LMFDB - Embedded newform 1849.2.a.o.1.9

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:	$0$
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			1.9
Root			$0.131407$ 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)

$f(q)$	$=$	$q+0.131407 q^{2} -1.32082 q^{3} -1.98273 q^{4} -1.78074 q^{5} -0.173564 q^{6} -0.0149856 q^{7} -0.523357 q^{8} -1.25544 q^{9} +O(q^{10})$	\(q+0.131407 q^{2} -1.32082 q^{3} -1.98273 q^{4} -1.78074 q^{5} -0.173564 q^{6} -0.0149856 q^{7} -0.523357 q^{8} -1.25544 q^{9} -0.234000 q^{10} -2.07972 q^{11} +2.61883 q^{12} -1.62441 q^{13} -0.00196921 q^{14} +2.35203 q^{15} +3.89669 q^{16} -6.03444 q^{17} -0.164973 q^{18} -7.62293 q^{19} +3.53072 q^{20} +0.0197933 q^{21} -0.273289 q^{22} -5.30206 q^{23} +0.691260 q^{24} -1.82898 q^{25} -0.213458 q^{26} +5.62066 q^{27} +0.0297125 q^{28} +7.17687 q^{29} +0.309072 q^{30} +2.38527 q^{31} +1.55877 q^{32} +2.74694 q^{33} -0.792965 q^{34} +0.0266854 q^{35} +2.48919 q^{36} -5.04085 q^{37} -1.00170 q^{38} +2.14555 q^{39} +0.931961 q^{40} +3.55296 q^{41} +0.00260097 q^{42} +4.12354 q^{44} +2.23560 q^{45} -0.696725 q^{46} -10.0228 q^{47} -5.14683 q^{48} -6.99978 q^{49} -0.240340 q^{50} +7.97041 q^{51} +3.22077 q^{52} -6.85699 q^{53} +0.738592 q^{54} +3.70344 q^{55} +0.00784283 q^{56} +10.0685 q^{57} +0.943088 q^{58} -1.66670 q^{59} -4.66345 q^{60} +6.05120 q^{61} +0.313440 q^{62} +0.0188135 q^{63} -7.58855 q^{64} +2.89265 q^{65} +0.360966 q^{66} +1.43303 q^{67} +11.9647 q^{68} +7.00306 q^{69} +0.00350664 q^{70} +7.04548 q^{71} +0.657042 q^{72} -9.76187 q^{73} -0.662401 q^{74} +2.41575 q^{75} +15.1142 q^{76} +0.0311659 q^{77} +0.281940 q^{78} +12.0115 q^{79} -6.93898 q^{80} -3.65757 q^{81} +0.466882 q^{82} +9.06798 q^{83} -0.0392448 q^{84} +10.7457 q^{85} -9.47935 q^{87} +1.08844 q^{88} +15.9043 q^{89} +0.293773 q^{90} +0.0243428 q^{91} +10.5126 q^{92} -3.15051 q^{93} -1.31706 q^{94} +13.5744 q^{95} -2.05885 q^{96} +13.5487 q^{97} -0.919817 q^{98} +2.61096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.131407	0.0929185	0.0464592	−	0.998920i	$-0.485206\pi$
$2$	0.131407	0.0929185	0.0464592	+	0.998920i	$0.485206\pi$
$3$	−1.32082	−0.762575	−0.381288	−	0.924456i	$-0.624519\pi$
$3$	−1.32082	−0.762575	−0.381288	+	0.924456i	$0.624519\pi$
$4$	−1.98273	−0.991366
$5$	−1.78074	−0.796369	−0.398185	−	0.917305i	$-0.630360\pi$
$5$	−1.78074	−0.796369	−0.398185	+	0.917305i	$0.630360\pi$
$6$	−0.173564	−0.0708573
$7$	−0.0149856	−0.00566403	−0.00283201	−	0.999996i	$-0.500901\pi$
$7$	−0.0149856	−0.00566403	−0.00283201	+	0.999996i	$0.500901\pi$
$8$	−0.523357	−0.185035
$9$	−1.25544	−0.418479
$10$	−0.234000	−0.0739974
$11$	−2.07972	−0.627061	−0.313530	−	0.949578i	$-0.601512\pi$
$11$	−2.07972	−0.627061	−0.313530	+	0.949578i	$0.601512\pi$
$12$	2.61883	0.755991
$13$	−1.62441	−0.450531	−0.225265	−	0.974297i	$-0.572325\pi$
$13$	−1.62441	−0.450531	−0.225265	+	0.974297i	$0.572325\pi$
$14$	−0.00196921	−0.000526293 0
$15$	2.35203	0.607292
$16$	3.89669	0.974173
$17$	−6.03444	−1.46357	−0.731783	−	0.681537i	$-0.761312\pi$
$17$	−6.03444	−1.46357	−0.731783	+	0.681537i	$0.761312\pi$
$18$	−0.164973	−0.0388844
$19$	−7.62293	−1.74882	−0.874410	−	0.485188i	$-0.838751\pi$
$19$	−7.62293	−1.74882	−0.874410	+	0.485188i	$0.838751\pi$
$20$	3.53072	0.789494
$21$	0.0197933	0.00431925
$22$	−0.273289	−0.0582655
$23$	−5.30206	−1.10556	−0.552778	−	0.833329i	$-0.686432\pi$
$23$	−5.30206	−1.10556	−0.552778	+	0.833329i	$0.686432\pi$
$24$	0.691260	0.141103
$25$	−1.82898	−0.365796
$26$	−0.213458	−0.0418626
$27$	5.62066	1.08170
$28$	0.0297125	0.00561513
$29$	7.17687	1.33271	0.666356	−	0.745634i	$-0.267853\pi$
$29$	7.17687	1.33271	0.666356	+	0.745634i	$0.267853\pi$
$30$	0.309072	0.0564286
$31$	2.38527	0.428407	0.214203	−	0.976789i	$-0.431284\pi$
$31$	2.38527	0.428407	0.214203	+	0.976789i	$0.431284\pi$
$32$	1.55877	0.275553
$33$	2.74694	0.478181
$34$	−0.792965	−0.135992
$35$	0.0266854	0.00451066
$36$	2.48919	0.414866
$37$	−5.04085	−0.828711	−0.414356	−	0.910115i	$-0.635993\pi$
$37$	−5.04085	−0.828711	−0.414356	+	0.910115i	$0.635993\pi$
$38$	−1.00170	−0.162498
$39$	2.14555	0.343563
$40$	0.931961	0.147356
$41$	3.55296	0.554879	0.277439	−	0.960743i	$-0.410514\pi$
$41$	3.55296	0.554879	0.277439	+	0.960743i	$0.410514\pi$
$42$	0.00260097	0.000401338 0
$43$	0	0
$43$	0	0
$44$	4.12354	0.621647
$45$	2.23560	0.333264
$46$	−0.696725	−0.102727
$47$	−10.0228	−1.46198	−0.730988	−	0.682390i	$-0.760940\pi$
$47$	−10.0228	−1.46198	−0.730988	+	0.682390i	$0.760940\pi$
$48$	−5.14683	−0.742880
$49$	−6.99978	−0.999968
$50$	−0.240340	−0.0339892
$51$	7.97041	1.11608
$52$	3.22077	0.446641
$53$	−6.85699	−0.941881	−0.470940	−	0.882165i	$-0.656085\pi$
$53$	−6.85699	−0.941881	−0.470940	+	0.882165i	$0.656085\pi$
$54$	0.738592	0.100510
$55$	3.70344	0.499372
$56$	0.00784283	0.00104804
$57$	10.0685	1.33361
$58$	0.943088	0.123833
$59$	−1.66670	−0.216986	−0.108493	−	0.994097i	$-0.534602\pi$
$59$	−1.66670	−0.216986	−0.108493	+	0.994097i	$0.534602\pi$
$60$	−4.66345	−0.602048
$61$	6.05120	0.774777	0.387389	−	0.921916i	$-0.373377\pi$
$61$	6.05120	0.774777	0.387389	+	0.921916i	$0.373377\pi$
$62$	0.313440	0.0398069
$63$	0.0188135	0.00237028
$64$	−7.58855	−0.948569
$65$	2.89265	0.358789
$66$	0.360966	0.0444318
$67$	1.43303	0.175073	0.0875363	−	0.996161i	$-0.472101\pi$
$67$	1.43303	0.175073	0.0875363	+	0.996161i	$0.472101\pi$
$68$	11.9647	1.45093
$69$	7.00306	0.843070
$70$	0.00350664	0.000419124 0
$71$	7.04548	0.836144	0.418072	−	0.908414i	$-0.362706\pi$
$71$	7.04548	0.836144	0.418072	+	0.908414i	$0.362706\pi$
$72$	0.657042	0.0774331
$73$	−9.76187	−1.14254	−0.571270	−	0.820762i	$-0.693549\pi$
$73$	−9.76187	−1.14254	−0.571270	+	0.820762i	$0.693549\pi$
$74$	−0.662401	−0.0770026
$75$	2.41575	0.278947
$76$	15.1142	1.73372
$77$	0.0311659	0.00355169
$78$	0.281940	0.0319234
$79$	12.0115	1.35139	0.675697	−	0.737179i	$-0.263843\pi$
$79$	12.0115	1.35139	0.675697	+	0.737179i	$0.263843\pi$
$80$	−6.93898	−0.775802
$81$	−3.65757	−0.406397
$82$	0.466882	0.0515585
$83$	9.06798	0.995340	0.497670	−	0.867366i	$-0.334189\pi$
$83$	9.06798	0.995340	0.497670	+	0.867366i	$0.334189\pi$
$84$	−0.0392448	−0.00428196
$85$	10.7457	1.16554
$86$	0	0
$87$	−9.47935	−1.01629
$88$	1.08844	0.116028
$89$	15.9043	1.68585	0.842925	−	0.538031i	$-0.180832\pi$
$89$	15.9043	1.68585	0.842925	+	0.538031i	$0.180832\pi$
$90$	0.293773	0.0309664
$91$	0.0243428	0.00255182
$92$	10.5126	1.09601
$93$	−3.15051	−0.326692
$94$	−1.31706	−0.135845
$95$	13.5744	1.39271
$96$	−2.05885	−0.210130
$97$	13.5487	1.37566	0.687832	−	0.725870i	$-0.258563\pi$
$97$	13.5487	1.37566	0.687832	+	0.725870i	$0.258563\pi$
$98$	−0.919817	−0.0929155
$99$	2.61096	0.262412
$100$	3.62637	0.362637
$101$	3.12321	0.310771	0.155385	−	0.987854i	$-0.450338\pi$
$101$	3.12321	0.310771	0.155385	+	0.987854i	$0.450338\pi$
$102$	1.04736	0.103704
$103$	−0.527236	−0.0519501	−0.0259751	−	0.999663i	$-0.508269\pi$
$103$	−0.527236	−0.0519501	−0.0259751	+	0.999663i	$0.508269\pi$
$104$	0.850147	0.0833638
$105$	−0.0352466	−0.00343972
$106$	−0.901054	−0.0875181
$107$	1.13567	0.109789	0.0548945	−	0.998492i	$-0.482518\pi$
$107$	1.13567	0.109789	0.0548945	+	0.998492i	$0.482518\pi$
$108$	−11.1443	−1.07236
$109$	−12.2005	−1.16859	−0.584297	−	0.811540i	$-0.698630\pi$
$109$	−12.2005	−1.16859	−0.584297	+	0.811540i	$0.698630\pi$
$110$	0.486657	0.0464009
$111$	6.65806	0.631955
$112$	−0.0583943	−0.00551774
$113$	4.40928	0.414790	0.207395	−	0.978257i	$-0.433501\pi$
$113$	4.40928	0.414790	0.207395	+	0.978257i	$0.433501\pi$
$114$	1.32307	0.123917
$115$	9.44157	0.880431
$116$	−14.2298	−1.32120
$117$	2.03934	0.188538
$118$	−0.219015	−0.0201620
$119$	0.0904298	0.00828968
$120$	−1.23095	−0.112370
$121$	−6.67475	−0.606795
$122$	0.795168	0.0719911
$123$	−4.69281	−0.423137
$124$	−4.72935	−0.424708
$125$	12.1606	1.08768
$126$	0.00247222	0.000220242 0
$127$	−9.00820	−0.799348	−0.399674	−	0.916657i	$-0.630877\pi$
$127$	−9.00820	−0.799348	−0.399674	+	0.916657i	$0.630877\pi$
$128$	−4.11472	−0.363693
$129$	0	0
$130$	0.380113	0.0333381
$131$	4.56448	0.398801	0.199400	−	0.979918i	$-0.436101\pi$
$131$	4.56448	0.398801	0.199400	+	0.979918i	$0.436101\pi$
$132$	−5.44645	−0.474052
$133$	0.114234	0.00990537
$134$	0.188310	0.0162675
$135$	−10.0089	−0.861430
$136$	3.15817	0.270811
$137$	15.5552	1.32897	0.664484	−	0.747302i	$-0.268651\pi$
$137$	15.5552	1.32897	0.664484	+	0.747302i	$0.268651\pi$
$138$	0.920248	0.0783367
$139$	−6.85934	−0.581802	−0.290901	−	0.956753i	$-0.593955\pi$
$139$	−6.85934	−0.581802	−0.290901	+	0.956753i	$0.593955\pi$
$140$	−0.0529101	−0.00447172
$141$	13.2383	1.11487
$142$	0.925822	0.0776933
$143$	3.37833	0.282510
$144$	−4.89205	−0.407671
$145$	−12.7801	−1.06133
$146$	−1.28277	−0.106163
$147$	9.24544	0.762551
$148$	9.99466	0.821556
$149$	−20.6396	−1.69087	−0.845433	−	0.534082i	$-0.820657\pi$
$149$	−20.6396	−1.69087	−0.845433	+	0.534082i	$0.820657\pi$
$150$	0.317445	0.0259193
$151$	3.87910	0.315676	0.157838	−	0.987465i	$-0.449548\pi$
$151$	3.87910	0.315676	0.157838	+	0.987465i	$0.449548\pi$
$152$	3.98951	0.323592
$153$	7.57586	0.612472
$154$	0.00409541	0.000330018 0
$155$	−4.24753	−0.341170
$156$	−4.25406	−0.340597
$157$	−1.37891	−0.110049	−0.0550244	−	0.998485i	$-0.517524\pi$
$157$	−1.37891	−0.110049	−0.0550244	+	0.998485i	$0.517524\pi$
$158$	1.57838	0.125570
$159$	9.05685	0.718255
$160$	−2.77575	−0.219442
$161$	0.0794546	0.00626190
$162$	−0.480629	−0.0377618
$163$	3.27038	0.256156	0.128078	−	0.991764i	$-0.459119\pi$
$163$	3.27038	0.256156	0.128078	+	0.991764i	$0.459119\pi$
$164$	−7.04456	−0.550088
$165$	−4.89158	−0.380809
$166$	1.19159	0.0924855
$167$	3.47025	0.268536	0.134268	−	0.990945i	$-0.457132\pi$
$167$	3.47025	0.268536	0.134268	+	0.990945i	$0.457132\pi$
$168$	−0.0103590	−0.000799211 0
$169$	−10.3613	−0.797022
$170$	1.41206	0.108300
$171$	9.57010	0.731844
$172$	0	0
$173$	16.9268	1.28692	0.643459	−	0.765480i	$-0.277499\pi$
$173$	16.9268	1.28692	0.643459	+	0.765480i	$0.277499\pi$
$174$	−1.24565	−0.0944324
$175$	0.0274084	0.00207188
$176$	−8.10405	−0.610865
$177$	2.20141	0.165468
$178$	2.08993	0.156647
$179$	−9.43773	−0.705409	−0.352705	−	0.935735i	$-0.614738\pi$
$179$	−9.43773	−0.705409	−0.352705	+	0.935735i	$0.614738\pi$
$180$	−4.43260	−0.330386
$181$	−7.36950	−0.547771	−0.273885	−	0.961762i	$-0.588309\pi$
$181$	−7.36950	−0.547771	−0.273885	+	0.961762i	$0.588309\pi$
$182$	0.00319880	0.000237111 0
$183$	−7.99255	−0.590826
$184$	2.77487	0.204566
$185$	8.97643	0.659960
$186$	−0.413997	−0.0303558
$187$	12.5500	0.917745
$188$	19.8725	1.44935
$189$	−0.0842291	−0.00612676
$190$	1.78377	0.129408
$191$	−19.3203	−1.39797	−0.698983	−	0.715138i	$-0.746364\pi$
$191$	−19.3203	−1.39797	−0.698983	+	0.715138i	$0.746364\pi$
$192$	10.0231	0.723355
$193$	2.11851	0.152493	0.0762467	−	0.997089i	$-0.475706\pi$
$193$	2.11851	0.152493	0.0762467	+	0.997089i	$0.475706\pi$
$194$	1.78039	0.127825
$195$	−3.82066	−0.273603
$196$	13.8787	0.991334
$197$	−18.5821	−1.32392	−0.661960	−	0.749539i	$-0.730275\pi$
$197$	−18.5821	−1.32392	−0.661960	+	0.749539i	$0.730275\pi$
$198$	0.343098	0.0243829
$199$	7.88855	0.559204	0.279602	−	0.960116i	$-0.409797\pi$
$199$	7.88855	0.559204	0.279602	+	0.960116i	$0.409797\pi$
$200$	0.957209	0.0676849
$201$	−1.89277	−0.133506
$202$	0.410410	0.0288764
$203$	−0.107550	−0.00754851
$204$	−15.8032	−1.10644
$205$	−6.32688	−0.441888
$206$	−0.0692823	−0.00482713
$207$	6.65640	0.462652
$208$	−6.32983	−0.438895
$209$	15.8536	1.09662
$210$	−0.00463164	−0.000319613 0
$211$	−8.05765	−0.554711	−0.277356	−	0.960767i	$-0.589458\pi$
$211$	−8.05765	−0.554711	−0.277356	+	0.960767i	$0.589458\pi$
$212$	13.5956	0.933749
$213$	−9.30580	−0.637623
$214$	0.149234	0.0102014
$215$	0	0
$216$	−2.94161	−0.200151
$217$	−0.0357447	−0.00242651
$218$	−1.60322	−0.108584
$219$	12.8937	0.871273
$220$	−7.34293	−0.495060
$221$	9.80241	0.659382
$222$	0.874912	0.0587203
$223$	−20.3361	−1.36180	−0.680902	−	0.732374i	$-0.738412\pi$
$223$	−20.3361	−1.36180	−0.680902	+	0.732374i	$0.738412\pi$
$224$	−0.0233591	−0.00156074
$225$	2.29617	0.153078
$226$	0.579408	0.0385416
$227$	−5.13351	−0.340723	−0.170361	−	0.985382i	$-0.554494\pi$
$227$	−5.13351	−0.340723	−0.170361	+	0.985382i	$0.554494\pi$
$228$	−19.9632	−1.32209
$229$	−2.86288	−0.189185	−0.0945923	−	0.995516i	$-0.530155\pi$
$229$	−2.86288	−0.189185	−0.0945923	+	0.995516i	$0.530155\pi$
$230$	1.24068	0.0818083
$231$	−0.0411646	−0.00270843
$232$	−3.75607	−0.246598
$233$	−12.4178	−0.813518	−0.406759	−	0.913535i	$-0.633341\pi$
$233$	−12.4178	−0.813518	−0.406759	+	0.913535i	$0.633341\pi$
$234$	0.267983	0.0175186
$235$	17.8480	1.16427
$236$	3.30461	0.215112
$237$	−15.8650	−1.03054
$238$	0.0118831	0.000770265 0
$239$	−23.2734	−1.50543	−0.752716	−	0.658345i	$-0.771257\pi$
$239$	−23.2734	−1.50543	−0.752716	+	0.658345i	$0.771257\pi$
$240$	9.16514	0.591607
$241$	−3.51552	−0.226455	−0.113227	−	0.993569i	$-0.536119\pi$
$241$	−3.51552	−0.226455	−0.113227	+	0.993569i	$0.536119\pi$
$242$	−0.877105	−0.0563825
$243$	−12.0310	−0.771789
$244$	−11.9979	−0.768088
$245$	12.4648	0.796344
$246$	−0.616667	−0.0393172
$247$	12.3828	0.787897
$248$	−1.24835	−0.0792701
$249$	−11.9772	−0.759022
$250$	1.59798	0.101065
$251$	−13.8483	−0.874097	−0.437048	−	0.899438i	$-0.643976\pi$
$251$	−13.8483	−0.874097	−0.437048	+	0.899438i	$0.643976\pi$
$252$	−0.0373021	−0.00234981
$253$	11.0268	0.693250
$254$	−1.18374	−0.0742742
$255$	−14.1932	−0.888812
$256$	14.6364	0.914775
$257$	−24.5832	−1.53346	−0.766728	−	0.641972i	$-0.778117\pi$
$257$	−24.5832	−1.53346	−0.766728	+	0.641972i	$0.778117\pi$
$258$	0	0
$259$	0.0755403	0.00469384
$260$	−5.73535	−0.355691
$261$	−9.01010	−0.557711
$262$	0.599803	0.0370560
$263$	7.08052	0.436603	0.218302	−	0.975881i	$-0.429948\pi$
$263$	7.08052	0.436603	0.218302	+	0.975881i	$0.429948\pi$
$264$	−1.43763	−0.0884801
$265$	12.2105	0.750085
$266$	0.0150111	0.000920392 0
$267$	−21.0067	−1.28559
$268$	−2.84132	−0.173561
$269$	−9.15068	−0.557927	−0.278963	−	0.960302i	$-0.589991\pi$
$269$	−9.15068	−0.557927	−0.278963	+	0.960302i	$0.589991\pi$
$270$	−1.31524	−0.0800428
$271$	3.31695	0.201490	0.100745	−	0.994912i	$-0.467877\pi$
$271$	3.31695	0.201490	0.100745	+	0.994912i	$0.467877\pi$
$272$	−23.5144	−1.42577
$273$	−0.0321524	−0.00194595
$274$	2.04405	0.123486
$275$	3.80377	0.229376
$276$	−13.8852	−0.835791
$277$	1.91138	0.114844	0.0574218	−	0.998350i	$-0.481712\pi$
$277$	1.91138	0.114844	0.0574218	+	0.998350i	$0.481712\pi$
$278$	−0.901363	−0.0540602
$279$	−2.99455	−0.179279
$280$	−0.0139660	−0.000834629 0
$281$	19.7462	1.17796	0.588981	−	0.808147i	$-0.299529\pi$
$281$	19.7462	1.17796	0.588981	+	0.808147i	$0.299529\pi$
$282$	1.73960	0.103592
$283$	−17.5592	−1.04378	−0.521892	−	0.853012i	$-0.674773\pi$
$283$	−17.5592	−1.04378	−0.521892	+	0.853012i	$0.674773\pi$
$284$	−13.9693	−0.828925
$285$	−17.9294	−1.06204
$286$	0.443934	0.0262504
$287$	−0.0532432	−0.00314285
$288$	−1.95693	−0.115313
$289$	19.4145	1.14203
$290$	−1.67939	−0.0986172
$291$	−17.8954	−1.04905
$292$	19.3552	1.13268
$293$	5.75228	0.336052	0.168026	−	0.985783i	$-0.446261\pi$
$293$	5.75228	0.336052	0.168026	+	0.985783i	$0.446261\pi$
$294$	1.21491	0.0708551
$295$	2.96795	0.172801
$296$	2.63817	0.153340
$297$	−11.6894	−0.678290
$298$	−2.71218	−0.157113
$299$	8.61272	0.498087
$300$	−4.78978	−0.276538
$301$	0	0
$302$	0.509739	0.0293322
$303$	−4.12519	−0.236986
$304$	−29.7042	−1.70365
$305$	−10.7756	−0.617009
$306$	0.995517	0.0569099
$307$	−15.2358	−0.869552	−0.434776	−	0.900539i	$-0.643172\pi$
$307$	−15.2358	−0.869552	−0.434776	+	0.900539i	$0.643172\pi$
$308$	−0.0617937	−0.00352102
$309$	0.696384	0.0396159
$310$	−0.558154	−0.0317010
$311$	32.8205	1.86108	0.930541	−	0.366189i	$-0.119338\pi$
$311$	32.8205	1.86108	0.930541	+	0.366189i	$0.119338\pi$
$312$	−1.12289	−0.0635712
$313$	−19.4958	−1.10197	−0.550984	−	0.834516i	$-0.685748\pi$
$313$	−19.4958	−1.10197	−0.550984	+	0.834516i	$0.685748\pi$
$314$	−0.181197	−0.0102256
$315$	−0.0335019	−0.00188762
$316$	−23.8155	−1.33973
$317$	−16.8983	−0.949102	−0.474551	−	0.880228i	$-0.657390\pi$
$317$	−16.8983	−0.949102	−0.474551	+	0.880228i	$0.657390\pi$
$318$	1.19013	0.0667392
$319$	−14.9259	−0.835691
$320$	13.5132	0.755411
$321$	−1.50001	−0.0837223
$322$	0.0104409	0.000581846 0
$323$	46.0001	2.55951
$324$	7.25198	0.402888
$325$	2.97101	0.164802
$326$	0.429749	0.0238016
$327$	16.1146	0.891141
$328$	−1.85947	−0.102672
$329$	0.150198	0.00828067
$330$	−0.642785	−0.0353842
$331$	28.7420	1.57980	0.789901	−	0.613235i	$-0.210132\pi$
$331$	28.7420	1.57980	0.789901	+	0.613235i	$0.210132\pi$
$332$	−17.9794	−0.986746
$333$	6.32847	0.346798
$334$	0.456013	0.0249519
$335$	−2.55185	−0.139422
$336$	0.0771283	0.00420770
$337$	17.0393	0.928190	0.464095	−	0.885786i	$-0.346380\pi$
$337$	17.0393	0.928190	0.464095	+	0.885786i	$0.346380\pi$
$338$	−1.36154	−0.0740581
$339$	−5.82386	−0.316309
$340$	−21.3059	−1.15548
$341$	−4.96070	−0.268637
$342$	1.25757	0.0680018
$343$	0.209795	0.0113279
$344$	0	0
$345$	−12.4706	−0.671395
$346$	2.22429	0.119578
$347$	27.8145	1.49316	0.746579	−	0.665296i	$-0.231695\pi$
$347$	27.8145	1.49316	0.746579	+	0.665296i	$0.231695\pi$
$348$	18.7950	1.00752
$349$	12.5352	0.670995	0.335498	−	0.942041i	$-0.391096\pi$
$349$	12.5352	0.670995	0.335498	+	0.942041i	$0.391096\pi$
$350$	0.00360164	0.000192516 0
$351$	−9.13027	−0.487338
$352$	−3.24180	−0.172789
$353$	−0.747503	−0.0397856	−0.0198928	−	0.999802i	$-0.506332\pi$
$353$	−0.747503	−0.0397856	−0.0198928	+	0.999802i	$0.506332\pi$
$354$	0.289279	0.0153750
$355$	−12.5461	−0.665880
$356$	−31.5339	−1.67129
$357$	−0.119441	−0.00632151
$358$	−1.24018	−0.0655455
$359$	0.379130	0.0200097	0.0100049	−	0.999950i	$-0.496815\pi$
$359$	0.379130	0.0200097	0.0100049	+	0.999950i	$0.496815\pi$
$360$	−1.17002	−0.0616654
$361$	39.1090	2.05837
$362$	−0.968401	−0.0508980
$363$	8.81613	0.462727
$364$	−0.0482652	−0.00252979
$365$	17.3833	0.909884
$366$	−1.05027	−0.0548987
$367$	17.2647	0.901207	0.450604	−	0.892724i	$-0.351209\pi$
$367$	17.2647	0.901207	0.450604	+	0.892724i	$0.351209\pi$
$368$	−20.6605	−1.07700
$369$	−4.46051	−0.232205
$370$	1.17956	0.0613225
$371$	0.102756	0.00533484
$372$	6.24661	0.323872
$373$	−28.8028	−1.49135	−0.745675	−	0.666310i	$-0.767873\pi$
$373$	−28.8028	−1.49135	−0.745675	+	0.666310i	$0.767873\pi$
$374$	1.64915	0.0852755
$375$	−16.0620	−0.829436
$376$	5.24550	0.270516
$377$	−11.6582	−0.600427
$378$	−0.0110683	−0.000569289 0
$379$	19.2545	0.989039	0.494519	−	0.869167i	$-0.335344\pi$
$379$	19.2545	0.989039	0.494519	+	0.869167i	$0.335344\pi$
$380$	−26.9145	−1.38068
$381$	11.8982	0.609563
$382$	−2.53881	−0.129897
$383$	13.7094	0.700515	0.350258	−	0.936653i	$-0.386094\pi$
$383$	13.7094	0.700515	0.350258	+	0.936653i	$0.386094\pi$
$384$	5.43480	0.277343
$385$	−0.0554983	−0.00282846
$386$	0.278386	0.0141695
$387$	0	0
$388$	−26.8635	−1.36379
$389$	−29.2387	−1.48246	−0.741229	−	0.671252i	$-0.765757\pi$
$389$	−29.2387	−1.48246	−0.741229	+	0.671252i	$0.765757\pi$
$390$	−0.502060	−0.0254228
$391$	31.9950	1.61805
$392$	3.66338	0.185029
$393$	−6.02886	−0.304116
$394$	−2.44181	−0.123017
$395$	−21.3892	−1.07621
$396$	−5.17684	−0.260146
$397$	18.6986	0.938457	0.469229	−	0.883077i	$-0.344532\pi$
$397$	18.6986	0.938457	0.469229	+	0.883077i	$0.344532\pi$
$398$	1.03661	0.0519604
$399$	−0.150883	−0.00755359
$400$	−7.12696	−0.356348
$401$	−5.29723	−0.264531	−0.132265	−	0.991214i	$-0.542225\pi$
$401$	−5.29723	−0.264531	−0.132265	+	0.991214i	$0.542225\pi$
$402$	−0.248723	−0.0124052
$403$	−3.87465	−0.193010
$404$	−6.19249	−0.308088
$405$	6.51317	0.323642
$406$	−0.0141327	−0.000701397 0
$407$	10.4836	0.519652
$408$	−4.17137	−0.206514
$409$	−6.09599	−0.301427	−0.150714	−	0.988577i	$-0.548157\pi$
$409$	−6.09599	−0.301427	−0.150714	+	0.988577i	$0.548157\pi$
$410$	−0.831394	−0.0410596
$411$	−20.5456	−1.01344
$412$	1.04537	0.0515016
$413$	0.0249765	0.00122901
$414$	0.874695	0.0429889
$415$	−16.1477	−0.792658
$416$	−2.53208	−0.124145
$417$	9.05995	0.443668
$418$	2.08327	0.101896
$419$	−5.38564	−0.263106	−0.131553	−	0.991309i	$-0.541996\pi$
$419$	−5.38564	−0.263106	−0.131553	+	0.991309i	$0.541996\pi$
$420$	0.0698846	0.00341002
$421$	−35.8102	−1.74528	−0.872641	−	0.488362i	$-0.837595\pi$
$421$	−35.8102	−1.74528	−0.872641	+	0.488362i	$0.837595\pi$
$422$	−1.05883	−0.0515429
$423$	12.5830	0.611806
$424$	3.58866	0.174281
$425$	11.0369	0.535366
$426$	−1.22284	−0.0592470
$427$	−0.0906810	−0.00438836
$428$	−2.25172	−0.108841
$429$	−4.46216	−0.215435
$430$	0	0
$431$	2.38810	0.115031	0.0575153	−	0.998345i	$-0.481682\pi$
$431$	2.38810	0.115031	0.0575153	+	0.998345i	$0.481682\pi$
$432$	21.9020	1.05376
$433$	8.45324	0.406237	0.203119	−	0.979154i	$-0.434892\pi$
$433$	8.45324	0.406237	0.203119	+	0.979154i	$0.434892\pi$
$434$	−0.00469709	−0.000225467 0
$435$	16.8802	0.809345
$436$	24.1903	1.15850
$437$	40.4172	1.93342
$438$	1.69431	0.0809573
$439$	3.89988	0.186131	0.0930655	−	0.995660i	$-0.470333\pi$
$439$	3.89988	0.186131	0.0930655	+	0.995660i	$0.470333\pi$
$440$	−1.93822	−0.0924011
$441$	8.78777	0.418465
$442$	1.28810	0.0612687
$443$	25.3153	1.20276	0.601382	−	0.798962i	$-0.294617\pi$
$443$	25.3153	1.20276	0.601382	+	0.798962i	$0.294617\pi$
$444$	−13.2011	−0.626499
$445$	−28.3213	−1.34256
$446$	−2.67229	−0.126537
$447$	27.2612	1.28941
$448$	0.113719	0.00537272
$449$	35.7482	1.68706	0.843531	−	0.537080i	$-0.180473\pi$
$449$	35.7482	1.68706	0.843531	+	0.537080i	$0.180473\pi$
$450$	0.301731	0.0142238
$451$	−7.38917	−0.347943
$452$	−8.74242	−0.411209
$453$	−5.12359	−0.240727
$454$	−0.674577	−0.0316594
$455$	−0.0433481	−0.00203219
$456$	−5.26943	−0.246764
$457$	−18.9542	−0.886641	−0.443321	−	0.896363i	$-0.646200\pi$
$457$	−18.9542	−0.886641	−0.443321	+	0.896363i	$0.646200\pi$
$458$	−0.376202	−0.0175787
$459$	−33.9176	−1.58314
$460$	−18.7201	−0.872829
$461$	14.0800	0.655773	0.327887	−	0.944717i	$-0.393664\pi$
$461$	14.0800	0.655773	0.327887	+	0.944717i	$0.393664\pi$
$462$	−0.00540930	−0.000251663 0
$463$	−18.7262	−0.870282	−0.435141	−	0.900362i	$-0.643301\pi$
$463$	−18.7262	−0.870282	−0.435141	+	0.900362i	$0.643301\pi$
$464$	27.9661	1.29829
$465$	5.61022	0.260168
$466$	−1.63178	−0.0755909
$467$	2.15149	0.0995592	0.0497796	−	0.998760i	$-0.484148\pi$
$467$	2.15149	0.0995592	0.0497796	+	0.998760i	$0.484148\pi$
$468$	−4.04348	−0.186910
$469$	−0.0214748	−0.000991616 0
$470$	2.34534	0.108182
$471$	1.82129	0.0839205
$472$	0.872278	0.0401499
$473$	0	0
$474$	−2.08476	−0.0957562
$475$	13.9422	0.639711
$476$	−0.179298	−0.00821811
$477$	8.60852	0.394157
$478$	−3.05828	−0.139882
$479$	28.0982	1.28384	0.641919	−	0.766772i	$-0.278138\pi$
$479$	28.0982	1.28384	0.641919	+	0.766772i	$0.278138\pi$
$480$	3.66626	0.167341
$481$	8.18842	0.373360
$482$	−0.461962	−0.0210418
$483$	−0.104945	−0.00477517
$484$	13.2342	0.601556
$485$	−24.1267	−1.09554
$486$	−1.58095	−0.0717135
$487$	−18.8948	−0.856206	−0.428103	−	0.903730i	$-0.640818\pi$
$487$	−18.8948	−0.856206	−0.428103	+	0.903730i	$0.640818\pi$
$488$	−3.16694	−0.143361
$489$	−4.31958	−0.195338
$490$	1.63795	0.0739951
$491$	27.0470	1.22061	0.610306	−	0.792166i	$-0.291046\pi$
$491$	27.0470	1.22061	0.610306	+	0.792166i	$0.291046\pi$
$492$	9.30459	0.419483
$493$	−43.3084	−1.95051
$494$	1.62718	0.0732102
$495$	−4.64944	−0.208977
$496$	9.29465	0.417342
$497$	−0.105581	−0.00473595
$498$	−1.57388	−0.0705271
$499$	−7.10029	−0.317853	−0.158926	−	0.987290i	$-0.550803\pi$
$499$	−7.10029	−0.317853	−0.158926	+	0.987290i	$0.550803\pi$
$500$	−24.1112	−1.07829
$501$	−4.58357	−0.204779
$502$	−1.81976	−0.0812197
$503$	19.3911	0.864608	0.432304	−	0.901728i	$-0.357701\pi$
$503$	19.3911	0.864608	0.432304	+	0.901728i	$0.357701\pi$
$504$	−0.00984617	−0.000438583 0
$505$	−5.56161	−0.247488
$506$	1.44900	0.0644158
$507$	13.6854	0.607789
$508$	17.8608	0.792447
$509$	−24.1473	−1.07031	−0.535156	−	0.844754i	$-0.679747\pi$
$509$	−24.1473	−1.07031	−0.535156	+	0.844754i	$0.679747\pi$
$510$	−1.86508	−0.0825871
$511$	0.146288	0.00647138
$512$	10.1528	0.448693
$513$	−42.8459	−1.89169
$514$	−3.23039	−0.142486
$515$	0.938868	0.0413715
$516$	0	0
$517$	20.8447	0.916747
$518$	0.00992649	0.000436145 0
$519$	−22.3572	−0.981372
$520$	−1.51389	−0.0663884
$521$	−2.26759	−0.0993450	−0.0496725	−	0.998766i	$-0.515818\pi$
$521$	−2.26759	−0.0993450	−0.0496725	+	0.998766i	$0.515818\pi$
$522$	−1.18399	−0.0518217
$523$	−31.4577	−1.37555	−0.687775	−	0.725923i	$-0.741413\pi$
$523$	−31.4577	−1.37555	−0.687775	+	0.725923i	$0.741413\pi$
$524$	−9.05015	−0.395358
$525$	−0.0362015	−0.00157996
$526$	0.930427	0.0405685
$527$	−14.3938	−0.627002
$528$	10.7040	0.465831
$529$	5.11183	0.222254
$530$	1.60454	0.0696968
$531$	2.09243	0.0908038
$532$	−0.226496	−0.00981984
$533$	−5.77146	−0.249990
$534$	−2.76042	−0.119455
$535$	−2.02232	−0.0874325
$536$	−0.749987	−0.0323945
$537$	12.4655	0.537928
$538$	−1.20246	−0.0518417
$539$	14.5576	0.627040
$540$	19.8450	0.853993
$541$	−0.910849	−0.0391605	−0.0195802	−	0.999808i	$-0.506233\pi$
$541$	−0.910849	−0.0391605	−0.0195802	+	0.999808i	$0.506233\pi$
$542$	0.435869	0.0187222
$543$	9.73378	0.417717
$544$	−9.40628	−0.403291
$545$	21.7258	0.930632
$546$	−0.00422504	−0.000180815 0
$547$	−37.6312	−1.60900	−0.804498	−	0.593956i	$-0.797565\pi$
$547$	−37.6312	−1.60900	−0.804498	+	0.593956i	$0.797565\pi$
$548$	−30.8417	−1.31749
$549$	−7.59690	−0.324228
$550$	0.499841	0.0213133
$551$	−54.7088	−2.33067
$552$	−3.66510	−0.155997
$553$	−0.179999	−0.00765434
$554$	0.251168	0.0106711
$555$	−11.8562	−0.503269
$556$	13.6002	0.576779
$557$	−41.4304	−1.75546	−0.877732	−	0.479153i	$-0.840944\pi$
$557$	−41.4304	−1.75546	−0.877732	+	0.479153i	$0.840944\pi$
$558$	−0.393504	−0.0166583
$559$	0	0
$560$	0.103985	0.00439416
$561$	−16.5762	−0.699850
$562$	2.59478	0.109454
$563$	23.6741	0.997743	0.498872	−	0.866676i	$-0.333748\pi$
$563$	23.6741	0.997743	0.498872	+	0.866676i	$0.333748\pi$
$564$	−26.2480	−1.10524
$565$	−7.85176	−0.330326
$566$	−2.30739	−0.0969868
$567$	0.0548109	0.00230184
$568$	−3.68730	−0.154716
$569$	4.74494	0.198918	0.0994591	−	0.995042i	$-0.468289\pi$
$569$	4.74494	0.198918	0.0994591	+	0.995042i	$0.468289\pi$
$570$	−2.35604	−0.0986835
$571$	36.2166	1.51562	0.757809	−	0.652477i	$-0.226270\pi$
$571$	36.2166	1.51562	0.757809	+	0.652477i	$0.226270\pi$
$572$	−6.69832	−0.280071
$573$	25.5186	1.06606
$574$	−0.00699651	−0.000292029 0
$575$	9.69735	0.404408
$576$	9.52695	0.396956
$577$	−20.7025	−0.861855	−0.430927	−	0.902387i	$-0.641814\pi$
$577$	−20.7025	−0.861855	−0.430927	+	0.902387i	$0.641814\pi$
$578$	2.55119	0.106115
$579$	−2.79816	−0.116288
$580$	25.3395	1.05217
$581$	−0.135889	−0.00563763
$582$	−2.35157	−0.0974759
$583$	14.2607	0.590616
$584$	5.10894	0.211410
$585$	−3.63154	−0.150146
$586$	0.755888	0.0312254
$587$	22.7426	0.938687	0.469344	−	0.883016i	$-0.344491\pi$
$587$	22.7426	0.938687	0.469344	+	0.883016i	$0.344491\pi$
$588$	−18.3312	−0.755967
$589$	−18.1827	−0.749206
$590$	0.390008	0.0160564
$591$	24.5436	1.00959
$592$	−19.6427	−0.807308
$593$	8.73804	0.358828	0.179414	−	0.983774i	$-0.442580\pi$
$593$	8.73804	0.358828	0.179414	+	0.983774i	$0.442580\pi$
$594$	−1.53607	−0.0630256
$595$	−0.161032	−0.00660165
$596$	40.9229	1.67627
$597$	−10.4193	−0.426435
$598$	1.13177	0.0462815
$599$	21.0835	0.861446	0.430723	−	0.902484i	$-0.358259\pi$
$599$	21.0835	0.861446	0.430723	+	0.902484i	$0.358259\pi$
$600$	−1.26430	−0.0516148
$601$	9.25003	0.377316	0.188658	−	0.982043i	$-0.439586\pi$
$601$	9.25003	0.377316	0.188658	+	0.982043i	$0.439586\pi$
$602$	0	0
$603$	−1.79908	−0.0732641
$604$	−7.69121	−0.312951
$605$	11.8860	0.483233
$606$	−0.542078	−0.0220204
$607$	36.0062	1.46145	0.730723	−	0.682674i	$-0.239183\pi$
$607$	36.0062	1.46145	0.730723	+	0.682674i	$0.239183\pi$
$608$	−11.8824	−0.481893
$609$	0.142054	0.00575631
$610$	−1.41598	−0.0573315
$611$	16.2811	0.658665
$612$	−15.0209	−0.607184
$613$	−7.55326	−0.305073	−0.152537	−	0.988298i	$-0.548744\pi$
$613$	−7.55326	−0.305073	−0.152537	+	0.988298i	$0.548744\pi$
$614$	−2.00208	−0.0807974
$615$	8.35666	0.336973
$616$	−0.0163109	−0.000657186 0
$617$	14.0622	0.566121	0.283061	−	0.959102i	$-0.408650\pi$
$617$	14.0622	0.566121	0.283061	+	0.959102i	$0.408650\pi$
$618$	0.0915094	0.00368105
$619$	−6.15010	−0.247194	−0.123597	−	0.992333i	$-0.539443\pi$
$619$	−6.15010	−0.247194	−0.123597	+	0.992333i	$0.539443\pi$
$620$	8.42172	0.338224
$621$	−29.8011	−1.19588
$622$	4.31283	0.172929
$623$	−0.238335	−0.00954870
$624$	8.36056	0.334690
$625$	−12.5099	−0.500398
$626$	−2.56188	−0.102393
$627$	−20.9397	−0.836252
$628$	2.73400	0.109099
$629$	30.4187	1.21287
$630$	−0.00440236	−0.000175394 0
$631$	31.1395	1.23965	0.619823	−	0.784742i	$-0.287204\pi$
$631$	31.1395	1.23965	0.619823	+	0.784742i	$0.287204\pi$
$632$	−6.28628	−0.250055
$633$	10.6427	0.423009
$634$	−2.22055	−0.0881891
$635$	16.0412	0.636577
$636$	−17.9573	−0.712054
$637$	11.3705	0.450516
$638$	−1.96136	−0.0776511
$639$	−8.84515	−0.349909
$640$	7.32722	0.289634
$641$	26.4675	1.04540	0.522701	−	0.852516i	$-0.324924\pi$
$641$	26.4675	1.04540	0.522701	+	0.852516i	$0.324924\pi$
$642$	−0.197111	−0.00777935
$643$	16.8687	0.665236	0.332618	−	0.943062i	$-0.392068\pi$
$643$	16.8687	0.665236	0.332618	+	0.943062i	$0.392068\pi$
$644$	−0.157537	−0.00620784
$645$	0	0
$646$	6.04472	0.237826
$647$	−8.85456	−0.348109	−0.174054	−	0.984736i	$-0.555687\pi$
$647$	−8.85456	−0.348109	−0.174054	+	0.984736i	$0.555687\pi$
$648$	1.91422	0.0751975
$649$	3.46627	0.136063
$650$	0.390411	0.0153132
$651$	0.0472123	0.00185040
$652$	−6.48429	−0.253944
$653$	−4.27841	−0.167427	−0.0837135	−	0.996490i	$-0.526678\pi$
$653$	−4.27841	−0.167427	−0.0837135	+	0.996490i	$0.526678\pi$
$654$	2.11757	0.0828035
$655$	−8.12814	−0.317593
$656$	13.8448	0.540548
$657$	12.2554	0.478129
$658$	0.0197370	0.000769427 0
$659$	−21.9991	−0.856963	−0.428481	−	0.903551i	$-0.640951\pi$
$659$	−21.9991	−0.856963	−0.428481	+	0.903551i	$0.640951\pi$
$660$	9.69869	0.377521
$661$	−15.1722	−0.590131	−0.295066	−	0.955477i	$-0.595342\pi$
$661$	−15.1722	−0.590131	−0.295066	+	0.955477i	$0.595342\pi$
$662$	3.77688	0.146793
$663$	−12.9472	−0.502828
$664$	−4.74579	−0.184172
$665$	−0.203421	−0.00788833
$666$	0.831603	0.0322240
$667$	−38.0522	−1.47339
$668$	−6.88057	−0.266217
$669$	26.8603	1.03848
$670$	−0.335330	−0.0129549
$671$	−12.5848	−0.485832
$672$	0.0308531	0.00119018
$673$	−18.4425	−0.710905	−0.355453	−	0.934694i	$-0.615673\pi$
$673$	−18.4425	−0.710905	−0.355453	+	0.934694i	$0.615673\pi$
$674$	2.23908	0.0862460
$675$	−10.2801	−0.395680
$676$	20.5437	0.790141
$677$	−23.0579	−0.886186	−0.443093	−	0.896476i	$-0.646119\pi$
$677$	−23.0579	−0.886186	−0.443093	+	0.896476i	$0.646119\pi$
$678$	−0.765293	−0.0293909
$679$	−0.203036	−0.00779180
$680$	−5.62386	−0.215665
$681$	6.78043	0.259827
$682$	−0.651869	−0.0249613
$683$	47.6757	1.82426	0.912129	−	0.409903i	$-0.134437\pi$
$683$	47.6757	1.82426	0.912129	+	0.409903i	$0.134437\pi$
$684$	−18.9750	−0.725525
$685$	−27.6997	−1.05835
$686$	0.0275685	0.00105257
$687$	3.78135	0.144268
$688$	0	0
$689$	11.1386	0.424346
$690$	−1.63872	−0.0623850
$691$	−16.1924	−0.615988	−0.307994	−	0.951388i	$-0.599658\pi$
$691$	−16.1924	−0.615988	−0.307994	+	0.951388i	$0.599658\pi$
$692$	−33.5612	−1.27581
$693$	−0.0391269	−0.00148631
$694$	3.65500	0.138742
$695$	12.2147	0.463329
$696$	4.96108	0.188049
$697$	−21.4401	−0.812102
$698$	1.64721	0.0623478
$699$	16.4017	0.620369
$700$	−0.0543434	−0.00205399
$701$	−29.5981	−1.11790	−0.558952	−	0.829200i	$-0.688796\pi$
$701$	−29.5981	−1.11790	−0.558952	+	0.829200i	$0.688796\pi$
$702$	−1.19978	−0.0452827
$703$	38.4261	1.44927
$704$	15.7821	0.594810
$705$	−23.5739	−0.887846
$706$	−0.0982268	−0.00369682
$707$	−0.0468032	−0.00176022
$708$	−4.36480	−0.164039
$709$	−18.1434	−0.681388	−0.340694	−	0.940174i	$-0.610662\pi$
$709$	−18.1434	−0.681388	−0.340694	+	0.940174i	$0.610662\pi$
$710$	−1.64865	−0.0618726
$711$	−15.0796	−0.565530
$712$	−8.32362	−0.311941
$713$	−12.6468	−0.473628
$714$	−0.0156954	−0.000587385 0
$715$	−6.01591	−0.224982
$716$	18.7125	0.699319
$717$	30.7400	1.14801
$718$	0.0498202	0.00185927
$719$	17.9498	0.669414	0.334707	−	0.942322i	$-0.391363\pi$
$719$	17.9498	0.669414	0.334707	+	0.942322i	$0.391363\pi$
$720$	8.71145	0.324657
$721$	0.00790095	0.000294247 0
$722$	5.13919	0.191261
$723$	4.64337	0.172689
$724$	14.6118	0.543042
$725$	−13.1263	−0.487500
$726$	1.15850	0.0429959
$727$	−12.3726	−0.458876	−0.229438	−	0.973323i	$-0.573689\pi$
$727$	−12.3726	−0.458876	−0.229438	+	0.973323i	$0.573689\pi$
$728$	−0.0127400	−0.000472175 0
$729$	26.8635	0.994944
$730$	2.28428	0.0845450
$731$	0	0
$732$	15.8471	0.585725
$733$	19.8125	0.731790	0.365895	−	0.930656i	$-0.380763\pi$
$733$	19.8125	0.731790	0.365895	+	0.930656i	$0.380763\pi$
$734$	2.26869	0.0837388
$735$	−16.4637	−0.607272
$736$	−8.26467	−0.304640
$737$	−2.98031	−0.109781
$738$	−0.586141	−0.0215761
$739$	29.2367	1.07549	0.537745	−	0.843108i	$-0.319276\pi$
$739$	29.2367	1.07549	0.537745	+	0.843108i	$0.319276\pi$
$740$	−17.7979	−0.654262
$741$	−16.3554	−0.600831
$742$	0.0135028	0.000495705 0
$743$	18.5545	0.680698	0.340349	−	0.940299i	$-0.389455\pi$
$743$	18.5545	0.680698	0.340349	+	0.940299i	$0.389455\pi$
$744$	1.64884	0.0604494
$745$	36.7538	1.34655
$746$	−3.78487	−0.138574
$747$	−11.3843	−0.416529
$748$	−24.8832	−0.909821
$749$	−0.0170186	−0.000621848 0
$750$	−2.11065	−0.0770700
$751$	41.5635	1.51668	0.758338	−	0.651862i	$-0.226012\pi$
$751$	41.5635	1.51668	0.758338	+	0.651862i	$0.226012\pi$
$752$	−39.0558	−1.42422
$753$	18.2911	0.666565
$754$	−1.53196	−0.0557908
$755$	−6.90765	−0.251395
$756$	0.167004	0.00607387
$757$	25.1239	0.913143	0.456572	−	0.889687i	$-0.349077\pi$
$757$	25.1239	0.913143	0.456572	+	0.889687i	$0.349077\pi$
$758$	2.53017	0.0919000
$759$	−14.5644	−0.528656
$760$	−7.10427	−0.257699
$761$	−2.67135	−0.0968363	−0.0484182	−	0.998827i	$-0.515418\pi$
$761$	−2.67135	−0.0968363	−0.0484182	+	0.998827i	$0.515418\pi$
$762$	1.56350	0.0566397
$763$	0.182832	0.00661895
$764$	38.3070	1.38590
$765$	−13.4906	−0.487754
$766$	1.80150	0.0650908
$767$	2.70740	0.0977586
$768$	−19.3320	−0.697585
$769$	−37.0496	−1.33604	−0.668022	−	0.744142i	$-0.732859\pi$
$769$	−37.0496	−1.33604	−0.668022	+	0.744142i	$0.732859\pi$
$770$	−0.00729285	−0.000262816 0
$771$	32.4699	1.16938
$772$	−4.20043	−0.151177
$773$	−46.2293	−1.66275	−0.831376	−	0.555711i	$-0.812446\pi$
$773$	−46.2293	−1.66275	−0.831376	+	0.555711i	$0.812446\pi$
$774$	0	0
$775$	−4.36260	−0.156709
$776$	−7.09082	−0.254546
$777$	−0.0997750	−0.00357941
$778$	−3.84215	−0.137748
$779$	−27.0839	−0.970383
$780$	7.57536	0.271241
$781$	−14.6527	−0.524313
$782$	4.20435	0.150347
$783$	40.3388	1.44159
$784$	−27.2760	−0.974142
$785$	2.45547	0.0876395
$786$	−0.792232	−0.0282580
$787$	12.9148	0.460364	0.230182	−	0.973148i	$-0.426068\pi$
$787$	12.9148	0.460364	0.230182	+	0.973148i	$0.426068\pi$
$788$	36.8433	1.31249
$789$	−9.35208	−0.332943
$790$	−2.81069	−0.0999997
$791$	−0.0660757	−0.00234938
$792$	−1.36647	−0.0485553
$793$	−9.82964	−0.349061
$794$	2.45712	0.0872000
$795$	−16.1279	−0.571996
$796$	−15.6409	−0.554376
$797$	34.9960	1.23962	0.619811	−	0.784751i	$-0.287209\pi$
$797$	34.9960	1.23962	0.619811	+	0.784751i	$0.287209\pi$
$798$	−0.0198270	−0.000701868 0
$799$	60.4820	2.13970
$800$	−2.85095	−0.100796
$801$	−19.9668	−0.705493
$802$	−0.696091	−0.0245798
$803$	20.3020	0.716442
$804$	3.75286	0.132353
$805$	−0.141488	−0.00498679
$806$	−0.509155	−0.0179342
$807$	12.0864	0.425461
$808$	−1.63455	−0.0575034
$809$	−20.2894	−0.713339	−0.356669	−	0.934231i	$-0.616088\pi$
$809$	−20.2894	−0.713339	−0.356669	+	0.934231i	$0.616088\pi$
$810$	0.855873	0.0300723
$811$	−7.05661	−0.247791	−0.123896	−	0.992295i	$-0.539539\pi$
$811$	−7.05661	−0.247791	−0.123896	+	0.992295i	$0.539539\pi$
$812$	0.213242	0.00748334
$813$	−4.38109	−0.153651
$814$	1.37761	0.0482853
$815$	−5.82369	−0.203995
$816$	31.0582	1.08726
$817$	0	0
$818$	−0.801053	−0.0280082
$819$	−0.0305608	−0.00106788
$820$	12.5445	0.438073
$821$	−29.1585	−1.01764	−0.508819	−	0.860874i	$-0.669918\pi$
$821$	−29.1585	−1.01764	−0.508819	+	0.860874i	$0.669918\pi$
$822$	−2.69982	−0.0941672
$823$	−49.0909	−1.71120	−0.855600	−	0.517637i	$-0.826812\pi$
$823$	−49.0909	−1.71120	−0.855600	+	0.517637i	$0.826812\pi$
$824$	0.275933	0.00961257
$825$	−5.02409	−0.174917
$826$	0.00328207	0.000114198 0
$827$	4.85202	0.168721	0.0843606	−	0.996435i	$-0.473115\pi$
$827$	4.85202	0.168721	0.0843606	+	0.996435i	$0.473115\pi$
$828$	−13.1979	−0.458657
$829$	−30.6618	−1.06493	−0.532465	−	0.846452i	$-0.678734\pi$
$829$	−30.6618	−1.06493	−0.532465	+	0.846452i	$0.678734\pi$
$830$	−2.12191	−0.0736526
$831$	−2.52459	−0.0875770
$832$	12.3269	0.427359
$833$	42.2397	1.46352
$834$	1.19054	0.0412249
$835$	−6.17960	−0.213854
$836$	−31.4334	−1.08715
$837$	13.4068	0.463406
$838$	−0.707709	−0.0244474
$839$	31.9485	1.10299	0.551493	−	0.834180i	$-0.314059\pi$
$839$	31.9485	1.10299	0.551493	+	0.834180i	$0.314059\pi$
$840$	0.0184466	0.000636467 0
$841$	22.5075	0.776119
$842$	−4.70570	−0.162169
$843$	−26.0812	−0.898284
$844$	15.9762	0.549922
$845$	18.4507	0.634724
$846$	1.65349	0.0568481
$847$	0.100025	0.00343690
$848$	−26.7196	−0.917555
$849$	23.1925	0.795963
$850$	1.45032	0.0497454
$851$	26.7269	0.916187
$852$	18.4509	0.632118
$853$	24.1240	0.825991	0.412996	−	0.910733i	$-0.364482\pi$
$853$	24.1240	0.825991	0.412996	+	0.910733i	$0.364482\pi$
$854$	−0.0119161	−0.000407760 0
$855$	−17.0418	−0.582818
$856$	−0.594359	−0.0203148
$857$	45.7278	1.56203	0.781016	−	0.624511i	$-0.214702\pi$
$857$	45.7278	1.56203	0.781016	+	0.624511i	$0.214702\pi$
$858$	−0.586357	−0.0200179
$859$	31.4601	1.07341	0.536703	−	0.843771i	$-0.319670\pi$
$859$	31.4601	1.07341	0.536703	+	0.843771i	$0.319670\pi$
$860$	0	0
$861$	0.0703247	0.00239666
$862$	0.313811	0.0106885
$863$	9.07754	0.309003	0.154501	−	0.987993i	$-0.450623\pi$
$863$	9.07754	0.309003	0.154501	+	0.987993i	$0.450623\pi$
$864$	8.76129	0.298065
$865$	−30.1421	−1.02486
$866$	1.11081	0.0377469
$867$	−25.6430	−0.870882
$868$	0.0708722	0.00240556
$869$	−24.9805	−0.847406
$870$	2.21817	0.0752031
$871$	−2.32783	−0.0788755
$872$	6.38521	0.216230
$873$	−17.0096	−0.575686
$874$	5.31109	0.179650
$875$	−0.182234	−0.00616064
$876$	−25.5647	−0.863750
$877$	−43.9606	−1.48444	−0.742221	−	0.670155i	$-0.766228\pi$
$877$	−43.9606	−1.48444	−0.742221	+	0.670155i	$0.766228\pi$
$878$	0.512469	0.0172950
$879$	−7.59772	−0.256265
$880$	14.4312	0.486475
$881$	20.8194	0.701424	0.350712	−	0.936483i	$-0.385940\pi$
$881$	20.8194	0.701424	0.350712	+	0.936483i	$0.385940\pi$
$882$	1.15477	0.0388832
$883$	−50.5651	−1.70165	−0.850825	−	0.525448i	$-0.823898\pi$
$883$	−50.5651	−1.70165	−0.850825	+	0.525448i	$0.823898\pi$
$884$	−19.4356	−0.653689
$885$	−3.92012	−0.131774
$886$	3.32659	0.111759
$887$	55.7000	1.87022	0.935111	−	0.354355i	$-0.115300\pi$
$887$	55.7000	1.87022	0.935111	+	0.354355i	$0.115300\pi$
$888$	−3.48454	−0.116934
$889$	0.134993	0.00452753
$890$	−3.72161	−0.124749
$891$	7.60674	0.254835
$892$	40.3210	1.35005
$893$	76.4031	2.55673
$894$	3.58231	0.119810
$895$	16.8061	0.561766
$896$	0.0616615	0.00205997
$897$	−11.3759	−0.379829
$898$	4.69755	0.156759
$899$	17.1188	0.570942
$900$	−4.55268	−0.151756
$901$	41.3781	1.37851
$902$	−0.970986	−0.0323303
$903$	0	0
$904$	−2.30763	−0.0767505
$905$	13.1231	0.436228
$906$	−0.673273	−0.0223680
$907$	−42.1173	−1.39848	−0.699241	−	0.714886i	$-0.746479\pi$
$907$	−42.1173	−1.39848	−0.699241	+	0.714886i	$0.746479\pi$
$908$	10.1784	0.337781
$909$	−3.92099	−0.130051
$910$	−0.00569622	−0.000188828 0
$911$	15.7963	0.523353	0.261677	−	0.965156i	$-0.415725\pi$
$911$	15.7963	0.523353	0.261677	+	0.965156i	$0.415725\pi$
$912$	39.2339	1.29916
$913$	−18.8589	−0.624138
$914$	−2.49071	−0.0823854
$915$	14.2326	0.470516
$916$	5.67633	0.187551
$917$	−0.0684016	−0.00225882
$918$	−4.45699	−0.147103
$919$	28.4300	0.937819	0.468909	−	0.883246i	$-0.344647\pi$
$919$	28.4300	0.937819	0.468909	+	0.883246i	$0.344647\pi$
$920$	−4.94131	−0.162910
$921$	20.1237	0.663099
$922$	1.85021	0.0609335
$923$	−11.4448	−0.376709
$924$	0.0816183	0.00268505
$925$	9.21961	0.303139
$926$	−2.46075	−0.0808653
$927$	0.661911	0.0217400
$928$	11.1871	0.367233
$929$	44.3206	1.45411	0.727056	−	0.686578i	$-0.240888\pi$
$929$	44.3206	1.45411	0.727056	+	0.686578i	$0.240888\pi$
$930$	0.737220	0.0241744
$931$	53.3588	1.74876
$932$	24.6212	0.806495
$933$	−43.3500	−1.41921
$934$	0.282720	0.00925089
$935$	−22.3482	−0.730864
$936$	−1.06731	−0.0348860
$937$	−30.6555	−1.00147	−0.500736	−	0.865600i	$-0.666937\pi$
$937$	−30.6555	−1.00147	−0.500736	+	0.865600i	$0.666937\pi$
$938$	−0.00282193	−9.21394e−5 0
$939$	25.7504	0.840334
$940$	−35.3877	−1.15422
$941$	−35.7206	−1.16446	−0.582229	−	0.813025i	$-0.697819\pi$
$941$	−35.7206	−1.16446	−0.582229	+	0.813025i	$0.697819\pi$
$942$	0.239329	0.00779776
$943$	−18.8380	−0.613449
$944$	−6.49461	−0.211381
$945$	0.149990	0.00487917
$946$	0	0
$947$	−40.7779	−1.32510	−0.662552	−	0.749016i	$-0.730527\pi$
$947$	−40.7779	−1.32510	−0.662552	+	0.749016i	$0.730527\pi$
$948$	31.4560	1.02164
$949$	15.8573	0.514749
$950$	1.83209	0.0594409
$951$	22.3196	0.723762
$952$	−0.0473271	−0.00153388
$953$	24.8562	0.805172	0.402586	−	0.915382i	$-0.368111\pi$
$953$	24.8562	0.805172	0.402586	+	0.915382i	$0.368111\pi$
$954$	1.13122	0.0366245
$955$	34.4043	1.11330
$956$	46.1450	1.49243
$957$	19.7144	0.637277
$958$	3.69228	0.119292
$959$	−0.233104	−0.00752732
$960$	−17.8485	−0.576058
$961$	−25.3105	−0.816468
$962$	1.07601	0.0346920
$963$	−1.42576	−0.0459443
$964$	6.97034	0.224499
$965$	−3.77250	−0.121441
$966$	−0.0137905	−0.000443702 0
$967$	−12.4470	−0.400269	−0.200135	−	0.979768i	$-0.564138\pi$
$967$	−12.4470	−0.400269	−0.200135	+	0.979768i	$0.564138\pi$
$968$	3.49328	0.112278
$969$	−60.7578	−1.95182
$970$	−3.17041	−0.101796
$971$	30.2774	0.971648	0.485824	−	0.874057i	$-0.338520\pi$
$971$	30.2774	0.971648	0.485824	+	0.874057i	$0.338520\pi$
$972$	23.8543	0.765125
$973$	0.102791	0.00329534
$974$	−2.48290	−0.0795574
$975$	−3.92417	−0.125674
$976$	23.5797	0.754767
$977$	35.9146	1.14901	0.574505	−	0.818501i	$-0.305195\pi$
$977$	35.9146	1.14901	0.574505	+	0.818501i	$0.305195\pi$
$978$	−0.567621	−0.0181505
$979$	−33.0765	−1.05713
$980$	−24.7143	−0.789468
$981$	15.3169	0.489032
$982$	3.55415	0.113417
$983$	−48.3080	−1.54078	−0.770392	−	0.637570i	$-0.779940\pi$
$983$	−48.3080	−1.54078	−0.770392	+	0.637570i	$0.779940\pi$
$984$	2.45602	0.0782950
$985$	33.0898	1.05433
$986$	−5.69101	−0.181239
$987$	−0.198384	−0.00631464
$988$	−24.5517	−0.781094
$989$	0	0
$990$	−0.610966	−0.0194178
$991$	11.1406	0.353893	0.176946	−	0.984220i	$-0.443378\pi$
$991$	11.1406	0.353893	0.176946	+	0.984220i	$0.443378\pi$
$992$	3.71807	0.118049
$993$	−37.9629	−1.20472
$994$	−0.0138740	−0.000440057 0
$995$	−14.0474	−0.445333
$996$	23.7475	0.752468
$997$	39.5782	1.25346	0.626728	−	0.779238i	$-0.284394\pi$
$997$	39.5782	1.25346	0.626728	+	0.779238i	$0.284394\pi$
$998$	−0.933024	−0.0295344
$999$	−28.3329	−0.896414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.o.1.9		18
43.5	odd	42		43.2.g.a.25.2	✓	36
43.26	odd	42		43.2.g.a.31.2	yes	36
43.42	odd	2		1849.2.a.n.1.10		18
129.5	even	42		387.2.y.c.154.2		36
129.26	even	42		387.2.y.c.289.2		36
172.91	even	42		688.2.bg.c.369.1		36
172.155	even	42		688.2.bg.c.289.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.25.2	✓	36	43.5	odd	42
43.2.g.a.31.2	yes	36	43.26	odd	42
387.2.y.c.154.2		36	129.5	even	42
387.2.y.c.289.2		36	129.26	even	42
688.2.bg.c.289.1		36	172.155	even	42
688.2.bg.c.369.1		36	172.91	even	42
1849.2.a.n.1.10		18	43.42	odd	2
1849.2.a.o.1.9		18	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+0.131407 q^{2} -1.32082 q^{3} -1.98273 q^{4} -1.78074 q^{5} -0.173564 q^{6} -0.0149856 q^{7} -0.523357 q^{8} -1.25544 q^{9} +O(q^{10})\)	\(q+0.131407 q^{2} -1.32082 q^{3} -1.98273 q^{4} -1.78074 q^{5} -0.173564 q^{6} -0.0149856 q^{7} -0.523357 q^{8} -1.25544 q^{9} -0.234000 q^{10} -2.07972 q^{11} +2.61883 q^{12} -1.62441 q^{13} -0.00196921 q^{14} +2.35203 q^{15} +3.89669 q^{16} -6.03444 q^{17} -0.164973 q^{18} -7.62293 q^{19} +3.53072 q^{20} +0.0197933 q^{21} -0.273289 q^{22} -5.30206 q^{23} +0.691260 q^{24} -1.82898 q^{25} -0.213458 q^{26} +5.62066 q^{27} +0.0297125 q^{28} +7.17687 q^{29} +0.309072 q^{30} +2.38527 q^{31} +1.55877 q^{32} +2.74694 q^{33} -0.792965 q^{34} +0.0266854 q^{35} +2.48919 q^{36} -5.04085 q^{37} -1.00170 q^{38} +2.14555 q^{39} +0.931961 q^{40} +3.55296 q^{41} +0.00260097 q^{42} +4.12354 q^{44} +2.23560 q^{45} -0.696725 q^{46} -10.0228 q^{47} -5.14683 q^{48} -6.99978 q^{49} -0.240340 q^{50} +7.97041 q^{51} +3.22077 q^{52} -6.85699 q^{53} +0.738592 q^{54} +3.70344 q^{55} +0.00784283 q^{56} +10.0685 q^{57} +0.943088 q^{58} -1.66670 q^{59} -4.66345 q^{60} +6.05120 q^{61} +0.313440 q^{62} +0.0188135 q^{63} -7.58855 q^{64} +2.89265 q^{65} +0.360966 q^{66} +1.43303 q^{67} +11.9647 q^{68} +7.00306 q^{69} +0.00350664 q^{70} +7.04548 q^{71} +0.657042 q^{72} -9.76187 q^{73} -0.662401 q^{74} +2.41575 q^{75} +15.1142 q^{76} +0.0311659 q^{77} +0.281940 q^{78} +12.0115 q^{79} -6.93898 q^{80} -3.65757 q^{81} +0.466882 q^{82} +9.06798 q^{83} -0.0392448 q^{84} +10.7457 q^{85} -9.47935 q^{87} +1.08844 q^{88} +15.9043 q^{89} +0.293773 q^{90} +0.0243428 q^{91} +10.5126 q^{92} -3.15051 q^{93} -1.31706 q^{94} +13.5744 q^{95} -2.05885 q^{96} +13.5487 q^{97} -0.919817 q^{98} +2.61096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more