LMFDB - Embedded newform 1849.2.a.p.1.13

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			1.13
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	$-0.458344\pi$
$2$	0.369089	0.260986	0.130493	+	0.991449i	$0.458344\pi$
$3$	−0.00229289	−0.00132380	−0.000661901	−	1.00000i	$-0.500211\pi$
$3$	−0.00229289	−0.00132380	−0.000661901		1.00000i	$0.500211\pi$
$4$	−1.86377	−0.931887
$5$	2.37597	1.06257	0.531283	−	0.847194i	$-0.321710\pi$
$5$	2.37597	1.06257	0.531283	+	0.847194i	$0.321710\pi$
$6$	−0.000846282 0	−0.000345493 0
$7$	−4.42543	−1.67266	−0.836328	−	0.548229i	$-0.815302\pi$
$7$	−4.42543	−1.67266	−0.836328	+	0.548229i	$0.815302\pi$
$8$	−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	$-0.430720\pi$
$19$	1.88247	0.431869	0.215934	+	0.976408i	$0.430720\pi$
$20$	−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	$-0.254827\pi$
$29$	7.49941	1.39260	0.696302	+	0.717749i	$0.254827\pi$
$30$	−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	$-0.435030\pi$
$37$	2.46588	0.405388	0.202694	+	0.979242i	$0.435030\pi$
$38$	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	$-0.693987\pi$
$61$	−8.94115	−1.14480	−0.572398	+	0.819976i	$0.693987\pi$
$62$	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	$-0.536757\pi$
$71$	−1.94173	−0.230441	−0.115221	+	0.993340i	$0.536757\pi$
$72$	4.27822	0.504194
$73$	−1.11112	−0.130047	−0.0650235	−	0.997884i	$-0.520712\pi$
$73$	−1.11112	−0.130047	−0.0650235	+	0.997884i	$0.520712\pi$
$74$	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	$-0.430301\pi$
$89$	4.09850	0.434440	0.217220	+	0.976123i	$0.430301\pi$
$90$	−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	$-0.802550\pi$
$113$	−17.2995	−1.62740	−0.813700	+	0.581286i	$0.802550\pi$
$114$	−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	$-0.459647\pi$
$131$	2.89419	0.252867	0.126433	+	0.991975i	$0.459647\pi$
$132$	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	$-0.619553\pi$
$137$	−8.58701	−0.733638	−0.366819	+	0.930292i	$0.619553\pi$
$138$	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	$-0.725842\pi$
$149$	−15.9041	−1.30291	−0.651456	+	0.758686i	$0.725842\pi$
$150$	−0.000546053 0	−4.45850e−5 0
$151$	4.16823	0.339206	0.169603	−	0.985513i	$-0.445752\pi$
$151$	4.16823	0.339206	0.169603	+	0.985513i	$0.445752\pi$
$152$	−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	$-0.261315\pi$
$157$	17.0791	1.36306	0.681529	+	0.731791i	$0.261315\pi$
$158$	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	$-0.344910\pi$
$163$	11.9547	0.936361	0.468180	+	0.883633i	$0.344910\pi$
$164$	−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	$-0.614466\pi$
$179$	−9.41632	−0.703809	−0.351904	+	0.936036i	$0.614466\pi$
$180$	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	$-0.438311\pi$
$191$	5.32331	0.385181	0.192591	+	0.981279i	$0.438311\pi$
$192$	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	$-0.178232\pi$
$199$	23.9050	1.69458	0.847291	+	0.531129i	$0.178232\pi$
$200$	−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	$-0.234448\pi$
$211$	21.5214	1.48159	0.740797	+	0.671729i	$0.234448\pi$
$212$	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	$-0.750147\pi$
$223$	−21.1285	−1.41487	−0.707434	+	0.706780i	$0.750147\pi$
$224$	−17.8508	−1.19271
$225$	−1.93571	−0.129047
$226$	−6.38506	−0.424728
$227$	−7.07079	−0.469305	−0.234652	−	0.972079i	$-0.575395\pi$
$227$	−7.07079	−0.469305	−0.234652	+	0.972079i	$0.575395\pi$
$228$	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	$-0.828003\pi$
$233$	−26.1793	−1.71506	−0.857532	+	0.514430i	$0.828003\pi$
$234$	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	$-0.285341\pi$
$241$	19.3868	1.24881	0.624406	+	0.781100i	$0.285341\pi$
$242$	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	$-0.273007\pi$
$257$	20.9751	1.30839	0.654196	+	0.756325i	$0.273007\pi$
$258$	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	$-0.589952\pi$
$263$	−9.04421	−0.557690	−0.278845	+	0.960336i	$0.589952\pi$
$264$	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	$-0.505296\pi$
$277$	−0.553836	−0.0332768	−0.0166384	+	0.999862i	$0.505296\pi$
$278$	−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	$-0.820771\pi$
$313$	−29.9212	−1.69125	−0.845624	+	0.533780i	$0.820771\pi$
$314$	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	$-0.578889\pi$
$331$	−8.92598	−0.490616	−0.245308	+	0.969445i	$0.578889\pi$
$332$	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	$-0.322779\pi$
$347$	19.6873	1.05687	0.528436	+	0.848973i	$0.322779\pi$
$348$	0.0320482	0.00171796
$349$	0.600699	0.0321547	0.0160773	−	0.999871i	$-0.494882\pi$
$349$	0.600699	0.0321547	0.0160773	+	0.999871i	$0.494882\pi$
$350$	−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	$-0.691470\pi$
$373$	−21.8586	−1.13179	−0.565897	+	0.824476i	$0.691470\pi$
$374$	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	$-0.584604\pi$
$383$	−10.2812	−0.525343	−0.262672	+	0.964885i	$0.584604\pi$
$384$	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	$-0.270725\pi$
$389$	26.0188	1.31920	0.659602	+	0.751615i	$0.270725\pi$
$390$	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	$-0.768654\pi$
$409$	−30.2267	−1.49462	−0.747308	+	0.664478i	$0.768654\pi$
$410$	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	$-0.748033\pi$
$419$	−28.7688	−1.40545	−0.702724	+	0.711463i	$0.748033\pi$
$420$	−0.0449338	−0.00219255
$421$	−13.0517	−0.636099	−0.318049	−	0.948074i	$-0.603028\pi$
$421$	−13.0517	−0.636099	−0.318049	+	0.948074i	$0.603028\pi$
$422$	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	$-0.595159\pi$
$433$	−12.2571	−0.589038	−0.294519	+	0.955646i	$0.595159\pi$
$434$	−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	$-0.525135\pi$
$449$	−3.34295	−0.157764	−0.0788818	+	0.996884i	$0.525135\pi$
$450$	−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	$-0.315692\pi$
$457$	23.3958	1.09441	0.547204	+	0.837000i	$0.315692\pi$
$458$	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	$-0.194440\pi$
$463$	35.2525	1.63832	0.819160	+	0.573564i	$0.194440\pi$
$464$	24.0071	1.11450
$465$	−0.0115725	−0.000536663 0
$466$	−9.66251	−0.447607
$467$	16.7731	0.776169	0.388084	−	0.921624i	$-0.373137\pi$
$467$	16.7731	0.776169	0.388084	+	0.921624i	$0.373137\pi$
$468$	−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	$-0.485289\pi$
$491$	2.04748	0.0924016	0.0462008	+	0.998932i	$0.485289\pi$
$492$	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	$-0.401152\pi$
$499$	13.6519	0.611143	0.305572	+	0.952169i	$0.401152\pi$
$500$	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	$-0.338192\pi$
$503$	21.8322	0.973448	0.486724	+	0.873556i	$0.338192\pi$
$504$	−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	$-0.815552\pi$
$521$	−38.1988	−1.67352	−0.836759	+	0.547571i	$0.815552\pi$
$522$	−8.30384	−0.363449
$523$	12.9728	0.567259	0.283629	−	0.958934i	$-0.408461\pi$
$523$	12.9728	0.567259	0.283629	+	0.958934i	$0.408461\pi$
$524$	−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	$-0.335425\pi$
$571$	23.6231	0.988594	0.494297	+	0.869293i	$0.335425\pi$
$572$	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	$-0.612083\pi$
$577$	−16.5690	−0.689777	−0.344889	+	0.938644i	$0.612083\pi$
$578$	−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	$-0.533596\pi$
$587$	−5.10477	−0.210696	−0.105348	+	0.994435i	$0.533596\pi$
$588$	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	$-0.431755\pi$
$593$	10.3620	0.425518	0.212759	+	0.977105i	$0.431755\pi$
$594$	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	$-0.339050\pi$
$601$	23.7489	0.968736	0.484368	+	0.874864i	$0.339050\pi$
$602$	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	$-0.587321\pi$
$607$	−13.3485	−0.541801	−0.270900	+	0.962607i	$0.587321\pi$
$608$	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	$-0.240449\pi$
$631$	36.5744	1.45600	0.728002	+	0.685575i	$0.240449\pi$
$632$	−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	$-0.410493\pi$
$641$	14.0516	0.555005	0.277503	+	0.960725i	$0.410493\pi$
$642$	−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	$-0.439367\pi$
$647$	9.63194	0.378671	0.189335	+	0.981912i	$0.439367\pi$
$648$	−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	$-0.288025\pi$
$653$	31.5742	1.23559	0.617797	+	0.786338i	$0.288025\pi$
$654$	−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	$-0.419890\pi$
$673$	12.9206	0.498051	0.249026	+	0.968497i	$0.419890\pi$
$674$	−3.87125	−0.149115
$675$	0.00887675	0.000341666 0
$676$	−7.87620	−0.302931
$677$	18.5700	0.713704	0.356852	−	0.934161i	$-0.383850\pi$
$677$	18.5700	0.713704	0.356852	+	0.934161i	$0.383850\pi$
$678$	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	$-0.732312\pi$
$691$	−35.0532	−1.33349	−0.666744	+	0.745287i	$0.732312\pi$
$692$	−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	$-0.485507\pi$
$727$	2.45445	0.0910306	0.0455153	+	0.998964i	$0.485507\pi$
$728$	−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	$-0.486193\pi$
$733$	2.34791	0.0867222	0.0433611	+	0.999059i	$0.486193\pi$
$734$	−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	$-0.490013\pi$
$739$	1.70561	0.0627419	0.0313709	+	0.999508i	$0.490013\pi$
$740$	−10.9196	−0.401411
$741$	0.0179145	0.000658104 0
$742$	0.871046	0.0319771
$743$	−50.6964	−1.85987	−0.929935	−	0.367725i	$-0.880137\pi$
$743$	−50.6964	−1.85987	−0.929935	+	0.367725i	$0.880137\pi$
$744$	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	$-0.520017\pi$
$751$	−3.44441	−0.125688	−0.0628442	+	0.998023i	$0.520017\pi$
$752$	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	$-0.228910\pi$
$757$	41.4010	1.50474	0.752372	+	0.658739i	$0.228910\pi$
$758$	9.51580	0.345629
$759$	0.0133110	0.000483159 0
$760$	−6.37841	−0.231369
$761$	19.4195	0.703955	0.351978	−	0.936008i	$-0.385509\pi$
$761$	19.4195	0.703955	0.351978	+	0.936008i	$0.385509\pi$
$762$	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	$-0.868849\pi$
$773$	−50.9523	−1.83263	−0.916313	+	0.400463i	$0.868849\pi$
$774$	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	$-0.260345\pi$
$811$	38.9442	1.36752	0.683758	+	0.729709i	$0.260345\pi$
$812$	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	$-0.189431\pi$
$829$	47.6850	1.65617	0.828084	+	0.560603i	$0.189431\pi$
$830$	−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	$-0.302639\pi$
$839$	33.6613	1.16212	0.581059	+	0.813862i	$0.302639\pi$
$840$	−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	$-0.646906\pi$
$859$	−26.1028	−0.890617	−0.445309	+	0.895377i	$0.646906\pi$
$860$	0	0
$861$	0.0863984	0.00294445
$862$	6.81384	0.232080
$863$	38.7535	1.31919	0.659593	−	0.751623i	$-0.270729\pi$
$863$	38.7535	1.31919	0.659593	+	0.751623i	$0.270729\pi$
$864$	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	$-0.696143\pi$
$887$	−34.4250	−1.15588	−0.577938	+	0.816080i	$0.696143\pi$
$888$	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	$-0.669667\pi$
$911$	−30.6741	−1.01628	−0.508140	+	0.861275i	$0.669667\pi$
$912$	−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	$-0.684993\pi$
$929$	−33.4667	−1.09801	−0.549004	+	0.835820i	$0.684993\pi$
$930$	−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	$-0.546439\pi$
$937$	−8.89994	−0.290748	−0.145374	+	0.989377i	$0.546439\pi$
$938$	−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	$-0.448983\pi$
$953$	9.85336	0.319182	0.159591	+	0.987183i	$0.448983\pi$
$954$	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	$-0.334619\pi$
$983$	31.1332	0.992996	0.496498	+	0.868038i	$0.334619\pi$
$984$	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	$-0.819731\pi$
$991$	−53.1306	−1.68775	−0.843874	+	0.536541i	$0.819731\pi$
$992$	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	$-0.485014\pi$
$997$	2.97207	0.0941264	0.0470632	+	0.998892i	$0.485014\pi$
$998$	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.p.1.13	✓	20
43.42	odd	2		1849.2.a.r.1.8	yes	20

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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