LMFDB - Embedded newform 1849.4.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,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, 4, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.45868.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} + 11x + 1 $ x^4 - x^3 - 10x^2 + 11x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.0844804$ 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)

$f(q)$	$=$	$q+5.19893 q^{2} -0.759721 q^{3} +19.0289 q^{4} +1.54763 q^{5} -3.94973 q^{6} +13.3169 q^{7} +57.3382 q^{8} -26.4228 q^{9} +O(q^{10})$	\(q+5.19893 q^{2} -0.759721 q^{3} +19.0289 q^{4} +1.54763 q^{5} -3.94973 q^{6} +13.3169 q^{7} +57.3382 q^{8} -26.4228 q^{9} +8.04602 q^{10} -37.7845 q^{11} -14.4566 q^{12} +6.24570 q^{13} +69.2335 q^{14} -1.17577 q^{15} +145.866 q^{16} -103.952 q^{17} -137.370 q^{18} -103.156 q^{19} +29.4496 q^{20} -10.1171 q^{21} -196.439 q^{22} -135.924 q^{23} -43.5610 q^{24} -122.605 q^{25} +32.4710 q^{26} +40.5864 q^{27} +253.405 q^{28} -272.908 q^{29} -6.11273 q^{30} +16.0386 q^{31} +299.644 q^{32} +28.7057 q^{33} -540.438 q^{34} +20.6096 q^{35} -502.796 q^{36} +157.028 q^{37} -536.300 q^{38} -4.74499 q^{39} +88.7384 q^{40} +304.427 q^{41} -52.5981 q^{42} -718.995 q^{44} -40.8928 q^{45} -706.658 q^{46} +547.763 q^{47} -110.818 q^{48} -165.661 q^{49} -637.414 q^{50} +78.9743 q^{51} +118.849 q^{52} -561.219 q^{53} +211.006 q^{54} -58.4764 q^{55} +763.566 q^{56} +78.3697 q^{57} -1418.83 q^{58} +169.891 q^{59} -22.3735 q^{60} +272.060 q^{61} +83.3837 q^{62} -351.869 q^{63} +390.894 q^{64} +9.66604 q^{65} +149.239 q^{66} -29.6347 q^{67} -1978.08 q^{68} +103.264 q^{69} +107.148 q^{70} +522.148 q^{71} -1515.04 q^{72} +518.694 q^{73} +816.376 q^{74} +93.1454 q^{75} -1962.94 q^{76} -503.171 q^{77} -24.6689 q^{78} -175.889 q^{79} +225.747 q^{80} +682.582 q^{81} +1582.69 q^{82} +990.336 q^{83} -192.517 q^{84} -160.879 q^{85} +207.334 q^{87} -2166.50 q^{88} +1175.00 q^{89} -212.599 q^{90} +83.1732 q^{91} -2586.48 q^{92} -12.1849 q^{93} +2847.78 q^{94} -159.647 q^{95} -227.645 q^{96} +557.250 q^{97} -861.260 q^{98} +998.373 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 11 q^{3} + 2 q^{4} + 27 q^{5} - 27 q^{6} + 20 q^{7} + 66 q^{8} - 9 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 11 * q^3 + 2 * q^4 + 27 * q^5 - 27 * q^6 + 20 * q^7 + 66 * q^8 - 9 * q^9	\( 4 q + 4 q^{2} + 11 q^{3} + 2 q^{4} + 27 q^{5} - 27 q^{6} + 20 q^{7} + 66 q^{8} - 9 q^{9} - 3 q^{10} - 62 q^{11} - 61 q^{12} - 2 q^{13} + 112 q^{14} + 92 q^{15} + 202 q^{16} - 207 q^{17} - 299 q^{18} - 99 q^{19} - 81 q^{20} - 90 q^{21} - 202 q^{22} - 103 q^{23} + 209 q^{24} - 101 q^{25} + 50 q^{26} + 218 q^{27} + 80 q^{28} + 99 q^{29} - 300 q^{30} + 131 q^{31} + 342 q^{32} + 32 q^{33} - 53 q^{34} - 374 q^{35} - 379 q^{36} + 449 q^{37} - 609 q^{38} - 98 q^{39} + 133 q^{40} - 491 q^{41} + 394 q^{42} - 764 q^{44} + 338 q^{45} - 1061 q^{46} + 19 q^{47} - 237 q^{48} + 236 q^{49} - 599 q^{50} - 1649 q^{51} + 224 q^{52} - 1220 q^{53} - 322 q^{54} - 1360 q^{55} + 344 q^{56} + 232 q^{57} - 771 q^{58} + 816 q^{59} - 156 q^{60} - 372 q^{61} + 97 q^{62} - 1914 q^{63} + 434 q^{64} + 350 q^{65} + 812 q^{66} + 110 q^{67} - 1697 q^{68} + 1238 q^{69} + 718 q^{70} - 468 q^{71} + 315 q^{72} - 628 q^{73} + 395 q^{74} - 62 q^{75} - 1671 q^{76} + 2044 q^{77} - 90 q^{78} + 1095 q^{79} + 31 q^{80} + 2056 q^{81} + 2287 q^{82} - 980 q^{83} - 610 q^{84} + 152 q^{85} - 507 q^{87} - 1816 q^{88} + 738 q^{89} - 2398 q^{90} - 852 q^{91} - 2517 q^{92} + 35 q^{93} + 2233 q^{94} + 1149 q^{95} - 1551 q^{96} - 1765 q^{97} - 1652 q^{98} - 58 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 11 * q^3 + 2 * q^4 + 27 * q^5 - 27 * q^6 + 20 * q^7 + 66 * q^8 - 9 * q^9 - 3 * q^10 - 62 * q^11 - 61 * q^12 - 2 * q^13 + 112 * q^14 + 92 * q^15 + 202 * q^16 - 207 * q^17 - 299 * q^18 - 99 * q^19 - 81 * q^20 - 90 * q^21 - 202 * q^22 - 103 * q^23 + 209 * q^24 - 101 * q^25 + 50 * q^26 + 218 * q^27 + 80 * q^28 + 99 * q^29 - 300 * q^30 + 131 * q^31 + 342 * q^32 + 32 * q^33 - 53 * q^34 - 374 * q^35 - 379 * q^36 + 449 * q^37 - 609 * q^38 - 98 * q^39 + 133 * q^40 - 491 * q^41 + 394 * q^42 - 764 * q^44 + 338 * q^45 - 1061 * q^46 + 19 * q^47 - 237 * q^48 + 236 * q^49 - 599 * q^50 - 1649 * q^51 + 224 * q^52 - 1220 * q^53 - 322 * q^54 - 1360 * q^55 + 344 * q^56 + 232 * q^57 - 771 * q^58 + 816 * q^59 - 156 * q^60 - 372 * q^61 + 97 * q^62 - 1914 * q^63 + 434 * q^64 + 350 * q^65 + 812 * q^66 + 110 * q^67 - 1697 * q^68 + 1238 * q^69 + 718 * q^70 - 468 * q^71 + 315 * q^72 - 628 * q^73 + 395 * q^74 - 62 * q^75 - 1671 * q^76 + 2044 * q^77 - 90 * q^78 + 1095 * q^79 + 31 * q^80 + 2056 * q^81 + 2287 * q^82 - 980 * q^83 - 610 * q^84 + 152 * q^85 - 507 * q^87 - 1816 * q^88 + 738 * q^89 - 2398 * q^90 - 852 * q^91 - 2517 * q^92 + 35 * q^93 + 2233 * q^94 + 1149 * q^95 - 1551 * q^96 - 1765 * q^97 - 1652 * q^98 - 58 * 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 $

$2$	5.19893	1.83810	0.919049	−	0.394142i	$-0.128958\pi$
$2$	5.19893	1.83810	0.919049	+	0.394142i	$0.128958\pi$
$3$	−0.759721	−0.146208	−0.0731042	−	0.997324i	$-0.523291\pi$
$3$	−0.759721	−0.146208	−0.0731042	+	0.997324i	$0.523291\pi$
$4$	19.0289	2.37861
$5$	1.54763	0.138424	0.0692121	−	0.997602i	$-0.477951\pi$
$5$	1.54763	0.138424	0.0692121	+	0.997602i	$0.477951\pi$
$6$	−3.94973	−0.268745
$7$	13.3169	0.719043	0.359522	−	0.933137i	$-0.382940\pi$
$7$	13.3169	0.719043	0.359522	+	0.933137i	$0.382940\pi$
$8$	57.3382	2.53402
$9$	−26.4228	−0.978623
$10$	8.04602	0.254437
$11$	−37.7845	−1.03568	−0.517839	−	0.855478i	$-0.673263\pi$
$11$	−37.7845	−1.03568	−0.517839	+	0.855478i	$0.673263\pi$
$12$	−14.4566	−0.347772
$13$	6.24570	0.133250	0.0666248	−	0.997778i	$-0.478777\pi$
$13$	6.24570	0.133250	0.0666248	+	0.997778i	$0.478777\pi$
$14$	69.2335	1.32167
$15$	−1.17577	−0.0202388
$16$	145.866	2.27916
$17$	−103.952	−1.48306	−0.741529	−	0.670920i	$-0.765899\pi$
$17$	−103.952	−1.48306	−0.741529	+	0.670920i	$0.765899\pi$
$18$	−137.370	−1.79881
$19$	−103.156	−1.24556	−0.622778	−	0.782398i	$-0.713996\pi$
$19$	−103.156	−1.24556	−0.622778	+	0.782398i	$0.713996\pi$
$20$	29.4496	0.329257
$21$	−10.1171	−0.105130
$22$	−196.439	−1.90368
$23$	−135.924	−1.23226	−0.616132	−	0.787643i	$-0.711301\pi$
$23$	−135.924	−1.23226	−0.616132	+	0.787643i	$0.711301\pi$
$24$	−43.5610	−0.370494
$25$	−122.605	−0.980839
$26$	32.4710	0.244926
$27$	40.5864	0.289291
$28$	253.405	1.71032
$29$	−272.908	−1.74751	−0.873753	−	0.486370i	$-0.838321\pi$
$29$	−272.908	−1.74751	−0.873753	+	0.486370i	$0.838321\pi$
$30$	−6.11273	−0.0372009
$31$	16.0386	0.0929234	0.0464617	−	0.998920i	$-0.485205\pi$
$31$	16.0386	0.0929234	0.0464617	+	0.998920i	$0.485205\pi$
$32$	299.644	1.65531
$33$	28.7057	0.151425
$34$	−540.438	−2.72601
$35$	20.6096	0.0995331
$36$	−502.796	−2.32776
$37$	157.028	0.697708	0.348854	−	0.937177i	$-0.386571\pi$
$37$	157.028	0.697708	0.348854	+	0.937177i	$0.386571\pi$
$38$	−536.300	−2.28946
$39$	−4.74499	−0.0194822
$40$	88.7384	0.350769
$41$	304.427	1.15960	0.579798	−	0.814760i	$-0.303131\pi$
$41$	304.427	1.15960	0.579798	+	0.814760i	$0.303131\pi$
$42$	−52.5981	−0.193240
$43$	0	0
$43$	0	0
$44$	−718.995	−2.46347
$45$	−40.8928	−0.135465
$46$	−706.658	−2.26502
$47$	547.763	1.69999	0.849995	−	0.526791i	$-0.176605\pi$
$47$	547.763	1.69999	0.849995	+	0.526791i	$0.176605\pi$
$48$	−110.818	−0.333233
$49$	−165.661	−0.482977
$50$	−637.414	−1.80288
$51$	78.9743	0.216836
$52$	118.849	0.316949
$53$	−561.219	−1.45452	−0.727258	−	0.686364i	$-0.759206\pi$
$53$	−561.219	−1.45452	−0.727258	+	0.686364i	$0.759206\pi$
$54$	211.006	0.531746
$55$	−58.4764	−0.143363
$56$	763.566	1.82207
$57$	78.3697	0.182111
$58$	−1418.83	−3.21209
$59$	169.891	0.374881	0.187441	−	0.982276i	$-0.439981\pi$
$59$	169.891	0.374881	0.187441	+	0.982276i	$0.439981\pi$
$60$	−22.3735	−0.0481401
$61$	272.060	0.571045	0.285522	−	0.958372i	$-0.407833\pi$
$61$	272.060	0.571045	0.285522	+	0.958372i	$0.407833\pi$
$62$	83.3837	0.170802
$63$	−351.869	−0.703672
$64$	390.894	0.763464
$65$	9.66604	0.0184450
$66$	149.239	0.278333
$67$	−29.6347	−0.0540367	−0.0270183	−	0.999635i	$-0.508601\pi$
$67$	−29.6347	−0.0540367	−0.0270183	+	0.999635i	$0.508601\pi$
$68$	−1978.08	−3.52761
$69$	103.264	0.180167
$70$	107.148	0.182952
$71$	522.148	0.872783	0.436392	−	0.899757i	$-0.356256\pi$
$71$	522.148	0.872783	0.436392	+	0.899757i	$0.356256\pi$
$72$	−1515.04	−2.47985
$73$	518.694	0.831624	0.415812	−	0.909451i	$-0.363497\pi$
$73$	518.694	0.831624	0.415812	+	0.909451i	$0.363497\pi$
$74$	816.376	1.28246
$75$	93.1454	0.143407
$76$	−1962.94	−2.96269
$77$	−503.171	−0.744697
$78$	−24.6689	−0.0358102
$79$	−175.889	−0.250494	−0.125247	−	0.992126i	$-0.539972\pi$
$79$	−175.889	−0.250494	−0.125247	+	0.992126i	$0.539972\pi$
$80$	225.747	0.315492
$81$	682.582	0.936326
$82$	1582.69	2.13145
$83$	990.336	1.30968	0.654840	−	0.755767i	$-0.272736\pi$
$83$	990.336	1.30968	0.654840	+	0.755767i	$0.272736\pi$
$84$	−192.517	−0.250063
$85$	−160.879	−0.205291
$86$	0	0
$87$	207.334	0.255500
$88$	−2166.50	−2.62442
$89$	1175.00	1.39944	0.699718	−	0.714419i	$-0.253309\pi$
$89$	1175.00	1.39944	0.699718	+	0.714419i	$0.253309\pi$
$90$	−212.599	−0.248998
$91$	83.1732	0.0958123
$92$	−2586.48	−2.93107
$93$	−12.1849	−0.0135862
$94$	2847.78	3.12475
$95$	−159.647	−0.172415
$96$	−227.645	−0.242021
$97$	557.250	0.583301	0.291650	−	0.956525i	$-0.405796\pi$
$97$	557.250	0.583301	0.291650	+	0.956525i	$0.405796\pi$
$98$	−861.260	−0.887759
$99$	998.373	1.01354
$100$	−2333.03	−2.33303
$101$	−1966.20	−1.93708	−0.968538	−	0.248866i	$-0.919942\pi$
$101$	−1966.20	−1.93708	−0.968538	+	0.248866i	$0.919942\pi$
$102$	410.582	0.398565
$103$	609.537	0.583101	0.291551	−	0.956555i	$-0.405829\pi$
$103$	609.537	0.583101	0.291551	+	0.956555i	$0.405829\pi$
$104$	358.117	0.337657
$105$	−15.6575	−0.0145526
$106$	−2917.74	−2.67354
$107$	1349.22	1.21901	0.609504	−	0.792783i	$-0.291369\pi$
$107$	1349.22	1.21901	0.609504	+	0.792783i	$0.291369\pi$
$108$	772.313	0.688110
$109$	−383.498	−0.336995	−0.168498	−	0.985702i	$-0.553892\pi$
$109$	−383.498	−0.336995	−0.168498	+	0.985702i	$0.553892\pi$
$110$	−304.015	−0.263515
$111$	−119.297	−0.102011
$112$	1942.49	1.63882
$113$	168.968	0.140666	0.0703328	−	0.997524i	$-0.477594\pi$
$113$	168.968	0.140666	0.0703328	+	0.997524i	$0.477594\pi$
$114$	407.438	0.334738
$115$	−210.360	−0.170575
$116$	−5193.12	−4.15663
$117$	−165.029	−0.130401
$118$	883.253	0.689068
$119$	−1384.31	−1.06638
$120$	−67.4164	−0.0512854
$121$	96.6669	0.0726273
$122$	1414.42	1.04964
$123$	−231.279	−0.169543
$124$	305.197	0.221028
$125$	−383.201	−0.274196
$126$	−1829.34	−1.29342
$127$	−1825.96	−1.27581	−0.637905	−	0.770115i	$-0.720199\pi$
$127$	−1825.96	−1.27581	−0.637905	+	0.770115i	$0.720199\pi$
$128$	−364.920	−0.251990
$129$	0	0
$130$	50.2530	0.0339037
$131$	−1148.18	−0.765778	−0.382889	−	0.923794i	$-0.625071\pi$
$131$	−1148.18	−0.765778	−0.382889	+	0.923794i	$0.625071\pi$
$132$	546.236	0.360180
$133$	−1373.71	−0.895609
$134$	−154.069	−0.0993247
$135$	62.8128	0.0400449
$136$	−5960.41	−3.75809
$137$	−173.728	−0.108340	−0.0541700	−	0.998532i	$-0.517251\pi$
$137$	−173.728	−0.108340	−0.0541700	+	0.998532i	$0.517251\pi$
$138$	536.863	0.331165
$139$	−154.363	−0.0941938	−0.0470969	−	0.998890i	$-0.514997\pi$
$139$	−154.363	−0.0941938	−0.0470969	+	0.998890i	$0.514997\pi$
$140$	392.177	0.236750
$141$	−416.147	−0.248553
$142$	2714.61	1.60426
$143$	−235.991	−0.138004
$144$	−3854.20	−2.23044
$145$	−422.360	−0.241897
$146$	2696.65	1.52861
$147$	125.856	0.0706152
$148$	2988.06	1.65957
$149$	2033.52	1.11807	0.559036	−	0.829143i	$-0.311171\pi$
$149$	2033.52	1.11807	0.559036	+	0.829143i	$0.311171\pi$
$150$	484.256	0.263596
$151$	−925.845	−0.498968	−0.249484	−	0.968379i	$-0.580261\pi$
$151$	−925.845	−0.498968	−0.249484	+	0.968379i	$0.580261\pi$
$152$	−5914.77	−3.15626
$153$	2746.70	1.45136
$154$	−2615.95	−1.36883
$155$	24.8219	0.0128628
$156$	−90.2917	−0.0463405
$157$	−69.0018	−0.0350761	−0.0175380	−	0.999846i	$-0.505583\pi$
$157$	−69.0018	−0.0350761	−0.0175380	+	0.999846i	$0.505583\pi$
$158$	−914.434	−0.460433
$159$	426.370	0.212662
$160$	463.738	0.229135
$161$	−1810.08	−0.886052
$162$	3548.69	1.72106
$163$	3172.22	1.52434	0.762171	−	0.647376i	$-0.224134\pi$
$163$	3172.22	1.52434	0.762171	+	0.647376i	$0.224134\pi$
$164$	5792.89	2.75823
$165$	44.4257	0.0209608
$166$	5148.68	2.40732
$167$	−2928.61	−1.35702	−0.678512	−	0.734589i	$-0.737375\pi$
$167$	−2928.61	−1.35702	−0.678512	+	0.734589i	$0.737375\pi$
$168$	−580.097	−0.266401
$169$	−2157.99	−0.982245
$170$	−836.398	−0.377346
$171$	2725.67	1.21893
$172$	0	0
$173$	−2766.71	−1.21589	−0.607946	−	0.793979i	$-0.708006\pi$
$173$	−2766.71	−1.21589	−0.607946	+	0.793979i	$0.708006\pi$
$174$	1077.91	0.469634
$175$	−1632.71	−0.705266
$176$	−5511.49	−2.36048
$177$	−129.070	−0.0548107
$178$	6108.74	2.57230
$179$	1147.03	0.478955	0.239477	−	0.970902i	$-0.423024\pi$
$179$	1147.03	0.478955	0.239477	+	0.970902i	$0.423024\pi$
$180$	−778.143	−0.322218
$181$	−53.7838	−0.0220868	−0.0110434	−	0.999939i	$-0.503515\pi$
$181$	−53.7838	−0.0220868	−0.0110434	+	0.999939i	$0.503515\pi$
$182$	432.411	0.176112
$183$	−206.690	−0.0834915
$184$	−7793.63	−3.12258
$185$	243.021	0.0965798
$186$	−63.3483	−0.0249727
$187$	3927.76	1.53597
$188$	10423.3	4.04361
$189$	540.484	0.208013
$190$	−829.994	−0.316916
$191$	−578.919	−0.219315	−0.109657	−	0.993969i	$-0.534975\pi$
$191$	−578.919	−0.219315	−0.109657	+	0.993969i	$0.534975\pi$
$192$	−296.970	−0.111625
$193$	−1304.10	−0.486378	−0.243189	−	0.969979i	$-0.578194\pi$
$193$	−1304.10	−0.486378	−0.243189	+	0.969979i	$0.578194\pi$
$194$	2897.10	1.07216
$195$	−7.34349	−0.00269681
$196$	−3152.34	−1.14881
$197$	−20.9616	−0.00758096	−0.00379048	−	0.999993i	$-0.501207\pi$
$197$	−20.9616	−0.00758096	−0.00379048	+	0.999993i	$0.501207\pi$
$198$	5190.47	1.86298
$199$	−4666.37	−1.66226	−0.831131	−	0.556077i	$-0.812306\pi$
$199$	−4666.37	−1.66226	−0.831131	+	0.556077i	$0.812306\pi$
$200$	−7029.94	−2.48546
$201$	22.5141	0.00790061
$202$	−10222.2	−3.56054
$203$	−3634.27	−1.25653
$204$	1502.79	0.515767
$205$	471.140	0.160516
$206$	3168.94	1.07180
$207$	3591.49	1.20592
$208$	911.039	0.303698
$209$	3897.69	1.28999
$210$	−81.4024	−0.0267490
$211$	2926.19	0.954726	0.477363	−	0.878706i	$-0.341593\pi$
$211$	2926.19	0.954726	0.477363	+	0.878706i	$0.341593\pi$
$212$	−10679.4	−3.45972
$213$	−396.687	−0.127608
$214$	7014.49	2.24066
$215$	0	0
$216$	2327.15	0.733068
$217$	213.584	0.0668159
$218$	−1993.78	−0.619430
$219$	−394.063	−0.121590
$220$	−1112.74	−0.341004
$221$	−649.251	−0.197617
$222$	−620.218	−0.187506
$223$	2449.44	0.735545	0.367773	−	0.929916i	$-0.380120\pi$
$223$	2449.44	0.735545	0.367773	+	0.929916i	$0.380120\pi$
$224$	3990.32	1.19024
$225$	3239.57	0.959871
$226$	878.454	0.258557
$227$	−2813.56	−0.822656	−0.411328	−	0.911487i	$-0.634935\pi$
$227$	−2813.56	−0.822656	−0.411328	+	0.911487i	$0.634935\pi$
$228$	1491.28	0.433170
$229$	4056.98	1.17071	0.585355	−	0.810777i	$-0.300955\pi$
$229$	4056.98	1.17071	0.585355	+	0.810777i	$0.300955\pi$
$230$	−1093.65	−0.313534
$231$	382.269	0.108881
$232$	−15648.0	−4.42821
$233$	−5438.36	−1.52909	−0.764546	−	0.644569i	$-0.777037\pi$
$233$	−5438.36	−1.52909	−0.764546	+	0.644569i	$0.777037\pi$
$234$	−857.974	−0.239690
$235$	847.735	0.235320
$236$	3232.84	0.891695
$237$	133.627	0.0366244
$238$	−7196.94	−1.96012
$239$	918.457	0.248577	0.124289	−	0.992246i	$-0.460335\pi$
$239$	918.457	0.248577	0.124289	+	0.992246i	$0.460335\pi$
$240$	−171.505	−0.0461275
$241$	−4620.36	−1.23495	−0.617477	−	0.786589i	$-0.711845\pi$
$241$	−4620.36	−1.23495	−0.617477	+	0.786589i	$0.711845\pi$
$242$	502.564	0.133496
$243$	−1614.41	−0.426190
$244$	5176.99	1.35829
$245$	−256.382	−0.0668557
$246$	−1202.40	−0.311636
$247$	−644.281	−0.165970
$248$	919.627	0.235469
$249$	−752.379	−0.191486
$250$	−1992.23	−0.504000
$251$	−369.842	−0.0930050	−0.0465025	−	0.998918i	$-0.514808\pi$
$251$	−369.842	−0.0930050	−0.0465025	+	0.998918i	$0.514808\pi$
$252$	−6695.67	−1.67376
$253$	5135.81	1.27623
$254$	−9493.04	−2.34506
$255$	122.223	0.0300153
$256$	−5024.34	−1.22665
$257$	−658.640	−0.159863	−0.0799316	−	0.996800i	$-0.525470\pi$
$257$	−658.640	−0.159863	−0.0799316	+	0.996800i	$0.525470\pi$
$258$	0	0
$259$	2091.12	0.501683
$260$	183.934	0.0438734
$261$	7210.99	1.71015
$262$	−5969.30	−1.40758
$263$	−1068.23	−0.250456	−0.125228	−	0.992128i	$-0.539966\pi$
$263$	−1068.23	−0.250456	−0.125228	+	0.992128i	$0.539966\pi$
$264$	1645.93	0.383712
$265$	−868.560	−0.201340
$266$	−7141.84	−1.64622
$267$	−892.672	−0.204609
$268$	−563.915	−0.128532
$269$	−3082.82	−0.698747	−0.349374	−	0.936984i	$-0.613606\pi$
$269$	−3082.82	−0.698747	−0.349374	+	0.936984i	$0.613606\pi$
$270$	326.559	0.0736065
$271$	−4535.71	−1.01670	−0.508348	−	0.861152i	$-0.669744\pi$
$271$	−4535.71	−1.01670	−0.508348	+	0.861152i	$0.669744\pi$
$272$	−15163.1	−3.38013
$273$	−63.1884	−0.0140086
$274$	−903.199	−0.199140
$275$	4632.56	1.01583
$276$	1965.00	0.428547
$277$	−4149.16	−0.899996	−0.449998	−	0.893030i	$-0.648575\pi$
$277$	−4149.16	−0.899996	−0.449998	+	0.893030i	$0.648575\pi$
$278$	−802.524	−0.173137
$279$	−423.786	−0.0909370
$280$	1181.72	0.252218
$281$	5989.98	1.27164	0.635822	−	0.771835i	$-0.280661\pi$
$281$	5989.98	1.27164	0.635822	+	0.771835i	$0.280661\pi$
$282$	−2163.52	−0.456864
$283$	−4823.94	−1.01326	−0.506632	−	0.862163i	$-0.669110\pi$
$283$	−4823.94	−1.01326	−0.506632	+	0.862163i	$0.669110\pi$
$284$	9935.89	2.07601
$285$	121.287	0.0252086
$286$	−1226.90	−0.253664
$287$	4054.01	0.833800
$288$	−7917.43	−1.61993
$289$	5892.96	1.19946
$290$	−2195.82	−0.444631
$291$	−423.354	−0.0852834
$292$	9870.16	1.97811
$293$	−1412.53	−0.281642	−0.140821	−	0.990035i	$-0.544974\pi$
$293$	−1412.53	−0.281642	−0.140821	+	0.990035i	$0.544974\pi$
$294$	654.317	0.129798
$295$	262.929	0.0518926
$296$	9003.69	1.76800
$297$	−1533.54	−0.299612
$298$	10572.1	2.05513
$299$	−848.940	−0.164199
$300$	1772.45	0.341108
$301$	0	0
$302$	−4813.40	−0.917153
$303$	1493.77	0.283217
$304$	−15047.0	−2.83883
$305$	421.048	0.0790464
$306$	14279.9	2.66773
$307$	8561.77	1.59168	0.795841	−	0.605506i	$-0.207029\pi$
$307$	8561.77	1.59168	0.795841	+	0.605506i	$0.207029\pi$
$308$	−9574.77	−1.77134
$309$	−463.078	−0.0852543
$310$	129.047	0.0236432
$311$	−9921.27	−1.80895	−0.904475	−	0.426526i	$-0.859737\pi$
$311$	−9921.27	−1.80895	−0.904475	+	0.426526i	$0.859737\pi$
$312$	−272.069	−0.0493682
$313$	−2341.57	−0.422854	−0.211427	−	0.977394i	$-0.567811\pi$
$313$	−2341.57	−0.422854	−0.211427	+	0.977394i	$0.567811\pi$
$314$	−358.735	−0.0644733
$315$	−544.564	−0.0974054
$316$	−3346.97	−0.595828
$317$	−848.830	−0.150394	−0.0751972	−	0.997169i	$-0.523959\pi$
$317$	−848.830	−0.150394	−0.0751972	+	0.997169i	$0.523959\pi$
$318$	2216.67	0.390895
$319$	10311.7	1.80985
$320$	604.959	0.105682
$321$	−1025.03	−0.178229
$322$	−9410.48	−1.62865
$323$	10723.2	1.84723
$324$	12988.8	2.22715
$325$	−765.753	−0.130696
$326$	16492.2	2.80189
$327$	291.352	0.0492715
$328$	17455.3	2.93844
$329$	7294.49	1.22237
$330$	230.966	0.0385281
$331$	9892.58	1.64273	0.821367	−	0.570400i	$-0.193212\pi$
$331$	9892.58	1.64273	0.821367	+	0.570400i	$0.193212\pi$
$332$	18845.0	3.11521
$333$	−4149.12	−0.682793
$334$	−15225.7	−2.49434
$335$	−45.8636	−0.00747998
$336$	−1475.75	−0.239609
$337$	3892.53	0.629198	0.314599	−	0.949225i	$-0.398130\pi$
$337$	3892.53	0.629198	0.314599	+	0.949225i	$0.398130\pi$
$338$	−11219.2	−1.80546
$339$	−128.369	−0.0205665
$340$	−3061.34	−0.488307
$341$	−606.012	−0.0962386
$342$	14170.6	2.24051
$343$	−6773.77	−1.06632
$344$	0	0
$345$	159.815	0.0249395
$346$	−14383.9	−2.23493
$347$	−3769.35	−0.583139	−0.291570	−	0.956550i	$-0.594177\pi$
$347$	−3769.35	−0.583139	−0.291570	+	0.956550i	$0.594177\pi$
$348$	3945.32	0.607734
$349$	7246.36	1.11143	0.555715	−	0.831373i	$-0.312445\pi$
$349$	7246.36	1.11143	0.555715	+	0.831373i	$0.312445\pi$
$350$	−8488.36	−1.29635
$351$	253.491	0.0385480
$352$	−11321.9	−1.71437
$353$	−10521.5	−1.58640	−0.793202	−	0.608959i	$-0.791588\pi$
$353$	−10521.5	−1.58640	−0.793202	+	0.608959i	$0.791588\pi$
$354$	−671.026	−0.100748
$355$	808.093	0.120814
$356$	22358.9	3.32871
$357$	1051.69	0.155914
$358$	5963.32	0.880366
$359$	−5843.44	−0.859066	−0.429533	−	0.903051i	$-0.641322\pi$
$359$	−5843.44	−0.859066	−0.429533	+	0.903051i	$0.641322\pi$
$360$	−2344.72	−0.343271
$361$	3782.13	0.551412
$362$	−279.618	−0.0405978
$363$	−73.4399	−0.0106187
$364$	1582.69	0.227900
$365$	802.747	0.115117
$366$	−1074.56	−0.153466
$367$	5347.03	0.760525	0.380263	−	0.924879i	$-0.375834\pi$
$367$	5347.03	0.760525	0.380263	+	0.924879i	$0.375834\pi$
$368$	−19826.7	−2.80853
$369$	−8043.81	−1.13481
$370$	1263.45	0.177523
$371$	−7473.68	−1.04586
$372$	−231.864	−0.0323162
$373$	−1550.04	−0.215169	−0.107584	−	0.994196i	$-0.534312\pi$
$373$	−1550.04	−0.215169	−0.107584	+	0.994196i	$0.534312\pi$
$374$	20420.2	2.82326
$375$	291.126	0.0400898
$376$	31407.8	4.30780
$377$	−1704.50	−0.232855
$378$	2809.94	0.382348
$379$	−4489.09	−0.608415	−0.304207	−	0.952606i	$-0.598392\pi$
$379$	−4489.09	−0.608415	−0.304207	+	0.952606i	$0.598392\pi$
$380$	−3037.90	−0.410108
$381$	1387.22	0.186534
$382$	−3009.76	−0.403122
$383$	1928.41	0.257277	0.128639	−	0.991692i	$-0.458939\pi$
$383$	1928.41	0.257277	0.128639	+	0.991692i	$0.458939\pi$
$384$	277.237	0.0368430
$385$	−778.723	−0.103084
$386$	−6779.91	−0.894012
$387$	0	0
$388$	10603.8	1.38744
$389$	5866.01	0.764572	0.382286	−	0.924044i	$-0.375137\pi$
$389$	5866.01	0.764572	0.382286	+	0.924044i	$0.375137\pi$
$390$	−38.1783	−0.00495701
$391$	14129.5	1.82752
$392$	−9498.71	−1.22387
$393$	872.296	0.111963
$394$	−108.978	−0.0139346
$395$	−272.211	−0.0346745
$396$	18997.9	2.41081
$397$	−4082.35	−0.516089	−0.258044	−	0.966133i	$-0.583078\pi$
$397$	−4082.35	−0.516089	−0.258044	+	0.966133i	$0.583078\pi$
$398$	−24260.1	−3.05540
$399$	1043.64	0.130946
$400$	−17883.9	−2.23549
$401$	3277.42	0.408146	0.204073	−	0.978956i	$-0.434582\pi$
$401$	3277.42	0.408146	0.204073	+	0.978956i	$0.434582\pi$
$402$	117.049	0.0145221
$403$	100.173	0.0123820
$404$	−37414.6	−4.60754
$405$	1056.38	0.129610
$406$	−18894.3	−2.30963
$407$	−5933.21	−0.722601
$408$	4528.25	0.549465
$409$	−13408.5	−1.62105	−0.810523	−	0.585706i	$-0.800817\pi$
$409$	−13408.5	−1.62105	−0.810523	+	0.585706i	$0.800817\pi$
$410$	2449.42	0.295045
$411$	131.985	0.0158402
$412$	11598.8	1.38697
$413$	2262.42	0.269556
$414$	18671.9	2.21660
$415$	1532.67	0.181292
$416$	1871.48	0.220570
$417$	117.273	0.0137719
$418$	20263.8	2.37114
$419$	−11682.9	−1.36217	−0.681083	−	0.732206i	$-0.738491\pi$
$419$	−11682.9	−1.36217	−0.681083	+	0.732206i	$0.738491\pi$
$420$	−297.945	−0.0346148
$421$	3248.77	0.376093	0.188047	−	0.982160i	$-0.439784\pi$
$421$	3248.77	0.376093	0.188047	+	0.982160i	$0.439784\pi$
$422$	15213.0	1.75488
$423$	−14473.5	−1.66365
$424$	−32179.3	−3.68577
$425$	12745.0	1.45464
$426$	−2062.35	−0.234556
$427$	3622.99	0.410606
$428$	25674.1	2.89954
$429$	179.287	0.0201773
$430$	0	0
$431$	−2773.39	−0.309952	−0.154976	−	0.987918i	$-0.549530\pi$
$431$	−2773.39	−0.309952	−0.154976	+	0.987918i	$0.549530\pi$
$432$	5920.20	0.659342
$433$	−14460.0	−1.60485	−0.802427	−	0.596751i	$-0.796458\pi$
$433$	−14460.0	−1.60485	−0.802427	+	0.596751i	$0.796458\pi$
$434$	1110.41	0.122814
$435$	320.876	0.0353674
$436$	−7297.53	−0.801579
$437$	14021.3	1.53486
$438$	−2048.70	−0.223495
$439$	−5799.58	−0.630522	−0.315261	−	0.949005i	$-0.602092\pi$
$439$	−5799.58	−0.630522	−0.315261	+	0.949005i	$0.602092\pi$
$440$	−3352.93	−0.363284
$441$	4377.23	0.472652
$442$	−3375.41	−0.363240
$443$	−656.688	−0.0704294	−0.0352147	−	0.999380i	$-0.511211\pi$
$443$	−656.688	−0.0704294	−0.0352147	+	0.999380i	$0.511211\pi$
$444$	−2270.09	−0.242644
$445$	1818.47	0.193716
$446$	12734.5	1.35200
$447$	−1544.91	−0.163472
$448$	5205.48	0.548964
$449$	−14512.4	−1.52535	−0.762677	−	0.646779i	$-0.776115\pi$
$449$	−14512.4	−1.52535	−0.762677	+	0.646779i	$0.776115\pi$
$450$	16842.3	1.76434
$451$	−11502.6	−1.20097
$452$	3215.27	0.334588
$453$	703.384	0.0729533
$454$	−14627.5	−1.51212
$455$	128.721	0.0132627
$456$	4493.58	0.461472
$457$	−1934.01	−0.197963	−0.0989817	−	0.995089i	$-0.531559\pi$
$457$	−1934.01	−0.197963	−0.0989817	+	0.995089i	$0.531559\pi$
$458$	21091.9	2.15188
$459$	−4219.03	−0.429036
$460$	−4002.91	−0.405732
$461$	−9190.71	−0.928534	−0.464267	−	0.885695i	$-0.653682\pi$
$461$	−9190.71	−0.928534	−0.464267	+	0.885695i	$0.653682\pi$
$462$	1987.39	0.200134
$463$	−9681.56	−0.971793	−0.485897	−	0.874016i	$-0.661507\pi$
$463$	−9681.56	−0.971793	−0.485897	+	0.874016i	$0.661507\pi$
$464$	−39808.1	−3.98285
$465$	−18.8577	−0.00188066
$466$	−28273.6	−2.81062
$467$	8408.67	0.833206	0.416603	−	0.909089i	$-0.363221\pi$
$467$	8408.67	0.833206	0.416603	+	0.909089i	$0.363221\pi$
$468$	−3140.31	−0.310173
$469$	−394.642	−0.0388547
$470$	4407.31	0.432541
$471$	52.4221	0.00512841
$472$	9741.28	0.949955
$473$	0	0
$474$	694.715	0.0673192
$475$	12647.4	1.22169
$476$	−26341.9	−2.53651
$477$	14829.0	1.42342
$478$	4774.99	0.456910
$479$	7395.21	0.705419	0.352709	−	0.935733i	$-0.385260\pi$
$479$	7395.21	0.705419	0.352709	+	0.935733i	$0.385260\pi$
$480$	−352.311	−0.0335015
$481$	980.749	0.0929694
$482$	−24020.9	−2.26997
$483$	1375.16	0.129548
$484$	1839.46	0.172752
$485$	862.417	0.0807430
$486$	−8393.18	−0.783379
$487$	18697.2	1.73974	0.869869	−	0.493283i	$-0.164203\pi$
$487$	18697.2	1.73974	0.869869	+	0.493283i	$0.164203\pi$
$488$	15599.4	1.44704
$489$	−2410.00	−0.222871
$490$	−1332.91	−0.122887
$491$	−16792.3	−1.54343	−0.771715	−	0.635969i	$-0.780601\pi$
$491$	−16792.3	−1.54343	−0.771715	+	0.635969i	$0.780601\pi$
$492$	−4400.98	−0.403275
$493$	28369.2	2.59165
$494$	−3349.57	−0.305069
$495$	1545.11	0.140298
$496$	2339.50	0.211788
$497$	6953.38	0.627569
$498$	−3911.56	−0.351971
$499$	339.483	0.0304556	0.0152278	−	0.999884i	$-0.495153\pi$
$499$	339.483	0.0304556	0.0152278	+	0.999884i	$0.495153\pi$
$500$	−7291.87	−0.652205
$501$	2224.93	0.198408
$502$	−1922.78	−0.170952
$503$	15526.9	1.37636	0.688181	−	0.725539i	$-0.258409\pi$
$503$	15526.9	1.37636	0.688181	+	0.725539i	$0.258409\pi$
$504$	−20175.6	−1.78312
$505$	−3042.96	−0.268138
$506$	26700.7	2.34583
$507$	1639.47	0.143612
$508$	−34745.9	−3.03465
$509$	16682.2	1.45271	0.726353	−	0.687322i	$-0.241214\pi$
$509$	16682.2	1.45271	0.726353	+	0.687322i	$0.241214\pi$
$510$	635.429	0.0551711
$511$	6907.38	0.597974
$512$	−23201.8	−2.00271
$513$	−4186.73	−0.360329
$514$	−3424.22	−0.293844
$515$	943.338	0.0807154
$516$	0	0
$517$	−20697.0	−1.76064
$518$	10871.6	0.922142
$519$	2101.93	0.177773
$520$	554.233	0.0467399
$521$	3161.97	0.265890	0.132945	−	0.991123i	$-0.457557\pi$
$521$	3161.97	0.265890	0.132945	+	0.991123i	$0.457557\pi$
$522$	37489.4	3.14342
$523$	9582.45	0.801169	0.400584	−	0.916260i	$-0.368807\pi$
$523$	9582.45	0.801169	0.400584	+	0.916260i	$0.368807\pi$
$524$	−21848.5	−1.82148
$525$	1240.41	0.103116
$526$	−5553.65	−0.460362
$527$	−1667.24	−0.137811
$528$	4187.19	0.345122
$529$	6308.30	0.518476
$530$	−4515.58	−0.370084
$531$	−4489.01	−0.366867
$532$	−26140.2	−2.13030
$533$	1901.36	0.154516
$534$	−4640.94	−0.376092
$535$	2088.09	0.168740
$536$	−1699.20	−0.136930
$537$	−871.421	−0.0700272
$538$	−16027.4	−1.28437
$539$	6259.41	0.500208
$540$	1195.26	0.0952511
$541$	−9357.70	−0.743658	−0.371829	−	0.928301i	$-0.621269\pi$
$541$	−9357.70	−0.743658	−0.371829	+	0.928301i	$0.621269\pi$
$542$	−23580.8	−1.86879
$543$	40.8607	0.00322928
$544$	−31148.5	−2.45493
$545$	−593.514	−0.0466483
$546$	−328.512	−0.0257491
$547$	9615.47	0.751605	0.375802	−	0.926700i	$-0.377367\pi$
$547$	9615.47	0.751605	0.375802	+	0.926700i	$0.377367\pi$
$548$	−3305.85	−0.257698
$549$	−7188.59	−0.558837
$550$	24084.3	1.86720
$551$	28152.0	2.17662
$552$	5920.99	0.456547
$553$	−2342.29	−0.180116
$554$	−21571.2	−1.65428
$555$	−184.628	−0.0141208
$556$	−2937.36	−0.224050
$557$	−14274.1	−1.08584	−0.542922	−	0.839783i	$-0.682682\pi$
$557$	−14274.1	−1.08584	−0.542922	+	0.839783i	$0.682682\pi$
$558$	−2203.23	−0.167151
$559$	0	0
$560$	3006.25	0.226852
$561$	−2984.00	−0.224572
$562$	31141.5	2.33741
$563$	−23539.5	−1.76212	−0.881058	−	0.473008i	$-0.843168\pi$
$563$	−23539.5	−1.76212	−0.881058	+	0.473008i	$0.843168\pi$
$564$	−7918.80	−0.591209
$565$	261.501	0.0194715
$566$	−25079.3	−1.86248
$567$	9089.85	0.673259
$568$	29939.1	2.21165
$569$	−13681.7	−1.00803	−0.504013	−	0.863696i	$-0.668144\pi$
$569$	−13681.7	−1.00803	−0.504013	+	0.863696i	$0.668144\pi$
$570$	630.564	0.0463358
$571$	−20623.5	−1.51150	−0.755750	−	0.654860i	$-0.772728\pi$
$571$	−20623.5	−1.51150	−0.755750	+	0.654860i	$0.772728\pi$
$572$	−4490.63	−0.328256
$573$	439.817	0.0320657
$574$	21076.5	1.53261
$575$	16664.9	1.20865
$576$	−10328.5	−0.747144
$577$	20097.6	1.45004	0.725022	−	0.688726i	$-0.241830\pi$
$577$	20097.6	1.45004	0.725022	+	0.688726i	$0.241830\pi$
$578$	30637.1	2.20473
$579$	990.750	0.0711126
$580$	−8037.03	−0.575378
$581$	13188.2	0.941717
$582$	−2200.99	−0.156759
$583$	21205.4	1.50641
$584$	29741.0	2.10735
$585$	−255.404	−0.0180507
$586$	−7343.67	−0.517686
$587$	−11803.2	−0.829929	−0.414965	−	0.909838i	$-0.636206\pi$
$587$	−11803.2	−0.829929	−0.414965	+	0.909838i	$0.636206\pi$
$588$	2394.90	0.167966
$589$	−1654.48	−0.115741
$590$	1366.95	0.0953838
$591$	15.9249	0.00110840
$592$	22905.1	1.59019
$593$	12440.0	0.861463	0.430732	−	0.902480i	$-0.358256\pi$
$593$	12440.0	0.861463	0.430732	+	0.902480i	$0.358256\pi$
$594$	−7972.75	−0.550717
$595$	−2142.40	−0.147613
$596$	38695.6	2.65946
$597$	3545.14	0.243036
$598$	−4413.58	−0.301814
$599$	−12.3439	−0.000841998 0	−0.000420999	−	1.00000i	$-0.500134\pi$
$599$	−12.3439	−0.000841998 0	−0.000420999		1.00000i	$0.500134\pi$
$600$	5340.79	0.363395
$601$	24805.2	1.68357	0.841784	−	0.539814i	$-0.181506\pi$
$601$	24805.2	1.68357	0.841784	+	0.539814i	$0.181506\pi$
$602$	0	0
$603$	783.033	0.0528815
$604$	−17617.8	−1.18685
$605$	149.605	0.0100534
$606$	7765.98	0.520580
$607$	9978.82	0.667262	0.333631	−	0.942704i	$-0.391726\pi$
$607$	9978.82	0.667262	0.333631	+	0.942704i	$0.391726\pi$
$608$	−30910.0	−2.06179
$609$	2761.03	0.183715
$610$	2189.00	0.145295
$611$	3421.17	0.226523
$612$	52266.5	3.45220
$613$	2908.44	0.191633	0.0958164	−	0.995399i	$-0.469454\pi$
$613$	2908.44	0.191633	0.0958164	+	0.995399i	$0.469454\pi$
$614$	44512.0	2.92567
$615$	−357.935	−0.0234688
$616$	−28850.9	−1.88707
$617$	14423.2	0.941095	0.470548	−	0.882375i	$-0.344056\pi$
$617$	14423.2	0.941095	0.470548	+	0.882375i	$0.344056\pi$
$618$	−2407.51	−0.156706
$619$	17175.3	1.11524	0.557619	−	0.830097i	$-0.311715\pi$
$619$	17175.3	1.11524	0.557619	+	0.830097i	$0.311715\pi$
$620$	472.332	0.0305957
$621$	−5516.66	−0.356483
$622$	−51580.0	−3.32503
$623$	15647.3	1.00626
$624$	−692.135	−0.0444032
$625$	14732.6	0.942883
$626$	−12173.6	−0.777247
$627$	−2961.16	−0.188608
$628$	−1313.02	−0.0834322
$629$	−16323.3	−1.03474
$630$	−2831.15	−0.179041
$631$	29159.8	1.83967	0.919836	−	0.392303i	$-0.128322\pi$
$631$	29159.8	1.83967	0.919836	+	0.392303i	$0.128322\pi$
$632$	−10085.2	−0.634757
$633$	−2223.09	−0.139589
$634$	−4413.01	−0.276440
$635$	−2825.91	−0.176603
$636$	8113.33	0.505840
$637$	−1034.67	−0.0643565
$638$	53609.6	3.32669
$639$	−13796.6	−0.854126
$640$	−564.762	−0.0348815
$641$	4435.81	0.273329	0.136665	−	0.990617i	$-0.456362\pi$
$641$	4435.81	0.273329	0.136665	+	0.990617i	$0.456362\pi$
$642$	−5329.05	−0.327603
$643$	−7982.01	−0.489549	−0.244774	−	0.969580i	$-0.578714\pi$
$643$	−7982.01	−0.489549	−0.244774	+	0.969580i	$0.578714\pi$
$644$	−34443.8	−2.10757
$645$	0	0
$646$	55749.3	3.39540
$647$	1298.36	0.0788927	0.0394464	−	0.999222i	$-0.487441\pi$
$647$	1298.36	0.0788927	0.0394464	+	0.999222i	$0.487441\pi$
$648$	39138.0	2.37267
$649$	−6419.26	−0.388256
$650$	−3981.10	−0.240233
$651$	−162.265	−0.00976904
$652$	60363.8	3.62581
$653$	18989.2	1.13798	0.568991	−	0.822343i	$-0.307334\pi$
$653$	18989.2	1.13798	0.568991	+	0.822343i	$0.307334\pi$
$654$	1514.72	0.0905659
$655$	−1776.96	−0.106002
$656$	44405.7	2.64291
$657$	−13705.4	−0.813846
$658$	37923.5	2.24683
$659$	11152.9	0.659266	0.329633	−	0.944109i	$-0.393075\pi$
$659$	11152.9	0.659266	0.329633	+	0.944109i	$0.393075\pi$
$660$	845.371	0.0498576
$661$	−2606.49	−0.153375	−0.0766873	−	0.997055i	$-0.524434\pi$
$661$	−2606.49	−0.153375	−0.0766873	+	0.997055i	$0.524434\pi$
$662$	51430.8	3.01951
$663$	493.250	0.0288933
$664$	56784.1	3.31875
$665$	−2126.00	−0.123974
$666$	−21571.0	−1.25504
$667$	37094.6	2.15339
$668$	−55728.2	−3.22783
$669$	−1860.89	−0.107543
$670$	−238.441	−0.0137490
$671$	−10279.6	−0.591418
$672$	−3031.53	−0.174023
$673$	−11770.5	−0.674175	−0.337088	−	0.941473i	$-0.609442\pi$
$673$	−11770.5	−0.674175	−0.337088	+	0.941473i	$0.609442\pi$
$674$	20237.0	1.15653
$675$	−4976.09	−0.283748
$676$	−41064.1	−2.33637
$677$	−32322.0	−1.83491	−0.917457	−	0.397836i	$-0.869761\pi$
$677$	−32322.0	−1.83491	−0.917457	+	0.397836i	$0.869761\pi$
$678$	−667.380	−0.0378032
$679$	7420.83	0.419419
$680$	−9224.51	−0.520211
$681$	2137.52	0.120279
$682$	−3150.61	−0.176896
$683$	7733.21	0.433240	0.216620	−	0.976256i	$-0.430497\pi$
$683$	7733.21	0.433240	0.216620	+	0.976256i	$0.430497\pi$
$684$	51866.4	2.89936
$685$	−268.867	−0.0149969
$686$	−35216.4	−1.96001
$687$	−3082.17	−0.171167
$688$	0	0
$689$	−3505.21	−0.193814
$690$	830.866	0.0458413
$691$	20271.3	1.11600	0.558000	−	0.829841i	$-0.311569\pi$
$691$	20271.3	1.11600	0.558000	+	0.829841i	$0.311569\pi$
$692$	−52647.4	−2.89213
$693$	13295.2	0.728778
$694$	−19596.6	−1.07187
$695$	−238.898	−0.0130387
$696$	11888.1	0.647441
$697$	−31645.7	−1.71975
$698$	37673.3	2.04292
$699$	4131.63	0.223566
$700$	−31068.7	−1.67755
$701$	−21437.3	−1.15503	−0.577516	−	0.816380i	$-0.695978\pi$
$701$	−21437.3	−1.15503	−0.577516	+	0.816380i	$0.695978\pi$
$702$	1317.88	0.0708550
$703$	−16198.3	−0.869035
$704$	−14769.7	−0.790703
$705$	−644.042	−0.0344057
$706$	−54700.3	−2.91597
$707$	−26183.7	−1.39284
$708$	−2456.06	−0.130373
$709$	18958.1	1.00421	0.502105	−	0.864806i	$-0.332559\pi$
$709$	18958.1	1.00421	0.502105	+	0.864806i	$0.332559\pi$
$710$	4201.22	0.222069
$711$	4647.48	0.245140
$712$	67372.5	3.54619
$713$	−2180.03	−0.114506
$714$	5467.66	0.286586
$715$	−365.226	−0.0191031
$716$	21826.6	1.13924
$717$	−697.770	−0.0363441
$718$	−30379.6	−1.57905
$719$	−11620.0	−0.602715	−0.301357	−	0.953511i	$-0.597440\pi$
$719$	−11620.0	−0.602715	−0.301357	+	0.953511i	$0.597440\pi$
$720$	−5964.88	−0.308747
$721$	8117.12	0.419275
$722$	19663.0	1.01355
$723$	3510.19	0.180561
$724$	−1023.44	−0.0525359
$725$	33459.8	1.71402
$726$	−381.809	−0.0195182
$727$	4977.52	0.253929	0.126964	−	0.991907i	$-0.459477\pi$
$727$	4977.52	0.253929	0.126964	+	0.991907i	$0.459477\pi$
$728$	4769.00	0.242790
$729$	−17203.2	−0.874014
$730$	4173.42	0.211596
$731$	0	0
$732$	−3933.07	−0.198593
$733$	−21266.7	−1.07163	−0.535815	−	0.844336i	$-0.679995\pi$
$733$	−21266.7	−1.07163	−0.535815	+	0.844336i	$0.679995\pi$
$734$	27798.8	1.39792
$735$	194.779	0.00977486
$736$	−40728.7	−2.03978
$737$	1119.73	0.0559645
$738$	−41819.2	−2.08589
$739$	−25736.8	−1.28111	−0.640556	−	0.767911i	$-0.721296\pi$
$739$	−25736.8	−1.28111	−0.640556	+	0.767911i	$0.721296\pi$
$740$	4624.41	0.229725
$741$	489.473	0.0242662
$742$	−38855.1	−1.92239
$743$	−15289.2	−0.754923	−0.377462	−	0.926025i	$-0.623203\pi$
$743$	−15289.2	−0.754923	−0.377462	+	0.926025i	$0.623203\pi$
$744$	−698.660	−0.0344276
$745$	3147.14	0.154768
$746$	−8058.54	−0.395502
$747$	−26167.5	−1.28168
$748$	74740.8	3.65347
$749$	17967.4	0.876520
$750$	1513.54	0.0736889
$751$	19407.1	0.942974	0.471487	−	0.881873i	$-0.343717\pi$
$751$	19407.1	0.942974	0.471487	+	0.881873i	$0.343717\pi$
$752$	79900.3	3.87455
$753$	280.977	0.0135981
$754$	−8861.57	−0.428010
$755$	−1432.87	−0.0690693
$756$	10284.8	0.494781
$757$	9636.00	0.462650	0.231325	−	0.972877i	$-0.425694\pi$
$757$	9636.00	0.462650	0.231325	+	0.972877i	$0.425694\pi$
$758$	−23338.5	−1.11833
$759$	−3901.78	−0.186595
$760$	−9153.89	−0.436903
$761$	4368.49	0.208092	0.104046	−	0.994573i	$-0.466821\pi$
$761$	4368.49	0.208092	0.104046	+	0.994573i	$0.466821\pi$
$762$	7212.06	0.342868
$763$	−5107.00	−0.242314
$764$	−11016.2	−0.521664
$765$	4250.87	0.200903
$766$	10025.7	0.472901
$767$	1061.09	0.0499528
$768$	3817.10	0.179346
$769$	11777.9	0.552304	0.276152	−	0.961114i	$-0.410941\pi$
$769$	11777.9	0.552304	0.276152	+	0.961114i	$0.410941\pi$
$770$	−4048.52	−0.189479
$771$	500.383	0.0233733
$772$	−24815.5	−1.15690
$773$	−6291.30	−0.292732	−0.146366	−	0.989230i	$-0.546758\pi$
$773$	−6291.30	−0.292732	−0.146366	+	0.989230i	$0.546758\pi$
$774$	0	0
$775$	−1966.41	−0.0911428
$776$	31951.7	1.47809
$777$	−1588.67	−0.0733502
$778$	30496.9	1.40536
$779$	−31403.4	−1.44434
$780$	−139.738	−0.00641465
$781$	−19729.1	−0.903922
$782$	73458.4	3.35916
$783$	−11076.3	−0.505538
$784$	−24164.4	−1.10078
$785$	−106.789	−0.00485538
$786$	4535.00	0.205799
$787$	24499.3	1.10966	0.554831	−	0.831963i	$-0.312783\pi$
$787$	24499.3	1.10966	0.554831	+	0.831963i	$0.312783\pi$
$788$	−398.875	−0.0180321
$789$	811.556	0.0366187
$790$	−1415.21	−0.0637352
$791$	2250.13	0.101145
$792$	57244.9	2.56832
$793$	1699.21	0.0760915
$794$	−21223.8	−0.948622
$795$	659.863	0.0294376
$796$	−88795.6	−3.95387
$797$	−26435.2	−1.17488	−0.587442	−	0.809266i	$-0.699865\pi$
$797$	−26435.2	−1.17488	−0.587442	+	0.809266i	$0.699865\pi$
$798$	5425.80	0.240691
$799$	−56940.9	−2.52118
$800$	−36737.8	−1.62359
$801$	−31046.8	−1.36952
$802$	17039.1	0.750212
$803$	−19598.6	−0.861294
$804$	428.418	0.0187924
$805$	−2801.34	−0.122651
$806$	520.790	0.0227594
$807$	2342.08	0.102163
$808$	−112739.	−4.90858
$809$	−3348.45	−0.145520	−0.0727598	−	0.997349i	$-0.523181\pi$
$809$	−3348.45	−0.145520	−0.0727598	+	0.997349i	$0.523181\pi$
$810$	5492.07	0.238237
$811$	33297.4	1.44171	0.720857	−	0.693084i	$-0.243748\pi$
$811$	33297.4	1.44171	0.720857	+	0.693084i	$0.243748\pi$
$812$	−69156.1	−2.98880
$813$	3445.87	0.148649
$814$	−30846.3	−1.32821
$815$	4909.43	0.211006
$816$	11519.7	0.494204
$817$	0	0
$818$	−69709.9	−2.97964
$819$	−2197.67	−0.0937641
$820$	8965.26	0.381805
$821$	22570.1	0.959443	0.479721	−	0.877421i	$-0.340738\pi$
$821$	22570.1	0.959443	0.479721	+	0.877421i	$0.340738\pi$
$822$	686.179	0.0291159
$823$	54.0301	0.00228842	0.00114421	−	0.999999i	$-0.499636\pi$
$823$	54.0301	0.00228842	0.00114421	+	0.999999i	$0.499636\pi$
$824$	34949.8	1.47759
$825$	−3519.45	−0.148523
$826$	11762.2	0.495470
$827$	−19326.3	−0.812624	−0.406312	−	0.913734i	$-0.633185\pi$
$827$	−19326.3	−0.812624	−0.406312	+	0.913734i	$0.633185\pi$
$828$	68342.0	2.86842
$829$	−2431.56	−0.101871	−0.0509357	−	0.998702i	$-0.516220\pi$
$829$	−2431.56	−0.101871	−0.0509357	+	0.998702i	$0.516220\pi$
$830$	7968.26	0.333232
$831$	3152.20	0.131587
$832$	2441.41	0.101731
$833$	17220.7	0.716283
$834$	609.694	0.0253141
$835$	−4532.41	−0.187845
$836$	74168.6	3.06839
$837$	650.951	0.0268819
$838$	−60738.6	−2.50380
$839$	−23086.8	−0.949993	−0.474997	−	0.879988i	$-0.657551\pi$
$839$	−23086.8	−0.949993	−0.474997	+	0.879988i	$0.657551\pi$
$840$	−897.775	−0.0368764
$841$	50089.5	2.05378
$842$	16890.1	0.691297
$843$	−4550.71	−0.185925
$844$	55682.0	2.27092
$845$	−3339.77	−0.135966
$846$	−75246.5	−3.05795
$847$	1287.30	0.0522222
$848$	−81863.1	−3.31508
$849$	3664.85	0.148148
$850$	66260.3	2.67377
$851$	−21343.8	−0.859761
$852$	−7548.50	−0.303530
$853$	−15247.9	−0.612051	−0.306025	−	0.952023i	$-0.598999\pi$
$853$	−15247.9	−0.612051	−0.306025	+	0.952023i	$0.598999\pi$
$854$	18835.7	0.754734
$855$	4218.33	0.168730
$856$	77361.8	3.08899
$857$	−6797.71	−0.270952	−0.135476	−	0.990781i	$-0.543256\pi$
$857$	−6797.71	−0.270952	−0.135476	+	0.990781i	$0.543256\pi$
$858$	932.100	0.0370878
$859$	19722.7	0.783388	0.391694	−	0.920095i	$-0.371889\pi$
$859$	19722.7	0.783388	0.391694	+	0.920095i	$0.371889\pi$
$860$	0	0
$861$	−3079.92	−0.121909
$862$	−14418.6	−0.569722
$863$	−22879.2	−0.902453	−0.451226	−	0.892410i	$-0.649013\pi$
$863$	−22879.2	−0.902453	−0.451226	+	0.892410i	$0.649013\pi$
$864$	12161.5	0.478867
$865$	−4281.85	−0.168309
$866$	−75176.3	−2.94988
$867$	−4477.01	−0.175372
$868$	4064.27	0.158929
$869$	6645.87	0.259431
$870$	1668.21	0.0650087
$871$	−185.090	−0.00720037
$872$	−21989.1	−0.853951
$873$	−14724.1	−0.570832
$874$	72896.0	2.82122
$875$	−5103.03	−0.197159
$876$	−7498.56	−0.289216
$877$	−15436.5	−0.594358	−0.297179	−	0.954822i	$-0.596046\pi$
$877$	−15436.5	−0.594358	−0.297179	+	0.954822i	$0.596046\pi$
$878$	−30151.6	−1.15896
$879$	1073.13	0.0411784
$880$	−8529.75	−0.326748
$881$	−5683.15	−0.217333	−0.108666	−	0.994078i	$-0.534658\pi$
$881$	−5683.15	−0.217333	−0.108666	+	0.994078i	$0.534658\pi$
$882$	22756.9	0.868781
$883$	34681.0	1.32175	0.660877	−	0.750494i	$-0.270184\pi$
$883$	34681.0	1.32175	0.660877	+	0.750494i	$0.270184\pi$
$884$	−12354.5	−0.470053
$885$	−199.753	−0.00758714
$886$	−3414.08	−0.129456
$887$	182.395	0.00690444	0.00345222	−	0.999994i	$-0.498901\pi$
$887$	182.395	0.00690444	0.00345222	+	0.999994i	$0.498901\pi$
$888$	−6840.29	−0.258497
$889$	−24316.1	−0.917362
$890$	9454.08	0.356069
$891$	−25791.0	−0.969732
$892$	46610.0	1.74957
$893$	−56505.0	−2.11743
$894$	−8031.88	−0.300477
$895$	1775.18	0.0662990
$896$	−4859.60	−0.181192
$897$	644.957	0.0240072
$898$	−75449.1	−2.80375
$899$	−4377.06	−0.162384
$900$	61645.2	2.28316
$901$	58339.7	2.15713
$902$	−59801.2	−2.20750
$903$	0	0
$904$	9688.35	0.356449
$905$	−83.2374	−0.00305735
$906$	3656.84	0.134095
$907$	−17963.1	−0.657614	−0.328807	−	0.944397i	$-0.606647\pi$
$907$	−17963.1	−0.657614	−0.328807	+	0.944397i	$0.606647\pi$
$908$	−53538.9	−1.95677
$909$	51952.7	1.89567
$910$	669.213	0.0243782
$911$	−4378.61	−0.159243	−0.0796213	−	0.996825i	$-0.525371\pi$
$911$	−4378.61	−0.159243	−0.0796213	+	0.996825i	$0.525371\pi$
$912$	11431.5	0.415060
$913$	−37419.3	−1.35641
$914$	−10054.8	−0.363876
$915$	−319.879	−0.0115572
$916$	77199.6	2.78466
$917$	−15290.2	−0.550627
$918$	−21934.4	−0.788610
$919$	17620.4	0.632475	0.316237	−	0.948680i	$-0.397580\pi$
$919$	17620.4	0.632475	0.316237	+	0.948680i	$0.397580\pi$
$920$	−12061.7	−0.432241
$921$	−6504.56	−0.232717
$922$	−47781.9	−1.70674
$923$	3261.18	0.116298
$924$	7274.15	0.258985
$925$	−19252.4	−0.684339
$926$	−50333.8	−1.78625
$927$	−16105.7	−0.570637
$928$	−81775.0	−2.89267
$929$	8531.15	0.301290	0.150645	−	0.988588i	$-0.451865\pi$
$929$	8531.15	0.301290	0.150645	+	0.988588i	$0.451865\pi$
$930$	−98.0398	−0.00345683
$931$	17088.9	0.601575
$932$	−103486.	−3.63711
$933$	7537.39	0.264484
$934$	43716.1	1.53151
$935$	6078.72	0.212616
$936$	−9462.47	−0.330439
$937$	−21687.1	−0.756123	−0.378062	−	0.925780i	$-0.623409\pi$
$937$	−21687.1	−0.756123	−0.378062	+	0.925780i	$0.623409\pi$
$938$	−2051.71	−0.0714188
$939$	1778.94	0.0618248
$940$	16131.4	0.559733
$941$	8811.91	0.305271	0.152636	−	0.988283i	$-0.451224\pi$
$941$	8811.91	0.305271	0.152636	+	0.988283i	$0.451224\pi$
$942$	272.539	0.00942653
$943$	−41378.9	−1.42893
$944$	24781.5	0.854415
$945$	836.470	0.0287940
$946$	0	0
$947$	−12721.0	−0.436511	−0.218255	−	0.975892i	$-0.570037\pi$
$947$	−12721.0	−0.436511	−0.218255	+	0.975892i	$0.570037\pi$
$948$	2542.76	0.0871150
$949$	3239.61	0.110814
$950$	65753.0	2.24559
$951$	644.874	0.0219889
$952$	−79374.0	−2.70223
$953$	38861.4	1.32093	0.660464	−	0.750858i	$-0.270360\pi$
$953$	38861.4	1.32093	0.660464	+	0.750858i	$0.270360\pi$
$954$	77094.9	2.61639
$955$	−895.953	−0.0303585
$956$	17477.2	0.591268
$957$	−7833.99	−0.264615
$958$	38447.2	1.29663
$959$	−2313.51	−0.0779012
$960$	−459.600	−0.0154516
$961$	−29533.8	−0.991365
$962$	5098.84	0.170887
$963$	−35650.2	−1.19295
$964$	−87920.3	−2.93747
$965$	−2018.26	−0.0673266
$966$	7149.34	0.238122
$967$	36221.1	1.20454	0.602271	−	0.798292i	$-0.294263\pi$
$967$	36221.1	1.20454	0.602271	+	0.798292i	$0.294263\pi$
$968$	5542.71	0.184039
$969$	−8146.66	−0.270081
$970$	4483.65	0.148414
$971$	−37637.0	−1.24390	−0.621952	−	0.783056i	$-0.713660\pi$
$971$	−37637.0	−1.24390	−0.621952	+	0.783056i	$0.713660\pi$
$972$	−30720.3	−1.01374
$973$	−2055.64	−0.0677294
$974$	97205.6	3.19781
$975$	581.759	0.0191089
$976$	39684.4	1.30150
$977$	29341.3	0.960809	0.480404	−	0.877047i	$-0.340490\pi$
$977$	29341.3	0.960809	0.480404	+	0.877047i	$0.340490\pi$
$978$	−12529.4	−0.409660
$979$	−44396.8	−1.44936
$980$	−4878.66	−0.159023
$981$	10133.1	0.329791
$982$	−87301.7	−2.83698
$983$	−24200.7	−0.785231	−0.392615	−	0.919703i	$-0.628430\pi$
$983$	−24200.7	−0.785231	−0.392615	+	0.919703i	$0.628430\pi$
$984$	−13261.1	−0.429624
$985$	−32.4408	−0.00104939
$986$	147489.	4.76371
$987$	−5541.78	−0.178720
$988$	−12259.9	−0.394778
$989$	0	0
$990$	8032.93	0.257882
$991$	61657.9	1.97642	0.988208	−	0.153120i	$-0.0489320\pi$
$991$	61657.9	1.97642	0.988208	+	0.153120i	$0.0489320\pi$
$992$	4805.88	0.153817
$993$	−7515.59	−0.240181
$994$	36150.1	1.15353
$995$	−7221.81	−0.230097
$996$	−14316.9	−0.455470
$997$	26103.4	0.829191	0.414596	−	0.910006i	$-0.363923\pi$
$997$	26103.4	0.829191	0.414596	+	0.910006i	$0.363923\pi$
$998$	1764.95	0.0559804
$999$	6373.20	0.201841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.b.1.4		4
43.42	odd	2		43.4.a.a.1.1	✓	4
129.128	even	2		387.4.a.e.1.4		4
172.171	even	2		688.4.a.f.1.2		4
215.214	odd	2		1075.4.a.a.1.4		4
301.300	even	2		2107.4.a.b.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.a.1.1	✓	4	43.42	odd	2
387.4.a.e.1.4		4	129.128	even	2
688.4.a.f.1.2		4	172.171	even	2
1075.4.a.a.1.4		4	215.214	odd	2
1849.4.a.b.1.4		4	1.1	even	1	trivial
2107.4.a.b.1.1		4	301.300	even	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+5.19893 q^{2} -0.759721 q^{3} +19.0289 q^{4} +1.54763 q^{5} -3.94973 q^{6} +13.3169 q^{7} +57.3382 q^{8} -26.4228 q^{9} +O(q^{10})\)	\(q+5.19893 q^{2} -0.759721 q^{3} +19.0289 q^{4} +1.54763 q^{5} -3.94973 q^{6} +13.3169 q^{7} +57.3382 q^{8} -26.4228 q^{9} +8.04602 q^{10} -37.7845 q^{11} -14.4566 q^{12} +6.24570 q^{13} +69.2335 q^{14} -1.17577 q^{15} +145.866 q^{16} -103.952 q^{17} -137.370 q^{18} -103.156 q^{19} +29.4496 q^{20} -10.1171 q^{21} -196.439 q^{22} -135.924 q^{23} -43.5610 q^{24} -122.605 q^{25} +32.4710 q^{26} +40.5864 q^{27} +253.405 q^{28} -272.908 q^{29} -6.11273 q^{30} +16.0386 q^{31} +299.644 q^{32} +28.7057 q^{33} -540.438 q^{34} +20.6096 q^{35} -502.796 q^{36} +157.028 q^{37} -536.300 q^{38} -4.74499 q^{39} +88.7384 q^{40} +304.427 q^{41} -52.5981 q^{42} -718.995 q^{44} -40.8928 q^{45} -706.658 q^{46} +547.763 q^{47} -110.818 q^{48} -165.661 q^{49} -637.414 q^{50} +78.9743 q^{51} +118.849 q^{52} -561.219 q^{53} +211.006 q^{54} -58.4764 q^{55} +763.566 q^{56} +78.3697 q^{57} -1418.83 q^{58} +169.891 q^{59} -22.3735 q^{60} +272.060 q^{61} +83.3837 q^{62} -351.869 q^{63} +390.894 q^{64} +9.66604 q^{65} +149.239 q^{66} -29.6347 q^{67} -1978.08 q^{68} +103.264 q^{69} +107.148 q^{70} +522.148 q^{71} -1515.04 q^{72} +518.694 q^{73} +816.376 q^{74} +93.1454 q^{75} -1962.94 q^{76} -503.171 q^{77} -24.6689 q^{78} -175.889 q^{79} +225.747 q^{80} +682.582 q^{81} +1582.69 q^{82} +990.336 q^{83} -192.517 q^{84} -160.879 q^{85} +207.334 q^{87} -2166.50 q^{88} +1175.00 q^{89} -212.599 q^{90} +83.1732 q^{91} -2586.48 q^{92} -12.1849 q^{93} +2847.78 q^{94} -159.647 q^{95} -227.645 q^{96} +557.250 q^{97} -861.260 q^{98} +998.373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 11 q^{3} + 2 q^{4} + 27 q^{5} - 27 q^{6} + 20 q^{7} + 66 q^{8} - 9 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 11 * q^3 + 2 * q^4 + 27 * q^5 - 27 * q^6 + 20 * q^7 + 66 * q^8 - 9 * q^9	\( 4 q + 4 q^{2} + 11 q^{3} + 2 q^{4} + 27 q^{5} - 27 q^{6} + 20 q^{7} + 66 q^{8} - 9 q^{9} - 3 q^{10} - 62 q^{11} - 61 q^{12} - 2 q^{13} + 112 q^{14} + 92 q^{15} + 202 q^{16} - 207 q^{17} - 299 q^{18} - 99 q^{19} - 81 q^{20} - 90 q^{21} - 202 q^{22} - 103 q^{23} + 209 q^{24} - 101 q^{25} + 50 q^{26} + 218 q^{27} + 80 q^{28} + 99 q^{29} - 300 q^{30} + 131 q^{31} + 342 q^{32} + 32 q^{33} - 53 q^{34} - 374 q^{35} - 379 q^{36} + 449 q^{37} - 609 q^{38} - 98 q^{39} + 133 q^{40} - 491 q^{41} + 394 q^{42} - 764 q^{44} + 338 q^{45} - 1061 q^{46} + 19 q^{47} - 237 q^{48} + 236 q^{49} - 599 q^{50} - 1649 q^{51} + 224 q^{52} - 1220 q^{53} - 322 q^{54} - 1360 q^{55} + 344 q^{56} + 232 q^{57} - 771 q^{58} + 816 q^{59} - 156 q^{60} - 372 q^{61} + 97 q^{62} - 1914 q^{63} + 434 q^{64} + 350 q^{65} + 812 q^{66} + 110 q^{67} - 1697 q^{68} + 1238 q^{69} + 718 q^{70} - 468 q^{71} + 315 q^{72} - 628 q^{73} + 395 q^{74} - 62 q^{75} - 1671 q^{76} + 2044 q^{77} - 90 q^{78} + 1095 q^{79} + 31 q^{80} + 2056 q^{81} + 2287 q^{82} - 980 q^{83} - 610 q^{84} + 152 q^{85} - 507 q^{87} - 1816 q^{88} + 738 q^{89} - 2398 q^{90} - 852 q^{91} - 2517 q^{92} + 35 q^{93} + 2233 q^{94} + 1149 q^{95} - 1551 q^{96} - 1765 q^{97} - 1652 q^{98} - 58 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 11 * q^3 + 2 * q^4 + 27 * q^5 - 27 * q^6 + 20 * q^7 + 66 * q^8 - 9 * q^9 - 3 * q^10 - 62 * q^11 - 61 * q^12 - 2 * q^13 + 112 * q^14 + 92 * q^15 + 202 * q^16 - 207 * q^17 - 299 * q^18 - 99 * q^19 - 81 * q^20 - 90 * q^21 - 202 * q^22 - 103 * q^23 + 209 * q^24 - 101 * q^25 + 50 * q^26 + 218 * q^27 + 80 * q^28 + 99 * q^29 - 300 * q^30 + 131 * q^31 + 342 * q^32 + 32 * q^33 - 53 * q^34 - 374 * q^35 - 379 * q^36 + 449 * q^37 - 609 * q^38 - 98 * q^39 + 133 * q^40 - 491 * q^41 + 394 * q^42 - 764 * q^44 + 338 * q^45 - 1061 * q^46 + 19 * q^47 - 237 * q^48 + 236 * q^49 - 599 * q^50 - 1649 * q^51 + 224 * q^52 - 1220 * q^53 - 322 * q^54 - 1360 * q^55 + 344 * q^56 + 232 * q^57 - 771 * q^58 + 816 * q^59 - 156 * q^60 - 372 * q^61 + 97 * q^62 - 1914 * q^63 + 434 * q^64 + 350 * q^65 + 812 * q^66 + 110 * q^67 - 1697 * q^68 + 1238 * q^69 + 718 * q^70 - 468 * q^71 + 315 * q^72 - 628 * q^73 + 395 * q^74 - 62 * q^75 - 1671 * q^76 + 2044 * q^77 - 90 * q^78 + 1095 * q^79 + 31 * q^80 + 2056 * q^81 + 2287 * q^82 - 980 * q^83 - 610 * q^84 + 152 * q^85 - 507 * q^87 - 1816 * q^88 + 738 * q^89 - 2398 * q^90 - 852 * q^91 - 2517 * q^92 + 35 * q^93 + 2233 * q^94 + 1149 * q^95 - 1551 * q^96 - 1765 * q^97 - 1652 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more