LMFDB - Embedded newform 3381.2.a.bg.1.2

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:	$0$
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} + 100x^{3} - 17x^{2} - 28x - 2 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 100x^3 - 17x^2 - 28x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.24407$ 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)

$f(q)$	$=$	$q-2.24407 q^{2} -1.00000 q^{3} +3.03587 q^{4} -4.44184 q^{5} +2.24407 q^{6} -2.32456 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.24407 q^{2} -1.00000 q^{3} +3.03587 q^{4} -4.44184 q^{5} +2.24407 q^{6} -2.32456 q^{8} +1.00000 q^{9} +9.96781 q^{10} -2.32829 q^{11} -3.03587 q^{12} +6.62385 q^{13} +4.44184 q^{15} -0.855252 q^{16} +5.41655 q^{17} -2.24407 q^{18} +6.50778 q^{19} -13.4848 q^{20} +5.22485 q^{22} +1.00000 q^{23} +2.32456 q^{24} +14.7299 q^{25} -14.8644 q^{26} -1.00000 q^{27} +1.22555 q^{29} -9.96781 q^{30} -1.65049 q^{31} +6.56836 q^{32} +2.32829 q^{33} -12.1551 q^{34} +3.03587 q^{36} -5.91137 q^{37} -14.6039 q^{38} -6.62385 q^{39} +10.3253 q^{40} +4.74138 q^{41} +0.311818 q^{43} -7.06837 q^{44} -4.44184 q^{45} -2.24407 q^{46} +0.868126 q^{47} +0.855252 q^{48} -33.0551 q^{50} -5.41655 q^{51} +20.1091 q^{52} -3.07677 q^{53} +2.24407 q^{54} +10.3419 q^{55} -6.50778 q^{57} -2.75021 q^{58} -0.204728 q^{59} +13.4848 q^{60} -0.134838 q^{61} +3.70382 q^{62} -13.0294 q^{64} -29.4221 q^{65} -5.22485 q^{66} +8.61255 q^{67} +16.4439 q^{68} -1.00000 q^{69} -6.97110 q^{71} -2.32456 q^{72} -10.6345 q^{73} +13.2656 q^{74} -14.7299 q^{75} +19.7568 q^{76} +14.8644 q^{78} -6.82320 q^{79} +3.79889 q^{80} +1.00000 q^{81} -10.6400 q^{82} +13.2209 q^{83} -24.0594 q^{85} -0.699743 q^{86} -1.22555 q^{87} +5.41224 q^{88} +15.6794 q^{89} +9.96781 q^{90} +3.03587 q^{92} +1.65049 q^{93} -1.94814 q^{94} -28.9065 q^{95} -6.56836 q^{96} -6.32960 q^{97} -2.32829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 16 q^{13} - 4 q^{15} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 26 q^{19} - 8 q^{22} + 10 q^{23} + 12 q^{24} + 14 q^{25} - 12 q^{26} - 10 q^{27} - 16 q^{29} - 8 q^{30} + 20 q^{31} - 8 q^{32} + 2 q^{33} - 4 q^{34} + 8 q^{36} + 8 q^{37} - 8 q^{38} - 16 q^{39} - 12 q^{40} + 22 q^{41} - 4 q^{43} - 24 q^{44} + 4 q^{45} - 4 q^{46} + 6 q^{47} - 4 q^{48} - 48 q^{50} - 12 q^{51} + 24 q^{52} - 30 q^{53} + 4 q^{54} + 48 q^{55} - 26 q^{57} + 24 q^{58} + 42 q^{59} + 14 q^{61} + 40 q^{62} + 8 q^{64} - 44 q^{65} + 8 q^{66} + 8 q^{68} - 10 q^{69} + 8 q^{71} - 12 q^{72} + 24 q^{73} + 8 q^{74} - 14 q^{75} + 32 q^{76} + 12 q^{78} + 32 q^{79} + 28 q^{80} + 10 q^{81} - 64 q^{82} + 28 q^{83} - 4 q^{85} - 4 q^{86} + 16 q^{87} + 20 q^{88} + 8 q^{90} + 8 q^{92} - 20 q^{93} + 8 q^{94} - 16 q^{95} + 8 q^{96} - 12 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 + 16 * q^13 - 4 * q^15 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 26 * q^19 - 8 * q^22 + 10 * q^23 + 12 * q^24 + 14 * q^25 - 12 * q^26 - 10 * q^27 - 16 * q^29 - 8 * q^30 + 20 * q^31 - 8 * q^32 + 2 * q^33 - 4 * q^34 + 8 * q^36 + 8 * q^37 - 8 * q^38 - 16 * q^39 - 12 * q^40 + 22 * q^41 - 4 * q^43 - 24 * q^44 + 4 * q^45 - 4 * q^46 + 6 * q^47 - 4 * q^48 - 48 * q^50 - 12 * q^51 + 24 * q^52 - 30 * q^53 + 4 * q^54 + 48 * q^55 - 26 * q^57 + 24 * q^58 + 42 * q^59 + 14 * q^61 + 40 * q^62 + 8 * q^64 - 44 * q^65 + 8 * q^66 + 8 * q^68 - 10 * q^69 + 8 * q^71 - 12 * q^72 + 24 * q^73 + 8 * q^74 - 14 * q^75 + 32 * q^76 + 12 * q^78 + 32 * q^79 + 28 * q^80 + 10 * q^81 - 64 * q^82 + 28 * q^83 - 4 * q^85 - 4 * q^86 + 16 * q^87 + 20 * q^88 + 8 * q^90 + 8 * q^92 - 20 * q^93 + 8 * q^94 - 16 * q^95 + 8 * q^96 - 12 * 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 $

$2$	−2.24407	−1.58680	−0.793400	−	0.608701i	$-0.791691\pi$
$2$	−2.24407	−1.58680	−0.793400	+	0.608701i	$0.791691\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.03587	1.51793
$5$	−4.44184	−1.98645	−0.993225	−	0.116203i	$-0.962928\pi$
$5$	−4.44184	−1.98645	−0.993225	+	0.116203i	$0.962928\pi$
$6$	2.24407	0.916139
$7$	0	0
$7$	0	0
$8$	−2.32456	−0.821855
$9$	1.00000	0.333333
$10$	9.96781	3.15210
$11$	−2.32829	−0.702005	−0.351003	−	0.936375i	$-0.614159\pi$
$11$	−2.32829	−0.702005	−0.351003	+	0.936375i	$0.614159\pi$
$12$	−3.03587	−0.876379
$13$	6.62385	1.83713	0.918563	−	0.395274i	$-0.129350\pi$
$13$	6.62385	1.83713	0.918563	+	0.395274i	$0.129350\pi$
$14$	0	0
$15$	4.44184	1.14688
$16$	−0.855252	−0.213813
$17$	5.41655	1.31371	0.656853	−	0.754019i	$-0.271887\pi$
$17$	5.41655	1.31371	0.656853	+	0.754019i	$0.271887\pi$
$18$	−2.24407	−0.528933
$19$	6.50778	1.49299	0.746494	−	0.665392i	$-0.231736\pi$
$19$	6.50778	1.49299	0.746494	+	0.665392i	$0.231736\pi$
$20$	−13.4848	−3.01530
$21$	0	0
$22$	5.22485	1.11394
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.32456	0.474498
$25$	14.7299	2.94599
$26$	−14.8644	−2.91515
$27$	−1.00000	−0.192450
$28$	0	0
$29$	1.22555	0.227578	0.113789	−	0.993505i	$-0.463701\pi$
$29$	1.22555	0.227578	0.113789	+	0.993505i	$0.463701\pi$
$30$	−9.96781	−1.81987
$31$	−1.65049	−0.296437	−0.148218	−	0.988955i	$-0.547354\pi$
$31$	−1.65049	−0.296437	−0.148218	+	0.988955i	$0.547354\pi$
$32$	6.56836	1.16113
$33$	2.32829	0.405303
$34$	−12.1551	−2.08459
$35$	0	0
$36$	3.03587	0.505978
$37$	−5.91137	−0.971824	−0.485912	−	0.874008i	$-0.661512\pi$
$37$	−5.91137	−0.971824	−0.485912	+	0.874008i	$0.661512\pi$
$38$	−14.6039	−2.36907
$39$	−6.62385	−1.06067
$40$	10.3253	1.63258
$41$	4.74138	0.740479	0.370239	−	0.928936i	$-0.379276\pi$
$41$	4.74138	0.740479	0.370239	+	0.928936i	$0.379276\pi$
$42$	0	0
$43$	0.311818	0.0475518	0.0237759	−	0.999717i	$-0.492431\pi$
$43$	0.311818	0.0475518	0.0237759	+	0.999717i	$0.492431\pi$
$44$	−7.06837	−1.06560
$45$	−4.44184	−0.662150
$46$	−2.24407	−0.330871
$47$	0.868126	0.126629	0.0633146	−	0.997994i	$-0.479833\pi$
$47$	0.868126	0.126629	0.0633146	+	0.997994i	$0.479833\pi$
$48$	0.855252	0.123445
$49$	0	0
$50$	−33.0551	−4.67469
$51$	−5.41655	−0.758469
$52$	20.1091	2.78863
$53$	−3.07677	−0.422628	−0.211314	−	0.977418i	$-0.567774\pi$
$53$	−3.07677	−0.422628	−0.211314	+	0.977418i	$0.567774\pi$
$54$	2.24407	0.305380
$55$	10.3419	1.39450
$56$	0	0
$57$	−6.50778	−0.861977
$58$	−2.75021	−0.361121
$59$	−0.204728	−0.0266533	−0.0133267	−	0.999911i	$-0.504242\pi$
$59$	−0.204728	−0.0266533	−0.0133267	+	0.999911i	$0.504242\pi$
$60$	13.4848	1.74088
$61$	−0.134838	−0.0172643	−0.00863213	−	0.999963i	$-0.502748\pi$
$61$	−0.134838	−0.0172643	−0.00863213	+	0.999963i	$0.502748\pi$
$62$	3.70382	0.470385
$63$	0	0
$64$	−13.0294	−1.62867
$65$	−29.4221	−3.64936
$66$	−5.22485	−0.643134
$67$	8.61255	1.05219	0.526096	−	0.850425i	$-0.323655\pi$
$67$	8.61255	1.05219	0.526096	+	0.850425i	$0.323655\pi$
$68$	16.4439	1.99412
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−6.97110	−0.827318	−0.413659	−	0.910432i	$-0.635749\pi$
$71$	−6.97110	−0.827318	−0.413659	+	0.910432i	$0.635749\pi$
$72$	−2.32456	−0.273952
$73$	−10.6345	−1.24467	−0.622336	−	0.782750i	$-0.713816\pi$
$73$	−10.6345	−1.24467	−0.622336	+	0.782750i	$0.713816\pi$
$74$	13.2656	1.54209
$75$	−14.7299	−1.70087
$76$	19.7568	2.26626
$77$	0	0
$78$	14.8644	1.68306
$79$	−6.82320	−0.767670	−0.383835	−	0.923402i	$-0.625397\pi$
$79$	−6.82320	−0.767670	−0.383835	+	0.923402i	$0.625397\pi$
$80$	3.79889	0.424729
$81$	1.00000	0.111111
$82$	−10.6400	−1.17499
$83$	13.2209	1.45118	0.725591	−	0.688126i	$-0.241566\pi$
$83$	13.2209	1.45118	0.725591	+	0.688126i	$0.241566\pi$
$84$	0	0
$85$	−24.0594	−2.60961
$86$	−0.699743	−0.0754552
$87$	−1.22555	−0.131392
$88$	5.41224	0.576947
$89$	15.6794	1.66201	0.831005	−	0.556264i	$-0.187766\pi$
$89$	15.6794	1.66201	0.831005	+	0.556264i	$0.187766\pi$
$90$	9.96781	1.05070
$91$	0	0
$92$	3.03587	0.316511
$93$	1.65049	0.171148
$94$	−1.94814	−0.200935
$95$	−28.9065	−2.96575
$96$	−6.56836	−0.670381
$97$	−6.32960	−0.642674	−0.321337	−	0.946965i	$-0.604132\pi$
$97$	−6.32960	−0.642674	−0.321337	+	0.946965i	$0.604132\pi$
$98$	0	0
$99$	−2.32829	−0.234002
$100$	44.7181	4.47181
$101$	−4.37582	−0.435410	−0.217705	−	0.976015i	$-0.569857\pi$
$101$	−4.37582	−0.435410	−0.217705	+	0.976015i	$0.569857\pi$
$102$	12.1551	1.20354
$103$	2.93155	0.288854	0.144427	−	0.989515i	$-0.453866\pi$
$103$	2.93155	0.288854	0.144427	+	0.989515i	$0.453866\pi$
$104$	−15.3975	−1.50985
$105$	0	0
$106$	6.90451	0.670625
$107$	19.8846	1.92232	0.961159	−	0.275994i	$-0.0890069\pi$
$107$	19.8846	1.92232	0.961159	+	0.275994i	$0.0890069\pi$
$108$	−3.03587	−0.292126
$109$	10.2475	0.981529	0.490765	−	0.871292i	$-0.336718\pi$
$109$	10.2475	0.981529	0.490765	+	0.871292i	$0.336718\pi$
$110$	−23.2079	−2.21279
$111$	5.91137	0.561083
$112$	0	0
$113$	−13.1144	−1.23370	−0.616849	−	0.787081i	$-0.711591\pi$
$113$	−13.1144	−1.23370	−0.616849	+	0.787081i	$0.711591\pi$
$114$	14.6039	1.36778
$115$	−4.44184	−0.414204
$116$	3.72059	0.345448
$117$	6.62385	0.612376
$118$	0.459425	0.0422935
$119$	0	0
$120$	−10.3253	−0.942568
$121$	−5.57908	−0.507189
$122$	0.302587	0.0273949
$123$	−4.74138	−0.427516
$124$	−5.01066	−0.449971
$125$	−43.2188	−3.86561
$126$	0	0
$127$	−4.35290	−0.386258	−0.193129	−	0.981173i	$-0.561864\pi$
$127$	−4.35290	−0.386258	−0.193129	+	0.981173i	$0.561864\pi$
$128$	16.1022	1.42324
$129$	−0.311818	−0.0274541
$130$	66.0253	5.79081
$131$	20.9835	1.83334	0.916670	−	0.399645i	$-0.130866\pi$
$131$	20.9835	1.83334	0.916670	+	0.399645i	$0.130866\pi$
$132$	7.06837	0.615222
$133$	0	0
$134$	−19.3272	−1.66962
$135$	4.44184	0.382293
$136$	−12.5911	−1.07968
$137$	−17.6900	−1.51136	−0.755678	−	0.654943i	$-0.772692\pi$
$137$	−17.6900	−1.51136	−0.755678	+	0.654943i	$0.772692\pi$
$138$	2.24407	0.191028
$139$	20.6301	1.74982	0.874910	−	0.484286i	$-0.160921\pi$
$139$	20.6301	1.74982	0.874910	+	0.484286i	$0.160921\pi$
$140$	0	0
$141$	−0.868126	−0.0731094
$142$	15.6437	1.31279
$143$	−15.4222	−1.28967
$144$	−0.855252	−0.0712710
$145$	−5.44368	−0.452073
$146$	23.8646	1.97505
$147$	0	0
$148$	−17.9461	−1.47516
$149$	−3.78263	−0.309885	−0.154943	−	0.987923i	$-0.549519\pi$
$149$	−3.78263	−0.309885	−0.154943	+	0.987923i	$0.549519\pi$
$150$	33.0551	2.69893
$151$	−9.44506	−0.768628	−0.384314	−	0.923202i	$-0.625562\pi$
$151$	−9.44506	−0.768628	−0.384314	+	0.923202i	$0.625562\pi$
$152$	−15.1277	−1.22702
$153$	5.41655	0.437902
$154$	0	0
$155$	7.33121	0.588857
$156$	−20.1091	−1.61002
$157$	7.81777	0.623926	0.311963	−	0.950094i	$-0.399014\pi$
$157$	7.81777	0.623926	0.311963	+	0.950094i	$0.399014\pi$
$158$	15.3118	1.21814
$159$	3.07677	0.244004
$160$	−29.1756	−2.30654
$161$	0	0
$162$	−2.24407	−0.176311
$163$	−12.4478	−0.974990	−0.487495	−	0.873126i	$-0.662089\pi$
$163$	−12.4478	−0.974990	−0.487495	+	0.873126i	$0.662089\pi$
$164$	14.3942	1.12400
$165$	−10.3419	−0.805114
$166$	−29.6687	−2.30273
$167$	−1.07030	−0.0828220	−0.0414110	−	0.999142i	$-0.513185\pi$
$167$	−1.07030	−0.0828220	−0.0414110	+	0.999142i	$0.513185\pi$
$168$	0	0
$169$	30.8754	2.37503
$170$	53.9912	4.14093
$171$	6.50778	0.497663
$172$	0.946638	0.0721805
$173$	6.58216	0.500432	0.250216	−	0.968190i	$-0.419498\pi$
$173$	6.58216	0.500432	0.250216	+	0.968190i	$0.419498\pi$
$174$	2.75021	0.208493
$175$	0	0
$176$	1.99127	0.150098
$177$	0.204728	0.0153883
$178$	−35.1857	−2.63728
$179$	5.61117	0.419399	0.209699	−	0.977766i	$-0.432751\pi$
$179$	5.61117	0.419399	0.209699	+	0.977766i	$0.432751\pi$
$180$	−13.4848	−1.00510
$181$	−19.0014	−1.41236	−0.706182	−	0.708030i	$-0.749584\pi$
$181$	−19.0014	−1.41236	−0.706182	+	0.708030i	$0.749584\pi$
$182$	0	0
$183$	0.134838	0.00996752
$184$	−2.32456	−0.171369
$185$	26.2574	1.93048
$186$	−3.70382	−0.271577
$187$	−12.6113	−0.922228
$188$	2.63551	0.192215
$189$	0	0
$190$	64.8684	4.70605
$191$	−0.684753	−0.0495470	−0.0247735	−	0.999693i	$-0.507886\pi$
$191$	−0.684753	−0.0495470	−0.0247735	+	0.999693i	$0.507886\pi$
$192$	13.0294	0.940315
$193$	14.9144	1.07356	0.536782	−	0.843721i	$-0.319640\pi$
$193$	14.9144	1.07356	0.536782	+	0.843721i	$0.319640\pi$
$194$	14.2041	1.01979
$195$	29.4221	2.10696
$196$	0	0
$197$	5.00661	0.356706	0.178353	−	0.983967i	$-0.442923\pi$
$197$	5.00661	0.356706	0.178353	+	0.983967i	$0.442923\pi$
$198$	5.22485	0.371314
$199$	13.9353	0.987848	0.493924	−	0.869505i	$-0.335562\pi$
$199$	13.9353	0.987848	0.493924	+	0.869505i	$0.335562\pi$
$200$	−34.2406	−2.42118
$201$	−8.61255	−0.607483
$202$	9.81965	0.690908
$203$	0	0
$204$	−16.4439	−1.15130
$205$	−21.0604	−1.47092
$206$	−6.57860	−0.458353
$207$	1.00000	0.0695048
$208$	−5.66507	−0.392802
$209$	−15.1520	−1.04809
$210$	0	0
$211$	8.40485	0.578614	0.289307	−	0.957236i	$-0.406575\pi$
$211$	8.40485	0.578614	0.289307	+	0.957236i	$0.406575\pi$
$212$	−9.34067	−0.641520
$213$	6.97110	0.477652
$214$	−44.6225	−3.05033
$215$	−1.38505	−0.0944594
$216$	2.32456	0.158166
$217$	0	0
$218$	−22.9961	−1.55749
$219$	10.6345	0.718612
$220$	31.3965	2.11675
$221$	35.8784	2.41345
$222$	−13.2656	−0.890326
$223$	−11.1980	−0.749872	−0.374936	−	0.927051i	$-0.622335\pi$
$223$	−11.1980	−0.749872	−0.374936	+	0.927051i	$0.622335\pi$
$224$	0	0
$225$	14.7299	0.981996
$226$	29.4297	1.95763
$227$	−20.9943	−1.39344	−0.696719	−	0.717344i	$-0.745358\pi$
$227$	−20.9943	−1.39344	−0.696719	+	0.717344i	$0.745358\pi$
$228$	−19.7568	−1.30842
$229$	−10.1670	−0.671855	−0.335928	−	0.941888i	$-0.609050\pi$
$229$	−10.1670	−0.671855	−0.335928	+	0.941888i	$0.609050\pi$
$230$	9.96781	0.657258
$231$	0	0
$232$	−2.84885	−0.187036
$233$	−7.22594	−0.473387	−0.236694	−	0.971584i	$-0.576064\pi$
$233$	−7.22594	−0.473387	−0.236694	+	0.971584i	$0.576064\pi$
$234$	−14.8644	−0.971717
$235$	−3.85607	−0.251543
$236$	−0.621527	−0.0404580
$237$	6.82320	0.443214
$238$	0	0
$239$	−16.6680	−1.07816	−0.539081	−	0.842254i	$-0.681228\pi$
$239$	−16.6680	−1.07816	−0.539081	+	0.842254i	$0.681228\pi$
$240$	−3.79889	−0.245217
$241$	−11.6655	−0.751443	−0.375722	−	0.926733i	$-0.622605\pi$
$241$	−11.6655	−0.751443	−0.375722	+	0.926733i	$0.622605\pi$
$242$	12.5199	0.804807
$243$	−1.00000	−0.0641500
$244$	−0.409351	−0.0262060
$245$	0	0
$246$	10.6400	0.678382
$247$	43.1066	2.74281
$248$	3.83666	0.243628
$249$	−13.2209	−0.837840
$250$	96.9862	6.13395
$251$	23.2184	1.46553	0.732766	−	0.680481i	$-0.238229\pi$
$251$	23.2184	1.46553	0.732766	+	0.680481i	$0.238229\pi$
$252$	0	0
$253$	−2.32829	−0.146378
$254$	9.76823	0.612914
$255$	24.0594	1.50666
$256$	−10.0757	−0.629730
$257$	18.4683	1.15202	0.576009	−	0.817443i	$-0.304609\pi$
$257$	18.4683	1.15202	0.576009	+	0.817443i	$0.304609\pi$
$258$	0.699743	0.0435641
$259$	0	0
$260$	−89.3215	−5.53949
$261$	1.22555	0.0758594
$262$	−47.0886	−2.90914
$263$	−8.22273	−0.507035	−0.253518	−	0.967331i	$-0.581588\pi$
$263$	−8.22273	−0.507035	−0.253518	+	0.967331i	$0.581588\pi$
$264$	−5.41224	−0.333100
$265$	13.6665	0.839529
$266$	0	0
$267$	−15.6794	−0.959562
$268$	26.1466	1.59716
$269$	−9.75233	−0.594610	−0.297305	−	0.954783i	$-0.596088\pi$
$269$	−9.75233	−0.594610	−0.297305	+	0.954783i	$0.596088\pi$
$270$	−9.96781	−0.606622
$271$	9.74037	0.591686	0.295843	−	0.955237i	$-0.404400\pi$
$271$	9.74037	0.591686	0.295843	+	0.955237i	$0.404400\pi$
$272$	−4.63252	−0.280888
$273$	0	0
$274$	39.6976	2.39822
$275$	−34.2955	−2.06810
$276$	−3.03587	−0.182738
$277$	2.89544	0.173970	0.0869850	−	0.996210i	$-0.472277\pi$
$277$	2.89544	0.173970	0.0869850	+	0.996210i	$0.472277\pi$
$278$	−46.2954	−2.77661
$279$	−1.65049	−0.0988122
$280$	0	0
$281$	−7.28895	−0.434822	−0.217411	−	0.976080i	$-0.569761\pi$
$281$	−7.28895	−0.434822	−0.217411	+	0.976080i	$0.569761\pi$
$282$	1.94814	0.116010
$283$	−28.4924	−1.69370	−0.846849	−	0.531833i	$-0.821503\pi$
$283$	−28.4924	−1.69370	−0.846849	+	0.531833i	$0.821503\pi$
$284$	−21.1633	−1.25581
$285$	28.9065	1.71228
$286$	34.6086	2.04645
$287$	0	0
$288$	6.56836	0.387045
$289$	12.3390	0.725824
$290$	12.2160	0.717349
$291$	6.32960	0.371048
$292$	−32.2849	−1.88933
$293$	2.34546	0.137023	0.0685115	−	0.997650i	$-0.478175\pi$
$293$	2.34546	0.137023	0.0685115	+	0.997650i	$0.478175\pi$
$294$	0	0
$295$	0.909370	0.0529456
$296$	13.7413	0.798699
$297$	2.32829	0.135101
$298$	8.48850	0.491726
$299$	6.62385	0.383067
$300$	−44.7181	−2.58180
$301$	0	0
$302$	21.1954	1.21966
$303$	4.37582	0.251384
$304$	−5.56580	−0.319220
$305$	0.598929	0.0342946
$306$	−12.1551	−0.694863
$307$	15.2646	0.871196	0.435598	−	0.900141i	$-0.356537\pi$
$307$	15.2646	0.871196	0.435598	+	0.900141i	$0.356537\pi$
$308$	0	0
$309$	−2.93155	−0.166770
$310$	−16.4518	−0.934397
$311$	32.5329	1.84477	0.922386	−	0.386269i	$-0.126236\pi$
$311$	32.5329	1.84477	0.922386	+	0.386269i	$0.126236\pi$
$312$	15.3975	0.871714
$313$	−8.79852	−0.497322	−0.248661	−	0.968591i	$-0.579991\pi$
$313$	−8.79852	−0.497322	−0.248661	+	0.968591i	$0.579991\pi$
$314$	−17.5436	−0.990045
$315$	0	0
$316$	−20.7143	−1.16527
$317$	−14.6920	−0.825187	−0.412593	−	0.910915i	$-0.635377\pi$
$317$	−14.6920	−0.825187	−0.412593	+	0.910915i	$0.635377\pi$
$318$	−6.90451	−0.387186
$319$	−2.85342	−0.159761
$320$	57.8744	3.23528
$321$	−19.8846	−1.10985
$322$	0	0
$323$	35.2497	1.96135
$324$	3.03587	0.168659
$325$	97.5690	5.41215
$326$	27.9339	1.54711
$327$	−10.2475	−0.566686
$328$	−11.0216	−0.608566
$329$	0	0
$330$	23.2079	1.27755
$331$	−5.57820	−0.306606	−0.153303	−	0.988179i	$-0.548991\pi$
$331$	−5.57820	−0.306606	−0.153303	+	0.988179i	$0.548991\pi$
$332$	40.1369	2.20280
$333$	−5.91137	−0.323941
$334$	2.40182	0.131422
$335$	−38.2556	−2.09013
$336$	0	0
$337$	−10.8312	−0.590015	−0.295008	−	0.955495i	$-0.595322\pi$
$337$	−10.8312	−0.590015	−0.295008	+	0.955495i	$0.595322\pi$
$338$	−69.2868	−3.76870
$339$	13.1144	0.712276
$340$	−73.0412	−3.96122
$341$	3.84281	0.208100
$342$	−14.6039	−0.789691
$343$	0	0
$344$	−0.724839	−0.0390807
$345$	4.44184	0.239141
$346$	−14.7708	−0.794086
$347$	−16.2578	−0.872766	−0.436383	−	0.899761i	$-0.643741\pi$
$347$	−16.2578	−0.872766	−0.436383	+	0.899761i	$0.643741\pi$
$348$	−3.72059	−0.199445
$349$	23.1851	1.24107	0.620536	−	0.784178i	$-0.286915\pi$
$349$	23.1851	1.24107	0.620536	+	0.784178i	$0.286915\pi$
$350$	0	0
$351$	−6.62385	−0.353555
$352$	−15.2930	−0.815122
$353$	−32.0103	−1.70374	−0.851868	−	0.523757i	$-0.824530\pi$
$353$	−32.0103	−1.70374	−0.851868	+	0.523757i	$0.824530\pi$
$354$	−0.459425	−0.0244182
$355$	30.9645	1.64343
$356$	47.6005	2.52282
$357$	0	0
$358$	−12.5919	−0.665502
$359$	7.88732	0.416277	0.208138	−	0.978099i	$-0.433260\pi$
$359$	7.88732	0.416277	0.208138	+	0.978099i	$0.433260\pi$
$360$	10.3253	0.544192
$361$	23.3513	1.22901
$362$	42.6406	2.24114
$363$	5.57908	0.292826
$364$	0	0
$365$	47.2367	2.47248
$366$	−0.302587	−0.0158165
$367$	20.4185	1.06584	0.532918	−	0.846167i	$-0.321095\pi$
$367$	20.4185	1.06584	0.532918	+	0.846167i	$0.321095\pi$
$368$	−0.855252	−0.0445831
$369$	4.74138	0.246826
$370$	−58.9235	−3.06328
$371$	0	0
$372$	5.01066	0.259791
$373$	25.5705	1.32399	0.661996	−	0.749507i	$-0.269709\pi$
$373$	25.5705	1.32399	0.661996	+	0.749507i	$0.269709\pi$
$374$	28.3006	1.46339
$375$	43.2188	2.23181
$376$	−2.01801	−0.104071
$377$	8.11784	0.418090
$378$	0	0
$379$	10.2246	0.525204	0.262602	−	0.964904i	$-0.415419\pi$
$379$	10.2246	0.525204	0.262602	+	0.964904i	$0.415419\pi$
$380$	−87.7563	−4.50180
$381$	4.35290	0.223006
$382$	1.53664	0.0786212
$383$	4.81269	0.245917	0.122958	−	0.992412i	$-0.460762\pi$
$383$	4.81269	0.245917	0.122958	+	0.992412i	$0.460762\pi$
$384$	−16.1022	−0.821711
$385$	0	0
$386$	−33.4691	−1.70353
$387$	0.311818	0.0158506
$388$	−19.2158	−0.975535
$389$	4.00176	0.202897	0.101449	−	0.994841i	$-0.467652\pi$
$389$	4.00176	0.202897	0.101449	+	0.994841i	$0.467652\pi$
$390$	−66.0253	−3.34332
$391$	5.41655	0.273927
$392$	0	0
$393$	−20.9835	−1.05848
$394$	−11.2352	−0.566021
$395$	30.3075	1.52494
$396$	−7.06837	−0.355199
$397$	14.5264	0.729062	0.364531	−	0.931191i	$-0.381229\pi$
$397$	14.5264	0.729062	0.364531	+	0.931191i	$0.381229\pi$
$398$	−31.2719	−1.56752
$399$	0	0
$400$	−12.5978	−0.629890
$401$	5.29064	0.264202	0.132101	−	0.991236i	$-0.457828\pi$
$401$	5.29064	0.264202	0.132101	+	0.991236i	$0.457828\pi$
$402$	19.3272	0.963953
$403$	−10.9326	−0.544591
$404$	−13.2844	−0.660923
$405$	−4.44184	−0.220717
$406$	0	0
$407$	13.7634	0.682225
$408$	12.5911	0.623352
$409$	21.7746	1.07668	0.538342	−	0.842726i	$-0.319051\pi$
$409$	21.7746	1.07668	0.538342	+	0.842726i	$0.319051\pi$
$410$	47.2612	2.33406
$411$	17.6900	0.872582
$412$	8.89978	0.438461
$413$	0	0
$414$	−2.24407	−0.110290
$415$	−58.7251	−2.88270
$416$	43.5079	2.13315
$417$	−20.6301	−1.01026
$418$	34.0022	1.66310
$419$	17.5761	0.858648	0.429324	−	0.903151i	$-0.358752\pi$
$419$	17.5761	0.858648	0.429324	+	0.903151i	$0.358752\pi$
$420$	0	0
$421$	35.3300	1.72188	0.860939	−	0.508709i	$-0.169877\pi$
$421$	35.3300	1.72188	0.860939	+	0.508709i	$0.169877\pi$
$422$	−18.8611	−0.918144
$423$	0.868126	0.0422097
$424$	7.15214	0.347339
$425$	79.7854	3.87016
$426$	−15.6437	−0.757938
$427$	0	0
$428$	60.3670	2.91795
$429$	15.4222	0.744593
$430$	3.10814	0.149888
$431$	7.57343	0.364799	0.182400	−	0.983224i	$-0.441614\pi$
$431$	7.57343	0.364799	0.182400	+	0.983224i	$0.441614\pi$
$432$	0.855252	0.0411483
$433$	−16.3571	−0.786072	−0.393036	−	0.919523i	$-0.628575\pi$
$433$	−16.3571	−0.786072	−0.393036	+	0.919523i	$0.628575\pi$
$434$	0	0
$435$	5.44368	0.261004
$436$	31.1099	1.48990
$437$	6.50778	0.311310
$438$	−23.8646	−1.14029
$439$	−28.2351	−1.34759	−0.673793	−	0.738920i	$-0.735336\pi$
$439$	−28.2351	−1.34759	−0.673793	+	0.738920i	$0.735336\pi$
$440$	−24.0403	−1.14608
$441$	0	0
$442$	−80.5139	−3.82965
$443$	31.3443	1.48921	0.744605	−	0.667505i	$-0.232638\pi$
$443$	31.3443	1.48921	0.744605	+	0.667505i	$0.232638\pi$
$444$	17.9461	0.851686
$445$	−69.6453	−3.30150
$446$	25.1291	1.18990
$447$	3.78263	0.178912
$448$	0	0
$449$	28.9362	1.36559	0.682793	−	0.730612i	$-0.260765\pi$
$449$	28.9362	1.36559	0.682793	+	0.730612i	$0.260765\pi$
$450$	−33.0551	−1.55823
$451$	−11.0393	−0.519820
$452$	−39.8135	−1.87267
$453$	9.44506	0.443768
$454$	47.1127	2.21111
$455$	0	0
$456$	15.1277	0.708420
$457$	15.9583	0.746496	0.373248	−	0.927732i	$-0.378244\pi$
$457$	15.9583	0.746496	0.373248	+	0.927732i	$0.378244\pi$
$458$	22.8155	1.06610
$459$	−5.41655	−0.252823
$460$	−13.4848	−0.628733
$461$	31.4141	1.46310	0.731550	−	0.681788i	$-0.238797\pi$
$461$	31.4141	1.46310	0.731550	+	0.681788i	$0.238797\pi$
$462$	0	0
$463$	−1.84491	−0.0857404	−0.0428702	−	0.999081i	$-0.513650\pi$
$463$	−1.84491	−0.0857404	−0.0428702	+	0.999081i	$0.513650\pi$
$464$	−1.04815	−0.0486592
$465$	−7.33121	−0.339977
$466$	16.2155	0.751171
$467$	−2.93182	−0.135669	−0.0678343	−	0.997697i	$-0.521609\pi$
$467$	−2.93182	−0.135669	−0.0678343	+	0.997697i	$0.521609\pi$
$468$	20.1091	0.929545
$469$	0	0
$470$	8.65331	0.399148
$471$	−7.81777	−0.360224
$472$	0.475903	0.0219052
$473$	−0.726002	−0.0333816
$474$	−15.3118	−0.703292
$475$	95.8592	4.39832
$476$	0	0
$477$	−3.07677	−0.140876
$478$	37.4042	1.71083
$479$	−26.5733	−1.21417	−0.607083	−	0.794638i	$-0.707661\pi$
$479$	−26.5733	−1.21417	−0.607083	+	0.794638i	$0.707661\pi$
$480$	29.1756	1.33168
$481$	−39.1561	−1.78536
$482$	26.1783	1.19239
$483$	0	0
$484$	−16.9373	−0.769879
$485$	28.1151	1.27664
$486$	2.24407	0.101793
$487$	−1.19973	−0.0543650	−0.0271825	−	0.999630i	$-0.508654\pi$
$487$	−1.19973	−0.0543650	−0.0271825	+	0.999630i	$0.508654\pi$
$488$	0.313439	0.0141887
$489$	12.4478	0.562910
$490$	0	0
$491$	23.9958	1.08292	0.541458	−	0.840728i	$-0.317872\pi$
$491$	23.9958	1.08292	0.541458	+	0.840728i	$0.317872\pi$
$492$	−14.3942	−0.648940
$493$	6.63823	0.298971
$494$	−96.7344	−4.35229
$495$	10.3419	0.464833
$496$	1.41158	0.0633820
$497$	0	0
$498$	29.6687	1.32948
$499$	−0.00378079	−0.000169251 0	−8.46256e−5	−	1.00000i	$-0.500027\pi$
$499$	−0.00378079	−0.000169251 0	−8.46256e−5		1.00000i	$0.500027\pi$
$500$	−131.206	−5.86773
$501$	1.07030	0.0478173
$502$	−52.1038	−2.32550
$503$	−26.6590	−1.18867	−0.594333	−	0.804219i	$-0.702584\pi$
$503$	−26.6590	−1.18867	−0.594333	+	0.804219i	$0.702584\pi$
$504$	0	0
$505$	19.4367	0.864921
$506$	5.22485	0.232273
$507$	−30.8754	−1.37123
$508$	−13.2148	−0.586313
$509$	−11.8688	−0.526073	−0.263037	−	0.964786i	$-0.584724\pi$
$509$	−11.8688	−0.526073	−0.263037	+	0.964786i	$0.584724\pi$
$510$	−53.9912	−2.39077
$511$	0	0
$512$	−9.59377	−0.423989
$513$	−6.50778	−0.287326
$514$	−41.4441	−1.82802
$515$	−13.0215	−0.573794
$516$	−0.946638	−0.0416734
$517$	−2.02125	−0.0888943
$518$	0	0
$519$	−6.58216	−0.288925
$520$	68.3934	2.99925
$521$	−21.6157	−0.947000	−0.473500	−	0.880794i	$-0.657010\pi$
$521$	−21.6157	−0.947000	−0.473500	+	0.880794i	$0.657010\pi$
$522$	−2.75021	−0.120374
$523$	−28.0184	−1.22516	−0.612580	−	0.790408i	$-0.709868\pi$
$523$	−28.0184	−1.22516	−0.612580	+	0.790408i	$0.709868\pi$
$524$	63.7032	2.78289
$525$	0	0
$526$	18.4524	0.804564
$527$	−8.93995	−0.389431
$528$	−1.99127	−0.0866590
$529$	1.00000	0.0434783
$530$	−30.6687	−1.33216
$531$	−0.204728	−0.00888445
$532$	0	0
$533$	31.4062	1.36035
$534$	35.1857	1.52263
$535$	−88.3243	−3.81859
$536$	−20.0204	−0.864749
$537$	−5.61117	−0.242140
$538$	21.8849	0.943527
$539$	0	0
$540$	13.4848	0.580295
$541$	16.9422	0.728403	0.364201	−	0.931320i	$-0.381342\pi$
$541$	16.9422	0.728403	0.364201	+	0.931320i	$0.381342\pi$
$542$	−21.8581	−0.938886
$543$	19.0014	0.815429
$544$	35.5779	1.52539
$545$	−45.5176	−1.94976
$546$	0	0
$547$	−19.2402	−0.822653	−0.411327	−	0.911488i	$-0.634934\pi$
$547$	−19.2402	−0.822653	−0.411327	+	0.911488i	$0.634934\pi$
$548$	−53.7044	−2.29414
$549$	−0.134838	−0.00575475
$550$	76.9617	3.28166
$551$	7.97559	0.339771
$552$	2.32456	0.0989398
$553$	0	0
$554$	−6.49758	−0.276056
$555$	−26.2574	−1.11456
$556$	62.6301	2.65611
$557$	−0.885679	−0.0375274	−0.0187637	−	0.999824i	$-0.505973\pi$
$557$	−0.885679	−0.0375274	−0.0187637	+	0.999824i	$0.505973\pi$
$558$	3.70382	0.156795
$559$	2.06544	0.0873587
$560$	0	0
$561$	12.6113	0.532449
$562$	16.3569	0.689976
$563$	10.7578	0.453387	0.226694	−	0.973966i	$-0.427208\pi$
$563$	10.7578	0.453387	0.226694	+	0.973966i	$0.427208\pi$
$564$	−2.63551	−0.110975
$565$	58.2520	2.45068
$566$	63.9391	2.68756
$567$	0	0
$568$	16.2047	0.679935
$569$	−9.76262	−0.409270	−0.204635	−	0.978838i	$-0.565601\pi$
$569$	−9.76262	−0.409270	−0.204635	+	0.978838i	$0.565601\pi$
$570$	−64.8684	−2.71704
$571$	1.89100	0.0791358	0.0395679	−	0.999217i	$-0.487402\pi$
$571$	1.89100	0.0791358	0.0395679	+	0.999217i	$0.487402\pi$
$572$	−46.8198	−1.95764
$573$	0.684753	0.0286060
$574$	0	0
$575$	14.7299	0.614281
$576$	−13.0294	−0.542891
$577$	−16.9444	−0.705406	−0.352703	−	0.935735i	$-0.614737\pi$
$577$	−16.9444	−0.705406	−0.352703	+	0.935735i	$0.614737\pi$
$578$	−27.6897	−1.15174
$579$	−14.9144	−0.619822
$580$	−16.5263	−0.686216
$581$	0	0
$582$	−14.2041	−0.588778
$583$	7.16362	0.296687
$584$	24.7205	1.02294
$585$	−29.4221	−1.21645
$586$	−5.26338	−0.217428
$587$	8.64168	0.356680	0.178340	−	0.983969i	$-0.442927\pi$
$587$	8.64168	0.356680	0.178340	+	0.983969i	$0.442927\pi$
$588$	0	0
$589$	−10.7410	−0.442576
$590$	−2.04069	−0.0840140
$591$	−5.00661	−0.205944
$592$	5.05571	0.207789
$593$	−26.0558	−1.06998	−0.534991	−	0.844858i	$-0.679685\pi$
$593$	−26.0558	−1.06998	−0.534991	+	0.844858i	$0.679685\pi$
$594$	−5.22485	−0.214378
$595$	0	0
$596$	−11.4836	−0.470385
$597$	−13.9353	−0.570334
$598$	−14.8644	−0.607851
$599$	42.4268	1.73351	0.866757	−	0.498731i	$-0.166200\pi$
$599$	42.4268	1.73351	0.866757	+	0.498731i	$0.166200\pi$
$600$	34.2406	1.39787
$601$	13.3951	0.546397	0.273199	−	0.961958i	$-0.411918\pi$
$601$	13.3951	0.546397	0.273199	+	0.961958i	$0.411918\pi$
$602$	0	0
$603$	8.61255	0.350730
$604$	−28.6739	−1.16673
$605$	24.7814	1.00751
$606$	−9.81965	−0.398896
$607$	22.8819	0.928746	0.464373	−	0.885640i	$-0.346280\pi$
$607$	22.8819	0.928746	0.464373	+	0.885640i	$0.346280\pi$
$608$	42.7455	1.73356
$609$	0	0
$610$	−1.34404	−0.0544187
$611$	5.75034	0.232634
$612$	16.4439	0.664706
$613$	−5.65808	−0.228528	−0.114264	−	0.993450i	$-0.536451\pi$
$613$	−5.65808	−0.228528	−0.114264	+	0.993450i	$0.536451\pi$
$614$	−34.2549	−1.38241
$615$	21.0604	0.849239
$616$	0	0
$617$	31.7080	1.27652	0.638259	−	0.769822i	$-0.279655\pi$
$617$	31.7080	1.27652	0.638259	+	0.769822i	$0.279655\pi$
$618$	6.57860	0.264630
$619$	17.2432	0.693062	0.346531	−	0.938039i	$-0.387360\pi$
$619$	17.2432	0.693062	0.346531	+	0.938039i	$0.387360\pi$
$620$	22.2566	0.893845
$621$	−1.00000	−0.0401286
$622$	−73.0063	−2.92728
$623$	0	0
$624$	5.66507	0.226784
$625$	118.321	4.73285
$626$	19.7445	0.789150
$627$	15.1520	0.605112
$628$	23.7337	0.947078
$629$	−32.0192	−1.27669
$630$	0	0
$631$	−41.6059	−1.65630	−0.828152	−	0.560504i	$-0.810607\pi$
$631$	−41.6059	−1.65630	−0.828152	+	0.560504i	$0.810607\pi$
$632$	15.8609	0.630913
$633$	−8.40485	−0.334063
$634$	32.9700	1.30941
$635$	19.3349	0.767282
$636$	9.34067	0.370382
$637$	0	0
$638$	6.40329	0.253509
$639$	−6.97110	−0.275773
$640$	−71.5233	−2.82721
$641$	−3.28505	−0.129752	−0.0648759	−	0.997893i	$-0.520665\pi$
$641$	−3.28505	−0.129752	−0.0648759	+	0.997893i	$0.520665\pi$
$642$	44.6225	1.76111
$643$	22.4085	0.883705	0.441853	−	0.897088i	$-0.354321\pi$
$643$	22.4085	0.883705	0.441853	+	0.897088i	$0.354321\pi$
$644$	0	0
$645$	1.38505	0.0545361
$646$	−79.1030	−3.11227
$647$	20.4170	0.802677	0.401338	−	0.915930i	$-0.368545\pi$
$647$	20.4170	0.802677	0.401338	+	0.915930i	$0.368545\pi$
$648$	−2.32456	−0.0913173
$649$	0.476666	0.0187108
$650$	−218.952	−8.58800
$651$	0	0
$652$	−37.7899	−1.47997
$653$	−0.686482	−0.0268641	−0.0134321	−	0.999910i	$-0.504276\pi$
$653$	−0.686482	−0.0268641	−0.0134321	+	0.999910i	$0.504276\pi$
$654$	22.9961	0.899217
$655$	−93.2055	−3.64184
$656$	−4.05507	−0.158324
$657$	−10.6345	−0.414891
$658$	0	0
$659$	4.83392	0.188303	0.0941514	−	0.995558i	$-0.469986\pi$
$659$	4.83392	0.188303	0.0941514	+	0.995558i	$0.469986\pi$
$660$	−31.3965	−1.22211
$661$	−25.5702	−0.994564	−0.497282	−	0.867589i	$-0.665669\pi$
$661$	−25.5702	−0.994564	−0.497282	+	0.867589i	$0.665669\pi$
$662$	12.5179	0.486522
$663$	−35.8784	−1.39340
$664$	−30.7327	−1.19266
$665$	0	0
$666$	13.2656	0.514030
$667$	1.22555	0.0474533
$668$	−3.24927	−0.125718
$669$	11.1980	0.432939
$670$	85.8483	3.31661
$671$	0.313942	0.0121196
$672$	0	0
$673$	14.6619	0.565175	0.282587	−	0.959242i	$-0.408807\pi$
$673$	14.6619	0.565175	0.282587	+	0.959242i	$0.408807\pi$
$674$	24.3061	0.936236
$675$	−14.7299	−0.566956
$676$	93.7337	3.60514
$677$	−19.8461	−0.762749	−0.381375	−	0.924421i	$-0.624549\pi$
$677$	−19.8461	−0.762749	−0.381375	+	0.924421i	$0.624549\pi$
$678$	−29.4297	−1.13024
$679$	0	0
$680$	55.9276	2.14472
$681$	20.9943	0.804502
$682$	−8.62355	−0.330213
$683$	−10.3009	−0.394154	−0.197077	−	0.980388i	$-0.563145\pi$
$683$	−10.3009	−0.394154	−0.197077	+	0.980388i	$0.563145\pi$
$684$	19.7568	0.755418
$685$	78.5760	3.00223
$686$	0	0
$687$	10.1670	0.387896
$688$	−0.266683	−0.0101672
$689$	−20.3801	−0.776420
$690$	−9.96781	−0.379468
$691$	23.4018	0.890247	0.445124	−	0.895469i	$-0.353160\pi$
$691$	23.4018	0.890247	0.445124	+	0.895469i	$0.353160\pi$
$692$	19.9825	0.759622
$693$	0	0
$694$	36.4838	1.38491
$695$	−91.6354	−3.47593
$696$	2.84885	0.107985
$697$	25.6819	0.972772
$698$	−52.0292	−1.96933
$699$	7.22594	0.273310
$700$	0	0
$701$	−47.7420	−1.80319	−0.901595	−	0.432581i	$-0.857603\pi$
$701$	−47.7420	−1.80319	−0.901595	+	0.432581i	$0.857603\pi$
$702$	14.8644	0.561021
$703$	−38.4699	−1.45092
$704$	30.3362	1.14334
$705$	3.85607	0.145228
$706$	71.8334	2.70349
$707$	0	0
$708$	0.621527	0.0233584
$709$	−20.1469	−0.756634	−0.378317	−	0.925676i	$-0.623497\pi$
$709$	−20.1469	−0.756634	−0.378317	+	0.925676i	$0.623497\pi$
$710$	−69.4866	−2.60779
$711$	−6.82320	−0.255890
$712$	−36.4476	−1.36593
$713$	−1.65049	−0.0618113
$714$	0	0
$715$	68.5031	2.56187
$716$	17.0348	0.636619
$717$	16.6680	0.622477
$718$	−17.6997	−0.660548
$719$	34.6742	1.29313	0.646565	−	0.762859i	$-0.276205\pi$
$719$	34.6742	1.29313	0.646565	+	0.762859i	$0.276205\pi$
$720$	3.79889	0.141576
$721$	0	0
$722$	−52.4019	−1.95020
$723$	11.6655	0.433846
$724$	−57.6857	−2.14387
$725$	18.0522	0.670442
$726$	−12.5199	−0.464656
$727$	−37.0801	−1.37523	−0.687613	−	0.726077i	$-0.741341\pi$
$727$	−37.0801	−1.37523	−0.687613	+	0.726077i	$0.741341\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−106.003	−3.92333
$731$	1.68898	0.0624691
$732$	0.409351	0.0151300
$733$	−36.8990	−1.36290	−0.681448	−	0.731866i	$-0.738650\pi$
$733$	−36.8990	−1.36290	−0.681448	+	0.731866i	$0.738650\pi$
$734$	−45.8206	−1.69127
$735$	0	0
$736$	6.56836	0.242113
$737$	−20.0525	−0.738643
$738$	−10.6400	−0.391664
$739$	−31.1337	−1.14527	−0.572636	−	0.819810i	$-0.694079\pi$
$739$	−31.1337	−1.14527	−0.572636	+	0.819810i	$0.694079\pi$
$740$	79.7138	2.93034
$741$	−43.1066	−1.58356
$742$	0	0
$743$	−15.7280	−0.577004	−0.288502	−	0.957479i	$-0.593157\pi$
$743$	−15.7280	−0.577004	−0.288502	+	0.957479i	$0.593157\pi$
$744$	−3.83666	−0.140659
$745$	16.8018	0.615572
$746$	−57.3822	−2.10091
$747$	13.2209	0.483727
$748$	−38.2862	−1.39988
$749$	0	0
$750$	−96.9862	−3.54143
$751$	6.56721	0.239641	0.119820	−	0.992796i	$-0.461768\pi$
$751$	6.56721	0.239641	0.119820	+	0.992796i	$0.461768\pi$
$752$	−0.742466	−0.0270750
$753$	−23.2184	−0.846125
$754$	−18.2170	−0.663425
$755$	41.9535	1.52684
$756$	0	0
$757$	−11.5504	−0.419806	−0.209903	−	0.977722i	$-0.567315\pi$
$757$	−11.5504	−0.419806	−0.209903	+	0.977722i	$0.567315\pi$
$758$	−22.9448	−0.833393
$759$	2.32829	0.0845115
$760$	67.1949	2.43742
$761$	−36.1319	−1.30978	−0.654890	−	0.755724i	$-0.727285\pi$
$761$	−36.1319	−1.30978	−0.654890	+	0.755724i	$0.727285\pi$
$762$	−9.76823	−0.353866
$763$	0	0
$764$	−2.07882	−0.0752090
$765$	−24.0594	−0.869871
$766$	−10.8000	−0.390221
$767$	−1.35609	−0.0489656
$768$	10.0757	0.363575
$769$	−49.0953	−1.77042	−0.885210	−	0.465191i	$-0.845986\pi$
$769$	−49.0953	−1.77042	−0.885210	+	0.465191i	$0.845986\pi$
$770$	0	0
$771$	−18.4683	−0.665118
$772$	45.2782	1.62960
$773$	−18.7199	−0.673307	−0.336653	−	0.941629i	$-0.609295\pi$
$773$	−18.7199	−0.673307	−0.336653	+	0.941629i	$0.609295\pi$
$774$	−0.699743	−0.0251517
$775$	−24.3116	−0.873298
$776$	14.7135	0.528185
$777$	0	0
$778$	−8.98024	−0.321957
$779$	30.8559	1.10553
$780$	89.3215	3.19822
$781$	16.2307	0.580781
$782$	−12.1551	−0.434667
$783$	−1.22555	−0.0437974
$784$	0	0
$785$	−34.7253	−1.23940
$786$	47.0886	1.67959
$787$	−22.3031	−0.795018	−0.397509	−	0.917598i	$-0.630125\pi$
$787$	−22.3031	−0.795018	−0.397509	+	0.917598i	$0.630125\pi$
$788$	15.1994	0.541456
$789$	8.22273	0.292737
$790$	−68.0124	−2.41977
$791$	0	0
$792$	5.41224	0.192316
$793$	−0.893148	−0.0317166
$794$	−32.5984	−1.15687
$795$	−13.6665	−0.484702
$796$	42.3057	1.49949
$797$	−4.11023	−0.145592	−0.0727960	−	0.997347i	$-0.523192\pi$
$797$	−4.11023	−0.145592	−0.0727960	+	0.997347i	$0.523192\pi$
$798$	0	0
$799$	4.70225	0.166354
$800$	96.7516	3.42069
$801$	15.6794	0.554004
$802$	−11.8726	−0.419236
$803$	24.7601	0.873766
$804$	−26.1466	−0.922118
$805$	0	0
$806$	24.5335	0.864157
$807$	9.75233	0.343298
$808$	10.1718	0.357844
$809$	38.3080	1.34684	0.673419	−	0.739261i	$-0.264825\pi$
$809$	38.3080	1.34684	0.673419	+	0.739261i	$0.264825\pi$
$810$	9.96781	0.350233
$811$	43.1899	1.51660	0.758302	−	0.651904i	$-0.226029\pi$
$811$	43.1899	1.51660	0.758302	+	0.651904i	$0.226029\pi$
$812$	0	0
$813$	−9.74037	−0.341610
$814$	−30.8860	−1.08255
$815$	55.2913	1.93677
$816$	4.63252	0.162170
$817$	2.02925	0.0709943
$818$	−48.8638	−1.70848
$819$	0	0
$820$	−63.9367	−2.23276
$821$	−31.6981	−1.10627	−0.553136	−	0.833091i	$-0.686569\pi$
$821$	−31.6981	−1.10627	−0.553136	+	0.833091i	$0.686569\pi$
$822$	−39.6976	−1.38461
$823$	−18.4147	−0.641898	−0.320949	−	0.947097i	$-0.604002\pi$
$823$	−18.4147	−0.641898	−0.320949	+	0.947097i	$0.604002\pi$
$824$	−6.81455	−0.237396
$825$	34.2955	1.19402
$826$	0	0
$827$	−43.6619	−1.51827	−0.759137	−	0.650931i	$-0.774379\pi$
$827$	−43.6619	−1.51827	−0.759137	+	0.650931i	$0.774379\pi$
$828$	3.03587	0.105504
$829$	22.4734	0.780533	0.390266	−	0.920702i	$-0.372383\pi$
$829$	22.4734	0.780533	0.390266	+	0.920702i	$0.372383\pi$
$830$	131.783	4.57427
$831$	−2.89544	−0.100442
$832$	−86.3048	−2.99208
$833$	0	0
$834$	46.2954	1.60308
$835$	4.75408	0.164522
$836$	−45.9994	−1.59092
$837$	1.65049	0.0570492
$838$	−39.4420	−1.36250
$839$	18.1056	0.625074	0.312537	−	0.949906i	$-0.398821\pi$
$839$	18.1056	0.625074	0.312537	+	0.949906i	$0.398821\pi$
$840$	0	0
$841$	−27.4980	−0.948208
$842$	−79.2831	−2.73227
$843$	7.28895	0.251045
$844$	25.5160	0.878297
$845$	−137.144	−4.71789
$846$	−1.94814	−0.0669784
$847$	0	0
$848$	2.63142	0.0903633
$849$	28.4924	0.977857
$850$	−179.044	−6.14117
$851$	−5.91137	−0.202639
$852$	21.1633	0.725044
$853$	31.3236	1.07250	0.536249	−	0.844060i	$-0.319841\pi$
$853$	31.3236	1.07250	0.536249	+	0.844060i	$0.319841\pi$
$854$	0	0
$855$	−28.9065	−0.988582
$856$	−46.2230	−1.57987
$857$	−29.0584	−0.992617	−0.496309	−	0.868146i	$-0.665312\pi$
$857$	−29.0584	−0.992617	−0.496309	+	0.868146i	$0.665312\pi$
$858$	−34.6086	−1.18152
$859$	−23.3532	−0.796799	−0.398400	−	0.917212i	$-0.630434\pi$
$859$	−23.3532	−0.796799	−0.398400	+	0.917212i	$0.630434\pi$
$860$	−4.20481	−0.143383
$861$	0	0
$862$	−16.9953	−0.578863
$863$	44.0945	1.50100	0.750498	−	0.660873i	$-0.229814\pi$
$863$	44.0945	1.50100	0.750498	+	0.660873i	$0.229814\pi$
$864$	−6.56836	−0.223460
$865$	−29.2369	−0.994084
$866$	36.7065	1.24734
$867$	−12.3390	−0.419055
$868$	0	0
$869$	15.8864	0.538908
$870$	−12.2160	−0.414162
$871$	57.0483	1.93301
$872$	−23.8208	−0.806675
$873$	−6.32960	−0.214225
$874$	−14.6039	−0.493986
$875$	0	0
$876$	32.2849	1.09080
$877$	−8.30360	−0.280393	−0.140196	−	0.990124i	$-0.544773\pi$
$877$	−8.30360	−0.280393	−0.140196	+	0.990124i	$0.544773\pi$
$878$	63.3616	2.13835
$879$	−2.34546	−0.0791103
$880$	−8.84491	−0.298162
$881$	−13.2926	−0.447839	−0.223919	−	0.974608i	$-0.571885\pi$
$881$	−13.2926	−0.447839	−0.223919	+	0.974608i	$0.571885\pi$
$882$	0	0
$883$	27.8661	0.937767	0.468884	−	0.883260i	$-0.344656\pi$
$883$	27.8661	0.937767	0.468884	+	0.883260i	$0.344656\pi$
$884$	108.922	3.66345
$885$	−0.909370	−0.0305681
$886$	−70.3388	−2.36308
$887$	−8.25357	−0.277128	−0.138564	−	0.990354i	$-0.544249\pi$
$887$	−8.25357	−0.277128	−0.138564	+	0.990354i	$0.544249\pi$
$888$	−13.7413	−0.461129
$889$	0	0
$890$	156.289	5.23882
$891$	−2.32829	−0.0780006
$892$	−33.9956	−1.13826
$893$	5.64957	0.189056
$894$	−8.48850	−0.283898
$895$	−24.9239	−0.833115
$896$	0	0
$897$	−6.62385	−0.221164
$898$	−64.9351	−2.16691
$899$	−2.02275	−0.0674625
$900$	44.7181	1.49060
$901$	−16.6655	−0.555208
$902$	24.7730	0.824850
$903$	0	0
$904$	30.4852	1.01392
$905$	84.4012	2.80559
$906$	−21.1954	−0.704171
$907$	29.0473	0.964501	0.482250	−	0.876033i	$-0.339820\pi$
$907$	29.0473	0.964501	0.482250	+	0.876033i	$0.339820\pi$
$908$	−63.7358	−2.11515
$909$	−4.37582	−0.145137
$910$	0	0
$911$	−29.3336	−0.971866	−0.485933	−	0.873996i	$-0.661520\pi$
$911$	−29.3336	−0.971866	−0.485933	+	0.873996i	$0.661520\pi$
$912$	5.56580	0.184302
$913$	−30.7820	−1.01874
$914$	−35.8115	−1.18454
$915$	−0.598929	−0.0198000
$916$	−30.8657	−1.01983
$917$	0	0
$918$	12.1551	0.401179
$919$	13.0477	0.430404	0.215202	−	0.976570i	$-0.430959\pi$
$919$	13.0477	0.430404	0.215202	+	0.976570i	$0.430959\pi$
$920$	10.3253	0.340415
$921$	−15.2646	−0.502986
$922$	−70.4955	−2.32165
$923$	−46.1756	−1.51989
$924$	0	0
$925$	−87.0741	−2.86298
$926$	4.14012	0.136053
$927$	2.93155	0.0962846
$928$	8.04983	0.264249
$929$	−17.5058	−0.574347	−0.287174	−	0.957879i	$-0.592716\pi$
$929$	−17.5058	−0.574347	−0.287174	+	0.957879i	$0.592716\pi$
$930$	16.4518	0.539475
$931$	0	0
$932$	−21.9370	−0.718570
$933$	−32.5329	−1.06508
$934$	6.57923	0.215279
$935$	56.0173	1.83196
$936$	−15.3975	−0.503284
$937$	−22.9983	−0.751322	−0.375661	−	0.926757i	$-0.622584\pi$
$937$	−22.9983	−0.751322	−0.375661	+	0.926757i	$0.622584\pi$
$938$	0	0
$939$	8.79852	0.287129
$940$	−11.7065	−0.381825
$941$	38.7996	1.26483	0.632415	−	0.774630i	$-0.282064\pi$
$941$	38.7996	1.26483	0.632415	+	0.774630i	$0.282064\pi$
$942$	17.5436	0.571603
$943$	4.74138	0.154401
$944$	0.175094	0.00569883
$945$	0	0
$946$	1.62920	0.0529699
$947$	−10.4328	−0.339019	−0.169510	−	0.985529i	$-0.554218\pi$
$947$	−10.4328	−0.339019	−0.169510	+	0.985529i	$0.554218\pi$
$948$	20.7143	0.672769
$949$	−70.4413	−2.28662
$950$	−215.115	−6.97926
$951$	14.6920	0.476422
$952$	0	0
$953$	40.2446	1.30365	0.651825	−	0.758370i	$-0.274004\pi$
$953$	40.2446	1.30365	0.651825	+	0.758370i	$0.274004\pi$
$954$	6.90451	0.223542
$955$	3.04156	0.0984227
$956$	−50.6018	−1.63658
$957$	2.85342	0.0922381
$958$	59.6325	1.92664
$959$	0	0
$960$	−57.8744	−1.86789
$961$	−28.2759	−0.912125
$962$	87.8691	2.83301
$963$	19.8846	0.640773
$964$	−35.4150	−1.14064
$965$	−66.2475	−2.13258
$966$	0	0
$967$	50.2630	1.61635	0.808175	−	0.588943i	$-0.200456\pi$
$967$	50.2630	1.61635	0.808175	+	0.588943i	$0.200456\pi$
$968$	12.9689	0.416836
$969$	−35.2497	−1.13238
$970$	−63.0923	−2.02577
$971$	57.8038	1.85501	0.927506	−	0.373808i	$-0.121948\pi$
$971$	57.8038	1.85501	0.927506	+	0.373808i	$0.121948\pi$
$972$	−3.03587	−0.0973754
$973$	0	0
$974$	2.69228	0.0862663
$975$	−97.5690	−3.12471
$976$	0.115321	0.00369132
$977$	0.550666	0.0176174	0.00880868	−	0.999961i	$-0.497196\pi$
$977$	0.550666	0.0176174	0.00880868	+	0.999961i	$0.497196\pi$
$978$	−27.9339	−0.893226
$979$	−36.5061	−1.16674
$980$	0	0
$981$	10.2475	0.327176
$982$	−53.8484	−1.71837
$983$	22.7867	0.726784	0.363392	−	0.931636i	$-0.381619\pi$
$983$	22.7867	0.726784	0.363392	+	0.931636i	$0.381619\pi$
$984$	11.0216	0.351356
$985$	−22.2385	−0.708579
$986$	−14.8967	−0.474407
$987$	0	0
$988$	130.866	4.16340
$989$	0.311818	0.00991524
$990$	−23.2079	−0.737597
$991$	55.3661	1.75876	0.879381	−	0.476119i	$-0.157957\pi$
$991$	55.3661	1.75876	0.879381	+	0.476119i	$0.157957\pi$
$992$	−10.8410	−0.344202
$993$	5.57820	0.177019
$994$	0	0
$995$	−61.8984	−1.96231
$996$	−40.1369	−1.27179
$997$	−5.83960	−0.184942	−0.0924710	−	0.995715i	$-0.529477\pi$
$997$	−5.83960	−0.184942	−0.0924710	+	0.995715i	$0.529477\pi$
$998$	0.00848436	0.000268568 0
$999$	5.91137	0.187028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bg.1.2	✓	10
7.6	odd	2		3381.2.a.bh.1.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bg.1.2	✓	10	1.1	even	1	trivial
3381.2.a.bh.1.2	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)

\(f(q)\)	\(=\)	\(q-2.24407 q^{2} -1.00000 q^{3} +3.03587 q^{4} -4.44184 q^{5} +2.24407 q^{6} -2.32456 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.24407 q^{2} -1.00000 q^{3} +3.03587 q^{4} -4.44184 q^{5} +2.24407 q^{6} -2.32456 q^{8} +1.00000 q^{9} +9.96781 q^{10} -2.32829 q^{11} -3.03587 q^{12} +6.62385 q^{13} +4.44184 q^{15} -0.855252 q^{16} +5.41655 q^{17} -2.24407 q^{18} +6.50778 q^{19} -13.4848 q^{20} +5.22485 q^{22} +1.00000 q^{23} +2.32456 q^{24} +14.7299 q^{25} -14.8644 q^{26} -1.00000 q^{27} +1.22555 q^{29} -9.96781 q^{30} -1.65049 q^{31} +6.56836 q^{32} +2.32829 q^{33} -12.1551 q^{34} +3.03587 q^{36} -5.91137 q^{37} -14.6039 q^{38} -6.62385 q^{39} +10.3253 q^{40} +4.74138 q^{41} +0.311818 q^{43} -7.06837 q^{44} -4.44184 q^{45} -2.24407 q^{46} +0.868126 q^{47} +0.855252 q^{48} -33.0551 q^{50} -5.41655 q^{51} +20.1091 q^{52} -3.07677 q^{53} +2.24407 q^{54} +10.3419 q^{55} -6.50778 q^{57} -2.75021 q^{58} -0.204728 q^{59} +13.4848 q^{60} -0.134838 q^{61} +3.70382 q^{62} -13.0294 q^{64} -29.4221 q^{65} -5.22485 q^{66} +8.61255 q^{67} +16.4439 q^{68} -1.00000 q^{69} -6.97110 q^{71} -2.32456 q^{72} -10.6345 q^{73} +13.2656 q^{74} -14.7299 q^{75} +19.7568 q^{76} +14.8644 q^{78} -6.82320 q^{79} +3.79889 q^{80} +1.00000 q^{81} -10.6400 q^{82} +13.2209 q^{83} -24.0594 q^{85} -0.699743 q^{86} -1.22555 q^{87} +5.41224 q^{88} +15.6794 q^{89} +9.96781 q^{90} +3.03587 q^{92} +1.65049 q^{93} -1.94814 q^{94} -28.9065 q^{95} -6.56836 q^{96} -6.32960 q^{97} -2.32829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 10 * q^3 + 8 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 + 10 * q^9	\( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9} + 8 q^{10} - 2 q^{11} - 8 q^{12} + 16 q^{13} - 4 q^{15} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 26 q^{19} - 8 q^{22} + 10 q^{23} + 12 q^{24} + 14 q^{25} - 12 q^{26} - 10 q^{27} - 16 q^{29} - 8 q^{30} + 20 q^{31} - 8 q^{32} + 2 q^{33} - 4 q^{34} + 8 q^{36} + 8 q^{37} - 8 q^{38} - 16 q^{39} - 12 q^{40} + 22 q^{41} - 4 q^{43} - 24 q^{44} + 4 q^{45} - 4 q^{46} + 6 q^{47} - 4 q^{48} - 48 q^{50} - 12 q^{51} + 24 q^{52} - 30 q^{53} + 4 q^{54} + 48 q^{55} - 26 q^{57} + 24 q^{58} + 42 q^{59} + 14 q^{61} + 40 q^{62} + 8 q^{64} - 44 q^{65} + 8 q^{66} + 8 q^{68} - 10 q^{69} + 8 q^{71} - 12 q^{72} + 24 q^{73} + 8 q^{74} - 14 q^{75} + 32 q^{76} + 12 q^{78} + 32 q^{79} + 28 q^{80} + 10 q^{81} - 64 q^{82} + 28 q^{83} - 4 q^{85} - 4 q^{86} + 16 q^{87} + 20 q^{88} + 8 q^{90} + 8 q^{92} - 20 q^{93} + 8 q^{94} - 16 q^{95} + 8 q^{96} - 12 q^{97} - 2 q^{99}+O(q^{100}) \) 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 + 16 * q^13 - 4 * q^15 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 26 * q^19 - 8 * q^22 + 10 * q^23 + 12 * q^24 + 14 * q^25 - 12 * q^26 - 10 * q^27 - 16 * q^29 - 8 * q^30 + 20 * q^31 - 8 * q^32 + 2 * q^33 - 4 * q^34 + 8 * q^36 + 8 * q^37 - 8 * q^38 - 16 * q^39 - 12 * q^40 + 22 * q^41 - 4 * q^43 - 24 * q^44 + 4 * q^45 - 4 * q^46 + 6 * q^47 - 4 * q^48 - 48 * q^50 - 12 * q^51 + 24 * q^52 - 30 * q^53 + 4 * q^54 + 48 * q^55 - 26 * q^57 + 24 * q^58 + 42 * q^59 + 14 * q^61 + 40 * q^62 + 8 * q^64 - 44 * q^65 + 8 * q^66 + 8 * q^68 - 10 * q^69 + 8 * q^71 - 12 * q^72 + 24 * q^73 + 8 * q^74 - 14 * q^75 + 32 * q^76 + 12 * q^78 + 32 * q^79 + 28 * q^80 + 10 * q^81 - 64 * q^82 + 28 * q^83 - 4 * q^85 - 4 * q^86 + 16 * q^87 + 20 * q^88 + 8 * q^90 + 8 * q^92 - 20 * q^93 + 8 * q^94 - 16 * q^95 + 8 * q^96 - 12 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

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Database

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