LMFDB - Embedded newform 2695.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
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} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 30x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 30*x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.62366$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62366 q^{2} -3.16125 q^{3} +4.88361 q^{4} +1.00000 q^{5} +8.29406 q^{6} -7.56562 q^{8} +6.99351 q^{9} +O(q^{10})$	\(q-2.62366 q^{2} -3.16125 q^{3} +4.88361 q^{4} +1.00000 q^{5} +8.29406 q^{6} -7.56562 q^{8} +6.99351 q^{9} -2.62366 q^{10} +1.00000 q^{11} -15.4383 q^{12} +2.92390 q^{13} -3.16125 q^{15} +10.0824 q^{16} -4.34355 q^{17} -18.3486 q^{18} +4.16701 q^{19} +4.88361 q^{20} -2.62366 q^{22} +7.46567 q^{23} +23.9168 q^{24} +1.00000 q^{25} -7.67132 q^{26} -12.6245 q^{27} -1.51081 q^{29} +8.29406 q^{30} -7.31788 q^{31} -11.3216 q^{32} -3.16125 q^{33} +11.3960 q^{34} +34.1536 q^{36} -11.4093 q^{37} -10.9328 q^{38} -9.24317 q^{39} -7.56562 q^{40} -9.30762 q^{41} +6.10291 q^{43} +4.88361 q^{44} +6.99351 q^{45} -19.5874 q^{46} -0.486833 q^{47} -31.8730 q^{48} -2.62366 q^{50} +13.7311 q^{51} +14.2792 q^{52} -14.0089 q^{53} +33.1224 q^{54} +1.00000 q^{55} -13.1730 q^{57} +3.96384 q^{58} -10.8022 q^{59} -15.4383 q^{60} +6.41820 q^{61} +19.1996 q^{62} +9.53929 q^{64} +2.92390 q^{65} +8.29406 q^{66} +5.11104 q^{67} -21.2122 q^{68} -23.6009 q^{69} +4.63039 q^{71} -52.9102 q^{72} +5.56874 q^{73} +29.9342 q^{74} -3.16125 q^{75} +20.3501 q^{76} +24.2510 q^{78} +1.62385 q^{79} +10.0824 q^{80} +18.9287 q^{81} +24.4200 q^{82} -3.35483 q^{83} -4.34355 q^{85} -16.0120 q^{86} +4.77604 q^{87} -7.56562 q^{88} -2.74617 q^{89} -18.3486 q^{90} +36.4594 q^{92} +23.1337 q^{93} +1.27729 q^{94} +4.16701 q^{95} +35.7905 q^{96} +4.34662 q^{97} +6.99351 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9	$ 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9} - 2 q^{10} + 10 q^{11} - 20 q^{12} - 8 q^{13} - 8 q^{15} + 6 q^{16} - 28 q^{17} - 14 q^{18} + 10 q^{20} - 2 q^{22} - 16 q^{23} + 8 q^{24} + 10 q^{25} - 20 q^{26} - 32 q^{27} - 4 q^{30} - 20 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} + 42 q^{36} - 36 q^{37} - 24 q^{38} + 24 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{43} + 10 q^{44} + 10 q^{45} - 4 q^{46} - 12 q^{47} - 40 q^{48} - 2 q^{50} + 20 q^{51} - 4 q^{52} - 16 q^{53} + 48 q^{54} + 10 q^{55} + 4 q^{57} + 16 q^{58} - 32 q^{59} - 20 q^{60} + 16 q^{61} + 4 q^{62} - 34 q^{64} - 8 q^{65} - 4 q^{66} - 20 q^{67} - 32 q^{68} - 28 q^{69} + 12 q^{71} - 2 q^{72} - 20 q^{73} + 32 q^{74} - 8 q^{75} - 12 q^{76} + 20 q^{78} + 12 q^{79} + 6 q^{80} + 42 q^{81} + 40 q^{82} - 8 q^{83} - 28 q^{85} - 4 q^{86} - 28 q^{87} - 6 q^{88} - 68 q^{89} - 14 q^{90} + 32 q^{92} - 32 q^{93} - 16 q^{94} + 80 q^{96} - 36 q^{97} + 10 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9 - 2 * q^10 + 10 * q^11 - 20 * q^12 - 8 * q^13 - 8 * q^15 + 6 * q^16 - 28 * q^17 - 14 * q^18 + 10 * q^20 - 2 * q^22 - 16 * q^23 + 8 * q^24 + 10 * q^25 - 20 * q^26 - 32 * q^27 - 4 * q^30 - 20 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 + 42 * q^36 - 36 * q^37 - 24 * q^38 + 24 * q^39 - 6 * q^40 - 36 * q^41 - 4 * q^43 + 10 * q^44 + 10 * q^45 - 4 * q^46 - 12 * q^47 - 40 * q^48 - 2 * q^50 + 20 * q^51 - 4 * q^52 - 16 * q^53 + 48 * q^54 + 10 * q^55 + 4 * q^57 + 16 * q^58 - 32 * q^59 - 20 * q^60 + 16 * q^61 + 4 * q^62 - 34 * q^64 - 8 * q^65 - 4 * q^66 - 20 * q^67 - 32 * q^68 - 28 * q^69 + 12 * q^71 - 2 * q^72 - 20 * q^73 + 32 * q^74 - 8 * q^75 - 12 * q^76 + 20 * q^78 + 12 * q^79 + 6 * q^80 + 42 * q^81 + 40 * q^82 - 8 * q^83 - 28 * q^85 - 4 * q^86 - 28 * q^87 - 6 * q^88 - 68 * q^89 - 14 * q^90 + 32 * q^92 - 32 * q^93 - 16 * q^94 + 80 * q^96 - 36 * q^97 + 10 * 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 $

$2$	−2.62366	−1.85521	−0.927605	−	0.373563i	$-0.878136\pi$
$2$	−2.62366	−1.85521	−0.927605	+	0.373563i	$0.878136\pi$
$3$	−3.16125	−1.82515	−0.912575	−	0.408910i	$-0.865909\pi$
$3$	−3.16125	−1.82515	−0.912575	+	0.408910i	$0.865909\pi$
$4$	4.88361	2.44180
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	8.29406	3.38604
$7$	0	0
$7$	0	0
$8$	−7.56562	−2.67485
$9$	6.99351	2.33117
$10$	−2.62366	−0.829675
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−15.4383	−4.45666
$13$	2.92390	0.810943	0.405471	−	0.914108i	$-0.367107\pi$
$13$	2.92390	0.810943	0.405471	+	0.914108i	$0.367107\pi$
$14$	0	0
$15$	−3.16125	−0.816232
$16$	10.0824	2.52060
$17$	−4.34355	−1.05347	−0.526733	−	0.850031i	$-0.676583\pi$
$17$	−4.34355	−1.05347	−0.526733	+	0.850031i	$0.676583\pi$
$18$	−18.3486	−4.32481
$19$	4.16701	0.955978	0.477989	−	0.878366i	$-0.341366\pi$
$19$	4.16701	0.955978	0.477989	+	0.878366i	$0.341366\pi$
$20$	4.88361	1.09201
$21$	0	0
$22$	−2.62366	−0.559367
$23$	7.46567	1.55670	0.778350	−	0.627831i	$-0.216057\pi$
$23$	7.46567	1.55670	0.778350	+	0.627831i	$0.216057\pi$
$24$	23.9168	4.88200
$25$	1.00000	0.200000
$26$	−7.67132	−1.50447
$27$	−12.6245	−2.42959
$28$	0	0
$29$	−1.51081	−0.280549	−0.140275	−	0.990113i	$-0.544799\pi$
$29$	−1.51081	−0.280549	−0.140275	+	0.990113i	$0.544799\pi$
$30$	8.29406	1.51428
$31$	−7.31788	−1.31433	−0.657165	−	0.753747i	$-0.728244\pi$
$31$	−7.31788	−1.31433	−0.657165	+	0.753747i	$0.728244\pi$
$32$	−11.3216	−2.00140
$33$	−3.16125	−0.550303
$34$	11.3960	1.95440
$35$	0	0
$36$	34.1536	5.69226
$37$	−11.4093	−1.87568	−0.937842	−	0.347064i	$-0.887179\pi$
$37$	−11.4093	−1.87568	−0.937842	+	0.347064i	$0.887179\pi$
$38$	−10.9328	−1.77354
$39$	−9.24317	−1.48009
$40$	−7.56562	−1.19623
$41$	−9.30762	−1.45361	−0.726803	−	0.686846i	$-0.758995\pi$
$41$	−9.30762	−1.45361	−0.726803	+	0.686846i	$0.758995\pi$
$42$	0	0
$43$	6.10291	0.930685	0.465342	−	0.885131i	$-0.345931\pi$
$43$	6.10291	0.930685	0.465342	+	0.885131i	$0.345931\pi$
$44$	4.88361	0.736232
$45$	6.99351	1.04253
$46$	−19.5874	−2.88800
$47$	−0.486833	−0.0710119	−0.0355059	−	0.999369i	$-0.511304\pi$
$47$	−0.486833	−0.0710119	−0.0355059	+	0.999369i	$0.511304\pi$
$48$	−31.8730	−4.60048
$49$	0	0
$50$	−2.62366	−0.371042
$51$	13.7311	1.92273
$52$	14.2792	1.98016
$53$	−14.0089	−1.92427	−0.962134	−	0.272576i	$-0.912125\pi$
$53$	−14.0089	−1.92427	−0.962134	+	0.272576i	$0.912125\pi$
$54$	33.1224	4.50739
$55$	1.00000	0.134840
$56$	0	0
$57$	−13.1730	−1.74480
$58$	3.96384	0.520478
$59$	−10.8022	−1.40633	−0.703164	−	0.711028i	$-0.748230\pi$
$59$	−10.8022	−1.40633	−0.703164	+	0.711028i	$0.748230\pi$
$60$	−15.4383	−1.99308
$61$	6.41820	0.821767	0.410883	−	0.911688i	$-0.365220\pi$
$61$	6.41820	0.821767	0.410883	+	0.911688i	$0.365220\pi$
$62$	19.1996	2.43836
$63$	0	0
$64$	9.53929	1.19241
$65$	2.92390	0.362665
$66$	8.29406	1.02093
$67$	5.11104	0.624413	0.312207	−	0.950014i	$-0.398932\pi$
$67$	5.11104	0.624413	0.312207	+	0.950014i	$0.398932\pi$
$68$	−21.2122	−2.57236
$69$	−23.6009	−2.84121
$70$	0	0
$71$	4.63039	0.549526	0.274763	−	0.961512i	$-0.411401\pi$
$71$	4.63039	0.549526	0.274763	+	0.961512i	$0.411401\pi$
$72$	−52.9102	−6.23553
$73$	5.56874	0.651771	0.325886	−	0.945409i	$-0.394338\pi$
$73$	5.56874	0.651771	0.325886	+	0.945409i	$0.394338\pi$
$74$	29.9342	3.47979
$75$	−3.16125	−0.365030
$76$	20.3501	2.33431
$77$	0	0
$78$	24.2510	2.74588
$79$	1.62385	0.182697	0.0913487	−	0.995819i	$-0.470882\pi$
$79$	1.62385	0.182697	0.0913487	+	0.995819i	$0.470882\pi$
$80$	10.0824	1.12725
$81$	18.9287	2.10319
$82$	24.4200	2.69674
$83$	−3.35483	−0.368241	−0.184120	−	0.982904i	$-0.558944\pi$
$83$	−3.35483	−0.368241	−0.184120	+	0.982904i	$0.558944\pi$
$84$	0	0
$85$	−4.34355	−0.471124
$86$	−16.0120	−1.72662
$87$	4.77604	0.512045
$88$	−7.56562	−0.806497
$89$	−2.74617	−0.291094	−0.145547	−	0.989351i	$-0.546494\pi$
$89$	−2.74617	−0.291094	−0.145547	+	0.989351i	$0.546494\pi$
$90$	−18.3486	−1.93411
$91$	0	0
$92$	36.4594	3.80115
$93$	23.1337	2.39885
$94$	1.27729	0.131742
$95$	4.16701	0.427526
$96$	35.7905	3.65285
$97$	4.34662	0.441333	0.220666	−	0.975349i	$-0.429177\pi$
$97$	4.34662	0.441333	0.220666	+	0.975349i	$0.429177\pi$
$98$	0	0
$99$	6.99351	0.702874
$100$	4.88361	0.488361
$101$	−6.42012	−0.638826	−0.319413	−	0.947616i	$-0.603486\pi$
$101$	−6.42012	−0.638826	−0.319413	+	0.947616i	$0.603486\pi$
$102$	−36.0257	−3.56707
$103$	−15.4170	−1.51908	−0.759539	−	0.650462i	$-0.774575\pi$
$103$	−15.4170	−1.51908	−0.759539	+	0.650462i	$0.774575\pi$
$104$	−22.1211	−2.16915
$105$	0	0
$106$	36.7546	3.56992
$107$	17.2574	1.66833	0.834166	−	0.551514i	$-0.185950\pi$
$107$	17.2574	1.66833	0.834166	+	0.551514i	$0.185950\pi$
$108$	−61.6531	−5.93257
$109$	15.3963	1.47469	0.737347	−	0.675514i	$-0.236078\pi$
$109$	15.3963	1.47469	0.737347	+	0.675514i	$0.236078\pi$
$110$	−2.62366	−0.250156
$111$	36.0678	3.42340
$112$	0	0
$113$	5.03571	0.473720	0.236860	−	0.971544i	$-0.423882\pi$
$113$	5.03571	0.473720	0.236860	+	0.971544i	$0.423882\pi$
$114$	34.5614	3.23698
$115$	7.46567	0.696177
$116$	−7.37818	−0.685047
$117$	20.4483	1.89045
$118$	28.3414	2.60903
$119$	0	0
$120$	23.9168	2.18330
$121$	1.00000	0.0909091
$122$	−16.8392	−1.52455
$123$	29.4237	2.65305
$124$	−35.7376	−3.20934
$125$	1.00000	0.0894427
$126$	0	0
$127$	−6.60626	−0.586211	−0.293105	−	0.956080i	$-0.594689\pi$
$127$	−6.60626	−0.586211	−0.293105	+	0.956080i	$0.594689\pi$
$128$	−2.38465	−0.210775
$129$	−19.2928	−1.69864
$130$	−7.67132	−0.672819
$131$	−13.9031	−1.21472	−0.607359	−	0.794428i	$-0.707771\pi$
$131$	−13.9031	−1.21472	−0.607359	+	0.794428i	$0.707771\pi$
$132$	−15.4383	−1.34373
$133$	0	0
$134$	−13.4096	−1.15842
$135$	−12.6245	−1.08654
$136$	32.8616	2.81786
$137$	−11.1474	−0.952389	−0.476195	−	0.879340i	$-0.657984\pi$
$137$	−11.1474	−0.952389	−0.476195	+	0.879340i	$0.657984\pi$
$138$	61.9207	5.27104
$139$	0.534743	0.0453563	0.0226782	−	0.999743i	$-0.492781\pi$
$139$	0.534743	0.0453563	0.0226782	+	0.999743i	$0.492781\pi$
$140$	0	0
$141$	1.53900	0.129607
$142$	−12.1486	−1.01949
$143$	2.92390	0.244508
$144$	70.5115	5.87596
$145$	−1.51081	−0.125466
$146$	−14.6105	−1.20917
$147$	0	0
$148$	−55.7187	−4.58005
$149$	−10.9169	−0.894350	−0.447175	−	0.894447i	$-0.647570\pi$
$149$	−10.9169	−0.894350	−0.447175	+	0.894447i	$0.647570\pi$
$150$	8.29406	0.677207
$151$	2.43820	0.198418	0.0992091	−	0.995067i	$-0.468369\pi$
$151$	2.43820	0.198418	0.0992091	+	0.995067i	$0.468369\pi$
$152$	−31.5260	−2.55710
$153$	−30.3767	−2.45581
$154$	0	0
$155$	−7.31788	−0.587786
$156$	−45.1400	−3.61409
$157$	10.1125	0.807062	0.403531	−	0.914966i	$-0.367783\pi$
$157$	10.1125	0.807062	0.403531	+	0.914966i	$0.367783\pi$
$158$	−4.26044	−0.338942
$159$	44.2856	3.51208
$160$	−11.3216	−0.895053
$161$	0	0
$162$	−49.6625	−3.90185
$163$	−1.74979	−0.137054	−0.0685270	−	0.997649i	$-0.521830\pi$
$163$	−1.74979	−0.137054	−0.0685270	+	0.997649i	$0.521830\pi$
$164$	−45.4547	−3.54942
$165$	−3.16125	−0.246103
$166$	8.80195	0.683164
$167$	16.9048	1.30813	0.654065	−	0.756438i	$-0.273062\pi$
$167$	16.9048	1.30813	0.654065	+	0.756438i	$0.273062\pi$
$168$	0	0
$169$	−4.45083	−0.342372
$170$	11.3960	0.874035
$171$	29.1421	2.22855
$172$	29.8042	2.27255
$173$	−10.3873	−0.789731	−0.394866	−	0.918739i	$-0.629209\pi$
$173$	−10.3873	−0.789731	−0.394866	+	0.918739i	$0.629209\pi$
$174$	−12.5307	−0.949950
$175$	0	0
$176$	10.0824	0.759990
$177$	34.1485	2.56676
$178$	7.20503	0.540040
$179$	−2.95045	−0.220527	−0.110263	−	0.993902i	$-0.535169\pi$
$179$	−2.95045	−0.220527	−0.110263	+	0.993902i	$0.535169\pi$
$180$	34.1536	2.54566
$181$	2.45782	0.182688	0.0913442	−	0.995819i	$-0.470884\pi$
$181$	2.45782	0.182688	0.0913442	+	0.995819i	$0.470884\pi$
$182$	0	0
$183$	−20.2896	−1.49985
$184$	−56.4824	−4.16394
$185$	−11.4093	−0.838831
$186$	−60.6949	−4.45037
$187$	−4.34355	−0.317632
$188$	−2.37750	−0.173397
$189$	0	0
$190$	−10.9328	−0.793151
$191$	7.94510	0.574888	0.287444	−	0.957798i	$-0.407195\pi$
$191$	7.94510	0.574888	0.287444	+	0.957798i	$0.407195\pi$
$192$	−30.1561	−2.17633
$193$	4.47938	0.322433	0.161216	−	0.986919i	$-0.448458\pi$
$193$	4.47938	0.322433	0.161216	+	0.986919i	$0.448458\pi$
$194$	−11.4041	−0.818765
$195$	−9.24317	−0.661917
$196$	0	0
$197$	−5.71469	−0.407155	−0.203577	−	0.979059i	$-0.565257\pi$
$197$	−5.71469	−0.407155	−0.203577	+	0.979059i	$0.565257\pi$
$198$	−18.3486	−1.30398
$199$	−5.46486	−0.387394	−0.193697	−	0.981061i	$-0.562048\pi$
$199$	−5.46486	−0.387394	−0.193697	+	0.981061i	$0.562048\pi$
$200$	−7.56562	−0.534970
$201$	−16.1573	−1.13965
$202$	16.8442	1.18516
$203$	0	0
$204$	67.0571	4.69494
$205$	−9.30762	−0.650072
$206$	40.4489	2.81821
$207$	52.2112	3.62893
$208$	29.4799	2.04406
$209$	4.16701	0.288238
$210$	0	0
$211$	−6.89786	−0.474868	−0.237434	−	0.971404i	$-0.576306\pi$
$211$	−6.89786	−0.474868	−0.237434	+	0.971404i	$0.576306\pi$
$212$	−68.4139	−4.69869
$213$	−14.6378	−1.00297
$214$	−45.2775	−3.09511
$215$	6.10291	0.416215
$216$	95.5121	6.49878
$217$	0	0
$218$	−40.3946	−2.73587
$219$	−17.6042	−1.18958
$220$	4.88361	0.329253
$221$	−12.7001	−0.854301
$222$	−94.6297	−6.35113
$223$	10.8430	0.726104	0.363052	−	0.931769i	$-0.381735\pi$
$223$	10.8430	0.726104	0.363052	+	0.931769i	$0.381735\pi$
$224$	0	0
$225$	6.99351	0.466234
$226$	−13.2120	−0.878850
$227$	15.2187	1.01010	0.505050	−	0.863090i	$-0.331474\pi$
$227$	15.2187	1.01010	0.505050	+	0.863090i	$0.331474\pi$
$228$	−64.3316	−4.26047
$229$	1.63918	0.108320	0.0541600	−	0.998532i	$-0.482752\pi$
$229$	1.63918	0.108320	0.0541600	+	0.998532i	$0.482752\pi$
$230$	−19.5874	−1.29155
$231$	0	0
$232$	11.4302	0.750428
$233$	−26.4609	−1.73351	−0.866757	−	0.498731i	$-0.833799\pi$
$233$	−26.4609	−1.73351	−0.866757	+	0.498731i	$0.833799\pi$
$234$	−53.6495	−3.50717
$235$	−0.486833	−0.0317575
$236$	−52.7538	−3.43398
$237$	−5.13340	−0.333450
$238$	0	0
$239$	11.5025	0.744035	0.372018	−	0.928226i	$-0.378666\pi$
$239$	11.5025	0.744035	0.372018	+	0.928226i	$0.378666\pi$
$240$	−31.8730	−2.05740
$241$	−13.6618	−0.880031	−0.440015	−	0.897990i	$-0.645027\pi$
$241$	−13.6618	−0.880031	−0.440015	+	0.897990i	$0.645027\pi$
$242$	−2.62366	−0.168655
$243$	−21.9648	−1.40904
$244$	31.3440	2.00659
$245$	0	0
$246$	−77.1979	−4.92196
$247$	12.1839	0.775244
$248$	55.3643	3.51563
$249$	10.6055	0.672094
$250$	−2.62366	−0.165935
$251$	−22.1548	−1.39840	−0.699200	−	0.714926i	$-0.746460\pi$
$251$	−22.1548	−1.39840	−0.699200	+	0.714926i	$0.746460\pi$
$252$	0	0
$253$	7.46567	0.469362
$254$	17.3326	1.08754
$255$	13.7311	0.859872
$256$	−12.8221	−0.801379
$257$	−10.6767	−0.665992	−0.332996	−	0.942928i	$-0.608059\pi$
$257$	−10.6767	−0.665992	−0.332996	+	0.942928i	$0.608059\pi$
$258$	50.6179	3.15133
$259$	0	0
$260$	14.2792	0.885556
$261$	−10.5658	−0.654009
$262$	36.4770	2.25356
$263$	23.3208	1.43802	0.719011	−	0.694998i	$-0.244595\pi$
$263$	23.3208	1.43802	0.719011	+	0.694998i	$0.244595\pi$
$264$	23.9168	1.47198
$265$	−14.0089	−0.860559
$266$	0	0
$267$	8.68134	0.531289
$268$	24.9603	1.52469
$269$	−6.84590	−0.417402	−0.208701	−	0.977979i	$-0.566924\pi$
$269$	−6.84590	−0.417402	−0.208701	+	0.977979i	$0.566924\pi$
$270$	33.1224	2.01577
$271$	5.52642	0.335706	0.167853	−	0.985812i	$-0.446317\pi$
$271$	5.52642	0.335706	0.167853	+	0.985812i	$0.446317\pi$
$272$	−43.7935	−2.65537
$273$	0	0
$274$	29.2471	1.76688
$275$	1.00000	0.0603023
$276$	−115.257	−6.93767
$277$	−19.2513	−1.15670	−0.578348	−	0.815790i	$-0.696302\pi$
$277$	−19.2513	−1.15670	−0.578348	+	0.815790i	$0.696302\pi$
$278$	−1.40299	−0.0841455
$279$	−51.1777	−3.06393
$280$	0	0
$281$	1.79588	0.107133	0.0535665	−	0.998564i	$-0.482941\pi$
$281$	1.79588	0.107133	0.0535665	+	0.998564i	$0.482941\pi$
$282$	−4.03782	−0.240449
$283$	2.99024	0.177751	0.0888755	−	0.996043i	$-0.471673\pi$
$283$	2.99024	0.177751	0.0888755	+	0.996043i	$0.471673\pi$
$284$	22.6130	1.34184
$285$	−13.1730	−0.780300
$286$	−7.67132	−0.453614
$287$	0	0
$288$	−79.1779	−4.66560
$289$	1.86645	0.109791
$290$	3.96384	0.232765
$291$	−13.7408	−0.805498
$292$	27.1955	1.59150
$293$	−24.8482	−1.45165	−0.725824	−	0.687881i	$-0.758541\pi$
$293$	−24.8482	−1.45165	−0.725824	+	0.687881i	$0.758541\pi$
$294$	0	0
$295$	−10.8022	−0.628929
$296$	86.3186	5.01717
$297$	−12.6245	−0.732548
$298$	28.6424	1.65921
$299$	21.8288	1.26239
$300$	−15.4383	−0.891331
$301$	0	0
$302$	−6.39702	−0.368107
$303$	20.2956	1.16595
$304$	42.0135	2.40964
$305$	6.41820	0.367505
$306$	79.6982	4.55604
$307$	12.8668	0.734348	0.367174	−	0.930152i	$-0.380325\pi$
$307$	12.8668	0.734348	0.367174	+	0.930152i	$0.380325\pi$
$308$	0	0
$309$	48.7369	2.77254
$310$	19.1996	1.09047
$311$	−22.2770	−1.26321	−0.631606	−	0.775289i	$-0.717604\pi$
$311$	−22.2770	−1.26321	−0.631606	+	0.775289i	$0.717604\pi$
$312$	69.9303	3.95902
$313$	−33.1958	−1.87634	−0.938170	−	0.346176i	$-0.887480\pi$
$313$	−33.1958	−1.87634	−0.938170	+	0.346176i	$0.887480\pi$
$314$	−26.5317	−1.49727
$315$	0	0
$316$	7.93025	0.446111
$317$	−21.1298	−1.18677	−0.593384	−	0.804919i	$-0.702209\pi$
$317$	−21.1298	−1.18677	−0.593384	+	0.804919i	$0.702209\pi$
$318$	−116.191	−6.51564
$319$	−1.51081	−0.0845888
$320$	9.53929	0.533263
$321$	−54.5548	−3.04495
$322$	0	0
$323$	−18.0996	−1.00709
$324$	92.4402	5.13557
$325$	2.92390	0.162189
$326$	4.59085	0.254264
$327$	−48.6714	−2.69154
$328$	70.4178	3.88817
$329$	0	0
$330$	8.29406	0.456573
$331$	−7.69397	−0.422899	−0.211449	−	0.977389i	$-0.567818\pi$
$331$	−7.69397	−0.422899	−0.211449	+	0.977389i	$0.567818\pi$
$332$	−16.3837	−0.899172
$333$	−79.7913	−4.37254
$334$	−44.3524	−2.42686
$335$	5.11104	0.279246
$336$	0	0
$337$	−26.0810	−1.42072	−0.710362	−	0.703837i	$-0.751469\pi$
$337$	−26.0810	−1.42072	−0.710362	+	0.703837i	$0.751469\pi$
$338$	11.6775	0.635172
$339$	−15.9191	−0.864609
$340$	−21.2122	−1.15039
$341$	−7.31788	−0.396285
$342$	−76.4589	−4.13443
$343$	0	0
$344$	−46.1723	−2.48944
$345$	−23.6009	−1.27063
$346$	27.2528	1.46512
$347$	7.26861	0.390199	0.195100	−	0.980783i	$-0.437497\pi$
$347$	7.26861	0.390199	0.195100	+	0.980783i	$0.437497\pi$
$348$	23.3243	1.25031
$349$	−7.27252	−0.389289	−0.194644	−	0.980874i	$-0.562355\pi$
$349$	−7.27252	−0.389289	−0.194644	+	0.980874i	$0.562355\pi$
$350$	0	0
$351$	−36.9127	−1.97025
$352$	−11.3216	−0.603444
$353$	28.5648	1.52035	0.760176	−	0.649717i	$-0.225113\pi$
$353$	28.5648	1.52035	0.760176	+	0.649717i	$0.225113\pi$
$354$	−89.5942	−4.76188
$355$	4.63039	0.245756
$356$	−13.4112	−0.710794
$357$	0	0
$358$	7.74099	0.409124
$359$	−27.5961	−1.45646	−0.728232	−	0.685330i	$-0.759658\pi$
$359$	−27.5961	−1.45646	−0.728232	+	0.685330i	$0.759658\pi$
$360$	−52.9102	−2.78861
$361$	−1.63601	−0.0861057
$362$	−6.44850	−0.338925
$363$	−3.16125	−0.165923
$364$	0	0
$365$	5.56874	0.291481
$366$	53.2330	2.78253
$367$	−11.7968	−0.615786	−0.307893	−	0.951421i	$-0.599624\pi$
$367$	−11.7968	−0.615786	−0.307893	+	0.951421i	$0.599624\pi$
$368$	75.2719	3.92382
$369$	−65.0929	−3.38860
$370$	29.9342	1.55621
$371$	0	0
$372$	112.976	5.85752
$373$	17.9430	0.929054	0.464527	−	0.885559i	$-0.346224\pi$
$373$	17.9430	0.929054	0.464527	+	0.885559i	$0.346224\pi$
$374$	11.3960	0.589274
$375$	−3.16125	−0.163246
$376$	3.68319	0.189946
$377$	−4.41744	−0.227510
$378$	0	0
$379$	27.1123	1.39267	0.696333	−	0.717718i	$-0.254814\pi$
$379$	27.1123	1.39267	0.696333	+	0.717718i	$0.254814\pi$
$380$	20.3501	1.04394
$381$	20.8841	1.06992
$382$	−20.8453	−1.06654
$383$	7.31702	0.373882	0.186941	−	0.982371i	$-0.440143\pi$
$383$	7.31702	0.373882	0.186941	+	0.982371i	$0.440143\pi$
$384$	7.53847	0.384696
$385$	0	0
$386$	−11.7524	−0.598181
$387$	42.6808	2.16958
$388$	21.2272	1.07765
$389$	5.90581	0.299436	0.149718	−	0.988729i	$-0.452163\pi$
$389$	5.90581	0.299436	0.149718	+	0.988729i	$0.452163\pi$
$390$	24.2510	1.22800
$391$	−32.4275	−1.63993
$392$	0	0
$393$	43.9511	2.21704
$394$	14.9934	0.755358
$395$	1.62385	0.0817048
$396$	34.1536	1.71628
$397$	11.4496	0.574641	0.287321	−	0.957834i	$-0.407235\pi$
$397$	11.4496	0.574641	0.287321	+	0.957834i	$0.407235\pi$
$398$	14.3380	0.718697
$399$	0	0
$400$	10.0824	0.504121
$401$	−13.8885	−0.693557	−0.346779	−	0.937947i	$-0.612725\pi$
$401$	−13.8885	−0.693557	−0.346779	+	0.937947i	$0.612725\pi$
$402$	42.3913	2.11428
$403$	−21.3967	−1.06585
$404$	−31.3534	−1.55989
$405$	18.9287	0.940574
$406$	0	0
$407$	−11.4093	−0.565540
$408$	−103.884	−5.14302
$409$	25.7937	1.27541	0.637707	−	0.770279i	$-0.279883\pi$
$409$	25.7937	1.27541	0.637707	+	0.770279i	$0.279883\pi$
$410$	24.4200	1.20602
$411$	35.2398	1.73825
$412$	−75.2904	−3.70929
$413$	0	0
$414$	−136.985	−6.73243
$415$	−3.35483	−0.164682
$416$	−33.1032	−1.62302
$417$	−1.69046	−0.0827821
$418$	−10.9328	−0.534742
$419$	23.1241	1.12969	0.564843	−	0.825199i	$-0.308937\pi$
$419$	23.1241	1.12969	0.564843	+	0.825199i	$0.308937\pi$
$420$	0	0
$421$	0.172946	0.00842886	0.00421443	−	0.999991i	$-0.498659\pi$
$421$	0.172946	0.00842886	0.00421443	+	0.999991i	$0.498659\pi$
$422$	18.0977	0.880980
$423$	−3.40467	−0.165541
$424$	105.986	5.14713
$425$	−4.34355	−0.210693
$426$	38.4047	1.86072
$427$	0	0
$428$	84.2782	4.07374
$429$	−9.24317	−0.446264
$430$	−16.0120	−0.772166
$431$	23.4406	1.12909	0.564547	−	0.825401i	$-0.309051\pi$
$431$	23.4406	1.12909	0.564547	+	0.825401i	$0.309051\pi$
$432$	−127.285	−6.12402
$433$	5.55138	0.266782	0.133391	−	0.991063i	$-0.457413\pi$
$433$	5.55138	0.266782	0.133391	+	0.991063i	$0.457413\pi$
$434$	0	0
$435$	4.77604	0.228993
$436$	75.1893	3.60091
$437$	31.1095	1.48817
$438$	46.1874	2.20692
$439$	−26.7771	−1.27800	−0.639002	−	0.769205i	$-0.720652\pi$
$439$	−26.7771	−1.27800	−0.639002	+	0.769205i	$0.720652\pi$
$440$	−7.56562	−0.360677
$441$	0	0
$442$	33.3208	1.58491
$443$	−33.6240	−1.59752	−0.798761	−	0.601648i	$-0.794511\pi$
$443$	−33.6240	−1.59752	−0.798761	+	0.601648i	$0.794511\pi$
$444$	176.141	8.35928
$445$	−2.74617	−0.130181
$446$	−28.4485	−1.34708
$447$	34.5112	1.63232
$448$	0	0
$449$	13.8607	0.654129	0.327064	−	0.945002i	$-0.393941\pi$
$449$	13.8607	0.654129	0.327064	+	0.945002i	$0.393941\pi$
$450$	−18.3486	−0.864962
$451$	−9.30762	−0.438278
$452$	24.5924	1.15673
$453$	−7.70777	−0.362143
$454$	−39.9287	−1.87395
$455$	0	0
$456$	99.6617	4.66709
$457$	−6.69316	−0.313093	−0.156546	−	0.987671i	$-0.550036\pi$
$457$	−6.69316	−0.313093	−0.156546	+	0.987671i	$0.550036\pi$
$458$	−4.30065	−0.200956
$459$	54.8352	2.55949
$460$	36.4594	1.69993
$461$	38.1454	1.77661	0.888304	−	0.459256i	$-0.151884\pi$
$461$	38.1454	1.77661	0.888304	+	0.459256i	$0.151884\pi$
$462$	0	0
$463$	−34.4052	−1.59894	−0.799472	−	0.600704i	$-0.794887\pi$
$463$	−34.4052	−1.59894	−0.799472	+	0.600704i	$0.794887\pi$
$464$	−15.2326	−0.707154
$465$	23.1337	1.07280
$466$	69.4246	3.21603
$467$	26.5929	1.23057	0.615286	−	0.788304i	$-0.289040\pi$
$467$	26.5929	1.23057	0.615286	+	0.788304i	$0.289040\pi$
$468$	99.8615	4.61610
$469$	0	0
$470$	1.27729	0.0589168
$471$	−31.9680	−1.47301
$472$	81.7254	3.76172
$473$	6.10291	0.280612
$474$	13.4683	0.618620
$475$	4.16701	0.191196
$476$	0	0
$477$	−97.9713	−4.48580
$478$	−30.1787	−1.38034
$479$	−31.6447	−1.44588	−0.722941	−	0.690909i	$-0.757210\pi$
$479$	−31.6447	−1.44588	−0.722941	+	0.690909i	$0.757210\pi$
$480$	35.7905	1.63360
$481$	−33.3597	−1.52107
$482$	35.8438	1.63264
$483$	0	0
$484$	4.88361	0.221982
$485$	4.34662	0.197370
$486$	57.6283	2.61407
$487$	3.68520	0.166992	0.0834962	−	0.996508i	$-0.473391\pi$
$487$	3.68520	0.166992	0.0834962	+	0.996508i	$0.473391\pi$
$488$	−48.5577	−2.19810
$489$	5.53152	0.250144
$490$	0	0
$491$	−22.4062	−1.01118	−0.505588	−	0.862775i	$-0.668725\pi$
$491$	−22.4062	−1.01118	−0.505588	+	0.862775i	$0.668725\pi$
$492$	143.694	6.47822
$493$	6.56226	0.295549
$494$	−31.9665	−1.43824
$495$	6.99351	0.314335
$496$	−73.7819	−3.31290
$497$	0	0
$498$	−27.8252	−1.24688
$499$	12.4575	0.557673	0.278836	−	0.960339i	$-0.410051\pi$
$499$	12.4575	0.557673	0.278836	+	0.960339i	$0.410051\pi$
$500$	4.88361	0.218402
$501$	−53.4402	−2.38753
$502$	58.1268	2.59433
$503$	−7.75511	−0.345783	−0.172892	−	0.984941i	$-0.555311\pi$
$503$	−7.75511	−0.345783	−0.172892	+	0.984941i	$0.555311\pi$
$504$	0	0
$505$	−6.42012	−0.285692
$506$	−19.5874	−0.870766
$507$	14.0702	0.624880
$508$	−32.2624	−1.43141
$509$	15.1594	0.671931	0.335965	−	0.941874i	$-0.390938\pi$
$509$	15.1594	0.671931	0.335965	+	0.941874i	$0.390938\pi$
$510$	−36.0257	−1.59524
$511$	0	0
$512$	38.4101	1.69750
$513$	−52.6064	−2.32263
$514$	28.0120	1.23555
$515$	−15.4170	−0.679352
$516$	−94.2186	−4.14774
$517$	−0.486833	−0.0214109
$518$	0	0
$519$	32.8369	1.44138
$520$	−22.1211	−0.970073
$521$	−4.75275	−0.208222	−0.104111	−	0.994566i	$-0.533200\pi$
$521$	−4.75275	−0.208222	−0.104111	+	0.994566i	$0.533200\pi$
$522$	27.7212	1.21332
$523$	13.0891	0.572346	0.286173	−	0.958178i	$-0.407617\pi$
$523$	13.0891	0.572346	0.286173	+	0.958178i	$0.407617\pi$
$524$	−67.8972	−2.96610
$525$	0	0
$526$	−61.1859	−2.66783
$527$	31.7856	1.38460
$528$	−31.8730	−1.38710
$529$	32.7362	1.42331
$530$	36.7546	1.59652
$531$	−75.5454	−3.27839
$532$	0	0
$533$	−27.2145	−1.17879
$534$	−22.7769	−0.985654
$535$	17.2574	0.746101
$536$	−38.6682	−1.67021
$537$	9.32711	0.402495
$538$	17.9613	0.774368
$539$	0	0
$540$	−61.6531	−2.65313
$541$	37.9131	1.63001	0.815007	−	0.579451i	$-0.196733\pi$
$541$	37.9131	1.63001	0.815007	+	0.579451i	$0.196733\pi$
$542$	−14.4995	−0.622805
$543$	−7.76979	−0.333434
$544$	49.1760	2.10841
$545$	15.3963	0.659503
$546$	0	0
$547$	21.3023	0.910822	0.455411	−	0.890281i	$-0.349492\pi$
$547$	21.3023	0.910822	0.455411	+	0.890281i	$0.349492\pi$
$548$	−54.4397	−2.32555
$549$	44.8858	1.91568
$550$	−2.62366	−0.111873
$551$	−6.29554	−0.268199
$552$	178.555	7.59980
$553$	0	0
$554$	50.5088	2.14591
$555$	36.0678	1.53099
$556$	2.61148	0.110751
$557$	−7.89950	−0.334713	−0.167356	−	0.985896i	$-0.553523\pi$
$557$	−7.89950	−0.334713	−0.167356	+	0.985896i	$0.553523\pi$
$558$	134.273	5.68423
$559$	17.8443	0.754732
$560$	0	0
$561$	13.7311	0.579726
$562$	−4.71178	−0.198754
$563$	−33.5955	−1.41588	−0.707941	−	0.706272i	$-0.750376\pi$
$563$	−33.5955	−1.41588	−0.707941	+	0.706272i	$0.750376\pi$
$564$	7.51588	0.316476
$565$	5.03571	0.211854
$566$	−7.84537	−0.329766
$567$	0	0
$568$	−35.0318	−1.46990
$569$	−0.213749	−0.00896082	−0.00448041	−	0.999990i	$-0.501426\pi$
$569$	−0.213749	−0.00896082	−0.00448041	+	0.999990i	$0.501426\pi$
$570$	34.5614	1.44762
$571$	31.1590	1.30397	0.651983	−	0.758234i	$-0.273937\pi$
$571$	31.1590	1.30397	0.651983	+	0.758234i	$0.273937\pi$
$572$	14.2792	0.597042
$573$	−25.1165	−1.04926
$574$	0	0
$575$	7.46567	0.311340
$576$	66.7132	2.77971
$577$	−24.1908	−1.00708	−0.503538	−	0.863973i	$-0.667969\pi$
$577$	−24.1908	−1.00708	−0.503538	+	0.863973i	$0.667969\pi$
$578$	−4.89692	−0.203685
$579$	−14.1604	−0.588488
$580$	−7.37818	−0.306362
$581$	0	0
$582$	36.0512	1.49437
$583$	−14.0089	−0.580189
$584$	−42.1309	−1.74339
$585$	20.4483	0.845433
$586$	65.1933	2.69311
$587$	15.6623	0.646450	0.323225	−	0.946322i	$-0.395233\pi$
$587$	15.6623	0.646450	0.323225	+	0.946322i	$0.395233\pi$
$588$	0	0
$589$	−30.4937	−1.25647
$590$	28.3414	1.16680
$591$	18.0656	0.743119
$592$	−115.034	−4.72785
$593$	−23.7201	−0.974067	−0.487034	−	0.873383i	$-0.661921\pi$
$593$	−23.7201	−0.974067	−0.487034	+	0.873383i	$0.661921\pi$
$594$	33.1224	1.35903
$595$	0	0
$596$	−53.3140	−2.18383
$597$	17.2758	0.707052
$598$	−57.2715	−2.34201
$599$	1.19318	0.0487518	0.0243759	−	0.999703i	$-0.492240\pi$
$599$	1.19318	0.0487518	0.0243759	+	0.999703i	$0.492240\pi$
$600$	23.9168	0.976400
$601$	−5.03409	−0.205345	−0.102672	−	0.994715i	$-0.532739\pi$
$601$	−5.03409	−0.205345	−0.102672	+	0.994715i	$0.532739\pi$
$602$	0	0
$603$	35.7441	1.45561
$604$	11.9072	0.484498
$605$	1.00000	0.0406558
$606$	−53.2489	−2.16309
$607$	−5.83761	−0.236941	−0.118471	−	0.992958i	$-0.537799\pi$
$607$	−5.83761	−0.236941	−0.118471	+	0.992958i	$0.537799\pi$
$608$	−47.1773	−1.91329
$609$	0	0
$610$	−16.8392	−0.681799
$611$	−1.42345	−0.0575866
$612$	−148.348	−5.99661
$613$	−29.6027	−1.19564	−0.597820	−	0.801630i	$-0.703966\pi$
$613$	−29.6027	−1.19564	−0.597820	+	0.801630i	$0.703966\pi$
$614$	−33.7582	−1.36237
$615$	29.4237	1.18648
$616$	0	0
$617$	−15.1868	−0.611399	−0.305700	−	0.952128i	$-0.598890\pi$
$617$	−15.1868	−0.611399	−0.305700	+	0.952128i	$0.598890\pi$
$618$	−127.869	−5.14365
$619$	−12.3382	−0.495915	−0.247958	−	0.968771i	$-0.579759\pi$
$619$	−12.3382	−0.495915	−0.247958	+	0.968771i	$0.579759\pi$
$620$	−35.7376	−1.43526
$621$	−94.2503	−3.78213
$622$	58.4473	2.34352
$623$	0	0
$624$	−93.1934	−3.73072
$625$	1.00000	0.0400000
$626$	87.0947	3.48100
$627$	−13.1730	−0.526078
$628$	49.3853	1.97069
$629$	49.5570	1.97597
$630$	0	0
$631$	−16.8787	−0.671932	−0.335966	−	0.941874i	$-0.609063\pi$
$631$	−16.8787	−0.671932	−0.335966	+	0.941874i	$0.609063\pi$
$632$	−12.2854	−0.488688
$633$	21.8059	0.866705
$634$	55.4375	2.20171
$635$	−6.60626	−0.262162
$636$	216.274	8.57581
$637$	0	0
$638$	3.96384	0.156930
$639$	32.3827	1.28104
$640$	−2.38465	−0.0942615
$641$	−28.2729	−1.11671	−0.558357	−	0.829601i	$-0.688568\pi$
$641$	−28.2729	−1.11671	−0.558357	+	0.829601i	$0.688568\pi$
$642$	143.134	5.64903
$643$	−3.34276	−0.131826	−0.0659128	−	0.997825i	$-0.520996\pi$
$643$	−3.34276	−0.131826	−0.0659128	+	0.997825i	$0.520996\pi$
$644$	0	0
$645$	−19.2928	−0.759654
$646$	47.4873	1.86836
$647$	−37.0144	−1.45519	−0.727593	−	0.686009i	$-0.759361\pi$
$647$	−37.0144	−1.45519	−0.727593	+	0.686009i	$0.759361\pi$
$648$	−143.207	−5.62571
$649$	−10.8022	−0.424024
$650$	−7.67132	−0.300894
$651$	0	0
$652$	−8.54528	−0.334659
$653$	5.53951	0.216778	0.108389	−	0.994109i	$-0.465431\pi$
$653$	5.53951	0.216778	0.108389	+	0.994109i	$0.465431\pi$
$654$	127.697	4.99336
$655$	−13.9031	−0.543238
$656$	−93.8432	−3.66396
$657$	38.9450	1.51939
$658$	0	0
$659$	−6.26375	−0.244001	−0.122001	−	0.992530i	$-0.538931\pi$
$659$	−6.26375	−0.244001	−0.122001	+	0.992530i	$0.538931\pi$
$660$	−15.4383	−0.600936
$661$	−0.923727	−0.0359288	−0.0179644	−	0.999839i	$-0.505719\pi$
$661$	−0.923727	−0.0359288	−0.0179644	+	0.999839i	$0.505719\pi$
$662$	20.1864	0.784566
$663$	40.1482	1.55923
$664$	25.3814	0.984988
$665$	0	0
$666$	209.346	8.11198
$667$	−11.2792	−0.436731
$668$	82.5563	3.19420
$669$	−34.2776	−1.32525
$670$	−13.4096	−0.518060
$671$	6.41820	0.247772
$672$	0	0
$673$	−11.8005	−0.454877	−0.227439	−	0.973792i	$-0.573035\pi$
$673$	−11.8005	−0.454877	−0.227439	+	0.973792i	$0.573035\pi$
$674$	68.4278	2.63574
$675$	−12.6245	−0.485917
$676$	−21.7361	−0.836005
$677$	39.8595	1.53192	0.765962	−	0.642885i	$-0.222263\pi$
$677$	39.8595	1.53192	0.765962	+	0.642885i	$0.222263\pi$
$678$	41.7665	1.60403
$679$	0	0
$680$	32.8616	1.26019
$681$	−48.1101	−1.84358
$682$	19.1996	0.735192
$683$	−29.5408	−1.13035	−0.565174	−	0.824972i	$-0.691191\pi$
$683$	−29.5408	−1.13035	−0.565174	+	0.824972i	$0.691191\pi$
$684$	142.318	5.44168
$685$	−11.1474	−0.425921
$686$	0	0
$687$	−5.18185	−0.197700
$688$	61.5320	2.34589
$689$	−40.9605	−1.56047
$690$	61.9207	2.35728
$691$	−17.2364	−0.655703	−0.327852	−	0.944729i	$-0.606325\pi$
$691$	−17.2364	−0.655703	−0.327852	+	0.944729i	$0.606325\pi$
$692$	−50.7275	−1.92837
$693$	0	0
$694$	−19.0704	−0.723901
$695$	0.534743	0.0202840
$696$	−36.1336	−1.36964
$697$	40.4281	1.53132
$698$	19.0806	0.722213
$699$	83.6497	3.16392
$700$	0	0
$701$	−26.4276	−0.998155	−0.499077	−	0.866557i	$-0.666328\pi$
$701$	−26.4276	−0.998155	−0.499077	+	0.866557i	$0.666328\pi$
$702$	96.8465	3.65524
$703$	−47.5428	−1.79311
$704$	9.53929	0.359526
$705$	1.53900	0.0579621
$706$	−74.9445	−2.82057
$707$	0	0
$708$	166.768	6.26752
$709$	4.78321	0.179637	0.0898186	−	0.995958i	$-0.471371\pi$
$709$	4.78321	0.179637	0.0898186	+	0.995958i	$0.471371\pi$
$710$	−12.1486	−0.455928
$711$	11.3564	0.425899
$712$	20.7765	0.778632
$713$	−54.6328	−2.04602
$714$	0	0
$715$	2.92390	0.109347
$716$	−14.4088	−0.538484
$717$	−36.3623	−1.35798
$718$	72.4028	2.70205
$719$	46.5322	1.73536	0.867679	−	0.497125i	$-0.165611\pi$
$719$	46.5322	1.73536	0.867679	+	0.497125i	$0.165611\pi$
$720$	70.5115	2.62781
$721$	0	0
$722$	4.29234	0.159744
$723$	43.1882	1.60619
$724$	12.0030	0.446089
$725$	−1.51081	−0.0561099
$726$	8.29406	0.307821
$727$	40.4101	1.49873	0.749363	−	0.662159i	$-0.230360\pi$
$727$	40.4101	1.49873	0.749363	+	0.662159i	$0.230360\pi$
$728$	0	0
$729$	12.6503	0.468530
$730$	−14.6105	−0.540758
$731$	−26.5083	−0.980445
$732$	−99.0863	−3.66233
$733$	13.5272	0.499638	0.249819	−	0.968293i	$-0.419629\pi$
$733$	13.5272	0.499638	0.249819	+	0.968293i	$0.419629\pi$
$734$	30.9507	1.14241
$735$	0	0
$736$	−84.5234	−3.11558
$737$	5.11104	0.188268
$738$	170.782	6.28657
$739$	−45.5490	−1.67555	−0.837774	−	0.546017i	$-0.816143\pi$
$739$	−45.5490	−1.67555	−0.837774	+	0.546017i	$0.816143\pi$
$740$	−55.7187	−2.04826
$741$	−38.5164	−1.41494
$742$	0	0
$743$	27.7972	1.01978	0.509890	−	0.860240i	$-0.329686\pi$
$743$	27.7972	1.01978	0.509890	+	0.860240i	$0.329686\pi$
$744$	−175.020	−6.41656
$745$	−10.9169	−0.399965
$746$	−47.0764	−1.72359
$747$	−23.4621	−0.858432
$748$	−21.2122	−0.775595
$749$	0	0
$750$	8.29406	0.302856
$751$	−13.8457	−0.505238	−0.252619	−	0.967566i	$-0.581292\pi$
$751$	−13.8457	−0.505238	−0.252619	+	0.967566i	$0.581292\pi$
$752$	−4.90845	−0.178993
$753$	70.0370	2.55229
$754$	11.5899	0.422078
$755$	2.43820	0.0887353
$756$	0	0
$757$	7.44333	0.270532	0.135266	−	0.990809i	$-0.456811\pi$
$757$	7.44333	0.270532	0.135266	+	0.990809i	$0.456811\pi$
$758$	−71.1336	−2.58369
$759$	−23.6009	−0.856657
$760$	−31.5260	−1.14357
$761$	−11.2003	−0.406011	−0.203005	−	0.979178i	$-0.565071\pi$
$761$	−11.2003	−0.406011	−0.203005	+	0.979178i	$0.565071\pi$
$762$	−54.7927	−1.98493
$763$	0	0
$764$	38.8008	1.40376
$765$	−30.3767	−1.09827
$766$	−19.1974	−0.693630
$767$	−31.5845	−1.14045
$768$	40.5338	1.46264
$769$	−16.1920	−0.583898	−0.291949	−	0.956434i	$-0.594304\pi$
$769$	−16.1920	−0.583898	−0.291949	+	0.956434i	$0.594304\pi$
$770$	0	0
$771$	33.7516	1.21553
$772$	21.8755	0.787318
$773$	−43.3138	−1.55789	−0.778944	−	0.627094i	$-0.784244\pi$
$773$	−43.3138	−1.55789	−0.778944	+	0.627094i	$0.784244\pi$
$774$	−111.980	−4.02504
$775$	−7.31788	−0.262866
$776$	−32.8849	−1.18050
$777$	0	0
$778$	−15.4948	−0.555517
$779$	−38.7849	−1.38961
$780$	−45.1400	−1.61627
$781$	4.63039	0.165688
$782$	85.0789	3.04241
$783$	19.0732	0.681619
$784$	0	0
$785$	10.1125	0.360929
$786$	−115.313	−4.11308
$787$	−33.0587	−1.17842	−0.589208	−	0.807981i	$-0.700560\pi$
$787$	−33.0587	−1.17842	−0.589208	+	0.807981i	$0.700560\pi$
$788$	−27.9083	−0.994193
$789$	−73.7229	−2.62461
$790$	−4.26044	−0.151580
$791$	0	0
$792$	−52.9102	−1.88008
$793$	18.7662	0.666406
$794$	−30.0400	−1.06608
$795$	44.2856	1.57065
$796$	−26.6882	−0.945940
$797$	−6.45547	−0.228664	−0.114332	−	0.993443i	$-0.536473\pi$
$797$	−6.45547	−0.228664	−0.114332	+	0.993443i	$0.536473\pi$
$798$	0	0
$799$	2.11458	0.0748086
$800$	−11.3216	−0.400280
$801$	−19.2054	−0.678589
$802$	36.4387	1.28669
$803$	5.56874	0.196516
$804$	−78.9059	−2.78280
$805$	0	0
$806$	56.1378	1.97737
$807$	21.6416	0.761821
$808$	48.5722	1.70876
$809$	−46.2479	−1.62599	−0.812994	−	0.582272i	$-0.802164\pi$
$809$	−46.2479	−1.62599	−0.812994	+	0.582272i	$0.802164\pi$
$810$	−49.6625	−1.74496
$811$	26.3444	0.925078	0.462539	−	0.886599i	$-0.346939\pi$
$811$	26.3444	0.925078	0.462539	+	0.886599i	$0.346939\pi$
$812$	0	0
$813$	−17.4704	−0.612714
$814$	29.9342	1.04919
$815$	−1.74979	−0.0612924
$816$	138.442	4.84645
$817$	25.4309	0.889714
$818$	−67.6739	−2.36616
$819$	0	0
$820$	−45.4547	−1.58735
$821$	−36.6502	−1.27910	−0.639550	−	0.768750i	$-0.720879\pi$
$821$	−36.6502	−1.27910	−0.639550	+	0.768750i	$0.720879\pi$
$822$	−92.4574	−3.22482
$823$	−14.4331	−0.503107	−0.251553	−	0.967843i	$-0.580941\pi$
$823$	−14.4331	−0.503107	−0.251553	+	0.967843i	$0.580941\pi$
$824$	116.639	4.06331
$825$	−3.16125	−0.110061
$826$	0	0
$827$	43.0370	1.49654	0.748271	−	0.663393i	$-0.230884\pi$
$827$	43.0370	1.49654	0.748271	+	0.663393i	$0.230884\pi$
$828$	254.979	8.86114
$829$	27.1661	0.943517	0.471759	−	0.881728i	$-0.343619\pi$
$829$	27.1661	0.943517	0.471759	+	0.881728i	$0.343619\pi$
$830$	8.80195	0.305520
$831$	60.8581	2.11114
$832$	27.8919	0.966977
$833$	0	0
$834$	4.43519	0.153578
$835$	16.9048	0.585014
$836$	20.3501	0.703821
$837$	92.3845	3.19328
$838$	−60.6698	−2.09580
$839$	−24.8868	−0.859186	−0.429593	−	0.903023i	$-0.641343\pi$
$839$	−24.8868	−0.859186	−0.429593	+	0.903023i	$0.641343\pi$
$840$	0	0
$841$	−26.7175	−0.921292
$842$	−0.453752	−0.0156373
$843$	−5.67722	−0.195534
$844$	−33.6864	−1.15953
$845$	−4.45083	−0.153113
$846$	8.93271	0.307113
$847$	0	0
$848$	−141.243	−4.85032
$849$	−9.45289	−0.324422
$850$	11.3960	0.390880
$851$	−85.1783	−2.91987
$852$	−71.4854	−2.44905
$853$	17.7400	0.607407	0.303704	−	0.952767i	$-0.401777\pi$
$853$	17.7400	0.607407	0.303704	+	0.952767i	$0.401777\pi$
$854$	0	0
$855$	29.1421	0.996637
$856$	−130.563	−4.46254
$857$	7.04835	0.240767	0.120384	−	0.992727i	$-0.461588\pi$
$857$	7.04835	0.240767	0.120384	+	0.992727i	$0.461588\pi$
$858$	24.2510	0.827914
$859$	−22.8691	−0.780284	−0.390142	−	0.920755i	$-0.627574\pi$
$859$	−22.8691	−0.780284	−0.390142	+	0.920755i	$0.627574\pi$
$860$	29.8042	1.01632
$861$	0	0
$862$	−61.5003	−2.09471
$863$	−12.7006	−0.432332	−0.216166	−	0.976357i	$-0.569355\pi$
$863$	−12.7006	−0.432332	−0.216166	+	0.976357i	$0.569355\pi$
$864$	142.930	4.86257
$865$	−10.3873	−0.353179
$866$	−14.5649	−0.494937
$867$	−5.90030	−0.200385
$868$	0	0
$869$	1.62385	0.0550854
$870$	−12.5307	−0.424831
$871$	14.9442	0.506363
$872$	−116.482	−3.94458
$873$	30.3982	1.02882
$874$	−81.6209	−2.76087
$875$	0	0
$876$	−85.9719	−2.90472
$877$	−45.0211	−1.52026	−0.760128	−	0.649774i	$-0.774864\pi$
$877$	−45.0211	−1.52026	−0.760128	+	0.649774i	$0.774864\pi$
$878$	70.2542	2.37097
$879$	78.5514	2.64947
$880$	10.0824	0.339878
$881$	34.8356	1.17364	0.586820	−	0.809717i	$-0.300380\pi$
$881$	34.8356	1.17364	0.586820	+	0.809717i	$0.300380\pi$
$882$	0	0
$883$	−41.8965	−1.40993	−0.704965	−	0.709242i	$-0.749037\pi$
$883$	−41.8965	−1.40993	−0.704965	+	0.709242i	$0.749037\pi$
$884$	−62.0223	−2.08603
$885$	34.1485	1.14789
$886$	88.2180	2.96374
$887$	16.4880	0.553614	0.276807	−	0.960926i	$-0.410724\pi$
$887$	16.4880	0.553614	0.276807	+	0.960926i	$0.410724\pi$
$888$	−272.875	−9.15708
$889$	0	0
$890$	7.20503	0.241513
$891$	18.9287	0.634135
$892$	52.9532	1.77300
$893$	−2.02864	−0.0678858
$894$	−90.5457	−3.02830
$895$	−2.95045	−0.0986227
$896$	0	0
$897$	−69.0064	−2.30406
$898$	−36.3659	−1.21355
$899$	11.0559	0.368734
$900$	34.1536	1.13845
$901$	60.8483	2.02715
$902$	24.4200	0.813099
$903$	0	0
$904$	−38.0982	−1.26713
$905$	2.45782	0.0817008
$906$	20.2226	0.671851
$907$	19.2426	0.638940	0.319470	−	0.947596i	$-0.396495\pi$
$907$	19.2426	0.638940	0.319470	+	0.947596i	$0.396495\pi$
$908$	74.3221	2.46646
$909$	−44.8992	−1.48921
$910$	0	0
$911$	−15.8165	−0.524024	−0.262012	−	0.965065i	$-0.584386\pi$
$911$	−15.8165	−0.524024	−0.262012	+	0.965065i	$0.584386\pi$
$912$	−132.815	−4.39796
$913$	−3.35483	−0.111029
$914$	17.5606	0.580853
$915$	−20.2896	−0.670752
$916$	8.00510	0.264496
$917$	0	0
$918$	−143.869	−4.74838
$919$	−44.9695	−1.48341	−0.741703	−	0.670728i	$-0.765982\pi$
$919$	−44.9695	−1.48341	−0.741703	+	0.670728i	$0.765982\pi$
$920$	−56.4824	−1.86217
$921$	−40.6753	−1.34030
$922$	−100.081	−3.29598
$923$	13.5388	0.445634
$924$	0	0
$925$	−11.4093	−0.375137
$926$	90.2675	2.96638
$927$	−107.819	−3.54123
$928$	17.1048	0.561491
$929$	8.57701	0.281403	0.140701	−	0.990052i	$-0.455064\pi$
$929$	8.57701	0.281403	0.140701	+	0.990052i	$0.455064\pi$
$930$	−60.6949	−1.99026
$931$	0	0
$932$	−129.225	−4.23290
$933$	70.4232	2.30555
$934$	−69.7708	−2.28297
$935$	−4.34355	−0.142049
$936$	−154.704	−5.05666
$937$	28.4452	0.929265	0.464632	−	0.885504i	$-0.346186\pi$
$937$	28.4452	0.929265	0.464632	+	0.885504i	$0.346186\pi$
$938$	0	0
$939$	104.940	3.42460
$940$	−2.37750	−0.0775455
$941$	29.0857	0.948167	0.474083	−	0.880480i	$-0.342779\pi$
$941$	29.0857	0.948167	0.474083	+	0.880480i	$0.342779\pi$
$942$	83.8733	2.73274
$943$	−69.4875	−2.26283
$944$	−108.912	−3.54479
$945$	0	0
$946$	−16.0120	−0.520594
$947$	−27.9775	−0.909148	−0.454574	−	0.890709i	$-0.650208\pi$
$947$	−27.9775	−0.909148	−0.454574	+	0.890709i	$0.650208\pi$
$948$	−25.0695	−0.814220
$949$	16.2824	0.528549
$950$	−10.9328	−0.354708
$951$	66.7967	2.16603
$952$	0	0
$953$	44.7703	1.45025	0.725126	−	0.688617i	$-0.241782\pi$
$953$	44.7703	1.45025	0.725126	+	0.688617i	$0.241782\pi$
$954$	257.044	8.32210
$955$	7.94510	0.257098
$956$	56.1737	1.81679
$957$	4.77604	0.154387
$958$	83.0250	2.68242
$959$	0	0
$960$	−30.1561	−0.973284
$961$	22.5513	0.727462
$962$	87.5246	2.82191
$963$	120.690	3.88917
$964$	−66.7186	−2.14886
$965$	4.47938	0.144196
$966$	0	0
$967$	8.96530	0.288305	0.144152	−	0.989556i	$-0.453954\pi$
$967$	8.96530	0.288305	0.144152	+	0.989556i	$0.453954\pi$
$968$	−7.56562	−0.243168
$969$	57.2175	1.83809
$970$	−11.4041	−0.366163
$971$	−9.11685	−0.292574	−0.146287	−	0.989242i	$-0.546732\pi$
$971$	−9.11685	−0.292574	−0.146287	+	0.989242i	$0.546732\pi$
$972$	−107.268	−3.44061
$973$	0	0
$974$	−9.66872	−0.309806
$975$	−9.24317	−0.296018
$976$	64.7110	2.07135
$977$	−25.7390	−0.823464	−0.411732	−	0.911305i	$-0.635076\pi$
$977$	−25.7390	−0.823464	−0.411732	+	0.911305i	$0.635076\pi$
$978$	−14.5128	−0.464070
$979$	−2.74617	−0.0877680
$980$	0	0
$981$	107.674	3.43776
$982$	58.7863	1.87594
$983$	−28.0974	−0.896167	−0.448084	−	0.893992i	$-0.647893\pi$
$983$	−28.0974	−0.896167	−0.448084	+	0.893992i	$0.647893\pi$
$984$	−222.609	−7.09650
$985$	−5.71469	−0.182085
$986$	−17.2172	−0.548306
$987$	0	0
$988$	59.5014	1.89299
$989$	45.5623	1.44880
$990$	−18.3486	−0.583157
$991$	−18.0139	−0.572232	−0.286116	−	0.958195i	$-0.592364\pi$
$991$	−18.0139	−0.572232	−0.286116	+	0.958195i	$0.592364\pi$
$992$	82.8502	2.63050
$993$	24.3226	0.771854
$994$	0	0
$995$	−5.46486	−0.173248
$996$	51.7930	1.64112
$997$	26.6311	0.843417	0.421708	−	0.906732i	$-0.361431\pi$
$997$	26.6311	0.843417	0.421708	+	0.906732i	$0.361431\pi$
$998$	−32.6842	−1.03460
$999$	144.037	4.55713

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.u.1.1	✓	10
7.6	odd	2		2695.2.a.v.1.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.u.1.1	✓	10	1.1	even	1	trivial
2695.2.a.v.1.1	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62366 q^{2} -3.16125 q^{3} +4.88361 q^{4} +1.00000 q^{5} +8.29406 q^{6} -7.56562 q^{8} +6.99351 q^{9} +O(q^{10})\)	\(q-2.62366 q^{2} -3.16125 q^{3} +4.88361 q^{4} +1.00000 q^{5} +8.29406 q^{6} -7.56562 q^{8} +6.99351 q^{9} -2.62366 q^{10} +1.00000 q^{11} -15.4383 q^{12} +2.92390 q^{13} -3.16125 q^{15} +10.0824 q^{16} -4.34355 q^{17} -18.3486 q^{18} +4.16701 q^{19} +4.88361 q^{20} -2.62366 q^{22} +7.46567 q^{23} +23.9168 q^{24} +1.00000 q^{25} -7.67132 q^{26} -12.6245 q^{27} -1.51081 q^{29} +8.29406 q^{30} -7.31788 q^{31} -11.3216 q^{32} -3.16125 q^{33} +11.3960 q^{34} +34.1536 q^{36} -11.4093 q^{37} -10.9328 q^{38} -9.24317 q^{39} -7.56562 q^{40} -9.30762 q^{41} +6.10291 q^{43} +4.88361 q^{44} +6.99351 q^{45} -19.5874 q^{46} -0.486833 q^{47} -31.8730 q^{48} -2.62366 q^{50} +13.7311 q^{51} +14.2792 q^{52} -14.0089 q^{53} +33.1224 q^{54} +1.00000 q^{55} -13.1730 q^{57} +3.96384 q^{58} -10.8022 q^{59} -15.4383 q^{60} +6.41820 q^{61} +19.1996 q^{62} +9.53929 q^{64} +2.92390 q^{65} +8.29406 q^{66} +5.11104 q^{67} -21.2122 q^{68} -23.6009 q^{69} +4.63039 q^{71} -52.9102 q^{72} +5.56874 q^{73} +29.9342 q^{74} -3.16125 q^{75} +20.3501 q^{76} +24.2510 q^{78} +1.62385 q^{79} +10.0824 q^{80} +18.9287 q^{81} +24.4200 q^{82} -3.35483 q^{83} -4.34355 q^{85} -16.0120 q^{86} +4.77604 q^{87} -7.56562 q^{88} -2.74617 q^{89} -18.3486 q^{90} +36.4594 q^{92} +23.1337 q^{93} +1.27729 q^{94} +4.16701 q^{95} +35.7905 q^{96} +4.34662 q^{97} +6.99351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9} - 2 q^{10} + 10 q^{11} - 20 q^{12} - 8 q^{13} - 8 q^{15} + 6 q^{16} - 28 q^{17} - 14 q^{18} + 10 q^{20} - 2 q^{22} - 16 q^{23} + 8 q^{24} + 10 q^{25} - 20 q^{26} - 32 q^{27} - 4 q^{30} - 20 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} + 42 q^{36} - 36 q^{37} - 24 q^{38} + 24 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{43} + 10 q^{44} + 10 q^{45} - 4 q^{46} - 12 q^{47} - 40 q^{48} - 2 q^{50} + 20 q^{51} - 4 q^{52} - 16 q^{53} + 48 q^{54} + 10 q^{55} + 4 q^{57} + 16 q^{58} - 32 q^{59} - 20 q^{60} + 16 q^{61} + 4 q^{62} - 34 q^{64} - 8 q^{65} - 4 q^{66} - 20 q^{67} - 32 q^{68} - 28 q^{69} + 12 q^{71} - 2 q^{72} - 20 q^{73} + 32 q^{74} - 8 q^{75} - 12 q^{76} + 20 q^{78} + 12 q^{79} + 6 q^{80} + 42 q^{81} + 40 q^{82} - 8 q^{83} - 28 q^{85} - 4 q^{86} - 28 q^{87} - 6 q^{88} - 68 q^{89} - 14 q^{90} + 32 q^{92} - 32 q^{93} - 16 q^{94} + 80 q^{96} - 36 q^{97} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9 - 2 * q^10 + 10 * q^11 - 20 * q^12 - 8 * q^13 - 8 * q^15 + 6 * q^16 - 28 * q^17 - 14 * q^18 + 10 * q^20 - 2 * q^22 - 16 * q^23 + 8 * q^24 + 10 * q^25 - 20 * q^26 - 32 * q^27 - 4 * q^30 - 20 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 + 42 * q^36 - 36 * q^37 - 24 * q^38 + 24 * q^39 - 6 * q^40 - 36 * q^41 - 4 * q^43 + 10 * q^44 + 10 * q^45 - 4 * q^46 - 12 * q^47 - 40 * q^48 - 2 * q^50 + 20 * q^51 - 4 * q^52 - 16 * q^53 + 48 * q^54 + 10 * q^55 + 4 * q^57 + 16 * q^58 - 32 * q^59 - 20 * q^60 + 16 * q^61 + 4 * q^62 - 34 * q^64 - 8 * q^65 - 4 * q^66 - 20 * q^67 - 32 * q^68 - 28 * q^69 + 12 * q^71 - 2 * q^72 - 20 * q^73 + 32 * q^74 - 8 * q^75 - 12 * q^76 + 20 * q^78 + 12 * q^79 + 6 * q^80 + 42 * q^81 + 40 * q^82 - 8 * q^83 - 28 * q^85 - 4 * q^86 - 28 * q^87 - 6 * q^88 - 68 * q^89 - 14 * q^90 + 32 * q^92 - 32 * q^93 - 16 * q^94 + 80 * q^96 - 36 * q^97 + 10 * q^99

Introduction

L-functions

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