LMFDB - Embedded newform 1859.4.a.o.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.78462 q^{2} -0.436688 q^{3} -4.81514 q^{4} +13.8087 q^{5} +0.779321 q^{6} -6.26730 q^{7} +22.8701 q^{8} -26.8093 q^{9} +O(q^{10})$	\(q-1.78462 q^{2} -0.436688 q^{3} -4.81514 q^{4} +13.8087 q^{5} +0.779321 q^{6} -6.26730 q^{7} +22.8701 q^{8} -26.8093 q^{9} -24.6433 q^{10} -11.0000 q^{11} +2.10272 q^{12} +11.1847 q^{14} -6.03011 q^{15} -2.29324 q^{16} +7.27787 q^{17} +47.8443 q^{18} -91.0329 q^{19} -66.4910 q^{20} +2.73686 q^{21} +19.6308 q^{22} +157.363 q^{23} -9.98711 q^{24} +65.6811 q^{25} +23.4979 q^{27} +30.1780 q^{28} +206.284 q^{29} +10.7614 q^{30} +8.76578 q^{31} -178.868 q^{32} +4.80357 q^{33} -12.9882 q^{34} -86.5435 q^{35} +129.091 q^{36} +132.380 q^{37} +162.459 q^{38} +315.807 q^{40} -58.6171 q^{41} -4.88424 q^{42} +23.3871 q^{43} +52.9666 q^{44} -370.203 q^{45} -280.832 q^{46} -1.21603 q^{47} +1.00143 q^{48} -303.721 q^{49} -117.216 q^{50} -3.17816 q^{51} -554.842 q^{53} -41.9347 q^{54} -151.896 q^{55} -143.334 q^{56} +39.7530 q^{57} -368.138 q^{58} -129.684 q^{59} +29.0358 q^{60} +242.582 q^{61} -15.6436 q^{62} +168.022 q^{63} +337.557 q^{64} -8.57253 q^{66} -398.720 q^{67} -35.0440 q^{68} -68.7184 q^{69} +154.447 q^{70} +757.901 q^{71} -613.132 q^{72} +872.123 q^{73} -236.247 q^{74} -28.6822 q^{75} +438.336 q^{76} +68.9403 q^{77} -773.280 q^{79} -31.6668 q^{80} +713.590 q^{81} +104.609 q^{82} -4.22184 q^{83} -13.1784 q^{84} +100.498 q^{85} -41.7370 q^{86} -90.0817 q^{87} -251.571 q^{88} +290.011 q^{89} +660.670 q^{90} -757.724 q^{92} -3.82791 q^{93} +2.17014 q^{94} -1257.05 q^{95} +78.1097 q^{96} -642.620 q^{97} +542.025 q^{98} +294.902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * 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 $

$2$	−1.78462	−0.630957	−0.315479	−	0.948933i	$-0.602165\pi$
$2$	−1.78462	−0.630957	−0.315479	+	0.948933i	$0.602165\pi$
$3$	−0.436688	−0.0840407	−0.0420203	−	0.999117i	$-0.513379\pi$
$3$	−0.436688	−0.0840407	−0.0420203	+	0.999117i	$0.513379\pi$
$4$	−4.81514	−0.601893
$5$	13.8087	1.23509	0.617545	−	0.786535i	$-0.288127\pi$
$5$	13.8087	1.23509	0.617545	+	0.786535i	$0.288127\pi$
$6$	0.779321	0.0530261
$7$	−6.26730	−0.338402	−0.169201	−	0.985582i	$-0.554119\pi$
$7$	−6.26730	−0.338402	−0.169201	+	0.985582i	$0.554119\pi$
$8$	22.8701	1.01073
$9$	−26.8093	−0.992937
$10$	−24.6433	−0.779289
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	2.10272	0.0505835
$13$	0	0
$13$	0	0
$14$	11.1847	0.213517
$15$	−6.03011	−0.103798
$16$	−2.29324	−0.0358319
$17$	7.27787	0.103832	0.0519160	−	0.998651i	$-0.483467\pi$
$17$	7.27787	0.103832	0.0519160	+	0.998651i	$0.483467\pi$
$18$	47.8443	0.626501
$19$	−91.0329	−1.09918	−0.549589	−	0.835435i	$-0.685216\pi$
$19$	−91.0329	−1.09918	−0.549589	+	0.835435i	$0.685216\pi$
$20$	−66.4910	−0.743392
$21$	2.73686	0.0284396
$22$	19.6308	0.190241
$23$	157.363	1.42663	0.713313	−	0.700846i	$-0.247194\pi$
$23$	157.363	1.42663	0.713313	+	0.700846i	$0.247194\pi$
$24$	−9.98711	−0.0849421
$25$	65.6811	0.525449
$26$	0	0
$27$	23.4979	0.167488
$28$	30.1780	0.203682
$29$	206.284	1.32090	0.660448	−	0.750872i	$-0.270367\pi$
$29$	206.284	1.32090	0.660448	+	0.750872i	$0.270367\pi$
$30$	10.7614	0.0654920
$31$	8.76578	0.0507865	0.0253932	−	0.999678i	$-0.491916\pi$
$31$	8.76578	0.0507865	0.0253932	+	0.999678i	$0.491916\pi$
$32$	−178.868	−0.988118
$33$	4.80357	0.0253392
$34$	−12.9882	−0.0655135
$35$	−86.5435	−0.417958
$36$	129.091	0.597642
$37$	132.380	0.588191	0.294096	−	0.955776i	$-0.404982\pi$
$37$	132.380	0.588191	0.294096	+	0.955776i	$0.404982\pi$
$38$	162.459	0.693534
$39$	0	0
$40$	315.807	1.24834
$41$	−58.6171	−0.223279	−0.111640	−	0.993749i	$-0.535610\pi$
$41$	−58.6171	−0.223279	−0.111640	+	0.993749i	$0.535610\pi$
$42$	−4.88424	−0.0179442
$43$	23.3871	0.0829419	0.0414709	−	0.999140i	$-0.486796\pi$
$43$	23.3871	0.0829419	0.0414709	+	0.999140i	$0.486796\pi$
$44$	52.9666	0.181478
$45$	−370.203	−1.22637
$46$	−280.832	−0.900140
$47$	−1.21603	−0.00377396	−0.00188698	−	0.999998i	$-0.500601\pi$
$47$	−1.21603	−0.00377396	−0.00188698	+	0.999998i	$0.500601\pi$
$48$	1.00143	0.00301134
$49$	−303.721	−0.885484
$50$	−117.216	−0.331536
$51$	−3.17816	−0.00872610
$52$	0	0
$53$	−554.842	−1.43799	−0.718994	−	0.695016i	$-0.755397\pi$
$53$	−554.842	−1.43799	−0.718994	+	0.695016i	$0.755397\pi$
$54$	−41.9347	−0.105678
$55$	−151.896	−0.372394
$56$	−143.334	−0.342032
$57$	39.7530	0.0923756
$58$	−368.138	−0.833428
$59$	−129.684	−0.286160	−0.143080	−	0.989711i	$-0.545701\pi$
$59$	−129.684	−0.286160	−0.143080	+	0.989711i	$0.545701\pi$
$60$	29.0358	0.0624752
$61$	242.582	0.509171	0.254585	−	0.967050i	$-0.418061\pi$
$61$	242.582	0.509171	0.254585	+	0.967050i	$0.418061\pi$
$62$	−15.6436	−0.0320441
$63$	168.022	0.336012
$64$	337.557	0.659292
$65$	0	0
$66$	−8.57253	−0.0159880
$67$	−398.720	−0.727036	−0.363518	−	0.931587i	$-0.618424\pi$
$67$	−398.720	−0.727036	−0.363518	+	0.931587i	$0.618424\pi$
$68$	−35.0440	−0.0624957
$69$	−68.7184	−0.119895
$70$	154.447	0.263713
$71$	757.901	1.26685	0.633425	−	0.773804i	$-0.281649\pi$
$71$	757.901	1.26685	0.633425	+	0.773804i	$0.281649\pi$
$72$	−613.132	−1.00359
$73$	872.123	1.39828	0.699139	−	0.714986i	$-0.253567\pi$
$73$	872.123	1.39828	0.699139	+	0.714986i	$0.253567\pi$
$74$	−236.247	−0.371124
$75$	−28.6822	−0.0441591
$76$	438.336	0.661587
$77$	68.9403	0.102032
$78$	0	0
$79$	−773.280	−1.10128	−0.550638	−	0.834744i	$-0.685615\pi$
$79$	−773.280	−1.10128	−0.550638	+	0.834744i	$0.685615\pi$
$80$	−31.6668	−0.0442557
$81$	713.590	0.978861
$82$	104.609	0.140880
$83$	−4.22184	−0.00558322	−0.00279161	−	0.999996i	$-0.500889\pi$
$83$	−4.22184	−0.00558322	−0.00279161	+	0.999996i	$0.500889\pi$
$84$	−13.1784	−0.0171176
$85$	100.498	0.128242
$86$	−41.7370	−0.0523328
$87$	−90.0817	−0.111009
$88$	−251.571	−0.304745
$89$	290.011	0.345405	0.172703	−	0.984974i	$-0.444750\pi$
$89$	290.011	0.345405	0.172703	+	0.984974i	$0.444750\pi$
$90$	660.670	0.773785
$91$	0	0
$92$	−757.724	−0.858676
$93$	−3.82791	−0.00426813
$94$	2.17014	0.00238121
$95$	−1257.05	−1.35758
$96$	78.1097	0.0830421
$97$	−642.620	−0.672661	−0.336331	−	0.941744i	$-0.609186\pi$
$97$	−642.620	−0.672661	−0.336331	+	0.941744i	$0.609186\pi$
$98$	542.025	0.558702
$99$	294.902	0.299382
$100$	−316.264	−0.316264
$101$	−1445.44	−1.42403	−0.712013	−	0.702167i	$-0.752216\pi$
$101$	−1445.44	−1.42403	−0.712013	+	0.702167i	$0.752216\pi$
$102$	5.67179	0.00550580
$103$	834.817	0.798611	0.399305	−	0.916818i	$-0.369251\pi$
$103$	834.817	0.798611	0.399305	+	0.916818i	$0.369251\pi$
$104$	0	0
$105$	37.7925	0.0351255
$106$	990.180	0.907309
$107$	743.849	0.672061	0.336031	−	0.941851i	$-0.390915\pi$
$107$	743.849	0.672061	0.336031	+	0.941851i	$0.390915\pi$
$108$	−113.146	−0.100810
$109$	−1199.27	−1.05385	−0.526925	−	0.849912i	$-0.676655\pi$
$109$	−1199.27	−1.05385	−0.526925	+	0.849912i	$0.676655\pi$
$110$	271.076	0.234965
$111$	−57.8086	−0.0494320
$112$	14.3724	0.0121256
$113$	−111.534	−0.0928519	−0.0464260	−	0.998922i	$-0.514783\pi$
$113$	−111.534	−0.0928519	−0.0464260	+	0.998922i	$0.514783\pi$
$114$	−70.9438	−0.0582851
$115$	2172.98	1.76201
$116$	−993.287	−0.795038
$117$	0	0
$118$	231.437	0.180555
$119$	−45.6126	−0.0351370
$120$	−137.909	−0.104911
$121$	121.000	0.0909091
$122$	−432.915	−0.321265
$123$	25.5974	0.0187646
$124$	−42.2085	−0.0305680
$125$	−819.118	−0.586113
$126$	−299.855	−0.212009
$127$	−1064.97	−0.744100	−0.372050	−	0.928213i	$-0.621345\pi$
$127$	−1064.97	−0.744100	−0.372050	+	0.928213i	$0.621345\pi$
$128$	828.536	0.572133
$129$	−10.2129	−0.00697049
$130$	0	0
$131$	830.151	0.553669	0.276835	−	0.960918i	$-0.410715\pi$
$131$	830.151	0.553669	0.276835	+	0.960918i	$0.410715\pi$
$132$	−23.1299	−0.0152515
$133$	570.530	0.371964
$134$	711.562	0.458729
$135$	324.476	0.206863
$136$	166.446	0.104946
$137$	2877.86	1.79468	0.897342	−	0.441335i	$-0.145495\pi$
$137$	2877.86	1.79468	0.897342	+	0.441335i	$0.145495\pi$
$138$	122.636	0.0756483
$139$	2262.22	1.38043	0.690213	−	0.723606i	$-0.257517\pi$
$139$	2262.22	1.38043	0.690213	+	0.723606i	$0.257517\pi$
$140$	416.719	0.251566
$141$	0.531025	0.000317166 0
$142$	−1352.56	−0.799328
$143$	0	0
$144$	61.4803	0.0355789
$145$	2848.52	1.63143
$146$	−1556.41	−0.882254
$147$	132.631	0.0744167
$148$	−637.427	−0.354028
$149$	−2142.18	−1.17782	−0.588908	−	0.808200i	$-0.700442\pi$
$149$	−2142.18	−1.17782	−0.588908	+	0.808200i	$0.700442\pi$
$150$	51.1867	0.0278625
$151$	−61.0245	−0.0328881	−0.0164441	−	0.999865i	$-0.505235\pi$
$151$	−61.0245	−0.0328881	−0.0164441	+	0.999865i	$0.505235\pi$
$152$	−2081.93	−1.11097
$153$	−195.115	−0.103099
$154$	−123.032	−0.0643779
$155$	121.044	0.0627259
$156$	0	0
$157$	1119.64	0.569152	0.284576	−	0.958653i	$-0.408147\pi$
$157$	1119.64	0.569152	0.284576	+	0.958653i	$0.408147\pi$
$158$	1380.01	0.694858
$159$	242.293	0.120849
$160$	−2469.95	−1.22041
$161$	−986.239	−0.482774
$162$	−1273.48	−0.617620
$163$	1187.64	0.570693	0.285346	−	0.958424i	$-0.407891\pi$
$163$	1187.64	0.570693	0.285346	+	0.958424i	$0.407891\pi$
$164$	282.250	0.134390
$165$	66.3312	0.0312962
$166$	7.53436	0.00352277
$167$	−80.7132	−0.0373999	−0.0186999	−	0.999825i	$-0.505953\pi$
$167$	−80.7132	−0.0373999	−0.0186999	+	0.999825i	$0.505953\pi$
$168$	62.5922	0.0287446
$169$	0	0
$170$	−179.351	−0.0809151
$171$	2440.53	1.09141
$172$	−112.612	−0.0499221
$173$	−2821.81	−1.24011	−0.620053	−	0.784560i	$-0.712889\pi$
$173$	−2821.81	−1.24011	−0.620053	+	0.784560i	$0.712889\pi$
$174$	160.761	0.0700419
$175$	−411.644	−0.177813
$176$	25.2257	0.0108037
$177$	56.6316	0.0240491
$178$	−517.558	−0.217936
$179$	−4276.88	−1.78586	−0.892930	−	0.450197i	$-0.851354\pi$
$179$	−4276.88	−1.78586	−0.892930	+	0.450197i	$0.851354\pi$
$180$	1782.58	0.738142
$181$	1075.77	0.441774	0.220887	−	0.975299i	$-0.429105\pi$
$181$	1075.77	0.441774	0.220887	+	0.975299i	$0.429105\pi$
$182$	0	0
$183$	−105.933	−0.0427910
$184$	3598.90	1.44193
$185$	1828.00	0.726470
$186$	6.83136	0.00269301
$187$	−80.0566	−0.0313065
$188$	5.85535	0.00227152
$189$	−147.268	−0.0566783
$190$	2243.35	0.856577
$191$	−1011.93	−0.383355	−0.191678	−	0.981458i	$-0.561393\pi$
$191$	−1011.93	−0.383355	−0.191678	+	0.981458i	$0.561393\pi$
$192$	−147.407	−0.0554073
$193$	−4392.92	−1.63839	−0.819195	−	0.573515i	$-0.805579\pi$
$193$	−4392.92	−1.63839	−0.819195	+	0.573515i	$0.805579\pi$
$194$	1146.83	0.424420
$195$	0	0
$196$	1462.46	0.532966
$197$	−862.072	−0.311777	−0.155889	−	0.987775i	$-0.549824\pi$
$197$	−862.072	−0.311777	−0.155889	+	0.987775i	$0.549824\pi$
$198$	−526.288	−0.188897
$199$	−2945.48	−1.04925	−0.524623	−	0.851335i	$-0.675794\pi$
$199$	−2945.48	−1.04925	−0.524623	+	0.851335i	$0.675794\pi$
$200$	1502.14	0.531085
$201$	174.116	0.0611006
$202$	2579.55	0.898499
$203$	−1292.84	−0.446994
$204$	15.3033	0.00525218
$205$	−809.428	−0.275770
$206$	−1489.83	−0.503889
$207$	−4218.78	−1.41655
$208$	0	0
$209$	1001.36	0.331414
$210$	−67.4452	−0.0221627
$211$	1900.32	0.620017	0.310008	−	0.950734i	$-0.399668\pi$
$211$	1900.32	0.620017	0.310008	+	0.950734i	$0.399668\pi$
$212$	2671.64	0.865515
$213$	−330.967	−0.106467
$214$	−1327.48	−0.424042
$215$	322.946	0.102441
$216$	537.399	0.169284
$217$	−54.9378	−0.0171863
$218$	2140.24	0.664934
$219$	−380.846	−0.117512
$220$	731.401	0.224141
$221$	0	0
$222$	103.166	0.0311895
$223$	341.505	0.102551	0.0512755	−	0.998685i	$-0.483671\pi$
$223$	341.505	0.102551	0.0512755	+	0.998685i	$0.483671\pi$
$224$	1121.02	0.334381
$225$	−1760.87	−0.521738
$226$	199.046	0.0585856
$227$	−5870.03	−1.71633	−0.858166	−	0.513372i	$-0.828396\pi$
$227$	−5870.03	−1.71633	−0.858166	+	0.513372i	$0.828396\pi$
$228$	−191.416	−0.0556002
$229$	3097.85	0.893937	0.446969	−	0.894550i	$-0.352504\pi$
$229$	3097.85	0.893937	0.446969	+	0.894550i	$0.352504\pi$
$230$	−3877.94	−1.11175
$231$	−30.1054	−0.00857485
$232$	4717.74	1.33506
$233$	1283.22	0.360800	0.180400	−	0.983593i	$-0.442261\pi$
$233$	1283.22	0.360800	0.180400	+	0.983593i	$0.442261\pi$
$234$	0	0
$235$	−16.7918	−0.00466118
$236$	624.449	0.172238
$237$	337.682	0.0925520
$238$	81.4010	0.0221699
$239$	1303.95	0.352910	0.176455	−	0.984309i	$-0.443537\pi$
$239$	1303.95	0.352910	0.176455	+	0.984309i	$0.443537\pi$
$240$	13.8285	0.00371928
$241$	2634.57	0.704181	0.352091	−	0.935966i	$-0.385471\pi$
$241$	2634.57	0.704181	0.352091	+	0.935966i	$0.385471\pi$
$242$	−215.939	−0.0573597
$243$	−946.059	−0.249752
$244$	−1168.07	−0.306466
$245$	−4194.00	−1.09365
$246$	−45.6815	−0.0118396
$247$	0	0
$248$	200.474	0.0513312
$249$	1.84363	0.000469217 0
$250$	1461.81	0.369812
$251$	−4637.86	−1.16629	−0.583146	−	0.812367i	$-0.698178\pi$
$251$	−4637.86	−1.16629	−0.583146	+	0.812367i	$0.698178\pi$
$252$	−809.050	−0.202243
$253$	−1730.99	−0.430144
$254$	1900.56	0.469496
$255$	−43.8864	−0.0107775
$256$	−4179.08	−1.02028
$257$	−5846.25	−1.41898	−0.709492	−	0.704713i	$-0.751076\pi$
$257$	−5846.25	−1.41898	−0.709492	+	0.704713i	$0.751076\pi$
$258$	18.2261	0.00439808
$259$	−829.663	−0.199045
$260$	0	0
$261$	−5530.33	−1.31157
$262$	−1481.50	−0.349342
$263$	−4194.29	−0.983388	−0.491694	−	0.870768i	$-0.663622\pi$
$263$	−4194.29	−0.983388	−0.491694	+	0.870768i	$0.663622\pi$
$264$	109.858	0.0256110
$265$	−7661.66	−1.77605
$266$	−1018.18	−0.234694
$267$	−126.644	−0.0290281
$268$	1919.89	0.437598
$269$	−4794.54	−1.08672	−0.543361	−	0.839499i	$-0.682849\pi$
$269$	−4794.54	−1.08672	−0.543361	+	0.839499i	$0.682849\pi$
$270$	−579.065	−0.130521
$271$	6126.50	1.37328	0.686639	−	0.726998i	$-0.259085\pi$
$271$	6126.50	1.37328	0.686639	+	0.726998i	$0.259085\pi$
$272$	−16.6899	−0.00372050
$273$	0	0
$274$	−5135.87	−1.13237
$275$	−722.493	−0.158429
$276$	330.889	0.0721637
$277$	107.307	0.0232761	0.0116380	−	0.999932i	$-0.496295\pi$
$277$	107.307	0.0232761	0.0116380	+	0.999932i	$0.496295\pi$
$278$	−4037.20	−0.870990
$279$	−235.004	−0.0504278
$280$	−1979.26	−0.422441
$281$	−1668.54	−0.354223	−0.177111	−	0.984191i	$-0.556675\pi$
$281$	−1668.54	−0.354223	−0.177111	+	0.984191i	$0.556675\pi$
$282$	−0.947677	−0.000200118 0
$283$	−7560.50	−1.58807	−0.794037	−	0.607869i	$-0.792025\pi$
$283$	−7560.50	−1.58807	−0.794037	+	0.607869i	$0.792025\pi$
$284$	−3649.40	−0.762508
$285$	548.938	0.114092
$286$	0	0
$287$	367.371	0.0755583
$288$	4795.34	0.981139
$289$	−4860.03	−0.989219
$290$	−5083.52	−1.02936
$291$	280.624	0.0565309
$292$	−4199.40	−0.841614
$293$	−5087.18	−1.01432	−0.507161	−	0.861851i	$-0.669305\pi$
$293$	−5087.18	−1.01432	−0.507161	+	0.861851i	$0.669305\pi$
$294$	−236.696	−0.0469537
$295$	−1790.78	−0.353434
$296$	3027.54	0.594500
$297$	−258.477	−0.0504995
$298$	3822.98	0.743151
$299$	0	0
$300$	138.109	0.0265791
$301$	−146.574	−0.0280677
$302$	108.905	0.0207510
$303$	631.206	0.119676
$304$	208.761	0.0393856
$305$	3349.75	0.628872
$306$	348.205	0.0650508
$307$	−1124.24	−0.209002	−0.104501	−	0.994525i	$-0.533325\pi$
$307$	−1124.24	−0.209002	−0.104501	+	0.994525i	$0.533325\pi$
$308$	−331.958	−0.0614125
$309$	−364.555	−0.0671158
$310$	−216.018	−0.0395774
$311$	10793.4	1.96796	0.983981	−	0.178273i	$-0.0570510\pi$
$311$	10793.4	1.96796	0.983981	+	0.178273i	$0.0570510\pi$
$312$	0	0
$313$	−7854.46	−1.41840	−0.709201	−	0.705006i	$-0.750944\pi$
$313$	−7854.46	−1.41840	−0.709201	+	0.705006i	$0.750944\pi$
$314$	−1998.13	−0.359111
$315$	2320.17	0.415006
$316$	3723.45	0.662850
$317$	−9045.35	−1.60264	−0.801321	−	0.598234i	$-0.795869\pi$
$317$	−9045.35	−1.60264	−0.801321	+	0.598234i	$0.795869\pi$
$318$	−432.400	−0.0762509
$319$	−2269.12	−0.398265
$320$	4661.24	0.814285
$321$	−324.830	−0.0564805
$322$	1760.06	0.304610
$323$	−662.525	−0.114130
$324$	−3436.04	−0.589170
$325$	0	0
$326$	−2119.48	−0.360083
$327$	523.709	0.0885663
$328$	−1340.58	−0.225674
$329$	7.62122	0.00127712
$330$	−118.376	−0.0197466
$331$	982.613	0.163170	0.0815851	−	0.996666i	$-0.474002\pi$
$331$	982.613	0.163170	0.0815851	+	0.996666i	$0.474002\pi$
$332$	20.3288	0.00336050
$333$	−3549.01	−0.584037
$334$	144.042	0.0235977
$335$	−5505.82	−0.897955
$336$	−6.27628	−0.00101904
$337$	1708.61	0.276184	0.138092	−	0.990419i	$-0.455903\pi$
$337$	1708.61	0.276184	0.138092	+	0.990419i	$0.455903\pi$
$338$	0	0
$339$	48.7057	0.00780334
$340$	−483.913	−0.0771878
$341$	−96.4236	−0.0153127
$342$	−4355.41	−0.688636
$343$	4053.20	0.638052
$344$	534.866	0.0838315
$345$	−948.914	−0.148081
$346$	5035.85	0.782454
$347$	−12030.7	−1.86121	−0.930604	−	0.366027i	$-0.880718\pi$
$347$	−12030.7	−1.86121	−0.930604	+	0.366027i	$0.880718\pi$
$348$	433.757	0.0668155
$349$	10029.2	1.53825	0.769124	−	0.639100i	$-0.220693\pi$
$349$	10029.2	1.53825	0.769124	+	0.639100i	$0.220693\pi$
$350$	734.626	0.112193
$351$	0	0
$352$	1967.55	0.297929
$353$	−8076.65	−1.21778	−0.608890	−	0.793254i	$-0.708385\pi$
$353$	−8076.65	−1.21778	−0.608890	+	0.793254i	$0.708385\pi$
$354$	−101.066	−0.0151740
$355$	10465.7	1.56467
$356$	−1396.44	−0.207897
$357$	19.9185	0.00295293
$358$	7632.58	1.12680
$359$	9147.36	1.34479	0.672394	−	0.740193i	$-0.265266\pi$
$359$	9147.36	1.34479	0.672394	+	0.740193i	$0.265266\pi$
$360$	−8466.58	−1.23952
$361$	1427.98	0.208191
$362$	−1919.83	−0.278741
$363$	−52.8393	−0.00764006
$364$	0	0
$365$	12042.9	1.72700
$366$	189.049	0.0269993
$367$	3621.72	0.515129	0.257565	−	0.966261i	$-0.417080\pi$
$367$	3621.72	0.515129	0.257565	+	0.966261i	$0.417080\pi$
$368$	−360.871	−0.0511187
$369$	1571.48	0.221702
$370$	−3262.27	−0.458371
$371$	3477.36	0.486619
$372$	18.4319	0.00256896
$373$	−11583.7	−1.60800	−0.803998	−	0.594631i	$-0.797298\pi$
$373$	−11583.7	−1.60800	−0.803998	+	0.594631i	$0.797298\pi$
$374$	142.870	0.0197531
$375$	357.699	0.0492574
$376$	−27.8107	−0.00381444
$377$	0	0
$378$	262.818	0.0357616
$379$	−7905.07	−1.07139	−0.535694	−	0.844412i	$-0.679950\pi$
$379$	−7905.07	−1.07139	−0.535694	+	0.844412i	$0.679950\pi$
$380$	6052.87	0.817120
$381$	465.060	0.0625347
$382$	1805.91	0.241881
$383$	−1210.01	−0.161433	−0.0807164	−	0.996737i	$-0.525721\pi$
$383$	−1210.01	−0.161433	−0.0807164	+	0.996737i	$0.525721\pi$
$384$	−361.812	−0.0480824
$385$	951.979	0.126019
$386$	7839.68	1.03375
$387$	−626.992	−0.0823561
$388$	3094.31	0.404870
$389$	9387.93	1.22362	0.611808	−	0.791006i	$-0.290442\pi$
$389$	9387.93	1.22362	0.611808	+	0.791006i	$0.290442\pi$
$390$	0	0
$391$	1145.26	0.148129
$392$	−6946.13	−0.894981
$393$	−362.517	−0.0465307
$394$	1538.47	0.196718
$395$	−10678.0	−1.36018
$396$	−1420.00	−0.180196
$397$	−9369.80	−1.18453	−0.592263	−	0.805745i	$-0.701765\pi$
$397$	−9369.80	−1.18453	−0.592263	+	0.805745i	$0.701765\pi$
$398$	5256.56	0.662029
$399$	−249.144	−0.0312601
$400$	−150.623	−0.0188279
$401$	−8435.01	−1.05043	−0.525217	−	0.850968i	$-0.676016\pi$
$401$	−8435.01	−1.05043	−0.525217	+	0.850968i	$0.676016\pi$
$402$	−310.731	−0.0385519
$403$	0	0
$404$	6960.00	0.857111
$405$	9853.77	1.20898
$406$	2307.23	0.282034
$407$	−1456.18	−0.177346
$408$	−72.6849	−0.00881970
$409$	−12957.1	−1.56647	−0.783234	−	0.621727i	$-0.786431\pi$
$409$	−12957.1	−1.56647	−0.783234	+	0.621727i	$0.786431\pi$
$410$	1444.52	0.173999
$411$	−1256.73	−0.150827
$412$	−4019.76	−0.480678
$413$	812.771	0.0968374
$414$	7528.91	0.893782
$415$	−58.2983	−0.00689578
$416$	0	0
$417$	−987.886	−0.116012
$418$	−1787.05	−0.209108
$419$	−16832.1	−1.96254	−0.981269	−	0.192645i	$-0.938294\pi$
$419$	−16832.1	−1.96254	−0.981269	+	0.192645i	$0.938294\pi$
$420$	−181.976	−0.0211418
$421$	−6636.81	−0.768310	−0.384155	−	0.923269i	$-0.625507\pi$
$421$	−6636.81	−0.768310	−0.384155	+	0.923269i	$0.625507\pi$
$422$	−3391.35	−0.391204
$423$	32.6009	0.00374730
$424$	−12689.3	−1.45341
$425$	478.019	0.0545584
$426$	590.648	0.0671761
$427$	−1520.33	−0.172305
$428$	−3581.74	−0.404509
$429$	0	0
$430$	−576.336	−0.0646357
$431$	8858.77	0.990051	0.495026	−	0.868878i	$-0.335159\pi$
$431$	8858.77	0.990051	0.495026	+	0.868878i	$0.335159\pi$
$432$	−53.8864	−0.00600141
$433$	2800.00	0.310761	0.155380	−	0.987855i	$-0.450340\pi$
$433$	2800.00	0.310761	0.155380	+	0.987855i	$0.450340\pi$
$434$	98.0429	0.0108438
$435$	−1243.91	−0.137106
$436$	5774.68	0.634305
$437$	−14325.2	−1.56811
$438$	679.664	0.0741452
$439$	−915.084	−0.0994865	−0.0497432	−	0.998762i	$-0.515840\pi$
$439$	−915.084	−0.0994865	−0.0497432	+	0.998762i	$0.515840\pi$
$440$	−3473.88	−0.376388
$441$	8142.55	0.879230
$442$	0	0
$443$	14368.8	1.54104	0.770522	−	0.637414i	$-0.219996\pi$
$443$	14368.8	1.54104	0.770522	+	0.637414i	$0.219996\pi$
$444$	278.357	0.0297528
$445$	4004.68	0.426607
$446$	−609.456	−0.0647053
$447$	935.466	0.0989844
$448$	−2115.57	−0.223106
$449$	−9106.61	−0.957165	−0.478583	−	0.878042i	$-0.658849\pi$
$449$	−9106.61	−0.957165	−0.478583	+	0.878042i	$0.658849\pi$
$450$	3142.47	0.329194
$451$	644.788	0.0673213
$452$	537.054	0.0558869
$453$	26.6487	0.00276394
$454$	10475.8	1.08293
$455$	0	0
$456$	909.155	0.0933664
$457$	6028.70	0.617091	0.308546	−	0.951210i	$-0.400158\pi$
$457$	6028.70	0.617091	0.308546	+	0.951210i	$0.400158\pi$
$458$	−5528.47	−0.564036
$459$	171.015	0.0173906
$460$	−10463.2	−1.06054
$461$	12229.5	1.23555	0.617773	−	0.786357i	$-0.288035\pi$
$461$	12229.5	1.23555	0.617773	+	0.786357i	$0.288035\pi$
$462$	53.7266	0.00541037
$463$	12787.0	1.28351	0.641753	−	0.766912i	$-0.278208\pi$
$463$	12787.0	1.28351	0.641753	+	0.766912i	$0.278208\pi$
$464$	−473.059	−0.0473302
$465$	−52.8586	−0.00527153
$466$	−2290.05	−0.227649
$467$	−18316.4	−1.81495	−0.907477	−	0.420101i	$-0.861995\pi$
$467$	−18316.4	−1.81495	−0.907477	+	0.420101i	$0.861995\pi$
$468$	0	0
$469$	2498.90	0.246031
$470$	29.9670	0.00294101
$471$	−488.933	−0.0478319
$472$	−2965.90	−0.289230
$473$	−257.258	−0.0250079
$474$	−602.633	−0.0583963
$475$	−5979.14	−0.577562
$476$	219.631	0.0211487
$477$	14874.9	1.42783
$478$	−2327.05	−0.222671
$479$	−14458.2	−1.37915	−0.689576	−	0.724214i	$-0.742203\pi$
$479$	−14458.2	−1.37915	−0.689576	+	0.724214i	$0.742203\pi$
$480$	1078.60	0.102564
$481$	0	0
$482$	−4701.70	−0.444308
$483$	430.679	0.0405726
$484$	−582.632	−0.0547175
$485$	−8873.76	−0.830797
$486$	1688.35	0.157583
$487$	1790.68	0.166619	0.0833096	−	0.996524i	$-0.473451\pi$
$487$	1790.68	0.166619	0.0833096	+	0.996524i	$0.473451\pi$
$488$	5547.87	0.514632
$489$	−518.627	−0.0479614
$490$	7484.68	0.690048
$491$	−10537.8	−0.968566	−0.484283	−	0.874911i	$-0.660919\pi$
$491$	−10537.8	−0.968566	−0.484283	+	0.874911i	$0.660919\pi$
$492$	−123.255	−0.0112943
$493$	1501.31	0.137151
$494$	0	0
$495$	4072.23	0.369764
$496$	−20.1021	−0.00181978
$497$	−4750.00	−0.428705
$498$	−3.29017	−0.000296056 0
$499$	−587.471	−0.0527031	−0.0263515	−	0.999653i	$-0.508389\pi$
$499$	−587.471	−0.0527031	−0.0263515	+	0.999653i	$0.508389\pi$
$500$	3944.17	0.352777
$501$	35.2465	0.00314311
$502$	8276.81	0.735880
$503$	−2626.00	−0.232779	−0.116389	−	0.993204i	$-0.537132\pi$
$503$	−2626.00	−0.232779	−0.116389	+	0.993204i	$0.537132\pi$
$504$	3842.68	0.339616
$505$	−19959.7	−1.75880
$506$	3089.15	0.271402
$507$	0	0
$508$	5127.98	0.447869
$509$	1866.54	0.162540	0.0812702	−	0.996692i	$-0.474102\pi$
$509$	1866.54	0.162540	0.0812702	+	0.996692i	$0.474102\pi$
$510$	78.3203	0.00680016
$511$	−5465.86	−0.473181
$512$	829.763	0.0716224
$513$	−2139.08	−0.184099
$514$	10433.3	0.895318
$515$	11527.8	0.986357
$516$	49.1765	0.00419549
$517$	13.3763	0.00113789
$518$	1480.63	0.125589
$519$	1232.25	0.104219
$520$	0	0
$521$	3222.27	0.270960	0.135480	−	0.990780i	$-0.456742\pi$
$521$	3222.27	0.270960	0.135480	+	0.990780i	$0.456742\pi$
$522$	9869.52	0.827542
$523$	−1966.70	−0.164432	−0.0822159	−	0.996615i	$-0.526200\pi$
$523$	−1966.70	−0.164432	−0.0822159	+	0.996615i	$0.526200\pi$
$524$	−3997.30	−0.333250
$525$	179.760	0.0149435
$526$	7485.20	0.620476
$527$	63.7962	0.00527326
$528$	−11.0158	−0.000907953 0
$529$	12596.0	1.03526
$530$	13673.1	1.12061
$531$	3476.75	0.284139
$532$	−2747.19	−0.223883
$533$	0	0
$534$	226.011	0.0183155
$535$	10271.6	0.830057
$536$	−9118.77	−0.734834
$537$	1867.66	0.150085
$538$	8556.42	0.685675
$539$	3340.93	0.266983
$540$	−1562.40	−0.124509
$541$	1738.55	0.138163	0.0690813	−	0.997611i	$-0.477993\pi$
$541$	1738.55	0.138163	0.0690813	+	0.997611i	$0.477993\pi$
$542$	−10933.5	−0.866480
$543$	−469.775	−0.0371270
$544$	−1301.78	−0.102598
$545$	−16560.5	−1.30160
$546$	0	0
$547$	−16088.2	−1.25756	−0.628778	−	0.777585i	$-0.716445\pi$
$547$	−16088.2	−1.25756	−0.628778	+	0.777585i	$0.716445\pi$
$548$	−13857.3	−1.08021
$549$	−6503.45	−0.505574
$550$	1289.37	0.0999619
$551$	−18778.6	−1.45190
$552$	−1571.60	−0.121181
$553$	4846.38	0.372674
$554$	−191.502	−0.0146862
$555$	−798.264	−0.0610530
$556$	−10892.9	−0.830869
$557$	5299.01	0.403100	0.201550	−	0.979478i	$-0.435402\pi$
$557$	5299.01	0.403100	0.201550	+	0.979478i	$0.435402\pi$
$558$	419.393	0.0318178
$559$	0	0
$560$	198.465	0.0149762
$561$	34.9597	0.00263102
$562$	2977.70	0.223500
$563$	4712.27	0.352751	0.176375	−	0.984323i	$-0.443563\pi$
$563$	4712.27	0.352751	0.176375	+	0.984323i	$0.443563\pi$
$564$	−2.55696	−0.000190900 0
$565$	−1540.15	−0.114681
$566$	13492.6	1.00201
$567$	−4472.28	−0.331249
$568$	17333.3	1.28044
$569$	6604.36	0.486589	0.243295	−	0.969952i	$-0.421772\pi$
$569$	6604.36	0.486589	0.243295	+	0.969952i	$0.421772\pi$
$570$	−979.644	−0.0719873
$571$	−24702.2	−1.81043	−0.905215	−	0.424955i	$-0.860290\pi$
$571$	−24702.2	−1.81043	−0.905215	+	0.424955i	$0.860290\pi$
$572$	0	0
$573$	441.899	0.0322174
$574$	−655.617	−0.0476741
$575$	10335.8	0.749619
$576$	−9049.68	−0.654635
$577$	7484.46	0.540004	0.270002	−	0.962860i	$-0.412976\pi$
$577$	7484.46	0.540004	0.270002	+	0.962860i	$0.412976\pi$
$578$	8673.29	0.624155
$579$	1918.34	0.137691
$580$	−13716.0	−0.981943
$581$	26.4595	0.00188937
$582$	−500.807	−0.0356686
$583$	6103.26	0.433570
$584$	19945.6	1.41328
$585$	0	0
$586$	9078.67	0.639994
$587$	−20384.9	−1.43335	−0.716673	−	0.697409i	$-0.754336\pi$
$587$	−20384.9	−1.43335	−0.716673	+	0.697409i	$0.754336\pi$
$588$	−638.639	−0.0447909
$589$	−797.974	−0.0558233
$590$	3195.85	0.223002
$591$	376.457	0.0262020
$592$	−303.579	−0.0210760
$593$	1619.94	0.112180	0.0560900	−	0.998426i	$-0.482137\pi$
$593$	1619.94	0.112180	0.0560900	+	0.998426i	$0.482137\pi$
$594$	461.282	0.0318630
$595$	−629.852	−0.0433974
$596$	10314.9	0.708919
$597$	1286.26	0.0881793
$598$	0	0
$599$	248.581	0.0169562	0.00847808	−	0.999964i	$-0.497301\pi$
$599$	248.581	0.0169562	0.00847808	+	0.999964i	$0.497301\pi$
$600$	−655.965	−0.0446327
$601$	−18586.0	−1.26146	−0.630730	−	0.776003i	$-0.717244\pi$
$601$	−18586.0	−1.26146	−0.630730	+	0.776003i	$0.717244\pi$
$602$	261.579	0.0177095
$603$	10689.4	0.721901
$604$	293.842	0.0197951
$605$	1670.86	0.112281
$606$	−1126.46	−0.0755105
$607$	−13617.1	−0.910543	−0.455272	−	0.890353i	$-0.650458\pi$
$607$	−13617.1	−0.910543	−0.455272	+	0.890353i	$0.650458\pi$
$608$	16282.9	1.08612
$609$	564.569	0.0375657
$610$	−5978.01	−0.396791
$611$	0	0
$612$	939.505	0.0620543
$613$	9699.81	0.639106	0.319553	−	0.947568i	$-0.396467\pi$
$613$	9699.81	0.639106	0.319553	+	0.947568i	$0.396467\pi$
$614$	2006.33	0.131871
$615$	353.468	0.0231759
$616$	1576.67	0.103127
$617$	25421.1	1.65869	0.829346	−	0.558735i	$-0.188713\pi$
$617$	25421.1	1.65869	0.829346	+	0.558735i	$0.188713\pi$
$618$	650.590	0.0423472
$619$	8673.10	0.563169	0.281584	−	0.959536i	$-0.409140\pi$
$619$	8673.10	0.563169	0.281584	+	0.959536i	$0.409140\pi$
$620$	−582.846	−0.0377543
$621$	3697.69	0.238942
$622$	−19262.0	−1.24170
$623$	−1817.59	−0.116886
$624$	0	0
$625$	−19521.1	−1.24935
$626$	14017.2	0.894952
$627$	−437.283	−0.0278523
$628$	−5391.22	−0.342569
$629$	963.442	0.0610730
$630$	−4140.62	−0.261851
$631$	5610.32	0.353951	0.176976	−	0.984215i	$-0.443369\pi$
$631$	5610.32	0.353951	0.176976	+	0.984215i	$0.443369\pi$
$632$	−17685.0	−1.11309
$633$	−829.848	−0.0521066
$634$	16142.5	1.01120
$635$	−14705.9	−0.919032
$636$	−1166.67	−0.0727384
$637$	0	0
$638$	4049.51	0.251288
$639$	−20318.8	−1.25790
$640$	11441.0	0.706636
$641$	6780.75	0.417822	0.208911	−	0.977935i	$-0.433008\pi$
$641$	6780.75	0.417822	0.208911	+	0.977935i	$0.433008\pi$
$642$	579.697	0.0356368
$643$	11928.3	0.731582	0.365791	−	0.930697i	$-0.380798\pi$
$643$	11928.3	0.731582	0.365791	+	0.930697i	$0.380798\pi$
$644$	4748.88	0.290578
$645$	−141.027	−0.00860919
$646$	1182.35	0.0720110
$647$	−1726.95	−0.104936	−0.0524679	−	0.998623i	$-0.516709\pi$
$647$	−1726.95	−0.104936	−0.0524679	+	0.998623i	$0.516709\pi$
$648$	16319.9	0.989361
$649$	1426.53	0.0862806
$650$	0	0
$651$	23.9907	0.00144435
$652$	−5718.64	−0.343496
$653$	19822.6	1.18793	0.593965	−	0.804491i	$-0.297562\pi$
$653$	19822.6	1.18793	0.593965	+	0.804491i	$0.297562\pi$
$654$	−934.620	−0.0558815
$655$	11463.3	0.683832
$656$	134.423	0.00800053
$657$	−23381.0	−1.38840
$658$	−13.6010	−0.000805806 0
$659$	−5159.82	−0.305004	−0.152502	−	0.988303i	$-0.548733\pi$
$659$	−5159.82	−0.305004	−0.152502	+	0.988303i	$0.548733\pi$
$660$	−319.394	−0.0188370
$661$	26522.0	1.56064	0.780321	−	0.625379i	$-0.215056\pi$
$661$	26522.0	1.56064	0.780321	+	0.625379i	$0.215056\pi$
$662$	−1753.59	−0.102953
$663$	0	0
$664$	−96.5540	−0.00564310
$665$	7878.30	0.459410
$666$	6333.62	0.368502
$667$	32461.4	1.88442
$668$	388.646	0.0225107
$669$	−149.131	−0.00861846
$670$	9825.77	0.566571
$671$	−2668.40	−0.153521
$672$	−489.537	−0.0281016
$673$	−1867.06	−0.106939	−0.0534694	−	0.998569i	$-0.517028\pi$
$673$	−1867.06	−0.106939	−0.0534694	+	0.998569i	$0.517028\pi$
$674$	−3049.21	−0.174260
$675$	1543.37	0.0880063
$676$	0	0
$677$	−27586.9	−1.56610	−0.783050	−	0.621959i	$-0.786337\pi$
$677$	−27586.9	−1.56610	−0.783050	+	0.621959i	$0.786337\pi$
$678$	−86.9211	−0.00492357
$679$	4027.49	0.227630
$680$	2298.40	0.129617
$681$	2563.37	0.144242
$682$	172.079	0.00966166
$683$	−29300.6	−1.64152	−0.820759	−	0.571275i	$-0.806449\pi$
$683$	−29300.6	−1.64152	−0.820759	+	0.571275i	$0.806449\pi$
$684$	−11751.5	−0.656914
$685$	39739.5	2.21660
$686$	−7233.40	−0.402584
$687$	−1352.79	−0.0751271
$688$	−53.6323	−0.00297197
$689$	0	0
$690$	1693.45	0.0934326
$691$	10058.7	0.553767	0.276883	−	0.960904i	$-0.410698\pi$
$691$	10058.7	0.553767	0.276883	+	0.960904i	$0.410698\pi$
$692$	13587.4	0.746411
$693$	−1848.24	−0.101312
$694$	21470.1	1.17434
$695$	31238.4	1.70495
$696$	−2060.18	−0.112200
$697$	−426.608	−0.0231835
$698$	−17898.2	−0.970569
$699$	−560.365	−0.0303218
$700$	1982.12	0.107025
$701$	−16442.7	−0.885923	−0.442961	−	0.896541i	$-0.646072\pi$
$701$	−16442.7	−0.885923	−0.442961	+	0.896541i	$0.646072\pi$
$702$	0	0
$703$	−12050.9	−0.646527
$704$	−3713.13	−0.198784
$705$	7.33279	0.000391729 0
$706$	14413.7	0.768367
$707$	9059.00	0.481894
$708$	−272.689	−0.0144750
$709$	5548.35	0.293897	0.146948	−	0.989144i	$-0.453055\pi$
$709$	5548.35	0.293897	0.146948	+	0.989144i	$0.453055\pi$
$710$	−18677.2	−0.987243
$711$	20731.1	1.09350
$712$	6632.58	0.349110
$713$	1379.41	0.0724533
$714$	−35.5468	−0.00186318
$715$	0	0
$716$	20593.8	1.07490
$717$	−569.420	−0.0296588
$718$	−16324.5	−0.848504
$719$	26188.1	1.35835	0.679173	−	0.733978i	$-0.262338\pi$
$719$	26188.1	1.35835	0.679173	+	0.733978i	$0.262338\pi$
$720$	848.965	0.0439431
$721$	−5232.05	−0.270252
$722$	−2548.40	−0.131360
$723$	−1150.49	−0.0591798
$724$	−5179.97	−0.265901
$725$	13549.0	0.694063
$726$	94.2978	0.00482055
$727$	−435.047	−0.0221939	−0.0110970	−	0.999938i	$-0.503532\pi$
$727$	−435.047	−0.0221939	−0.0110970	+	0.999938i	$0.503532\pi$
$728$	0	0
$729$	−18853.8	−0.957872
$730$	−21492.0	−1.08966
$731$	170.208	0.00861201
$732$	510.080	0.0257556
$733$	−26121.5	−1.31626	−0.658130	−	0.752904i	$-0.728652\pi$
$733$	−26121.5	−1.31626	−0.658130	+	0.752904i	$0.728652\pi$
$734$	−6463.39	−0.325025
$735$	1831.47	0.0919113
$736$	−28147.2	−1.40967
$737$	4385.92	0.219210
$738$	−2804.50	−0.139885
$739$	20720.3	1.03141	0.515704	−	0.856767i	$-0.327530\pi$
$739$	20720.3	1.03141	0.515704	+	0.856767i	$0.327530\pi$
$740$	−8802.06	−0.437257
$741$	0	0
$742$	−6205.75	−0.307036
$743$	4650.94	0.229645	0.114823	−	0.993386i	$-0.463370\pi$
$743$	4650.94	0.229645	0.114823	+	0.993386i	$0.463370\pi$
$744$	−87.5448	−0.00431391
$745$	−29580.8	−1.45471
$746$	20672.5	1.01458
$747$	113.185	0.00554378
$748$	385.484	0.0188432
$749$	−4661.92	−0.227427
$750$	−638.356	−0.0310793
$751$	−3081.63	−0.149734	−0.0748670	−	0.997194i	$-0.523853\pi$
$751$	−3081.63	−0.149734	−0.0748670	+	0.997194i	$0.523853\pi$
$752$	2.78865	0.000135228 0
$753$	2025.30	0.0980160
$754$	0	0
$755$	−842.672	−0.0406198
$756$	709.118	0.0341143
$757$	8628.74	0.414289	0.207144	−	0.978310i	$-0.433583\pi$
$757$	8628.74	0.414289	0.207144	+	0.978310i	$0.433583\pi$
$758$	14107.5	0.676001
$759$	755.903	0.0361496
$760$	−28748.9	−1.37215
$761$	−16292.8	−0.776103	−0.388051	−	0.921638i	$-0.626852\pi$
$761$	−16292.8	−0.776103	−0.388051	+	0.921638i	$0.626852\pi$
$762$	−829.953	−0.0394567
$763$	7516.21	0.356625
$764$	4872.60	0.230739
$765$	−2694.29	−0.127336
$766$	2159.41	0.101857
$767$	0	0
$768$	1824.95	0.0857453
$769$	2003.48	0.0939496	0.0469748	−	0.998896i	$-0.485042\pi$
$769$	2003.48	0.0939496	0.0469748	+	0.998896i	$0.485042\pi$
$770$	−1698.92	−0.0795126
$771$	2552.99	0.119252
$772$	21152.5	0.986135
$773$	−27470.7	−1.27821	−0.639103	−	0.769121i	$-0.720694\pi$
$773$	−27470.7	−1.27821	−0.639103	+	0.769121i	$0.720694\pi$
$774$	1118.94	0.0519632
$775$	575.746	0.0266857
$776$	−14696.8	−0.679876
$777$	362.304	0.0167279
$778$	−16753.8	−0.772050
$779$	5336.08	0.245424
$780$	0	0
$781$	−8336.91	−0.381970
$782$	−2043.86	−0.0934632
$783$	4847.24	0.221234
$784$	696.506	0.0317286
$785$	15460.8	0.702954
$786$	646.954	0.0293589
$787$	22793.4	1.03240	0.516199	−	0.856469i	$-0.327346\pi$
$787$	22793.4	1.03240	0.516199	+	0.856469i	$0.327346\pi$
$788$	4151.00	0.187657
$789$	1831.60	0.0826446
$790$	19056.2	0.858213
$791$	699.019	0.0314213
$792$	6744.45	0.302593
$793$	0	0
$794$	16721.5	0.747386
$795$	3345.76	0.149260
$796$	14182.9	0.631533
$797$	16623.9	0.738833	0.369416	−	0.929264i	$-0.379558\pi$
$797$	16623.9	0.738833	0.369416	+	0.929264i	$0.379558\pi$
$798$	444.626	0.0197238
$799$	−8.85010	−0.000391857 0
$800$	−11748.3	−0.519206
$801$	−7774.99	−0.342966
$802$	15053.3	0.662779
$803$	−9593.35	−0.421597
$804$	−838.395	−0.0367760
$805$	−13618.7	−0.596269
$806$	0	0
$807$	2093.72	0.0913289
$808$	−33057.4	−1.43930
$809$	7610.80	0.330756	0.165378	−	0.986230i	$-0.447116\pi$
$809$	7610.80	0.330756	0.165378	+	0.986230i	$0.447116\pi$
$810$	−17585.2	−0.762816
$811$	37978.3	1.64439	0.822195	−	0.569206i	$-0.192749\pi$
$811$	37978.3	1.64439	0.822195	+	0.569206i	$0.192749\pi$
$812$	6225.23	0.269043
$813$	−2675.37	−0.115411
$814$	2598.72	0.111898
$815$	16399.8	0.704857
$816$	7.28829	0.000312673 0
$817$	−2129.00	−0.0911679
$818$	23123.4	0.988374
$819$	0	0
$820$	3897.51	0.165984
$821$	−15185.2	−0.645513	−0.322757	−	0.946482i	$-0.604610\pi$
$821$	−15185.2	−0.645513	−0.322757	+	0.946482i	$0.604610\pi$
$822$	2242.77	0.0951651
$823$	41072.6	1.73961	0.869805	−	0.493395i	$-0.164244\pi$
$823$	41072.6	1.73961	0.869805	+	0.493395i	$0.164244\pi$
$824$	19092.4	0.807177
$825$	315.504	0.0133145
$826$	−1450.48	−0.0611003
$827$	32185.8	1.35334	0.676669	−	0.736288i	$-0.263423\pi$
$827$	32185.8	1.35334	0.676669	+	0.736288i	$0.263423\pi$
$828$	20314.0	0.852611
$829$	−7591.68	−0.318058	−0.159029	−	0.987274i	$-0.550836\pi$
$829$	−7591.68	−0.318058	−0.159029	+	0.987274i	$0.550836\pi$
$830$	104.040	0.00435094
$831$	−46.8598	−0.00195614
$832$	0	0
$833$	−2210.44	−0.0919415
$834$	1763.00	0.0731986
$835$	−1114.55	−0.0461922
$836$	−4821.70	−0.199476
$837$	205.977	0.00850611
$838$	30038.9	1.23828
$839$	−43099.2	−1.77348	−0.886740	−	0.462269i	$-0.847035\pi$
$839$	−43099.2	−1.77348	−0.886740	+	0.462269i	$0.847035\pi$
$840$	864.319	0.0355022
$841$	18164.1	0.744764
$842$	11844.2	0.484771
$843$	728.631	0.0297691
$844$	−9150.32	−0.373184
$845$	0	0
$846$	−58.1801	−0.00236439
$847$	−758.343	−0.0307639
$848$	1272.39	0.0515259
$849$	3301.58	0.133463
$850$	−853.080	−0.0344240
$851$	20831.6	0.839129
$852$	1593.65	0.0640817
$853$	−34783.3	−1.39620	−0.698099	−	0.716002i	$-0.745970\pi$
$853$	−34783.3	−1.39620	−0.698099	+	0.716002i	$0.745970\pi$
$854$	2713.21	0.108717
$855$	33700.6	1.34800
$856$	17011.9	0.679270
$857$	−7297.35	−0.290866	−0.145433	−	0.989368i	$-0.546458\pi$
$857$	−7297.35	−0.290866	−0.145433	+	0.989368i	$0.546458\pi$
$858$	0	0
$859$	26293.7	1.04439	0.522193	−	0.852827i	$-0.325114\pi$
$859$	26293.7	1.04439	0.522193	+	0.852827i	$0.325114\pi$
$860$	−1555.03	−0.0616584
$861$	−160.427	−0.00634997
$862$	−15809.5	−0.624680
$863$	38584.9	1.52195	0.760976	−	0.648780i	$-0.224721\pi$
$863$	38584.9	1.52195	0.760976	+	0.648780i	$0.224721\pi$
$864$	−4203.03	−0.165498
$865$	−38965.6	−1.53164
$866$	−4996.93	−0.196077
$867$	2122.32	0.0831346
$868$	264.533	0.0103443
$869$	8506.08	0.332047
$870$	2219.91	0.0865081
$871$	0	0
$872$	−27427.5	−1.06515
$873$	17228.2	0.667910
$874$	25564.9	0.989413
$875$	5133.66	0.198342
$876$	1833.83	0.0707298
$877$	−12142.2	−0.467517	−0.233758	−	0.972295i	$-0.575102\pi$
$877$	−12142.2	−0.467517	−0.233758	+	0.972295i	$0.575102\pi$
$878$	1633.07	0.0627717
$879$	2221.51	0.0852443
$880$	348.335	0.0133436
$881$	−7010.46	−0.268091	−0.134046	−	0.990975i	$-0.542797\pi$
$881$	−7010.46	−0.268091	−0.134046	+	0.990975i	$0.542797\pi$
$882$	−14531.3	−0.554756
$883$	−29064.0	−1.10768	−0.553839	−	0.832624i	$-0.686838\pi$
$883$	−29064.0	−1.10768	−0.553839	+	0.832624i	$0.686838\pi$
$884$	0	0
$885$	782.011	0.0297028
$886$	−25642.8	−0.972332
$887$	20079.6	0.760097	0.380049	−	0.924967i	$-0.375907\pi$
$887$	20079.6	0.760097	0.380049	+	0.924967i	$0.375907\pi$
$888$	−1322.09	−0.0499622
$889$	6674.49	0.251805
$890$	−7146.82	−0.269171
$891$	−7849.49	−0.295138
$892$	−1644.40	−0.0617247
$893$	110.699	0.00414825
$894$	−1669.45	−0.0624549
$895$	−59058.3	−2.20570
$896$	−5192.69	−0.193611
$897$	0	0
$898$	16251.8	0.603930
$899$	1808.24	0.0670836
$900$	8478.82	0.314030
$901$	−4038.06	−0.149309
$902$	−1150.70	−0.0424768
$903$	64.0072	0.00235883
$904$	−2550.80	−0.0938479
$905$	14855.0	0.545631
$906$	−47.5577	−0.00174393
$907$	−16287.4	−0.596267	−0.298133	−	0.954524i	$-0.596364\pi$
$907$	−16287.4	−0.596267	−0.298133	+	0.954524i	$0.596364\pi$
$908$	28265.0	1.03305
$909$	38751.2	1.41397
$910$	0	0
$911$	17983.5	0.654028	0.327014	−	0.945020i	$-0.393958\pi$
$911$	17983.5	0.654028	0.327014	+	0.945020i	$0.393958\pi$
$912$	−91.1632	−0.00331000
$913$	46.4402	0.00168340
$914$	−10758.9	−0.389358
$915$	−1462.79	−0.0528508
$916$	−14916.6	−0.538055
$917$	−5202.81	−0.187363
$918$	−305.195	−0.0109727
$919$	31433.3	1.12828	0.564139	−	0.825680i	$-0.309208\pi$
$919$	31433.3	1.12828	0.564139	+	0.825680i	$0.309208\pi$
$920$	49696.3	1.78091
$921$	490.941	0.0175647
$922$	−21825.0	−0.779576
$923$	0	0
$924$	144.962	0.00516114
$925$	8694.85	0.309065
$926$	−22819.9	−0.809837
$927$	−22380.9	−0.792970
$928$	−36897.7	−1.30520
$929$	24872.5	0.878406	0.439203	−	0.898388i	$-0.355261\pi$
$929$	24872.5	0.878406	0.439203	+	0.898388i	$0.355261\pi$
$930$	94.3324	0.00332611
$931$	27648.6	0.973304
$932$	−6178.87	−0.217163
$933$	−4713.34	−0.165389
$934$	32687.8	1.14516
$935$	−1105.48	−0.0386664
$936$	0	0
$937$	−53379.0	−1.86106	−0.930531	−	0.366212i	$-0.880654\pi$
$937$	−53379.0	−1.86106	−0.930531	+	0.366212i	$0.880654\pi$
$938$	−4459.58	−0.155235
$939$	3429.95	0.119204
$940$	80.8550	0.00280553
$941$	7194.22	0.249230	0.124615	−	0.992205i	$-0.460230\pi$
$941$	7194.22	0.249230	0.124615	+	0.992205i	$0.460230\pi$
$942$	872.558	0.0301799
$943$	−9224.15	−0.318536
$944$	297.398	0.0102537
$945$	−2033.59	−0.0700028
$946$	459.107	0.0157789
$947$	14187.4	0.486829	0.243414	−	0.969922i	$-0.421732\pi$
$947$	14187.4	0.486829	0.243414	+	0.969922i	$0.421732\pi$
$948$	−1625.99	−0.0557064
$949$	0	0
$950$	10670.5	0.364417
$951$	3950.00	0.134687
$952$	−1043.17	−0.0355139
$953$	24263.6	0.824739	0.412369	−	0.911017i	$-0.364701\pi$
$953$	24263.6	0.824739	0.412369	+	0.911017i	$0.364701\pi$
$954$	−26546.0	−0.900901
$955$	−13973.5	−0.473479
$956$	−6278.71	−0.212414
$957$	990.899	0.0334705
$958$	25802.4	0.870185
$959$	−18036.4	−0.607326
$960$	−2035.51	−0.0684331
$961$	−29714.2	−0.997421
$962$	0	0
$963$	−19942.1	−0.667315
$964$	−12685.8	−0.423842
$965$	−60660.7	−2.02356
$966$	−768.597	−0.0255996
$967$	33519.9	1.11471	0.557357	−	0.830273i	$-0.311816\pi$
$967$	33519.9	1.11471	0.557357	+	0.830273i	$0.311816\pi$
$968$	2767.28	0.0918842
$969$	289.317	0.00959154
$970$	15836.3	0.524198
$971$	50383.3	1.66517	0.832584	−	0.553899i	$-0.186861\pi$
$971$	50383.3	1.66517	0.832584	+	0.553899i	$0.186861\pi$
$972$	4555.41	0.150324
$973$	−14178.0	−0.467140
$974$	−3195.68	−0.105130
$975$	0	0
$976$	−556.299	−0.0182446
$977$	6899.67	0.225936	0.112968	−	0.993599i	$-0.463964\pi$
$977$	6899.67	0.225936	0.112968	+	0.993599i	$0.463964\pi$
$978$	925.550	0.0302616
$979$	−3190.12	−0.104144
$980$	20194.7	0.658262
$981$	32151.7	1.04641
$982$	18806.0	0.611124
$983$	23448.4	0.760822	0.380411	−	0.924818i	$-0.375783\pi$
$983$	23448.4	0.760822	0.380411	+	0.924818i	$0.375783\pi$
$984$	585.416	0.0189658
$985$	−11904.1	−0.385073
$986$	−2679.26	−0.0865365
$987$	−3.32810	−0.000107330 0
$988$	0	0
$989$	3680.26	0.118327
$990$	−7267.37	−0.233305
$991$	−40065.0	−1.28427	−0.642133	−	0.766594i	$-0.721950\pi$
$991$	−40065.0	−1.28427	−0.642133	+	0.766594i	$0.721950\pi$
$992$	−1567.92	−0.0501830
$993$	−429.096	−0.0137129
$994$	8476.92	0.270495
$995$	−40673.4	−1.29591
$996$	−8.87733	−0.000282419 0
$997$	−5206.10	−0.165375	−0.0826874	−	0.996576i	$-0.526350\pi$
$997$	−5206.10	−0.165375	−0.0826874	+	0.996576i	$0.526350\pi$
$998$	1048.41	0.0332534
$999$	3110.64	0.0985149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.14	yes	39
13.12	even	2		1859.4.a.n.1.26	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.26	✓	39	13.12	even	2
1859.4.a.o.1.14	yes	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.78462 q^{2} -0.436688 q^{3} -4.81514 q^{4} +13.8087 q^{5} +0.779321 q^{6} -6.26730 q^{7} +22.8701 q^{8} -26.8093 q^{9} +O(q^{10})\)	\(q-1.78462 q^{2} -0.436688 q^{3} -4.81514 q^{4} +13.8087 q^{5} +0.779321 q^{6} -6.26730 q^{7} +22.8701 q^{8} -26.8093 q^{9} -24.6433 q^{10} -11.0000 q^{11} +2.10272 q^{12} +11.1847 q^{14} -6.03011 q^{15} -2.29324 q^{16} +7.27787 q^{17} +47.8443 q^{18} -91.0329 q^{19} -66.4910 q^{20} +2.73686 q^{21} +19.6308 q^{22} +157.363 q^{23} -9.98711 q^{24} +65.6811 q^{25} +23.4979 q^{27} +30.1780 q^{28} +206.284 q^{29} +10.7614 q^{30} +8.76578 q^{31} -178.868 q^{32} +4.80357 q^{33} -12.9882 q^{34} -86.5435 q^{35} +129.091 q^{36} +132.380 q^{37} +162.459 q^{38} +315.807 q^{40} -58.6171 q^{41} -4.88424 q^{42} +23.3871 q^{43} +52.9666 q^{44} -370.203 q^{45} -280.832 q^{46} -1.21603 q^{47} +1.00143 q^{48} -303.721 q^{49} -117.216 q^{50} -3.17816 q^{51} -554.842 q^{53} -41.9347 q^{54} -151.896 q^{55} -143.334 q^{56} +39.7530 q^{57} -368.138 q^{58} -129.684 q^{59} +29.0358 q^{60} +242.582 q^{61} -15.6436 q^{62} +168.022 q^{63} +337.557 q^{64} -8.57253 q^{66} -398.720 q^{67} -35.0440 q^{68} -68.7184 q^{69} +154.447 q^{70} +757.901 q^{71} -613.132 q^{72} +872.123 q^{73} -236.247 q^{74} -28.6822 q^{75} +438.336 q^{76} +68.9403 q^{77} -773.280 q^{79} -31.6668 q^{80} +713.590 q^{81} +104.609 q^{82} -4.22184 q^{83} -13.1784 q^{84} +100.498 q^{85} -41.7370 q^{86} -90.0817 q^{87} -251.571 q^{88} +290.011 q^{89} +660.670 q^{90} -757.724 q^{92} -3.82791 q^{93} +2.17014 q^{94} -1257.05 q^{95} +78.1097 q^{96} -642.620 q^{97} +542.025 q^{98} +294.902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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