LMFDB - Embedded newform 1075.6.a.j.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.156002 q^{2} +15.3198 q^{3} -31.9757 q^{4} +2.38992 q^{6} +16.1051 q^{7} -9.98030 q^{8} -8.30330 q^{9} +O(q^{10})$	\(q+0.156002 q^{2} +15.3198 q^{3} -31.9757 q^{4} +2.38992 q^{6} +16.1051 q^{7} -9.98030 q^{8} -8.30330 q^{9} +199.918 q^{11} -489.861 q^{12} +1160.67 q^{13} +2.51242 q^{14} +1021.66 q^{16} -1474.33 q^{17} -1.29533 q^{18} -1782.44 q^{19} +246.727 q^{21} +31.1875 q^{22} +2700.63 q^{23} -152.896 q^{24} +181.066 q^{26} -3849.92 q^{27} -514.972 q^{28} -3146.99 q^{29} +3290.44 q^{31} +478.751 q^{32} +3062.70 q^{33} -229.998 q^{34} +265.504 q^{36} +8453.91 q^{37} -278.063 q^{38} +17781.3 q^{39} +1192.60 q^{41} +38.4898 q^{42} +1849.00 q^{43} -6392.50 q^{44} +421.303 q^{46} +24114.3 q^{47} +15651.7 q^{48} -16547.6 q^{49} -22586.5 q^{51} -37113.2 q^{52} -23222.0 q^{53} -600.594 q^{54} -160.734 q^{56} -27306.6 q^{57} -490.935 q^{58} -3648.27 q^{59} -40345.9 q^{61} +513.314 q^{62} -133.726 q^{63} -32618.6 q^{64} +477.786 q^{66} +67650.8 q^{67} +47142.8 q^{68} +41373.2 q^{69} -26217.5 q^{71} +82.8695 q^{72} +44737.2 q^{73} +1318.82 q^{74} +56994.7 q^{76} +3219.70 q^{77} +2773.90 q^{78} +31278.4 q^{79} -56962.4 q^{81} +186.048 q^{82} +3919.54 q^{83} -7889.27 q^{84} +288.447 q^{86} -48211.2 q^{87} -1995.24 q^{88} -126237. q^{89} +18692.7 q^{91} -86354.6 q^{92} +50409.0 q^{93} +3761.87 q^{94} +7334.38 q^{96} -108547. q^{97} -2581.46 q^{98} -1659.98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9}+O(q^{10}) $ 37 * q + 630 * q^4 + 291 * q^6 + 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9} + 675 q^{11} - 4446 q^{12} + 1241 q^{13} + 2375 q^{14} + 10518 q^{16} + 1153 q^{17} - 6680 q^{18} + 4065 q^{19} + 9953 q^{21} + 9283 q^{22} - 360 q^{23} + 2265 q^{24} + 23695 q^{26} + 1323 q^{27} - 30375 q^{28} + 19290 q^{29} + 23291 q^{31} + 8166 q^{32} - 10388 q^{33} - 13153 q^{34} + 148705 q^{36} + 13501 q^{37} - 8127 q^{38} - 1327 q^{39} + 38345 q^{41} - 21835 q^{42} + 68413 q^{43} + 47768 q^{44} + 48755 q^{46} + 84859 q^{47} - 208720 q^{48} + 107255 q^{49} + 62027 q^{51} + 128320 q^{52} - 53559 q^{53} + 44158 q^{54} + 107538 q^{56} + 104239 q^{57} - 85186 q^{58} + 48186 q^{59} + 82364 q^{61} + 206506 q^{62} - 75269 q^{63} + 161467 q^{64} + 91969 q^{66} + 38168 q^{67} + 95991 q^{68} + 287103 q^{69} + 155302 q^{71} + 9979 q^{72} + 31927 q^{73} + 59946 q^{74} + 225407 q^{76} - 80007 q^{77} - 67815 q^{78} + 150174 q^{79} + 417489 q^{81} + 60603 q^{82} + 266568 q^{83} + 586273 q^{84} - 57554 q^{87} + 323054 q^{88} + 334356 q^{89} + 51747 q^{91} - 258529 q^{92} - 285287 q^{93} + 302744 q^{94} + 287282 q^{96} - 78640 q^{97} - 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 + 213 * q^8 + 3535 * q^9 + 675 * q^11 - 4446 * q^12 + 1241 * q^13 + 2375 * q^14 + 10518 * q^16 + 1153 * q^17 - 6680 * q^18 + 4065 * q^19 + 9953 * q^21 + 9283 * q^22 - 360 * q^23 + 2265 * q^24 + 23695 * q^26 + 1323 * q^27 - 30375 * q^28 + 19290 * q^29 + 23291 * q^31 + 8166 * q^32 - 10388 * q^33 - 13153 * q^34 + 148705 * q^36 + 13501 * q^37 - 8127 * q^38 - 1327 * q^39 + 38345 * q^41 - 21835 * q^42 + 68413 * q^43 + 47768 * q^44 + 48755 * q^46 + 84859 * q^47 - 208720 * q^48 + 107255 * q^49 + 62027 * q^51 + 128320 * q^52 - 53559 * q^53 + 44158 * q^54 + 107538 * q^56 + 104239 * q^57 - 85186 * q^58 + 48186 * q^59 + 82364 * q^61 + 206506 * q^62 - 75269 * q^63 + 161467 * q^64 + 91969 * q^66 + 38168 * q^67 + 95991 * q^68 + 287103 * q^69 + 155302 * q^71 + 9979 * q^72 + 31927 * q^73 + 59946 * q^74 + 225407 * q^76 - 80007 * q^77 - 67815 * q^78 + 150174 * q^79 + 417489 * q^81 + 60603 * q^82 + 266568 * q^83 + 586273 * q^84 - 57554 * q^87 + 323054 * q^88 + 334356 * q^89 + 51747 * q^91 - 258529 * q^92 - 285287 * q^93 + 302744 * q^94 + 287282 * q^96 - 78640 * q^97 - 397117 * q^98 + 362152 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.156002	0.0275774	0.0137887	−	0.999905i	$-0.495611\pi$
$2$	0.156002	0.0275774	0.0137887	+	0.999905i	$0.495611\pi$
$3$	15.3198	0.982767	0.491383	−	0.870943i	$-0.336491\pi$
$3$	15.3198	0.982767	0.491383	+	0.870943i	$0.336491\pi$
$4$	−31.9757	−0.999239
$5$	0	0
$5$	0	0
$6$	2.38992	0.0271022
$7$	16.1051	0.124228	0.0621139	−	0.998069i	$-0.480216\pi$
$7$	16.1051	0.124228	0.0621139	+	0.998069i	$0.480216\pi$
$8$	−9.98030	−0.0551339
$9$	−8.30330	−0.0341700
$10$	0	0
$11$	199.918	0.498161	0.249080	−	0.968483i	$-0.419872\pi$
$11$	199.918	0.498161	0.249080	+	0.968483i	$0.419872\pi$
$12$	−489.861	−0.982019
$13$	1160.67	1.90481	0.952403	−	0.304842i	$-0.0986038\pi$
$13$	1160.67	1.90481	0.952403	+	0.304842i	$0.0986038\pi$
$14$	2.51242	0.00342588
$15$	0	0
$16$	1021.66	0.997719
$17$	−1474.33	−1.23730	−0.618648	−	0.785669i	$-0.712319\pi$
$17$	−1474.33	−1.23730	−0.618648	+	0.785669i	$0.712319\pi$
$18$	−1.29533	−0.000942320 0
$19$	−1782.44	−1.13274	−0.566371	−	0.824151i	$-0.691653\pi$
$19$	−1782.44	−1.13274	−0.566371	+	0.824151i	$0.691653\pi$
$20$	0	0
$21$	246.727	0.122087
$22$	31.1875	0.0137380
$23$	2700.63	1.06450	0.532251	−	0.846587i	$-0.321346\pi$
$23$	2700.63	1.06450	0.532251	+	0.846587i	$0.321346\pi$
$24$	−152.896	−0.0541838
$25$	0	0
$26$	181.066	0.0525297
$27$	−3849.92	−1.01635
$28$	−514.972	−0.124133
$29$	−3146.99	−0.694864	−0.347432	−	0.937705i	$-0.612946\pi$
$29$	−3146.99	−0.694864	−0.347432	+	0.937705i	$0.612946\pi$
$30$	0	0
$31$	3290.44	0.614965	0.307482	−	0.951554i	$-0.400514\pi$
$31$	3290.44	0.614965	0.307482	+	0.951554i	$0.400514\pi$
$32$	478.751	0.0826485
$33$	3062.70	0.489576
$34$	−229.998	−0.0341214
$35$	0	0
$36$	265.504	0.0341440
$37$	8453.91	1.01520	0.507602	−	0.861592i	$-0.330532\pi$
$37$	8453.91	1.01520	0.507602	+	0.861592i	$0.330532\pi$
$38$	−278.063	−0.0312381
$39$	17781.3	1.87198
$40$	0	0
$41$	1192.60	0.110799	0.0553996	−	0.998464i	$-0.482357\pi$
$41$	1192.60	0.110799	0.0553996	+	0.998464i	$0.482357\pi$
$42$	38.4898	0.00336684
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	−6392.50	−0.497782
$45$	0	0
$46$	421.303	0.0293562
$47$	24114.3	1.59232	0.796161	−	0.605085i	$-0.206861\pi$
$47$	24114.3	1.59232	0.796161	+	0.605085i	$0.206861\pi$
$48$	15651.7	0.980525
$49$	−16547.6	−0.984567
$50$	0	0
$51$	−22586.5	−1.21597
$52$	−37113.2	−1.90336
$53$	−23222.0	−1.13556	−0.567779	−	0.823181i	$-0.692197\pi$
$53$	−23222.0	−1.13556	−0.567779	+	0.823181i	$0.692197\pi$
$54$	−600.594	−0.0280283
$55$	0	0
$56$	−160.734	−0.00684916
$57$	−27306.6	−1.11322
$58$	−490.935	−0.0191626
$59$	−3648.27	−0.136445	−0.0682223	−	0.997670i	$-0.521733\pi$
$59$	−3648.27	−0.136445	−0.0682223	+	0.997670i	$0.521733\pi$
$60$	0	0
$61$	−40345.9	−1.38827	−0.694136	−	0.719844i	$-0.744213\pi$
$61$	−40345.9	−1.38827	−0.694136	+	0.719844i	$0.744213\pi$
$62$	513.314	0.0169591
$63$	−133.726	−0.00424486
$64$	−32618.6	−0.995440
$65$	0	0
$66$	477.786	0.0135012
$67$	67650.8	1.84114	0.920568	−	0.390583i	$-0.127726\pi$
$67$	67650.8	1.84114	0.920568	+	0.390583i	$0.127726\pi$
$68$	47142.8	1.23635
$69$	41373.2	1.04616
$70$	0	0
$71$	−26217.5	−0.617227	−0.308613	−	0.951188i	$-0.599865\pi$
$71$	−26217.5	−0.617227	−0.308613	+	0.951188i	$0.599865\pi$
$72$	82.8695	0.00188392
$73$	44737.2	0.982565	0.491282	−	0.871000i	$-0.336528\pi$
$73$	44737.2	0.982565	0.491282	+	0.871000i	$0.336528\pi$
$74$	1318.82	0.0279967
$75$	0	0
$76$	56994.7	1.13188
$77$	3219.70	0.0618854
$78$	2773.90	0.0516244
$79$	31278.4	0.563867	0.281933	−	0.959434i	$-0.409024\pi$
$79$	31278.4	0.563867	0.281933	+	0.959434i	$0.409024\pi$
$80$	0	0
$81$	−56962.4	−0.964662
$82$	186.048	0.00305556
$83$	3919.54	0.0624511	0.0312255	−	0.999512i	$-0.490059\pi$
$83$	3919.54	0.0624511	0.0312255	+	0.999512i	$0.490059\pi$
$84$	−7889.27	−0.121994
$85$	0	0
$86$	288.447	0.00420552
$87$	−48211.2	−0.682889
$88$	−1995.24	−0.0274655
$89$	−126237.	−1.68931	−0.844657	−	0.535307i	$-0.820196\pi$
$89$	−126237.	−1.68931	−0.844657	+	0.535307i	$0.820196\pi$
$90$	0	0
$91$	18692.7	0.236630
$92$	−86354.6	−1.06369
$93$	50409.0	0.604367
$94$	3761.87	0.0439122
$95$	0	0
$96$	7334.38	0.0812241
$97$	−108547.	−1.17135	−0.585677	−	0.810544i	$-0.699171\pi$
$97$	−108547.	−1.17135	−0.585677	+	0.810544i	$0.699171\pi$
$98$	−2581.46	−0.0271519
$99$	−1659.98	−0.0170221
$100$	0	0
$101$	60325.8	0.588436	0.294218	−	0.955738i	$-0.404941\pi$
$101$	60325.8	0.588436	0.294218	+	0.955738i	$0.404941\pi$
$102$	−3523.53	−0.0335334
$103$	158095.	1.46834	0.734169	−	0.678966i	$-0.237572\pi$
$103$	158095.	1.46834	0.734169	+	0.678966i	$0.237572\pi$
$104$	−11583.8	−0.105019
$105$	0	0
$106$	−3622.67	−0.0313158
$107$	141572.	1.19541	0.597705	−	0.801716i	$-0.296079\pi$
$107$	141572.	1.19541	0.597705	+	0.801716i	$0.296079\pi$
$108$	123104.	1.01557
$109$	−89995.3	−0.725527	−0.362764	−	0.931881i	$-0.618167\pi$
$109$	−89995.3	−0.725527	−0.362764	+	0.931881i	$0.618167\pi$
$110$	0	0
$111$	129512.	0.997708
$112$	16454.0	0.123944
$113$	182820.	1.34688	0.673439	−	0.739242i	$-0.264816\pi$
$113$	182820.	1.34688	0.673439	+	0.739242i	$0.264816\pi$
$114$	−4259.88	−0.0306998
$115$	0	0
$116$	100627.	0.694336
$117$	−9637.40	−0.0650871
$118$	−569.135	−0.00376279
$119$	−23744.3	−0.153706
$120$	0	0
$121$	−121084.	−0.751836
$122$	−6294.02	−0.0382850
$123$	18270.5	0.108890
$124$	−105214.	−0.614497
$125$	0	0
$126$	−20.8614	−0.000117062 0
$127$	81153.5	0.446476	0.223238	−	0.974764i	$-0.428337\pi$
$127$	81153.5	0.446476	0.223238	+	0.974764i	$0.428337\pi$
$128$	−20408.6	−0.110100
$129$	28326.3	0.149870
$130$	0	0
$131$	113628.	0.578504	0.289252	−	0.957253i	$-0.406593\pi$
$131$	113628.	0.578504	0.289252	+	0.957253i	$0.406593\pi$
$132$	−97931.9	−0.489203
$133$	−28706.4	−0.140718
$134$	10553.6	0.0507738
$135$	0	0
$136$	14714.3	0.0682169
$137$	319591.	1.45477	0.727383	−	0.686232i	$-0.240736\pi$
$137$	319591.	1.45477	0.727383	+	0.686232i	$0.240736\pi$
$138$	6454.29	0.0288503
$139$	156012.	0.684891	0.342445	−	0.939538i	$-0.388745\pi$
$139$	156012.	0.684891	0.342445	+	0.939538i	$0.388745\pi$
$140$	0	0
$141$	369427.	1.56488
$142$	−4089.97	−0.0170215
$143$	232039.	0.948899
$144$	−8483.19	−0.0340920
$145$	0	0
$146$	6979.07	0.0270966
$147$	−253507.	−0.967600
$148$	−270319.	−1.01443
$149$	234019.	0.863546	0.431773	−	0.901982i	$-0.357888\pi$
$149$	234019.	0.863546	0.431773	+	0.901982i	$0.357888\pi$
$150$	0	0
$151$	−101665.	−0.362851	−0.181426	−	0.983405i	$-0.558071\pi$
$151$	−101665.	−0.362851	−0.181426	+	0.983405i	$0.558071\pi$
$152$	17789.3	0.0624525
$153$	12241.8	0.0422783
$154$	502.278	0.00170664
$155$	0	0
$156$	−568568.	−1.87056
$157$	−199163.	−0.644850	−0.322425	−	0.946595i	$-0.604498\pi$
$157$	−199163.	−0.644850	−0.322425	+	0.946595i	$0.604498\pi$
$158$	4879.48	0.0155500
$159$	−355756.	−1.11599
$160$	0	0
$161$	43494.0	0.132241
$162$	−8886.22	−0.0266029
$163$	131334.	0.387175	0.193588	−	0.981083i	$-0.437988\pi$
$163$	131334.	0.387175	0.193588	+	0.981083i	$0.437988\pi$
$164$	−38134.3	−0.110715
$165$	0	0
$166$	611.454	0.00172224
$167$	101575.	0.281836	0.140918	−	0.990021i	$-0.454995\pi$
$167$	101575.	0.281836	0.140918	+	0.990021i	$0.454995\pi$
$168$	−2462.41	−0.00673113
$169$	975864.	2.62828
$170$	0	0
$171$	14800.1	0.0387057
$172$	−59123.0	−0.152383
$173$	741466.	1.88355	0.941773	−	0.336249i	$-0.109158\pi$
$173$	741466.	1.88355	0.941773	+	0.336249i	$0.109158\pi$
$174$	−7521.03	−0.0188323
$175$	0	0
$176$	204249.	0.497024
$177$	−55890.8	−0.134093
$178$	−19693.1	−0.0465870
$179$	319582.	0.745503	0.372752	−	0.927931i	$-0.378414\pi$
$179$	319582.	0.745503	0.372752	+	0.927931i	$0.378414\pi$
$180$	0	0
$181$	−613718.	−1.39243	−0.696213	−	0.717835i	$-0.745133\pi$
$181$	−613718.	−1.39243	−0.696213	+	0.717835i	$0.745133\pi$
$182$	2916.10	0.00652564
$183$	−618091.	−1.36435
$184$	−26953.2	−0.0586901
$185$	0	0
$186$	7863.88	0.0166669
$187$	−294745.	−0.616372
$188$	−771072.	−1.59111
$189$	−62003.4	−0.126259
$190$	0	0
$191$	742875.	1.47344	0.736719	−	0.676198i	$-0.236374\pi$
$191$	742875.	1.47344	0.736719	+	0.676198i	$0.236374\pi$
$192$	−499710.	−0.978285
$193$	−583437.	−1.12746	−0.563730	−	0.825959i	$-0.690634\pi$
$193$	−583437.	−1.12746	−0.563730	+	0.825959i	$0.690634\pi$
$194$	−16933.5	−0.0323030
$195$	0	0
$196$	529121.	0.983819
$197$	267075.	0.490307	0.245154	−	0.969484i	$-0.421162\pi$
$197$	267075.	0.490307	0.245154	+	0.969484i	$0.421162\pi$
$198$	−258.959	−0.000469427 0
$199$	591624.	1.05904	0.529521	−	0.848297i	$-0.322372\pi$
$199$	591624.	1.05904	0.529521	+	0.848297i	$0.322372\pi$
$200$	0	0
$201$	1.03640e6	1.80941
$202$	9410.91	0.0162276
$203$	−50682.6	−0.0863214
$204$	722219.	1.21505
$205$	0	0
$206$	24663.1	0.0404930
$207$	−22424.2	−0.0363740
$208$	1.18582e6	1.90046
$209$	−356341.	−0.564287
$210$	0	0
$211$	1.02428e6	1.58385	0.791926	−	0.610617i	$-0.209079\pi$
$211$	1.02428e6	1.58385	0.791926	+	0.610617i	$0.209079\pi$
$212$	742538.	1.13470
$213$	−401647.	−0.606590
$214$	22085.4	0.0329664
$215$	0	0
$216$	38423.4	0.0560352
$217$	52992.9	0.0763957
$218$	−14039.4	−0.0200082
$219$	685365.	0.965632
$220$	0	0
$221$	−1.71122e6	−2.35681
$222$	20204.1	0.0275142
$223$	72443.6	0.0975523	0.0487762	−	0.998810i	$-0.484468\pi$
$223$	72443.6	0.0975523	0.0487762	+	0.998810i	$0.484468\pi$
$224$	7710.34	0.0102672
$225$	0	0
$226$	28520.3	0.0371435
$227$	1.22913e6	1.58319	0.791596	−	0.611045i	$-0.209251\pi$
$227$	1.22913e6	1.58319	0.791596	+	0.611045i	$0.209251\pi$
$228$	873148.	1.11237
$229$	−842507.	−1.06166	−0.530829	−	0.847479i	$-0.678120\pi$
$229$	−842507.	−1.06166	−0.530829	+	0.847479i	$0.678120\pi$
$230$	0	0
$231$	49325.1	0.0608189
$232$	31407.9	0.0383106
$233$	711133.	0.858146	0.429073	−	0.903270i	$-0.358840\pi$
$233$	711133.	0.858146	0.429073	+	0.903270i	$0.358840\pi$
$234$	−1503.45	−0.00179494
$235$	0	0
$236$	116656.	0.136341
$237$	479179.	0.554149
$238$	−3704.15	−0.00423883
$239$	626313.	0.709245	0.354623	−	0.935009i	$-0.384609\pi$
$239$	626313.	0.709245	0.354623	+	0.935009i	$0.384609\pi$
$240$	0	0
$241$	1.44334e6	1.60076	0.800381	−	0.599491i	$-0.204630\pi$
$241$	1.44334e6	1.60076	0.800381	+	0.599491i	$0.204630\pi$
$242$	−18889.3	−0.0207337
$243$	62877.9	0.0683097
$244$	1.29009e6	1.38722
$245$	0	0
$246$	2850.22	0.00300290
$247$	−2.06883e6	−2.15765
$248$	−32839.6	−0.0339054
$249$	60046.6	0.0613748
$250$	0	0
$251$	−1.59237e6	−1.59536	−0.797680	−	0.603081i	$-0.793940\pi$
$251$	−1.59237e6	−1.59536	−0.797680	+	0.603081i	$0.793940\pi$
$252$	4275.96	0.00424163
$253$	539904.	0.530293
$254$	12660.1	0.0123127
$255$	0	0
$256$	1.04061e6	0.992404
$257$	−1.06223e6	−1.00319	−0.501596	−	0.865102i	$-0.667253\pi$
$257$	−1.06223e6	−1.00319	−0.501596	+	0.865102i	$0.667253\pi$
$258$	4418.95	0.00413304
$259$	136151.	0.126116
$260$	0	0
$261$	26130.4	0.0237435
$262$	17726.1	0.0159537
$263$	−48907.5	−0.0436000	−0.0218000	−	0.999762i	$-0.506940\pi$
$263$	−48907.5	−0.0436000	−0.0218000	+	0.999762i	$0.506940\pi$
$264$	−30566.7	−0.0269922
$265$	0	0
$266$	−4478.24	−0.00388064
$267$	−1.93392e6	−1.66020
$268$	−2.16318e6	−1.83974
$269$	1.40505e6	1.18389	0.591945	−	0.805978i	$-0.298360\pi$
$269$	1.40505e6	1.18389	0.591945	+	0.805978i	$0.298360\pi$
$270$	0	0
$271$	117173.	0.0969182	0.0484591	−	0.998825i	$-0.484569\pi$
$271$	117173.	0.0969182	0.0484591	+	0.998825i	$0.484569\pi$
$272$	−1.50627e6	−1.23447
$273$	286369.	0.232552
$274$	49856.7	0.0401187
$275$	0	0
$276$	−1.32294e6	−1.04536
$277$	521976.	0.408744	0.204372	−	0.978893i	$-0.434485\pi$
$277$	521976.	0.408744	0.204372	+	0.978893i	$0.434485\pi$
$278$	24338.1	0.0188875
$279$	−27321.5	−0.0210133
$280$	0	0
$281$	1.54480e6	1.16710	0.583549	−	0.812078i	$-0.301664\pi$
$281$	1.54480e6	1.16710	0.583549	+	0.812078i	$0.301664\pi$
$282$	57631.2	0.0431554
$283$	−427711.	−0.317457	−0.158728	−	0.987322i	$-0.550739\pi$
$283$	−427711.	−0.317457	−0.158728	+	0.987322i	$0.550739\pi$
$284$	838321.	0.616757
$285$	0	0
$286$	36198.4	0.0261682
$287$	19207.0	0.0137643
$288$	−3975.21	−0.00282409
$289$	753802.	0.530900
$290$	0	0
$291$	−1.66292e6	−1.15117
$292$	−1.43050e6	−0.981818
$293$	−2.84393e6	−1.93531	−0.967654	−	0.252280i	$-0.918820\pi$
$293$	−2.84393e6	−1.93531	−0.967654	+	0.252280i	$0.918820\pi$
$294$	−39547.4	−0.0266839
$295$	0	0
$296$	−84372.6	−0.0559721
$297$	−769667.	−0.506304
$298$	36507.3	0.0238144
$299$	3.13455e6	2.02767
$300$	0	0
$301$	29778.4	0.0189446
$302$	−15859.9	−0.0100065
$303$	924180.	0.578295
$304$	−1.82105e6	−1.13016
$305$	0	0
$306$	1909.75	0.00116593
$307$	−2.28792e6	−1.38546	−0.692730	−	0.721197i	$-0.743592\pi$
$307$	−2.28792e6	−1.38546	−0.692730	+	0.721197i	$0.743592\pi$
$308$	−102952.	−0.0618383
$309$	2.42199e6	1.44303
$310$	0	0
$311$	−2.12226e6	−1.24422	−0.622112	−	0.782928i	$-0.713725\pi$
$311$	−2.12226e6	−1.24422	−0.622112	+	0.782928i	$0.713725\pi$
$312$	−177462.	−0.103210
$313$	2.24624e6	1.29597	0.647985	−	0.761653i	$-0.275612\pi$
$313$	2.24624e6	1.29597	0.647985	+	0.761653i	$0.275612\pi$
$314$	−31069.7	−0.0177833
$315$	0	0
$316$	−1.00015e6	−0.563438
$317$	1.70892e6	0.955157	0.477578	−	0.878589i	$-0.341515\pi$
$317$	1.70892e6	0.955157	0.477578	+	0.878589i	$0.341515\pi$
$318$	−55498.6	−0.0307761
$319$	−629138.	−0.346154
$320$	0	0
$321$	2.16885e6	1.17481
$322$	6785.14	0.00364686
$323$	2.62791e6	1.40154
$324$	1.82141e6	0.963929
$325$	0	0
$326$	20488.3	0.0106773
$327$	−1.37871e6	−0.713024
$328$	−11902.6	−0.00610879
$329$	388364.	0.197811
$330$	0	0
$331$	−308875.	−0.154958	−0.0774788	−	0.996994i	$-0.524687\pi$
$331$	−308875.	−0.154958	−0.0774788	+	0.996994i	$0.524687\pi$
$332$	−125330.	−0.0624036
$333$	−70195.3	−0.0346895
$334$	15845.9	0.00777230
$335$	0	0
$336$	252072.	0.121808
$337$	−1.73652e6	−0.832923	−0.416462	−	0.909153i	$-0.636730\pi$
$337$	−1.73652e6	−0.832923	−0.416462	+	0.909153i	$0.636730\pi$
$338$	152236.	0.0724814
$339$	2.80077e6	1.32367
$340$	0	0
$341$	657818.	0.306351
$342$	2308.84	0.00106741
$343$	−537180.	−0.246538
$344$	−18453.6	−0.00840784
$345$	0	0
$346$	115670.	0.0519434
$347$	1.23059e6	0.548642	0.274321	−	0.961638i	$-0.411547\pi$
$347$	1.23059e6	0.548642	0.274321	+	0.961638i	$0.411547\pi$
$348$	1.54159e6	0.682370
$349$	1.37703e6	0.605172	0.302586	−	0.953122i	$-0.402150\pi$
$349$	1.37703e6	0.605172	0.302586	+	0.953122i	$0.402150\pi$
$350$	0	0
$351$	−4.46849e6	−1.93594
$352$	95710.8	0.0411722
$353$	2.60647e6	1.11331	0.556655	−	0.830744i	$-0.312084\pi$
$353$	2.60647e6	1.11331	0.556655	+	0.830744i	$0.312084\pi$
$354$	−8719.05	−0.00369795
$355$	0	0
$356$	4.03650e6	1.68803
$357$	−363758.	−0.151058
$358$	49855.3	0.0205591
$359$	−1.33972e6	−0.548627	−0.274314	−	0.961640i	$-0.588451\pi$
$359$	−1.33972e6	−0.548627	−0.274314	+	0.961640i	$0.588451\pi$
$360$	0	0
$361$	700992.	0.283103
$362$	−95740.9	−0.0383996
$363$	−1.85498e6	−0.738879
$364$	−597713.	−0.236450
$365$	0	0
$366$	−96423.2	−0.0376252
$367$	3.30685e6	1.28159	0.640795	−	0.767712i	$-0.278605\pi$
$367$	3.30685e6	1.28159	0.640795	+	0.767712i	$0.278605\pi$
$368$	2.75914e6	1.06207
$369$	−9902.55	−0.00378600
$370$	0	0
$371$	−373993.	−0.141068
$372$	−1.61186e6	−0.603907
$373$	−4.15246e6	−1.54537	−0.772687	−	0.634787i	$-0.781088\pi$
$373$	−4.15246e6	−1.54537	−0.772687	+	0.634787i	$0.781088\pi$
$374$	−45980.7	−0.0169980
$375$	0	0
$376$	−240668.	−0.0877909
$377$	−3.65262e6	−1.32358
$378$	−9672.63	−0.00348189
$379$	4.09943e6	1.46597	0.732985	−	0.680245i	$-0.238126\pi$
$379$	4.09943e6	1.46597	0.732985	+	0.680245i	$0.238126\pi$
$380$	0	0
$381$	1.24326e6	0.438782
$382$	115890.	0.0406337
$383$	5.20135e6	1.81184	0.905919	−	0.423451i	$-0.139181\pi$
$383$	5.20135e6	1.81184	0.905919	+	0.423451i	$0.139181\pi$
$384$	−312656.	−0.108203
$385$	0	0
$386$	−91017.2	−0.0310925
$387$	−15352.8	−0.00521087
$388$	3.47086e6	1.17046
$389$	−4.06260e6	−1.36123	−0.680613	−	0.732644i	$-0.738286\pi$
$389$	−4.06260e6	−1.36123	−0.680613	+	0.732644i	$0.738286\pi$
$390$	0	0
$391$	−3.98164e6	−1.31710
$392$	165150.	0.0542831
$393$	1.74076e6	0.568535
$394$	41664.2	0.0135214
$395$	0	0
$396$	53078.8	0.0170092
$397$	2.53252e6	0.806450	0.403225	−	0.915101i	$-0.367889\pi$
$397$	2.53252e6	0.806450	0.403225	+	0.915101i	$0.367889\pi$
$398$	92294.2	0.0292056
$399$	−439777.	−0.138293
$400$	0	0
$401$	−3.58153e6	−1.11226	−0.556132	−	0.831094i	$-0.687715\pi$
$401$	−3.58153e6	−1.11226	−0.556132	+	0.831094i	$0.687715\pi$
$402$	161680.	0.0498988
$403$	3.81912e6	1.17139
$404$	−1.92896e6	−0.587989
$405$	0	0
$406$	−7906.56	−0.00238052
$407$	1.69009e6	0.505734
$408$	225420.	0.0670413
$409$	−3.39036e6	−1.00216	−0.501081	−	0.865400i	$-0.667064\pi$
$409$	−3.39036e6	−1.00216	−0.501081	+	0.865400i	$0.667064\pi$
$410$	0	0
$411$	4.89608e6	1.42970
$412$	−5.05521e6	−1.46722
$413$	−58755.7	−0.0169502
$414$	−3498.21	−0.00100310
$415$	0	0
$416$	555672.	0.157429
$417$	2.39008e6	0.673088
$418$	−55589.8	−0.0155616
$419$	2.44291e6	0.679787	0.339894	−	0.940464i	$-0.389609\pi$
$419$	2.44291e6	0.679787	0.339894	+	0.940464i	$0.389609\pi$
$420$	0	0
$421$	4.21031e6	1.15773	0.578867	−	0.815422i	$-0.303495\pi$
$421$	4.21031e6	1.15773	0.578867	+	0.815422i	$0.303495\pi$
$422$	159790.	0.0436786
$423$	−200229.	−0.0544096
$424$	231762.	0.0626078
$425$	0	0
$426$	−62657.5	−0.0167282
$427$	−649775.	−0.172462
$428$	−4.52685e6	−1.19450
$429$	3.55479e6	0.932546
$430$	0	0
$431$	123145.	0.0319318	0.0159659	−	0.999873i	$-0.494918\pi$
$431$	123145.	0.0319318	0.0159659	+	0.999873i	$0.494918\pi$
$432$	−3.93333e6	−1.01403
$433$	6.16019e6	1.57897	0.789486	−	0.613769i	$-0.210347\pi$
$433$	6.16019e6	1.57897	0.789486	+	0.613769i	$0.210347\pi$
$434$	8266.98	0.00210680
$435$	0	0
$436$	2.87766e6	0.724975
$437$	−4.81372e6	−1.20580
$438$	106918.	0.0266297
$439$	1.94645e6	0.482038	0.241019	−	0.970520i	$-0.422518\pi$
$439$	1.94645e6	0.482038	0.241019	+	0.970520i	$0.422518\pi$
$440$	0	0
$441$	137400.	0.0336426
$442$	−266952.	−0.0649947
$443$	4.12045e6	0.997551	0.498776	−	0.866731i	$-0.333783\pi$
$443$	4.12045e6	0.997551	0.498776	+	0.866731i	$0.333783\pi$
$444$	−4.14124e6	−0.996949
$445$	0	0
$446$	11301.3	0.00269024
$447$	3.58513e6	0.848664
$448$	−525326.	−0.123661
$449$	−2.68306e6	−0.628079	−0.314040	−	0.949410i	$-0.601682\pi$
$449$	−2.68306e6	−0.628079	−0.314040	+	0.949410i	$0.601682\pi$
$450$	0	0
$451$	238423.	0.0551958
$452$	−5.84580e6	−1.34585
$453$	−1.55749e6	−0.356598
$454$	191746.	0.0436604
$455$	0	0
$456$	272529.	0.0613762
$457$	−963555.	−0.215817	−0.107909	−	0.994161i	$-0.534415\pi$
$457$	−963555.	−0.215817	−0.107909	+	0.994161i	$0.534415\pi$
$458$	−131432.	−0.0292778
$459$	5.67607e6	1.25752
$460$	0	0
$461$	6.84506e6	1.50012	0.750059	−	0.661371i	$-0.230025\pi$
$461$	6.84506e6	1.50012	0.750059	+	0.661371i	$0.230025\pi$
$462$	7694.80	0.00167723
$463$	−1.43307e6	−0.310681	−0.155340	−	0.987861i	$-0.549647\pi$
$463$	−1.43307e6	−0.310681	−0.155340	+	0.987861i	$0.549647\pi$
$464$	−3.21516e6	−0.693279
$465$	0	0
$466$	110938.	0.0236655
$467$	−1.54974e6	−0.328827	−0.164414	−	0.986391i	$-0.552573\pi$
$467$	−1.54974e6	−0.328827	−0.164414	+	0.986391i	$0.552573\pi$
$468$	308162.	0.0650376
$469$	1.08952e6	0.228720
$470$	0	0
$471$	−3.05113e6	−0.633737
$472$	36410.8	0.00752273
$473$	369648.	0.0759688
$474$	74752.7	0.0152820
$475$	0	0
$476$	759240.	0.153590
$477$	192819.	0.0388020
$478$	97705.8	0.0195592
$479$	3.69111e6	0.735052	0.367526	−	0.930013i	$-0.380205\pi$
$479$	3.69111e6	0.735052	0.367526	+	0.930013i	$0.380205\pi$
$480$	0	0
$481$	9.81220e6	1.93377
$482$	225164.	0.0441449
$483$	666320.	0.129962
$484$	3.87174e6	0.751264
$485$	0	0
$486$	9809.05	0.00188381
$487$	5.40345e6	1.03240	0.516201	−	0.856468i	$-0.327346\pi$
$487$	5.40345e6	1.03240	0.516201	+	0.856468i	$0.327346\pi$
$488$	402664.	0.0765409
$489$	2.01201e6	0.380503
$490$	0	0
$491$	673978.	0.126166	0.0630830	−	0.998008i	$-0.479907\pi$
$491$	673978.	0.126166	0.0630830	+	0.998008i	$0.479907\pi$
$492$	−584210.	−0.108807
$493$	4.63971e6	0.859752
$494$	−322740.	−0.0595025
$495$	0	0
$496$	3.36173e6	0.613562
$497$	−422235.	−0.0766767
$498$	9367.37	0.00169256
$499$	−2.38895e6	−0.429492	−0.214746	−	0.976670i	$-0.568892\pi$
$499$	−2.38895e6	−0.429492	−0.214746	+	0.976670i	$0.568892\pi$
$500$	0	0
$501$	1.55611e6	0.276979
$502$	−248412.	−0.0439960
$503$	−1.07774e7	−1.89930	−0.949650	−	0.313314i	$-0.898561\pi$
$503$	−1.07774e7	−1.89930	−0.949650	+	0.313314i	$0.898561\pi$
$504$	1334.62	0.000234036 0
$505$	0	0
$506$	84225.9	0.0146241
$507$	1.49500e7	2.58299
$508$	−2.59494e6	−0.446136
$509$	9.52953e6	1.63034	0.815168	−	0.579225i	$-0.196645\pi$
$509$	9.52953e6	1.63034	0.815168	+	0.579225i	$0.196645\pi$
$510$	0	0
$511$	720497.	0.122062
$512$	815411.	0.137468
$513$	6.86225e6	1.15126
$514$	−165709.	−0.0276654
$515$	0	0
$516$	−905753.	−0.149757
$517$	4.82088e6	0.793232
$518$	21239.8	0.00347797
$519$	1.13591e7	1.85109
$520$	0	0
$521$	−6.93728e6	−1.11968	−0.559841	−	0.828600i	$-0.689138\pi$
$521$	−6.93728e6	−1.11968	−0.559841	+	0.828600i	$0.689138\pi$
$522$	4076.38	0.000654784 0
$523$	8.52785e6	1.36328	0.681640	−	0.731687i	$-0.261267\pi$
$523$	8.52785e6	1.36328	0.681640	+	0.731687i	$0.261267\pi$
$524$	−3.63333e6	−0.578064
$525$	0	0
$526$	−7629.65	−0.00120238
$527$	−4.85121e6	−0.760893
$528$	3.12905e6	0.488459
$529$	857083.	0.133163
$530$	0	0
$531$	30292.6	0.00466231
$532$	917906.	0.140611
$533$	1.38422e6	0.211051
$534$	−301695.	−0.0457841
$535$	0	0
$536$	−675175.	−0.101509
$537$	4.89594e6	0.732656
$538$	219190.	0.0326487
$539$	−3.30816e6	−0.490473
$540$	0	0
$541$	−4.64917e6	−0.682940	−0.341470	−	0.939893i	$-0.610925\pi$
$541$	−4.64917e6	−0.682940	−0.341470	+	0.939893i	$0.610925\pi$
$542$	18279.2	0.00267276
$543$	−9.40204e6	−1.36843
$544$	−705839.	−0.102261
$545$	0	0
$546$	44674.0	0.00641318
$547$	−6.51750e6	−0.931349	−0.465675	−	0.884956i	$-0.654188\pi$
$547$	−6.51750e6	−0.931349	−0.465675	+	0.884956i	$0.654188\pi$
$548$	−1.02191e7	−1.45366
$549$	335004.	0.0474372
$550$	0	0
$551$	5.60931e6	0.787101
$552$	−412917.	−0.0576787
$553$	503742.	0.0700479
$554$	81429.1	0.0112721
$555$	0	0
$556$	−4.98859e6	−0.684370
$557$	−5.59844e6	−0.764591	−0.382295	−	0.924040i	$-0.624866\pi$
$557$	−5.59844e6	−0.764591	−0.382295	+	0.924040i	$0.624866\pi$
$558$	−4262.20	−0.000579493 0
$559$	2.14608e6	0.290480
$560$	0	0
$561$	−4.51544e6	−0.605750
$562$	240992.	0.0321856
$563$	−4.87671e6	−0.648420	−0.324210	−	0.945985i	$-0.605098\pi$
$563$	−4.87671e6	−0.648420	−0.324210	+	0.945985i	$0.605098\pi$
$564$	−1.18127e7	−1.56369
$565$	0	0
$566$	−66723.6	−0.00875465
$567$	−917385.	−0.119838
$568$	261658.	0.0340301
$569$	−7.20436e6	−0.932856	−0.466428	−	0.884559i	$-0.654459\pi$
$569$	−7.20436e6	−0.932856	−0.466428	+	0.884559i	$0.654459\pi$
$570$	0	0
$571$	1.01161e7	1.29844	0.649220	−	0.760601i	$-0.275096\pi$
$571$	1.01161e7	1.29844	0.649220	+	0.760601i	$0.275096\pi$
$572$	−7.41959e6	−0.948178
$573$	1.13807e7	1.44805
$574$	2996.33	0.000379585 0
$575$	0	0
$576$	270842.	0.0340141
$577$	7.86343e6	0.983270	0.491635	−	0.870802i	$-0.336400\pi$
$577$	7.86343e6	0.983270	0.491635	+	0.870802i	$0.336400\pi$
$578$	117594.	0.0146409
$579$	−8.93815e6	−1.10803
$580$	0	0
$581$	63124.6	0.00775815
$582$	−259418.	−0.0317463
$583$	−4.64248e6	−0.565691
$584$	−446490.	−0.0541726
$585$	0	0
$586$	−443658.	−0.0533709
$587$	1.24195e7	1.48768	0.743841	−	0.668356i	$-0.233002\pi$
$587$	1.24195e7	1.48768	0.743841	+	0.668356i	$0.233002\pi$
$588$	8.10604e6	0.966864
$589$	−5.86502e6	−0.696596
$590$	0	0
$591$	4.09155e6	0.481858
$592$	8.63705e6	1.01289
$593$	−1.22515e7	−1.43072	−0.715359	−	0.698757i	$-0.753737\pi$
$593$	−1.22515e7	−1.43072	−0.715359	+	0.698757i	$0.753737\pi$
$594$	−120069.	−0.0139626
$595$	0	0
$596$	−7.48291e6	−0.862889
$597$	9.06356e6	1.04079
$598$	488994.	0.0559179
$599$	−1.20969e7	−1.37755	−0.688774	−	0.724976i	$-0.741851\pi$
$599$	−1.20969e7	−1.37755	−0.688774	+	0.724976i	$0.741851\pi$
$600$	0	0
$601$	110723.	0.0125041	0.00625203	−	0.999980i	$-0.498010\pi$
$601$	110723.	0.0125041	0.00625203	+	0.999980i	$0.498010\pi$
$602$	4645.47	0.000522442 0
$603$	−561725.	−0.0629115
$604$	3.25080e6	0.362575
$605$	0	0
$606$	144173.	0.0159479
$607$	886922.	0.0977043	0.0488521	−	0.998806i	$-0.484444\pi$
$607$	886922.	0.0977043	0.0488521	+	0.998806i	$0.484444\pi$
$608$	−853345.	−0.0936193
$609$	−776448.	−0.0848338
$610$	0	0
$611$	2.79888e7	3.03306
$612$	−391441.	−0.0422462
$613$	403565.	0.0433773	0.0216886	−	0.999765i	$-0.493096\pi$
$613$	403565.	0.0433773	0.0216886	+	0.999765i	$0.493096\pi$
$614$	−356919.	−0.0382075
$615$	0	0
$616$	−32133.5	−0.00341198
$617$	1.49287e7	1.57874	0.789370	−	0.613918i	$-0.210407\pi$
$617$	1.49287e7	1.57874	0.789370	+	0.613918i	$0.210407\pi$
$618$	377835.	0.0397952
$619$	1.13264e7	1.18813	0.594067	−	0.804416i	$-0.297521\pi$
$619$	1.13264e7	1.18813	0.594067	+	0.804416i	$0.297521\pi$
$620$	0	0
$621$	−1.03972e7	−1.08190
$622$	−331077.	−0.0343125
$623$	−2.03306e6	−0.209860
$624$	1.81665e7	1.86771
$625$	0	0
$626$	350417.	0.0357395
$627$	−5.45908e6	−0.554563
$628$	6.36835e6	0.644359
$629$	−1.24639e7	−1.25611
$630$	0	0
$631$	−1.49821e7	−1.49796	−0.748981	−	0.662592i	$-0.769456\pi$
$631$	−1.49821e7	−1.49796	−0.748981	+	0.662592i	$0.769456\pi$
$632$	−312168.	−0.0310882
$633$	1.56919e7	1.55656
$634$	266595.	0.0263408
$635$	0	0
$636$	1.13755e7	1.11514
$637$	−1.92063e7	−1.87541
$638$	−98146.5	−0.00954604
$639$	217691.	0.0210906
$640$	0	0
$641$	−1.11162e7	−1.06859	−0.534294	−	0.845299i	$-0.679423\pi$
$641$	−1.11162e7	−1.06859	−0.534294	+	0.845299i	$0.679423\pi$
$642$	338344.	0.0323982
$643$	756694.	0.0721760	0.0360880	−	0.999349i	$-0.488510\pi$
$643$	756694.	0.0721760	0.0360880	+	0.999349i	$0.488510\pi$
$644$	−1.39075e6	−0.132140
$645$	0	0
$646$	409958.	0.0386508
$647$	−1.13005e7	−1.06129	−0.530647	−	0.847593i	$-0.678051\pi$
$647$	−1.13005e7	−1.06129	−0.530647	+	0.847593i	$0.678051\pi$
$648$	568502.	0.0531856
$649$	−729353.	−0.0679713
$650$	0	0
$651$	811842.	0.0750791
$652$	−4.19949e6	−0.386881
$653$	−8.95338e6	−0.821683	−0.410841	−	0.911707i	$-0.634765\pi$
$653$	−8.95338e6	−0.821683	−0.410841	+	0.911707i	$0.634765\pi$
$654$	−215081.	−0.0196634
$655$	0	0
$656$	1.21844e6	0.110546
$657$	−371466.	−0.0335742
$658$	60585.4	0.00545511
$659$	−1.17404e7	−1.05310	−0.526548	−	0.850145i	$-0.676514\pi$
$659$	−1.17404e7	−1.05310	−0.526548	+	0.850145i	$0.676514\pi$
$660$	0	0
$661$	3.25091e6	0.289402	0.144701	−	0.989475i	$-0.453778\pi$
$661$	3.25091e6	0.289402	0.144701	+	0.989475i	$0.453778\pi$
$662$	−48185.0	−0.00427334
$663$	−2.62155e7	−2.31619
$664$	−39118.2	−0.00344317
$665$	0	0
$666$	−10950.6	−0.000956647 0
$667$	−8.49886e6	−0.739684
$668$	−3.24793e6	−0.281621
$669$	1.10982e6	0.0958712
$670$	0	0
$671$	−8.06585e6	−0.691582
$672$	118121.	0.0100903
$673$	−1.89394e7	−1.61186	−0.805932	−	0.592008i	$-0.798335\pi$
$673$	−1.89394e7	−1.61186	−0.805932	+	0.592008i	$0.798335\pi$
$674$	−270900.	−0.0229699
$675$	0	0
$676$	−3.12039e7	−2.62629
$677$	2.00764e7	1.68350	0.841751	−	0.539867i	$-0.181525\pi$
$677$	2.00764e7	1.68350	0.841751	+	0.539867i	$0.181525\pi$
$678$	436925.	0.0365034
$679$	−1.74816e6	−0.145515
$680$	0	0
$681$	1.88301e7	1.55591
$682$	102621.	0.00844838
$683$	−1.81167e7	−1.48603	−0.743016	−	0.669273i	$-0.766606\pi$
$683$	−1.81167e7	−1.48603	−0.743016	+	0.669273i	$0.766606\pi$
$684$	−473244.	−0.0386763
$685$	0	0
$686$	−83800.9	−0.00679890
$687$	−1.29071e7	−1.04336
$688$	1.88906e6	0.152151
$689$	−2.69531e7	−2.16302
$690$	0	0
$691$	−7.11877e6	−0.567166	−0.283583	−	0.958948i	$-0.591523\pi$
$691$	−7.11877e6	−0.567166	−0.283583	+	0.958948i	$0.591523\pi$
$692$	−2.37089e7	−1.88211
$693$	−26734.1	−0.00211462
$694$	191974.	0.0151301
$695$	0	0
$696$	481163.	0.0376504
$697$	−1.75830e6	−0.137091
$698$	214818.	0.0166891
$699$	1.08944e7	0.843357
$700$	0	0
$701$	−3.11470e6	−0.239399	−0.119699	−	0.992810i	$-0.538193\pi$
$701$	−3.11470e6	−0.239399	−0.119699	+	0.992810i	$0.538193\pi$
$702$	−697091.	−0.0533884
$703$	−1.50686e7	−1.14996
$704$	−6.52103e6	−0.495889
$705$	0	0
$706$	406614.	0.0307023
$707$	971553.	0.0731001
$708$	1.78714e6	0.133991
$709$	3.60687e6	0.269473	0.134736	−	0.990881i	$-0.456981\pi$
$709$	3.60687e6	0.269473	0.134736	+	0.990881i	$0.456981\pi$
$710$	0	0
$711$	−259714.	−0.0192673
$712$	1.25988e6	0.0931385
$713$	8.88628e6	0.654631
$714$	−56746.9	−0.00416578
$715$	0	0
$716$	−1.02188e7	−0.744936
$717$	9.59499e6	0.697023
$718$	−208998.	−0.0151297
$719$	1.24229e6	0.0896192	0.0448096	−	0.998996i	$-0.485732\pi$
$719$	1.24229e6	0.0896192	0.0448096	+	0.998996i	$0.485732\pi$
$720$	0	0
$721$	2.54614e6	0.182408
$722$	109356.	0.00780727
$723$	2.21117e7	1.57318
$724$	1.96240e7	1.39137
$725$	0	0
$726$	−289380.	−0.0203764
$727$	−1.41045e7	−0.989741	−0.494871	−	0.868967i	$-0.664785\pi$
$727$	−1.41045e7	−0.989741	−0.494871	+	0.868967i	$0.664785\pi$
$728$	−186559.	−0.0130463
$729$	1.48051e7	1.03179
$730$	0	0
$731$	−2.72604e6	−0.188686
$732$	1.97639e7	1.36331
$733$	−2.19590e7	−1.50957	−0.754783	−	0.655974i	$-0.772258\pi$
$733$	−2.19590e7	−1.50957	−0.754783	+	0.655974i	$0.772258\pi$
$734$	515873.	0.0353430
$735$	0	0
$736$	1.29293e6	0.0879794
$737$	1.35246e7	0.917181
$738$	−1544.81	−0.000104408 0
$739$	1.56128e7	1.05165	0.525823	−	0.850594i	$-0.323758\pi$
$739$	1.56128e7	1.05165	0.525823	+	0.850594i	$0.323758\pi$
$740$	0	0
$741$	−3.16940e7	−2.12047
$742$	−58343.4	−0.00389029
$743$	−1.11040e7	−0.737917	−0.368959	−	0.929446i	$-0.620286\pi$
$743$	−1.11040e7	−0.737917	−0.368959	+	0.929446i	$0.620286\pi$
$744$	−503097.	−0.0333211
$745$	0	0
$746$	−647791.	−0.0426175
$747$	−32545.1	−0.00213395
$748$	9.42467e6	0.615903
$749$	2.28003e6	0.148503
$750$	0	0
$751$	−2.39825e7	−1.55165	−0.775825	−	0.630948i	$-0.782666\pi$
$751$	−2.39825e7	−1.55165	−0.775825	+	0.630948i	$0.782666\pi$
$752$	2.46368e7	1.58869
$753$	−2.43948e7	−1.56787
$754$	−569814.	−0.0365010
$755$	0	0
$756$	1.98260e6	0.126163
$757$	−2.57134e7	−1.63087	−0.815437	−	0.578846i	$-0.803503\pi$
$757$	−2.57134e7	−1.63087	−0.815437	+	0.578846i	$0.803503\pi$
$758$	639517.	0.0404277
$759$	8.27124e6	0.521154
$760$	0	0
$761$	−1.61036e7	−1.00800	−0.504002	−	0.863702i	$-0.668140\pi$
$761$	−1.61036e7	−1.00800	−0.504002	+	0.863702i	$0.668140\pi$
$762$	193950.	0.0121005
$763$	−1.44938e6	−0.0901306
$764$	−2.37539e7	−1.47232
$765$	0	0
$766$	811419.	0.0499659
$767$	−4.23444e6	−0.259901
$768$	1.59420e7	0.975301
$769$	1.18549e6	0.0722909	0.0361455	−	0.999347i	$-0.488492\pi$
$769$	1.18549e6	0.0722909	0.0361455	+	0.999347i	$0.488492\pi$
$770$	0	0
$771$	−1.62731e7	−0.985903
$772$	1.86558e7	1.12660
$773$	6.09554e6	0.366913	0.183457	−	0.983028i	$-0.441271\pi$
$773$	6.09554e6	0.366913	0.183457	+	0.983028i	$0.441271\pi$
$774$	−2395.06	−0.000143702 0
$775$	0	0
$776$	1.08333e6	0.0645814
$777$	2.08581e6	0.123943
$778$	−633772.	−0.0375391
$779$	−2.12574e6	−0.125507
$780$	0	0
$781$	−5.24133e6	−0.307478
$782$	−621141.	−0.0363223
$783$	1.21156e7	0.706223
$784$	−1.69061e7	−0.982322
$785$	0	0
$786$	271561.	0.0156787
$787$	1.87506e7	1.07914	0.539570	−	0.841941i	$-0.318587\pi$
$787$	1.87506e7	1.07914	0.539570	+	0.841941i	$0.318587\pi$
$788$	−8.53991e6	−0.489934
$789$	−749255.	−0.0428486
$790$	0	0
$791$	2.94434e6	0.167320
$792$	16567.1	0.000938497 0
$793$	−4.68283e7	−2.64439
$794$	395078.	0.0222398
$795$	0	0
$796$	−1.89176e7	−1.05824
$797$	3.59822e6	0.200651	0.100326	−	0.994955i	$-0.468012\pi$
$797$	3.59822e6	0.200651	0.100326	+	0.994955i	$0.468012\pi$
$798$	−68605.8	−0.00381376
$799$	−3.55526e7	−1.97017
$800$	0	0
$801$	1.04818e6	0.0577238
$802$	−558724.	−0.0306734
$803$	8.94375e6	0.489475
$804$	−3.31395e7	−1.80803
$805$	0	0
$806$	595789.	0.0323039
$807$	2.15251e7	1.16349
$808$	−602070.	−0.0324428
$809$	−1.31628e6	−0.0707096	−0.0353548	−	0.999375i	$-0.511256\pi$
$809$	−1.31628e6	−0.0707096	−0.0353548	+	0.999375i	$0.511256\pi$
$810$	0	0
$811$	1.45817e6	0.0778493	0.0389246	−	0.999242i	$-0.487607\pi$
$811$	1.45817e6	0.0778493	0.0389246	+	0.999242i	$0.487607\pi$
$812$	1.62061e6	0.0862558
$813$	1.79507e6	0.0952480
$814$	263656.	0.0139469
$815$	0	0
$816$	−2.30758e7	−1.21320
$817$	−3.29573e6	−0.172741
$818$	−528902.	−0.0276371
$819$	−155211.	−0.00808563
$820$	0	0
$821$	−5.40144e6	−0.279674	−0.139837	−	0.990175i	$-0.544658\pi$
$821$	−5.40144e6	−0.279674	−0.139837	+	0.990175i	$0.544658\pi$
$822$	763796.	0.0394274
$823$	2.34244e7	1.20551	0.602753	−	0.797928i	$-0.294070\pi$
$823$	2.34244e7	1.20551	0.602753	+	0.797928i	$0.294070\pi$
$824$	−1.57784e6	−0.0809553
$825$	0	0
$826$	−9165.99	−0.000467443 0
$827$	2.07710e7	1.05607	0.528036	−	0.849222i	$-0.322929\pi$
$827$	2.07710e7	1.05607	0.528036	+	0.849222i	$0.322929\pi$
$828$	717028.	0.0363463
$829$	6.32167e6	0.319481	0.159741	−	0.987159i	$-0.448934\pi$
$829$	6.32167e6	0.319481	0.159741	+	0.987159i	$0.448934\pi$
$830$	0	0
$831$	7.99658e6	0.401700
$832$	−3.78594e7	−1.89612
$833$	2.43967e7	1.21820
$834$	372856.	0.0185620
$835$	0	0
$836$	1.13942e7	0.563858
$837$	−1.26679e7	−0.625018
$838$	381098.	0.0187468
$839$	−2.97405e7	−1.45862	−0.729311	−	0.684182i	$-0.760159\pi$
$839$	−2.97405e7	−1.45862	−0.729311	+	0.684182i	$0.760159\pi$
$840$	0	0
$841$	−1.06076e7	−0.517164
$842$	656815.	0.0319273
$843$	2.36661e7	1.14698
$844$	−3.27522e7	−1.58265
$845$	0	0
$846$	−31236.0	−0.00150048
$847$	−1.95007e6	−0.0933989
$848$	−2.37251e7	−1.13297
$849$	−6.55246e6	−0.311986
$850$	0	0
$851$	2.28309e7	1.08069
$852$	1.28429e7	0.606128
$853$	2.71443e6	0.127734	0.0638670	−	0.997958i	$-0.479657\pi$
$853$	2.71443e6	0.127734	0.0638670	+	0.997958i	$0.479657\pi$
$854$	−101366.	−0.00475606
$855$	0	0
$856$	−1.41293e6	−0.0659077
$857$	8.75694e6	0.407287	0.203643	−	0.979045i	$-0.434722\pi$
$857$	8.75694e6	0.407287	0.203643	+	0.979045i	$0.434722\pi$
$858$	554552.	0.0257172
$859$	−2.27559e7	−1.05223	−0.526115	−	0.850413i	$-0.676352\pi$
$859$	−2.27559e7	−1.05223	−0.526115	+	0.850413i	$0.676352\pi$
$860$	0	0
$861$	294248.	0.0135271
$862$	19210.8	0.000880597 0
$863$	−1.33638e7	−0.610806	−0.305403	−	0.952223i	$-0.598791\pi$
$863$	−1.33638e7	−0.610806	−0.305403	+	0.952223i	$0.598791\pi$
$864$	−1.84315e6	−0.0839996
$865$	0	0
$866$	960999.	0.0435440
$867$	1.15481e7	0.521751
$868$	−1.69448e6	−0.0763376
$869$	6.25310e6	0.280896
$870$	0	0
$871$	7.85203e7	3.50701
$872$	898181.	0.0400012
$873$	901298.	0.0400251
$874$	−750948.	−0.0332530
$875$	0	0
$876$	−2.19150e7	−0.964897
$877$	−2.31621e7	−1.01690	−0.508451	−	0.861091i	$-0.669782\pi$
$877$	−2.31621e7	−1.01690	−0.508451	+	0.861091i	$0.669782\pi$
$878$	303649.	0.0132934
$879$	−4.35685e7	−1.90196
$880$	0	0
$881$	1.97084e7	0.855481	0.427741	−	0.903901i	$-0.359310\pi$
$881$	1.97084e7	0.855481	0.427741	+	0.903901i	$0.359310\pi$
$882$	21434.6	0.000927778 0
$883$	3.15439e7	1.36149	0.680744	−	0.732521i	$-0.261657\pi$
$883$	3.15439e7	1.36149	0.680744	+	0.732521i	$0.261657\pi$
$884$	5.47173e7	2.35501
$885$	0	0
$886$	642796.	0.0275099
$887$	2.80635e7	1.19766	0.598829	−	0.800877i	$-0.295633\pi$
$887$	2.80635e7	1.19766	0.598829	+	0.800877i	$0.295633\pi$
$888$	−1.29257e6	−0.0550076
$889$	1.30699e6	0.0554647
$890$	0	0
$891$	−1.13878e7	−0.480557
$892$	−2.31643e6	−0.0974781
$893$	−4.29824e7	−1.80369
$894$	559286.	0.0234040
$895$	0	0
$896$	−328682.	−0.0136775
$897$	4.80207e7	1.99272
$898$	−418561.	−0.0173208
$899$	−1.03550e7	−0.427317
$900$	0	0
$901$	3.42369e7	1.40502
$902$	37194.3	0.00152216
$903$	456199.	0.0186181
$904$	−1.82460e6	−0.0742587
$905$	0	0
$906$	−242970.	−0.00983406
$907$	−2.09399e7	−0.845194	−0.422597	−	0.906318i	$-0.638881\pi$
$907$	−2.09399e7	−0.845194	−0.422597	+	0.906318i	$0.638881\pi$
$908$	−3.93023e7	−1.58199
$909$	−500903.	−0.0201068
$910$	0	0
$911$	7.93865e6	0.316921	0.158460	−	0.987365i	$-0.449347\pi$
$911$	7.93865e6	0.316921	0.158460	+	0.987365i	$0.449347\pi$
$912$	−2.78982e7	−1.11068
$913$	783585.	0.0311107
$914$	−150316.	−0.00595168
$915$	0	0
$916$	2.69397e7	1.06085
$917$	1.82999e6	0.0718663
$918$	885475.	0.0346792
$919$	−3.09848e7	−1.21021	−0.605103	−	0.796147i	$-0.706868\pi$
$919$	−3.09848e7	−1.21021	−0.605103	+	0.796147i	$0.706868\pi$
$920$	0	0
$921$	−3.50505e7	−1.36158
$922$	1.06784e6	0.0413694
$923$	−3.04298e7	−1.17570
$924$	−1.57720e6	−0.0607726
$925$	0	0
$926$	−223561.	−0.00856779
$927$	−1.31271e6	−0.0501731
$928$	−1.50662e6	−0.0574294
$929$	−5.39203e6	−0.204981	−0.102490	−	0.994734i	$-0.532681\pi$
$929$	−5.39203e6	−0.204981	−0.102490	+	0.994734i	$0.532681\pi$
$930$	0	0
$931$	2.94951e7	1.11526
$932$	−2.27389e7	−0.857493
$933$	−3.25127e7	−1.22278
$934$	−241762.	−0.00906821
$935$	0	0
$936$	96184.2	0.00358851
$937$	1.96672e7	0.731802	0.365901	−	0.930654i	$-0.380761\pi$
$937$	1.96672e7	0.731802	0.365901	+	0.930654i	$0.380761\pi$
$938$	169967.	0.00630752
$939$	3.44120e7	1.27364
$940$	0	0
$941$	−2.04623e7	−0.753323	−0.376661	−	0.926351i	$-0.622928\pi$
$941$	−2.04623e7	−0.753323	−0.376661	+	0.926351i	$0.622928\pi$
$942$	−475982.	−0.0174768
$943$	3.22079e6	0.117946
$944$	−3.72730e6	−0.136133
$945$	0	0
$946$	57665.6	0.00209502
$947$	1.14254e7	0.413995	0.206998	−	0.978341i	$-0.433631\pi$
$947$	1.14254e7	0.413995	0.206998	+	0.978341i	$0.433631\pi$
$948$	−1.53221e7	−0.553728
$949$	5.19251e7	1.87160
$950$	0	0
$951$	2.61804e7	0.938696
$952$	236975.	0.00847444
$953$	4.87166e7	1.73758	0.868789	−	0.495183i	$-0.164899\pi$
$953$	4.87166e7	1.73758	0.868789	+	0.495183i	$0.164899\pi$
$954$	30080.1	0.00107006
$955$	0	0
$956$	−2.00268e7	−0.708706
$957$	−9.63828e6	−0.340189
$958$	575819.	0.0202709
$959$	5.14705e6	0.180722
$960$	0	0
$961$	−1.78021e7	−0.621819
$962$	1.53072e6	0.0533283
$963$	−1.17551e6	−0.0408471
$964$	−4.61518e7	−1.59955
$965$	0	0
$966$	103947.	0.00358401
$967$	2.71815e7	0.934777	0.467388	−	0.884052i	$-0.345195\pi$
$967$	2.71815e7	0.934777	0.467388	+	0.884052i	$0.345195\pi$
$968$	1.20845e6	0.0414517
$969$	4.02591e7	1.37738
$970$	0	0
$971$	1.25052e7	0.425642	0.212821	−	0.977091i	$-0.431735\pi$
$971$	1.25052e7	0.425642	0.212821	+	0.977091i	$0.431735\pi$
$972$	−2.01056e6	−0.0682577
$973$	2.51259e6	0.0850824
$974$	842947.	0.0284710
$975$	0	0
$976$	−4.12199e7	−1.38511
$977$	1.16639e7	0.390938	0.195469	−	0.980710i	$-0.437377\pi$
$977$	1.16639e7	0.390938	0.195469	+	0.980710i	$0.437377\pi$
$978$	313877.	0.0104933
$979$	−2.52369e7	−0.841550
$980$	0	0
$981$	747258.	0.0247912
$982$	105142.	0.00347934
$983$	1.12255e7	0.370530	0.185265	−	0.982689i	$-0.440686\pi$
$983$	1.12255e7	0.370530	0.185265	+	0.982689i	$0.440686\pi$
$984$	−182345.	−0.00600352
$985$	0	0
$986$	723802.	0.0237098
$987$	5.94967e6	0.194402
$988$	6.61521e7	2.15601
$989$	4.99347e6	0.162335
$990$	0	0
$991$	−8.86302e6	−0.286680	−0.143340	−	0.989673i	$-0.545784\pi$
$991$	−8.86302e6	−0.286680	−0.143340	+	0.989673i	$0.545784\pi$
$992$	1.57530e6	0.0508259
$993$	−4.73191e6	−0.152287
$994$	−65869.3	−0.00211455
$995$	0	0
$996$	−1.92003e6	−0.0613281
$997$	−3.41641e7	−1.08851	−0.544254	−	0.838920i	$-0.683187\pi$
$997$	−3.41641e7	−1.08851	−0.544254	+	0.838920i	$0.683187\pi$
$998$	−372680.	−0.0118443
$999$	−3.25469e7	−1.03180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.j.1.20	yes	37
5.4	even	2		1075.6.a.i.1.18	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.6.a.i.1.18	✓	37	5.4	even	2
1075.6.a.j.1.20	yes	37	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q+0.156002 q^{2} +15.3198 q^{3} -31.9757 q^{4} +2.38992 q^{6} +16.1051 q^{7} -9.98030 q^{8} -8.30330 q^{9} +O(q^{10})\)	\(q+0.156002 q^{2} +15.3198 q^{3} -31.9757 q^{4} +2.38992 q^{6} +16.1051 q^{7} -9.98030 q^{8} -8.30330 q^{9} +199.918 q^{11} -489.861 q^{12} +1160.67 q^{13} +2.51242 q^{14} +1021.66 q^{16} -1474.33 q^{17} -1.29533 q^{18} -1782.44 q^{19} +246.727 q^{21} +31.1875 q^{22} +2700.63 q^{23} -152.896 q^{24} +181.066 q^{26} -3849.92 q^{27} -514.972 q^{28} -3146.99 q^{29} +3290.44 q^{31} +478.751 q^{32} +3062.70 q^{33} -229.998 q^{34} +265.504 q^{36} +8453.91 q^{37} -278.063 q^{38} +17781.3 q^{39} +1192.60 q^{41} +38.4898 q^{42} +1849.00 q^{43} -6392.50 q^{44} +421.303 q^{46} +24114.3 q^{47} +15651.7 q^{48} -16547.6 q^{49} -22586.5 q^{51} -37113.2 q^{52} -23222.0 q^{53} -600.594 q^{54} -160.734 q^{56} -27306.6 q^{57} -490.935 q^{58} -3648.27 q^{59} -40345.9 q^{61} +513.314 q^{62} -133.726 q^{63} -32618.6 q^{64} +477.786 q^{66} +67650.8 q^{67} +47142.8 q^{68} +41373.2 q^{69} -26217.5 q^{71} +82.8695 q^{72} +44737.2 q^{73} +1318.82 q^{74} +56994.7 q^{76} +3219.70 q^{77} +2773.90 q^{78} +31278.4 q^{79} -56962.4 q^{81} +186.048 q^{82} +3919.54 q^{83} -7889.27 q^{84} +288.447 q^{86} -48211.2 q^{87} -1995.24 q^{88} -126237. q^{89} +18692.7 q^{91} -86354.6 q^{92} +50409.0 q^{93} +3761.87 q^{94} +7334.38 q^{96} -108547. q^{97} -2581.46 q^{98} -1659.98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 37 * q + 630 * q^4 + 291 * q^6 + 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9} + 675 q^{11} - 4446 q^{12} + 1241 q^{13} + 2375 q^{14} + 10518 q^{16} + 1153 q^{17} - 6680 q^{18} + 4065 q^{19} + 9953 q^{21} + 9283 q^{22} - 360 q^{23} + 2265 q^{24} + 23695 q^{26} + 1323 q^{27} - 30375 q^{28} + 19290 q^{29} + 23291 q^{31} + 8166 q^{32} - 10388 q^{33} - 13153 q^{34} + 148705 q^{36} + 13501 q^{37} - 8127 q^{38} - 1327 q^{39} + 38345 q^{41} - 21835 q^{42} + 68413 q^{43} + 47768 q^{44} + 48755 q^{46} + 84859 q^{47} - 208720 q^{48} + 107255 q^{49} + 62027 q^{51} + 128320 q^{52} - 53559 q^{53} + 44158 q^{54} + 107538 q^{56} + 104239 q^{57} - 85186 q^{58} + 48186 q^{59} + 82364 q^{61} + 206506 q^{62} - 75269 q^{63} + 161467 q^{64} + 91969 q^{66} + 38168 q^{67} + 95991 q^{68} + 287103 q^{69} + 155302 q^{71} + 9979 q^{72} + 31927 q^{73} + 59946 q^{74} + 225407 q^{76} - 80007 q^{77} - 67815 q^{78} + 150174 q^{79} + 417489 q^{81} + 60603 q^{82} + 266568 q^{83} + 586273 q^{84} - 57554 q^{87} + 323054 q^{88} + 334356 q^{89} + 51747 q^{91} - 258529 q^{92} - 285287 q^{93} + 302744 q^{94} + 287282 q^{96} - 78640 q^{97} - 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 + 213 * q^8 + 3535 * q^9 + 675 * q^11 - 4446 * q^12 + 1241 * q^13 + 2375 * q^14 + 10518 * q^16 + 1153 * q^17 - 6680 * q^18 + 4065 * q^19 + 9953 * q^21 + 9283 * q^22 - 360 * q^23 + 2265 * q^24 + 23695 * q^26 + 1323 * q^27 - 30375 * q^28 + 19290 * q^29 + 23291 * q^31 + 8166 * q^32 - 10388 * q^33 - 13153 * q^34 + 148705 * q^36 + 13501 * q^37 - 8127 * q^38 - 1327 * q^39 + 38345 * q^41 - 21835 * q^42 + 68413 * q^43 + 47768 * q^44 + 48755 * q^46 + 84859 * q^47 - 208720 * q^48 + 107255 * q^49 + 62027 * q^51 + 128320 * q^52 - 53559 * q^53 + 44158 * q^54 + 107538 * q^56 + 104239 * q^57 - 85186 * q^58 + 48186 * q^59 + 82364 * q^61 + 206506 * q^62 - 75269 * q^63 + 161467 * q^64 + 91969 * q^66 + 38168 * q^67 + 95991 * q^68 + 287103 * q^69 + 155302 * q^71 + 9979 * q^72 + 31927 * q^73 + 59946 * q^74 + 225407 * q^76 - 80007 * q^77 - 67815 * q^78 + 150174 * q^79 + 417489 * q^81 + 60603 * q^82 + 266568 * q^83 + 586273 * q^84 - 57554 * q^87 + 323054 * q^88 + 334356 * q^89 + 51747 * q^91 - 258529 * q^92 - 285287 * q^93 + 302744 * q^94 + 287282 * q^96 - 78640 * q^97 - 397117 * q^98 + 362152 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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