LMFDB - Embedded newform 4334.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} + \cdots + 16 $ x^17 - 5x^16 - 19x^15 + 121x^14 + 112x^13 - 1172x^12 - 25x^11 + 5845x^10 - 2233x^9 - 16035x^8 + 9174x^7 + 23882x^6 - 15232x^5 - 17609x^4 + 10764x^3 + 4764x^2 - 2368x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.70875$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.70875 q^{3} +1.00000 q^{4} +1.80981 q^{5} +2.70875 q^{6} -1.02803 q^{7} -1.00000 q^{8} +4.33730 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.70875 q^{3} +1.00000 q^{4} +1.80981 q^{5} +2.70875 q^{6} -1.02803 q^{7} -1.00000 q^{8} +4.33730 q^{9} -1.80981 q^{10} -1.00000 q^{11} -2.70875 q^{12} -3.68449 q^{13} +1.02803 q^{14} -4.90233 q^{15} +1.00000 q^{16} +0.383918 q^{17} -4.33730 q^{18} +1.48084 q^{19} +1.80981 q^{20} +2.78468 q^{21} +1.00000 q^{22} +7.06154 q^{23} +2.70875 q^{24} -1.72457 q^{25} +3.68449 q^{26} -3.62241 q^{27} -1.02803 q^{28} -4.21022 q^{29} +4.90233 q^{30} +0.673305 q^{31} -1.00000 q^{32} +2.70875 q^{33} -0.383918 q^{34} -1.86055 q^{35} +4.33730 q^{36} +2.90539 q^{37} -1.48084 q^{38} +9.98033 q^{39} -1.80981 q^{40} -1.05710 q^{41} -2.78468 q^{42} +9.11349 q^{43} -1.00000 q^{44} +7.84971 q^{45} -7.06154 q^{46} -7.00242 q^{47} -2.70875 q^{48} -5.94315 q^{49} +1.72457 q^{50} -1.03994 q^{51} -3.68449 q^{52} +4.18429 q^{53} +3.62241 q^{54} -1.80981 q^{55} +1.02803 q^{56} -4.01121 q^{57} +4.21022 q^{58} -8.91020 q^{59} -4.90233 q^{60} -6.12688 q^{61} -0.673305 q^{62} -4.45888 q^{63} +1.00000 q^{64} -6.66824 q^{65} -2.70875 q^{66} +11.7253 q^{67} +0.383918 q^{68} -19.1279 q^{69} +1.86055 q^{70} -0.171090 q^{71} -4.33730 q^{72} -7.55576 q^{73} -2.90539 q^{74} +4.67142 q^{75} +1.48084 q^{76} +1.02803 q^{77} -9.98033 q^{78} +6.71949 q^{79} +1.80981 q^{80} -3.19972 q^{81} +1.05710 q^{82} -2.82289 q^{83} +2.78468 q^{84} +0.694820 q^{85} -9.11349 q^{86} +11.4044 q^{87} +1.00000 q^{88} -0.122506 q^{89} -7.84971 q^{90} +3.78777 q^{91} +7.06154 q^{92} -1.82381 q^{93} +7.00242 q^{94} +2.68004 q^{95} +2.70875 q^{96} +6.44296 q^{97} +5.94315 q^{98} -4.33730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * 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
$3$	−2.70875	−1.56389	−0.781947	−	0.623344i	$-0.785774\pi$
$3$	−2.70875	−1.56389	−0.781947	+	0.623344i	$0.785774\pi$
$4$	1.00000	0.500000
$5$	1.80981	0.809374	0.404687	−	0.914455i	$-0.367381\pi$
$5$	1.80981	0.809374	0.404687	+	0.914455i	$0.367381\pi$
$6$	2.70875	1.10584
$7$	−1.02803	−0.388559	−0.194280	−	0.980946i	$-0.562237\pi$
$7$	−1.02803	−0.388559	−0.194280	+	0.980946i	$0.562237\pi$
$8$	−1.00000	−0.353553
$9$	4.33730	1.44577
$10$	−1.80981	−0.572314
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.70875	−0.781947
$13$	−3.68449	−1.02189	−0.510946	−	0.859613i	$-0.670705\pi$
$13$	−3.68449	−1.02189	−0.510946	+	0.859613i	$0.670705\pi$
$14$	1.02803	0.274753
$15$	−4.90233	−1.26578
$16$	1.00000	0.250000
$17$	0.383918	0.0931137	0.0465569	−	0.998916i	$-0.485175\pi$
$17$	0.383918	0.0931137	0.0465569	+	0.998916i	$0.485175\pi$
$18$	−4.33730	−1.02231
$19$	1.48084	0.339727	0.169864	−	0.985468i	$-0.445667\pi$
$19$	1.48084	0.339727	0.169864	+	0.985468i	$0.445667\pi$
$20$	1.80981	0.404687
$21$	2.78468	0.607666
$22$	1.00000	0.213201
$23$	7.06154	1.47243	0.736217	−	0.676746i	$-0.236610\pi$
$23$	7.06154	1.47243	0.736217	+	0.676746i	$0.236610\pi$
$24$	2.70875	0.552920
$25$	−1.72457	−0.344914
$26$	3.68449	0.722587
$27$	−3.62241	−0.697133
$28$	−1.02803	−0.194280
$29$	−4.21022	−0.781819	−0.390910	−	0.920429i	$-0.627839\pi$
$29$	−4.21022	−0.781819	−0.390910	+	0.920429i	$0.627839\pi$
$30$	4.90233	0.895039
$31$	0.673305	0.120929	0.0604646	−	0.998170i	$-0.480742\pi$
$31$	0.673305	0.120929	0.0604646	+	0.998170i	$0.480742\pi$
$32$	−1.00000	−0.176777
$33$	2.70875	0.471532
$34$	−0.383918	−0.0658413
$35$	−1.86055	−0.314490
$36$	4.33730	0.722884
$37$	2.90539	0.477643	0.238822	−	0.971063i	$-0.423239\pi$
$37$	2.90539	0.477643	0.238822	+	0.971063i	$0.423239\pi$
$38$	−1.48084	−0.240224
$39$	9.98033	1.59813
$40$	−1.80981	−0.286157
$41$	−1.05710	−0.165091	−0.0825455	−	0.996587i	$-0.526305\pi$
$41$	−1.05710	−0.165091	−0.0825455	+	0.996587i	$0.526305\pi$
$42$	−2.78468	−0.429685
$43$	9.11349	1.38979	0.694897	−	0.719109i	$-0.255450\pi$
$43$	9.11349	1.38979	0.694897	+	0.719109i	$0.255450\pi$
$44$	−1.00000	−0.150756
$45$	7.84971	1.17017
$46$	−7.06154	−1.04117
$47$	−7.00242	−1.02141	−0.510704	−	0.859756i	$-0.670615\pi$
$47$	−7.00242	−1.02141	−0.510704	+	0.859756i	$0.670615\pi$
$48$	−2.70875	−0.390974
$49$	−5.94315	−0.849022
$50$	1.72457	0.243891
$51$	−1.03994	−0.145620
$52$	−3.68449	−0.510946
$53$	4.18429	0.574757	0.287378	−	0.957817i	$-0.407216\pi$
$53$	4.18429	0.574757	0.287378	+	0.957817i	$0.407216\pi$
$54$	3.62241	0.492948
$55$	−1.80981	−0.244035
$56$	1.02803	0.137376
$57$	−4.01121	−0.531298
$58$	4.21022	0.552830
$59$	−8.91020	−1.16001	−0.580004	−	0.814613i	$-0.696949\pi$
$59$	−8.91020	−1.16001	−0.580004	+	0.814613i	$0.696949\pi$
$60$	−4.90233	−0.632888
$61$	−6.12688	−0.784466	−0.392233	−	0.919866i	$-0.628297\pi$
$61$	−6.12688	−0.784466	−0.392233	+	0.919866i	$0.628297\pi$
$62$	−0.673305	−0.0855098
$63$	−4.45888	−0.561766
$64$	1.00000	0.125000
$65$	−6.66824	−0.827093
$66$	−2.70875	−0.333424
$67$	11.7253	1.43247	0.716236	−	0.697858i	$-0.245863\pi$
$67$	11.7253	1.43247	0.716236	+	0.697858i	$0.245863\pi$
$68$	0.383918	0.0465569
$69$	−19.1279	−2.30273
$70$	1.86055	0.222378
$71$	−0.171090	−0.0203047	−0.0101523	−	0.999948i	$-0.503232\pi$
$71$	−0.171090	−0.0203047	−0.0101523	+	0.999948i	$0.503232\pi$
$72$	−4.33730	−0.511156
$73$	−7.55576	−0.884335	−0.442167	−	0.896933i	$-0.645790\pi$
$73$	−7.55576	−0.884335	−0.442167	+	0.896933i	$0.645790\pi$
$74$	−2.90539	−0.337745
$75$	4.67142	0.539409
$76$	1.48084	0.169864
$77$	1.02803	0.117155
$78$	−9.98033	−1.13005
$79$	6.71949	0.756001	0.378001	−	0.925805i	$-0.376612\pi$
$79$	6.71949	0.756001	0.378001	+	0.925805i	$0.376612\pi$
$80$	1.80981	0.202343
$81$	−3.19972	−0.355524
$82$	1.05710	0.116737
$83$	−2.82289	−0.309852	−0.154926	−	0.987926i	$-0.549514\pi$
$83$	−2.82289	−0.309852	−0.154926	+	0.987926i	$0.549514\pi$
$84$	2.78468	0.303833
$85$	0.694820	0.0753638
$86$	−9.11349	−0.982733
$87$	11.4044	1.22268
$88$	1.00000	0.106600
$89$	−0.122506	−0.0129857	−0.00649283	−	0.999979i	$-0.502067\pi$
$89$	−0.122506	−0.0129857	−0.00649283	+	0.999979i	$0.502067\pi$
$90$	−7.84971	−0.827433
$91$	3.78777	0.397066
$92$	7.06154	0.736217
$93$	−1.82381	−0.189120
$94$	7.00242	0.722245
$95$	2.68004	0.274967
$96$	2.70875	0.276460
$97$	6.44296	0.654183	0.327092	−	0.944993i	$-0.393931\pi$
$97$	6.44296	0.654183	0.327092	+	0.944993i	$0.393931\pi$
$98$	5.94315	0.600349
$99$	−4.33730	−0.435915
$100$	−1.72457	−0.172457
$101$	−2.20686	−0.219591	−0.109795	−	0.993954i	$-0.535020\pi$
$101$	−2.20686	−0.219591	−0.109795	+	0.993954i	$0.535020\pi$
$102$	1.03994	0.102969
$103$	16.3758	1.61356	0.806779	−	0.590854i	$-0.201209\pi$
$103$	16.3758	1.61356	0.806779	+	0.590854i	$0.201209\pi$
$104$	3.68449	0.361293
$105$	5.03975	0.491829
$106$	−4.18429	−0.406414
$107$	11.5019	1.11193	0.555964	−	0.831206i	$-0.312349\pi$
$107$	11.5019	1.11193	0.555964	+	0.831206i	$0.312349\pi$
$108$	−3.62241	−0.348567
$109$	−11.5823	−1.10938	−0.554691	−	0.832056i	$-0.687164\pi$
$109$	−11.5823	−1.10938	−0.554691	+	0.832056i	$0.687164\pi$
$110$	1.80981	0.172559
$111$	−7.86996	−0.746984
$112$	−1.02803	−0.0971398
$113$	7.57336	0.712442	0.356221	−	0.934402i	$-0.384065\pi$
$113$	7.57336	0.712442	0.356221	+	0.934402i	$0.384065\pi$
$114$	4.01121	0.375684
$115$	12.7801	1.19175
$116$	−4.21022	−0.390910
$117$	−15.9807	−1.47742
$118$	8.91020	0.820250
$119$	−0.394679	−0.0361802
$120$	4.90233	0.447519
$121$	1.00000	0.0909091
$122$	6.12688	0.554701
$123$	2.86341	0.258185
$124$	0.673305	0.0604646
$125$	−12.1702	−1.08854
$126$	4.45888	0.397229
$127$	5.19006	0.460544	0.230272	−	0.973126i	$-0.426038\pi$
$127$	5.19006	0.460544	0.230272	+	0.973126i	$0.426038\pi$
$128$	−1.00000	−0.0883883
$129$	−24.6861	−2.17349
$130$	6.66824	0.584843
$131$	−10.6535	−0.930801	−0.465401	−	0.885100i	$-0.654090\pi$
$131$	−10.6535	−0.930801	−0.465401	+	0.885100i	$0.654090\pi$
$132$	2.70875	0.235766
$133$	−1.52235	−0.132004
$134$	−11.7253	−1.01291
$135$	−6.55589	−0.564242
$136$	−0.383918	−0.0329207
$137$	−4.39067	−0.375120	−0.187560	−	0.982253i	$-0.560058\pi$
$137$	−4.39067	−0.375120	−0.187560	+	0.982253i	$0.560058\pi$
$138$	19.1279	1.62828
$139$	5.28118	0.447944	0.223972	−	0.974596i	$-0.428098\pi$
$139$	5.28118	0.447944	0.223972	+	0.974596i	$0.428098\pi$
$140$	−1.86055	−0.157245
$141$	18.9678	1.59738
$142$	0.171090	0.0143576
$143$	3.68449	0.308112
$144$	4.33730	0.361442
$145$	−7.61973	−0.632784
$146$	7.55576	0.625319
$147$	16.0985	1.32778
$148$	2.90539	0.238822
$149$	22.4755	1.84126	0.920631	−	0.390433i	$-0.127675\pi$
$149$	22.4755	1.84126	0.920631	+	0.390433i	$0.127675\pi$
$150$	−4.67142	−0.381420
$151$	−14.0797	−1.14579	−0.572895	−	0.819629i	$-0.694180\pi$
$151$	−14.0797	−1.14579	−0.572895	+	0.819629i	$0.694180\pi$
$152$	−1.48084	−0.120112
$153$	1.66517	0.134621
$154$	−1.02803	−0.0828411
$155$	1.21856	0.0978769
$156$	9.98033	0.799066
$157$	−13.1199	−1.04708	−0.523542	−	0.852000i	$-0.675390\pi$
$157$	−13.1199	−1.04708	−0.523542	+	0.852000i	$0.675390\pi$
$158$	−6.71949	−0.534574
$159$	−11.3342	−0.898859
$160$	−1.80981	−0.143078
$161$	−7.25949	−0.572128
$162$	3.19972	0.251393
$163$	7.33349	0.574403	0.287202	−	0.957870i	$-0.407275\pi$
$163$	7.33349	0.574403	0.287202	+	0.957870i	$0.407275\pi$
$164$	−1.05710	−0.0825455
$165$	4.90233	0.381646
$166$	2.82289	0.219099
$167$	−3.94190	−0.305033	−0.152517	−	0.988301i	$-0.548738\pi$
$167$	−3.94190	−0.305033	−0.152517	+	0.988301i	$0.548738\pi$
$168$	−2.78468	−0.214842
$169$	0.575430	0.0442639
$170$	−0.694820	−0.0532903
$171$	6.42284	0.491167
$172$	9.11349	0.694897
$173$	0.191973	0.0145954	0.00729772	−	0.999973i	$-0.497677\pi$
$173$	0.191973	0.0145954	0.00729772	+	0.999973i	$0.497677\pi$
$174$	−11.4044	−0.864567
$175$	1.77291	0.134020
$176$	−1.00000	−0.0753778
$177$	24.1355	1.81413
$178$	0.122506	0.00918224
$179$	−7.67948	−0.573991	−0.286996	−	0.957932i	$-0.592657\pi$
$179$	−7.67948	−0.573991	−0.286996	+	0.957932i	$0.592657\pi$
$180$	7.84971	0.585083
$181$	24.9030	1.85103	0.925513	−	0.378716i	$-0.123634\pi$
$181$	24.9030	1.85103	0.925513	+	0.378716i	$0.123634\pi$
$182$	−3.78777	−0.280768
$183$	16.5962	1.22682
$184$	−7.06154	−0.520584
$185$	5.25822	0.386592
$186$	1.82381	0.133728
$187$	−0.383918	−0.0280748
$188$	−7.00242	−0.510704
$189$	3.72395	0.270878
$190$	−2.68004	−0.194431
$191$	25.3403	1.83356	0.916778	−	0.399397i	$-0.130780\pi$
$191$	25.3403	1.83356	0.916778	+	0.399397i	$0.130780\pi$
$192$	−2.70875	−0.195487
$193$	−16.6511	−1.19857	−0.599286	−	0.800535i	$-0.704549\pi$
$193$	−16.6511	−1.19857	−0.599286	+	0.800535i	$0.704549\pi$
$194$	−6.44296	−0.462578
$195$	18.0626	1.29349
$196$	−5.94315	−0.424511
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	4.33730	0.308239
$199$	−24.1244	−1.71013	−0.855066	−	0.518519i	$-0.826484\pi$
$199$	−24.1244	−1.71013	−0.855066	+	0.518519i	$0.826484\pi$
$200$	1.72457	0.121946
$201$	−31.7608	−2.24024
$202$	2.20686	0.155274
$203$	4.32824	0.303783
$204$	−1.03994	−0.0728100
$205$	−1.91315	−0.133620
$206$	−16.3758	−1.14096
$207$	30.6280	2.12880
$208$	−3.68449	−0.255473
$209$	−1.48084	−0.102432
$210$	−5.03975	−0.347776
$211$	11.8987	0.819142	0.409571	−	0.912278i	$-0.365678\pi$
$211$	11.8987	0.819142	0.409571	+	0.912278i	$0.365678\pi$
$212$	4.18429	0.287378
$213$	0.463439	0.0317543
$214$	−11.5019	−0.786252
$215$	16.4937	1.12486
$216$	3.62241	0.246474
$217$	−0.692178	−0.0469881
$218$	11.5823	0.784452
$219$	20.4666	1.38301
$220$	−1.80981	−0.122018
$221$	−1.41454	−0.0951522
$222$	7.86996	0.528197
$223$	−16.8520	−1.12849	−0.564246	−	0.825607i	$-0.690833\pi$
$223$	−16.8520	−1.12849	−0.564246	+	0.825607i	$0.690833\pi$
$224$	1.02803	0.0686882
$225$	−7.47998	−0.498665
$226$	−7.57336	−0.503772
$227$	−13.5443	−0.898968	−0.449484	−	0.893288i	$-0.648392\pi$
$227$	−13.5443	−0.898968	−0.449484	+	0.893288i	$0.648392\pi$
$228$	−4.01121	−0.265649
$229$	−10.5498	−0.697148	−0.348574	−	0.937281i	$-0.613334\pi$
$229$	−10.5498	−0.697148	−0.348574	+	0.937281i	$0.613334\pi$
$230$	−12.7801	−0.842694
$231$	−2.78468	−0.183218
$232$	4.21022	0.276415
$233$	7.92349	0.519085	0.259542	−	0.965732i	$-0.416428\pi$
$233$	7.92349	0.519085	0.259542	+	0.965732i	$0.416428\pi$
$234$	15.9807	1.04469
$235$	−12.6731	−0.826701
$236$	−8.91020	−0.580004
$237$	−18.2014	−1.18231
$238$	0.394679	0.0255833
$239$	−26.7180	−1.72825	−0.864123	−	0.503280i	$-0.832126\pi$
$239$	−26.7180	−1.72825	−0.864123	+	0.503280i	$0.832126\pi$
$240$	−4.90233	−0.316444
$241$	−25.1533	−1.62026	−0.810132	−	0.586247i	$-0.800605\pi$
$241$	−25.1533	−1.62026	−0.810132	+	0.586247i	$0.800605\pi$
$242$	−1.00000	−0.0642824
$243$	19.5345	1.25314
$244$	−6.12688	−0.392233
$245$	−10.7560	−0.687176
$246$	−2.86341	−0.182564
$247$	−5.45612	−0.347165
$248$	−0.673305	−0.0427549
$249$	7.64648	0.484576
$250$	12.1702	0.769713
$251$	2.38310	0.150420	0.0752101	−	0.997168i	$-0.476037\pi$
$251$	2.38310	0.150420	0.0752101	+	0.997168i	$0.476037\pi$
$252$	−4.45888	−0.280883
$253$	−7.06154	−0.443955
$254$	−5.19006	−0.325654
$255$	−1.88209	−0.117861
$256$	1.00000	0.0625000
$257$	24.3481	1.51879	0.759395	−	0.650630i	$-0.225495\pi$
$257$	24.3481	1.51879	0.759395	+	0.650630i	$0.225495\pi$
$258$	24.6861	1.53689
$259$	−2.98683	−0.185593
$260$	−6.66824	−0.413546
$261$	−18.2610	−1.13033
$262$	10.6535	0.658176
$263$	−23.8407	−1.47008	−0.735041	−	0.678023i	$-0.762837\pi$
$263$	−23.8407	−1.47008	−0.735041	+	0.678023i	$0.762837\pi$
$264$	−2.70875	−0.166712
$265$	7.57279	0.465193
$266$	1.52235	0.0933411
$267$	0.331839	0.0203082
$268$	11.7253	0.716236
$269$	19.6338	1.19709	0.598547	−	0.801088i	$-0.295745\pi$
$269$	19.6338	1.19709	0.598547	+	0.801088i	$0.295745\pi$
$270$	6.55589	0.398979
$271$	−19.7100	−1.19730	−0.598649	−	0.801011i	$-0.704296\pi$
$271$	−19.7100	−1.19730	−0.598649	+	0.801011i	$0.704296\pi$
$272$	0.383918	0.0232784
$273$	−10.2601	−0.620969
$274$	4.39067	0.265250
$275$	1.72457	0.103995
$276$	−19.1279	−1.15137
$277$	6.24188	0.375038	0.187519	−	0.982261i	$-0.439955\pi$
$277$	6.24188	0.375038	0.187519	+	0.982261i	$0.439955\pi$
$278$	−5.28118	−0.316744
$279$	2.92033	0.174835
$280$	1.86055	0.111189
$281$	−20.2062	−1.20540	−0.602700	−	0.797968i	$-0.705908\pi$
$281$	−20.2062	−1.20540	−0.602700	+	0.797968i	$0.705908\pi$
$282$	−18.9678	−1.12952
$283$	13.4770	0.801123	0.400562	−	0.916270i	$-0.368815\pi$
$283$	13.4770	0.801123	0.400562	+	0.916270i	$0.368815\pi$
$284$	−0.171090	−0.0101523
$285$	−7.25955	−0.430019
$286$	−3.68449	−0.217868
$287$	1.08673	0.0641477
$288$	−4.33730	−0.255578
$289$	−16.8526	−0.991330
$290$	7.61973	0.447446
$291$	−17.4523	−1.02307
$292$	−7.55576	−0.442167
$293$	−15.5346	−0.907543	−0.453772	−	0.891118i	$-0.649922\pi$
$293$	−15.5346	−0.907543	−0.453772	+	0.891118i	$0.649922\pi$
$294$	−16.0985	−0.938883
$295$	−16.1258	−0.938881
$296$	−2.90539	−0.168872
$297$	3.62241	0.210194
$298$	−22.4755	−1.30197
$299$	−26.0181	−1.50467
$300$	4.67142	0.269705
$301$	−9.36895	−0.540017
$302$	14.0797	0.810195
$303$	5.97782	0.343417
$304$	1.48084	0.0849319
$305$	−11.0885	−0.634926
$306$	−1.66517	−0.0951913
$307$	6.57539	0.375277	0.187639	−	0.982238i	$-0.439917\pi$
$307$	6.57539	0.375277	0.187639	+	0.982238i	$0.439917\pi$
$308$	1.02803	0.0585775
$309$	−44.3579	−2.52343
$310$	−1.21856	−0.0692094
$311$	−19.7037	−1.11730	−0.558648	−	0.829405i	$-0.688680\pi$
$311$	−19.7037	−1.11730	−0.558648	+	0.829405i	$0.688680\pi$
$312$	−9.98033	−0.565025
$313$	1.79777	0.101616	0.0508081	−	0.998708i	$-0.483820\pi$
$313$	1.79777	0.101616	0.0508081	+	0.998708i	$0.483820\pi$
$314$	13.1199	0.740400
$315$	−8.06975	−0.454679
$316$	6.71949	0.378001
$317$	−22.2336	−1.24876	−0.624382	−	0.781119i	$-0.714649\pi$
$317$	−22.2336	−1.24876	−0.624382	+	0.781119i	$0.714649\pi$
$318$	11.3342	0.635589
$319$	4.21022	0.235727
$320$	1.80981	0.101172
$321$	−31.1556	−1.73894
$322$	7.25949	0.404555
$323$	0.568520	0.0316333
$324$	−3.19972	−0.177762
$325$	6.35415	0.352465
$326$	−7.33349	−0.406164
$327$	31.3735	1.73496
$328$	1.05710	0.0583685
$329$	7.19871	0.396878
$330$	−4.90233	−0.269864
$331$	−17.2848	−0.950057	−0.475029	−	0.879970i	$-0.657562\pi$
$331$	−17.2848	−0.950057	−0.475029	+	0.879970i	$0.657562\pi$
$332$	−2.82289	−0.154926
$333$	12.6016	0.690561
$334$	3.94190	0.215691
$335$	21.2206	1.15941
$336$	2.78468	0.151916
$337$	−30.5466	−1.66398	−0.831989	−	0.554792i	$-0.812798\pi$
$337$	−30.5466	−1.66398	−0.831989	+	0.554792i	$0.812798\pi$
$338$	−0.575430	−0.0312993
$339$	−20.5143	−1.11418
$340$	0.694820	0.0376819
$341$	−0.673305	−0.0364615
$342$	−6.42284	−0.347307
$343$	13.3060	0.718455
$344$	−9.11349	−0.491366
$345$	−34.6180	−1.86377
$346$	−0.191973	−0.0103205
$347$	8.50271	0.456449	0.228225	−	0.973609i	$-0.426708\pi$
$347$	8.50271	0.456449	0.228225	+	0.973609i	$0.426708\pi$
$348$	11.4044	0.611341
$349$	−17.3331	−0.927818	−0.463909	−	0.885883i	$-0.653554\pi$
$349$	−17.3331	−0.927818	−0.463909	+	0.885883i	$0.653554\pi$
$350$	−1.77291	−0.0947661
$351$	13.3467	0.712395
$352$	1.00000	0.0533002
$353$	−12.3367	−0.656615	−0.328308	−	0.944571i	$-0.606478\pi$
$353$	−12.3367	−0.656615	−0.328308	+	0.944571i	$0.606478\pi$
$354$	−24.1355	−1.28278
$355$	−0.309641	−0.0164341
$356$	−0.122506	−0.00649283
$357$	1.06909	0.0565820
$358$	7.67948	0.405873
$359$	6.42568	0.339135	0.169567	−	0.985519i	$-0.445763\pi$
$359$	6.42568	0.339135	0.169567	+	0.985519i	$0.445763\pi$
$360$	−7.84971	−0.413716
$361$	−16.8071	−0.884585
$362$	−24.9030	−1.30887
$363$	−2.70875	−0.142172
$364$	3.78777	0.198533
$365$	−13.6745	−0.715757
$366$	−16.5962	−0.867495
$367$	−22.1908	−1.15835	−0.579175	−	0.815203i	$-0.696625\pi$
$367$	−22.1908	−1.15835	−0.579175	+	0.815203i	$0.696625\pi$
$368$	7.06154	0.368108
$369$	−4.58496	−0.238683
$370$	−5.25822	−0.273362
$371$	−4.30158	−0.223327
$372$	−1.82381	−0.0945602
$373$	−37.6429	−1.94908	−0.974538	−	0.224224i	$-0.928015\pi$
$373$	−37.6429	−1.94908	−0.974538	+	0.224224i	$0.928015\pi$
$374$	0.383918	0.0198519
$375$	32.9660	1.70236
$376$	7.00242	0.361122
$377$	15.5125	0.798935
$378$	−3.72395	−0.191539
$379$	−9.52813	−0.489427	−0.244714	−	0.969595i	$-0.578694\pi$
$379$	−9.52813	−0.489427	−0.244714	+	0.969595i	$0.578694\pi$
$380$	2.68004	0.137483
$381$	−14.0586	−0.720242
$382$	−25.3403	−1.29652
$383$	32.4206	1.65662	0.828308	−	0.560273i	$-0.189304\pi$
$383$	32.4206	1.65662	0.828308	+	0.560273i	$0.189304\pi$
$384$	2.70875	0.138230
$385$	1.86055	0.0948222
$386$	16.6511	0.847518
$387$	39.5279	2.00932
$388$	6.44296	0.327092
$389$	21.6585	1.09813	0.549066	−	0.835779i	$-0.314984\pi$
$389$	21.6585	1.09813	0.549066	+	0.835779i	$0.314984\pi$
$390$	−18.0626	−0.914633
$391$	2.71105	0.137104
$392$	5.94315	0.300174
$393$	28.8576	1.45568
$394$	1.00000	0.0503793
$395$	12.1610	0.611888
$396$	−4.33730	−0.217958
$397$	−24.7391	−1.24162	−0.620809	−	0.783962i	$-0.713196\pi$
$397$	−24.7391	−1.24162	−0.620809	+	0.783962i	$0.713196\pi$
$398$	24.1244	1.20925
$399$	4.12365	0.206441
$400$	−1.72457	−0.0862285
$401$	−10.5068	−0.524684	−0.262342	−	0.964975i	$-0.584495\pi$
$401$	−10.5068	−0.524684	−0.262342	+	0.964975i	$0.584495\pi$
$402$	31.7608	1.58409
$403$	−2.48078	−0.123577
$404$	−2.20686	−0.109795
$405$	−5.79089	−0.287752
$406$	−4.32824	−0.214807
$407$	−2.90539	−0.144015
$408$	1.03994	0.0514845
$409$	5.49779	0.271848	0.135924	−	0.990719i	$-0.456600\pi$
$409$	5.49779	0.271848	0.135924	+	0.990719i	$0.456600\pi$
$410$	1.91315	0.0944839
$411$	11.8932	0.586648
$412$	16.3758	0.806779
$413$	9.15996	0.450732
$414$	−30.6280	−1.50529
$415$	−5.10890	−0.250786
$416$	3.68449	0.180647
$417$	−14.3054	−0.700537
$418$	1.48084	0.0724301
$419$	−36.4229	−1.77938	−0.889688	−	0.456570i	$-0.849078\pi$
$419$	−36.4229	−1.77938	−0.889688	+	0.456570i	$0.849078\pi$
$420$	5.03975	0.245914
$421$	14.6138	0.712232	0.356116	−	0.934442i	$-0.384101\pi$
$421$	14.6138	0.712232	0.356116	+	0.934442i	$0.384101\pi$
$422$	−11.8987	−0.579221
$423$	−30.3716	−1.47672
$424$	−4.18429	−0.203207
$425$	−0.662093	−0.0321162
$426$	−0.463439	−0.0224537
$427$	6.29862	0.304812
$428$	11.5019	0.555964
$429$	−9.98033	−0.481855
$430$	−16.4937	−0.795398
$431$	−3.76658	−0.181430	−0.0907148	−	0.995877i	$-0.528915\pi$
$431$	−3.76658	−0.181430	−0.0907148	+	0.995877i	$0.528915\pi$
$432$	−3.62241	−0.174283
$433$	−14.1809	−0.681492	−0.340746	−	0.940155i	$-0.610680\pi$
$433$	−14.1809	−0.681492	−0.340746	+	0.940155i	$0.610680\pi$
$434$	0.692178	0.0332256
$435$	20.6399	0.989608
$436$	−11.5823	−0.554691
$437$	10.4570	0.500226
$438$	−20.4666	−0.977933
$439$	13.8475	0.660905	0.330452	−	0.943823i	$-0.392799\pi$
$439$	13.8475	0.660905	0.330452	+	0.943823i	$0.392799\pi$
$440$	1.80981	0.0862795
$441$	−25.7772	−1.22749
$442$	1.41454	0.0672828
$443$	−9.33250	−0.443400	−0.221700	−	0.975115i	$-0.571161\pi$
$443$	−9.33250	−0.443400	−0.221700	+	0.975115i	$0.571161\pi$
$444$	−7.86996	−0.373492
$445$	−0.221714	−0.0105102
$446$	16.8520	0.797964
$447$	−60.8803	−2.87954
$448$	−1.02803	−0.0485699
$449$	11.0633	0.522111	0.261055	−	0.965324i	$-0.415929\pi$
$449$	11.0633	0.522111	0.261055	+	0.965324i	$0.415929\pi$
$450$	7.47998	0.352610
$451$	1.05710	0.0497768
$452$	7.57336	0.356221
$453$	38.1383	1.79189
$454$	13.5443	0.635666
$455$	6.85516	0.321375
$456$	4.01121	0.187842
$457$	18.8133	0.880050	0.440025	−	0.897986i	$-0.354970\pi$
$457$	18.8133	0.880050	0.440025	+	0.897986i	$0.354970\pi$
$458$	10.5498	0.492958
$459$	−1.39071	−0.0649127
$460$	12.7801	0.595874
$461$	−7.27756	−0.338950	−0.169475	−	0.985534i	$-0.554207\pi$
$461$	−7.27756	−0.338950	−0.169475	+	0.985534i	$0.554207\pi$
$462$	2.78468	0.129555
$463$	29.1565	1.35502	0.677508	−	0.735516i	$-0.263060\pi$
$463$	29.1565	1.35502	0.677508	+	0.735516i	$0.263060\pi$
$464$	−4.21022	−0.195455
$465$	−3.30076	−0.153069
$466$	−7.92349	−0.367048
$467$	24.2888	1.12395	0.561975	−	0.827154i	$-0.310042\pi$
$467$	24.2888	1.12395	0.561975	+	0.827154i	$0.310042\pi$
$468$	−15.9807	−0.738709
$469$	−12.0540	−0.556600
$470$	12.6731	0.584566
$471$	35.5385	1.63753
$472$	8.91020	0.410125
$473$	−9.11349	−0.419039
$474$	18.2014	0.836017
$475$	−2.55381	−0.117177
$476$	−0.394679	−0.0180901
$477$	18.1485	0.830965
$478$	26.7180	1.22205
$479$	23.6743	1.08171	0.540853	−	0.841117i	$-0.318102\pi$
$479$	23.6743	1.08171	0.540853	+	0.841117i	$0.318102\pi$
$480$	4.90233	0.223760
$481$	−10.7049	−0.488100
$482$	25.1533	1.14570
$483$	19.6641	0.894748
$484$	1.00000	0.0454545
$485$	11.6606	0.529479
$486$	−19.5345	−0.886101
$487$	−29.9710	−1.35812	−0.679059	−	0.734084i	$-0.737612\pi$
$487$	−29.9710	−1.35812	−0.679059	+	0.734084i	$0.737612\pi$
$488$	6.12688	0.277351
$489$	−19.8646	−0.898306
$490$	10.7560	0.485907
$491$	−35.8665	−1.61863	−0.809317	−	0.587372i	$-0.800163\pi$
$491$	−35.8665	−1.61863	−0.809317	+	0.587372i	$0.800163\pi$
$492$	2.86341	0.129093
$493$	−1.61638	−0.0727981
$494$	5.45612	0.245483
$495$	−7.84971	−0.352818
$496$	0.673305	0.0302323
$497$	0.175886	0.00788956
$498$	−7.64648	−0.342647
$499$	−9.88539	−0.442531	−0.221266	−	0.975214i	$-0.571019\pi$
$499$	−9.88539	−0.442531	−0.221266	+	0.975214i	$0.571019\pi$
$500$	−12.1702	−0.544269
$501$	10.6776	0.477040
$502$	−2.38310	−0.106363
$503$	−29.4156	−1.31158	−0.655788	−	0.754945i	$-0.727664\pi$
$503$	−29.4156	−1.31158	−0.655788	+	0.754945i	$0.727664\pi$
$504$	4.45888	0.198614
$505$	−3.99400	−0.177731
$506$	7.06154	0.313924
$507$	−1.55869	−0.0692241
$508$	5.19006	0.230272
$509$	2.48806	0.110281	0.0551406	−	0.998479i	$-0.482439\pi$
$509$	2.48806	0.110281	0.0551406	+	0.998479i	$0.482439\pi$
$510$	1.88209	0.0833404
$511$	7.76756	0.343616
$512$	−1.00000	−0.0441942
$513$	−5.36420	−0.236835
$514$	−24.3481	−1.07395
$515$	29.6372	1.30597
$516$	−24.6861	−1.08675
$517$	7.00242	0.307966
$518$	2.98683	0.131234
$519$	−0.520006	−0.0228257
$520$	6.66824	0.292421
$521$	−3.40868	−0.149337	−0.0746684	−	0.997208i	$-0.523790\pi$
$521$	−3.40868	−0.149337	−0.0746684	+	0.997208i	$0.523790\pi$
$522$	18.2610	0.799263
$523$	0.0771254	0.00337246	0.00168623	−	0.999999i	$-0.499463\pi$
$523$	0.0771254	0.00337246	0.00168623	+	0.999999i	$0.499463\pi$
$524$	−10.6535	−0.465401
$525$	−4.80237	−0.209593
$526$	23.8407	1.03950
$527$	0.258494	0.0112602
$528$	2.70875	0.117883
$529$	26.8654	1.16806
$530$	−7.57279	−0.328941
$531$	−38.6462	−1.67710
$532$	−1.52235	−0.0660021
$533$	3.89486	0.168705
$534$	−0.331839	−0.0143601
$535$	20.8163	0.899965
$536$	−11.7253	−0.506455
$537$	20.8018	0.897662
$538$	−19.6338	−0.846473
$539$	5.94315	0.255990
$540$	−6.55589	−0.282121
$541$	−43.9508	−1.88959	−0.944796	−	0.327661i	$-0.893740\pi$
$541$	−43.9508	−1.88959	−0.944796	+	0.327661i	$0.893740\pi$
$542$	19.7100	0.846618
$543$	−67.4559	−2.89481
$544$	−0.383918	−0.0164603
$545$	−20.9618	−0.897905
$546$	10.2601	0.439092
$547$	−17.6442	−0.754411	−0.377205	−	0.926130i	$-0.623115\pi$
$547$	−17.6442	−0.754411	−0.377205	+	0.926130i	$0.623115\pi$
$548$	−4.39067	−0.187560
$549$	−26.5741	−1.13416
$550$	−1.72457	−0.0735359
$551$	−6.23466	−0.265605
$552$	19.1279	0.814138
$553$	−6.90784	−0.293751
$554$	−6.24188	−0.265192
$555$	−14.2432	−0.604589
$556$	5.28118	0.223972
$557$	−11.9958	−0.508278	−0.254139	−	0.967168i	$-0.581792\pi$
$557$	−11.9958	−0.508278	−0.254139	+	0.967168i	$0.581792\pi$
$558$	−2.92033	−0.123627
$559$	−33.5785	−1.42022
$560$	−1.86055	−0.0786224
$561$	1.03994	0.0439061
$562$	20.2062	0.852346
$563$	−21.8180	−0.919520	−0.459760	−	0.888043i	$-0.652065\pi$
$563$	−21.8180	−0.919520	−0.459760	+	0.888043i	$0.652065\pi$
$564$	18.9678	0.798688
$565$	13.7064	0.576632
$566$	−13.4770	−0.566480
$567$	3.28941	0.138142
$568$	0.171090	0.00717878
$569$	43.6209	1.82868	0.914341	−	0.404946i	$-0.132710\pi$
$569$	43.6209	1.82868	0.914341	+	0.404946i	$0.132710\pi$
$570$	7.25955	0.304069
$571$	23.8250	0.997044	0.498522	−	0.866877i	$-0.333876\pi$
$571$	23.8250	0.997044	0.498522	+	0.866877i	$0.333876\pi$
$572$	3.68449	0.154056
$573$	−68.6403	−2.86749
$574$	−1.08673	−0.0453592
$575$	−12.1781	−0.507863
$576$	4.33730	0.180721
$577$	−30.3854	−1.26496	−0.632481	−	0.774576i	$-0.717963\pi$
$577$	−30.3854	−1.26496	−0.632481	+	0.774576i	$0.717963\pi$
$578$	16.8526	0.700976
$579$	45.1036	1.87444
$580$	−7.61973	−0.316392
$581$	2.90202	0.120396
$582$	17.4523	0.723423
$583$	−4.18429	−0.173296
$584$	7.55576	0.312659
$585$	−28.9222	−1.19578
$586$	15.5346	0.641730
$587$	7.61772	0.314417	0.157208	−	0.987565i	$-0.449751\pi$
$587$	7.61772	0.314417	0.157208	+	0.987565i	$0.449751\pi$
$588$	16.0985	0.663890
$589$	0.997055	0.0410829
$590$	16.1258	0.663889
$591$	2.70875	0.111423
$592$	2.90539	0.119411
$593$	−16.9697	−0.696861	−0.348430	−	0.937335i	$-0.613285\pi$
$593$	−16.9697	−0.696861	−0.348430	+	0.937335i	$0.613285\pi$
$594$	−3.62241	−0.148629
$595$	−0.714297	−0.0292833
$596$	22.4755	0.920631
$597$	65.3468	2.67447
$598$	26.0181	1.06396
$599$	12.6699	0.517680	0.258840	−	0.965920i	$-0.416660\pi$
$599$	12.6699	0.517680	0.258840	+	0.965920i	$0.416660\pi$
$600$	−4.67142	−0.190710
$601$	−33.2164	−1.35493	−0.677463	−	0.735557i	$-0.736921\pi$
$601$	−33.2164	−1.35493	−0.677463	+	0.735557i	$0.736921\pi$
$602$	9.36895	0.381850
$603$	50.8561	2.07102
$604$	−14.0797	−0.572895
$605$	1.80981	0.0735794
$606$	−5.97782	−0.242832
$607$	−17.5721	−0.713230	−0.356615	−	0.934251i	$-0.616069\pi$
$607$	−17.5721	−0.713230	−0.356615	+	0.934251i	$0.616069\pi$
$608$	−1.48084	−0.0600559
$609$	−11.7241	−0.475085
$610$	11.0885	0.448961
$611$	25.8003	1.04377
$612$	1.66517	0.0673104
$613$	−2.36495	−0.0955196	−0.0477598	−	0.998859i	$-0.515208\pi$
$613$	−2.36495	−0.0955196	−0.0477598	+	0.998859i	$0.515208\pi$
$614$	−6.57539	−0.265361
$615$	5.18224	0.208968
$616$	−1.02803	−0.0414206
$617$	−4.22597	−0.170131	−0.0850655	−	0.996375i	$-0.527110\pi$
$617$	−4.22597	−0.170131	−0.0850655	+	0.996375i	$0.527110\pi$
$618$	44.3579	1.78434
$619$	−24.5503	−0.986761	−0.493380	−	0.869814i	$-0.664239\pi$
$619$	−24.5503	−0.986761	−0.493380	+	0.869814i	$0.664239\pi$
$620$	1.21856	0.0489384
$621$	−25.5798	−1.02648
$622$	19.7037	0.790047
$623$	0.125940	0.00504570
$624$	9.98033	0.399533
$625$	−13.4030	−0.536120
$626$	−1.79777	−0.0718535
$627$	4.01121	0.160192
$628$	−13.1199	−0.523542
$629$	1.11543	0.0444751
$630$	8.06975	0.321507
$631$	−41.2656	−1.64276	−0.821378	−	0.570384i	$-0.806794\pi$
$631$	−41.2656	−1.64276	−0.821378	+	0.570384i	$0.806794\pi$
$632$	−6.71949	−0.267287
$633$	−32.2306	−1.28105
$634$	22.2336	0.883010
$635$	9.39306	0.372752
$636$	−11.3342	−0.449430
$637$	21.8975	0.867609
$638$	−4.21022	−0.166684
$639$	−0.742069	−0.0293558
$640$	−1.80981	−0.0715392
$641$	−27.1080	−1.07070	−0.535350	−	0.844630i	$-0.679820\pi$
$641$	−27.1080	−1.07070	−0.535350	+	0.844630i	$0.679820\pi$
$642$	31.1556	1.22962
$643$	3.91443	0.154370	0.0771850	−	0.997017i	$-0.475407\pi$
$643$	3.91443	0.154370	0.0771850	+	0.997017i	$0.475407\pi$
$644$	−7.25949	−0.286064
$645$	−44.6773	−1.75917
$646$	−0.568520	−0.0223681
$647$	38.9905	1.53287	0.766436	−	0.642320i	$-0.222028\pi$
$647$	38.9905	1.53287	0.766436	+	0.642320i	$0.222028\pi$
$648$	3.19972	0.125697
$649$	8.91020	0.349756
$650$	−6.35415	−0.249230
$651$	1.87494	0.0734845
$652$	7.33349	0.287202
$653$	−16.3999	−0.641776	−0.320888	−	0.947117i	$-0.603981\pi$
$653$	−16.3999	−0.641776	−0.320888	+	0.947117i	$0.603981\pi$
$654$	−31.3735	−1.22680
$655$	−19.2809	−0.753366
$656$	−1.05710	−0.0412728
$657$	−32.7716	−1.27854
$658$	−7.19871	−0.280635
$659$	28.4300	1.10748	0.553738	−	0.832691i	$-0.313201\pi$
$659$	28.4300	1.10748	0.553738	+	0.832691i	$0.313201\pi$
$660$	4.90233	0.190823
$661$	30.0909	1.17040	0.585200	−	0.810889i	$-0.301016\pi$
$661$	30.0909	1.17040	0.585200	+	0.810889i	$0.301016\pi$
$662$	17.2848	0.671792
$663$	3.83163	0.148808
$664$	2.82289	0.109549
$665$	−2.75517	−0.106841
$666$	−12.6016	−0.488300
$667$	−29.7307	−1.15118
$668$	−3.94190	−0.152517
$669$	45.6477	1.76484
$670$	−21.2206	−0.819824
$671$	6.12688	0.236525
$672$	−2.78468	−0.107421
$673$	−29.0362	−1.11926	−0.559632	−	0.828741i	$-0.689058\pi$
$673$	−29.0362	−1.11926	−0.559632	+	0.828741i	$0.689058\pi$
$674$	30.5466	1.17661
$675$	6.24710	0.240451
$676$	0.575430	0.0221319
$677$	28.6617	1.10156	0.550779	−	0.834651i	$-0.314331\pi$
$677$	28.6617	1.10156	0.550779	+	0.834651i	$0.314331\pi$
$678$	20.5143	0.787847
$679$	−6.62356	−0.254189
$680$	−0.694820	−0.0266451
$681$	36.6881	1.40589
$682$	0.673305	0.0257822
$683$	−29.2228	−1.11818	−0.559090	−	0.829107i	$-0.688849\pi$
$683$	−29.2228	−1.11818	−0.559090	+	0.829107i	$0.688849\pi$
$684$	6.42284	0.245583
$685$	−7.94629	−0.303612
$686$	−13.3060	−0.508024
$687$	28.5766	1.09027
$688$	9.11349	0.347448
$689$	−15.4170	−0.587340
$690$	34.6180	1.31788
$691$	1.87910	0.0714842	0.0357421	−	0.999361i	$-0.488621\pi$
$691$	1.87910	0.0714842	0.0357421	+	0.999361i	$0.488621\pi$
$692$	0.191973	0.00729772
$693$	4.45888	0.169379
$694$	−8.50271	−0.322758
$695$	9.55796	0.362554
$696$	−11.4044	−0.432284
$697$	−0.405839	−0.0153722
$698$	17.3331	0.656067
$699$	−21.4627	−0.811794
$700$	1.77291	0.0670098
$701$	9.89790	0.373838	0.186919	−	0.982375i	$-0.440150\pi$
$701$	9.89790	0.373838	0.186919	+	0.982375i	$0.440150\pi$
$702$	−13.3467	−0.503740
$703$	4.30241	0.162268
$704$	−1.00000	−0.0376889
$705$	34.3282	1.29287
$706$	12.3367	0.464297
$707$	2.26872	0.0853240
$708$	24.1355	0.907066
$709$	29.2330	1.09787	0.548934	−	0.835866i	$-0.315034\pi$
$709$	29.2330	1.09787	0.548934	+	0.835866i	$0.315034\pi$
$710$	0.309641	0.0116206
$711$	29.1444	1.09300
$712$	0.122506	0.00459112
$713$	4.75457	0.178060
$714$	−1.06909	−0.0400095
$715$	6.66824	0.249378
$716$	−7.67948	−0.286996
$717$	72.3724	2.70280
$718$	−6.42568	−0.239804
$719$	−0.829816	−0.0309469	−0.0154735	−	0.999880i	$-0.504926\pi$
$719$	−0.829816	−0.0309469	−0.0154735	+	0.999880i	$0.504926\pi$
$720$	7.84971	0.292542
$721$	−16.8349	−0.626963
$722$	16.8071	0.625496
$723$	68.1338	2.53392
$724$	24.9030	0.925513
$725$	7.26083	0.269660
$726$	2.70875	0.100531
$727$	−9.33583	−0.346247	−0.173123	−	0.984900i	$-0.555386\pi$
$727$	−9.33583	−0.346247	−0.173123	+	0.984900i	$0.555386\pi$
$728$	−3.78777	−0.140384
$729$	−43.3147	−1.60425
$730$	13.6745	0.506117
$731$	3.49883	0.129409
$732$	16.5962	0.613411
$733$	−8.65678	−0.319745	−0.159873	−	0.987138i	$-0.551108\pi$
$733$	−8.65678	−0.319745	−0.159873	+	0.987138i	$0.551108\pi$
$734$	22.1908	0.819077
$735$	29.1353	1.07467
$736$	−7.06154	−0.260292
$737$	−11.7253	−0.431907
$738$	4.58496	0.168775
$739$	0.187305	0.00689012	0.00344506	−	0.999994i	$-0.498903\pi$
$739$	0.187305	0.00689012	0.00344506	+	0.999994i	$0.498903\pi$
$740$	5.25822	0.193296
$741$	14.7793	0.542929
$742$	4.30158	0.157916
$743$	17.9070	0.656945	0.328473	−	0.944513i	$-0.393466\pi$
$743$	17.9070	0.656945	0.328473	+	0.944513i	$0.393466\pi$
$744$	1.82381	0.0668642
$745$	40.6764	1.49027
$746$	37.6429	1.37820
$747$	−12.2437	−0.447974
$748$	−0.383918	−0.0140374
$749$	−11.8243	−0.432050
$750$	−32.9660	−1.20375
$751$	−6.77489	−0.247219	−0.123610	−	0.992331i	$-0.539447\pi$
$751$	−6.77489	−0.247219	−0.123610	+	0.992331i	$0.539447\pi$
$752$	−7.00242	−0.255352
$753$	−6.45522	−0.235241
$754$	−15.5125	−0.564932
$755$	−25.4816	−0.927372
$756$	3.72395	0.135439
$757$	36.9896	1.34441	0.672205	−	0.740365i	$-0.265347\pi$
$757$	36.9896	1.34441	0.672205	+	0.740365i	$0.265347\pi$
$758$	9.52813	0.346077
$759$	19.1279	0.694300
$760$	−2.68004	−0.0972153
$761$	15.9311	0.577503	0.288752	−	0.957404i	$-0.406760\pi$
$761$	15.9311	0.577503	0.288752	+	0.957404i	$0.406760\pi$
$762$	14.0586	0.509288
$763$	11.9070	0.431061
$764$	25.3403	0.916778
$765$	3.01364	0.108959
$766$	−32.4206	−1.17140
$767$	32.8295	1.18540
$768$	−2.70875	−0.0977434
$769$	37.9667	1.36912	0.684558	−	0.728959i	$-0.259995\pi$
$769$	37.9667	1.36912	0.684558	+	0.728959i	$0.259995\pi$
$770$	−1.86055	−0.0670494
$771$	−65.9527	−2.37523
$772$	−16.6511	−0.599286
$773$	3.63185	0.130628	0.0653142	−	0.997865i	$-0.479195\pi$
$773$	3.63185	0.130628	0.0653142	+	0.997865i	$0.479195\pi$
$774$	−39.5279	−1.42080
$775$	−1.16116	−0.0417101
$776$	−6.44296	−0.231289
$777$	8.09057	0.290247
$778$	−21.6585	−0.776496
$779$	−1.56539	−0.0560860
$780$	18.0626	0.646743
$781$	0.171090	0.00612208
$782$	−2.71105	−0.0969470
$783$	15.2512	0.545032
$784$	−5.94315	−0.212255
$785$	−23.7446	−0.847482
$786$	−28.8576	−1.02932
$787$	−40.6073	−1.44749	−0.723746	−	0.690066i	$-0.757581\pi$
$787$	−40.6073	−1.44749	−0.723746	+	0.690066i	$0.757581\pi$
$788$	−1.00000	−0.0356235
$789$	64.5784	2.29905
$790$	−12.1610	−0.432670
$791$	−7.78565	−0.276826
$792$	4.33730	0.154119
$793$	22.5744	0.801640
$794$	24.7391	0.877957
$795$	−20.5128	−0.727513
$796$	−24.1244	−0.855066
$797$	24.1020	0.853738	0.426869	−	0.904314i	$-0.359617\pi$
$797$	24.1020	0.853738	0.426869	+	0.904314i	$0.359617\pi$
$798$	−4.12365	−0.145976
$799$	−2.68835	−0.0951071
$800$	1.72457	0.0609728
$801$	−0.531347	−0.0187742
$802$	10.5068	0.371007
$803$	7.55576	0.266637
$804$	−31.7608	−1.12012
$805$	−13.1383	−0.463065
$806$	2.48078	0.0873818
$807$	−53.1830	−1.87213
$808$	2.20686	0.0776370
$809$	−3.67611	−0.129245	−0.0646226	−	0.997910i	$-0.520584\pi$
$809$	−3.67611	−0.129245	−0.0646226	+	0.997910i	$0.520584\pi$
$810$	5.79089	0.203471
$811$	19.6775	0.690970	0.345485	−	0.938424i	$-0.387714\pi$
$811$	19.6775	0.690970	0.345485	+	0.938424i	$0.387714\pi$
$812$	4.32824	0.151892
$813$	53.3894	1.87245
$814$	2.90539	0.101834
$815$	13.2723	0.464907
$816$	−1.03994	−0.0364050
$817$	13.4956	0.472151
$818$	−5.49779	−0.192226
$819$	16.4287	0.574065
$820$	−1.91315	−0.0668102
$821$	5.89601	0.205772	0.102886	−	0.994693i	$-0.467192\pi$
$821$	5.89601	0.205772	0.102886	+	0.994693i	$0.467192\pi$
$822$	−11.8932	−0.414823
$823$	21.9387	0.764735	0.382368	−	0.924010i	$-0.375109\pi$
$823$	21.9387	0.764735	0.382368	+	0.924010i	$0.375109\pi$
$824$	−16.3758	−0.570479
$825$	−4.67142	−0.162638
$826$	−9.15996	−0.318716
$827$	−10.9898	−0.382152	−0.191076	−	0.981575i	$-0.561198\pi$
$827$	−10.9898	−0.382152	−0.191076	+	0.981575i	$0.561198\pi$
$828$	30.6280	1.06440
$829$	45.6228	1.58454	0.792272	−	0.610168i	$-0.208898\pi$
$829$	45.6228	1.58454	0.792272	+	0.610168i	$0.208898\pi$
$830$	5.10890	0.177333
$831$	−16.9077	−0.586521
$832$	−3.68449	−0.127737
$833$	−2.28168	−0.0790556
$834$	14.3054	0.495355
$835$	−7.13410	−0.246886
$836$	−1.48084	−0.0512158
$837$	−2.43899	−0.0843037
$838$	36.4229	1.25821
$839$	−15.2270	−0.525695	−0.262847	−	0.964837i	$-0.584662\pi$
$839$	−15.2270	−0.525695	−0.262847	+	0.964837i	$0.584662\pi$
$840$	−5.03975	−0.173888
$841$	−11.2740	−0.388759
$842$	−14.6138	−0.503624
$843$	54.7334	1.88512
$844$	11.8987	0.409571
$845$	1.04142	0.0358260
$846$	30.3716	1.04420
$847$	−1.02803	−0.0353236
$848$	4.18429	0.143689
$849$	−36.5057	−1.25287
$850$	0.662093	0.0227096
$851$	20.5165	0.703298
$852$	0.463439	0.0158772
$853$	−39.2348	−1.34337	−0.671686	−	0.740836i	$-0.734430\pi$
$853$	−39.2348	−1.34337	−0.671686	+	0.740836i	$0.734430\pi$
$854$	−6.29862	−0.215534
$855$	11.6242	0.397538
$856$	−11.5019	−0.393126
$857$	−8.50870	−0.290652	−0.145326	−	0.989384i	$-0.546423\pi$
$857$	−8.50870	−0.290652	−0.145326	+	0.989384i	$0.546423\pi$
$858$	9.98033	0.340723
$859$	30.1076	1.02726	0.513629	−	0.858012i	$-0.328301\pi$
$859$	30.1076	1.02726	0.513629	+	0.858012i	$0.328301\pi$
$860$	16.4937	0.562431
$861$	−2.94368	−0.100320
$862$	3.76658	0.128290
$863$	−17.5864	−0.598648	−0.299324	−	0.954152i	$-0.596761\pi$
$863$	−17.5864	−0.598648	−0.299324	+	0.954152i	$0.596761\pi$
$864$	3.62241	0.123237
$865$	0.347436	0.0118132
$866$	14.1809	0.481888
$867$	45.6494	1.55034
$868$	−0.692178	−0.0234941
$869$	−6.71949	−0.227943
$870$	−20.6399	−0.699758
$871$	−43.2017	−1.46383
$872$	11.5823	0.392226
$873$	27.9451	0.945797
$874$	−10.4570	−0.353713
$875$	12.5114	0.422962
$876$	20.4666	0.691503
$877$	−18.3633	−0.620085	−0.310042	−	0.950723i	$-0.600343\pi$
$877$	−18.3633	−0.620085	−0.310042	+	0.950723i	$0.600343\pi$
$878$	−13.8475	−0.467330
$879$	42.0794	1.41930
$880$	−1.80981	−0.0610088
$881$	−24.0919	−0.811675	−0.405838	−	0.913945i	$-0.633020\pi$
$881$	−24.0919	−0.811675	−0.405838	+	0.913945i	$0.633020\pi$
$882$	25.7772	0.867965
$883$	−28.9964	−0.975807	−0.487903	−	0.872898i	$-0.662238\pi$
$883$	−28.9964	−0.975807	−0.487903	+	0.872898i	$0.662238\pi$
$884$	−1.41454	−0.0475761
$885$	43.6807	1.46831
$886$	9.33250	0.313531
$887$	12.6541	0.424883	0.212442	−	0.977174i	$-0.431858\pi$
$887$	12.6541	0.424883	0.212442	+	0.977174i	$0.431858\pi$
$888$	7.86996	0.264099
$889$	−5.33555	−0.178949
$890$	0.221714	0.00743187
$891$	3.19972	0.107195
$892$	−16.8520	−0.564246
$893$	−10.3695	−0.347001
$894$	60.8803	2.03614
$895$	−13.8984	−0.464573
$896$	1.02803	0.0343441
$897$	70.4765	2.35314
$898$	−11.0633	−0.369188
$899$	−2.83476	−0.0945447
$900$	−7.47998	−0.249333
$901$	1.60642	0.0535177
$902$	−1.05710	−0.0351975
$903$	25.3781	0.844530
$904$	−7.57336	−0.251886
$905$	45.0698	1.49817
$906$	−38.1383	−1.26706
$907$	22.0243	0.731304	0.365652	−	0.930752i	$-0.380846\pi$
$907$	22.0243	0.731304	0.365652	+	0.930752i	$0.380846\pi$
$908$	−13.5443	−0.449484
$909$	−9.57181	−0.317477
$910$	−6.85516	−0.227246
$911$	5.77411	0.191305	0.0956524	−	0.995415i	$-0.469506\pi$
$911$	5.77411	0.191305	0.0956524	+	0.995415i	$0.469506\pi$
$912$	−4.01121	−0.132825
$913$	2.82289	0.0934239
$914$	−18.8133	−0.622289
$915$	30.0360	0.992958
$916$	−10.5498	−0.348574
$917$	10.9521	0.361671
$918$	1.39071	0.0459002
$919$	−2.85839	−0.0942896	−0.0471448	−	0.998888i	$-0.515012\pi$
$919$	−2.85839	−0.0942896	−0.0471448	+	0.998888i	$0.515012\pi$
$920$	−12.7801	−0.421347
$921$	−17.8111	−0.586894
$922$	7.27756	0.239674
$923$	0.630379	0.0207492
$924$	−2.78468	−0.0916091
$925$	−5.01055	−0.164746
$926$	−29.1565	−0.958141
$927$	71.0269	2.33283
$928$	4.21022	0.138207
$929$	−1.34120	−0.0440034	−0.0220017	−	0.999758i	$-0.507004\pi$
$929$	−1.34120	−0.0440034	−0.0220017	+	0.999758i	$0.507004\pi$
$930$	3.30076	0.108236
$931$	−8.80084	−0.288436
$932$	7.92349	0.259542
$933$	53.3724	1.74733
$934$	−24.2888	−0.794753
$935$	−0.694820	−0.0227230
$936$	15.9807	0.522346
$937$	−9.87688	−0.322663	−0.161332	−	0.986900i	$-0.551579\pi$
$937$	−9.87688	−0.322663	−0.161332	+	0.986900i	$0.551579\pi$
$938$	12.0540	0.393576
$939$	−4.86971	−0.158917
$940$	−12.6731	−0.413351
$941$	35.6915	1.16351	0.581754	−	0.813365i	$-0.302367\pi$
$941$	35.6915	1.16351	0.581754	+	0.813365i	$0.302367\pi$
$942$	−35.5385	−1.15791
$943$	−7.46474	−0.243086
$944$	−8.91020	−0.290002
$945$	6.73966	0.219241
$946$	9.11349	0.296305
$947$	−47.1591	−1.53246	−0.766232	−	0.642564i	$-0.777871\pi$
$947$	−47.1591	−1.53246	−0.766232	+	0.642564i	$0.777871\pi$
$948$	−18.2014	−0.591153
$949$	27.8391	0.903695
$950$	2.55381	0.0828565
$951$	60.2252	1.95294
$952$	0.394679	0.0127916
$953$	5.98618	0.193911	0.0969557	−	0.995289i	$-0.469089\pi$
$953$	5.98618	0.193911	0.0969557	+	0.995289i	$0.469089\pi$
$954$	−18.1485	−0.587581
$955$	45.8612	1.48403
$956$	−26.7180	−0.864123
$957$	−11.4044	−0.368653
$958$	−23.6743	−0.764881
$959$	4.51374	0.145756
$960$	−4.90233	−0.158222
$961$	−30.5467	−0.985376
$962$	10.7049	0.345139
$963$	49.8871	1.60759
$964$	−25.1533	−0.810132
$965$	−30.1354	−0.970092
$966$	−19.6641	−0.632682
$967$	32.6796	1.05091	0.525453	−	0.850823i	$-0.323896\pi$
$967$	32.6796	1.05091	0.525453	+	0.850823i	$0.323896\pi$
$968$	−1.00000	−0.0321412
$969$	−1.53998	−0.0494711
$970$	−11.6606	−0.374398
$971$	29.2814	0.939685	0.469843	−	0.882750i	$-0.344311\pi$
$971$	29.2814	0.939685	0.469843	+	0.882750i	$0.344311\pi$
$972$	19.5345	0.626568
$973$	−5.42922	−0.174053
$974$	29.9710	0.960334
$975$	−17.2118	−0.551218
$976$	−6.12688	−0.196117
$977$	−27.4376	−0.877807	−0.438903	−	0.898534i	$-0.644633\pi$
$977$	−27.4376	−0.877807	−0.438903	+	0.898534i	$0.644633\pi$
$978$	19.8646	0.635199
$979$	0.122506	0.00391532
$980$	−10.7560	−0.343588
$981$	−50.2359	−1.60391
$982$	35.8665	1.14455
$983$	2.56800	0.0819063	0.0409532	−	0.999161i	$-0.486961\pi$
$983$	2.56800	0.0819063	0.0409532	+	0.999161i	$0.486961\pi$
$984$	−2.86341	−0.0912822
$985$	−1.80981	−0.0576655
$986$	1.61638	0.0514760
$987$	−19.4995	−0.620675
$988$	−5.45612	−0.173582
$989$	64.3553	2.04638
$990$	7.84971	0.249480
$991$	17.0825	0.542642	0.271321	−	0.962489i	$-0.412539\pi$
$991$	17.0825	0.542642	0.271321	+	0.962489i	$0.412539\pi$
$992$	−0.673305	−0.0213774
$993$	46.8201	1.48579
$994$	−0.175886	−0.00557876
$995$	−43.6607	−1.38414
$996$	7.64648	0.242288
$997$	−44.1932	−1.39961	−0.699806	−	0.714332i	$-0.746730\pi$
$997$	−44.1932	−1.39961	−0.699806	+	0.714332i	$0.746730\pi$
$998$	9.88539	0.312917
$999$	−10.5245	−0.332981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.c.1.1	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.c.1.1	✓	17	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.70875 q^{3} +1.00000 q^{4} +1.80981 q^{5} +2.70875 q^{6} -1.02803 q^{7} -1.00000 q^{8} +4.33730 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.70875 q^{3} +1.00000 q^{4} +1.80981 q^{5} +2.70875 q^{6} -1.02803 q^{7} -1.00000 q^{8} +4.33730 q^{9} -1.80981 q^{10} -1.00000 q^{11} -2.70875 q^{12} -3.68449 q^{13} +1.02803 q^{14} -4.90233 q^{15} +1.00000 q^{16} +0.383918 q^{17} -4.33730 q^{18} +1.48084 q^{19} +1.80981 q^{20} +2.78468 q^{21} +1.00000 q^{22} +7.06154 q^{23} +2.70875 q^{24} -1.72457 q^{25} +3.68449 q^{26} -3.62241 q^{27} -1.02803 q^{28} -4.21022 q^{29} +4.90233 q^{30} +0.673305 q^{31} -1.00000 q^{32} +2.70875 q^{33} -0.383918 q^{34} -1.86055 q^{35} +4.33730 q^{36} +2.90539 q^{37} -1.48084 q^{38} +9.98033 q^{39} -1.80981 q^{40} -1.05710 q^{41} -2.78468 q^{42} +9.11349 q^{43} -1.00000 q^{44} +7.84971 q^{45} -7.06154 q^{46} -7.00242 q^{47} -2.70875 q^{48} -5.94315 q^{49} +1.72457 q^{50} -1.03994 q^{51} -3.68449 q^{52} +4.18429 q^{53} +3.62241 q^{54} -1.80981 q^{55} +1.02803 q^{56} -4.01121 q^{57} +4.21022 q^{58} -8.91020 q^{59} -4.90233 q^{60} -6.12688 q^{61} -0.673305 q^{62} -4.45888 q^{63} +1.00000 q^{64} -6.66824 q^{65} -2.70875 q^{66} +11.7253 q^{67} +0.383918 q^{68} -19.1279 q^{69} +1.86055 q^{70} -0.171090 q^{71} -4.33730 q^{72} -7.55576 q^{73} -2.90539 q^{74} +4.67142 q^{75} +1.48084 q^{76} +1.02803 q^{77} -9.98033 q^{78} +6.71949 q^{79} +1.80981 q^{80} -3.19972 q^{81} +1.05710 q^{82} -2.82289 q^{83} +2.78468 q^{84} +0.694820 q^{85} -9.11349 q^{86} +11.4044 q^{87} +1.00000 q^{88} -0.122506 q^{89} -7.84971 q^{90} +3.78777 q^{91} +7.06154 q^{92} -1.82381 q^{93} +7.00242 q^{94} +2.68004 q^{95} +2.70875 q^{96} +6.44296 q^{97} +5.94315 q^{98} -4.33730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more