$	3.57586	0.271867	0.135934	+	0.990718i	$0.456597\pi$
$174$	−0.676479	−0.0512838
$175$	6.20938	0.469385
$176$	1.00000	0.0753778
$177$	−1.14966	−0.0864140
$178$	−17.9441	−1.34496
$179$	−10.1630	−0.759621	−0.379811	−	0.925064i	$-0.624011\pi$
$179$	−10.1630	−0.759621	−0.379811	+	0.925064i	$0.624011\pi$
$180$	3.34804	0.249548
$181$	−14.7803	−1.09861	−0.549306	−	0.835621i	$-0.685108\pi$
$181$	−14.7803	−1.09861	−0.549306	+	0.835621i	$0.685108\pi$
$182$	−1.00000	−0.0741249
$183$	−1.74242	−0.128803
$184$	5.00365	0.368874
$185$	13.9055	1.02235
$186$	3.96223	0.290525
$187$	1.19473	0.0873672
$188$	7.28631	0.531409
$189$	−1.00000	−0.0727393
$190$	−17.0100	−1.23404
$191$	10.3566	0.749378	0.374689	−	0.927151i	$-0.377750\pi$
$191$	10.3566	0.749378	0.374689	+	0.927151i	$0.377750\pi$
$192$	−1.00000	−0.0721688
$193$	19.3396	1.39209	0.696046	−	0.717997i	$-0.254941\pi$
$193$	19.3396	1.39209	0.696046	+	0.717997i	$0.254941\pi$
$194$	−1.53912	−0.110502
$195$	3.34804	0.239758
$196$	1.00000	0.0714286
$197$	14.1410	1.00751	0.503754	−	0.863847i	$-0.331952\pi$
$197$	14.1410	1.00751	0.503754	+	0.863847i	$0.331952\pi$
$198$	1.00000	0.0710669
$199$	−6.03332	−0.427691	−0.213845	−	0.976868i	$-0.568599\pi$
$199$	−6.03332	−0.427691	−0.213845	+	0.976868i	$0.568599\pi$
$200$	6.20938	0.439069
$201$	−14.9190	−1.05230
$202$	4.77981	0.336306
$203$	0.676479	0.0474796
$204$	−1.19473	−0.0836477
$205$	−27.0663	−1.89040
$206$	−7.28631	−0.507661
$207$	5.00365	0.347778
$208$	−1.00000	−0.0693375
$209$	−5.08058	−0.351431
$210$	−3.34804	−0.231037
$211$	−11.9946	−0.825743	−0.412871	−	0.910789i	$-0.635474\pi$
$211$	−11.9946	−0.825743	−0.412871	+	0.910789i	$0.635474\pi$
$212$	0.0518562	0.00356150
$213$	5.54642	0.380034
$214$	−5.05269	−0.345395
$215$	41.9493	2.86092
$216$	−1.00000	−0.0680414
$217$	−3.96223	−0.268974
$218$	−5.92446	−0.401255
$219$	−6.13609	−0.414638
$220$	3.34804	0.225725
$221$	−1.19473	−0.0803661
$222$	−4.15331	−0.278752
$223$	−18.3810	−1.23088	−0.615441	−	0.788183i	$-0.711022\pi$
$223$	−18.3810	−1.23088	−0.615441	+	0.788183i	$0.711022\pi$
$224$	1.00000	0.0668153
$225$	6.20938	0.413958
$226$	−8.84995	−0.588690
$227$	4.22782	0.280610	0.140305	−	0.990108i	$-0.455192\pi$
$227$	4.22782	0.280610	0.140305	+	0.990108i	$0.455192\pi$
$228$	5.08058	0.336470
$229$	1.35717	0.0896846	0.0448423	−	0.998994i	$-0.485721\pi$
$229$	1.35717	0.0896846	0.0448423	+	0.998994i	$0.485721\pi$
$230$	16.7524	1.10462
$231$	−1.00000	−0.0657952
$232$	0.676479	0.0444131
$233$	−25.8471	−1.69330	−0.846650	−	0.532151i	$-0.821384\pi$
$233$	−25.8471	−1.69330	−0.846650	+	0.532151i	$0.821384\pi$
$234$	−1.00000	−0.0653720
$235$	24.3949	1.59135
$236$	1.14966	0.0748367
$237$	−5.47739	−0.355795
$238$	1.19473	0.0774428
$239$	29.4412	1.90439	0.952197	−	0.305486i	$-0.0988189\pi$
$239$	29.4412	1.90439	0.952197	+	0.305486i	$0.0988189\pi$
$240$	−3.34804	−0.216115
$241$	22.2342	1.43223	0.716114	−	0.697983i	$-0.245919\pi$
$241$	22.2342	1.43223	0.716114	+	0.697983i	$0.245919\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.74242	0.111547
$245$	3.34804	0.213898
$246$	8.08423	0.515432
$247$	5.08058	0.323270
$248$	−3.96223	−0.251602
$249$	−17.4464	−1.10562
$250$	4.04904	0.256084
$251$	−23.4288	−1.47881	−0.739405	−	0.673261i	$-0.764893\pi$
$251$	−23.4288	−1.47881	−0.739405	+	0.673261i	$0.764893\pi$
$252$	1.00000	0.0629941
$253$	5.00365	0.314577
$254$	−3.63744	−0.228233
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	−24.9136	−1.55407	−0.777033	−	0.629459i	$-0.783276\pi$
$257$	−24.9136	−1.55407	−0.777033	+	0.629459i	$0.783276\pi$
$258$	−12.5295	−0.780054
$259$	4.15331	0.258074
$260$	−3.34804	−0.207637
$261$	0.676479	0.0418730
$262$	15.4469	0.954314
$263$	9.39367	0.579238	0.289619	−	0.957142i	$-0.406471\pi$
$263$	9.39367	0.579238	0.289619	+	0.957142i	$0.406471\pi$
$264$	−1.00000	−0.0615457
$265$	0.173617	0.0106652
$266$	−5.08058	−0.311511
$267$	17.9441	1.09816
$268$	14.9190	0.911322
$269$	−21.0351	−1.28253	−0.641266	−	0.767319i	$-0.721590\pi$
$269$	−21.0351	−1.28253	−0.641266	+	0.767319i	$0.721590\pi$
$270$	−3.34804	−0.203755
$271$	−32.5769	−1.97891	−0.989453	−	0.144852i	$-0.953729\pi$
$271$	−32.5769	−1.97891	−0.989453	+	0.144852i	$0.953729\pi$
$272$	1.19473	0.0724411
$273$	1.00000	0.0605228
$274$	0.830735	0.0501865
$275$	6.20938	0.374439
$276$	−5.00365	−0.301184
$277$	−2.53642	−0.152398	−0.0761992	−	0.997093i	$-0.524278\pi$
$277$	−2.53642	−0.152398	−0.0761992	+	0.997093i	$0.524278\pi$
$278$	18.9238	1.13497
$279$	−3.96223	−0.237213
$280$	3.34804	0.200084
$281$	−15.4068	−0.919090	−0.459545	−	0.888154i	$-0.651988\pi$
$281$	−15.4068	−0.919090	−0.459545	+	0.888154i	$0.651988\pi$
$282$	−7.28631	−0.433894
$283$	6.06650	0.360616	0.180308	−	0.983610i	$-0.442291\pi$
$283$	6.06650	0.360616	0.180308	+	0.983610i	$0.442291\pi$
$284$	−5.54642	−0.329119
$285$	17.0100	1.00759
$286$	−1.00000	−0.0591312
$287$	−8.08423	−0.477197
$288$	1.00000	0.0589256
$289$	−15.5726	−0.916037
$290$	2.26488	0.132998
$291$	1.53912	0.0902249
$292$	6.13609	0.359087
$293$	−5.53762	−0.323511	−0.161756	−	0.986831i	$-0.551716\pi$
$293$	−5.53762	−0.323511	−0.161756	+	0.986831i	$0.551716\pi$
$294$	−1.00000	−0.0583212
$295$	3.84912	0.224104
$296$	4.15331	0.241406
$297$	−1.00000	−0.0580259
$298$	−21.2976	−1.23374
$299$	−5.00365	−0.289368
$300$	−6.20938	−0.358498
$301$	12.5295	0.722190
$302$	−7.41117	−0.426465
$303$	−4.77981	−0.274593
$304$	−5.08058	−0.291391
$305$	5.83368	0.334036
$306$	1.19473	0.0682981
$307$	3.12420	0.178308	0.0891538	−	0.996018i	$-0.471584\pi$
$307$	3.12420	0.178308	0.0891538	+	0.996018i	$0.471584\pi$
$308$	1.00000	0.0569803
$309$	7.28631	0.414504
$310$	−13.2657	−0.753442
$311$	−9.91041	−0.561968	−0.280984	−	0.959712i	$-0.590661\pi$
$311$	−9.91041	−0.561968	−0.280984	+	0.959712i	$0.590661\pi$
$312$	1.00000	0.0566139
$313$	−22.2410	−1.25714	−0.628568	−	0.777755i	$-0.716359\pi$
$313$	−22.2410	−1.25714	−0.628568	+	0.777755i	$0.716359\pi$
$314$	−1.40977	−0.0795579
$315$	3.34804	0.188641
$316$	5.47739	0.308127
$317$	29.9452	1.68189	0.840945	−	0.541121i	$-0.182000\pi$
$317$	29.9452	1.68189	0.840945	+	0.541121i	$0.182000\pi$
$318$	−0.0518562	−0.00290795
$319$	0.676479	0.0378756
$320$	3.34804	0.187161
$321$	5.05269	0.282014
$322$	5.00365	0.278842
$323$	−6.06992	−0.337739
$324$	1.00000	0.0555556
$325$	−6.20938	−0.344434
$326$	−4.32773	−0.239691
$327$	5.92446	0.327624
$328$	−8.08423	−0.446377
$329$	7.28631	0.401707
$330$	−3.34804	−0.184304
$331$	−5.44659	−0.299372	−0.149686	−	0.988734i	$-0.547826\pi$
$331$	−5.44659	−0.299372	−0.149686	+	0.988734i	$0.547826\pi$
$332$	17.4464	0.957493
$333$	4.15331	0.227600
$334$	17.5233	0.958832
$335$	49.9493	2.72902
$336$	−1.00000	−0.0545545
$337$	22.9063	1.24779	0.623893	−	0.781510i	$-0.285550\pi$
$337$	22.9063	1.24779	0.623893	+	0.781510i	$0.285550\pi$
$338$	1.00000	0.0543928
$339$	8.84995	0.480663
$340$	4.00000	0.216930
$341$	−3.96223	−0.214567
$342$	−5.08058	−0.274727
$343$	1.00000	0.0539949
$344$	12.5295	0.675547
$345$	−16.7524	−0.901920
$346$	3.57586	0.192239
$347$	−14.1185	−0.757920	−0.378960	−	0.925413i	$-0.623718\pi$
$347$	−14.1185	−0.757920	−0.378960	+	0.925413i	$0.623718\pi$
$348$	−0.676479	−0.0362631
$349$	20.5989	1.10264	0.551318	−	0.834295i	$-0.314125\pi$
$349$	20.5989	1.10264	0.551318	+	0.834295i	$0.314125\pi$
$350$	6.20938	0.331905
$351$	1.00000	0.0533761
$352$	1.00000	0.0533002
$353$	26.9259	1.43312	0.716560	−	0.697525i	$-0.245715\pi$
$353$	26.9259	1.43312	0.716560	+	0.697525i	$0.245715\pi$
$354$	−1.14966	−0.0611039
$355$	−18.5696	−0.985574
$356$	−17.9441	−0.951034
$357$	−1.19473	−0.0632317
$358$	−10.1630	−0.537133
$359$	37.2822	1.96768	0.983839	−	0.179055i	$-0.0573039\pi$
$359$	37.2822	1.96768	0.983839	+	0.179055i	$0.0573039\pi$
$360$	3.34804	0.176457
$361$	6.81234	0.358544
$362$	−14.7803	−0.776836
$363$	−1.00000	−0.0524864
$364$	−1.00000	−0.0524142
$365$	20.5439	1.07532
$366$	−1.74242	−0.0910776
$367$	25.3526	1.32339	0.661696	−	0.749772i	$-0.269837\pi$
$367$	25.3526	1.32339	0.661696	+	0.749772i	$0.269837\pi$
$368$	5.00365	0.260833
$369$	−8.08423	−0.420848
$370$	13.9055	0.722910
$371$	0.0518562	0.00269224
$372$	3.96223	0.205432
$373$	28.7103	1.48656	0.743281	−	0.668979i	$-0.233268\pi$
$373$	28.7103	1.48656	0.743281	+	0.668979i	$0.233268\pi$
$374$	1.19473	0.0617779
$375$	−4.04904	−0.209092
$376$	7.28631	0.375763
$377$	−0.676479	−0.0348405
$378$	−1.00000	−0.0514344
$379$	−3.44510	−0.176963	−0.0884815	−	0.996078i	$-0.528201\pi$
$379$	−3.44510	−0.176963	−0.0884815	+	0.996078i	$0.528201\pi$
$380$	−17.0100	−0.872595
$381$	3.63744	0.186352
$382$	10.3566	0.529890
$383$	−9.61886	−0.491501	−0.245750	−	0.969333i	$-0.579034\pi$
$383$	−9.61886	−0.491501	−0.245750	+	0.969333i	$0.579034\pi$
$384$	−1.00000	−0.0510310
$385$	3.34804	0.170632
$386$	19.3396	0.984358
$387$	12.5295	0.636911
$388$	−1.53912	−0.0781370
$389$	−20.3969	−1.03417	−0.517083	−	0.855935i	$-0.672982\pi$
$389$	−20.3969	−1.03417	−0.517083	+	0.855935i	$0.672982\pi$
$390$	3.34804	0.169535
$391$	5.97800	0.302321
$392$	1.00000	0.0505076
$393$	−15.4469	−0.779194
$394$	14.1410	0.712415
$395$	18.3385	0.922712
$396$	1.00000	0.0502519
$397$	−20.7764	−1.04274	−0.521368	−	0.853332i	$-0.674578\pi$
$397$	−20.7764	−1.04274	−0.521368	+	0.853332i	$0.674578\pi$
$398$	−6.03332	−0.302423
$399$	5.08058	0.254347
$400$	6.20938	0.310469
$401$	8.42414	0.420682	0.210341	−	0.977628i	$-0.432543\pi$
$401$	8.42414	0.420682	0.210341	+	0.977628i	$0.432543\pi$
$402$	−14.9190	−0.744091
$403$	3.96223	0.197373
$404$	4.77981	0.237804
$405$	3.34804	0.166365
$406$	0.676479	0.0335731
$407$	4.15331	0.205872
$408$	−1.19473	−0.0591479
$409$	−20.6383	−1.02050	−0.510250	−	0.860026i	$-0.670447\pi$
$409$	−20.6383	−1.02050	−0.510250	+	0.860026i	$0.670447\pi$
$410$	−27.0663	−1.33671
$411$	−0.830735	−0.0409771
$412$	−7.28631	−0.358971
$413$	1.14966	0.0565712
$414$	5.00365	0.245916
$415$	58.4111	2.86729
$416$	−1.00000	−0.0490290
$417$	−18.9238	−0.926700
$418$	−5.08058	−0.248499
$419$	−6.33853	−0.309657	−0.154829	−	0.987941i	$-0.549483\pi$
$419$	−6.33853	−0.309657	−0.154829	+	0.987941i	$0.549483\pi$
$420$	−3.34804	−0.163368
$421$	32.5284	1.58534	0.792669	−	0.609652i	$-0.208691\pi$
$421$	32.5284	1.58534	0.792669	+	0.609652i	$0.208691\pi$
$422$	−11.9946	−0.583888
$423$	7.28631	0.354273
$424$	0.0518562	0.00251836
$425$	7.41852	0.359851
$426$	5.54642	0.268725
$427$	1.74242	0.0843214
$428$	−5.05269	−0.244231
$429$	1.00000	0.0482805
$430$	41.9493	2.02298
$431$	−22.2660	−1.07252	−0.536258	−	0.844054i	$-0.680162\pi$
$431$	−22.2660	−1.07252	−0.536258	+	0.844054i	$0.680162\pi$
$432$	−1.00000	−0.0481125
$433$	16.8136	0.808011	0.404006	−	0.914757i	$-0.367618\pi$
$433$	16.8136	0.808011	0.404006	+	0.914757i	$0.367618\pi$
$434$	−3.96223	−0.190193
$435$	−2.26488	−0.108593
$436$	−5.92446	−0.283730
$437$	−25.4215	−1.21607
$438$	−6.13609	−0.293194
$439$	−3.07285	−0.146659	−0.0733296	−	0.997308i	$-0.523362\pi$
$439$	−3.07285	−0.146659	−0.0733296	+	0.997308i	$0.523362\pi$
$440$	3.34804	0.159612
$441$	1.00000	0.0476190
$442$	−1.19473	−0.0568274
$443$	−9.00009	−0.427607	−0.213804	−	0.976877i	$-0.568585\pi$
$443$	−9.00009	−0.427607	−0.213804	+	0.976877i	$0.568585\pi$
$444$	−4.15331	−0.197107
$445$	−60.0775	−2.84794
$446$	−18.3810	−0.870365
$447$	21.2976	1.00734
$448$	1.00000	0.0472456
$449$	26.6541	1.25788	0.628942	−	0.777452i	$-0.283488\pi$
$449$	26.6541	1.25788	0.628942	+	0.777452i	$0.283488\pi$
$450$	6.20938	0.292713
$451$	−8.08423	−0.380672
$452$	−8.84995	−0.416267
$453$	7.41117	0.348207
$454$	4.22782	0.198421
$455$	−3.34804	−0.156959
$456$	5.08058	0.237920
$457$	−12.9277	−0.604734	−0.302367	−	0.953192i	$-0.597777\pi$
$457$	−12.9277	−0.604734	−0.302367	+	0.953192i	$0.597777\pi$
$458$	1.35717	0.0634166
$459$	−1.19473	−0.0557652
$460$	16.7524	0.781086
$461$	−26.3703	−1.22819	−0.614093	−	0.789234i	$-0.710478\pi$
$461$	−26.3703	−1.22819	−0.614093	+	0.789234i	$0.710478\pi$
$462$	−1.00000	−0.0465242
$463$	26.9550	1.25271	0.626353	−	0.779540i	$-0.284547\pi$
$463$	26.9550	1.25271	0.626353	+	0.779540i	$0.284547\pi$
$464$	0.676479	0.0314048
$465$	13.2657	0.615183
$466$	−25.8471	−1.19734
$467$	17.3873	0.804588	0.402294	−	0.915510i	$-0.368213\pi$
$467$	17.3873	0.804588	0.402294	+	0.915510i	$0.368213\pi$
$468$	−1.00000	−0.0462250
$469$	14.9190	0.688894
$470$	24.3949	1.12525
$471$	1.40977	0.0649588
$472$	1.14966	0.0529176
$473$	12.5295	0.576108
$474$	−5.47739	−0.251585
$475$	−31.5473	−1.44749
$476$	1.19473	0.0547603
$477$	0.0518562	0.00237433
$478$	29.4412	1.34661
$479$	16.6543	0.760956	0.380478	−	0.924790i	$-0.375759\pi$
$479$	16.6543	0.760956	0.380478	+	0.924790i	$0.375759\pi$
$480$	−3.34804	−0.152816
$481$	−4.15331	−0.189375
$482$	22.2342	1.01274
$483$	−5.00365	−0.227674
$484$	1.00000	0.0454545
$485$	−5.15304	−0.233987
$486$	−1.00000	−0.0453609
$487$	−19.3028	−0.874695	−0.437347	−	0.899293i	$-0.644082\pi$
$487$	−19.3028	−0.874695	−0.437347	+	0.899293i	$0.644082\pi$
$488$	1.74242	0.0788755
$489$	4.32773	0.195707
$490$	3.34804	0.151249
$491$	24.1591	1.09029	0.545143	−	0.838343i	$-0.316476\pi$
$491$	24.1591	1.09029	0.545143	+	0.838343i	$0.316476\pi$
$492$	8.08423	0.364465
$493$	0.808209	0.0363999
$494$	5.08058	0.228586
$495$	3.34804	0.150483
$496$	−3.96223	−0.177909
$497$	−5.54642	−0.248791
$498$	−17.4464	−0.781790
$499$	−27.8154	−1.24519	−0.622593	−	0.782546i	$-0.713921\pi$
$499$	−27.8154	−1.24519	−0.622593	+	0.782546i	$0.713921\pi$
$500$	4.04904	0.181079
$501$	−17.5233	−0.782883
$502$	−23.4288	−1.04568
$503$	−43.7697	−1.95160	−0.975798	−	0.218676i	$-0.929826\pi$
$503$	−43.7697	−1.95160	−0.975798	+	0.218676i	$0.929826\pi$
$504$	1.00000	0.0445435
$505$	16.0030	0.712124
$506$	5.00365	0.222439
$507$	−1.00000	−0.0444116
$508$	−3.63744	−0.161385
$509$	−18.5593	−0.822626	−0.411313	−	0.911494i	$-0.634930\pi$
$509$	−18.5593	−0.822626	−0.411313	+	0.911494i	$0.634930\pi$
$510$	−4.00000	−0.177123
$511$	6.13609	0.271445
$512$	1.00000	0.0441942
$513$	5.08058	0.224313
$514$	−24.9136	−1.09889
$515$	−24.3949	−1.07497
$516$	−12.5295	−0.551581
$517$	7.28631	0.320452
$518$	4.15331	0.182486
$519$	−3.57586	−0.156963
$520$	−3.34804	−0.146821
$521$	44.7245	1.95942	0.979708	−	0.200430i	$-0.0642340\pi$
$521$	44.7245	1.95942	0.979708	+	0.200430i	$0.0642340\pi$
$522$	0.676479	0.0296087
$523$	14.7846	0.646485	0.323242	−	0.946316i	$-0.395227\pi$
$523$	14.7846	0.646485	0.323242	+	0.946316i	$0.395227\pi$
$524$	15.4469	0.674802
$525$	−6.20938	−0.270999
$526$	9.39367	0.409583
$527$	−4.73379	−0.206207
$528$	−1.00000	−0.0435194
$529$	2.03650	0.0885434
$530$	0.173617	0.00754143
$531$	1.14966	0.0498911
$532$	−5.08058	−0.220271
$533$	8.08423	0.350167
$534$	17.9441	0.776516
$535$	−16.9166	−0.731369
$536$	14.9190	0.644402
$537$	10.1630	0.438568
$538$	−21.0351	−0.906887
$539$	1.00000	0.0430730
$540$	−3.34804	−0.144077
$541$	−5.70808	−0.245409	−0.122705	−	0.992443i	$-0.539157\pi$
$541$	−5.70808	−0.245409	−0.122705	+	0.992443i	$0.539157\pi$
$542$	−32.5769	−1.39930
$543$	14.7803	0.634284
$544$	1.19473	0.0512236
$545$	−19.8353	−0.849653
$546$	1.00000	0.0427960
$547$	−13.3231	−0.569656	−0.284828	−	0.958579i	$-0.591937\pi$
$547$	−13.3231	−0.569656	−0.284828	+	0.958579i	$0.591937\pi$
$548$	0.830735	0.0354872
$549$	1.74242	0.0743645
$550$	6.20938	0.264769
$551$	−3.43691	−0.146417
$552$	−5.00365	−0.212969
$553$	5.47739	0.232922
$554$	−2.53642	−0.107762
$555$	−13.9055	−0.590254
$556$	18.9238	0.802546
$557$	−25.6277	−1.08588	−0.542941	−	0.839771i	$-0.682689\pi$
$557$	−25.6277	−1.08588	−0.542941	+	0.839771i	$0.682689\pi$
$558$	−3.96223	−0.167735
$559$	−12.5295	−0.529942
$560$	3.34804	0.141481
$561$	−1.19473	−0.0504415
$562$	−15.4068	−0.649895
$563$	−40.8900	−1.72331	−0.861654	−	0.507496i	$-0.830571\pi$
$563$	−40.8900	−1.72331	−0.861654	+	0.507496i	$0.830571\pi$
$564$	−7.28631	−0.306809
$565$	−29.6300	−1.24654
$566$	6.06650	0.254994
$567$	1.00000	0.0419961
$568$	−5.54642	−0.232723
$569$	41.0839	1.72233	0.861163	−	0.508329i	$-0.169737\pi$
$569$	41.0839	1.72233	0.861163	+	0.508329i	$0.169737\pi$
$570$	17.0100	0.712471
$571$	31.7408	1.32831	0.664155	−	0.747595i	$-0.268792\pi$
$571$	31.7408	1.32831	0.664155	+	0.747595i	$0.268792\pi$
$572$	−1.00000	−0.0418121
$573$	−10.3566	−0.432653
$574$	−8.08423	−0.337429
$575$	31.0695	1.29569
$576$	1.00000	0.0416667
$577$	6.24250	0.259879	0.129939	−	0.991522i	$-0.458522\pi$
$577$	6.24250	0.259879	0.129939	+	0.991522i	$0.458522\pi$
$578$	−15.5726	−0.647736
$579$	−19.3396	−0.803725
$580$	2.26488	0.0940441
$581$	17.4464	0.723797
$582$	1.53912	0.0637986
$583$	0.0518562	0.00214766
$584$	6.13609	0.253913
$585$	−3.34804	−0.138424
$586$	−5.53762	−0.228757
$587$	0.872334	0.0360051	0.0180025	−	0.999838i	$-0.494269\pi$
$587$	0.872334	0.0360051	0.0180025	+	0.999838i	$0.494269\pi$
$588$	−1.00000	−0.0412393
$589$	20.1305	0.829461
$590$	3.84912	0.158466
$591$	−14.1410	−0.581685
$592$	4.15331	0.170700
$593$	43.9785	1.80598	0.902991	−	0.429660i	$-0.141367\pi$
$593$	43.9785	1.80598	0.902991	+	0.429660i	$0.141367\pi$
$594$	−1.00000	−0.0410305
$595$	4.00000	0.163984
$596$	−21.2976	−0.872385
$597$	6.03332	0.246927
$598$	−5.00365	−0.204614
$599$	−12.8852	−0.526476	−0.263238	−	0.964731i	$-0.584791\pi$
$599$	−12.8852	−0.526476	−0.263238	+	0.964731i	$0.584791\pi$
$600$	−6.20938	−0.253497
$601$	−2.68401	−0.109483	−0.0547415	−	0.998501i	$-0.517433\pi$
$601$	−2.68401	−0.109483	−0.0547415	+	0.998501i	$0.517433\pi$
$602$	12.5295	0.510665
$603$	14.9190	0.607548
$604$	−7.41117	−0.301556
$605$	3.34804	0.136117
$606$	−4.77981	−0.194166
$607$	−27.8518	−1.13047	−0.565234	−	0.824931i	$-0.691214\pi$
$607$	−27.8518	−1.13047	−0.565234	+	0.824931i	$0.691214\pi$
$608$	−5.08058	−0.206045
$609$	−0.676479	−0.0274123
$610$	5.83368	0.236199
$611$	−7.28631	−0.294773
$612$	1.19473	0.0482940
$613$	−39.0100	−1.57560	−0.787800	−	0.615932i	$-0.788780\pi$
$613$	−39.0100	−1.57560	−0.787800	+	0.615932i	$0.788780\pi$
$614$	3.12420	0.126082
$615$	27.0663	1.09142
$616$	1.00000	0.0402911
$617$	23.0546	0.928143	0.464072	−	0.885798i	$-0.346388\pi$
$617$	23.0546	0.928143	0.464072	+	0.885798i	$0.346388\pi$
$618$	7.28631	0.293098
$619$	−22.8684	−0.919160	−0.459580	−	0.888136i	$-0.652000\pi$
$619$	−22.8684	−0.919160	−0.459580	+	0.888136i	$0.652000\pi$
$620$	−13.2657	−0.532764
$621$	−5.00365	−0.200789
$622$	−9.91041	−0.397371
$623$	−17.9441	−0.718914
$624$	1.00000	0.0400320
$625$	−17.4905	−0.699621
$626$	−22.2410	−0.888929
$627$	5.08058	0.202899
$628$	−1.40977	−0.0562559
$629$	4.96208	0.197851
$630$	3.34804	0.133389
$631$	21.3653	0.850540	0.425270	−	0.905066i	$-0.360179\pi$
$631$	21.3653	0.850540	0.425270	+	0.905066i	$0.360179\pi$
$632$	5.47739	0.217879
$633$	11.9946	0.476743
$634$	29.9452	1.18928
$635$	−12.1783	−0.483281
$636$	−0.0518562	−0.00205623
$637$	−1.00000	−0.0396214
$638$	0.676479	0.0267821
$639$	−5.54642	−0.219413
$640$	3.34804	0.132343
$641$	−22.5349	−0.890076	−0.445038	−	0.895512i	$-0.646810\pi$
$641$	−22.5349	−0.890076	−0.445038	+	0.895512i	$0.646810\pi$
$642$	5.05269	0.199414
$643$	−7.86573	−0.310194	−0.155097	−	0.987899i	$-0.549569\pi$
$643$	−7.86573	−0.310194	−0.155097	+	0.987899i	$0.549569\pi$
$644$	5.00365	0.197171
$645$	−41.9493	−1.65175
$646$	−6.06992	−0.238818
$647$	−30.6822	−1.20624	−0.603121	−	0.797650i	$-0.706076\pi$
$647$	−30.6822	−1.20624	−0.603121	+	0.797650i	$0.706076\pi$
$648$	1.00000	0.0392837
$649$	1.14966	0.0451282
$650$	−6.20938	−0.243552
$651$	3.96223	0.155292
$652$	−4.32773	−0.169487
$653$	−11.4759	−0.449088	−0.224544	−	0.974464i	$-0.572089\pi$
$653$	−11.4759	−0.449088	−0.224544	+	0.974464i	$0.572089\pi$
$654$	5.92446	0.231665
$655$	51.7169	2.02075
$656$	−8.08423	−0.315636
$657$	6.13609	0.239392
$658$	7.28631	0.284050
$659$	31.3286	1.22039	0.610194	−	0.792252i	$-0.291091\pi$
$659$	31.3286	1.22039	0.610194	+	0.792252i	$0.291091\pi$
$660$	−3.34804	−0.130322
$661$	−10.3165	−0.401264	−0.200632	−	0.979667i	$-0.564299\pi$
$661$	−10.3165	−0.401264	−0.200632	+	0.979667i	$0.564299\pi$
$662$	−5.44659	−0.211688
$663$	1.19473	0.0463994
$664$	17.4464	0.677050
$665$	−17.0100	−0.659620
$666$	4.15331	0.160938
$667$	3.38487	0.131063
$668$	17.5233	0.677997
$669$	18.3810	0.710650
$670$	49.9493	1.92971
$671$	1.74242	0.0672652
$672$	−1.00000	−0.0385758
$673$	−31.2589	−1.20494	−0.602470	−	0.798141i	$-0.705817\pi$
$673$	−31.2589	−1.20494	−0.602470	+	0.798141i	$0.705817\pi$
$674$	22.9063	0.882317
$675$	−6.20938	−0.238999
$676$	1.00000	0.0384615
$677$	−7.34757	−0.282390	−0.141195	−	0.989982i	$-0.545094\pi$
$677$	−7.34757	−0.282390	−0.141195	+	0.989982i	$0.545094\pi$
$678$	8.84995	0.339880
$679$	−1.53912	−0.0590660
$680$	4.00000	0.153393
$681$	−4.22782	−0.162010
$682$	−3.96223	−0.151722
$683$	−42.4923	−1.62592	−0.812961	−	0.582318i	$-0.802146\pi$
$683$	−42.4923	−1.62592	−0.812961	+	0.582318i	$0.802146\pi$
$684$	−5.08058	−0.194261
$685$	2.78133	0.106269
$686$	1.00000	0.0381802
$687$	−1.35717	−0.0517794
$688$	12.5295	0.477684
$689$	−0.0518562	−0.00197556
$690$	−16.7524	−0.637754
$691$	2.01811	0.0767725	0.0383862	−	0.999263i	$-0.487778\pi$
$691$	2.01811	0.0767725	0.0383862	+	0.999263i	$0.487778\pi$
$692$	3.57586	0.135934
$693$	1.00000	0.0379869
$694$	−14.1185	−0.535930
$695$	63.3575	2.40329
$696$	−0.676479	−0.0256419
$697$	−9.65846	−0.365840
$698$	20.5989	0.779681
$699$	25.8471	0.977627
$700$	6.20938	0.234692
$701$	11.6705	0.440787	0.220394	−	0.975411i	$-0.429266\pi$
$701$	11.6705	0.440787	0.220394	+	0.975411i	$0.429266\pi$
$702$	1.00000	0.0377426
$703$	−21.1013	−0.795849
$704$	1.00000	0.0376889
$705$	−24.3949	−0.918764
$706$	26.9259	1.01337
$707$	4.77981	0.179763
$708$	−1.14966	−0.0432070
$709$	1.50627	0.0565692	0.0282846	−	0.999600i	$-0.490996\pi$
$709$	1.50627	0.0565692	0.0282846	+	0.999600i	$0.490996\pi$
$710$	−18.5696	−0.696906
$711$	5.47739	0.205418
$712$	−17.9441	−0.672482
$713$	−19.8256	−0.742475
$714$	−1.19473	−0.0447116
$715$	−3.34804	−0.125210
$716$	−10.1630	−0.379811
$717$	−29.4412	−1.09950
$718$	37.2822	1.39136
$719$	6.19542	0.231050	0.115525	−	0.993305i	$-0.463145\pi$
$719$	6.19542	0.231050	0.115525	+	0.993305i	$0.463145\pi$
$720$	3.34804	0.124774
$721$	−7.28631	−0.271356
$722$	6.81234	0.253529
$723$	−22.2342	−0.826898
$724$	−14.7803	−0.549306
$725$	4.20052	0.156003
$726$	−1.00000	−0.0371135
$727$	−12.5246	−0.464512	−0.232256	−	0.972655i	$-0.574611\pi$
$727$	−12.5246	−0.464512	−0.232256	+	0.972655i	$0.574611\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	20.5439	0.760363
$731$	14.9694	0.553662
$732$	−1.74242	−0.0644016
$733$	−24.3660	−0.899977	−0.449988	−	0.893034i	$-0.648572\pi$
$733$	−24.3660	−0.899977	−0.449988	+	0.893034i	$0.648572\pi$
$734$	25.3526	0.935780
$735$	−3.34804	−0.123494
$736$	5.00365	0.184437
$737$	14.9190	0.549548
$738$	−8.08423	−0.297585
$739$	−36.5079	−1.34297	−0.671483	−	0.741020i	$-0.734342\pi$
$739$	−36.5079	−1.34297	−0.671483	+	0.741020i	$0.734342\pi$
$740$	13.9055	0.511175
$741$	−5.08058	−0.186640
$742$	0.0518562	0.00190370
$743$	42.0298	1.54193	0.770963	−	0.636880i	$-0.219775\pi$
$743$	42.0298	1.54193	0.770963	+	0.636880i	$0.219775\pi$
$744$	3.96223	0.145262
$745$	−71.3053	−2.61242
$746$	28.7103	1.05116
$747$	17.4464	0.638329
$748$	1.19473	0.0436836
$749$	−5.05269	−0.184621
$750$	−4.04904	−0.147850
$751$	−9.38917	−0.342616	−0.171308	−	0.985218i	$-0.554799\pi$
$751$	−9.38917	−0.342616	−0.171308	+	0.985218i	$0.554799\pi$
$752$	7.28631	0.265704
$753$	23.4288	0.853791
$754$	−0.676479	−0.0246359
$755$	−24.8129	−0.903034
$756$	−1.00000	−0.0363696
$757$	2.50674	0.0911089	0.0455544	−	0.998962i	$-0.485495\pi$
$757$	2.50674	0.0911089	0.0455544	+	0.998962i	$0.485495\pi$
$758$	−3.44510	−0.125132
$759$	−5.00365	−0.181621
$760$	−17.0100	−0.617018
$761$	27.2691	0.988503	0.494252	−	0.869319i	$-0.335442\pi$
$761$	27.2691	0.988503	0.494252	+	0.869319i	$0.335442\pi$
$762$	3.63744	0.131771
$763$	−5.92446	−0.214480
$764$	10.3566	0.374689
$765$	4.00000	0.144620
$766$	−9.61886	−0.347544
$767$	−1.14966	−0.0415119
$768$	−1.00000	−0.0360844
$769$	−20.8480	−0.751798	−0.375899	−	0.926661i	$-0.622666\pi$
$769$	−20.8480	−0.751798	−0.375899	+	0.926661i	$0.622666\pi$
$770$	3.34804	0.120655
$771$	24.9136	0.897241
$772$	19.3396	0.696046
$773$	−19.0414	−0.684872	−0.342436	−	0.939541i	$-0.611252\pi$
$773$	−19.0414	−0.684872	−0.342436	+	0.939541i	$0.611252\pi$
$774$	12.5295	0.450364
$775$	−24.6030	−0.883765
$776$	−1.53912	−0.0552512
$777$	−4.15331	−0.148999
$778$	−20.3969	−0.731265
$779$	41.0726	1.47158
$780$	3.34804	0.119879
$781$	−5.54642	−0.198466
$782$	5.97800	0.213773
$783$	−0.676479	−0.0241754
$784$	1.00000	0.0357143
$785$	−4.71997	−0.168463
$786$	−15.4469	−0.550973
$787$	−26.3953	−0.940892	−0.470446	−	0.882429i	$-0.655907\pi$
$787$	−26.3953	−0.940892	−0.470446	+	0.882429i	$0.655907\pi$
$788$	14.1410	0.503754
$789$	−9.39367	−0.334423
$790$	18.3385	0.652456
$791$	−8.84995	−0.314668
$792$	1.00000	0.0355335
$793$	−1.74242	−0.0618750
$794$	−20.7764	−0.737326
$795$	−0.173617	−0.00615755
$796$	−6.03332	−0.213845
$797$	3.47921	0.123240	0.0616200	−	0.998100i	$-0.480373\pi$
$797$	3.47921	0.123240	0.0616200	+	0.998100i	$0.480373\pi$
$798$	5.08058	0.179851
$799$	8.70517	0.307967
$800$	6.20938	0.219535
$801$	−17.9441	−0.634022
$802$	8.42414	0.297467
$803$	6.13609	0.216538
$804$	−14.9190	−0.526152
$805$	16.7524	0.590445
$806$	3.96223	0.139564
$807$	21.0351	0.740470
$808$	4.77981	0.168153
$809$	−5.47571	−0.192516	−0.0962579	−	0.995356i	$-0.530687\pi$
$809$	−5.47571	−0.192516	−0.0962579	+	0.995356i	$0.530687\pi$
$810$	3.34804	0.117638
$811$	33.9690	1.19281	0.596406	−	0.802683i	$-0.296595\pi$
$811$	33.9690	1.19281	0.596406	+	0.802683i	$0.296595\pi$
$812$	0.676479	0.0237398
$813$	32.5769	1.14252
$814$	4.15331	0.145574
$815$	−14.4894	−0.507542
$816$	−1.19473	−0.0418239
$817$	−63.6573	−2.22709
$818$	−20.6383	−0.721602
$819$	−1.00000	−0.0349428
$820$	−27.0663	−0.945198
$821$	−26.2977	−0.917797	−0.458899	−	0.888489i	$-0.651756\pi$
$821$	−26.2977	−0.917797	−0.458899	+	0.888489i	$0.651756\pi$
$822$	−0.830735	−0.0289752
$823$	6.91359	0.240992	0.120496	−	0.992714i	$-0.461551\pi$
$823$	6.91359	0.240992	0.120496	+	0.992714i	$0.461551\pi$
$824$	−7.28631	−0.253831
$825$	−6.20938	−0.216183
$826$	1.14966	0.0400019
$827$	−37.6214	−1.30822	−0.654112	−	0.756398i	$-0.726957\pi$
$827$	−37.6214	−1.30822	−0.654112	+	0.756398i	$0.726957\pi$
$828$	5.00365	0.173889
$829$	24.9661	0.867108	0.433554	−	0.901128i	$-0.357259\pi$
$829$	24.9661	0.867108	0.433554	+	0.901128i	$0.357259\pi$
$830$	58.4111	2.02748
$831$	2.53642	0.0879873
$832$	−1.00000	−0.0346688
$833$	1.19473	0.0413949
$834$	−18.9238	−0.655276
$835$	58.6687	2.03031
$836$	−5.08058	−0.175716
$837$	3.96223	0.136955
$838$	−6.33853	−0.218961
$839$	−6.62682	−0.228783	−0.114392	−	0.993436i	$-0.536492\pi$
$839$	−6.62682	−0.228783	−0.114392	+	0.993436i	$0.536492\pi$
$840$	−3.34804	−0.115518
$841$	−28.5424	−0.984220
$842$	32.5284	1.12100
$843$	15.4068	0.530637
$844$	−11.9946	−0.412871
$845$	3.34804	0.115176
$846$	7.28631	0.250509
$847$	1.00000	0.0343604
$848$	0.0518562	0.00178075
$849$	−6.06650	−0.208202
$850$	7.41852	0.254453
$851$	20.7817	0.712388
$852$	5.54642	0.190017
$853$	−32.3220	−1.10668	−0.553341	−	0.832955i	$-0.686647\pi$
$853$	−32.3220	−1.10668	−0.553341	+	0.832955i	$0.686647\pi$
$854$	1.74242	0.0596243
$855$	−17.0100	−0.581730
$856$	−5.05269	−0.172697
$857$	47.1012	1.60895	0.804473	−	0.593989i	$-0.202448\pi$
$857$	47.1012	1.60895	0.804473	+	0.593989i	$0.202448\pi$
$858$	1.00000	0.0341394
$859$	−2.20928	−0.0753797	−0.0376899	−	0.999289i	$-0.512000\pi$
$859$	−2.20928	−0.0753797	−0.0376899	+	0.999289i	$0.512000\pi$
$860$	41.9493	1.43046
$861$	8.08423	0.275510
$862$	−22.2660	−0.758383
$863$	14.7664	0.502653	0.251327	−	0.967902i	$-0.419133\pi$
$863$	14.7664	0.502653	0.251327	+	0.967902i	$0.419133\pi$
$864$	−1.00000	−0.0340207
$865$	11.9721	0.407064
$866$	16.8136	0.571350
$867$	15.5726	0.528874
$868$	−3.96223	−0.134487
$869$	5.47739	0.185808
$870$	−2.26488	−0.0767866
$871$	−14.9190	−0.505510
$872$	−5.92446	−0.200628
$873$	−1.53912	−0.0520913
$874$	−25.4215	−0.859894
$875$	4.04904	0.136883
$876$	−6.13609	−0.207319
$877$	−45.9834	−1.55275	−0.776375	−	0.630272i	$-0.782944\pi$
$877$	−45.9834	−1.55275	−0.776375	+	0.630272i	$0.782944\pi$
$878$	−3.07285	−0.103704
$879$	5.53762	0.186779
$880$	3.34804	0.112862
$881$	−30.7670	−1.03657	−0.518283	−	0.855209i	$-0.673429\pi$
$881$	−30.7670	−1.03657	−0.518283	+	0.855209i	$0.673429\pi$
$882$	1.00000	0.0336718
$883$	−4.50842	−0.151720	−0.0758602	−	0.997118i	$-0.524170\pi$
$883$	−4.50842	−0.151720	−0.0758602	+	0.997118i	$0.524170\pi$
$884$	−1.19473	−0.0401831
$885$	−3.84912	−0.129387
$886$	−9.00009	−0.302364
$887$	19.5005	0.654764	0.327382	−	0.944892i	$-0.393834\pi$
$887$	19.5005	0.654764	0.327382	+	0.944892i	$0.393834\pi$
$888$	−4.15331	−0.139376
$889$	−3.63744	−0.121996
$890$	−60.0775	−2.01380
$891$	1.00000	0.0335013
$892$	−18.3810	−0.615441
$893$	−37.0187	−1.23878
$894$	21.2976	0.712299
$895$	−34.0263	−1.13737
$896$	1.00000	0.0334077
$897$	5.00365	0.167067
$898$	26.6541	0.889459
$899$	−2.68037	−0.0893953
$900$	6.20938	0.206979
$901$	0.0619541	0.00206399
$902$	−8.08423	−0.269176
$903$	−12.5295	−0.416956
$904$	−8.84995	−0.294345
$905$	−49.4851	−1.64494
$906$	7.41117	0.246220
$907$	−26.2630	−0.872048	−0.436024	−	0.899935i	$-0.643614\pi$
$907$	−26.2630	−0.872048	−0.436024	+	0.899935i	$0.643614\pi$
$908$	4.22782	0.140305
$909$	4.77981	0.158536
$910$	−3.34804	−0.110986
$911$	−10.5790	−0.350497	−0.175249	−	0.984524i	$-0.556073\pi$
$911$	−10.5790	−0.350497	−0.175249	+	0.984524i	$0.556073\pi$
$912$	5.08058	0.168235
$913$	17.4464	0.577390
$914$	−12.9277	−0.427611
$915$	−5.83368	−0.192856
$916$	1.35717	0.0448423
$917$	15.4469	0.510102
$918$	−1.19473	−0.0394319
$919$	−43.8285	−1.44577	−0.722884	−	0.690970i	$-0.757184\pi$
$919$	−43.8285	−1.44577	−0.722884	+	0.690970i	$0.757184\pi$
$920$	16.7524	0.552311
$921$	−3.12420	−0.102946
$922$	−26.3703	−0.868458
$923$	5.54642	0.182563
$924$	−1.00000	−0.0328976
$925$	25.7895	0.847953
$926$	26.9550	0.885797
$927$	−7.28631	−0.239314
$928$	0.676479	0.0222065
$929$	−8.26894	−0.271295	−0.135648	−	0.990757i	$-0.543311\pi$
$929$	−8.26894	−0.271295	−0.135648	+	0.990757i	$0.543311\pi$
$930$	13.2657	0.435000
$931$	−5.08058	−0.166509
$932$	−25.8471	−0.846650
$933$	9.91041	0.324452
$934$	17.3873	0.568930
$935$	4.00000	0.130814
$936$	−1.00000	−0.0326860
$937$	−30.4850	−0.995902	−0.497951	−	0.867205i	$-0.665914\pi$
$937$	−30.4850	−0.995902	−0.497951	+	0.867205i	$0.665914\pi$
$938$	14.9190	0.487122
$939$	22.2410	0.725807
$940$	24.3949	0.795673
$941$	−31.4705	−1.02591	−0.512954	−	0.858416i	$-0.671449\pi$
$941$	−31.4705	−1.02591	−0.512954	+	0.858416i	$0.671449\pi$
$942$	1.40977	0.0459328
$943$	−40.4507	−1.31725
$944$	1.14966	0.0374184
$945$	−3.34804	−0.108912
$946$	12.5295	0.407370
$947$	51.3199	1.66767	0.833836	−	0.552012i	$-0.186140\pi$
$947$	51.3199	1.66767	0.833836	+	0.552012i	$0.186140\pi$
$948$	−5.47739	−0.177897
$949$	−6.13609	−0.199186
$950$	−31.5473	−1.02353
$951$	−29.9452	−0.971039
$952$	1.19473	0.0387214
$953$	−19.3856	−0.627960	−0.313980	−	0.949430i	$-0.601663\pi$
$953$	−19.3856	−0.627960	−0.313980	+	0.949430i	$0.601663\pi$
$954$	0.0518562	0.00167891
$955$	34.6743	1.12204
$956$	29.4412	0.952197
$957$	−0.676479	−0.0218675
$958$	16.6543	0.538077
$959$	0.830735	0.0268258
$960$	−3.34804	−0.108058
$961$	−15.3007	−0.493572
$962$	−4.15331	−0.133908
$963$	−5.05269	−0.162821
$964$	22.2342	0.716114
$965$	64.7497	2.08437
$966$	−5.00365	−0.160990
$967$	51.2957	1.64956	0.824780	−	0.565454i	$-0.191299\pi$
$967$	51.2957	1.64956	0.824780	+	0.565454i	$0.191299\pi$
$968$	1.00000	0.0321412
$969$	6.06992	0.194994
$970$	−5.15304	−0.165454
$971$	−5.66154	−0.181688	−0.0908438	−	0.995865i	$-0.528956\pi$
$971$	−5.66154	−0.181688	−0.0908438	+	0.995865i	$0.528956\pi$
$972$	−1.00000	−0.0320750
$973$	18.9238	0.606668
$974$	−19.3028	−0.618503
$975$	6.20938	0.198859
$976$	1.74242	0.0557734
$977$	−33.4666	−1.07069	−0.535346	−	0.844633i	$-0.679819\pi$
$977$	−33.4666	−1.07069	−0.535346	+	0.844633i	$0.679819\pi$
$978$	4.32773	0.138385
$979$	−17.9441	−0.573495
$980$	3.34804	0.106949
$981$	−5.92446	−0.189154
$982$	24.1591	0.770948
$983$	32.3189	1.03081	0.515406	−	0.856946i	$-0.327641\pi$
$983$	32.3189	1.03081	0.515406	+	0.856946i	$0.327641\pi$
$984$	8.08423	0.257716
$985$	47.3448	1.50853
$986$	0.808209	0.0257386
$987$	−7.28631	−0.231926
$988$	5.08058	0.161635
$989$	62.6933	1.99353
$990$	3.34804	0.106408
$991$	43.2769	1.37474	0.687368	−	0.726309i	$-0.258766\pi$
$991$	43.2769	1.37474	0.687368	+	0.726309i	$0.258766\pi$
$992$	−3.96223	−0.125801
$993$	5.44659	0.172842
$994$	−5.54642	−0.175922
$995$	−20.1998	−0.640377
$996$	−17.4464	−0.552809
$997$	−20.0528	−0.635078	−0.317539	−	0.948245i	$-0.602856\pi$
$997$	−20.0528	−0.635078	−0.317539	+	0.948245i	$0.602856\pi$
$998$	−27.8154	−0.880480
$999$	−4.15331	−0.131405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6006.2.a.cf.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6006.2.a.cf.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.34804 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.34804 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.34804 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} -3.34804 q^{15} +1.00000 q^{16} +1.19473 q^{17} +1.00000 q^{18} -5.08058 q^{19} +3.34804 q^{20} -1.00000 q^{21} +1.00000 q^{22} +5.00365 q^{23} -1.00000 q^{24} +6.20938 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +0.676479 q^{29} -3.34804 q^{30} -3.96223 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.19473 q^{34} +3.34804 q^{35} +1.00000 q^{36} +4.15331 q^{37} -5.08058 q^{38} +1.00000 q^{39} +3.34804 q^{40} -8.08423 q^{41} -1.00000 q^{42} +12.5295 q^{43} +1.00000 q^{44} +3.34804 q^{45} +5.00365 q^{46} +7.28631 q^{47} -1.00000 q^{48} +1.00000 q^{49} +6.20938 q^{50} -1.19473 q^{51} -1.00000 q^{52} +0.0518562 q^{53} -1.00000 q^{54} +3.34804 q^{55} +1.00000 q^{56} +5.08058 q^{57} +0.676479 q^{58} +1.14966 q^{59} -3.34804 q^{60} +1.74242 q^{61} -3.96223 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.34804 q^{65} -1.00000 q^{66} +14.9190 q^{67} +1.19473 q^{68} -5.00365 q^{69} +3.34804 q^{70} -5.54642 q^{71} +1.00000 q^{72} +6.13609 q^{73} +4.15331 q^{74} -6.20938 q^{75} -5.08058 q^{76} +1.00000 q^{77} +1.00000 q^{78} +5.47739 q^{79} +3.34804 q^{80} +1.00000 q^{81} -8.08423 q^{82} +17.4464 q^{83} -1.00000 q^{84} +4.00000 q^{85} +12.5295 q^{86} -0.676479 q^{87} +1.00000 q^{88} -17.9441 q^{89} +3.34804 q^{90} -1.00000 q^{91} +5.00365 q^{92} +3.96223 q^{93} +7.28631 q^{94} -17.0100 q^{95} -1.00000 q^{96} -1.53912 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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