LMFDB - Embedded newform 1849.2.a.r.1.8

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 19 x^{18} + 127 x^{17} + 95 x^{16} - 1293 x^{15} + 329 x^{14} + 6765 x^{13} + \cdots - 43 $ x^20 - 5x^19 - 19x^18 + 127x^17 + 95x^16 - 1293x^15 + 329x^14 + 6765x^13 - 5068x^12 - 19360x^11 + 20357x^10 + 29618x^9 - 37889x^8 - 21700x^7 + 32885x^6 + 6093x^5 - 11330x^4 - 1004x^3 + 1386x^2 + 87*x - 43
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.369089$ 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)

$f(q)$	$=$	$q-0.369089 q^{2} +0.00229289 q^{3} -1.86377 q^{4} -2.37597 q^{5} -0.000846282 q^{6} +4.42543 q^{7} +1.42608 q^{8} -2.99999 q^{9} +O(q^{10})$	\(q-0.369089 q^{2} +0.00229289 q^{3} -1.86377 q^{4} -2.37597 q^{5} -0.000846282 q^{6} +4.42543 q^{7} +1.42608 q^{8} -2.99999 q^{9} +0.876946 q^{10} +4.37936 q^{11} -0.00427343 q^{12} -4.15041 q^{13} -1.63338 q^{14} -0.00544785 q^{15} +3.20120 q^{16} +2.13613 q^{17} +1.10727 q^{18} -1.88247 q^{19} +4.42827 q^{20} +0.0101470 q^{21} -1.61638 q^{22} -1.32561 q^{23} +0.00326984 q^{24} +0.645237 q^{25} +1.53187 q^{26} -0.0137573 q^{27} -8.24800 q^{28} -7.49941 q^{29} +0.00201074 q^{30} +2.12424 q^{31} -4.03368 q^{32} +0.0100414 q^{33} -0.788425 q^{34} -10.5147 q^{35} +5.59131 q^{36} -2.46588 q^{37} +0.694800 q^{38} -0.00951645 q^{39} -3.38832 q^{40} +8.51464 q^{41} -0.00374517 q^{42} -8.16214 q^{44} +7.12790 q^{45} +0.489269 q^{46} +8.63973 q^{47} +0.00734000 q^{48} +12.5845 q^{49} -0.238150 q^{50} +0.00489793 q^{51} +7.73543 q^{52} -0.533278 q^{53} +0.00507769 q^{54} -10.4052 q^{55} +6.31101 q^{56} -0.00431630 q^{57} +2.76795 q^{58} +0.466153 q^{59} +0.0101535 q^{60} +8.94115 q^{61} -0.784034 q^{62} -13.2763 q^{63} -4.91360 q^{64} +9.86126 q^{65} -0.00370618 q^{66} +6.26411 q^{67} -3.98127 q^{68} -0.00303948 q^{69} +3.88086 q^{70} +1.94173 q^{71} -4.27822 q^{72} +1.11112 q^{73} +0.910129 q^{74} +0.00147946 q^{75} +3.50850 q^{76} +19.3806 q^{77} +0.00351242 q^{78} +15.8475 q^{79} -7.60595 q^{80} +8.99995 q^{81} -3.14266 q^{82} -12.5731 q^{83} -0.0189118 q^{84} -5.07539 q^{85} -0.0171953 q^{87} +6.24531 q^{88} -4.09850 q^{89} -2.63083 q^{90} -18.3674 q^{91} +2.47064 q^{92} +0.00487065 q^{93} -3.18883 q^{94} +4.47270 q^{95} -0.00924880 q^{96} +0.625574 q^{97} -4.64479 q^{98} -13.1381 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 + 23 * q^4 - 3 * q^5 + 5 * q^6 - 2 * q^7 + 9 * q^8 + 27 * q^9	\( 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9} + 21 q^{11} - 12 q^{12} + 11 q^{13} + 8 q^{14} + 4 q^{15} + 29 q^{16} + 15 q^{17} + 9 q^{18} - 7 q^{19} - 17 q^{20} + 8 q^{21} + 47 q^{22} + 26 q^{23} - q^{24} + 11 q^{25} + 58 q^{26} - 22 q^{27} - 28 q^{28} - 12 q^{29} - 24 q^{30} + 26 q^{31} + 3 q^{32} - 17 q^{33} + 54 q^{34} + 26 q^{35} + 14 q^{36} - 19 q^{37} + 5 q^{38} - 7 q^{39} - 16 q^{40} + 27 q^{41} - 52 q^{42} + 32 q^{44} + 75 q^{45} + 59 q^{46} + 45 q^{47} - 66 q^{48} + 20 q^{49} + 75 q^{51} + 11 q^{52} + 3 q^{53} + 57 q^{54} - 2 q^{55} + 87 q^{56} - 24 q^{57} - 46 q^{58} + 66 q^{59} + 29 q^{60} + 30 q^{61} + 72 q^{62} - 21 q^{63} - 7 q^{64} - 6 q^{65} + 41 q^{66} - 6 q^{67} + 28 q^{68} - 35 q^{69} - 80 q^{70} - 31 q^{71} - 15 q^{72} - 26 q^{73} + 87 q^{74} + 73 q^{75} - 68 q^{76} - 21 q^{77} - 50 q^{78} + 39 q^{79} - 60 q^{80} + 16 q^{81} + 45 q^{82} + 13 q^{83} + 31 q^{84} - 22 q^{85} + 61 q^{87} + 50 q^{88} - 4 q^{89} - 13 q^{90} - 25 q^{91} + 5 q^{92} + 67 q^{93} + 42 q^{94} + 79 q^{95} + 36 q^{96} - 2 q^{97} - 35 q^{98} + 13 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 + 23 * q^4 - 3 * q^5 + 5 * q^6 - 2 * q^7 + 9 * q^8 + 27 * q^9 + 21 * q^11 - 12 * q^12 + 11 * q^13 + 8 * q^14 + 4 * q^15 + 29 * q^16 + 15 * q^17 + 9 * q^18 - 7 * q^19 - 17 * q^20 + 8 * q^21 + 47 * q^22 + 26 * q^23 - q^24 + 11 * q^25 + 58 * q^26 - 22 * q^27 - 28 * q^28 - 12 * q^29 - 24 * q^30 + 26 * q^31 + 3 * q^32 - 17 * q^33 + 54 * q^34 + 26 * q^35 + 14 * q^36 - 19 * q^37 + 5 * q^38 - 7 * q^39 - 16 * q^40 + 27 * q^41 - 52 * q^42 + 32 * q^44 + 75 * q^45 + 59 * q^46 + 45 * q^47 - 66 * q^48 + 20 * q^49 + 75 * q^51 + 11 * q^52 + 3 * q^53 + 57 * q^54 - 2 * q^55 + 87 * q^56 - 24 * q^57 - 46 * q^58 + 66 * q^59 + 29 * q^60 + 30 * q^61 + 72 * q^62 - 21 * q^63 - 7 * q^64 - 6 * q^65 + 41 * q^66 - 6 * q^67 + 28 * q^68 - 35 * q^69 - 80 * q^70 - 31 * q^71 - 15 * q^72 - 26 * q^73 + 87 * q^74 + 73 * q^75 - 68 * q^76 - 21 * q^77 - 50 * q^78 + 39 * q^79 - 60 * q^80 + 16 * q^81 + 45 * q^82 + 13 * q^83 + 31 * q^84 - 22 * q^85 + 61 * q^87 + 50 * q^88 - 4 * q^89 - 13 * q^90 - 25 * q^91 + 5 * q^92 + 67 * q^93 + 42 * q^94 + 79 * q^95 + 36 * q^96 - 2 * q^97 - 35 * q^98 + 13 * 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 $

$2$	−0.369089	−0.260986	−0.130493	−	0.991449i	$-0.541656\pi$
$2$	−0.369089	−0.260986	−0.130493	+	0.991449i	$0.541656\pi$
$3$	0.00229289	0.00132380	0.000661901	−	1.00000i	$-0.499789\pi$
$3$	0.00229289	0.00132380	0.000661901		1.00000i	$0.499789\pi$
$4$	−1.86377	−0.931887
$5$	−2.37597	−1.06257	−0.531283	−	0.847194i	$-0.678290\pi$
$5$	−2.37597	−1.06257	−0.531283	+	0.847194i	$0.678290\pi$
$6$	−0.000846282 0	−0.000345493 0
$7$	4.42543	1.67266	0.836328	−	0.548229i	$-0.184698\pi$
$7$	4.42543	1.67266	0.836328	+	0.548229i	$0.184698\pi$
$8$	1.42608	0.504195
$9$	−2.99999	−0.999998
$10$	0.876946	0.277315
$11$	4.37936	1.32043	0.660214	−	0.751078i	$-0.270466\pi$
$11$	4.37936	1.32043	0.660214	+	0.751078i	$0.270466\pi$
$12$	−0.00427343	−0.00123363
$13$	−4.15041	−1.15112	−0.575559	−	0.817760i	$-0.695215\pi$
$13$	−4.15041	−1.15112	−0.575559	+	0.817760i	$0.695215\pi$
$14$	−1.63338	−0.436539
$15$	−0.00544785	−0.00140663
$16$	3.20120	0.800299
$17$	2.13613	0.518089	0.259044	−	0.965865i	$-0.416592\pi$
$17$	2.13613	0.518089	0.259044	+	0.965865i	$0.416592\pi$
$18$	1.10727	0.260985
$19$	−1.88247	−0.431869	−0.215934	−	0.976408i	$-0.569280\pi$
$19$	−1.88247	−0.431869	−0.215934	+	0.976408i	$0.569280\pi$
$20$	4.42827	0.990191
$21$	0.0101470	0.00221427
$22$	−1.61638	−0.344613
$23$	−1.32561	−0.276409	−0.138204	−	0.990404i	$-0.544133\pi$
$23$	−1.32561	−0.276409	−0.138204	+	0.990404i	$0.544133\pi$
$24$	0.00326984	0.000667454 0
$25$	0.645237	0.129047
$26$	1.53187	0.300425
$27$	−0.0137573	−0.00264760
$28$	−8.24800	−1.55873
$29$	−7.49941	−1.39260	−0.696302	−	0.717749i	$-0.745173\pi$
$29$	−7.49941	−1.39260	−0.696302	+	0.717749i	$0.745173\pi$
$30$	0.00201074	0.000367110 0
$31$	2.12424	0.381525	0.190762	−	0.981636i	$-0.438904\pi$
$31$	2.12424	0.381525	0.190762	+	0.981636i	$0.438904\pi$
$32$	−4.03368	−0.713061
$33$	0.0100414	0.00174798
$34$	−0.788425	−0.135214
$35$	−10.5147	−1.77731
$36$	5.59131	0.931885
$37$	−2.46588	−0.405388	−0.202694	−	0.979242i	$-0.564970\pi$
$37$	−2.46588	−0.405388	−0.202694	+	0.979242i	$0.564970\pi$
$38$	0.694800	0.112711
$39$	−0.00951645	−0.00152385
$40$	−3.38832	−0.535740
$41$	8.51464	1.32976	0.664882	−	0.746949i	$-0.268482\pi$
$41$	8.51464	1.32976	0.664882	+	0.746949i	$0.268482\pi$
$42$	−0.00374517	−0.000577892 0
$43$	0	0
$43$	0	0
$44$	−8.16214	−1.23049
$45$	7.12790	1.06256
$46$	0.489269	0.0721387
$47$	8.63973	1.26023	0.630117	−	0.776500i	$-0.283007\pi$
$47$	8.63973	1.26023	0.630117	+	0.776500i	$0.283007\pi$
$48$	0.00734000	0.00105944
$49$	12.5845	1.79778
$50$	−0.238150	−0.0336795
$51$	0.00489793	0.000685847 0
$52$	7.73543	1.07271
$53$	−0.533278	−0.0732514	−0.0366257	−	0.999329i	$-0.511661\pi$
$53$	−0.533278	−0.0732514	−0.0366257	+	0.999329i	$0.511661\pi$
$54$	0.00507769	0.000690986 0
$55$	−10.4052	−1.40304
$56$	6.31101	0.843344
$57$	−0.00431630	−0.000571708 0
$58$	2.76795	0.363450
$59$	0.466153	0.0606879	0.0303440	−	0.999540i	$-0.490340\pi$
$59$	0.466153	0.0606879	0.0303440	+	0.999540i	$0.490340\pi$
$60$	0.0101535	0.00131082
$61$	8.94115	1.14480	0.572398	−	0.819976i	$-0.306013\pi$
$61$	8.94115	1.14480	0.572398	+	0.819976i	$0.306013\pi$
$62$	−0.784034	−0.0995724
$63$	−13.2763	−1.67265
$64$	−4.91360	−0.614200
$65$	9.86126	1.22314
$66$	−0.00370618	−0.000456199 0
$67$	6.26411	0.765283	0.382642	−	0.923897i	$-0.375014\pi$
$67$	6.26411	0.765283	0.382642	+	0.923897i	$0.375014\pi$
$68$	−3.98127	−0.482800
$69$	−0.00303948	−0.000365911 0
$70$	3.88086	0.463852
$71$	1.94173	0.230441	0.115221	−	0.993340i	$-0.463243\pi$
$71$	1.94173	0.230441	0.115221	+	0.993340i	$0.463243\pi$
$72$	−4.27822	−0.504194
$73$	1.11112	0.130047	0.0650235	−	0.997884i	$-0.479288\pi$
$73$	1.11112	0.130047	0.0650235	+	0.997884i	$0.479288\pi$
$74$	0.910129	0.105800
$75$	0.00147946	0.000170833 0
$76$	3.50850	0.402452
$77$	19.3806	2.20862
$78$	0.00351242	0.000397703 0
$79$	15.8475	1.78298	0.891489	−	0.453042i	$-0.149661\pi$
$79$	15.8475	1.78298	0.891489	+	0.453042i	$0.149661\pi$
$80$	−7.60595	−0.850371
$81$	8.99995	0.999995
$82$	−3.14266	−0.347049
$83$	−12.5731	−1.38008	−0.690041	−	0.723771i	$-0.742407\pi$
$83$	−12.5731	−1.38008	−0.690041	+	0.723771i	$0.742407\pi$
$84$	−0.0189118	−0.00206344
$85$	−5.07539	−0.550504
$86$	0	0
$87$	−0.0171953	−0.00184353
$88$	6.24531	0.665752
$89$	−4.09850	−0.434440	−0.217220	−	0.976123i	$-0.569699\pi$
$89$	−4.09850	−0.434440	−0.217220	+	0.976123i	$0.569699\pi$
$90$	−2.63083	−0.277314
$91$	−18.3674	−1.92542
$92$	2.47064	0.257582
$93$	0.00487065	0.000505063 0
$94$	−3.18883	−0.328903
$95$	4.47270	0.458889
$96$	−0.00924880	−0.000943952 0
$97$	0.625574	0.0635174	0.0317587	−	0.999496i	$-0.489889\pi$
$97$	0.625574	0.0635174	0.0317587	+	0.999496i	$0.489889\pi$
$98$	−4.64479	−0.469195
$99$	−13.1381	−1.32043
$100$	−1.20258	−0.120258
$101$	9.45307	0.940616	0.470308	−	0.882502i	$-0.344143\pi$
$101$	9.45307	0.940616	0.470308	+	0.882502i	$0.344143\pi$
$102$	−0.00180777	−0.000178996 0
$103$	11.9461	1.17709	0.588544	−	0.808465i	$-0.299701\pi$
$103$	11.9461	1.17709	0.588544	+	0.808465i	$0.299701\pi$
$104$	−5.91881	−0.580387
$105$	−0.0241091	−0.00235280
$106$	0.196827	0.0191176
$107$	11.3267	1.09499	0.547495	−	0.836809i	$-0.315582\pi$
$107$	11.3267	1.09499	0.547495	+	0.836809i	$0.315582\pi$
$108$	0.0256406	0.00246726
$109$	3.05362	0.292484	0.146242	−	0.989249i	$-0.453282\pi$
$109$	3.05362	0.292484	0.146242	+	0.989249i	$0.453282\pi$
$110$	3.84046	0.366174
$111$	−0.00565399	−0.000536653 0
$112$	14.1667	1.33863
$113$	17.2995	1.62740	0.813700	−	0.581286i	$-0.197450\pi$
$113$	17.2995	1.62740	0.813700	+	0.581286i	$0.197450\pi$
$114$	0.00159310	0.000149208 0
$115$	3.14961	0.293703
$116$	13.9772	1.29775
$117$	12.4512	1.15112
$118$	−0.172052	−0.0158387
$119$	9.45332	0.866585
$120$	−0.00776905	−0.000709214 0
$121$	8.17882	0.743529
$122$	−3.30008	−0.298775
$123$	0.0195232	0.00176034
$124$	−3.95910	−0.355538
$125$	10.3468	0.925445
$126$	4.90013	0.436538
$127$	−3.78501	−0.335866	−0.167933	−	0.985798i	$-0.553709\pi$
$127$	−3.78501	−0.335866	−0.167933	+	0.985798i	$0.553709\pi$
$128$	9.88092	0.873358
$129$	0	0
$130$	−3.63969	−0.319222
$131$	−2.89419	−0.252867	−0.126433	−	0.991975i	$-0.540353\pi$
$131$	−2.89419	−0.252867	−0.126433	+	0.991975i	$0.540353\pi$
$132$	−0.0187149	−0.00162892
$133$	−8.33075	−0.722368
$134$	−2.31202	−0.199728
$135$	0.0326870	0.00281325
$136$	3.04629	0.261218
$137$	8.58701	0.733638	0.366819	−	0.930292i	$-0.380447\pi$
$137$	8.58701	0.733638	0.366819	+	0.930292i	$0.380447\pi$
$138$	0.00112184	9.54974e−5 0
$139$	−3.89309	−0.330207	−0.165104	−	0.986276i	$-0.552796\pi$
$139$	−3.89309	−0.330207	−0.165104	+	0.986276i	$0.552796\pi$
$140$	19.5970	1.65625
$141$	0.0198100	0.00166830
$142$	−0.716672	−0.0601418
$143$	−18.1762	−1.51997
$144$	−9.60357	−0.800298
$145$	17.8184	1.47974
$146$	−0.410103	−0.0339404
$147$	0.0288548	0.00237990
$148$	4.59583	0.377775
$149$	15.9041	1.30291	0.651456	−	0.758686i	$-0.274158\pi$
$149$	15.9041	1.30291	0.651456	+	0.758686i	$0.274158\pi$
$150$	−0.000546053 0	−4.45850e−5 0
$151$	−4.16823	−0.339206	−0.169603	−	0.985513i	$-0.554248\pi$
$151$	−4.16823	−0.339206	−0.169603	+	0.985513i	$0.554248\pi$
$152$	−2.68455	−0.217746
$153$	−6.40839	−0.518088
$154$	−7.15316	−0.576418
$155$	−5.04713	−0.405395
$156$	0.0177365	0.00142006
$157$	−17.0791	−1.36306	−0.681529	−	0.731791i	$-0.738685\pi$
$157$	−17.0791	−1.36306	−0.681529	+	0.731791i	$0.738685\pi$
$158$	−5.84913	−0.465332
$159$	−0.00122275	−9.69704e−5 0
$160$	9.58391	0.757675
$161$	−5.86640	−0.462337
$162$	−3.32179	−0.260984
$163$	−11.9547	−0.936361	−0.468180	−	0.883633i	$-0.655090\pi$
$163$	−11.9547	−0.936361	−0.468180	+	0.883633i	$0.655090\pi$
$164$	−15.8694	−1.23919
$165$	−0.0238581	−0.00185735
$166$	4.64061	0.360181
$167$	0.434445	0.0336184	0.0168092	−	0.999859i	$-0.494649\pi$
$167$	0.434445	0.0336184	0.0168092	+	0.999859i	$0.494649\pi$
$168$	0.0144705	0.00111642
$169$	4.22594	0.325072
$170$	1.87327	0.143674
$171$	5.64740	0.431868
$172$	0	0
$173$	17.0351	1.29516	0.647578	−	0.761999i	$-0.275782\pi$
$173$	17.0351	1.29516	0.647578	+	0.761999i	$0.275782\pi$
$174$	0.00634661	0.000481136 0
$175$	2.85545	0.215852
$176$	14.0192	1.05674
$177$	0.00106884	8.03388e−5 0
$178$	1.51271	0.113383
$179$	9.41632	0.703809	0.351904	−	0.936036i	$-0.385534\pi$
$179$	9.41632	0.703809	0.351904	+	0.936036i	$0.385534\pi$
$180$	−13.2848	−0.990190
$181$	1.73857	0.129227	0.0646135	−	0.997910i	$-0.479419\pi$
$181$	1.73857	0.129227	0.0646135	+	0.997910i	$0.479419\pi$
$182$	6.77921	0.502508
$183$	0.0205011	0.00151548
$184$	−1.89042	−0.139364
$185$	5.85885	0.430751
$186$	−0.00179771	−0.000131814 0
$187$	9.35491	0.684099
$188$	−16.1025	−1.17440
$189$	−0.0608822	−0.00442853
$190$	−1.65082	−0.119763
$191$	−5.32331	−0.385181	−0.192591	−	0.981279i	$-0.561689\pi$
$191$	−5.32331	−0.385181	−0.192591	+	0.981279i	$0.561689\pi$
$192$	−0.0112664	−0.000813080 0
$193$	−7.82045	−0.562928	−0.281464	−	0.959572i	$-0.590820\pi$
$193$	−7.82045	−0.562928	−0.281464	+	0.959572i	$0.590820\pi$
$194$	−0.230893	−0.0165771
$195$	0.0226108	0.00161919
$196$	−23.4546	−1.67533
$197$	17.2566	1.22948	0.614739	−	0.788730i	$-0.289261\pi$
$197$	17.2566	1.22948	0.614739	+	0.788730i	$0.289261\pi$
$198$	4.84912	0.344612
$199$	−23.9050	−1.69458	−0.847291	−	0.531129i	$-0.821768\pi$
$199$	−23.9050	−1.69458	−0.847291	+	0.531129i	$0.821768\pi$
$200$	0.920158	0.0650650
$201$	0.0143629	0.00101308
$202$	−3.48903	−0.245487
$203$	−33.1881	−2.32935
$204$	−0.00912862	−0.000639132 0
$205$	−20.2305	−1.41296
$206$	−4.40919	−0.307203
$207$	3.97682	0.276408
$208$	−13.2863	−0.921239
$209$	−8.24402	−0.570251
$210$	0.00889840	0.000614048 0
$211$	−21.5214	−1.48159	−0.740797	−	0.671729i	$-0.765552\pi$
$211$	−21.5214	−1.48159	−0.740797	+	0.671729i	$0.765552\pi$
$212$	0.993910	0.0682620
$213$	0.00445218	0.000305058 0
$214$	−4.18055	−0.285776
$215$	0	0
$216$	−0.0196190	−0.00133491
$217$	9.40068	0.638159
$218$	−1.12706	−0.0763341
$219$	0.00254768	0.000172156 0
$220$	19.3930	1.30748
$221$	−8.86584	−0.596381
$222$	0.00208683	0.000140059 0
$223$	21.1285	1.41487	0.707434	−	0.706780i	$-0.249853\pi$
$223$	21.1285	1.41487	0.707434	+	0.706780i	$0.249853\pi$
$224$	−17.8508	−1.19271
$225$	−1.93571	−0.129047
$226$	−6.38506	−0.424728
$227$	7.07079	0.469305	0.234652	−	0.972079i	$-0.424605\pi$
$227$	7.07079	0.469305	0.234652	+	0.972079i	$0.424605\pi$
$228$	0.00804461	0.000532767 0
$229$	10.2048	0.674353	0.337176	−	0.941442i	$-0.390528\pi$
$229$	10.2048	0.674353	0.337176	+	0.941442i	$0.390528\pi$
$230$	−1.16249	−0.0766522
$231$	0.0444376	0.00292378
$232$	−10.6947	−0.702144
$233$	26.1793	1.71506	0.857532	−	0.514430i	$-0.171997\pi$
$233$	26.1793	1.71506	0.857532	+	0.514430i	$0.171997\pi$
$234$	−4.59561	−0.300425
$235$	−20.5278	−1.33908
$236$	−0.868803	−0.0565543
$237$	0.0363365	0.00236031
$238$	−3.48912	−0.226166
$239$	22.3247	1.44406	0.722032	−	0.691859i	$-0.243208\pi$
$239$	22.3247	1.44406	0.722032	+	0.691859i	$0.243208\pi$
$240$	−0.0174396	−0.00112572
$241$	−19.3868	−1.24881	−0.624406	−	0.781100i	$-0.714659\pi$
$241$	−19.3868	−1.24881	−0.624406	+	0.781100i	$0.714659\pi$
$242$	−3.01871	−0.194050
$243$	0.0619079	0.00397140
$244$	−16.6643	−1.06682
$245$	−29.9003	−1.91026
$246$	−0.00720579	−0.000459424 0
$247$	7.81304	0.497132
$248$	3.02933	0.192363
$249$	−0.0288289	−0.00182695
$250$	−3.81889	−0.241528
$251$	−4.72044	−0.297952	−0.148976	−	0.988841i	$-0.547598\pi$
$251$	−4.72044	−0.297952	−0.148976	+	0.988841i	$0.547598\pi$
$252$	24.7440	1.55872
$253$	−5.80533	−0.364978
$254$	1.39701	0.0876561
$255$	−0.0116373	−0.000728758 0
$256$	6.18026	0.386266
$257$	−20.9751	−1.30839	−0.654196	−	0.756325i	$-0.726993\pi$
$257$	−20.9751	−1.30839	−0.654196	+	0.756325i	$0.726993\pi$
$258$	0	0
$259$	−10.9126	−0.678074
$260$	−18.3792	−1.13983
$261$	22.4982	1.39260
$262$	1.06822	0.0659946
$263$	9.04421	0.557690	0.278845	−	0.960336i	$-0.410048\pi$
$263$	9.04421	0.557690	0.278845	+	0.960336i	$0.410048\pi$
$264$	0.0143198	0.000881324 0
$265$	1.26705	0.0778345
$266$	3.07479	0.188528
$267$	−0.00939742	−0.000575113 0
$268$	−11.6749	−0.713157
$269$	−26.5472	−1.61861	−0.809306	−	0.587387i	$-0.800157\pi$
$269$	−26.5472	−1.61861	−0.809306	+	0.587387i	$0.800157\pi$
$270$	−0.0120644	−0.000734218 0
$271$	7.49971	0.455575	0.227787	−	0.973711i	$-0.426851\pi$
$271$	7.49971	0.455575	0.227787	+	0.973711i	$0.426851\pi$
$272$	6.83819	0.414626
$273$	−0.0421144	−0.00254888
$274$	−3.16937	−0.191469
$275$	2.82573	0.170398
$276$	0.00566491	0.000340987 0
$277$	0.553836	0.0332768	0.0166384	−	0.999862i	$-0.494704\pi$
$277$	0.553836	0.0332768	0.0166384	+	0.999862i	$0.494704\pi$
$278$	1.43690	0.0861794
$279$	−6.37270	−0.381524
$280$	−14.9948	−0.896109
$281$	17.5130	1.04474	0.522370	−	0.852719i	$-0.325048\pi$
$281$	17.5130	1.04474	0.522370	+	0.852719i	$0.325048\pi$
$282$	−0.00731165	−0.000435403 0
$283$	5.04269	0.299757	0.149878	−	0.988704i	$-0.452112\pi$
$283$	5.04269	0.299757	0.149878	+	0.988704i	$0.452112\pi$
$284$	−3.61895	−0.214745
$285$	0.0102554	0.000607478 0
$286$	6.70863	0.396690
$287$	37.6810	2.22424
$288$	12.1010	0.713060
$289$	−12.4369	−0.731584
$290$	−6.57657	−0.386190
$291$	0.00143437	8.40845e−5 0
$292$	−2.07088	−0.121189
$293$	20.3722	1.19016	0.595078	−	0.803668i	$-0.297121\pi$
$293$	20.3722	1.19016	0.595078	+	0.803668i	$0.297121\pi$
$294$	−0.0106500	−0.000621121 0
$295$	−1.10757	−0.0644850
$296$	−3.51653	−0.204394
$297$	−0.0602484	−0.00349597
$298$	−5.87003	−0.340041
$299$	5.50183	0.318179
$300$	−0.00275738	−0.000159197 0
$301$	0	0
$302$	1.53845	0.0885278
$303$	0.0216749	0.00124519
$304$	−6.02616	−0.345624
$305$	−21.2439	−1.21642
$306$	2.36527	0.135213
$307$	−28.6732	−1.63647	−0.818233	−	0.574886i	$-0.805046\pi$
$307$	−28.6732	−1.63647	−0.818233	+	0.574886i	$0.805046\pi$
$308$	−36.1210	−2.05818
$309$	0.0273912	0.00155823
$310$	1.86284	0.105802
$311$	15.0840	0.855338	0.427669	−	0.903935i	$-0.359335\pi$
$311$	15.0840	0.855338	0.427669	+	0.903935i	$0.359335\pi$
$312$	−0.0135712	−0.000768318 0
$313$	29.9212	1.69125	0.845624	−	0.533780i	$-0.179229\pi$
$313$	29.9212	1.69125	0.845624	+	0.533780i	$0.179229\pi$
$314$	6.30370	0.355738
$315$	31.5440	1.77731
$316$	−29.5361	−1.66153
$317$	−19.3582	−1.08727	−0.543633	−	0.839323i	$-0.682952\pi$
$317$	−19.3582	−1.08727	−0.543633	+	0.839323i	$0.682952\pi$
$318$	0.000451304 0	2.53079e−5 0
$319$	−32.8426	−1.83883
$320$	11.6746	0.652629
$321$	0.0259708	0.00144955
$322$	2.16523	0.120663
$323$	−4.02121	−0.223746
$324$	−16.7739	−0.931882
$325$	−2.67800	−0.148549
$326$	4.41234	0.244377
$327$	0.00700163	0.000387191 0
$328$	12.1425	0.670459
$329$	38.2346	2.10794
$330$	0.00880577	0.000484742 0
$331$	8.92598	0.490616	0.245308	−	0.969445i	$-0.421111\pi$
$331$	8.92598	0.490616	0.245308	+	0.969445i	$0.421111\pi$
$332$	23.4335	1.28608
$333$	7.39762	0.405387
$334$	−0.160349	−0.00877391
$335$	−14.8833	−0.813164
$336$	0.0324827	0.00177207
$337$	−10.4886	−0.571353	−0.285677	−	0.958326i	$-0.592218\pi$
$337$	−10.4886	−0.571353	−0.285677	+	0.958326i	$0.592218\pi$
$338$	−1.55975	−0.0848392
$339$	0.0396659	0.00215435
$340$	9.45938	0.513007
$341$	9.30281	0.503775
$342$	−2.08440	−0.112711
$343$	24.7136	1.33441
$344$	0	0
$345$	0.00722172	0.000388804 0
$346$	−6.28748	−0.338017
$347$	−19.6873	−1.05687	−0.528436	−	0.848973i	$-0.677221\pi$
$347$	−19.6873	−1.05687	−0.528436	+	0.848973i	$0.677221\pi$
$348$	0.0320482	0.00171796
$349$	−0.600699	−0.0321547	−0.0160773	−	0.999871i	$-0.505118\pi$
$349$	−0.600699	−0.0321547	−0.0160773	+	0.999871i	$0.505118\pi$
$350$	−1.05392	−0.0563343
$351$	0.0570987	0.00304770
$352$	−17.6650	−0.941545
$353$	−3.53348	−0.188068	−0.0940341	−	0.995569i	$-0.529976\pi$
$353$	−3.53348	−0.188068	−0.0940341	+	0.995569i	$0.529976\pi$
$354$	−0.000394497 0	−2.09673e−5 0
$355$	−4.61350	−0.244859
$356$	7.63867	0.404849
$357$	0.0216754	0.00114719
$358$	−3.47546	−0.183684
$359$	−2.26432	−0.119506	−0.0597530	−	0.998213i	$-0.519031\pi$
$359$	−2.26432	−0.119506	−0.0597530	+	0.998213i	$0.519031\pi$
$360$	10.1649	0.535739
$361$	−15.4563	−0.813490
$362$	−0.641688	−0.0337264
$363$	0.0187532	0.000984285 0
$364$	34.2326	1.79428
$365$	−2.63999	−0.138183
$366$	−0.00756673	−0.000395519 0
$367$	−14.2503	−0.743860	−0.371930	−	0.928261i	$-0.621304\pi$
$367$	−14.2503	−0.743860	−0.371930	+	0.928261i	$0.621304\pi$
$368$	−4.24354	−0.221210
$369$	−25.5439	−1.32976
$370$	−2.16244	−0.112420
$371$	−2.35999	−0.122524
$372$	−0.00907779	−0.000470661 0
$373$	21.8586	1.13179	0.565897	−	0.824476i	$-0.308530\pi$
$373$	21.8586	1.13179	0.565897	+	0.824476i	$0.308530\pi$
$374$	−3.45280	−0.178540
$375$	0.0237241	0.00122511
$376$	12.3209	0.635404
$377$	31.1256	1.60305
$378$	0.0224710	0.00115578
$379$	25.7818	1.32432	0.662162	−	0.749361i	$-0.269639\pi$
$379$	25.7818	1.32432	0.662162	+	0.749361i	$0.269639\pi$
$380$	−8.33609	−0.427632
$381$	−0.00867863	−0.000444620 0
$382$	1.96478	0.100527
$383$	10.2812	0.525343	0.262672	−	0.964885i	$-0.415396\pi$
$383$	10.2812	0.525343	0.262672	+	0.964885i	$0.415396\pi$
$384$	0.0226559	0.00115615
$385$	−46.0477	−2.34681
$386$	2.88644	0.146916
$387$	0	0
$388$	−1.16593	−0.0591910
$389$	−26.0188	−1.31920	−0.659602	−	0.751615i	$-0.729275\pi$
$389$	−26.0188	−1.31920	−0.659602	+	0.751615i	$0.729275\pi$
$390$	−0.00834541	−0.000422586 0
$391$	−2.83168	−0.143204
$392$	17.9464	0.906431
$393$	−0.00663608	−0.000334746 0
$394$	−6.36921	−0.320876
$395$	−37.6531	−1.89453
$396$	24.4864	1.23049
$397$	10.5448	0.529230	0.264615	−	0.964354i	$-0.414755\pi$
$397$	10.5448	0.529230	0.264615	+	0.964354i	$0.414755\pi$
$398$	8.82309	0.442262
$399$	−0.0191015	−0.000956272 0
$400$	2.06553	0.103277
$401$	−23.0748	−1.15230	−0.576151	−	0.817343i	$-0.695446\pi$
$401$	−23.0748	−1.15230	−0.576151	+	0.817343i	$0.695446\pi$
$402$	−0.00530121	−0.000264400 0
$403$	−8.81647	−0.439180
$404$	−17.6184	−0.876547
$405$	−21.3836	−1.06256
$406$	12.2494	0.607927
$407$	−10.7990	−0.535285
$408$	0.00698482	0.000345800 0
$409$	30.2267	1.49462	0.747308	−	0.664478i	$-0.231346\pi$
$409$	30.2267	1.49462	0.747308	+	0.664478i	$0.231346\pi$
$410$	7.46687	0.368763
$411$	0.0196891	0.000971191 0
$412$	−22.2649	−1.09691
$413$	2.06293	0.101510
$414$	−1.46780	−0.0721386
$415$	29.8734	1.46643
$416$	16.7415	0.820817
$417$	−0.00892643	−0.000437129 0
$418$	3.04278	0.148827
$419$	28.7688	1.40545	0.702724	−	0.711463i	$-0.251967\pi$
$419$	28.7688	1.40545	0.702724	+	0.711463i	$0.251967\pi$
$420$	0.0449338	0.00219255
$421$	13.0517	0.636099	0.318049	−	0.948074i	$-0.396972\pi$
$421$	13.0517	0.636099	0.318049	+	0.948074i	$0.396972\pi$
$422$	7.94332	0.386675
$423$	−25.9192	−1.26023
$424$	−0.760496	−0.0369330
$425$	1.37831	0.0668580
$426$	−0.00164325	−7.96158e−5 0
$427$	39.5684	1.91485
$428$	−21.1103	−1.02041
$429$	−0.0416760	−0.00201214
$430$	0	0
$431$	18.4612	0.889246	0.444623	−	0.895718i	$-0.353338\pi$
$431$	18.4612	0.889246	0.444623	+	0.895718i	$0.353338\pi$
$432$	−0.0440399	−0.00211887
$433$	12.2571	0.589038	0.294519	−	0.955646i	$-0.404841\pi$
$433$	12.2571	0.589038	0.294519	+	0.955646i	$0.404841\pi$
$434$	−3.46969	−0.166550
$435$	0.0408556	0.00195888
$436$	−5.69126	−0.272562
$437$	2.49542	0.119372
$438$	−0.000940322 0	−4.49303e−5 0
$439$	−27.9984	−1.33629	−0.668145	−	0.744031i	$-0.732912\pi$
$439$	−27.9984	−1.33629	−0.668145	+	0.744031i	$0.732912\pi$
$440$	−14.8387	−0.707406
$441$	−37.7533	−1.79778
$442$	3.27229	0.155647
$443$	8.59516	0.408368	0.204184	−	0.978933i	$-0.434546\pi$
$443$	8.59516	0.408368	0.204184	+	0.978933i	$0.434546\pi$
$444$	0.0105378	0.000500100 0
$445$	9.73792	0.461622
$446$	−7.79830	−0.369260
$447$	0.0364663	0.00172480
$448$	−21.7448	−1.02735
$449$	3.34295	0.157764	0.0788818	−	0.996884i	$-0.474865\pi$
$449$	3.34295	0.157764	0.0788818	+	0.996884i	$0.474865\pi$
$450$	0.714449	0.0336795
$451$	37.2887	1.75586
$452$	−32.2423	−1.51655
$453$	−0.00955730	−0.000449041 0
$454$	−2.60975	−0.122482
$455$	43.6404	2.04589
$456$	−0.00615538	−0.000288252 0
$457$	−23.3958	−1.09441	−0.547204	−	0.837000i	$-0.684308\pi$
$457$	−23.3958	−1.09441	−0.547204	+	0.837000i	$0.684308\pi$
$458$	−3.76649	−0.175996
$459$	−0.0293875	−0.00137169
$460$	−5.87016	−0.273698
$461$	−9.00448	−0.419381	−0.209690	−	0.977768i	$-0.567246\pi$
$461$	−9.00448	−0.419381	−0.209690	+	0.977768i	$0.567246\pi$
$462$	−0.0164014	−0.000763064 0
$463$	−35.2525	−1.63832	−0.819160	−	0.573564i	$-0.805560\pi$
$463$	−35.2525	−1.63832	−0.819160	+	0.573564i	$0.805560\pi$
$464$	−24.0071	−1.11450
$465$	−0.0115725	−0.000536663 0
$466$	−9.66251	−0.447607
$467$	−16.7731	−0.776169	−0.388084	−	0.921624i	$-0.626863\pi$
$467$	−16.7731	−0.776169	−0.388084	+	0.921624i	$0.626863\pi$
$468$	−23.2063	−1.07271
$469$	27.7214	1.28006
$470$	7.57658	0.349481
$471$	−0.0391604	−0.00180442
$472$	0.664770	0.0305985
$473$	0	0
$474$	−0.0134114	−0.000616007 0
$475$	−1.21464	−0.0557315
$476$	−17.6188	−0.807558
$477$	1.59983	0.0732513
$478$	−8.23981	−0.376880
$479$	19.5964	0.895383	0.447691	−	0.894188i	$-0.352246\pi$
$479$	19.5964	0.895383	0.447691	+	0.894188i	$0.352246\pi$
$480$	0.0219749	0.00100301
$481$	10.2344	0.466649
$482$	7.15545	0.325922
$483$	−0.0134510	−0.000612043 0
$484$	−15.2435	−0.692885
$485$	−1.48635	−0.0674915
$486$	−0.0228496	−0.00103648
$487$	21.3074	0.965532	0.482766	−	0.875749i	$-0.339632\pi$
$487$	21.3074	0.965532	0.482766	+	0.875749i	$0.339632\pi$
$488$	12.7508	0.577200
$489$	−0.0274107	−0.00123956
$490$	11.0359	0.498550
$491$	−2.04748	−0.0924016	−0.0462008	−	0.998932i	$-0.514711\pi$
$491$	−2.04748	−0.0924016	−0.0462008	+	0.998932i	$0.514711\pi$
$492$	−0.0363867	−0.00164044
$493$	−16.0197	−0.721493
$494$	−2.88371	−0.129744
$495$	31.2157	1.40304
$496$	6.80010	0.305334
$497$	8.59300	0.385449
$498$	0.0106404	0.000476809 0
$499$	−13.6519	−0.611143	−0.305572	−	0.952169i	$-0.598848\pi$
$499$	−13.6519	−0.611143	−0.305572	+	0.952169i	$0.598848\pi$
$500$	−19.2841	−0.862410
$501$	0.000996136 0	4.45041e−5 0
$502$	1.74227	0.0777611
$503$	−21.8322	−0.973448	−0.486724	−	0.873556i	$-0.661808\pi$
$503$	−21.8322	−0.973448	−0.486724	+	0.873556i	$0.661808\pi$
$504$	−18.9330	−0.843343
$505$	−22.4602	−0.999467
$506$	2.14269	0.0952540
$507$	0.00968963	0.000430332 0
$508$	7.05440	0.312989
$509$	34.4634	1.52756	0.763781	−	0.645475i	$-0.223341\pi$
$509$	34.4634	1.52756	0.763781	+	0.645475i	$0.223341\pi$
$510$	0.00429522	0.000190195 0
$511$	4.91719	0.217524
$512$	−22.0429	−0.974168
$513$	0.0258978	0.00114342
$514$	7.74169	0.341471
$515$	−28.3837	−1.25073
$516$	0	0
$517$	37.8365	1.66405
$518$	4.02771	0.176968
$519$	0.0390597	0.00171453
$520$	14.0629	0.616700
$521$	38.1988	1.67352	0.836759	−	0.547571i	$-0.184448\pi$
$521$	38.1988	1.67352	0.836759	+	0.547571i	$0.184448\pi$
$522$	−8.30384	−0.363449
$523$	−12.9728	−0.567259	−0.283629	−	0.958934i	$-0.591539\pi$
$523$	−12.9728	−0.567259	−0.283629	+	0.958934i	$0.591539\pi$
$524$	5.39412	0.235643
$525$	0.00654725	0.000285745 0
$526$	−3.33812	−0.145549
$527$	4.53766	0.197664
$528$	0.0321445	0.00139891
$529$	−21.2428	−0.923598
$530$	−0.467656	−0.0203137
$531$	−1.39846	−0.0606878
$532$	15.5266	0.673165
$533$	−35.3393	−1.53071
$534$	0.00346849	0.000150096 0
$535$	−26.9118	−1.16350
$536$	8.93311	0.385852
$537$	0.0215906	0.000931703 0
$538$	9.79829	0.422434
$539$	55.1119	2.37384
$540$	−0.0609212	−0.00262163
$541$	−17.5721	−0.755486	−0.377743	−	0.925911i	$-0.623300\pi$
$541$	−17.5721	−0.755486	−0.377743	+	0.925911i	$0.623300\pi$
$542$	−2.76806	−0.118898
$543$	0.00398635	0.000171071 0
$544$	−8.61649	−0.369429
$545$	−7.25532	−0.310784
$546$	0.0155440	0.000665221 0
$547$	−12.3117	−0.526411	−0.263206	−	0.964740i	$-0.584780\pi$
$547$	−12.3117	−0.526411	−0.263206	+	0.964740i	$0.584780\pi$
$548$	−16.0042	−0.683667
$549$	−26.8234	−1.14479
$550$	−1.04295	−0.0444714
$551$	14.1174	0.601422
$552$	−0.00433454	−0.000184490 0
$553$	70.1318	2.98231
$554$	−0.204415	−0.00868475
$555$	0.0134337	0.000570229 0
$556$	7.25583	0.307716
$557$	17.2759	0.732003	0.366002	−	0.930614i	$-0.380726\pi$
$557$	17.2759	0.732003	0.366002	+	0.930614i	$0.380726\pi$
$558$	2.35210	0.0995722
$559$	0	0
$560$	−33.6596	−1.42238
$561$	0.0214498	0.000905611 0
$562$	−6.46388	−0.272662
$563$	5.53465	0.233258	0.116629	−	0.993176i	$-0.462791\pi$
$563$	5.53465	0.233258	0.116629	+	0.993176i	$0.462791\pi$
$564$	−0.0369213	−0.00155467
$565$	−41.1031	−1.72922
$566$	−1.86120	−0.0782322
$567$	39.8287	1.67265
$568$	2.76906	0.116187
$569$	−27.7111	−1.16171	−0.580854	−	0.814007i	$-0.697281\pi$
$569$	−27.7111	−1.16171	−0.580854	+	0.814007i	$0.697281\pi$
$570$	−0.00378516	−0.000158543 0
$571$	−23.6231	−0.988594	−0.494297	−	0.869293i	$-0.664575\pi$
$571$	−23.6231	−0.988594	−0.494297	+	0.869293i	$0.664575\pi$
$572$	33.8763	1.41644
$573$	−0.0122058	−0.000509904 0
$574$	−13.9076	−0.580494
$575$	−0.855333	−0.0356699
$576$	14.7408	0.614199
$577$	16.5690	0.689777	0.344889	−	0.938644i	$-0.387917\pi$
$577$	16.5690	0.689777	0.344889	+	0.938644i	$0.387917\pi$
$578$	4.59034	0.190933
$579$	−0.0179314	−0.000745205 0
$580$	−33.2094	−1.37895
$581$	−55.6416	−2.30840
$582$	−0.000529412 0	−2.19448e−5 0
$583$	−2.33542	−0.0967232
$584$	1.58455	0.0655689
$585$	−29.5837	−1.22314
$586$	−7.51916	−0.310614
$587$	5.10477	0.210696	0.105348	−	0.994435i	$-0.466404\pi$
$587$	5.10477	0.210696	0.105348	+	0.994435i	$0.466404\pi$
$588$	−0.0537788	−0.00221780
$589$	−3.99882	−0.164768
$590$	0.408791	0.0168296
$591$	0.0395674	0.00162759
$592$	−7.89375	−0.324431
$593$	−10.3620	−0.425518	−0.212759	−	0.977105i	$-0.568245\pi$
$593$	−10.3620	−0.425518	−0.212759	+	0.977105i	$0.568245\pi$
$594$	0.0222370	0.000912397 0
$595$	−22.4608	−0.920804
$596$	−29.6416	−1.21417
$597$	−0.0548116	−0.00224329
$598$	−2.03067	−0.0830402
$599$	−8.55613	−0.349594	−0.174797	−	0.984604i	$-0.555927\pi$
$599$	−8.55613	−0.349594	−0.174797	+	0.984604i	$0.555927\pi$
$600$	0.00210982	8.61332e−5 0
$601$	−23.7489	−0.968736	−0.484368	−	0.874864i	$-0.660950\pi$
$601$	−23.7489	−0.968736	−0.484368	+	0.874864i	$0.660950\pi$
$602$	0	0
$603$	−18.7923	−0.765282
$604$	7.76863	0.316101
$605$	−19.4326	−0.790049
$606$	−0.00799997	−0.000324977 0
$607$	13.3485	0.541801	0.270900	−	0.962607i	$-0.412679\pi$
$607$	13.3485	0.541801	0.270900	+	0.962607i	$0.412679\pi$
$608$	7.59329	0.307949
$609$	−0.0760968	−0.00308360
$610$	7.84090	0.317469
$611$	−35.8585	−1.45068
$612$	11.9438	0.482799
$613$	11.0943	0.448093	0.224046	−	0.974578i	$-0.428073\pi$
$613$	11.0943	0.448093	0.224046	+	0.974578i	$0.428073\pi$
$614$	10.5830	0.427094
$615$	−0.0463864	−0.00187048
$616$	27.6382	1.11358
$617$	−12.2343	−0.492536	−0.246268	−	0.969202i	$-0.579204\pi$
$617$	−12.2343	−0.492536	−0.246268	+	0.969202i	$0.579204\pi$
$618$	−0.0101098	−0.000406676 0
$619$	8.45853	0.339977	0.169989	−	0.985446i	$-0.445627\pi$
$619$	8.45853	0.339977	0.169989	+	0.985446i	$0.445627\pi$
$620$	9.40670	0.377782
$621$	0.0182369	0.000731821 0
$622$	−5.56736	−0.223231
$623$	−18.1376	−0.726669
$624$	−0.0304640	−0.00121954
$625$	−27.8099	−1.11239
$626$	−11.0436	−0.441391
$627$	−0.0189027	−0.000754900 0
$628$	31.8315	1.27021
$629$	−5.26744	−0.210027
$630$	−11.6426	−0.463851
$631$	−36.5744	−1.45600	−0.728002	−	0.685575i	$-0.759551\pi$
$631$	−36.5744	−1.45600	−0.728002	+	0.685575i	$0.759551\pi$
$632$	22.5997	0.898968
$633$	−0.0493462	−0.00196134
$634$	7.14491	0.283761
$635$	8.99308	0.356879
$636$	0.00227893	9.03654e−5 0
$637$	−52.2307	−2.06946
$638$	12.1219	0.479909
$639$	−5.82518	−0.230441
$640$	−23.4768	−0.928001
$641$	−14.0516	−0.555005	−0.277503	−	0.960725i	$-0.589507\pi$
$641$	−14.0516	−0.555005	−0.277503	+	0.960725i	$0.589507\pi$
$642$	−0.00958555	−0.000378311 0
$643$	36.2301	1.42878	0.714389	−	0.699749i	$-0.246705\pi$
$643$	36.2301	1.42878	0.714389	+	0.699749i	$0.246705\pi$
$644$	10.9336	0.430846
$645$	0	0
$646$	1.48419	0.0583945
$647$	−9.63194	−0.378671	−0.189335	−	0.981912i	$-0.560633\pi$
$647$	−9.63194	−0.378671	−0.189335	+	0.981912i	$0.560633\pi$
$648$	12.8346	0.504192
$649$	2.04145	0.0801340
$650$	0.988422	0.0387691
$651$	0.0215547	0.000844797 0
$652$	22.2808	0.872582
$653$	−31.5742	−1.23559	−0.617797	−	0.786338i	$-0.711975\pi$
$653$	−31.5742	−1.23559	−0.617797	+	0.786338i	$0.711975\pi$
$654$	−0.00258423	−0.000101051 0
$655$	6.87652	0.268688
$656$	27.2570	1.06421
$657$	−3.33336	−0.130047
$658$	−14.1120	−0.550142
$659$	0.851227	0.0331591	0.0165796	−	0.999863i	$-0.494722\pi$
$659$	0.851227	0.0331591	0.0165796	+	0.999863i	$0.494722\pi$
$660$	0.0444661	0.00173084
$661$	−20.2062	−0.785929	−0.392964	−	0.919554i	$-0.628550\pi$
$661$	−20.2062	−0.785929	−0.392964	+	0.919554i	$0.628550\pi$
$662$	−3.29448	−0.128044
$663$	−0.0203284	−0.000789491 0
$664$	−17.9303	−0.695829
$665$	19.7936	0.767564
$666$	−2.73038	−0.105800
$667$	9.94129	0.384928
$668$	−0.809707	−0.0313285
$669$	0.0484453	0.00187300
$670$	5.49328	0.212224
$671$	39.1565	1.51162
$672$	−0.0409299	−0.00157891
$673$	−12.9206	−0.498051	−0.249026	−	0.968497i	$-0.580110\pi$
$673$	−12.9206	−0.498051	−0.249026	+	0.968497i	$0.580110\pi$
$674$	3.87125	0.149115
$675$	−0.00887675	−0.000341666 0
$676$	−7.87620	−0.302931
$677$	−18.5700	−0.713704	−0.356852	−	0.934161i	$-0.616150\pi$
$677$	−18.5700	−0.713704	−0.356852	+	0.934161i	$0.616150\pi$
$678$	−0.0146403	−0.000562255 0
$679$	2.76844	0.106243
$680$	−7.23790	−0.277561
$681$	0.0162126	0.000621267 0
$682$	−3.43357	−0.131478
$683$	1.36977	0.0524126	0.0262063	−	0.999657i	$-0.491657\pi$
$683$	1.36977	0.0524126	0.0262063	+	0.999657i	$0.491657\pi$
$684$	−10.5255	−0.402452
$685$	−20.4025	−0.779539
$686$	−9.12154	−0.348262
$687$	0.0233985	0.000892709 0
$688$	0	0
$689$	2.21333	0.0843210
$690$	−0.00266546	−0.000101472 0
$691$	35.0532	1.33349	0.666744	−	0.745287i	$-0.267688\pi$
$691$	35.0532	1.33349	0.666744	+	0.745287i	$0.267688\pi$
$692$	−31.7496	−1.20694
$693$	−58.1416	−2.20862
$694$	7.26639	0.275828
$695$	9.24986	0.350867
$696$	−0.0245219	−0.000929499 0
$697$	18.1884	0.688935
$698$	0.221712	0.00839191
$699$	0.0600264	0.00227041
$700$	−5.32192	−0.201150
$701$	2.05955	0.0777881	0.0388940	−	0.999243i	$-0.487617\pi$
$701$	2.05955	0.0777881	0.0388940	+	0.999243i	$0.487617\pi$
$702$	−0.0210745	−0.000795406 0
$703$	4.64194	0.175074
$704$	−21.5184	−0.811007
$705$	−0.0470679	−0.00177268
$706$	1.30417	0.0490831
$707$	41.8339	1.57333
$708$	−0.00199207	−7.48667e−5 0
$709$	5.17917	0.194508	0.0972539	−	0.995260i	$-0.468994\pi$
$709$	5.17917	0.194508	0.0972539	+	0.995260i	$0.468994\pi$
$710$	1.70279	0.0639046
$711$	−47.5423	−1.78297
$712$	−5.84478	−0.219042
$713$	−2.81591	−0.105457
$714$	−0.00800018	−0.000299399 0
$715$	43.1861	1.61507
$716$	−17.5499	−0.655870
$717$	0.0511881	0.00191166
$718$	0.835735	0.0311894
$719$	36.2525	1.35199	0.675994	−	0.736907i	$-0.263714\pi$
$719$	36.2525	1.35199	0.675994	+	0.736907i	$0.263714\pi$
$720$	22.8178	0.850369
$721$	52.8668	1.96886
$722$	5.70476	0.212309
$723$	−0.0444518	−0.00165318
$724$	−3.24030	−0.120425
$725$	−4.83890	−0.179712
$726$	−0.00692159	−0.000256884 0
$727$	−2.45445	−0.0910306	−0.0455153	−	0.998964i	$-0.514493\pi$
$727$	−2.45445	−0.0910306	−0.0455153	+	0.998964i	$0.514493\pi$
$728$	−26.1933	−0.970789
$729$	−26.9997	−0.999989
$730$	0.974393	0.0360639
$731$	0	0
$732$	−0.0382094	−0.00141226
$733$	−2.34791	−0.0867222	−0.0433611	−	0.999059i	$-0.513807\pi$
$733$	−2.34791	−0.0867222	−0.0433611	+	0.999059i	$0.513807\pi$
$734$	5.25964	0.194137
$735$	−0.0685582	−0.00252881
$736$	5.34709	0.197096
$737$	27.4328	1.01050
$738$	9.42797	0.347048
$739$	−1.70561	−0.0627419	−0.0313709	−	0.999508i	$-0.509987\pi$
$739$	−1.70561	−0.0627419	−0.0313709	+	0.999508i	$0.509987\pi$
$740$	−10.9196	−0.401411
$741$	0.0179145	0.000658104 0
$742$	0.871046	0.0319771
$743$	50.6964	1.85987	0.929935	−	0.367725i	$-0.119863\pi$
$743$	50.6964	1.85987	0.929935	+	0.367725i	$0.119863\pi$
$744$	0.00694593	0.000254650 0
$745$	−37.7876	−1.38443
$746$	−8.06776	−0.295382
$747$	37.7194	1.38008
$748$	−17.4354	−0.637502
$749$	50.1254	1.83154
$750$	−0.00875630	−0.000319735 0
$751$	3.44441	0.125688	0.0628442	−	0.998023i	$-0.479983\pi$
$751$	3.44441	0.125688	0.0628442	+	0.998023i	$0.479983\pi$
$752$	27.6575	1.00856
$753$	−0.0108235	−0.000394429 0
$754$	−11.4881	−0.418374
$755$	9.90359	0.360428
$756$	0.113471	0.00412689
$757$	−41.4010	−1.50474	−0.752372	−	0.658739i	$-0.771090\pi$
$757$	−41.4010	−1.50474	−0.752372	+	0.658739i	$0.771090\pi$
$758$	−9.51580	−0.345629
$759$	−0.0133110	−0.000483159 0
$760$	6.37841	0.231369
$761$	−19.4195	−0.703955	−0.351978	−	0.936008i	$-0.614491\pi$
$761$	−19.4195	−0.703955	−0.351978	+	0.936008i	$0.614491\pi$
$762$	0.00320319	0.000116039 0
$763$	13.5136	0.489225
$764$	9.92144	0.358945
$765$	15.2262	0.550503
$766$	−3.79467	−0.137107
$767$	−1.93473	−0.0698590
$768$	0.0141707	0.000511340 0
$769$	35.0901	1.26538	0.632690	−	0.774405i	$-0.281951\pi$
$769$	35.0901	1.26538	0.632690	+	0.774405i	$0.281951\pi$
$770$	16.9957	0.612483
$771$	−0.0480937	−0.00173205
$772$	14.5755	0.524585
$773$	50.9523	1.83263	0.916313	−	0.400463i	$-0.131151\pi$
$773$	50.9523	1.83263	0.916313	+	0.400463i	$0.131151\pi$
$774$	0	0
$775$	1.37064	0.0492348
$776$	0.892117	0.0320251
$777$	−0.0250214	−0.000897636 0
$778$	9.60325	0.344293
$779$	−16.0286	−0.574283
$780$	−0.0421414	−0.00150891
$781$	8.50354	0.304281
$782$	1.04514	0.0373743
$783$	0.103172	0.00368706
$784$	40.2853	1.43876
$785$	40.5793	1.44834
$786$	0.00244931	8.73638e−5 0
$787$	−34.2796	−1.22194	−0.610968	−	0.791655i	$-0.709220\pi$
$787$	−34.2796	−1.22194	−0.610968	+	0.791655i	$0.709220\pi$
$788$	−32.1623	−1.14573
$789$	0.0207374	0.000738271 0
$790$	13.8974	0.494446
$791$	76.5577	2.72208
$792$	−18.7359	−0.665751
$793$	−37.1095	−1.31780
$794$	−3.89198	−0.138121
$795$	0.00290522	0.000103037 0
$796$	44.5535	1.57916
$797$	−18.3684	−0.650643	−0.325321	−	0.945603i	$-0.605473\pi$
$797$	−18.3684	−0.650643	−0.325321	+	0.945603i	$0.605473\pi$
$798$	0.00705017	0.000249573 0
$799$	18.4556	0.652914
$800$	−2.60268	−0.0920187
$801$	12.2955	0.434439
$802$	8.51668	0.300734
$803$	4.86600	0.171718
$804$	−0.0267692	−0.000944079 0
$805$	13.9384	0.491264
$806$	3.25407	0.114620
$807$	−0.0608699	−0.00214272
$808$	13.4808	0.474253
$809$	9.94153	0.349526	0.174763	−	0.984611i	$-0.444084\pi$
$809$	9.94153	0.349526	0.174763	+	0.984611i	$0.444084\pi$
$810$	7.89247	0.277313
$811$	−38.9442	−1.36752	−0.683758	−	0.729709i	$-0.739655\pi$
$811$	−38.9442	−1.36752	−0.683758	+	0.729709i	$0.739655\pi$
$812$	61.8551	2.17069
$813$	0.0171960	0.000603091 0
$814$	3.98578	0.139702
$815$	28.4039	0.994946
$816$	0.0156792	0.000548883 0
$817$	0	0
$818$	−11.1564	−0.390073
$819$	55.1021	1.92542
$820$	37.7051	1.31672
$821$	−12.0689	−0.421206	−0.210603	−	0.977572i	$-0.567543\pi$
$821$	−12.0689	−0.421206	−0.210603	+	0.977572i	$0.567543\pi$
$822$	−0.00726703	−0.000253467 0
$823$	53.3967	1.86129	0.930646	−	0.365920i	$-0.119246\pi$
$823$	53.3967	1.86129	0.930646	+	0.365920i	$0.119246\pi$
$824$	17.0361	0.593481
$825$	0.00647909	0.000225573 0
$826$	−0.761405	−0.0264927
$827$	44.1558	1.53545	0.767724	−	0.640780i	$-0.221389\pi$
$827$	44.1558	1.53545	0.767724	+	0.640780i	$0.221389\pi$
$828$	−7.41190	−0.257581
$829$	−47.6850	−1.65617	−0.828084	−	0.560603i	$-0.810569\pi$
$829$	−47.6850	−1.65617	−0.828084	+	0.560603i	$0.810569\pi$
$830$	−11.0260	−0.382717
$831$	0.00126989	4.40518e−5 0
$832$	20.3935	0.707017
$833$	26.8821	0.931409
$834$	0.00329465	0.000114084 0
$835$	−1.03223	−0.0357218
$836$	15.3650	0.531409
$837$	−0.0292239	−0.00101012
$838$	−10.6183	−0.366802
$839$	−33.6613	−1.16212	−0.581059	−	0.813862i	$-0.697361\pi$
$839$	−33.6613	−1.16212	−0.581059	+	0.813862i	$0.697361\pi$
$840$	−0.0343814	−0.00118627
$841$	27.2411	0.939348
$842$	−4.81723	−0.166013
$843$	0.0401555	0.00138303
$844$	40.1110	1.38068
$845$	−10.0407	−0.345411
$846$	9.56649	0.328903
$847$	36.1948	1.24367
$848$	−1.70713	−0.0586230
$849$	0.0115623	0.000396819 0
$850$	−0.508721	−0.0174490
$851$	3.26879	0.112053
$852$	−0.00829785	−0.000284280 0
$853$	29.6416	1.01491	0.507454	−	0.861679i	$-0.330587\pi$
$853$	29.6416	1.01491	0.507454	+	0.861679i	$0.330587\pi$
$854$	−14.6043	−0.499749
$855$	−13.4181	−0.458888
$856$	16.1527	0.552088
$857$	−41.9713	−1.43371	−0.716856	−	0.697221i	$-0.754420\pi$
$857$	−41.9713	−1.43371	−0.716856	+	0.697221i	$0.754420\pi$
$858$	0.0153822	0.000525139 0
$859$	26.1028	0.890617	0.445309	−	0.895377i	$-0.353094\pi$
$859$	26.1028	0.890617	0.445309	+	0.895377i	$0.353094\pi$
$860$	0	0
$861$	0.0863984	0.00294445
$862$	−6.81384	−0.232080
$863$	−38.7535	−1.31919	−0.659593	−	0.751623i	$-0.729271\pi$
$863$	−38.7535	−1.31919	−0.659593	+	0.751623i	$0.729271\pi$
$864$	0.0554927	0.00188790
$865$	−40.4749	−1.37619
$866$	−4.52396	−0.153730
$867$	−0.0285165	−0.000968472 0
$868$	−17.5207	−0.594692
$869$	69.4018	2.35429
$870$	−0.0150794	−0.000511239 0
$871$	−25.9987	−0.880931
$872$	4.35470	0.147469
$873$	−1.87672	−0.0635173
$874$	−0.921034	−0.0311545
$875$	45.7890	1.54795
$876$	−0.00474830	−0.000160430 0
$877$	20.6264	0.696503	0.348252	−	0.937401i	$-0.386775\pi$
$877$	20.6264	0.696503	0.348252	+	0.937401i	$0.386775\pi$
$878$	10.3339	0.348753
$879$	0.0467112	0.00157553
$880$	−33.3092	−1.12285
$881$	34.2252	1.15307	0.576537	−	0.817071i	$-0.304403\pi$
$881$	34.2252	1.15307	0.576537	+	0.817071i	$0.304403\pi$
$882$	13.9343	0.469194
$883$	36.7828	1.23784	0.618920	−	0.785454i	$-0.287571\pi$
$883$	36.7828	1.23784	0.618920	+	0.785454i	$0.287571\pi$
$884$	16.5239	0.555760
$885$	−0.00253953	−8.53653e−5 0
$886$	−3.17238	−0.106578
$887$	34.4250	1.15588	0.577938	−	0.816080i	$-0.303857\pi$
$887$	34.4250	1.15588	0.577938	+	0.816080i	$0.303857\pi$
$888$	−0.00806303	−0.000270577 0
$889$	−16.7503	−0.561788
$890$	−3.59416	−0.120477
$891$	39.4141	1.32042
$892$	−39.3787	−1.31850
$893$	−16.2641	−0.544256
$894$	−0.0134593	−0.000450148 0
$895$	−22.3729	−0.747843
$896$	43.7274	1.46083
$897$	0.0126151	0.000421206 0
$898$	−1.23385	−0.0411740
$899$	−15.9305	−0.531313
$900$	3.60772	0.120257
$901$	−1.13915	−0.0379507
$902$	−13.7629	−0.458253
$903$	0	0
$904$	24.6704	0.820526
$905$	−4.13079	−0.137312
$906$	0.00352750	0.000117193 0
$907$	40.5072	1.34502	0.672510	−	0.740088i	$-0.265216\pi$
$907$	40.5072	1.34502	0.672510	+	0.740088i	$0.265216\pi$
$908$	−13.1784	−0.437339
$909$	−28.3592	−0.940614
$910$	−16.1072	−0.533948
$911$	30.6741	1.01628	0.508140	−	0.861275i	$-0.330333\pi$
$911$	30.6741	1.01628	0.508140	+	0.861275i	$0.330333\pi$
$912$	−0.0138173	−0.000457538 0
$913$	−55.0623	−1.82230
$914$	8.63512	0.285624
$915$	−0.0487100	−0.00161030
$916$	−19.0194	−0.628420
$917$	−12.8081	−0.422960
$918$	0.0108466	0.000357992 0
$919$	−5.57144	−0.183785	−0.0918925	−	0.995769i	$-0.529292\pi$
$919$	−5.57144	−0.183785	−0.0918925	+	0.995769i	$0.529292\pi$
$920$	4.49159	0.148083
$921$	−0.0657446	−0.00216636
$922$	3.32346	0.109452
$923$	−8.05899	−0.265265
$924$	−0.0828216	−0.00272463
$925$	−1.59108	−0.0523142
$926$	13.0113	0.427578
$927$	−35.8383	−1.17709
$928$	30.2502	0.993012
$929$	33.4667	1.09801	0.549004	−	0.835820i	$-0.315007\pi$
$929$	33.4667	1.09801	0.549004	+	0.835820i	$0.315007\pi$
$930$	0.00427130	0.000140061 0
$931$	−23.6899	−0.776404
$932$	−48.7923	−1.59825
$933$	0.0345861	0.00113230
$934$	6.19079	0.202569
$935$	−22.2270	−0.726900
$936$	17.7564	0.580386
$937$	8.89994	0.290748	0.145374	−	0.989377i	$-0.453561\pi$
$937$	8.89994	0.290748	0.145374	+	0.989377i	$0.453561\pi$
$938$	−10.2317	−0.334076
$939$	0.0686061	0.00223888
$940$	38.2591	1.24787
$941$	1.96856	0.0641732	0.0320866	−	0.999485i	$-0.489785\pi$
$941$	1.96856	0.0641732	0.0320866	+	0.999485i	$0.489785\pi$
$942$	0.0144537	0.000470927 0
$943$	−11.2871	−0.367558
$944$	1.49225	0.0485685
$945$	0.144654	0.00470561
$946$	0	0
$947$	−27.3742	−0.889543	−0.444771	−	0.895644i	$-0.646715\pi$
$947$	−27.3742	−0.889543	−0.444771	+	0.895644i	$0.646715\pi$
$948$	−0.0677230	−0.00219954
$949$	−4.61161	−0.149699
$950$	0.448311	0.0145451
$951$	−0.0443863	−0.00143932
$952$	13.4812	0.436927
$953$	−9.85336	−0.319182	−0.159591	−	0.987183i	$-0.551017\pi$
$953$	−9.85336	−0.319182	−0.159591	+	0.987183i	$0.551017\pi$
$954$	−0.590481	−0.0191175
$955$	12.6480	0.409281
$956$	−41.6082	−1.34570
$957$	−0.0753046	−0.00243425
$958$	−7.23283	−0.233682
$959$	38.0012	1.22712
$960$	0.0267685	0.000863951 0
$961$	−26.4876	−0.854439
$962$	−3.77741	−0.121789
$963$	−33.9799	−1.09499
$964$	36.1326	1.16375
$965$	18.5812	0.598148
$966$	0.00496463	0.000159734 0
$967$	−28.9916	−0.932307	−0.466154	−	0.884704i	$-0.654361\pi$
$967$	−28.9916	−0.932307	−0.466154	+	0.884704i	$0.654361\pi$
$968$	11.6636	0.374883
$969$	−0.00922021	−0.000296196 0
$970$	0.548594	0.0176143
$971$	−54.9685	−1.76402	−0.882011	−	0.471228i	$-0.843811\pi$
$971$	−54.9685	−1.76402	−0.882011	+	0.471228i	$0.843811\pi$
$972$	−0.115382	−0.00370089
$973$	−17.2286	−0.552324
$974$	−7.86435	−0.251990
$975$	−0.00614037	−0.000196649 0
$976$	28.6224	0.916180
$977$	−43.0678	−1.37786	−0.688930	−	0.724828i	$-0.741919\pi$
$977$	−43.0678	−1.37786	−0.688930	+	0.724828i	$0.741919\pi$
$978$	0.0101170	0.000323506 0
$979$	−17.9488	−0.573647
$980$	55.7274	1.78015
$981$	−9.16085	−0.292483
$982$	0.755704	0.0241155
$983$	−31.1332	−0.992996	−0.496498	−	0.868038i	$-0.665381\pi$
$983$	−31.1332	−0.992996	−0.496498	+	0.868038i	$0.665381\pi$
$984$	0.0278415	0.000887555 0
$985$	−41.0011	−1.30640
$986$	5.91272	0.188299
$987$	0.0876678	0.00279050
$988$	−14.5617	−0.463270
$989$	0	0
$990$	−11.5214	−0.366173
$991$	53.1306	1.68775	0.843874	−	0.536541i	$-0.180269\pi$
$991$	53.1306	1.68775	0.843874	+	0.536541i	$0.180269\pi$
$992$	−8.56850	−0.272050
$993$	0.0204663	0.000649479 0
$994$	−3.17158	−0.100597
$995$	56.7976	1.80061
$996$	0.0537304	0.00170251
$997$	−2.97207	−0.0941264	−0.0470632	−	0.998892i	$-0.514986\pi$
$997$	−2.97207	−0.0941264	−0.0470632	+	0.998892i	$0.514986\pi$
$998$	5.03877	0.159500
$999$	0.0339239	0.00107330

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.r.1.8	yes	20
43.42	odd	2		1849.2.a.p.1.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.p.1.13	✓	20	43.42	odd	2
1849.2.a.r.1.8	yes	20	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)

\(f(q)\)	\(=\)	\(q-0.369089 q^{2} +0.00229289 q^{3} -1.86377 q^{4} -2.37597 q^{5} -0.000846282 q^{6} +4.42543 q^{7} +1.42608 q^{8} -2.99999 q^{9} +O(q^{10})\)	\(q-0.369089 q^{2} +0.00229289 q^{3} -1.86377 q^{4} -2.37597 q^{5} -0.000846282 q^{6} +4.42543 q^{7} +1.42608 q^{8} -2.99999 q^{9} +0.876946 q^{10} +4.37936 q^{11} -0.00427343 q^{12} -4.15041 q^{13} -1.63338 q^{14} -0.00544785 q^{15} +3.20120 q^{16} +2.13613 q^{17} +1.10727 q^{18} -1.88247 q^{19} +4.42827 q^{20} +0.0101470 q^{21} -1.61638 q^{22} -1.32561 q^{23} +0.00326984 q^{24} +0.645237 q^{25} +1.53187 q^{26} -0.0137573 q^{27} -8.24800 q^{28} -7.49941 q^{29} +0.00201074 q^{30} +2.12424 q^{31} -4.03368 q^{32} +0.0100414 q^{33} -0.788425 q^{34} -10.5147 q^{35} +5.59131 q^{36} -2.46588 q^{37} +0.694800 q^{38} -0.00951645 q^{39} -3.38832 q^{40} +8.51464 q^{41} -0.00374517 q^{42} -8.16214 q^{44} +7.12790 q^{45} +0.489269 q^{46} +8.63973 q^{47} +0.00734000 q^{48} +12.5845 q^{49} -0.238150 q^{50} +0.00489793 q^{51} +7.73543 q^{52} -0.533278 q^{53} +0.00507769 q^{54} -10.4052 q^{55} +6.31101 q^{56} -0.00431630 q^{57} +2.76795 q^{58} +0.466153 q^{59} +0.0101535 q^{60} +8.94115 q^{61} -0.784034 q^{62} -13.2763 q^{63} -4.91360 q^{64} +9.86126 q^{65} -0.00370618 q^{66} +6.26411 q^{67} -3.98127 q^{68} -0.00303948 q^{69} +3.88086 q^{70} +1.94173 q^{71} -4.27822 q^{72} +1.11112 q^{73} +0.910129 q^{74} +0.00147946 q^{75} +3.50850 q^{76} +19.3806 q^{77} +0.00351242 q^{78} +15.8475 q^{79} -7.60595 q^{80} +8.99995 q^{81} -3.14266 q^{82} -12.5731 q^{83} -0.0189118 q^{84} -5.07539 q^{85} -0.0171953 q^{87} +6.24531 q^{88} -4.09850 q^{89} -2.63083 q^{90} -18.3674 q^{91} +2.47064 q^{92} +0.00487065 q^{93} -3.18883 q^{94} +4.47270 q^{95} -0.00924880 q^{96} +0.625574 q^{97} -4.64479 q^{98} -13.1381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 + 23 * q^4 - 3 * q^5 + 5 * q^6 - 2 * q^7 + 9 * q^8 + 27 * q^9	\( 20 q + 5 q^{2} - q^{3} + 23 q^{4} - 3 q^{5} + 5 q^{6} - 2 q^{7} + 9 q^{8} + 27 q^{9} + 21 q^{11} - 12 q^{12} + 11 q^{13} + 8 q^{14} + 4 q^{15} + 29 q^{16} + 15 q^{17} + 9 q^{18} - 7 q^{19} - 17 q^{20} + 8 q^{21} + 47 q^{22} + 26 q^{23} - q^{24} + 11 q^{25} + 58 q^{26} - 22 q^{27} - 28 q^{28} - 12 q^{29} - 24 q^{30} + 26 q^{31} + 3 q^{32} - 17 q^{33} + 54 q^{34} + 26 q^{35} + 14 q^{36} - 19 q^{37} + 5 q^{38} - 7 q^{39} - 16 q^{40} + 27 q^{41} - 52 q^{42} + 32 q^{44} + 75 q^{45} + 59 q^{46} + 45 q^{47} - 66 q^{48} + 20 q^{49} + 75 q^{51} + 11 q^{52} + 3 q^{53} + 57 q^{54} - 2 q^{55} + 87 q^{56} - 24 q^{57} - 46 q^{58} + 66 q^{59} + 29 q^{60} + 30 q^{61} + 72 q^{62} - 21 q^{63} - 7 q^{64} - 6 q^{65} + 41 q^{66} - 6 q^{67} + 28 q^{68} - 35 q^{69} - 80 q^{70} - 31 q^{71} - 15 q^{72} - 26 q^{73} + 87 q^{74} + 73 q^{75} - 68 q^{76} - 21 q^{77} - 50 q^{78} + 39 q^{79} - 60 q^{80} + 16 q^{81} + 45 q^{82} + 13 q^{83} + 31 q^{84} - 22 q^{85} + 61 q^{87} + 50 q^{88} - 4 q^{89} - 13 q^{90} - 25 q^{91} + 5 q^{92} + 67 q^{93} + 42 q^{94} + 79 q^{95} + 36 q^{96} - 2 q^{97} - 35 q^{98} + 13 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 + 23 * q^4 - 3 * q^5 + 5 * q^6 - 2 * q^7 + 9 * q^8 + 27 * q^9 + 21 * q^11 - 12 * q^12 + 11 * q^13 + 8 * q^14 + 4 * q^15 + 29 * q^16 + 15 * q^17 + 9 * q^18 - 7 * q^19 - 17 * q^20 + 8 * q^21 + 47 * q^22 + 26 * q^23 - q^24 + 11 * q^25 + 58 * q^26 - 22 * q^27 - 28 * q^28 - 12 * q^29 - 24 * q^30 + 26 * q^31 + 3 * q^32 - 17 * q^33 + 54 * q^34 + 26 * q^35 + 14 * q^36 - 19 * q^37 + 5 * q^38 - 7 * q^39 - 16 * q^40 + 27 * q^41 - 52 * q^42 + 32 * q^44 + 75 * q^45 + 59 * q^46 + 45 * q^47 - 66 * q^48 + 20 * q^49 + 75 * q^51 + 11 * q^52 + 3 * q^53 + 57 * q^54 - 2 * q^55 + 87 * q^56 - 24 * q^57 - 46 * q^58 + 66 * q^59 + 29 * q^60 + 30 * q^61 + 72 * q^62 - 21 * q^63 - 7 * q^64 - 6 * q^65 + 41 * q^66 - 6 * q^67 + 28 * q^68 - 35 * q^69 - 80 * q^70 - 31 * q^71 - 15 * q^72 - 26 * q^73 + 87 * q^74 + 73 * q^75 - 68 * q^76 - 21 * q^77 - 50 * q^78 + 39 * q^79 - 60 * q^80 + 16 * q^81 + 45 * q^82 + 13 * q^83 + 31 * q^84 - 22 * q^85 + 61 * q^87 + 50 * q^88 - 4 * q^89 - 13 * q^90 - 25 * q^91 + 5 * q^92 + 67 * q^93 + 42 * q^94 + 79 * q^95 + 36 * q^96 - 2 * q^97 - 35 * q^98 + 13 * q^99

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