LMFDB - Embedded newform 1859.4.a.g.1.13

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:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 93 x^{15} - 7 x^{14} + 3449 x^{13} + 406 x^{12} - 65242 x^{11} - 7942 x^{10} + 669163 x^{9} + \cdots - 2210688 $ x^17 - 93x^15 - 7x^14 + 3449x^13 + 406x^12 - 65242x^11 - 7942x^10 + 669163x^9 + 59532x^8 - 3663297x^7 - 79027x^6 + 9967603x^5 - 984554x^4 - 12177120x^3 + 3207432x^2 + 5215872*x - 2210688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-2.78419$ of defining polynomial
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)

$f(q)$	$=$	$q+2.78419 q^{2} -8.94641 q^{3} -0.248293 q^{4} -17.0433 q^{5} -24.9085 q^{6} -30.9353 q^{7} -22.9648 q^{8} +53.0382 q^{9} +O(q^{10})$	\(q+2.78419 q^{2} -8.94641 q^{3} -0.248293 q^{4} -17.0433 q^{5} -24.9085 q^{6} -30.9353 q^{7} -22.9648 q^{8} +53.0382 q^{9} -47.4517 q^{10} +11.0000 q^{11} +2.22133 q^{12} -86.1296 q^{14} +152.476 q^{15} -61.9520 q^{16} -25.5564 q^{17} +147.668 q^{18} -119.151 q^{19} +4.23172 q^{20} +276.759 q^{21} +30.6261 q^{22} +39.1307 q^{23} +205.453 q^{24} +165.474 q^{25} -232.949 q^{27} +7.68100 q^{28} +240.200 q^{29} +424.522 q^{30} -175.056 q^{31} +11.2323 q^{32} -98.4105 q^{33} -71.1539 q^{34} +527.238 q^{35} -13.1690 q^{36} -197.907 q^{37} -331.739 q^{38} +391.396 q^{40} +33.6304 q^{41} +770.551 q^{42} +450.702 q^{43} -2.73122 q^{44} -903.945 q^{45} +108.947 q^{46} +146.461 q^{47} +554.248 q^{48} +613.990 q^{49} +460.710 q^{50} +228.638 q^{51} +240.842 q^{53} -648.573 q^{54} -187.476 q^{55} +710.422 q^{56} +1065.97 q^{57} +668.763 q^{58} +46.3962 q^{59} -37.8587 q^{60} -242.500 q^{61} -487.389 q^{62} -1640.75 q^{63} +526.889 q^{64} -273.993 q^{66} +565.666 q^{67} +6.34547 q^{68} -350.080 q^{69} +1467.93 q^{70} +82.7588 q^{71} -1218.01 q^{72} -643.157 q^{73} -551.010 q^{74} -1480.39 q^{75} +29.5844 q^{76} -340.288 q^{77} +534.566 q^{79} +1055.87 q^{80} +652.021 q^{81} +93.6334 q^{82} -375.952 q^{83} -68.7174 q^{84} +435.565 q^{85} +1254.84 q^{86} -2148.93 q^{87} -252.613 q^{88} -1361.50 q^{89} -2516.75 q^{90} -9.71588 q^{92} +1566.12 q^{93} +407.776 q^{94} +2030.73 q^{95} -100.489 q^{96} -257.882 q^{97} +1709.47 q^{98} +583.420 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * 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 $

$2$	2.78419	0.984359	0.492180	−	0.870494i	$-0.336200\pi$
$2$	2.78419	0.984359	0.492180	+	0.870494i	$0.336200\pi$
$3$	−8.94641	−1.72174	−0.860869	−	0.508827i	$-0.830079\pi$
$3$	−8.94641	−1.72174	−0.860869	+	0.508827i	$0.830079\pi$
$4$	−0.248293	−0.0310366
$5$	−17.0433	−1.52440	−0.762199	−	0.647343i	$-0.775880\pi$
$5$	−17.0433	−1.52440	−0.762199	+	0.647343i	$0.775880\pi$
$6$	−24.9085	−1.69481
$7$	−30.9353	−1.67035	−0.835174	−	0.549986i	$-0.814633\pi$
$7$	−30.9353	−1.67035	−0.835174	+	0.549986i	$0.814633\pi$
$8$	−22.9648	−1.01491
$9$	53.0382	1.96438
$10$	−47.4517	−1.50056
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	2.22133	0.0534369
$13$	0	0
$13$	0	0
$14$	−86.1296	−1.64422
$15$	152.476	2.62461
$16$	−61.9520	−0.968000
$17$	−25.5564	−0.364608	−0.182304	−	0.983242i	$-0.558356\pi$
$17$	−25.5564	−0.364608	−0.182304	+	0.983242i	$0.558356\pi$
$18$	147.668	1.93365
$19$	−119.151	−1.43869	−0.719346	−	0.694652i	$-0.755558\pi$
$19$	−119.151	−1.43869	−0.719346	+	0.694652i	$0.755558\pi$
$20$	4.23172	0.0473121
$21$	276.759	2.87590
$22$	30.6261	0.296796
$23$	39.1307	0.354753	0.177377	−	0.984143i	$-0.443239\pi$
$23$	39.1307	0.354753	0.177377	+	0.984143i	$0.443239\pi$
$24$	205.453	1.74741
$25$	165.474	1.32379
$26$	0	0
$27$	−232.949	−1.66041
$28$	7.68100	0.0518419
$29$	240.200	1.53807	0.769036	−	0.639206i	$-0.220737\pi$
$29$	240.200	1.53807	0.769036	+	0.639206i	$0.220737\pi$
$30$	424.522	2.58356
$31$	−175.056	−1.01423	−0.507113	−	0.861880i	$-0.669287\pi$
$31$	−175.056	−1.01423	−0.507113	+	0.861880i	$0.669287\pi$
$32$	11.2323	0.0620505
$33$	−98.4105	−0.519123
$34$	−71.1539	−0.358905
$35$	527.238	2.54627
$36$	−13.1690	−0.0609676
$37$	−197.907	−0.879343	−0.439671	−	0.898159i	$-0.644905\pi$
$37$	−197.907	−0.879343	−0.439671	+	0.898159i	$0.644905\pi$
$38$	−331.739	−1.41619
$39$	0	0
$40$	391.396	1.54713
$41$	33.6304	0.128102	0.0640511	−	0.997947i	$-0.479598\pi$
$41$	33.6304	0.128102	0.0640511	+	0.997947i	$0.479598\pi$
$42$	770.551	2.83092
$43$	450.702	1.59841	0.799203	−	0.601062i	$-0.205255\pi$
$43$	450.702	1.59841	0.799203	+	0.601062i	$0.205255\pi$
$44$	−2.73122	−0.00935789
$45$	−903.945	−2.99449
$46$	108.947	0.349205
$47$	146.461	0.454544	0.227272	−	0.973831i	$-0.427019\pi$
$47$	146.461	0.454544	0.227272	+	0.973831i	$0.427019\pi$
$48$	554.248	1.66664
$49$	613.990	1.79006
$50$	460.710	1.30308
$51$	228.638	0.627759
$52$	0	0
$53$	240.842	0.624193	0.312096	−	0.950050i	$-0.398969\pi$
$53$	240.842	0.624193	0.312096	+	0.950050i	$0.398969\pi$
$54$	−648.573	−1.63444
$55$	−187.476	−0.459623
$56$	710.422	1.69525
$57$	1065.97	2.47705
$58$	668.763	1.51402
$59$	46.3962	0.102378	0.0511888	−	0.998689i	$-0.483699\pi$
$59$	46.3962	0.102378	0.0511888	+	0.998689i	$0.483699\pi$
$60$	−37.8587	−0.0814590
$61$	−242.500	−0.509000	−0.254500	−	0.967073i	$-0.581911\pi$
$61$	−242.500	−0.509000	−0.254500	+	0.967073i	$0.581911\pi$
$62$	−487.389	−0.998363
$63$	−1640.75	−3.28119
$64$	526.889	1.02908
$65$	0	0
$66$	−273.993	−0.511004
$67$	565.666	1.03145	0.515725	−	0.856754i	$-0.327523\pi$
$67$	565.666	1.03145	0.515725	+	0.856754i	$0.327523\pi$
$68$	6.34547	0.0113162
$69$	−350.080	−0.610792
$70$	1467.93	2.50645
$71$	82.7588	0.138333	0.0691666	−	0.997605i	$-0.477966\pi$
$71$	82.7588	0.138333	0.0691666	+	0.997605i	$0.477966\pi$
$72$	−1218.01	−1.99367
$73$	−643.157	−1.03118	−0.515588	−	0.856837i	$-0.672426\pi$
$73$	−643.157	−1.03118	−0.515588	+	0.856837i	$0.672426\pi$
$74$	−551.010	−0.865589
$75$	−1480.39	−2.27922
$76$	29.5844	0.0446521
$77$	−340.288	−0.503629
$78$	0	0
$79$	534.566	0.761309	0.380654	−	0.924717i	$-0.375699\pi$
$79$	534.566	0.761309	0.380654	+	0.924717i	$0.375699\pi$
$80$	1055.87	1.47562
$81$	652.021	0.894404
$82$	93.6334	0.126099
$83$	−375.952	−0.497181	−0.248591	−	0.968609i	$-0.579967\pi$
$83$	−375.952	−0.497181	−0.248591	+	0.968609i	$0.579967\pi$
$84$	−68.7174	−0.0892581
$85$	435.565	0.555808
$86$	1254.84	1.57341
$87$	−2148.93	−2.64815
$88$	−252.613	−0.306007
$89$	−1361.50	−1.62155	−0.810777	−	0.585355i	$-0.800955\pi$
$89$	−1361.50	−1.62155	−0.810777	+	0.585355i	$0.800955\pi$
$90$	−2516.75	−2.94766
$91$	0	0
$92$	−9.71588	−0.0110103
$93$	1566.12	1.74623
$94$	407.776	0.447435
$95$	2030.73	2.19314
$96$	−100.489	−0.106835
$97$	−257.882	−0.269938	−0.134969	−	0.990850i	$-0.543093\pi$
$97$	−257.882	−0.269938	−0.134969	+	0.990850i	$0.543093\pi$
$98$	1709.47	1.76206
$99$	583.420	0.592282
$100$	−41.0859	−0.0410859
$101$	−1251.54	−1.23300	−0.616500	−	0.787355i	$-0.711450\pi$
$101$	−1251.54	−1.23300	−0.616500	+	0.787355i	$0.711450\pi$
$102$	636.571	0.617941
$103$	1175.16	1.12420	0.562099	−	0.827070i	$-0.309994\pi$
$103$	1175.16	1.12420	0.562099	+	0.827070i	$0.309994\pi$
$104$	0	0
$105$	−4716.89	−4.38401
$106$	670.550	0.614430
$107$	48.1633	0.0435151	0.0217576	−	0.999763i	$-0.493074\pi$
$107$	48.1633	0.0435151	0.0217576	+	0.999763i	$0.493074\pi$
$108$	57.8394	0.0515333
$109$	−512.050	−0.449959	−0.224979	−	0.974364i	$-0.572231\pi$
$109$	−512.050	−0.449959	−0.224979	+	0.974364i	$0.572231\pi$
$110$	−521.969	−0.452434
$111$	1770.56	1.51400
$112$	1916.50	1.61690
$113$	−1607.36	−1.33812	−0.669060	−	0.743208i	$-0.733303\pi$
$113$	−1607.36	−1.33812	−0.669060	+	0.743208i	$0.733303\pi$
$114$	2967.87	2.43831
$115$	−666.916	−0.540785
$116$	−59.6400	−0.0477365
$117$	0	0
$118$	129.176	0.100776
$119$	790.594	0.609022
$120$	−3501.59	−2.66375
$121$	121.000	0.0909091
$122$	−675.167	−0.501039
$123$	−300.871	−0.220558
$124$	43.4652	0.0314781
$125$	−689.802	−0.493582
$126$	−4568.16	−3.22987
$127$	351.126	0.245334	0.122667	−	0.992448i	$-0.460855\pi$
$127$	351.126	0.245334	0.122667	+	0.992448i	$0.460855\pi$
$128$	1377.10	0.950934
$129$	−4032.16	−2.75203
$130$	0	0
$131$	−1347.95	−0.899013	−0.449506	−	0.893277i	$-0.648400\pi$
$131$	−1347.95	−0.899013	−0.449506	+	0.893277i	$0.648400\pi$
$132$	24.4346	0.0161118
$133$	3685.97	2.40311
$134$	1574.92	1.01532
$135$	3970.21	2.53112
$136$	586.898	0.370045
$137$	−1685.23	−1.05094	−0.525470	−	0.850812i	$-0.676110\pi$
$137$	−1685.23	−1.05094	−0.525470	+	0.850812i	$0.676110\pi$
$138$	−974.688	−0.601239
$139$	345.486	0.210818	0.105409	−	0.994429i	$-0.466385\pi$
$139$	345.486	0.210818	0.105409	+	0.994429i	$0.466385\pi$
$140$	−130.909	−0.0790277
$141$	−1310.30	−0.782605
$142$	230.416	0.136170
$143$	0	0
$144$	−3285.82	−1.90152
$145$	−4093.80	−2.34463
$146$	−1790.67	−1.01505
$147$	−5493.01	−3.08201
$148$	49.1388	0.0272918
$149$	−2619.19	−1.44009	−0.720043	−	0.693930i	$-0.755878\pi$
$149$	−2619.19	−1.44009	−0.720043	+	0.693930i	$0.755878\pi$
$150$	−4121.70	−2.24357
$151$	2603.50	1.40311	0.701554	−	0.712616i	$-0.252490\pi$
$151$	2603.50	1.40311	0.701554	+	0.712616i	$0.252490\pi$
$152$	2736.28	1.46014
$153$	−1355.47	−0.716228
$154$	−947.426	−0.495752
$155$	2983.53	1.54608
$156$	0	0
$157$	1263.89	0.642482	0.321241	−	0.946997i	$-0.395900\pi$
$157$	1263.89	0.642482	0.321241	+	0.946997i	$0.395900\pi$
$158$	1488.33	0.749402
$159$	−2154.67	−1.07470
$160$	−191.436	−0.0945897
$161$	−1210.52	−0.592561
$162$	1815.35	0.880415
$163$	2269.28	1.09045	0.545227	−	0.838289i	$-0.316444\pi$
$163$	2269.28	1.09045	0.545227	+	0.838289i	$0.316444\pi$
$164$	−8.35019	−0.00397585
$165$	1677.24	0.791350
$166$	−1046.72	−0.489405
$167$	2975.45	1.37873	0.689363	−	0.724416i	$-0.257890\pi$
$167$	2975.45	1.37873	0.689363	+	0.724416i	$0.257890\pi$
$168$	−6355.73	−2.91878
$169$	0	0
$170$	1212.70	0.547115
$171$	−6319.56	−2.82614
$172$	−111.906	−0.0496091
$173$	−303.822	−0.133521	−0.0667606	−	0.997769i	$-0.521266\pi$
$173$	−303.822	−0.133521	−0.0667606	+	0.997769i	$0.521266\pi$
$174$	−5983.03	−2.60674
$175$	−5118.97	−2.21119
$176$	−681.472	−0.291863
$177$	−415.080	−0.176267
$178$	−3790.66	−1.59619
$179$	683.220	0.285287	0.142643	−	0.989774i	$-0.454440\pi$
$179$	683.220	0.285287	0.142643	+	0.989774i	$0.454440\pi$
$180$	224.443	0.0929389
$181$	−425.289	−0.174649	−0.0873246	−	0.996180i	$-0.527832\pi$
$181$	−425.289	−0.174649	−0.0873246	+	0.996180i	$0.527832\pi$
$182$	0	0
$183$	2169.51	0.876364
$184$	−898.630	−0.360043
$185$	3372.98	1.34047
$186$	4360.38	1.71892
$187$	−281.120	−0.109933
$188$	−36.3653	−0.0141075
$189$	7206.32	2.77345
$190$	5653.93	2.15884
$191$	−2501.24	−0.947559	−0.473779	−	0.880644i	$-0.657111\pi$
$191$	−2501.24	−0.947559	−0.473779	+	0.880644i	$0.657111\pi$
$192$	−4713.76	−1.77181
$193$	68.4563	0.0255316	0.0127658	−	0.999919i	$-0.495936\pi$
$193$	68.4563	0.0255316	0.0127658	+	0.999919i	$0.495936\pi$
$194$	−717.993	−0.265716
$195$	0	0
$196$	−152.449	−0.0555574
$197$	2460.38	0.889820	0.444910	−	0.895575i	$-0.353236\pi$
$197$	2460.38	0.889820	0.444910	+	0.895575i	$0.353236\pi$
$198$	1624.35	0.583019
$199$	−745.419	−0.265535	−0.132767	−	0.991147i	$-0.542386\pi$
$199$	−745.419	−0.265535	−0.132767	+	0.991147i	$0.542386\pi$
$200$	−3800.07	−1.34353
$201$	−5060.68	−1.77588
$202$	−3484.53	−1.21372
$203$	−7430.66	−2.56911
$204$	−56.7692	−0.0194835
$205$	−573.173	−0.195279
$206$	3271.88	1.10661
$207$	2075.42	0.696870
$208$	0	0
$209$	−1310.66	−0.433782
$210$	−13132.7	−4.31544
$211$	−889.480	−0.290210	−0.145105	−	0.989416i	$-0.546352\pi$
$211$	−889.480	−0.290210	−0.145105	+	0.989416i	$0.546352\pi$
$212$	−59.7994	−0.0193728
$213$	−740.394	−0.238173
$214$	134.096	0.0428345
$215$	−7681.44	−2.43661
$216$	5349.62	1.68516
$217$	5415.41	1.69411
$218$	−1425.64	−0.442921
$219$	5753.94	1.77541
$220$	46.5490	0.0142651
$221$	0	0
$222$	4929.56	1.49032
$223$	3739.64	1.12298	0.561491	−	0.827483i	$-0.310228\pi$
$223$	3739.64	1.12298	0.561491	+	0.827483i	$0.310228\pi$
$224$	−347.476	−0.103646
$225$	8776.42	2.60042
$226$	−4475.19	−1.31719
$227$	778.524	0.227632	0.113816	−	0.993502i	$-0.463693\pi$
$227$	778.524	0.227632	0.113816	+	0.993502i	$0.463693\pi$
$228$	−264.674	−0.0768792
$229$	6113.27	1.76409	0.882045	−	0.471165i	$-0.156166\pi$
$229$	6113.27	1.76409	0.882045	+	0.471165i	$0.156166\pi$
$230$	−1856.82	−0.532327
$231$	3044.35	0.867116
$232$	−5516.15	−1.56101
$233$	2872.78	0.807733	0.403867	−	0.914818i	$-0.367666\pi$
$233$	2872.78	0.807733	0.403867	+	0.914818i	$0.367666\pi$
$234$	0	0
$235$	−2496.18	−0.692906
$236$	−11.5199	−0.00317745
$237$	−4782.45	−1.31077
$238$	2201.16	0.599497
$239$	1064.76	0.288173	0.144086	−	0.989565i	$-0.453976\pi$
$239$	1064.76	0.288173	0.144086	+	0.989565i	$0.453976\pi$
$240$	−9446.21	−2.54062
$241$	655.096	0.175097	0.0875487	−	0.996160i	$-0.472097\pi$
$241$	655.096	0.175097	0.0875487	+	0.996160i	$0.472097\pi$
$242$	336.887	0.0894872
$243$	456.367	0.120477
$244$	60.2111	0.0157976
$245$	−10464.4	−2.72876
$246$	−837.683	−0.217108
$247$	0	0
$248$	4020.13	1.02935
$249$	3363.42	0.856016
$250$	−1920.54	−0.485862
$251$	−40.2062	−0.0101107	−0.00505536	−	0.999987i	$-0.501609\pi$
$251$	−40.2062	−0.0101107	−0.00505536	+	0.999987i	$0.501609\pi$
$252$	407.387	0.101837
$253$	430.438	0.106962
$254$	977.602	0.241497
$255$	−3896.74	−0.956955
$256$	−381.006	−0.0930192
$257$	4673.93	1.13444	0.567221	−	0.823566i	$-0.308019\pi$
$257$	4673.93	1.13444	0.567221	+	0.823566i	$0.308019\pi$
$258$	−11226.3	−2.70899
$259$	6122.30	1.46881
$260$	0	0
$261$	12739.8	3.02135
$262$	−3752.94	−0.884952
$263$	−650.798	−0.152585	−0.0762927	−	0.997085i	$-0.524308\pi$
$263$	−650.798	−0.152585	−0.0762927	+	0.997085i	$0.524308\pi$
$264$	2259.98	0.526864
$265$	−4104.74	−0.951518
$266$	10262.4	2.36553
$267$	12180.5	2.79189
$268$	−140.451	−0.0320127
$269$	4437.66	1.00583	0.502917	−	0.864335i	$-0.332260\pi$
$269$	4437.66	1.00583	0.502917	+	0.864335i	$0.332260\pi$
$270$	11053.8	2.49153
$271$	6600.83	1.47960	0.739801	−	0.672826i	$-0.234920\pi$
$271$	6600.83	1.47960	0.739801	+	0.672826i	$0.234920\pi$
$272$	1583.27	0.352941
$273$	0	0
$274$	−4691.99	−1.03450
$275$	1820.21	0.399137
$276$	86.9222	0.0189569
$277$	−7741.10	−1.67912	−0.839562	−	0.543263i	$-0.817189\pi$
$277$	−7741.10	−1.67912	−0.839562	+	0.543263i	$0.817189\pi$
$278$	961.898	0.207521
$279$	−9284.67	−1.99232
$280$	−12107.9	−2.58424
$281$	5156.69	1.09474	0.547371	−	0.836890i	$-0.315629\pi$
$281$	5156.69	1.09474	0.547371	+	0.836890i	$0.315629\pi$
$282$	−3648.13	−0.770365
$283$	2867.40	0.602294	0.301147	−	0.953578i	$-0.402630\pi$
$283$	2867.40	0.602294	0.301147	+	0.953578i	$0.402630\pi$
$284$	−20.5484	−0.00429339
$285$	−18167.7	−3.77601
$286$	0	0
$287$	−1040.37	−0.213975
$288$	595.744	0.121891
$289$	−4259.87	−0.867061
$290$	−11397.9	−2.30796
$291$	2307.12	0.464762
$292$	159.691	0.0320042
$293$	7190.16	1.43363	0.716815	−	0.697263i	$-0.245599\pi$
$293$	7190.16	1.43363	0.716815	+	0.697263i	$0.245599\pi$
$294$	−15293.6	−3.03381
$295$	−790.744	−0.156064
$296$	4544.89	0.892454
$297$	−2562.43	−0.500631
$298$	−7292.33	−1.41756
$299$	0	0
$300$	367.571	0.0707391
$301$	−13942.6	−2.66989
$302$	7248.62	1.38116
$303$	11196.8	2.12290
$304$	7381.65	1.39265
$305$	4133.00	0.775919
$306$	−3773.87	−0.705026
$307$	6709.43	1.24732	0.623660	−	0.781695i	$-0.285645\pi$
$307$	6709.43	1.24732	0.623660	+	0.781695i	$0.285645\pi$
$308$	84.4910	0.0156309
$309$	−10513.5	−1.93557
$310$	8306.71	1.52190
$311$	6167.68	1.12456	0.562278	−	0.826948i	$-0.309925\pi$
$311$	6167.68	1.12456	0.562278	+	0.826948i	$0.309925\pi$
$312$	0	0
$313$	3803.93	0.686935	0.343468	−	0.939164i	$-0.388398\pi$
$313$	3803.93	0.686935	0.343468	+	0.939164i	$0.388398\pi$
$314$	3518.92	0.632434
$315$	27963.8	5.00184
$316$	−132.729	−0.0236284
$317$	−1782.39	−0.315801	−0.157900	−	0.987455i	$-0.550472\pi$
$317$	−1782.39	−0.315801	−0.157900	+	0.987455i	$0.550472\pi$
$318$	−5999.02	−1.05789
$319$	2642.20	0.463746
$320$	−8979.92	−1.56873
$321$	−430.888	−0.0749216
$322$	−3370.32	−0.583293
$323$	3045.07	0.524559
$324$	−161.892	−0.0277593
$325$	0	0
$326$	6318.11	1.07340
$327$	4581.01	0.774711
$328$	−772.316	−0.130012
$329$	−4530.82	−0.759246
$330$	4669.75	0.778973
$331$	8191.95	1.36033	0.680166	−	0.733058i	$-0.261908\pi$
$331$	8191.95	1.36033	0.680166	+	0.733058i	$0.261908\pi$
$332$	93.3461	0.0154308
$333$	−10496.6	−1.72736
$334$	8284.22	1.35716
$335$	−9640.81	−1.57234
$336$	−17145.8	−2.78387
$337$	684.679	0.110673	0.0553366	−	0.998468i	$-0.482377\pi$
$337$	684.679	0.110673	0.0553366	+	0.998468i	$0.482377\pi$
$338$	0	0
$339$	14380.1	2.30389
$340$	−108.148	−0.0172504
$341$	−1925.62	−0.305801
$342$	−17594.9	−2.78193
$343$	−8383.16	−1.31967
$344$	−10350.3	−1.62224
$345$	5966.51	0.931090
$346$	−845.898	−0.131433
$347$	−10216.0	−1.58047	−0.790234	−	0.612805i	$-0.790041\pi$
$347$	−10216.0	−1.58047	−0.790234	+	0.612805i	$0.790041\pi$
$348$	533.564	0.0821897
$349$	−9850.14	−1.51079	−0.755395	−	0.655269i	$-0.772555\pi$
$349$	−9850.14	−1.51079	−0.755395	+	0.655269i	$0.772555\pi$
$350$	−14252.2	−2.17660
$351$	0	0
$352$	123.556	0.0187089
$353$	−5440.87	−0.820363	−0.410182	−	0.912004i	$-0.634535\pi$
$353$	−5440.87	−0.820363	−0.410182	+	0.912004i	$0.634535\pi$
$354$	−1155.66	−0.173510
$355$	−1410.48	−0.210875
$356$	338.050	0.0503275
$357$	−7072.98	−1.04858
$358$	1902.21	0.280824
$359$	−745.414	−0.109586	−0.0547931	−	0.998498i	$-0.517450\pi$
$359$	−745.414	−0.109586	−0.0547931	+	0.998498i	$0.517450\pi$
$360$	20758.9	3.03914
$361$	7337.99	1.06983
$362$	−1184.09	−0.171918
$363$	−1082.52	−0.156522
$364$	0	0
$365$	10961.5	1.57192
$366$	6040.32	0.862657
$367$	3355.85	0.477313	0.238656	−	0.971104i	$-0.423293\pi$
$367$	3355.85	0.477313	0.238656	+	0.971104i	$0.423293\pi$
$368$	−2424.23	−0.343401
$369$	1783.70	0.251641
$370$	9391.02	1.31950
$371$	−7450.52	−1.04262
$372$	−388.857	−0.0541970
$373$	7929.22	1.10070	0.550348	−	0.834936i	$-0.314495\pi$
$373$	7929.22	1.10070	0.550348	+	0.834936i	$0.314495\pi$
$374$	−782.692	−0.108214
$375$	6171.25	0.849819
$376$	−3363.45	−0.461322
$377$	0	0
$378$	20063.8	2.73008
$379$	−3400.29	−0.460847	−0.230423	−	0.973090i	$-0.574011\pi$
$379$	−3400.29	−0.460847	−0.230423	+	0.973090i	$0.574011\pi$
$380$	−504.215	−0.0680676
$381$	−3141.32	−0.422401
$382$	−6963.94	−0.932738
$383$	724.079	0.0966024	0.0483012	−	0.998833i	$-0.484619\pi$
$383$	724.079	0.0966024	0.0483012	+	0.998833i	$0.484619\pi$
$384$	−12320.1	−1.63726
$385$	5799.62	0.767730
$386$	190.595	0.0251323
$387$	23904.4	3.13987
$388$	64.0303	0.00837796
$389$	−10213.1	−1.33117	−0.665587	−	0.746320i	$-0.731819\pi$
$389$	−10213.1	−1.33117	−0.665587	+	0.746320i	$0.731819\pi$
$390$	0	0
$391$	−1000.04	−0.129346
$392$	−14100.2	−1.81675
$393$	12059.3	1.54786
$394$	6850.15	0.875902
$395$	−9110.77	−1.16054
$396$	−144.859	−0.0183824
$397$	5232.41	0.661479	0.330740	−	0.943722i	$-0.392702\pi$
$397$	5232.41	0.661479	0.330740	+	0.943722i	$0.392702\pi$
$398$	−2075.39	−0.261381
$399$	−32976.2	−4.13753
$400$	−10251.4	−1.28143
$401$	12778.6	1.59135	0.795676	−	0.605723i	$-0.207116\pi$
$401$	12778.6	1.59135	0.795676	+	0.605723i	$0.207116\pi$
$402$	−14089.9	−1.74811
$403$	0	0
$404$	310.749	0.0382681
$405$	−11112.6	−1.36343
$406$	−20688.4	−2.52893
$407$	−2176.97	−0.265132
$408$	−5250.63	−0.637120
$409$	4613.54	0.557763	0.278882	−	0.960326i	$-0.410036\pi$
$409$	4613.54	0.557763	0.278882	+	0.960326i	$0.410036\pi$
$410$	−1595.82	−0.192224
$411$	15076.7	1.80944
$412$	−291.785	−0.0348913
$413$	−1435.28	−0.171006
$414$	5778.37	0.685970
$415$	6407.45	0.757902
$416$	0	0
$417$	−3090.86	−0.362973
$418$	−3649.13	−0.426997
$419$	−8104.43	−0.944934	−0.472467	−	0.881348i	$-0.656636\pi$
$419$	−8104.43	−0.944934	−0.472467	+	0.881348i	$0.656636\pi$
$420$	1171.17	0.136065
$421$	−12776.6	−1.47908	−0.739540	−	0.673113i	$-0.764957\pi$
$421$	−12776.6	−1.47908	−0.739540	+	0.673113i	$0.764957\pi$
$422$	−2476.48	−0.285671
$423$	7768.05	0.892897
$424$	−5530.90	−0.633500
$425$	−4228.91	−0.482664
$426$	−2061.40	−0.234448
$427$	7501.82	0.850207
$428$	−11.9586	−0.00135056
$429$	0	0
$430$	−21386.6	−2.39850
$431$	−9594.58	−1.07228	−0.536142	−	0.844128i	$-0.680119\pi$
$431$	−9594.58	−1.07228	−0.536142	+	0.844128i	$0.680119\pi$
$432$	14431.6	1.60727
$433$	−3303.48	−0.366640	−0.183320	−	0.983053i	$-0.558684\pi$
$433$	−3303.48	−0.366640	−0.183320	+	0.983053i	$0.558684\pi$
$434$	15077.5	1.66761
$435$	36624.8	4.03684
$436$	127.138	0.0139652
$437$	−4662.47	−0.510381
$438$	16020.1	1.74764
$439$	−12325.4	−1.34000	−0.670000	−	0.742361i	$-0.733706\pi$
$439$	−12325.4	−1.34000	−0.670000	+	0.742361i	$0.733706\pi$
$440$	4305.35	0.466476
$441$	32565.0	3.51635
$442$	0	0
$443$	−17375.7	−1.86353	−0.931764	−	0.363065i	$-0.881730\pi$
$443$	−17375.7	−1.86353	−0.931764	+	0.363065i	$0.881730\pi$
$444$	−439.616	−0.0469893
$445$	23204.4	2.47189
$446$	10411.9	1.10542
$447$	23432.4	2.47945
$448$	−16299.5	−1.71892
$449$	−361.407	−0.0379863	−0.0189931	−	0.999820i	$-0.506046\pi$
$449$	−361.407	−0.0379863	−0.0189931	+	0.999820i	$0.506046\pi$
$450$	24435.2	2.55975
$451$	369.934	0.0386242
$452$	399.095	0.0415307
$453$	−23291.9	−2.41578
$454$	2167.56	0.224072
$455$	0	0
$456$	−24479.9	−2.51398
$457$	−4479.44	−0.458510	−0.229255	−	0.973366i	$-0.573629\pi$
$457$	−4479.44	−0.458510	−0.229255	+	0.973366i	$0.573629\pi$
$458$	17020.5	1.73650
$459$	5953.33	0.605398
$460$	165.591	0.0167841
$461$	−4276.49	−0.432052	−0.216026	−	0.976388i	$-0.569310\pi$
$461$	−4276.49	−0.432052	−0.216026	+	0.976388i	$0.569310\pi$
$462$	8476.06	0.853554
$463$	14592.9	1.46477	0.732386	−	0.680890i	$-0.238407\pi$
$463$	14592.9	1.46477	0.732386	+	0.680890i	$0.238407\pi$
$464$	−14880.9	−1.48885
$465$	−26691.9	−2.66195
$466$	7998.35	0.795100
$467$	6631.84	0.657141	0.328571	−	0.944479i	$-0.393433\pi$
$467$	6631.84	0.657141	0.328571	+	0.944479i	$0.393433\pi$
$468$	0	0
$469$	−17499.0	−1.72288
$470$	−6949.84	−0.682069
$471$	−11307.3	−1.10619
$472$	−1065.48	−0.103904
$473$	4957.72	0.481937
$474$	−13315.2	−1.29027
$475$	−19716.4	−1.90452
$476$	−196.299	−0.0189020
$477$	12773.8	1.22615
$478$	2964.48	0.283666
$479$	3196.24	0.304885	0.152442	−	0.988312i	$-0.451286\pi$
$479$	3196.24	0.304885	0.152442	+	0.988312i	$0.451286\pi$
$480$	1712.67	0.162859
$481$	0	0
$482$	1823.91	0.172359
$483$	10829.8	1.02023
$484$	−30.0434	−0.00282151
$485$	4395.16	0.411493
$486$	1270.61	0.118593
$487$	−18413.1	−1.71330	−0.856651	−	0.515897i	$-0.827459\pi$
$487$	−18413.1	−1.71330	−0.856651	+	0.515897i	$0.827459\pi$
$488$	5568.98	0.516590
$489$	−20301.9	−1.87747
$490$	−29134.9	−2.68608
$491$	−8914.76	−0.819384	−0.409692	−	0.912224i	$-0.634364\pi$
$491$	−8914.76	−0.819384	−0.409692	+	0.912224i	$0.634364\pi$
$492$	74.7042	0.00684537
$493$	−6138.66	−0.560793
$494$	0	0
$495$	−9943.40	−0.902874
$496$	10845.1	0.981771
$497$	−2560.16	−0.231064
$498$	9364.39	0.842627
$499$	−13841.2	−1.24172	−0.620858	−	0.783923i	$-0.713216\pi$
$499$	−13841.2	−1.24172	−0.620858	+	0.783923i	$0.713216\pi$
$500$	171.273	0.0153191
$501$	−26619.6	−2.37381
$502$	−111.942	−0.00995258
$503$	−1022.16	−0.0906079	−0.0453039	−	0.998973i	$-0.514426\pi$
$503$	−1022.16	−0.0906079	−0.0453039	+	0.998973i	$0.514426\pi$
$504$	37679.5	3.33012
$505$	21330.4	1.87958
$506$	1198.42	0.105289
$507$	0	0
$508$	−87.1821	−0.00761433
$509$	−13710.1	−1.19389	−0.596943	−	0.802284i	$-0.703618\pi$
$509$	−13710.1	−1.19389	−0.596943	+	0.802284i	$0.703618\pi$
$510$	−10849.3	−0.941988
$511$	19896.2	1.72242
$512$	−12077.6	−1.04250
$513$	27756.1	2.38881
$514$	13013.1	1.11670
$515$	−20028.7	−1.71372
$516$	1001.16	0.0854137
$517$	1611.07	0.137050
$518$	17045.6	1.44583
$519$	2718.12	0.229888
$520$	0	0
$521$	23529.0	1.97855	0.989276	−	0.146056i	$-0.0466580\pi$
$521$	23529.0	1.97855	0.989276	+	0.146056i	$0.0466580\pi$
$522$	35470.0	2.97410
$523$	−3200.59	−0.267594	−0.133797	−	0.991009i	$-0.542717\pi$
$523$	−3200.59	−0.267594	−0.133797	+	0.991009i	$0.542717\pi$
$524$	334.685	0.0279023
$525$	45796.4	3.80708
$526$	−1811.95	−0.150199
$527$	4473.81	0.369795
$528$	6096.73	0.502511
$529$	−10635.8	−0.874150
$530$	−11428.4	−0.936636
$531$	2460.77	0.201108
$532$	−915.200	−0.0745845
$533$	0	0
$534$	33912.8	2.74822
$535$	−820.860	−0.0663344
$536$	−12990.4	−1.04683
$537$	−6112.37	−0.491188
$538$	12355.3	0.990102
$539$	6753.89	0.539723
$540$	−985.774	−0.0785573
$541$	−17056.5	−1.35548	−0.677740	−	0.735302i	$-0.737040\pi$
$541$	−17056.5	−1.35548	−0.677740	+	0.735302i	$0.737040\pi$
$542$	18378.0	1.45646
$543$	3804.81	0.300700
$544$	−287.058	−0.0226241
$545$	8727.02	0.685916
$546$	0	0
$547$	−16192.8	−1.26573	−0.632864	−	0.774263i	$-0.718121\pi$
$547$	−16192.8	−1.26573	−0.632864	+	0.774263i	$0.718121\pi$
$548$	418.430	0.0326176
$549$	−12861.8	−0.999869
$550$	5067.81	0.392894
$551$	−28620.1	−2.21281
$552$	8039.51	0.619899
$553$	−16536.9	−1.27165
$554$	−21552.7	−1.65286
$555$	−30176.1	−2.30793
$556$	−85.7816	−0.00654308
$557$	16672.1	1.26826	0.634129	−	0.773227i	$-0.281359\pi$
$557$	16672.1	1.26826	0.634129	+	0.773227i	$0.281359\pi$
$558$	−25850.3	−1.96116
$559$	0	0
$560$	−32663.5	−2.46479
$561$	2515.02	0.189277
$562$	14357.2	1.07762
$563$	−6474.98	−0.484703	−0.242352	−	0.970188i	$-0.577919\pi$
$563$	−6474.98	−0.484703	−0.242352	+	0.970188i	$0.577919\pi$
$564$	325.339	0.0242894
$565$	27394.7	2.03983
$566$	7983.39	0.592874
$567$	−20170.4	−1.49397
$568$	−1900.54	−0.140396
$569$	15783.5	1.16288	0.581441	−	0.813589i	$-0.302489\pi$
$569$	15783.5	1.16288	0.581441	+	0.813589i	$0.302489\pi$
$570$	−50582.3	−3.71695
$571$	13667.2	1.00167	0.500836	−	0.865542i	$-0.333026\pi$
$571$	13667.2	1.00167	0.500836	+	0.865542i	$0.333026\pi$
$572$	0	0
$573$	22377.2	1.63145
$574$	−2896.57	−0.210628
$575$	6475.10	0.469618
$576$	27945.3	2.02150
$577$	−26656.2	−1.92325	−0.961624	−	0.274372i	$-0.911530\pi$
$577$	−26656.2	−1.92325	−0.961624	+	0.274372i	$0.911530\pi$
$578$	−11860.3	−0.853500
$579$	−612.438	−0.0439587
$580$	1016.46	0.0727694
$581$	11630.2	0.830465
$582$	6423.46	0.457493
$583$	2649.26	0.188201
$584$	14770.0	1.04655
$585$	0	0
$586$	20018.8	1.41121
$587$	10710.7	0.753116	0.376558	−	0.926393i	$-0.377108\pi$
$587$	10710.7	0.753116	0.376558	+	0.926393i	$0.377108\pi$
$588$	1363.87	0.0956551
$589$	20858.1	1.45916
$590$	−2201.58	−0.153623
$591$	−22011.5	−1.53204
$592$	12260.7	0.851204
$593$	20103.6	1.39217	0.696084	−	0.717960i	$-0.254924\pi$
$593$	20103.6	1.39217	0.696084	+	0.717960i	$0.254924\pi$
$594$	−7134.30	−0.492801
$595$	−13474.3	−0.928392
$596$	650.327	0.0446953
$597$	6668.82	0.457181
$598$	0	0
$599$	16671.1	1.13717	0.568583	−	0.822626i	$-0.307492\pi$
$599$	16671.1	1.13717	0.568583	+	0.822626i	$0.307492\pi$
$600$	33997.0	2.31320
$601$	−230.036	−0.0156129	−0.00780646	−	0.999970i	$-0.502485\pi$
$601$	−230.036	−0.0156129	−0.00780646	+	0.999970i	$0.502485\pi$
$602$	−38818.8	−2.62813
$603$	30001.9	2.02616
$604$	−646.429	−0.0435477
$605$	−2062.24	−0.138582
$606$	31174.0	2.08970
$607$	−2266.30	−0.151542	−0.0757711	−	0.997125i	$-0.524142\pi$
$607$	−2266.30	−0.151542	−0.0757711	+	0.997125i	$0.524142\pi$
$608$	−1338.35	−0.0892716
$609$	66477.7	4.42334
$610$	11507.1	0.763783
$611$	0	0
$612$	336.552	0.0222293
$613$	13320.1	0.877642	0.438821	−	0.898574i	$-0.355396\pi$
$613$	13320.1	0.877642	0.438821	+	0.898574i	$0.355396\pi$
$614$	18680.3	1.22781
$615$	5127.84	0.336218
$616$	7814.64	0.511138
$617$	15863.6	1.03508	0.517541	−	0.855658i	$-0.326847\pi$
$617$	15863.6	1.03508	0.517541	+	0.855658i	$0.326847\pi$
$618$	−29271.6	−1.90530
$619$	16354.4	1.06194	0.530969	−	0.847391i	$-0.321828\pi$
$619$	16354.4	1.06194	0.530969	+	0.847391i	$0.321828\pi$
$620$	−740.789	−0.0479852
$621$	−9115.45	−0.589034
$622$	17172.0	1.10697
$623$	42118.3	2.70856
$624$	0	0
$625$	−8927.70	−0.571373
$626$	10590.9	0.676191
$627$	11725.7	0.746858
$628$	−313.816	−0.0199405
$629$	5057.79	0.320616
$630$	77856.5	4.92361
$631$	−242.340	−0.0152891	−0.00764453	−	0.999971i	$-0.502433\pi$
$631$	−242.340	−0.0152891	−0.00764453	+	0.999971i	$0.502433\pi$
$632$	−12276.2	−0.772661
$633$	7957.65	0.499666
$634$	−4962.50	−0.310861
$635$	−5984.35	−0.373987
$636$	534.990	0.0333549
$637$	0	0
$638$	7356.39	0.456493
$639$	4389.38	0.271739
$640$	−23470.3	−1.44960
$641$	11682.8	0.719877	0.359938	−	0.932976i	$-0.382798\pi$
$641$	11682.8	0.719877	0.359938	+	0.932976i	$0.382798\pi$
$642$	−1199.67	−0.0737498
$643$	−4387.86	−0.269114	−0.134557	−	0.990906i	$-0.542961\pi$
$643$	−4387.86	−0.269114	−0.134557	+	0.990906i	$0.542961\pi$
$644$	300.563	0.0183911
$645$	68721.3	4.19519
$646$	8478.06	0.516354
$647$	−5118.78	−0.311035	−0.155518	−	0.987833i	$-0.549705\pi$
$647$	−5118.78	−0.311035	−0.155518	+	0.987833i	$0.549705\pi$
$648$	−14973.5	−0.907740
$649$	510.359	0.0308680
$650$	0	0
$651$	−48448.4	−2.91681
$652$	−563.446	−0.0338440
$653$	−15299.0	−0.916837	−0.458419	−	0.888736i	$-0.651584\pi$
$653$	−15299.0	−0.916837	−0.458419	+	0.888736i	$0.651584\pi$
$654$	12754.4	0.762594
$655$	22973.4	1.37045
$656$	−2083.47	−0.124003
$657$	−34111.9	−2.02562
$658$	−12614.7	−0.747371
$659$	18484.3	1.09263	0.546316	−	0.837579i	$-0.316030\pi$
$659$	18484.3	1.09263	0.546316	+	0.837579i	$0.316030\pi$
$660$	−416.446	−0.0245608
$661$	−19446.9	−1.14432	−0.572160	−	0.820142i	$-0.693894\pi$
$661$	−19446.9	−1.14432	−0.572160	+	0.820142i	$0.693894\pi$
$662$	22807.9	1.33906
$663$	0	0
$664$	8633.66	0.504595
$665$	−62821.1	−3.66330
$666$	−29224.6	−1.70034
$667$	9399.22	0.545636
$668$	−738.783	−0.0427910
$669$	−33456.4	−1.93348
$670$	−26841.8	−1.54775
$671$	−2667.51	−0.153469
$672$	3108.66	0.178451
$673$	−1360.80	−0.0779421	−0.0389711	−	0.999240i	$-0.512408\pi$
$673$	−1360.80	−0.0779421	−0.0389711	+	0.999240i	$0.512408\pi$
$674$	1906.28	0.108942
$675$	−38546.8	−2.19803
$676$	0	0
$677$	−8989.99	−0.510360	−0.255180	−	0.966894i	$-0.582135\pi$
$677$	−8989.99	−0.510360	−0.255180	+	0.966894i	$0.582135\pi$
$678$	40036.9	2.26786
$679$	7977.66	0.450890
$680$	−10002.7	−0.564095
$681$	−6965.00	−0.391923
$682$	−5361.28	−0.301018
$683$	−15019.1	−0.841421	−0.420711	−	0.907195i	$-0.638219\pi$
$683$	−15019.1	−0.841421	−0.420711	+	0.907195i	$0.638219\pi$
$684$	1569.10	0.0877136
$685$	28721.8	1.60205
$686$	−23340.3	−1.29903
$687$	−54691.9	−3.03730
$688$	−27921.9	−1.54726
$689$	0	0
$690$	16611.9	0.916527
$691$	−4748.76	−0.261435	−0.130717	−	0.991420i	$-0.541728\pi$
$691$	−4748.76	−0.261435	−0.130717	+	0.991420i	$0.541728\pi$
$692$	75.4368	0.00414404
$693$	−18048.3	−0.989317
$694$	−28443.2	−1.55575
$695$	−5888.21	−0.321371
$696$	49349.8	2.68764
$697$	−859.472	−0.0467071
$698$	−27424.7	−1.48716
$699$	−25701.0	−1.39070
$700$	1271.00	0.0686277
$701$	−18117.1	−0.976141	−0.488070	−	0.872804i	$-0.662299\pi$
$701$	−18117.1	−0.976141	−0.488070	+	0.872804i	$0.662299\pi$
$702$	0	0
$703$	23580.8	1.26510
$704$	5795.78	0.310279
$705$	22331.9	1.19300
$706$	−15148.4	−0.807532
$707$	38716.8	2.05954
$708$	103.061	0.00547074
$709$	−7473.16	−0.395854	−0.197927	−	0.980217i	$-0.563421\pi$
$709$	−7473.16	−0.395854	−0.197927	+	0.980217i	$0.563421\pi$
$710$	−3927.05	−0.207577
$711$	28352.4	1.49550
$712$	31266.5	1.64573
$713$	−6850.08	−0.359800
$714$	−19692.5	−1.03218
$715$	0	0
$716$	−169.639	−0.00885432
$717$	−9525.74	−0.496158
$718$	−2075.37	−0.107872
$719$	−9072.64	−0.470587	−0.235294	−	0.971924i	$-0.575605\pi$
$719$	−9072.64	−0.470587	−0.235294	+	0.971924i	$0.575605\pi$
$720$	56001.2	2.89867
$721$	−36354.0	−1.87780
$722$	20430.4	1.05310
$723$	−5860.76	−0.301472
$724$	105.596	0.00542052
$725$	39746.8	2.03608
$726$	−3013.93	−0.154073
$727$	−16802.9	−0.857200	−0.428600	−	0.903494i	$-0.640993\pi$
$727$	−16802.9	−0.857200	−0.428600	+	0.903494i	$0.640993\pi$
$728$	0	0
$729$	−21687.4	−1.10183
$730$	30518.9	1.54734
$731$	−11518.3	−0.582792
$732$	−538.673	−0.0271994
$733$	−38260.7	−1.92796	−0.963978	−	0.265982i	$-0.914304\pi$
$733$	−38260.7	−1.92796	−0.963978	+	0.265982i	$0.914304\pi$
$734$	9343.31	0.469847
$735$	93618.9	4.69821
$736$	439.530	0.0220126
$737$	6222.33	0.310994
$738$	4966.15	0.247705
$739$	−32944.7	−1.63991	−0.819953	−	0.572431i	$-0.806001\pi$
$739$	−32944.7	−1.63991	−0.819953	+	0.572431i	$0.806001\pi$
$740$	−837.487	−0.0416036
$741$	0	0
$742$	−20743.6	−1.02631
$743$	27786.8	1.37200	0.686002	−	0.727599i	$-0.259364\pi$
$743$	27786.8	1.37200	0.686002	+	0.727599i	$0.259364\pi$
$744$	−35965.7	−1.77227
$745$	44639.7	2.19526
$746$	22076.4	1.08348
$747$	−19939.8	−0.976652
$748$	69.8002	0.00341196
$749$	−1489.94	−0.0726854
$750$	17181.9	0.836527
$751$	−3543.62	−0.172182	−0.0860909	−	0.996287i	$-0.527438\pi$
$751$	−3543.62	−0.172182	−0.0860909	+	0.996287i	$0.527438\pi$
$752$	−9073.57	−0.439999
$753$	359.701	0.0174080
$754$	0	0
$755$	−44372.1	−2.13890
$756$	−1789.28	−0.0860786
$757$	17124.6	0.822199	0.411099	−	0.911591i	$-0.365145\pi$
$757$	17124.6	0.822199	0.411099	+	0.911591i	$0.365145\pi$
$758$	−9467.04	−0.453639
$759$	−3850.88	−0.184161
$760$	−46635.2	−2.22584
$761$	−20135.7	−0.959157	−0.479579	−	0.877499i	$-0.659210\pi$
$761$	−20135.7	−0.959157	−0.479579	+	0.877499i	$0.659210\pi$
$762$	−8746.03	−0.415794
$763$	15840.4	0.751588
$764$	621.041	0.0294090
$765$	23101.6	1.09182
$766$	2015.97	0.0950915
$767$	0	0
$768$	3408.64	0.160155
$769$	25507.1	1.19611	0.598056	−	0.801455i	$-0.295940\pi$
$769$	25507.1	1.19611	0.598056	+	0.801455i	$0.295940\pi$
$770$	16147.2	0.755723
$771$	−41814.9	−1.95321
$772$	−16.9972	−0.000792413 0
$773$	1323.23	0.0615696	0.0307848	−	0.999526i	$-0.490199\pi$
$773$	1323.23	0.0615696	0.0307848	+	0.999526i	$0.490199\pi$
$774$	66554.5	3.09076
$775$	−28967.2	−1.34262
$776$	5922.22	0.273963
$777$	−54772.6	−2.52890
$778$	−28435.3	−1.31035
$779$	−4007.10	−0.184299
$780$	0	0
$781$	910.346	0.0417090
$782$	−2784.30	−0.127323
$783$	−55954.3	−2.55382
$784$	−38037.9	−1.73278
$785$	−21540.9	−0.979399
$786$	33575.3	1.52365
$787$	32874.8	1.48902	0.744511	−	0.667610i	$-0.232683\pi$
$787$	32874.8	1.48902	0.744511	+	0.667610i	$0.232683\pi$
$788$	−610.893	−0.0276170
$789$	5822.31	0.262712
$790$	−25366.1	−1.14239
$791$	49724.0	2.23512
$792$	−13398.1	−0.601114
$793$	0	0
$794$	14568.0	0.651133
$795$	36722.7	1.63826
$796$	185.082	0.00824129
$797$	14456.7	0.642511	0.321255	−	0.946993i	$-0.395895\pi$
$797$	14456.7	0.642511	0.321255	+	0.946993i	$0.395895\pi$
$798$	−91812.0	−4.07282
$799$	−3743.02	−0.165730
$800$	1858.66	0.0821418
$801$	−72211.4	−3.18535
$802$	35578.0	1.56646
$803$	−7074.72	−0.310911
$804$	1256.53	0.0551174
$805$	20631.2	0.903299
$806$	0	0
$807$	−39701.2	−1.73178
$808$	28741.4	1.25138
$809$	−14910.6	−0.647995	−0.323998	−	0.946058i	$-0.605027\pi$
$809$	−14910.6	−0.647995	−0.323998	+	0.946058i	$0.605027\pi$
$810$	−30939.5	−1.34210
$811$	11353.9	0.491603	0.245802	−	0.969320i	$-0.420949\pi$
$811$	11353.9	0.491603	0.245802	+	0.969320i	$0.420949\pi$
$812$	1844.98	0.0797365
$813$	−59053.8	−2.54749
$814$	−6061.11	−0.260985
$815$	−38676.0	−1.66228
$816$	−14164.6	−0.607671
$817$	−53701.7	−2.29961
$818$	12845.0	0.549039
$819$	0	0
$820$	142.315	0.00606078
$821$	13672.6	0.581216	0.290608	−	0.956842i	$-0.406142\pi$
$821$	13672.6	0.581216	0.290608	+	0.956842i	$0.406142\pi$
$822$	41976.5	1.78114
$823$	−27315.2	−1.15692	−0.578462	−	0.815709i	$-0.696347\pi$
$823$	−27315.2	−1.15692	−0.578462	+	0.815709i	$0.696347\pi$
$824$	−26987.4	−1.14096
$825$	−16284.3	−0.687209
$826$	−3996.09	−0.168331
$827$	30785.2	1.29444	0.647222	−	0.762302i	$-0.275931\pi$
$827$	30785.2	1.29444	0.647222	+	0.762302i	$0.275931\pi$
$828$	−515.313	−0.0216285
$829$	33025.0	1.38360	0.691801	−	0.722089i	$-0.256818\pi$
$829$	33025.0	1.38360	0.691801	+	0.722089i	$0.256818\pi$
$830$	17839.6	0.746048
$831$	69255.0	2.89101
$832$	0	0
$833$	−15691.4	−0.652670
$834$	−8605.53	−0.357296
$835$	−50711.5	−2.10173
$836$	325.428	0.0134631
$837$	40779.1	1.68403
$838$	−22564.3	−0.930155
$839$	8155.30	0.335581	0.167790	−	0.985823i	$-0.446337\pi$
$839$	8155.30	0.335581	0.167790	+	0.985823i	$0.446337\pi$
$840$	108322.	4.44938
$841$	33307.2	1.36566
$842$	−35572.4	−1.45595
$843$	−46133.9	−1.88486
$844$	220.851	0.00900714
$845$	0	0
$846$	21627.7	0.878931
$847$	−3743.17	−0.151850
$848$	−14920.7	−0.604219
$849$	−25652.9	−1.03699
$850$	−11774.1	−0.475115
$851$	−7744.24	−0.311950
$852$	183.834	0.00739209
$853$	−11187.7	−0.449074	−0.224537	−	0.974466i	$-0.572087\pi$
$853$	−11187.7	−0.449074	−0.224537	+	0.974466i	$0.572087\pi$
$854$	20886.5	0.836909
$855$	107706.	4.30815
$856$	−1106.06	−0.0441640
$857$	27766.6	1.10675	0.553377	−	0.832931i	$-0.313339\pi$
$857$	27766.6	1.10675	0.553377	+	0.832931i	$0.313339\pi$
$858$	0	0
$859$	−1365.75	−0.0542478	−0.0271239	−	0.999632i	$-0.508635\pi$
$859$	−1365.75	−0.0542478	−0.0271239	+	0.999632i	$0.508635\pi$
$860$	1907.25	0.0756239
$861$	9307.53	0.368409
$862$	−26713.1	−1.05551
$863$	6976.15	0.275169	0.137584	−	0.990490i	$-0.456066\pi$
$863$	6976.15	0.275169	0.137584	+	0.990490i	$0.456066\pi$
$864$	−2616.56	−0.103029
$865$	5178.12	0.203539
$866$	−9197.50	−0.360905
$867$	38110.5	1.49285
$868$	−1344.61	−0.0525794
$869$	5880.23	0.229543
$870$	101970.	3.97370
$871$	0	0
$872$	11759.1	0.456668
$873$	−13677.6	−0.530260
$874$	−12981.2	−0.502398
$875$	21339.2	0.824454
$876$	−1428.66	−0.0551028
$877$	−36526.6	−1.40640	−0.703201	−	0.710991i	$-0.748246\pi$
$877$	−36526.6	−1.40640	−0.703201	+	0.710991i	$0.748246\pi$
$878$	−34316.3	−1.31904
$879$	−64326.1	−2.46833
$880$	11614.5	0.444915
$881$	−17459.6	−0.667682	−0.333841	−	0.942629i	$-0.608345\pi$
$881$	−17459.6	−0.667682	−0.333841	+	0.942629i	$0.608345\pi$
$882$	90667.0	3.46136
$883$	1542.46	0.0587858	0.0293929	−	0.999568i	$-0.490643\pi$
$883$	1542.46	0.0587858	0.0293929	+	0.999568i	$0.490643\pi$
$884$	0	0
$885$	7074.32	0.268701
$886$	−48377.1	−1.83438
$887$	21994.9	0.832600	0.416300	−	0.909227i	$-0.363327\pi$
$887$	21994.9	0.832600	0.416300	+	0.909227i	$0.363327\pi$
$888$	−40660.4	−1.53657
$889$	−10862.2	−0.409793
$890$	64605.4	2.43323
$891$	7172.23	0.269673
$892$	−928.527	−0.0348536
$893$	−17451.0	−0.653949
$894$	65240.1	2.44067
$895$	−11644.3	−0.434890
$896$	−42600.9	−1.58839
$897$	0	0
$898$	−1006.22	−0.0373921
$899$	−42048.5	−1.55995
$900$	−2179.12	−0.0807082
$901$	−6155.06	−0.227586
$902$	1029.97	0.0380201
$903$	124736.	4.59685
$904$	36912.7	1.35807
$905$	7248.33	0.266235
$906$	−64849.1	−2.37800
$907$	46347.2	1.69673	0.848364	−	0.529413i	$-0.177588\pi$
$907$	46347.2	1.69673	0.848364	+	0.529413i	$0.177588\pi$
$908$	−193.302	−0.00706492
$909$	−66379.5	−2.42208
$910$	0	0
$911$	−14026.4	−0.510116	−0.255058	−	0.966926i	$-0.582095\pi$
$911$	−14026.4	−0.510116	−0.255058	+	0.966926i	$0.582095\pi$
$912$	−66039.3	−2.39778
$913$	−4135.47	−0.149906
$914$	−12471.6	−0.451339
$915$	−36975.5	−1.33593
$916$	−1517.88	−0.0547513
$917$	41699.1	1.50166
$918$	16575.2	0.595929
$919$	19382.1	0.695710	0.347855	−	0.937548i	$-0.386910\pi$
$919$	19382.1	0.695710	0.347855	+	0.937548i	$0.386910\pi$
$920$	15315.6	0.548848
$921$	−60025.3	−2.14756
$922$	−11906.5	−0.425294
$923$	0	0
$924$	−755.891	−0.0269123
$925$	−32748.3	−1.16406
$926$	40629.4	1.44186
$927$	62328.6	2.20835
$928$	2698.01	0.0954382
$929$	−12163.1	−0.429556	−0.214778	−	0.976663i	$-0.568903\pi$
$929$	−12163.1	−0.429556	−0.214778	+	0.976663i	$0.568903\pi$
$930$	−74315.3	−2.62032
$931$	−73157.7	−2.57534
$932$	−713.289	−0.0250693
$933$	−55178.6	−1.93619
$934$	18464.3	0.646863
$935$	4791.22	0.167582
$936$	0	0
$937$	−13024.9	−0.454114	−0.227057	−	0.973881i	$-0.572910\pi$
$937$	−13024.9	−0.454114	−0.227057	+	0.973881i	$0.572910\pi$
$938$	−48720.6	−1.69593
$939$	−34031.5	−1.18272
$940$	619.784	0.0215054
$941$	3546.16	0.122850	0.0614249	−	0.998112i	$-0.480436\pi$
$941$	3546.16	0.122850	0.0614249	+	0.998112i	$0.480436\pi$
$942$	−31481.7	−1.08888
$943$	1315.98	0.0454446
$944$	−2874.34	−0.0991015
$945$	−122819.	−4.22785
$946$	13803.2	0.474400
$947$	16896.8	0.579803	0.289901	−	0.957056i	$-0.406377\pi$
$947$	16896.8	0.579803	0.289901	+	0.957056i	$0.406377\pi$
$948$	1187.45	0.0406820
$949$	0	0
$950$	−54894.1	−1.87474
$951$	15946.0	0.543726
$952$	−18155.8	−0.618103
$953$	7878.85	0.267808	0.133904	−	0.990994i	$-0.457249\pi$
$953$	7878.85	0.267808	0.133904	+	0.990994i	$0.457249\pi$
$954$	35564.8	1.20697
$955$	42629.4	1.44446
$956$	−264.371	−0.00894390
$957$	−23638.2	−0.798449
$958$	8898.93	0.300116
$959$	52132.9	1.75543
$960$	80338.0	2.70094
$961$	853.647	0.0286545
$962$	0	0
$963$	2554.49	0.0854802
$964$	−162.656	−0.00543443
$965$	−1166.72	−0.0389203
$966$	30152.2	1.00428
$967$	−29992.3	−0.997401	−0.498700	−	0.866774i	$-0.666189\pi$
$967$	−29992.3	−0.997401	−0.498700	+	0.866774i	$0.666189\pi$
$968$	−2778.74	−0.0922646
$969$	−27242.5	−0.903152
$970$	12237.0	0.405057
$971$	−27884.0	−0.921565	−0.460782	−	0.887513i	$-0.652431\pi$
$971$	−27884.0	−0.921565	−0.460782	+	0.887513i	$0.652431\pi$
$972$	−113.313	−0.00373920
$973$	−10687.7	−0.352139
$974$	−51265.6	−1.68650
$975$	0	0
$976$	15023.4	0.492712
$977$	43532.5	1.42551	0.712757	−	0.701411i	$-0.247446\pi$
$977$	43532.5	1.42551	0.712757	+	0.701411i	$0.247446\pi$
$978$	−56524.4	−1.84811
$979$	−14976.5	−0.488917
$980$	2598.24	0.0846915
$981$	−27158.2	−0.883890
$982$	−24820.4	−0.806569
$983$	−14650.1	−0.475346	−0.237673	−	0.971345i	$-0.576385\pi$
$983$	−14650.1	−0.475346	−0.237673	+	0.971345i	$0.576385\pi$
$984$	6909.45	0.223847
$985$	−41932.9	−1.35644
$986$	−17091.2	−0.552022
$987$	40534.5	1.30722
$988$	0	0
$989$	17636.3	0.567039
$990$	−27684.3	−0.888752
$991$	−3391.31	−0.108707	−0.0543534	−	0.998522i	$-0.517310\pi$
$991$	−3391.31	−0.108707	−0.0543534	+	0.998522i	$0.517310\pi$
$992$	−1966.29	−0.0629333
$993$	−73288.5	−2.34213
$994$	−7127.98	−0.227450
$995$	12704.4	0.404780
$996$	−835.112	−0.0265678
$997$	−31095.9	−0.987781	−0.493891	−	0.869524i	$-0.664426\pi$
$997$	−31095.9	−0.987781	−0.493891	+	0.869524i	$0.664426\pi$
$998$	−38536.5	−1.22230
$999$	46102.1	1.46007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.13		17
13.3	even	3		143.4.e.b.100.5	✓	34
13.9	even	3		143.4.e.b.133.5	yes	34
13.12	even	2		1859.4.a.h.1.5		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.5	✓	34	13.3	even	3
143.4.e.b.133.5	yes	34	13.9	even	3
1859.4.a.g.1.13		17	1.1	even	1	trivial
1859.4.a.h.1.5		17	13.12	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.78419 q^{2} -8.94641 q^{3} -0.248293 q^{4} -17.0433 q^{5} -24.9085 q^{6} -30.9353 q^{7} -22.9648 q^{8} +53.0382 q^{9} +O(q^{10})\)	\(q+2.78419 q^{2} -8.94641 q^{3} -0.248293 q^{4} -17.0433 q^{5} -24.9085 q^{6} -30.9353 q^{7} -22.9648 q^{8} +53.0382 q^{9} -47.4517 q^{10} +11.0000 q^{11} +2.22133 q^{12} -86.1296 q^{14} +152.476 q^{15} -61.9520 q^{16} -25.5564 q^{17} +147.668 q^{18} -119.151 q^{19} +4.23172 q^{20} +276.759 q^{21} +30.6261 q^{22} +39.1307 q^{23} +205.453 q^{24} +165.474 q^{25} -232.949 q^{27} +7.68100 q^{28} +240.200 q^{29} +424.522 q^{30} -175.056 q^{31} +11.2323 q^{32} -98.4105 q^{33} -71.1539 q^{34} +527.238 q^{35} -13.1690 q^{36} -197.907 q^{37} -331.739 q^{38} +391.396 q^{40} +33.6304 q^{41} +770.551 q^{42} +450.702 q^{43} -2.73122 q^{44} -903.945 q^{45} +108.947 q^{46} +146.461 q^{47} +554.248 q^{48} +613.990 q^{49} +460.710 q^{50} +228.638 q^{51} +240.842 q^{53} -648.573 q^{54} -187.476 q^{55} +710.422 q^{56} +1065.97 q^{57} +668.763 q^{58} +46.3962 q^{59} -37.8587 q^{60} -242.500 q^{61} -487.389 q^{62} -1640.75 q^{63} +526.889 q^{64} -273.993 q^{66} +565.666 q^{67} +6.34547 q^{68} -350.080 q^{69} +1467.93 q^{70} +82.7588 q^{71} -1218.01 q^{72} -643.157 q^{73} -551.010 q^{74} -1480.39 q^{75} +29.5844 q^{76} -340.288 q^{77} +534.566 q^{79} +1055.87 q^{80} +652.021 q^{81} +93.6334 q^{82} -375.952 q^{83} -68.7174 q^{84} +435.565 q^{85} +1254.84 q^{86} -2148.93 q^{87} -252.613 q^{88} -1361.50 q^{89} -2516.75 q^{90} -9.71588 q^{92} +1566.12 q^{93} +407.776 q^{94} +2030.73 q^{95} -100.489 q^{96} -257.882 q^{97} +1709.47 q^{98} +583.420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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