LMFDB - Embedded newform 2011.2.a.a.1.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, 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("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.41
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.00378745 q^{2} +0.933952 q^{3} -1.99999 q^{4} -0.391294 q^{5} -0.00353729 q^{6} +0.694814 q^{7} +0.0151497 q^{8} -2.12773 q^{9} +O(q^{10})$	\(q-0.00378745 q^{2} +0.933952 q^{3} -1.99999 q^{4} -0.391294 q^{5} -0.00353729 q^{6} +0.694814 q^{7} +0.0151497 q^{8} -2.12773 q^{9} +0.00148200 q^{10} -2.36081 q^{11} -1.86789 q^{12} +2.09810 q^{13} -0.00263157 q^{14} -0.365450 q^{15} +3.99991 q^{16} +6.36824 q^{17} +0.00805868 q^{18} -3.57576 q^{19} +0.782582 q^{20} +0.648923 q^{21} +0.00894145 q^{22} +5.57199 q^{23} +0.0141491 q^{24} -4.84689 q^{25} -0.00794646 q^{26} -4.78906 q^{27} -1.38962 q^{28} +4.10359 q^{29} +0.00138412 q^{30} -3.95056 q^{31} -0.0454489 q^{32} -2.20489 q^{33} -0.0241194 q^{34} -0.271876 q^{35} +4.25544 q^{36} -2.37596 q^{37} +0.0135430 q^{38} +1.95953 q^{39} -0.00592800 q^{40} -9.42509 q^{41} -0.00245776 q^{42} -9.39941 q^{43} +4.72159 q^{44} +0.832569 q^{45} -0.0211036 q^{46} +1.19169 q^{47} +3.73573 q^{48} -6.51723 q^{49} +0.0183573 q^{50} +5.94763 q^{51} -4.19618 q^{52} -4.65715 q^{53} +0.0181383 q^{54} +0.923772 q^{55} +0.0105262 q^{56} -3.33959 q^{57} -0.0155421 q^{58} -13.4814 q^{59} +0.730894 q^{60} -6.78436 q^{61} +0.0149625 q^{62} -1.47838 q^{63} -7.99966 q^{64} -0.820975 q^{65} +0.00835089 q^{66} +6.39793 q^{67} -12.7364 q^{68} +5.20397 q^{69} +0.00102972 q^{70} -2.22767 q^{71} -0.0322346 q^{72} -12.4964 q^{73} +0.00899880 q^{74} -4.52676 q^{75} +7.15148 q^{76} -1.64033 q^{77} -0.00742161 q^{78} +13.4387 q^{79} -1.56514 q^{80} +1.91045 q^{81} +0.0356970 q^{82} +2.21611 q^{83} -1.29784 q^{84} -2.49185 q^{85} +0.0355997 q^{86} +3.83256 q^{87} -0.0357657 q^{88} -8.28286 q^{89} -0.00315331 q^{90} +1.45779 q^{91} -11.1439 q^{92} -3.68963 q^{93} -0.00451346 q^{94} +1.39917 q^{95} -0.0424471 q^{96} -2.37535 q^{97} +0.0246837 q^{98} +5.02318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9}+O(q^{10}) $ 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9} - 21 q^{10} - 34 q^{11} - 36 q^{12} - 34 q^{13} - 49 q^{14} - 12 q^{15} + 47 q^{16} - 59 q^{17} - 24 q^{18} - 31 q^{19} - 82 q^{20} - 71 q^{21} - 3 q^{22} - 28 q^{23} - 50 q^{24} + 68 q^{25} - 54 q^{26} - 43 q^{27} - 2 q^{28} - 151 q^{29} + q^{30} - 37 q^{31} - 59 q^{32} - 35 q^{33} - q^{34} - 58 q^{35} + 19 q^{36} - 29 q^{37} - 22 q^{38} - 40 q^{39} - 41 q^{40} - 142 q^{41} + 16 q^{42} - 23 q^{43} - 89 q^{44} - 119 q^{45} - 6 q^{46} - 36 q^{47} - 46 q^{48} + 45 q^{49} - 29 q^{50} - 53 q^{51} - 11 q^{52} - 69 q^{53} - 50 q^{54} - 13 q^{55} - 122 q^{56} - 14 q^{57} + 31 q^{58} - 92 q^{59} + 20 q^{60} - 115 q^{61} - 66 q^{62} - 25 q^{63} + 37 q^{64} - 57 q^{65} - 17 q^{66} - 108 q^{68} - 160 q^{69} + 40 q^{70} - 67 q^{71} - 35 q^{72} - 36 q^{73} - 55 q^{74} - 51 q^{75} - 56 q^{76} - 116 q^{77} + 22 q^{78} - 42 q^{79} - 114 q^{80} + 37 q^{81} + 18 q^{82} - 42 q^{83} - 77 q^{84} - 18 q^{85} - 33 q^{86} - 7 q^{87} - 2 q^{88} - 93 q^{89} - 34 q^{90} - 37 q^{91} - 55 q^{92} - 8 q^{93} - 35 q^{94} - 64 q^{95} - 83 q^{96} - 16 q^{97} - 57 q^{98} - 65 q^{99}+O(q^{100}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9 - 21 * q^10 - 34 * q^11 - 36 * q^12 - 34 * q^13 - 49 * q^14 - 12 * q^15 + 47 * q^16 - 59 * q^17 - 24 * q^18 - 31 * q^19 - 82 * q^20 - 71 * q^21 - 3 * q^22 - 28 * q^23 - 50 * q^24 + 68 * q^25 - 54 * q^26 - 43 * q^27 - 2 * q^28 - 151 * q^29 + q^30 - 37 * q^31 - 59 * q^32 - 35 * q^33 - q^34 - 58 * q^35 + 19 * q^36 - 29 * q^37 - 22 * q^38 - 40 * q^39 - 41 * q^40 - 142 * q^41 + 16 * q^42 - 23 * q^43 - 89 * q^44 - 119 * q^45 - 6 * q^46 - 36 * q^47 - 46 * q^48 + 45 * q^49 - 29 * q^50 - 53 * q^51 - 11 * q^52 - 69 * q^53 - 50 * q^54 - 13 * q^55 - 122 * q^56 - 14 * q^57 + 31 * q^58 - 92 * q^59 + 20 * q^60 - 115 * q^61 - 66 * q^62 - 25 * q^63 + 37 * q^64 - 57 * q^65 - 17 * q^66 - 108 * q^68 - 160 * q^69 + 40 * q^70 - 67 * q^71 - 35 * q^72 - 36 * q^73 - 55 * q^74 - 51 * q^75 - 56 * q^76 - 116 * q^77 + 22 * q^78 - 42 * q^79 - 114 * q^80 + 37 * q^81 + 18 * q^82 - 42 * q^83 - 77 * q^84 - 18 * q^85 - 33 * q^86 - 7 * q^87 - 2 * q^88 - 93 * q^89 - 34 * q^90 - 37 * q^91 - 55 * q^92 - 8 * q^93 - 35 * q^94 - 64 * q^95 - 83 * q^96 - 16 * q^97 - 57 * q^98 - 65 * 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 $

$2$	−0.00378745	−0.00267813	−0.00133906	−	0.999999i	$-0.500426\pi$
$2$	−0.00378745	−0.00267813	−0.00133906	+	0.999999i	$0.500426\pi$
$3$	0.933952	0.539217	0.269609	−	0.962970i	$-0.413106\pi$
$3$	0.933952	0.539217	0.269609	+	0.962970i	$0.413106\pi$
$4$	−1.99999	−0.999993
$5$	−0.391294	−0.174992	−0.0874960	−	0.996165i	$-0.527886\pi$
$5$	−0.391294	−0.174992	−0.0874960	+	0.996165i	$0.527886\pi$
$6$	−0.00353729	−0.00144409
$7$	0.694814	0.262615	0.131307	−	0.991342i	$-0.458082\pi$
$7$	0.694814	0.262615	0.131307	+	0.991342i	$0.458082\pi$
$8$	0.0151497	0.00535624
$9$	−2.12773	−0.709245
$10$	0.00148200	0.000468651 0
$11$	−2.36081	−0.711812	−0.355906	−	0.934522i	$-0.615828\pi$
$11$	−2.36081	−0.711812	−0.355906	+	0.934522i	$0.615828\pi$
$12$	−1.86789	−0.539214
$13$	2.09810	0.581910	0.290955	−	0.956737i	$-0.406027\pi$
$13$	2.09810	0.581910	0.290955	+	0.956737i	$0.406027\pi$
$14$	−0.00263157	−0.000703317 0
$15$	−0.365450	−0.0943587
$16$	3.99991	0.999978
$17$	6.36824	1.54453	0.772263	−	0.635303i	$-0.219125\pi$
$17$	6.36824	1.54453	0.772263	+	0.635303i	$0.219125\pi$
$18$	0.00805868	0.00189945
$19$	−3.57576	−0.820337	−0.410168	−	0.912010i	$-0.634530\pi$
$19$	−3.57576	−0.820337	−0.410168	+	0.912010i	$0.634530\pi$
$20$	0.782582	0.174991
$21$	0.648923	0.141607
$22$	0.00894145	0.00190632
$23$	5.57199	1.16184	0.580920	−	0.813961i	$-0.302693\pi$
$23$	5.57199	1.16184	0.580920	+	0.813961i	$0.302693\pi$
$24$	0.0141491	0.00288818
$25$	−4.84689	−0.969378
$26$	−0.00794646	−0.00155843
$27$	−4.78906	−0.921655
$28$	−1.38962	−0.262613
$29$	4.10359	0.762018	0.381009	−	0.924571i	$-0.375577\pi$
$29$	4.10359	0.762018	0.381009	+	0.924571i	$0.375577\pi$
$30$	0.00138412	0.000252705 0
$31$	−3.95056	−0.709541	−0.354770	−	0.934953i	$-0.615441\pi$
$31$	−3.95056	−0.709541	−0.354770	+	0.934953i	$0.615441\pi$
$32$	−0.0454489	−0.00803431
$33$	−2.20489	−0.383822
$34$	−0.0241194	−0.00413644
$35$	−0.271876	−0.0459555
$36$	4.25544	0.709239
$37$	−2.37596	−0.390605	−0.195302	−	0.980743i	$-0.562569\pi$
$37$	−2.37596	−0.390605	−0.195302	+	0.980743i	$0.562569\pi$
$38$	0.0135430	0.00219697
$39$	1.95953	0.313776
$40$	−0.00592800	−0.000937298 0
$41$	−9.42509	−1.47195	−0.735976	−	0.677008i	$-0.763276\pi$
$41$	−9.42509	−1.47195	−0.735976	+	0.677008i	$0.763276\pi$
$42$	−0.00245776	−0.000379241 0
$43$	−9.39941	−1.43340	−0.716698	−	0.697384i	$-0.754347\pi$
$43$	−9.39941	−1.43340	−0.716698	+	0.697384i	$0.754347\pi$
$44$	4.72159	0.711807
$45$	0.832569	0.124112
$46$	−0.0211036	−0.00311156
$47$	1.19169	0.173826	0.0869130	−	0.996216i	$-0.472300\pi$
$47$	1.19169	0.173826	0.0869130	+	0.996216i	$0.472300\pi$
$48$	3.73573	0.539206
$49$	−6.51723	−0.931033
$50$	0.0183573	0.00259612
$51$	5.94763	0.832835
$52$	−4.19618	−0.581905
$53$	−4.65715	−0.639708	−0.319854	−	0.947467i	$-0.603634\pi$
$53$	−4.65715	−0.639708	−0.319854	+	0.947467i	$0.603634\pi$
$54$	0.0181383	0.00246831
$55$	0.923772	0.124561
$56$	0.0105262	0.00140663
$57$	−3.33959	−0.442340
$58$	−0.0155421	−0.00204078
$59$	−13.4814	−1.75512	−0.877562	−	0.479462i	$-0.840832\pi$
$59$	−13.4814	−1.75512	−0.877562	+	0.479462i	$0.840832\pi$
$60$	0.730894	0.0943580
$61$	−6.78436	−0.868648	−0.434324	−	0.900757i	$-0.643013\pi$
$61$	−6.78436	−0.868648	−0.434324	+	0.900757i	$0.643013\pi$
$62$	0.0149625	0.00190024
$63$	−1.47838	−0.186258
$64$	−7.99966	−0.999957
$65$	−0.820975	−0.101829
$66$	0.00835089	0.00102792
$67$	6.39793	0.781632	0.390816	−	0.920469i	$-0.372193\pi$
$67$	6.39793	0.781632	0.390816	+	0.920469i	$0.372193\pi$
$68$	−12.7364	−1.54451
$69$	5.20397	0.626484
$70$	0.00102972	0.000123075 0
$71$	−2.22767	−0.264376	−0.132188	−	0.991225i	$-0.542200\pi$
$71$	−2.22767	−0.264376	−0.132188	+	0.991225i	$0.542200\pi$
$72$	−0.0322346	−0.00379888
$73$	−12.4964	−1.46260	−0.731298	−	0.682058i	$-0.761085\pi$
$73$	−12.4964	−1.46260	−0.731298	+	0.682058i	$0.761085\pi$
$74$	0.00899880	0.00104609
$75$	−4.52676	−0.522705
$76$	7.15148	0.820331
$77$	−1.64033	−0.186933
$78$	−0.00742161	−0.000840332 0
$79$	13.4387	1.51197	0.755987	−	0.654587i	$-0.227157\pi$
$79$	13.4387	1.51197	0.755987	+	0.654587i	$0.227157\pi$
$80$	−1.56514	−0.174988
$81$	1.91045	0.212272
$82$	0.0356970	0.00394208
$83$	2.21611	0.243250	0.121625	−	0.992576i	$-0.461189\pi$
$83$	2.21611	0.243250	0.121625	+	0.992576i	$0.461189\pi$
$84$	−1.29784	−0.141606
$85$	−2.49185	−0.270279
$86$	0.0355997	0.00383882
$87$	3.83256	0.410893
$88$	−0.0357657	−0.00381264
$89$	−8.28286	−0.877982	−0.438991	−	0.898491i	$-0.644664\pi$
$89$	−8.28286	−0.877982	−0.438991	+	0.898491i	$0.644664\pi$
$90$	−0.00315331	−0.000332388 0
$91$	1.45779	0.152818
$92$	−11.1439	−1.16183
$93$	−3.68963	−0.382597
$94$	−0.00451346	−0.000465528 0
$95$	1.39917	0.143552
$96$	−0.0424471	−0.00433224
$97$	−2.37535	−0.241180	−0.120590	−	0.992702i	$-0.538479\pi$
$97$	−2.37535	−0.241180	−0.120590	+	0.992702i	$0.538479\pi$
$98$	0.0246837	0.00249343
$99$	5.02318	0.504849
$100$	9.69371	0.969371
$101$	13.1219	1.30567	0.652837	−	0.757499i	$-0.273579\pi$
$101$	13.1219	1.30567	0.652837	+	0.757499i	$0.273579\pi$
$102$	−0.0225263	−0.00223044
$103$	−3.28153	−0.323339	−0.161669	−	0.986845i	$-0.551688\pi$
$103$	−3.28153	−0.323339	−0.161669	+	0.986845i	$0.551688\pi$
$104$	0.0317857	0.00311685
$105$	−0.253920	−0.0247800
$106$	0.0176387	0.00171322
$107$	−2.48399	−0.240137	−0.120068	−	0.992766i	$-0.538311\pi$
$107$	−2.48399	−0.240137	−0.120068	+	0.992766i	$0.538311\pi$
$108$	9.57805	0.921648
$109$	12.2600	1.17430	0.587149	−	0.809479i	$-0.300250\pi$
$109$	12.2600	1.17430	0.587149	+	0.809479i	$0.300250\pi$
$110$	−0.00349874	−0.000333591 0
$111$	−2.21903	−0.210621
$112$	2.77920	0.262609
$113$	−8.33115	−0.783729	−0.391865	−	0.920023i	$-0.628170\pi$
$113$	−8.33115	−0.783729	−0.391865	+	0.920023i	$0.628170\pi$
$114$	0.0126485	0.00118464
$115$	−2.18028	−0.203313
$116$	−8.20712	−0.762012
$117$	−4.46421	−0.412716
$118$	0.0510600	0.00470045
$119$	4.42474	0.405615
$120$	−0.00553646	−0.000505408 0
$121$	−5.42656	−0.493324
$122$	0.0256954	0.00232635
$123$	−8.80258	−0.793702
$124$	7.90106	0.709536
$125$	3.85303	0.344625
$126$	0.00559928	0.000498824 0
$127$	9.61788	0.853448	0.426724	−	0.904382i	$-0.359667\pi$
$127$	9.61788	0.853448	0.426724	+	0.904382i	$0.359667\pi$
$128$	0.121196	0.0107123
$129$	−8.77859	−0.772912
$130$	0.00310940	0.000272712 0
$131$	−20.9997	−1.83475	−0.917375	−	0.398025i	$-0.869696\pi$
$131$	−20.9997	−1.83475	−0.917375	+	0.398025i	$0.869696\pi$
$132$	4.40974	0.383819
$133$	−2.48449	−0.215433
$134$	−0.0242318	−0.00209331
$135$	1.87393	0.161282
$136$	0.0964771	0.00827285
$137$	4.63685	0.396153	0.198076	−	0.980187i	$-0.436531\pi$
$137$	4.63685	0.396153	0.198076	+	0.980187i	$0.436531\pi$
$138$	−0.0197098	−0.00167781
$139$	4.70586	0.399146	0.199573	−	0.979883i	$-0.436045\pi$
$139$	4.70586	0.399146	0.199573	+	0.979883i	$0.436045\pi$
$140$	0.543749	0.0459552
$141$	1.11298	0.0937300
$142$	0.00843717	0.000708032 0
$143$	−4.95323	−0.414210
$144$	−8.51075	−0.709229
$145$	−1.60571	−0.133347
$146$	0.0473295	0.00391702
$147$	−6.08678	−0.502029
$148$	4.75188	0.390602
$149$	−7.06636	−0.578898	−0.289449	−	0.957193i	$-0.593472\pi$
$149$	−7.06636	−0.578898	−0.289449	+	0.957193i	$0.593472\pi$
$150$	0.0171449	0.00139987
$151$	11.5198	0.937468	0.468734	−	0.883339i	$-0.344710\pi$
$151$	11.5198	0.937468	0.468734	+	0.883339i	$0.344710\pi$
$152$	−0.0541719	−0.00439392
$153$	−13.5499	−1.09545
$154$	0.00621265	0.000500629 0
$155$	1.54583	0.124164
$156$	−3.91903	−0.313774
$157$	3.07791	0.245644	0.122822	−	0.992429i	$-0.460806\pi$
$157$	3.07791	0.245644	0.122822	+	0.992429i	$0.460806\pi$
$158$	−0.0508984	−0.00404926
$159$	−4.34955	−0.344942
$160$	0.0177839	0.00140594
$161$	3.87149	0.305117
$162$	−0.00723573	−0.000568493 0
$163$	−11.9761	−0.938038	−0.469019	−	0.883188i	$-0.655392\pi$
$163$	−11.9761	−0.938038	−0.469019	+	0.883188i	$0.655392\pi$
$164$	18.8500	1.47194
$165$	0.862759	0.0671657
$166$	−0.00839341	−0.000651455 0
$167$	8.55394	0.661923	0.330962	−	0.943644i	$-0.392627\pi$
$167$	8.55394	0.661923	0.330962	+	0.943644i	$0.392627\pi$
$168$	0.00983101	0.000758479 0
$169$	−8.59796	−0.661381
$170$	0.00943776	0.000723843 0
$171$	7.60828	0.581819
$172$	18.7987	1.43339
$173$	−19.4733	−1.48053	−0.740265	−	0.672315i	$-0.765300\pi$
$173$	−19.4733	−1.48053	−0.740265	+	0.672315i	$0.765300\pi$
$174$	−0.0145156	−0.00110043
$175$	−3.36769	−0.254573
$176$	−9.44305	−0.711797
$177$	−12.5910	−0.946394
$178$	0.0313709	0.00235135
$179$	11.5141	0.860602	0.430301	−	0.902685i	$-0.358407\pi$
$179$	11.5141	0.860602	0.430301	+	0.902685i	$0.358407\pi$
$180$	−1.66513	−0.124111
$181$	−6.26016	−0.465314	−0.232657	−	0.972559i	$-0.574742\pi$
$181$	−6.26016	−0.465314	−0.232657	+	0.972559i	$0.574742\pi$
$182$	−0.00552131	−0.000409267 0
$183$	−6.33626	−0.468390
$184$	0.0844141	0.00622309
$185$	0.929697	0.0683527
$186$	0.0139743	0.00102464
$187$	−15.0342	−1.09941
$188$	−2.38336	−0.173825
$189$	−3.32750	−0.242040
$190$	−0.00529930	−0.000384452 0
$191$	−12.4804	−0.903052	−0.451526	−	0.892258i	$-0.649120\pi$
$191$	−12.4804	−0.903052	−0.451526	+	0.892258i	$0.649120\pi$
$192$	−7.47129	−0.539194
$193$	2.35506	0.169521	0.0847603	−	0.996401i	$-0.472988\pi$
$193$	2.35506	0.169521	0.0847603	+	0.996401i	$0.472988\pi$
$194$	0.00899651	0.000645912 0
$195$	−0.766752	−0.0549082
$196$	13.0344	0.931027
$197$	−8.12715	−0.579036	−0.289518	−	0.957173i	$-0.593495\pi$
$197$	−8.12715	−0.579036	−0.289518	+	0.957173i	$0.593495\pi$
$198$	−0.0190250	−0.00135205
$199$	6.29085	0.445947	0.222973	−	0.974825i	$-0.428424\pi$
$199$	6.29085	0.445947	0.222973	+	0.974825i	$0.428424\pi$
$200$	−0.0734291	−0.00519222
$201$	5.97536	0.421470
$202$	−0.0496983	−0.00349676
$203$	2.85123	0.200117
$204$	−11.8952	−0.832829
$205$	3.68798	0.257580
$206$	0.0124286	0.000865943 0
$207$	−11.8557	−0.824028
$208$	8.39224	0.581897
$209$	8.44171	0.583926
$210$	0.000961707 0	6.63641e−5 0
$211$	8.99877	0.619501	0.309750	−	0.950818i	$-0.399754\pi$
$211$	8.99877	0.619501	0.309750	+	0.950818i	$0.399754\pi$
$212$	9.31423	0.639704
$213$	−2.08054	−0.142556
$214$	0.00940799	0.000643117 0
$215$	3.67793	0.250833
$216$	−0.0725529	−0.00493660
$217$	−2.74490	−0.186336
$218$	−0.0464342	−0.00314492
$219$	−11.6711	−0.788657
$220$	−1.84753	−0.124560
$221$	13.3612	0.898774
$222$	0.00840445	0.000564070 0
$223$	−7.92190	−0.530490	−0.265245	−	0.964181i	$-0.585453\pi$
$223$	−7.92190	−0.530490	−0.265245	+	0.964181i	$0.585453\pi$
$224$	−0.0315785	−0.00210993
$225$	10.3129	0.687526
$226$	0.0315538	0.00209893
$227$	−19.6617	−1.30499	−0.652497	−	0.757792i	$-0.726278\pi$
$227$	−19.6617	−1.30499	−0.652497	+	0.757792i	$0.726278\pi$
$228$	6.67914	0.442337
$229$	8.31707	0.549607	0.274804	−	0.961500i	$-0.411387\pi$
$229$	8.31707	0.549607	0.274804	+	0.961500i	$0.411387\pi$
$230$	0.00825771	0.000544497 0
$231$	−1.53199	−0.100797
$232$	0.0621683	0.00408155
$233$	8.61399	0.564321	0.282161	−	0.959367i	$-0.408949\pi$
$233$	8.61399	0.564321	0.282161	+	0.959367i	$0.408949\pi$
$234$	0.0169079	0.00110531
$235$	−0.466301	−0.0304181
$236$	26.9625	1.75511
$237$	12.5511	0.815283
$238$	−0.0167585	−0.00108629
$239$	18.2063	1.17767	0.588834	−	0.808254i	$-0.299587\pi$
$239$	18.2063	1.17767	0.588834	+	0.808254i	$0.299587\pi$
$240$	−1.46177	−0.0943567
$241$	23.3306	1.50285	0.751427	−	0.659816i	$-0.229366\pi$
$241$	23.3306	1.50285	0.751427	+	0.659816i	$0.229366\pi$
$242$	0.0205528	0.00132118
$243$	16.1514	1.03612
$244$	13.5686	0.868641
$245$	2.55015	0.162923
$246$	0.0333393	0.00212564
$247$	−7.50233	−0.477362
$248$	−0.0598499	−0.00380047
$249$	2.06974	0.131165
$250$	−0.0145931	−0.000922951 0
$251$	7.67918	0.484706	0.242353	−	0.970188i	$-0.422081\pi$
$251$	7.67918	0.484706	0.242353	+	0.970188i	$0.422081\pi$
$252$	2.95674	0.186257
$253$	−13.1544	−0.827011
$254$	−0.0364272	−0.00228564
$255$	−2.32727	−0.145739
$256$	15.9989	0.999928
$257$	−1.29603	−0.0808441	−0.0404220	−	0.999183i	$-0.512870\pi$
$257$	−1.29603	−0.0808441	−0.0404220	+	0.999183i	$0.512870\pi$
$258$	0.0332485	0.00206996
$259$	−1.65085	−0.102579
$260$	1.64194	0.101829
$261$	−8.73135	−0.540457
$262$	0.0795351	0.00491370
$263$	−9.10519	−0.561450	−0.280725	−	0.959788i	$-0.590575\pi$
$263$	−9.10519	−0.561450	−0.280725	+	0.959788i	$0.590575\pi$
$264$	−0.0334034	−0.00205584
$265$	1.82231	0.111944
$266$	0.00940988	0.000576957 0
$267$	−7.73580	−0.473423
$268$	−12.7958	−0.781626
$269$	−21.5681	−1.31503	−0.657515	−	0.753442i	$-0.728392\pi$
$269$	−21.5681	−1.31503	−0.657515	+	0.753442i	$0.728392\pi$
$270$	−0.00709740	−0.000431934 0
$271$	3.87570	0.235432	0.117716	−	0.993047i	$-0.462443\pi$
$271$	3.87570	0.235432	0.117716	+	0.993047i	$0.462443\pi$
$272$	25.4724	1.54449
$273$	1.36151	0.0824022
$274$	−0.0175618	−0.00106095
$275$	11.4426	0.690015
$276$	−10.4079	−0.626480
$277$	−8.53522	−0.512832	−0.256416	−	0.966567i	$-0.582542\pi$
$277$	−8.53522	−0.512832	−0.256416	+	0.966567i	$0.582542\pi$
$278$	−0.0178232	−0.00106896
$279$	8.40573	0.503238
$280$	−0.00411885	−0.000246149 0
$281$	−2.43284	−0.145131	−0.0725655	−	0.997364i	$-0.523119\pi$
$281$	−2.43284	−0.145131	−0.0725655	+	0.997364i	$0.523119\pi$
$282$	−0.00421536	−0.000251021 0
$283$	−26.2510	−1.56046	−0.780231	−	0.625492i	$-0.784898\pi$
$283$	−26.2510	−1.56046	−0.780231	+	0.625492i	$0.784898\pi$
$284$	4.45530	0.264374
$285$	1.30676	0.0774059
$286$	0.0187601	0.00110931
$287$	−6.54868	−0.386557
$288$	0.0967032	0.00569829
$289$	23.5545	1.38556
$290$	0.00608154	0.000357120 0
$291$	−2.21846	−0.130049
$292$	24.9927	1.46259
$293$	18.9934	1.10960	0.554802	−	0.831983i	$-0.312794\pi$
$293$	18.9934	1.10960	0.554802	+	0.831983i	$0.312794\pi$
$294$	0.0230534	0.00134450
$295$	5.27518	0.307133
$296$	−0.0359951	−0.00209217
$297$	11.3061	0.656045
$298$	0.0267634	0.00155036
$299$	11.6906	0.676086
$300$	9.05346	0.522702
$301$	−6.53084	−0.376431
$302$	−0.0436306	−0.00251066
$303$	12.2552	0.704042
$304$	−14.3028	−0.820319
$305$	2.65468	0.152006
$306$	0.0513196	0.00293375
$307$	25.3013	1.44402	0.722011	−	0.691881i	$-0.243218\pi$
$307$	25.3013	1.44402	0.722011	+	0.691881i	$0.243218\pi$
$308$	3.28063	0.186931
$309$	−3.06479	−0.174350
$310$	−0.00585474	−0.000332527 0
$311$	−24.2012	−1.37233	−0.686163	−	0.727448i	$-0.740706\pi$
$311$	−24.2012	−1.37233	−0.686163	+	0.727448i	$0.740706\pi$
$312$	0.0296863	0.00168066
$313$	0.602460	0.0340531	0.0170265	−	0.999855i	$-0.494580\pi$
$313$	0.602460	0.0340531	0.0170265	+	0.999855i	$0.494580\pi$
$314$	−0.0116574	−0.000657867 0
$315$	0.578481	0.0325937
$316$	−26.8772	−1.51196
$317$	31.5149	1.77005	0.885026	−	0.465541i	$-0.154140\pi$
$317$	31.5149	1.77005	0.885026	+	0.465541i	$0.154140\pi$
$318$	0.0164737	0.000923799 0
$319$	−9.68781	−0.542413
$320$	3.13022	0.174984
$321$	−2.31993	−0.129486
$322$	−0.0146631	−0.000817141 0
$323$	−22.7713	−1.26703
$324$	−3.82087	−0.212271
$325$	−10.1693	−0.564090
$326$	0.0453587	0.00251219
$327$	11.4503	0.633202
$328$	−0.142788	−0.00788413
$329$	0.828003	0.0456493
$330$	−0.00326765	−0.000179878 0
$331$	11.3545	0.624100	0.312050	−	0.950066i	$-0.398984\pi$
$331$	11.3545	0.624100	0.312050	+	0.950066i	$0.398984\pi$
$332$	−4.43219	−0.243248
$333$	5.05540	0.277034
$334$	−0.0323976	−0.00177272
$335$	−2.50347	−0.136779
$336$	2.59564	0.141604
$337$	21.2285	1.15639	0.578195	−	0.815898i	$-0.303757\pi$
$337$	21.2285	1.15639	0.578195	+	0.815898i	$0.303757\pi$
$338$	0.0325643	0.00177126
$339$	−7.78090	−0.422600
$340$	4.98367	0.270277
$341$	9.32653	0.505060
$342$	−0.0288159	−0.00155819
$343$	−9.39196	−0.507118
$344$	−0.142398	−0.00767761
$345$	−2.03628	−0.109630
$346$	0.0737542	0.00396505
$347$	−0.423897	−0.0227560	−0.0113780	−	0.999935i	$-0.503622\pi$
$347$	−0.423897	−0.0227560	−0.0113780	+	0.999935i	$0.503622\pi$
$348$	−7.66506	−0.410890
$349$	7.07938	0.378951	0.189475	−	0.981885i	$-0.439321\pi$
$349$	7.07938	0.378951	0.189475	+	0.981885i	$0.439321\pi$
$350$	0.0127549	0.000681780 0
$351$	−10.0479	−0.536320
$352$	0.107296	0.00571892
$353$	−13.8155	−0.735323	−0.367661	−	0.929960i	$-0.619841\pi$
$353$	−13.8155	−0.735323	−0.367661	+	0.929960i	$0.619841\pi$
$354$	0.0476876	0.00253456
$355$	0.871673	0.0462636
$356$	16.5656	0.877976
$357$	4.13250	0.218715
$358$	−0.0436089	−0.00230480
$359$	0.514589	0.0271590	0.0135795	−	0.999908i	$-0.495677\pi$
$359$	0.514589	0.0271590	0.0135795	+	0.999908i	$0.495677\pi$
$360$	0.0126132	0.000664774 0
$361$	−6.21391	−0.327048
$362$	0.0237100	0.00124617
$363$	−5.06815	−0.266009
$364$	−2.91556	−0.152817
$365$	4.88977	0.255943
$366$	0.0239983	0.00125441
$367$	−10.9800	−0.573150	−0.286575	−	0.958058i	$-0.592517\pi$
$367$	−10.9800	−0.573150	−0.286575	+	0.958058i	$0.592517\pi$
$368$	22.2875	1.16181
$369$	20.0541	1.04397
$370$	−0.00352118	−0.000183057 0
$371$	−3.23585	−0.167997
$372$	7.37921	0.382594
$373$	−38.2274	−1.97934	−0.989670	−	0.143367i	$-0.954207\pi$
$373$	−38.2274	−1.97934	−0.989670	+	0.143367i	$0.954207\pi$
$374$	0.0569413	0.00294437
$375$	3.59854	0.185828
$376$	0.0180538	0.000931053 0
$377$	8.60976	0.443425
$378$	0.0126027	0.000648215 0
$379$	−14.5860	−0.749235	−0.374617	−	0.927179i	$-0.622226\pi$
$379$	−14.5860	−0.749235	−0.374617	+	0.927179i	$0.622226\pi$
$380$	−2.79833	−0.143551
$381$	8.98263	0.460194
$382$	0.0472690	0.00241849
$383$	4.62373	0.236262	0.118131	−	0.992998i	$-0.462310\pi$
$383$	4.62373	0.236262	0.118131	+	0.992998i	$0.462310\pi$
$384$	0.113191	0.00577627
$385$	0.641850	0.0327117
$386$	−0.00891965	−0.000453998 0
$387$	19.9994	1.01663
$388$	4.75067	0.241178
$389$	−25.1496	−1.27513	−0.637567	−	0.770395i	$-0.720059\pi$
$389$	−25.1496	−1.27513	−0.637567	+	0.770395i	$0.720059\pi$
$390$	0.00290403	0.000147051 0
$391$	35.4838	1.79449
$392$	−0.0987343	−0.00498684
$393$	−19.6127	−0.989329
$394$	0.0307812	0.00155073
$395$	−5.25849	−0.264583
$396$	−10.0463	−0.504845
$397$	−1.42172	−0.0713542	−0.0356771	−	0.999363i	$-0.511359\pi$
$397$	−1.42172	−0.0713542	−0.0356771	+	0.999363i	$0.511359\pi$
$398$	−0.0238263	−0.00119430
$399$	−2.32040	−0.116165
$400$	−19.3871	−0.969357
$401$	21.7984	1.08856	0.544280	−	0.838904i	$-0.316803\pi$
$401$	21.7984	1.08856	0.544280	+	0.838904i	$0.316803\pi$
$402$	−0.0226314	−0.00112875
$403$	−8.28868	−0.412889
$404$	−26.2435	−1.30566
$405$	−0.747548	−0.0371459
$406$	−0.0107989	−0.000535940 0
$407$	5.60919	0.278037
$408$	0.0901050	0.00446086
$409$	−5.66080	−0.279909	−0.139954	−	0.990158i	$-0.544696\pi$
$409$	−5.66080	−0.279909	−0.139954	+	0.990158i	$0.544696\pi$
$410$	−0.0139680	−0.000689832 0
$411$	4.33060	0.213613
$412$	6.56301	0.323336
$413$	−9.36704	−0.460922
$414$	0.0449028	0.00220685
$415$	−0.867151	−0.0425668
$416$	−0.0953566	−0.00467524
$417$	4.39505	0.215226
$418$	−0.0319725	−0.00156383
$419$	−4.62739	−0.226063	−0.113031	−	0.993591i	$-0.536056\pi$
$419$	−4.62739	−0.226063	−0.113031	+	0.993591i	$0.536056\pi$
$420$	0.507835	0.0247798
$421$	20.8821	1.01773	0.508866	−	0.860845i	$-0.330065\pi$
$421$	20.8821	1.01773	0.508866	+	0.860845i	$0.330065\pi$
$422$	−0.0340824	−0.00165910
$423$	−2.53560	−0.123285
$424$	−0.0705545	−0.00342643
$425$	−30.8662	−1.49723
$426$	0.00787992	0.000381783 0
$427$	−4.71386	−0.228120
$428$	4.96795	0.240135
$429$	−4.62608	−0.223349
$430$	−0.0139300	−0.000671762 0
$431$	4.00855	0.193085	0.0965424	−	0.995329i	$-0.469222\pi$
$431$	4.00855	0.193085	0.0965424	+	0.995329i	$0.469222\pi$
$432$	−19.1558	−0.921635
$433$	−1.26381	−0.0607349	−0.0303674	−	0.999539i	$-0.509668\pi$
$433$	−1.26381	−0.0607349	−0.0303674	+	0.999539i	$0.509668\pi$
$434$	0.0103962	0.000499032 0
$435$	−1.49966	−0.0719030
$436$	−24.5199	−1.17429
$437$	−19.9241	−0.953100
$438$	0.0442035	0.00211213
$439$	8.85336	0.422548	0.211274	−	0.977427i	$-0.432239\pi$
$439$	8.85336	0.422548	0.211274	+	0.977427i	$0.432239\pi$
$440$	0.0139949	0.000667180 0
$441$	13.8669	0.660330
$442$	−0.0506050	−0.00240703
$443$	−23.8330	−1.13234	−0.566169	−	0.824289i	$-0.691575\pi$
$443$	−23.8330	−1.13234	−0.566169	+	0.824289i	$0.691575\pi$
$444$	4.43802	0.210619
$445$	3.24103	0.153640
$446$	0.0300038	0.00142072
$447$	−6.59964	−0.312152
$448$	−5.55827	−0.262604
$449$	−22.8679	−1.07920	−0.539602	−	0.841920i	$-0.681425\pi$
$449$	−22.8679	−1.07920	−0.539602	+	0.841920i	$0.681425\pi$
$450$	−0.0390595	−0.00184128
$451$	22.2509	1.04775
$452$	16.6622	0.783723
$453$	10.7589	0.505499
$454$	0.0744676	0.00349494
$455$	−0.570425	−0.0267419
$456$	−0.0505939	−0.00236928
$457$	−33.5336	−1.56863	−0.784317	−	0.620361i	$-0.786986\pi$
$457$	−33.5336	−1.56863	−0.784317	+	0.620361i	$0.786986\pi$
$458$	−0.0315004	−0.00147192
$459$	−30.4979	−1.42352
$460$	4.36054	0.203311
$461$	23.9772	1.11673	0.558364	−	0.829596i	$-0.311429\pi$
$461$	23.9772	1.11673	0.558364	+	0.829596i	$0.311429\pi$
$462$	0.00580231	0.000269948 0
$463$	17.2083	0.799735	0.399868	−	0.916573i	$-0.369056\pi$
$463$	17.2083	0.799735	0.399868	+	0.916573i	$0.369056\pi$
$464$	16.4140	0.762001
$465$	1.44373	0.0669514
$466$	−0.0326250	−0.00151133
$467$	−29.0457	−1.34407	−0.672037	−	0.740517i	$-0.734581\pi$
$467$	−29.0457	−1.34407	−0.672037	+	0.740517i	$0.734581\pi$
$468$	8.92835	0.412713
$469$	4.44537	0.205268
$470$	0.00176609	8.14637e−5 0
$471$	2.87462	0.132456
$472$	−0.204239	−0.00940087
$473$	22.1902	1.02031
$474$	−0.0475367	−0.00218343
$475$	17.3313	0.795216
$476$	−8.84942	−0.405613
$477$	9.90917	0.453710
$478$	−0.0689554	−0.00315395
$479$	40.4572	1.84853	0.924267	−	0.381746i	$-0.124677\pi$
$479$	40.4572	1.84853	0.924267	+	0.381746i	$0.124677\pi$
$480$	0.0166093	0.000758107 0
$481$	−4.98500	−0.227297
$482$	−0.0883633	−0.00402484
$483$	3.61579	0.164524
$484$	10.8530	0.493320
$485$	0.929460	0.0422046
$486$	−0.0611727	−0.00277485
$487$	14.8148	0.671323	0.335662	−	0.941983i	$-0.391040\pi$
$487$	14.8148	0.671323	0.335662	+	0.941983i	$0.391040\pi$
$488$	−0.102781	−0.00465268
$489$	−11.1851	−0.505806
$490$	−0.00965857	−0.000436330 0
$491$	19.6007	0.884568	0.442284	−	0.896875i	$-0.354168\pi$
$491$	19.6007	0.884568	0.442284	+	0.896875i	$0.354168\pi$
$492$	17.6050	0.793696
$493$	26.1327	1.17696
$494$	0.0284147	0.00127844
$495$	−1.96554	−0.0883445
$496$	−15.8019	−0.709526
$497$	−1.54782	−0.0694290
$498$	−0.00783904	−0.000351276 0
$499$	2.78788	0.124803	0.0624013	−	0.998051i	$-0.480124\pi$
$499$	2.78788	0.124803	0.0624013	+	0.998051i	$0.480124\pi$
$500$	−7.70600	−0.344623
$501$	7.98897	0.356921
$502$	−0.0290845	−0.00129810
$503$	27.2144	1.21343	0.606715	−	0.794920i	$-0.292487\pi$
$503$	27.2144	1.21343	0.606715	+	0.794920i	$0.292487\pi$
$504$	−0.0223970	−0.000997644 0
$505$	−5.13450	−0.228482
$506$	0.0498217	0.00221484
$507$	−8.03008	−0.356628
$508$	−19.2356	−0.853442
$509$	13.0241	0.577284	0.288642	−	0.957437i	$-0.406796\pi$
$509$	13.0241	0.577284	0.288642	+	0.957437i	$0.406796\pi$
$510$	0.00881441	0.000390309 0
$511$	−8.68269	−0.384100
$512$	−0.302987	−0.0133903
$513$	17.1245	0.756067
$514$	0.00490864	0.000216511 0
$515$	1.28404	0.0565817
$516$	17.5571	0.772907
$517$	−2.81336	−0.123731
$518$	0.00625249	0.000274719 0
$519$	−18.1872	−0.798328
$520$	−0.0124376	−0.000545423 0
$521$	7.05570	0.309116	0.154558	−	0.987984i	$-0.450605\pi$
$521$	7.05570	0.309116	0.154558	+	0.987984i	$0.450605\pi$
$522$	0.0330695	0.00144741
$523$	−20.8962	−0.913729	−0.456864	−	0.889536i	$-0.651027\pi$
$523$	−20.8962	−0.913729	−0.456864	+	0.889536i	$0.651027\pi$
$524$	41.9990	1.83474
$525$	−3.14526	−0.137270
$526$	0.0344854	0.00150364
$527$	−25.1581	−1.09590
$528$	−8.81936	−0.383813
$529$	8.04704	0.349871
$530$	−0.00690191	−0.000299800 0
$531$	28.6848	1.24481
$532$	4.96895	0.215431
$533$	−19.7748	−0.856543
$534$	0.0292989	0.00126789
$535$	0.971971	0.0420220
$536$	0.0969270	0.00418661
$537$	10.7536	0.464052
$538$	0.0816880	0.00352182
$539$	15.3860	0.662721
$540$	−3.74783	−0.161281
$541$	18.7471	0.806000	0.403000	−	0.915200i	$-0.367968\pi$
$541$	18.7471	0.806000	0.403000	+	0.915200i	$0.367968\pi$
$542$	−0.0146790	−0.000630517 0
$543$	−5.84669	−0.250905
$544$	−0.289430	−0.0124092
$545$	−4.79727	−0.205493
$546$	−0.00515664	−0.000220684 0
$547$	11.3694	0.486121	0.243060	−	0.970011i	$-0.421849\pi$
$547$	11.3694	0.486121	0.243060	+	0.970011i	$0.421849\pi$
$548$	−9.27363	−0.396150
$549$	14.4353	0.616084
$550$	−0.0433382	−0.00184795
$551$	−14.6735	−0.625111
$552$	0.0788387	0.00335560
$553$	9.33741	0.397067
$554$	0.0323267	0.00137343
$555$	0.868292	0.0368569
$556$	−9.41165	−0.399143
$557$	−24.8715	−1.05384	−0.526920	−	0.849915i	$-0.676653\pi$
$557$	−24.8715	−1.05384	−0.526920	+	0.849915i	$0.676653\pi$
$558$	−0.0318363	−0.00134774
$559$	−19.7209	−0.834107
$560$	−1.08748	−0.0459545
$561$	−14.0412	−0.592822
$562$	0.00921425	0.000388680 0
$563$	4.15891	0.175277	0.0876385	−	0.996152i	$-0.472068\pi$
$563$	4.15891	0.175277	0.0876385	+	0.996152i	$0.472068\pi$
$564$	−2.22595	−0.0937293
$565$	3.25993	0.137146
$566$	0.0994244	0.00417912
$567$	1.32741	0.0557459
$568$	−0.0337486	−0.00141606
$569$	−13.6274	−0.571290	−0.285645	−	0.958336i	$-0.592208\pi$
$569$	−13.6274	−0.571290	−0.285645	+	0.958336i	$0.592208\pi$
$570$	−0.00494929	−0.000207303 0
$571$	−8.44039	−0.353219	−0.176610	−	0.984281i	$-0.556513\pi$
$571$	−8.44039	−0.353219	−0.176610	+	0.984281i	$0.556513\pi$
$572$	9.90640	0.414207
$573$	−11.6561	−0.486942
$574$	0.0248028	0.00103525
$575$	−27.0068	−1.12626
$576$	17.0211	0.709214
$577$	38.9986	1.62353	0.811767	−	0.583982i	$-0.198506\pi$
$577$	38.9986	1.62353	0.811767	+	0.583982i	$0.198506\pi$
$578$	−0.0892113	−0.00371070
$579$	2.19951	0.0914085
$580$	3.21140	0.133346
$581$	1.53979	0.0638811
$582$	0.00840231	0.000348287 0
$583$	10.9947	0.455352
$584$	−0.189317	−0.00783401
$585$	1.74682	0.0722220
$586$	−0.0719363	−0.00297166
$587$	10.8086	0.446118	0.223059	−	0.974805i	$-0.428396\pi$
$587$	10.8086	0.446118	0.223059	+	0.974805i	$0.428396\pi$
$588$	12.1735	0.502026
$589$	14.1263	0.582063
$590$	−0.0199794	−0.000822541 0
$591$	−7.59037	−0.312226
$592$	−9.50362	−0.390596
$593$	17.1302	0.703455	0.351727	−	0.936103i	$-0.385594\pi$
$593$	17.1302	0.703455	0.351727	+	0.936103i	$0.385594\pi$
$594$	−0.0428211	−0.00175697
$595$	−1.73137	−0.0709794
$596$	14.1326	0.578894
$597$	5.87536	0.240462
$598$	−0.0442776	−0.00181064
$599$	6.16279	0.251805	0.125902	−	0.992043i	$-0.459817\pi$
$599$	6.16279	0.251805	0.125902	+	0.992043i	$0.459817\pi$
$600$	−0.0685792	−0.00279974
$601$	19.7337	0.804954	0.402477	−	0.915430i	$-0.368149\pi$
$601$	19.7337	0.804954	0.402477	+	0.915430i	$0.368149\pi$
$602$	0.0247352	0.00100813
$603$	−13.6131	−0.554368
$604$	−23.0394	−0.937462
$605$	2.12338	0.0863276
$606$	−0.0464158	−0.00188551
$607$	2.67674	0.108646	0.0543228	−	0.998523i	$-0.482700\pi$
$607$	2.67674	0.108646	0.0543228	+	0.998523i	$0.482700\pi$
$608$	0.162515	0.00659084
$609$	2.66291	0.107907
$610$	−0.0100544	−0.000407093 0
$611$	2.50029	0.101151
$612$	27.0996	1.09544
$613$	29.6776	1.19867	0.599333	−	0.800500i	$-0.295433\pi$
$613$	29.6776	1.19867	0.599333	+	0.800500i	$0.295433\pi$
$614$	−0.0958274	−0.00386728
$615$	3.44440	0.138891
$616$	−0.0248505	−0.00100126
$617$	−6.41351	−0.258198	−0.129099	−	0.991632i	$-0.541209\pi$
$617$	−6.41351	−0.258198	−0.129099	+	0.991632i	$0.541209\pi$
$618$	0.0116077	0.000466931 0
$619$	−16.4429	−0.660897	−0.330448	−	0.943824i	$-0.607200\pi$
$619$	−16.4429	−0.660897	−0.330448	+	0.943824i	$0.607200\pi$
$620$	−3.09164	−0.124163
$621$	−26.6846	−1.07081
$622$	0.0916609	0.00367527
$623$	−5.75505	−0.230571
$624$	7.83795	0.313769
$625$	22.7268	0.909071
$626$	−0.00228179	−9.11985e−5 0
$627$	7.88416	0.314863
$628$	−6.15578	−0.245642
$629$	−15.1307	−0.603299
$630$	−0.00219096	−8.72901e−5 0
$631$	11.0395	0.439476	0.219738	−	0.975559i	$-0.429480\pi$
$631$	11.0395	0.439476	0.219738	+	0.975559i	$0.429480\pi$
$632$	0.203593	0.00809849
$633$	8.40442	0.334046
$634$	−0.119361	−0.00474043
$635$	−3.76342	−0.149347
$636$	8.69904	0.344939
$637$	−13.6738	−0.541777
$638$	0.0366921	0.00145265
$639$	4.73988	0.187507
$640$	−0.0474233	−0.00187457
$641$	−41.3434	−1.63297	−0.816484	−	0.577368i	$-0.804080\pi$
$641$	−41.3434	−1.63297	−0.816484	+	0.577368i	$0.804080\pi$
$642$	0.00878661	0.000346780 0
$643$	−32.5703	−1.28445	−0.642224	−	0.766517i	$-0.721988\pi$
$643$	−32.5703	−1.28445	−0.642224	+	0.766517i	$0.721988\pi$
$644$	−7.74293	−0.305114
$645$	3.43501	0.135253
$646$	0.0862452	0.00339327
$647$	−3.64127	−0.143153	−0.0715765	−	0.997435i	$-0.522803\pi$
$647$	−3.64127	−0.143153	−0.0715765	+	0.997435i	$0.522803\pi$
$648$	0.0289428	0.00113698
$649$	31.8270	1.24932
$650$	0.0385156	0.00151071
$651$	−2.56361	−0.100476
$652$	23.9520	0.938031
$653$	−21.5380	−0.842847	−0.421423	−	0.906864i	$-0.638469\pi$
$653$	−21.5380	−0.842847	−0.421423	+	0.906864i	$0.638469\pi$
$654$	−0.0433673	−0.00169580
$655$	8.21704	0.321066
$656$	−37.6996	−1.47192
$657$	26.5891	1.03734
$658$	−0.00313602	−0.000122255 0
$659$	−0.349854	−0.0136284	−0.00681418	−	0.999977i	$-0.502169\pi$
$659$	−0.349854	−0.0136284	−0.00681418	+	0.999977i	$0.502169\pi$
$660$	−1.72550	−0.0671652
$661$	−29.4855	−1.14685	−0.573426	−	0.819257i	$-0.694386\pi$
$661$	−29.4855	−1.14685	−0.573426	+	0.819257i	$0.694386\pi$
$662$	−0.0430046	−0.00167142
$663$	12.4788	0.484635
$664$	0.0335735	0.00130290
$665$	0.972166	0.0376990
$666$	−0.0191471	−0.000741933 0
$667$	22.8652	0.885342
$668$	−17.1077	−0.661919
$669$	−7.39868	−0.286049
$670$	0.00948177	0.000366313 0
$671$	16.0166	0.618314
$672$	−0.0294928	−0.00113771
$673$	35.8685	1.38263	0.691314	−	0.722555i	$-0.257032\pi$
$673$	35.8685	1.38263	0.691314	+	0.722555i	$0.257032\pi$
$674$	−0.0804018	−0.00309696
$675$	23.2120	0.893431
$676$	17.1958	0.661377
$677$	11.6486	0.447692	0.223846	−	0.974625i	$-0.428139\pi$
$677$	11.6486	0.447692	0.223846	+	0.974625i	$0.428139\pi$
$678$	0.0294697	0.00113178
$679$	−1.65043	−0.0633375
$680$	−0.0377509	−0.00144768
$681$	−18.3631	−0.703675
$682$	−0.0353237	−0.00135262
$683$	−5.85285	−0.223953	−0.111976	−	0.993711i	$-0.535718\pi$
$683$	−5.85285	−0.223953	−0.111976	+	0.993711i	$0.535718\pi$
$684$	−15.2164	−0.581815
$685$	−1.81437	−0.0693235
$686$	0.0355716	0.00135813
$687$	7.76774	0.296358
$688$	−37.5968	−1.43337
$689$	−9.77118	−0.372252
$690$	0.00771230	0.000293602 0
$691$	43.1525	1.64160	0.820799	−	0.571218i	$-0.193529\pi$
$691$	43.1525	1.64160	0.820799	+	0.571218i	$0.193529\pi$
$692$	38.9464	1.48052
$693$	3.49018	0.132581
$694$	0.00160549	6.09435e−5 0
$695$	−1.84137	−0.0698473
$696$	0.0580622	0.00220084
$697$	−60.0212	−2.27347
$698$	−0.0268128	−0.00101488
$699$	8.04506	0.304292
$700$	6.73532	0.254571
$701$	−29.4754	−1.11327	−0.556635	−	0.830757i	$-0.687908\pi$
$701$	−29.4754	−1.11327	−0.556635	+	0.830757i	$0.687908\pi$
$702$	0.0380560	0.00143633
$703$	8.49586	0.320427
$704$	18.8857	0.711781
$705$	−0.435503	−0.0164020
$706$	0.0523253	0.00196929
$707$	9.11725	0.342889
$708$	25.1817	0.946387
$709$	22.2729	0.836475	0.418237	−	0.908338i	$-0.362648\pi$
$709$	22.2729	0.836475	0.418237	+	0.908338i	$0.362648\pi$
$710$	−0.00330141	−0.000123900 0
$711$	−28.5940	−1.07236
$712$	−0.125483	−0.00470268
$713$	−22.0125	−0.824373
$714$	−0.0156516	−0.000585747 0
$715$	1.93817	0.0724834
$716$	−23.0280	−0.860596
$717$	17.0038	0.635019
$718$	−0.00194898	−7.27352e−5 0
$719$	−11.1810	−0.416983	−0.208491	−	0.978024i	$-0.566855\pi$
$719$	−11.1810	−0.416983	−0.208491	+	0.978024i	$0.566855\pi$
$720$	3.33020	0.124109
$721$	−2.28005	−0.0849136
$722$	0.0235348	0.000875876 0
$723$	21.7896	0.810365
$724$	12.5202	0.465311
$725$	−19.8897	−0.738683
$726$	0.0191953	0.000712406 0
$727$	20.3271	0.753890	0.376945	−	0.926236i	$-0.376974\pi$
$727$	20.3271	0.753890	0.376945	+	0.926236i	$0.376974\pi$
$728$	0.0220852	0.000818530 0
$729$	9.35332	0.346419
$730$	−0.0185198	−0.000685447 0
$731$	−59.8577	−2.21392
$732$	12.6724	0.468387
$733$	14.2356	0.525803	0.262902	−	0.964823i	$-0.415320\pi$
$733$	14.2356	0.525803	0.262902	+	0.964823i	$0.415320\pi$
$734$	0.0415861	0.00153497
$735$	2.38172	0.0878511
$736$	−0.253241	−0.00933458
$737$	−15.1043	−0.556375
$738$	−0.0759538	−0.00279590
$739$	40.2446	1.48042	0.740211	−	0.672374i	$-0.234726\pi$
$739$	40.2446	1.48042	0.740211	+	0.672374i	$0.234726\pi$
$740$	−1.85938	−0.0683522
$741$	−7.00682	−0.257402
$742$	0.0122556	0.000449918 0
$743$	33.5371	1.23036	0.615179	−	0.788387i	$-0.289084\pi$
$743$	33.5371	1.23036	0.615179	+	0.788387i	$0.289084\pi$
$744$	−0.0558969	−0.00204928
$745$	2.76502	0.101303
$746$	0.144784	0.00530093
$747$	−4.71530	−0.172524
$748$	30.0682	1.09940
$749$	−1.72591	−0.0630635
$750$	−0.0136293	−0.000497671 0
$751$	37.5102	1.36877	0.684383	−	0.729122i	$-0.260072\pi$
$751$	37.5102	1.36877	0.684383	+	0.729122i	$0.260072\pi$
$752$	4.76666	0.173822
$753$	7.17199	0.261362
$754$	−0.0326090	−0.00118755
$755$	−4.50763	−0.164049
$756$	6.65496	0.242039
$757$	−48.8186	−1.77434	−0.887172	−	0.461440i	$-0.847333\pi$
$757$	−48.8186	−1.77434	−0.887172	+	0.461440i	$0.847333\pi$
$758$	0.0552439	0.00200655
$759$	−12.2856	−0.445939
$760$	0.0211971	0.000768900 0
$761$	−42.3833	−1.53639	−0.768197	−	0.640214i	$-0.778846\pi$
$761$	−42.3833	−1.53639	−0.768197	+	0.640214i	$0.778846\pi$
$762$	−0.0340212	−0.00123246
$763$	8.51844	0.308388
$764$	24.9607	0.903046
$765$	5.30200	0.191694
$766$	−0.0175121	−0.000632740 0
$767$	−28.2853	−1.02132
$768$	14.9422	0.539179
$769$	18.1864	0.655819	0.327909	−	0.944709i	$-0.393656\pi$
$769$	18.1864	0.655819	0.327909	+	0.944709i	$0.393656\pi$
$770$	−0.00243097	−8.76061e−5 0
$771$	−1.21043	−0.0435925
$772$	−4.71008	−0.169519
$773$	−28.2688	−1.01676	−0.508380	−	0.861133i	$-0.669755\pi$
$773$	−28.2688	−1.01676	−0.508380	+	0.861133i	$0.669755\pi$
$774$	−0.0757468	−0.00272266
$775$	19.1479	0.687813
$776$	−0.0359859	−0.00129182
$777$	−1.54181	−0.0553122
$778$	0.0952527	0.00341498
$779$	33.7019	1.20750
$780$	1.53349	0.0549078
$781$	5.25911	0.188186
$782$	−0.134393	−0.00480588
$783$	−19.6523	−0.702317
$784$	−26.0684	−0.931013
$785$	−1.20437	−0.0429857
$786$	0.0742820	0.00264955
$787$	32.7750	1.16830	0.584152	−	0.811644i	$-0.301427\pi$
$787$	32.7750	1.16830	0.584152	+	0.811644i	$0.301427\pi$
$788$	16.2542	0.579032
$789$	−8.50381	−0.302744
$790$	0.0199162	0.000708588 0
$791$	−5.78860	−0.205819
$792$	0.0760999	0.00270409
$793$	−14.2343	−0.505474
$794$	0.00538470	0.000191096 0
$795$	1.70195	0.0603620
$796$	−12.5816	−0.445944
$797$	−16.0719	−0.569294	−0.284647	−	0.958632i	$-0.591876\pi$
$797$	−16.0719	−0.569294	−0.284647	+	0.958632i	$0.591876\pi$
$798$	0.00878837	0.000311105 0
$799$	7.58897	0.268479
$800$	0.220286	0.00778828
$801$	17.6237	0.622704
$802$	−0.0825602	−0.00291530
$803$	29.5017	1.04109
$804$	−11.9506	−0.421467
$805$	−1.51489	−0.0533929
$806$	0.0313929	0.00110577
$807$	−20.1436	−0.709087
$808$	0.198793	0.00699350
$809$	−51.6220	−1.81493	−0.907467	−	0.420123i	$-0.861987\pi$
$809$	−51.6220	−1.81493	−0.907467	+	0.420123i	$0.861987\pi$
$810$	0.00283130	9.94816e−5 0
$811$	−32.3448	−1.13578	−0.567890	−	0.823104i	$-0.692240\pi$
$811$	−32.3448	−1.13578	−0.567890	+	0.823104i	$0.692240\pi$
$812$	−5.70242	−0.200116
$813$	3.61972	0.126949
$814$	−0.0212445	−0.000744619 0
$815$	4.68616	0.164149
$816$	23.7900	0.832817
$817$	33.6101	1.17587
$818$	0.0214400	0.000749632 0
$819$	−3.10179	−0.108385
$820$	−7.37591	−0.257578
$821$	19.5142	0.681050	0.340525	−	0.940235i	$-0.389395\pi$
$821$	19.5142	0.681050	0.340525	+	0.940235i	$0.389395\pi$
$822$	−0.0164019	−0.000572082 0
$823$	−34.9384	−1.21788	−0.608938	−	0.793218i	$-0.708404\pi$
$823$	−34.9384	−1.21788	−0.608938	+	0.793218i	$0.708404\pi$
$824$	−0.0497143	−0.00173188
$825$	10.6868	0.372068
$826$	0.0354772	0.00123441
$827$	33.4982	1.16485	0.582423	−	0.812886i	$-0.302105\pi$
$827$	33.4982	1.16485	0.582423	+	0.812886i	$0.302105\pi$
$828$	23.7112	0.824022
$829$	50.3308	1.74806	0.874031	−	0.485870i	$-0.161497\pi$
$829$	50.3308	1.74806	0.874031	+	0.485870i	$0.161497\pi$
$830$	0.00328429	0.000113999 0
$831$	−7.97149	−0.276528
$832$	−16.7841	−0.581884
$833$	−41.5033	−1.43800
$834$	−0.0166460	−0.000576404 0
$835$	−3.34710	−0.115831
$836$	−16.8833	−0.583921
$837$	18.9194	0.653952
$838$	0.0175260	0.000605425 0
$839$	−15.6729	−0.541089	−0.270544	−	0.962708i	$-0.587204\pi$
$839$	−15.6729	−0.541089	−0.270544	+	0.962708i	$0.587204\pi$
$840$	−0.00384681	−0.000132728 0
$841$	−12.1605	−0.419329
$842$	−0.0790900	−0.00272562
$843$	−2.27216	−0.0782572
$844$	−17.9974	−0.619496
$845$	3.36433	0.115736
$846$	0.00960345	0.000330173 0
$847$	−3.77045	−0.129554
$848$	−18.6282	−0.639695
$849$	−24.5172	−0.841428
$850$	0.116904	0.00400977
$851$	−13.2388	−0.453820
$852$	4.16104	0.142555
$853$	−25.7139	−0.880427	−0.440214	−	0.897893i	$-0.645097\pi$
$853$	−25.7139	−0.880427	−0.440214	+	0.897893i	$0.645097\pi$
$854$	0.0178535	0.000610935 0
$855$	−2.97707	−0.101814
$856$	−0.0376318	−0.00128623
$857$	−4.24618	−0.145047	−0.0725234	−	0.997367i	$-0.523105\pi$
$857$	−4.24618	−0.145047	−0.0725234	+	0.997367i	$0.523105\pi$
$858$	0.0175210	0.000598158 0
$859$	0.0793334	0.00270682	0.00135341	−	0.999999i	$-0.499569\pi$
$859$	0.0793334	0.00270682	0.00135341	+	0.999999i	$0.499569\pi$
$860$	−7.35581	−0.250831
$861$	−6.11616	−0.208438
$862$	−0.0151822	−0.000517106 0
$863$	34.9838	1.19086	0.595432	−	0.803406i	$-0.296981\pi$
$863$	34.9838	1.19086	0.595432	+	0.803406i	$0.296981\pi$
$864$	0.217657	0.00740486
$865$	7.61979	0.259081
$866$	0.00478662	0.000162656 0
$867$	21.9988	0.747117
$868$	5.48976	0.186335
$869$	−31.7263	−1.07624
$870$	0.00567987	0.000192565 0
$871$	13.4235	0.454839
$872$	0.185736	0.00628982
$873$	5.05411	0.171056
$874$	0.0754615	0.00255252
$875$	2.67714	0.0905037
$876$	23.3420	0.788652
$877$	5.32883	0.179942	0.0899709	−	0.995944i	$-0.471323\pi$
$877$	5.32883	0.179942	0.0899709	+	0.995944i	$0.471323\pi$
$878$	−0.0335316	−0.00113164
$879$	17.7389	0.598318
$880$	3.69501	0.124559
$881$	4.74910	0.160001	0.0800007	−	0.996795i	$-0.474508\pi$
$881$	4.74910	0.160001	0.0800007	+	0.996795i	$0.474508\pi$
$882$	−0.0525203	−0.00176845
$883$	−31.6012	−1.06347	−0.531733	−	0.846912i	$-0.678459\pi$
$883$	−31.6012	−1.06347	−0.531733	+	0.846912i	$0.678459\pi$
$884$	−26.7223	−0.898767
$885$	4.92676	0.165611
$886$	0.0902661	0.00303255
$887$	−49.9219	−1.67622	−0.838108	−	0.545505i	$-0.816338\pi$
$887$	−49.9219	−1.67622	−0.838108	+	0.545505i	$0.816338\pi$
$888$	−0.0336177	−0.00112814
$889$	6.68263	0.224128
$890$	−0.0122752	−0.000411467 0
$891$	−4.51022	−0.151098
$892$	15.8437	0.530486
$893$	−4.26121	−0.142596
$894$	0.0249958	0.000835984 0
$895$	−4.50539	−0.150598
$896$	0.0842087	0.00281322
$897$	10.9185	0.364557
$898$	0.0866110	0.00289025
$899$	−16.2115	−0.540683
$900$	−20.6256	−0.687521
$901$	−29.6578	−0.988046
$902$	−0.0842740	−0.00280602
$903$	−6.09949	−0.202978
$904$	−0.126215	−0.00419784
$905$	2.44956	0.0814262
$906$	−0.0407489	−0.00135379
$907$	2.96367	0.0984071	0.0492035	−	0.998789i	$-0.484332\pi$
$907$	2.96367	0.0984071	0.0492035	+	0.998789i	$0.484332\pi$
$908$	39.3231	1.30498
$909$	−27.9198	−0.926042
$910$	0.00216045	7.16184e−5 0
$911$	−36.2836	−1.20213	−0.601065	−	0.799200i	$-0.705257\pi$
$911$	−36.2836	−1.20213	−0.601065	+	0.799200i	$0.705257\pi$
$912$	−13.3581	−0.442330
$913$	−5.23183	−0.173148
$914$	0.127007	0.00420100
$915$	2.47934	0.0819645
$916$	−16.6340	−0.549603
$917$	−14.5909	−0.481833
$918$	0.115509	0.00381237
$919$	−2.26107	−0.0745857	−0.0372928	−	0.999304i	$-0.511873\pi$
$919$	−2.26107	−0.0745857	−0.0372928	+	0.999304i	$0.511873\pi$
$920$	−0.0330307	−0.00108899
$921$	23.6302	0.778642
$922$	−0.0908123	−0.00299074
$923$	−4.67388	−0.153843
$924$	3.06395	0.100797
$925$	11.5160	0.378643
$926$	−0.0651753	−0.00214179
$927$	6.98222	0.229326
$928$	−0.186504	−0.00612229
$929$	−18.3382	−0.601658	−0.300829	−	0.953678i	$-0.597263\pi$
$929$	−18.3382	−0.601658	−0.300829	+	0.953678i	$0.597263\pi$
$930$	−0.00546805	−0.000179304 0
$931$	23.3041	0.763761
$932$	−17.2279	−0.564317
$933$	−22.6028	−0.739982
$934$	0.110009	0.00359960
$935$	5.88280	0.192388
$936$	−0.0676315	−0.00221061
$937$	20.1379	0.657876	0.328938	−	0.944352i	$-0.393309\pi$
$937$	20.1379	0.657876	0.328938	+	0.944352i	$0.393309\pi$
$938$	−0.0168366	−0.000549735 0
$939$	0.562669	0.0183620
$940$	0.932596	0.0304179
$941$	−23.1576	−0.754915	−0.377457	−	0.926027i	$-0.623202\pi$
$941$	−23.1576	−0.754915	−0.377457	+	0.926027i	$0.623202\pi$
$942$	−0.0108875	−0.000354733 0
$943$	−52.5165	−1.71017
$944$	−53.9243	−1.75509
$945$	1.30203	0.0423551
$946$	−0.0840444	−0.00273252
$947$	−19.1799	−0.623262	−0.311631	−	0.950203i	$-0.600875\pi$
$947$	−19.1799	−0.623262	−0.311631	+	0.950203i	$0.600875\pi$
$948$	−25.1021	−0.815277
$949$	−26.2188	−0.851099
$950$	−0.0656415	−0.00212969
$951$	29.4334	0.954443
$952$	0.0670337	0.00217257
$953$	17.0370	0.551883	0.275942	−	0.961174i	$-0.411010\pi$
$953$	17.0370	0.551883	0.275942	+	0.961174i	$0.411010\pi$
$954$	−0.0375304	−0.00121509
$955$	4.88352	0.158027
$956$	−36.4124	−1.17766
$957$	−9.04795	−0.292479
$958$	−0.153229	−0.00495061
$959$	3.22175	0.104036
$960$	2.92347	0.0943546
$961$	−15.3931	−0.496552
$962$	0.0188804	0.000608729 0
$963$	5.28528	0.170316
$964$	−46.6608	−1.50284
$965$	−0.921519	−0.0296647
$966$	−0.0136946	−0.000440617 0
$967$	48.9019	1.57258	0.786289	−	0.617859i	$-0.212000\pi$
$967$	48.9019	1.57258	0.786289	+	0.617859i	$0.212000\pi$
$968$	−0.0822109	−0.00264236
$969$	−21.2673	−0.683205
$970$	−0.00352028	−0.000113029 0
$971$	−56.4444	−1.81139	−0.905694	−	0.423933i	$-0.860649\pi$
$971$	−56.4444	−1.81139	−0.905694	+	0.423933i	$0.860649\pi$
$972$	−32.3027	−1.03611
$973$	3.26970	0.104822
$974$	−0.0561103	−0.00179789
$975$	−9.49762	−0.304167
$976$	−27.1368	−0.868629
$977$	−36.4401	−1.16582	−0.582911	−	0.812536i	$-0.698086\pi$
$977$	−36.4401	−1.16582	−0.582911	+	0.812536i	$0.698086\pi$
$978$	0.0423628	0.00135461
$979$	19.5543	0.624958
$980$	−5.10027	−0.162922
$981$	−26.0861	−0.832864
$982$	−0.0742367	−0.00236899
$983$	6.38184	0.203549	0.101775	−	0.994807i	$-0.467548\pi$
$983$	6.38184	0.203549	0.101775	+	0.994807i	$0.467548\pi$
$984$	−0.133357	−0.00425126
$985$	3.18010	0.101327
$986$	−0.0989760	−0.00315204
$987$	0.773315	0.0246149
$988$	15.0045	0.477358
$989$	−52.3734	−1.66538
$990$	0.00744438	0.000236598 0
$991$	27.2317	0.865044	0.432522	−	0.901623i	$-0.357624\pi$
$991$	27.2317	0.865044	0.432522	+	0.901623i	$0.357624\pi$
$992$	0.179549	0.00570067
$993$	10.6046	0.336526
$994$	0.00586227	0.000185940 0
$995$	−2.46157	−0.0780371
$996$	−4.13946	−0.131164
$997$	−1.18939	−0.0376685	−0.0188342	−	0.999823i	$-0.505995\pi$
$997$	−1.18939	−0.0376685	−0.0188342	+	0.999823i	$0.505995\pi$
$998$	−0.0105589	−0.000334237 0
$999$	11.3786	0.360002

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.a.1.41	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.a.1.41	✓	77	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:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q-0.00378745 q^{2} +0.933952 q^{3} -1.99999 q^{4} -0.391294 q^{5} -0.00353729 q^{6} +0.694814 q^{7} +0.0151497 q^{8} -2.12773 q^{9} +O(q^{10})\)	\(q-0.00378745 q^{2} +0.933952 q^{3} -1.99999 q^{4} -0.391294 q^{5} -0.00353729 q^{6} +0.694814 q^{7} +0.0151497 q^{8} -2.12773 q^{9} +0.00148200 q^{10} -2.36081 q^{11} -1.86789 q^{12} +2.09810 q^{13} -0.00263157 q^{14} -0.365450 q^{15} +3.99991 q^{16} +6.36824 q^{17} +0.00805868 q^{18} -3.57576 q^{19} +0.782582 q^{20} +0.648923 q^{21} +0.00894145 q^{22} +5.57199 q^{23} +0.0141491 q^{24} -4.84689 q^{25} -0.00794646 q^{26} -4.78906 q^{27} -1.38962 q^{28} +4.10359 q^{29} +0.00138412 q^{30} -3.95056 q^{31} -0.0454489 q^{32} -2.20489 q^{33} -0.0241194 q^{34} -0.271876 q^{35} +4.25544 q^{36} -2.37596 q^{37} +0.0135430 q^{38} +1.95953 q^{39} -0.00592800 q^{40} -9.42509 q^{41} -0.00245776 q^{42} -9.39941 q^{43} +4.72159 q^{44} +0.832569 q^{45} -0.0211036 q^{46} +1.19169 q^{47} +3.73573 q^{48} -6.51723 q^{49} +0.0183573 q^{50} +5.94763 q^{51} -4.19618 q^{52} -4.65715 q^{53} +0.0181383 q^{54} +0.923772 q^{55} +0.0105262 q^{56} -3.33959 q^{57} -0.0155421 q^{58} -13.4814 q^{59} +0.730894 q^{60} -6.78436 q^{61} +0.0149625 q^{62} -1.47838 q^{63} -7.99966 q^{64} -0.820975 q^{65} +0.00835089 q^{66} +6.39793 q^{67} -12.7364 q^{68} +5.20397 q^{69} +0.00102972 q^{70} -2.22767 q^{71} -0.0322346 q^{72} -12.4964 q^{73} +0.00899880 q^{74} -4.52676 q^{75} +7.15148 q^{76} -1.64033 q^{77} -0.00742161 q^{78} +13.4387 q^{79} -1.56514 q^{80} +1.91045 q^{81} +0.0356970 q^{82} +2.21611 q^{83} -1.29784 q^{84} -2.49185 q^{85} +0.0355997 q^{86} +3.83256 q^{87} -0.0357657 q^{88} -8.28286 q^{89} -0.00315331 q^{90} +1.45779 q^{91} -11.1439 q^{92} -3.68963 q^{93} -0.00451346 q^{94} +1.39917 q^{95} -0.0424471 q^{96} -2.37535 q^{97} +0.0246837 q^{98} +5.02318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9}+O(q^{10}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9} - 21 q^{10} - 34 q^{11} - 36 q^{12} - 34 q^{13} - 49 q^{14} - 12 q^{15} + 47 q^{16} - 59 q^{17} - 24 q^{18} - 31 q^{19} - 82 q^{20} - 71 q^{21} - 3 q^{22} - 28 q^{23} - 50 q^{24} + 68 q^{25} - 54 q^{26} - 43 q^{27} - 2 q^{28} - 151 q^{29} + q^{30} - 37 q^{31} - 59 q^{32} - 35 q^{33} - q^{34} - 58 q^{35} + 19 q^{36} - 29 q^{37} - 22 q^{38} - 40 q^{39} - 41 q^{40} - 142 q^{41} + 16 q^{42} - 23 q^{43} - 89 q^{44} - 119 q^{45} - 6 q^{46} - 36 q^{47} - 46 q^{48} + 45 q^{49} - 29 q^{50} - 53 q^{51} - 11 q^{52} - 69 q^{53} - 50 q^{54} - 13 q^{55} - 122 q^{56} - 14 q^{57} + 31 q^{58} - 92 q^{59} + 20 q^{60} - 115 q^{61} - 66 q^{62} - 25 q^{63} + 37 q^{64} - 57 q^{65} - 17 q^{66} - 108 q^{68} - 160 q^{69} + 40 q^{70} - 67 q^{71} - 35 q^{72} - 36 q^{73} - 55 q^{74} - 51 q^{75} - 56 q^{76} - 116 q^{77} + 22 q^{78} - 42 q^{79} - 114 q^{80} + 37 q^{81} + 18 q^{82} - 42 q^{83} - 77 q^{84} - 18 q^{85} - 33 q^{86} - 7 q^{87} - 2 q^{88} - 93 q^{89} - 34 q^{90} - 37 q^{91} - 55 q^{92} - 8 q^{93} - 35 q^{94} - 64 q^{95} - 83 q^{96} - 16 q^{97} - 57 q^{98} - 65 q^{99}+O(q^{100}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9 - 21 * q^10 - 34 * q^11 - 36 * q^12 - 34 * q^13 - 49 * q^14 - 12 * q^15 + 47 * q^16 - 59 * q^17 - 24 * q^18 - 31 * q^19 - 82 * q^20 - 71 * q^21 - 3 * q^22 - 28 * q^23 - 50 * q^24 + 68 * q^25 - 54 * q^26 - 43 * q^27 - 2 * q^28 - 151 * q^29 + q^30 - 37 * q^31 - 59 * q^32 - 35 * q^33 - q^34 - 58 * q^35 + 19 * q^36 - 29 * q^37 - 22 * q^38 - 40 * q^39 - 41 * q^40 - 142 * q^41 + 16 * q^42 - 23 * q^43 - 89 * q^44 - 119 * q^45 - 6 * q^46 - 36 * q^47 - 46 * q^48 + 45 * q^49 - 29 * q^50 - 53 * q^51 - 11 * q^52 - 69 * q^53 - 50 * q^54 - 13 * q^55 - 122 * q^56 - 14 * q^57 + 31 * q^58 - 92 * q^59 + 20 * q^60 - 115 * q^61 - 66 * q^62 - 25 * q^63 + 37 * q^64 - 57 * q^65 - 17 * q^66 - 108 * q^68 - 160 * q^69 + 40 * q^70 - 67 * q^71 - 35 * q^72 - 36 * q^73 - 55 * q^74 - 51 * q^75 - 56 * q^76 - 116 * q^77 + 22 * q^78 - 42 * q^79 - 114 * q^80 + 37 * q^81 + 18 * q^82 - 42 * q^83 - 77 * q^84 - 18 * q^85 - 33 * q^86 - 7 * q^87 - 2 * q^88 - 93 * q^89 - 34 * q^90 - 37 * q^91 - 55 * q^92 - 8 * q^93 - 35 * q^94 - 64 * q^95 - 83 * q^96 - 16 * q^97 - 57 * q^98 - 65 * q^99

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