LMFDB - Embedded newform 1815.4.a.bo.1.10

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 69 x^{10} + 157 x^{9} + 1812 x^{8} - 2703 x^{7} - 22379 x^{6} + 16453 x^{5} + \cdots + 196416 $ x^12 - 3x^11 - 69x^10 + 157x^9 + 1812x^8 - 2703x^7 - 22379x^6 + 16453x^5 + 129167x^4 - 22672x^3 - 298084x^2 - 19392*x + 196416
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.71454$ 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)

$f(q)$	$=$	$q+3.71454 q^{2} +3.00000 q^{3} +5.79777 q^{4} -5.00000 q^{5} +11.1436 q^{6} +21.2047 q^{7} -8.18025 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.71454 q^{2} +3.00000 q^{3} +5.79777 q^{4} -5.00000 q^{5} +11.1436 q^{6} +21.2047 q^{7} -8.18025 q^{8} +9.00000 q^{9} -18.5727 q^{10} +17.3933 q^{12} +28.0040 q^{13} +78.7657 q^{14} -15.0000 q^{15} -76.7680 q^{16} -81.0229 q^{17} +33.4308 q^{18} +85.4976 q^{19} -28.9889 q^{20} +63.6142 q^{21} +145.578 q^{23} -24.5408 q^{24} +25.0000 q^{25} +104.022 q^{26} +27.0000 q^{27} +122.940 q^{28} +135.407 q^{29} -55.7180 q^{30} -34.8036 q^{31} -219.715 q^{32} -300.962 q^{34} -106.024 q^{35} +52.1799 q^{36} +245.367 q^{37} +317.584 q^{38} +84.0121 q^{39} +40.9013 q^{40} +107.559 q^{41} +236.297 q^{42} -105.298 q^{43} -45.0000 q^{45} +540.756 q^{46} -540.058 q^{47} -230.304 q^{48} +106.640 q^{49} +92.8634 q^{50} -243.069 q^{51} +162.361 q^{52} +682.347 q^{53} +100.292 q^{54} -173.460 q^{56} +256.493 q^{57} +502.975 q^{58} +604.915 q^{59} -86.9666 q^{60} +32.8475 q^{61} -129.279 q^{62} +190.843 q^{63} -201.997 q^{64} -140.020 q^{65} +278.910 q^{67} -469.752 q^{68} +436.735 q^{69} -393.829 q^{70} +325.852 q^{71} -73.6223 q^{72} +529.794 q^{73} +911.423 q^{74} +75.0000 q^{75} +495.696 q^{76} +312.066 q^{78} -1086.78 q^{79} +383.840 q^{80} +81.0000 q^{81} +399.531 q^{82} +675.157 q^{83} +368.820 q^{84} +405.114 q^{85} -391.132 q^{86} +406.221 q^{87} +1051.26 q^{89} -167.154 q^{90} +593.818 q^{91} +844.031 q^{92} -104.411 q^{93} -2006.07 q^{94} -427.488 q^{95} -659.146 q^{96} -492.913 q^{97} +396.120 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} + 27 q^{6} + 21 q^{7} + 123 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q + 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 + 27 * q^6 + 21 * q^7 + 123 * q^8 + 108 * q^9	\( 12 q + 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} + 27 q^{6} + 21 q^{7} + 123 q^{8} + 108 q^{9} - 45 q^{10} + 171 q^{12} + 78 q^{13} + 262 q^{14} - 180 q^{15} + 225 q^{16} + 313 q^{17} + 81 q^{18} + 51 q^{19} - 285 q^{20} + 63 q^{21} - 34 q^{23} + 369 q^{24} + 300 q^{25} + 28 q^{26} + 324 q^{27} + 376 q^{28} + 31 q^{29} - 135 q^{30} + 655 q^{31} + 1578 q^{32} - 10 q^{34} - 105 q^{35} + 513 q^{36} + 84 q^{37} - 1076 q^{38} + 234 q^{39} - 615 q^{40} + 1463 q^{41} + 786 q^{42} - 111 q^{43} - 540 q^{45} - q^{46} + 278 q^{47} + 675 q^{48} - 325 q^{49} + 225 q^{50} + 939 q^{51} + 1957 q^{52} + 517 q^{53} + 243 q^{54} + 1543 q^{56} + 153 q^{57} + 442 q^{58} - 308 q^{59} - 855 q^{60} + 604 q^{61} + 1773 q^{62} + 189 q^{63} + 4323 q^{64} - 390 q^{65} - 357 q^{67} + 2192 q^{68} - 102 q^{69} - 1310 q^{70} - 620 q^{71} + 1107 q^{72} + 1892 q^{73} + 581 q^{74} + 900 q^{75} + 378 q^{76} + 84 q^{78} + 415 q^{79} - 1125 q^{80} + 972 q^{81} - 2802 q^{82} + 3158 q^{83} + 1128 q^{84} - 1565 q^{85} + 747 q^{86} + 93 q^{87} + 1563 q^{89} - 405 q^{90} + 1434 q^{91} - 3466 q^{92} + 1965 q^{93} - 3 q^{94} - 255 q^{95} + 4734 q^{96} + 714 q^{97} + 6586 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 + 27 * q^6 + 21 * q^7 + 123 * q^8 + 108 * q^9 - 45 * q^10 + 171 * q^12 + 78 * q^13 + 262 * q^14 - 180 * q^15 + 225 * q^16 + 313 * q^17 + 81 * q^18 + 51 * q^19 - 285 * q^20 + 63 * q^21 - 34 * q^23 + 369 * q^24 + 300 * q^25 + 28 * q^26 + 324 * q^27 + 376 * q^28 + 31 * q^29 - 135 * q^30 + 655 * q^31 + 1578 * q^32 - 10 * q^34 - 105 * q^35 + 513 * q^36 + 84 * q^37 - 1076 * q^38 + 234 * q^39 - 615 * q^40 + 1463 * q^41 + 786 * q^42 - 111 * q^43 - 540 * q^45 - q^46 + 278 * q^47 + 675 * q^48 - 325 * q^49 + 225 * q^50 + 939 * q^51 + 1957 * q^52 + 517 * q^53 + 243 * q^54 + 1543 * q^56 + 153 * q^57 + 442 * q^58 - 308 * q^59 - 855 * q^60 + 604 * q^61 + 1773 * q^62 + 189 * q^63 + 4323 * q^64 - 390 * q^65 - 357 * q^67 + 2192 * q^68 - 102 * q^69 - 1310 * q^70 - 620 * q^71 + 1107 * q^72 + 1892 * q^73 + 581 * q^74 + 900 * q^75 + 378 * q^76 + 84 * q^78 + 415 * q^79 - 1125 * q^80 + 972 * q^81 - 2802 * q^82 + 3158 * q^83 + 1128 * q^84 - 1565 * q^85 + 747 * q^86 + 93 * q^87 + 1563 * q^89 - 405 * q^90 + 1434 * q^91 - 3466 * q^92 + 1965 * q^93 - 3 * q^94 - 255 * q^95 + 4734 * q^96 + 714 * q^97 + 6586 * 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 $

$2$	3.71454	1.31329	0.656643	−	0.754201i	$-0.271976\pi$
$2$	3.71454	1.31329	0.656643	+	0.754201i	$0.271976\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.79777	0.724721
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	11.1436	0.758226
$7$	21.2047	1.14495	0.572474	−	0.819923i	$-0.305984\pi$
$7$	21.2047	1.14495	0.572474	+	0.819923i	$0.305984\pi$
$8$	−8.18025	−0.361520
$9$	9.00000	0.333333
$10$	−18.5727	−0.587320
$11$	0	0
$11$	0	0
$12$	17.3933	0.418418
$13$	28.0040	0.597455	0.298728	−	0.954338i	$-0.403438\pi$
$13$	28.0040	0.597455	0.298728	+	0.954338i	$0.403438\pi$
$14$	78.7657	1.50364
$15$	−15.0000	−0.258199
$16$	−76.7680	−1.19950
$17$	−81.0229	−1.15594	−0.577969	−	0.816059i	$-0.696154\pi$
$17$	−81.0229	−1.15594	−0.577969	+	0.816059i	$0.696154\pi$
$18$	33.4308	0.437762
$19$	85.4976	1.03234	0.516171	−	0.856486i	$-0.327357\pi$
$19$	85.4976	1.03234	0.516171	+	0.856486i	$0.327357\pi$
$20$	−28.9889	−0.324105
$21$	63.6142	0.661036
$22$	0	0
$23$	145.578	1.31979	0.659896	−	0.751357i	$-0.270600\pi$
$23$	145.578	1.31979	0.659896	+	0.751357i	$0.270600\pi$
$24$	−24.5408	−0.208723
$25$	25.0000	0.200000
$26$	104.022	0.784630
$27$	27.0000	0.192450
$28$	122.940	0.829768
$29$	135.407	0.867051	0.433525	−	0.901141i	$-0.357269\pi$
$29$	135.407	0.867051	0.433525	+	0.901141i	$0.357269\pi$
$30$	−55.7180	−0.339089
$31$	−34.8036	−0.201643	−0.100821	−	0.994905i	$-0.532147\pi$
$31$	−34.8036	−0.201643	−0.100821	+	0.994905i	$0.532147\pi$
$32$	−219.715	−1.21377
$33$	0	0
$34$	−300.962	−1.51808
$35$	−106.024	−0.512036
$36$	52.1799	0.241574
$37$	245.367	1.09022	0.545108	−	0.838366i	$-0.316489\pi$
$37$	245.367	1.09022	0.545108	+	0.838366i	$0.316489\pi$
$38$	317.584	1.35576
$39$	84.0121	0.344941
$40$	40.9013	0.161676
$41$	107.559	0.409704	0.204852	−	0.978793i	$-0.434329\pi$
$41$	107.559	0.409704	0.204852	+	0.978793i	$0.434329\pi$
$42$	236.297	0.868129
$43$	−105.298	−0.373436	−0.186718	−	0.982414i	$-0.559785\pi$
$43$	−105.298	−0.373436	−0.186718	+	0.982414i	$0.559785\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	540.756	1.73326
$47$	−540.058	−1.67608	−0.838038	−	0.545612i	$-0.816297\pi$
$47$	−540.058	−1.67608	−0.838038	+	0.545612i	$0.816297\pi$
$48$	−230.304	−0.692532
$49$	106.640	0.310905
$50$	92.8634	0.262657
$51$	−243.069	−0.667381
$52$	162.361	0.432989
$53$	682.347	1.76844	0.884222	−	0.467066i	$-0.154689\pi$
$53$	682.347	1.76844	0.884222	+	0.467066i	$0.154689\pi$
$54$	100.292	0.252742
$55$	0	0
$56$	−173.460	−0.413921
$57$	256.493	0.596023
$58$	502.975	1.13869
$59$	604.915	1.33480	0.667401	−	0.744699i	$-0.267407\pi$
$59$	604.915	1.33480	0.667401	+	0.744699i	$0.267407\pi$
$60$	−86.9666	−0.187122
$61$	32.8475	0.0689458	0.0344729	−	0.999406i	$-0.489025\pi$
$61$	32.8475	0.0689458	0.0344729	+	0.999406i	$0.489025\pi$
$62$	−129.279	−0.264814
$63$	190.843	0.381649
$64$	−201.997	−0.394525
$65$	−140.020	−0.267190
$66$	0	0
$67$	278.910	0.508571	0.254286	−	0.967129i	$-0.418160\pi$
$67$	278.910	0.508571	0.254286	+	0.967129i	$0.418160\pi$
$68$	−469.752	−0.837733
$69$	436.735	0.761982
$70$	−393.829	−0.672450
$71$	325.852	0.544669	0.272335	−	0.962203i	$-0.412204\pi$
$71$	325.852	0.544669	0.272335	+	0.962203i	$0.412204\pi$
$72$	−73.6223	−0.120507
$73$	529.794	0.849420	0.424710	−	0.905329i	$-0.360376\pi$
$73$	529.794	0.849420	0.424710	+	0.905329i	$0.360376\pi$
$74$	911.423	1.43177
$75$	75.0000	0.115470
$76$	495.696	0.748160
$77$	0	0
$78$	312.066	0.453006
$79$	−1086.78	−1.54774	−0.773872	−	0.633342i	$-0.781683\pi$
$79$	−1086.78	−1.54774	−0.773872	+	0.633342i	$0.781683\pi$
$80$	383.840	0.536433
$81$	81.0000	0.111111
$82$	399.531	0.538058
$83$	675.157	0.892868	0.446434	−	0.894817i	$-0.352694\pi$
$83$	675.157	0.892868	0.446434	+	0.894817i	$0.352694\pi$
$84$	368.820	0.479067
$85$	405.114	0.516951
$86$	−391.132	−0.490428
$87$	406.221	0.500592
$88$	0	0
$89$	1051.26	1.25206	0.626030	−	0.779799i	$-0.284679\pi$
$89$	1051.26	1.25206	0.626030	+	0.779799i	$0.284679\pi$
$90$	−167.154	−0.195773
$91$	593.818	0.684055
$92$	844.031	0.956481
$93$	−104.411	−0.116418
$94$	−2006.07	−2.20117
$95$	−427.488	−0.461677
$96$	−659.146	−0.700769
$97$	−492.913	−0.515955	−0.257978	−	0.966151i	$-0.583056\pi$
$97$	−492.913	−0.515955	−0.257978	+	0.966151i	$0.583056\pi$
$98$	396.120	0.408307
$99$	0	0
$100$	144.944	0.144944
$101$	1022.93	1.00778	0.503890	−	0.863768i	$-0.331902\pi$
$101$	1022.93	1.00778	0.503890	+	0.863768i	$0.331902\pi$
$102$	−902.887	−0.876462
$103$	−79.8655	−0.0764018	−0.0382009	−	0.999270i	$-0.512163\pi$
$103$	−79.8655	−0.0764018	−0.0382009	+	0.999270i	$0.512163\pi$
$104$	−229.080	−0.215992
$105$	−318.071	−0.295624
$106$	2534.60	2.32247
$107$	1724.34	1.55793	0.778964	−	0.627068i	$-0.215745\pi$
$107$	1724.34	1.55793	0.778964	+	0.627068i	$0.215745\pi$
$108$	156.540	0.139473
$109$	−1209.81	−1.06311	−0.531554	−	0.847024i	$-0.678392\pi$
$109$	−1209.81	−1.06311	−0.531554	+	0.847024i	$0.678392\pi$
$110$	0	0
$111$	736.100	0.629437
$112$	−1627.84	−1.37336
$113$	−2346.81	−1.95371	−0.976854	−	0.213909i	$-0.931380\pi$
$113$	−2346.81	−1.95371	−0.976854	+	0.213909i	$0.931380\pi$
$114$	952.751	0.782749
$115$	−727.892	−0.590229
$116$	785.060	0.628370
$117$	252.036	0.199152
$118$	2246.98	1.75298
$119$	−1718.07	−1.32349
$120$	122.704	0.0933440
$121$	0	0
$122$	122.013	0.0905456
$123$	322.676	0.236543
$124$	−201.784	−0.146135
$125$	−125.000	−0.0894427
$126$	708.891	0.501215
$127$	−225.901	−0.157838	−0.0789192	−	0.996881i	$-0.525147\pi$
$127$	−225.901	−0.157838	−0.0789192	+	0.996881i	$0.525147\pi$
$128$	1007.40	0.695644
$129$	−315.893	−0.215603
$130$	−520.110	−0.350897
$131$	−1.81608	−0.00121123	−0.000605617	−	1.00000i	$-0.500193\pi$
$131$	−1.81608	−0.00121123	−0.000605617		1.00000i	$0.500193\pi$
$132$	0	0
$133$	1812.95	1.18198
$134$	1036.02	0.667899
$135$	−135.000	−0.0860663
$136$	662.788	0.417894
$137$	2404.39	1.49942	0.749711	−	0.661766i	$-0.230193\pi$
$137$	2404.39	1.49942	0.749711	+	0.661766i	$0.230193\pi$
$138$	1622.27	1.00070
$139$	−859.965	−0.524757	−0.262379	−	0.964965i	$-0.584507\pi$
$139$	−859.965	−0.524757	−0.262379	+	0.964965i	$0.584507\pi$
$140$	−614.701	−0.371084
$141$	−1620.17	−0.967683
$142$	1210.39	0.715307
$143$	0	0
$144$	−690.912	−0.399833
$145$	−677.036	−0.387757
$146$	1967.94	1.11553
$147$	319.921	0.179501
$148$	1422.58	0.790103
$149$	1519.00	0.835178	0.417589	−	0.908636i	$-0.362875\pi$
$149$	1519.00	0.835178	0.417589	+	0.908636i	$0.362875\pi$
$150$	278.590	0.151645
$151$	−1136.24	−0.612355	−0.306177	−	0.951975i	$-0.599050\pi$
$151$	−1136.24	−0.612355	−0.306177	+	0.951975i	$0.599050\pi$
$152$	−699.392	−0.373212
$153$	−729.206	−0.385312
$154$	0	0
$155$	174.018	0.0901773
$156$	487.083	0.249986
$157$	3284.87	1.66982	0.834909	−	0.550388i	$-0.185520\pi$
$157$	3284.87	1.66982	0.834909	+	0.550388i	$0.185520\pi$
$158$	−4036.87	−2.03263
$159$	2047.04	1.02101
$160$	1098.58	0.542814
$161$	3086.95	1.51109
$162$	300.877	0.145921
$163$	−3751.09	−1.80250	−0.901251	−	0.433298i	$-0.857350\pi$
$163$	−3751.09	−1.80250	−0.901251	+	0.433298i	$0.857350\pi$
$164$	623.601	0.296921
$165$	0	0
$166$	2507.89	1.17259
$167$	−878.302	−0.406977	−0.203488	−	0.979077i	$-0.565228\pi$
$167$	−878.302	−0.406977	−0.203488	+	0.979077i	$0.565228\pi$
$168$	−520.380	−0.238977
$169$	−1412.77	−0.643047
$170$	1504.81	0.678905
$171$	769.478	0.344114
$172$	−610.492	−0.270637
$173$	2220.44	0.975818	0.487909	−	0.872894i	$-0.337760\pi$
$173$	2220.44	0.975818	0.487909	+	0.872894i	$0.337760\pi$
$174$	1508.92	0.657421
$175$	530.118	0.228990
$176$	0	0
$177$	1814.75	0.770648
$178$	3904.94	1.64431
$179$	3310.99	1.38254	0.691271	−	0.722596i	$-0.257051\pi$
$179$	3310.99	1.38254	0.691271	+	0.722596i	$0.257051\pi$
$180$	−260.900	−0.108035
$181$	−2202.62	−0.904528	−0.452264	−	0.891884i	$-0.649384\pi$
$181$	−2202.62	−0.904528	−0.452264	+	0.891884i	$0.649384\pi$
$182$	2205.76	0.898360
$183$	98.5426	0.0398059
$184$	−1190.87	−0.477131
$185$	−1226.83	−0.487560
$186$	−387.838	−0.152891
$187$	0	0
$188$	−3131.13	−1.21469
$189$	572.528	0.220345
$190$	−1587.92	−0.606314
$191$	−560.598	−0.212374	−0.106187	−	0.994346i	$-0.533864\pi$
$191$	−560.598	−0.212374	−0.106187	+	0.994346i	$0.533864\pi$
$192$	−605.990	−0.227779
$193$	−2790.87	−1.04089	−0.520443	−	0.853896i	$-0.674233\pi$
$193$	−2790.87	−1.04089	−0.520443	+	0.853896i	$0.674233\pi$
$194$	−1830.94	−0.677597
$195$	−420.060	−0.154262
$196$	618.277	0.225320
$197$	1928.01	0.697286	0.348643	−	0.937256i	$-0.386643\pi$
$197$	1928.01	0.697286	0.348643	+	0.937256i	$0.386643\pi$
$198$	0	0
$199$	944.274	0.336371	0.168185	−	0.985755i	$-0.446209\pi$
$199$	944.274	0.336371	0.168185	+	0.985755i	$0.446209\pi$
$200$	−204.506	−0.0723039
$201$	836.729	0.293624
$202$	3799.72	1.32350
$203$	2871.27	0.992728
$204$	−1409.26	−0.483665
$205$	−537.794	−0.183225
$206$	−296.663	−0.100337
$207$	1310.21	0.439931
$208$	−2149.81	−0.716648
$209$	0	0
$210$	−1181.49	−0.388239
$211$	−1802.63	−0.588144	−0.294072	−	0.955783i	$-0.595010\pi$
$211$	−1802.63	−0.588144	−0.294072	+	0.955783i	$0.595010\pi$
$212$	3956.09	1.28163
$213$	977.556	0.314465
$214$	6405.13	2.04601
$215$	526.488	0.167006
$216$	−220.867	−0.0695745
$217$	−738.002	−0.230870
$218$	−4493.88	−1.39617
$219$	1589.38	0.490413
$220$	0	0
$221$	−2268.97	−0.690621
$222$	2734.27	0.826631
$223$	−1566.38	−0.470369	−0.235185	−	0.971951i	$-0.575569\pi$
$223$	−1566.38	−0.470369	−0.235185	+	0.971951i	$0.575569\pi$
$224$	−4659.01	−1.38970
$225$	225.000	0.0666667
$226$	−8717.29	−2.56578
$227$	558.164	0.163201	0.0816005	−	0.996665i	$-0.473997\pi$
$227$	558.164	0.163201	0.0816005	+	0.996665i	$0.473997\pi$
$228$	1487.09	0.431950
$229$	−4506.96	−1.30056	−0.650280	−	0.759694i	$-0.725349\pi$
$229$	−4506.96	−1.30056	−0.650280	+	0.759694i	$0.725349\pi$
$230$	−2703.78	−0.775140
$231$	0	0
$232$	−1107.66	−0.313456
$233$	−6926.32	−1.94746	−0.973730	−	0.227705i	$-0.926878\pi$
$233$	−6926.32	−1.94746	−0.973730	+	0.227705i	$0.926878\pi$
$234$	936.198	0.261543
$235$	2700.29	0.749564
$236$	3507.16	0.967359
$237$	−3260.33	−0.893591
$238$	−6381.82	−1.73812
$239$	1934.51	0.523569	0.261784	−	0.965126i	$-0.415689\pi$
$239$	1934.51	0.523569	0.261784	+	0.965126i	$0.415689\pi$
$240$	1151.52	0.309710
$241$	2289.61	0.611978	0.305989	−	0.952035i	$-0.401013\pi$
$241$	2289.61	0.611978	0.305989	+	0.952035i	$0.401013\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	190.442	0.0499665
$245$	−533.202	−0.139041
$246$	1198.59	0.310648
$247$	2394.28	0.616778
$248$	284.703	0.0728977
$249$	2025.47	0.515498
$250$	−464.317	−0.117464
$251$	5666.73	1.42502	0.712512	−	0.701660i	$-0.247558\pi$
$251$	5666.73	1.42502	0.712512	+	0.701660i	$0.247558\pi$
$252$	1106.46	0.276589
$253$	0	0
$254$	−839.117	−0.207287
$255$	1215.34	0.298462
$256$	5358.00	1.30810
$257$	−3957.80	−0.960626	−0.480313	−	0.877097i	$-0.659477\pi$
$257$	−3957.80	−0.960626	−0.480313	+	0.877097i	$0.659477\pi$
$258$	−1173.40	−0.283149
$259$	5202.93	1.24824
$260$	−811.805	−0.193638
$261$	1218.66	0.289017
$262$	−6.74589	−0.00159070
$263$	5451.43	1.27814	0.639068	−	0.769150i	$-0.279320\pi$
$263$	5451.43	1.27814	0.639068	+	0.769150i	$0.279320\pi$
$264$	0	0
$265$	−3411.73	−0.790873
$266$	6734.28	1.55227
$267$	3153.78	0.722877
$268$	1617.06	0.368572
$269$	2717.80	0.616011	0.308006	−	0.951384i	$-0.400338\pi$
$269$	2717.80	0.616011	0.308006	+	0.951384i	$0.400338\pi$
$270$	−501.462	−0.113030
$271$	542.067	0.121506	0.0607531	−	0.998153i	$-0.480650\pi$
$271$	542.067	0.121506	0.0607531	+	0.998153i	$0.480650\pi$
$272$	6219.97	1.38655
$273$	1781.45	0.394939
$274$	8931.18	1.96917
$275$	0	0
$276$	2532.09	0.552225
$277$	−1483.24	−0.321730	−0.160865	−	0.986976i	$-0.551428\pi$
$277$	−1483.24	−0.321730	−0.160865	+	0.986976i	$0.551428\pi$
$278$	−3194.37	−0.689157
$279$	−313.233	−0.0672142
$280$	867.300	0.185111
$281$	−259.185	−0.0550238	−0.0275119	−	0.999621i	$-0.508758\pi$
$281$	−259.185	−0.0550238	−0.0275119	+	0.999621i	$0.508758\pi$
$282$	−6018.20	−1.27085
$283$	3542.63	0.744125	0.372063	−	0.928208i	$-0.378651\pi$
$283$	3542.63	0.744125	0.372063	+	0.928208i	$0.378651\pi$
$284$	1889.22	0.394734
$285$	−1282.46	−0.266549
$286$	0	0
$287$	2280.75	0.469089
$288$	−1977.44	−0.404589
$289$	1651.71	0.336191
$290$	−2514.87	−0.509236
$291$	−1478.74	−0.297887
$292$	3071.62	0.615593
$293$	7435.06	1.48246	0.741230	−	0.671251i	$-0.234243\pi$
$293$	7435.06	1.48246	0.741230	+	0.671251i	$0.234243\pi$
$294$	1188.36	0.235736
$295$	−3024.58	−0.596941
$296$	−2007.16	−0.394135
$297$	0	0
$298$	5642.39	1.09683
$299$	4076.78	0.788517
$300$	434.833	0.0836836
$301$	−2232.81	−0.427564
$302$	−4220.59	−0.804197
$303$	3068.80	0.581842
$304$	−6563.48	−1.23829
$305$	−164.238	−0.0308335
$306$	−2708.66	−0.506026
$307$	9776.47	1.81750	0.908750	−	0.417340i	$-0.137038\pi$
$307$	9776.47	1.81750	0.908750	+	0.417340i	$0.137038\pi$
$308$	0	0
$309$	−239.596	−0.0441106
$310$	646.397	0.118429
$311$	−4367.12	−0.796260	−0.398130	−	0.917329i	$-0.630341\pi$
$311$	−4367.12	−0.796260	−0.398130	+	0.917329i	$0.630341\pi$
$312$	−687.240	−0.124703
$313$	−9651.99	−1.74301	−0.871506	−	0.490386i	$-0.836856\pi$
$313$	−9651.99	−1.74301	−0.871506	+	0.490386i	$0.836856\pi$
$314$	12201.8	2.19295
$315$	−954.213	−0.170679
$316$	−6300.88	−1.12168
$317$	−2745.04	−0.486361	−0.243181	−	0.969981i	$-0.578191\pi$
$317$	−2745.04	−0.486361	−0.243181	+	0.969981i	$0.578191\pi$
$318$	7603.81	1.34088
$319$	0	0
$320$	1009.98	0.176437
$321$	5173.02	0.899470
$322$	11466.6	1.98450
$323$	−6927.26	−1.19332
$324$	469.620	0.0805246
$325$	700.101	0.119491
$326$	−13933.5	−2.36720
$327$	−3629.43	−0.613786
$328$	−879.858	−0.148116
$329$	−11451.8	−1.91902
$330$	0	0
$331$	−2935.70	−0.487495	−0.243747	−	0.969839i	$-0.578377\pi$
$331$	−2935.70	−0.487495	−0.243747	+	0.969839i	$0.578377\pi$
$332$	3914.40	0.647081
$333$	2208.30	0.363406
$334$	−3262.49	−0.534477
$335$	−1394.55	−0.227440
$336$	−4883.53	−0.792913
$337$	48.8906	0.00790280	0.00395140	−	0.999992i	$-0.498742\pi$
$337$	48.8906	0.00790280	0.00395140	+	0.999992i	$0.498742\pi$
$338$	−5247.80	−0.844505
$339$	−7040.42	−1.12797
$340$	2348.76	0.374645
$341$	0	0
$342$	2858.25	0.451920
$343$	−5011.94	−0.788978
$344$	861.361	0.135004
$345$	−2183.68	−0.340769
$346$	8247.88	1.28153
$347$	−9685.05	−1.49833	−0.749165	−	0.662383i	$-0.769545\pi$
$347$	−9685.05	−1.49833	−0.749165	+	0.662383i	$0.769545\pi$
$348$	2355.18	0.362790
$349$	−7918.97	−1.21459	−0.607296	−	0.794476i	$-0.707746\pi$
$349$	−7918.97	−1.21459	−0.607296	+	0.794476i	$0.707746\pi$
$350$	1969.14	0.300729
$351$	756.109	0.114980
$352$	0	0
$353$	−9232.67	−1.39208	−0.696042	−	0.718001i	$-0.745057\pi$
$353$	−9232.67	−1.39208	−0.696042	+	0.718001i	$0.745057\pi$
$354$	6740.94	1.01208
$355$	−1629.26	−0.243584
$356$	6094.97	0.907395
$357$	−5154.20	−0.764116
$358$	12298.8	1.81567
$359$	−3136.97	−0.461178	−0.230589	−	0.973051i	$-0.574065\pi$
$359$	−3136.97	−0.461178	−0.230589	+	0.973051i	$0.574065\pi$
$360$	368.111	0.0538922
$361$	450.838	0.0657294
$362$	−8181.72	−1.18790
$363$	0	0
$364$	3442.82	0.495749
$365$	−2648.97	−0.379872
$366$	366.040	0.0522765
$367$	1392.29	0.198030	0.0990151	−	0.995086i	$-0.468431\pi$
$367$	1392.29	0.198030	0.0990151	+	0.995086i	$0.468431\pi$
$368$	−11175.8	−1.58309
$369$	968.028	0.136568
$370$	−4557.11	−0.640306
$371$	14469.0	2.02478
$372$	−605.351	−0.0843709
$373$	8848.60	1.22832	0.614159	−	0.789182i	$-0.289495\pi$
$373$	8848.60	1.22832	0.614159	+	0.789182i	$0.289495\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	4417.81	0.605934
$377$	3791.95	0.518024
$378$	2126.67	0.289376
$379$	−6740.09	−0.913497	−0.456748	−	0.889596i	$-0.650986\pi$
$379$	−6740.09	−0.913497	−0.456748	+	0.889596i	$0.650986\pi$
$380$	−2478.48	−0.334587
$381$	−677.703	−0.0911280
$382$	−2082.36	−0.278908
$383$	−7547.43	−1.00693	−0.503467	−	0.864015i	$-0.667942\pi$
$383$	−7547.43	−1.00693	−0.503467	+	0.864015i	$0.667942\pi$
$384$	3022.20	0.401630
$385$	0	0
$386$	−10366.8	−1.36698
$387$	−947.679	−0.124479
$388$	−2857.79	−0.373924
$389$	−8662.64	−1.12908	−0.564542	−	0.825405i	$-0.690947\pi$
$389$	−8662.64	−1.12908	−0.564542	+	0.825405i	$0.690947\pi$
$390$	−1560.33	−0.202591
$391$	−11795.2	−1.52560
$392$	−872.346	−0.112398
$393$	−5.44824	−0.000699306 0
$394$	7161.68	0.915736
$395$	5433.88	0.692172
$396$	0	0
$397$	−7328.45	−0.926460	−0.463230	−	0.886238i	$-0.653310\pi$
$397$	−7328.45	−0.926460	−0.463230	+	0.886238i	$0.653310\pi$
$398$	3507.54	0.441751
$399$	5438.86	0.682415
$400$	−1919.20	−0.239900
$401$	−6191.66	−0.771064	−0.385532	−	0.922694i	$-0.625982\pi$
$401$	−6191.66	−0.771064	−0.385532	+	0.922694i	$0.625982\pi$
$402$	3108.06	0.385612
$403$	−974.642	−0.120472
$404$	5930.74	0.730359
$405$	−405.000	−0.0496904
$406$	10665.4	1.30374
$407$	0	0
$408$	1988.36	0.241271
$409$	9979.21	1.20646	0.603228	−	0.797569i	$-0.293881\pi$
$409$	9979.21	1.20646	0.603228	+	0.797569i	$0.293881\pi$
$410$	−1997.65	−0.240627
$411$	7213.16	0.865691
$412$	−463.042	−0.0553700
$413$	12827.1	1.52828
$414$	4866.81	0.577755
$415$	−3375.78	−0.399303
$416$	−6152.92	−0.725172
$417$	−2579.89	−0.302969
$418$	0	0
$419$	−11273.5	−1.31443	−0.657216	−	0.753702i	$-0.728266\pi$
$419$	−11273.5	−1.31443	−0.657216	+	0.753702i	$0.728266\pi$
$420$	−1844.10	−0.214245
$421$	−215.058	−0.0248961	−0.0124481	−	0.999923i	$-0.503962\pi$
$421$	−215.058	−0.0248961	−0.0124481	+	0.999923i	$0.503962\pi$
$422$	−6695.94	−0.772401
$423$	−4860.52	−0.558692
$424$	−5581.77	−0.639327
$425$	−2025.57	−0.231187
$426$	3631.17	0.412983
$427$	696.523	0.0789393
$428$	9997.34	1.12906
$429$	0	0
$430$	1955.66	0.219326
$431$	10862.0	1.21393	0.606965	−	0.794729i	$-0.292387\pi$
$431$	10862.0	1.21393	0.606965	+	0.794729i	$0.292387\pi$
$432$	−2072.74	−0.230844
$433$	−4847.38	−0.537991	−0.268995	−	0.963141i	$-0.586692\pi$
$433$	−4847.38	−0.537991	−0.268995	+	0.963141i	$0.586692\pi$
$434$	−2741.33	−0.303199
$435$	−2031.11	−0.223872
$436$	−7014.20	−0.770457
$437$	12446.6	1.36248
$438$	5903.81	0.644053
$439$	800.449	0.0870236	0.0435118	−	0.999053i	$-0.486145\pi$
$439$	800.449	0.0870236	0.0435118	+	0.999053i	$0.486145\pi$
$440$	0	0
$441$	959.764	0.103635
$442$	−8428.16	−0.906983
$443$	−16786.4	−1.80033	−0.900166	−	0.435547i	$-0.856555\pi$
$443$	−16786.4	−1.80033	−0.900166	+	0.435547i	$0.856555\pi$
$444$	4267.74	0.456166
$445$	−5256.30	−0.559938
$446$	−5818.36	−0.617729
$447$	4557.01	0.482190
$448$	−4283.28	−0.451710
$449$	−4987.10	−0.524178	−0.262089	−	0.965044i	$-0.584411\pi$
$449$	−4987.10	−0.524178	−0.262089	+	0.965044i	$0.584411\pi$
$450$	835.770	0.0875524
$451$	0	0
$452$	−13606.2	−1.41589
$453$	−3408.71	−0.353543
$454$	2073.32	0.214330
$455$	−2969.09	−0.305919
$456$	−2098.18	−0.215474
$457$	400.553	0.0410002	0.0205001	−	0.999790i	$-0.493474\pi$
$457$	400.553	0.0410002	0.0205001	+	0.999790i	$0.493474\pi$
$458$	−16741.3	−1.70801
$459$	−2187.62	−0.222460
$460$	−4220.15	−0.427752
$461$	−6192.51	−0.625627	−0.312813	−	0.949815i	$-0.601271\pi$
$461$	−6192.51	−0.625627	−0.312813	+	0.949815i	$0.601271\pi$
$462$	0	0
$463$	15107.1	1.51639	0.758193	−	0.652030i	$-0.226082\pi$
$463$	15107.1	1.51639	0.758193	+	0.652030i	$0.226082\pi$
$464$	−10394.9	−1.04003
$465$	522.055	0.0520639
$466$	−25728.1	−2.55757
$467$	−8820.04	−0.873968	−0.436984	−	0.899469i	$-0.643953\pi$
$467$	−8820.04	−0.873968	−0.436984	+	0.899469i	$0.643953\pi$
$468$	1461.25	0.144330
$469$	5914.21	0.582287
$470$	10030.3	0.984392
$471$	9854.62	0.964070
$472$	−4948.36	−0.482557
$473$	0	0
$474$	−12110.6	−1.17354
$475$	2137.44	0.206468
$476$	−9960.97	−0.959160
$477$	6141.12	0.589482
$478$	7185.80	0.687596
$479$	−10067.2	−0.960295	−0.480148	−	0.877188i	$-0.659417\pi$
$479$	−10067.2	−0.960295	−0.480148	+	0.877188i	$0.659417\pi$
$480$	3295.73	0.313394
$481$	6871.25	0.651356
$482$	8504.84	0.803703
$483$	9260.86	0.872430
$484$	0	0
$485$	2464.56	0.230742
$486$	902.632	0.0842474
$487$	807.840	0.0751679	0.0375839	−	0.999293i	$-0.488034\pi$
$487$	807.840	0.0751679	0.0375839	+	0.999293i	$0.488034\pi$
$488$	−268.701	−0.0249253
$489$	−11253.3	−1.04067
$490$	−1980.60	−0.182601
$491$	13876.2	1.27540	0.637701	−	0.770284i	$-0.279885\pi$
$491$	13876.2	1.27540	0.637701	+	0.770284i	$0.279885\pi$
$492$	1870.80	0.171427
$493$	−10971.1	−1.00226
$494$	8893.63	0.810006
$495$	0	0
$496$	2671.81	0.241870
$497$	6909.60	0.623618
$498$	7523.68	0.676996
$499$	9879.00	0.886262	0.443131	−	0.896457i	$-0.353868\pi$
$499$	9879.00	0.886262	0.443131	+	0.896457i	$0.353868\pi$
$500$	−724.721	−0.0648211
$501$	−2634.91	−0.234968
$502$	21049.3	1.87146
$503$	717.319	0.0635858	0.0317929	−	0.999494i	$-0.489878\pi$
$503$	717.319	0.0635858	0.0317929	+	0.999494i	$0.489878\pi$
$504$	−1561.14	−0.137974
$505$	−5114.67	−0.450693
$506$	0	0
$507$	−4238.32	−0.371263
$508$	−1309.72	−0.114389
$509$	5602.06	0.487833	0.243916	−	0.969796i	$-0.421568\pi$
$509$	5602.06	0.487833	0.243916	+	0.969796i	$0.421568\pi$
$510$	4514.44	0.391966
$511$	11234.1	0.972541
$512$	11843.3	1.02227
$513$	2308.43	0.198674
$514$	−14701.4	−1.26158
$515$	399.327	0.0341679
$516$	−1831.47	−0.156252
$517$	0	0
$518$	19326.5	1.63930
$519$	6661.31	0.563389
$520$	1145.40	0.0965945
$521$	−21752.2	−1.82914	−0.914569	−	0.404431i	$-0.867470\pi$
$521$	−21752.2	−1.82914	−0.914569	+	0.404431i	$0.867470\pi$
$522$	4526.77	0.379562
$523$	−13920.0	−1.16382	−0.581910	−	0.813253i	$-0.697694\pi$
$523$	−13920.0	−1.16382	−0.581910	+	0.813253i	$0.697694\pi$
$524$	−10.5292	−0.000877807 0
$525$	1590.35	0.132207
$526$	20249.5	1.67856
$527$	2819.89	0.233086
$528$	0	0
$529$	9026.09	0.741850
$530$	−12673.0	−1.03864
$531$	5444.24	0.444934
$532$	10511.1	0.856604
$533$	3012.08	0.244780
$534$	11714.8	0.949345
$535$	−8621.71	−0.696727
$536$	−2281.55	−0.183858
$537$	9932.97	0.798211
$538$	10095.4	0.809000
$539$	0	0
$540$	−782.699	−0.0623741
$541$	17528.3	1.39298	0.696490	−	0.717567i	$-0.254744\pi$
$541$	17528.3	1.39298	0.696490	+	0.717567i	$0.254744\pi$
$542$	2013.53	0.159573
$543$	−6607.87	−0.522230
$544$	17802.0	1.40304
$545$	6049.05	0.475436
$546$	6617.27	0.518669
$547$	−15441.6	−1.20701	−0.603507	−	0.797358i	$-0.706230\pi$
$547$	−15441.6	−1.20701	−0.603507	+	0.797358i	$0.706230\pi$
$548$	13940.1	1.08666
$549$	295.628	0.0229819
$550$	0	0
$551$	11577.0	0.895093
$552$	−3572.61	−0.275471
$553$	−23044.8	−1.77209
$554$	−5509.55	−0.422524
$555$	−3680.50	−0.281493
$556$	−4985.88	−0.380303
$557$	−7175.87	−0.545873	−0.272936	−	0.962032i	$-0.587995\pi$
$557$	−7175.87	−0.545873	−0.272936	+	0.962032i	$0.587995\pi$
$558$	−1163.51	−0.0882715
$559$	−2948.76	−0.223111
$560$	8139.22	0.614187
$561$	0	0
$562$	−962.753	−0.0722620
$563$	10680.1	0.799491	0.399745	−	0.916626i	$-0.369099\pi$
$563$	10680.1	0.799491	0.399745	+	0.916626i	$0.369099\pi$
$564$	−9393.40	−0.701301
$565$	11734.0	0.873724
$566$	13159.2	0.977250
$567$	1717.58	0.127216
$568$	−2665.55	−0.196909
$569$	16334.2	1.20345	0.601726	−	0.798702i	$-0.294480\pi$
$569$	16334.2	1.20345	0.601726	+	0.798702i	$0.294480\pi$
$570$	−4763.76	−0.350056
$571$	−7832.73	−0.574062	−0.287031	−	0.957921i	$-0.592668\pi$
$571$	−7832.73	−0.574062	−0.287031	+	0.957921i	$0.592668\pi$
$572$	0	0
$573$	−1681.79	−0.122614
$574$	8471.94	0.616049
$575$	3639.46	0.263958
$576$	−1817.97	−0.131508
$577$	−12009.8	−0.866505	−0.433253	−	0.901273i	$-0.642634\pi$
$577$	−12009.8	−0.866505	−0.433253	+	0.901273i	$0.642634\pi$
$578$	6135.32	0.441515
$579$	−8372.60	−0.600956
$580$	−3925.30	−0.281016
$581$	14316.5	1.02229
$582$	−5492.82	−0.391211
$583$	0	0
$584$	−4333.85	−0.307082
$585$	−1260.18	−0.0890634
$586$	27617.8	1.94690
$587$	−2249.68	−0.158184	−0.0790922	−	0.996867i	$-0.525202\pi$
$587$	−2249.68	−0.158184	−0.0790922	+	0.996867i	$0.525202\pi$
$588$	1854.83	0.130088
$589$	−2975.63	−0.208164
$590$	−11234.9	−0.783955
$591$	5784.04	0.402578
$592$	−18836.3	−1.30772
$593$	−12389.9	−0.857998	−0.428999	−	0.903305i	$-0.641134\pi$
$593$	−12389.9	−0.857998	−0.428999	+	0.903305i	$0.641134\pi$
$594$	0	0
$595$	8590.34	0.591882
$596$	8806.83	0.605272
$597$	2832.82	0.194204
$598$	15143.4	1.03555
$599$	11027.4	0.752200	0.376100	−	0.926579i	$-0.377265\pi$
$599$	11027.4	0.752200	0.376100	+	0.926579i	$0.377265\pi$
$600$	−613.519	−0.0417447
$601$	18985.3	1.28856	0.644282	−	0.764788i	$-0.277156\pi$
$601$	18985.3	1.28856	0.644282	+	0.764788i	$0.277156\pi$
$602$	−8293.84	−0.561514
$603$	2510.19	0.169524
$604$	−6587.63	−0.443787
$605$	0	0
$606$	11399.2	0.764125
$607$	−2654.58	−0.177506	−0.0887530	−	0.996054i	$-0.528288\pi$
$607$	−2654.58	−0.177506	−0.0887530	+	0.996054i	$0.528288\pi$
$608$	−18785.1	−1.25302
$609$	8613.81	0.573152
$610$	−610.066	−0.0404932
$611$	−15123.8	−1.00138
$612$	−4227.77	−0.279244
$613$	−12026.0	−0.792373	−0.396186	−	0.918170i	$-0.629667\pi$
$613$	−12026.0	−0.792373	−0.396186	+	0.918170i	$0.629667\pi$
$614$	36315.0	2.38690
$615$	−1613.38	−0.105785
$616$	0	0
$617$	−22514.9	−1.46907	−0.734536	−	0.678570i	$-0.762600\pi$
$617$	−22514.9	−1.46907	−0.734536	+	0.678570i	$0.762600\pi$
$618$	−889.990	−0.0579298
$619$	−4301.37	−0.279300	−0.139650	−	0.990201i	$-0.544598\pi$
$619$	−4301.37	−0.279300	−0.139650	+	0.990201i	$0.544598\pi$
$620$	1008.92	0.0653534
$621$	3930.62	0.253994
$622$	−16221.8	−1.04572
$623$	22291.7	1.43354
$624$	−6449.44	−0.413757
$625$	625.000	0.0400000
$626$	−35852.6	−2.28907
$627$	0	0
$628$	19044.9	1.21015
$629$	−19880.3	−1.26022
$630$	−3544.46	−0.224150
$631$	−5340.09	−0.336903	−0.168451	−	0.985710i	$-0.553877\pi$
$631$	−5340.09	−0.336903	−0.168451	+	0.985710i	$0.553877\pi$
$632$	8890.10	0.559540
$633$	−5407.90	−0.339565
$634$	−10196.5	−0.638732
$635$	1129.50	0.0705874
$636$	11868.3	0.739949
$637$	2986.36	0.185752
$638$	0	0
$639$	2932.67	0.181556
$640$	−5037.00	−0.311101
$641$	24580.3	1.51461	0.757303	−	0.653063i	$-0.226516\pi$
$641$	24580.3	1.51461	0.757303	+	0.653063i	$0.226516\pi$
$642$	19215.4	1.18126
$643$	−3779.39	−0.231796	−0.115898	−	0.993261i	$-0.536975\pi$
$643$	−3779.39	−0.231796	−0.115898	+	0.993261i	$0.536975\pi$
$644$	17897.4	1.09512
$645$	1579.46	0.0964207
$646$	−25731.6	−1.56717
$647$	−31348.5	−1.90485	−0.952425	−	0.304772i	$-0.901420\pi$
$647$	−31348.5	−1.90485	−0.952425	+	0.304772i	$0.901420\pi$
$648$	−662.601	−0.0401688
$649$	0	0
$650$	2600.55	0.156926
$651$	−2214.00	−0.133293
$652$	−21747.9	−1.30631
$653$	23893.6	1.43190	0.715949	−	0.698152i	$-0.245994\pi$
$653$	23893.6	1.43190	0.715949	+	0.698152i	$0.245994\pi$
$654$	−13481.6	−0.806076
$655$	9.08040	0.000541680 0
$656$	−8257.07	−0.491440
$657$	4768.14	0.283140
$658$	−42538.1	−2.52022
$659$	−21134.4	−1.24928	−0.624642	−	0.780912i	$-0.714755\pi$
$659$	−21134.4	−1.24928	−0.624642	+	0.780912i	$0.714755\pi$
$660$	0	0
$661$	−2722.03	−0.160174	−0.0800868	−	0.996788i	$-0.525520\pi$
$661$	−2722.03	−0.160174	−0.0800868	+	0.996788i	$0.525520\pi$
$662$	−10904.8	−0.640220
$663$	−6806.90	−0.398730
$664$	−5522.95	−0.322789
$665$	−9064.77	−0.528596
$666$	8202.80	0.477256
$667$	19712.4	1.14433
$668$	−5092.20	−0.294945
$669$	−4699.13	−0.271568
$670$	−5180.10	−0.298694
$671$	0	0
$672$	−13977.0	−0.802344
$673$	−22785.2	−1.30506	−0.652529	−	0.757764i	$-0.726292\pi$
$673$	−22785.2	−1.30506	−0.652529	+	0.757764i	$0.726292\pi$
$674$	181.606	0.0103786
$675$	675.000	0.0384900
$676$	−8190.94	−0.466030
$677$	11182.3	0.634814	0.317407	−	0.948289i	$-0.397188\pi$
$677$	11182.3	0.634814	0.317407	+	0.948289i	$0.397188\pi$
$678$	−26151.9	−1.48135
$679$	−10452.1	−0.590742
$680$	−3313.94	−0.186888
$681$	1674.49	0.0942241
$682$	0	0
$683$	−5921.94	−0.331767	−0.165883	−	0.986145i	$-0.553048\pi$
$683$	−5921.94	−0.331767	−0.165883	+	0.986145i	$0.553048\pi$
$684$	4461.26	0.249387
$685$	−12021.9	−0.670562
$686$	−18617.0	−1.03615
$687$	−13520.9	−0.750879
$688$	8083.49	0.447936
$689$	19108.5	1.05657
$690$	−8111.35	−0.447527
$691$	−3853.12	−0.212127	−0.106063	−	0.994359i	$-0.533825\pi$
$691$	−3853.12	−0.212127	−0.106063	+	0.994359i	$0.533825\pi$
$692$	12873.6	0.707196
$693$	0	0
$694$	−35975.5	−1.96774
$695$	4299.82	0.234679
$696$	−3322.99	−0.180974
$697$	−8714.72	−0.473592
$698$	−29415.3	−1.59511
$699$	−20779.0	−1.12437
$700$	3073.50	0.165954
$701$	−8326.68	−0.448637	−0.224318	−	0.974516i	$-0.572016\pi$
$701$	−8326.68	−0.448637	−0.224318	+	0.974516i	$0.572016\pi$
$702$	2808.59	0.151002
$703$	20978.2	1.12548
$704$	0	0
$705$	8100.87	0.432761
$706$	−34295.1	−1.82820
$707$	21691.0	1.15385
$708$	10521.5	0.558505
$709$	21068.4	1.11600	0.557998	−	0.829843i	$-0.311570\pi$
$709$	21068.4	1.11600	0.557998	+	0.829843i	$0.311570\pi$
$710$	−6051.94	−0.319895
$711$	−9780.98	−0.515915
$712$	−8599.58	−0.452644
$713$	−5066.66	−0.266126
$714$	−19145.5	−1.00350
$715$	0	0
$716$	19196.4	1.00196
$717$	5803.52	0.302283
$718$	−11652.4	−0.605659
$719$	30379.6	1.57576	0.787879	−	0.615830i	$-0.211179\pi$
$719$	30379.6	1.57576	0.787879	+	0.615830i	$0.211179\pi$
$720$	3454.56	0.178811
$721$	−1693.53	−0.0874760
$722$	1674.65	0.0863215
$723$	6868.83	0.353326
$724$	−12770.3	−0.655531
$725$	3385.18	0.173410
$726$	0	0
$727$	26894.4	1.37202	0.686010	−	0.727592i	$-0.259361\pi$
$727$	26894.4	1.37202	0.686010	+	0.727592i	$0.259361\pi$
$728$	−4857.58	−0.247299
$729$	729.000	0.0370370
$730$	−9839.69	−0.498881
$731$	8531.52	0.431668
$732$	571.327	0.0288482
$733$	16811.5	0.847129	0.423565	−	0.905866i	$-0.360779\pi$
$733$	16811.5	0.847129	0.423565	+	0.905866i	$0.360779\pi$
$734$	5171.72	0.260070
$735$	−1599.61	−0.0802753
$736$	−31985.8	−1.60192
$737$	0	0
$738$	3595.78	0.179353
$739$	−10378.1	−0.516598	−0.258299	−	0.966065i	$-0.583162\pi$
$739$	−10378.1	−0.516598	−0.258299	+	0.966065i	$0.583162\pi$
$740$	−7112.90	−0.353345
$741$	7182.83	0.356097
$742$	53745.5	2.65911
$743$	16328.4	0.806233	0.403117	−	0.915149i	$-0.367927\pi$
$743$	16328.4	0.806233	0.403117	+	0.915149i	$0.367927\pi$
$744$	854.108	0.0420875
$745$	−7595.01	−0.373503
$746$	32868.4	1.61313
$747$	6076.41	0.297623
$748$	0	0
$749$	36564.2	1.78375
$750$	−1392.95	−0.0678178
$751$	1657.39	0.0805313	0.0402656	−	0.999189i	$-0.487180\pi$
$751$	1657.39	0.0805313	0.0402656	+	0.999189i	$0.487180\pi$
$752$	41459.2	2.01045
$753$	17000.2	0.822738
$754$	14085.3	0.680314
$755$	5681.18	0.273853
$756$	3319.38	0.159689
$757$	15688.2	0.753232	0.376616	−	0.926370i	$-0.377088\pi$
$757$	15688.2	0.753232	0.376616	+	0.926370i	$0.377088\pi$
$758$	−25036.3	−1.19968
$759$	0	0
$760$	3496.96	0.166905
$761$	−36603.6	−1.74360	−0.871800	−	0.489862i	$-0.837047\pi$
$761$	−36603.6	−1.74360	−0.871800	+	0.489862i	$0.837047\pi$
$762$	−2517.35	−0.119677
$763$	−25653.7	−1.21720
$764$	−3250.22	−0.153912
$765$	3646.03	0.172317
$766$	−28035.2	−1.32239
$767$	16940.1	0.797484
$768$	16074.0	0.755234
$769$	25913.0	1.21515	0.607573	−	0.794264i	$-0.292143\pi$
$769$	25913.0	1.21515	0.607573	+	0.794264i	$0.292143\pi$
$770$	0	0
$771$	−11873.4	−0.554617
$772$	−16180.8	−0.754353
$773$	−41817.7	−1.94577	−0.972884	−	0.231292i	$-0.925705\pi$
$773$	−41817.7	−1.94577	−0.972884	+	0.231292i	$0.925705\pi$
$774$	−3520.19	−0.163476
$775$	−870.091	−0.0403285
$776$	4032.15	0.186528
$777$	15608.8	0.720672
$778$	−32177.7	−1.48281
$779$	9196.01	0.422954
$780$	−2435.41	−0.111797
$781$	0	0
$782$	−43813.6	−2.00355
$783$	3655.99	0.166864
$784$	−8186.57	−0.372931
$785$	−16424.4	−0.746765
$786$	−20.2377	−0.000918389 0
$787$	−21321.3	−0.965723	−0.482861	−	0.875697i	$-0.660403\pi$
$787$	−21321.3	−0.965723	−0.482861	+	0.875697i	$0.660403\pi$
$788$	11178.2	0.505338
$789$	16354.3	0.737932
$790$	20184.3	0.909021
$791$	−49763.4	−2.23689
$792$	0	0
$793$	919.863	0.0411920
$794$	−27221.8	−1.21671
$795$	−10235.2	−0.456610
$796$	5474.68	0.243775
$797$	9036.84	0.401633	0.200816	−	0.979629i	$-0.435641\pi$
$797$	9036.84	0.401633	0.200816	+	0.979629i	$0.435641\pi$
$798$	20202.8	0.896206
$799$	43757.1	1.93744
$800$	−5492.89	−0.242754
$801$	9461.34	0.417353
$802$	−22999.1	−1.01263
$803$	0	0
$804$	4851.17	0.212795
$805$	−15434.8	−0.675781
$806$	−3620.34	−0.158215
$807$	8153.40	0.355654
$808$	−8367.86	−0.364332
$809$	−11669.3	−0.507134	−0.253567	−	0.967318i	$-0.581604\pi$
$809$	−11669.3	−0.507134	−0.253567	+	0.967318i	$0.581604\pi$
$810$	−1504.39	−0.0652577
$811$	26020.5	1.12664	0.563320	−	0.826239i	$-0.309524\pi$
$811$	26020.5	1.12664	0.563320	+	0.826239i	$0.309524\pi$
$812$	16647.0	0.719451
$813$	1626.20	0.0701517
$814$	0	0
$815$	18755.4	0.806103
$816$	18659.9	0.800523
$817$	−9002.69	−0.385513
$818$	37068.1	1.58442
$819$	5344.36	0.228018
$820$	−3118.00	−0.132787
$821$	14726.2	0.626002	0.313001	−	0.949753i	$-0.398666\pi$
$821$	14726.2	0.626002	0.313001	+	0.949753i	$0.398666\pi$
$822$	26793.6	1.13690
$823$	−37392.8	−1.58376	−0.791878	−	0.610679i	$-0.790896\pi$
$823$	−37392.8	−1.58376	−0.791878	+	0.610679i	$0.790896\pi$
$824$	653.320	0.0276207
$825$	0	0
$826$	47646.6	2.00707
$827$	15375.6	0.646508	0.323254	−	0.946312i	$-0.395223\pi$
$827$	15375.6	0.646508	0.323254	+	0.946312i	$0.395223\pi$
$828$	7596.28	0.318827
$829$	30372.5	1.27247	0.636237	−	0.771493i	$-0.280490\pi$
$829$	30372.5	1.27247	0.636237	+	0.771493i	$0.280490\pi$
$830$	−12539.5	−0.524399
$831$	−4449.72	−0.185751
$832$	−5656.72	−0.235711
$833$	−8640.32	−0.359387
$834$	−9583.11	−0.397885
$835$	4391.51	0.182005
$836$	0	0
$837$	−939.698	−0.0388061
$838$	−41875.8	−1.72623
$839$	−43507.1	−1.79026	−0.895132	−	0.445802i	$-0.852919\pi$
$839$	−43507.1	−1.79026	−0.895132	+	0.445802i	$0.852919\pi$
$840$	2601.90	0.106874
$841$	−6053.91	−0.248223
$842$	−798.839	−0.0326957
$843$	−777.556	−0.0317680
$844$	−10451.2	−0.426240
$845$	7063.87	0.287579
$846$	−18054.6	−0.733723
$847$	0	0
$848$	−52382.4	−2.12125
$849$	10627.9	0.429621
$850$	−7524.06	−0.303615
$851$	35720.1	1.43886
$852$	5667.65	0.227900
$853$	7932.67	0.318417	0.159208	−	0.987245i	$-0.449106\pi$
$853$	7932.67	0.318417	0.159208	+	0.987245i	$0.449106\pi$
$854$	2587.26	0.103670
$855$	−3847.39	−0.153892
$856$	−14105.5	−0.563222
$857$	−1469.02	−0.0585540	−0.0292770	−	0.999571i	$-0.509320\pi$
$857$	−1469.02	−0.0585540	−0.0292770	+	0.999571i	$0.509320\pi$
$858$	0	0
$859$	22.7919	0.000905298 0	0.000452649	−	1.00000i	$-0.499856\pi$
$859$	22.7919	0.000905298 0	0.000452649		1.00000i	$0.499856\pi$
$860$	3052.46	0.121032
$861$	6842.26	0.270829
$862$	40347.3	1.59424
$863$	−9487.61	−0.374232	−0.187116	−	0.982338i	$-0.559914\pi$
$863$	−9487.61	−0.374232	−0.187116	+	0.982338i	$0.559914\pi$
$864$	−5932.32	−0.233590
$865$	−11102.2	−0.436399
$866$	−18005.8	−0.706536
$867$	4955.12	0.194100
$868$	−4278.76	−0.167317
$869$	0	0
$870$	−7544.62	−0.294007
$871$	7810.60	0.303848
$872$	9896.55	0.384334
$873$	−4436.21	−0.171985
$874$	46233.4	1.78932
$875$	−2650.59	−0.102407
$876$	9214.87	0.355413
$877$	48255.5	1.85801	0.929003	−	0.370071i	$-0.120667\pi$
$877$	48255.5	1.85801	0.929003	+	0.370071i	$0.120667\pi$
$878$	2973.30	0.114287
$879$	22305.2	0.855899
$880$	0	0
$881$	−12933.6	−0.494603	−0.247302	−	0.968939i	$-0.579544\pi$
$881$	−12933.6	−0.494603	−0.247302	+	0.968939i	$0.579544\pi$
$882$	3565.08	0.136102
$883$	18184.5	0.693043	0.346521	−	0.938042i	$-0.387363\pi$
$883$	18184.5	0.693043	0.346521	+	0.938042i	$0.387363\pi$
$884$	−13155.0	−0.500508
$885$	−9073.73	−0.344644
$886$	−62353.8	−2.36435
$887$	7795.26	0.295084	0.147542	−	0.989056i	$-0.452864\pi$
$887$	7795.26	0.295084	0.147542	+	0.989056i	$0.452864\pi$
$888$	−6021.48	−0.227554
$889$	−4790.17	−0.180717
$890$	−19524.7	−0.735360
$891$	0	0
$892$	−9081.49	−0.340887
$893$	−46173.7	−1.73028
$894$	16927.2	0.633254
$895$	−16555.0	−0.618292
$896$	21361.6	0.796476
$897$	12230.4	0.455250
$898$	−18524.8	−0.688396
$899$	−4712.66	−0.174834
$900$	1304.50	0.0483148
$901$	−55285.7	−2.04421
$902$	0	0
$903$	−6698.42	−0.246854
$904$	19197.5	0.706303
$905$	11013.1	0.404517
$906$	−12661.8	−0.464303
$907$	−99.7631	−0.00365224	−0.00182612	−	0.999998i	$-0.500581\pi$
$907$	−99.7631	−0.00365224	−0.00182612	+	0.999998i	$0.500581\pi$
$908$	3236.11	0.118275
$909$	9206.40	0.335926
$910$	−11028.8	−0.401759
$911$	23707.9	0.862215	0.431108	−	0.902300i	$-0.358123\pi$
$911$	23707.9	0.862215	0.431108	+	0.902300i	$0.358123\pi$
$912$	−19690.4	−0.714929
$913$	0	0
$914$	1487.87	0.0538450
$915$	−492.713	−0.0178017
$916$	−26130.3	−0.942544
$917$	−38.5095	−0.00138680
$918$	−8125.98	−0.292154
$919$	47348.3	1.69954	0.849769	−	0.527155i	$-0.176741\pi$
$919$	47348.3	1.69954	0.849769	+	0.527155i	$0.176741\pi$
$920$	5954.34	0.213379
$921$	29329.4	1.04933
$922$	−23002.3	−0.821627
$923$	9125.17	0.325416
$924$	0	0
$925$	6134.16	0.218043
$926$	56115.9	1.99145
$927$	−718.789	−0.0254673
$928$	−29751.0	−1.05240
$929$	−26802.4	−0.946564	−0.473282	−	0.880911i	$-0.656931\pi$
$929$	−26802.4	−0.946564	−0.473282	+	0.880911i	$0.656931\pi$
$930$	1939.19	0.0683748
$931$	9117.50	0.320960
$932$	−40157.2	−1.41137
$933$	−13101.4	−0.459721
$934$	−32762.4	−1.14777
$935$	0	0
$936$	−2061.72	−0.0719973
$937$	−10657.7	−0.371580	−0.185790	−	0.982589i	$-0.559484\pi$
$937$	−10657.7	−0.371580	−0.185790	+	0.982589i	$0.559484\pi$
$938$	21968.5	0.764710
$939$	−28956.0	−1.00633
$940$	15655.7	0.543225
$941$	−50278.4	−1.74179	−0.870897	−	0.491465i	$-0.836462\pi$
$941$	−50278.4	−1.74179	−0.870897	+	0.491465i	$0.836462\pi$
$942$	36605.3	1.26610
$943$	15658.2	0.540724
$944$	−46438.1	−1.60109
$945$	−2862.64	−0.0985414
$946$	0	0
$947$	25502.5	0.875099	0.437550	−	0.899194i	$-0.355846\pi$
$947$	25502.5	0.875099	0.437550	+	0.899194i	$0.355846\pi$
$948$	−18902.6	−0.647604
$949$	14836.4	0.507490
$950$	7939.60	0.271152
$951$	−8235.11	−0.280801
$952$	14054.2	0.478467
$953$	−21624.9	−0.735045	−0.367523	−	0.930015i	$-0.619794\pi$
$953$	−21624.9	−0.735045	−0.367523	+	0.930015i	$0.619794\pi$
$954$	22811.4	0.774158
$955$	2802.99	0.0949766
$956$	11215.8	0.379441
$957$	0	0
$958$	−37394.9	−1.26114
$959$	50984.4	1.71676
$960$	3029.95	0.101866
$961$	−28579.7	−0.959340
$962$	25523.5	0.855417
$963$	15519.1	0.519309
$964$	13274.6	0.443514
$965$	13954.3	0.465498
$966$	34399.8	1.14575
$967$	−55058.0	−1.83097	−0.915484	−	0.402353i	$-0.868192\pi$
$967$	−55058.0	−1.83097	−0.915484	+	0.402353i	$0.868192\pi$
$968$	0	0
$969$	−20781.8	−0.688965
$970$	9154.70	0.303031
$971$	57920.6	1.91427	0.957136	−	0.289637i	$-0.0935347\pi$
$971$	57920.6	1.91427	0.957136	+	0.289637i	$0.0935347\pi$
$972$	1408.86	0.0464909
$973$	−18235.3	−0.600820
$974$	3000.75	0.0987169
$975$	2100.30	0.0689882
$976$	−2521.64	−0.0827005
$977$	6308.33	0.206572	0.103286	−	0.994652i	$-0.467064\pi$
$977$	6308.33	0.206572	0.103286	+	0.994652i	$0.467064\pi$
$978$	−41800.6	−1.36670
$979$	0	0
$980$	−3091.38	−0.100766
$981$	−10888.3	−0.354369
$982$	51543.5	1.67497
$983$	−5233.66	−0.169815	−0.0849073	−	0.996389i	$-0.527059\pi$
$983$	−5233.66	−0.169815	−0.0849073	+	0.996389i	$0.527059\pi$
$984$	−2639.57	−0.0855148
$985$	−9640.07	−0.311836
$986$	−40752.4	−1.31625
$987$	−34355.4	−1.10795
$988$	13881.5	0.446992
$989$	−15329.1	−0.492857
$990$	0	0
$991$	41353.9	1.32558	0.662789	−	0.748806i	$-0.269372\pi$
$991$	41353.9	1.32558	0.662789	+	0.748806i	$0.269372\pi$
$992$	7646.90	0.244747
$993$	−8807.10	−0.281455
$994$	25666.0	0.818989
$995$	−4721.37	−0.150430
$996$	11743.2	0.373592
$997$	−44993.4	−1.42924	−0.714622	−	0.699511i	$-0.753401\pi$
$997$	−44993.4	−1.42924	−0.714622	+	0.699511i	$0.753401\pi$
$998$	36695.9	1.16392
$999$	6624.90	0.209812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bo.1.10		12
11.2	odd	10		165.4.m.d.136.5	yes	24
11.6	odd	10		165.4.m.d.91.5	✓	24
11.10	odd	2		1815.4.a.bg.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.m.d.91.5	✓	24	11.6	odd	10
165.4.m.d.136.5	yes	24	11.2	odd	10
1815.4.a.bg.1.3		12	11.10	odd	2
1815.4.a.bo.1.10		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.71454 q^{2} +3.00000 q^{3} +5.79777 q^{4} -5.00000 q^{5} +11.1436 q^{6} +21.2047 q^{7} -8.18025 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.71454 q^{2} +3.00000 q^{3} +5.79777 q^{4} -5.00000 q^{5} +11.1436 q^{6} +21.2047 q^{7} -8.18025 q^{8} +9.00000 q^{9} -18.5727 q^{10} +17.3933 q^{12} +28.0040 q^{13} +78.7657 q^{14} -15.0000 q^{15} -76.7680 q^{16} -81.0229 q^{17} +33.4308 q^{18} +85.4976 q^{19} -28.9889 q^{20} +63.6142 q^{21} +145.578 q^{23} -24.5408 q^{24} +25.0000 q^{25} +104.022 q^{26} +27.0000 q^{27} +122.940 q^{28} +135.407 q^{29} -55.7180 q^{30} -34.8036 q^{31} -219.715 q^{32} -300.962 q^{34} -106.024 q^{35} +52.1799 q^{36} +245.367 q^{37} +317.584 q^{38} +84.0121 q^{39} +40.9013 q^{40} +107.559 q^{41} +236.297 q^{42} -105.298 q^{43} -45.0000 q^{45} +540.756 q^{46} -540.058 q^{47} -230.304 q^{48} +106.640 q^{49} +92.8634 q^{50} -243.069 q^{51} +162.361 q^{52} +682.347 q^{53} +100.292 q^{54} -173.460 q^{56} +256.493 q^{57} +502.975 q^{58} +604.915 q^{59} -86.9666 q^{60} +32.8475 q^{61} -129.279 q^{62} +190.843 q^{63} -201.997 q^{64} -140.020 q^{65} +278.910 q^{67} -469.752 q^{68} +436.735 q^{69} -393.829 q^{70} +325.852 q^{71} -73.6223 q^{72} +529.794 q^{73} +911.423 q^{74} +75.0000 q^{75} +495.696 q^{76} +312.066 q^{78} -1086.78 q^{79} +383.840 q^{80} +81.0000 q^{81} +399.531 q^{82} +675.157 q^{83} +368.820 q^{84} +405.114 q^{85} -391.132 q^{86} +406.221 q^{87} +1051.26 q^{89} -167.154 q^{90} +593.818 q^{91} +844.031 q^{92} -104.411 q^{93} -2006.07 q^{94} -427.488 q^{95} -659.146 q^{96} -492.913 q^{97} +396.120 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} + 27 q^{6} + 21 q^{7} + 123 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q + 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 + 27 * q^6 + 21 * q^7 + 123 * q^8 + 108 * q^9	\( 12 q + 9 q^{2} + 36 q^{3} + 57 q^{4} - 60 q^{5} + 27 q^{6} + 21 q^{7} + 123 q^{8} + 108 q^{9} - 45 q^{10} + 171 q^{12} + 78 q^{13} + 262 q^{14} - 180 q^{15} + 225 q^{16} + 313 q^{17} + 81 q^{18} + 51 q^{19} - 285 q^{20} + 63 q^{21} - 34 q^{23} + 369 q^{24} + 300 q^{25} + 28 q^{26} + 324 q^{27} + 376 q^{28} + 31 q^{29} - 135 q^{30} + 655 q^{31} + 1578 q^{32} - 10 q^{34} - 105 q^{35} + 513 q^{36} + 84 q^{37} - 1076 q^{38} + 234 q^{39} - 615 q^{40} + 1463 q^{41} + 786 q^{42} - 111 q^{43} - 540 q^{45} - q^{46} + 278 q^{47} + 675 q^{48} - 325 q^{49} + 225 q^{50} + 939 q^{51} + 1957 q^{52} + 517 q^{53} + 243 q^{54} + 1543 q^{56} + 153 q^{57} + 442 q^{58} - 308 q^{59} - 855 q^{60} + 604 q^{61} + 1773 q^{62} + 189 q^{63} + 4323 q^{64} - 390 q^{65} - 357 q^{67} + 2192 q^{68} - 102 q^{69} - 1310 q^{70} - 620 q^{71} + 1107 q^{72} + 1892 q^{73} + 581 q^{74} + 900 q^{75} + 378 q^{76} + 84 q^{78} + 415 q^{79} - 1125 q^{80} + 972 q^{81} - 2802 q^{82} + 3158 q^{83} + 1128 q^{84} - 1565 q^{85} + 747 q^{86} + 93 q^{87} + 1563 q^{89} - 405 q^{90} + 1434 q^{91} - 3466 q^{92} + 1965 q^{93} - 3 q^{94} - 255 q^{95} + 4734 q^{96} + 714 q^{97} + 6586 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 + 36 * q^3 + 57 * q^4 - 60 * q^5 + 27 * q^6 + 21 * q^7 + 123 * q^8 + 108 * q^9 - 45 * q^10 + 171 * q^12 + 78 * q^13 + 262 * q^14 - 180 * q^15 + 225 * q^16 + 313 * q^17 + 81 * q^18 + 51 * q^19 - 285 * q^20 + 63 * q^21 - 34 * q^23 + 369 * q^24 + 300 * q^25 + 28 * q^26 + 324 * q^27 + 376 * q^28 + 31 * q^29 - 135 * q^30 + 655 * q^31 + 1578 * q^32 - 10 * q^34 - 105 * q^35 + 513 * q^36 + 84 * q^37 - 1076 * q^38 + 234 * q^39 - 615 * q^40 + 1463 * q^41 + 786 * q^42 - 111 * q^43 - 540 * q^45 - q^46 + 278 * q^47 + 675 * q^48 - 325 * q^49 + 225 * q^50 + 939 * q^51 + 1957 * q^52 + 517 * q^53 + 243 * q^54 + 1543 * q^56 + 153 * q^57 + 442 * q^58 - 308 * q^59 - 855 * q^60 + 604 * q^61 + 1773 * q^62 + 189 * q^63 + 4323 * q^64 - 390 * q^65 - 357 * q^67 + 2192 * q^68 - 102 * q^69 - 1310 * q^70 - 620 * q^71 + 1107 * q^72 + 1892 * q^73 + 581 * q^74 + 900 * q^75 + 378 * q^76 + 84 * q^78 + 415 * q^79 - 1125 * q^80 + 972 * q^81 - 2802 * q^82 + 3158 * q^83 + 1128 * q^84 - 1565 * q^85 + 747 * q^86 + 93 * q^87 + 1563 * q^89 - 405 * q^90 + 1434 * q^91 - 3466 * q^92 + 1965 * q^93 - 3 * q^94 - 255 * q^95 + 4734 * q^96 + 714 * q^97 + 6586 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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