LMFDB - Embedded newform 1815.4.a.r.1.1

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:	$0$
Dimension:	$3$
Coefficient field:	3.3.47528.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 26x - 22 $ x^3 - x^2 - 26*x - 22
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.97123$ 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)

$f(q)$	$=$	$q-4.97123 q^{2} +3.00000 q^{3} +16.7131 q^{4} -5.00000 q^{5} -14.9137 q^{6} -5.48376 q^{7} -43.3148 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.97123 q^{2} +3.00000 q^{3} +16.7131 q^{4} -5.00000 q^{5} -14.9137 q^{6} -5.48376 q^{7} -43.3148 q^{8} +9.00000 q^{9} +24.8561 q^{10} +50.1393 q^{12} -24.5738 q^{13} +27.2610 q^{14} -15.0000 q^{15} +81.6231 q^{16} +59.3687 q^{17} -44.7411 q^{18} -5.89234 q^{19} -83.5655 q^{20} -16.4513 q^{21} -68.4570 q^{23} -129.945 q^{24} +25.0000 q^{25} +122.162 q^{26} +27.0000 q^{27} -91.6506 q^{28} +265.022 q^{29} +74.5684 q^{30} -196.554 q^{31} -59.2482 q^{32} -295.135 q^{34} +27.4188 q^{35} +150.418 q^{36} +166.575 q^{37} +29.2922 q^{38} -73.7214 q^{39} +216.574 q^{40} -424.101 q^{41} +81.7830 q^{42} +177.351 q^{43} -45.0000 q^{45} +340.316 q^{46} +141.148 q^{47} +244.869 q^{48} -312.928 q^{49} -124.281 q^{50} +178.106 q^{51} -410.704 q^{52} -339.828 q^{53} -134.223 q^{54} +237.528 q^{56} -17.6770 q^{57} -1317.48 q^{58} +416.784 q^{59} -250.697 q^{60} -662.146 q^{61} +977.115 q^{62} -49.3538 q^{63} -358.448 q^{64} +122.869 q^{65} +313.713 q^{67} +992.235 q^{68} -205.371 q^{69} -136.305 q^{70} -153.693 q^{71} -389.834 q^{72} -153.866 q^{73} -828.084 q^{74} +75.0000 q^{75} -98.4793 q^{76} +366.486 q^{78} -403.000 q^{79} -408.115 q^{80} +81.0000 q^{81} +2108.30 q^{82} +652.313 q^{83} -274.952 q^{84} -296.843 q^{85} -881.650 q^{86} +795.065 q^{87} +1226.77 q^{89} +223.705 q^{90} +134.757 q^{91} -1144.13 q^{92} -589.662 q^{93} -701.677 q^{94} +29.4617 q^{95} -177.745 q^{96} +959.746 q^{97} +1555.64 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} - 10 q^{10} + 90 q^{12} - 114 q^{13} - 68 q^{14} - 45 q^{15} + 178 q^{16} + 104 q^{17} + 18 q^{18} + 58 q^{19} - 150 q^{20} - 30 q^{21} + 120 q^{23} - 54 q^{24} + 75 q^{25} - 120 q^{26} + 81 q^{27} - 676 q^{28} + 220 q^{29} - 30 q^{30} + 248 q^{31} + 258 q^{32} - 80 q^{34} + 50 q^{35} + 270 q^{36} + 838 q^{37} + 600 q^{38} - 342 q^{39} + 90 q^{40} - 156 q^{41} - 204 q^{42} - 122 q^{43} - 135 q^{45} + 1256 q^{46} + 504 q^{47} + 534 q^{48} + 279 q^{49} + 50 q^{50} + 312 q^{51} - 520 q^{52} + 282 q^{53} + 54 q^{54} - 1644 q^{56} + 174 q^{57} - 1644 q^{58} + 548 q^{59} - 450 q^{60} - 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} + 570 q^{65} - 428 q^{67} + 1704 q^{68} + 360 q^{69} + 340 q^{70} - 912 q^{71} - 162 q^{72} - 618 q^{73} + 1612 q^{74} + 225 q^{75} + 2752 q^{76} - 360 q^{78} + 542 q^{79} - 890 q^{80} + 243 q^{81} + 3372 q^{82} - 2028 q^{84} - 520 q^{85} - 1548 q^{86} + 660 q^{87} + 790 q^{89} - 90 q^{90} - 772 q^{91} + 1912 q^{92} + 744 q^{93} + 424 q^{94} - 290 q^{95} + 774 q^{96} + 2074 q^{97} + 3978 q^{98}+O(q^{100}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 - 10 * q^10 + 90 * q^12 - 114 * q^13 - 68 * q^14 - 45 * q^15 + 178 * q^16 + 104 * q^17 + 18 * q^18 + 58 * q^19 - 150 * q^20 - 30 * q^21 + 120 * q^23 - 54 * q^24 + 75 * q^25 - 120 * q^26 + 81 * q^27 - 676 * q^28 + 220 * q^29 - 30 * q^30 + 248 * q^31 + 258 * q^32 - 80 * q^34 + 50 * q^35 + 270 * q^36 + 838 * q^37 + 600 * q^38 - 342 * q^39 + 90 * q^40 - 156 * q^41 - 204 * q^42 - 122 * q^43 - 135 * q^45 + 1256 * q^46 + 504 * q^47 + 534 * q^48 + 279 * q^49 + 50 * q^50 + 312 * q^51 - 520 * q^52 + 282 * q^53 + 54 * q^54 - 1644 * q^56 + 174 * q^57 - 1644 * q^58 + 548 * q^59 - 450 * q^60 - 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 + 570 * q^65 - 428 * q^67 + 1704 * q^68 + 360 * q^69 + 340 * q^70 - 912 * q^71 - 162 * q^72 - 618 * q^73 + 1612 * q^74 + 225 * q^75 + 2752 * q^76 - 360 * q^78 + 542 * q^79 - 890 * q^80 + 243 * q^81 + 3372 * q^82 - 2028 * q^84 - 520 * q^85 - 1548 * q^86 + 660 * q^87 + 790 * q^89 - 90 * q^90 - 772 * q^91 + 1912 * q^92 + 744 * q^93 + 424 * q^94 - 290 * q^95 + 774 * q^96 + 2074 * q^97 + 3978 * 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 $

$2$	−4.97123	−1.75759	−0.878797	−	0.477195i	$-0.841653\pi$
$2$	−4.97123	−1.75759	−0.878797	+	0.477195i	$0.841653\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	16.7131	2.08914
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−14.9137	−1.01475
$7$	−5.48376	−0.296095	−0.148048	−	0.988980i	$-0.547299\pi$
$7$	−5.48376	−0.296095	−0.148048	+	0.988980i	$0.547299\pi$
$8$	−43.3148	−1.91426
$9$	9.00000	0.333333
$10$	24.8561	0.786020
$11$	0	0
$11$	0	0
$12$	50.1393	1.20616
$13$	−24.5738	−0.524272	−0.262136	−	0.965031i	$-0.584427\pi$
$13$	−24.5738	−0.524272	−0.262136	+	0.965031i	$0.584427\pi$
$14$	27.2610	0.520415
$15$	−15.0000	−0.258199
$16$	81.6231	1.27536
$17$	59.3687	0.847001	0.423501	−	0.905896i	$-0.360801\pi$
$17$	59.3687	0.847001	0.423501	+	0.905896i	$0.360801\pi$
$18$	−44.7411	−0.585865
$19$	−5.89234	−0.0711471	−0.0355736	−	0.999367i	$-0.511326\pi$
$19$	−5.89234	−0.0711471	−0.0355736	+	0.999367i	$0.511326\pi$
$20$	−83.5655	−0.934291
$21$	−16.4513	−0.170951
$22$	0	0
$23$	−68.4570	−0.620621	−0.310310	−	0.950635i	$-0.600433\pi$
$23$	−68.4570	−0.620621	−0.310310	+	0.950635i	$0.600433\pi$
$24$	−129.945	−1.10520
$25$	25.0000	0.200000
$26$	122.162	0.921458
$27$	27.0000	0.192450
$28$	−91.6506	−0.618584
$29$	265.022	1.69701	0.848505	−	0.529187i	$-0.177503\pi$
$29$	265.022	1.69701	0.848505	+	0.529187i	$0.177503\pi$
$30$	74.5684	0.453809
$31$	−196.554	−1.13878	−0.569389	−	0.822068i	$-0.692820\pi$
$31$	−196.554	−1.13878	−0.569389	+	0.822068i	$0.692820\pi$
$32$	−59.2482	−0.327303
$33$	0	0
$34$	−295.135	−1.48868
$35$	27.4188	0.132418
$36$	150.418	0.696379
$37$	166.575	0.740131	0.370065	−	0.929006i	$-0.379335\pi$
$37$	166.575	0.740131	0.370065	+	0.929006i	$0.379335\pi$
$38$	29.2922	0.125048
$39$	−73.7214	−0.302689
$40$	216.574	0.856085
$41$	−424.101	−1.61545	−0.807725	−	0.589559i	$-0.799301\pi$
$41$	−424.101	−1.61545	−0.807725	+	0.589559i	$0.799301\pi$
$42$	81.7830	0.300462
$43$	177.351	0.628970	0.314485	−	0.949262i	$-0.398168\pi$
$43$	177.351	0.628970	0.314485	+	0.949262i	$0.398168\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	340.316	1.09080
$47$	141.148	0.438053	0.219026	−	0.975719i	$-0.429712\pi$
$47$	141.148	0.438053	0.219026	+	0.975719i	$0.429712\pi$
$48$	244.869	0.736330
$49$	−312.928	−0.912328
$50$	−124.281	−0.351519
$51$	178.106	0.489016
$52$	−410.704	−1.09528
$53$	−339.828	−0.880736	−0.440368	−	0.897817i	$-0.645152\pi$
$53$	−339.828	−0.880736	−0.440368	+	0.897817i	$0.645152\pi$
$54$	−134.223	−0.338249
$55$	0	0
$56$	237.528	0.566804
$57$	−17.6770	−0.0410768
$58$	−1317.48	−2.98266
$59$	416.784	0.919672	0.459836	−	0.888004i	$-0.347908\pi$
$59$	416.784	0.919672	0.459836	+	0.888004i	$0.347908\pi$
$60$	−250.697	−0.539413
$61$	−662.146	−1.38982	−0.694911	−	0.719096i	$-0.744556\pi$
$61$	−662.146	−1.38982	−0.694911	+	0.719096i	$0.744556\pi$
$62$	977.115	2.00151
$63$	−49.3538	−0.0986984
$64$	−358.448	−0.700094
$65$	122.869	0.234462
$66$	0	0
$67$	313.713	0.572032	0.286016	−	0.958225i	$-0.407669\pi$
$67$	313.713	0.572032	0.286016	+	0.958225i	$0.407669\pi$
$68$	992.235	1.76950
$69$	−205.371	−0.358316
$70$	−136.305	−0.232737
$71$	−153.693	−0.256902	−0.128451	−	0.991716i	$-0.541000\pi$
$71$	−153.693	−0.256902	−0.128451	+	0.991716i	$0.541000\pi$
$72$	−389.834	−0.638088
$73$	−153.866	−0.246694	−0.123347	−	0.992364i	$-0.539363\pi$
$73$	−153.866	−0.246694	−0.123347	+	0.992364i	$0.539363\pi$
$74$	−828.084	−1.30085
$75$	75.0000	0.115470
$76$	−98.4793	−0.148636
$77$	0	0
$78$	366.486	0.532004
$79$	−403.000	−0.573938	−0.286969	−	0.957940i	$-0.592648\pi$
$79$	−403.000	−0.573938	−0.286969	+	0.957940i	$0.592648\pi$
$80$	−408.115	−0.570359
$81$	81.0000	0.111111
$82$	2108.30	2.83931
$83$	652.313	0.862659	0.431329	−	0.902195i	$-0.358045\pi$
$83$	652.313	0.862659	0.431329	+	0.902195i	$0.358045\pi$
$84$	−274.952	−0.357139
$85$	−296.843	−0.378790
$86$	−881.650	−1.10547
$87$	795.065	0.979769
$88$	0	0
$89$	1226.77	1.46109	0.730545	−	0.682864i	$-0.239266\pi$
$89$	1226.77	1.46109	0.730545	+	0.682864i	$0.239266\pi$
$90$	223.705	0.262007
$91$	134.757	0.155234
$92$	−1144.13	−1.29656
$93$	−589.662	−0.657474
$94$	−701.677	−0.769919
$95$	29.4617	0.0318180
$96$	−177.745	−0.188969
$97$	959.746	1.00461	0.502306	−	0.864690i	$-0.332485\pi$
$97$	959.746	1.00461	0.502306	+	0.864690i	$0.332485\pi$
$98$	1555.64	1.60350
$99$	0	0
$100$	417.828	0.417828
$101$	1258.52	1.23988	0.619939	−	0.784650i	$-0.287157\pi$
$101$	1258.52	1.23988	0.619939	+	0.784650i	$0.287157\pi$
$102$	−885.406	−0.859492
$103$	−493.175	−0.471786	−0.235893	−	0.971779i	$-0.575802\pi$
$103$	−493.175	−0.471786	−0.235893	+	0.971779i	$0.575802\pi$
$104$	1064.41	1.00360
$105$	82.2564	0.0764514
$106$	1689.36	1.54798
$107$	1099.05	0.992983	0.496492	−	0.868042i	$-0.334621\pi$
$107$	1099.05	0.992983	0.496492	+	0.868042i	$0.334621\pi$
$108$	451.254	0.402055
$109$	−1275.04	−1.12043	−0.560216	−	0.828347i	$-0.689282\pi$
$109$	−1275.04	−1.12043	−0.560216	+	0.828347i	$0.689282\pi$
$110$	0	0
$111$	499.726	0.427315
$112$	−447.601	−0.377628
$113$	−946.433	−0.787902	−0.393951	−	0.919131i	$-0.628892\pi$
$113$	−946.433	−0.787902	−0.393951	+	0.919131i	$0.628892\pi$
$114$	87.8765	0.0721964
$115$	342.285	0.277550
$116$	4429.34	3.54529
$117$	−221.164	−0.174757
$118$	−2071.93	−1.61641
$119$	−325.563	−0.250793
$120$	649.723	0.494261
$121$	0	0
$122$	3291.68	2.44274
$123$	−1272.30	−0.932681
$124$	−3285.03	−2.37907
$125$	−125.000	−0.0894427
$126$	245.349	0.173472
$127$	−2260.77	−1.57962	−0.789808	−	0.613354i	$-0.789820\pi$
$127$	−2260.77	−1.57962	−0.789808	+	0.613354i	$0.789820\pi$
$128$	2255.91	1.55778
$129$	532.052	0.363136
$130$	−610.809	−0.412089
$131$	57.1277	0.0381013	0.0190507	−	0.999819i	$-0.493936\pi$
$131$	57.1277	0.0381013	0.0190507	+	0.999819i	$0.493936\pi$
$132$	0	0
$133$	32.3122	0.0210663
$134$	−1559.54	−1.00540
$135$	−135.000	−0.0860663
$136$	−2571.54	−1.62138
$137$	1919.27	1.19689	0.598447	−	0.801162i	$-0.295785\pi$
$137$	1919.27	1.19689	0.598447	+	0.801162i	$0.295785\pi$
$138$	1020.95	0.629774
$139$	1690.46	1.03153	0.515766	−	0.856729i	$-0.327507\pi$
$139$	1690.46	1.03153	0.515766	+	0.856729i	$0.327507\pi$
$140$	458.253	0.276639
$141$	423.443	0.252910
$142$	764.044	0.451529
$143$	0	0
$144$	734.608	0.425120
$145$	−1325.11	−0.758926
$146$	764.904	0.433588
$147$	−938.785	−0.526733
$148$	2783.99	1.54624
$149$	2077.88	1.14246	0.571231	−	0.820789i	$-0.306466\pi$
$149$	2077.88	1.14246	0.571231	+	0.820789i	$0.306466\pi$
$150$	−372.842	−0.202950
$151$	−2711.16	−1.46113	−0.730566	−	0.682842i	$-0.760744\pi$
$151$	−2711.16	−1.46113	−0.730566	+	0.682842i	$0.760744\pi$
$152$	255.226	0.136194
$153$	534.318	0.282334
$154$	0	0
$155$	982.770	0.509277
$156$	−1232.11	−0.632359
$157$	2341.23	1.19013	0.595066	−	0.803677i	$-0.297126\pi$
$157$	2341.23	1.19013	0.595066	+	0.803677i	$0.297126\pi$
$158$	2003.41	1.00875
$159$	−1019.48	−0.508493
$160$	296.241	0.146374
$161$	375.402	0.183763
$162$	−402.669	−0.195288
$163$	3523.01	1.69291	0.846453	−	0.532464i	$-0.178734\pi$
$163$	3523.01	1.69291	0.846453	+	0.532464i	$0.178734\pi$
$164$	−7088.05	−3.37490
$165$	0	0
$166$	−3242.80	−1.51620
$167$	−4011.90	−1.85898	−0.929492	−	0.368842i	$-0.879754\pi$
$167$	−4011.90	−1.85898	−0.929492	+	0.368842i	$0.879754\pi$
$168$	712.584	0.327244
$169$	−1593.13	−0.725138
$170$	1475.68	0.665760
$171$	−53.0310	−0.0237157
$172$	2964.08	1.31400
$173$	−3325.30	−1.46137	−0.730687	−	0.682713i	$-0.760800\pi$
$173$	−3325.30	−1.46137	−0.730687	+	0.682713i	$0.760800\pi$
$174$	−3952.45	−1.72204
$175$	−137.094	−0.0592190
$176$	0	0
$177$	1250.35	0.530973
$178$	−6098.54	−2.56800
$179$	−26.6350	−0.0111217	−0.00556087	−	0.999985i	$-0.501770\pi$
$179$	−26.6350	−0.0111217	−0.00556087	+	0.999985i	$0.501770\pi$
$180$	−752.090	−0.311430
$181$	1934.25	0.794320	0.397160	−	0.917749i	$-0.369996\pi$
$181$	1934.25	0.794320	0.397160	+	0.917749i	$0.369996\pi$
$182$	−669.906	−0.272839
$183$	−1986.44	−0.802414
$184$	2965.21	1.18803
$185$	−832.877	−0.330996
$186$	2931.34	1.15557
$187$	0	0
$188$	2359.01	0.915153
$189$	−148.061	−0.0569835
$190$	−146.461	−0.0559231
$191$	−3341.59	−1.26591	−0.632956	−	0.774188i	$-0.718158\pi$
$191$	−3341.59	−1.26591	−0.632956	+	0.774188i	$0.718158\pi$
$192$	−1075.34	−0.404200
$193$	1293.97	0.482600	0.241300	−	0.970451i	$-0.422426\pi$
$193$	1293.97	0.482600	0.241300	+	0.970451i	$0.422426\pi$
$194$	−4771.12	−1.76570
$195$	368.607	0.135367
$196$	−5230.01	−1.90598
$197$	2301.17	0.832240	0.416120	−	0.909310i	$-0.363390\pi$
$197$	2301.17	0.832240	0.416120	+	0.909310i	$0.363390\pi$
$198$	0	0
$199$	−3039.64	−1.08279	−0.541393	−	0.840770i	$-0.682103\pi$
$199$	−3039.64	−1.08279	−0.541393	+	0.840770i	$0.682103\pi$
$200$	−1082.87	−0.382853
$201$	941.139	0.330263
$202$	−6256.40	−2.17920
$203$	−1453.31	−0.502476
$204$	2976.70	1.02162
$205$	2120.51	0.722451
$206$	2451.69	0.829209
$207$	−616.113	−0.206874
$208$	−2005.79	−0.668636
$209$	0	0
$210$	−408.915	−0.134371
$211$	−2807.86	−0.916119	−0.458060	−	0.888921i	$-0.651455\pi$
$211$	−2807.86	−0.916119	−0.458060	+	0.888921i	$0.651455\pi$
$212$	−5679.58	−1.83998
$213$	−461.080	−0.148322
$214$	−5463.63	−1.74526
$215$	−886.753	−0.281284
$216$	−1169.50	−0.368400
$217$	1077.85	0.337187
$218$	6338.53	1.96926
$219$	−461.598	−0.142429
$220$	0	0
$221$	−1458.91	−0.444059
$222$	−2484.25	−0.751046
$223$	1443.09	0.433348	0.216674	−	0.976244i	$-0.430479\pi$
$223$	1443.09	0.433348	0.216674	+	0.976244i	$0.430479\pi$
$224$	324.903	0.0969129
$225$	225.000	0.0666667
$226$	4704.94	1.38481
$227$	−3658.71	−1.06977	−0.534884	−	0.844926i	$-0.679645\pi$
$227$	−3658.71	−1.06977	−0.534884	+	0.844926i	$0.679645\pi$
$228$	−295.438	−0.0858151
$229$	−1695.50	−0.489265	−0.244632	−	0.969616i	$-0.578667\pi$
$229$	−1695.50	−0.489265	−0.244632	+	0.969616i	$0.578667\pi$
$230$	−1701.58	−0.487821
$231$	0	0
$232$	−11479.4	−3.24853
$233$	5782.24	1.62578	0.812890	−	0.582417i	$-0.197893\pi$
$233$	5782.24	1.62578	0.812890	+	0.582417i	$0.197893\pi$
$234$	1099.46	0.307153
$235$	−705.738	−0.195903
$236$	6965.76	1.92132
$237$	−1209.00	−0.331363
$238$	1618.45	0.440792
$239$	5836.16	1.57954	0.789770	−	0.613404i	$-0.210200\pi$
$239$	5836.16	1.57954	0.789770	+	0.613404i	$0.210200\pi$
$240$	−1224.35	−0.329297
$241$	982.308	0.262556	0.131278	−	0.991346i	$-0.458092\pi$
$241$	982.308	0.262556	0.131278	+	0.991346i	$0.458092\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−11066.5	−2.90353
$245$	1564.64	0.408005
$246$	6324.91	1.63927
$247$	144.797	0.0373005
$248$	8513.70	2.17992
$249$	1956.94	0.498056
$250$	621.403	0.157204
$251$	4320.23	1.08642	0.543209	−	0.839598i	$-0.317209\pi$
$251$	4320.23	1.08642	0.543209	+	0.839598i	$0.317209\pi$
$252$	−824.856	−0.206195
$253$	0	0
$254$	11238.8	2.77633
$255$	−890.530	−0.218695
$256$	−8347.07	−2.03786
$257$	−6224.29	−1.51074	−0.755371	−	0.655298i	$-0.772543\pi$
$257$	−6224.29	−1.51074	−0.755371	+	0.655298i	$0.772543\pi$
$258$	−2644.95	−0.638246
$259$	−913.459	−0.219149
$260$	2053.52	0.489823
$261$	2385.20	0.565670
$262$	−283.995	−0.0669666
$263$	2588.95	0.607002	0.303501	−	0.952831i	$-0.401844\pi$
$263$	2588.95	0.607002	0.303501	+	0.952831i	$0.401844\pi$
$264$	0	0
$265$	1699.14	0.393877
$266$	−160.631	−0.0370260
$267$	3680.30	0.843561
$268$	5243.12	1.19505
$269$	−5871.53	−1.33083	−0.665415	−	0.746473i	$-0.731746\pi$
$269$	−5871.53	−1.33083	−0.665415	+	0.746473i	$0.731746\pi$
$270$	671.116	0.151270
$271$	3306.93	0.741261	0.370630	−	0.928780i	$-0.379142\pi$
$271$	3306.93	0.741261	0.370630	+	0.928780i	$0.379142\pi$
$272$	4845.85	1.08023
$273$	404.270	0.0896247
$274$	−9541.14	−2.10366
$275$	0	0
$276$	−3432.39	−0.748571
$277$	2861.37	0.620660	0.310330	−	0.950629i	$-0.399560\pi$
$277$	2861.37	0.620660	0.310330	+	0.950629i	$0.399560\pi$
$278$	−8403.66	−1.81302
$279$	−1768.99	−0.379593
$280$	−1187.64	−0.253482
$281$	2988.05	0.634349	0.317174	−	0.948367i	$-0.397266\pi$
$281$	2988.05	0.634349	0.317174	+	0.948367i	$0.397266\pi$
$282$	−2105.03	−0.444513
$283$	−1454.60	−0.305536	−0.152768	−	0.988262i	$-0.548819\pi$
$283$	−1454.60	−0.305536	−0.152768	+	0.988262i	$0.548819\pi$
$284$	−2568.69	−0.536704
$285$	88.3851	0.0183701
$286$	0	0
$287$	2325.67	0.478327
$288$	−533.234	−0.109101
$289$	−1388.36	−0.282589
$290$	6587.42	1.33388
$291$	2879.24	0.580014
$292$	−2571.58	−0.515378
$293$	8586.52	1.71205	0.856023	−	0.516937i	$-0.172928\pi$
$293$	8586.52	1.71205	0.856023	+	0.516937i	$0.172928\pi$
$294$	4666.92	0.925782
$295$	−2083.92	−0.411290
$296$	−7215.19	−1.41681
$297$	0	0
$298$	−10329.6	−2.00798
$299$	1682.25	0.325374
$300$	1253.48	0.241233
$301$	−972.547	−0.186235
$302$	13477.8	2.56808
$303$	3775.57	0.715844
$304$	−480.951	−0.0907382
$305$	3310.73	0.621547
$306$	−2656.22	−0.496228
$307$	−529.029	−0.0983495	−0.0491748	−	0.998790i	$-0.515659\pi$
$307$	−529.029	−0.0983495	−0.0491748	+	0.998790i	$0.515659\pi$
$308$	0	0
$309$	−1479.53	−0.272386
$310$	−4885.57	−0.895103
$311$	−5008.00	−0.913111	−0.456555	−	0.889695i	$-0.650917\pi$
$311$	−5008.00	−0.913111	−0.456555	+	0.889695i	$0.650917\pi$
$312$	3193.23	0.579426
$313$	7858.53	1.41914	0.709570	−	0.704635i	$-0.248889\pi$
$313$	7858.53	1.41914	0.709570	+	0.704635i	$0.248889\pi$
$314$	−11638.8	−2.09177
$315$	246.769	0.0441392
$316$	−6735.39	−1.19904
$317$	7747.04	1.37261	0.686304	−	0.727315i	$-0.259232\pi$
$317$	7747.04	1.37261	0.686304	+	0.727315i	$0.259232\pi$
$318$	5068.09	0.893724
$319$	0	0
$320$	1792.24	0.313092
$321$	3297.15	0.573299
$322$	−1866.21	−0.322980
$323$	−349.820	−0.0602617
$324$	1353.76	0.232126
$325$	−614.345	−0.104854
$326$	−17513.7	−2.97544
$327$	−3825.13	−0.646882
$328$	18369.9	3.09240
$329$	−774.019	−0.129705
$330$	0	0
$331$	1355.08	0.225022	0.112511	−	0.993650i	$-0.464111\pi$
$331$	1355.08	0.225022	0.112511	+	0.993650i	$0.464111\pi$
$332$	10902.2	1.80221
$333$	1499.18	0.246710
$334$	19944.1	3.26734
$335$	−1568.57	−0.255821
$336$	−1342.80	−0.218024
$337$	−2596.97	−0.419780	−0.209890	−	0.977725i	$-0.567311\pi$
$337$	−2596.97	−0.419780	−0.209890	+	0.977725i	$0.567311\pi$
$338$	7919.81	1.27450
$339$	−2839.30	−0.454896
$340$	−4961.17	−0.791345
$341$	0	0
$342$	263.629	0.0416826
$343$	3596.95	0.566231
$344$	−7681.91	−1.20401
$345$	1026.86	0.160244
$346$	16530.8	2.56850
$347$	−266.820	−0.0412785	−0.0206392	−	0.999787i	$-0.506570\pi$
$347$	−266.820	−0.0412785	−0.0206392	+	0.999787i	$0.506570\pi$
$348$	13288.0	2.04687
$349$	10549.4	1.61804	0.809021	−	0.587780i	$-0.199998\pi$
$349$	10549.4	1.61804	0.809021	+	0.587780i	$0.199998\pi$
$350$	681.525	0.104083
$351$	−663.492	−0.100896
$352$	0	0
$353$	7152.63	1.07846	0.539229	−	0.842159i	$-0.318716\pi$
$353$	7152.63	1.07846	0.539229	+	0.842159i	$0.318716\pi$
$354$	−6215.79	−0.933235
$355$	768.467	0.114890
$356$	20503.1	3.05242
$357$	−976.690	−0.144795
$358$	132.409	0.0195475
$359$	−359.182	−0.0528047	−0.0264024	−	0.999651i	$-0.508405\pi$
$359$	−359.182	−0.0528047	−0.0264024	+	0.999651i	$0.508405\pi$
$360$	1949.17	0.285362
$361$	−6824.28	−0.994938
$362$	−9615.62	−1.39609
$363$	0	0
$364$	2252.20	0.324306
$365$	769.331	0.110325
$366$	9875.04	1.41032
$367$	9042.47	1.28614	0.643070	−	0.765808i	$-0.277661\pi$
$367$	9042.47	1.28614	0.643070	+	0.765808i	$0.277661\pi$
$368$	−5587.67	−0.791515
$369$	−3816.91	−0.538483
$370$	4140.42	0.581758
$371$	1863.54	0.260781
$372$	−9855.08	−1.37355
$373$	11929.0	1.65592	0.827960	−	0.560787i	$-0.189501\pi$
$373$	11929.0	1.65592	0.827960	+	0.560787i	$0.189501\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	−6113.78	−0.838549
$377$	−6512.59	−0.889696
$378$	736.047	0.100154
$379$	6556.08	0.888557	0.444279	−	0.895889i	$-0.353460\pi$
$379$	6556.08	0.888557	0.444279	+	0.895889i	$0.353460\pi$
$380$	492.396	0.0664721
$381$	−6782.32	−0.911992
$382$	16611.8	2.22496
$383$	10703.1	1.42795	0.713975	−	0.700172i	$-0.246893\pi$
$383$	10703.1	1.42795	0.713975	+	0.700172i	$0.246893\pi$
$384$	6767.74	0.899388
$385$	0	0
$386$	−6432.60	−0.848214
$387$	1596.15	0.209657
$388$	16040.3	2.09878
$389$	−6450.30	−0.840728	−0.420364	−	0.907355i	$-0.638098\pi$
$389$	−6450.30	−0.840728	−0.420364	+	0.907355i	$0.638098\pi$
$390$	−1832.43	−0.237920
$391$	−4064.20	−0.525667
$392$	13554.4	1.74644
$393$	171.383	0.0219978
$394$	−11439.6	−1.46274
$395$	2015.00	0.256673
$396$	0	0
$397$	−12526.0	−1.58353	−0.791764	−	0.610828i	$-0.790837\pi$
$397$	−12526.0	−1.58353	−0.791764	+	0.610828i	$0.790837\pi$
$398$	15110.7	1.90310
$399$	96.9365	0.0121626
$400$	2040.58	0.255072
$401$	9119.52	1.13568	0.567839	−	0.823139i	$-0.307779\pi$
$401$	9119.52	1.13568	0.567839	+	0.823139i	$0.307779\pi$
$402$	−4678.62	−0.580468
$403$	4830.08	0.597030
$404$	21033.8	2.59028
$405$	−405.000	−0.0496904
$406$	7224.76	0.883150
$407$	0	0
$408$	−7714.63	−0.936106
$409$	596.921	0.0721658	0.0360829	−	0.999349i	$-0.488512\pi$
$409$	596.921	0.0721658	0.0360829	+	0.999349i	$0.488512\pi$
$410$	−10541.5	−1.26978
$411$	5757.82	0.691027
$412$	−8242.49	−0.985627
$413$	−2285.54	−0.272310
$414$	3062.84	0.363600
$415$	−3261.57	−0.385793
$416$	1455.95	0.171596
$417$	5071.38	0.595555
$418$	0	0
$419$	11560.5	1.34789	0.673944	−	0.738782i	$-0.264599\pi$
$419$	11560.5	1.34789	0.673944	+	0.738782i	$0.264599\pi$
$420$	1374.76	0.159718
$421$	15182.6	1.75761	0.878805	−	0.477182i	$-0.158342\pi$
$421$	15182.6	1.75761	0.878805	+	0.477182i	$0.158342\pi$
$422$	13958.5	1.61017
$423$	1270.33	0.146018
$424$	14719.6	1.68596
$425$	1484.22	0.169400
$426$	2292.13	0.260691
$427$	3631.05	0.411519
$428$	18368.5	2.07448
$429$	0	0
$430$	4408.25	0.494383
$431$	14902.7	1.66551	0.832757	−	0.553639i	$-0.186761\pi$
$431$	14902.7	1.66551	0.832757	+	0.553639i	$0.186761\pi$
$432$	2203.82	0.245443
$433$	−2269.85	−0.251922	−0.125961	−	0.992035i	$-0.540201\pi$
$433$	−2269.85	−0.251922	−0.125961	+	0.992035i	$0.540201\pi$
$434$	−5358.26	−0.592637
$435$	−3975.33	−0.438166
$436$	−21309.9	−2.34074
$437$	403.372	0.0441554
$438$	2294.71	0.250332
$439$	13418.7	1.45886	0.729431	−	0.684054i	$-0.239785\pi$
$439$	13418.7	1.45886	0.729431	+	0.684054i	$0.239785\pi$
$440$	0	0
$441$	−2816.36	−0.304109
$442$	7252.59	0.780476
$443$	11507.5	1.23417	0.617086	−	0.786896i	$-0.288313\pi$
$443$	11507.5	1.23417	0.617086	+	0.786896i	$0.288313\pi$
$444$	8351.98	0.892719
$445$	−6133.84	−0.653420
$446$	−7173.94	−0.761650
$447$	6233.65	0.659601
$448$	1965.64	0.207294
$449$	−16203.8	−1.70313	−0.851564	−	0.524250i	$-0.824346\pi$
$449$	−16203.8	−1.70313	−0.851564	+	0.524250i	$0.824346\pi$
$450$	−1118.53	−0.117173
$451$	0	0
$452$	−15817.8	−1.64604
$453$	−8133.48	−0.843585
$454$	18188.3	1.88022
$455$	−673.783	−0.0694230
$456$	765.677	0.0786318
$457$	−4912.79	−0.502868	−0.251434	−	0.967874i	$-0.580902\pi$
$457$	−4912.79	−0.502868	−0.251434	+	0.967874i	$0.580902\pi$
$458$	8428.70	0.859929
$459$	1602.95	0.163005
$460$	5720.65	0.579841
$461$	14270.8	1.44178	0.720888	−	0.693051i	$-0.243734\pi$
$461$	14270.8	1.44178	0.720888	+	0.693051i	$0.243734\pi$
$462$	0	0
$463$	6656.46	0.668146	0.334073	−	0.942547i	$-0.391577\pi$
$463$	6656.46	0.668146	0.334073	+	0.942547i	$0.391577\pi$
$464$	21631.9	2.16430
$465$	2948.31	0.294031
$466$	−28744.8	−2.85746
$467$	19347.7	1.91714	0.958571	−	0.284853i	$-0.0919446\pi$
$467$	19347.7	1.91714	0.958571	+	0.284853i	$0.0919446\pi$
$468$	−3696.34	−0.365093
$469$	−1720.33	−0.169376
$470$	3508.38	0.344318
$471$	7023.70	0.687123
$472$	−18052.9	−1.76050
$473$	0	0
$474$	6010.22	0.582402
$475$	−147.308	−0.0142294
$476$	−5441.18	−0.523941
$477$	−3058.45	−0.293579
$478$	−29012.9	−2.77619
$479$	−9826.69	−0.937355	−0.468678	−	0.883369i	$-0.655269\pi$
$479$	−9826.69	−0.937355	−0.468678	+	0.883369i	$0.655269\pi$
$480$	888.723	0.0845093
$481$	−4093.39	−0.388030
$482$	−4883.28	−0.461467
$483$	1126.21	0.106095
$484$	0	0
$485$	−4798.73	−0.449277
$486$	−1208.01	−0.112750
$487$	10278.1	0.956353	0.478176	−	0.878264i	$-0.341298\pi$
$487$	10278.1	0.956353	0.478176	+	0.878264i	$0.341298\pi$
$488$	28680.7	2.66048
$489$	10569.0	0.977400
$490$	−7778.19	−0.717108
$491$	−11397.1	−1.04755	−0.523773	−	0.851858i	$-0.675476\pi$
$491$	−11397.1	−1.04755	−0.523773	+	0.851858i	$0.675476\pi$
$492$	−21264.1	−1.94850
$493$	15734.0	1.43737
$494$	−719.819	−0.0655591
$495$	0	0
$496$	−16043.3	−1.45235
$497$	842.817	0.0760674
$498$	−9728.39	−0.875381
$499$	−9179.17	−0.823479	−0.411740	−	0.911302i	$-0.635079\pi$
$499$	−9179.17	−0.823479	−0.411740	+	0.911302i	$0.635079\pi$
$500$	−2089.14	−0.186858
$501$	−12035.7	−1.07329
$502$	−21476.9	−1.90948
$503$	−6782.80	−0.601253	−0.300626	−	0.953742i	$-0.597196\pi$
$503$	−6782.80	−0.601253	−0.300626	+	0.953742i	$0.597196\pi$
$504$	2137.75	0.188935
$505$	−6292.61	−0.554490
$506$	0	0
$507$	−4779.39	−0.418659
$508$	−37784.6	−3.30004
$509$	6814.24	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$509$	6814.24	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$510$	4427.03	0.384377
$511$	843.765	0.0730449
$512$	23447.9	2.02395
$513$	−159.093	−0.0136923
$514$	30942.4	2.65527
$515$	2465.88	0.210989
$516$	8892.23	0.758641
$517$	0	0
$518$	4541.01	0.385175
$519$	−9975.89	−0.843724
$520$	−5322.05	−0.448822
$521$	206.712	0.0173824	0.00869118	−	0.999962i	$-0.497233\pi$
$521$	206.712	0.0173824	0.00869118	+	0.999962i	$0.497233\pi$
$522$	−11857.4	−0.994219
$523$	11375.9	0.951118	0.475559	−	0.879684i	$-0.342246\pi$
$523$	11375.9	0.951118	0.475559	+	0.879684i	$0.342246\pi$
$524$	954.781	0.0795989
$525$	−411.282	−0.0341901
$526$	−12870.3	−1.06686
$527$	−11669.1	−0.964547
$528$	0	0
$529$	−7480.63	−0.614830
$530$	−8446.82	−0.692276
$531$	3751.06	0.306557
$532$	540.036	0.0440104
$533$	10421.8	0.846936
$534$	−18295.6	−1.48264
$535$	−5495.25	−0.444076
$536$	−13588.4	−1.09502
$537$	−79.9049	−0.00642114
$538$	29188.7	2.33906
$539$	0	0
$540$	−2256.27	−0.179804
$541$	10228.1	0.812831	0.406415	−	0.913688i	$-0.366779\pi$
$541$	10228.1	0.812831	0.406415	+	0.913688i	$0.366779\pi$
$542$	−16439.5	−1.30284
$543$	5802.76	0.458601
$544$	−3517.49	−0.277226
$545$	6375.22	0.501072
$546$	−2009.72	−0.157524
$547$	15538.9	1.21461	0.607307	−	0.794467i	$-0.292250\pi$
$547$	15538.9	1.21461	0.607307	+	0.794467i	$0.292250\pi$
$548$	32077.0	2.50048
$549$	−5959.31	−0.463274
$550$	0	0
$551$	−1561.60	−0.120737
$552$	8895.62	0.685911
$553$	2209.96	0.169940
$554$	−14224.5	−1.09087
$555$	−2498.63	−0.191101
$556$	28252.8	2.15501
$557$	5191.17	0.394896	0.197448	−	0.980313i	$-0.436735\pi$
$557$	5191.17	0.394896	0.197448	+	0.980313i	$0.436735\pi$
$558$	8794.03	0.667170
$559$	−4358.17	−0.329752
$560$	2238.01	0.168880
$561$	0	0
$562$	−14854.3	−1.11493
$563$	−13722.9	−1.02727	−0.513635	−	0.858009i	$-0.671701\pi$
$563$	−13722.9	−1.02727	−0.513635	+	0.858009i	$0.671701\pi$
$564$	7077.04	0.528364
$565$	4732.17	0.352361
$566$	7231.13	0.537009
$567$	−444.184	−0.0328995
$568$	6657.20	0.491778
$569$	−23209.0	−1.70997	−0.854986	−	0.518652i	$-0.826434\pi$
$569$	−23209.0	−1.70997	−0.854986	+	0.518652i	$0.826434\pi$
$570$	−439.382	−0.0322872
$571$	13130.5	0.962337	0.481168	−	0.876628i	$-0.340213\pi$
$571$	13130.5	0.962337	0.481168	+	0.876628i	$0.340213\pi$
$572$	0	0
$573$	−10024.8	−0.730874
$574$	−11561.4	−0.840705
$575$	−1711.43	−0.124124
$576$	−3226.03	−0.233365
$577$	−12261.0	−0.884633	−0.442317	−	0.896859i	$-0.645843\pi$
$577$	−12261.0	−0.884633	−0.442317	+	0.896859i	$0.645843\pi$
$578$	6901.86	0.496677
$579$	3881.90	0.278629
$580$	−22146.7	−1.58550
$581$	−3577.13	−0.255429
$582$	−14313.3	−1.01943
$583$	0	0
$584$	6664.69	0.472238
$585$	1105.82	0.0781539
$586$	−42685.5	−3.00908
$587$	−3553.42	−0.249856	−0.124928	−	0.992166i	$-0.539870\pi$
$587$	−3553.42	−0.249856	−0.124928	+	0.992166i	$0.539870\pi$
$588$	−15690.0	−1.10042
$589$	1158.16	0.0810208
$590$	10359.6	0.722881
$591$	6903.50	0.480494
$592$	13596.4	0.943933
$593$	−1942.83	−0.134540	−0.0672701	−	0.997735i	$-0.521429\pi$
$593$	−1942.83	−0.134540	−0.0672701	+	0.997735i	$0.521429\pi$
$594$	0	0
$595$	1627.82	0.112158
$596$	34727.9	2.38676
$597$	−9118.92	−0.625147
$598$	−8362.84	−0.571876
$599$	18585.4	1.26774	0.633871	−	0.773439i	$-0.281465\pi$
$599$	18585.4	1.26774	0.633871	+	0.773439i	$0.281465\pi$
$600$	−3248.61	−0.221040
$601$	−8010.10	−0.543658	−0.271829	−	0.962346i	$-0.587629\pi$
$601$	−8010.10	−0.543658	−0.271829	+	0.962346i	$0.587629\pi$
$602$	4834.75	0.327325
$603$	2823.42	0.190677
$604$	−45311.9	−3.05251
$605$	0	0
$606$	−18769.2	−1.25816
$607$	1537.69	0.102822	0.0514111	−	0.998678i	$-0.483628\pi$
$607$	1537.69	0.102822	0.0514111	+	0.998678i	$0.483628\pi$
$608$	349.110	0.0232867
$609$	−4359.94	−0.290105
$610$	−16458.4	−1.09243
$611$	−3468.53	−0.229659
$612$	8930.11	0.589834
$613$	−2298.75	−0.151461	−0.0757304	−	0.997128i	$-0.524129\pi$
$613$	−2298.75	−0.151461	−0.0757304	+	0.997128i	$0.524129\pi$
$614$	2629.93	0.172859
$615$	6361.52	0.417107
$616$	0	0
$617$	6089.51	0.397333	0.198666	−	0.980067i	$-0.436339\pi$
$617$	6089.51	0.397333	0.198666	+	0.980067i	$0.436339\pi$
$618$	7355.06	0.478744
$619$	12255.4	0.795775	0.397887	−	0.917434i	$-0.369743\pi$
$619$	12255.4	0.795775	0.397887	+	0.917434i	$0.369743\pi$
$620$	16425.1	1.06395
$621$	−1848.34	−0.119439
$622$	24895.9	1.60488
$623$	−6727.29	−0.432622
$624$	−6017.36	−0.386037
$625$	625.000	0.0400000
$626$	−39066.6	−2.49427
$627$	0	0
$628$	39129.3	2.48635
$629$	9889.36	0.626891
$630$	−1226.75	−0.0775789
$631$	−25746.5	−1.62433	−0.812165	−	0.583428i	$-0.801711\pi$
$631$	−25746.5	−1.62433	−0.812165	+	0.583428i	$0.801711\pi$
$632$	17455.9	1.09867
$633$	−8423.58	−0.528922
$634$	−38512.3	−2.41249
$635$	11303.9	0.706426
$636$	−17038.8	−1.06231
$637$	7689.84	0.478308
$638$	0	0
$639$	−1383.24	−0.0856340
$640$	−11279.6	−0.696663
$641$	−598.022	−0.0368494	−0.0184247	−	0.999830i	$-0.505865\pi$
$641$	−598.022	−0.0368494	−0.0184247	+	0.999830i	$0.505865\pi$
$642$	−16390.9	−1.00763
$643$	14610.9	0.896109	0.448054	−	0.894006i	$-0.352117\pi$
$643$	14610.9	0.896109	0.448054	+	0.894006i	$0.352117\pi$
$644$	6274.13	0.383906
$645$	−2660.26	−0.162399
$646$	1739.04	0.105916
$647$	−17252.3	−1.04831	−0.524156	−	0.851622i	$-0.675619\pi$
$647$	−17252.3	−1.04831	−0.524156	+	0.851622i	$0.675619\pi$
$648$	−3508.50	−0.212696
$649$	0	0
$650$	3054.05	0.184292
$651$	3233.56	0.194675
$652$	58880.5	3.53671
$653$	−17768.6	−1.06484	−0.532418	−	0.846481i	$-0.678717\pi$
$653$	−17768.6	−1.06484	−0.532418	+	0.846481i	$0.678717\pi$
$654$	19015.6	1.13696
$655$	−285.639	−0.0170394
$656$	−34616.4	−2.06028
$657$	−1384.80	−0.0822314
$658$	3847.82	0.227969
$659$	17594.9	1.04006	0.520031	−	0.854147i	$-0.325920\pi$
$659$	17594.9	1.04006	0.520031	+	0.854147i	$0.325920\pi$
$660$	0	0
$661$	23355.9	1.37434	0.687170	−	0.726497i	$-0.258853\pi$
$661$	23355.9	1.37434	0.687170	+	0.726497i	$0.258853\pi$
$662$	−6736.44	−0.395497
$663$	−4376.74	−0.256378
$664$	−28254.8	−1.65136
$665$	−161.561	−0.00942114
$666$	−7452.76	−0.433617
$667$	−18142.6	−1.05320
$668$	−67051.4	−3.88368
$669$	4329.28	0.250194
$670$	7797.70	0.449629
$671$	0	0
$672$	974.708	0.0559527
$673$	2340.47	0.134054	0.0670271	−	0.997751i	$-0.478649\pi$
$673$	2340.47	0.134054	0.0670271	+	0.997751i	$0.478649\pi$
$674$	12910.1	0.737803
$675$	675.000	0.0384900
$676$	−26626.1	−1.51491
$677$	16562.2	0.940234	0.470117	−	0.882604i	$-0.344212\pi$
$677$	16562.2	0.940234	0.470117	+	0.882604i	$0.344212\pi$
$678$	14114.8	0.799522
$679$	−5263.01	−0.297461
$680$	12857.7	0.725105
$681$	−10976.1	−0.617630
$682$	0	0
$683$	22303.4	1.24951	0.624755	−	0.780821i	$-0.285199\pi$
$683$	22303.4	1.24951	0.624755	+	0.780821i	$0.285199\pi$
$684$	−886.313	−0.0495454
$685$	−9596.36	−0.535268
$686$	−17881.3	−0.995204
$687$	−5086.49	−0.282477
$688$	14475.9	0.802163
$689$	8350.87	0.461745
$690$	−5104.73	−0.281643
$691$	6244.91	0.343802	0.171901	−	0.985114i	$-0.445009\pi$
$691$	6244.91	0.343802	0.171901	+	0.985114i	$0.445009\pi$
$692$	−55576.0	−3.05301
$693$	0	0
$694$	1326.42	0.0725508
$695$	−8452.30	−0.461315
$696$	−34438.1	−1.87554
$697$	−25178.3	−1.36829
$698$	−52443.5	−2.84386
$699$	17346.7	0.938645
$700$	−2291.27	−0.123717
$701$	15277.7	0.823154	0.411577	−	0.911375i	$-0.364978\pi$
$701$	15277.7	0.823154	0.411577	+	0.911375i	$0.364978\pi$
$702$	3298.37	0.177335
$703$	−981.519	−0.0526582
$704$	0	0
$705$	−2117.21	−0.113105
$706$	−35557.3	−1.89549
$707$	−6901.43	−0.367122
$708$	20897.3	1.10928
$709$	−11732.1	−0.621449	−0.310725	−	0.950500i	$-0.600572\pi$
$709$	−11732.1	−0.621449	−0.310725	+	0.950500i	$0.600572\pi$
$710$	−3820.22	−0.201930
$711$	−3627.00	−0.191313
$712$	−53137.2	−2.79691
$713$	13455.5	0.706750
$714$	4855.35	0.254491
$715$	0	0
$716$	−445.153	−0.0232349
$717$	17508.5	0.911947
$718$	1785.57	0.0928093
$719$	−19006.2	−0.985828	−0.492914	−	0.870078i	$-0.664068\pi$
$719$	−19006.2	−0.985828	−0.492914	+	0.870078i	$0.664068\pi$
$720$	−3673.04	−0.190120
$721$	2704.45	0.139694
$722$	33925.1	1.74870
$723$	2946.92	0.151587
$724$	32327.4	1.65945
$725$	6625.54	0.339402
$726$	0	0
$727$	2650.77	0.135229	0.0676146	−	0.997712i	$-0.478461\pi$
$727$	2650.77	0.135229	0.0676146	+	0.997712i	$0.478461\pi$
$728$	−5836.96	−0.297160
$729$	729.000	0.0370370
$730$	−3824.52	−0.193907
$731$	10529.1	0.532738
$732$	−33199.5	−1.67635
$733$	8854.22	0.446164	0.223082	−	0.974800i	$-0.428388\pi$
$733$	8854.22	0.446164	0.223082	+	0.974800i	$0.428388\pi$
$734$	−44952.2	−2.26051
$735$	4693.93	0.235562
$736$	4055.96	0.203131
$737$	0	0
$738$	18974.7	0.946435
$739$	−17174.8	−0.854921	−0.427460	−	0.904034i	$-0.640592\pi$
$739$	−17174.8	−0.854921	−0.427460	+	0.904034i	$0.640592\pi$
$740$	−13920.0	−0.691497
$741$	434.391	0.0215354
$742$	−9264.06	−0.458348
$743$	9800.30	0.483901	0.241950	−	0.970289i	$-0.422213\pi$
$743$	9800.30	0.483901	0.241950	+	0.970289i	$0.422213\pi$
$744$	25541.1	1.25858
$745$	−10389.4	−0.510925
$746$	−59301.6	−2.91044
$747$	5870.82	0.287553
$748$	0	0
$749$	−6026.92	−0.294017
$750$	1864.21	0.0907618
$751$	2781.25	0.135139	0.0675695	−	0.997715i	$-0.478476\pi$
$751$	2781.25	0.135139	0.0675695	+	0.997715i	$0.478476\pi$
$752$	11520.9	0.558675
$753$	12960.7	0.627243
$754$	32375.6	1.56372
$755$	13555.8	0.653438
$756$	−2474.57	−0.119046
$757$	3010.87	0.144560	0.0722800	−	0.997384i	$-0.476972\pi$
$757$	3010.87	0.144560	0.0722800	+	0.997384i	$0.476972\pi$
$758$	−32591.8	−1.56172
$759$	0	0
$760$	−1276.13	−0.0609079
$761$	2709.54	0.129068	0.0645340	−	0.997916i	$-0.479444\pi$
$761$	2709.54	0.129068	0.0645340	+	0.997916i	$0.479444\pi$
$762$	33716.5	1.60291
$763$	6992.03	0.331754
$764$	−55848.4	−2.64466
$765$	−2671.59	−0.126263
$766$	−53207.7	−2.50976
$767$	−10242.0	−0.482159
$768$	−25041.2	−1.17656
$769$	28121.1	1.31869	0.659345	−	0.751841i	$-0.270834\pi$
$769$	28121.1	1.31869	0.659345	+	0.751841i	$0.270834\pi$
$770$	0	0
$771$	−18672.9	−0.872227
$772$	21626.2	1.00822
$773$	4274.61	0.198897	0.0994483	−	0.995043i	$-0.468292\pi$
$773$	4274.61	0.198897	0.0994483	+	0.995043i	$0.468292\pi$
$774$	−7934.85	−0.368491
$775$	−4913.85	−0.227756
$776$	−41571.2	−1.92309
$777$	−2740.38	−0.126526
$778$	32065.9	1.47766
$779$	2498.95	0.114935
$780$	6160.56	0.282799
$781$	0	0
$782$	20204.1	0.923909
$783$	7155.59	0.326590
$784$	−25542.2	−1.16355
$785$	−11706.2	−0.532243
$786$	−851.985	−0.0386632
$787$	−19107.9	−0.865469	−0.432734	−	0.901522i	$-0.642451\pi$
$787$	−19107.9	−0.865469	−0.432734	+	0.901522i	$0.642451\pi$
$788$	38459.6	1.73866
$789$	7766.85	0.350453
$790$	−10017.0	−0.451127
$791$	5190.01	0.233294
$792$	0	0
$793$	16271.4	0.728645
$794$	62269.4	2.78320
$795$	5097.42	0.227405
$796$	−50801.9	−2.26209
$797$	27518.4	1.22303	0.611513	−	0.791234i	$-0.290561\pi$
$797$	27518.4	1.22303	0.611513	+	0.791234i	$0.290561\pi$
$798$	−481.893	−0.0213770
$799$	8379.74	0.371031
$800$	−1481.21	−0.0654606
$801$	11040.9	0.487030
$802$	−45335.2	−1.99606
$803$	0	0
$804$	15729.4	0.689965
$805$	−1877.01	−0.0821812
$806$	−24011.4	−1.04934
$807$	−17614.6	−0.768356
$808$	−54512.7	−2.37345
$809$	−21986.6	−0.955511	−0.477755	−	0.878493i	$-0.658550\pi$
$809$	−21986.6	−0.955511	−0.477755	+	0.878493i	$0.658550\pi$
$810$	2013.35	0.0873356
$811$	−11835.1	−0.512437	−0.256218	−	0.966619i	$-0.582477\pi$
$811$	−11835.1	−0.512437	−0.256218	+	0.966619i	$0.582477\pi$
$812$	−24289.4	−1.04974
$813$	9920.79	0.427967
$814$	0	0
$815$	−17615.1	−0.757090
$816$	14537.6	0.623672
$817$	−1045.01	−0.0447494
$818$	−2967.43	−0.126838
$819$	1212.81	0.0517448
$820$	35440.2	1.50930
$821$	7890.58	0.335424	0.167712	−	0.985836i	$-0.446362\pi$
$821$	7890.58	0.335424	0.167712	+	0.985836i	$0.446362\pi$
$822$	−28623.4	−1.21455
$823$	1000.74	0.0423861	0.0211930	−	0.999775i	$-0.493254\pi$
$823$	1000.74	0.0423861	0.0211930	+	0.999775i	$0.493254\pi$
$824$	21361.8	0.903123
$825$	0	0
$826$	11362.0	0.478611
$827$	−22764.2	−0.957181	−0.478590	−	0.878038i	$-0.658852\pi$
$827$	−22764.2	−0.957181	−0.478590	+	0.878038i	$0.658852\pi$
$828$	−10297.2	−0.432188
$829$	39835.8	1.66894	0.834471	−	0.551051i	$-0.185773\pi$
$829$	39835.8	1.66894	0.834471	+	0.551051i	$0.185773\pi$
$830$	16214.0	0.678067
$831$	8584.10	0.358338
$832$	8808.43	0.367040
$833$	−18578.1	−0.772742
$834$	−25211.0	−1.04674
$835$	20059.5	0.831363
$836$	0	0
$837$	−5306.96	−0.219158
$838$	−57469.7	−2.36904
$839$	23330.9	0.960037	0.480019	−	0.877258i	$-0.340630\pi$
$839$	23330.9	0.960037	0.480019	+	0.877258i	$0.340630\pi$
$840$	−3562.92	−0.146348
$841$	45847.5	1.87984
$842$	−75476.0	−3.08916
$843$	8964.14	0.366241
$844$	−46928.1	−1.91390
$845$	7965.64	0.324292
$846$	−6315.09	−0.256640
$847$	0	0
$848$	−27737.8	−1.12326
$849$	−4363.79	−0.176402
$850$	−7378.38	−0.297737
$851$	−11403.3	−0.459341
$852$	−7706.08	−0.309866
$853$	−22937.3	−0.920701	−0.460351	−	0.887737i	$-0.652276\pi$
$853$	−22937.3	−0.920701	−0.460351	+	0.887737i	$0.652276\pi$
$854$	−18050.8	−0.723284
$855$	265.155	0.0106060
$856$	−47605.2	−1.90083
$857$	38472.3	1.53348	0.766738	−	0.641961i	$-0.221879\pi$
$857$	38472.3	1.53348	0.766738	+	0.641961i	$0.221879\pi$
$858$	0	0
$859$	−22970.3	−0.912384	−0.456192	−	0.889881i	$-0.650787\pi$
$859$	−22970.3	−0.912384	−0.456192	+	0.889881i	$0.650787\pi$
$860$	−14820.4	−0.587641
$861$	6977.00	0.276162
$862$	−74084.5	−2.92730
$863$	−33587.6	−1.32484	−0.662420	−	0.749133i	$-0.730470\pi$
$863$	−33587.6	−1.32484	−0.662420	+	0.749133i	$0.730470\pi$
$864$	−1599.70	−0.0629895
$865$	16626.5	0.653546
$866$	11284.0	0.442777
$867$	−4165.08	−0.163153
$868$	18014.3	0.704430
$869$	0	0
$870$	19762.3	0.770119
$871$	−7709.12	−0.299901
$872$	55228.3	2.14480
$873$	8637.71	0.334871
$874$	−2005.25	−0.0776073
$875$	685.470	0.0264835
$876$	−7714.74	−0.297554
$877$	704.130	0.0271115	0.0135558	−	0.999908i	$-0.495685\pi$
$877$	704.130	0.0271115	0.0135558	+	0.999908i	$0.495685\pi$
$878$	−66707.5	−2.56409
$879$	25759.5	0.988450
$880$	0	0
$881$	9746.33	0.372715	0.186358	−	0.982482i	$-0.440332\pi$
$881$	9746.33	0.372715	0.186358	+	0.982482i	$0.440332\pi$
$882$	14000.7	0.534501
$883$	−8774.24	−0.334402	−0.167201	−	0.985923i	$-0.553473\pi$
$883$	−8774.24	−0.334402	−0.167201	+	0.985923i	$0.553473\pi$
$884$	−24383.0	−0.927701
$885$	−6251.76	−0.237458
$886$	−57206.4	−2.16917
$887$	13505.1	0.511224	0.255612	−	0.966779i	$-0.417723\pi$
$887$	13505.1	0.511224	0.255612	+	0.966779i	$0.417723\pi$
$888$	−21645.6	−0.817993
$889$	12397.5	0.467717
$890$	30492.7	1.14845
$891$	0	0
$892$	24118.6	0.905324
$893$	−831.689	−0.0311662
$894$	−30988.9	−1.15931
$895$	133.175	0.00497379
$896$	−12370.9	−0.461252
$897$	5046.75	0.187855
$898$	80552.8	2.99341
$899$	−52091.1	−1.93252
$900$	3760.45	0.139276
$901$	−20175.1	−0.745984
$902$	0	0
$903$	−2917.64	−0.107523
$904$	40994.6	1.50825
$905$	−9671.27	−0.355231
$906$	40433.4	1.48268
$907$	−2523.23	−0.0923732	−0.0461866	−	0.998933i	$-0.514707\pi$
$907$	−2523.23	−0.0923732	−0.0461866	+	0.998933i	$0.514707\pi$
$908$	−61148.4	−2.23489
$909$	11326.7	0.413293
$910$	3349.53	0.122017
$911$	−32285.3	−1.17416	−0.587080	−	0.809529i	$-0.699723\pi$
$911$	−32285.3	−1.17416	−0.587080	+	0.809529i	$0.699723\pi$
$912$	−1442.85	−0.0523877
$913$	0	0
$914$	24422.6	0.883838
$915$	9932.19	0.358850
$916$	−28337.0	−1.02214
$917$	−313.274	−0.0112816
$918$	−7968.65	−0.286497
$919$	40956.5	1.47011	0.735055	−	0.678008i	$-0.237156\pi$
$919$	40956.5	1.47011	0.735055	+	0.678008i	$0.237156\pi$
$920$	−14826.0	−0.531304
$921$	−1587.09	−0.0567821
$922$	−70943.6	−2.53406
$923$	3776.83	0.134687
$924$	0	0
$925$	4164.39	0.148026
$926$	−33090.8	−1.17433
$927$	−4438.58	−0.157262
$928$	−15702.1	−0.555437
$929$	−6728.41	−0.237623	−0.118812	−	0.992917i	$-0.537908\pi$
$929$	−6728.41	−0.237623	−0.118812	+	0.992917i	$0.537908\pi$
$930$	−14656.7	−0.516788
$931$	1843.88	0.0649095
$932$	96639.1	3.39648
$933$	−15024.0	−0.527185
$934$	−96181.9	−3.36956
$935$	0	0
$936$	9579.69	0.334532
$937$	36377.8	1.26831	0.634157	−	0.773205i	$-0.281347\pi$
$937$	36377.8	1.26831	0.634157	+	0.773205i	$0.281347\pi$
$938$	8552.13	0.297694
$939$	23575.6	0.819340
$940$	−11795.1	−0.409269
$941$	−25907.0	−0.897496	−0.448748	−	0.893658i	$-0.648130\pi$
$941$	−25907.0	−0.897496	−0.448748	+	0.893658i	$0.648130\pi$
$942$	−34916.4	−1.20768
$943$	29032.7	1.00258
$944$	34019.2	1.17291
$945$	740.307	0.0254838
$946$	0	0
$947$	37096.3	1.27293	0.636466	−	0.771304i	$-0.280395\pi$
$947$	37096.3	1.27293	0.636466	+	0.771304i	$0.280395\pi$
$948$	−20206.2	−0.692263
$949$	3781.07	0.129335
$950$	732.304	0.0250096
$951$	23241.1	0.792476
$952$	14101.7	0.480084
$953$	15323.7	0.520865	0.260432	−	0.965492i	$-0.416135\pi$
$953$	15323.7	0.520865	0.260432	+	0.965492i	$0.416135\pi$
$954$	15204.3	0.515992
$955$	16708.0	0.566133
$956$	97540.4	3.29988
$957$	0	0
$958$	48850.7	1.64749
$959$	−10524.8	−0.354395
$960$	5376.72	0.180764
$961$	8842.46	0.296817
$962$	20349.2	0.682000
$963$	9891.45	0.330994
$964$	16417.4	0.548516
$965$	−6469.83	−0.215825
$966$	−5598.62	−0.186473
$967$	53388.0	1.77543	0.887716	−	0.460391i	$-0.152291\pi$
$967$	53388.0	1.77543	0.887716	+	0.460391i	$0.152291\pi$
$968$	0	0
$969$	−1049.46	−0.0347921
$970$	23855.6	0.789646
$971$	−36325.7	−1.20056	−0.600281	−	0.799789i	$-0.704945\pi$
$971$	−36325.7	−1.20056	−0.600281	+	0.799789i	$0.704945\pi$
$972$	4061.28	0.134018
$973$	−9270.07	−0.305432
$974$	−51094.6	−1.68088
$975$	−1843.03	−0.0605378
$976$	−54046.4	−1.77252
$977$	48608.7	1.59174	0.795870	−	0.605468i	$-0.207014\pi$
$977$	48608.7	1.59174	0.795870	+	0.605468i	$0.207014\pi$
$978$	−52541.1	−1.71787
$979$	0	0
$980$	26150.0	0.852380
$981$	−11475.4	−0.373477
$982$	56657.7	1.84116
$983$	31762.6	1.03059	0.515295	−	0.857013i	$-0.327682\pi$
$983$	31762.6	1.03059	0.515295	+	0.857013i	$0.327682\pi$
$984$	55109.6	1.78540
$985$	−11505.8	−0.372189
$986$	−78217.2	−2.52631
$987$	−2322.06	−0.0748854
$988$	2420.01	0.0779258
$989$	−12140.9	−0.390352
$990$	0	0
$991$	−5073.82	−0.162639	−0.0813195	−	0.996688i	$-0.525913\pi$
$991$	−5073.82	−0.162639	−0.0813195	+	0.996688i	$0.525913\pi$
$992$	11645.5	0.372726
$993$	4065.25	0.129916
$994$	−4189.83	−0.133696
$995$	15198.2	0.484237
$996$	32706.5	1.04051
$997$	−24607.0	−0.781657	−0.390828	−	0.920464i	$-0.627811\pi$
$997$	−24607.0	−0.781657	−0.390828	+	0.920464i	$0.627811\pi$
$998$	45631.8	1.44734
$999$	4497.54	0.142438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.r.1.1		3
11.10	odd	2		165.4.a.e.1.3	✓	3
33.32	even	2		495.4.a.k.1.1		3
55.32	even	4		825.4.c.k.199.5		6
55.43	even	4		825.4.c.k.199.2		6
55.54	odd	2		825.4.a.r.1.1		3
165.164	even	2		2475.4.a.t.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.e.1.3	✓	3	11.10	odd	2
495.4.a.k.1.1		3	33.32	even	2
825.4.a.r.1.1		3	55.54	odd	2
825.4.c.k.199.2		6	55.43	even	4
825.4.c.k.199.5		6	55.32	even	4
1815.4.a.r.1.1		3	1.1	even	1	trivial
2475.4.a.t.1.3		3	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)

\(f(q)\)	\(=\)	\(q-4.97123 q^{2} +3.00000 q^{3} +16.7131 q^{4} -5.00000 q^{5} -14.9137 q^{6} -5.48376 q^{7} -43.3148 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.97123 q^{2} +3.00000 q^{3} +16.7131 q^{4} -5.00000 q^{5} -14.9137 q^{6} -5.48376 q^{7} -43.3148 q^{8} +9.00000 q^{9} +24.8561 q^{10} +50.1393 q^{12} -24.5738 q^{13} +27.2610 q^{14} -15.0000 q^{15} +81.6231 q^{16} +59.3687 q^{17} -44.7411 q^{18} -5.89234 q^{19} -83.5655 q^{20} -16.4513 q^{21} -68.4570 q^{23} -129.945 q^{24} +25.0000 q^{25} +122.162 q^{26} +27.0000 q^{27} -91.6506 q^{28} +265.022 q^{29} +74.5684 q^{30} -196.554 q^{31} -59.2482 q^{32} -295.135 q^{34} +27.4188 q^{35} +150.418 q^{36} +166.575 q^{37} +29.2922 q^{38} -73.7214 q^{39} +216.574 q^{40} -424.101 q^{41} +81.7830 q^{42} +177.351 q^{43} -45.0000 q^{45} +340.316 q^{46} +141.148 q^{47} +244.869 q^{48} -312.928 q^{49} -124.281 q^{50} +178.106 q^{51} -410.704 q^{52} -339.828 q^{53} -134.223 q^{54} +237.528 q^{56} -17.6770 q^{57} -1317.48 q^{58} +416.784 q^{59} -250.697 q^{60} -662.146 q^{61} +977.115 q^{62} -49.3538 q^{63} -358.448 q^{64} +122.869 q^{65} +313.713 q^{67} +992.235 q^{68} -205.371 q^{69} -136.305 q^{70} -153.693 q^{71} -389.834 q^{72} -153.866 q^{73} -828.084 q^{74} +75.0000 q^{75} -98.4793 q^{76} +366.486 q^{78} -403.000 q^{79} -408.115 q^{80} +81.0000 q^{81} +2108.30 q^{82} +652.313 q^{83} -274.952 q^{84} -296.843 q^{85} -881.650 q^{86} +795.065 q^{87} +1226.77 q^{89} +223.705 q^{90} +134.757 q^{91} -1144.13 q^{92} -589.662 q^{93} -701.677 q^{94} +29.4617 q^{95} -177.745 q^{96} +959.746 q^{97} +1555.64 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} - 10 q^{10} + 90 q^{12} - 114 q^{13} - 68 q^{14} - 45 q^{15} + 178 q^{16} + 104 q^{17} + 18 q^{18} + 58 q^{19} - 150 q^{20} - 30 q^{21} + 120 q^{23} - 54 q^{24} + 75 q^{25} - 120 q^{26} + 81 q^{27} - 676 q^{28} + 220 q^{29} - 30 q^{30} + 248 q^{31} + 258 q^{32} - 80 q^{34} + 50 q^{35} + 270 q^{36} + 838 q^{37} + 600 q^{38} - 342 q^{39} + 90 q^{40} - 156 q^{41} - 204 q^{42} - 122 q^{43} - 135 q^{45} + 1256 q^{46} + 504 q^{47} + 534 q^{48} + 279 q^{49} + 50 q^{50} + 312 q^{51} - 520 q^{52} + 282 q^{53} + 54 q^{54} - 1644 q^{56} + 174 q^{57} - 1644 q^{58} + 548 q^{59} - 450 q^{60} - 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} + 570 q^{65} - 428 q^{67} + 1704 q^{68} + 360 q^{69} + 340 q^{70} - 912 q^{71} - 162 q^{72} - 618 q^{73} + 1612 q^{74} + 225 q^{75} + 2752 q^{76} - 360 q^{78} + 542 q^{79} - 890 q^{80} + 243 q^{81} + 3372 q^{82} - 2028 q^{84} - 520 q^{85} - 1548 q^{86} + 660 q^{87} + 790 q^{89} - 90 q^{90} - 772 q^{91} + 1912 q^{92} + 744 q^{93} + 424 q^{94} - 290 q^{95} + 774 q^{96} + 2074 q^{97} + 3978 q^{98}+O(q^{100}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 - 10 * q^10 + 90 * q^12 - 114 * q^13 - 68 * q^14 - 45 * q^15 + 178 * q^16 + 104 * q^17 + 18 * q^18 + 58 * q^19 - 150 * q^20 - 30 * q^21 + 120 * q^23 - 54 * q^24 + 75 * q^25 - 120 * q^26 + 81 * q^27 - 676 * q^28 + 220 * q^29 - 30 * q^30 + 248 * q^31 + 258 * q^32 - 80 * q^34 + 50 * q^35 + 270 * q^36 + 838 * q^37 + 600 * q^38 - 342 * q^39 + 90 * q^40 - 156 * q^41 - 204 * q^42 - 122 * q^43 - 135 * q^45 + 1256 * q^46 + 504 * q^47 + 534 * q^48 + 279 * q^49 + 50 * q^50 + 312 * q^51 - 520 * q^52 + 282 * q^53 + 54 * q^54 - 1644 * q^56 + 174 * q^57 - 1644 * q^58 + 548 * q^59 - 450 * q^60 - 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 + 570 * q^65 - 428 * q^67 + 1704 * q^68 + 360 * q^69 + 340 * q^70 - 912 * q^71 - 162 * q^72 - 618 * q^73 + 1612 * q^74 + 225 * q^75 + 2752 * q^76 - 360 * q^78 + 542 * q^79 - 890 * q^80 + 243 * q^81 + 3372 * q^82 - 2028 * q^84 - 520 * q^85 - 1548 * q^86 + 660 * q^87 + 790 * q^89 - 90 * q^90 - 772 * q^91 + 1912 * q^92 + 744 * q^93 + 424 * q^94 - 290 * q^95 + 774 * q^96 + 2074 * q^97 + 3978 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more