LMFDB - Embedded newform 1859.4.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.05441 q^{2} +0.801365 q^{3} +17.5470 q^{4} -17.5680 q^{5} -4.05042 q^{6} +1.71020 q^{7} -48.2547 q^{8} -26.3578 q^{9} +O(q^{10})$	\(q-5.05441 q^{2} +0.801365 q^{3} +17.5470 q^{4} -17.5680 q^{5} -4.05042 q^{6} +1.71020 q^{7} -48.2547 q^{8} -26.3578 q^{9} +88.7960 q^{10} +11.0000 q^{11} +14.0616 q^{12} -8.64404 q^{14} -14.0784 q^{15} +103.522 q^{16} +47.2534 q^{17} +133.223 q^{18} -150.092 q^{19} -308.267 q^{20} +1.37049 q^{21} -55.5985 q^{22} +59.4061 q^{23} -38.6696 q^{24} +183.636 q^{25} -42.7591 q^{27} +30.0089 q^{28} -91.1947 q^{29} +71.1580 q^{30} +74.1614 q^{31} -137.207 q^{32} +8.81501 q^{33} -238.838 q^{34} -30.0448 q^{35} -462.502 q^{36} +83.8911 q^{37} +758.624 q^{38} +847.740 q^{40} -378.855 q^{41} -6.92703 q^{42} +329.816 q^{43} +193.017 q^{44} +463.055 q^{45} -300.263 q^{46} -539.208 q^{47} +82.9592 q^{48} -340.075 q^{49} -928.171 q^{50} +37.8672 q^{51} -7.33959 q^{53} +216.122 q^{54} -193.248 q^{55} -82.5250 q^{56} -120.278 q^{57} +460.935 q^{58} -676.124 q^{59} -247.034 q^{60} -359.563 q^{61} -374.842 q^{62} -45.0771 q^{63} -134.678 q^{64} -44.5547 q^{66} -318.437 q^{67} +829.157 q^{68} +47.6059 q^{69} +151.859 q^{70} -704.480 q^{71} +1271.89 q^{72} +1043.78 q^{73} -424.020 q^{74} +147.159 q^{75} -2633.66 q^{76} +18.8122 q^{77} -112.511 q^{79} -1818.69 q^{80} +677.395 q^{81} +1914.89 q^{82} -614.013 q^{83} +24.0481 q^{84} -830.149 q^{85} -1667.02 q^{86} -73.0802 q^{87} -530.801 q^{88} +410.480 q^{89} -2340.47 q^{90} +1042.40 q^{92} +59.4303 q^{93} +2725.38 q^{94} +2636.81 q^{95} -109.953 q^{96} +934.568 q^{97} +1718.88 q^{98} -289.936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * 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 $

$2$	−5.05441	−1.78700	−0.893502	−	0.449060i	$-0.851759\pi$
$2$	−5.05441	−1.78700	−0.893502	+	0.449060i	$0.851759\pi$
$3$	0.801365	0.154223	0.0771114	−	0.997022i	$-0.475430\pi$
$3$	0.801365	0.154223	0.0771114	+	0.997022i	$0.475430\pi$
$4$	17.5470	2.19338
$5$	−17.5680	−1.57133	−0.785666	−	0.618650i	$-0.787680\pi$
$5$	−17.5680	−1.57133	−0.785666	+	0.618650i	$0.787680\pi$
$6$	−4.05042	−0.275596
$7$	1.71020	0.0923420	0.0461710	−	0.998934i	$-0.485298\pi$
$7$	1.71020	0.0923420	0.0461710	+	0.998934i	$0.485298\pi$
$8$	−48.2547	−2.13257
$9$	−26.3578	−0.976215
$10$	88.7960	2.80798
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	14.0616	0.338269
$13$	0	0
$13$	0	0
$14$	−8.64404	−0.165015
$15$	−14.0784	−0.242335
$16$	103.522	1.61754
$17$	47.2534	0.674154	0.337077	−	0.941477i	$-0.390562\pi$
$17$	47.2534	0.674154	0.337077	+	0.941477i	$0.390562\pi$
$18$	133.223	1.74450
$19$	−150.092	−1.81228	−0.906141	−	0.422975i	$-0.860986\pi$
$19$	−150.092	−1.81228	−0.906141	+	0.422975i	$0.860986\pi$
$20$	−308.267	−3.44653
$21$	1.37049	0.0142412
$22$	−55.5985	−0.538802
$23$	59.4061	0.538566	0.269283	−	0.963061i	$-0.413213\pi$
$23$	59.4061	0.538566	0.269283	+	0.963061i	$0.413213\pi$
$24$	−38.6696	−0.328891
$25$	183.636	1.46909
$26$	0	0
$27$	−42.7591	−0.304777
$28$	30.0089	0.202541
$29$	−91.1947	−0.583946	−0.291973	−	0.956427i	$-0.594312\pi$
$29$	−91.1947	−0.583946	−0.291973	+	0.956427i	$0.594312\pi$
$30$	71.1580	0.433054
$31$	74.1614	0.429670	0.214835	−	0.976650i	$-0.431079\pi$
$31$	74.1614	0.429670	0.214835	+	0.976650i	$0.431079\pi$
$32$	−137.207	−0.757970
$33$	8.81501	0.0464999
$34$	−238.838	−1.20472
$35$	−30.0448	−0.145100
$36$	−462.502	−2.14121
$37$	83.8911	0.372746	0.186373	−	0.982479i	$-0.440327\pi$
$37$	83.8911	0.372746	0.186373	+	0.982479i	$0.440327\pi$
$38$	758.624	3.23855
$39$	0	0
$40$	847.740	3.35098
$41$	−378.855	−1.44310	−0.721550	−	0.692362i	$-0.756570\pi$
$41$	−378.855	−1.44310	−0.721550	+	0.692362i	$0.756570\pi$
$42$	−6.92703	−0.0254491
$43$	329.816	1.16969	0.584843	−	0.811147i	$-0.301156\pi$
$43$	329.816	1.16969	0.584843	+	0.811147i	$0.301156\pi$
$44$	193.017	0.661329
$45$	463.055	1.53396
$46$	−300.263	−0.962420
$47$	−539.208	−1.67344	−0.836719	−	0.547632i	$-0.815529\pi$
$47$	−539.208	−1.67344	−0.836719	+	0.547632i	$0.815529\pi$
$48$	82.9592	0.249461
$49$	−340.075	−0.991473
$50$	−928.171	−2.62526
$51$	37.8672	0.103970
$52$	0	0
$53$	−7.33959	−0.0190221	−0.00951104	−	0.999955i	$-0.503028\pi$
$53$	−7.33959	−0.0190221	−0.00951104	+	0.999955i	$0.503028\pi$
$54$	216.122	0.544638
$55$	−193.248	−0.473775
$56$	−82.5250	−0.196926
$57$	−120.278	−0.279495
$58$	460.935	1.04351
$59$	−676.124	−1.49193	−0.745965	−	0.665985i	$-0.768011\pi$
$59$	−676.124	−1.49193	−0.745965	+	0.665985i	$0.768011\pi$
$60$	−247.034	−0.531533
$61$	−359.563	−0.754711	−0.377355	−	0.926069i	$-0.623166\pi$
$61$	−359.563	−0.754711	−0.377355	+	0.926069i	$0.623166\pi$
$62$	−374.842	−0.767822
$63$	−45.0771	−0.0901457
$64$	−134.678	−0.263043
$65$	0	0
$66$	−44.5547	−0.0830955
$67$	−318.437	−0.580645	−0.290323	−	0.956929i	$-0.593763\pi$
$67$	−318.437	−0.580645	−0.290323	+	0.956929i	$0.593763\pi$
$68$	829.157	1.47868
$69$	47.6059	0.0830592
$70$	151.859	0.259294
$71$	−704.480	−1.17755	−0.588777	−	0.808295i	$-0.700390\pi$
$71$	−704.480	−1.17755	−0.588777	+	0.808295i	$0.700390\pi$
$72$	1271.89	2.08185
$73$	1043.78	1.67350	0.836750	−	0.547584i	$-0.184453\pi$
$73$	1043.78	1.67350	0.836750	+	0.547584i	$0.184453\pi$
$74$	−424.020	−0.666099
$75$	147.159	0.226567
$76$	−2633.66	−3.97502
$77$	18.8122	0.0278422
$78$	0	0
$79$	−112.511	−0.160234	−0.0801172	−	0.996785i	$-0.525529\pi$
$79$	−112.511	−0.160234	−0.0801172	+	0.996785i	$0.525529\pi$
$80$	−1818.69	−2.54169
$81$	677.395	0.929212
$82$	1914.89	2.57883
$83$	−614.013	−0.812009	−0.406004	−	0.913871i	$-0.633078\pi$
$83$	−614.013	−0.812009	−0.406004	+	0.913871i	$0.633078\pi$
$84$	24.0481	0.0312364
$85$	−830.149	−1.05932
$86$	−1667.02	−2.09023
$87$	−73.0802	−0.0900577
$88$	−530.801	−0.642995
$89$	410.480	0.488886	0.244443	−	0.969664i	$-0.421395\pi$
$89$	410.480	0.488886	0.244443	+	0.969664i	$0.421395\pi$
$90$	−2340.47	−2.74119
$91$	0	0
$92$	1042.40	1.18128
$93$	59.4303	0.0662649
$94$	2725.38	2.99044
$95$	2636.81	2.84770
$96$	−109.953	−0.116896
$97$	934.568	0.978257	0.489129	−	0.872212i	$-0.337315\pi$
$97$	934.568	0.978257	0.489129	+	0.872212i	$0.337315\pi$
$98$	1718.88	1.77177
$99$	−289.936	−0.294340
$100$	3222.27	3.22227
$101$	−1119.39	−1.10280	−0.551401	−	0.834240i	$-0.685907\pi$
$101$	−1119.39	−1.10280	−0.551401	+	0.834240i	$0.685907\pi$
$102$	−191.396	−0.185795
$103$	−1125.40	−1.07659	−0.538297	−	0.842755i	$-0.680932\pi$
$103$	−1125.40	−1.07659	−0.538297	+	0.842755i	$0.680932\pi$
$104$	0	0
$105$	−24.0769	−0.0223777
$106$	37.0973	0.0339925
$107$	−396.565	−0.358293	−0.179147	−	0.983822i	$-0.557334\pi$
$107$	−396.565	−0.358293	−0.179147	+	0.983822i	$0.557334\pi$
$108$	−750.295	−0.668493
$109$	1066.11	0.936831	0.468416	−	0.883508i	$-0.344825\pi$
$109$	1066.11	0.936831	0.468416	+	0.883508i	$0.344825\pi$
$110$	976.756	0.846637
$111$	67.2274	0.0574860
$112$	177.044	0.149367
$113$	−452.392	−0.376615	−0.188307	−	0.982110i	$-0.560300\pi$
$113$	−452.392	−0.376615	−0.188307	+	0.982110i	$0.560300\pi$
$114$	607.935	0.499459
$115$	−1043.65	−0.846267
$116$	−1600.20	−1.28082
$117$	0	0
$118$	3417.41	2.66608
$119$	80.8126	0.0622528
$120$	679.349	0.516798
$121$	121.000	0.0909091
$122$	1817.38	1.34867
$123$	−303.601	−0.222559
$124$	1301.31	0.942430
$125$	−1030.12	−0.737092
$126$	227.838	0.161091
$127$	−2645.14	−1.84818	−0.924089	−	0.382177i	$-0.875174\pi$
$127$	−2645.14	−1.84818	−0.924089	+	0.382177i	$0.875174\pi$
$128$	1778.38	1.22803
$129$	264.303	0.180392
$130$	0	0
$131$	−2440.09	−1.62742	−0.813708	−	0.581274i	$-0.802554\pi$
$131$	−2440.09	−1.62742	−0.813708	+	0.581274i	$0.802554\pi$
$132$	154.677	0.101992
$133$	−256.686	−0.167350
$134$	1609.51	1.03761
$135$	751.193	0.478907
$136$	−2280.19	−1.43768
$137$	−2290.65	−1.42849	−0.714247	−	0.699894i	$-0.753231\pi$
$137$	−2290.65	−1.42849	−0.714247	+	0.699894i	$0.753231\pi$
$138$	−240.620	−0.148427
$139$	2186.12	1.33399	0.666993	−	0.745064i	$-0.267581\pi$
$139$	2186.12	1.33399	0.666993	+	0.745064i	$0.267581\pi$
$140$	−527.198	−0.318260
$141$	−432.102	−0.258082
$142$	3560.73	2.10429
$143$	0	0
$144$	−2728.62	−1.57906
$145$	1602.11	0.917574
$146$	−5275.71	−2.99055
$147$	−272.524	−0.152908
$148$	1472.04	0.817575
$149$	−41.5941	−0.0228692	−0.0114346	−	0.999935i	$-0.503640\pi$
$149$	−41.5941	−0.0228692	−0.0114346	+	0.999935i	$0.503640\pi$
$150$	−743.803	−0.404875
$151$	−863.170	−0.465191	−0.232595	−	0.972574i	$-0.574722\pi$
$151$	−863.170	−0.465191	−0.232595	+	0.972574i	$0.574722\pi$
$152$	7242.62	3.86483
$153$	−1245.50	−0.658120
$154$	−95.0844	−0.0497540
$155$	−1302.87	−0.675155
$156$	0	0
$157$	−3156.39	−1.60450	−0.802252	−	0.596985i	$-0.796365\pi$
$157$	−3156.39	−1.60450	−0.802252	+	0.596985i	$0.796365\pi$
$158$	568.678	0.286339
$159$	−5.88169	−0.00293364
$160$	2410.46	1.19102
$161$	101.596	0.0497323
$162$	−3423.83	−1.66050
$163$	2922.79	1.40448	0.702242	−	0.711939i	$-0.252183\pi$
$163$	2922.79	1.40448	0.702242	+	0.711939i	$0.252183\pi$
$164$	−6647.78	−3.16527
$165$	−154.862	−0.0730668
$166$	3103.47	1.45106
$167$	3492.78	1.61844	0.809219	−	0.587507i	$-0.199891\pi$
$167$	3492.78	1.61844	0.809219	+	0.587507i	$0.199891\pi$
$168$	−66.1326	−0.0303705
$169$	0	0
$170$	4195.91	1.89301
$171$	3956.09	1.76918
$172$	5787.30	2.56556
$173$	106.998	0.0470225	0.0235112	−	0.999724i	$-0.492515\pi$
$173$	106.998	0.0470225	0.0235112	+	0.999724i	$0.492515\pi$
$174$	369.377	0.160933
$175$	314.054	0.135658
$176$	1138.75	0.487706
$177$	−541.822	−0.230090
$178$	−2074.73	−0.873640
$179$	−2294.50	−0.958096	−0.479048	−	0.877789i	$-0.659018\pi$
$179$	−2294.50	−0.958096	−0.479048	+	0.877789i	$0.659018\pi$
$180$	8125.25	3.36456
$181$	2829.84	1.16210	0.581051	−	0.813867i	$-0.302642\pi$
$181$	2829.84	1.16210	0.581051	+	0.813867i	$0.302642\pi$
$182$	0	0
$183$	−288.141	−0.116394
$184$	−2866.62	−1.14853
$185$	−1473.80	−0.585709
$186$	−300.385	−0.118416
$187$	519.787	0.203265
$188$	−9461.51	−3.67049
$189$	−73.1265	−0.0281437
$190$	−13327.5	−5.08885
$191$	49.4608	0.0187375	0.00936873	−	0.999956i	$-0.497018\pi$
$191$	49.4608	0.0187375	0.00936873	+	0.999956i	$0.497018\pi$
$192$	−107.926	−0.0405672
$193$	−4071.33	−1.51845	−0.759224	−	0.650829i	$-0.774421\pi$
$193$	−4071.33	−1.51845	−0.759224	+	0.650829i	$0.774421\pi$
$194$	−4723.69	−1.74815
$195$	0	0
$196$	−5967.31	−2.17468
$197$	−3822.34	−1.38239	−0.691193	−	0.722670i	$-0.742915\pi$
$197$	−3822.34	−1.38239	−0.691193	+	0.722670i	$0.742915\pi$
$198$	1465.45	0.525987
$199$	−1985.09	−0.707133	−0.353567	−	0.935409i	$-0.615031\pi$
$199$	−1985.09	−0.707133	−0.353567	+	0.935409i	$0.615031\pi$
$200$	−8861.29	−3.13294
$201$	−255.184	−0.0895487
$202$	5657.83	1.97071
$203$	−155.961	−0.0539227
$204$	664.457	0.228046
$205$	6655.73	2.26759
$206$	5688.24	1.92388
$207$	−1565.81	−0.525757
$208$	0	0
$209$	−1651.01	−0.546424
$210$	121.694	0.0399890
$211$	−4338.68	−1.41558	−0.707789	−	0.706424i	$-0.750307\pi$
$211$	−4338.68	−1.41558	−0.707789	+	0.706424i	$0.750307\pi$
$212$	−128.788	−0.0417227
$213$	−564.545	−0.181606
$214$	2004.40	0.640271
$215$	−5794.22	−1.83797
$216$	2063.32	0.649960
$217$	126.831	0.0396766
$218$	−5388.55	−1.67412
$219$	836.451	0.258092
$220$	−3390.94	−1.03917
$221$	0	0
$222$	−339.795	−0.102728
$223$	−3353.82	−1.00712	−0.503562	−	0.863959i	$-0.667977\pi$
$223$	−3353.82	−1.00712	−0.503562	+	0.863959i	$0.667977\pi$
$224$	−234.651	−0.0699924
$225$	−4840.24	−1.43415
$226$	2286.57	0.673012
$227$	−632.027	−0.184798	−0.0923989	−	0.995722i	$-0.529453\pi$
$227$	−632.027	−0.184798	−0.0923989	+	0.995722i	$0.529453\pi$
$228$	−2110.52	−0.613039
$229$	6681.76	1.92814	0.964068	−	0.265657i	$-0.0855888\pi$
$229$	6681.76	1.92814	0.964068	+	0.265657i	$0.0855888\pi$
$230$	5275.03	1.51228
$231$	15.0754	0.00429389
$232$	4400.57	1.24531
$233$	−3663.81	−1.03015	−0.515073	−	0.857146i	$-0.672235\pi$
$233$	−3663.81	−1.03015	−0.515073	+	0.857146i	$0.672235\pi$
$234$	0	0
$235$	9472.83	2.62953
$236$	−11864.0	−3.27237
$237$	−90.1627	−0.0247118
$238$	−408.460	−0.111246
$239$	−1524.34	−0.412558	−0.206279	−	0.978493i	$-0.566136\pi$
$239$	−1524.34	−0.412558	−0.206279	+	0.978493i	$0.566136\pi$
$240$	−1457.43	−0.391986
$241$	−1797.61	−0.480473	−0.240236	−	0.970714i	$-0.577225\pi$
$241$	−1797.61	−0.480473	−0.240236	+	0.970714i	$0.577225\pi$
$242$	−611.583	−0.162455
$243$	1697.34	0.448083
$244$	−6309.27	−1.65537
$245$	5974.45	1.55793
$246$	1534.52	0.397714
$247$	0	0
$248$	−3578.63	−0.916304
$249$	−492.049	−0.125230
$250$	5206.64	1.31719
$251$	−990.602	−0.249109	−0.124554	−	0.992213i	$-0.539750\pi$
$251$	−990.602	−0.249109	−0.124554	+	0.992213i	$0.539750\pi$
$252$	−790.969	−0.197724
$253$	653.467	0.162384
$254$	13369.6	3.30270
$255$	−665.252	−0.163371
$256$	−7911.21	−1.93145
$257$	−2923.16	−0.709502	−0.354751	−	0.934961i	$-0.615434\pi$
$257$	−2923.16	−0.709502	−0.354751	+	0.934961i	$0.615434\pi$
$258$	−1335.89	−0.322361
$259$	143.470	0.0344201
$260$	0	0
$261$	2403.69	0.570057
$262$	12333.2	2.90820
$263$	−1139.81	−0.267239	−0.133620	−	0.991033i	$-0.542660\pi$
$263$	−1139.81	−0.267239	−0.133620	+	0.991033i	$0.542660\pi$
$264$	−425.365	−0.0991645
$265$	128.942	0.0298900
$266$	1297.40	0.299055
$267$	328.944	0.0753973
$268$	−5587.62	−1.27358
$269$	7416.52	1.68102	0.840508	−	0.541799i	$-0.182257\pi$
$269$	7416.52	1.68102	0.840508	+	0.541799i	$0.182257\pi$
$270$	−3796.84	−0.855808
$271$	242.405	0.0543359	0.0271680	−	0.999631i	$-0.491351\pi$
$271$	242.405	0.0543359	0.0271680	+	0.999631i	$0.491351\pi$
$272$	4891.78	1.09047
$273$	0	0
$274$	11577.9	2.55272
$275$	2019.99	0.442946
$276$	835.344	0.182180
$277$	7060.55	1.53151	0.765753	−	0.643135i	$-0.222367\pi$
$277$	7060.55	1.53151	0.765753	+	0.643135i	$0.222367\pi$
$278$	−11049.5	−2.38384
$279$	−1954.73	−0.419451
$280$	1449.80	0.309437
$281$	303.622	0.0644576	0.0322288	−	0.999481i	$-0.489739\pi$
$281$	303.622	0.0644576	0.0322288	+	0.999481i	$0.489739\pi$
$282$	2184.02	0.461194
$283$	−3634.00	−0.763317	−0.381659	−	0.924303i	$-0.624647\pi$
$283$	−3634.00	−0.763317	−0.381659	+	0.924303i	$0.624647\pi$
$284$	−12361.5	−2.58283
$285$	2113.05	0.439180
$286$	0	0
$287$	−647.916	−0.133259
$288$	3616.48	0.739942
$289$	−2680.12	−0.545516
$290$	−8097.73	−1.63971
$291$	748.929	0.150869
$292$	18315.3	3.67062
$293$	267.520	0.0533402	0.0266701	−	0.999644i	$-0.491510\pi$
$293$	267.520	0.0533402	0.0266701	+	0.999644i	$0.491510\pi$
$294$	1377.45	0.273246
$295$	11878.2	2.34432
$296$	−4048.14	−0.794909
$297$	−470.350	−0.0918938
$298$	210.233	0.0408674
$299$	0	0
$300$	2582.21	0.496947
$301$	564.051	0.108011
$302$	4362.82	0.831297
$303$	−897.036	−0.170077
$304$	−15537.8	−2.93143
$305$	6316.82	1.18590
$306$	6295.24	1.17606
$307$	7557.05	1.40490	0.702449	−	0.711734i	$-0.252090\pi$
$307$	7557.05	1.40490	0.702449	+	0.711734i	$0.252090\pi$
$308$	330.098	0.0610684
$309$	−901.857	−0.166035
$310$	6585.24	1.20650
$311$	−443.116	−0.0807935	−0.0403967	−	0.999184i	$-0.512862\pi$
$311$	−443.116	−0.0807935	−0.0403967	+	0.999184i	$0.512862\pi$
$312$	0	0
$313$	6088.18	1.09944	0.549719	−	0.835350i	$-0.314735\pi$
$313$	6088.18	1.09944	0.549719	+	0.835350i	$0.314735\pi$
$314$	15953.7	2.86726
$315$	791.916	0.141649
$316$	−1974.24	−0.351455
$317$	−5007.99	−0.887308	−0.443654	−	0.896198i	$-0.646318\pi$
$317$	−5007.99	−0.887308	−0.443654	+	0.896198i	$0.646318\pi$
$318$	29.7285	0.00524242
$319$	−1003.14	−0.176066
$320$	2366.03	0.413328
$321$	−317.793	−0.0552570
$322$	−513.508	−0.0888718
$323$	−7092.33	−1.22176
$324$	11886.3	2.03811
$325$	0	0
$326$	−14773.0	−2.50982
$327$	854.341	0.144481
$328$	18281.5	3.07752
$329$	−922.153	−0.154529
$330$	782.738	0.130571
$331$	2719.77	0.451637	0.225819	−	0.974169i	$-0.427494\pi$
$331$	2719.77	0.451637	0.225819	+	0.974169i	$0.427494\pi$
$332$	−10774.1	−1.78104
$333$	−2211.19	−0.363881
$334$	−17653.9	−2.89215
$335$	5594.31	0.912387
$336$	141.877	0.0230357
$337$	6163.20	0.996235	0.498117	−	0.867110i	$-0.334025\pi$
$337$	6163.20	0.996235	0.498117	+	0.867110i	$0.334025\pi$
$338$	0	0
$339$	−362.531	−0.0580826
$340$	−14566.7	−2.32349
$341$	815.775	0.129550
$342$	−19995.7	−3.16153
$343$	−1168.19	−0.183897
$344$	−15915.2	−2.49444
$345$	−836.343	−0.130514
$346$	−540.810	−0.0840293
$347$	−792.015	−0.122529	−0.0612646	−	0.998122i	$-0.519513\pi$
$347$	−792.015	−0.122529	−0.0612646	+	0.998122i	$0.519513\pi$
$348$	−1282.34	−0.197531
$349$	−4167.64	−0.639223	−0.319612	−	0.947549i	$-0.603552\pi$
$349$	−4167.64	−0.639223	−0.319612	+	0.947549i	$0.603552\pi$
$350$	−1587.36	−0.242422
$351$	0	0
$352$	−1509.28	−0.228536
$353$	−5628.56	−0.848664	−0.424332	−	0.905507i	$-0.639491\pi$
$353$	−5628.56	−0.848664	−0.424332	+	0.905507i	$0.639491\pi$
$354$	2738.59	0.411171
$355$	12376.3	1.85033
$356$	7202.71	1.07231
$357$	64.7604	0.00960079
$358$	11597.3	1.71212
$359$	5896.12	0.866812	0.433406	−	0.901199i	$-0.357312\pi$
$359$	5896.12	0.866812	0.433406	+	0.901199i	$0.357312\pi$
$360$	−22344.6	−3.27128
$361$	15668.5	2.28437
$362$	−14303.2	−2.07668
$363$	96.9651	0.0140202
$364$	0	0
$365$	−18337.2	−2.62963
$366$	1456.38	0.207996
$367$	−3532.30	−0.502411	−0.251205	−	0.967934i	$-0.580827\pi$
$367$	−3532.30	−0.502411	−0.251205	+	0.967934i	$0.580827\pi$
$368$	6149.86	0.871151
$369$	9985.78	1.40878
$370$	7449.20	1.04666
$371$	−12.5521	−0.00175654
$372$	1042.83	0.145344
$373$	6024.05	0.836230	0.418115	−	0.908394i	$-0.362691\pi$
$373$	6024.05	0.836230	0.418115	+	0.908394i	$0.362691\pi$
$374$	−2627.22	−0.363236
$375$	−825.500	−0.113676
$376$	26019.3	3.56873
$377$	0	0
$378$	369.611	0.0502930
$379$	1592.25	0.215801	0.107900	−	0.994162i	$-0.465587\pi$
$379$	1592.25	0.215801	0.107900	+	0.994162i	$0.465587\pi$
$380$	46268.3	6.24609
$381$	−2119.73	−0.285031
$382$	−249.995	−0.0334839
$383$	10634.6	1.41881	0.709405	−	0.704801i	$-0.248964\pi$
$383$	10634.6	1.41881	0.709405	+	0.704801i	$0.248964\pi$
$384$	1425.13	0.189390
$385$	−330.493	−0.0437493
$386$	20578.1	2.71347
$387$	−8693.23	−1.14186
$388$	16398.9	2.14569
$389$	14601.6	1.90316	0.951582	−	0.307395i	$-0.0994574\pi$
$389$	14601.6	1.90316	0.951582	+	0.307395i	$0.0994574\pi$
$390$	0	0
$391$	2807.14	0.363077
$392$	16410.2	2.11439
$393$	−1955.40	−0.250984
$394$	19319.6	2.47033
$395$	1976.60	0.251782
$396$	−5087.52	−0.645600
$397$	−1454.84	−0.183920	−0.0919599	−	0.995763i	$-0.529313\pi$
$397$	−1454.84	−0.183920	−0.0919599	+	0.995763i	$0.529313\pi$
$398$	10033.5	1.26365
$399$	−205.699	−0.0258091
$400$	19010.4	2.37630
$401$	9348.07	1.16414	0.582071	−	0.813138i	$-0.302243\pi$
$401$	9348.07	1.16414	0.582071	+	0.813138i	$0.302243\pi$
$402$	1289.80	0.160024
$403$	0	0
$404$	−19641.9	−2.41887
$405$	−11900.5	−1.46010
$406$	788.290	0.0963601
$407$	922.802	0.112387
$408$	−1827.27	−0.221724
$409$	12053.0	1.45717	0.728587	−	0.684953i	$-0.240177\pi$
$409$	12053.0	1.45717	0.728587	+	0.684953i	$0.240177\pi$
$410$	−33640.8	−4.05219
$411$	−1835.65	−0.220306
$412$	−19747.5	−2.36138
$413$	−1156.31	−0.137768
$414$	7914.27	0.939529
$415$	10787.0	1.27594
$416$	0	0
$417$	1751.88	0.205731
$418$	8344.86	0.976461
$419$	7881.55	0.918947	0.459474	−	0.888191i	$-0.348038\pi$
$419$	7881.55	0.918947	0.459474	+	0.888191i	$0.348038\pi$
$420$	−422.478	−0.0490828
$421$	3976.29	0.460314	0.230157	−	0.973153i	$-0.426076\pi$
$421$	3976.29	0.460314	0.230157	+	0.973153i	$0.426076\pi$
$422$	21929.5	2.52964
$423$	14212.4	1.63364
$424$	354.169	0.0405660
$425$	8677.41	0.990392
$426$	2853.44	0.324530
$427$	−614.924	−0.0696915
$428$	−6958.54	−0.785873
$429$	0	0
$430$	29286.4	3.28445
$431$	−5827.46	−0.651273	−0.325637	−	0.945495i	$-0.605579\pi$
$431$	−5827.46	−0.651273	−0.325637	+	0.945495i	$0.605579\pi$
$432$	−4426.52	−0.492989
$433$	−10716.4	−1.18937	−0.594683	−	0.803960i	$-0.702722\pi$
$433$	−10716.4	−1.18937	−0.594683	+	0.803960i	$0.702722\pi$
$434$	−641.054	−0.0709022
$435$	1283.88	0.141511
$436$	18707.0	2.05483
$437$	−8916.35	−0.976034
$438$	−4227.76	−0.461211
$439$	9200.09	1.00022	0.500110	−	0.865962i	$-0.333293\pi$
$439$	9200.09	1.00022	0.500110	+	0.865962i	$0.333293\pi$
$440$	9325.14	1.01036
$441$	8963.64	0.967891
$442$	0	0
$443$	14983.8	1.60700	0.803499	−	0.595306i	$-0.202969\pi$
$443$	14983.8	1.60700	0.803499	+	0.595306i	$0.202969\pi$
$444$	1179.64	0.126089
$445$	−7211.33	−0.768202
$446$	16951.6	1.79973
$447$	−33.3320	−0.00352696
$448$	−230.326	−0.0242899
$449$	−11881.8	−1.24886	−0.624429	−	0.781082i	$-0.714668\pi$
$449$	−11881.8	−1.24886	−0.624429	+	0.781082i	$0.714668\pi$
$450$	24464.6	2.56282
$451$	−4167.40	−0.435111
$452$	−7938.15	−0.826060
$453$	−691.714	−0.0717430
$454$	3194.52	0.330234
$455$	0	0
$456$	5803.98	0.596044
$457$	10407.3	1.06528	0.532642	−	0.846341i	$-0.321199\pi$
$457$	10407.3	1.06528	0.532642	+	0.846341i	$0.321199\pi$
$458$	−33772.3	−3.44558
$459$	−2020.51	−0.205467
$460$	−18312.9	−1.85619
$461$	3496.97	0.353297	0.176649	−	0.984274i	$-0.443474\pi$
$461$	3496.97	0.353297	0.176649	+	0.984274i	$0.443474\pi$
$462$	−76.1973	−0.00767320
$463$	8674.65	0.870724	0.435362	−	0.900255i	$-0.356620\pi$
$463$	8674.65	0.870724	0.435362	+	0.900255i	$0.356620\pi$
$464$	−9440.70	−0.944554
$465$	−1044.07	−0.104124
$466$	18518.4	1.84087
$467$	14013.8	1.38861	0.694304	−	0.719682i	$-0.255712\pi$
$467$	14013.8	1.38861	0.694304	+	0.719682i	$0.255712\pi$
$468$	0	0
$469$	−544.590	−0.0536179
$470$	−47879.5	−4.69898
$471$	−2529.42	−0.247451
$472$	32626.1	3.18165
$473$	3627.98	0.352673
$474$	455.719	0.0441600
$475$	−27562.2	−2.66240
$476$	1418.02	0.136544
$477$	193.456	0.0185696
$478$	7704.64	0.737243
$479$	−1228.41	−0.117177	−0.0585883	−	0.998282i	$-0.518660\pi$
$479$	−1228.41	−0.117177	−0.0585883	+	0.998282i	$0.518660\pi$
$480$	1931.66	0.183683
$481$	0	0
$482$	9085.83	0.858606
$483$	81.4156	0.00766985
$484$	2123.19	0.199398
$485$	−16418.5	−1.53717
$486$	−8579.03	−0.800725
$487$	−4729.64	−0.440083	−0.220042	−	0.975490i	$-0.570619\pi$
$487$	−4729.64	−0.440083	−0.220042	+	0.975490i	$0.570619\pi$
$488$	17350.6	1.60948
$489$	2342.22	0.216603
$490$	−30197.3	−2.78403
$491$	−16502.5	−1.51680	−0.758399	−	0.651791i	$-0.774018\pi$
$491$	−16502.5	−1.51680	−0.758399	+	0.651791i	$0.774018\pi$
$492$	−5327.29	−0.488156
$493$	−4309.26	−0.393670
$494$	0	0
$495$	5093.61	0.462506
$496$	7677.36	0.695008
$497$	−1204.80	−0.108738
$498$	2487.01	0.223787
$499$	6605.63	0.592602	0.296301	−	0.955095i	$-0.404247\pi$
$499$	6605.63	0.592602	0.296301	+	0.955095i	$0.404247\pi$
$500$	−18075.5	−1.61672
$501$	2798.99	0.249600
$502$	5006.91	0.445158
$503$	−8775.25	−0.777871	−0.388936	−	0.921265i	$-0.627157\pi$
$503$	−8775.25	−0.777871	−0.388936	+	0.921265i	$0.627157\pi$
$504$	2175.18	0.192242
$505$	19665.4	1.73287
$506$	−3302.89	−0.290180
$507$	0	0
$508$	−46414.5	−4.05376
$509$	8368.70	0.728755	0.364377	−	0.931251i	$-0.381282\pi$
$509$	8368.70	0.728755	0.364377	+	0.931251i	$0.381282\pi$
$510$	3362.46	0.291945
$511$	1785.08	0.154534
$512$	25759.5	2.22347
$513$	6417.78	0.552343
$514$	14774.9	1.26788
$515$	19771.1	1.69169
$516$	4637.73	0.395668
$517$	−5931.29	−0.504561
$518$	−725.158	−0.0615089
$519$	85.7442	0.00725193
$520$	0	0
$521$	18387.7	1.54622	0.773111	−	0.634271i	$-0.218700\pi$
$521$	18387.7	1.54622	0.773111	+	0.634271i	$0.218700\pi$
$522$	−12149.2	−1.01869
$523$	−16182.8	−1.35301	−0.676506	−	0.736437i	$-0.736507\pi$
$523$	−16182.8	−1.35301	−0.676506	+	0.736437i	$0.736507\pi$
$524$	−42816.3	−3.56954
$525$	251.672	0.0209216
$526$	5761.08	0.477557
$527$	3504.38	0.289664
$528$	912.551	0.0752153
$529$	−8637.92	−0.709946
$530$	−651.726	−0.0534136
$531$	17821.2	1.45645
$532$	−4504.08	−0.367062
$533$	0	0
$534$	−1662.62	−0.134735
$535$	6966.87	0.562998
$536$	15366.1	1.23827
$537$	−1838.73	−0.147760
$538$	−37486.1	−3.00398
$539$	−3740.83	−0.298940
$540$	13181.2	1.05042
$541$	−22465.6	−1.78534	−0.892672	−	0.450708i	$-0.851172\pi$
$541$	−22465.6	−1.78534	−0.892672	+	0.450708i	$0.851172\pi$
$542$	−1225.21	−0.0970985
$543$	2267.74	0.179223
$544$	−6483.50	−0.510989
$545$	−18729.4	−1.47207
$546$	0	0
$547$	−3952.30	−0.308936	−0.154468	−	0.987998i	$-0.549366\pi$
$547$	−3952.30	−0.308936	−0.154468	+	0.987998i	$0.549366\pi$
$548$	−40194.2	−3.13323
$549$	9477.30	0.736760
$550$	−10209.9	−0.791547
$551$	13687.6	1.05828
$552$	−2297.21	−0.177130
$553$	−192.417	−0.0147964
$554$	−35686.9	−2.73681
$555$	−1181.05	−0.0903296
$556$	38359.9	2.92594
$557$	−15390.6	−1.17077	−0.585387	−	0.810754i	$-0.699057\pi$
$557$	−15390.6	−1.17077	−0.585387	+	0.810754i	$0.699057\pi$
$558$	9880.01	0.749560
$559$	0	0
$560$	−3110.31	−0.234705
$561$	416.539	0.0313481
$562$	−1534.63	−0.115186
$563$	19916.1	1.49088	0.745440	−	0.666573i	$-0.232240\pi$
$563$	19916.1	1.49088	0.745440	+	0.666573i	$0.232240\pi$
$564$	−7582.12	−0.566072
$565$	7947.64	0.591787
$566$	18367.7	1.36405
$567$	1158.48	0.0858053
$568$	33994.4	2.51122
$569$	−2301.12	−0.169540	−0.0847699	−	0.996401i	$-0.527016\pi$
$569$	−2301.12	−0.169540	−0.0847699	+	0.996401i	$0.527016\pi$
$570$	−10680.2	−0.784816
$571$	−4880.64	−0.357703	−0.178851	−	0.983876i	$-0.557238\pi$
$571$	−4880.64	−0.357703	−0.178851	+	0.983876i	$0.557238\pi$
$572$	0	0
$573$	39.6361	0.00288974
$574$	3274.83	0.238134
$575$	10909.1	0.791201
$576$	3549.82	0.256787
$577$	9536.18	0.688036	0.344018	−	0.938963i	$-0.388212\pi$
$577$	9536.18	0.688036	0.344018	+	0.938963i	$0.388212\pi$
$578$	13546.4	0.974839
$579$	−3262.62	−0.234179
$580$	28112.3	2.01259
$581$	−1050.08	−0.0749825
$582$	−3785.40	−0.269604
$583$	−80.7355	−0.00573537
$584$	−50367.4	−3.56887
$585$	0	0
$586$	−1352.15	−0.0953190
$587$	23781.1	1.67215	0.836075	−	0.548615i	$-0.184845\pi$
$587$	23781.1	1.67215	0.836075	+	0.548615i	$0.184845\pi$
$588$	−4782.00	−0.335385
$589$	−11131.0	−0.778684
$590$	−60037.2	−4.18931
$591$	−3063.09	−0.213195
$592$	8684.61	0.602931
$593$	7770.77	0.538124	0.269062	−	0.963123i	$-0.413286\pi$
$593$	7770.77	0.538124	0.269062	+	0.963123i	$0.413286\pi$
$594$	2377.34	0.164215
$595$	−1419.72	−0.0978198
$596$	−729.853	−0.0501610
$597$	−1590.78	−0.109056
$598$	0	0
$599$	−5961.65	−0.406655	−0.203327	−	0.979111i	$-0.565176\pi$
$599$	−5961.65	−0.406655	−0.203327	+	0.979111i	$0.565176\pi$
$600$	−7101.12	−0.483170
$601$	−19316.2	−1.31102	−0.655510	−	0.755187i	$-0.727546\pi$
$601$	−19316.2	−1.31102	−0.655510	+	0.755187i	$0.727546\pi$
$602$	−2850.94	−0.193016
$603$	8393.30	0.566835
$604$	−15146.1	−1.02034
$605$	−2125.73	−0.142848
$606$	4533.99	0.303928
$607$	2167.44	0.144932	0.0724659	−	0.997371i	$-0.476913\pi$
$607$	2167.44	0.144932	0.0724659	+	0.997371i	$0.476913\pi$
$608$	20593.6	1.37366
$609$	−124.982	−0.00831611
$610$	−31927.8	−2.11921
$611$	0	0
$612$	−21854.8	−1.44351
$613$	15066.7	0.992724	0.496362	−	0.868116i	$-0.334669\pi$
$613$	15066.7	0.992724	0.496362	+	0.868116i	$0.334669\pi$
$614$	−38196.4	−2.51056
$615$	5333.67	0.349714
$616$	−907.775	−0.0593755
$617$	−1215.95	−0.0793390	−0.0396695	−	0.999213i	$-0.512631\pi$
$617$	−1215.95	−0.0793390	−0.0396695	+	0.999213i	$0.512631\pi$
$618$	4558.35	0.296705
$619$	−16027.7	−1.04072	−0.520361	−	0.853946i	$-0.674203\pi$
$619$	−16027.7	−1.04072	−0.520361	+	0.853946i	$0.674203\pi$
$620$	−22861.5	−1.48087
$621$	−2540.15	−0.164143
$622$	2239.69	0.144378
$623$	702.002	0.0451447
$624$	0	0
$625$	−4857.34	−0.310870
$626$	−30772.1	−1.96470
$627$	−1323.06	−0.0842709
$628$	−55385.3	−3.51929
$629$	3964.14	0.251289
$630$	−4002.66	−0.253127
$631$	18434.2	1.16300	0.581502	−	0.813545i	$-0.302465\pi$
$631$	18434.2	1.16300	0.581502	+	0.813545i	$0.302465\pi$
$632$	5429.20	0.341712
$633$	−3476.86	−0.218314
$634$	25312.4	1.58562
$635$	46470.0	2.90410
$636$	−103.206	−0.00643458
$637$	0	0
$638$	5070.29	0.314631
$639$	18568.5	1.14955
$640$	−31242.6	−1.92964
$641$	−4728.47	−0.291363	−0.145681	−	0.989332i	$-0.546537\pi$
$641$	−4728.47	−0.291363	−0.145681	+	0.989332i	$0.546537\pi$
$642$	1606.26	0.0987444
$643$	25872.7	1.58681	0.793407	−	0.608692i	$-0.208306\pi$
$643$	25872.7	1.58681	0.793407	+	0.608692i	$0.208306\pi$
$644$	1782.71	0.109082
$645$	−4643.28	−0.283456
$646$	35847.5	2.18329
$647$	4202.15	0.255338	0.127669	−	0.991817i	$-0.459250\pi$
$647$	4202.15	0.255338	0.127669	+	0.991817i	$0.459250\pi$
$648$	−32687.5	−1.98161
$649$	−7437.37	−0.449834
$650$	0	0
$651$	101.638	0.00611903
$652$	51286.4	3.08057
$653$	23050.1	1.38135	0.690674	−	0.723166i	$-0.257314\pi$
$653$	23050.1	1.38135	0.690674	+	0.723166i	$0.257314\pi$
$654$	−4318.19	−0.258187
$655$	42867.5	2.55721
$656$	−39219.9	−2.33427
$657$	−27511.8	−1.63370
$658$	4660.94	0.276143
$659$	19591.7	1.15810	0.579048	−	0.815293i	$-0.303424\pi$
$659$	19591.7	1.15810	0.579048	+	0.815293i	$0.303424\pi$
$660$	−2717.38	−0.160263
$661$	1640.20	0.0965149	0.0482575	−	0.998835i	$-0.484633\pi$
$661$	1640.20	0.0965149	0.0482575	+	0.998835i	$0.484633\pi$
$662$	−13746.8	−0.807077
$663$	0	0
$664$	29629.0	1.73167
$665$	4509.47	0.262962
$666$	11176.2	0.650256
$667$	−5417.52	−0.314494
$668$	61287.9	3.54985
$669$	−2687.64	−0.155321
$670$	−28275.9	−1.63044
$671$	−3955.19	−0.227554
$672$	−188.041	−0.0107944
$673$	−31619.1	−1.81104	−0.905518	−	0.424307i	$-0.860518\pi$
$673$	−31619.1	−1.81104	−0.905518	+	0.424307i	$0.860518\pi$
$674$	−31151.4	−1.78027
$675$	−7852.10	−0.447744
$676$	0	0
$677$	16571.5	0.940758	0.470379	−	0.882465i	$-0.344117\pi$
$677$	16571.5	0.940758	0.470379	+	0.882465i	$0.344117\pi$
$678$	1832.38	0.103794
$679$	1598.30	0.0903342
$680$	40058.5	2.25908
$681$	−506.484	−0.0285000
$682$	−4123.26	−0.231507
$683$	−7731.49	−0.433144	−0.216572	−	0.976267i	$-0.569488\pi$
$683$	−7731.49	−0.433144	−0.216572	+	0.976267i	$0.569488\pi$
$684$	69417.6	3.88048
$685$	40242.3	2.24464
$686$	5904.53	0.328624
$687$	5354.52	0.297362
$688$	34143.3	1.89201
$689$	0	0
$690$	4227.22	0.233228
$691$	27672.4	1.52346	0.761728	−	0.647896i	$-0.224351\pi$
$691$	27672.4	1.52346	0.761728	+	0.647896i	$0.224351\pi$
$692$	1877.49	0.103138
$693$	−495.848	−0.0271799
$694$	4003.17	0.218960
$695$	−38405.8	−2.09614
$696$	3526.46	0.192055
$697$	−17902.2	−0.972873
$698$	21065.0	1.14229
$699$	−2936.05	−0.158872
$700$	5510.71	0.297551
$701$	−22346.8	−1.20403	−0.602016	−	0.798484i	$-0.705636\pi$
$701$	−22346.8	−1.20403	−0.602016	+	0.798484i	$0.705636\pi$
$702$	0	0
$703$	−12591.4	−0.675522
$704$	−1481.46	−0.0793105
$705$	7591.19	0.405533
$706$	28449.1	1.51656
$707$	−1914.37	−0.101835
$708$	−9507.38	−0.504674
$709$	−21669.3	−1.14782	−0.573912	−	0.818917i	$-0.694575\pi$
$709$	−21669.3	−1.14782	−0.573912	+	0.818917i	$0.694575\pi$
$710$	−62555.0	−3.30655
$711$	2965.55	0.156423
$712$	−19807.6	−1.04258
$713$	4405.64	0.231406
$714$	−327.325	−0.0171566
$715$	0	0
$716$	−40261.7	−2.10147
$717$	−1221.55	−0.0636259
$718$	−29801.4	−1.54900
$719$	−18738.1	−0.971922	−0.485961	−	0.873980i	$-0.661530\pi$
$719$	−18738.1	−0.971922	−0.485961	+	0.873980i	$0.661530\pi$
$720$	47936.6	2.48124
$721$	−1924.66	−0.0994148
$722$	−79194.9	−4.08217
$723$	−1440.54	−0.0740998
$724$	49655.4	2.54893
$725$	−16746.6	−0.857868
$726$	−490.101	−0.0250542
$727$	25718.6	1.31203	0.656017	−	0.754746i	$-0.272240\pi$
$727$	25718.6	1.31203	0.656017	+	0.754746i	$0.272240\pi$
$728$	0	0
$729$	−16929.5	−0.860107
$730$	92683.8	4.69915
$731$	15584.9	0.788549
$732$	−5056.03	−0.255295
$733$	−32080.0	−1.61651	−0.808255	−	0.588833i	$-0.799588\pi$
$733$	−32080.0	−1.61651	−0.808255	+	0.588833i	$0.799588\pi$
$734$	17853.7	0.897809
$735$	4787.72	0.240269
$736$	−8150.94	−0.408217
$737$	−3502.80	−0.175071
$738$	−50472.2	−2.51749
$739$	−4913.72	−0.244593	−0.122296	−	0.992494i	$-0.539026\pi$
$739$	−4913.72	−0.244593	−0.122296	+	0.992494i	$0.539026\pi$
$740$	−25860.9	−1.28468
$741$	0	0
$742$	63.4437	0.00313894
$743$	−9600.61	−0.474040	−0.237020	−	0.971505i	$-0.576171\pi$
$743$	−9600.61	−0.474040	−0.237020	+	0.971505i	$0.576171\pi$
$744$	−2867.79	−0.141315
$745$	730.726	0.0359352
$746$	−30448.0	−1.49435
$747$	16184.1	0.792695
$748$	9120.73	0.445838
$749$	−678.204	−0.0330855
$750$	4172.41	0.203140
$751$	10638.9	0.516937	0.258468	−	0.966020i	$-0.416782\pi$
$751$	10638.9	0.516937	0.258468	+	0.966020i	$0.416782\pi$
$752$	−55820.1	−2.70685
$753$	−793.833	−0.0384182
$754$	0	0
$755$	15164.2	0.730970
$756$	−1283.15	−0.0617299
$757$	−19884.8	−0.954724	−0.477362	−	0.878707i	$-0.658407\pi$
$757$	−19884.8	−0.954724	−0.477362	+	0.878707i	$0.658407\pi$
$758$	−8047.88	−0.385636
$759$	523.665	0.0250433
$760$	−127239.	−6.07293
$761$	−11501.5	−0.547872	−0.273936	−	0.961748i	$-0.588326\pi$
$761$	−11501.5	−0.547872	−0.273936	+	0.961748i	$0.588326\pi$
$762$	10714.0	0.509351
$763$	1823.26	0.0865089
$764$	867.890	0.0410984
$765$	21880.9	1.03413
$766$	−53751.8	−2.53542
$767$	0	0
$768$	−6339.76	−0.297873
$769$	−17605.9	−0.825599	−0.412800	−	0.910822i	$-0.635449\pi$
$769$	−17605.9	−0.825599	−0.412800	+	0.910822i	$0.635449\pi$
$770$	1670.45	0.0781801
$771$	−2342.52	−0.109421
$772$	−71439.7	−3.33053
$773$	17110.3	0.796140	0.398070	−	0.917355i	$-0.369680\pi$
$773$	17110.3	0.796140	0.398070	+	0.917355i	$0.369680\pi$
$774$	43939.1	2.04052
$775$	13618.7	0.631223
$776$	−45097.2	−2.08621
$777$	114.972	0.00530837
$778$	−73802.5	−3.40096
$779$	56862.9	2.61531
$780$	0	0
$781$	−7749.28	−0.355046
$782$	−14188.4	−0.648820
$783$	3899.40	0.177973
$784$	−35205.4	−1.60374
$785$	55451.6	2.52121
$786$	9883.39	0.448510
$787$	−9878.70	−0.447443	−0.223722	−	0.974653i	$-0.571821\pi$
$787$	−9878.70	−0.447443	−0.223722	+	0.974653i	$0.571821\pi$
$788$	−67070.7	−3.03210
$789$	−913.406	−0.0412144
$790$	−9990.56	−0.449935
$791$	−773.680	−0.0347774
$792$	13990.8	0.627702
$793$	0	0
$794$	7353.34	0.328665
$795$	103.330	0.00460972
$796$	−34832.5	−1.55101
$797$	−19082.4	−0.848095	−0.424048	−	0.905640i	$-0.639391\pi$
$797$	−19082.4	−0.848095	−0.424048	+	0.905640i	$0.639391\pi$
$798$	1039.69	0.0461210
$799$	−25479.4	−1.12816
$800$	−25196.2	−1.11352
$801$	−10819.4	−0.477258
$802$	−47249.0	−2.08032
$803$	11481.6	0.504579
$804$	−4477.72	−0.196414
$805$	−1784.84	−0.0781460
$806$	0	0
$807$	5943.34	0.259251
$808$	54015.6	2.35181
$809$	−19459.3	−0.845676	−0.422838	−	0.906205i	$-0.638966\pi$
$809$	−19459.3	−0.845676	−0.422838	+	0.906205i	$0.638966\pi$
$810$	60150.0	2.60921
$811$	28347.0	1.22737	0.613685	−	0.789551i	$-0.289687\pi$
$811$	28347.0	1.22737	0.613685	+	0.789551i	$0.289687\pi$
$812$	−2736.65	−0.118273
$813$	194.255	0.00837984
$814$	−4664.22	−0.200836
$815$	−51347.7	−2.20691
$816$	3920.10	0.168175
$817$	−49502.6	−2.11980
$818$	−60920.9	−2.60397
$819$	0	0
$820$	116788.	4.97369
$821$	−24053.7	−1.02251	−0.511255	−	0.859429i	$-0.670819\pi$
$821$	−24053.7	−1.02251	−0.511255	+	0.859429i	$0.670819\pi$
$822$	9278.12	0.393688
$823$	15125.6	0.640637	0.320319	−	0.947310i	$-0.396210\pi$
$823$	15125.6	0.640637	0.320319	+	0.947310i	$0.396210\pi$
$824$	54305.9	2.29592
$825$	1618.75	0.0683124
$826$	5844.44	0.246192
$827$	−14415.0	−0.606116	−0.303058	−	0.952972i	$-0.598008\pi$
$827$	−14415.0	−0.606116	−0.303058	+	0.952972i	$0.598008\pi$
$828$	−27475.4	−1.15318
$829$	45122.0	1.89041	0.945205	−	0.326476i	$-0.105861\pi$
$829$	45122.0	1.89041	0.945205	+	0.326476i	$0.105861\pi$
$830$	−54522.0	−2.28010
$831$	5658.07	0.236193
$832$	0	0
$833$	−16069.7	−0.668406
$834$	−8854.70	−0.367642
$835$	−61361.2	−2.54311
$836$	−28970.3	−1.19852
$837$	−3171.07	−0.130954
$838$	−39836.6	−1.64216
$839$	16425.6	0.675896	0.337948	−	0.941165i	$-0.390267\pi$
$839$	16425.6	0.675896	0.337948	+	0.941165i	$0.390267\pi$
$840$	1161.82	0.0477221
$841$	−16072.5	−0.659007
$842$	−20097.8	−0.822583
$843$	243.312	0.00994082
$844$	−76131.0	−3.10490
$845$	0	0
$846$	−71835.0	−2.91931
$847$	206.934	0.00839473
$848$	−759.812	−0.0307689
$849$	−2912.16	−0.117721
$850$	−43859.2	−1.76983
$851$	4983.64	0.200749
$852$	−9906.10	−0.398330
$853$	−20888.5	−0.838462	−0.419231	−	0.907880i	$-0.637700\pi$
$853$	−20888.5	−0.838462	−0.419231	+	0.907880i	$0.637700\pi$
$854$	3108.08	0.124539
$855$	−69500.7	−2.77997
$856$	19136.1	0.764087
$857$	24417.9	0.973280	0.486640	−	0.873603i	$-0.338222\pi$
$857$	24417.9	0.973280	0.486640	+	0.873603i	$0.338222\pi$
$858$	0	0
$859$	3483.23	0.138354	0.0691770	−	0.997604i	$-0.477963\pi$
$859$	3483.23	0.138354	0.0691770	+	0.997604i	$0.477963\pi$
$860$	−101671.	−4.03136
$861$	−519.217	−0.0205515
$862$	29454.4	1.16383
$863$	−11435.6	−0.451068	−0.225534	−	0.974235i	$-0.572413\pi$
$863$	−11435.6	−0.451068	−0.225534	+	0.974235i	$0.572413\pi$
$864$	5866.85	0.231012
$865$	−1879.74	−0.0738879
$866$	54164.9	2.12540
$867$	−2147.75	−0.0841309
$868$	2225.50	0.0870259
$869$	−1237.63	−0.0483125
$870$	−6489.23	−0.252880
$871$	0	0
$872$	−51444.7	−1.99786
$873$	−24633.2	−0.954990
$874$	45066.9	1.74418
$875$	−1761.70	−0.0680646
$876$	14677.2	0.566094
$877$	−10625.5	−0.409121	−0.204560	−	0.978854i	$-0.565576\pi$
$877$	−10625.5	−0.409121	−0.204560	+	0.978854i	$0.565576\pi$
$878$	−46501.0	−1.78740
$879$	214.381	0.00822626
$880$	−20005.5	−0.766348
$881$	33230.0	1.27077	0.635384	−	0.772197i	$-0.280842\pi$
$881$	33230.0	1.27077	0.635384	+	0.772197i	$0.280842\pi$
$882$	−45305.9	−1.72962
$883$	−5296.26	−0.201850	−0.100925	−	0.994894i	$-0.532180\pi$
$883$	−5296.26	−0.201850	−0.100925	+	0.994894i	$0.532180\pi$
$884$	0	0
$885$	9518.75	0.361547
$886$	−75734.1	−2.87171
$887$	4568.43	0.172935	0.0864673	−	0.996255i	$-0.472442\pi$
$887$	4568.43	0.172935	0.0864673	+	0.996255i	$0.472442\pi$
$888$	−3244.03	−0.122593
$889$	−4523.72	−0.170664
$890$	36449.0	1.37278
$891$	7451.35	0.280168
$892$	−58849.7	−2.20901
$893$	80930.6	3.03274
$894$	168.474	0.00630268
$895$	40309.9	1.50549
$896$	3041.37	0.113399
$897$	0	0
$898$	60055.5	2.23171
$899$	−6763.13	−0.250904
$900$	−84931.9	−3.14563
$901$	−346.820	−0.0128238
$902$	21063.7	0.777545
$903$	452.010	0.0166578
$904$	21830.0	0.803159
$905$	−49714.8	−1.82605
$906$	3496.21	0.128205
$907$	−42923.5	−1.57139	−0.785696	−	0.618613i	$-0.787695\pi$
$907$	−42923.5	−1.57139	−0.785696	+	0.618613i	$0.787695\pi$
$908$	−11090.2	−0.405332
$909$	29504.6	1.07657
$910$	0	0
$911$	−18684.8	−0.679532	−0.339766	−	0.940510i	$-0.610348\pi$
$911$	−18684.8	−0.679532	−0.339766	+	0.940510i	$0.610348\pi$
$912$	−12451.5	−0.452094
$913$	−6754.15	−0.244830
$914$	−52602.9	−1.90367
$915$	5062.08	0.182893
$916$	117245.	4.22913
$917$	−4173.03	−0.150279
$918$	10212.5	0.367170
$919$	1260.71	0.0452524	0.0226262	−	0.999744i	$-0.492797\pi$
$919$	1260.71	0.0452524	0.0226262	+	0.999744i	$0.492797\pi$
$920$	50360.9	1.80473
$921$	6055.95	0.216667
$922$	−17675.1	−0.631343
$923$	0	0
$924$	264.529	0.00941814
$925$	15405.4	0.547597
$926$	−43845.2	−1.55599
$927$	29663.1	1.05099
$928$	12512.6	0.442613
$929$	16768.3	0.592197	0.296099	−	0.955157i	$-0.404314\pi$
$929$	16768.3	0.592197	0.296099	+	0.955157i	$0.404314\pi$
$930$	5277.18	0.186070
$931$	51042.4	1.79683
$932$	−64289.0	−2.25950
$933$	−355.097	−0.0124602
$934$	−70831.3	−2.48145
$935$	−9131.64	−0.319397
$936$	0	0
$937$	29827.7	1.03994	0.519972	−	0.854183i	$-0.325942\pi$
$937$	29827.7	1.03994	0.519972	+	0.854183i	$0.325942\pi$
$938$	2752.58	0.0958154
$939$	4878.85	0.169558
$940$	166220.	5.76756
$941$	43342.2	1.50151	0.750753	−	0.660583i	$-0.229691\pi$
$941$	43342.2	1.50151	0.750753	+	0.660583i	$0.229691\pi$
$942$	12784.7	0.442196
$943$	−22506.3	−0.777206
$944$	−69994.0	−2.41325
$945$	1284.69	0.0442232
$946$	−18337.3	−0.630229
$947$	45482.3	1.56069	0.780347	−	0.625347i	$-0.215042\pi$
$947$	45482.3	1.56069	0.780347	+	0.625347i	$0.215042\pi$
$948$	−1582.09	−0.0542024
$949$	0	0
$950$	139311.	4.75772
$951$	−4013.23	−0.136843
$952$	−3899.58	−0.132759
$953$	48062.2	1.63367	0.816835	−	0.576871i	$-0.195727\pi$
$953$	48062.2	1.63367	0.816835	+	0.576871i	$0.195727\pi$
$954$	−977.803	−0.0331840
$955$	−868.929	−0.0294428
$956$	−26747.7	−0.904897
$957$	−803.883	−0.0271534
$958$	6208.90	0.209395
$959$	−3917.47	−0.131910
$960$	1896.05	0.0637446
$961$	−24291.1	−0.815383
$962$	0	0
$963$	10452.6	0.349771
$964$	−31542.7	−1.05386
$965$	71525.2	2.38599
$966$	−411.508	−0.0137060
$967$	−47131.2	−1.56736	−0.783680	−	0.621165i	$-0.786660\pi$
$967$	−47131.2	−1.56736	−0.783680	+	0.621165i	$0.786660\pi$
$968$	−5838.81	−0.193870
$969$	−5683.54	−0.188423
$970$	82985.9	2.74692
$971$	54154.9	1.78982	0.894908	−	0.446250i	$-0.147241\pi$
$971$	54154.9	1.78982	0.894908	+	0.446250i	$0.147241\pi$
$972$	29783.2	0.982816
$973$	3738.69	0.123183
$974$	23905.6	0.786430
$975$	0	0
$976$	−37222.8	−1.22077
$977$	−6195.54	−0.202879	−0.101440	−	0.994842i	$-0.532345\pi$
$977$	−6195.54	−0.202879	−0.101440	+	0.994842i	$0.532345\pi$
$978$	−11838.5	−0.387071
$979$	4515.28	0.147405
$980$	104834.	3.41714
$981$	−28100.3	−0.914549
$982$	83410.4	2.71052
$983$	−7154.91	−0.232153	−0.116076	−	0.993240i	$-0.537032\pi$
$983$	−7154.91	−0.232153	−0.116076	+	0.993240i	$0.537032\pi$
$984$	14650.1	0.474624
$985$	67150.9	2.17219
$986$	21780.7	0.703489
$987$	−738.980	−0.0238318
$988$	0	0
$989$	19593.1	0.629953
$990$	−25745.2	−0.826500
$991$	11663.3	0.373862	0.186931	−	0.982373i	$-0.440146\pi$
$991$	11663.3	0.373862	0.186931	+	0.982373i	$0.440146\pi$
$992$	−10175.5	−0.325677
$993$	2179.52	0.0696527
$994$	6089.55	0.194315
$995$	34874.2	1.11114
$996$	−8634.00	−0.274677
$997$	−3625.68	−0.115172	−0.0575860	−	0.998341i	$-0.518340\pi$
$997$	−3625.68	−0.115172	−0.0575860	+	0.998341i	$0.518340\pi$
$998$	−33387.5	−1.05898
$999$	−3587.11	−0.113605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.4	yes	51
13.12	even	2		1859.4.a.p.1.48	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.48	✓	51	13.12	even	2
1859.4.a.q.1.4	yes	51	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-5.05441 q^{2} +0.801365 q^{3} +17.5470 q^{4} -17.5680 q^{5} -4.05042 q^{6} +1.71020 q^{7} -48.2547 q^{8} -26.3578 q^{9} +O(q^{10})\)	\(q-5.05441 q^{2} +0.801365 q^{3} +17.5470 q^{4} -17.5680 q^{5} -4.05042 q^{6} +1.71020 q^{7} -48.2547 q^{8} -26.3578 q^{9} +88.7960 q^{10} +11.0000 q^{11} +14.0616 q^{12} -8.64404 q^{14} -14.0784 q^{15} +103.522 q^{16} +47.2534 q^{17} +133.223 q^{18} -150.092 q^{19} -308.267 q^{20} +1.37049 q^{21} -55.5985 q^{22} +59.4061 q^{23} -38.6696 q^{24} +183.636 q^{25} -42.7591 q^{27} +30.0089 q^{28} -91.1947 q^{29} +71.1580 q^{30} +74.1614 q^{31} -137.207 q^{32} +8.81501 q^{33} -238.838 q^{34} -30.0448 q^{35} -462.502 q^{36} +83.8911 q^{37} +758.624 q^{38} +847.740 q^{40} -378.855 q^{41} -6.92703 q^{42} +329.816 q^{43} +193.017 q^{44} +463.055 q^{45} -300.263 q^{46} -539.208 q^{47} +82.9592 q^{48} -340.075 q^{49} -928.171 q^{50} +37.8672 q^{51} -7.33959 q^{53} +216.122 q^{54} -193.248 q^{55} -82.5250 q^{56} -120.278 q^{57} +460.935 q^{58} -676.124 q^{59} -247.034 q^{60} -359.563 q^{61} -374.842 q^{62} -45.0771 q^{63} -134.678 q^{64} -44.5547 q^{66} -318.437 q^{67} +829.157 q^{68} +47.6059 q^{69} +151.859 q^{70} -704.480 q^{71} +1271.89 q^{72} +1043.78 q^{73} -424.020 q^{74} +147.159 q^{75} -2633.66 q^{76} +18.8122 q^{77} -112.511 q^{79} -1818.69 q^{80} +677.395 q^{81} +1914.89 q^{82} -614.013 q^{83} +24.0481 q^{84} -830.149 q^{85} -1667.02 q^{86} -73.0802 q^{87} -530.801 q^{88} +410.480 q^{89} -2340.47 q^{90} +1042.40 q^{92} +59.4303 q^{93} +2725.38 q^{94} +2636.81 q^{95} -109.953 q^{96} +934.568 q^{97} +1718.88 q^{98} -289.936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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