LMFDB - Embedded newform 845.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(1,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("845.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.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:	$6.74735897080$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.571993$ of defining polynomial
Character	$\chi$	$=$	845.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.571993 q^{2} -0.428007 q^{3} -1.67282 q^{4} +1.00000 q^{5} +0.244817 q^{6} +2.67282 q^{7} +2.10083 q^{8} -2.81681 q^{9} -0.571993 q^{10} -5.10083 q^{11} +0.715980 q^{12} -1.52884 q^{14} -0.428007 q^{15} +2.14399 q^{16} +5.34565 q^{17} +1.61120 q^{18} -6.24482 q^{19} -1.67282 q^{20} -1.14399 q^{21} +2.91764 q^{22} -2.42801 q^{23} -0.899170 q^{24} +1.00000 q^{25} +2.48963 q^{27} -4.47116 q^{28} +2.67282 q^{29} +0.244817 q^{30} +0.244817 q^{31} -5.42801 q^{32} +2.18319 q^{33} -3.05767 q^{34} +2.67282 q^{35} +4.71203 q^{36} -3.32718 q^{37} +3.57199 q^{38} +2.10083 q^{40} -6.48963 q^{41} +0.654353 q^{42} -10.9176 q^{43} +8.53279 q^{44} -2.81681 q^{45} +1.38880 q^{46} -2.67282 q^{47} -0.917641 q^{48} +0.143987 q^{49} -0.571993 q^{50} -2.28797 q^{51} -4.20166 q^{53} -1.42405 q^{54} -5.10083 q^{55} +5.61515 q^{56} +2.67282 q^{57} -1.52884 q^{58} +0.899170 q^{59} +0.715980 q^{60} -5.81681 q^{61} -0.140034 q^{62} -7.52884 q^{63} -1.18319 q^{64} -1.24877 q^{66} -2.18319 q^{67} -8.94233 q^{68} +1.03920 q^{69} -1.52884 q^{70} -6.24482 q^{71} -5.91764 q^{72} -10.9608 q^{73} +1.90312 q^{74} -0.428007 q^{75} +10.4465 q^{76} -13.6336 q^{77} -3.63362 q^{79} +2.14399 q^{80} +7.38485 q^{81} +3.71203 q^{82} -9.81681 q^{83} +1.91369 q^{84} +5.34565 q^{85} +6.24482 q^{86} -1.14399 q^{87} -10.7160 q^{88} -7.63362 q^{89} +1.61120 q^{90} +4.06163 q^{92} -0.104783 q^{93} +1.52884 q^{94} -6.24482 q^{95} +2.32322 q^{96} +11.3456 q^{97} -0.0823593 q^{98} +14.3681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 2 q^{3} + 5 q^{4} + 3 q^{5} - 10 q^{6} - 2 q^{7} - 3 q^{8} + 3 q^{9} - q^{10} - 6 q^{11} + 4 q^{14} - 2 q^{15} + 5 q^{16} - 4 q^{17} + 17 q^{18} - 8 q^{19} + 5 q^{20} - 2 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) $ 3 * q - q^2 - 2 * q^3 + 5 * q^4 + 3 * q^5 - 10 * q^6 - 2 * q^7 - 3 * q^8 + 3 * q^9 - q^10 - 6 * q^11 + 4 * q^14 - 2 * q^15 + 5 * q^16 - 4 * q^17 + 17 * q^18 - 8 * q^19 + 5 * q^20 - 2 * q^21 - 12 * q^22 - 8 * q^23 - 12 * q^24 + 3 * q^25 - 14 * q^27 - 22 * q^28 - 2 * q^29 - 10 * q^30 - 10 * q^31 - 17 * q^32 + 18 * q^33 + 8 * q^34 - 2 * q^35 + 17 * q^36 - 20 * q^37 + 10 * q^38 - 3 * q^40 + 2 * q^41 + 22 * q^42 - 12 * q^43 + 12 * q^44 + 3 * q^45 - 8 * q^46 + 2 * q^47 + 18 * q^48 - q^49 - q^50 - 4 * q^51 + 6 * q^53 - 10 * q^54 - 6 * q^55 + 24 * q^56 - 2 * q^57 + 4 * q^58 + 12 * q^59 - 6 * q^61 - 4 * q^62 - 14 * q^63 - 15 * q^64 + 12 * q^66 - 18 * q^67 - 44 * q^68 + 16 * q^69 + 4 * q^70 - 8 * q^71 + 3 * q^72 - 20 * q^73 + 10 * q^74 - 2 * q^75 + 2 * q^76 - 18 * q^77 + 12 * q^79 + 5 * q^80 + 15 * q^81 + 14 * q^82 - 18 * q^83 - 10 * q^84 - 4 * q^85 + 8 * q^86 - 2 * q^87 - 30 * q^88 + 17 * q^90 - 10 * q^92 + 14 * q^93 - 4 * q^94 - 8 * q^95 + 22 * q^96 + 14 * q^97 - 21 * q^98 - 12 * q^99

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 $

$2$	−0.571993	−0.404460	−0.202230	−	0.979338i	$-0.564819\pi$
$2$	−0.571993	−0.404460	−0.202230	+	0.979338i	$0.564819\pi$
$3$	−0.428007	−0.247110	−0.123555	−	0.992338i	$-0.539430\pi$
$3$	−0.428007	−0.247110	−0.123555	+	0.992338i	$0.539430\pi$
$4$	−1.67282	−0.836412
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.244817	0.0999461
$7$	2.67282	1.01023	0.505116	−	0.863051i	$-0.331450\pi$
$7$	2.67282	1.01023	0.505116	+	0.863051i	$0.331450\pi$
$8$	2.10083	0.742756
$9$	−2.81681	−0.938937
$10$	−0.571993	−0.180880
$11$	−5.10083	−1.53796	−0.768979	−	0.639274i	$-0.779235\pi$
$11$	−5.10083	−1.53796	−0.768979	+	0.639274i	$0.779235\pi$
$12$	0.715980	0.206686
$13$	0	0
$13$	0	0
$14$	−1.52884	−0.408599
$15$	−0.428007	−0.110511
$16$	2.14399	0.535997
$17$	5.34565	1.29651	0.648255	−	0.761423i	$-0.275499\pi$
$17$	5.34565	1.29651	0.648255	+	0.761423i	$0.275499\pi$
$18$	1.61120	0.379763
$19$	−6.24482	−1.43266	−0.716330	−	0.697762i	$-0.754179\pi$
$19$	−6.24482	−1.43266	−0.716330	+	0.697762i	$0.754179\pi$
$20$	−1.67282	−0.374055
$21$	−1.14399	−0.249638
$22$	2.91764	0.622043
$23$	−2.42801	−0.506274	−0.253137	−	0.967430i	$-0.581462\pi$
$23$	−2.42801	−0.506274	−0.253137	+	0.967430i	$0.581462\pi$
$24$	−0.899170	−0.183542
$25$	1.00000	0.200000
$26$	0	0
$27$	2.48963	0.479130
$28$	−4.47116	−0.844970
$29$	2.67282	0.496331	0.248165	−	0.968718i	$-0.420172\pi$
$29$	2.67282	0.496331	0.248165	+	0.968718i	$0.420172\pi$
$30$	0.244817	0.0446973
$31$	0.244817	0.0439704	0.0219852	−	0.999758i	$-0.493001\pi$
$31$	0.244817	0.0439704	0.0219852	+	0.999758i	$0.493001\pi$
$32$	−5.42801	−0.959545
$33$	2.18319	0.380045
$34$	−3.05767	−0.524387
$35$	2.67282	0.451790
$36$	4.71203	0.785338
$37$	−3.32718	−0.546984	−0.273492	−	0.961874i	$-0.588179\pi$
$37$	−3.32718	−0.546984	−0.273492	+	0.961874i	$0.588179\pi$
$38$	3.57199	0.579454
$39$	0	0
$40$	2.10083	0.332170
$41$	−6.48963	−1.01351	−0.506755	−	0.862090i	$-0.669155\pi$
$41$	−6.48963	−1.01351	−0.506755	+	0.862090i	$0.669155\pi$
$42$	0.654353	0.100969
$43$	−10.9176	−1.66492	−0.832462	−	0.554082i	$-0.813070\pi$
$43$	−10.9176	−1.66492	−0.832462	+	0.554082i	$0.813070\pi$
$44$	8.53279	1.28637
$45$	−2.81681	−0.419905
$46$	1.38880	0.204768
$47$	−2.67282	−0.389871	−0.194936	−	0.980816i	$-0.562450\pi$
$47$	−2.67282	−0.389871	−0.194936	+	0.980816i	$0.562450\pi$
$48$	−0.917641	−0.132450
$49$	0.143987	0.0205695
$50$	−0.571993	−0.0808921
$51$	−2.28797	−0.320380
$52$	0	0
$53$	−4.20166	−0.577143	−0.288571	−	0.957458i	$-0.593180\pi$
$53$	−4.20166	−0.577143	−0.288571	+	0.957458i	$0.593180\pi$
$54$	−1.42405	−0.193789
$55$	−5.10083	−0.687796
$56$	5.61515	0.750356
$57$	2.67282	0.354024
$58$	−1.52884	−0.200746
$59$	0.899170	0.117062	0.0585310	−	0.998286i	$-0.481358\pi$
$59$	0.899170	0.117062	0.0585310	+	0.998286i	$0.481358\pi$
$60$	0.715980	0.0924326
$61$	−5.81681	−0.744766	−0.372383	−	0.928079i	$-0.621459\pi$
$61$	−5.81681	−0.744766	−0.372383	+	0.928079i	$0.621459\pi$
$62$	−0.140034	−0.0177843
$63$	−7.52884	−0.948544
$64$	−1.18319	−0.147899
$65$	0	0
$66$	−1.24877	−0.153713
$67$	−2.18319	−0.266719	−0.133360	−	0.991068i	$-0.542577\pi$
$67$	−2.18319	−0.266719	−0.133360	+	0.991068i	$0.542577\pi$
$68$	−8.94233	−1.08442
$69$	1.03920	0.125105
$70$	−1.52884	−0.182731
$71$	−6.24482	−0.741123	−0.370562	−	0.928808i	$-0.620835\pi$
$71$	−6.24482	−0.741123	−0.370562	+	0.928808i	$0.620835\pi$
$72$	−5.91764	−0.697401
$73$	−10.9608	−1.28286	−0.641432	−	0.767180i	$-0.721659\pi$
$73$	−10.9608	−1.28286	−0.641432	+	0.767180i	$0.721659\pi$
$74$	1.90312	0.221233
$75$	−0.428007	−0.0494220
$76$	10.4465	1.19829
$77$	−13.6336	−1.55370
$78$	0	0
$79$	−3.63362	−0.408814	−0.204407	−	0.978886i	$-0.565527\pi$
$79$	−3.63362	−0.408814	−0.204407	+	0.978886i	$0.565527\pi$
$80$	2.14399	0.239705
$81$	7.38485	0.820539
$82$	3.71203	0.409925
$83$	−9.81681	−1.07753	−0.538767	−	0.842455i	$-0.681110\pi$
$83$	−9.81681	−1.07753	−0.538767	+	0.842455i	$0.681110\pi$
$84$	1.91369	0.208800
$85$	5.34565	0.579817
$86$	6.24482	0.673396
$87$	−1.14399	−0.122648
$88$	−10.7160	−1.14233
$89$	−7.63362	−0.809162	−0.404581	−	0.914502i	$-0.632583\pi$
$89$	−7.63362	−0.809162	−0.404581	+	0.914502i	$0.632583\pi$
$90$	1.61120	0.169835
$91$	0	0
$92$	4.06163	0.423454
$93$	−0.104783	−0.0108655
$94$	1.52884	0.157688
$95$	−6.24482	−0.640705
$96$	2.32322	0.237113
$97$	11.3456	1.15198	0.575988	−	0.817458i	$-0.304617\pi$
$97$	11.3456	1.15198	0.575988	+	0.817458i	$0.304617\pi$
$98$	−0.0823593	−0.00831955
$99$	14.3681	1.44405
$100$	−1.67282	−0.167282
$101$	10.8560	1.08021	0.540107	−	0.841596i	$-0.318384\pi$
$101$	10.8560	1.08021	0.540107	+	0.841596i	$0.318384\pi$
$102$	1.30871	0.129581
$103$	10.6297	1.04737	0.523686	−	0.851911i	$-0.324556\pi$
$103$	10.6297	1.04737	0.523686	+	0.851911i	$0.324556\pi$
$104$	0	0
$105$	−1.14399	−0.111642
$106$	2.40332	0.233431
$107$	0.140034	0.0135376	0.00676878	−	0.999977i	$-0.497845\pi$
$107$	0.140034	0.0135376	0.00676878	+	0.999977i	$0.497845\pi$
$108$	−4.16472	−0.400750
$109$	−9.05767	−0.867568	−0.433784	−	0.901017i	$-0.642822\pi$
$109$	−9.05767	−0.867568	−0.433784	+	0.901017i	$0.642822\pi$
$110$	2.91764	0.278186
$111$	1.42405	0.135165
$112$	5.73050	0.541481
$113$	12.9793	1.22099	0.610493	−	0.792021i	$-0.290971\pi$
$113$	12.9793	1.22099	0.610493	+	0.792021i	$0.290971\pi$
$114$	−1.52884	−0.143189
$115$	−2.42801	−0.226413
$116$	−4.47116	−0.415137
$117$	0	0
$118$	−0.514319	−0.0473469
$119$	14.2880	1.30978
$120$	−0.899170	−0.0820826
$121$	15.0185	1.36532
$122$	3.32718	0.301228
$123$	2.77761	0.250448
$124$	−0.409536	−0.0367774
$125$	1.00000	0.0894427
$126$	4.30644	0.383649
$127$	12.0616	1.07030	0.535148	−	0.844758i	$-0.320256\pi$
$127$	12.0616	1.07030	0.535148	+	0.844758i	$0.320256\pi$
$128$	11.5328	1.01936
$129$	4.67282	0.411419
$130$	0	0
$131$	7.63362	0.666953	0.333476	−	0.942758i	$-0.391778\pi$
$131$	7.63362	0.666953	0.333476	+	0.942758i	$0.391778\pi$
$132$	−3.65209	−0.317874
$133$	−16.6913	−1.44732
$134$	1.24877	0.107877
$135$	2.48963	0.214274
$136$	11.2303	0.962990
$137$	3.43196	0.293212	0.146606	−	0.989195i	$-0.453165\pi$
$137$	3.43196	0.293212	0.146606	+	0.989195i	$0.453165\pi$
$138$	−0.594417	−0.0506002
$139$	−0.942326	−0.0799270	−0.0399635	−	0.999201i	$-0.512724\pi$
$139$	−0.942326	−0.0799270	−0.0399635	+	0.999201i	$0.512724\pi$
$140$	−4.47116	−0.377882
$141$	1.14399	0.0963410
$142$	3.57199	0.299755
$143$	0	0
$144$	−6.03920	−0.503267
$145$	2.67282	0.221966
$146$	6.26950	0.518868
$147$	−0.0616272	−0.00508293
$148$	5.56578	0.457504
$149$	11.3456	0.929472	0.464736	−	0.885449i	$-0.346149\pi$
$149$	11.3456	0.929472	0.464736	+	0.885449i	$0.346149\pi$
$150$	0.244817	0.0199892
$151$	−21.0224	−1.71078	−0.855390	−	0.517984i	$-0.826683\pi$
$151$	−21.0224	−1.71078	−0.855390	+	0.517984i	$0.826683\pi$
$152$	−13.1193	−1.06412
$153$	−15.0577	−1.21734
$154$	7.79834	0.628408
$155$	0.244817	0.0196642
$156$	0	0
$157$	−9.83528	−0.784941	−0.392470	−	0.919765i	$-0.628379\pi$
$157$	−9.83528	−0.784941	−0.392470	+	0.919765i	$0.628379\pi$
$158$	2.07841	0.165349
$159$	1.79834	0.142618
$160$	−5.42801	−0.429122
$161$	−6.48963	−0.511455
$162$	−4.22408	−0.331875
$163$	−12.3849	−0.970056	−0.485028	−	0.874499i	$-0.661191\pi$
$163$	−12.3849	−0.970056	−0.485028	+	0.874499i	$0.661191\pi$
$164$	10.8560	0.847712
$165$	2.18319	0.169961
$166$	5.61515	0.435820
$167$	8.50811	0.658377	0.329188	−	0.944264i	$-0.393225\pi$
$167$	8.50811	0.658377	0.329188	+	0.944264i	$0.393225\pi$
$168$	−2.40332	−0.185420
$169$	0	0
$170$	−3.05767	−0.234513
$171$	17.5905	1.34518
$172$	18.2633	1.39256
$173$	−21.5473	−1.63821	−0.819106	−	0.573643i	$-0.805530\pi$
$173$	−21.5473	−1.63821	−0.819106	+	0.573643i	$0.805530\pi$
$174$	0.654353	0.0496063
$175$	2.67282	0.202046
$176$	−10.9361	−0.824340
$177$	−0.384851	−0.0289271
$178$	4.36638	0.327274
$179$	2.56804	0.191944	0.0959722	−	0.995384i	$-0.469404\pi$
$179$	2.56804	0.191944	0.0959722	+	0.995384i	$0.469404\pi$
$180$	4.71203	0.351214
$181$	−13.7305	−1.02058	−0.510290	−	0.860002i	$-0.670462\pi$
$181$	−13.7305	−1.02058	−0.510290	+	0.860002i	$0.670462\pi$
$182$	0	0
$183$	2.48963	0.184039
$184$	−5.10083	−0.376038
$185$	−3.32718	−0.244619
$186$	0.0599353	0.00439467
$187$	−27.2672	−1.99398
$188$	4.47116	0.326093
$189$	6.65435	0.484033
$190$	3.57199	0.259140
$191$	−10.6913	−0.773595	−0.386797	−	0.922165i	$-0.626419\pi$
$191$	−10.6913	−0.773595	−0.386797	+	0.922165i	$0.626419\pi$
$192$	0.506413	0.0365472
$193$	19.2593	1.38632	0.693159	−	0.720785i	$-0.256219\pi$
$193$	19.2593	1.38632	0.693159	+	0.720785i	$0.256219\pi$
$194$	−6.48963	−0.465929
$195$	0	0
$196$	−0.240864	−0.0172046
$197$	17.1809	1.22409	0.612045	−	0.790823i	$-0.290347\pi$
$197$	17.1809	1.22409	0.612045	+	0.790823i	$0.290347\pi$
$198$	−8.21844	−0.584059
$199$	11.5473	0.818567	0.409283	−	0.912407i	$-0.365779\pi$
$199$	11.5473	0.818567	0.409283	+	0.912407i	$0.365779\pi$
$200$	2.10083	0.148551
$201$	0.934420	0.0659089
$202$	−6.20957	−0.436904
$203$	7.14399	0.501410
$204$	3.82738	0.267970
$205$	−6.48963	−0.453256
$206$	−6.08010	−0.423621
$207$	6.83923	0.475360
$208$	0	0
$209$	31.8538	2.20337
$210$	0.654353	0.0451546
$211$	24.1233	1.66071	0.830357	−	0.557232i	$-0.188137\pi$
$211$	24.1233	1.66071	0.830357	+	0.557232i	$0.188137\pi$
$212$	7.02864	0.482729
$213$	2.67282	0.183139
$214$	−0.0800983	−0.00547541
$215$	−10.9176	−0.744577
$216$	5.23030	0.355877
$217$	0.654353	0.0444203
$218$	5.18093	0.350897
$219$	4.69129	0.317008
$220$	8.53279	0.575281
$221$	0	0
$222$	−0.814549	−0.0546690
$223$	−5.73050	−0.383743	−0.191871	−	0.981420i	$-0.561456\pi$
$223$	−5.73050	−0.383743	−0.191871	+	0.981420i	$0.561456\pi$
$224$	−14.5081	−0.969364
$225$	−2.81681	−0.187787
$226$	−7.42405	−0.493841
$227$	−2.95289	−0.195990	−0.0979951	−	0.995187i	$-0.531243\pi$
$227$	−2.95289	−0.195990	−0.0979951	+	0.995187i	$0.531243\pi$
$228$	−4.47116	−0.296110
$229$	−25.2593	−1.66918	−0.834592	−	0.550869i	$-0.814297\pi$
$229$	−25.2593	−1.66918	−0.834592	+	0.550869i	$0.814297\pi$
$230$	1.38880	0.0915750
$231$	5.83528	0.383933
$232$	5.61515	0.368653
$233$	23.3456	1.52942	0.764712	−	0.644372i	$-0.222881\pi$
$233$	23.3456	1.52942	0.764712	+	0.644372i	$0.222881\pi$
$234$	0	0
$235$	−2.67282	−0.174356
$236$	−1.50415	−0.0979120
$237$	1.55521	0.101022
$238$	−8.17262	−0.529753
$239$	3.79213	0.245292	0.122646	−	0.992450i	$-0.460862\pi$
$239$	3.79213	0.245292	0.122646	+	0.992450i	$0.460862\pi$
$240$	−0.917641	−0.0592335
$241$	3.43196	0.221072	0.110536	−	0.993872i	$-0.464743\pi$
$241$	3.43196	0.221072	0.110536	+	0.993872i	$0.464743\pi$
$242$	−8.59046	−0.552216
$243$	−10.6297	−0.681893
$244$	9.73050	0.622931
$245$	0.143987	0.00919896
$246$	−1.58877	−0.101296
$247$	0	0
$248$	0.514319	0.0326593
$249$	4.20166	0.266269
$250$	−0.571993	−0.0361760
$251$	25.4689	1.60758	0.803791	−	0.594911i	$-0.202813\pi$
$251$	25.4689	1.60758	0.803791	+	0.594911i	$0.202813\pi$
$252$	12.5944	0.793374
$253$	12.3849	0.778629
$254$	−6.89917	−0.432892
$255$	−2.28797	−0.143278
$256$	−4.23030	−0.264394
$257$	−9.26724	−0.578075	−0.289037	−	0.957318i	$-0.593335\pi$
$257$	−9.26724	−0.578075	−0.289037	+	0.957318i	$0.593335\pi$
$258$	−2.67282	−0.166403
$259$	−8.89296	−0.552581
$260$	0	0
$261$	−7.52884	−0.466023
$262$	−4.36638	−0.269756
$263$	−8.14794	−0.502423	−0.251212	−	0.967932i	$-0.580829\pi$
$263$	−8.14794	−0.502423	−0.251212	+	0.967932i	$0.580829\pi$
$264$	4.58651	0.282280
$265$	−4.20166	−0.258106
$266$	9.54731	0.585383
$267$	3.26724	0.199952
$268$	3.65209	0.223087
$269$	1.14399	0.0697501	0.0348750	−	0.999392i	$-0.488897\pi$
$269$	1.14399	0.0697501	0.0348750	+	0.999392i	$0.488897\pi$
$270$	−1.42405	−0.0866652
$271$	3.18714	0.193605	0.0968026	−	0.995304i	$-0.469138\pi$
$271$	3.18714	0.193605	0.0968026	+	0.995304i	$0.469138\pi$
$272$	11.4610	0.694925
$273$	0	0
$274$	−1.96306	−0.118593
$275$	−5.10083	−0.307592
$276$	−1.73840	−0.104640
$277$	−7.62571	−0.458185	−0.229092	−	0.973405i	$-0.573576\pi$
$277$	−7.62571	−0.458185	−0.229092	+	0.973405i	$0.573576\pi$
$278$	0.539004	0.0323273
$279$	−0.689603	−0.0412854
$280$	5.61515	0.335569
$281$	20.2386	1.20733	0.603667	−	0.797237i	$-0.293706\pi$
$281$	20.2386	1.20733	0.603667	+	0.797237i	$0.293706\pi$
$282$	−0.654353	−0.0389661
$283$	−19.8969	−1.18275	−0.591374	−	0.806397i	$-0.701414\pi$
$283$	−19.8969	−1.18275	−0.591374	+	0.806397i	$0.701414\pi$
$284$	10.4465	0.619884
$285$	2.67282	0.158324
$286$	0	0
$287$	−17.3456	−1.02388
$288$	15.2897	0.900952
$289$	11.5759	0.680938
$290$	−1.52884	−0.0897764
$291$	−4.85601	−0.284665
$292$	18.3355	1.07300
$293$	26.0185	1.52002	0.760008	−	0.649914i	$-0.225195\pi$
$293$	26.0185	1.52002	0.760008	+	0.649914i	$0.225195\pi$
$294$	0.0352503	0.00205584
$295$	0.899170	0.0523517
$296$	−6.98983	−0.406276
$297$	−12.6992	−0.736882
$298$	−6.48963	−0.375934
$299$	0	0
$300$	0.715980	0.0413371
$301$	−29.1809	−1.68196
$302$	12.0247	0.691943
$303$	−4.64645	−0.266931
$304$	−13.3888	−0.767901
$305$	−5.81681	−0.333070
$306$	8.61289	0.492366
$307$	2.39276	0.136562	0.0682809	−	0.997666i	$-0.478249\pi$
$307$	2.39276	0.136562	0.0682809	+	0.997666i	$0.478249\pi$
$308$	22.8066	1.29953
$309$	−4.54957	−0.258816
$310$	−0.140034	−0.00795338
$311$	−3.54731	−0.201149	−0.100575	−	0.994930i	$-0.532068\pi$
$311$	−3.54731	−0.201149	−0.100575	+	0.994930i	$0.532068\pi$
$312$	0	0
$313$	4.97927	0.281445	0.140722	−	0.990049i	$-0.455057\pi$
$313$	4.97927	0.281445	0.140722	+	0.990049i	$0.455057\pi$
$314$	5.62571	0.317477
$315$	−7.52884	−0.424202
$316$	6.07841	0.341937
$317$	18.5944	1.04437	0.522183	−	0.852833i	$-0.325118\pi$
$317$	18.5944	1.04437	0.522183	+	0.852833i	$0.325118\pi$
$318$	−1.02864	−0.0576831
$319$	−13.6336	−0.763336
$320$	−1.18319	−0.0661423
$321$	−0.0599353	−0.00334526
$322$	3.71203	0.206863
$323$	−33.3826	−1.85746
$324$	−12.3536	−0.686309
$325$	0	0
$326$	7.08405	0.392349
$327$	3.87675	0.214385
$328$	−13.6336	−0.752791
$329$	−7.14399	−0.393861
$330$	−1.24877	−0.0687425
$331$	−5.91990	−0.325387	−0.162694	−	0.986677i	$-0.552018\pi$
$331$	−5.91990	−0.325387	−0.162694	+	0.986677i	$0.552018\pi$
$332$	16.4218	0.901263
$333$	9.37202	0.513584
$334$	−4.86658	−0.266287
$335$	−2.18319	−0.119280
$336$	−2.45269	−0.133805
$337$	−13.9216	−0.758358	−0.379179	−	0.925323i	$-0.623793\pi$
$337$	−13.9216	−0.758358	−0.379179	+	0.925323i	$0.623793\pi$
$338$	0	0
$339$	−5.55521	−0.301718
$340$	−8.94233	−0.484966
$341$	−1.24877	−0.0676247
$342$	−10.0616	−0.544070
$343$	−18.3249	−0.989452
$344$	−22.9361	−1.23663
$345$	1.03920	0.0559488
$346$	12.3249	0.662592
$347$	7.65831	0.411119	0.205560	−	0.978645i	$-0.434099\pi$
$347$	7.65831	0.411119	0.205560	+	0.978645i	$0.434099\pi$
$348$	1.91369	0.102584
$349$	−11.1809	−0.598501	−0.299251	−	0.954175i	$-0.596737\pi$
$349$	−11.1809	−0.598501	−0.299251	+	0.954175i	$0.596737\pi$
$350$	−1.52884	−0.0817198
$351$	0	0
$352$	27.6873	1.47574
$353$	9.65209	0.513729	0.256864	−	0.966447i	$-0.417311\pi$
$353$	9.65209	0.513729	0.256864	+	0.966447i	$0.417311\pi$
$354$	0.220132	0.0116999
$355$	−6.24482	−0.331440
$356$	12.7697	0.676793
$357$	−6.11535	−0.323659
$358$	−1.46890	−0.0776339
$359$	−9.51206	−0.502027	−0.251014	−	0.967984i	$-0.580764\pi$
$359$	−9.51206	−0.502027	−0.251014	+	0.967984i	$0.580764\pi$
$360$	−5.91764	−0.311887
$361$	19.9977	1.05251
$362$	7.85375	0.412784
$363$	−6.42801	−0.337383
$364$	0	0
$365$	−10.9608	−0.573714
$366$	−1.42405	−0.0744365
$367$	−17.0040	−0.887599	−0.443800	−	0.896126i	$-0.646370\pi$
$367$	−17.0040	−0.887599	−0.443800	+	0.896126i	$0.646370\pi$
$368$	−5.20561	−0.271361
$369$	18.2801	0.951622
$370$	1.90312	0.0989386
$371$	−11.2303	−0.583048
$372$	0.175284	0.00908805
$373$	−1.83528	−0.0950273	−0.0475136	−	0.998871i	$-0.515130\pi$
$373$	−1.83528	−0.0950273	−0.0475136	+	0.998871i	$0.515130\pi$
$374$	15.5967	0.806485
$375$	−0.428007	−0.0221022
$376$	−5.61515	−0.289579
$377$	0	0
$378$	−3.80624	−0.195772
$379$	−32.3681	−1.66264	−0.831318	−	0.555797i	$-0.812413\pi$
$379$	−32.3681	−1.66264	−0.831318	+	0.555797i	$0.812413\pi$
$380$	10.4465	0.535893
$381$	−5.16246	−0.264481
$382$	6.11535	0.312888
$383$	−28.1417	−1.43798	−0.718988	−	0.695023i	$-0.755394\pi$
$383$	−28.1417	−1.43798	−0.718988	+	0.695023i	$0.755394\pi$
$384$	−4.93611	−0.251895
$385$	−13.6336	−0.694834
$386$	−11.0162	−0.560710
$387$	30.7529	1.56326
$388$	−18.9793	−0.963526
$389$	31.9585	1.62036	0.810181	−	0.586180i	$-0.199369\pi$
$389$	31.9585	1.62036	0.810181	+	0.586180i	$0.199369\pi$
$390$	0	0
$391$	−12.9793	−0.656390
$392$	0.302491	0.0152781
$393$	−3.26724	−0.164811
$394$	−9.82738	−0.495096
$395$	−3.63362	−0.182827
$396$	−24.0353	−1.20782
$397$	−12.7098	−0.637885	−0.318942	−	0.947774i	$-0.603328\pi$
$397$	−12.7098	−0.637885	−0.318942	+	0.947774i	$0.603328\pi$
$398$	−6.60498	−0.331078
$399$	7.14399	0.357647
$400$	2.14399	0.107199
$401$	0.979268	0.0489023	0.0244512	−	0.999701i	$-0.492216\pi$
$401$	0.979268	0.0489023	0.0244512	+	0.999701i	$0.492216\pi$
$402$	−0.534482	−0.0266575
$403$	0	0
$404$	−18.1602	−0.903504
$405$	7.38485	0.366956
$406$	−4.08631	−0.202800
$407$	16.9714	0.841239
$408$	−4.80664	−0.237964
$409$	7.79834	0.385603	0.192802	−	0.981238i	$-0.438243\pi$
$409$	7.79834	0.385603	0.192802	+	0.981238i	$0.438243\pi$
$410$	3.71203	0.183324
$411$	−1.46890	−0.0724556
$412$	−17.7816	−0.876035
$413$	2.40332	0.118260
$414$	−3.91200	−0.192264
$415$	−9.81681	−0.481888
$416$	0	0
$417$	0.403322	0.0197508
$418$	−18.2201	−0.891176
$419$	10.2017	0.498384	0.249192	−	0.968454i	$-0.419835\pi$
$419$	10.2017	0.498384	0.249192	+	0.968454i	$0.419835\pi$
$420$	1.91369	0.0933784
$421$	31.1888	1.52005	0.760025	−	0.649893i	$-0.225186\pi$
$421$	31.1888	1.52005	0.760025	+	0.649893i	$0.225186\pi$
$422$	−13.7983	−0.671693
$423$	7.52884	0.366065
$424$	−8.82698	−0.428676
$425$	5.34565	0.259302
$426$	−1.52884	−0.0740724
$427$	−15.5473	−0.752387
$428$	−0.234252	−0.0113230
$429$	0	0
$430$	6.24482	0.301152
$431$	22.9361	1.10479	0.552397	−	0.833581i	$-0.313713\pi$
$431$	22.9361	1.10479	0.552397	+	0.833581i	$0.313713\pi$
$432$	5.33774	0.256812
$433$	16.2880	0.782750	0.391375	−	0.920231i	$-0.372000\pi$
$433$	16.2880	0.782750	0.391375	+	0.920231i	$0.372000\pi$
$434$	−0.374285	−0.0179663
$435$	−1.14399	−0.0548500
$436$	15.1519	0.725644
$437$	15.1625	0.725319
$438$	−2.68339	−0.128217
$439$	−23.7569	−1.13385	−0.566927	−	0.823768i	$-0.691868\pi$
$439$	−23.7569	−1.13385	−0.566927	+	0.823768i	$0.691868\pi$
$440$	−10.7160	−0.510864
$441$	−0.405583	−0.0193135
$442$	0	0
$443$	−2.75292	−0.130795	−0.0653976	−	0.997859i	$-0.520832\pi$
$443$	−2.75292	−0.130795	−0.0653976	+	0.997859i	$0.520832\pi$
$444$	−2.38219	−0.113054
$445$	−7.63362	−0.361868
$446$	3.27781	0.155209
$447$	−4.85601	−0.229682
$448$	−3.16246	−0.149412
$449$	27.1025	1.27905	0.639524	−	0.768772i	$-0.279132\pi$
$449$	27.1025	1.27905	0.639524	+	0.768772i	$0.279132\pi$
$450$	1.61120	0.0759525
$451$	33.1025	1.55874
$452$	−21.7120	−1.02125
$453$	8.99774	0.422751
$454$	1.68903	0.0792703
$455$	0	0
$456$	5.61515	0.262953
$457$	−40.1523	−1.87824	−0.939122	−	0.343583i	$-0.888359\pi$
$457$	−40.1523	−1.87824	−0.939122	+	0.343583i	$0.888359\pi$
$458$	14.4482	0.675119
$459$	13.3087	0.621197
$460$	4.06163	0.189374
$461$	−2.00791	−0.0935175	−0.0467587	−	0.998906i	$-0.514889\pi$
$461$	−2.00791	−0.0935175	−0.0467587	+	0.998906i	$0.514889\pi$
$462$	−3.33774	−0.155286
$463$	−2.67282	−0.124217	−0.0621083	−	0.998069i	$-0.519782\pi$
$463$	−2.67282	−0.124217	−0.0621083	+	0.998069i	$0.519782\pi$
$464$	5.73050	0.266032
$465$	−0.104783	−0.00485921
$466$	−13.3536	−0.618591
$467$	−31.8890	−1.47565	−0.737824	−	0.674994i	$-0.764146\pi$
$467$	−31.8890	−1.47565	−0.737824	+	0.674994i	$0.764146\pi$
$468$	0	0
$469$	−5.83528	−0.269448
$470$	1.52884	0.0705200
$471$	4.20957	0.193967
$472$	1.88900	0.0869484
$473$	55.6890	2.56058
$474$	−0.889572	−0.0408594
$475$	−6.24482	−0.286532
$476$	−23.9013	−1.09551
$477$	11.8353	0.541900
$478$	−2.16907	−0.0992110
$479$	6.73445	0.307705	0.153852	−	0.988094i	$-0.450832\pi$
$479$	6.73445	0.307705	0.153852	+	0.988094i	$0.450832\pi$
$480$	2.32322	0.106040
$481$	0	0
$482$	−1.96306	−0.0894148
$483$	2.77761	0.126385
$484$	−25.1233	−1.14197
$485$	11.3456	0.515179
$486$	6.08010	0.275799
$487$	−39.6521	−1.79681	−0.898404	−	0.439170i	$-0.855273\pi$
$487$	−39.6521	−1.79681	−0.898404	+	0.439170i	$0.855273\pi$
$488$	−12.2201	−0.553179
$489$	5.30080	0.239710
$490$	−0.0823593	−0.00372062
$491$	−31.0946	−1.40328	−0.701640	−	0.712531i	$-0.747549\pi$
$491$	−31.0946	−1.40328	−0.701640	+	0.712531i	$0.747549\pi$
$492$	−4.64645	−0.209478
$493$	14.2880	0.643498
$494$	0	0
$495$	14.3681	0.645797
$496$	0.524884	0.0235680
$497$	−16.6913	−0.748707
$498$	−2.40332	−0.107695
$499$	−13.1087	−0.586828	−0.293414	−	0.955986i	$-0.594791\pi$
$499$	−13.1087	−0.586828	−0.293414	+	0.955986i	$0.594791\pi$
$500$	−1.67282	−0.0748110
$501$	−3.64153	−0.162691
$502$	−14.5680	−0.650203
$503$	−8.59273	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$503$	−8.59273	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$504$	−15.8168	−0.704537
$505$	10.8560	0.483086
$506$	−7.08405	−0.314924
$507$	0	0
$508$	−20.1770	−0.895209
$509$	−29.8353	−1.32243	−0.661213	−	0.750198i	$-0.729958\pi$
$509$	−29.8353	−1.32243	−0.661213	+	0.750198i	$0.729958\pi$
$510$	1.30871	0.0579504
$511$	−29.2963	−1.29599
$512$	−20.6459	−0.912428
$513$	−15.5473	−0.686430
$514$	5.30080	0.233808
$515$	10.6297	0.468399
$516$	−7.81681	−0.344116
$517$	13.6336	0.599606
$518$	5.08671	0.223497
$519$	9.22239	0.404818
$520$	0	0
$521$	10.0969	0.442352	0.221176	−	0.975234i	$-0.429010\pi$
$521$	10.0969	0.442352	0.221176	+	0.975234i	$0.429010\pi$
$522$	4.30644	0.188488
$523$	16.1479	0.706100	0.353050	−	0.935604i	$-0.385145\pi$
$523$	16.1479	0.706100	0.353050	+	0.935604i	$0.385145\pi$
$524$	−12.7697	−0.557847
$525$	−1.14399	−0.0499277
$526$	4.66057	0.203210
$527$	1.30871	0.0570081
$528$	4.68073	0.203703
$529$	−17.1048	−0.743686
$530$	2.40332	0.104394
$531$	−2.53279	−0.109914
$532$	27.9216	1.21055
$533$	0	0
$534$	−1.86884	−0.0808726
$535$	0.140034	0.00605418
$536$	−4.58651	−0.198107
$537$	−1.09914	−0.0474313
$538$	−0.654353	−0.0282111
$539$	−0.734451	−0.0316350
$540$	−4.16472	−0.179221
$541$	−26.7776	−1.15126	−0.575630	−	0.817711i	$-0.695243\pi$
$541$	−26.7776	−1.15126	−0.575630	+	0.817711i	$0.695243\pi$
$542$	−1.82302	−0.0783056
$543$	5.87675	0.252195
$544$	−29.0162	−1.24406
$545$	−9.05767	−0.387988
$546$	0	0
$547$	12.3865	0.529610	0.264805	−	0.964302i	$-0.414692\pi$
$547$	12.3865	0.529610	0.264805	+	0.964302i	$0.414692\pi$
$548$	−5.74106	−0.245246
$549$	16.3849	0.699288
$550$	2.91764	0.124409
$551$	−16.6913	−0.711073
$552$	2.18319	0.0929227
$553$	−9.71203	−0.412997
$554$	4.36186	0.185318
$555$	1.42405	0.0604477
$556$	1.57634	0.0668519
$557$	−10.4218	−0.441586	−0.220793	−	0.975321i	$-0.570864\pi$
$557$	−10.4218	−0.441586	−0.220793	+	0.975321i	$0.570864\pi$
$558$	0.394448	0.0166983
$559$	0	0
$560$	5.73050	0.242158
$561$	11.6706	0.492732
$562$	−11.5763	−0.488319
$563$	−9.78156	−0.412244	−0.206122	−	0.978526i	$-0.566084\pi$
$563$	−9.78156	−0.412244	−0.206122	+	0.978526i	$0.566084\pi$
$564$	−1.91369	−0.0805808
$565$	12.9793	0.546042
$566$	11.3809	0.478375
$567$	19.7384	0.828935
$568$	−13.1193	−0.550474
$569$	30.2201	1.26689	0.633447	−	0.773786i	$-0.281639\pi$
$569$	30.2201	1.26689	0.633447	+	0.773786i	$0.281639\pi$
$570$	−1.52884	−0.0640359
$571$	39.8643	1.66827	0.834135	−	0.551561i	$-0.185967\pi$
$571$	39.8643	1.66827	0.834135	+	0.551561i	$0.185967\pi$
$572$	0	0
$573$	4.57595	0.191163
$574$	9.92159	0.414119
$575$	−2.42801	−0.101255
$576$	3.33282	0.138868
$577$	8.46326	0.352330	0.176165	−	0.984361i	$-0.443631\pi$
$577$	8.46326	0.352330	0.176165	+	0.984361i	$0.443631\pi$
$578$	−6.62136	−0.275412
$579$	−8.24313	−0.342573
$580$	−4.47116	−0.185655
$581$	−26.2386	−1.08856
$582$	2.77761	0.115136
$583$	21.4320	0.887621
$584$	−23.0268	−0.952855
$585$	0	0
$586$	−14.8824	−0.614786
$587$	9.32718	0.384974	0.192487	−	0.981300i	$-0.438345\pi$
$587$	9.32718	0.384974	0.192487	+	0.981300i	$0.438345\pi$
$588$	0.103091	0.00425142
$589$	−1.52884	−0.0629946
$590$	−0.514319	−0.0211742
$591$	−7.35355	−0.302485
$592$	−7.13342	−0.293182
$593$	8.07841	0.331740	0.165870	−	0.986148i	$-0.446957\pi$
$593$	8.07841	0.331740	0.165870	+	0.986148i	$0.446957\pi$
$594$	7.26386	0.298040
$595$	14.2880	0.585750
$596$	−18.9793	−0.777421
$597$	−4.94233	−0.202276
$598$	0	0
$599$	19.1440	0.782202	0.391101	−	0.920348i	$-0.372094\pi$
$599$	19.1440	0.782202	0.391101	+	0.920348i	$0.372094\pi$
$600$	−0.899170	−0.0367084
$601$	−4.28797	−0.174910	−0.0874550	−	0.996168i	$-0.527873\pi$
$601$	−4.28797	−0.174910	−0.0874550	+	0.996168i	$0.527873\pi$
$602$	16.6913	0.680286
$603$	6.14963	0.250432
$604$	35.1668	1.43092
$605$	15.0185	0.610588
$606$	2.65774	0.107963
$607$	29.2426	1.18692	0.593459	−	0.804864i	$-0.297762\pi$
$607$	29.2426	1.18692	0.593459	+	0.804864i	$0.297762\pi$
$608$	33.8969	1.37470
$609$	−3.05767	−0.123903
$610$	3.32718	0.134713
$611$	0	0
$612$	25.1888	1.01820
$613$	−1.42405	−0.0575170	−0.0287585	−	0.999586i	$-0.509155\pi$
$613$	−1.42405	−0.0575170	−0.0287585	+	0.999586i	$0.509155\pi$
$614$	−1.36864	−0.0552338
$615$	2.77761	0.112004
$616$	−28.6419	−1.15402
$617$	46.5266	1.87309	0.936545	−	0.350548i	$-0.114005\pi$
$617$	46.5266	1.87309	0.936545	+	0.350548i	$0.114005\pi$
$618$	2.60232	0.104681
$619$	34.2818	1.37790	0.688950	−	0.724809i	$-0.258072\pi$
$619$	34.2818	1.37790	0.688950	+	0.724809i	$0.258072\pi$
$620$	−0.409536	−0.0164473
$621$	−6.04485	−0.242571
$622$	2.02904	0.0813569
$623$	−20.4033	−0.817442
$624$	0	0
$625$	1.00000	0.0400000
$626$	−2.84811	−0.113833
$627$	−13.6336	−0.544474
$628$	16.4527	0.656534
$629$	−17.7859	−0.709171
$630$	4.30644	0.171573
$631$	−2.32322	−0.0924861	−0.0462430	−	0.998930i	$-0.514725\pi$
$631$	−2.32322	−0.0924861	−0.0462430	+	0.998930i	$0.514725\pi$
$632$	−7.63362	−0.303649
$633$	−10.3249	−0.410379
$634$	−10.6359	−0.422405
$635$	12.0616	0.478651
$636$	−3.00830	−0.119287
$637$	0	0
$638$	7.79834	0.308739
$639$	17.5905	0.695868
$640$	11.5328	0.455874
$641$	−28.1312	−1.11111	−0.555557	−	0.831478i	$-0.687495\pi$
$641$	−28.1312	−1.11111	−0.555557	+	0.831478i	$0.687495\pi$
$642$	0.0342826	0.00135303
$643$	14.1338	0.557383	0.278692	−	0.960381i	$-0.410099\pi$
$643$	14.1338	0.557383	0.278692	+	0.960381i	$0.410099\pi$
$644$	10.8560	0.427787
$645$	4.67282	0.183992
$646$	19.0946	0.751268
$647$	−45.8969	−1.80439	−0.902197	−	0.431325i	$-0.858046\pi$
$647$	−45.8969	−1.80439	−0.902197	+	0.431325i	$0.858046\pi$
$648$	15.5143	0.609460
$649$	−4.58651	−0.180036
$650$	0	0
$651$	−0.280067	−0.0109767
$652$	20.7177	0.811367
$653$	50.4482	1.97419	0.987095	−	0.160137i	$-0.0511938\pi$
$653$	50.4482	1.97419	0.987095	+	0.160137i	$0.0511938\pi$
$654$	−2.21747	−0.0867100
$655$	7.63362	0.298270
$656$	−13.9137	−0.543238
$657$	30.8745	1.20453
$658$	4.08631	0.159301
$659$	−45.8722	−1.78693	−0.893464	−	0.449135i	$-0.851732\pi$
$659$	−45.8722	−1.78693	−0.893464	+	0.449135i	$0.851732\pi$
$660$	−3.65209	−0.142157
$661$	25.8432	1.00518	0.502592	−	0.864524i	$-0.332380\pi$
$661$	25.8432	1.00518	0.502592	+	0.864524i	$0.332380\pi$
$662$	3.38614	0.131606
$663$	0	0
$664$	−20.6235	−0.800345
$665$	−16.6913	−0.647261
$666$	−5.36073	−0.207724
$667$	−6.48963	−0.251280
$668$	−14.2326	−0.550674
$669$	2.45269	0.0948265
$670$	1.24877	0.0482442
$671$	29.6706	1.14542
$672$	6.20957	0.239539
$673$	4.97927	0.191937	0.0959683	−	0.995384i	$-0.469405\pi$
$673$	4.97927	0.191937	0.0959683	+	0.995384i	$0.469405\pi$
$674$	7.96306	0.306726
$675$	2.48963	0.0958261
$676$	0	0
$677$	−35.8353	−1.37726	−0.688631	−	0.725112i	$-0.741788\pi$
$677$	−35.8353	−1.37726	−0.688631	+	0.725112i	$0.741788\pi$
$678$	3.17755	0.122033
$679$	30.3249	1.16376
$680$	11.2303	0.430662
$681$	1.26386	0.0484311
$682$	0.714288	0.0273515
$683$	−40.4712	−1.54859	−0.774293	−	0.632827i	$-0.781894\pi$
$683$	−40.4712	−1.54859	−0.774293	+	0.632827i	$0.781894\pi$
$684$	−29.4257	−1.12512
$685$	3.43196	0.131128
$686$	10.4817	0.400194
$687$	10.8112	0.412472
$688$	−23.4073	−0.892394
$689$	0	0
$690$	−0.594417	−0.0226291
$691$	−12.2448	−0.465815	−0.232907	−	0.972499i	$-0.574824\pi$
$691$	−12.2448	−0.465815	−0.232907	+	0.972499i	$0.574824\pi$
$692$	36.0448	1.37022
$693$	38.4033	1.45882
$694$	−4.38050	−0.166281
$695$	−0.942326	−0.0357445
$696$	−2.40332	−0.0910977
$697$	−34.6913	−1.31403
$698$	6.39542	0.242070
$699$	−9.99209	−0.377936
$700$	−4.47116	−0.168994
$701$	11.8353	0.447012	0.223506	−	0.974703i	$-0.428250\pi$
$701$	11.8353	0.447012	0.223506	+	0.974703i	$0.428250\pi$
$702$	0	0
$703$	20.7776	0.783642
$704$	6.03525	0.227462
$705$	1.14399	0.0430850
$706$	−5.52093	−0.207783
$707$	29.0162	1.09127
$708$	0.643787	0.0241950
$709$	−6.37429	−0.239391	−0.119696	−	0.992811i	$-0.538192\pi$
$709$	−6.37429	−0.239391	−0.119696	+	0.992811i	$0.538192\pi$
$710$	3.57199	0.134055
$711$	10.2352	0.383851
$712$	−16.0369	−0.601010
$713$	−0.594417	−0.0222611
$714$	3.49794	0.130907
$715$	0	0
$716$	−4.29588	−0.160545
$717$	−1.62306	−0.0606141
$718$	5.44083	0.203050
$719$	−34.9009	−1.30158	−0.650791	−	0.759257i	$-0.725563\pi$
$719$	−34.9009	−1.30158	−0.650791	+	0.759257i	$0.725563\pi$
$720$	−6.03920	−0.225068
$721$	28.4112	1.05809
$722$	−11.4386	−0.425700
$723$	−1.46890	−0.0546290
$724$	22.9687	0.853625
$725$	2.67282	0.0992662
$726$	3.67678	0.136458
$727$	19.8106	0.734734	0.367367	−	0.930076i	$-0.380259\pi$
$727$	19.8106	0.734734	0.367367	+	0.930076i	$0.380259\pi$
$728$	0	0
$729$	−17.6050	−0.652036
$730$	6.26950	0.232045
$731$	−58.3619	−2.15859
$732$	−4.16472	−0.153932
$733$	−12.6050	−0.465576	−0.232788	−	0.972528i	$-0.574785\pi$
$733$	−12.6050	−0.465576	−0.232788	+	0.972528i	$0.574785\pi$
$734$	9.72615	0.358999
$735$	−0.0616272	−0.00227315
$736$	13.1792	0.485793
$737$	11.1361	0.410203
$738$	−10.4561	−0.384893
$739$	37.1747	1.36749	0.683747	−	0.729719i	$-0.260349\pi$
$739$	37.1747	1.36749	0.683747	+	0.729719i	$0.260349\pi$
$740$	5.56578	0.204602
$741$	0	0
$742$	6.42366	0.235820
$743$	27.9322	1.02473	0.512366	−	0.858767i	$-0.328769\pi$
$743$	27.9322	1.02473	0.512366	+	0.858767i	$0.328769\pi$
$744$	−0.220132	−0.00807043
$745$	11.3456	0.415672
$746$	1.04977	0.0384348
$747$	27.6521	1.01174
$748$	45.6133	1.66779
$749$	0.374285	0.0136761
$750$	0.244817	0.00893945
$751$	−13.6257	−0.497209	−0.248605	−	0.968605i	$-0.579972\pi$
$751$	−13.6257	−0.497209	−0.248605	+	0.968605i	$0.579972\pi$
$752$	−5.73050	−0.208970
$753$	−10.9009	−0.397249
$754$	0	0
$755$	−21.0224	−0.765084
$756$	−11.1316	−0.404851
$757$	−30.8560	−1.12148	−0.560740	−	0.827992i	$-0.689483\pi$
$757$	−30.8560	−1.12148	−0.560740	+	0.827992i	$0.689483\pi$
$758$	18.5143	0.672470
$759$	−5.30080	−0.192407
$760$	−13.1193	−0.475887
$761$	−17.0162	−0.616837	−0.308419	−	0.951251i	$-0.599800\pi$
$761$	−17.0162	−0.616837	−0.308419	+	0.951251i	$0.599800\pi$
$762$	2.95289	0.106972
$763$	−24.2096	−0.876445
$764$	17.8847	0.647044
$765$	−15.0577	−0.544411
$766$	16.0969	0.581604
$767$	0	0
$768$	1.81060	0.0653343
$769$	29.0162	1.04635	0.523176	−	0.852225i	$-0.324747\pi$
$769$	29.0162	1.04635	0.523176	+	0.852225i	$0.324747\pi$
$770$	7.79834	0.281033
$771$	3.96644	0.142848
$772$	−32.2175	−1.15953
$773$	40.5160	1.45726	0.728630	−	0.684908i	$-0.240158\pi$
$773$	40.5160	1.45726	0.728630	+	0.684908i	$0.240158\pi$
$774$	−17.5905	−0.632276
$775$	0.244817	0.00879409
$776$	23.8353	0.855637
$777$	3.80624	0.136548
$778$	−18.2801	−0.655372
$779$	40.5266	1.45202
$780$	0	0
$781$	31.8538	1.13982
$782$	7.42405	0.265484
$783$	6.65435	0.237807
$784$	0.308705	0.0110252
$785$	−9.83528	−0.351036
$786$	1.86884	0.0666593
$787$	−34.0264	−1.21291	−0.606455	−	0.795118i	$-0.707409\pi$
$787$	−34.0264	−1.21291	−0.606455	+	0.795118i	$0.707409\pi$
$788$	−28.7407	−1.02384
$789$	3.48737	0.124154
$790$	2.07841	0.0739464
$791$	34.6913	1.23348
$792$	30.1849	1.07257
$793$	0	0
$794$	7.26990	0.257999
$795$	1.79834	0.0637805
$796$	−19.3166	−0.684659
$797$	−14.7776	−0.523450	−0.261725	−	0.965143i	$-0.584291\pi$
$797$	−14.7776	−0.523450	−0.261725	+	0.965143i	$0.584291\pi$
$798$	−4.08631	−0.144654
$799$	−14.2880	−0.505472
$800$	−5.42801	−0.191909
$801$	21.5025	0.759752
$802$	−0.560135	−0.0197790
$803$	55.9092	1.97299
$804$	−1.56312	−0.0551270
$805$	−6.48963	−0.228730
$806$	0	0
$807$	−0.489634	−0.0172359
$808$	22.8066	0.802335
$809$	−36.0554	−1.26764	−0.633820	−	0.773480i	$-0.718514\pi$
$809$	−36.0554	−1.26764	−0.633820	+	0.773480i	$0.718514\pi$
$810$	−4.22408	−0.148419
$811$	5.31040	0.186473	0.0932366	−	0.995644i	$-0.470279\pi$
$811$	5.31040	0.186473	0.0932366	+	0.995644i	$0.470279\pi$
$812$	−11.9506	−0.419385
$813$	−1.36412	−0.0478417
$814$	−9.70750	−0.340248
$815$	−12.3849	−0.433822
$816$	−4.90538	−0.171723
$817$	68.1787	2.38527
$818$	−4.46060	−0.155961
$819$	0	0
$820$	10.8560	0.379108
$821$	13.6336	0.475817	0.237908	−	0.971288i	$-0.423538\pi$
$821$	13.6336	0.475817	0.237908	+	0.971288i	$0.423538\pi$
$822$	0.840202	0.0293054
$823$	39.6459	1.38197	0.690984	−	0.722870i	$-0.257177\pi$
$823$	39.6459	1.38197	0.690984	+	0.722870i	$0.257177\pi$
$824$	22.3311	0.777942
$825$	2.18319	0.0760089
$826$	−1.37468	−0.0478314
$827$	23.8952	0.830918	0.415459	−	0.909612i	$-0.363621\pi$
$827$	23.8952	0.830918	0.415459	+	0.909612i	$0.363621\pi$
$828$	−11.4408	−0.397596
$829$	−27.3562	−0.950121	−0.475060	−	0.879953i	$-0.657574\pi$
$829$	−27.3562	−0.950121	−0.475060	+	0.879953i	$0.657574\pi$
$830$	5.61515	0.194905
$831$	3.26386	0.113222
$832$	0	0
$833$	0.769701	0.0266686
$834$	−0.230697	−0.00798839
$835$	8.50811	0.294435
$836$	−53.2857	−1.84292
$837$	0.609505	0.0210676
$838$	−5.83528	−0.201576
$839$	−29.5411	−1.01987	−0.509936	−	0.860212i	$-0.670331\pi$
$839$	−29.5411	−1.01987	−0.509936	+	0.860212i	$0.670331\pi$
$840$	−2.40332	−0.0829225
$841$	−21.8560	−0.753656
$842$	−17.8398	−0.614800
$843$	−8.66226	−0.298344
$844$	−40.3540	−1.38904
$845$	0	0
$846$	−4.30644	−0.148059
$847$	40.1417	1.37929
$848$	−9.00830	−0.309346
$849$	8.51601	0.292269
$850$	−3.05767	−0.104877
$851$	8.07841	0.276924
$852$	−4.47116	−0.153180
$853$	5.61515	0.192259	0.0961295	−	0.995369i	$-0.469354\pi$
$853$	5.61515	0.192259	0.0961295	+	0.995369i	$0.469354\pi$
$854$	8.89296	0.304311
$855$	17.5905	0.601581
$856$	0.294187	0.0100551
$857$	−39.9216	−1.36370	−0.681848	−	0.731494i	$-0.738823\pi$
$857$	−39.9216	−1.36370	−0.681848	+	0.731494i	$0.738823\pi$
$858$	0	0
$859$	28.6498	0.977520	0.488760	−	0.872418i	$-0.337449\pi$
$859$	28.6498	0.977520	0.488760	+	0.872418i	$0.337449\pi$
$860$	18.2633	0.622773
$861$	7.42405	0.253011
$862$	−13.1193	−0.446845
$863$	−38.5530	−1.31236	−0.656179	−	0.754605i	$-0.727828\pi$
$863$	−38.5530	−1.31236	−0.656179	+	0.754605i	$0.727828\pi$
$864$	−13.5137	−0.459747
$865$	−21.5473	−0.732630
$866$	−9.31661	−0.316591
$867$	−4.95458	−0.168266
$868$	−1.09462	−0.0371537
$869$	18.5345	0.628739
$870$	0.654353	0.0221846
$871$	0	0
$872$	−19.0286	−0.644391
$873$	−31.9585	−1.08163
$874$	−8.67282	−0.293363
$875$	2.67282	0.0903579
$876$	−7.84771	−0.265150
$877$	−27.3826	−0.924644	−0.462322	−	0.886712i	$-0.652984\pi$
$877$	−27.3826	−0.924644	−0.462322	+	0.886712i	$0.652984\pi$
$878$	13.5888	0.458599
$879$	−11.1361	−0.375611
$880$	−10.9361	−0.368656
$881$	−25.0841	−0.845103	−0.422552	−	0.906339i	$-0.638865\pi$
$881$	−25.0841	−0.845103	−0.422552	+	0.906339i	$0.638865\pi$
$882$	0.231991	0.00781153
$883$	−50.5513	−1.70119	−0.850593	−	0.525825i	$-0.823757\pi$
$883$	−50.5513	−1.70119	−0.850593	+	0.525825i	$0.823757\pi$
$884$	0	0
$885$	−0.384851	−0.0129366
$886$	1.57465	0.0529015
$887$	−19.6583	−0.660061	−0.330031	−	0.943970i	$-0.607059\pi$
$887$	−19.6583	−0.660061	−0.330031	+	0.943970i	$0.607059\pi$
$888$	2.99170	0.100395
$889$	32.2386	1.08125
$890$	4.36638	0.146361
$891$	−37.6689	−1.26195
$892$	9.58611	0.320967
$893$	16.6913	0.558553
$894$	2.77761	0.0928971
$895$	2.56804	0.0858401
$896$	30.8251	1.02979
$897$	0	0
$898$	−15.5025	−0.517324
$899$	0.654353	0.0218239
$900$	4.71203	0.157068
$901$	−22.4606	−0.748271
$902$	−18.9344	−0.630447
$903$	12.4896	0.415629
$904$	27.2672	0.906895
$905$	−13.7305	−0.456417
$906$	−5.14665	−0.170986
$907$	22.0537	0.732282	0.366141	−	0.930559i	$-0.380679\pi$
$907$	22.0537	0.732282	0.366141	+	0.930559i	$0.380679\pi$
$908$	4.93967	0.163929
$909$	−30.5793	−1.01425
$910$	0	0
$911$	−14.0079	−0.464103	−0.232051	−	0.972704i	$-0.574544\pi$
$911$	−14.0079	−0.464103	−0.232051	+	0.972704i	$0.574544\pi$
$912$	5.73050	0.189756
$913$	50.0739	1.65720
$914$	22.9668	0.759676
$915$	2.48963	0.0823048
$916$	42.2544	1.39613
$917$	20.4033	0.673777
$918$	−7.61249	−0.251250
$919$	21.8353	0.720279	0.360140	−	0.932898i	$-0.382729\pi$
$919$	21.8353	0.720279	0.360140	+	0.932898i	$0.382729\pi$
$920$	−5.10083	−0.168169
$921$	−1.02412	−0.0337458
$922$	1.14851	0.0378241
$923$	0	0
$924$	−9.76140	−0.321126
$925$	−3.32718	−0.109397
$926$	1.52884	0.0502407
$927$	−29.9418	−0.983416
$928$	−14.5081	−0.476252
$929$	−15.2224	−0.499431	−0.249715	−	0.968319i	$-0.580337\pi$
$929$	−15.2224	−0.499431	−0.249715	+	0.968319i	$0.580337\pi$
$930$	0.0599353	0.00196536
$931$	−0.899170	−0.0294691
$932$	−39.0532	−1.27923
$933$	1.51827	0.0497060
$934$	18.2403	0.596841
$935$	−27.2672	−0.891734
$936$	0	0
$937$	−25.4610	−0.831774	−0.415887	−	0.909416i	$-0.636529\pi$
$937$	−25.4610	−0.831774	−0.415887	+	0.909416i	$0.636529\pi$
$938$	3.33774	0.108981
$939$	−2.13116	−0.0695478
$940$	4.47116	0.145833
$941$	24.9299	0.812691	0.406346	−	0.913719i	$-0.366803\pi$
$941$	24.9299	0.812691	0.406346	+	0.913719i	$0.366803\pi$
$942$	−2.40784	−0.0784518
$943$	15.7569	0.513114
$944$	1.92781	0.0627448
$945$	6.65435	0.216466
$946$	−31.8538	−1.03565
$947$	−16.6807	−0.542051	−0.271025	−	0.962572i	$-0.587363\pi$
$947$	−16.6807	−0.542051	−0.271025	+	0.962572i	$0.587363\pi$
$948$	−2.60160	−0.0844960
$949$	0	0
$950$	3.57199	0.115891
$951$	−7.95854	−0.258073
$952$	30.0166	0.972844
$953$	27.1730	0.880221	0.440110	−	0.897944i	$-0.354939\pi$
$953$	27.1730	0.880221	0.440110	+	0.897944i	$0.354939\pi$
$954$	−6.76970	−0.219177
$955$	−10.6913	−0.345962
$956$	−6.34356	−0.205165
$957$	5.83528	0.188628
$958$	−3.85206	−0.124454
$959$	9.17302	0.296212
$960$	0.506413	0.0163444
$961$	−30.9401	−0.998067
$962$	0	0
$963$	−0.394448	−0.0127109
$964$	−5.74106	−0.184907
$965$	19.2593	0.619980
$966$	−1.58877	−0.0511179
$967$	6.75914	0.217359	0.108680	−	0.994077i	$-0.465338\pi$
$967$	6.75914	0.217359	0.108680	+	0.994077i	$0.465338\pi$
$968$	31.5513	1.01410
$969$	14.2880	0.458996
$970$	−6.48963	−0.208370
$971$	46.6419	1.49681	0.748405	−	0.663242i	$-0.230820\pi$
$971$	46.6419	1.49681	0.748405	+	0.663242i	$0.230820\pi$
$972$	17.7816	0.570344
$973$	−2.51867	−0.0807449
$974$	22.6807	0.726737
$975$	0	0
$976$	−12.4712	−0.399192
$977$	−52.7467	−1.68752	−0.843758	−	0.536723i	$-0.819662\pi$
$977$	−52.7467	−1.68752	−0.843758	+	0.536723i	$0.819662\pi$
$978$	−3.03202	−0.0969534
$979$	38.9378	1.24446
$980$	−0.240864	−0.00769412
$981$	25.5137	0.814591
$982$	17.7859	0.567571
$983$	20.9977	0.669724	0.334862	−	0.942267i	$-0.391310\pi$
$983$	20.9977	0.669724	0.334862	+	0.942267i	$0.391310\pi$
$984$	5.83528	0.186022
$985$	17.1809	0.547430
$986$	−8.17262	−0.260269
$987$	3.05767	0.0973268
$988$	0	0
$989$	26.5081	0.842909
$990$	−8.21844	−0.261199
$991$	−32.3170	−1.02658	−0.513292	−	0.858214i	$-0.671574\pi$
$991$	−32.3170	−1.02658	−0.513292	+	0.858214i	$0.671574\pi$
$992$	−1.32887	−0.0421916
$993$	2.53376	0.0804064
$994$	9.54731	0.302822
$995$	11.5473	0.366074
$996$	−7.02864	−0.222711
$997$	−21.3905	−0.677444	−0.338722	−	0.940887i	$-0.609995\pi$
$997$	−21.3905	−0.677444	−0.338722	+	0.940887i	$0.609995\pi$
$998$	7.49811	0.237348
$999$	−8.28345	−0.262077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.a.i.1.2		3
3.2	odd	2		7605.2.a.cc.1.2		3
5.4	even	2		4225.2.a.be.1.2		3
13.2	odd	12		845.2.m.h.316.3		12
13.3	even	3		845.2.e.k.191.2		6
13.4	even	6		845.2.e.i.146.2		6
13.5	odd	4		65.2.c.a.51.4	yes	6
13.6	odd	12		845.2.m.h.361.4		12
13.7	odd	12		845.2.m.h.361.3		12
13.8	odd	4		65.2.c.a.51.3	✓	6
13.9	even	3		845.2.e.k.146.2		6
13.10	even	6		845.2.e.i.191.2		6
13.11	odd	12		845.2.m.h.316.4		12
13.12	even	2		845.2.a.k.1.2		3
39.5	even	4		585.2.b.g.181.3		6
39.8	even	4		585.2.b.g.181.4		6
39.38	odd	2		7605.2.a.bs.1.2		3
52.31	even	4		1040.2.k.d.961.3		6
52.47	even	4		1040.2.k.d.961.4		6
65.8	even	4		325.2.d.e.324.3		6
65.18	even	4		325.2.d.f.324.3		6
65.34	odd	4		325.2.c.g.51.4		6
65.44	odd	4		325.2.c.g.51.3		6
65.47	even	4		325.2.d.f.324.4		6
65.57	even	4		325.2.d.e.324.4		6
65.64	even	2		4225.2.a.bc.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.c.a.51.3	✓	6	13.8	odd	4
65.2.c.a.51.4	yes	6	13.5	odd	4
325.2.c.g.51.3		6	65.44	odd	4
325.2.c.g.51.4		6	65.34	odd	4
325.2.d.e.324.3		6	65.8	even	4
325.2.d.e.324.4		6	65.57	even	4
325.2.d.f.324.3		6	65.18	even	4
325.2.d.f.324.4		6	65.47	even	4
585.2.b.g.181.3		6	39.5	even	4
585.2.b.g.181.4		6	39.8	even	4
845.2.a.i.1.2		3	1.1	even	1	trivial
845.2.a.k.1.2		3	13.12	even	2
845.2.e.i.146.2		6	13.4	even	6
845.2.e.i.191.2		6	13.10	even	6
845.2.e.k.146.2		6	13.9	even	3
845.2.e.k.191.2		6	13.3	even	3
845.2.m.h.316.3		12	13.2	odd	12
845.2.m.h.316.4		12	13.11	odd	12
845.2.m.h.361.3		12	13.7	odd	12
845.2.m.h.361.4		12	13.6	odd	12
1040.2.k.d.961.3		6	52.31	even	4
1040.2.k.d.961.4		6	52.47	even	4
4225.2.a.bc.1.2		3	65.64	even	2
4225.2.a.be.1.2		3	5.4	even	2
7605.2.a.bs.1.2		3	39.38	odd	2
7605.2.a.cc.1.2		3	3.2	odd	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.a (trivial)

\(f(q)\)	\(=\)	\(q-0.571993 q^{2} -0.428007 q^{3} -1.67282 q^{4} +1.00000 q^{5} +0.244817 q^{6} +2.67282 q^{7} +2.10083 q^{8} -2.81681 q^{9} -0.571993 q^{10} -5.10083 q^{11} +0.715980 q^{12} -1.52884 q^{14} -0.428007 q^{15} +2.14399 q^{16} +5.34565 q^{17} +1.61120 q^{18} -6.24482 q^{19} -1.67282 q^{20} -1.14399 q^{21} +2.91764 q^{22} -2.42801 q^{23} -0.899170 q^{24} +1.00000 q^{25} +2.48963 q^{27} -4.47116 q^{28} +2.67282 q^{29} +0.244817 q^{30} +0.244817 q^{31} -5.42801 q^{32} +2.18319 q^{33} -3.05767 q^{34} +2.67282 q^{35} +4.71203 q^{36} -3.32718 q^{37} +3.57199 q^{38} +2.10083 q^{40} -6.48963 q^{41} +0.654353 q^{42} -10.9176 q^{43} +8.53279 q^{44} -2.81681 q^{45} +1.38880 q^{46} -2.67282 q^{47} -0.917641 q^{48} +0.143987 q^{49} -0.571993 q^{50} -2.28797 q^{51} -4.20166 q^{53} -1.42405 q^{54} -5.10083 q^{55} +5.61515 q^{56} +2.67282 q^{57} -1.52884 q^{58} +0.899170 q^{59} +0.715980 q^{60} -5.81681 q^{61} -0.140034 q^{62} -7.52884 q^{63} -1.18319 q^{64} -1.24877 q^{66} -2.18319 q^{67} -8.94233 q^{68} +1.03920 q^{69} -1.52884 q^{70} -6.24482 q^{71} -5.91764 q^{72} -10.9608 q^{73} +1.90312 q^{74} -0.428007 q^{75} +10.4465 q^{76} -13.6336 q^{77} -3.63362 q^{79} +2.14399 q^{80} +7.38485 q^{81} +3.71203 q^{82} -9.81681 q^{83} +1.91369 q^{84} +5.34565 q^{85} +6.24482 q^{86} -1.14399 q^{87} -10.7160 q^{88} -7.63362 q^{89} +1.61120 q^{90} +4.06163 q^{92} -0.104783 q^{93} +1.52884 q^{94} -6.24482 q^{95} +2.32322 q^{96} +11.3456 q^{97} -0.0823593 q^{98} +14.3681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 2 q^{3} + 5 q^{4} + 3 q^{5} - 10 q^{6} - 2 q^{7} - 3 q^{8} + 3 q^{9} - q^{10} - 6 q^{11} + 4 q^{14} - 2 q^{15} + 5 q^{16} - 4 q^{17} + 17 q^{18} - 8 q^{19} + 5 q^{20} - 2 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) 3 * q - q^2 - 2 * q^3 + 5 * q^4 + 3 * q^5 - 10 * q^6 - 2 * q^7 - 3 * q^8 + 3 * q^9 - q^10 - 6 * q^11 + 4 * q^14 - 2 * q^15 + 5 * q^16 - 4 * q^17 + 17 * q^18 - 8 * q^19 + 5 * q^20 - 2 * q^21 - 12 * q^22 - 8 * q^23 - 12 * q^24 + 3 * q^25 - 14 * q^27 - 22 * q^28 - 2 * q^29 - 10 * q^30 - 10 * q^31 - 17 * q^32 + 18 * q^33 + 8 * q^34 - 2 * q^35 + 17 * q^36 - 20 * q^37 + 10 * q^38 - 3 * q^40 + 2 * q^41 + 22 * q^42 - 12 * q^43 + 12 * q^44 + 3 * q^45 - 8 * q^46 + 2 * q^47 + 18 * q^48 - q^49 - q^50 - 4 * q^51 + 6 * q^53 - 10 * q^54 - 6 * q^55 + 24 * q^56 - 2 * q^57 + 4 * q^58 + 12 * q^59 - 6 * q^61 - 4 * q^62 - 14 * q^63 - 15 * q^64 + 12 * q^66 - 18 * q^67 - 44 * q^68 + 16 * q^69 + 4 * q^70 - 8 * q^71 + 3 * q^72 - 20 * q^73 + 10 * q^74 - 2 * q^75 + 2 * q^76 - 18 * q^77 + 12 * q^79 + 5 * q^80 + 15 * q^81 + 14 * q^82 - 18 * q^83 - 10 * q^84 - 4 * q^85 + 8 * q^86 - 2 * q^87 - 30 * q^88 + 17 * q^90 - 10 * q^92 + 14 * q^93 - 4 * q^94 - 8 * q^95 + 22 * q^96 + 14 * q^97 - 21 * q^98 - 12 * q^99

Introduction

L-functions

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