LMFDB - Embedded newform 1815.4.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.1540841.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 27x^{2} - 18x + 92 $ x^4 - 27x^2 - 18x + 92
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.63835$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.63835 q^{2} +3.00000 q^{3} +5.23763 q^{4} +5.00000 q^{5} -10.9151 q^{6} -20.8444 q^{7} +10.0505 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.63835 q^{2} +3.00000 q^{3} +5.23763 q^{4} +5.00000 q^{5} -10.9151 q^{6} -20.8444 q^{7} +10.0505 q^{8} +9.00000 q^{9} -18.1918 q^{10} +15.7129 q^{12} -67.4988 q^{13} +75.8394 q^{14} +15.0000 q^{15} -78.4683 q^{16} +57.8120 q^{17} -32.7452 q^{18} +7.98646 q^{19} +26.1881 q^{20} -62.5333 q^{21} +67.5185 q^{23} +30.1515 q^{24} +25.0000 q^{25} +245.585 q^{26} +27.0000 q^{27} -109.175 q^{28} +56.1558 q^{29} -54.5753 q^{30} -127.085 q^{31} +205.091 q^{32} -210.341 q^{34} -104.222 q^{35} +47.1386 q^{36} -95.4222 q^{37} -29.0576 q^{38} -202.497 q^{39} +50.2525 q^{40} +485.903 q^{41} +227.518 q^{42} +146.216 q^{43} +45.0000 q^{45} -245.656 q^{46} +164.296 q^{47} -235.405 q^{48} +91.4901 q^{49} -90.9589 q^{50} +173.436 q^{51} -353.534 q^{52} +431.492 q^{53} -98.2356 q^{54} -209.497 q^{56} +23.9594 q^{57} -204.315 q^{58} -804.178 q^{59} +78.5644 q^{60} +120.847 q^{61} +462.381 q^{62} -187.600 q^{63} -118.449 q^{64} -337.494 q^{65} -371.469 q^{67} +302.798 q^{68} +202.555 q^{69} +379.197 q^{70} +529.835 q^{71} +90.4545 q^{72} -1059.19 q^{73} +347.180 q^{74} +75.0000 q^{75} +41.8301 q^{76} +736.754 q^{78} +168.663 q^{79} -392.341 q^{80} +81.0000 q^{81} -1767.89 q^{82} +144.130 q^{83} -327.526 q^{84} +289.060 q^{85} -531.986 q^{86} +168.468 q^{87} -1400.20 q^{89} -163.726 q^{90} +1406.97 q^{91} +353.637 q^{92} -381.256 q^{93} -597.767 q^{94} +39.9323 q^{95} +615.274 q^{96} +29.6912 q^{97} -332.873 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 12 q^{3} + 26 q^{4} + 20 q^{5} - 12 q^{6} - 34 q^{7} - 48 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 12 * q^3 + 26 * q^4 + 20 * q^5 - 12 * q^6 - 34 * q^7 - 48 * q^8 + 36 * q^9	\( 4 q - 4 q^{2} + 12 q^{3} + 26 q^{4} + 20 q^{5} - 12 q^{6} - 34 q^{7} - 48 q^{8} + 36 q^{9} - 20 q^{10} + 78 q^{12} - 2 q^{13} - 52 q^{14} + 60 q^{15} + 66 q^{16} - 74 q^{17} - 36 q^{18} - 136 q^{19} + 130 q^{20} - 102 q^{21} - 64 q^{23} - 144 q^{24} + 100 q^{25} - 320 q^{26} + 108 q^{27} + 20 q^{28} - 52 q^{29} - 60 q^{30} + 492 q^{31} - 208 q^{32} + 244 q^{34} - 170 q^{35} + 234 q^{36} - 4 q^{37} - 404 q^{38} - 6 q^{39} - 240 q^{40} - 268 q^{41} - 156 q^{42} - 546 q^{43} + 180 q^{45} - 368 q^{46} - 276 q^{47} + 198 q^{48} - 496 q^{49} - 100 q^{50} - 222 q^{51} + 1084 q^{52} - 184 q^{53} - 108 q^{54} - 852 q^{56} - 408 q^{57} - 444 q^{58} - 1032 q^{59} + 390 q^{60} - 116 q^{61} + 1240 q^{62} - 306 q^{63} - 918 q^{64} - 10 q^{65} - 552 q^{67} + 720 q^{68} - 192 q^{69} - 260 q^{70} - 920 q^{71} - 432 q^{72} - 926 q^{73} + 2856 q^{74} + 300 q^{75} - 1572 q^{76} - 960 q^{78} - 1152 q^{79} + 330 q^{80} + 324 q^{81} - 1924 q^{82} + 134 q^{83} + 60 q^{84} - 370 q^{85} + 236 q^{86} - 156 q^{87} - 1064 q^{89} - 180 q^{90} + 2780 q^{91} - 4896 q^{92} + 1476 q^{93} + 1432 q^{94} - 680 q^{95} - 624 q^{96} - 1648 q^{97} + 188 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 12 * q^3 + 26 * q^4 + 20 * q^5 - 12 * q^6 - 34 * q^7 - 48 * q^8 + 36 * q^9 - 20 * q^10 + 78 * q^12 - 2 * q^13 - 52 * q^14 + 60 * q^15 + 66 * q^16 - 74 * q^17 - 36 * q^18 - 136 * q^19 + 130 * q^20 - 102 * q^21 - 64 * q^23 - 144 * q^24 + 100 * q^25 - 320 * q^26 + 108 * q^27 + 20 * q^28 - 52 * q^29 - 60 * q^30 + 492 * q^31 - 208 * q^32 + 244 * q^34 - 170 * q^35 + 234 * q^36 - 4 * q^37 - 404 * q^38 - 6 * q^39 - 240 * q^40 - 268 * q^41 - 156 * q^42 - 546 * q^43 + 180 * q^45 - 368 * q^46 - 276 * q^47 + 198 * q^48 - 496 * q^49 - 100 * q^50 - 222 * q^51 + 1084 * q^52 - 184 * q^53 - 108 * q^54 - 852 * q^56 - 408 * q^57 - 444 * q^58 - 1032 * q^59 + 390 * q^60 - 116 * q^61 + 1240 * q^62 - 306 * q^63 - 918 * q^64 - 10 * q^65 - 552 * q^67 + 720 * q^68 - 192 * q^69 - 260 * q^70 - 920 * q^71 - 432 * q^72 - 926 * q^73 + 2856 * q^74 + 300 * q^75 - 1572 * q^76 - 960 * q^78 - 1152 * q^79 + 330 * q^80 + 324 * q^81 - 1924 * q^82 + 134 * q^83 + 60 * q^84 - 370 * q^85 + 236 * q^86 - 156 * q^87 - 1064 * q^89 - 180 * q^90 + 2780 * q^91 - 4896 * q^92 + 1476 * q^93 + 1432 * q^94 - 680 * q^95 - 624 * q^96 - 1648 * q^97 + 188 * q^98

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 $

$2$	−3.63835	−1.28635	−0.643176	−	0.765718i	$-0.722384\pi$
$2$	−3.63835	−1.28635	−0.643176	+	0.765718i	$0.722384\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.23763	0.654703
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−10.9151	−0.742676
$7$	−20.8444	−1.12549	−0.562747	−	0.826629i	$-0.690255\pi$
$7$	−20.8444	−1.12549	−0.562747	+	0.826629i	$0.690255\pi$
$8$	10.0505	0.444173
$9$	9.00000	0.333333
$10$	−18.1918	−0.575274
$11$	0	0
$11$	0	0
$12$	15.7129	0.377993
$13$	−67.4988	−1.44006	−0.720031	−	0.693942i	$-0.755872\pi$
$13$	−67.4988	−1.44006	−0.720031	+	0.693942i	$0.755872\pi$
$14$	75.8394	1.44778
$15$	15.0000	0.258199
$16$	−78.4683	−1.22607
$17$	57.8120	0.824792	0.412396	−	0.911005i	$-0.364692\pi$
$17$	57.8120	0.824792	0.412396	+	0.911005i	$0.364692\pi$
$18$	−32.7452	−0.428784
$19$	7.98646	0.0964326	0.0482163	−	0.998837i	$-0.484646\pi$
$19$	7.98646	0.0964326	0.0482163	+	0.998837i	$0.484646\pi$
$20$	26.1881	0.292792
$21$	−62.5333	−0.649804
$22$	0	0
$23$	67.5185	0.612112	0.306056	−	0.952013i	$-0.400990\pi$
$23$	67.5185	0.612112	0.306056	+	0.952013i	$0.400990\pi$
$24$	30.1515	0.256444
$25$	25.0000	0.200000
$26$	245.585	1.85243
$27$	27.0000	0.192450
$28$	−109.175	−0.736864
$29$	56.1558	0.359582	0.179791	−	0.983705i	$-0.442458\pi$
$29$	56.1558	0.359582	0.179791	+	0.983705i	$0.442458\pi$
$30$	−54.5753	−0.332135
$31$	−127.085	−0.736296	−0.368148	−	0.929767i	$-0.620008\pi$
$31$	−127.085	−0.736296	−0.368148	+	0.929767i	$0.620008\pi$
$32$	205.091	1.13298
$33$	0	0
$34$	−210.341	−1.06097
$35$	−104.222	−0.503336
$36$	47.1386	0.218234
$37$	−95.4222	−0.423981	−0.211991	−	0.977272i	$-0.567995\pi$
$37$	−95.4222	−0.423981	−0.211991	+	0.977272i	$0.567995\pi$
$38$	−29.0576	−0.124046
$39$	−202.497	−0.831420
$40$	50.2525	0.198640
$41$	485.903	1.85086	0.925431	−	0.378917i	$-0.123703\pi$
$41$	485.903	1.85086	0.925431	+	0.378917i	$0.123703\pi$
$42$	227.518	0.835877
$43$	146.216	0.518552	0.259276	−	0.965803i	$-0.416516\pi$
$43$	146.216	0.518552	0.259276	+	0.965803i	$0.416516\pi$
$44$	0	0
$45$	45.0000	0.149071
$46$	−245.656	−0.787392
$47$	164.296	0.509894	0.254947	−	0.966955i	$-0.417942\pi$
$47$	164.296	0.509894	0.254947	+	0.966955i	$0.417942\pi$
$48$	−235.405	−0.707870
$49$	91.4901	0.266735
$50$	−90.9589	−0.257271
$51$	173.436	0.476194
$52$	−353.534	−0.942813
$53$	431.492	1.11830	0.559151	−	0.829066i	$-0.311127\pi$
$53$	431.492	1.11830	0.559151	+	0.829066i	$0.311127\pi$
$54$	−98.2356	−0.247559
$55$	0	0
$56$	−209.497	−0.499914
$57$	23.9594	0.0556754
$58$	−204.315	−0.462549
$59$	−804.178	−1.77449	−0.887246	−	0.461296i	$-0.847385\pi$
$59$	−804.178	−1.77449	−0.887246	+	0.461296i	$0.847385\pi$
$60$	78.5644	0.169044
$61$	120.847	0.253653	0.126826	−	0.991925i	$-0.459521\pi$
$61$	120.847	0.253653	0.126826	+	0.991925i	$0.459521\pi$
$62$	462.381	0.947137
$63$	−187.600	−0.375164
$64$	−118.449	−0.231346
$65$	−337.494	−0.644015
$66$	0	0
$67$	−371.469	−0.677346	−0.338673	−	0.940904i	$-0.609978\pi$
$67$	−371.469	−0.677346	−0.338673	+	0.940904i	$0.609978\pi$
$68$	302.798	0.539994
$69$	202.555	0.353403
$70$	379.197	0.647467
$71$	529.835	0.885631	0.442816	−	0.896613i	$-0.353980\pi$
$71$	529.835	0.885631	0.442816	+	0.896613i	$0.353980\pi$
$72$	90.4545	0.148058
$73$	−1059.19	−1.69820	−0.849100	−	0.528232i	$-0.822855\pi$
$73$	−1059.19	−1.69820	−0.849100	+	0.528232i	$0.822855\pi$
$74$	347.180	0.545389
$75$	75.0000	0.115470
$76$	41.8301	0.0631348
$77$	0	0
$78$	736.754	1.06950
$79$	168.663	0.240204	0.120102	−	0.992762i	$-0.461678\pi$
$79$	168.663	0.240204	0.120102	+	0.992762i	$0.461678\pi$
$80$	−392.341	−0.548314
$81$	81.0000	0.111111
$82$	−1767.89	−2.38086
$83$	144.130	0.190606	0.0953032	−	0.995448i	$-0.469618\pi$
$83$	144.130	0.190606	0.0953032	+	0.995448i	$0.469618\pi$
$84$	−327.526	−0.425429
$85$	289.060	0.368858
$86$	−531.986	−0.667041
$87$	168.468	0.207605
$88$	0	0
$89$	−1400.20	−1.66765	−0.833823	−	0.552032i	$-0.813853\pi$
$89$	−1400.20	−1.66765	−0.833823	+	0.552032i	$0.813853\pi$
$90$	−163.726	−0.191758
$91$	1406.97	1.62078
$92$	353.637	0.400752
$93$	−381.256	−0.425101
$94$	−597.767	−0.655904
$95$	39.9323	0.0431260
$96$	615.274	0.654127
$97$	29.6912	0.0310792	0.0155396	−	0.999879i	$-0.495053\pi$
$97$	29.6912	0.0310792	0.0155396	+	0.999879i	$0.495053\pi$
$98$	−332.873	−0.343115
$99$	0	0
$100$	130.941	0.130941
$101$	17.5982	0.0173375	0.00866874	−	0.999962i	$-0.497241\pi$
$101$	17.5982	0.0173375	0.00866874	+	0.999962i	$0.497241\pi$
$102$	−631.022	−0.612553
$103$	1423.03	1.36131	0.680655	−	0.732604i	$-0.261695\pi$
$103$	1423.03	1.36131	0.680655	+	0.732604i	$0.261695\pi$
$104$	−678.397	−0.639637
$105$	−312.666	−0.290601
$106$	−1569.92	−1.43853
$107$	1335.15	1.20629	0.603147	−	0.797630i	$-0.293913\pi$
$107$	1335.15	1.20629	0.603147	+	0.797630i	$0.293913\pi$
$108$	141.416	0.125998
$109$	−1565.39	−1.37557	−0.687784	−	0.725916i	$-0.741416\pi$
$109$	−1565.39	−1.37557	−0.687784	+	0.725916i	$0.741416\pi$
$110$	0	0
$111$	−286.266	−0.244786
$112$	1635.63	1.37993
$113$	1176.83	0.979709	0.489854	−	0.871804i	$-0.337050\pi$
$113$	1176.83	0.979709	0.489854	+	0.871804i	$0.337050\pi$
$114$	−87.1728	−0.0716182
$115$	337.592	0.273745
$116$	294.123	0.235420
$117$	−607.490	−0.480021
$118$	2925.89	2.28262
$119$	−1205.06	−0.928298
$120$	150.757	0.114685
$121$	0	0
$122$	−439.683	−0.326287
$123$	1457.71	1.06860
$124$	−665.625	−0.482056
$125$	125.000	0.0894427
$126$	682.555	0.482594
$127$	−311.155	−0.217406	−0.108703	−	0.994074i	$-0.534670\pi$
$127$	−311.155	−0.217406	−0.108703	+	0.994074i	$0.534670\pi$
$128$	−1209.77	−0.835388
$129$	438.648	0.299386
$130$	1227.92	0.828431
$131$	−582.818	−0.388711	−0.194355	−	0.980931i	$-0.562261\pi$
$131$	−582.818	−0.388711	−0.194355	+	0.980931i	$0.562261\pi$
$132$	0	0
$133$	−166.473	−0.108534
$134$	1351.54	0.871306
$135$	135.000	0.0860663
$136$	581.039	0.366351
$137$	−2367.98	−1.47672	−0.738358	−	0.674410i	$-0.764398\pi$
$137$	−2367.98	−1.47672	−0.738358	+	0.674410i	$0.764398\pi$
$138$	−736.969	−0.454601
$139$	−2573.48	−1.57036	−0.785179	−	0.619269i	$-0.787429\pi$
$139$	−2573.48	−1.57036	−0.785179	+	0.619269i	$0.787429\pi$
$140$	−545.877	−0.329536
$141$	492.888	0.294388
$142$	−1927.73	−1.13923
$143$	0	0
$144$	−706.215	−0.408689
$145$	280.779	0.160810
$146$	3853.70	2.18448
$147$	274.470	0.153999
$148$	−499.786	−0.277582
$149$	−1992.38	−1.09545	−0.547724	−	0.836659i	$-0.684506\pi$
$149$	−1992.38	−1.09545	−0.547724	+	0.836659i	$0.684506\pi$
$150$	−272.877	−0.148535
$151$	−2961.20	−1.59589	−0.797944	−	0.602731i	$-0.794079\pi$
$151$	−2961.20	−1.59589	−0.797944	+	0.602731i	$0.794079\pi$
$152$	80.2679	0.0428328
$153$	520.308	0.274931
$154$	0	0
$155$	−635.426	−0.329282
$156$	−1060.60	−0.544334
$157$	1302.56	0.662139	0.331070	−	0.943606i	$-0.392591\pi$
$157$	1302.56	0.662139	0.331070	+	0.943606i	$0.392591\pi$
$158$	−613.657	−0.308987
$159$	1294.48	0.645652
$160$	1025.46	0.506685
$161$	−1407.38	−0.688928
$162$	−294.707	−0.142928
$163$	−563.163	−0.270615	−0.135308	−	0.990804i	$-0.543202\pi$
$163$	−563.163	−0.270615	−0.135308	+	0.990804i	$0.543202\pi$
$164$	2544.98	1.21176
$165$	0	0
$166$	−524.396	−0.245187
$167$	−1128.96	−0.523124	−0.261562	−	0.965187i	$-0.584238\pi$
$167$	−1128.96	−0.523124	−0.261562	+	0.965187i	$0.584238\pi$
$168$	−628.490	−0.288626
$169$	2359.09	1.07378
$170$	−1051.70	−0.474482
$171$	71.8782	0.0321442
$172$	765.825	0.339498
$173$	−3091.97	−1.35883	−0.679416	−	0.733754i	$-0.737767\pi$
$173$	−3091.97	−1.35883	−0.679416	+	0.733754i	$0.737767\pi$
$174$	−612.945	−0.267053
$175$	−521.111	−0.225099
$176$	0	0
$177$	−2412.53	−1.02450
$178$	5094.41	2.14518
$179$	2879.27	1.20227	0.601136	−	0.799147i	$-0.294715\pi$
$179$	2879.27	1.20227	0.601136	+	0.799147i	$0.294715\pi$
$180$	235.693	0.0975974
$181$	−702.137	−0.288339	−0.144170	−	0.989553i	$-0.546051\pi$
$181$	−702.137	−0.288339	−0.144170	+	0.989553i	$0.546051\pi$
$182$	−5119.07	−2.08489
$183$	362.540	0.146447
$184$	678.594	0.271884
$185$	−477.111	−0.189610
$186$	1387.14	0.546830
$187$	0	0
$188$	860.521	0.333829
$189$	−562.799	−0.216601
$190$	−145.288	−0.0554752
$191$	4294.28	1.62682	0.813412	−	0.581688i	$-0.197608\pi$
$191$	4294.28	1.62682	0.813412	+	0.581688i	$0.197608\pi$
$192$	−355.348	−0.133568
$193$	3888.11	1.45012	0.725059	−	0.688687i	$-0.241813\pi$
$193$	3888.11	1.45012	0.725059	+	0.688687i	$0.241813\pi$
$194$	−108.027	−0.0399788
$195$	−1012.48	−0.371822
$196$	479.191	0.174632
$197$	3062.26	1.10750	0.553748	−	0.832684i	$-0.313197\pi$
$197$	3062.26	1.10750	0.553748	+	0.832684i	$0.313197\pi$
$198$	0	0
$199$	4874.64	1.73645	0.868226	−	0.496168i	$-0.165260\pi$
$199$	4874.64	1.73645	0.868226	+	0.496168i	$0.165260\pi$
$200$	251.262	0.0888347
$201$	−1114.41	−0.391066
$202$	−64.0285	−0.0223021
$203$	−1170.54	−0.404707
$204$	908.393	0.311766
$205$	2429.52	0.827730
$206$	−5177.47	−1.75112
$207$	607.666	0.204037
$208$	5296.52	1.76561
$209$	0	0
$210$	1137.59	0.373815
$211$	4324.02	1.41080	0.705398	−	0.708811i	$-0.250768\pi$
$211$	4324.02	1.41080	0.705398	+	0.708811i	$0.250768\pi$
$212$	2259.99	0.732156
$213$	1589.50	0.511319
$214$	−4857.74	−1.55172
$215$	731.081	0.231904
$216$	271.363	0.0854812
$217$	2649.02	0.828697
$218$	5695.43	1.76947
$219$	−3177.56	−0.980456
$220$	0	0
$221$	−3902.24	−1.18775
$222$	1041.54	0.314881
$223$	−6205.69	−1.86351	−0.931757	−	0.363084i	$-0.881724\pi$
$223$	−6205.69	−1.86351	−0.931757	+	0.363084i	$0.881724\pi$
$224$	−4275.01	−1.27516
$225$	225.000	0.0666667
$226$	−4281.73	−1.26025
$227$	−1535.81	−0.449055	−0.224528	−	0.974468i	$-0.572084\pi$
$227$	−1535.81	−0.449055	−0.224528	+	0.974468i	$0.572084\pi$
$228$	125.490	0.0364509
$229$	94.7362	0.0273378	0.0136689	−	0.999907i	$-0.495649\pi$
$229$	94.7362	0.0273378	0.0136689	+	0.999907i	$0.495649\pi$
$230$	−1228.28	−0.352132
$231$	0	0
$232$	564.394	0.159717
$233$	−654.983	−0.184160	−0.0920801	−	0.995752i	$-0.529352\pi$
$233$	−654.983	−0.184160	−0.0920801	+	0.995752i	$0.529352\pi$
$234$	2210.26	0.617476
$235$	821.480	0.228032
$236$	−4211.98	−1.16177
$237$	505.990	0.138682
$238$	4384.43	1.19412
$239$	5660.64	1.53204	0.766018	−	0.642819i	$-0.222235\pi$
$239$	5660.64	1.53204	0.766018	+	0.642819i	$0.222235\pi$
$240$	−1177.02	−0.316569
$241$	4156.88	1.11107	0.555536	−	0.831493i	$-0.312513\pi$
$241$	4156.88	1.11107	0.555536	+	0.831493i	$0.312513\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	632.950	0.166067
$245$	457.450	0.119287
$246$	−5303.66	−1.37459
$247$	−539.077	−0.138869
$248$	−1277.27	−0.327043
$249$	432.390	0.110047
$250$	−454.794	−0.115055
$251$	−7156.50	−1.79966	−0.899829	−	0.436243i	$-0.856309\pi$
$251$	−7156.50	−1.79966	−0.899829	+	0.436243i	$0.856309\pi$
$252$	−982.578	−0.245621
$253$	0	0
$254$	1132.09	0.279660
$255$	867.180	0.212960
$256$	5349.17	1.30595
$257$	−2188.36	−0.531152	−0.265576	−	0.964090i	$-0.585562\pi$
$257$	−2188.36	−0.531152	−0.265576	+	0.964090i	$0.585562\pi$
$258$	−1595.96	−0.385116
$259$	1989.02	0.477188
$260$	−1767.67	−0.421639
$261$	505.403	0.119861
$262$	2120.50	0.500019
$263$	−757.388	−0.177576	−0.0887881	−	0.996051i	$-0.528299\pi$
$263$	−757.388	−0.177576	−0.0887881	+	0.996051i	$0.528299\pi$
$264$	0	0
$265$	2157.46	0.500120
$266$	605.689	0.139613
$267$	−4200.59	−0.962816
$268$	−1945.62	−0.443461
$269$	−6782.64	−1.53734	−0.768671	−	0.639645i	$-0.779081\pi$
$269$	−6782.64	−1.53734	−0.768671	+	0.639645i	$0.779081\pi$
$270$	−491.178	−0.110712
$271$	−7040.87	−1.57824	−0.789119	−	0.614241i	$-0.789462\pi$
$271$	−7040.87	−1.57824	−0.789119	+	0.614241i	$0.789462\pi$
$272$	−4536.41	−1.01125
$273$	4220.92	0.935758
$274$	8615.54	1.89958
$275$	0	0
$276$	1060.91	0.231374
$277$	3211.46	0.696599	0.348300	−	0.937383i	$-0.386759\pi$
$277$	3211.46	0.696599	0.348300	+	0.937383i	$0.386759\pi$
$278$	9363.24	2.02003
$279$	−1143.77	−0.245432
$280$	−1047.48	−0.223568
$281$	−3986.15	−0.846241	−0.423120	−	0.906073i	$-0.639065\pi$
$281$	−3986.15	−0.846241	−0.423120	+	0.906073i	$0.639065\pi$
$282$	−1793.30	−0.378686
$283$	−7838.75	−1.64652	−0.823260	−	0.567664i	$-0.807847\pi$
$283$	−7838.75	−1.64652	−0.823260	+	0.567664i	$0.807847\pi$
$284$	2775.08	0.579826
$285$	119.797	0.0248988
$286$	0	0
$287$	−10128.4	−2.08313
$288$	1845.82	0.377660
$289$	−1570.77	−0.319718
$290$	−1021.57	−0.206858
$291$	89.0735	0.0179436
$292$	−5547.63	−1.11182
$293$	5430.65	1.08280	0.541402	−	0.840764i	$-0.317894\pi$
$293$	5430.65	1.08280	0.541402	+	0.840764i	$0.317894\pi$
$294$	−998.620	−0.198098
$295$	−4020.89	−0.793577
$296$	−959.040	−0.188321
$297$	0	0
$298$	7248.97	1.40913
$299$	−4557.42	−0.881480
$300$	392.822	0.0755986
$301$	−3047.79	−0.583627
$302$	10773.9	2.05288
$303$	52.7946	0.0100098
$304$	−626.684	−0.118233
$305$	604.233	0.113437
$306$	−1893.06	−0.353658
$307$	−8045.25	−1.49566	−0.747828	−	0.663892i	$-0.768903\pi$
$307$	−8045.25	−1.49566	−0.747828	+	0.663892i	$0.768903\pi$
$308$	0	0
$309$	4269.08	0.785952
$310$	2311.91	0.423573
$311$	−4712.06	−0.859152	−0.429576	−	0.903031i	$-0.641337\pi$
$311$	−4712.06	−0.859152	−0.429576	+	0.903031i	$0.641337\pi$
$312$	−2035.19	−0.369295
$313$	−1425.19	−0.257369	−0.128684	−	0.991686i	$-0.541075\pi$
$313$	−1425.19	−0.257369	−0.128684	+	0.991686i	$0.541075\pi$
$314$	−4739.19	−0.851744
$315$	−937.999	−0.167779
$316$	883.395	0.157262
$317$	−2031.54	−0.359944	−0.179972	−	0.983672i	$-0.557601\pi$
$317$	−2031.54	−0.359944	−0.179972	+	0.983672i	$0.557601\pi$
$318$	−4709.76	−0.830536
$319$	0	0
$320$	−592.247	−0.103461
$321$	4005.44	0.696454
$322$	5120.56	0.886204
$323$	461.713	0.0795369
$324$	424.248	0.0727448
$325$	−1687.47	−0.288012
$326$	2048.99	0.348107
$327$	−4696.16	−0.794184
$328$	4883.57	0.822103
$329$	−3424.65	−0.573882
$330$	0	0
$331$	316.790	0.0526054	0.0263027	−	0.999654i	$-0.491627\pi$
$331$	316.790	0.0526054	0.0263027	+	0.999654i	$0.491627\pi$
$332$	754.899	0.124791
$333$	−858.799	−0.141327
$334$	4107.57	0.672922
$335$	−1857.35	−0.302918
$336$	4906.88	0.796703
$337$	−4441.65	−0.717958	−0.358979	−	0.933346i	$-0.616875\pi$
$337$	−4441.65	−0.717958	−0.358979	+	0.933346i	$0.616875\pi$
$338$	−8583.22	−1.38126
$339$	3530.50	0.565635
$340$	1513.99	0.241493
$341$	0	0
$342$	−261.518	−0.0413488
$343$	5242.58	0.825285
$344$	1469.54	0.230327
$345$	1012.78	0.158047
$346$	11249.7	1.74794
$347$	−258.695	−0.0400215	−0.0200108	−	0.999800i	$-0.506370\pi$
$347$	−258.695	−0.0400215	−0.0200108	+	0.999800i	$0.506370\pi$
$348$	882.370	0.135920
$349$	−9929.62	−1.52298	−0.761491	−	0.648176i	$-0.775532\pi$
$349$	−9929.62	−1.52298	−0.761491	+	0.648176i	$0.775532\pi$
$350$	1895.99	0.289556
$351$	−1822.47	−0.277140
$352$	0	0
$353$	−1008.73	−0.152095	−0.0760474	−	0.997104i	$-0.524230\pi$
$353$	−1008.73	−0.152095	−0.0760474	+	0.997104i	$0.524230\pi$
$354$	8777.66	1.31787
$355$	2649.17	0.396066
$356$	−7333.70	−1.09181
$357$	−3615.17	−0.535953
$358$	−10475.8	−1.54655
$359$	−5813.26	−0.854630	−0.427315	−	0.904103i	$-0.640540\pi$
$359$	−5813.26	−0.854630	−0.427315	+	0.904103i	$0.640540\pi$
$360$	452.272	0.0662135
$361$	−6795.22	−0.990701
$362$	2554.62	0.370906
$363$	0	0
$364$	7369.21	1.06113
$365$	−5295.94	−0.759458
$366$	−1319.05	−0.188382
$367$	−10247.0	−1.45747	−0.728733	−	0.684798i	$-0.759890\pi$
$367$	−10247.0	−1.45747	−0.728733	+	0.684798i	$0.759890\pi$
$368$	−5298.06	−0.750490
$369$	4373.13	0.616954
$370$	1735.90	0.243906
$371$	−8994.20	−1.25864
$372$	−1996.88	−0.278315
$373$	2202.63	0.305759	0.152879	−	0.988245i	$-0.451145\pi$
$373$	2202.63	0.305759	0.152879	+	0.988245i	$0.451145\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	1651.26	0.226481
$377$	−3790.45	−0.517821
$378$	2047.66	0.278626
$379$	−1851.13	−0.250887	−0.125444	−	0.992101i	$-0.540035\pi$
$379$	−1851.13	−0.250887	−0.125444	+	0.992101i	$0.540035\pi$
$380$	209.151	0.0282347
$381$	−933.464	−0.125519
$382$	−15624.1	−2.09267
$383$	5880.65	0.784562	0.392281	−	0.919846i	$-0.371686\pi$
$383$	5880.65	0.784562	0.392281	+	0.919846i	$0.371686\pi$
$384$	−3629.31	−0.482311
$385$	0	0
$386$	−14146.3	−1.86536
$387$	1315.95	0.172851
$388$	155.511	0.0203476
$389$	−6963.66	−0.907639	−0.453820	−	0.891094i	$-0.649939\pi$
$389$	−6963.66	−0.907639	−0.453820	+	0.891094i	$0.649939\pi$
$390$	3683.77	0.478295
$391$	3903.38	0.504865
$392$	919.520	0.118477
$393$	−1748.46	−0.224422
$394$	−11141.6	−1.42463
$395$	843.316	0.107422
$396$	0	0
$397$	3024.31	0.382332	0.191166	−	0.981558i	$-0.438773\pi$
$397$	3024.31	0.382332	0.191166	+	0.981558i	$0.438773\pi$
$398$	−17735.7	−2.23369
$399$	−499.420	−0.0626623
$400$	−1961.71	−0.245213
$401$	−13392.7	−1.66783	−0.833914	−	0.551895i	$-0.813905\pi$
$401$	−13392.7	−1.66783	−0.833914	+	0.551895i	$0.813905\pi$
$402$	4054.61	0.503049
$403$	8578.11	1.06031
$404$	92.1728	0.0113509
$405$	405.000	0.0496904
$406$	4258.83	0.520596
$407$	0	0
$408$	1743.12	0.211513
$409$	−7637.16	−0.923308	−0.461654	−	0.887060i	$-0.652744\pi$
$409$	−7637.16	−0.923308	−0.461654	+	0.887060i	$0.652744\pi$
$410$	−8839.44	−1.06475
$411$	−7103.93	−0.852582
$412$	7453.28	0.891254
$413$	16762.6	1.99718
$414$	−2210.91	−0.262464
$415$	720.650	0.0852417
$416$	−13843.4	−1.63156
$417$	−7720.44	−0.906647
$418$	0	0
$419$	12523.9	1.46022	0.730112	−	0.683328i	$-0.239468\pi$
$419$	12523.9	1.46022	0.730112	+	0.683328i	$0.239468\pi$
$420$	−1637.63	−0.190257
$421$	−11150.0	−1.29078	−0.645391	−	0.763852i	$-0.723306\pi$
$421$	−11150.0	−1.29078	−0.645391	+	0.763852i	$0.723306\pi$
$422$	−15732.3	−1.81478
$423$	1478.66	0.169965
$424$	4336.71	0.496720
$425$	1445.30	0.164958
$426$	−5783.18	−0.657737
$427$	−2518.98	−0.285485
$428$	6993.00	0.789765
$429$	0	0
$430$	−2659.93	−0.298310
$431$	2093.77	0.233998	0.116999	−	0.993132i	$-0.462673\pi$
$431$	2093.77	0.233998	0.116999	+	0.993132i	$0.462673\pi$
$432$	−2118.64	−0.235957
$433$	−4391.47	−0.487392	−0.243696	−	0.969852i	$-0.578360\pi$
$433$	−4391.47	−0.487392	−0.243696	+	0.969852i	$0.578360\pi$
$434$	−9638.07	−1.06600
$435$	842.338	0.0928437
$436$	−8198.91	−0.900589
$437$	539.234	0.0590276
$438$	11561.1	1.26121
$439$	−15614.6	−1.69759	−0.848797	−	0.528719i	$-0.822672\pi$
$439$	−15614.6	−1.69759	−0.848797	+	0.528719i	$0.822672\pi$
$440$	0	0
$441$	823.411	0.0889116
$442$	14197.7	1.52787
$443$	7909.57	0.848296	0.424148	−	0.905593i	$-0.360574\pi$
$443$	7909.57	0.848296	0.424148	+	0.905593i	$0.360574\pi$
$444$	−1499.36	−0.160262
$445$	−7000.98	−0.745794
$446$	22578.5	2.39714
$447$	−5977.13	−0.632458
$448$	2469.01	0.260379
$449$	−14958.7	−1.57226	−0.786128	−	0.618064i	$-0.787917\pi$
$449$	−14958.7	−1.57226	−0.786128	+	0.618064i	$0.787917\pi$
$450$	−818.630	−0.0857568
$451$	0	0
$452$	6163.81	0.641419
$453$	−8883.61	−0.921387
$454$	5587.84	0.577644
$455$	7034.87	0.724835
$456$	240.804	0.0247295
$457$	−14584.6	−1.49286	−0.746430	−	0.665464i	$-0.768234\pi$
$457$	−14584.6	−1.49286	−0.746430	+	0.665464i	$0.768234\pi$
$458$	−344.684	−0.0351660
$459$	1560.92	0.158731
$460$	1768.18	0.179222
$461$	1802.35	0.182091	0.0910454	−	0.995847i	$-0.470979\pi$
$461$	1802.35	0.182091	0.0910454	+	0.995847i	$0.470979\pi$
$462$	0	0
$463$	6753.79	0.677916	0.338958	−	0.940801i	$-0.389926\pi$
$463$	6753.79	0.677916	0.338958	+	0.940801i	$0.389926\pi$
$464$	−4406.45	−0.440872
$465$	−1906.28	−0.190111
$466$	2383.06	0.236895
$467$	−1744.55	−0.172866	−0.0864329	−	0.996258i	$-0.527547\pi$
$467$	−1744.55	−0.172866	−0.0864329	+	0.996258i	$0.527547\pi$
$468$	−3181.80	−0.314271
$469$	7743.06	0.762349
$470$	−2988.83	−0.293329
$471$	3907.69	0.382286
$472$	−8082.39	−0.788182
$473$	0	0
$474$	−1840.97	−0.178394
$475$	199.662	0.0192865
$476$	−6311.64	−0.607760
$477$	3883.43	0.372767
$478$	−20595.4	−1.97074
$479$	−16930.6	−1.61499	−0.807495	−	0.589874i	$-0.799177\pi$
$479$	−16930.6	−1.61499	−0.807495	+	0.589874i	$0.799177\pi$
$480$	3076.37	0.292534
$481$	6440.88	0.610559
$482$	−15124.2	−1.42923
$483$	−4222.15	−0.397753
$484$	0	0
$485$	148.456	0.0138990
$486$	−884.120	−0.0825196
$487$	−3932.10	−0.365874	−0.182937	−	0.983125i	$-0.558560\pi$
$487$	−3932.10	−0.365874	−0.182937	+	0.983125i	$0.558560\pi$
$488$	1214.57	0.112666
$489$	−1689.49	−0.156240
$490$	−1664.37	−0.153446
$491$	−11477.9	−1.05497	−0.527484	−	0.849565i	$-0.676864\pi$
$491$	−11477.9	−1.05497	−0.527484	+	0.849565i	$0.676864\pi$
$492$	7634.94	0.699613
$493$	3246.48	0.296580
$494$	1961.35	0.178635
$495$	0	0
$496$	9972.16	0.902749
$497$	−11044.1	−0.996772
$498$	−1573.19	−0.141559
$499$	12806.6	1.14890	0.574451	−	0.818539i	$-0.305215\pi$
$499$	12806.6	1.14890	0.574451	+	0.818539i	$0.305215\pi$
$500$	654.703	0.0585584
$501$	−3386.89	−0.302026
$502$	26037.9	2.31500
$503$	−1319.41	−0.116958	−0.0584789	−	0.998289i	$-0.518625\pi$
$503$	−1319.41	−0.116958	−0.0584789	+	0.998289i	$0.518625\pi$
$504$	−1885.47	−0.166638
$505$	87.9910	0.00775356
$506$	0	0
$507$	7077.28	0.619947
$508$	−1629.71	−0.142336
$509$	1658.45	0.144419	0.0722097	−	0.997389i	$-0.476995\pi$
$509$	1658.45	0.144419	0.0722097	+	0.997389i	$0.476995\pi$
$510$	−3155.11	−0.273942
$511$	22078.2	1.91131
$512$	−9784.02	−0.844524
$513$	215.635	0.0185585
$514$	7962.02	0.683248
$515$	7115.13	0.608796
$516$	2297.48	0.196009
$517$	0	0
$518$	−7236.76	−0.613832
$519$	−9275.90	−0.784522
$520$	−3391.98	−0.286054
$521$	2790.40	0.234644	0.117322	−	0.993094i	$-0.462569\pi$
$521$	2790.40	0.234644	0.117322	+	0.993094i	$0.462569\pi$
$522$	−1838.83	−0.154183
$523$	2440.70	0.204062	0.102031	−	0.994781i	$-0.467466\pi$
$523$	2440.70	0.204062	0.102031	+	0.994781i	$0.467466\pi$
$524$	−3052.59	−0.254490
$525$	−1563.33	−0.129961
$526$	2755.64	0.228426
$527$	−7347.05	−0.607292
$528$	0	0
$529$	−7608.25	−0.625319
$530$	−7849.61	−0.643330
$531$	−7237.60	−0.591498
$532$	−871.925	−0.0710578
$533$	−32797.9	−2.66536
$534$	15283.2	1.23852
$535$	6675.73	0.539471
$536$	−3733.45	−0.300859
$537$	8637.81	0.694132
$538$	24677.6	1.97756
$539$	0	0
$540$	707.080	0.0563479
$541$	7756.41	0.616403	0.308202	−	0.951321i	$-0.400273\pi$
$541$	7756.41	0.616403	0.308202	+	0.951321i	$0.400273\pi$
$542$	25617.2	2.03017
$543$	−2106.41	−0.166473
$544$	11856.7	0.934474
$545$	−7826.93	−0.615173
$546$	−15357.2	−1.20371
$547$	13056.6	1.02058	0.510290	−	0.860002i	$-0.329538\pi$
$547$	13056.6	1.02058	0.510290	+	0.860002i	$0.329538\pi$
$548$	−12402.6	−0.966810
$549$	1087.62	0.0845510
$550$	0	0
$551$	448.487	0.0346754
$552$	2035.78	0.156972
$553$	−3515.69	−0.270348
$554$	−11684.4	−0.896072
$555$	−1431.33	−0.109471
$556$	−13478.9	−1.02812
$557$	1837.48	0.139778	0.0698892	−	0.997555i	$-0.477735\pi$
$557$	1837.48	0.139778	0.0698892	+	0.997555i	$0.477735\pi$
$558$	4161.43	0.315712
$559$	−9869.42	−0.746748
$560$	8178.13	0.617123
$561$	0	0
$562$	14503.0	1.08856
$563$	−11473.6	−0.858890	−0.429445	−	0.903093i	$-0.641291\pi$
$563$	−11473.6	−0.858890	−0.429445	+	0.903093i	$0.641291\pi$
$564$	2581.56	0.192736
$565$	5884.16	0.438139
$566$	28520.1	2.11801
$567$	−1688.40	−0.125055
$568$	5325.10	0.393374
$569$	−9698.61	−0.714564	−0.357282	−	0.933997i	$-0.616297\pi$
$569$	−9698.61	−0.714564	−0.357282	+	0.933997i	$0.616297\pi$
$570$	−435.864	−0.0320286
$571$	−14019.8	−1.02752	−0.513758	−	0.857935i	$-0.671747\pi$
$571$	−14019.8	−1.02752	−0.513758	+	0.857935i	$0.671747\pi$
$572$	0	0
$573$	12882.8	0.939247
$574$	36850.6	2.67964
$575$	1687.96	0.122422
$576$	−1066.04	−0.0771155
$577$	3912.25	0.282269	0.141134	−	0.989990i	$-0.454925\pi$
$577$	3912.25	0.282269	0.141134	+	0.989990i	$0.454925\pi$
$578$	5715.03	0.411270
$579$	11664.3	0.837226
$580$	1470.62	0.105283
$581$	−3004.31	−0.214526
$582$	−324.081	−0.0230818
$583$	0	0
$584$	−10645.4	−0.754295
$585$	−3037.45	−0.214672
$586$	−19758.6	−1.39287
$587$	11148.5	0.783899	0.391949	−	0.919987i	$-0.371801\pi$
$587$	11148.5	0.783899	0.391949	+	0.919987i	$0.371801\pi$
$588$	1437.57	0.100824
$589$	−1014.96	−0.0710030
$590$	14629.4	1.02082
$591$	9186.77	0.639413
$592$	7487.61	0.519829
$593$	17155.0	1.18798	0.593989	−	0.804473i	$-0.297552\pi$
$593$	17155.0	1.18798	0.593989	+	0.804473i	$0.297552\pi$
$594$	0	0
$595$	−6025.29	−0.415147
$596$	−10435.3	−0.717194
$597$	14623.9	1.00254
$598$	16581.5	1.13389
$599$	−2891.03	−0.197203	−0.0986014	−	0.995127i	$-0.531437\pi$
$599$	−2891.03	−0.197203	−0.0986014	+	0.995127i	$0.531437\pi$
$600$	753.787	0.0512887
$601$	−11439.4	−0.776412	−0.388206	−	0.921573i	$-0.626905\pi$
$601$	−11439.4	−0.776412	−0.388206	+	0.921573i	$0.626905\pi$
$602$	11088.9	0.750750
$603$	−3343.22	−0.225782
$604$	−15509.7	−1.04483
$605$	0	0
$606$	−192.085	−0.0128761
$607$	7768.78	0.519481	0.259741	−	0.965678i	$-0.416363\pi$
$607$	7768.78	0.519481	0.259741	+	0.965678i	$0.416363\pi$
$608$	1637.96	0.109256
$609$	−3511.61	−0.233658
$610$	−2198.41	−0.145920
$611$	−11089.8	−0.734279
$612$	2725.18	0.179998
$613$	6469.74	0.426281	0.213140	−	0.977022i	$-0.431631\pi$
$613$	6469.74	0.426281	0.213140	+	0.977022i	$0.431631\pi$
$614$	29271.5	1.92394
$615$	7288.55	0.477890
$616$	0	0
$617$	−18323.7	−1.19560	−0.597799	−	0.801646i	$-0.703958\pi$
$617$	−18323.7	−1.19560	−0.597799	+	0.801646i	$0.703958\pi$
$618$	−15532.4	−1.01101
$619$	−16697.1	−1.08419	−0.542096	−	0.840317i	$-0.682369\pi$
$619$	−16697.1	−1.08419	−0.542096	+	0.840317i	$0.682369\pi$
$620$	−3328.13	−0.215582
$621$	1823.00	0.117801
$622$	17144.1	1.10517
$623$	29186.3	1.87692
$624$	15889.6	1.01938
$625$	625.000	0.0400000
$626$	5185.35	0.331067
$627$	0	0
$628$	6822.34	0.433505
$629$	−5516.54	−0.349696
$630$	3412.77	0.215822
$631$	20458.8	1.29073	0.645367	−	0.763873i	$-0.276705\pi$
$631$	20458.8	1.29073	0.645367	+	0.763873i	$0.276705\pi$
$632$	1695.15	0.106692
$633$	12972.1	0.814524
$634$	7391.45	0.463016
$635$	−1555.77	−0.0972267
$636$	6779.98	0.422710
$637$	−6175.47	−0.384115
$638$	0	0
$639$	4768.51	0.295210
$640$	−6048.86	−0.373597
$641$	4676.71	0.288173	0.144087	−	0.989565i	$-0.453976\pi$
$641$	4676.71	0.288173	0.144087	+	0.989565i	$0.453976\pi$
$642$	−14573.2	−0.895886
$643$	−2321.97	−0.142410	−0.0712049	−	0.997462i	$-0.522684\pi$
$643$	−2321.97	−0.142410	−0.0712049	+	0.997462i	$0.522684\pi$
$644$	−7371.35	−0.451043
$645$	2193.24	0.133890
$646$	−1679.88	−0.102312
$647$	18149.3	1.10282	0.551408	−	0.834236i	$-0.314091\pi$
$647$	18149.3	1.10282	0.551408	+	0.834236i	$0.314091\pi$
$648$	814.090	0.0493526
$649$	0	0
$650$	6139.62	0.370486
$651$	7947.06	0.478448
$652$	−2949.64	−0.177173
$653$	23089.9	1.38374	0.691868	−	0.722024i	$-0.256788\pi$
$653$	23089.9	1.38374	0.691868	+	0.722024i	$0.256788\pi$
$654$	17086.3	1.02160
$655$	−2914.09	−0.173837
$656$	−38128.0	−2.26928
$657$	−9532.69	−0.566067
$658$	12460.1	0.738215
$659$	−415.639	−0.0245690	−0.0122845	−	0.999925i	$-0.503910\pi$
$659$	−415.639	−0.0245690	−0.0122845	+	0.999925i	$0.503910\pi$
$660$	0	0
$661$	12044.0	0.708710	0.354355	−	0.935111i	$-0.384700\pi$
$661$	12044.0	0.708710	0.354355	+	0.935111i	$0.384700\pi$
$662$	−1152.60	−0.0676691
$663$	−11706.7	−0.685749
$664$	1448.58	0.0846622
$665$	−832.366	−0.0485380
$666$	3124.62	0.181796
$667$	3791.56	0.220105
$668$	−5913.09	−0.342491
$669$	−18617.1	−1.07590
$670$	6757.69	0.389660
$671$	0	0
$672$	−12825.0	−0.736215
$673$	−8699.88	−0.498300	−0.249150	−	0.968465i	$-0.580151\pi$
$673$	−8699.88	−0.498300	−0.249150	+	0.968465i	$0.580151\pi$
$674$	16160.3	0.923547
$675$	675.000	0.0384900
$676$	12356.0	0.703007
$677$	29389.8	1.66845	0.834225	−	0.551424i	$-0.185915\pi$
$677$	29389.8	1.66845	0.834225	+	0.551424i	$0.185915\pi$
$678$	−12845.2	−0.727606
$679$	−618.895	−0.0349794
$680$	2905.20	0.163837
$681$	−4607.44	−0.259262
$682$	0	0
$683$	12261.0	0.686905	0.343452	−	0.939170i	$-0.388404\pi$
$683$	12261.0	0.686905	0.343452	+	0.939170i	$0.388404\pi$
$684$	376.471	0.0210449
$685$	−11839.9	−0.660407
$686$	−19074.4	−1.06161
$687$	284.209	0.0157835
$688$	−11473.3	−0.635780
$689$	−29125.2	−1.61042
$690$	−3684.84	−0.203304
$691$	−22711.4	−1.25034	−0.625168	−	0.780490i	$-0.714970\pi$
$691$	−22711.4	−1.25034	−0.625168	+	0.780490i	$0.714970\pi$
$692$	−16194.6	−0.889631
$693$	0	0
$694$	941.224	0.0514818
$695$	−12867.4	−0.702286
$696$	1693.18	0.0922125
$697$	28091.0	1.52658
$698$	36127.5	1.95909
$699$	−1964.95	−0.106325
$700$	−2729.38	−0.147373
$701$	21070.9	1.13529	0.567643	−	0.823275i	$-0.307855\pi$
$701$	21070.9	1.13529	0.567643	+	0.823275i	$0.307855\pi$
$702$	6630.79	0.356500
$703$	−762.086	−0.0408856
$704$	0	0
$705$	2464.44	0.131654
$706$	3670.13	0.195648
$707$	−366.824	−0.0195132
$708$	−12636.0	−0.670746
$709$	8521.30	0.451374	0.225687	−	0.974200i	$-0.427537\pi$
$709$	8521.30	0.451374	0.225687	+	0.974200i	$0.427537\pi$
$710$	−9638.63	−0.509481
$711$	1517.97	0.0800679
$712$	−14072.7	−0.740724
$713$	−8580.61	−0.450696
$714$	13153.3	0.689425
$715$	0	0
$716$	15080.5	0.787132
$717$	16981.9	0.884521
$718$	21150.7	1.09936
$719$	8217.19	0.426216	0.213108	−	0.977029i	$-0.431641\pi$
$719$	8217.19	0.426216	0.213108	+	0.977029i	$0.431641\pi$
$720$	−3531.07	−0.182771
$721$	−29662.1	−1.53214
$722$	24723.4	1.27439
$723$	12470.6	0.641478
$724$	−3677.53	−0.188777
$725$	1403.90	0.0719164
$726$	0	0
$727$	−20870.8	−1.06473	−0.532363	−	0.846516i	$-0.678696\pi$
$727$	−20870.8	−1.06473	−0.532363	+	0.846516i	$0.678696\pi$
$728$	14140.8	0.719907
$729$	729.000	0.0370370
$730$	19268.5	0.976931
$731$	8453.04	0.427698
$732$	1898.85	0.0958790
$733$	33776.4	1.70199	0.850997	−	0.525171i	$-0.175998\pi$
$733$	33776.4	1.70199	0.850997	+	0.525171i	$0.175998\pi$
$734$	37282.3	1.87482
$735$	1372.35	0.0688706
$736$	13847.5	0.693512
$737$	0	0
$738$	−15911.0	−0.793620
$739$	14342.3	0.713922	0.356961	−	0.934119i	$-0.383813\pi$
$739$	14342.3	0.713922	0.356961	+	0.934119i	$0.383813\pi$
$740$	−2498.93	−0.124138
$741$	−1617.23	−0.0801761
$742$	32724.1	1.61906
$743$	19225.5	0.949279	0.474640	−	0.880180i	$-0.342578\pi$
$743$	19225.5	0.949279	0.474640	+	0.880180i	$0.342578\pi$
$744$	−3831.81	−0.188819
$745$	−9961.88	−0.489900
$746$	−8013.96	−0.393313
$747$	1297.17	0.0635354
$748$	0	0
$749$	−27830.4	−1.35768
$750$	−1364.38	−0.0664270
$751$	−19629.4	−0.953776	−0.476888	−	0.878964i	$-0.658235\pi$
$751$	−19629.4	−0.953776	−0.476888	+	0.878964i	$0.658235\pi$
$752$	−12892.0	−0.625164
$753$	−21469.5	−1.03903
$754$	13791.0	0.666100
$755$	−14806.0	−0.713703
$756$	−2947.73	−0.141810
$757$	−26801.5	−1.28681	−0.643406	−	0.765525i	$-0.722479\pi$
$757$	−26801.5	−1.28681	−0.643406	+	0.765525i	$0.722479\pi$
$758$	6735.07	0.322729
$759$	0	0
$760$	401.340	0.0191554
$761$	−6490.31	−0.309164	−0.154582	−	0.987980i	$-0.549403\pi$
$761$	−6490.31	−0.309164	−0.154582	+	0.987980i	$0.549403\pi$
$762$	3396.27	0.161462
$763$	32629.6	1.54819
$764$	22491.8	1.06509
$765$	2601.54	0.122953
$766$	−21395.9	−1.00922
$767$	54281.1	2.55538
$768$	16047.5	0.753991
$769$	−14356.1	−0.673204	−0.336602	−	0.941647i	$-0.609278\pi$
$769$	−14356.1	−0.673204	−0.336602	+	0.941647i	$0.609278\pi$
$770$	0	0
$771$	−6565.07	−0.306661
$772$	20364.5	0.949397
$773$	19127.6	0.890004	0.445002	−	0.895529i	$-0.353203\pi$
$773$	19127.6	0.890004	0.445002	+	0.895529i	$0.353203\pi$
$774$	−4787.88	−0.222347
$775$	−3177.13	−0.147259
$776$	298.411	0.0138045
$777$	5967.06	0.275505
$778$	25336.3	1.16754
$779$	3880.65	0.178483
$780$	−5303.01	−0.243433
$781$	0	0
$782$	−14201.9	−0.649435
$783$	1516.21	0.0692016
$784$	−7179.07	−0.327035
$785$	6512.81	0.296118
$786$	6361.50	0.288686
$787$	−23509.7	−1.06484	−0.532420	−	0.846480i	$-0.678717\pi$
$787$	−23509.7	−1.06484	−0.532420	+	0.846480i	$0.678717\pi$
$788$	16039.0	0.725082
$789$	−2272.16	−0.102524
$790$	−3068.28	−0.138183
$791$	−24530.4	−1.10266
$792$	0	0
$793$	−8157.01	−0.365276
$794$	−11003.5	−0.491814
$795$	6472.38	0.288744
$796$	25531.5	1.13686
$797$	43145.1	1.91754	0.958769	−	0.284187i	$-0.0917236\pi$
$797$	43145.1	1.91754	0.958769	+	0.284187i	$0.0917236\pi$
$798$	1817.07	0.0806058
$799$	9498.27	0.420557
$800$	5127.29	0.226596
$801$	−12601.8	−0.555882
$802$	48727.3	2.14541
$803$	0	0
$804$	−5836.85	−0.256032
$805$	−7036.92	−0.308098
$806$	−31210.2	−1.36394
$807$	−20347.9	−0.887584
$808$	176.871	0.00770085
$809$	23470.4	1.02000	0.509998	−	0.860176i	$-0.329646\pi$
$809$	23470.4	1.02000	0.509998	+	0.860176i	$0.329646\pi$
$810$	−1473.53	−0.0639194
$811$	4906.52	0.212443	0.106221	−	0.994343i	$-0.466125\pi$
$811$	4906.52	0.212443	0.106221	+	0.994343i	$0.466125\pi$
$812$	−6130.83	−0.264963
$813$	−21122.6	−0.911196
$814$	0	0
$815$	−2815.81	−0.121023
$816$	−13609.2	−0.583846
$817$	1167.75	0.0500054
$818$	27786.7	1.18770
$819$	12662.8	0.540260
$820$	12724.9	0.541918
$821$	−45229.6	−1.92268	−0.961342	−	0.275356i	$-0.911204\pi$
$821$	−45229.6	−1.92268	−0.961342	+	0.275356i	$0.911204\pi$
$822$	25846.6	1.09672
$823$	24192.1	1.02465	0.512323	−	0.858793i	$-0.328785\pi$
$823$	24192.1	1.02465	0.512323	+	0.858793i	$0.328785\pi$
$824$	14302.1	0.604657
$825$	0	0
$826$	−60988.4	−2.56908
$827$	−2031.70	−0.0854282	−0.0427141	−	0.999087i	$-0.513600\pi$
$827$	−2031.70	−0.0854282	−0.0427141	+	0.999087i	$0.513600\pi$
$828$	3182.73	0.133584
$829$	17010.6	0.712671	0.356335	−	0.934358i	$-0.384026\pi$
$829$	17010.6	0.712671	0.356335	+	0.934358i	$0.384026\pi$
$830$	−2621.98	−0.109651
$831$	9634.38	0.402182
$832$	7995.20	0.333153
$833$	5289.22	0.220001
$834$	28089.7	1.16627
$835$	−5644.81	−0.233948
$836$	0	0
$837$	−3431.30	−0.141700
$838$	−45566.5	−1.87836
$839$	3184.10	0.131022	0.0655109	−	0.997852i	$-0.479132\pi$
$839$	3184.10	0.131022	0.0655109	+	0.997852i	$0.479132\pi$
$840$	−3142.45	−0.129077
$841$	−21235.5	−0.870701
$842$	40567.8	1.66040
$843$	−11958.4	−0.488577
$844$	22647.6	0.923653
$845$	11795.5	0.480209
$846$	−5379.90	−0.218635
$847$	0	0
$848$	−33858.4	−1.37111
$849$	−23516.2	−0.950619
$850$	−5258.51	−0.212195
$851$	−6442.76	−0.259524
$852$	8325.23	0.334762
$853$	−20566.8	−0.825548	−0.412774	−	0.910833i	$-0.635440\pi$
$853$	−20566.8	−0.825548	−0.412774	+	0.910833i	$0.635440\pi$
$854$	9164.94	0.367234
$855$	359.391	0.0143753
$856$	13418.9	0.535804
$857$	−48125.8	−1.91826	−0.959129	−	0.282971i	$-0.908680\pi$
$857$	−48125.8	−1.91826	−0.959129	+	0.282971i	$0.908680\pi$
$858$	0	0
$859$	−22013.7	−0.874387	−0.437194	−	0.899367i	$-0.644028\pi$
$859$	−22013.7	−0.874387	−0.437194	+	0.899367i	$0.644028\pi$
$860$	3829.13	0.151828
$861$	−30385.1	−1.20270
$862$	−7617.86	−0.301004
$863$	−23417.0	−0.923667	−0.461834	−	0.886967i	$-0.652808\pi$
$863$	−23417.0	−0.923667	−0.461834	+	0.886967i	$0.652808\pi$
$864$	5537.47	0.218042
$865$	−15459.8	−0.607688
$866$	15977.7	0.626958
$867$	−4712.32	−0.184589
$868$	13874.6	0.542550
$869$	0	0
$870$	−3064.72	−0.119430
$871$	25073.7	0.975421
$872$	−15732.9	−0.610991
$873$	267.221	0.0103597
$874$	−1961.92	−0.0759303
$875$	−2605.55	−0.100667
$876$	−16642.9	−0.641908
$877$	29017.9	1.11729	0.558645	−	0.829407i	$-0.311321\pi$
$877$	29017.9	1.11729	0.558645	+	0.829407i	$0.311321\pi$
$878$	56811.4	2.18370
$879$	16291.9	0.625158
$880$	0	0
$881$	−33241.1	−1.27119	−0.635597	−	0.772021i	$-0.719246\pi$
$881$	−33241.1	−1.27119	−0.635597	+	0.772021i	$0.719246\pi$
$882$	−2995.86	−0.114372
$883$	−5618.39	−0.214127	−0.107063	−	0.994252i	$-0.534145\pi$
$883$	−5618.39	−0.214127	−0.107063	+	0.994252i	$0.534145\pi$
$884$	−20438.5	−0.777625
$885$	−12062.7	−0.458172
$886$	−28777.8	−1.09121
$887$	14334.2	0.542612	0.271306	−	0.962493i	$-0.412545\pi$
$887$	14334.2	0.542612	0.271306	+	0.962493i	$0.412545\pi$
$888$	−2877.12	−0.108727
$889$	6485.84	0.244688
$890$	25472.1	0.959354
$891$	0	0
$892$	−32503.1	−1.22005
$893$	1312.14	0.0491704
$894$	21746.9	0.813564
$895$	14396.3	0.537672
$896$	25217.0	0.940223
$897$	−13672.3	−0.508922
$898$	54424.9	2.02247
$899$	−7136.58	−0.264759
$900$	1178.47	0.0436469
$901$	24945.4	0.922367
$902$	0	0
$903$	−9143.37	−0.336957
$904$	11827.7	0.435161
$905$	−3510.68	−0.128949
$906$	32321.7	1.18523
$907$	−36659.3	−1.34207	−0.671033	−	0.741428i	$-0.734149\pi$
$907$	−36659.3	−1.34207	−0.671033	+	0.741428i	$0.734149\pi$
$908$	−8044.02	−0.293998
$909$	158.384	0.00577916
$910$	−25595.4	−0.932393
$911$	−9050.97	−0.329168	−0.164584	−	0.986363i	$-0.552628\pi$
$911$	−9050.97	−0.329168	−0.164584	+	0.986363i	$0.552628\pi$
$912$	−1880.05	−0.0682618
$913$	0	0
$914$	53063.8	1.92035
$915$	1812.70	0.0654929
$916$	496.193	0.0178981
$917$	12148.5	0.437491
$918$	−5679.19	−0.204184
$919$	46444.5	1.66710	0.833549	−	0.552445i	$-0.186305\pi$
$919$	46444.5	1.66710	0.833549	+	0.552445i	$0.186305\pi$
$920$	3392.97	0.121590
$921$	−24135.7	−0.863518
$922$	−6557.59	−0.234233
$923$	−35763.2	−1.27536
$924$	0	0
$925$	−2385.55	−0.0847962
$926$	−24572.7	−0.872039
$927$	12807.2	0.453770
$928$	11517.1	0.407400
$929$	−18695.8	−0.660267	−0.330133	−	0.943934i	$-0.607094\pi$
$929$	−18695.8	−0.660267	−0.330133	+	0.943934i	$0.607094\pi$
$930$	6935.72	0.244550
$931$	730.682	0.0257219
$932$	−3430.55	−0.120570
$933$	−14136.2	−0.496032
$934$	6347.30	0.222366
$935$	0	0
$936$	−6105.57	−0.213212
$937$	13323.6	0.464530	0.232265	−	0.972653i	$-0.425386\pi$
$937$	13323.6	0.464530	0.232265	+	0.972653i	$0.425386\pi$
$938$	−28172.0	−0.980649
$939$	−4275.57	−0.148592
$940$	4302.60	0.149293
$941$	9500.50	0.329126	0.164563	−	0.986367i	$-0.447379\pi$
$941$	9500.50	0.329126	0.164563	+	0.986367i	$0.447379\pi$
$942$	−14217.6	−0.491755
$943$	32807.4	1.13293
$944$	63102.5	2.17565
$945$	−2814.00	−0.0968670
$946$	0	0
$947$	15179.4	0.520869	0.260435	−	0.965491i	$-0.416134\pi$
$947$	15179.4	0.520869	0.260435	+	0.965491i	$0.416134\pi$
$948$	2650.18	0.0907953
$949$	71494.0	2.44551
$950$	−726.440	−0.0248093
$951$	−6094.61	−0.207814
$952$	−12111.4	−0.412325
$953$	−5051.55	−0.171706	−0.0858530	−	0.996308i	$-0.527362\pi$
$953$	−5051.55	−0.171706	−0.0858530	+	0.996308i	$0.527362\pi$
$954$	−14129.3	−0.479510
$955$	21471.4	0.727538
$956$	29648.3	1.00303
$957$	0	0
$958$	61599.6	2.07745
$959$	49359.1	1.66203
$960$	−1776.74	−0.0597334
$961$	−13640.3	−0.457867
$962$	−23434.2	−0.785395
$963$	12016.3	0.402098
$964$	21772.2	0.727422
$965$	19440.6	0.648512
$966$	15361.7	0.511650
$967$	−15341.1	−0.510172	−0.255086	−	0.966918i	$-0.582104\pi$
$967$	−15341.1	−0.510172	−0.255086	+	0.966918i	$0.582104\pi$
$968$	0	0
$969$	1385.14	0.0459206
$970$	−540.135	−0.0178791
$971$	−5397.65	−0.178392	−0.0891961	−	0.996014i	$-0.528430\pi$
$971$	−5397.65	−0.178392	−0.0891961	+	0.996014i	$0.528430\pi$
$972$	1272.74	0.0419992
$973$	53642.7	1.76743
$974$	14306.4	0.470643
$975$	−5062.41	−0.166284
$976$	−9482.63	−0.310995
$977$	24180.4	0.791812	0.395906	−	0.918291i	$-0.370431\pi$
$977$	24180.4	0.791812	0.395906	+	0.918291i	$0.370431\pi$
$978$	6146.96	0.200980
$979$	0	0
$980$	2395.95	0.0780979
$981$	−14088.5	−0.458523
$982$	41760.5	1.35706
$983$	15159.6	0.491877	0.245938	−	0.969285i	$-0.420904\pi$
$983$	15159.6	0.491877	0.245938	+	0.969285i	$0.420904\pi$
$984$	14650.7	0.474642
$985$	15311.3	0.495288
$986$	−11811.9	−0.381507
$987$	−10274.0	−0.331331
$988$	−2823.48	−0.0909180
$989$	9872.29	0.317412
$990$	0	0
$991$	−3654.97	−0.117158	−0.0585792	−	0.998283i	$-0.518657\pi$
$991$	−3654.97	−0.117158	−0.0585792	+	0.998283i	$0.518657\pi$
$992$	−26064.1	−0.834210
$993$	950.371	0.0303717
$994$	40182.4	1.28220
$995$	24373.2	0.776565
$996$	2264.70	0.0720479
$997$	−46219.9	−1.46820	−0.734102	−	0.679040i	$-0.762396\pi$
$997$	−46219.9	−1.46820	−0.734102	+	0.679040i	$0.762396\pi$
$998$	−46595.0	−1.47789
$999$	−2576.40	−0.0815952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.t.1.2		4
11.10	odd	2		165.4.a.h.1.3	✓	4
33.32	even	2		495.4.a.m.1.2		4
55.32	even	4		825.4.c.p.199.6		8
55.43	even	4		825.4.c.p.199.3		8
55.54	odd	2		825.4.a.t.1.2		4
165.164	even	2		2475.4.a.be.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.h.1.3	✓	4	11.10	odd	2
495.4.a.m.1.2		4	33.32	even	2
825.4.a.t.1.2		4	55.54	odd	2
825.4.c.p.199.3		8	55.43	even	4
825.4.c.p.199.6		8	55.32	even	4
1815.4.a.t.1.2		4	1.1	even	1	trivial
2475.4.a.be.1.3		4	165.164	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q-3.63835 q^{2} +3.00000 q^{3} +5.23763 q^{4} +5.00000 q^{5} -10.9151 q^{6} -20.8444 q^{7} +10.0505 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.63835 q^{2} +3.00000 q^{3} +5.23763 q^{4} +5.00000 q^{5} -10.9151 q^{6} -20.8444 q^{7} +10.0505 q^{8} +9.00000 q^{9} -18.1918 q^{10} +15.7129 q^{12} -67.4988 q^{13} +75.8394 q^{14} +15.0000 q^{15} -78.4683 q^{16} +57.8120 q^{17} -32.7452 q^{18} +7.98646 q^{19} +26.1881 q^{20} -62.5333 q^{21} +67.5185 q^{23} +30.1515 q^{24} +25.0000 q^{25} +245.585 q^{26} +27.0000 q^{27} -109.175 q^{28} +56.1558 q^{29} -54.5753 q^{30} -127.085 q^{31} +205.091 q^{32} -210.341 q^{34} -104.222 q^{35} +47.1386 q^{36} -95.4222 q^{37} -29.0576 q^{38} -202.497 q^{39} +50.2525 q^{40} +485.903 q^{41} +227.518 q^{42} +146.216 q^{43} +45.0000 q^{45} -245.656 q^{46} +164.296 q^{47} -235.405 q^{48} +91.4901 q^{49} -90.9589 q^{50} +173.436 q^{51} -353.534 q^{52} +431.492 q^{53} -98.2356 q^{54} -209.497 q^{56} +23.9594 q^{57} -204.315 q^{58} -804.178 q^{59} +78.5644 q^{60} +120.847 q^{61} +462.381 q^{62} -187.600 q^{63} -118.449 q^{64} -337.494 q^{65} -371.469 q^{67} +302.798 q^{68} +202.555 q^{69} +379.197 q^{70} +529.835 q^{71} +90.4545 q^{72} -1059.19 q^{73} +347.180 q^{74} +75.0000 q^{75} +41.8301 q^{76} +736.754 q^{78} +168.663 q^{79} -392.341 q^{80} +81.0000 q^{81} -1767.89 q^{82} +144.130 q^{83} -327.526 q^{84} +289.060 q^{85} -531.986 q^{86} +168.468 q^{87} -1400.20 q^{89} -163.726 q^{90} +1406.97 q^{91} +353.637 q^{92} -381.256 q^{93} -597.767 q^{94} +39.9323 q^{95} +615.274 q^{96} +29.6912 q^{97} -332.873 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 12 q^{3} + 26 q^{4} + 20 q^{5} - 12 q^{6} - 34 q^{7} - 48 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 12 * q^3 + 26 * q^4 + 20 * q^5 - 12 * q^6 - 34 * q^7 - 48 * q^8 + 36 * q^9	\( 4 q - 4 q^{2} + 12 q^{3} + 26 q^{4} + 20 q^{5} - 12 q^{6} - 34 q^{7} - 48 q^{8} + 36 q^{9} - 20 q^{10} + 78 q^{12} - 2 q^{13} - 52 q^{14} + 60 q^{15} + 66 q^{16} - 74 q^{17} - 36 q^{18} - 136 q^{19} + 130 q^{20} - 102 q^{21} - 64 q^{23} - 144 q^{24} + 100 q^{25} - 320 q^{26} + 108 q^{27} + 20 q^{28} - 52 q^{29} - 60 q^{30} + 492 q^{31} - 208 q^{32} + 244 q^{34} - 170 q^{35} + 234 q^{36} - 4 q^{37} - 404 q^{38} - 6 q^{39} - 240 q^{40} - 268 q^{41} - 156 q^{42} - 546 q^{43} + 180 q^{45} - 368 q^{46} - 276 q^{47} + 198 q^{48} - 496 q^{49} - 100 q^{50} - 222 q^{51} + 1084 q^{52} - 184 q^{53} - 108 q^{54} - 852 q^{56} - 408 q^{57} - 444 q^{58} - 1032 q^{59} + 390 q^{60} - 116 q^{61} + 1240 q^{62} - 306 q^{63} - 918 q^{64} - 10 q^{65} - 552 q^{67} + 720 q^{68} - 192 q^{69} - 260 q^{70} - 920 q^{71} - 432 q^{72} - 926 q^{73} + 2856 q^{74} + 300 q^{75} - 1572 q^{76} - 960 q^{78} - 1152 q^{79} + 330 q^{80} + 324 q^{81} - 1924 q^{82} + 134 q^{83} + 60 q^{84} - 370 q^{85} + 236 q^{86} - 156 q^{87} - 1064 q^{89} - 180 q^{90} + 2780 q^{91} - 4896 q^{92} + 1476 q^{93} + 1432 q^{94} - 680 q^{95} - 624 q^{96} - 1648 q^{97} + 188 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 12 * q^3 + 26 * q^4 + 20 * q^5 - 12 * q^6 - 34 * q^7 - 48 * q^8 + 36 * q^9 - 20 * q^10 + 78 * q^12 - 2 * q^13 - 52 * q^14 + 60 * q^15 + 66 * q^16 - 74 * q^17 - 36 * q^18 - 136 * q^19 + 130 * q^20 - 102 * q^21 - 64 * q^23 - 144 * q^24 + 100 * q^25 - 320 * q^26 + 108 * q^27 + 20 * q^28 - 52 * q^29 - 60 * q^30 + 492 * q^31 - 208 * q^32 + 244 * q^34 - 170 * q^35 + 234 * q^36 - 4 * q^37 - 404 * q^38 - 6 * q^39 - 240 * q^40 - 268 * q^41 - 156 * q^42 - 546 * q^43 + 180 * q^45 - 368 * q^46 - 276 * q^47 + 198 * q^48 - 496 * q^49 - 100 * q^50 - 222 * q^51 + 1084 * q^52 - 184 * q^53 - 108 * q^54 - 852 * q^56 - 408 * q^57 - 444 * q^58 - 1032 * q^59 + 390 * q^60 - 116 * q^61 + 1240 * q^62 - 306 * q^63 - 918 * q^64 - 10 * q^65 - 552 * q^67 + 720 * q^68 - 192 * q^69 - 260 * q^70 - 920 * q^71 - 432 * q^72 - 926 * q^73 + 2856 * q^74 + 300 * q^75 - 1572 * q^76 - 960 * q^78 - 1152 * q^79 + 330 * q^80 + 324 * q^81 - 1924 * q^82 + 134 * q^83 + 60 * q^84 - 370 * q^85 + 236 * q^86 - 156 * q^87 - 1064 * q^89 - 180 * q^90 + 2780 * q^91 - 4896 * q^92 + 1476 * q^93 + 1432 * q^94 - 680 * q^95 - 624 * q^96 - 1648 * q^97 + 188 * q^98

Introduction

L-functions

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Database

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