LMFDB - Embedded newform 4017.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} + \cdots + 4 $ x^19 - 4x^18 - 16x^17 + 77x^16 + 88x^15 - 594x^14 - 154x^13 + 2388x^12 - 278x^11 - 5460x^10 + 1491x^9 + 7285x^8 - 2223x^7 - 5579x^6 + 1430x^5 + 2261x^4 - 352x^3 - 378x^2 + 11x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.02307$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02307 q^{2} +1.00000 q^{3} +2.09279 q^{4} -0.298497 q^{5} -2.02307 q^{6} +0.750849 q^{7} -0.187724 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.02307 q^{2} +1.00000 q^{3} +2.09279 q^{4} -0.298497 q^{5} -2.02307 q^{6} +0.750849 q^{7} -0.187724 q^{8} +1.00000 q^{9} +0.603878 q^{10} +0.237705 q^{11} +2.09279 q^{12} +1.00000 q^{13} -1.51902 q^{14} -0.298497 q^{15} -3.80581 q^{16} +0.0113846 q^{17} -2.02307 q^{18} +0.0257012 q^{19} -0.624692 q^{20} +0.750849 q^{21} -0.480892 q^{22} +4.72507 q^{23} -0.187724 q^{24} -4.91090 q^{25} -2.02307 q^{26} +1.00000 q^{27} +1.57137 q^{28} -8.18147 q^{29} +0.603878 q^{30} -6.60774 q^{31} +8.07484 q^{32} +0.237705 q^{33} -0.0230318 q^{34} -0.224126 q^{35} +2.09279 q^{36} +1.89574 q^{37} -0.0519952 q^{38} +1.00000 q^{39} +0.0560351 q^{40} -0.113872 q^{41} -1.51902 q^{42} -11.0396 q^{43} +0.497466 q^{44} -0.298497 q^{45} -9.55912 q^{46} -2.55917 q^{47} -3.80581 q^{48} -6.43623 q^{49} +9.93507 q^{50} +0.0113846 q^{51} +2.09279 q^{52} +11.1605 q^{53} -2.02307 q^{54} -0.0709541 q^{55} -0.140953 q^{56} +0.0257012 q^{57} +16.5517 q^{58} -3.79069 q^{59} -0.624692 q^{60} +2.16784 q^{61} +13.3679 q^{62} +0.750849 q^{63} -8.72432 q^{64} -0.298497 q^{65} -0.480892 q^{66} -2.16200 q^{67} +0.0238256 q^{68} +4.72507 q^{69} +0.453421 q^{70} -8.40881 q^{71} -0.187724 q^{72} -1.85534 q^{73} -3.83521 q^{74} -4.91090 q^{75} +0.0537873 q^{76} +0.178480 q^{77} -2.02307 q^{78} -2.96608 q^{79} +1.13602 q^{80} +1.00000 q^{81} +0.230371 q^{82} -8.50437 q^{83} +1.57137 q^{84} -0.00339826 q^{85} +22.3339 q^{86} -8.18147 q^{87} -0.0446230 q^{88} -4.70287 q^{89} +0.603878 q^{90} +0.750849 q^{91} +9.88859 q^{92} -6.60774 q^{93} +5.17736 q^{94} -0.00767173 q^{95} +8.07484 q^{96} -14.3192 q^{97} +13.0209 q^{98} +0.237705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.02307	−1.43052	−0.715261	−	0.698857i	$-0.753692\pi$
$2$	−2.02307	−1.43052	−0.715261	+	0.698857i	$0.753692\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.09279	1.04640
$5$	−0.298497	−0.133492	−0.0667459	−	0.997770i	$-0.521262\pi$
$5$	−0.298497	−0.133492	−0.0667459	+	0.997770i	$0.521262\pi$
$6$	−2.02307	−0.825913
$7$	0.750849	0.283794	0.141897	−	0.989881i	$-0.454680\pi$
$7$	0.750849	0.283794	0.141897	+	0.989881i	$0.454680\pi$
$8$	−0.187724	−0.0663706
$9$	1.00000	0.333333
$10$	0.603878	0.190963
$11$	0.237705	0.0716707	0.0358353	−	0.999358i	$-0.488591\pi$
$11$	0.237705	0.0716707	0.0358353	+	0.999358i	$0.488591\pi$
$12$	2.09279	0.604137
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.51902	−0.405974
$15$	−0.298497	−0.0770715
$16$	−3.80581	−0.951451
$17$	0.0113846	0.00276117	0.00138058	−	0.999999i	$-0.499561\pi$
$17$	0.0113846	0.00276117	0.00138058	+	0.999999i	$0.499561\pi$
$18$	−2.02307	−0.476841
$19$	0.0257012	0.00589627	0.00294813	−	0.999996i	$-0.499062\pi$
$19$	0.0257012	0.00589627	0.00294813	+	0.999996i	$0.499062\pi$
$20$	−0.624692	−0.139685
$21$	0.750849	0.163849
$22$	−0.480892	−0.102527
$23$	4.72507	0.985245	0.492623	−	0.870243i	$-0.336038\pi$
$23$	4.72507	0.985245	0.492623	+	0.870243i	$0.336038\pi$
$24$	−0.187724	−0.0383191
$25$	−4.91090	−0.982180
$26$	−2.02307	−0.396756
$27$	1.00000	0.192450
$28$	1.57137	0.296961
$29$	−8.18147	−1.51926	−0.759631	−	0.650355i	$-0.774620\pi$
$29$	−8.18147	−1.51926	−0.759631	+	0.650355i	$0.774620\pi$
$30$	0.603878	0.110253
$31$	−6.60774	−1.18678	−0.593392	−	0.804913i	$-0.702212\pi$
$31$	−6.60774	−1.18678	−0.593392	+	0.804913i	$0.702212\pi$
$32$	8.07484	1.42744
$33$	0.237705	0.0413791
$34$	−0.0230318	−0.00394991
$35$	−0.224126	−0.0378842
$36$	2.09279	0.348799
$37$	1.89574	0.311658	0.155829	−	0.987784i	$-0.450195\pi$
$37$	1.89574	0.311658	0.155829	+	0.987784i	$0.450195\pi$
$38$	−0.0519952	−0.00843474
$39$	1.00000	0.160128
$40$	0.0560351	0.00885993
$41$	−0.113872	−0.0177838	−0.00889192	−	0.999960i	$-0.502830\pi$
$41$	−0.113872	−0.0177838	−0.00889192	+	0.999960i	$0.502830\pi$
$42$	−1.51902	−0.234389
$43$	−11.0396	−1.68353	−0.841765	−	0.539844i	$-0.818483\pi$
$43$	−11.0396	−1.68353	−0.841765	+	0.539844i	$0.818483\pi$
$44$	0.497466	0.0749959
$45$	−0.298497	−0.0444973
$46$	−9.55912	−1.40942
$47$	−2.55917	−0.373293	−0.186647	−	0.982427i	$-0.559762\pi$
$47$	−2.55917	−0.373293	−0.186647	+	0.982427i	$0.559762\pi$
$48$	−3.80581	−0.549321
$49$	−6.43623	−0.919461
$50$	9.93507	1.40503
$51$	0.0113846	0.00159416
$52$	2.09279	0.290218
$53$	11.1605	1.53302	0.766508	−	0.642235i	$-0.221992\pi$
$53$	11.1605	1.53302	0.766508	+	0.642235i	$0.221992\pi$
$54$	−2.02307	−0.275304
$55$	−0.0709541	−0.00956744
$56$	−0.140953	−0.0188356
$57$	0.0257012	0.00340421
$58$	16.5517	2.17334
$59$	−3.79069	−0.493506	−0.246753	−	0.969078i	$-0.579364\pi$
$59$	−3.79069	−0.493506	−0.246753	+	0.969078i	$0.579364\pi$
$60$	−0.624692	−0.0806473
$61$	2.16784	0.277564	0.138782	−	0.990323i	$-0.455681\pi$
$61$	2.16784	0.277564	0.138782	+	0.990323i	$0.455681\pi$
$62$	13.3679	1.69772
$63$	0.750849	0.0945980
$64$	−8.72432	−1.09054
$65$	−0.298497	−0.0370240
$66$	−0.480892	−0.0591937
$67$	−2.16200	−0.264130	−0.132065	−	0.991241i	$-0.542161\pi$
$67$	−2.16200	−0.264130	−0.132065	+	0.991241i	$0.542161\pi$
$68$	0.0238256	0.00288928
$69$	4.72507	0.568831
$70$	0.453421	0.0541942
$71$	−8.40881	−0.997942	−0.498971	−	0.866619i	$-0.666289\pi$
$71$	−8.40881	−0.997942	−0.498971	+	0.866619i	$0.666289\pi$
$72$	−0.187724	−0.0221235
$73$	−1.85534	−0.217151	−0.108576	−	0.994088i	$-0.534629\pi$
$73$	−1.85534	−0.217151	−0.108576	+	0.994088i	$0.534629\pi$
$74$	−3.83521	−0.445834
$75$	−4.91090	−0.567062
$76$	0.0537873	0.00616983
$77$	0.178480	0.0203397
$78$	−2.02307	−0.229067
$79$	−2.96608	−0.333710	−0.166855	−	0.985981i	$-0.553361\pi$
$79$	−2.96608	−0.333710	−0.166855	+	0.985981i	$0.553361\pi$
$80$	1.13602	0.127011
$81$	1.00000	0.111111
$82$	0.230371	0.0254402
$83$	−8.50437	−0.933476	−0.466738	−	0.884396i	$-0.654571\pi$
$83$	−8.50437	−0.933476	−0.466738	+	0.884396i	$0.654571\pi$
$84$	1.57137	0.171451
$85$	−0.00339826	−0.000368593 0
$86$	22.3339	2.40833
$87$	−8.18147	−0.877146
$88$	−0.0446230	−0.00475682
$89$	−4.70287	−0.498504	−0.249252	−	0.968439i	$-0.580185\pi$
$89$	−4.70287	−0.498504	−0.249252	+	0.968439i	$0.580185\pi$
$90$	0.603878	0.0636544
$91$	0.750849	0.0787103
$92$	9.88859	1.03096
$93$	−6.60774	−0.685190
$94$	5.17736	0.534004
$95$	−0.00767173	−0.000787103 0
$96$	8.07484	0.824135
$97$	−14.3192	−1.45390	−0.726948	−	0.686692i	$-0.759062\pi$
$97$	−14.3192	−1.45390	−0.726948	+	0.686692i	$0.759062\pi$
$98$	13.0209	1.31531
$99$	0.237705	0.0238902
$100$	−10.2775	−1.02775
$101$	0.631177	0.0628044	0.0314022	−	0.999507i	$-0.490003\pi$
$101$	0.631177	0.0628044	0.0314022	+	0.999507i	$0.490003\pi$
$102$	−0.0230318	−0.00228048
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−0.187724	−0.0184079
$105$	−0.224126	−0.0218724
$106$	−22.5785	−2.19302
$107$	18.4606	1.78465	0.892325	−	0.451393i	$-0.149073\pi$
$107$	18.4606	1.78465	0.892325	+	0.451393i	$0.149073\pi$
$108$	2.09279	0.201379
$109$	2.95254	0.282802	0.141401	−	0.989952i	$-0.454839\pi$
$109$	2.95254	0.282802	0.141401	+	0.989952i	$0.454839\pi$
$110$	0.143545	0.0136864
$111$	1.89574	0.179936
$112$	−2.85758	−0.270016
$113$	12.4175	1.16814	0.584070	−	0.811703i	$-0.301459\pi$
$113$	12.4175	1.16814	0.584070	+	0.811703i	$0.301459\pi$
$114$	−0.0519952	−0.00486980
$115$	−1.41042	−0.131522
$116$	−17.1221	−1.58975
$117$	1.00000	0.0924500
$118$	7.66882	0.705972
$119$	0.00854810	0.000783603 0
$120$	0.0560351	0.00511528
$121$	−10.9435	−0.994863
$122$	−4.38569	−0.397062
$123$	−0.113872	−0.0102675
$124$	−13.8286	−1.24185
$125$	2.95837	0.264605
$126$	−1.51902	−0.135325
$127$	7.57139	0.671853	0.335926	−	0.941888i	$-0.390951\pi$
$127$	7.57139	0.671853	0.335926	+	0.941888i	$0.390951\pi$
$128$	1.50018	0.132598
$129$	−11.0396	−0.971987
$130$	0.603878	0.0529636
$131$	10.4303	0.911303	0.455652	−	0.890158i	$-0.349406\pi$
$131$	10.4303	0.911303	0.455652	+	0.890158i	$0.349406\pi$
$132$	0.497466	0.0432989
$133$	0.0192977	0.00167333
$134$	4.37386	0.377844
$135$	−0.298497	−0.0256905
$136$	−0.00213716	−0.000183260 0
$137$	11.7705	1.00562	0.502812	−	0.864396i	$-0.332299\pi$
$137$	11.7705	1.00562	0.502812	+	0.864396i	$0.332299\pi$
$138$	−9.55912	−0.813727
$139$	4.37973	0.371484	0.185742	−	0.982599i	$-0.440531\pi$
$139$	4.37973	0.371484	0.185742	+	0.982599i	$0.440531\pi$
$140$	−0.469049	−0.0396419
$141$	−2.55917	−0.215521
$142$	17.0116	1.42758
$143$	0.237705	0.0198779
$144$	−3.80581	−0.317150
$145$	2.44214	0.202809
$146$	3.75348	0.310640
$147$	−6.43623	−0.530851
$148$	3.96739	0.326118
$149$	−12.1640	−0.996518	−0.498259	−	0.867028i	$-0.666027\pi$
$149$	−12.1640	−0.996518	−0.498259	+	0.867028i	$0.666027\pi$
$150$	9.93507	0.811195
$151$	−1.81737	−0.147895	−0.0739477	−	0.997262i	$-0.523560\pi$
$151$	−1.81737	−0.147895	−0.0739477	+	0.997262i	$0.523560\pi$
$152$	−0.00482475	−0.000391339 0
$153$	0.0113846	0.000920389 0
$154$	−0.361077	−0.0290964
$155$	1.97239	0.158426
$156$	2.09279	0.167557
$157$	0.698694	0.0557618	0.0278809	−	0.999611i	$-0.491124\pi$
$157$	0.698694	0.0557618	0.0278809	+	0.999611i	$0.491124\pi$
$158$	6.00057	0.477380
$159$	11.1605	0.885087
$160$	−2.41031	−0.190552
$161$	3.54781	0.279607
$162$	−2.02307	−0.158947
$163$	−5.52864	−0.433036	−0.216518	−	0.976279i	$-0.569470\pi$
$163$	−5.52864	−0.433036	−0.216518	+	0.976279i	$0.569470\pi$
$164$	−0.238311	−0.0186089
$165$	−0.0709541	−0.00552377
$166$	17.2049	1.33536
$167$	−2.91337	−0.225444	−0.112722	−	0.993627i	$-0.535957\pi$
$167$	−2.91337	−0.225444	−0.112722	+	0.993627i	$0.535957\pi$
$168$	−0.140953	−0.0108747
$169$	1.00000	0.0769231
$170$	0.00687490	0.000527281 0
$171$	0.0257012	0.00196542
$172$	−23.1037	−1.76164
$173$	−18.8203	−1.43088	−0.715440	−	0.698674i	$-0.753774\pi$
$173$	−18.8203	−1.43088	−0.715440	+	0.698674i	$0.753774\pi$
$174$	16.5517	1.25478
$175$	−3.68734	−0.278737
$176$	−0.904658	−0.0681911
$177$	−3.79069	−0.284926
$178$	9.51422	0.713121
$179$	−20.1999	−1.50981	−0.754905	−	0.655834i	$-0.772317\pi$
$179$	−20.1999	−1.50981	−0.754905	+	0.655834i	$0.772317\pi$
$180$	−0.624692	−0.0465618
$181$	−3.91651	−0.291112	−0.145556	−	0.989350i	$-0.546497\pi$
$181$	−3.91651	−0.291112	−0.145556	+	0.989350i	$0.546497\pi$
$182$	−1.51902	−0.112597
$183$	2.16784	0.160252
$184$	−0.887011	−0.0653913
$185$	−0.565872	−0.0416038
$186$	13.3679	0.980181
$187$	0.00270617	0.000197895 0
$188$	−5.35581	−0.390612
$189$	0.750849	0.0546162
$190$	0.0155204	0.00112597
$191$	3.10053	0.224346	0.112173	−	0.993689i	$-0.464219\pi$
$191$	3.10053	0.224346	0.112173	+	0.993689i	$0.464219\pi$
$192$	−8.72432	−0.629623
$193$	−15.5985	−1.12281	−0.561403	−	0.827542i	$-0.689738\pi$
$193$	−15.5985	−1.12281	−0.561403	+	0.827542i	$0.689738\pi$
$194$	28.9687	2.07983
$195$	−0.298497	−0.0213758
$196$	−13.4697	−0.962120
$197$	−23.4396	−1.67000	−0.835002	−	0.550246i	$-0.814534\pi$
$197$	−23.4396	−1.67000	−0.835002	+	0.550246i	$0.814534\pi$
$198$	−0.480892	−0.0341755
$199$	−1.83086	−0.129786	−0.0648930	−	0.997892i	$-0.520671\pi$
$199$	−1.83086	−0.129786	−0.0648930	+	0.997892i	$0.520671\pi$
$200$	0.921896	0.0651879
$201$	−2.16200	−0.152496
$202$	−1.27691	−0.0898432
$203$	−6.14305	−0.431157
$204$	0.0238256	0.00166812
$205$	0.0339904	0.00237400
$206$	2.02307	0.140954
$207$	4.72507	0.328415
$208$	−3.80581	−0.263885
$209$	0.00610930	0.000422589 0
$210$	0.453421	0.0312890
$211$	−25.6348	−1.76477	−0.882385	−	0.470529i	$-0.844063\pi$
$211$	−25.6348	−1.76477	−0.882385	+	0.470529i	$0.844063\pi$
$212$	23.3567	1.60414
$213$	−8.40881	−0.576162
$214$	−37.3469	−2.55298
$215$	3.29530	0.224737
$216$	−0.187724	−0.0127730
$217$	−4.96141	−0.336803
$218$	−5.97318	−0.404555
$219$	−1.85534	−0.125372
$220$	−0.148492	−0.0100113
$221$	0.0113846	0.000765810 0
$222$	−3.83521	−0.257402
$223$	26.2600	1.75850	0.879250	−	0.476360i	$-0.158044\pi$
$223$	26.2600	1.75850	0.879250	+	0.476360i	$0.158044\pi$
$224$	6.06298	0.405100
$225$	−4.91090	−0.327393
$226$	−25.1214	−1.67105
$227$	−8.01089	−0.531702	−0.265851	−	0.964014i	$-0.585653\pi$
$227$	−8.01089	−0.531702	−0.265851	+	0.964014i	$0.585653\pi$
$228$	0.0537873	0.00356215
$229$	−11.7976	−0.779605	−0.389803	−	0.920898i	$-0.627457\pi$
$229$	−11.7976	−0.779605	−0.389803	+	0.920898i	$0.627457\pi$
$230$	2.85337	0.188145
$231$	0.178480	0.0117431
$232$	1.53586	0.100834
$233$	25.1752	1.64928	0.824641	−	0.565657i	$-0.191377\pi$
$233$	25.1752	1.64928	0.824641	+	0.565657i	$0.191377\pi$
$234$	−2.02307	−0.132252
$235$	0.763903	0.0498316
$236$	−7.93313	−0.516403
$237$	−2.96608	−0.192667
$238$	−0.0172934	−0.00112096
$239$	7.54505	0.488049	0.244024	−	0.969769i	$-0.421532\pi$
$239$	7.54505	0.488049	0.244024	+	0.969769i	$0.421532\pi$
$240$	1.13602	0.0733298
$241$	8.92600	0.574974	0.287487	−	0.957785i	$-0.407180\pi$
$241$	8.92600	0.574974	0.287487	+	0.957785i	$0.407180\pi$
$242$	22.1394	1.42317
$243$	1.00000	0.0641500
$244$	4.53685	0.290442
$245$	1.92119	0.122740
$246$	0.230371	0.0146879
$247$	0.0257012	0.00163533
$248$	1.24043	0.0787676
$249$	−8.50437	−0.538943
$250$	−5.98498	−0.378523
$251$	20.0548	1.26585	0.632925	−	0.774213i	$-0.281854\pi$
$251$	20.0548	1.26585	0.632925	+	0.774213i	$0.281854\pi$
$252$	1.57137	0.0989870
$253$	1.12317	0.0706132
$254$	−15.3174	−0.961101
$255$	−0.00339826	−0.000212807 0
$256$	14.4137	0.900855
$257$	14.3931	0.897819	0.448909	−	0.893577i	$-0.351813\pi$
$257$	14.3931	0.897819	0.448909	+	0.893577i	$0.351813\pi$
$258$	22.3339	1.39045
$259$	1.42341	0.0884467
$260$	−0.624692	−0.0387417
$261$	−8.18147	−0.506420
$262$	−21.1013	−1.30364
$263$	15.5763	0.960473	0.480236	−	0.877139i	$-0.340551\pi$
$263$	15.5763	0.960473	0.480236	+	0.877139i	$0.340551\pi$
$264$	−0.0446230	−0.00274635
$265$	−3.33138	−0.204645
$266$	−0.0390406	−0.00239373
$267$	−4.70287	−0.287811
$268$	−4.52461	−0.276385
$269$	25.1284	1.53211	0.766053	−	0.642778i	$-0.222218\pi$
$269$	25.1284	1.53211	0.766053	+	0.642778i	$0.222218\pi$
$270$	0.603878	0.0367509
$271$	15.0469	0.914031	0.457016	−	0.889459i	$-0.348918\pi$
$271$	15.0469	0.914031	0.457016	+	0.889459i	$0.348918\pi$
$272$	−0.0433275	−0.00262712
$273$	0.750849	0.0454434
$274$	−23.8125	−1.43857
$275$	−1.16734	−0.0703935
$276$	9.88859	0.595223
$277$	14.8725	0.893601	0.446801	−	0.894634i	$-0.352563\pi$
$277$	14.8725	0.893601	0.446801	+	0.894634i	$0.352563\pi$
$278$	−8.86049	−0.531417
$279$	−6.60774	−0.395595
$280$	0.0420739	0.00251440
$281$	8.91658	0.531919	0.265959	−	0.963984i	$-0.414311\pi$
$281$	8.91658	0.531919	0.265959	+	0.963984i	$0.414311\pi$
$282$	5.17736	0.308308
$283$	14.4516	0.859059	0.429530	−	0.903053i	$-0.358679\pi$
$283$	14.4516	0.859059	0.429530	+	0.903053i	$0.358679\pi$
$284$	−17.5979	−1.04424
$285$	−0.00767173	−0.000454434 0
$286$	−0.480892	−0.0284357
$287$	−0.0855007	−0.00504695
$288$	8.07484	0.475815
$289$	−16.9999	−0.999992
$290$	−4.94061	−0.290123
$291$	−14.3192	−0.839408
$292$	−3.88284	−0.227226
$293$	−16.3947	−0.957791	−0.478895	−	0.877872i	$-0.658963\pi$
$293$	−16.3947	−0.957791	−0.478895	+	0.877872i	$0.658963\pi$
$294$	13.0209	0.759395
$295$	1.13151	0.0658790
$296$	−0.355877	−0.0206849
$297$	0.237705	0.0137930
$298$	24.6087	1.42554
$299$	4.72507	0.273258
$300$	−10.2775	−0.593371
$301$	−8.28910	−0.477776
$302$	3.67666	0.211568
$303$	0.631177	0.0362602
$304$	−0.0978139	−0.00561001
$305$	−0.647094	−0.0370525
$306$	−0.0230318	−0.00131664
$307$	−0.369547	−0.0210911	−0.0105456	−	0.999944i	$-0.503357\pi$
$307$	−0.369547	−0.0210911	−0.0105456	+	0.999944i	$0.503357\pi$
$308$	0.373522	0.0212834
$309$	−1.00000	−0.0568880
$310$	−3.99027	−0.226632
$311$	18.6922	1.05994	0.529970	−	0.848017i	$-0.322203\pi$
$311$	18.6922	1.05994	0.529970	+	0.848017i	$0.322203\pi$
$312$	−0.187724	−0.0106278
$313$	−13.3835	−0.756479	−0.378239	−	0.925708i	$-0.623470\pi$
$313$	−13.3835	−0.756479	−0.378239	+	0.925708i	$0.623470\pi$
$314$	−1.41350	−0.0797686
$315$	−0.224126	−0.0126281
$316$	−6.20738	−0.349193
$317$	−21.7909	−1.22390	−0.611950	−	0.790897i	$-0.709614\pi$
$317$	−21.7909	−1.22390	−0.611950	+	0.790897i	$0.709614\pi$
$318$	−22.5785	−1.26614
$319$	−1.94477	−0.108886
$320$	2.60418	0.145578
$321$	18.4606	1.03037
$322$	−7.17745	−0.399984
$323$	0.000292598 0	1.62806e−5 0
$324$	2.09279	0.116266
$325$	−4.91090	−0.272408
$326$	11.1848	0.619468
$327$	2.95254	0.163276
$328$	0.0213766	0.00118032
$329$	−1.92155	−0.105938
$330$	0.143545	0.00790187
$331$	−27.7510	−1.52533	−0.762667	−	0.646792i	$-0.776110\pi$
$331$	−27.7510	−1.52533	−0.762667	+	0.646792i	$0.776110\pi$
$332$	−17.7979	−0.976786
$333$	1.89574	0.103886
$334$	5.89394	0.322502
$335$	0.645349	0.0352592
$336$	−2.85758	−0.155894
$337$	−0.178388	−0.00971743	−0.00485872	−	0.999988i	$-0.501547\pi$
$337$	−0.178388	−0.00971743	−0.00485872	+	0.999988i	$0.501547\pi$
$338$	−2.02307	−0.110040
$339$	12.4175	0.674426
$340$	−0.00711186	−0.000385695 0
$341$	−1.57069	−0.0850576
$342$	−0.0519952	−0.00281158
$343$	−10.0886	−0.544732
$344$	2.07241	0.111737
$345$	−1.41042	−0.0759343
$346$	38.0747	2.04691
$347$	−20.9680	−1.12562	−0.562810	−	0.826586i	$-0.690280\pi$
$347$	−20.9680	−1.12562	−0.562810	+	0.826586i	$0.690280\pi$
$348$	−17.1221	−0.917842
$349$	−33.2238	−1.77843	−0.889214	−	0.457492i	$-0.848748\pi$
$349$	−33.2238	−1.77843	−0.889214	+	0.457492i	$0.848748\pi$
$350$	7.45973	0.398740
$351$	1.00000	0.0533761
$352$	1.91943	0.102306
$353$	−10.0246	−0.533555	−0.266778	−	0.963758i	$-0.585959\pi$
$353$	−10.0246	−0.533555	−0.266778	+	0.963758i	$0.585959\pi$
$354$	7.66882	0.407593
$355$	2.51000	0.133217
$356$	−9.84214	−0.521632
$357$	0.00854810	0.000452414 0
$358$	40.8657	2.15982
$359$	−4.30436	−0.227176	−0.113588	−	0.993528i	$-0.536234\pi$
$359$	−4.30436	−0.227176	−0.113588	+	0.993528i	$0.536234\pi$
$360$	0.0560351	0.00295331
$361$	−18.9993	−0.999965
$362$	7.92335	0.416442
$363$	−10.9435	−0.574385
$364$	1.57137	0.0823622
$365$	0.553813	0.0289879
$366$	−4.38569	−0.229244
$367$	−20.5845	−1.07450	−0.537250	−	0.843423i	$-0.680537\pi$
$367$	−20.5845	−1.07450	−0.537250	+	0.843423i	$0.680537\pi$
$368$	−17.9827	−0.937413
$369$	−0.113872	−0.00592794
$370$	1.14480	0.0595151
$371$	8.37987	0.435061
$372$	−13.8286	−0.716981
$373$	9.38464	0.485918	0.242959	−	0.970037i	$-0.421882\pi$
$373$	9.38464	0.485918	0.242959	+	0.970037i	$0.421882\pi$
$374$	−0.00547476	−0.000283093 0
$375$	2.95837	0.152770
$376$	0.480418	0.0247757
$377$	−8.18147	−0.421367
$378$	−1.51902	−0.0781297
$379$	14.6851	0.754325	0.377162	−	0.926147i	$-0.376900\pi$
$379$	14.6851	0.754325	0.377162	+	0.926147i	$0.376900\pi$
$380$	−0.0160553	−0.000823621 0
$381$	7.57139	0.387894
$382$	−6.27257	−0.320933
$383$	−28.6716	−1.46505	−0.732525	−	0.680740i	$-0.761658\pi$
$383$	−28.6716	−1.46505	−0.732525	+	0.680740i	$0.761658\pi$
$384$	1.50018	0.0765557
$385$	−0.0532758	−0.00271518
$386$	31.5568	1.60620
$387$	−11.0396	−0.561177
$388$	−29.9672	−1.52135
$389$	10.0883	0.511499	0.255750	−	0.966743i	$-0.417678\pi$
$389$	10.0883	0.511499	0.255750	+	0.966743i	$0.417678\pi$
$390$	0.603878	0.0305786
$391$	0.0537930	0.00272043
$392$	1.20824	0.0610252
$393$	10.4303	0.526141
$394$	47.4199	2.38898
$395$	0.885365	0.0445475
$396$	0.497466	0.0249986
$397$	−10.6979	−0.536914	−0.268457	−	0.963292i	$-0.586514\pi$
$397$	−10.6979	−0.536914	−0.268457	+	0.963292i	$0.586514\pi$
$398$	3.70394	0.185662
$399$	0.0192977	0.000966095 0
$400$	18.6899	0.934496
$401$	8.65396	0.432158	0.216079	−	0.976376i	$-0.430673\pi$
$401$	8.65396	0.432158	0.216079	+	0.976376i	$0.430673\pi$
$402$	4.37386	0.218148
$403$	−6.60774	−0.329155
$404$	1.32092	0.0657183
$405$	−0.298497	−0.0148324
$406$	12.4278	0.616781
$407$	0.450626	0.0223367
$408$	−0.00213716	−0.000105805 0
$409$	−11.4910	−0.568192	−0.284096	−	0.958796i	$-0.591693\pi$
$409$	−11.4910	−0.568192	−0.284096	+	0.958796i	$0.591693\pi$
$410$	−0.0687649	−0.00339606
$411$	11.7705	0.580597
$412$	−2.09279	−0.103104
$413$	−2.84624	−0.140054
$414$	−9.55912	−0.469805
$415$	2.53853	0.124611
$416$	8.07484	0.395902
$417$	4.37973	0.214476
$418$	−0.0123595	−0.000604524 0
$419$	−27.5243	−1.34465	−0.672325	−	0.740256i	$-0.734704\pi$
$419$	−27.5243	−1.34465	−0.672325	+	0.740256i	$0.734704\pi$
$420$	−0.469049	−0.0228872
$421$	29.1400	1.42020	0.710098	−	0.704103i	$-0.248651\pi$
$421$	29.1400	1.42020	0.710098	+	0.704103i	$0.248651\pi$
$422$	51.8608	2.52454
$423$	−2.55917	−0.124431
$424$	−2.09510	−0.101747
$425$	−0.0559086	−0.00271196
$426$	17.0116	0.824214
$427$	1.62772	0.0787710
$428$	38.6341	1.86745
$429$	0.237705	0.0114765
$430$	−6.66660	−0.321492
$431$	−25.9674	−1.25081	−0.625404	−	0.780301i	$-0.715066\pi$
$431$	−25.9674	−1.25081	−0.625404	+	0.780301i	$0.715066\pi$
$432$	−3.80581	−0.183107
$433$	−6.52516	−0.313579	−0.156790	−	0.987632i	$-0.550114\pi$
$433$	−6.52516	−0.313579	−0.156790	+	0.987632i	$0.550114\pi$
$434$	10.0373	0.481804
$435$	2.44214	0.117092
$436$	6.17905	0.295923
$437$	0.121440	0.00580927
$438$	3.75348	0.179348
$439$	−6.78536	−0.323848	−0.161924	−	0.986803i	$-0.551770\pi$
$439$	−6.78536	−0.323848	−0.161924	+	0.986803i	$0.551770\pi$
$440$	0.0133198	0.000634997 0
$441$	−6.43623	−0.306487
$442$	−0.0230318	−0.00109551
$443$	−20.2857	−0.963803	−0.481902	−	0.876225i	$-0.660054\pi$
$443$	−20.2857	−0.963803	−0.481902	+	0.876225i	$0.660054\pi$
$444$	3.96739	0.188284
$445$	1.40379	0.0665462
$446$	−53.1257	−2.51557
$447$	−12.1640	−0.575340
$448$	−6.55064	−0.309489
$449$	−1.17348	−0.0553802	−0.0276901	−	0.999617i	$-0.508815\pi$
$449$	−1.17348	−0.0553802	−0.0276901	+	0.999617i	$0.508815\pi$
$450$	9.93507	0.468344
$451$	−0.0270679	−0.00127458
$452$	25.9873	1.22234
$453$	−1.81737	−0.0853874
$454$	16.2066	0.760611
$455$	−0.224126	−0.0105072
$456$	−0.00482475	−0.000225939 0
$457$	−29.2991	−1.37055	−0.685276	−	0.728283i	$-0.740318\pi$
$457$	−29.2991	−1.37055	−0.685276	+	0.728283i	$0.740318\pi$
$458$	23.8672	1.11524
$459$	0.0113846	0.000531387 0
$460$	−2.95171	−0.137624
$461$	33.0029	1.53710	0.768550	−	0.639790i	$-0.220979\pi$
$461$	33.0029	1.53710	0.768550	+	0.639790i	$0.220979\pi$
$462$	−0.361077	−0.0167988
$463$	−0.848963	−0.0394547	−0.0197273	−	0.999805i	$-0.506280\pi$
$463$	−0.848963	−0.0394547	−0.0197273	+	0.999805i	$0.506280\pi$
$464$	31.1371	1.44550
$465$	1.97239	0.0914673
$466$	−50.9310	−2.35934
$467$	−20.2741	−0.938175	−0.469088	−	0.883152i	$-0.655417\pi$
$467$	−20.2741	−0.938175	−0.469088	+	0.883152i	$0.655417\pi$
$468$	2.09279	0.0967393
$469$	−1.62333	−0.0749586
$470$	−1.54543	−0.0712852
$471$	0.698694	0.0321941
$472$	0.711605	0.0327543
$473$	−2.62418	−0.120660
$474$	6.00057	0.275615
$475$	−0.126216	−0.00579119
$476$	0.0178894	0.000819959 0
$477$	11.1605	0.511005
$478$	−15.2641	−0.698165
$479$	−27.2168	−1.24357	−0.621784	−	0.783189i	$-0.713592\pi$
$479$	−27.2168	−1.24357	−0.621784	+	0.783189i	$0.713592\pi$
$480$	−2.41031	−0.110015
$481$	1.89574	0.0864383
$482$	−18.0579	−0.822514
$483$	3.54781	0.161431
$484$	−22.9025	−1.04102
$485$	4.27424	0.194083
$486$	−2.02307	−0.0917681
$487$	−25.1480	−1.13956	−0.569781	−	0.821796i	$-0.692972\pi$
$487$	−25.1480	−1.13956	−0.569781	+	0.821796i	$0.692972\pi$
$488$	−0.406957	−0.0184221
$489$	−5.52864	−0.250014
$490$	−3.88670	−0.175583
$491$	13.3242	0.601311	0.300656	−	0.953733i	$-0.402794\pi$
$491$	13.3242	0.601311	0.300656	+	0.953733i	$0.402794\pi$
$492$	−0.238311	−0.0107439
$493$	−0.0931427	−0.00419494
$494$	−0.0519952	−0.00233938
$495$	−0.0709541	−0.00318915
$496$	25.1478	1.12917
$497$	−6.31375	−0.283210
$498$	17.2049	0.770970
$499$	−13.6035	−0.608978	−0.304489	−	0.952516i	$-0.598486\pi$
$499$	−13.6035	−0.608978	−0.304489	+	0.952516i	$0.598486\pi$
$500$	6.19126	0.276881
$501$	−2.91337	−0.130160
$502$	−40.5722	−1.81083
$503$	−33.0106	−1.47187	−0.735935	−	0.677052i	$-0.763257\pi$
$503$	−33.0106	−1.47187	−0.735935	+	0.677052i	$0.763257\pi$
$504$	−0.140953	−0.00627853
$505$	−0.188404	−0.00838388
$506$	−2.27225	−0.101014
$507$	1.00000	0.0444116
$508$	15.8454	0.703024
$509$	10.0734	0.446497	0.223248	−	0.974762i	$-0.428334\pi$
$509$	10.0734	0.446497	0.223248	+	0.974762i	$0.428334\pi$
$510$	0.00687490	0.000304426 0
$511$	−1.39308	−0.0616262
$512$	−32.1602	−1.42129
$513$	0.0257012	0.00113474
$514$	−29.1182	−1.28435
$515$	0.298497	0.0131533
$516$	−23.1037	−1.01708
$517$	−0.608326	−0.0267542
$518$	−2.87966	−0.126525
$519$	−18.8203	−0.826119
$520$	0.0560351	0.00245730
$521$	−23.5560	−1.03201	−0.516004	−	0.856586i	$-0.672581\pi$
$521$	−23.5560	−1.03201	−0.516004	+	0.856586i	$0.672581\pi$
$522$	16.5517	0.724446
$523$	−4.16023	−0.181914	−0.0909571	−	0.995855i	$-0.528993\pi$
$523$	−4.16023	−0.181914	−0.0909571	+	0.995855i	$0.528993\pi$
$524$	21.8285	0.953584
$525$	−3.68734	−0.160929
$526$	−31.5118	−1.37398
$527$	−0.0752264	−0.00327691
$528$	−0.904658	−0.0393702
$529$	−0.673720	−0.0292922
$530$	6.73960	0.292750
$531$	−3.79069	−0.164502
$532$	0.0403861	0.00175096
$533$	−0.113872	−0.00493235
$534$	9.51422	0.411721
$535$	−5.51042	−0.238236
$536$	0.405860	0.0175305
$537$	−20.1999	−0.871690
$538$	−50.8364	−2.19171
$539$	−1.52992	−0.0658984
$540$	−0.624692	−0.0268824
$541$	−11.3274	−0.487001	−0.243500	−	0.969901i	$-0.578296\pi$
$541$	−11.3274	−0.487001	−0.243500	+	0.969901i	$0.578296\pi$
$542$	−30.4408	−1.30754
$543$	−3.91651	−0.168073
$544$	0.0919287	0.00394141
$545$	−0.881323	−0.0377517
$546$	−1.51902	−0.0650079
$547$	21.2483	0.908511	0.454256	−	0.890871i	$-0.349905\pi$
$547$	21.2483	0.908511	0.454256	+	0.890871i	$0.349905\pi$
$548$	24.6333	1.05228
$549$	2.16784	0.0925213
$550$	2.36161	0.100699
$551$	−0.210274	−0.00895797
$552$	−0.887011	−0.0377537
$553$	−2.22708	−0.0947049
$554$	−30.0880	−1.27832
$555$	−0.565872	−0.0240199
$556$	9.16587	0.388720
$557$	−7.05762	−0.299041	−0.149520	−	0.988759i	$-0.547773\pi$
$557$	−7.05762	−0.299041	−0.149520	+	0.988759i	$0.547773\pi$
$558$	13.3679	0.565908
$559$	−11.0396	−0.466927
$560$	0.852979	0.0360450
$561$	0.00270617	0.000114255 0
$562$	−18.0388	−0.760922
$563$	22.2144	0.936224	0.468112	−	0.883669i	$-0.344934\pi$
$563$	22.2144	0.936224	0.468112	+	0.883669i	$0.344934\pi$
$564$	−5.35581	−0.225520
$565$	−3.70658	−0.155937
$566$	−29.2365	−1.22890
$567$	0.750849	0.0315327
$568$	1.57854	0.0662340
$569$	−11.9904	−0.502665	−0.251332	−	0.967901i	$-0.580869\pi$
$569$	−11.9904	−0.502665	−0.251332	+	0.967901i	$0.580869\pi$
$570$	0.0155204	0.000650078 0
$571$	−40.5710	−1.69784	−0.848921	−	0.528520i	$-0.822747\pi$
$571$	−40.5710	−1.69784	−0.848921	+	0.528520i	$0.822747\pi$
$572$	0.497466	0.0208001
$573$	3.10053	0.129526
$574$	0.172973	0.00721977
$575$	−23.2043	−0.967688
$576$	−8.72432	−0.363513
$577$	7.30531	0.304124	0.152062	−	0.988371i	$-0.451409\pi$
$577$	7.30531	0.304124	0.152062	+	0.988371i	$0.451409\pi$
$578$	34.3918	1.43051
$579$	−15.5985	−0.648253
$580$	5.11090	0.212218
$581$	−6.38550	−0.264915
$582$	28.9687	1.20079
$583$	2.65291	0.109872
$584$	0.348293	0.0144125
$585$	−0.298497	−0.0123413
$586$	33.1676	1.37014
$587$	3.69201	0.152386	0.0761929	−	0.997093i	$-0.475724\pi$
$587$	3.69201	0.152386	0.0761929	+	0.997093i	$0.475724\pi$
$588$	−13.4697	−0.555480
$589$	−0.169827	−0.00699760
$590$	−2.28912	−0.0942414
$591$	−23.4396	−0.964178
$592$	−7.21482	−0.296527
$593$	26.3558	1.08230	0.541152	−	0.840925i	$-0.317988\pi$
$593$	26.3558	1.08230	0.541152	+	0.840925i	$0.317988\pi$
$594$	−0.480892	−0.0197312
$595$	−0.00255158	−0.000104605 0
$596$	−25.4568	−1.04275
$597$	−1.83086	−0.0749319
$598$	−9.55912	−0.390902
$599$	−15.1909	−0.620683	−0.310342	−	0.950625i	$-0.600443\pi$
$599$	−15.1909	−0.620683	−0.310342	+	0.950625i	$0.600443\pi$
$600$	0.921896	0.0376362
$601$	−2.29576	−0.0936459	−0.0468230	−	0.998903i	$-0.514910\pi$
$601$	−2.29576	−0.0936459	−0.0468230	+	0.998903i	$0.514910\pi$
$602$	16.7694	0.683470
$603$	−2.16200	−0.0880434
$604$	−3.80338	−0.154757
$605$	3.26660	0.132806
$606$	−1.27691	−0.0518710
$607$	38.2390	1.55207	0.776036	−	0.630689i	$-0.217228\pi$
$607$	38.2390	1.55207	0.776036	+	0.630689i	$0.217228\pi$
$608$	0.207533	0.00841659
$609$	−6.14305	−0.248929
$610$	1.30911	0.0530045
$611$	−2.55917	−0.103533
$612$	0.0238256	0.000963092 0
$613$	2.58621	0.104456	0.0522281	−	0.998635i	$-0.483368\pi$
$613$	2.58621	0.104456	0.0522281	+	0.998635i	$0.483368\pi$
$614$	0.747617	0.0301714
$615$	0.0339904	0.00137063
$616$	−0.0335051	−0.00134996
$617$	−13.1387	−0.528943	−0.264471	−	0.964394i	$-0.585197\pi$
$617$	−13.1387	−0.528943	−0.264471	+	0.964394i	$0.585197\pi$
$618$	2.02307	0.0813796
$619$	23.1480	0.930396	0.465198	−	0.885207i	$-0.345983\pi$
$619$	23.1480	0.930396	0.465198	+	0.885207i	$0.345983\pi$
$620$	4.12780	0.165776
$621$	4.72507	0.189610
$622$	−37.8156	−1.51627
$623$	−3.53115	−0.141472
$624$	−3.80581	−0.152354
$625$	23.6714	0.946857
$626$	27.0756	1.08216
$627$	0.00610930	0.000243982 0
$628$	1.46222	0.0583490
$629$	0.0215822	0.000860540 0
$630$	0.453421	0.0180647
$631$	−15.9805	−0.636173	−0.318087	−	0.948062i	$-0.603040\pi$
$631$	−15.9805	−0.636173	−0.318087	+	0.948062i	$0.603040\pi$
$632$	0.556805	0.0221485
$633$	−25.6348	−1.01889
$634$	44.0844	1.75082
$635$	−2.26004	−0.0896868
$636$	23.3567	0.926152
$637$	−6.43623	−0.255013
$638$	3.93440	0.155765
$639$	−8.40881	−0.332647
$640$	−0.447798	−0.0177008
$641$	19.0287	0.751590	0.375795	−	0.926703i	$-0.377370\pi$
$641$	19.0287	0.751590	0.375795	+	0.926703i	$0.377370\pi$
$642$	−37.3469	−1.47397
$643$	27.5698	1.08725	0.543623	−	0.839329i	$-0.317052\pi$
$643$	27.5698	1.08725	0.543623	+	0.839329i	$0.317052\pi$
$644$	7.42483	0.292579
$645$	3.29530	0.129752
$646$	−0.000591944 0	−2.32897e−5 0
$647$	−4.12275	−0.162082	−0.0810409	−	0.996711i	$-0.525824\pi$
$647$	−4.12275	−0.162082	−0.0810409	+	0.996711i	$0.525824\pi$
$648$	−0.187724	−0.00737451
$649$	−0.901065	−0.0353699
$650$	9.93507	0.389685
$651$	−4.96141	−0.194453
$652$	−11.5703	−0.453128
$653$	−12.3881	−0.484784	−0.242392	−	0.970178i	$-0.577932\pi$
$653$	−12.3881	−0.484784	−0.242392	+	0.970178i	$0.577932\pi$
$654$	−5.97318	−0.233570
$655$	−3.11342	−0.121652
$656$	0.433375	0.0169205
$657$	−1.85534	−0.0723837
$658$	3.88742	0.151547
$659$	4.06952	0.158526	0.0792630	−	0.996854i	$-0.474743\pi$
$659$	4.06952	0.158526	0.0792630	+	0.996854i	$0.474743\pi$
$660$	−0.148492	−0.00578005
$661$	34.4959	1.34174	0.670868	−	0.741576i	$-0.265922\pi$
$661$	34.4959	1.34174	0.670868	+	0.741576i	$0.265922\pi$
$662$	56.1421	2.18202
$663$	0.0113846	0.000442141 0
$664$	1.59648	0.0619554
$665$	−0.00576031	−0.000223375 0
$666$	−3.83521	−0.148611
$667$	−38.6580	−1.49684
$668$	−6.09708	−0.235903
$669$	26.2600	1.01527
$670$	−1.30558	−0.0504391
$671$	0.515307	0.0198932
$672$	6.06298	0.233885
$673$	4.54822	0.175321	0.0876605	−	0.996150i	$-0.472061\pi$
$673$	4.54822	0.175321	0.0876605	+	0.996150i	$0.472061\pi$
$674$	0.360891	0.0139010
$675$	−4.91090	−0.189021
$676$	2.09279	0.0804920
$677$	−23.3740	−0.898338	−0.449169	−	0.893447i	$-0.648280\pi$
$677$	−23.3740	−0.898338	−0.449169	+	0.893447i	$0.648280\pi$
$678$	−25.1214	−0.964782
$679$	−10.7516	−0.412607
$680$	0.000637937 0	2.44638e−5 0
$681$	−8.01089	−0.306978
$682$	3.17761	0.121677
$683$	−20.4551	−0.782691	−0.391346	−	0.920244i	$-0.627990\pi$
$683$	−20.4551	−0.782691	−0.391346	+	0.920244i	$0.627990\pi$
$684$	0.0537873	0.00205661
$685$	−3.51346	−0.134243
$686$	20.4098	0.779251
$687$	−11.7976	−0.450105
$688$	42.0147	1.60180
$689$	11.1605	0.425182
$690$	2.85337	0.108626
$691$	17.6090	0.669878	0.334939	−	0.942240i	$-0.391284\pi$
$691$	17.6090	0.669878	0.334939	+	0.942240i	$0.391284\pi$
$692$	−39.3870	−1.49727
$693$	0.178480	0.00677990
$694$	42.4196	1.61022
$695$	−1.30734	−0.0495901
$696$	1.53586	0.0582167
$697$	−0.00129639	−4.91042e−5 0
$698$	67.2139	2.54408
$699$	25.1752	0.952213
$700$	−7.71684	−0.291669
$701$	37.5140	1.41689	0.708443	−	0.705769i	$-0.249398\pi$
$701$	37.5140	1.41689	0.708443	+	0.705769i	$0.249398\pi$
$702$	−2.02307	−0.0763557
$703$	0.0487229	0.00183762
$704$	−2.07381	−0.0781597
$705$	0.763903	0.0287703
$706$	20.2804	0.763263
$707$	0.473918	0.0178235
$708$	−7.93313	−0.298145
$709$	−10.4742	−0.393368	−0.196684	−	0.980467i	$-0.563017\pi$
$709$	−10.4742	−0.393368	−0.196684	+	0.980467i	$0.563017\pi$
$710$	−5.07790	−0.190570
$711$	−2.96608	−0.111237
$712$	0.882844	0.0330860
$713$	−31.2220	−1.16927
$714$	−0.0172934	−0.000647188 0
$715$	−0.0709541	−0.00265353
$716$	−42.2742	−1.57986
$717$	7.54505	0.281775
$718$	8.70800	0.324980
$719$	14.5594	0.542973	0.271486	−	0.962442i	$-0.412485\pi$
$719$	14.5594	0.542973	0.271486	+	0.962442i	$0.412485\pi$
$720$	1.13602	0.0423370
$721$	−0.750849	−0.0279631
$722$	38.4369	1.43047
$723$	8.92600	0.331961
$724$	−8.19643	−0.304618
$725$	40.1784	1.49219
$726$	22.1394	0.821670
$727$	2.13455	0.0791661	0.0395830	−	0.999216i	$-0.487397\pi$
$727$	2.13455	0.0791661	0.0395830	+	0.999216i	$0.487397\pi$
$728$	−0.140953	−0.00522405
$729$	1.00000	0.0370370
$730$	−1.12040	−0.0414679
$731$	−0.125682	−0.00464851
$732$	4.53685	0.167687
$733$	−35.6939	−1.31838	−0.659192	−	0.751974i	$-0.729102\pi$
$733$	−35.6939	−1.31838	−0.659192	+	0.751974i	$0.729102\pi$
$734$	41.6437	1.53710
$735$	1.92119	0.0708642
$736$	38.1542	1.40638
$737$	−0.513917	−0.0189304
$738$	0.230371	0.00848006
$739$	33.7804	1.24263	0.621316	−	0.783560i	$-0.286598\pi$
$739$	33.7804	1.24263	0.621316	+	0.783560i	$0.286598\pi$
$740$	−1.18425	−0.0435340
$741$	0.0257012	0.000944158 0
$742$	−16.9530	−0.622365
$743$	−12.0539	−0.442216	−0.221108	−	0.975249i	$-0.570967\pi$
$743$	−12.0539	−0.442216	−0.221108	+	0.975249i	$0.570967\pi$
$744$	1.24043	0.0454765
$745$	3.63093	0.133027
$746$	−18.9857	−0.695117
$747$	−8.50437	−0.311159
$748$	0.00566345	0.000207076 0
$749$	13.8611	0.506473
$750$	−5.98498	−0.218540
$751$	−44.3124	−1.61698	−0.808490	−	0.588509i	$-0.799715\pi$
$751$	−44.3124	−1.61698	−0.808490	+	0.588509i	$0.799715\pi$
$752$	9.73970	0.355170
$753$	20.0548	0.730839
$754$	16.5517	0.602776
$755$	0.542479	0.0197428
$756$	1.57137	0.0571502
$757$	31.5271	1.14587	0.572936	−	0.819600i	$-0.305805\pi$
$757$	31.5271	1.14587	0.572936	+	0.819600i	$0.305805\pi$
$758$	−29.7090	−1.07908
$759$	1.12317	0.0407685
$760$	0.00144017	5.22405e−5 0
$761$	51.1633	1.85467	0.927333	−	0.374236i	$-0.122095\pi$
$761$	51.1633	1.85467	0.927333	+	0.374236i	$0.122095\pi$
$762$	−15.3174	−0.554892
$763$	2.21691	0.0802575
$764$	6.48876	0.234755
$765$	−0.00339826	−0.000122864 0
$766$	58.0045	2.09579
$767$	−3.79069	−0.136874
$768$	14.4137	0.520109
$769$	−33.6742	−1.21432	−0.607161	−	0.794579i	$-0.707692\pi$
$769$	−33.6742	−1.21432	−0.607161	+	0.794579i	$0.707692\pi$
$770$	0.107780	0.00388413
$771$	14.3931	0.518356
$772$	−32.6445	−1.17490
$773$	−22.8760	−0.822792	−0.411396	−	0.911457i	$-0.634959\pi$
$773$	−22.8760	−0.822792	−0.411396	+	0.911457i	$0.634959\pi$
$774$	22.3339	0.802776
$775$	32.4499	1.16564
$776$	2.68807	0.0964960
$777$	1.42341	0.0510647
$778$	−20.4094	−0.731712
$779$	−0.00292665	−0.000104858 0
$780$	−0.624692	−0.0223675
$781$	−1.99881	−0.0715232
$782$	−0.108827	−0.00389163
$783$	−8.18147	−0.292382
$784$	24.4950	0.874822
$785$	−0.208558	−0.00744375
$786$	−21.1013	−0.752657
$787$	−28.0481	−0.999807	−0.499904	−	0.866081i	$-0.666631\pi$
$787$	−28.0481	−0.999807	−0.499904	+	0.866081i	$0.666631\pi$
$788$	−49.0543	−1.74749
$789$	15.5763	0.554529
$790$	−1.79115	−0.0637263
$791$	9.32367	0.331511
$792$	−0.0446230	−0.00158561
$793$	2.16784	0.0769824
$794$	21.6426	0.768068
$795$	−3.33138	−0.118152
$796$	−3.83160	−0.135807
$797$	−36.4690	−1.29180	−0.645898	−	0.763423i	$-0.723517\pi$
$797$	−36.4690	−1.29180	−0.645898	+	0.763423i	$0.723517\pi$
$798$	−0.0390406	−0.00138202
$799$	−0.0291351	−0.00103072
$800$	−39.6547	−1.40201
$801$	−4.70287	−0.166168
$802$	−17.5075	−0.618212
$803$	−0.441023	−0.0155634
$804$	−4.52461	−0.159571
$805$	−1.05901	−0.0373252
$806$	13.3679	0.470864
$807$	25.1284	0.884561
$808$	−0.118487	−0.00416837
$809$	2.46768	0.0867592	0.0433796	−	0.999059i	$-0.486188\pi$
$809$	2.46768	0.0867592	0.0433796	+	0.999059i	$0.486188\pi$
$810$	0.603878	0.0212181
$811$	40.9422	1.43768	0.718838	−	0.695177i	$-0.244674\pi$
$811$	40.9422	1.43768	0.718838	+	0.695177i	$0.244674\pi$
$812$	−12.8561	−0.451161
$813$	15.0469	0.527716
$814$	−0.911647	−0.0319532
$815$	1.65028	0.0578068
$816$	−0.0433275	−0.00151677
$817$	−0.283732	−0.00992654
$818$	23.2470	0.812811
$819$	0.750849	0.0262368
$820$	0.0711349	0.00248414
$821$	−24.3132	−0.848537	−0.424269	−	0.905536i	$-0.639469\pi$
$821$	−24.3132	−0.848537	−0.424269	+	0.905536i	$0.639469\pi$
$822$	−23.8125	−0.830558
$823$	20.1482	0.702324	0.351162	−	0.936315i	$-0.385787\pi$
$823$	20.1482	0.702324	0.351162	+	0.936315i	$0.385787\pi$
$824$	0.187724	0.00653969
$825$	−1.16734	−0.0406417
$826$	5.75812	0.200351
$827$	25.7669	0.896001	0.448001	−	0.894033i	$-0.352136\pi$
$827$	25.7669	0.896001	0.448001	+	0.894033i	$0.352136\pi$
$828$	9.88859	0.343652
$829$	1.90021	0.0659971	0.0329986	−	0.999455i	$-0.489494\pi$
$829$	1.90021	0.0659971	0.0329986	+	0.999455i	$0.489494\pi$
$830$	−5.13560	−0.178259
$831$	14.8725	0.515921
$832$	−8.72432	−0.302461
$833$	−0.0732738	−0.00253879
$834$	−8.86049	−0.306814
$835$	0.869632	0.0300949
$836$	0.0127855	0.000442196 0
$837$	−6.60774	−0.228397
$838$	55.6834	1.92355
$839$	−15.6998	−0.542018	−0.271009	−	0.962577i	$-0.587357\pi$
$839$	−15.6998	−0.542018	−0.271009	+	0.962577i	$0.587357\pi$
$840$	0.0420739	0.00145169
$841$	37.9365	1.30816
$842$	−58.9521	−2.03162
$843$	8.91658	0.307103
$844$	−53.6482	−1.84665
$845$	−0.298497	−0.0102686
$846$	5.17736	0.178001
$847$	−8.21691	−0.282336
$848$	−42.4748	−1.45859
$849$	14.4516	0.495978
$850$	0.113107	0.00387953
$851$	8.95751	0.307059
$852$	−17.5979	−0.602894
$853$	20.8262	0.713076	0.356538	−	0.934281i	$-0.383957\pi$
$853$	20.8262	0.713076	0.356538	+	0.934281i	$0.383957\pi$
$854$	−3.29299	−0.112684
$855$	−0.00767173	−0.000262368 0
$856$	−3.46550	−0.118448
$857$	56.4305	1.92763	0.963814	−	0.266577i	$-0.0858925\pi$
$857$	56.4305	1.92763	0.963814	+	0.266577i	$0.0858925\pi$
$858$	−0.480892	−0.0164174
$859$	3.25567	0.111082	0.0555411	−	0.998456i	$-0.482312\pi$
$859$	3.25567	0.111082	0.0555411	+	0.998456i	$0.482312\pi$
$860$	6.89637	0.235164
$861$	−0.0855007	−0.00291386
$862$	52.5338	1.78931
$863$	42.5466	1.44830	0.724152	−	0.689640i	$-0.242231\pi$
$863$	42.5466	1.44830	0.724152	+	0.689640i	$0.242231\pi$
$864$	8.07484	0.274712
$865$	5.61780	0.191011
$866$	13.2008	0.448583
$867$	−16.9999	−0.577346
$868$	−10.3832	−0.352429
$869$	−0.705051	−0.0239172
$870$	−4.94061	−0.167502
$871$	−2.16200	−0.0732565
$872$	−0.554264	−0.0187697
$873$	−14.3192	−0.484632
$874$	−0.245681	−0.00831029
$875$	2.22129	0.0750933
$876$	−3.88284	−0.131189
$877$	−14.1498	−0.477803	−0.238902	−	0.971044i	$-0.576787\pi$
$877$	−14.1498	−0.477803	−0.238902	+	0.971044i	$0.576787\pi$
$878$	13.7272	0.463272
$879$	−16.3947	−0.552981
$880$	0.270037	0.00910296
$881$	−25.8761	−0.871790	−0.435895	−	0.899998i	$-0.643568\pi$
$881$	−25.8761	−0.871790	−0.435895	+	0.899998i	$0.643568\pi$
$882$	13.0209	0.438437
$883$	47.7063	1.60545	0.802723	−	0.596352i	$-0.203384\pi$
$883$	47.7063	1.60545	0.802723	+	0.596352i	$0.203384\pi$
$884$	0.0238256	0.000801341 0
$885$	1.13151	0.0380353
$886$	41.0393	1.37874
$887$	−10.6186	−0.356536	−0.178268	−	0.983982i	$-0.557049\pi$
$887$	−10.6186	−0.356536	−0.178268	+	0.983982i	$0.557049\pi$
$888$	−0.355877	−0.0119424
$889$	5.68497	0.190668
$890$	−2.83996	−0.0951958
$891$	0.237705	0.00796341
$892$	54.9567	1.84009
$893$	−0.0657738	−0.00220103
$894$	24.6087	0.823037
$895$	6.02960	0.201547
$896$	1.12641	0.0376306
$897$	4.72507	0.157765
$898$	2.37404	0.0792226
$899$	54.0610	1.80304
$900$	−10.2775	−0.342583
$901$	0.127058	0.00423292
$902$	0.0547602	0.00182331
$903$	−8.28910	−0.275844
$904$	−2.33107	−0.0775302
$905$	1.16906	0.0388610
$906$	3.67666	0.122149
$907$	−1.96940	−0.0653928	−0.0326964	−	0.999465i	$-0.510409\pi$
$907$	−1.96940	−0.0653928	−0.0326964	+	0.999465i	$0.510409\pi$
$908$	−16.7651	−0.556370
$909$	0.631177	0.0209348
$910$	0.453421	0.0150308
$911$	37.5276	1.24335	0.621673	−	0.783277i	$-0.286453\pi$
$911$	37.5276	1.24335	0.621673	+	0.783277i	$0.286453\pi$
$912$	−0.0978139	−0.00323894
$913$	−2.02153	−0.0669028
$914$	59.2739	1.96061
$915$	−0.647094	−0.0213923
$916$	−24.6899	−0.815776
$917$	7.83161	0.258623
$918$	−0.0230318	−0.000760161 0
$919$	32.7293	1.07964	0.539820	−	0.841780i	$-0.318492\pi$
$919$	32.7293	1.07964	0.539820	+	0.841780i	$0.318492\pi$
$920$	0.264770	0.00872920
$921$	−0.369547	−0.0121770
$922$	−66.7671	−2.19886
$923$	−8.40881	−0.276779
$924$	0.373522	0.0122880
$925$	−9.30979	−0.306104
$926$	1.71751	0.0564408
$927$	−1.00000	−0.0328443
$928$	−66.0641	−2.16866
$929$	10.0988	0.331331	0.165666	−	0.986182i	$-0.447023\pi$
$929$	10.0988	0.331331	0.165666	+	0.986182i	$0.447023\pi$
$930$	−3.99027	−0.130846
$931$	−0.165419	−0.00542139
$932$	52.6864	1.72580
$933$	18.6922	0.611956
$934$	41.0159	1.34208
$935$	−0.000807783 0	−2.64173e−5 0
$936$	−0.187724	−0.00613596
$937$	50.7213	1.65699	0.828496	−	0.559996i	$-0.189197\pi$
$937$	50.7213	1.65699	0.828496	+	0.559996i	$0.189197\pi$
$938$	3.28411	0.107230
$939$	−13.3835	−0.436753
$940$	1.59869	0.0521435
$941$	−5.12404	−0.167039	−0.0835195	−	0.996506i	$-0.526616\pi$
$941$	−5.12404	−0.167039	−0.0835195	+	0.996506i	$0.526616\pi$
$942$	−1.41350	−0.0460544
$943$	−0.538054	−0.0175214
$944$	14.4266	0.469547
$945$	−0.224126	−0.00729081
$946$	5.30888	0.172606
$947$	45.1006	1.46557	0.732786	−	0.680459i	$-0.238220\pi$
$947$	45.1006	1.46557	0.732786	+	0.680459i	$0.238220\pi$
$948$	−6.20738	−0.201606
$949$	−1.85534	−0.0602269
$950$	0.255343	0.00828444
$951$	−21.7909	−0.706619
$952$	−0.00160469	−5.20082e−5 0
$953$	−11.9737	−0.387866	−0.193933	−	0.981015i	$-0.562124\pi$
$953$	−11.9737	−0.387866	−0.193933	+	0.981015i	$0.562124\pi$
$954$	−22.5785	−0.731005
$955$	−0.925498	−0.0299484
$956$	15.7902	0.510692
$957$	−1.94477	−0.0628656
$958$	55.0614	1.77895
$959$	8.83788	0.285390
$960$	2.60418	0.0840495
$961$	12.6622	0.408458
$962$	−3.83521	−0.123652
$963$	18.4606	0.594883
$964$	18.6803	0.601651
$965$	4.65611	0.149885
$966$	−7.17745	−0.230931
$967$	36.3133	1.16776	0.583879	−	0.811841i	$-0.301534\pi$
$967$	36.3133	1.16776	0.583879	+	0.811841i	$0.301534\pi$
$968$	2.05436	0.0660297
$969$	0.000292598 0	9.39960e−6 0
$970$	−8.64707	−0.277641
$971$	−40.6827	−1.30557	−0.652785	−	0.757543i	$-0.726399\pi$
$971$	−40.6827	−1.30557	−0.652785	+	0.757543i	$0.726399\pi$
$972$	2.09279	0.0671263
$973$	3.28852	0.105425
$974$	50.8759	1.63017
$975$	−4.91090	−0.157275
$976$	−8.25039	−0.264089
$977$	−51.9480	−1.66197	−0.830983	−	0.556298i	$-0.812221\pi$
$977$	−51.9480	−1.66197	−0.830983	+	0.556298i	$0.812221\pi$
$978$	11.1848	0.357650
$979$	−1.11790	−0.0357281
$980$	4.02066	0.128435
$981$	2.95254	0.0942673
$982$	−26.9557	−0.860190
$983$	3.80556	0.121379	0.0606893	−	0.998157i	$-0.480670\pi$
$983$	3.80556	0.121379	0.0606893	+	0.998157i	$0.480670\pi$
$984$	0.0213766	0.000681460 0
$985$	6.99665	0.222932
$986$	0.188434	0.00600095
$987$	−1.92155	−0.0611635
$988$	0.0537873	0.00171120
$989$	−52.1631	−1.65869
$990$	0.143545	0.00456215
$991$	0.897755	0.0285181	0.0142591	−	0.999898i	$-0.495461\pi$
$991$	0.897755	0.0285181	0.0142591	+	0.999898i	$0.495461\pi$
$992$	−53.3564	−1.69407
$993$	−27.7510	−0.880652
$994$	12.7731	0.405139
$995$	0.546504	0.0173254
$996$	−17.7979	−0.563947
$997$	−42.7432	−1.35369	−0.676845	−	0.736126i	$-0.736653\pi$
$997$	−42.7432	−1.35369	−0.676845	+	0.736126i	$0.736653\pi$
$998$	27.5208	0.871157
$999$	1.89574	0.0599786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.f.1.4	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.f.1.4	✓	19	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02307 q^{2} +1.00000 q^{3} +2.09279 q^{4} -0.298497 q^{5} -2.02307 q^{6} +0.750849 q^{7} -0.187724 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.02307 q^{2} +1.00000 q^{3} +2.09279 q^{4} -0.298497 q^{5} -2.02307 q^{6} +0.750849 q^{7} -0.187724 q^{8} +1.00000 q^{9} +0.603878 q^{10} +0.237705 q^{11} +2.09279 q^{12} +1.00000 q^{13} -1.51902 q^{14} -0.298497 q^{15} -3.80581 q^{16} +0.0113846 q^{17} -2.02307 q^{18} +0.0257012 q^{19} -0.624692 q^{20} +0.750849 q^{21} -0.480892 q^{22} +4.72507 q^{23} -0.187724 q^{24} -4.91090 q^{25} -2.02307 q^{26} +1.00000 q^{27} +1.57137 q^{28} -8.18147 q^{29} +0.603878 q^{30} -6.60774 q^{31} +8.07484 q^{32} +0.237705 q^{33} -0.0230318 q^{34} -0.224126 q^{35} +2.09279 q^{36} +1.89574 q^{37} -0.0519952 q^{38} +1.00000 q^{39} +0.0560351 q^{40} -0.113872 q^{41} -1.51902 q^{42} -11.0396 q^{43} +0.497466 q^{44} -0.298497 q^{45} -9.55912 q^{46} -2.55917 q^{47} -3.80581 q^{48} -6.43623 q^{49} +9.93507 q^{50} +0.0113846 q^{51} +2.09279 q^{52} +11.1605 q^{53} -2.02307 q^{54} -0.0709541 q^{55} -0.140953 q^{56} +0.0257012 q^{57} +16.5517 q^{58} -3.79069 q^{59} -0.624692 q^{60} +2.16784 q^{61} +13.3679 q^{62} +0.750849 q^{63} -8.72432 q^{64} -0.298497 q^{65} -0.480892 q^{66} -2.16200 q^{67} +0.0238256 q^{68} +4.72507 q^{69} +0.453421 q^{70} -8.40881 q^{71} -0.187724 q^{72} -1.85534 q^{73} -3.83521 q^{74} -4.91090 q^{75} +0.0537873 q^{76} +0.178480 q^{77} -2.02307 q^{78} -2.96608 q^{79} +1.13602 q^{80} +1.00000 q^{81} +0.230371 q^{82} -8.50437 q^{83} +1.57137 q^{84} -0.00339826 q^{85} +22.3339 q^{86} -8.18147 q^{87} -0.0446230 q^{88} -4.70287 q^{89} +0.603878 q^{90} +0.750849 q^{91} +9.88859 q^{92} -6.60774 q^{93} +5.17736 q^{94} -0.00767173 q^{95} +8.07484 q^{96} -14.3192 q^{97} +13.0209 q^{98} +0.237705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * q^99

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