LMFDB - Embedded newform 1849.2.a.n.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-2.17399$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17399 q^{2} +0.327650 q^{3} +2.72622 q^{4} -0.0263127 q^{5} +0.712306 q^{6} -3.12927 q^{7} +1.57880 q^{8} -2.89265 q^{9} +O(q^{10})$	\(q+2.17399 q^{2} +0.327650 q^{3} +2.72622 q^{4} -0.0263127 q^{5} +0.712306 q^{6} -3.12927 q^{7} +1.57880 q^{8} -2.89265 q^{9} -0.0572034 q^{10} -3.73669 q^{11} +0.893246 q^{12} -4.89571 q^{13} -6.80300 q^{14} -0.00862134 q^{15} -2.02015 q^{16} +5.91371 q^{17} -6.28858 q^{18} +3.96946 q^{19} -0.0717342 q^{20} -1.02531 q^{21} -8.12353 q^{22} +0.343863 q^{23} +0.517294 q^{24} -4.99931 q^{25} -10.6432 q^{26} -1.93072 q^{27} -8.53110 q^{28} -1.32570 q^{29} -0.0187427 q^{30} +2.16577 q^{31} -7.54939 q^{32} -1.22433 q^{33} +12.8563 q^{34} +0.0823396 q^{35} -7.88600 q^{36} -10.0363 q^{37} +8.62956 q^{38} -1.60408 q^{39} -0.0415425 q^{40} +1.94056 q^{41} -2.22900 q^{42} -10.1871 q^{44} +0.0761133 q^{45} +0.747555 q^{46} +11.1145 q^{47} -0.661902 q^{48} +2.79235 q^{49} -10.8684 q^{50} +1.93762 q^{51} -13.3468 q^{52} -5.81886 q^{53} -4.19737 q^{54} +0.0983224 q^{55} -4.94050 q^{56} +1.30059 q^{57} -2.88205 q^{58} +0.172353 q^{59} -0.0235037 q^{60} +5.56236 q^{61} +4.70835 q^{62} +9.05188 q^{63} -12.3720 q^{64} +0.128819 q^{65} -2.66167 q^{66} -1.10095 q^{67} +16.1221 q^{68} +0.112667 q^{69} +0.179005 q^{70} -5.29439 q^{71} -4.56691 q^{72} -7.39621 q^{73} -21.8187 q^{74} -1.63802 q^{75} +10.8216 q^{76} +11.6931 q^{77} -3.48724 q^{78} -5.41531 q^{79} +0.0531556 q^{80} +8.04534 q^{81} +4.21874 q^{82} +2.03440 q^{83} -2.79521 q^{84} -0.155605 q^{85} -0.434365 q^{87} -5.89950 q^{88} -4.00190 q^{89} +0.165469 q^{90} +15.3200 q^{91} +0.937448 q^{92} +0.709612 q^{93} +24.1628 q^{94} -0.104447 q^{95} -2.47355 q^{96} +9.00196 q^{97} +6.07054 q^{98} +10.8089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * 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 $

$2$	2.17399	1.53724	0.768621	−	0.639705i	$-0.220943\pi$
$2$	2.17399	1.53724	0.768621	+	0.639705i	$0.220943\pi$
$3$	0.327650	0.189169	0.0945843	−	0.995517i	$-0.469848\pi$
$3$	0.327650	0.189169	0.0945843	+	0.995517i	$0.469848\pi$
$4$	2.72622	1.36311
$5$	−0.0263127	−0.0117674	−0.00588369	−	0.999983i	$-0.501873\pi$
$5$	−0.0263127	−0.0117674	−0.00588369	+	0.999983i	$0.501873\pi$
$6$	0.712306	0.290798
$7$	−3.12927	−1.18275	−0.591377	−	0.806395i	$-0.701416\pi$
$7$	−3.12927	−1.18275	−0.591377	+	0.806395i	$0.701416\pi$
$8$	1.57880	0.558191
$9$	−2.89265	−0.964215
$10$	−0.0572034	−0.0180893
$11$	−3.73669	−1.12666	−0.563328	−	0.826233i	$-0.690479\pi$
$11$	−3.73669	−1.12666	−0.563328	+	0.826233i	$0.690479\pi$
$12$	0.893246	0.257858
$13$	−4.89571	−1.35782	−0.678912	−	0.734219i	$-0.737548\pi$
$13$	−4.89571	−1.35782	−0.678912	+	0.734219i	$0.737548\pi$
$14$	−6.80300	−1.81818
$15$	−0.00862134	−0.00222602
$16$	−2.02015	−0.505038
$17$	5.91371	1.43428	0.717142	−	0.696927i	$-0.245450\pi$
$17$	5.91371	1.43428	0.717142	+	0.696927i	$0.245450\pi$
$18$	−6.28858	−1.48223
$19$	3.96946	0.910657	0.455328	−	0.890324i	$-0.349522\pi$
$19$	3.96946	0.910657	0.455328	+	0.890324i	$0.349522\pi$
$20$	−0.0717342	−0.0160403
$21$	−1.02531	−0.223740
$22$	−8.12353	−1.73194
$23$	0.343863	0.0717004	0.0358502	−	0.999357i	$-0.488586\pi$
$23$	0.343863	0.0717004	0.0358502	+	0.999357i	$0.488586\pi$
$24$	0.517294	0.105592
$25$	−4.99931	−0.999862
$26$	−10.6432	−2.08730
$27$	−1.93072	−0.371568
$28$	−8.53110	−1.61223
$29$	−1.32570	−0.246176	−0.123088	−	0.992396i	$-0.539280\pi$
$29$	−1.32570	−0.246176	−0.123088	+	0.992396i	$0.539280\pi$
$30$	−0.0187427	−0.00342193
$31$	2.16577	0.388983	0.194492	−	0.980904i	$-0.437694\pi$
$31$	2.16577	0.388983	0.194492	+	0.980904i	$0.437694\pi$
$32$	−7.54939	−1.33456
$33$	−1.22433	−0.213128
$34$	12.8563	2.20484
$35$	0.0823396	0.0139179
$36$	−7.88600	−1.31433
$37$	−10.0363	−1.64995	−0.824977	−	0.565166i	$-0.808812\pi$
$37$	−10.0363	−1.64995	−0.824977	+	0.565166i	$0.808812\pi$
$38$	8.62956	1.39990
$39$	−1.60408	−0.256858
$40$	−0.0415425	−0.00656845
$41$	1.94056	0.303064	0.151532	−	0.988452i	$-0.451579\pi$
$41$	1.94056	0.303064	0.151532	+	0.988452i	$0.451579\pi$
$42$	−2.22900	−0.343942
$43$	0	0
$43$	0	0
$44$	−10.1871	−1.53576
$45$	0.0761133	0.0113463
$46$	0.747555	0.110221
$47$	11.1145	1.62122	0.810608	−	0.585589i	$-0.199137\pi$
$47$	11.1145	1.62122	0.810608	+	0.585589i	$0.199137\pi$
$48$	−0.661902	−0.0955373
$49$	2.79235	0.398908
$50$	−10.8684	−1.53703
$51$	1.93762	0.271322
$52$	−13.3468	−1.85087
$53$	−5.81886	−0.799282	−0.399641	−	0.916672i	$-0.630865\pi$
$53$	−5.81886	−0.799282	−0.399641	+	0.916672i	$0.630865\pi$
$54$	−4.19737	−0.571189
$55$	0.0983224	0.0132578
$56$	−4.94050	−0.660202
$57$	1.30059	0.172268
$58$	−2.88205	−0.378432
$59$	0.172353	0.0224384	0.0112192	−	0.999937i	$-0.496429\pi$
$59$	0.172353	0.0224384	0.0112192	+	0.999937i	$0.496429\pi$
$60$	−0.0235037	−0.00303431
$61$	5.56236	0.712187	0.356094	−	0.934450i	$-0.384108\pi$
$61$	5.56236	0.712187	0.356094	+	0.934450i	$0.384108\pi$
$62$	4.70835	0.597961
$63$	9.05188	1.14043
$64$	−12.3720	−1.54650
$65$	0.128819	0.0159780
$66$	−2.66167	−0.327629
$67$	−1.10095	−0.134503	−0.0672513	−	0.997736i	$-0.521423\pi$
$67$	−1.10095	−0.134503	−0.0672513	+	0.997736i	$0.521423\pi$
$68$	16.1221	1.95509
$69$	0.112667	0.0135635
$70$	0.179005	0.0213952
$71$	−5.29439	−0.628329	−0.314164	−	0.949369i	$-0.601724\pi$
$71$	−5.29439	−0.628329	−0.314164	+	0.949369i	$0.601724\pi$
$72$	−4.56691	−0.538216
$73$	−7.39621	−0.865661	−0.432830	−	0.901475i	$-0.642485\pi$
$73$	−7.39621	−0.865661	−0.432830	+	0.901475i	$0.642485\pi$
$74$	−21.8187	−2.53638
$75$	−1.63802	−0.189142
$76$	10.8216	1.24133
$77$	11.6931	1.33256
$78$	−3.48724	−0.394852
$79$	−5.41531	−0.609269	−0.304635	−	0.952469i	$-0.598534\pi$
$79$	−5.41531	−0.609269	−0.304635	+	0.952469i	$0.598534\pi$
$80$	0.0531556	0.00594298
$81$	8.04534	0.893926
$82$	4.21874	0.465882
$83$	2.03440	0.223304	0.111652	−	0.993747i	$-0.464386\pi$
$83$	2.03440	0.223304	0.111652	+	0.993747i	$0.464386\pi$
$84$	−2.79521	−0.304983
$85$	−0.155605	−0.0168778
$86$	0	0
$87$	−0.434365	−0.0465688
$88$	−5.89950	−0.628889
$89$	−4.00190	−0.424201	−0.212100	−	0.977248i	$-0.568030\pi$
$89$	−4.00190	−0.424201	−0.212100	+	0.977248i	$0.568030\pi$
$90$	0.165469	0.0174420
$91$	15.3200	1.60597
$92$	0.937448	0.0977357
$93$	0.709612	0.0735834
$94$	24.1628	2.49220
$95$	−0.104447	−0.0107161
$96$	−2.47355	−0.252456
$97$	9.00196	0.914011	0.457005	−	0.889464i	$-0.348922\pi$
$97$	9.00196	0.914011	0.457005	+	0.889464i	$0.348922\pi$
$98$	6.07054	0.613217
$99$	10.8089	1.08634
$100$	−13.6292	−1.36292
$101$	15.2982	1.52223	0.761115	−	0.648617i	$-0.224652\pi$
$101$	15.2982	1.52223	0.761115	+	0.648617i	$0.224652\pi$
$102$	4.21237	0.417087
$103$	−16.0098	−1.57749	−0.788744	−	0.614722i	$-0.789268\pi$
$103$	−16.0098	−1.57749	−0.788744	+	0.614722i	$0.789268\pi$
$104$	−7.72935	−0.757925
$105$	0.0269785	0.00263283
$106$	−12.6501	−1.22869
$107$	16.5529	1.60023	0.800115	−	0.599847i	$-0.204772\pi$
$107$	16.5529	1.60023	0.800115	+	0.599847i	$0.204772\pi$
$108$	−5.26358	−0.506488
$109$	2.05750	0.197073	0.0985366	−	0.995133i	$-0.468584\pi$
$109$	2.05750	0.197073	0.0985366	+	0.995133i	$0.468584\pi$
$110$	0.213752	0.0203804
$111$	−3.28838	−0.312119
$112$	6.32161	0.597336
$113$	11.6657	1.09741	0.548707	−	0.836015i	$-0.315120\pi$
$113$	11.6657	1.09741	0.548707	+	0.836015i	$0.315120\pi$
$114$	2.82747	0.264817
$115$	−0.00904796	−0.000843727 0
$116$	−3.61415	−0.335566
$117$	14.1615	1.30924
$118$	0.374693	0.0344933
$119$	−18.5056	−1.69641
$120$	−0.0136114	−0.00124254
$121$	2.96289	0.269353
$122$	12.0925	1.09480
$123$	0.635822	0.0573302
$124$	5.90436	0.530228
$125$	0.263109	0.0235331
$126$	19.6787	1.75312
$127$	7.54163	0.669212	0.334606	−	0.942358i	$-0.391397\pi$
$127$	7.54163	0.669212	0.334606	+	0.942358i	$0.391397\pi$
$128$	−11.7978	−1.04278
$129$	0	0
$130$	0.280051	0.0245621
$131$	−8.86410	−0.774460	−0.387230	−	0.921983i	$-0.626568\pi$
$131$	−8.86410	−0.774460	−0.387230	+	0.921983i	$0.626568\pi$
$132$	−3.33779	−0.290517
$133$	−12.4215	−1.07708
$134$	−2.39345	−0.206763
$135$	0.0508025	0.00437238
$136$	9.33657	0.800604
$137$	−17.5689	−1.50101	−0.750504	−	0.660866i	$-0.770189\pi$
$137$	−17.5689	−1.50101	−0.750504	+	0.660866i	$0.770189\pi$
$138$	0.244936	0.0208503
$139$	−15.4463	−1.31014	−0.655068	−	0.755570i	$-0.727360\pi$
$139$	−15.4463	−1.31014	−0.655068	+	0.755570i	$0.727360\pi$
$140$	0.224476	0.0189717
$141$	3.64166	0.306683
$142$	−11.5099	−0.965893
$143$	18.2938	1.52980
$144$	5.84358	0.486965
$145$	0.0348827	0.00289685
$146$	−16.0793	−1.33073
$147$	0.914913	0.0754608
$148$	−27.3611	−2.24907
$149$	−7.25959	−0.594729	−0.297364	−	0.954764i	$-0.596108\pi$
$149$	−7.25959	−0.594729	−0.297364	+	0.954764i	$0.596108\pi$
$150$	−3.56104	−0.290758
$151$	−10.0324	−0.816429	−0.408215	−	0.912886i	$-0.633848\pi$
$151$	−10.0324	−0.816429	−0.408215	+	0.912886i	$0.633848\pi$
$152$	6.26699	0.508320
$153$	−17.1063	−1.38296
$154$	25.4207	2.04846
$155$	−0.0569871	−0.00457732
$156$	−4.37307	−0.350126
$157$	9.66028	0.770974	0.385487	−	0.922713i	$-0.374033\pi$
$157$	9.66028	0.770974	0.385487	+	0.922713i	$0.374033\pi$
$158$	−11.7728	−0.936594
$159$	−1.90655	−0.151199
$160$	0.198645	0.0157042
$161$	−1.07604	−0.0848040
$162$	17.4905	1.37418
$163$	−6.78724	−0.531618	−0.265809	−	0.964026i	$-0.585639\pi$
$163$	−6.78724	−0.531618	−0.265809	+	0.964026i	$0.585639\pi$
$164$	5.29039	0.413110
$165$	0.0322153	0.00250796
$166$	4.42276	0.343272
$167$	−13.9602	−1.08027	−0.540136	−	0.841578i	$-0.681627\pi$
$167$	−13.9602	−1.08027	−0.540136	+	0.841578i	$0.681627\pi$
$168$	−1.61875	−0.124890
$169$	10.9679	0.843688
$170$	−0.338284	−0.0259452
$171$	−11.4822	−0.878069
$172$	0	0
$173$	11.5110	0.875168	0.437584	−	0.899178i	$-0.355834\pi$
$173$	11.5110	0.875168	0.437584	+	0.899178i	$0.355834\pi$
$174$	−0.944304	−0.0715875
$175$	15.6442	1.18259
$176$	7.54869	0.569004
$177$	0.0564713	0.00424464
$178$	−8.70008	−0.652099
$179$	0.756719	0.0565598	0.0282799	−	0.999600i	$-0.490997\pi$
$179$	0.756719	0.0565598	0.0282799	+	0.999600i	$0.490997\pi$
$180$	0.207502	0.0154663
$181$	−1.04038	−0.0773306	−0.0386653	−	0.999252i	$-0.512311\pi$
$181$	−1.04038	−0.0773306	−0.0386653	+	0.999252i	$0.512311\pi$
$182$	33.3055	2.46877
$183$	1.82250	0.134723
$184$	0.542892	0.0400225
$185$	0.264081	0.0194156
$186$	1.54269	0.113115
$187$	−22.0977	−1.61595
$188$	30.3006	2.20990
$189$	6.04176	0.439473
$190$	−0.227067	−0.0164732
$191$	−13.8616	−1.00299	−0.501494	−	0.865161i	$-0.667216\pi$
$191$	−13.8616	−1.00299	−0.501494	+	0.865161i	$0.667216\pi$
$192$	−4.05367	−0.292549
$193$	14.7704	1.06319	0.531597	−	0.846998i	$-0.321592\pi$
$193$	14.7704	1.06319	0.531597	+	0.846998i	$0.321592\pi$
$194$	19.5702	1.40506
$195$	0.0422075	0.00302254
$196$	7.61258	0.543756
$197$	−7.59311	−0.540987	−0.270493	−	0.962722i	$-0.587187\pi$
$197$	−7.59311	−0.540987	−0.270493	+	0.962722i	$0.587187\pi$
$198$	23.4985	1.66997
$199$	−25.0893	−1.77853	−0.889265	−	0.457392i	$-0.848783\pi$
$199$	−25.0893	−1.77853	−0.889265	+	0.457392i	$0.848783\pi$
$200$	−7.89291	−0.558113
$201$	−0.360726	−0.0254437
$202$	33.2582	2.34004
$203$	4.14847	0.291166
$204$	5.28240	0.369842
$205$	−0.0510612	−0.00356627
$206$	−34.8050	−2.42498
$207$	−0.994675	−0.0691347
$208$	9.89007	0.685753
$209$	−14.8327	−1.02600
$210$	0.0586510	0.00404730
$211$	−16.0533	−1.10516	−0.552579	−	0.833461i	$-0.686356\pi$
$211$	−16.0533	−1.10516	−0.552579	+	0.833461i	$0.686356\pi$
$212$	−15.8635	−1.08951
$213$	−1.73471	−0.118860
$214$	35.9858	2.45994
$215$	0	0
$216$	−3.04823	−0.207406
$217$	−6.77728	−0.460071
$218$	4.47299	0.302949
$219$	−2.42336	−0.163756
$220$	0.268049	0.0180719
$221$	−28.9518	−1.94751
$222$	−7.14890	−0.479803
$223$	−15.0941	−1.01078	−0.505388	−	0.862892i	$-0.668651\pi$
$223$	−15.0941	−1.01078	−0.505388	+	0.862892i	$0.668651\pi$
$224$	23.6241	1.57845
$225$	14.4612	0.964082
$226$	25.3610	1.68699
$227$	20.1627	1.33824	0.669121	−	0.743153i	$-0.266671\pi$
$227$	20.1627	1.33824	0.669121	+	0.743153i	$0.266671\pi$
$228$	3.54571	0.234820
$229$	13.3813	0.884261	0.442130	−	0.896951i	$-0.354223\pi$
$229$	13.3813	0.884261	0.442130	+	0.896951i	$0.354223\pi$
$230$	−0.0196702	−0.00129701
$231$	3.83125	0.252078
$232$	−2.09302	−0.137413
$233$	9.26082	0.606697	0.303348	−	0.952880i	$-0.401895\pi$
$233$	9.26082	0.606697	0.303348	+	0.952880i	$0.401895\pi$
$234$	30.7870	2.01261
$235$	−0.292452	−0.0190775
$236$	0.469872	0.0305861
$237$	−1.77432	−0.115255
$238$	−40.2310	−2.60779
$239$	−19.2261	−1.24363	−0.621815	−	0.783164i	$-0.713604\pi$
$239$	−19.2261	−1.24363	−0.621815	+	0.783164i	$0.713604\pi$
$240$	0.0174164	0.00112422
$241$	5.78762	0.372813	0.186407	−	0.982473i	$-0.440316\pi$
$241$	5.78762	0.372813	0.186407	+	0.982473i	$0.440316\pi$
$242$	6.44128	0.414061
$243$	8.42822	0.540671
$244$	15.1642	0.970791
$245$	−0.0734743	−0.00469410
$246$	1.38227	0.0881303
$247$	−19.4333	−1.23651
$248$	3.41932	0.217127
$249$	0.666569	0.0422421
$250$	0.571995	0.0361761
$251$	7.42033	0.468367	0.234184	−	0.972192i	$-0.424758\pi$
$251$	7.42033	0.468367	0.234184	+	0.972192i	$0.424758\pi$
$252$	24.6774	1.55453
$253$	−1.28491	−0.0807817
$254$	16.3954	1.02874
$255$	−0.0509841	−0.00319275
$256$	−0.904216	−0.0565135
$257$	−22.5274	−1.40522	−0.702609	−	0.711576i	$-0.747982\pi$
$257$	−22.5274	−1.40522	−0.702609	+	0.711576i	$0.747982\pi$
$258$	0	0
$259$	31.4063	1.95149
$260$	0.351190	0.0217799
$261$	3.83478	0.237367
$262$	−19.2704	−1.19053
$263$	−5.43157	−0.334925	−0.167462	−	0.985878i	$-0.553557\pi$
$263$	−5.43157	−0.334925	−0.167462	+	0.985878i	$0.553557\pi$
$264$	−1.93297	−0.118966
$265$	0.153110	0.00940546
$266$	−27.0043	−1.65574
$267$	−1.31122	−0.0802454
$268$	−3.00144	−0.183342
$269$	−2.40577	−0.146683	−0.0733413	−	0.997307i	$-0.523366\pi$
$269$	−2.40577	−0.146683	−0.0733413	+	0.997307i	$0.523366\pi$
$270$	0.110444	0.00672141
$271$	−3.29877	−0.200386	−0.100193	−	0.994968i	$-0.531946\pi$
$271$	−3.29877	−0.200386	−0.100193	+	0.994968i	$0.531946\pi$
$272$	−11.9466	−0.724368
$273$	5.01959	0.303800
$274$	−38.1945	−2.30741
$275$	18.6809	1.12650
$276$	0.307154	0.0184885
$277$	−13.8128	−0.829929	−0.414965	−	0.909838i	$-0.636206\pi$
$277$	−13.8128	−0.829929	−0.414965	+	0.909838i	$0.636206\pi$
$278$	−33.5800	−2.01400
$279$	−6.26480	−0.375064
$280$	0.129998	0.00776886
$281$	18.0080	1.07427	0.537135	−	0.843497i	$-0.319507\pi$
$281$	18.0080	1.07427	0.537135	+	0.843497i	$0.319507\pi$
$282$	7.91692	0.471446
$283$	−13.2926	−0.790161	−0.395081	−	0.918646i	$-0.629283\pi$
$283$	−13.2926	−0.790161	−0.395081	+	0.918646i	$0.629283\pi$
$284$	−14.4337	−0.856483
$285$	−0.0342221	−0.00202714
$286$	39.7704	2.35167
$287$	−6.07253	−0.358450
$288$	21.8377	1.28680
$289$	17.9719	1.05717
$290$	0.0758345	0.00445316
$291$	2.94949	0.172902
$292$	−20.1637	−1.17999
$293$	−3.71669	−0.217132	−0.108566	−	0.994089i	$-0.534626\pi$
$293$	−3.71669	−0.217132	−0.108566	+	0.994089i	$0.534626\pi$
$294$	1.98901	0.116001
$295$	−0.00453506	−0.000264041 0
$296$	−15.8453	−0.920989
$297$	7.21452	0.418629
$298$	−15.7823	−0.914242
$299$	−1.68345	−0.0973566
$300$	−4.46561	−0.257822
$301$	0	0
$302$	−21.8104	−1.25505
$303$	5.01246	0.287958
$304$	−8.01891	−0.459916
$305$	−0.146361	−0.00838058
$306$	−37.1888	−2.12594
$307$	9.75456	0.556722	0.278361	−	0.960476i	$-0.410209\pi$
$307$	9.75456	0.556722	0.278361	+	0.960476i	$0.410209\pi$
$308$	31.8781	1.81642
$309$	−5.24559	−0.298411
$310$	−0.123889	−0.00703644
$311$	−3.94014	−0.223425	−0.111712	−	0.993741i	$-0.535634\pi$
$311$	−3.94014	−0.223425	−0.111712	+	0.993741i	$0.535634\pi$
$312$	−2.53252	−0.143376
$313$	−22.8913	−1.29389	−0.646947	−	0.762535i	$-0.723954\pi$
$313$	−22.8913	−1.29389	−0.646947	+	0.762535i	$0.723954\pi$
$314$	21.0013	1.18517
$315$	−0.238179	−0.0134199
$316$	−14.7633	−0.830502
$317$	10.3014	0.578583	0.289291	−	0.957241i	$-0.406580\pi$
$317$	10.3014	0.578583	0.289291	+	0.957241i	$0.406580\pi$
$318$	−4.14481	−0.232429
$319$	4.95373	0.277356
$320$	0.325540	0.0181982
$321$	5.42355	0.302713
$322$	−2.33930	−0.130364
$323$	23.4742	1.30614
$324$	21.9334	1.21852
$325$	24.4751	1.35764
$326$	−14.7554	−0.817225
$327$	0.674140	0.0372800
$328$	3.06375	0.169167
$329$	−34.7803	−1.91750
$330$	0.0700357	0.00385534
$331$	−11.9131	−0.654801	−0.327400	−	0.944886i	$-0.606173\pi$
$331$	−11.9131	−0.654801	−0.327400	+	0.944886i	$0.606173\pi$
$332$	5.54622	0.304389
$333$	29.0314	1.59091
$334$	−30.3493	−1.66064
$335$	0.0289690	0.00158274
$336$	2.07127	0.112997
$337$	−3.27987	−0.178666	−0.0893330	−	0.996002i	$-0.528474\pi$
$337$	−3.27987	−0.178666	−0.0893330	+	0.996002i	$0.528474\pi$
$338$	23.8442	1.29695
$339$	3.82225	0.207596
$340$	−0.424215	−0.0230063
$341$	−8.09281	−0.438250
$342$	−24.9623	−1.34980
$343$	13.1669	0.710945
$344$	0	0
$345$	−0.00296456	−0.000159607 0
$346$	25.0249	1.34534
$347$	−12.5267	−0.672468	−0.336234	−	0.941779i	$-0.609153\pi$
$347$	−12.5267	−0.672468	−0.336234	+	0.941779i	$0.609153\pi$
$348$	−1.18418	−0.0634785
$349$	32.0034	1.71311	0.856553	−	0.516060i	$-0.172602\pi$
$349$	32.0034	1.71311	0.856553	+	0.516060i	$0.172602\pi$
$350$	34.0103	1.81793
$351$	9.45225	0.504524
$352$	28.2098	1.50359
$353$	−2.40099	−0.127792	−0.0638958	−	0.997957i	$-0.520353\pi$
$353$	−2.40099	−0.127792	−0.0638958	+	0.997957i	$0.520353\pi$
$354$	0.122768	0.00652504
$355$	0.139310	0.00739379
$356$	−10.9101	−0.578233
$357$	−6.06335	−0.320907
$358$	1.64510	0.0869461
$359$	8.24617	0.435216	0.217608	−	0.976036i	$-0.430175\pi$
$359$	8.24617	0.435216	0.217608	+	0.976036i	$0.430175\pi$
$360$	0.120168	0.00633340
$361$	−3.24338	−0.170704
$362$	−2.26177	−0.118876
$363$	0.970788	0.0509532
$364$	41.7658	2.18912
$365$	0.194614	0.0101866
$366$	3.96210	0.207102
$367$	10.3568	0.540622	0.270311	−	0.962773i	$-0.412873\pi$
$367$	10.3568	0.540622	0.270311	+	0.962773i	$0.412873\pi$
$368$	−0.694656	−0.0362114
$369$	−5.61334	−0.292219
$370$	0.574110	0.0298465
$371$	18.2088	0.945354
$372$	1.93456	0.100302
$373$	11.5647	0.598799	0.299399	−	0.954128i	$-0.403214\pi$
$373$	11.5647	0.598799	0.299399	+	0.954128i	$0.403214\pi$
$374$	−48.0402	−2.48410
$375$	0.0862074	0.00445173
$376$	17.5476	0.904947
$377$	6.49023	0.334264
$378$	13.1347	0.675577
$379$	11.6208	0.596922	0.298461	−	0.954422i	$-0.403527\pi$
$379$	11.6208	0.596922	0.298461	+	0.954422i	$0.403527\pi$
$380$	−0.284746	−0.0146072
$381$	2.47101	0.126594
$382$	−30.1349	−1.54184
$383$	−17.5710	−0.897834	−0.448917	−	0.893573i	$-0.648190\pi$
$383$	−17.5710	−0.897834	−0.448917	+	0.893573i	$0.648190\pi$
$384$	−3.86553	−0.197262
$385$	−0.307678	−0.0156807
$386$	32.1106	1.63439
$387$	0	0
$388$	24.5414	1.24590
$389$	6.55712	0.332459	0.166230	−	0.986087i	$-0.446841\pi$
$389$	6.55712	0.332459	0.166230	+	0.986087i	$0.446841\pi$
$390$	0.0917587	0.00464638
$391$	2.03351	0.102839
$392$	4.40857	0.222666
$393$	−2.90432	−0.146503
$394$	−16.5073	−0.831627
$395$	0.142491	0.00716951
$396$	29.4676	1.48080
$397$	−29.5184	−1.48149	−0.740744	−	0.671787i	$-0.765527\pi$
$397$	−29.5184	−1.48149	−0.740744	+	0.671787i	$0.765527\pi$
$398$	−54.5437	−2.73403
$399$	−4.06991	−0.203750
$400$	10.0994	0.504968
$401$	24.8918	1.24304	0.621518	−	0.783400i	$-0.286516\pi$
$401$	24.8918	1.24304	0.621518	+	0.783400i	$0.286516\pi$
$402$	−0.784214	−0.0391131
$403$	−10.6030	−0.528171
$404$	41.7064	2.07497
$405$	−0.211694	−0.0105192
$406$	9.01873	0.447592
$407$	37.5025	1.85893
$408$	3.05912	0.151449
$409$	−12.8004	−0.632941	−0.316470	−	0.948602i	$-0.602498\pi$
$409$	−12.8004	−0.632941	−0.316470	+	0.948602i	$0.602498\pi$
$410$	−0.111006	−0.00548222
$411$	−5.75643	−0.283944
$412$	−43.6462	−2.15029
$413$	−0.539339	−0.0265391
$414$	−2.16241	−0.106277
$415$	−0.0535304	−0.00262771
$416$	36.9596	1.81209
$417$	−5.06097	−0.247837
$418$	−32.2460	−1.57720
$419$	27.9958	1.36768	0.683841	−	0.729631i	$-0.260308\pi$
$419$	27.9958	1.36768	0.683841	+	0.729631i	$0.260308\pi$
$420$	0.0735495	0.00358885
$421$	13.8349	0.674274	0.337137	−	0.941456i	$-0.390542\pi$
$421$	13.8349	0.674274	0.337137	+	0.941456i	$0.390542\pi$
$422$	−34.8998	−1.69889
$423$	−32.1503	−1.56320
$424$	−9.18682	−0.446152
$425$	−29.5644	−1.43409
$426$	−3.77123	−0.182717
$427$	−17.4061	−0.842342
$428$	45.1269	2.18129
$429$	5.99394	0.289390
$430$	0	0
$431$	−32.0319	−1.54292	−0.771462	−	0.636276i	$-0.780474\pi$
$431$	−32.0319	−1.54292	−0.771462	+	0.636276i	$0.780474\pi$
$432$	3.90035	0.187656
$433$	0.379554	0.0182402	0.00912011	−	0.999958i	$-0.497097\pi$
$433$	0.379554	0.0182402	0.00912011	+	0.999958i	$0.497097\pi$
$434$	−14.7337	−0.707241
$435$	0.0114293	0.000547993 0
$436$	5.60922	0.268633
$437$	1.36495	0.0652945
$438$	−5.26837	−0.251732
$439$	4.87777	0.232803	0.116402	−	0.993202i	$-0.462864\pi$
$439$	4.87777	0.232803	0.116402	+	0.993202i	$0.462864\pi$
$440$	0.155232	0.00740038
$441$	−8.07729	−0.384633
$442$	−62.9408	−2.99379
$443$	5.93506	0.281983	0.140992	−	0.990011i	$-0.454971\pi$
$443$	5.93506	0.281983	0.140992	+	0.990011i	$0.454971\pi$
$444$	−8.96486	−0.425454
$445$	0.105301	0.00499173
$446$	−32.8144	−1.55381
$447$	−2.37860	−0.112504
$448$	38.7153	1.82913
$449$	32.7108	1.54372	0.771858	−	0.635795i	$-0.219328\pi$
$449$	32.7108	1.54372	0.771858	+	0.635795i	$0.219328\pi$
$450$	31.4385	1.48203
$451$	−7.25126	−0.341449
$452$	31.8032	1.49590
$453$	−3.28713	−0.154443
$454$	43.8334	2.05720
$455$	−0.403110	−0.0188981
$456$	2.05338	0.0961582
$457$	29.0617	1.35945	0.679724	−	0.733468i	$-0.262100\pi$
$457$	29.0617	1.35945	0.679724	+	0.733468i	$0.262100\pi$
$458$	29.0908	1.35932
$459$	−11.4177	−0.532934
$460$	−0.0246668	−0.00115009
$461$	−14.5408	−0.677233	−0.338617	−	0.940924i	$-0.609959\pi$
$461$	−14.5408	−0.677233	−0.338617	+	0.940924i	$0.609959\pi$
$462$	8.32910	0.387505
$463$	−6.18240	−0.287321	−0.143660	−	0.989627i	$-0.545887\pi$
$463$	−6.18240	−0.287321	−0.143660	+	0.989627i	$0.545887\pi$
$464$	2.67811	0.124328
$465$	−0.0186718	−0.000865884 0
$466$	20.1329	0.932639
$467$	−15.8073	−0.731473	−0.365736	−	0.930718i	$-0.619183\pi$
$467$	−15.8073	−0.731473	−0.365736	+	0.930718i	$0.619183\pi$
$468$	38.6075	1.78463
$469$	3.44518	0.159084
$470$	−0.635787	−0.0293267
$471$	3.16519	0.145844
$472$	0.272111	0.0125249
$473$	0	0
$474$	−3.85736	−0.177174
$475$	−19.8446	−0.910531
$476$	−50.4504	−2.31239
$477$	16.8319	0.770680
$478$	−41.7972	−1.91176
$479$	38.5242	1.76021	0.880107	−	0.474775i	$-0.157471\pi$
$479$	38.5242	1.76021	0.880107	+	0.474775i	$0.157471\pi$
$480$	0.0650858	0.00297075
$481$	49.1347	2.24035
$482$	12.5822	0.573104
$483$	−0.352565	−0.0160423
$484$	8.07749	0.367159
$485$	−0.236866	−0.0107555
$486$	18.3228	0.831141
$487$	−12.4415	−0.563777	−0.281888	−	0.959447i	$-0.590961\pi$
$487$	−12.4415	−0.563777	−0.281888	+	0.959447i	$0.590961\pi$
$488$	8.78186	0.397536
$489$	−2.22384	−0.100565
$490$	−0.159732	−0.00721597
$491$	−38.5366	−1.73913	−0.869567	−	0.493814i	$-0.835602\pi$
$491$	−38.5366	−1.73913	−0.869567	+	0.493814i	$0.835602\pi$
$492$	1.73339	0.0781474
$493$	−7.83980	−0.353087
$494$	−42.2478	−1.90082
$495$	−0.284412	−0.0127834
$496$	−4.37518	−0.196451
$497$	16.5676	0.743159
$498$	1.44911	0.0649364
$499$	−41.8655	−1.87416	−0.937078	−	0.349119i	$-0.886481\pi$
$499$	−41.8655	−1.87416	−0.937078	+	0.349119i	$0.886481\pi$
$500$	0.717293	0.0320783
$501$	−4.57405	−0.204353
$502$	16.1317	0.719993
$503$	−14.6859	−0.654810	−0.327405	−	0.944884i	$-0.606174\pi$
$503$	−14.6859	−0.654810	−0.327405	+	0.944884i	$0.606174\pi$
$504$	14.2911	0.636577
$505$	−0.402537	−0.0179127
$506$	−2.79338	−0.124181
$507$	3.59364	0.159599
$508$	20.5602	0.912210
$509$	−22.1264	−0.980736	−0.490368	−	0.871516i	$-0.663138\pi$
$509$	−22.1264	−0.980736	−0.490368	+	0.871516i	$0.663138\pi$
$510$	−0.110839	−0.00490802
$511$	23.1448	1.02386
$512$	21.6297	0.955909
$513$	−7.66393	−0.338371
$514$	−48.9742	−2.16016
$515$	0.421259	0.0185629
$516$	0	0
$517$	−41.5315	−1.82655
$518$	68.2768	2.99991
$519$	3.77159	0.165554
$520$	0.203380	0.00891880
$521$	−25.5288	−1.11844	−0.559218	−	0.829020i	$-0.688899\pi$
$521$	−25.5288	−1.11844	−0.559218	+	0.829020i	$0.688899\pi$
$522$	8.33676	0.364890
$523$	28.5656	1.24909	0.624544	−	0.780990i	$-0.285285\pi$
$523$	28.5656	1.24909	0.624544	+	0.780990i	$0.285285\pi$
$524$	−24.1655	−1.05568
$525$	5.12582	0.223709
$526$	−11.8082	−0.514860
$527$	12.8077	0.557913
$528$	2.47332	0.107638
$529$	−22.8818	−0.994859
$530$	0.332859	0.0144585
$531$	−0.498555	−0.0216355
$532$	−33.8639	−1.46818
$533$	−9.50039	−0.411508
$534$	−2.85058	−0.123357
$535$	−0.435551	−0.0188305
$536$	−1.73818	−0.0750781
$537$	0.247939	0.0106993
$538$	−5.23012	−0.225487
$539$	−10.4342	−0.449431
$540$	0.138499	0.00596005
$541$	−1.74251	−0.0749162	−0.0374581	−	0.999298i	$-0.511926\pi$
$541$	−1.74251	−0.0749162	−0.0374581	+	0.999298i	$0.511926\pi$
$542$	−7.17149	−0.308042
$543$	−0.340879	−0.0146285
$544$	−44.6449	−1.91413
$545$	−0.0541384	−0.00231904
$546$	10.9125	0.467013
$547$	10.8159	0.462455	0.231227	−	0.972900i	$-0.425726\pi$
$547$	10.8159	0.462455	0.231227	+	0.972900i	$0.425726\pi$
$548$	−47.8966	−2.04604
$549$	−16.0899	−0.686702
$550$	40.6120	1.73170
$551$	−5.26231	−0.224182
$552$	0.177878	0.00757100
$553$	16.9460	0.720616
$554$	−30.0288	−1.27580
$555$	0.0865261	0.00367283
$556$	−42.1100	−1.78586
$557$	0.152401	0.00645745	0.00322872	−	0.999995i	$-0.498972\pi$
$557$	0.152401	0.00645745	0.00322872	+	0.999995i	$0.498972\pi$
$558$	−13.6196	−0.576563
$559$	0	0
$560$	−0.166338	−0.00702908
$561$	−7.24031	−0.305686
$562$	39.1492	1.65141
$563$	−23.8190	−1.00385	−0.501925	−	0.864911i	$-0.667374\pi$
$563$	−23.8190	−1.00385	−0.501925	+	0.864911i	$0.667374\pi$
$564$	9.92798	0.418043
$565$	−0.306955	−0.0129137
$566$	−28.8979	−1.21467
$567$	−25.1761	−1.05730
$568$	−8.35880	−0.350727
$569$	31.3030	1.31229	0.656144	−	0.754635i	$-0.272186\pi$
$569$	31.3030	1.31229	0.656144	+	0.754635i	$0.272186\pi$
$570$	−0.0743984	−0.00311620
$571$	−4.40841	−0.184486	−0.0922431	−	0.995737i	$-0.529404\pi$
$571$	−4.40841	−0.184486	−0.0922431	+	0.995737i	$0.529404\pi$
$572$	49.8729	2.08529
$573$	−4.54174	−0.189734
$574$	−13.2016	−0.551024
$575$	−1.71908	−0.0716905
$576$	35.7877	1.49116
$577$	25.6119	1.06624	0.533119	−	0.846040i	$-0.321020\pi$
$577$	25.6119	1.06624	0.533119	+	0.846040i	$0.321020\pi$
$578$	39.0708	1.62513
$579$	4.83950	0.201123
$580$	0.0950980	0.00394873
$581$	−6.36619	−0.264114
$582$	6.41215	0.265792
$583$	21.7433	0.900515
$584$	−11.6771	−0.483204
$585$	−0.372628	−0.0154063
$586$	−8.08005	−0.333784
$587$	26.4584	1.09205	0.546027	−	0.837767i	$-0.316140\pi$
$587$	26.4584	1.09205	0.546027	+	0.837767i	$0.316140\pi$
$588$	2.49426	0.102861
$589$	8.59693	0.354230
$590$	−0.00985917	−0.000405896 0
$591$	−2.48788	−0.102338
$592$	20.2748	0.833289
$593$	−37.8574	−1.55462	−0.777309	−	0.629119i	$-0.783416\pi$
$593$	−37.8574	−1.55462	−0.777309	+	0.629119i	$0.783416\pi$
$594$	15.6843	0.643534
$595$	0.486932	0.0199623
$596$	−19.7913	−0.810682
$597$	−8.22048	−0.336442
$598$	−3.65981	−0.149661
$599$	−7.23028	−0.295421	−0.147711	−	0.989031i	$-0.547190\pi$
$599$	−7.23028	−0.295421	−0.147711	+	0.989031i	$0.547190\pi$
$600$	−2.58611	−0.105577
$601$	1.42190	0.0580006	0.0290003	−	0.999579i	$-0.490768\pi$
$601$	1.42190	0.0580006	0.0290003	+	0.999579i	$0.490768\pi$
$602$	0	0
$603$	3.18466	0.129689
$604$	−27.3507	−1.11288
$605$	−0.0779614	−0.00316958
$606$	10.8970	0.442661
$607$	11.7959	0.478779	0.239390	−	0.970924i	$-0.423053\pi$
$607$	11.7959	0.478779	0.239390	+	0.970924i	$0.423053\pi$
$608$	−29.9670	−1.21532
$609$	1.35925	0.0550794
$610$	−0.318186	−0.0128830
$611$	−54.4133	−2.20133
$612$	−46.6355	−1.88513
$613$	−24.0217	−0.970228	−0.485114	−	0.874451i	$-0.661222\pi$
$613$	−24.0217	−0.970228	−0.485114	+	0.874451i	$0.661222\pi$
$614$	21.2063	0.855817
$615$	−0.0167302	−0.000674626 0
$616$	18.4611	0.743821
$617$	1.60543	0.0646320	0.0323160	−	0.999478i	$-0.489712\pi$
$617$	1.60543	0.0646320	0.0323160	+	0.999478i	$0.489712\pi$
$618$	−11.4038	−0.458730
$619$	48.5926	1.95310	0.976551	−	0.215285i	$-0.0690681\pi$
$619$	48.5926	1.95310	0.976551	+	0.215285i	$0.0690681\pi$
$620$	−0.155360	−0.00623939
$621$	−0.663905	−0.0266416
$622$	−8.56582	−0.343458
$623$	12.5230	0.501725
$624$	3.24048	0.129723
$625$	24.9896	0.999585
$626$	−49.7654	−1.98903
$627$	−4.85992	−0.194086
$628$	26.3361	1.05092
$629$	−59.3516	−2.36650
$630$	−0.517799	−0.0206296
$631$	−19.9083	−0.792537	−0.396268	−	0.918135i	$-0.629695\pi$
$631$	−19.9083	−0.792537	−0.396268	+	0.918135i	$0.629695\pi$
$632$	−8.54969	−0.340089
$633$	−5.25987	−0.209061
$634$	22.3951	0.889421
$635$	−0.198440	−0.00787487
$636$	−5.19767	−0.206101
$637$	−13.6705	−0.541647
$638$	10.7694	0.426363
$639$	15.3148	0.605844
$640$	0.310430	0.0122708
$641$	21.6495	0.855106	0.427553	−	0.903990i	$-0.359376\pi$
$641$	21.6495	0.855106	0.427553	+	0.903990i	$0.359376\pi$
$642$	11.7907	0.465343
$643$	2.12679	0.0838722	0.0419361	−	0.999120i	$-0.486647\pi$
$643$	2.12679	0.0838722	0.0419361	+	0.999120i	$0.486647\pi$
$644$	−2.93353	−0.115597
$645$	0	0
$646$	51.0327	2.00785
$647$	−2.66503	−0.104773	−0.0523867	−	0.998627i	$-0.516683\pi$
$647$	−2.66503	−0.104773	−0.0523867	+	0.998627i	$0.516683\pi$
$648$	12.7020	0.498981
$649$	−0.644029	−0.0252804
$650$	53.2087	2.08702
$651$	−2.22057	−0.0870311
$652$	−18.5035	−0.724655
$653$	12.8870	0.504306	0.252153	−	0.967687i	$-0.418861\pi$
$653$	12.8870	0.504306	0.252153	+	0.967687i	$0.418861\pi$
$654$	1.46557	0.0573084
$655$	0.233238	0.00911337
$656$	−3.92022	−0.153059
$657$	21.3946	0.834683
$658$	−75.6119	−2.94766
$659$	−38.9594	−1.51764	−0.758822	−	0.651298i	$-0.774225\pi$
$659$	−38.9594	−1.51764	−0.758822	+	0.651298i	$0.774225\pi$
$660$	0.0878261	0.00341863
$661$	39.8082	1.54836	0.774180	−	0.632965i	$-0.218162\pi$
$661$	39.8082	1.54836	0.774180	+	0.632965i	$0.218162\pi$
$662$	−25.8988	−1.00659
$663$	−9.48604	−0.368407
$664$	3.21191	0.124646
$665$	0.326844	0.0126745
$666$	63.1139	2.44561
$667$	−0.455859	−0.0176509
$668$	−38.0586	−1.47253
$669$	−4.94558	−0.191207
$670$	0.0629782	0.00243306
$671$	−20.7848	−0.802390
$672$	7.74043	0.298593
$673$	−37.4248	−1.44262	−0.721311	−	0.692612i	$-0.756460\pi$
$673$	−37.4248	−1.44262	−0.721311	+	0.692612i	$0.756460\pi$
$674$	−7.13040	−0.274653
$675$	9.65228	0.371516
$676$	29.9011	1.15004
$677$	−4.46503	−0.171605	−0.0858026	−	0.996312i	$-0.527345\pi$
$677$	−4.46503	−0.171605	−0.0858026	+	0.996312i	$0.527345\pi$
$678$	8.30953	0.319126
$679$	−28.1696	−1.08105
$680$	−0.245670	−0.00942102
$681$	6.60628	0.253153
$682$	−17.5937	−0.673696
$683$	38.0115	1.45447	0.727236	−	0.686388i	$-0.240805\pi$
$683$	38.0115	1.45447	0.727236	+	0.686388i	$0.240805\pi$
$684$	−31.3032	−1.19691
$685$	0.462284	0.0176629
$686$	28.6246	1.09289
$687$	4.38437	0.167274
$688$	0	0
$689$	28.4874	1.08528
$690$	−0.00644492	−0.000245354 0
$691$	−5.66536	−0.215520	−0.107760	−	0.994177i	$-0.534368\pi$
$691$	−5.66536	−0.215520	−0.107760	+	0.994177i	$0.534368\pi$
$692$	31.3817	1.19295
$693$	−33.8241	−1.28487
$694$	−27.2329	−1.03375
$695$	0.406433	0.0154169
$696$	−0.685776	−0.0259943
$697$	11.4759	0.434680
$698$	69.5751	2.63346
$699$	3.03430	0.114768
$700$	42.6496	1.61200
$701$	−25.5591	−0.965354	−0.482677	−	0.875798i	$-0.660335\pi$
$701$	−25.5591	−0.965354	−0.482677	+	0.875798i	$0.660335\pi$
$702$	20.5491	0.775575
$703$	−39.8386	−1.50254
$704$	46.2303	1.74237
$705$	−0.0958218	−0.00360886
$706$	−5.21971	−0.196447
$707$	−47.8723	−1.80042
$708$	0.153953	0.00578592
$709$	−35.1520	−1.32016	−0.660080	−	0.751196i	$-0.729478\pi$
$709$	−35.1520	−1.32016	−0.660080	+	0.751196i	$0.729478\pi$
$710$	0.302858	0.0113660
$711$	15.6646	0.587467
$712$	−6.31821	−0.236785
$713$	0.744728	0.0278903
$714$	−13.1817	−0.493311
$715$	−0.481358	−0.0180018
$716$	2.06299	0.0770974
$717$	−6.29941	−0.235256
$718$	17.9271	0.669033
$719$	5.04887	0.188291	0.0941456	−	0.995558i	$-0.469988\pi$
$719$	5.04887	0.188291	0.0941456	+	0.995558i	$0.469988\pi$
$720$	−0.153760	−0.00573031
$721$	50.0989	1.86578
$722$	−7.05106	−0.262413
$723$	1.89631	0.0705245
$724$	−2.83630	−0.105410
$725$	6.62758	0.246142
$726$	2.11048	0.0783273
$727$	−16.4699	−0.610835	−0.305417	−	0.952219i	$-0.598796\pi$
$727$	−16.4699	−0.610835	−0.305417	+	0.952219i	$0.598796\pi$
$728$	24.1872	0.896439
$729$	−21.3745	−0.791648
$730$	0.423089	0.0156592
$731$	0	0
$732$	4.96856	0.183643
$733$	11.3611	0.419632	0.209816	−	0.977741i	$-0.432713\pi$
$733$	11.3611	0.419632	0.209816	+	0.977741i	$0.432713\pi$
$734$	22.5156	0.831066
$735$	−0.0240738	−0.000887976 0
$736$	−2.59596	−0.0956883
$737$	4.11392	0.151538
$738$	−12.2033	−0.449211
$739$	−29.5197	−1.08590	−0.542949	−	0.839765i	$-0.682693\pi$
$739$	−29.5197	−1.08590	−0.542949	+	0.839765i	$0.682693\pi$
$740$	0.719945	0.0264657
$741$	−6.36732	−0.233909
$742$	39.5857	1.45324
$743$	−16.7847	−0.615771	−0.307886	−	0.951423i	$-0.599621\pi$
$743$	−16.7847	−0.615771	−0.307886	+	0.951423i	$0.599621\pi$
$744$	1.12034	0.0410736
$745$	0.191019	0.00699840
$746$	25.1416	0.920498
$747$	−5.88479	−0.215313
$748$	−60.2433	−2.20271
$749$	−51.7986	−1.89268
$750$	0.187414	0.00684339
$751$	−53.9644	−1.96919	−0.984595	−	0.174849i	$-0.944056\pi$
$751$	−53.9644	−1.96919	−0.984595	+	0.174849i	$0.944056\pi$
$752$	−22.4530	−0.818775
$753$	2.43127	0.0886003
$754$	14.1097	0.513845
$755$	0.263981	0.00960724
$756$	16.4712	0.599051
$757$	19.6811	0.715322	0.357661	−	0.933852i	$-0.383574\pi$
$757$	19.6811	0.715322	0.357661	+	0.933852i	$0.383574\pi$
$758$	25.2636	0.917614
$759$	−0.421001	−0.0152814
$760$	−0.164901	−0.00598160
$761$	37.5368	1.36071	0.680353	−	0.732884i	$-0.261826\pi$
$761$	37.5368	1.36071	0.680353	+	0.732884i	$0.261826\pi$
$762$	5.37195	0.194605
$763$	−6.43849	−0.233089
$764$	−37.7897	−1.36719
$765$	0.450112	0.0162738
$766$	−38.1991	−1.38019
$767$	−0.843788	−0.0304674
$768$	−0.296266	−0.0106906
$769$	−30.7637	−1.10937	−0.554683	−	0.832062i	$-0.687161\pi$
$769$	−30.7637	−1.10937	−0.554683	+	0.832062i	$0.687161\pi$
$770$	−0.668888	−0.0241050
$771$	−7.38108	−0.265823
$772$	40.2673	1.44925
$773$	−41.3365	−1.48677	−0.743386	−	0.668863i	$-0.766781\pi$
$773$	−41.3365	−1.48677	−0.743386	+	0.668863i	$0.766781\pi$
$774$	0	0
$775$	−10.8273	−0.388929
$776$	14.2123	0.510192
$777$	10.2902	0.369161
$778$	14.2551	0.511070
$779$	7.70296	0.275987
$780$	0.115067	0.00412007
$781$	19.7835	0.707910
$782$	4.42082	0.158088
$783$	2.55956	0.0914711
$784$	−5.64098	−0.201463
$785$	−0.254188	−0.00907235
$786$	−6.31395	−0.225211
$787$	9.84858	0.351064	0.175532	−	0.984474i	$-0.443835\pi$
$787$	9.84858	0.351064	0.175532	+	0.984474i	$0.443835\pi$
$788$	−20.7005	−0.737425
$789$	−1.77965	−0.0633573
$790$	0.309774	0.0110213
$791$	−36.5051	−1.29797
$792$	17.0652	0.606384
$793$	−27.2317	−0.967025
$794$	−64.1727	−2.27741
$795$	0.0501663	0.00177922
$796$	−68.3989	−2.42434
$797$	−15.6603	−0.554716	−0.277358	−	0.960767i	$-0.589459\pi$
$797$	−15.6603	−0.554716	−0.277358	+	0.960767i	$0.589459\pi$
$798$	−8.84793	−0.313213
$799$	65.7279	2.32528
$800$	37.7417	1.33437
$801$	11.5761	0.409021
$802$	54.1144	1.91085
$803$	27.6374	0.975302
$804$	−0.983420	−0.0346826
$805$	0.0283136	0.000997922 0
$806$	−23.0507	−0.811926
$807$	−0.788250	−0.0277477
$808$	24.1529	0.849695
$809$	51.8827	1.82410	0.912049	−	0.410081i	$-0.134500\pi$
$809$	51.8827	1.82410	0.912049	+	0.410081i	$0.134500\pi$
$810$	−0.460221	−0.0161705
$811$	11.3471	0.398451	0.199226	−	0.979954i	$-0.436157\pi$
$811$	11.3471	0.398451	0.199226	+	0.979954i	$0.436157\pi$
$812$	11.3097	0.396892
$813$	−1.08084	−0.0379068
$814$	81.5300	2.85762
$815$	0.178591	0.00625575
$816$	−3.91429	−0.137028
$817$	0	0
$818$	−27.8280	−0.972983
$819$	−44.3153	−1.54850
$820$	−0.139204	−0.00486122
$821$	−14.0496	−0.490333	−0.245167	−	0.969481i	$-0.578843\pi$
$821$	−14.0496	−0.490333	−0.245167	+	0.969481i	$0.578843\pi$
$822$	−12.5144	−0.436490
$823$	−9.51232	−0.331579	−0.165789	−	0.986161i	$-0.553017\pi$
$823$	−9.51232	−0.331579	−0.165789	+	0.986161i	$0.553017\pi$
$824$	−25.2762	−0.880539
$825$	6.12078	0.213098
$826$	−1.17252	−0.0407970
$827$	33.8180	1.17597	0.587983	−	0.808873i	$-0.299922\pi$
$827$	33.8180	1.17597	0.587983	+	0.808873i	$0.299922\pi$
$828$	−2.71171	−0.0942383
$829$	30.8291	1.07074	0.535369	−	0.844618i	$-0.320173\pi$
$829$	30.8291	1.07074	0.535369	+	0.844618i	$0.320173\pi$
$830$	−0.116375	−0.00403942
$831$	−4.52575	−0.156997
$832$	60.5696	2.09987
$833$	16.5132	0.572147
$834$	−11.0025	−0.380985
$835$	0.367330	0.0127120
$836$	−40.4372	−1.39855
$837$	−4.18149	−0.144534
$838$	60.8625	2.10246
$839$	−19.7462	−0.681713	−0.340857	−	0.940115i	$-0.610717\pi$
$839$	−19.7462	−0.681713	−0.340857	+	0.940115i	$0.610717\pi$
$840$	0.0425937	0.00146962
$841$	−27.2425	−0.939397
$842$	30.0770	1.03652
$843$	5.90032	0.203218
$844$	−43.7650	−1.50645
$845$	−0.288596	−0.00992800
$846$	−69.8944	−2.40302
$847$	−9.27168	−0.318579
$848$	11.7550	0.403668
$849$	−4.35530	−0.149474
$850$	−64.2728	−2.20454
$851$	−3.45111	−0.118302
$852$	−4.72920	−0.162020
$853$	52.6080	1.80126	0.900632	−	0.434583i	$-0.143104\pi$
$853$	52.6080	1.80126	0.900632	+	0.434583i	$0.143104\pi$
$854$	−37.8407	−1.29488
$855$	0.302129	0.0103326
$856$	26.1338	0.893233
$857$	40.7453	1.39183	0.695917	−	0.718122i	$-0.254998\pi$
$857$	40.7453	1.39183	0.695917	+	0.718122i	$0.254998\pi$
$858$	13.0308	0.444863
$859$	36.3447	1.24006	0.620032	−	0.784577i	$-0.287120\pi$
$859$	36.3447	1.24006	0.620032	+	0.784577i	$0.287120\pi$
$860$	0	0
$861$	−1.98966	−0.0678075
$862$	−69.6370	−2.37185
$863$	−28.8462	−0.981937	−0.490968	−	0.871177i	$-0.663357\pi$
$863$	−28.8462	−0.981937	−0.490968	+	0.871177i	$0.663357\pi$
$864$	14.5758	0.495878
$865$	−0.302886	−0.0102984
$866$	0.825147	0.0280396
$867$	5.88850	0.199984
$868$	−18.4764	−0.627129
$869$	20.2353	0.686437
$870$	0.0248472	0.000842397 0
$871$	5.38993	0.182631
$872$	3.24839	0.110004
$873$	−26.0395	−0.881303
$874$	2.96739	0.100373
$875$	−0.823339	−0.0278339
$876$	−6.60663	−0.223218
$877$	−4.77398	−0.161206	−0.0806030	−	0.996746i	$-0.525685\pi$
$877$	−4.77398	−0.161206	−0.0806030	+	0.996746i	$0.525685\pi$
$878$	10.6042	0.357875
$879$	−1.21777	−0.0410745
$880$	−0.198626	−0.00669569
$881$	−30.7057	−1.03450	−0.517251	−	0.855834i	$-0.673045\pi$
$881$	−30.7057	−1.03450	−0.517251	+	0.855834i	$0.673045\pi$
$882$	−17.5599	−0.591273
$883$	−20.6882	−0.696213	−0.348107	−	0.937455i	$-0.613175\pi$
$883$	−20.6882	−0.696213	−0.348107	+	0.937455i	$0.613175\pi$
$884$	−78.9290	−2.65467
$885$	−0.00148591	−4.99483e−5 0
$886$	12.9027	0.433476
$887$	−2.49616	−0.0838130	−0.0419065	−	0.999122i	$-0.513343\pi$
$887$	−2.49616	−0.0838130	−0.0419065	+	0.999122i	$0.513343\pi$
$888$	−5.19170	−0.174222
$889$	−23.5998	−0.791513
$890$	0.228922	0.00767350
$891$	−30.0630	−1.00715
$892$	−41.1499	−1.37780
$893$	44.1186	1.47637
$894$	−5.17105	−0.172946
$895$	−0.0199113	−0.000665561 0
$896$	36.9184	1.23336
$897$	−0.551583	−0.0184168
$898$	71.1128	2.37306
$899$	−2.87115	−0.0957584
$900$	39.4245	1.31415
$901$	−34.4110	−1.14640
$902$	−15.7642	−0.524889
$903$	0	0
$904$	18.4178	0.612566
$905$	0.0273751	0.000909979 0
$906$	−7.14618	−0.237416
$907$	−23.1548	−0.768843	−0.384421	−	0.923158i	$-0.625599\pi$
$907$	−23.1548	−0.768843	−0.384421	+	0.923158i	$0.625599\pi$
$908$	54.9679	1.82417
$909$	−44.2524	−1.46776
$910$	−0.876357	−0.0290510
$911$	17.4194	0.577130	0.288565	−	0.957460i	$-0.406822\pi$
$911$	17.4194	0.577130	0.288565	+	0.957460i	$0.406822\pi$
$912$	−2.62739	−0.0870017
$913$	−7.60192	−0.251587
$914$	63.1797	2.08980
$915$	−0.0479550	−0.00158534
$916$	36.4804	1.20535
$917$	27.7382	0.915996
$918$	−24.8220	−0.819248
$919$	14.1125	0.465529	0.232764	−	0.972533i	$-0.425223\pi$
$919$	14.1125	0.465529	0.232764	+	0.972533i	$0.425223\pi$
$920$	−0.0142849	−0.000470960 0
$921$	3.19608	0.105314
$922$	−31.6116	−1.04107
$923$	25.9198	0.853161
$924$	10.4448	0.343610
$925$	50.1744	1.64973
$926$	−13.4405	−0.441681
$927$	46.3105	1.52104
$928$	10.0082	0.328536
$929$	23.1546	0.759677	0.379839	−	0.925053i	$-0.375980\pi$
$929$	23.1546	0.759677	0.379839	+	0.925053i	$0.375980\pi$
$930$	−0.0405923	−0.00133107
$931$	11.0841	0.363268
$932$	25.2471	0.826995
$933$	−1.29099	−0.0422650
$934$	−34.3648	−1.12445
$935$	0.581450	0.0190155
$936$	22.3583	0.730803
$937$	40.0950	1.30985	0.654924	−	0.755695i	$-0.272701\pi$
$937$	40.0950	1.30985	0.654924	+	0.755695i	$0.272701\pi$
$938$	7.48977	0.244550
$939$	−7.50033	−0.244764
$940$	−0.797290	−0.0260047
$941$	−33.7796	−1.10118	−0.550591	−	0.834775i	$-0.685598\pi$
$941$	−33.7796	−1.10118	−0.550591	+	0.834775i	$0.685598\pi$
$942$	6.88108	0.224198
$943$	0.667286	0.0217298
$944$	−0.348179	−0.0113322
$945$	−0.158975	−0.00517145
$946$	0	0
$947$	−6.10756	−0.198469	−0.0992345	−	0.995064i	$-0.531639\pi$
$947$	−6.10756	−0.198469	−0.0992345	+	0.995064i	$0.531639\pi$
$948$	−4.83720	−0.157105
$949$	36.2097	1.17542
$950$	−43.1418	−1.39971
$951$	3.37524	0.109450
$952$	−29.2167	−0.946918
$953$	44.3018	1.43508	0.717538	−	0.696520i	$-0.245269\pi$
$953$	44.3018	1.43508	0.717538	+	0.696520i	$0.245269\pi$
$954$	36.5923	1.18472
$955$	0.364735	0.0118025
$956$	−52.4145	−1.69521
$957$	1.62309	0.0524670
$958$	83.7511	2.70587
$959$	54.9778	1.77532
$960$	0.106663	0.00344253
$961$	−26.3095	−0.848692
$962$	106.818	3.44396
$963$	−47.8817	−1.54297
$964$	15.7783	0.508186
$965$	−0.388648	−0.0125110
$966$	−0.766472	−0.0246608
$967$	51.8507	1.66741	0.833704	−	0.552212i	$-0.186216\pi$
$967$	51.8507	1.66741	0.833704	+	0.552212i	$0.186216\pi$
$968$	4.67781	0.150350
$969$	7.69132	0.247081
$970$	−0.514943	−0.0165338
$971$	41.0199	1.31639	0.658195	−	0.752847i	$-0.271320\pi$
$971$	41.0199	1.31639	0.658195	+	0.752847i	$0.271320\pi$
$972$	22.9772	0.736994
$973$	48.3356	1.54957
$974$	−27.0476	−0.866661
$975$	8.01927	0.256822
$976$	−11.2368	−0.359682
$977$	−40.1799	−1.28547	−0.642734	−	0.766089i	$-0.722200\pi$
$977$	−40.1799	−1.28547	−0.642734	+	0.766089i	$0.722200\pi$
$978$	−4.83460	−0.154593
$979$	14.9539	0.477928
$980$	−0.200307	−0.00639858
$981$	−5.95163	−0.190021
$982$	−83.7782	−2.67347
$983$	43.4810	1.38683	0.693414	−	0.720539i	$-0.256106\pi$
$983$	43.4810	1.38683	0.693414	+	0.720539i	$0.256106\pi$
$984$	1.00384	0.0320012
$985$	0.199795	0.00636600
$986$	−17.0436	−0.542780
$987$	−11.3957	−0.362731
$988$	−52.9796	−1.68550
$989$	0	0
$990$	−0.618308	−0.0196511
$991$	24.8448	0.789220	0.394610	−	0.918849i	$-0.370880\pi$
$991$	24.8448	0.789220	0.394610	+	0.918849i	$0.370880\pi$
$992$	−16.3502	−0.519120
$993$	−3.90331	−0.123868
$994$	36.0178	1.14241
$995$	0.660165	0.0209286
$996$	1.81722	0.0575807
$997$	28.5319	0.903614	0.451807	−	0.892116i	$-0.350779\pi$
$997$	28.5319	0.903614	0.451807	+	0.892116i	$0.350779\pi$
$998$	−91.0151	−2.88103
$999$	19.3773	0.613070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.16		18
43.15	even	21		43.2.g.a.10.1	✓	36
43.23	even	21		43.2.g.a.13.1	yes	36
43.42	odd	2		1849.2.a.o.1.3		18
129.23	odd	42		387.2.y.c.271.3		36
129.101	odd	42		387.2.y.c.10.3		36
172.15	odd	42		688.2.bg.c.225.2		36
172.23	odd	42		688.2.bg.c.529.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.1	✓	36	43.15	even	21
43.2.g.a.13.1	yes	36	43.23	even	21
387.2.y.c.10.3		36	129.101	odd	42
387.2.y.c.271.3		36	129.23	odd	42
688.2.bg.c.225.2		36	172.15	odd	42
688.2.bg.c.529.2		36	172.23	odd	42
1849.2.a.n.1.16		18	1.1	even	1	trivial
1849.2.a.o.1.3		18	43.42	odd	2

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+2.17399 q^{2} +0.327650 q^{3} +2.72622 q^{4} -0.0263127 q^{5} +0.712306 q^{6} -3.12927 q^{7} +1.57880 q^{8} -2.89265 q^{9} +O(q^{10})\)	\(q+2.17399 q^{2} +0.327650 q^{3} +2.72622 q^{4} -0.0263127 q^{5} +0.712306 q^{6} -3.12927 q^{7} +1.57880 q^{8} -2.89265 q^{9} -0.0572034 q^{10} -3.73669 q^{11} +0.893246 q^{12} -4.89571 q^{13} -6.80300 q^{14} -0.00862134 q^{15} -2.02015 q^{16} +5.91371 q^{17} -6.28858 q^{18} +3.96946 q^{19} -0.0717342 q^{20} -1.02531 q^{21} -8.12353 q^{22} +0.343863 q^{23} +0.517294 q^{24} -4.99931 q^{25} -10.6432 q^{26} -1.93072 q^{27} -8.53110 q^{28} -1.32570 q^{29} -0.0187427 q^{30} +2.16577 q^{31} -7.54939 q^{32} -1.22433 q^{33} +12.8563 q^{34} +0.0823396 q^{35} -7.88600 q^{36} -10.0363 q^{37} +8.62956 q^{38} -1.60408 q^{39} -0.0415425 q^{40} +1.94056 q^{41} -2.22900 q^{42} -10.1871 q^{44} +0.0761133 q^{45} +0.747555 q^{46} +11.1145 q^{47} -0.661902 q^{48} +2.79235 q^{49} -10.8684 q^{50} +1.93762 q^{51} -13.3468 q^{52} -5.81886 q^{53} -4.19737 q^{54} +0.0983224 q^{55} -4.94050 q^{56} +1.30059 q^{57} -2.88205 q^{58} +0.172353 q^{59} -0.0235037 q^{60} +5.56236 q^{61} +4.70835 q^{62} +9.05188 q^{63} -12.3720 q^{64} +0.128819 q^{65} -2.66167 q^{66} -1.10095 q^{67} +16.1221 q^{68} +0.112667 q^{69} +0.179005 q^{70} -5.29439 q^{71} -4.56691 q^{72} -7.39621 q^{73} -21.8187 q^{74} -1.63802 q^{75} +10.8216 q^{76} +11.6931 q^{77} -3.48724 q^{78} -5.41531 q^{79} +0.0531556 q^{80} +8.04534 q^{81} +4.21874 q^{82} +2.03440 q^{83} -2.79521 q^{84} -0.155605 q^{85} -0.434365 q^{87} -5.89950 q^{88} -4.00190 q^{89} +0.165469 q^{90} +15.3200 q^{91} +0.937448 q^{92} +0.709612 q^{93} +24.1628 q^{94} -0.104447 q^{95} -2.47355 q^{96} +9.00196 q^{97} +6.07054 q^{98} +10.8089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

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