LMFDB - Embedded newform 1075.6.a.j.1.13

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			1.13
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)

$f(q)$	$=$	$q-4.20568 q^{2} -17.5719 q^{3} -14.3123 q^{4} +73.9018 q^{6} +253.679 q^{7} +194.775 q^{8} +65.7719 q^{9} +O(q^{10})$	\(q-4.20568 q^{2} -17.5719 q^{3} -14.3123 q^{4} +73.9018 q^{6} +253.679 q^{7} +194.775 q^{8} +65.7719 q^{9} -360.960 q^{11} +251.494 q^{12} +40.7093 q^{13} -1066.89 q^{14} -361.167 q^{16} -218.989 q^{17} -276.616 q^{18} -807.463 q^{19} -4457.62 q^{21} +1518.08 q^{22} +4173.72 q^{23} -3422.56 q^{24} -171.210 q^{26} +3114.24 q^{27} -3630.72 q^{28} +8778.52 q^{29} +2577.20 q^{31} -4713.83 q^{32} +6342.76 q^{33} +920.997 q^{34} -941.345 q^{36} +6238.31 q^{37} +3395.93 q^{38} -715.339 q^{39} +5496.57 q^{41} +18747.3 q^{42} +1849.00 q^{43} +5166.16 q^{44} -17553.3 q^{46} -13022.4 q^{47} +6346.40 q^{48} +47546.0 q^{49} +3848.05 q^{51} -582.641 q^{52} +23606.6 q^{53} -13097.5 q^{54} +49410.2 q^{56} +14188.7 q^{57} -36919.6 q^{58} +8137.06 q^{59} -18074.7 q^{61} -10838.9 q^{62} +16685.0 q^{63} +31382.2 q^{64} -26675.6 q^{66} +33163.2 q^{67} +3134.22 q^{68} -73340.3 q^{69} -66159.0 q^{71} +12810.7 q^{72} -2493.41 q^{73} -26236.3 q^{74} +11556.6 q^{76} -91568.1 q^{77} +3008.49 q^{78} +88535.5 q^{79} -70705.6 q^{81} -23116.8 q^{82} +15958.3 q^{83} +63798.6 q^{84} -7776.30 q^{86} -154255. q^{87} -70305.9 q^{88} -28879.9 q^{89} +10327.1 q^{91} -59735.4 q^{92} -45286.3 q^{93} +54768.3 q^{94} +82831.0 q^{96} -143575. q^{97} -199963. q^{98} -23741.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.20568	−0.743466	−0.371733	−	0.928340i	$-0.621236\pi$
$2$	−4.20568	−0.743466	−0.371733	+	0.928340i	$0.621236\pi$
$3$	−17.5719	−1.12724	−0.563619	−	0.826035i	$-0.690591\pi$
$3$	−17.5719	−1.12724	−0.563619	+	0.826035i	$0.690591\pi$
$4$	−14.3123	−0.447258
$5$	0	0
$5$	0	0
$6$	73.9018	0.838064
$7$	253.679	1.95677	0.978384	−	0.206797i	$-0.0663041\pi$
$7$	253.679	1.95677	0.978384	+	0.206797i	$0.0663041\pi$
$8$	194.775	1.07599
$9$	65.7719	0.270666
$10$	0	0
$11$	−360.960	−0.899452	−0.449726	−	0.893167i	$-0.648478\pi$
$11$	−360.960	−0.899452	−0.449726	+	0.893167i	$0.648478\pi$
$12$	251.494	0.504166
$13$	40.7093	0.0668090	0.0334045	−	0.999442i	$-0.489365\pi$
$13$	40.7093	0.0668090	0.0334045	+	0.999442i	$0.489365\pi$
$14$	−1066.89	−1.45479
$15$	0	0
$16$	−361.167	−0.352702
$17$	−218.989	−0.183781	−0.0918903	−	0.995769i	$-0.529291\pi$
$17$	−218.989	−0.183781	−0.0918903	+	0.995769i	$0.529291\pi$
$18$	−276.616	−0.201231
$19$	−807.463	−0.513143	−0.256572	−	0.966525i	$-0.582593\pi$
$19$	−807.463	−0.513143	−0.256572	+	0.966525i	$0.582593\pi$
$20$	0	0
$21$	−4457.62	−2.20574
$22$	1518.08	0.668712
$23$	4173.72	1.64514	0.822572	−	0.568661i	$-0.192538\pi$
$23$	4173.72	1.64514	0.822572	+	0.568661i	$0.192538\pi$
$24$	−3422.56	−1.21289
$25$	0	0
$26$	−171.210	−0.0496702
$27$	3114.24	0.822133
$28$	−3630.72	−0.875180
$29$	8778.52	1.93832	0.969161	−	0.246427i	$-0.0792565\pi$
$29$	8778.52	1.93832	0.969161	+	0.246427i	$0.0792565\pi$
$30$	0	0
$31$	2577.20	0.481663	0.240832	−	0.970567i	$-0.422580\pi$
$31$	2577.20	0.481663	0.240832	+	0.970567i	$0.422580\pi$
$32$	−4713.83	−0.813765
$33$	6342.76	1.01390
$34$	920.997	0.136635
$35$	0	0
$36$	−941.345	−0.121058
$37$	6238.31	0.749139	0.374569	−	0.927199i	$-0.377791\pi$
$37$	6238.31	0.749139	0.374569	+	0.927199i	$0.377791\pi$
$38$	3395.93	0.381505
$39$	−715.339	−0.0753096
$40$	0	0
$41$	5496.57	0.510661	0.255330	−	0.966854i	$-0.417816\pi$
$41$	5496.57	0.510661	0.255330	+	0.966854i	$0.417816\pi$
$42$	18747.3	1.63990
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	5166.16	0.402287
$45$	0	0
$46$	−17553.3	−1.22311
$47$	−13022.4	−0.859900	−0.429950	−	0.902853i	$-0.641469\pi$
$47$	−13022.4	−0.859900	−0.429950	+	0.902853i	$0.641469\pi$
$48$	6346.40	0.397580
$49$	47546.0	2.82894
$50$	0	0
$51$	3848.05	0.207165
$52$	−582.641	−0.0298808
$53$	23606.6	1.15437	0.577183	−	0.816615i	$-0.304152\pi$
$53$	23606.6	1.15437	0.577183	+	0.816615i	$0.304152\pi$
$54$	−13097.5	−0.611228
$55$	0	0
$56$	49410.2	2.10546
$57$	14188.7	0.578435
$58$	−36919.6	−1.44108
$59$	8137.06	0.304325	0.152162	−	0.988355i	$-0.451376\pi$
$59$	8137.06	0.304325	0.152162	+	0.988355i	$0.451376\pi$
$60$	0	0
$61$	−18074.7	−0.621937	−0.310969	−	0.950420i	$-0.600653\pi$
$61$	−18074.7	−0.621937	−0.310969	+	0.950420i	$0.600653\pi$
$62$	−10838.9	−0.358100
$63$	16685.0	0.529631
$64$	31382.2	0.957709
$65$	0	0
$66$	−26675.6	−0.753798
$67$	33163.2	0.902546	0.451273	−	0.892386i	$-0.350970\pi$
$67$	33163.2	0.902546	0.451273	+	0.892386i	$0.350970\pi$
$68$	3134.22	0.0821974
$69$	−73340.3	−1.85447
$70$	0	0
$71$	−66159.0	−1.55755	−0.778777	−	0.627301i	$-0.784159\pi$
$71$	−66159.0	−1.55755	−0.778777	+	0.627301i	$0.784159\pi$
$72$	12810.7	0.291234
$73$	−2493.41	−0.0547629	−0.0273815	−	0.999625i	$-0.508717\pi$
$73$	−2493.41	−0.0547629	−0.0273815	+	0.999625i	$0.508717\pi$
$74$	−26236.3	−0.556959
$75$	0	0
$76$	11556.6	0.229507
$77$	−91568.1	−1.76002
$78$	3008.49	0.0559902
$79$	88535.5	1.59606	0.798031	−	0.602617i	$-0.205875\pi$
$79$	88535.5	1.59606	0.798031	+	0.602617i	$0.205875\pi$
$80$	0	0
$81$	−70705.6	−1.19741
$82$	−23116.8	−0.379659
$83$	15958.3	0.254267	0.127134	−	0.991886i	$-0.459422\pi$
$83$	15958.3	0.254267	0.127134	+	0.991886i	$0.459422\pi$
$84$	63798.6	0.986536
$85$	0	0
$86$	−7776.30	−0.113378
$87$	−154255.	−2.18495
$88$	−70305.9	−0.967799
$89$	−28879.9	−0.386475	−0.193238	−	0.981152i	$-0.561899\pi$
$89$	−28879.9	−0.386475	−0.193238	+	0.981152i	$0.561899\pi$
$90$	0	0
$91$	10327.1	0.130730
$92$	−59735.4	−0.735804
$93$	−45286.3	−0.542949
$94$	54768.3	0.639307
$95$	0	0
$96$	82831.0	0.917307
$97$	−143575.	−1.54935	−0.774676	−	0.632358i	$-0.782087\pi$
$97$	−143575.	−1.54935	−0.774676	+	0.632358i	$0.782087\pi$
$98$	−199963.	−2.10322
$99$	−23741.1	−0.243451
$100$	0	0
$101$	152588.	1.48839	0.744196	−	0.667961i	$-0.232833\pi$
$101$	152588.	1.48839	0.744196	+	0.667961i	$0.232833\pi$
$102$	−16183.7	−0.154020
$103$	55735.8	0.517656	0.258828	−	0.965923i	$-0.416664\pi$
$103$	55735.8	0.517656	0.258828	+	0.965923i	$0.416664\pi$
$104$	7929.13	0.0718856
$105$	0	0
$106$	−99281.7	−0.858232
$107$	−73165.1	−0.617796	−0.308898	−	0.951095i	$-0.599960\pi$
$107$	−73165.1	−0.617796	−0.308898	+	0.951095i	$0.599960\pi$
$108$	−44571.7	−0.367705
$109$	38862.1	0.313300	0.156650	−	0.987654i	$-0.449931\pi$
$109$	38862.1	0.313300	0.156650	+	0.987654i	$0.449931\pi$
$110$	0	0
$111$	−109619.	−0.844458
$112$	−91620.5	−0.690156
$113$	−153829.	−1.13329	−0.566646	−	0.823961i	$-0.691759\pi$
$113$	−153829.	−1.13329	−0.566646	+	0.823961i	$0.691759\pi$
$114$	−59673.0	−0.430047
$115$	0	0
$116$	−125640.	−0.866930
$117$	2677.53	0.0180829
$118$	−34221.9	−0.226255
$119$	−55552.9	−0.359616
$120$	0	0
$121$	−30758.5	−0.190986
$122$	76016.4	0.462389
$123$	−96585.3	−0.575636
$124$	−36885.5	−0.215428
$125$	0	0
$126$	−70171.6	−0.393763
$127$	−225122.	−1.23854	−0.619269	−	0.785179i	$-0.712571\pi$
$127$	−225122.	−1.23854	−0.619269	+	0.785179i	$0.712571\pi$
$128$	18859.0	0.101741
$129$	−32490.5	−0.171902
$130$	0	0
$131$	19196.7	0.0977345	0.0488673	−	0.998805i	$-0.484439\pi$
$131$	19196.7	0.0977345	0.0488673	+	0.998805i	$0.484439\pi$
$132$	−90779.3	−0.453473
$133$	−204836.	−1.00410
$134$	−139474.	−0.671012
$135$	0	0
$136$	−42653.5	−0.197746
$137$	270809.	1.23271	0.616357	−	0.787467i	$-0.288608\pi$
$137$	270809.	1.23271	0.616357	+	0.787467i	$0.288608\pi$
$138$	308446.	1.37874
$139$	−149584.	−0.656669	−0.328335	−	0.944561i	$-0.606487\pi$
$139$	−149584.	−0.656669	−0.328335	+	0.944561i	$0.606487\pi$
$140$	0	0
$141$	228829.	0.969312
$142$	278244.	1.15799
$143$	−14694.4	−0.0600915
$144$	−23754.7	−0.0954647
$145$	0	0
$146$	10486.5	0.0407144
$147$	−835474.	−3.18889
$148$	−89284.2	−0.335058
$149$	−134118.	−0.494905	−0.247453	−	0.968900i	$-0.579593\pi$
$149$	−134118.	−0.494905	−0.247453	+	0.968900i	$0.579593\pi$
$150$	0	0
$151$	23875.0	0.0852119	0.0426060	−	0.999092i	$-0.486434\pi$
$151$	23875.0	0.0852119	0.0426060	+	0.999092i	$0.486434\pi$
$152$	−157273.	−0.552136
$153$	−14403.3	−0.0497432
$154$	385106.	1.30851
$155$	0	0
$156$	10238.1	0.0336828
$157$	214681.	0.695095	0.347548	−	0.937662i	$-0.387014\pi$
$157$	214681.	0.695095	0.347548	+	0.937662i	$0.387014\pi$
$158$	−372352.	−1.18662
$159$	−414813.	−1.30125
$160$	0	0
$161$	1.05879e6	3.21917
$162$	297365.	0.890231
$163$	108407.	0.319586	0.159793	−	0.987151i	$-0.448917\pi$
$163$	108407.	0.319586	0.159793	+	0.987151i	$0.448917\pi$
$164$	−78668.4	−0.228397
$165$	0	0
$166$	−67115.4	−0.189039
$167$	44321.9	0.122978	0.0614889	−	0.998108i	$-0.480415\pi$
$167$	44321.9	0.122978	0.0614889	+	0.998108i	$0.480415\pi$
$168$	−868231.	−2.37335
$169$	−369636.	−0.995537
$170$	0	0
$171$	−53108.4	−0.138891
$172$	−26463.4	−0.0682062
$173$	131546.	0.334167	0.167083	−	0.985943i	$-0.446565\pi$
$173$	131546.	0.334167	0.167083	+	0.985943i	$0.446565\pi$
$174$	648748.	1.62444
$175$	0	0
$176$	130367.	0.317239
$177$	−142984.	−0.343047
$178$	121460.	0.287331
$179$	344190.	0.802907	0.401453	−	0.915879i	$-0.368505\pi$
$179$	344190.	0.802907	0.401453	+	0.915879i	$0.368505\pi$
$180$	0	0
$181$	125323.	0.284338	0.142169	−	0.989842i	$-0.454592\pi$
$181$	125323.	0.284338	0.142169	+	0.989842i	$0.454592\pi$
$182$	−43432.4	−0.0971931
$183$	317607.	0.701072
$184$	812935.	1.77015
$185$	0	0
$186$	190460.	0.403664
$187$	79046.3	0.165302
$188$	186381.	0.384597
$189$	790016.	1.60872
$190$	0	0
$191$	705482.	1.39927	0.699636	−	0.714499i	$-0.253345\pi$
$191$	705482.	1.39927	0.699636	+	0.714499i	$0.253345\pi$
$192$	−551445.	−1.07957
$193$	64331.3	0.124317	0.0621583	−	0.998066i	$-0.480202\pi$
$193$	64331.3	0.124317	0.0621583	+	0.998066i	$0.480202\pi$
$194$	603832.	1.15189
$195$	0	0
$196$	−680490.	−1.26527
$197$	−58943.4	−0.108211	−0.0541053	−	0.998535i	$-0.517231\pi$
$197$	−58943.4	−0.108211	−0.0541053	+	0.998535i	$0.517231\pi$
$198$	99847.3	0.180998
$199$	−280730.	−0.502523	−0.251262	−	0.967919i	$-0.580845\pi$
$199$	−280730.	−0.502523	−0.251262	+	0.967919i	$0.580845\pi$
$200$	0	0
$201$	−582740.	−1.01738
$202$	−641737.	−1.10657
$203$	2.22692e6	3.79285
$204$	−55074.3	−0.0926560
$205$	0	0
$206$	−234407.	−0.384859
$207$	274514.	0.445285
$208$	−14702.8	−0.0235637
$209$	291462.	0.461548
$210$	0	0
$211$	−819624.	−1.26739	−0.633693	−	0.773585i	$-0.718462\pi$
$211$	−819624.	−1.26739	−0.633693	+	0.773585i	$0.718462\pi$
$212$	−337863.	−0.516299
$213$	1.16254e6	1.75573
$214$	307709.	0.459310
$215$	0	0
$216$	606574.	0.884605
$217$	653781.	0.942503
$218$	−163442.	−0.232928
$219$	43814.0	0.0617309
$220$	0	0
$221$	−8914.87	−0.0122782
$222$	461022.	0.627826
$223$	1.23348e6	1.66099	0.830497	−	0.557022i	$-0.188056\pi$
$223$	1.23348e6	1.66099	0.830497	+	0.557022i	$0.188056\pi$
$224$	−1.19580e6	−1.59235
$225$	0	0
$226$	646955.	0.842564
$227$	−793589.	−1.02219	−0.511094	−	0.859525i	$-0.670760\pi$
$227$	−793589.	−1.02219	−0.511094	+	0.859525i	$0.670760\pi$
$228$	−203072.	−0.258710
$229$	−1.11761e6	−1.40832	−0.704162	−	0.710039i	$-0.748677\pi$
$229$	−1.11761e6	−1.40832	−0.704162	+	0.710039i	$0.748677\pi$
$230$	0	0
$231$	1.60903e6	1.98396
$232$	1.70983e6	2.08561
$233$	−985627.	−1.18939	−0.594693	−	0.803953i	$-0.702726\pi$
$233$	−985627.	−1.18939	−0.594693	+	0.803953i	$0.702726\pi$
$234$	−11260.8	−0.0134441
$235$	0	0
$236$	−116460.	−0.136112
$237$	−1.55574e6	−1.79914
$238$	233638.	0.267362
$239$	866646.	0.981402	0.490701	−	0.871328i	$-0.336741\pi$
$239$	866646.	0.981402	0.490701	+	0.871328i	$0.336741\pi$
$240$	0	0
$241$	1.13881e6	1.26302	0.631508	−	0.775370i	$-0.282436\pi$
$241$	1.13881e6	1.26302	0.631508	+	0.775370i	$0.282436\pi$
$242$	129360.	0.141992
$243$	485674.	0.527629
$244$	258690.	0.278166
$245$	0	0
$246$	406207.	0.427966
$247$	−32871.2	−0.0342826
$248$	501972.	0.518264
$249$	−280417.	−0.286620
$250$	0	0
$251$	−1.70001e6	−1.70321	−0.851604	−	0.524185i	$-0.824370\pi$
$251$	−1.70001e6	−1.70321	−0.851604	+	0.524185i	$0.824370\pi$
$252$	−238799.	−0.236882
$253$	−1.50655e6	−1.47973
$254$	946793.	0.920812
$255$	0	0
$256$	−1.08355e6	−1.03335
$257$	−1.06707e6	−1.00777	−0.503883	−	0.863772i	$-0.668096\pi$
$257$	−1.06707e6	−1.00777	−0.503883	+	0.863772i	$0.668096\pi$
$258$	136644.	0.127804
$259$	1.58253e6	1.46589
$260$	0	0
$261$	577380.	0.524639
$262$	−80735.1	−0.0726623
$263$	1.44042e6	1.28411	0.642053	−	0.766660i	$-0.278083\pi$
$263$	1.44042e6	1.28411	0.642053	+	0.766660i	$0.278083\pi$
$264$	1.23541e6	1.09094
$265$	0	0
$266$	861476.	0.746516
$267$	507476.	0.435649
$268$	−474640.	−0.403671
$269$	177448.	0.149517	0.0747586	−	0.997202i	$-0.476181\pi$
$269$	177448.	0.149517	0.0747586	+	0.997202i	$0.476181\pi$
$270$	0	0
$271$	306686.	0.253671	0.126836	−	0.991924i	$-0.459518\pi$
$271$	306686.	0.253671	0.126836	+	0.991924i	$0.459518\pi$
$272$	79091.6	0.0648199
$273$	−181466.	−0.147363
$274$	−1.13894e6	−0.916481
$275$	0	0
$276$	1.04966e6	0.829427
$277$	−1.48116e6	−1.15985	−0.579927	−	0.814668i	$-0.696919\pi$
$277$	−1.48116e6	−1.15985	−0.579927	+	0.814668i	$0.696919\pi$
$278$	629100.	0.488211
$279$	169507.	0.130370
$280$	0	0
$281$	−1.30910e6	−0.989024	−0.494512	−	0.869171i	$-0.664653\pi$
$281$	−1.30910e6	−0.989024	−0.494512	+	0.869171i	$0.664653\pi$
$282$	−962383.	−0.720651
$283$	−1.90418e6	−1.41332	−0.706662	−	0.707551i	$-0.749800\pi$
$283$	−1.90418e6	−1.41332	−0.706662	+	0.707551i	$0.749800\pi$
$284$	946884.	0.696628
$285$	0	0
$286$	61800.1	0.0446760
$287$	1.39436e6	0.999244
$288$	−310038.	−0.220259
$289$	−1.37190e6	−0.966225
$290$	0	0
$291$	2.52289e6	1.74649
$292$	35686.3	0.0244931
$293$	2.43083e6	1.65419	0.827095	−	0.562063i	$-0.189992\pi$
$293$	2.43083e6	1.65419	0.827095	+	0.562063i	$0.189992\pi$
$294$	3.51373e6	2.37083
$295$	0	0
$296$	1.21506e6	0.806064
$297$	−1.12412e6	−0.739469
$298$	564058.	0.367945
$299$	169909.	0.109910
$300$	0	0
$301$	469052.	0.298404
$302$	−100410.	−0.0633522
$303$	−2.68127e6	−1.67777
$304$	291629.	0.180987
$305$	0	0
$306$	60575.8	0.0369824
$307$	105980.	0.0641769	0.0320885	−	0.999485i	$-0.489784\pi$
$307$	105980.	0.0641769	0.0320885	+	0.999485i	$0.489784\pi$
$308$	1.31055e6	0.787182
$309$	−979384.	−0.583521
$310$	0	0
$311$	3.34217e6	1.95942	0.979709	−	0.200426i	$-0.0642325\pi$
$311$	3.34217e6	1.95942	0.979709	+	0.200426i	$0.0642325\pi$
$312$	−139330.	−0.0810322
$313$	−1.39140e6	−0.802772	−0.401386	−	0.915909i	$-0.631471\pi$
$313$	−1.39140e6	−0.802772	−0.401386	+	0.915909i	$0.631471\pi$
$314$	−902879.	−0.516780
$315$	0	0
$316$	−1.26714e6	−0.713851
$317$	−1.28885e6	−0.720369	−0.360184	−	0.932881i	$-0.617286\pi$
$317$	−1.28885e6	−0.720369	−0.360184	+	0.932881i	$0.617286\pi$
$318$	1.74457e6	0.967432
$319$	−3.16870e6	−1.74343
$320$	0	0
$321$	1.28565e6	0.696403
$322$	−4.45291e6	−2.39334
$323$	176825.	0.0943058
$324$	1.01196e6	0.535549
$325$	0	0
$326$	−455925.	−0.237602
$327$	−682881.	−0.353163
$328$	1.07059e6	0.549464
$329$	−3.30352e6	−1.68262
$330$	0	0
$331$	−3.91326e6	−1.96322	−0.981610	−	0.190895i	$-0.938861\pi$
$331$	−3.91326e6	−1.96322	−0.981610	+	0.190895i	$0.938861\pi$
$332$	−228399.	−0.113723
$333$	410305.	0.202767
$334$	−186404.	−0.0914299
$335$	0	0
$336$	1.60995e6	0.777971
$337$	−380330.	−0.182426	−0.0912128	−	0.995831i	$-0.529074\pi$
$337$	−380330.	−0.182426	−0.0912128	+	0.995831i	$0.529074\pi$
$338$	1.55457e6	0.740148
$339$	2.70307e6	1.27749
$340$	0	0
$341$	−930267.	−0.433233
$342$	223357.	0.103261
$343$	7.79783e6	3.57881
$344$	360138.	0.164087
$345$	0	0
$346$	−553241.	−0.248442
$347$	428128.	0.190875	0.0954377	−	0.995435i	$-0.469575\pi$
$347$	428128.	0.190875	0.0954377	+	0.995435i	$0.469575\pi$
$348$	2.20774e6	0.977237
$349$	3.08789e6	1.35706	0.678528	−	0.734575i	$-0.262618\pi$
$349$	3.08789e6	1.35706	0.678528	+	0.734575i	$0.262618\pi$
$350$	0	0
$351$	126778.	0.0549259
$352$	1.70151e6	0.731943
$353$	2.25486e6	0.963127	0.481563	−	0.876411i	$-0.340069\pi$
$353$	2.25486e6	0.963127	0.481563	+	0.876411i	$0.340069\pi$
$354$	601344.	0.255044
$355$	0	0
$356$	413337.	0.172854
$357$	976170.	0.405373
$358$	−1.44755e6	−0.596934
$359$	−2.65092e6	−1.08558	−0.542788	−	0.839870i	$-0.682631\pi$
$359$	−2.65092e6	−1.08558	−0.542788	+	0.839870i	$0.682631\pi$
$360$	0	0
$361$	−1.82410e6	−0.736684
$362$	−527068.	−0.211395
$363$	540486.	0.215287
$364$	−147804.	−0.0584699
$365$	0	0
$366$	−1.33575e6	−0.521223
$367$	2.48788e6	0.964195	0.482098	−	0.876117i	$-0.339875\pi$
$367$	2.48788e6	0.964195	0.482098	+	0.876117i	$0.339875\pi$
$368$	−1.50741e6	−0.580246
$369$	361520.	0.138219
$370$	0	0
$371$	5.98849e6	2.25883
$372$	648149.	0.242838
$373$	−338692.	−0.126047	−0.0630235	−	0.998012i	$-0.520074\pi$
$373$	−338692.	−0.126047	−0.0630235	+	0.998012i	$0.520074\pi$
$374$	−332444.	−0.122896
$375$	0	0
$376$	−2.53644e6	−0.925242
$377$	357367.	0.129497
$378$	−3.32255e6	−1.19603
$379$	3.47206e6	1.24162	0.620810	−	0.783961i	$-0.286804\pi$
$379$	3.47206e6	1.24162	0.620810	+	0.783961i	$0.286804\pi$
$380$	0	0
$381$	3.95583e6	1.39613
$382$	−2.96703e6	−1.04031
$383$	−2.87258e6	−1.00064	−0.500318	−	0.865842i	$-0.666783\pi$
$383$	−2.87258e6	−1.00064	−0.500318	+	0.865842i	$0.666783\pi$
$384$	−331389.	−0.114686
$385$	0	0
$386$	−270557.	−0.0924252
$387$	121612.	0.0412762
$388$	2.05489e6	0.692960
$389$	4.17956e6	1.40041	0.700207	−	0.713939i	$-0.253091\pi$
$389$	4.17956e6	1.40041	0.700207	+	0.713939i	$0.253091\pi$
$390$	0	0
$391$	−913999.	−0.302346
$392$	9.26075e6	3.04390
$393$	−337322.	−0.110170
$394$	247897.	0.0804509
$395$	0	0
$396$	339788.	0.108886
$397$	−2.76571e6	−0.880705	−0.440353	−	0.897825i	$-0.645147\pi$
$397$	−2.76571e6	−0.880705	−0.440353	+	0.897825i	$0.645147\pi$
$398$	1.18066e6	0.373609
$399$	3.59937e6	1.13186
$400$	0	0
$401$	−3.45914e6	−1.07425	−0.537127	−	0.843501i	$-0.680491\pi$
$401$	−3.45914e6	−1.07425	−0.537127	+	0.843501i	$0.680491\pi$
$402$	2.45082e6	0.756391
$403$	104916.	0.0321794
$404$	−2.18388e6	−0.665696
$405$	0	0
$406$	−9.36573e6	−2.81985
$407$	−2.25178e6	−0.673814
$408$	749503.	0.222906
$409$	5.79389e6	1.71262	0.856312	−	0.516459i	$-0.172750\pi$
$409$	5.79389e6	1.71262	0.856312	+	0.516459i	$0.172750\pi$
$410$	0	0
$411$	−4.75864e6	−1.38956
$412$	−797705.	−0.231526
$413$	2.06420e6	0.595493
$414$	−1.15452e6	−0.331055
$415$	0	0
$416$	−191897.	−0.0543668
$417$	2.62847e6	0.740223
$418$	−1.22580e6	−0.343145
$419$	4.91818e6	1.36858	0.684288	−	0.729212i	$-0.260113\pi$
$419$	4.91818e6	1.36858	0.684288	+	0.729212i	$0.260113\pi$
$420$	0	0
$421$	5.90130e6	1.62272	0.811358	−	0.584549i	$-0.198729\pi$
$421$	5.90130e6	1.62272	0.811358	+	0.584549i	$0.198729\pi$
$422$	3.44708e6	0.942258
$423$	−856512.	−0.232746
$424$	4.59796e6	1.24208
$425$	0	0
$426$	−4.88927e6	−1.30533
$427$	−4.58517e6	−1.21699
$428$	1.04716e6	0.276314
$429$	258209.	0.0677374
$430$	0	0
$431$	−3.87125e6	−1.00383	−0.501913	−	0.864918i	$-0.667370\pi$
$431$	−3.87125e6	−1.00383	−0.501913	+	0.864918i	$0.667370\pi$
$432$	−1.12476e6	−0.289968
$433$	−2.92658e6	−0.750137	−0.375069	−	0.926997i	$-0.622381\pi$
$433$	−2.92658e6	−0.750137	−0.375069	+	0.926997i	$0.622381\pi$
$434$	−2.74959e6	−0.700719
$435$	0	0
$436$	−556204.	−0.140126
$437$	−3.37013e6	−0.844195
$438$	−184268.	−0.0458948
$439$	7.33878e6	1.81745	0.908725	−	0.417396i	$-0.137057\pi$
$439$	7.33878e6	1.81745	0.908725	+	0.417396i	$0.137057\pi$
$440$	0	0
$441$	3.12719e6	0.765699
$442$	37493.1	0.00912842
$443$	5.50508e6	1.33277	0.666384	−	0.745609i	$-0.267841\pi$
$443$	5.50508e6	1.33277	0.666384	+	0.745609i	$0.267841\pi$
$444$	1.56889e6	0.377691
$445$	0	0
$446$	−5.18760e6	−1.23489
$447$	2.35671e6	0.557876
$448$	7.96101e6	1.87401
$449$	−631636.	−0.147860	−0.0739301	−	0.997263i	$-0.523554\pi$
$449$	−631636.	−0.147860	−0.0739301	+	0.997263i	$0.523554\pi$
$450$	0	0
$451$	−1.98405e6	−0.459315
$452$	2.20164e6	0.506874
$453$	−419529.	−0.0960542
$454$	3.33758e6	0.759962
$455$	0	0
$456$	2.76359e6	0.622389
$457$	4.22113e6	0.945449	0.472724	−	0.881210i	$-0.343271\pi$
$457$	4.22113e6	0.945449	0.472724	+	0.881210i	$0.343271\pi$
$458$	4.70032e6	1.04704
$459$	−681983.	−0.151092
$460$	0	0
$461$	8.71424e6	1.90975	0.954877	−	0.297003i	$-0.0959871\pi$
$461$	8.71424e6	1.90975	0.954877	+	0.297003i	$0.0959871\pi$
$462$	−6.76705e6	−1.47501
$463$	2.41735e6	0.524066	0.262033	−	0.965059i	$-0.415607\pi$
$463$	2.41735e6	0.524066	0.262033	+	0.965059i	$0.415607\pi$
$464$	−3.17051e6	−0.683651
$465$	0	0
$466$	4.14523e6	0.884268
$467$	4.82492e6	1.02376	0.511879	−	0.859057i	$-0.328949\pi$
$467$	4.82492e6	1.02376	0.511879	+	0.859057i	$0.328949\pi$
$468$	−38321.4	−0.00808774
$469$	8.41280e6	1.76607
$470$	0	0
$471$	−3.77235e6	−0.783538
$472$	1.58489e6	0.327450
$473$	−667416.	−0.137165
$474$	6.54293e6	1.33760
$475$	0	0
$476$	795087.	0.160841
$477$	1.55265e6	0.312448
$478$	−3.64483e6	−0.729639
$479$	−3.48862e6	−0.694729	−0.347364	−	0.937730i	$-0.612923\pi$
$479$	−3.48862e6	−0.694729	−0.347364	+	0.937730i	$0.612923\pi$
$480$	0	0
$481$	253957.	0.0500492
$482$	−4.78947e6	−0.939009
$483$	−1.86049e7	−3.62877
$484$	440224.	0.0854201
$485$	0	0
$486$	−2.04259e6	−0.392275
$487$	447441.	0.0854897	0.0427448	−	0.999086i	$-0.486390\pi$
$487$	447441.	0.0854897	0.0427448	+	0.999086i	$0.486390\pi$
$488$	−3.52049e6	−0.669197
$489$	−1.90492e6	−0.360250
$490$	0	0
$491$	47857.1	0.00895865	0.00447933	−	0.999990i	$-0.498574\pi$
$491$	47857.1	0.00895865	0.00447933	+	0.999990i	$0.498574\pi$
$492$	1.38235e6	0.257458
$493$	−1.92240e6	−0.356226
$494$	138246.	0.0254879
$495$	0	0
$496$	−930799.	−0.169884
$497$	−1.67831e7	−3.04777
$498$	1.17935e6	0.213092
$499$	−763264.	−0.137222	−0.0686110	−	0.997643i	$-0.521857\pi$
$499$	−763264.	−0.137222	−0.0686110	+	0.997643i	$0.521857\pi$
$500$	0	0
$501$	−778820.	−0.138625
$502$	7.14971e6	1.26628
$503$	−2.60799e6	−0.459607	−0.229803	−	0.973237i	$-0.573808\pi$
$503$	−2.60799e6	−0.459607	−0.229803	+	0.973237i	$0.573808\pi$
$504$	3.24980e6	0.569877
$505$	0	0
$506$	6.33606e6	1.10013
$507$	6.49521e6	1.12221
$508$	3.22201e6	0.553946
$509$	2.54521e6	0.435441	0.217720	−	0.976011i	$-0.430138\pi$
$509$	2.54521e6	0.435441	0.217720	+	0.976011i	$0.430138\pi$
$510$	0	0
$511$	−632525.	−0.107158
$512$	3.95356e6	0.666520
$513$	−2.51463e6	−0.421872
$514$	4.48775e6	0.749240
$515$	0	0
$516$	465012.	0.0768847
$517$	4.70059e6	0.773439
$518$	−6.65560e6	−1.08984
$519$	−2.31152e6	−0.376686
$520$	0	0
$521$	−6.19477e6	−0.999841	−0.499920	−	0.866071i	$-0.666637\pi$
$521$	−6.19477e6	−0.999841	−0.499920	+	0.866071i	$0.666637\pi$
$522$	−2.42828e6	−0.390051
$523$	−8.41734e6	−1.34561	−0.672807	−	0.739818i	$-0.734912\pi$
$523$	−8.41734e6	−1.34561	−0.672807	+	0.739818i	$0.734912\pi$
$524$	−274748.	−0.0437125
$525$	0	0
$526$	−6.05796e6	−0.954690
$527$	−564378.	−0.0885204
$528$	−2.29080e6	−0.357604
$529$	1.09836e7	1.70650
$530$	0	0
$531$	535190.	0.0823705
$532$	2.93167e6	0.449093
$533$	223761.	0.0341167
$534$	−2.13428e6	−0.323891
$535$	0	0
$536$	6.45934e6	0.971128
$537$	−6.04807e6	−0.905068
$538$	−746291.	−0.111161
$539$	−1.71622e7	−2.54449
$540$	0	0
$541$	−192997.	−0.0283503	−0.0141751	−	0.999900i	$-0.504512\pi$
$541$	−192997.	−0.0283503	−0.0141751	+	0.999900i	$0.504512\pi$
$542$	−1.28982e6	−0.188596
$543$	−2.20216e6	−0.320516
$544$	1.03228e6	0.149554
$545$	0	0
$546$	763190.	0.109560
$547$	−8.50208e6	−1.21495	−0.607473	−	0.794341i	$-0.707817\pi$
$547$	−8.50208e6	−1.21495	−0.607473	+	0.794341i	$0.707817\pi$
$548$	−3.87589e6	−0.551341
$549$	−1.18881e6	−0.168338
$550$	0	0
$551$	−7.08833e6	−0.994638
$552$	−1.42848e7	−1.99539
$553$	2.24596e7	3.12312
$554$	6.22930e6	0.862313
$555$	0	0
$556$	2.14088e6	0.293701
$557$	1.70937e6	0.233452	0.116726	−	0.993164i	$-0.462760\pi$
$557$	1.70937e6	0.233452	0.116726	+	0.993164i	$0.462760\pi$
$558$	−712893.	−0.0969257
$559$	75271.4	0.0101883
$560$	0	0
$561$	−1.38899e6	−0.186335
$562$	5.50566e6	0.735306
$563$	6.36289e6	0.846026	0.423013	−	0.906124i	$-0.360972\pi$
$563$	6.36289e6	0.846026	0.423013	+	0.906124i	$0.360972\pi$
$564$	−3.27506e6	−0.433533
$565$	0	0
$566$	8.00837e6	1.05076
$567$	−1.79365e7	−2.34305
$568$	−1.28861e7	−1.67591
$569$	−463621.	−0.0600320	−0.0300160	−	0.999549i	$-0.509556\pi$
$569$	−463621.	−0.0600320	−0.0300160	+	0.999549i	$0.509556\pi$
$570$	0	0
$571$	1.76216e6	0.226180	0.113090	−	0.993585i	$-0.463925\pi$
$571$	1.76216e6	0.226180	0.113090	+	0.993585i	$0.463925\pi$
$572$	210310.	0.0268764
$573$	−1.23967e7	−1.57731
$574$	−5.86425e6	−0.742904
$575$	0	0
$576$	2.06407e6	0.259220
$577$	−3.41336e6	−0.426817	−0.213409	−	0.976963i	$-0.568457\pi$
$577$	−3.41336e6	−0.426817	−0.213409	+	0.976963i	$0.568457\pi$
$578$	5.76978e6	0.718355
$579$	−1.13042e6	−0.140134
$580$	0	0
$581$	4.04828e6	0.497542
$582$	−1.06105e7	−1.29846
$583$	−8.52105e6	−1.03830
$584$	−485653.	−0.0589242
$585$	0	0
$586$	−1.02233e7	−1.22983
$587$	1.17288e7	1.40494	0.702469	−	0.711715i	$-0.252081\pi$
$587$	1.17288e7	1.40494	0.702469	+	0.711715i	$0.252081\pi$
$588$	1.19575e7	1.42626
$589$	−2.08099e6	−0.247162
$590$	0	0
$591$	1.03575e6	0.121979
$592$	−2.25307e6	−0.264223
$593$	1.24399e7	1.45271	0.726354	−	0.687321i	$-0.241213\pi$
$593$	1.24399e7	1.45271	0.726354	+	0.687321i	$0.241213\pi$
$594$	4.72767e6	0.549770
$595$	0	0
$596$	1.91953e6	0.221350
$597$	4.93296e6	0.566464
$598$	−714584.	−0.0817147
$599$	9.53463e6	1.08577	0.542884	−	0.839808i	$-0.317332\pi$
$599$	9.53463e6	1.08577	0.542884	+	0.839808i	$0.317332\pi$
$600$	0	0
$601$	1.23478e7	1.39445	0.697226	−	0.716851i	$-0.254417\pi$
$601$	1.23478e7	1.39445	0.697226	+	0.716851i	$0.254417\pi$
$602$	−1.97268e6	−0.221853
$603$	2.18121e6	0.244289
$604$	−341705.	−0.0381117
$605$	0	0
$606$	1.12765e7	1.24737
$607$	148783.	0.0163901	0.00819503	−	0.999966i	$-0.497391\pi$
$607$	148783.	0.0163901	0.00819503	+	0.999966i	$0.497391\pi$
$608$	3.80625e6	0.417578
$609$	−3.91313e7	−4.27544
$610$	0	0
$611$	−530134.	−0.0574490
$612$	206144.	0.0222481
$613$	−3.87776e6	−0.416802	−0.208401	−	0.978043i	$-0.566826\pi$
$613$	−3.87776e6	−0.416802	−0.208401	+	0.978043i	$0.566826\pi$
$614$	−445719.	−0.0477134
$615$	0	0
$616$	−1.78351e7	−1.89376
$617$	−1.50460e7	−1.59114	−0.795571	−	0.605860i	$-0.792829\pi$
$617$	−1.50460e7	−1.59114	−0.795571	+	0.605860i	$0.792829\pi$
$618$	4.11897e6	0.433828
$619$	7.84064e6	0.822479	0.411240	−	0.911527i	$-0.365096\pi$
$619$	7.84064e6	0.822479	0.411240	+	0.911527i	$0.365096\pi$
$620$	0	0
$621$	1.29980e7	1.35253
$622$	−1.40561e7	−1.45676
$623$	−7.32623e6	−0.756242
$624$	258357.	0.0265619
$625$	0	0
$626$	5.85180e6	0.596834
$627$	−5.12155e6	−0.520274
$628$	−3.07257e6	−0.310887
$629$	−1.36612e6	−0.137677
$630$	0	0
$631$	1.71876e7	1.71847	0.859237	−	0.511578i	$-0.170939\pi$
$631$	1.71876e7	1.71847	0.859237	+	0.511578i	$0.170939\pi$
$632$	1.72445e7	1.71734
$633$	1.44024e7	1.42865
$634$	5.42050e6	0.535570
$635$	0	0
$636$	5.93691e6	0.581993
$637$	1.93556e6	0.188999
$638$	1.33265e7	1.29618
$639$	−4.35140e6	−0.421577
$640$	0	0
$641$	915397.	0.0879963	0.0439982	−	0.999032i	$-0.485990\pi$
$641$	915397.	0.0879963	0.0439982	+	0.999032i	$0.485990\pi$
$642$	−5.40704e6	−0.517752
$643$	−4.31500e6	−0.411579	−0.205790	−	0.978596i	$-0.565976\pi$
$643$	−4.31500e6	−0.411579	−0.205790	+	0.978596i	$0.565976\pi$
$644$	−1.51536e7	−1.43980
$645$	0	0
$646$	−743671.	−0.0701132
$647$	8.88579e6	0.834517	0.417258	−	0.908788i	$-0.362991\pi$
$647$	8.88579e6	0.834517	0.417258	+	0.908788i	$0.362991\pi$
$648$	−1.37717e7	−1.28839
$649$	−2.93716e6	−0.273726
$650$	0	0
$651$	−1.14882e7	−1.06243
$652$	−1.55155e6	−0.142938
$653$	−3.23188e6	−0.296601	−0.148300	−	0.988942i	$-0.547380\pi$
$653$	−3.23188e6	−0.296601	−0.148300	+	0.988942i	$0.547380\pi$
$654$	2.87198e6	0.262565
$655$	0	0
$656$	−1.98518e6	−0.180111
$657$	−163996.	−0.0148225
$658$	1.38936e7	1.25097
$659$	−9.95173e6	−0.892658	−0.446329	−	0.894869i	$-0.647269\pi$
$659$	−9.95173e6	−0.892658	−0.446329	+	0.894869i	$0.647269\pi$
$660$	0	0
$661$	4.59979e6	0.409481	0.204741	−	0.978816i	$-0.434365\pi$
$661$	4.59979e6	0.409481	0.204741	+	0.978816i	$0.434365\pi$
$662$	1.64579e7	1.45959
$663$	156651.	0.0138405
$664$	3.10827e6	0.273589
$665$	0	0
$666$	−1.72561e6	−0.150750
$667$	3.66391e7	3.18882
$668$	−634346.	−0.0550028
$669$	−2.16745e7	−1.87234
$670$	0	0
$671$	6.52425e6	0.559403
$672$	2.10125e7	1.79496
$673$	−2.10051e7	−1.78767	−0.893835	−	0.448396i	$-0.851995\pi$
$673$	−2.10051e7	−1.78767	−0.893835	+	0.448396i	$0.851995\pi$
$674$	1.59955e6	0.135627
$675$	0	0
$676$	5.29032e6	0.445262
$677$	1.88543e6	0.158102	0.0790511	−	0.996871i	$-0.474811\pi$
$677$	1.88543e6	0.158102	0.0790511	+	0.996871i	$0.474811\pi$
$678$	−1.13682e7	−0.949771
$679$	−3.64220e7	−3.03172
$680$	0	0
$681$	1.39449e7	1.15225
$682$	3.91240e6	0.322094
$683$	1.47917e7	1.21329	0.606646	−	0.794972i	$-0.292515\pi$
$683$	1.47917e7	1.21329	0.606646	+	0.794972i	$0.292515\pi$
$684$	760101.	0.0621200
$685$	0	0
$686$	−3.27952e7	−2.66072
$687$	1.96386e7	1.58752
$688$	−667798.	−0.0537866
$689$	961007.	0.0771220
$690$	0	0
$691$	8.73952e6	0.696294	0.348147	−	0.937440i	$-0.386811\pi$
$691$	8.73952e6	0.696294	0.348147	+	0.937440i	$0.386811\pi$
$692$	−1.88272e6	−0.149459
$693$	−6.02261e6	−0.476378
$694$	−1.80057e6	−0.141909
$695$	0	0
$696$	−3.00450e7	−2.35098
$697$	−1.20369e6	−0.0938495
$698$	−1.29867e7	−1.00892
$699$	1.73193e7	1.34072
$700$	0	0
$701$	9.97613e6	0.766773	0.383387	−	0.923588i	$-0.374758\pi$
$701$	9.97613e6	0.766773	0.383387	+	0.923588i	$0.374758\pi$
$702$	−533189.	−0.0408355
$703$	−5.03720e6	−0.384416
$704$	−1.13277e7	−0.861413
$705$	0	0
$706$	−9.48323e6	−0.716052
$707$	3.87084e7	2.91244
$708$	2.04642e6	0.153430
$709$	6.47718e6	0.483916	0.241958	−	0.970287i	$-0.422210\pi$
$709$	6.47718e6	0.483916	0.241958	+	0.970287i	$0.422210\pi$
$710$	0	0
$711$	5.82315e6	0.432000
$712$	−5.62508e6	−0.415842
$713$	1.07565e7	0.792406
$714$	−4.10546e6	−0.301381
$715$	0	0
$716$	−4.92613e6	−0.359107
$717$	−1.52286e7	−1.10627
$718$	1.11489e7	0.807089
$719$	−1.39191e7	−1.00413	−0.502065	−	0.864830i	$-0.667426\pi$
$719$	−1.39191e7	−1.00413	−0.502065	+	0.864830i	$0.667426\pi$
$720$	0	0
$721$	1.41390e7	1.01293
$722$	7.67159e6	0.547700
$723$	−2.00111e7	−1.42372
$724$	−1.79365e6	−0.127172
$725$	0	0
$726$	−2.27311e6	−0.160059
$727$	−843139.	−0.0591648	−0.0295824	−	0.999562i	$-0.509418\pi$
$727$	−843139.	−0.0591648	−0.0295824	+	0.999562i	$0.509418\pi$
$728$	2.01145e6	0.140663
$729$	8.64726e6	0.602642
$730$	0	0
$731$	−404910.	−0.0280263
$732$	−4.54567e6	−0.313560
$733$	−655160.	−0.0450388	−0.0225194	−	0.999746i	$-0.507169\pi$
$733$	−655160.	−0.0450388	−0.0225194	+	0.999746i	$0.507169\pi$
$734$	−1.04632e7	−0.716847
$735$	0	0
$736$	−1.96742e7	−1.33876
$737$	−1.19706e7	−0.811797
$738$	−1.52044e6	−0.102761
$739$	−7.27526e6	−0.490047	−0.245023	−	0.969517i	$-0.578796\pi$
$739$	−7.27526e6	−0.490047	−0.245023	+	0.969517i	$0.578796\pi$
$740$	0	0
$741$	577610.	0.0386446
$742$	−2.51857e7	−1.67936
$743$	−1.47146e7	−0.977862	−0.488931	−	0.872322i	$-0.662613\pi$
$743$	−1.47146e7	−0.977862	−0.488931	+	0.872322i	$0.662613\pi$
$744$	−8.82061e6	−0.584207
$745$	0	0
$746$	1.42443e6	0.0937117
$747$	1.04961e6	0.0688217
$748$	−1.13133e6	−0.0739326
$749$	−1.85605e7	−1.20888
$750$	0	0
$751$	−2.30764e7	−1.49303	−0.746515	−	0.665369i	$-0.768274\pi$
$751$	−2.30764e7	−1.49303	−0.746515	+	0.665369i	$0.768274\pi$
$752$	4.70328e6	0.303289
$753$	2.98725e7	1.91992
$754$	−1.50297e6	−0.0962769
$755$	0	0
$756$	−1.13069e7	−0.719514
$757$	−332831.	−0.0211098	−0.0105549	−	0.999944i	$-0.503360\pi$
$757$	−332831.	−0.0211098	−0.0105549	+	0.999944i	$0.503360\pi$
$758$	−1.46024e7	−0.923103
$759$	2.64729e7	1.66801
$760$	0	0
$761$	−2.59438e6	−0.162395	−0.0811975	−	0.996698i	$-0.525874\pi$
$761$	−2.59438e6	−0.162395	−0.0811975	+	0.996698i	$0.525874\pi$
$762$	−1.66370e7	−1.03797
$763$	9.85849e6	0.613055
$764$	−1.00970e7	−0.625836
$765$	0	0
$766$	1.20812e7	0.743939
$767$	331254.	0.0203316
$768$	1.90400e7	1.16483
$769$	−3.11577e7	−1.89999	−0.949993	−	0.312273i	$-0.898910\pi$
$769$	−3.11577e7	−1.89999	−0.949993	+	0.312273i	$0.898910\pi$
$770$	0	0
$771$	1.87504e7	1.13599
$772$	−920726.	−0.0556016
$773$	1.48790e7	0.895620	0.447810	−	0.894129i	$-0.352204\pi$
$773$	1.48790e7	0.895620	0.447810	+	0.894129i	$0.352204\pi$
$774$	−511462.	−0.0306875
$775$	0	0
$776$	−2.79648e7	−1.66708
$777$	−2.78080e7	−1.65241
$778$	−1.75779e7	−1.04116
$779$	−4.43828e6	−0.262042
$780$	0	0
$781$	2.38808e7	1.40094
$782$	3.84399e6	0.224784
$783$	2.73384e7	1.59356
$784$	−1.71720e7	−0.997773
$785$	0	0
$786$	1.41867e6	0.0819077
$787$	1.33119e7	0.766132	0.383066	−	0.923721i	$-0.374868\pi$
$787$	1.33119e7	0.766132	0.383066	+	0.923721i	$0.374868\pi$
$788$	843614.	0.0483981
$789$	−2.53110e7	−1.44749
$790$	0	0
$791$	−3.90231e7	−2.21759
$792$	−4.62416e6	−0.261951
$793$	−735808.	−0.0415510
$794$	1.16317e7	0.654775
$795$	0	0
$796$	4.01788e6	0.224758
$797$	2.51126e7	1.40038	0.700189	−	0.713958i	$-0.253099\pi$
$797$	2.51126e7	1.40038	0.700189	+	0.713958i	$0.253099\pi$
$798$	−1.51378e7	−0.841502
$799$	2.85177e6	0.158033
$800$	0	0
$801$	−1.89949e6	−0.104606
$802$	1.45480e7	0.798672
$803$	900022.	0.0492566
$804$	8.34033e6	0.455033
$805$	0	0
$806$	−441242.	−0.0239243
$807$	−3.11811e6	−0.168542
$808$	2.97203e7	1.60149
$809$	2.25755e7	1.21274	0.606368	−	0.795184i	$-0.292626\pi$
$809$	2.25755e7	1.21274	0.606368	+	0.795184i	$0.292626\pi$
$810$	0	0
$811$	−3.09517e7	−1.65247	−0.826234	−	0.563327i	$-0.809521\pi$
$811$	−3.09517e7	−1.65247	−0.826234	+	0.563327i	$0.809521\pi$
$812$	−3.18723e7	−1.69638
$813$	−5.38906e6	−0.285948
$814$	9.47027e6	0.500958
$815$	0	0
$816$	−1.38979e6	−0.0730674
$817$	−1.49300e6	−0.0782536
$818$	−2.43672e7	−1.27328
$819$	679232.	0.0353841
$820$	0	0
$821$	8.98932e6	0.465446	0.232723	−	0.972543i	$-0.425237\pi$
$821$	8.98932e6	0.465446	0.232723	+	0.972543i	$0.425237\pi$
$822$	2.00133e7	1.03309
$823$	−6.97234e6	−0.358822	−0.179411	−	0.983774i	$-0.557419\pi$
$823$	−6.97234e6	−0.358822	−0.179411	+	0.983774i	$0.557419\pi$
$824$	1.08559e7	0.556991
$825$	0	0
$826$	−8.68137e6	−0.442729
$827$	−3.52799e7	−1.79376	−0.896878	−	0.442277i	$-0.854171\pi$
$827$	−3.52799e7	−1.79376	−0.896878	+	0.442277i	$0.854171\pi$
$828$	−3.92891e6	−0.199157
$829$	1.78972e7	0.904480	0.452240	−	0.891896i	$-0.350625\pi$
$829$	1.78972e7	0.904480	0.452240	+	0.891896i	$0.350625\pi$
$830$	0	0
$831$	2.60269e7	1.30743
$832$	1.27755e6	0.0639836
$833$	−1.04120e7	−0.519904
$834$	−1.10545e7	−0.550331
$835$	0	0
$836$	−4.17148e6	−0.206431
$837$	8.02600e6	0.395991
$838$	−2.06843e7	−1.01749
$839$	−4.70631e6	−0.230821	−0.115411	−	0.993318i	$-0.536818\pi$
$839$	−4.70631e6	−0.230821	−0.115411	+	0.993318i	$0.536818\pi$
$840$	0	0
$841$	5.65512e7	2.75710
$842$	−2.48190e7	−1.20643
$843$	2.30034e7	1.11487
$844$	1.17307e7	0.566848
$845$	0	0
$846$	3.60221e6	0.173039
$847$	−7.80279e6	−0.373716
$848$	−8.52592e6	−0.407148
$849$	3.34601e7	1.59315
$850$	0	0
$851$	2.60370e7	1.23244
$852$	−1.66386e7	−0.785266
$853$	−3.17206e7	−1.49269	−0.746344	−	0.665560i	$-0.768193\pi$
$853$	−3.17206e7	−1.49269	−0.746344	+	0.665560i	$0.768193\pi$
$854$	1.92838e7	0.904788
$855$	0	0
$856$	−1.42507e7	−0.664740
$857$	3.47688e7	1.61710	0.808552	−	0.588425i	$-0.200252\pi$
$857$	3.47688e7	1.61710	0.808552	+	0.588425i	$0.200252\pi$
$858$	−1.08595e6	−0.0503605
$859$	2.69492e7	1.24613	0.623065	−	0.782170i	$-0.285887\pi$
$859$	2.69492e7	1.24613	0.623065	+	0.782170i	$0.285887\pi$
$860$	0	0
$861$	−2.45016e7	−1.12639
$862$	1.62812e7	0.746310
$863$	2.55597e7	1.16823	0.584116	−	0.811670i	$-0.301441\pi$
$863$	2.55597e7	1.16823	0.584116	+	0.811670i	$0.301441\pi$
$864$	−1.46800e7	−0.669023
$865$	0	0
$866$	1.23083e7	0.557702
$867$	2.41069e7	1.08917
$868$	−9.35708e6	−0.421542
$869$	−3.19578e7	−1.43558
$870$	0	0
$871$	1.35005e6	0.0602982
$872$	7.56935e6	0.337107
$873$	−9.44322e6	−0.419358
$874$	1.41737e7	0.627631
$875$	0	0
$876$	−627077.	−0.0276096
$877$	2.40751e7	1.05699	0.528493	−	0.848938i	$-0.322757\pi$
$877$	2.40751e7	1.05699	0.528493	+	0.848938i	$0.322757\pi$
$878$	−3.08645e7	−1.35121
$879$	−4.27143e7	−1.86467
$880$	0	0
$881$	2.80319e7	1.21678	0.608392	−	0.793637i	$-0.291815\pi$
$881$	2.80319e7	1.21678	0.608392	+	0.793637i	$0.291815\pi$
$882$	−1.31520e7	−0.569271
$883$	1.08829e7	0.469725	0.234863	−	0.972029i	$-0.424536\pi$
$883$	1.08829e7	0.469725	0.234863	+	0.972029i	$0.424536\pi$
$884$	127592.	0.00549152
$885$	0	0
$886$	−2.31526e7	−0.990868
$887$	1.56070e7	0.666055	0.333027	−	0.942917i	$-0.391930\pi$
$887$	1.56070e7	0.666055	0.333027	+	0.942917i	$0.391930\pi$
$888$	−2.13510e7	−0.908626
$889$	−5.71088e7	−2.42353
$890$	0	0
$891$	2.55219e7	1.07701
$892$	−1.76538e7	−0.742893
$893$	1.05151e7	0.441252
$894$	−9.91158e6	−0.414762
$895$	0	0
$896$	4.78414e6	0.199083
$897$	−2.98563e6	−0.123895
$898$	2.65646e6	0.109929
$899$	2.26240e7	0.933619
$900$	0	0
$901$	−5.16958e6	−0.212150
$902$	8.34426e6	0.341485
$903$	−8.24214e6	−0.336373
$904$	−2.99619e7	−1.21941
$905$	0	0
$906$	1.76440e6	0.0714130
$907$	−1.27443e7	−0.514397	−0.257198	−	0.966359i	$-0.582799\pi$
$907$	−1.27443e7	−0.514397	−0.257198	+	0.966359i	$0.582799\pi$
$908$	1.13580e7	0.457182
$909$	1.00360e7	0.402858
$910$	0	0
$911$	−2.45516e7	−0.980130	−0.490065	−	0.871686i	$-0.663027\pi$
$911$	−2.45516e7	−0.980130	−0.490065	+	0.871686i	$0.663027\pi$
$912$	−5.12448e6	−0.204015
$913$	−5.76031e6	−0.228701
$914$	−1.77527e7	−0.702909
$915$	0	0
$916$	1.59956e7	0.629884
$917$	4.86979e6	0.191244
$918$	2.86820e6	0.112332
$919$	−4.35947e7	−1.70273	−0.851364	−	0.524575i	$-0.824224\pi$
$919$	−4.35947e7	−1.70273	−0.851364	+	0.524575i	$0.824224\pi$
$920$	0	0
$921$	−1.86228e6	−0.0723427
$922$	−3.66493e7	−1.41984
$923$	−2.69328e6	−0.104059
$924$	−2.30288e7	−0.887342
$925$	0	0
$926$	−1.01666e7	−0.389626
$927$	3.66585e6	0.140112
$928$	−4.13804e7	−1.57734
$929$	1.26241e7	0.479912	0.239956	−	0.970784i	$-0.422867\pi$
$929$	1.26241e7	0.479912	0.239956	+	0.970784i	$0.422867\pi$
$930$	0	0
$931$	−3.83916e7	−1.45165
$932$	1.41065e7	0.531962
$933$	−5.87282e7	−2.20873
$934$	−2.02921e7	−0.761130
$935$	0	0
$936$	521514.	0.0194570
$937$	−3.38149e7	−1.25823	−0.629114	−	0.777313i	$-0.716582\pi$
$937$	−3.38149e7	−1.25823	−0.629114	+	0.777313i	$0.716582\pi$
$938$	−3.53815e7	−1.31302
$939$	2.44496e7	0.904915
$940$	0	0
$941$	−1.85140e7	−0.681594	−0.340797	−	0.940137i	$-0.610697\pi$
$941$	−1.85140e7	−0.681594	−0.340797	+	0.940137i	$0.610697\pi$
$942$	1.58653e7	0.582534
$943$	2.29412e7	0.840110
$944$	−2.93884e6	−0.107336
$945$	0	0
$946$	2.80694e6	0.101978
$947$	−1.21694e7	−0.440956	−0.220478	−	0.975392i	$-0.570762\pi$
$947$	−1.21694e7	−0.440956	−0.220478	+	0.975392i	$0.570762\pi$
$948$	2.22661e7	0.804681
$949$	−101505.	−0.00365865
$950$	0	0
$951$	2.26476e7	0.812027
$952$	−1.08203e7	−0.386942
$953$	−2.04820e7	−0.730535	−0.365268	−	0.930903i	$-0.619023\pi$
$953$	−2.04820e7	−0.730535	−0.365268	+	0.930903i	$0.619023\pi$
$954$	−6.52995e6	−0.232295
$955$	0	0
$956$	−1.24037e7	−0.438940
$957$	5.56801e7	1.96526
$958$	1.46720e7	0.516507
$959$	6.86986e7	2.41213
$960$	0	0
$961$	−2.19872e7	−0.768001
$962$	−1.06806e6	−0.0372099
$963$	−4.81221e6	−0.167217
$964$	−1.62989e7	−0.564894
$965$	0	0
$966$	7.82462e7	2.69787
$967$	1.18003e6	0.0405815	0.0202907	−	0.999794i	$-0.493541\pi$
$967$	1.18003e6	0.0405815	0.0202907	+	0.999794i	$0.493541\pi$
$968$	−5.99098e6	−0.205499
$969$	−3.10716e6	−0.106305
$970$	0	0
$971$	−3.67004e7	−1.24917	−0.624587	−	0.780955i	$-0.714733\pi$
$971$	−3.67004e7	−1.24917	−0.624587	+	0.780955i	$0.714733\pi$
$972$	−6.95109e6	−0.235986
$973$	−3.79462e7	−1.28495
$974$	−1.88180e6	−0.0635587
$975$	0	0
$976$	6.52799e6	0.219359
$977$	3.51070e7	1.17668	0.588338	−	0.808615i	$-0.299782\pi$
$977$	3.51070e7	1.17668	0.588338	+	0.808615i	$0.299782\pi$
$978$	8.01148e6	0.267834
$979$	1.04245e7	0.347616
$980$	0	0
$981$	2.55604e6	0.0847997
$982$	−201272.	−0.00666046
$983$	1.18985e6	0.0392744	0.0196372	−	0.999807i	$-0.493749\pi$
$983$	1.18985e6	0.0392744	0.0196372	+	0.999807i	$0.493749\pi$
$984$	−1.88124e7	−0.619377
$985$	0	0
$986$	8.08499e6	0.264842
$987$	5.80492e7	1.89672
$988$	470461.	0.0153332
$989$	7.71721e6	0.250882
$990$	0	0
$991$	−1.32754e7	−0.429401	−0.214701	−	0.976680i	$-0.568878\pi$
$991$	−1.32754e7	−0.429401	−0.214701	+	0.976680i	$0.568878\pi$
$992$	−1.21485e7	−0.391961
$993$	6.87635e7	2.21302
$994$	7.05845e7	2.26591
$995$	0	0
$996$	4.01341e6	0.128193
$997$	−7.48358e6	−0.238436	−0.119218	−	0.992868i	$-0.538039\pi$
$997$	−7.48358e6	−0.238436	−0.119218	+	0.992868i	$0.538039\pi$
$998$	3.21005e6	0.102020
$999$	1.94276e7	0.615892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.j.1.13	yes	37
5.4	even	2		1075.6.a.i.1.25	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.6.a.i.1.25	✓	37	5.4	even	2
1075.6.a.j.1.13	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)

\(f(q)\)	\(=\)	\(q-4.20568 q^{2} -17.5719 q^{3} -14.3123 q^{4} +73.9018 q^{6} +253.679 q^{7} +194.775 q^{8} +65.7719 q^{9} +O(q^{10})\)	\(q-4.20568 q^{2} -17.5719 q^{3} -14.3123 q^{4} +73.9018 q^{6} +253.679 q^{7} +194.775 q^{8} +65.7719 q^{9} -360.960 q^{11} +251.494 q^{12} +40.7093 q^{13} -1066.89 q^{14} -361.167 q^{16} -218.989 q^{17} -276.616 q^{18} -807.463 q^{19} -4457.62 q^{21} +1518.08 q^{22} +4173.72 q^{23} -3422.56 q^{24} -171.210 q^{26} +3114.24 q^{27} -3630.72 q^{28} +8778.52 q^{29} +2577.20 q^{31} -4713.83 q^{32} +6342.76 q^{33} +920.997 q^{34} -941.345 q^{36} +6238.31 q^{37} +3395.93 q^{38} -715.339 q^{39} +5496.57 q^{41} +18747.3 q^{42} +1849.00 q^{43} +5166.16 q^{44} -17553.3 q^{46} -13022.4 q^{47} +6346.40 q^{48} +47546.0 q^{49} +3848.05 q^{51} -582.641 q^{52} +23606.6 q^{53} -13097.5 q^{54} +49410.2 q^{56} +14188.7 q^{57} -36919.6 q^{58} +8137.06 q^{59} -18074.7 q^{61} -10838.9 q^{62} +16685.0 q^{63} +31382.2 q^{64} -26675.6 q^{66} +33163.2 q^{67} +3134.22 q^{68} -73340.3 q^{69} -66159.0 q^{71} +12810.7 q^{72} -2493.41 q^{73} -26236.3 q^{74} +11556.6 q^{76} -91568.1 q^{77} +3008.49 q^{78} +88535.5 q^{79} -70705.6 q^{81} -23116.8 q^{82} +15958.3 q^{83} +63798.6 q^{84} -7776.30 q^{86} -154255. q^{87} -70305.9 q^{88} -28879.9 q^{89} +10327.1 q^{91} -59735.4 q^{92} -45286.3 q^{93} +54768.3 q^{94} +82831.0 q^{96} -143575. q^{97} -199963. q^{98} -23741.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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