LMFDB - Embedded newform 3381.2.a.bk.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 108x^{3} - 33x^{2} - 36x + 14 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 108x^3 - 33x^2 - 36x + 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.46930$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.46930 q^{2} -1.00000 q^{3} +0.158829 q^{4} +2.14842 q^{5} -1.46930 q^{6} -2.70522 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.46930 q^{2} -1.00000 q^{3} +0.158829 q^{4} +2.14842 q^{5} -1.46930 q^{6} -2.70522 q^{8} +1.00000 q^{9} +3.15666 q^{10} +2.16247 q^{11} -0.158829 q^{12} -3.08320 q^{13} -2.14842 q^{15} -4.29243 q^{16} -0.354774 q^{17} +1.46930 q^{18} -4.96083 q^{19} +0.341232 q^{20} +3.17731 q^{22} -1.00000 q^{23} +2.70522 q^{24} -0.384310 q^{25} -4.53014 q^{26} -1.00000 q^{27} -2.50055 q^{29} -3.15666 q^{30} +1.83663 q^{31} -0.896404 q^{32} -2.16247 q^{33} -0.521268 q^{34} +0.158829 q^{36} -4.50032 q^{37} -7.28892 q^{38} +3.08320 q^{39} -5.81195 q^{40} -10.5155 q^{41} +7.96942 q^{43} +0.343465 q^{44} +2.14842 q^{45} -1.46930 q^{46} -7.83688 q^{47} +4.29243 q^{48} -0.564665 q^{50} +0.354774 q^{51} -0.489703 q^{52} +8.86015 q^{53} -1.46930 q^{54} +4.64589 q^{55} +4.96083 q^{57} -3.67404 q^{58} -6.79270 q^{59} -0.341232 q^{60} +2.35137 q^{61} +2.69856 q^{62} +7.26778 q^{64} -6.62400 q^{65} -3.17731 q^{66} -2.20673 q^{67} -0.0563485 q^{68} +1.00000 q^{69} +3.08130 q^{71} -2.70522 q^{72} -3.33525 q^{73} -6.61229 q^{74} +0.384310 q^{75} -0.787926 q^{76} +4.53014 q^{78} -5.15275 q^{79} -9.22193 q^{80} +1.00000 q^{81} -15.4504 q^{82} -4.70908 q^{83} -0.762202 q^{85} +11.7094 q^{86} +2.50055 q^{87} -5.84998 q^{88} -1.87944 q^{89} +3.15666 q^{90} -0.158829 q^{92} -1.83663 q^{93} -11.5147 q^{94} -10.6579 q^{95} +0.896404 q^{96} -8.12795 q^{97} +2.16247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} - 8 q^{12} + 4 q^{15} + 4 q^{16} - 12 q^{17} + 4 q^{18} - 26 q^{19} - 24 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} - 2 q^{25} - 4 q^{26} - 10 q^{27} + 16 q^{29} + 8 q^{30} - 12 q^{31} + 8 q^{32} - 2 q^{33} - 28 q^{34} + 8 q^{36} - 8 q^{37} - 32 q^{38} - 4 q^{40} - 10 q^{41} - 4 q^{43} - 16 q^{44} - 4 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 8 q^{50} + 12 q^{51} - 24 q^{52} + 14 q^{53} - 4 q^{54} - 16 q^{55} + 26 q^{57} - 8 q^{58} - 38 q^{59} + 24 q^{60} - 14 q^{61} + 8 q^{62} + 8 q^{64} + 12 q^{65} + 8 q^{66} - 8 q^{68} + 10 q^{69} + 24 q^{71} + 12 q^{72} - 8 q^{73} - 8 q^{74} + 2 q^{75} - 64 q^{76} + 4 q^{78} - 16 q^{79} - 28 q^{80} + 10 q^{81} + 40 q^{82} - 28 q^{83} - 4 q^{85} + 20 q^{86} - 16 q^{87} - 68 q^{88} - 32 q^{89} - 8 q^{90} - 8 q^{92} + 12 q^{93} - 56 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} + 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 - 8 * q^12 + 4 * q^15 + 4 * q^16 - 12 * q^17 + 4 * q^18 - 26 * q^19 - 24 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 2 * q^25 - 4 * q^26 - 10 * q^27 + 16 * q^29 + 8 * q^30 - 12 * q^31 + 8 * q^32 - 2 * q^33 - 28 * q^34 + 8 * q^36 - 8 * q^37 - 32 * q^38 - 4 * q^40 - 10 * q^41 - 4 * q^43 - 16 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 8 * q^50 + 12 * q^51 - 24 * q^52 + 14 * q^53 - 4 * q^54 - 16 * q^55 + 26 * q^57 - 8 * q^58 - 38 * q^59 + 24 * q^60 - 14 * q^61 + 8 * q^62 + 8 * q^64 + 12 * q^65 + 8 * q^66 - 8 * q^68 + 10 * q^69 + 24 * q^71 + 12 * q^72 - 8 * q^73 - 8 * q^74 + 2 * q^75 - 64 * q^76 + 4 * q^78 - 16 * q^79 - 28 * q^80 + 10 * q^81 + 40 * q^82 - 28 * q^83 - 4 * q^85 + 20 * q^86 - 16 * q^87 - 68 * q^88 - 32 * q^89 - 8 * q^90 - 8 * q^92 + 12 * q^93 - 56 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.46930	1.03895	0.519474	−	0.854486i	$-0.326128\pi$
$2$	1.46930	1.03895	0.519474	+	0.854486i	$0.326128\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.158829	0.0794147
$5$	2.14842	0.960801	0.480400	−	0.877049i	$-0.340491\pi$
$5$	2.14842	0.960801	0.480400	+	0.877049i	$0.340491\pi$
$6$	−1.46930	−0.599837
$7$	0	0
$7$	0	0
$8$	−2.70522	−0.956441
$9$	1.00000	0.333333
$10$	3.15666	0.998223
$11$	2.16247	0.652011	0.326005	−	0.945368i	$-0.394297\pi$
$11$	2.16247	0.652011	0.326005	+	0.945368i	$0.394297\pi$
$12$	−0.158829	−0.0458501
$13$	−3.08320	−0.855127	−0.427563	−	0.903985i	$-0.640628\pi$
$13$	−3.08320	−0.855127	−0.427563	+	0.903985i	$0.640628\pi$
$14$	0	0
$15$	−2.14842	−0.554719
$16$	−4.29243	−1.07311
$17$	−0.354774	−0.0860453	−0.0430227	−	0.999074i	$-0.513699\pi$
$17$	−0.354774	−0.0860453	−0.0430227	+	0.999074i	$0.513699\pi$
$18$	1.46930	0.346316
$19$	−4.96083	−1.13809	−0.569046	−	0.822306i	$-0.692687\pi$
$19$	−4.96083	−1.13809	−0.569046	+	0.822306i	$0.692687\pi$
$20$	0.341232	0.0763017
$21$	0	0
$22$	3.17731	0.677406
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.70522	0.552201
$25$	−0.384310	−0.0768621
$26$	−4.53014	−0.888433
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.50055	−0.464340	−0.232170	−	0.972675i	$-0.574583\pi$
$29$	−2.50055	−0.464340	−0.232170	+	0.972675i	$0.574583\pi$
$30$	−3.15666	−0.576324
$31$	1.83663	0.329869	0.164934	−	0.986305i	$-0.447259\pi$
$31$	1.83663	0.329869	0.164934	+	0.986305i	$0.447259\pi$
$32$	−0.896404	−0.158463
$33$	−2.16247	−0.376438
$34$	−0.521268	−0.0893967
$35$	0	0
$36$	0.158829	0.0264716
$37$	−4.50032	−0.739847	−0.369924	−	0.929062i	$-0.620616\pi$
$37$	−4.50032	−0.739847	−0.369924	+	0.929062i	$0.620616\pi$
$38$	−7.28892	−1.18242
$39$	3.08320	0.493708
$40$	−5.81195	−0.918949
$41$	−10.5155	−1.64225	−0.821124	−	0.570749i	$-0.806653\pi$
$41$	−10.5155	−1.64225	−0.821124	+	0.570749i	$0.806653\pi$
$42$	0	0
$43$	7.96942	1.21533	0.607663	−	0.794195i	$-0.292107\pi$
$43$	7.96942	1.21533	0.607663	+	0.794195i	$0.292107\pi$
$44$	0.343465	0.0517792
$45$	2.14842	0.320267
$46$	−1.46930	−0.216636
$47$	−7.83688	−1.14313	−0.571564	−	0.820558i	$-0.693663\pi$
$47$	−7.83688	−1.14313	−0.571564	+	0.820558i	$0.693663\pi$
$48$	4.29243	0.619559
$49$	0	0
$50$	−0.564665	−0.0798557
$51$	0.354774	0.0496783
$52$	−0.489703	−0.0679096
$53$	8.86015	1.21703	0.608517	−	0.793541i	$-0.291765\pi$
$53$	8.86015	1.21703	0.608517	+	0.793541i	$0.291765\pi$
$54$	−1.46930	−0.199946
$55$	4.64589	0.626452
$56$	0	0
$57$	4.96083	0.657078
$58$	−3.67404	−0.482425
$59$	−6.79270	−0.884334	−0.442167	−	0.896933i	$-0.645790\pi$
$59$	−6.79270	−0.884334	−0.442167	+	0.896933i	$0.645790\pi$
$60$	−0.341232	−0.0440528
$61$	2.35137	0.301062	0.150531	−	0.988605i	$-0.451902\pi$
$61$	2.35137	0.301062	0.150531	+	0.988605i	$0.451902\pi$
$62$	2.69856	0.342717
$63$	0	0
$64$	7.26778	0.908473
$65$	−6.62400	−0.821606
$66$	−3.17731	−0.391100
$67$	−2.20673	−0.269595	−0.134798	−	0.990873i	$-0.543038\pi$
$67$	−2.20673	−0.269595	−0.134798	+	0.990873i	$0.543038\pi$
$68$	−0.0563485	−0.00683326
$69$	1.00000	0.120386
$70$	0	0
$71$	3.08130	0.365683	0.182841	−	0.983142i	$-0.441471\pi$
$71$	3.08130	0.365683	0.182841	+	0.983142i	$0.441471\pi$
$72$	−2.70522	−0.318814
$73$	−3.33525	−0.390362	−0.195181	−	0.980767i	$-0.562529\pi$
$73$	−3.33525	−0.390362	−0.195181	+	0.980767i	$0.562529\pi$
$74$	−6.61229	−0.768664
$75$	0.384310	0.0443763
$76$	−0.787926	−0.0903813
$77$	0	0
$78$	4.53014	0.512937
$79$	−5.15275	−0.579729	−0.289865	−	0.957068i	$-0.593610\pi$
$79$	−5.15275	−0.579729	−0.289865	+	0.957068i	$0.593610\pi$
$80$	−9.22193	−1.03104
$81$	1.00000	0.111111
$82$	−15.4504	−1.70621
$83$	−4.70908	−0.516889	−0.258445	−	0.966026i	$-0.583210\pi$
$83$	−4.70908	−0.516889	−0.258445	+	0.966026i	$0.583210\pi$
$84$	0	0
$85$	−0.762202	−0.0826724
$86$	11.7094	1.26266
$87$	2.50055	0.268087
$88$	−5.84998	−0.623610
$89$	−1.87944	−0.199220	−0.0996101	−	0.995027i	$-0.531760\pi$
$89$	−1.87944	−0.199220	−0.0996101	+	0.995027i	$0.531760\pi$
$90$	3.15666	0.332741
$91$	0	0
$92$	−0.158829	−0.0165591
$93$	−1.83663	−0.190450
$94$	−11.5147	−1.18765
$95$	−10.6579	−1.09348
$96$	0.896404	0.0914888
$97$	−8.12795	−0.825268	−0.412634	−	0.910897i	$-0.635391\pi$
$97$	−8.12795	−0.825268	−0.412634	+	0.910897i	$0.635391\pi$
$98$	0	0
$99$	2.16247	0.217337
$100$	−0.0610398	−0.00610398
$101$	−18.1335	−1.80435	−0.902174	−	0.431371i	$-0.858030\pi$
$101$	−18.1335	−1.80435	−0.902174	+	0.431371i	$0.858030\pi$
$102$	0.521268	0.0516132
$103$	−3.90946	−0.385210	−0.192605	−	0.981276i	$-0.561694\pi$
$103$	−3.90946	−0.385210	−0.192605	+	0.981276i	$0.561694\pi$
$104$	8.34076	0.817878
$105$	0	0
$106$	13.0182	1.26444
$107$	−5.42225	−0.524188	−0.262094	−	0.965042i	$-0.584413\pi$
$107$	−5.42225	−0.524188	−0.262094	+	0.965042i	$0.584413\pi$
$108$	−0.158829	−0.0152834
$109$	15.2859	1.46412	0.732060	−	0.681240i	$-0.238559\pi$
$109$	15.2859	1.46412	0.732060	+	0.681240i	$0.238559\pi$
$110$	6.82619	0.650852
$111$	4.50032	0.427151
$112$	0	0
$113$	5.97105	0.561709	0.280854	−	0.959750i	$-0.409382\pi$
$113$	5.97105	0.561709	0.280854	+	0.959750i	$0.409382\pi$
$114$	7.28892	0.682670
$115$	−2.14842	−0.200341
$116$	−0.397160	−0.0368754
$117$	−3.08320	−0.285042
$118$	−9.98048	−0.918778
$119$	0	0
$120$	5.81195	0.530556
$121$	−6.32370	−0.574882
$122$	3.45486	0.312788
$123$	10.5155	0.948153
$124$	0.291711	0.0261964
$125$	−11.5677	−1.03465
$126$	0	0
$127$	−7.84667	−0.696279	−0.348140	−	0.937443i	$-0.613186\pi$
$127$	−7.84667	−0.696279	−0.348140	+	0.937443i	$0.613186\pi$
$128$	12.4713	1.10232
$129$	−7.96942	−0.701669
$130$	−9.73262	−0.853607
$131$	5.14450	0.449477	0.224738	−	0.974419i	$-0.427847\pi$
$131$	5.14450	0.449477	0.224738	+	0.974419i	$0.427847\pi$
$132$	−0.343465	−0.0298948
$133$	0	0
$134$	−3.24234	−0.280096
$135$	−2.14842	−0.184906
$136$	0.959743	0.0822973
$137$	11.7090	1.00037	0.500183	−	0.865920i	$-0.333266\pi$
$137$	11.7090	1.00037	0.500183	+	0.865920i	$0.333266\pi$
$138$	1.46930	0.125075
$139$	3.57676	0.303377	0.151688	−	0.988428i	$-0.451529\pi$
$139$	3.57676	0.303377	0.151688	+	0.988428i	$0.451529\pi$
$140$	0	0
$141$	7.83688	0.659985
$142$	4.52734	0.379926
$143$	−6.66735	−0.557552
$144$	−4.29243	−0.357703
$145$	−5.37221	−0.446138
$146$	−4.90047	−0.405566
$147$	0	0
$148$	−0.714783	−0.0587548
$149$	−9.49709	−0.778032	−0.389016	−	0.921231i	$-0.627185\pi$
$149$	−9.49709	−0.778032	−0.389016	+	0.921231i	$0.627185\pi$
$150$	0.564665	0.0461047
$151$	−12.8737	−1.04765	−0.523825	−	0.851826i	$-0.675496\pi$
$151$	−12.8737	−1.04765	−0.523825	+	0.851826i	$0.675496\pi$
$152$	13.4202	1.08852
$153$	−0.354774	−0.0286818
$154$	0	0
$155$	3.94585	0.316938
$156$	0.489703	0.0392077
$157$	7.53352	0.601241	0.300620	−	0.953744i	$-0.402806\pi$
$157$	7.53352	0.601241	0.300620	+	0.953744i	$0.402806\pi$
$158$	−7.57091	−0.602309
$159$	−8.86015	−0.702655
$160$	−1.92585	−0.152252
$161$	0	0
$162$	1.46930	0.115439
$163$	−18.0136	−1.41094	−0.705468	−	0.708742i	$-0.749263\pi$
$163$	−18.0136	−1.41094	−0.705468	+	0.708742i	$0.749263\pi$
$164$	−1.67017	−0.130419
$165$	−4.64589	−0.361682
$166$	−6.91904	−0.537021
$167$	−16.8365	−1.30285	−0.651425	−	0.758713i	$-0.725829\pi$
$167$	−16.8365	−1.30285	−0.651425	+	0.758713i	$0.725829\pi$
$168$	0	0
$169$	−3.49385	−0.268758
$170$	−1.11990	−0.0858924
$171$	−4.96083	−0.379364
$172$	1.26578	0.0965147
$173$	16.8181	1.27865	0.639327	−	0.768935i	$-0.279213\pi$
$173$	16.8181	1.27865	0.639327	+	0.768935i	$0.279213\pi$
$174$	3.67404	0.278528
$175$	0	0
$176$	−9.28227	−0.699678
$177$	6.79270	0.510571
$178$	−2.76145	−0.206980
$179$	3.16675	0.236694	0.118347	−	0.992972i	$-0.462241\pi$
$179$	3.16675	0.236694	0.118347	+	0.992972i	$0.462241\pi$
$180$	0.341232	0.0254339
$181$	23.1662	1.72193	0.860965	−	0.508664i	$-0.169861\pi$
$181$	23.1662	1.72193	0.860965	+	0.508664i	$0.169861\pi$
$182$	0	0
$183$	−2.35137	−0.173818
$184$	2.70522	0.199432
$185$	−9.66855	−0.710846
$186$	−2.69856	−0.197868
$187$	−0.767190	−0.0561025
$188$	−1.24473	−0.0907811
$189$	0	0
$190$	−15.6596	−1.13607
$191$	−4.73960	−0.342945	−0.171473	−	0.985189i	$-0.554853\pi$
$191$	−4.73960	−0.342945	−0.171473	+	0.985189i	$0.554853\pi$
$192$	−7.26778	−0.524507
$193$	20.9142	1.50544	0.752720	−	0.658341i	$-0.228742\pi$
$193$	20.9142	1.50544	0.752720	+	0.658341i	$0.228742\pi$
$194$	−11.9424	−0.857411
$195$	6.62400	0.474355
$196$	0	0
$197$	−19.8120	−1.41155	−0.705773	−	0.708438i	$-0.749400\pi$
$197$	−19.8120	−1.41155	−0.705773	+	0.708438i	$0.749400\pi$
$198$	3.17731	0.225802
$199$	−12.7673	−0.905051	−0.452525	−	0.891751i	$-0.649477\pi$
$199$	−12.7673	−0.905051	−0.452525	+	0.891751i	$0.649477\pi$
$200$	1.03965	0.0735140
$201$	2.20673	0.155651
$202$	−26.6434	−1.87463
$203$	0	0
$204$	0.0563485	0.00394519
$205$	−22.5917	−1.57787
$206$	−5.74415	−0.400214
$207$	−1.00000	−0.0695048
$208$	13.2344	0.917644
$209$	−10.7277	−0.742048
$210$	0	0
$211$	3.77646	0.259983	0.129991	−	0.991515i	$-0.458505\pi$
$211$	3.77646	0.259983	0.129991	+	0.991515i	$0.458505\pi$
$212$	1.40725	0.0966504
$213$	−3.08130	−0.211127
$214$	−7.96688	−0.544605
$215$	17.1216	1.16769
$216$	2.70522	0.184067
$217$	0	0
$218$	22.4594	1.52115
$219$	3.33525	0.225376
$220$	0.737905	0.0497495
$221$	1.09384	0.0735797
$222$	6.61229	0.443788
$223$	−3.14153	−0.210373	−0.105186	−	0.994453i	$-0.533544\pi$
$223$	−3.14153	−0.210373	−0.105186	+	0.994453i	$0.533544\pi$
$224$	0	0
$225$	−0.384310	−0.0256207
$226$	8.77323	0.583587
$227$	−19.6642	−1.30516	−0.652579	−	0.757721i	$-0.726313\pi$
$227$	−19.6642	−1.30516	−0.652579	+	0.757721i	$0.726313\pi$
$228$	0.787926	0.0521816
$229$	3.40015	0.224688	0.112344	−	0.993669i	$-0.464164\pi$
$229$	3.40015	0.224688	0.112344	+	0.993669i	$0.464164\pi$
$230$	−3.15666	−0.208144
$231$	0	0
$232$	6.76454	0.444114
$233$	−19.1227	−1.25277	−0.626385	−	0.779514i	$-0.715466\pi$
$233$	−19.1227	−1.25277	−0.626385	+	0.779514i	$0.715466\pi$
$234$	−4.53014	−0.296144
$235$	−16.8369	−1.09832
$236$	−1.07888	−0.0702291
$237$	5.15275	0.334707
$238$	0	0
$239$	3.10915	0.201114	0.100557	−	0.994931i	$-0.467937\pi$
$239$	3.10915	0.201114	0.100557	+	0.994931i	$0.467937\pi$
$240$	9.22193	0.595273
$241$	20.0711	1.29289	0.646445	−	0.762961i	$-0.276255\pi$
$241$	20.0711	1.29289	0.646445	+	0.762961i	$0.276255\pi$
$242$	−9.29139	−0.597273
$243$	−1.00000	−0.0641500
$244$	0.373467	0.0239088
$245$	0	0
$246$	15.4504	0.985082
$247$	15.2952	0.973213
$248$	−4.96850	−0.315500
$249$	4.70908	0.298426
$250$	−16.9964	−1.07495
$251$	4.73370	0.298788	0.149394	−	0.988778i	$-0.452268\pi$
$251$	4.73370	0.298788	0.149394	+	0.988778i	$0.452268\pi$
$252$	0	0
$253$	−2.16247	−0.135954
$254$	−11.5291	−0.723398
$255$	0.762202	0.0477309
$256$	3.78850	0.236781
$257$	3.68563	0.229903	0.114952	−	0.993371i	$-0.463329\pi$
$257$	3.68563	0.229903	0.114952	+	0.993371i	$0.463329\pi$
$258$	−11.7094	−0.728998
$259$	0	0
$260$	−1.05209	−0.0652476
$261$	−2.50055	−0.154780
$262$	7.55879	0.466983
$263$	−4.58029	−0.282433	−0.141216	−	0.989979i	$-0.545101\pi$
$263$	−4.58029	−0.282433	−0.141216	+	0.989979i	$0.545101\pi$
$264$	5.84998	0.360041
$265$	19.0353	1.16933
$266$	0	0
$267$	1.87944	0.115020
$268$	−0.350494	−0.0214098
$269$	18.9657	1.15636	0.578181	−	0.815909i	$-0.303763\pi$
$269$	18.9657	1.15636	0.578181	+	0.815909i	$0.303763\pi$
$270$	−3.15666	−0.192108
$271$	−5.77817	−0.350999	−0.175499	−	0.984480i	$-0.556154\pi$
$271$	−5.77817	−0.350999	−0.175499	+	0.984480i	$0.556154\pi$
$272$	1.52284	0.0923359
$273$	0	0
$274$	17.2040	1.03933
$275$	−0.831061	−0.0501149
$276$	0.158829	0.00956041
$277$	−15.5279	−0.932981	−0.466490	−	0.884526i	$-0.654482\pi$
$277$	−15.5279	−0.932981	−0.466490	+	0.884526i	$0.654482\pi$
$278$	5.25532	0.315193
$279$	1.83663	0.109956
$280$	0	0
$281$	22.5853	1.34733	0.673664	−	0.739038i	$-0.264720\pi$
$281$	22.5853	1.34733	0.673664	+	0.739038i	$0.264720\pi$
$282$	11.5147	0.685690
$283$	22.4715	1.33579	0.667897	−	0.744254i	$-0.267195\pi$
$283$	22.4715	1.33579	0.667897	+	0.744254i	$0.267195\pi$
$284$	0.489401	0.0290406
$285$	10.6579	0.631321
$286$	−9.79631	−0.579268
$287$	0	0
$288$	−0.896404	−0.0528211
$289$	−16.8741	−0.992596
$290$	−7.89337	−0.463514
$291$	8.12795	0.476469
$292$	−0.529736	−0.0310005
$293$	−5.71918	−0.334118	−0.167059	−	0.985947i	$-0.553427\pi$
$293$	−5.71918	−0.334118	−0.167059	+	0.985947i	$0.553427\pi$
$294$	0	0
$295$	−14.5935	−0.849669
$296$	12.1744	0.707620
$297$	−2.16247	−0.125479
$298$	−13.9540	−0.808335
$299$	3.08320	0.178306
$300$	0.0610398	0.00352413
$301$	0	0
$302$	−18.9153	−1.08846
$303$	18.1335	1.04174
$304$	21.2940	1.22130
$305$	5.05173	0.289261
$306$	−0.521268	−0.0297989
$307$	−9.95544	−0.568187	−0.284093	−	0.958797i	$-0.591693\pi$
$307$	−9.95544	−0.568187	−0.284093	+	0.958797i	$0.591693\pi$
$308$	0	0
$309$	3.90946	0.222401
$310$	5.79762	0.329283
$311$	17.6774	1.00239	0.501197	−	0.865333i	$-0.332893\pi$
$311$	17.6774	1.00239	0.501197	+	0.865333i	$0.332893\pi$
$312$	−8.34076	−0.472202
$313$	17.1317	0.968339	0.484169	−	0.874974i	$-0.339122\pi$
$313$	17.1317	0.968339	0.484169	+	0.874974i	$0.339122\pi$
$314$	11.0690	0.624658
$315$	0	0
$316$	−0.818408	−0.0460390
$317$	6.44673	0.362084	0.181042	−	0.983475i	$-0.442053\pi$
$317$	6.44673	0.362084	0.181042	+	0.983475i	$0.442053\pi$
$318$	−13.0182	−0.730023
$319$	−5.40737	−0.302754
$320$	15.6142	0.872861
$321$	5.42225	0.302640
$322$	0	0
$323$	1.75997	0.0979275
$324$	0.158829	0.00882386
$325$	1.18491	0.0657268
$326$	−26.4673	−1.46589
$327$	−15.2859	−0.845310
$328$	28.4468	1.57071
$329$	0	0
$330$	−6.82619	−0.375769
$331$	−6.58020	−0.361681	−0.180840	−	0.983512i	$-0.557882\pi$
$331$	−6.58020	−0.361681	−0.180840	+	0.983512i	$0.557882\pi$
$332$	−0.747941	−0.0410486
$333$	−4.50032	−0.246616
$334$	−24.7378	−1.35359
$335$	−4.74098	−0.259028
$336$	0	0
$337$	34.4661	1.87749	0.938744	−	0.344615i	$-0.111990\pi$
$337$	34.4661	1.87749	0.938744	+	0.344615i	$0.111990\pi$
$338$	−5.13350	−0.279226
$339$	−5.97105	−0.324303
$340$	−0.121060	−0.00656540
$341$	3.97167	0.215078
$342$	−7.28892	−0.394140
$343$	0	0
$344$	−21.5591	−1.16239
$345$	2.14842	0.115667
$346$	24.7107	1.32846
$347$	−23.6184	−1.26790	−0.633950	−	0.773374i	$-0.718567\pi$
$347$	−23.6184	−1.26790	−0.633950	+	0.773374i	$0.718567\pi$
$348$	0.397160	0.0212900
$349$	−14.7497	−0.789536	−0.394768	−	0.918781i	$-0.629175\pi$
$349$	−14.7497	−0.789536	−0.394768	+	0.918781i	$0.629175\pi$
$350$	0	0
$351$	3.08320	0.164569
$352$	−1.93845	−0.103320
$353$	20.6050	1.09669	0.548346	−	0.836252i	$-0.315258\pi$
$353$	20.6050	1.09669	0.548346	+	0.836252i	$0.315258\pi$
$354$	9.98048	0.530457
$355$	6.61991	0.351348
$356$	−0.298510	−0.0158210
$357$	0	0
$358$	4.65289	0.245913
$359$	−26.7302	−1.41077	−0.705383	−	0.708826i	$-0.749225\pi$
$359$	−26.7302	−1.41077	−0.705383	+	0.708826i	$0.749225\pi$
$360$	−5.81195	−0.306316
$361$	5.60983	0.295254
$362$	34.0380	1.78900
$363$	6.32370	0.331908
$364$	0	0
$365$	−7.16551	−0.375060
$366$	−3.45486	−0.180589
$367$	33.4515	1.74616	0.873078	−	0.487580i	$-0.162120\pi$
$367$	33.4515	1.74616	0.873078	+	0.487580i	$0.162120\pi$
$368$	4.29243	0.223758
$369$	−10.5155	−0.547416
$370$	−14.2060	−0.738533
$371$	0	0
$372$	−0.291711	−0.0151245
$373$	26.3427	1.36397	0.681985	−	0.731366i	$-0.261117\pi$
$373$	26.3427	1.36397	0.681985	+	0.731366i	$0.261117\pi$
$374$	−1.12723	−0.0582876
$375$	11.5677	0.597355
$376$	21.2005	1.09333
$377$	7.70969	0.397069
$378$	0	0
$379$	19.2340	0.987984	0.493992	−	0.869466i	$-0.335537\pi$
$379$	19.2340	0.987984	0.493992	+	0.869466i	$0.335537\pi$
$380$	−1.69279	−0.0868384
$381$	7.84667	0.401997
$382$	−6.96387	−0.356303
$383$	16.3969	0.837842	0.418921	−	0.908023i	$-0.362408\pi$
$383$	16.3969	0.837842	0.418921	+	0.908023i	$0.362408\pi$
$384$	−12.4713	−0.636425
$385$	0	0
$386$	30.7292	1.56407
$387$	7.96942	0.405109
$388$	−1.29096	−0.0655384
$389$	22.6519	1.14849	0.574247	−	0.818682i	$-0.305295\pi$
$389$	22.6519	1.14849	0.574247	+	0.818682i	$0.305295\pi$
$390$	9.73262	0.492830
$391$	0.354774	0.0179417
$392$	0	0
$393$	−5.14450	−0.259506
$394$	−29.1097	−1.46652
$395$	−11.0702	−0.557004
$396$	0.343465	0.0172597
$397$	−15.2035	−0.763040	−0.381520	−	0.924361i	$-0.624599\pi$
$397$	−15.2035	−0.763040	−0.381520	+	0.924361i	$0.624599\pi$
$398$	−18.7590	−0.940302
$399$	0	0
$400$	1.64963	0.0824813
$401$	7.05495	0.352307	0.176154	−	0.984363i	$-0.443634\pi$
$401$	7.05495	0.352307	0.176154	+	0.984363i	$0.443634\pi$
$402$	3.24234	0.161713
$403$	−5.66271	−0.282080
$404$	−2.88013	−0.143292
$405$	2.14842	0.106756
$406$	0	0
$407$	−9.73182	−0.482388
$408$	−0.959743	−0.0475144
$409$	−27.4335	−1.35650	−0.678249	−	0.734832i	$-0.737261\pi$
$409$	−27.4335	−1.35650	−0.678249	+	0.734832i	$0.737261\pi$
$410$	−33.1939	−1.63933
$411$	−11.7090	−0.577561
$412$	−0.620937	−0.0305913
$413$	0	0
$414$	−1.46930	−0.0722119
$415$	−10.1171	−0.496627
$416$	2.76380	0.135506
$417$	−3.57676	−0.175155
$418$	−15.7621	−0.770950
$419$	−8.06199	−0.393854	−0.196927	−	0.980418i	$-0.563096\pi$
$419$	−8.06199	−0.393854	−0.196927	+	0.980418i	$0.563096\pi$
$420$	0	0
$421$	−3.26503	−0.159128	−0.0795640	−	0.996830i	$-0.525353\pi$
$421$	−3.26503	−0.159128	−0.0795640	+	0.996830i	$0.525353\pi$
$422$	5.54874	0.270109
$423$	−7.83688	−0.381042
$424$	−23.9687	−1.16402
$425$	0.136343	0.00661362
$426$	−4.52734	−0.219350
$427$	0	0
$428$	−0.861212	−0.0416283
$429$	6.66735	0.321903
$430$	25.1567	1.21317
$431$	18.7612	0.903697	0.451848	−	0.892095i	$-0.350765\pi$
$431$	18.7612	0.903697	0.451848	+	0.892095i	$0.350765\pi$
$432$	4.29243	0.206520
$433$	−4.07674	−0.195915	−0.0979577	−	0.995191i	$-0.531231\pi$
$433$	−4.07674	−0.195915	−0.0979577	+	0.995191i	$0.531231\pi$
$434$	0	0
$435$	5.37221	0.257578
$436$	2.42784	0.116273
$437$	4.96083	0.237309
$438$	4.90047	0.234154
$439$	−20.0760	−0.958173	−0.479087	−	0.877768i	$-0.659032\pi$
$439$	−20.0760	−0.958173	−0.479087	+	0.877768i	$0.659032\pi$
$440$	−12.5682	−0.599165
$441$	0	0
$442$	1.60717	0.0764455
$443$	18.1100	0.860433	0.430216	−	0.902726i	$-0.358437\pi$
$443$	18.1100	0.860433	0.430216	+	0.902726i	$0.358437\pi$
$444$	0.714783	0.0339221
$445$	−4.03782	−0.191411
$446$	−4.61584	−0.218566
$447$	9.49709	0.449197
$448$	0	0
$449$	21.9396	1.03539	0.517697	−	0.855564i	$-0.326790\pi$
$449$	21.9396	1.03539	0.517697	+	0.855564i	$0.326790\pi$
$450$	−0.564665	−0.0266186
$451$	−22.7396	−1.07076
$452$	0.948378	0.0446079
$453$	12.8737	0.604861
$454$	−28.8925	−1.35599
$455$	0	0
$456$	−13.4202	−0.628456
$457$	25.7102	1.20267	0.601336	−	0.798997i	$-0.294636\pi$
$457$	25.7102	1.20267	0.601336	+	0.798997i	$0.294636\pi$
$458$	4.99583	0.233440
$459$	0.354774	0.0165594
$460$	−0.341232	−0.0159100
$461$	29.6004	1.37863	0.689313	−	0.724464i	$-0.257912\pi$
$461$	29.6004	1.37863	0.689313	+	0.724464i	$0.257912\pi$
$462$	0	0
$463$	7.00166	0.325395	0.162697	−	0.986676i	$-0.447981\pi$
$463$	7.00166	0.325395	0.162697	+	0.986676i	$0.447981\pi$
$464$	10.7334	0.498287
$465$	−3.94585	−0.182984
$466$	−28.0969	−1.30156
$467$	−21.5522	−0.997317	−0.498659	−	0.866798i	$-0.666174\pi$
$467$	−21.5522	−0.997317	−0.498659	+	0.866798i	$0.666174\pi$
$468$	−0.489703	−0.0226365
$469$	0	0
$470$	−24.7384	−1.14110
$471$	−7.53352	−0.347126
$472$	18.3758	0.845813
$473$	17.2337	0.792405
$474$	7.57091	0.347743
$475$	1.90650	0.0874761
$476$	0	0
$477$	8.86015	0.405678
$478$	4.56826	0.208947
$479$	−1.45000	−0.0662524	−0.0331262	−	0.999451i	$-0.510546\pi$
$479$	−1.45000	−0.0662524	−0.0331262	+	0.999451i	$0.510546\pi$
$480$	1.92585	0.0879025
$481$	13.8754	0.632663
$482$	29.4903	1.34325
$483$	0	0
$484$	−1.00439	−0.0456541
$485$	−17.4622	−0.792918
$486$	−1.46930	−0.0666486
$487$	−29.3715	−1.33095	−0.665474	−	0.746421i	$-0.731770\pi$
$487$	−29.3715	−1.33095	−0.665474	+	0.746421i	$0.731770\pi$
$488$	−6.36099	−0.287948
$489$	18.0136	0.814605
$490$	0	0
$491$	−22.0308	−0.994235	−0.497117	−	0.867683i	$-0.665608\pi$
$491$	−22.0308	−0.994235	−0.497117	+	0.867683i	$0.665608\pi$
$492$	1.67017	0.0752973
$493$	0.887129	0.0399543
$494$	22.4732	1.01112
$495$	4.64589	0.208817
$496$	−7.88362	−0.353985
$497$	0	0
$498$	6.91904	0.310049
$499$	−13.0025	−0.582074	−0.291037	−	0.956712i	$-0.594000\pi$
$499$	−13.0025	−0.582074	−0.291037	+	0.956712i	$0.594000\pi$
$500$	−1.83730	−0.0821664
$501$	16.8365	0.752201
$502$	6.95520	0.310426
$503$	27.4378	1.22339	0.611695	−	0.791094i	$-0.290488\pi$
$503$	27.4378	1.22339	0.611695	+	0.791094i	$0.290488\pi$
$504$	0	0
$505$	−38.9583	−1.73362
$506$	−3.17731	−0.141249
$507$	3.49385	0.155168
$508$	−1.24628	−0.0552948
$509$	−10.7217	−0.475231	−0.237615	−	0.971359i	$-0.576366\pi$
$509$	−10.7217	−0.475231	−0.237615	+	0.971359i	$0.576366\pi$
$510$	1.11990	0.0495900
$511$	0	0
$512$	−19.3762	−0.856316
$513$	4.96083	0.219026
$514$	5.41528	0.238858
$515$	−8.39914	−0.370110
$516$	−1.26578	−0.0557228
$517$	−16.9471	−0.745331
$518$	0	0
$519$	−16.8181	−0.738231
$520$	17.9194	0.785818
$521$	−35.8465	−1.57046	−0.785232	−	0.619202i	$-0.787456\pi$
$521$	−35.8465	−1.57046	−0.785232	+	0.619202i	$0.787456\pi$
$522$	−3.67404	−0.160808
$523$	−17.0049	−0.743573	−0.371787	−	0.928318i	$-0.621255\pi$
$523$	−17.0049	−0.743573	−0.371787	+	0.928318i	$0.621255\pi$
$524$	0.817097	0.0356951
$525$	0	0
$526$	−6.72980	−0.293433
$527$	−0.651589	−0.0283837
$528$	9.28227	0.403959
$529$	1.00000	0.0434783
$530$	27.9684	1.21487
$531$	−6.79270	−0.294778
$532$	0	0
$533$	32.4215	1.40433
$534$	2.76145	0.119500
$535$	−11.6492	−0.503641
$536$	5.96971	0.257852
$537$	−3.16675	−0.136655
$538$	27.8663	1.20140
$539$	0	0
$540$	−0.341232	−0.0146843
$541$	−34.8174	−1.49692	−0.748459	−	0.663181i	$-0.769206\pi$
$541$	−34.8174	−1.49692	−0.748459	+	0.663181i	$0.769206\pi$
$542$	−8.48983	−0.364670
$543$	−23.1662	−0.994157
$544$	0.318021	0.0136350
$545$	32.8404	1.40673
$546$	0	0
$547$	−33.3988	−1.42803	−0.714015	−	0.700130i	$-0.753125\pi$
$547$	−33.3988	−1.42803	−0.714015	+	0.700130i	$0.753125\pi$
$548$	1.85973	0.0794437
$549$	2.35137	0.100354
$550$	−1.22107	−0.0520668
$551$	12.4048	0.528461
$552$	−2.70522	−0.115142
$553$	0	0
$554$	−22.8151	−0.969319
$555$	9.66855	0.410407
$556$	0.568095	0.0240926
$557$	39.5811	1.67711	0.838553	−	0.544820i	$-0.183402\pi$
$557$	39.5811	1.67711	0.838553	+	0.544820i	$0.183402\pi$
$558$	2.69856	0.114239
$559$	−24.5714	−1.03926
$560$	0	0
$561$	0.767190	0.0323908
$562$	33.1845	1.39980
$563$	−15.5253	−0.654314	−0.327157	−	0.944970i	$-0.606091\pi$
$563$	−15.5253	−0.654314	−0.327157	+	0.944970i	$0.606091\pi$
$564$	1.24473	0.0524125
$565$	12.8283	0.539690
$566$	33.0173	1.38782
$567$	0	0
$568$	−8.33560	−0.349754
$569$	34.0553	1.42767	0.713836	−	0.700313i	$-0.246956\pi$
$569$	34.0553	1.42767	0.713836	+	0.700313i	$0.246956\pi$
$570$	15.6596	0.655910
$571$	29.7572	1.24530	0.622650	−	0.782500i	$-0.286056\pi$
$571$	29.7572	1.24530	0.622650	+	0.782500i	$0.286056\pi$
$572$	−1.05897	−0.0442778
$573$	4.73960	0.198000
$574$	0	0
$575$	0.384310	0.0160268
$576$	7.26778	0.302824
$577$	2.09294	0.0871304	0.0435652	−	0.999051i	$-0.486128\pi$
$577$	2.09294	0.0871304	0.0435652	+	0.999051i	$0.486128\pi$
$578$	−24.7931	−1.03126
$579$	−20.9142	−0.869166
$580$	−0.853265	−0.0354299
$581$	0	0
$582$	11.9424	0.495026
$583$	19.1598	0.793519
$584$	9.02261	0.373358
$585$	−6.62400	−0.273869
$586$	−8.40317	−0.347132
$587$	35.6427	1.47113	0.735565	−	0.677454i	$-0.236917\pi$
$587$	35.6427	1.47113	0.735565	+	0.677454i	$0.236917\pi$
$588$	0	0
$589$	−9.11122	−0.375421
$590$	−21.4422	−0.882762
$591$	19.8120	0.814956
$592$	19.3173	0.793936
$593$	24.5094	1.00648	0.503240	−	0.864147i	$-0.332141\pi$
$593$	24.5094	1.00648	0.503240	+	0.864147i	$0.332141\pi$
$594$	−3.17731	−0.130367
$595$	0	0
$596$	−1.50842	−0.0617871
$597$	12.7673	0.522531
$598$	4.53014	0.185251
$599$	5.61551	0.229443	0.114722	−	0.993398i	$-0.463402\pi$
$599$	5.61551	0.229443	0.114722	+	0.993398i	$0.463402\pi$
$600$	−1.03965	−0.0424433
$601$	−13.1302	−0.535594	−0.267797	−	0.963475i	$-0.586296\pi$
$601$	−13.1302	−0.535594	−0.267797	+	0.963475i	$0.586296\pi$
$602$	0	0
$603$	−2.20673	−0.0898652
$604$	−2.04473	−0.0831989
$605$	−13.5859	−0.552347
$606$	26.6434	1.08232
$607$	−0.0961849	−0.00390403	−0.00195201	−	0.999998i	$-0.500621\pi$
$607$	−0.0961849	−0.00390403	−0.00195201	+	0.999998i	$0.500621\pi$
$608$	4.44691	0.180346
$609$	0	0
$610$	7.42248	0.300527
$611$	24.1627	0.977519
$612$	−0.0563485	−0.00227775
$613$	2.52392	0.101940	0.0509701	−	0.998700i	$-0.483769\pi$
$613$	2.52392	0.101940	0.0509701	+	0.998700i	$0.483769\pi$
$614$	−14.6275	−0.590317
$615$	22.5917	0.910986
$616$	0	0
$617$	22.7394	0.915453	0.457727	−	0.889093i	$-0.348664\pi$
$617$	22.7394	0.915453	0.457727	+	0.889093i	$0.348664\pi$
$618$	5.74415	0.231063
$619$	23.8721	0.959500	0.479750	−	0.877405i	$-0.340727\pi$
$619$	23.8721	0.959500	0.479750	+	0.877405i	$0.340727\pi$
$620$	0.626717	0.0251696
$621$	1.00000	0.0401286
$622$	25.9734	1.04144
$623$	0	0
$624$	−13.2344	−0.529802
$625$	−22.9308	−0.917230
$626$	25.1715	1.00605
$627$	10.7277	0.428422
$628$	1.19654	0.0477473
$629$	1.59659	0.0636604
$630$	0	0
$631$	13.5166	0.538086	0.269043	−	0.963128i	$-0.413293\pi$
$631$	13.5166	0.538086	0.269043	+	0.963128i	$0.413293\pi$
$632$	13.9393	0.554477
$633$	−3.77646	−0.150101
$634$	9.47215	0.376187
$635$	−16.8579	−0.668985
$636$	−1.40725	−0.0558012
$637$	0	0
$638$	−7.94502	−0.314546
$639$	3.08130	0.121894
$640$	26.7936	1.05911
$641$	17.3683	0.686005	0.343002	−	0.939335i	$-0.388556\pi$
$641$	17.3683	0.686005	0.343002	+	0.939335i	$0.388556\pi$
$642$	7.96688	0.314428
$643$	−10.2840	−0.405561	−0.202780	−	0.979224i	$-0.564998\pi$
$643$	−10.2840	−0.405561	−0.202780	+	0.979224i	$0.564998\pi$
$644$	0	0
$645$	−17.1216	−0.674164
$646$	2.58592	0.101742
$647$	43.6516	1.71612	0.858060	−	0.513550i	$-0.171670\pi$
$647$	43.6516	1.71612	0.858060	+	0.513550i	$0.171670\pi$
$648$	−2.70522	−0.106271
$649$	−14.6890	−0.576595
$650$	1.74098	0.0682868
$651$	0	0
$652$	−2.86109	−0.112049
$653$	5.79970	0.226960	0.113480	−	0.993540i	$-0.463800\pi$
$653$	5.79970	0.226960	0.113480	+	0.993540i	$0.463800\pi$
$654$	−22.4594	−0.878234
$655$	11.0525	0.431858
$656$	45.1372	1.76231
$657$	−3.33525	−0.130121
$658$	0	0
$659$	4.50649	0.175548	0.0877740	−	0.996140i	$-0.472025\pi$
$659$	4.50649	0.175548	0.0877740	+	0.996140i	$0.472025\pi$
$660$	−0.737905	−0.0287229
$661$	19.2687	0.749467	0.374734	−	0.927133i	$-0.377734\pi$
$661$	19.2687	0.749467	0.374734	+	0.927133i	$0.377734\pi$
$662$	−9.66826	−0.375768
$663$	−1.09384	−0.0424812
$664$	12.7391	0.494374
$665$	0	0
$666$	−6.61229	−0.256221
$667$	2.50055	0.0968215
$668$	−2.67414	−0.103465
$669$	3.14153	0.121459
$670$	−6.96590	−0.269116
$671$	5.08478	0.196296
$672$	0	0
$673$	−40.9683	−1.57921	−0.789606	−	0.613615i	$-0.789715\pi$
$673$	−40.9683	−1.57921	−0.789606	+	0.613615i	$0.789715\pi$
$674$	50.6409	1.95061
$675$	0.384310	0.0147921
$676$	−0.554927	−0.0213433
$677$	−20.8977	−0.803165	−0.401582	−	0.915823i	$-0.631540\pi$
$677$	−20.8977	−0.803165	−0.401582	+	0.915823i	$0.631540\pi$
$678$	−8.77323	−0.336934
$679$	0	0
$680$	2.06193	0.0790713
$681$	19.6642	0.753533
$682$	5.83556	0.223455
$683$	50.4475	1.93032	0.965159	−	0.261663i	$-0.0842709\pi$
$683$	50.4475	1.93032	0.965159	+	0.261663i	$0.0842709\pi$
$684$	−0.787926	−0.0301271
$685$	25.1558	0.961152
$686$	0	0
$687$	−3.40015	−0.129724
$688$	−34.2082	−1.30418
$689$	−27.3176	−1.04072
$690$	3.15666	0.120172
$691$	−21.7766	−0.828422	−0.414211	−	0.910181i	$-0.635943\pi$
$691$	−21.7766	−0.828422	−0.414211	+	0.910181i	$0.635943\pi$
$692$	2.67120	0.101544
$693$	0	0
$694$	−34.7023	−1.31728
$695$	7.68437	0.291485
$696$	−6.76454	−0.256409
$697$	3.73063	0.141308
$698$	−21.6717	−0.820287
$699$	19.1227	0.723287
$700$	0	0
$701$	5.05307	0.190852	0.0954259	−	0.995437i	$-0.469579\pi$
$701$	5.05307	0.190852	0.0954259	+	0.995437i	$0.469579\pi$
$702$	4.53014	0.170979
$703$	22.3253	0.842015
$704$	15.7164	0.592334
$705$	16.8369	0.634114
$706$	30.2748	1.13941
$707$	0	0
$708$	1.07888	0.0405468
$709$	−19.4725	−0.731304	−0.365652	−	0.930752i	$-0.619154\pi$
$709$	−19.4725	−0.731304	−0.365652	+	0.930752i	$0.619154\pi$
$710$	9.72660	0.365033
$711$	−5.15275	−0.193243
$712$	5.08431	0.190542
$713$	−1.83663	−0.0687824
$714$	0	0
$715$	−14.3242	−0.535696
$716$	0.502973	0.0187970
$717$	−3.10915	−0.116113
$718$	−39.2746	−1.46571
$719$	−21.1483	−0.788698	−0.394349	−	0.918961i	$-0.629030\pi$
$719$	−21.1483	−0.788698	−0.394349	+	0.918961i	$0.629030\pi$
$720$	−9.22193	−0.343681
$721$	0	0
$722$	8.24249	0.306754
$723$	−20.0711	−0.746450
$724$	3.67947	0.136747
$725$	0.960985	0.0356901
$726$	9.29139	0.344836
$727$	−36.0941	−1.33866	−0.669328	−	0.742967i	$-0.733418\pi$
$727$	−36.0941	−1.33866	−0.669328	+	0.742967i	$0.733418\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−10.5283	−0.389668
$731$	−2.82734	−0.104573
$732$	−0.373467	−0.0138037
$733$	12.5279	0.462728	0.231364	−	0.972867i	$-0.425681\pi$
$733$	12.5279	0.462728	0.231364	+	0.972867i	$0.425681\pi$
$734$	49.1502	1.81417
$735$	0	0
$736$	0.896404	0.0330419
$737$	−4.77201	−0.175779
$738$	−15.4504	−0.568738
$739$	28.8783	1.06230	0.531152	−	0.847276i	$-0.321759\pi$
$739$	28.8783	1.06230	0.531152	+	0.847276i	$0.321759\pi$
$740$	−1.53565	−0.0564516
$741$	−15.2952	−0.561885
$742$	0	0
$743$	4.69965	0.172413	0.0862066	−	0.996277i	$-0.472525\pi$
$743$	4.69965	0.172413	0.0862066	+	0.996277i	$0.472525\pi$
$744$	4.96850	0.182154
$745$	−20.4037	−0.747533
$746$	38.7051	1.41710
$747$	−4.70908	−0.172296
$748$	−0.121852	−0.00445536
$749$	0	0
$750$	16.9964	0.620622
$751$	−49.0318	−1.78920	−0.894598	−	0.446871i	$-0.852538\pi$
$751$	−49.0318	−1.78920	−0.894598	+	0.446871i	$0.852538\pi$
$752$	33.6393	1.22670
$753$	−4.73370	−0.172505
$754$	11.3278	0.412535
$755$	−27.6582	−1.00658
$756$	0	0
$757$	−9.25720	−0.336459	−0.168229	−	0.985748i	$-0.553805\pi$
$757$	−9.25720	−0.336459	−0.168229	+	0.985748i	$0.553805\pi$
$758$	28.2604	1.02646
$759$	2.16247	0.0784929
$760$	28.8321	1.04585
$761$	−9.75714	−0.353696	−0.176848	−	0.984238i	$-0.556590\pi$
$761$	−9.75714	−0.353696	−0.176848	+	0.984238i	$0.556590\pi$
$762$	11.5291	0.417654
$763$	0	0
$764$	−0.752788	−0.0272349
$765$	−0.762202	−0.0275575
$766$	24.0919	0.870475
$767$	20.9433	0.756218
$768$	−3.78850	−0.136706
$769$	3.88254	0.140008	0.0700041	−	0.997547i	$-0.477699\pi$
$769$	3.88254	0.140008	0.0700041	+	0.997547i	$0.477699\pi$
$770$	0	0
$771$	−3.68563	−0.132735
$772$	3.32180	0.119554
$773$	32.6917	1.17584	0.587919	−	0.808920i	$-0.299947\pi$
$773$	32.6917	1.17584	0.587919	+	0.808920i	$0.299947\pi$
$774$	11.7094	0.420887
$775$	−0.705836	−0.0253544
$776$	21.9879	0.789320
$777$	0	0
$778$	33.2823	1.19323
$779$	52.1657	1.86903
$780$	1.05209	0.0376707
$781$	6.66323	0.238429
$782$	0.521268	0.0186405
$783$	2.50055	0.0893622
$784$	0	0
$785$	16.1851	0.577672
$786$	−7.55879	−0.269613
$787$	−29.4878	−1.05113	−0.525563	−	0.850755i	$-0.676145\pi$
$787$	−29.4878	−1.05113	−0.525563	+	0.850755i	$0.676145\pi$
$788$	−3.14673	−0.112097
$789$	4.58029	0.163063
$790$	−16.2655	−0.578699
$791$	0	0
$792$	−5.84998	−0.207870
$793$	−7.24976	−0.257447
$794$	−22.3384	−0.792759
$795$	−19.0353	−0.675112
$796$	−2.02783	−0.0718744
$797$	−31.2478	−1.10685	−0.553427	−	0.832897i	$-0.686680\pi$
$797$	−31.2478	−1.10685	−0.553427	+	0.832897i	$0.686680\pi$
$798$	0	0
$799$	2.78032	0.0983607
$800$	0.344497	0.0121798
$801$	−1.87944	−0.0664068
$802$	10.3658	0.366029
$803$	−7.21240	−0.254520
$804$	0.350494	0.0123610
$805$	0	0
$806$	−8.32020	−0.293066
$807$	−18.9657	−0.667626
$808$	49.0551	1.72575
$809$	−6.47854	−0.227773	−0.113887	−	0.993494i	$-0.536330\pi$
$809$	−6.47854	−0.227773	−0.113887	+	0.993494i	$0.536330\pi$
$810$	3.15666	0.110914
$811$	16.2398	0.570257	0.285128	−	0.958489i	$-0.407964\pi$
$811$	16.2398	0.570257	0.285128	+	0.958489i	$0.407964\pi$
$812$	0	0
$813$	5.77817	0.202649
$814$	−14.2989	−0.501177
$815$	−38.7008	−1.35563
$816$	−1.52284	−0.0533102
$817$	−39.5349	−1.38315
$818$	−40.3079	−1.40933
$819$	0	0
$820$	−3.58823	−0.125306
$821$	−39.9374	−1.39382	−0.696912	−	0.717157i	$-0.745443\pi$
$821$	−39.9374	−1.39382	−0.696912	+	0.717157i	$0.745443\pi$
$822$	−17.2040	−0.600057
$823$	51.5045	1.79533	0.897667	−	0.440675i	$-0.145261\pi$
$823$	51.5045	1.79533	0.897667	+	0.440675i	$0.145261\pi$
$824$	10.5760	0.368431
$825$	0.831061	0.0289338
$826$	0	0
$827$	−11.0594	−0.384571	−0.192286	−	0.981339i	$-0.561590\pi$
$827$	−11.0594	−0.384571	−0.192286	+	0.981339i	$0.561590\pi$
$828$	−0.158829	−0.00551970
$829$	−9.76537	−0.339165	−0.169583	−	0.985516i	$-0.554242\pi$
$829$	−9.76537	−0.339165	−0.169583	+	0.985516i	$0.554242\pi$
$830$	−14.8650	−0.515971
$831$	15.5279	0.538657
$832$	−22.4081	−0.776859
$833$	0	0
$834$	−5.25532	−0.181977
$835$	−36.1719	−1.25178
$836$	−1.70387	−0.0589295
$837$	−1.83663	−0.0634833
$838$	−11.8454	−0.409194
$839$	−27.3798	−0.945254	−0.472627	−	0.881262i	$-0.656694\pi$
$839$	−27.3798	−0.945254	−0.472627	+	0.881262i	$0.656694\pi$
$840$	0	0
$841$	−22.7473	−0.784389
$842$	−4.79730	−0.165326
$843$	−22.5853	−0.777880
$844$	0.599814	0.0206464
$845$	−7.50625	−0.258223
$846$	−11.5147	−0.395884
$847$	0	0
$848$	−38.0316	−1.30601
$849$	−22.4715	−0.771221
$850$	0.200329	0.00687121
$851$	4.50032	0.154269
$852$	−0.489401	−0.0167666
$853$	29.0973	0.996274	0.498137	−	0.867098i	$-0.334018\pi$
$853$	29.0973	0.996274	0.498137	+	0.867098i	$0.334018\pi$
$854$	0	0
$855$	−10.6579	−0.364493
$856$	14.6684	0.501355
$857$	44.9912	1.53687	0.768435	−	0.639928i	$-0.221036\pi$
$857$	44.9912	1.53687	0.768435	+	0.639928i	$0.221036\pi$
$858$	9.79631	0.334440
$859$	9.64929	0.329230	0.164615	−	0.986358i	$-0.447362\pi$
$859$	9.64929	0.329230	0.164615	+	0.986358i	$0.447362\pi$
$860$	2.71942	0.0927314
$861$	0	0
$862$	27.5658	0.938895
$863$	12.9216	0.439856	0.219928	−	0.975516i	$-0.429418\pi$
$863$	12.9216	0.439856	0.219928	+	0.975516i	$0.429418\pi$
$864$	0.896404	0.0304963
$865$	36.1322	1.22853
$866$	−5.98993	−0.203546
$867$	16.8741	0.573076
$868$	0	0
$869$	−11.1427	−0.377990
$870$	7.89337	0.267610
$871$	6.80381	0.230538
$872$	−41.3517	−1.40034
$873$	−8.12795	−0.275089
$874$	7.28892	0.246552
$875$	0	0
$876$	0.529736	0.0178981
$877$	32.3173	1.09128	0.545639	−	0.838020i	$-0.316287\pi$
$877$	32.3173	1.09128	0.545639	+	0.838020i	$0.316287\pi$
$878$	−29.4975	−0.995493
$879$	5.71918	0.192903
$880$	−19.9422	−0.672251
$881$	−46.4011	−1.56329	−0.781647	−	0.623721i	$-0.785620\pi$
$881$	−46.4011	−1.56329	−0.781647	+	0.623721i	$0.785620\pi$
$882$	0	0
$883$	−4.37111	−0.147100	−0.0735498	−	0.997292i	$-0.523433\pi$
$883$	−4.37111	−0.147100	−0.0735498	+	0.997292i	$0.523433\pi$
$884$	0.173734	0.00584331
$885$	14.5935	0.490557
$886$	26.6090	0.893946
$887$	−25.3672	−0.851749	−0.425874	−	0.904782i	$-0.640033\pi$
$887$	−25.3672	−0.851749	−0.425874	+	0.904782i	$0.640033\pi$
$888$	−12.1744	−0.408545
$889$	0	0
$890$	−5.93275	−0.198866
$891$	2.16247	0.0724456
$892$	−0.498968	−0.0167067
$893$	38.8774	1.30098
$894$	13.9540	0.466692
$895$	6.80349	0.227416
$896$	0	0
$897$	−3.08320	−0.102945
$898$	32.2358	1.07572
$899$	−4.59258	−0.153171
$900$	−0.0610398	−0.00203466
$901$	−3.14335	−0.104720
$902$	−33.4111	−1.11247
$903$	0	0
$904$	−16.1530	−0.537241
$905$	49.7706	1.65443
$906$	18.9153	0.628420
$907$	−50.6441	−1.68161	−0.840804	−	0.541340i	$-0.817917\pi$
$907$	−50.6441	−1.68161	−0.840804	+	0.541340i	$0.817917\pi$
$908$	−3.12325	−0.103649
$909$	−18.1335	−0.601450
$910$	0	0
$911$	−6.29108	−0.208433	−0.104216	−	0.994555i	$-0.533233\pi$
$911$	−6.29108	−0.208433	−0.104216	+	0.994555i	$0.533233\pi$
$912$	−21.2940	−0.705116
$913$	−10.1833	−0.337017
$914$	37.7758	1.24951
$915$	−5.05173	−0.167005
$916$	0.540044	0.0178436
$917$	0	0
$918$	0.521268	0.0172044
$919$	26.3435	0.868991	0.434496	−	0.900674i	$-0.356927\pi$
$919$	26.3435	0.868991	0.434496	+	0.900674i	$0.356927\pi$
$920$	5.81195	0.191614
$921$	9.95544	0.328043
$922$	43.4917	1.43232
$923$	−9.50027	−0.312705
$924$	0	0
$925$	1.72952	0.0568662
$926$	10.2875	0.338069
$927$	−3.90946	−0.128403
$928$	2.24150	0.0735808
$929$	−51.3944	−1.68619	−0.843097	−	0.537762i	$-0.819270\pi$
$929$	−51.3944	−1.68619	−0.843097	+	0.537762i	$0.819270\pi$
$930$	−5.79762	−0.190111
$931$	0	0
$932$	−3.03725	−0.0994884
$933$	−17.6774	−0.578733
$934$	−31.6666	−1.03616
$935$	−1.64824	−0.0539033
$936$	8.34076	0.272626
$937$	9.83635	0.321339	0.160670	−	0.987008i	$-0.448635\pi$
$937$	9.83635	0.321339	0.160670	+	0.987008i	$0.448635\pi$
$938$	0	0
$939$	−17.1317	−0.559071
$940$	−2.67419	−0.0872225
$941$	−43.7737	−1.42698	−0.713491	−	0.700664i	$-0.752887\pi$
$941$	−43.7737	−1.42698	−0.713491	+	0.700664i	$0.752887\pi$
$942$	−11.0690	−0.360647
$943$	10.5155	0.342433
$944$	29.1572	0.948986
$945$	0	0
$946$	25.3214	0.823268
$947$	−29.6306	−0.962865	−0.481432	−	0.876483i	$-0.659883\pi$
$947$	−29.6306	−0.962865	−0.481432	+	0.876483i	$0.659883\pi$
$948$	0.818408	0.0265806
$949$	10.2833	0.333809
$950$	2.80121	0.0908832
$951$	−6.44673	−0.209049
$952$	0	0
$953$	38.6354	1.25152	0.625762	−	0.780014i	$-0.284788\pi$
$953$	38.6354	1.25152	0.625762	+	0.780014i	$0.284788\pi$
$954$	13.0182	0.421479
$955$	−10.1826	−0.329502
$956$	0.493825	0.0159714
$957$	5.40737	0.174795
$958$	−2.13048	−0.0688328
$959$	0	0
$960$	−15.6142	−0.503947
$961$	−27.6268	−0.891187
$962$	20.3871	0.657305
$963$	−5.42225	−0.174729
$964$	3.18787	0.102674
$965$	44.9325	1.44643
$966$	0	0
$967$	−46.5223	−1.49606	−0.748028	−	0.663668i	$-0.768999\pi$
$967$	−46.5223	−1.49606	−0.748028	+	0.663668i	$0.768999\pi$
$968$	17.1070	0.549841
$969$	−1.75997	−0.0565385
$970$	−25.6571	−0.823801
$971$	5.98111	0.191943	0.0959715	−	0.995384i	$-0.469404\pi$
$971$	5.98111	0.191943	0.0959715	+	0.995384i	$0.469404\pi$
$972$	−0.158829	−0.00509446
$973$	0	0
$974$	−43.1553	−1.38279
$975$	−1.18491	−0.0379474
$976$	−10.0931	−0.323073
$977$	−10.9369	−0.349901	−0.174950	−	0.984577i	$-0.555977\pi$
$977$	−10.9369	−0.349901	−0.174950	+	0.984577i	$0.555977\pi$
$978$	26.4673	0.846332
$979$	−4.06424	−0.129894
$980$	0	0
$981$	15.2859	0.488040
$982$	−32.3697	−1.03296
$983$	56.6707	1.80751	0.903757	−	0.428045i	$-0.140798\pi$
$983$	56.6707	1.80751	0.903757	+	0.428045i	$0.140798\pi$
$984$	−28.4468	−0.906852
$985$	−42.5644	−1.35621
$986$	1.30345	0.0415104
$987$	0	0
$988$	2.42934	0.0772874
$989$	−7.96942	−0.253413
$990$	6.82619	0.216951
$991$	9.57119	0.304039	0.152019	−	0.988378i	$-0.451422\pi$
$991$	9.57119	0.304039	0.152019	+	0.988378i	$0.451422\pi$
$992$	−1.64636	−0.0522721
$993$	6.58020	0.208816
$994$	0	0
$995$	−27.4295	−0.869574
$996$	0.747941	0.0236994
$997$	56.0202	1.77418	0.887089	−	0.461598i	$-0.152724\pi$
$997$	56.0202	1.77418	0.887089	+	0.461598i	$0.152724\pi$
$998$	−19.1046	−0.604745
$999$	4.50032	0.142384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bk.1.7	✓	10
7.6	odd	2		3381.2.a.bl.1.7	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bk.1.7	✓	10	1.1	even	1	trivial
3381.2.a.bl.1.7	yes	10	7.6	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+1.46930 q^{2} -1.00000 q^{3} +0.158829 q^{4} +2.14842 q^{5} -1.46930 q^{6} -2.70522 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.46930 q^{2} -1.00000 q^{3} +0.158829 q^{4} +2.14842 q^{5} -1.46930 q^{6} -2.70522 q^{8} +1.00000 q^{9} +3.15666 q^{10} +2.16247 q^{11} -0.158829 q^{12} -3.08320 q^{13} -2.14842 q^{15} -4.29243 q^{16} -0.354774 q^{17} +1.46930 q^{18} -4.96083 q^{19} +0.341232 q^{20} +3.17731 q^{22} -1.00000 q^{23} +2.70522 q^{24} -0.384310 q^{25} -4.53014 q^{26} -1.00000 q^{27} -2.50055 q^{29} -3.15666 q^{30} +1.83663 q^{31} -0.896404 q^{32} -2.16247 q^{33} -0.521268 q^{34} +0.158829 q^{36} -4.50032 q^{37} -7.28892 q^{38} +3.08320 q^{39} -5.81195 q^{40} -10.5155 q^{41} +7.96942 q^{43} +0.343465 q^{44} +2.14842 q^{45} -1.46930 q^{46} -7.83688 q^{47} +4.29243 q^{48} -0.564665 q^{50} +0.354774 q^{51} -0.489703 q^{52} +8.86015 q^{53} -1.46930 q^{54} +4.64589 q^{55} +4.96083 q^{57} -3.67404 q^{58} -6.79270 q^{59} -0.341232 q^{60} +2.35137 q^{61} +2.69856 q^{62} +7.26778 q^{64} -6.62400 q^{65} -3.17731 q^{66} -2.20673 q^{67} -0.0563485 q^{68} +1.00000 q^{69} +3.08130 q^{71} -2.70522 q^{72} -3.33525 q^{73} -6.61229 q^{74} +0.384310 q^{75} -0.787926 q^{76} +4.53014 q^{78} -5.15275 q^{79} -9.22193 q^{80} +1.00000 q^{81} -15.4504 q^{82} -4.70908 q^{83} -0.762202 q^{85} +11.7094 q^{86} +2.50055 q^{87} -5.84998 q^{88} -1.87944 q^{89} +3.15666 q^{90} -0.158829 q^{92} -1.83663 q^{93} -11.5147 q^{94} -10.6579 q^{95} +0.896404 q^{96} -8.12795 q^{97} +2.16247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} - 8 q^{12} + 4 q^{15} + 4 q^{16} - 12 q^{17} + 4 q^{18} - 26 q^{19} - 24 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} - 2 q^{25} - 4 q^{26} - 10 q^{27} + 16 q^{29} + 8 q^{30} - 12 q^{31} + 8 q^{32} - 2 q^{33} - 28 q^{34} + 8 q^{36} - 8 q^{37} - 32 q^{38} - 4 q^{40} - 10 q^{41} - 4 q^{43} - 16 q^{44} - 4 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 8 q^{50} + 12 q^{51} - 24 q^{52} + 14 q^{53} - 4 q^{54} - 16 q^{55} + 26 q^{57} - 8 q^{58} - 38 q^{59} + 24 q^{60} - 14 q^{61} + 8 q^{62} + 8 q^{64} + 12 q^{65} + 8 q^{66} - 8 q^{68} + 10 q^{69} + 24 q^{71} + 12 q^{72} - 8 q^{73} - 8 q^{74} + 2 q^{75} - 64 q^{76} + 4 q^{78} - 16 q^{79} - 28 q^{80} + 10 q^{81} + 40 q^{82} - 28 q^{83} - 4 q^{85} + 20 q^{86} - 16 q^{87} - 68 q^{88} - 32 q^{89} - 8 q^{90} - 8 q^{92} + 12 q^{93} - 56 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} + 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 - 8 * q^12 + 4 * q^15 + 4 * q^16 - 12 * q^17 + 4 * q^18 - 26 * q^19 - 24 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 2 * q^25 - 4 * q^26 - 10 * q^27 + 16 * q^29 + 8 * q^30 - 12 * q^31 + 8 * q^32 - 2 * q^33 - 28 * q^34 + 8 * q^36 - 8 * q^37 - 32 * q^38 - 4 * q^40 - 10 * q^41 - 4 * q^43 - 16 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 8 * q^50 + 12 * q^51 - 24 * q^52 + 14 * q^53 - 4 * q^54 - 16 * q^55 + 26 * q^57 - 8 * q^58 - 38 * q^59 + 24 * q^60 - 14 * q^61 + 8 * q^62 + 8 * q^64 + 12 * q^65 + 8 * q^66 - 8 * q^68 + 10 * q^69 + 24 * q^71 + 12 * q^72 - 8 * q^73 - 8 * q^74 + 2 * q^75 - 64 * q^76 + 4 * q^78 - 16 * q^79 - 28 * q^80 + 10 * q^81 + 40 * q^82 - 28 * q^83 - 4 * q^85 + 20 * q^86 - 16 * q^87 - 68 * q^88 - 32 * q^89 - 8 * q^90 - 8 * q^92 + 12 * q^93 - 56 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

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