LMFDB - Embedded newform 324.5.k.a.17.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,5,Mod(17,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("324.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	324.k (of order $18$, degree $6$, not minimal)

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:	no
Analytic conductor:	$33.4918680392$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	324.17
Dual form			324.5.k.a.305.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0223 + 5.64639i) q^{5} +(-0.626400 + 0.525612i) q^{7} +O(q^{10})$	$q+(32.0223 + 5.64639i) q^{5} +(-0.626400 + 0.525612i) q^{7} +(64.1736 - 11.3155i) q^{11} +(201.230 - 73.2417i) q^{13} +(-227.814 - 131.529i) q^{17} +(126.708 + 219.465i) q^{19} +(162.645 - 193.833i) q^{23} +(406.237 + 147.858i) q^{25} +(123.728 - 339.941i) q^{29} +(826.999 + 693.935i) q^{31} +(-23.0266 + 13.2944i) q^{35} +(-756.733 + 1310.70i) q^{37} +(-947.625 - 2603.58i) q^{41} +(-301.907 - 1712.20i) q^{43} +(1963.42 + 2339.92i) q^{47} +(-416.813 + 2363.86i) q^{49} -1072.38i q^{53} +2118.88 q^{55} +(4673.98 + 824.148i) q^{59} +(2209.58 - 1854.06i) q^{61} +(6857.39 - 1209.14i) q^{65} +(5924.45 - 2156.32i) q^{67} +(1573.20 + 908.285i) q^{71} +(1647.68 + 2853.87i) q^{73} +(-34.2508 + 40.8185i) q^{77} +(3482.95 + 1267.69i) q^{79} +(470.324 - 1292.20i) q^{83} +(-6552.47 - 5498.18i) q^{85} +(8830.06 - 5098.04i) q^{89} +(-87.5538 + 151.648i) q^{91} +(2818.30 + 7743.22i) q^{95} +(1550.17 + 8791.48i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 9 q^{5}+O(q^{10}) $ 72 * q - 9 * q^5	$ 72 q - 9 q^{5} - 18 q^{11} + 1278 q^{23} + 441 q^{25} - 1854 q^{29} - 1665 q^{31} + 2673 q^{35} + 5472 q^{41} + 1260 q^{43} - 5103 q^{47} - 5904 q^{49} + 10944 q^{59} + 8352 q^{61} - 8757 q^{65} + 378 q^{67} + 19764 q^{71} + 6111 q^{73} + 5679 q^{77} - 5652 q^{79} + 20061 q^{83} + 26100 q^{85} - 15633 q^{89} - 6039 q^{91} - 48024 q^{95} - 37530 q^{97}+O(q^{100}) $ 72 * q - 9 * q^5 - 18 * q^11 + 1278 * q^23 + 441 * q^25 - 1854 * q^29 - 1665 * q^31 + 2673 * q^35 + 5472 * q^41 + 1260 * q^43 - 5103 * q^47 - 5904 * q^49 + 10944 * q^59 + 8352 * q^61 - 8757 * q^65 + 378 * q^67 + 19764 * q^71 + 6111 * q^73 + 5679 * q^77 - 5652 * q^79 + 20061 * q^83 + 26100 * q^85 - 15633 * q^89 - 6039 * q^91 - 48024 * q^95 - 37530 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	32.0223	+	5.64639i	1.28089	+	0.225856i	0.772359	−	0.635187i	$-0.219077\pi$
$5$	32.0223	+	5.64639i	1.28089	+	0.225856i	0.508533	+	0.861043i	$0.330188\pi$
$6$		0			0
$7$	−0.626400	+	0.525612i	−0.0127837	+	0.0107268i	−0.649157	−	0.760654i	$-0.724878\pi$
$7$	−0.626400	+	0.525612i	−0.0127837	+	0.0107268i	0.636373	+	0.771381i	$0.280434\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	64.1736	−	11.3155i	0.530360	−	0.0935169i	0.0979458	−	0.995192i	$-0.468773\pi$
$11$	64.1736	−	11.3155i	0.530360	−	0.0935169i	0.432415	+	0.901675i	$0.357662\pi$
$12$		0			0
$13$	201.230	−	73.2417i	1.19071	−	0.433383i	0.330737	−	0.943723i	$-0.392703\pi$
$13$	201.230	−	73.2417i	1.19071	−	0.433383i	0.859973	+	0.510340i	$0.170480\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−227.814	−	131.529i	−0.788285	−	0.455117i	0.0510735	−	0.998695i	$-0.483736\pi$
$17$	−227.814	−	131.529i	−0.788285	−	0.455117i	−0.839358	+	0.543578i	$0.817069\pi$
$18$		0			0
$19$	126.708	+	219.465i	0.350993	+	0.607937i	0.986424	−	0.164221i	$-0.0525109\pi$
$19$	126.708	+	219.465i	0.350993	+	0.607937i	−0.635431	+	0.772158i	$0.719178\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	162.645	−	193.833i	0.307457	−	0.366413i	−0.590086	−	0.807341i	$-0.700906\pi$
$23$	162.645	−	193.833i	0.307457	−	0.366413i	0.897543	+	0.440928i	$0.145350\pi$
$24$		0			0
$25$	406.237	+	147.858i	0.649980	+	0.236573i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	123.728	−	339.941i	0.147121	−	0.404211i	−0.844141	−	0.536121i	$-0.819889\pi$
$29$	123.728	−	339.941i	0.147121	−	0.404211i	0.991262	+	0.131911i	$0.0421112\pi$
$30$		0			0
$31$	826.999	+	693.935i	0.860561	+	0.722096i	0.962089	−	0.272736i	$-0.0879286\pi$
$31$	826.999	+	693.935i	0.860561	+	0.722096i	−0.101528	+	0.994833i	$0.532373\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−23.0266	+	13.2944i	−0.0187972	+	0.0108526i
$36$		0			0
$37$	−756.733	+	1310.70i	−0.552763	+	0.957414i	0.445311	+	0.895376i	$0.353093\pi$
$37$	−756.733	+	1310.70i	−0.552763	+	0.957414i	−0.998074	+	0.0620378i	$0.980240\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−947.625	−	2603.58i	−0.563727	−	1.54883i	−0.814128	−	0.580685i	$-0.802785\pi$
$41$	−947.625	−	2603.58i	−0.563727	−	1.54883i	0.250401	−	0.968142i	$-0.419437\pi$
$42$		0			0
$43$	−301.907	−	1712.20i	−0.163281	−	0.926015i	−0.950819	−	0.309748i	$-0.899755\pi$
$43$	−301.907	−	1712.20i	−0.163281	−	0.926015i	0.787537	−	0.616267i	$-0.211356\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1963.42	+	2339.92i	0.888829	+	1.05926i	0.997870	+	0.0652278i	$0.0207774\pi$
$47$	1963.42	+	2339.92i	0.888829	+	1.05926i	−0.109042	+	0.994037i	$0.534778\pi$
$48$		0			0
$49$	−416.813	+	2363.86i	−0.173600	+	0.984533i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	1072.38i		−	0.381765i	−0.981613	−	0.190882i	$-0.938865\pi$
$53$		−	1072.38i		−	0.381765i	0.981613	−	0.190882i	$-0.0611349\pi$
$54$		0			0
$55$	2118.88			0.700455
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4673.98	+	824.148i	1.34271	+	0.236756i	0.798400	−	0.602127i	$-0.205680\pi$
$59$	4673.98	+	824.148i	1.34271	+	0.236756i	0.544311	+	0.838884i	$0.316791\pi$
$60$		0			0
$61$	2209.58	−	1854.06i	0.593814	−	0.498269i	−0.295637	−	0.955300i	$-0.595532\pi$
$61$	2209.58	−	1854.06i	0.593814	−	0.498269i	0.889451	+	0.457031i	$0.151087\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6857.39	−	1209.14i	1.62305	−	0.286188i
$66$		0			0
$67$	5924.45	−	2156.32i	1.31977	−	0.480357i	0.416385	−	0.909188i	$-0.363297\pi$
$67$	5924.45	−	2156.32i	1.31977	−	0.480357i	0.903385	+	0.428831i	$0.141075\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1573.20	+	908.285i	0.312080	+	0.180180i	0.647857	−	0.761762i	$-0.275665\pi$
$71$	1573.20	+	908.285i	0.312080	+	0.180180i	−0.335777	+	0.941942i	$0.608999\pi$
$72$		0			0
$73$	1647.68	+	2853.87i	0.309191	+	0.535535i	0.978186	−	0.207732i	$-0.0666083\pi$
$73$	1647.68	+	2853.87i	0.309191	+	0.535535i	−0.668994	+	0.743268i	$0.733275\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−34.2508	+	40.8185i	−0.00577682	+	0.00688455i
$78$		0			0
$79$	3482.95	+	1267.69i	0.558075	+	0.203123i	0.605631	−	0.795746i	$-0.292921\pi$
$79$	3482.95	+	1267.69i	0.558075	+	0.203123i	−0.0475555	+	0.998869i	$0.515143\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	470.324	−	1292.20i	0.0682717	−	0.187575i	−0.900865	−	0.434100i	$-0.857066\pi$
$83$	470.324	−	1292.20i	0.0682717	−	0.187575i	0.969136	+	0.246525i	$0.0792887\pi$
$84$		0			0
$85$	−6552.47	−	5498.18i	−0.906917	−	0.760994i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8830.06	−	5098.04i	1.11477	−	0.643610i	0.174706	−	0.984621i	$-0.444102\pi$
$89$	8830.06	−	5098.04i	1.11477	−	0.643610i	0.940060	+	0.341010i	$0.110769\pi$
$90$		0			0
$91$	−87.5538	+	151.648i	−0.0105729	+	0.0183127i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2818.30	+	7743.22i	0.312277	+	0.857975i
$96$		0			0
$97$	1550.17	+	8791.48i	0.164754	+	0.934369i	0.949317	+	0.314319i	$0.101776\pi$
$97$	1550.17	+	8791.48i	0.164754	+	0.934369i	−0.784563	+	0.620049i	$0.787113\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4742.86	−	5652.32i	−0.464941	−	0.554095i	0.481721	−	0.876325i	$-0.340012\pi$
$101$	−4742.86	−	5652.32i	−0.464941	−	0.554095i	−0.946661	+	0.322230i	$0.895568\pi$
$102$		0			0
$103$	−2700.81	+	15317.1i	−0.254578	+	1.44378i	0.542577	+	0.840006i	$0.317449\pi$
$103$	−2700.81	+	15317.1i	−0.254578	+	1.44378i	−0.797154	+	0.603776i	$0.793662\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	16462.3i		−	1.43789i	−0.695069	−	0.718943i	$-0.744626\pi$
$107$		−	16462.3i		−	1.43789i	0.695069	−	0.718943i	$-0.255374\pi$
$108$		0			0
$109$	17712.9			1.49086			0.745428	−	0.666587i	$-0.232245\pi$
$109$	17712.9			1.49086			0.745428	+	0.666587i	$0.232245\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−21631.8	−	3814.28i	−1.69409	−	0.298714i	−0.758466	−	0.651712i	$-0.774051\pi$
$113$	−21631.8	−	3814.28i	−1.69409	−	0.298714i	−0.935624	+	0.352999i	$0.885162\pi$
$114$		0			0
$115$	6302.71	−	5288.60i	0.476576	−	0.399894i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	211.836	−	37.3524i	0.0149591	−	0.00263770i
$120$		0			0
$121$	−9767.83	+	3555.20i	−0.667156	+	0.242825i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5426.18	−	3132.80i	−0.347275	−	0.200499i
$126$		0			0
$127$	12090.6	+	20941.5i	0.749617	+	1.29837i	0.948007	+	0.318251i	$0.103095\pi$
$127$	12090.6	+	20941.5i	0.749617	+	1.29837i	−0.198390	+	0.980123i	$0.563571\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8379.80	+	9986.66i	−0.488305	+	0.581939i	−0.952786	−	0.303644i	$-0.901797\pi$
$131$	−8379.80	+	9986.66i	−0.488305	+	0.581939i	0.464481	+	0.885583i	$0.346241\pi$
$132$		0			0
$133$	−194.724	−	70.8737i	−0.0110082	−	0.00400665i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1646.39	+	4523.42i	−0.0877186	+	0.241005i	−0.975794	−	0.218694i	$-0.929820\pi$
$137$	−1646.39	+	4523.42i	−0.0877186	+	0.241005i	0.888075	+	0.459699i	$0.152043\pi$
$138$		0			0
$139$	−27041.7	−	22690.7i	−1.39960	−	1.17441i	−0.961275	−	0.275590i	$-0.911127\pi$
$139$	−27041.7	−	22690.7i	−1.39960	−	1.17441i	−0.438326	−	0.898816i	$-0.644429\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	12084.9	−	6977.21i	0.590977	−	0.341201i
$144$		0			0
$145$	5881.51	−	10187.1i	0.279739	−	0.484522i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3472.62	+	9540.93i	0.156417	+	0.429752i	0.993004	−	0.118082i	$-0.0376746\pi$
$149$	3472.62	+	9540.93i	0.156417	+	0.429752i	−0.836587	+	0.547834i	$0.815452\pi$
$150$		0			0
$151$	−5606.40	−	31795.4i	−0.245884	−	1.39448i	−0.818431	−	0.574605i	$-0.805156\pi$
$151$	−5606.40	−	31795.4i	−0.245884	−	1.39448i	0.572547	−	0.819872i	$-0.305955\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	22564.2	+	26890.9i	0.939196	+	1.11929i
$156$		0			0
$157$	−2655.95	+	15062.6i	−0.107751	+	0.611085i	0.882335	+	0.470621i	$0.155970\pi$
$157$	−2655.95	+	15062.6i	−0.107751	+	0.611085i	−0.990086	+	0.140463i	$0.955141\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			206.905i			0.00798213i
$162$		0			0
$163$	−21291.3			−0.801358			−0.400679	−	0.916219i	$-0.631226\pi$
$163$	−21291.3			−0.801358			−0.400679	+	0.916219i	$0.631226\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−15713.5	−	2770.72i	−0.563431	−	0.0993481i	−0.115324	−	0.993328i	$-0.536791\pi$
$167$	−15713.5	−	2770.72i	−0.563431	−	0.0993481i	−0.448107	+	0.893980i	$0.647902\pi$
$168$		0			0
$169$	13250.1	−	11118.2i	0.463925	−	0.389279i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	26958.7	−	4753.55i	0.900756	−	0.158828i	0.295953	−	0.955203i	$-0.404363\pi$
$173$	26958.7	−	4753.55i	0.900756	−	0.158828i	0.604803	+	0.796375i	$0.293252\pi$
$174$		0			0
$175$	−332.183	+	120.905i	−0.0108468	+	0.00394791i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−19928.5	−	11505.7i	−0.621970	−	0.359094i	0.155666	−	0.987810i	$-0.450248\pi$
$179$	−19928.5	−	11505.7i	−0.621970	−	0.359094i	−0.777635	+	0.628715i	$0.783581\pi$
$180$		0			0
$181$	−7649.80	−	13249.8i	−0.233503	−	0.404439i	0.725333	−	0.688398i	$-0.241686\pi$
$181$	−7649.80	−	13249.8i	−0.233503	−	0.404439i	−0.958837	+	0.283958i	$0.908352\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−31633.0	+	37698.8i	−0.924267	+	1.10150i
$186$		0			0
$187$	−16108.0	−	5862.83i	−0.460636	−	0.167658i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−14485.2	+	39797.9i	−0.397063	+	1.09092i	0.566645	+	0.823962i	$0.308241\pi$
$191$	−14485.2	+	39797.9i	−0.397063	+	1.09092i	−0.963708	+	0.266959i	$0.913981\pi$
$192$		0			0
$193$	−46967.8	−	39410.7i	−1.26092	−	1.05803i	−0.995584	−	0.0938764i	$-0.970074\pi$
$193$	−46967.8	−	39410.7i	−1.26092	−	1.05803i	−0.265332	−	0.964157i	$-0.585481\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−49343.8	+	28488.7i	−1.27145	+	0.734074i	−0.975261	−	0.221055i	$-0.929050\pi$
$197$	−49343.8	+	28488.7i	−1.27145	+	0.734074i	−0.296191	+	0.955129i	$0.595717\pi$
$198$		0			0
$199$	−31505.5	+	54569.2i	−0.795574	+	1.37797i	0.126900	+	0.991916i	$0.459497\pi$
$199$	−31505.5	+	54569.2i	−0.795574	+	1.37797i	−0.922474	+	0.386059i	$0.873836\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	101.174	+	277.972i	0.00245514	+	0.00674543i
$204$		0			0
$205$	−15644.3	−	88723.2i	−0.372262	−	2.11120i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10614.7	+	12650.1i	0.243005	+	0.289602i
$210$		0			0
$211$	−4090.36	+	23197.6i	−0.0918747	+	0.521048i	0.903786	+	0.427986i	$0.140777\pi$
$211$	−4090.36	+	23197.6i	−0.0918747	+	0.521048i	−0.995660	+	0.0930620i	$0.970335\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	56533.3i		−	1.22300i
$216$		0			0
$217$	−882.773			−0.0187469
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−55476.5	−	9782.00i	−1.13586	−	0.200282i
$222$		0			0
$223$	12832.7	−	10767.9i	0.258052	−	0.216531i	−0.504578	−	0.863366i	$-0.668352\pi$
$223$	12832.7	−	10767.9i	0.258052	−	0.216531i	0.762630	+	0.646835i	$0.223908\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	48389.9	−	8532.45i	0.939081	−	0.165585i	0.316900	−	0.948459i	$-0.397358\pi$
$227$	48389.9	−	8532.45i	0.939081	−	0.165585i	0.622181	+	0.782873i	$0.286247\pi$
$228$		0			0
$229$	−68136.6	+	24799.7i	−1.29930	+	0.472906i	−0.896769	−	0.442500i	$-0.854092\pi$
$229$	−68136.6	+	24799.7i	−1.29930	+	0.472906i	−0.402531	+	0.915406i	$0.631870\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−43708.9	−	25235.3i	−0.805115	−	0.464834i	0.0401414	−	0.999194i	$-0.487219\pi$
$233$	−43708.9	−	25235.3i	−0.805115	−	0.464834i	−0.845257	+	0.534360i	$0.820552\pi$
$234$		0			0
$235$	49661.2	+	86015.7i	0.899252	+	1.55755i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−24701.5	+	29438.1i	−0.432442	+	0.515364i	−0.937625	−	0.347648i	$-0.886980\pi$
$239$	−24701.5	+	29438.1i	−0.432442	+	0.515364i	0.505183	+	0.863012i	$0.331425\pi$
$240$		0			0
$241$	−53245.2	−	19379.7i	−0.916740	−	0.333666i	−0.159799	−	0.987149i	$-0.551085\pi$
$241$	−53245.2	−	19379.7i	−0.916740	−	0.333666i	−0.756941	+	0.653483i	$0.773307\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−26694.6	+	73342.9i	−0.444725	+	1.22187i
$246$		0			0
$247$	41571.5	+	34882.6i	0.681400	+	0.571762i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	52230.0	−	30155.0i	0.829034	−	0.478643i	−0.0244875	−	0.999700i	$-0.507795\pi$
$251$	52230.0	−	30155.0i	0.829034	−	0.478643i	0.853522	+	0.521057i	$0.174462\pi$
$252$		0			0
$253$	8244.18	−	14279.3i	0.128797	−	0.223083i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−31430.6	−	86354.9i	−0.475868	−	1.30744i	−0.912971	−	0.408025i	$-0.866218\pi$
$257$	−31430.6	−	86354.9i	−0.475868	−	1.30744i	0.437103	−	0.899412i	$-0.356005\pi$
$258$		0			0
$259$	−214.902	−	1218.77i	−0.00320362	−	0.0181686i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	19365.9	+	23079.4i	0.279980	+	0.333667i	0.887647	−	0.460525i	$-0.152339\pi$
$263$	19365.9	+	23079.4i	0.279980	+	0.333667i	−0.607667	+	0.794192i	$0.707894\pi$
$264$		0			0
$265$	6055.06	−	34340.0i	0.0862238	−	0.488999i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	18684.3i		−	0.258209i	−0.991631	−	0.129105i	$-0.958790\pi$
$269$		−	18684.3i		−	0.258209i	0.991631	−	0.129105i	$-0.0412103\pi$
$270$		0			0
$271$	88004.5			1.19830			0.599151	−	0.800636i	$-0.295505\pi$
$271$	88004.5			1.19830			0.599151	+	0.800636i	$0.295505\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	27742.8	+	4891.80i	0.366847	+	0.0646850i
$276$		0			0
$277$	98425.6	−	82588.9i	1.28277	−	1.07637i	0.289914	−	0.957053i	$-0.406373\pi$
$277$	98425.6	−	82588.9i	1.28277	−	1.07637i	0.992856	−	0.119319i	$-0.0380711\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	69324.8	−	12223.8i	0.877963	−	0.154808i	0.283539	−	0.958961i	$-0.408491\pi$
$281$	69324.8	−	12223.8i	0.877963	−	0.154808i	0.594423	+	0.804152i	$0.297380\pi$
$282$		0			0
$283$	−55263.9	+	20114.4i	−0.690031	+	0.251151i	−0.663148	−	0.748488i	$-0.730780\pi$
$283$	−55263.9	+	20114.4i	−0.690031	+	0.251151i	−0.0268825	+	0.999639i	$0.508558\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1962.07	+	1132.80i	0.0238204	+	0.0137527i
$288$		0			0
$289$	−7160.91	−	12403.1i	−0.0857379	−	0.148502i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−51755.6	+	61679.9i	−0.602868	+	0.718470i	−0.978024	−	0.208492i	$-0.933145\pi$
$293$	−51755.6	+	61679.9i	−0.602868	+	0.718470i	0.375156	+	0.926962i	$0.377589\pi$
$294$		0			0
$295$	145018.	+	52782.2i	1.66639	+	0.606518i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	18532.4	−	50917.3i	0.207295	−	0.569538i
$300$		0			0
$301$	1089.07	+	913.837i	0.0120205	+	0.0100864i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	81224.6	−	46895.1i	0.873148	−	0.504112i
$306$		0			0
$307$	−17464.5	+	30249.4i	−0.185302	+	0.320952i	−0.943678	−	0.330865i	$-0.892660\pi$
$307$	−17464.5	+	30249.4i	−0.185302	+	0.320952i	0.758376	+	0.651817i	$0.225993\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	43308.4	+	118989.i	0.447766	+	1.23023i	0.934276	+	0.356551i	$0.116047\pi$
$311$	43308.4	+	118989.i	0.447766	+	1.23023i	−0.486510	+	0.873675i	$0.661730\pi$
$312$		0			0
$313$	17650.8	+	100103.i	0.180167	+	1.02178i	0.932009	+	0.362436i	$0.118055\pi$
$313$	17650.8	+	100103.i	0.180167	+	1.02178i	−0.751841	+	0.659344i	$0.770834\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−107949.	−	128649.i	−1.07424	−	1.28023i	−0.957925	−	0.287018i	$-0.907336\pi$
$317$	−107949.	−	128649.i	−1.07424	−	1.28023i	−0.116316	−	0.993212i	$-0.537108\pi$
$318$		0			0
$319$	4093.48	−	23215.3i	0.0402265	−	0.228136i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	66663.1i		−	0.638970i
$324$		0			0
$325$	92576.5			0.876464
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2459.78	−	433.725i	−0.0227250	−	0.00400703i
$330$		0			0
$331$	−64718.4	+	54305.2i	−0.590707	+	0.495662i	−0.888443	−	0.458986i	$-0.848213\pi$
$331$	−64718.4	+	54305.2i	−0.590707	+	0.495662i	0.297737	+	0.954648i	$0.403768\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	201890.	−	35598.6i	1.79897	−	0.317208i
$336$		0			0
$337$	−125092.	+	45529.8i	−1.10146	+	0.400900i	−0.827856	−	0.560941i	$-0.810439\pi$
$337$	−125092.	+	45529.8i	−1.10146	+	0.400900i	−0.273608	+	0.961841i	$0.588217\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	60923.8	+	35174.4i	0.523936	+	0.302494i
$342$		0			0
$343$	−1963.04	−	3400.09i	−0.0166856	−	0.0289003i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	32534.2	−	38772.8i	0.270198	−	0.322009i	−0.613835	−	0.789434i	$-0.710374\pi$
$347$	32534.2	−	38772.8i	0.270198	−	0.322009i	0.884032	+	0.467425i	$0.154818\pi$
$348$		0			0
$349$	−106866.	−	38896.0i	−0.877381	−	0.319341i	−0.136229	−	0.990677i	$-0.543498\pi$
$349$	−106866.	−	38896.0i	−0.877381	−	0.319341i	−0.741152	+	0.671337i	$0.765720\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−30240.3	+	83084.5i	−0.242681	+	0.666762i	0.757226	+	0.653153i	$0.226554\pi$
$353$	−30240.3	+	83084.5i	−0.242681	+	0.666762i	−0.999907	+	0.0136087i	$0.995668\pi$
$354$		0			0
$355$	45248.8	+	37968.3i	0.359046	+	0.301276i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	57834.2	−	33390.6i	0.448741	−	0.259081i	−0.258557	−	0.965996i	$-0.583247\pi$
$359$	57834.2	−	33390.6i	0.448741	−	0.259081i	0.707298	+	0.706915i	$0.249914\pi$
$360$		0			0
$361$	33050.5	−	57245.2i	0.253608	−	0.439263i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	36648.5	+	100691.i	0.275087	+	0.755795i
$366$		0			0
$367$	4445.85	+	25213.6i	0.0330082	+	0.187199i	0.996854	−	0.0792626i	$-0.0252566\pi$
$367$	4445.85	+	25213.6i	0.0330082	+	0.187199i	−0.963846	+	0.266462i	$0.914145\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	563.655	+	671.738i	0.00409511	+	0.00488036i
$372$		0			0
$373$	31316.4	−	177604.i	0.225089	−	1.27654i	−0.637425	−	0.770512i	$-0.720000\pi$
$373$	31316.4	−	177604.i	0.225089	−	1.27654i	0.862514	−	0.506033i	$-0.168888\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	77468.4i		−	0.545057i
$378$		0			0
$379$	25959.6			0.180725			0.0903627	−	0.995909i	$-0.471197\pi$
$379$	25959.6			0.180725			0.0903627	+	0.995909i	$0.471197\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−29611.2	−	5221.26i	−0.201864	−	0.0355941i	0.0718017	−	0.997419i	$-0.477125\pi$
$383$	−29611.2	−	5221.26i	−0.201864	−	0.0355941i	−0.273666	+	0.961825i	$0.588236\pi$
$384$		0			0
$385$	−1327.27	+	1113.71i	−0.00895440	+	0.00751363i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−101226.	+	17848.9i	−0.668949	+	0.117954i	−0.497801	−	0.867291i	$-0.665859\pi$
$389$	−101226.	+	17848.9i	−0.668949	+	0.117954i	−0.171149	+	0.985245i	$0.554748\pi$
$390$		0			0
$391$	−62547.4	+	22765.4i	−0.409124	+	0.148909i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	104374.	+	60260.4i	0.668957	+	0.386223i
$396$		0			0
$397$	88748.5	+	153717.i	0.563093	+	0.975306i	0.997224	+	0.0744562i	$0.0237221\pi$
$397$	88748.5	+	153717.i	0.563093	+	0.975306i	−0.434131	+	0.900850i	$0.642945\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	179356.	−	213748.i	1.11539	−	1.32927i	0.176797	−	0.984247i	$-0.443426\pi$
$401$	179356.	−	213748.i	1.11539	−	1.32927i	0.938594	−	0.345024i	$-0.112129\pi$
$402$		0			0
$403$	217242.	+	79069.6i	1.33762	+	0.486855i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−33731.0	+	92675.2i	−0.203629	+	0.559467i
$408$		0			0
$409$	214342.	+	179854.i	1.28133	+	1.07516i	0.993060	+	0.117613i	$0.0375242\pi$
$409$	214342.	+	179854.i	1.28133	+	1.07516i	0.288269	+	0.957549i	$0.406920\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3360.96	+	1940.45i	−0.0197044	+	0.0113764i
$414$		0			0
$415$	22357.1	−	38723.7i	0.129814	−	0.224844i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−35321.3	−	97044.6i	−0.201191	−	0.552769i	0.797532	−	0.603276i	$-0.206138\pi$
$419$	−35321.3	−	97044.6i	−0.201191	−	0.552769i	−0.998724	+	0.0505076i	$0.983916\pi$
$420$		0			0
$421$	−24823.5	−	140781.i	−0.140055	−	0.794290i	−0.971206	−	0.238243i	$-0.923428\pi$
$421$	−24823.5	−	140781.i	−0.140055	−	0.794290i	0.831151	−	0.556047i	$-0.187683\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−73099.1	−	87116.1i	−0.404701	−	0.482304i
$426$		0			0
$427$	−409.567	+	2322.77i	−0.00224631	+	0.0127394i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			160792.i			0.865585i	0.901494	+	0.432792i	$0.142472\pi$
$431$			160792.i			0.865585i	−0.901494	+	0.432792i	$0.857528\pi$
$432$		0			0
$433$	−121665.			−0.648919			−0.324459	−	0.945900i	$-0.605182\pi$
$433$	−121665.			−0.648919			−0.324459	+	0.945900i	$0.605182\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	63147.9	+	11134.7i	0.330671	+	0.0583062i
$438$		0			0
$439$	−34415.6	+	28878.1i	−0.178577	+	0.149844i	−0.727695	−	0.685901i	$-0.759408\pi$
$439$	−34415.6	+	28878.1i	−0.178577	+	0.149844i	0.549118	+	0.835745i	$0.314964\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	325180.	−	57338.0i	1.65698	−	0.292169i	0.734610	−	0.678489i	$-0.237365\pi$
$443$	325180.	−	57338.0i	1.65698	−	0.292169i	0.922365	+	0.386320i	$0.126254\pi$
$444$		0			0
$445$	311544.	−	113393.i	1.57326	−	0.572619i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−93307.3	−	53871.0i	−0.462832	−	0.267216i	0.250402	−	0.968142i	$-0.419437\pi$
$449$	−93307.3	−	53871.0i	−0.462832	−	0.267216i	−0.713234	+	0.700926i	$0.752770\pi$
$450$		0			0
$451$	−90273.4	−	156358.i	−0.443820	−	0.768719i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3659.93	+	4361.74i	−0.0176787	+	0.0210687i
$456$		0			0
$457$	−138582.	−	50439.6i	−0.663549	−	0.241512i	−0.0117811	−	0.999931i	$-0.503750\pi$
$457$	−138582.	−	50439.6i	−0.663549	−	0.241512i	−0.651768	+	0.758419i	$0.725972\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−34531.3	+	94873.8i	−0.162484	+	0.446421i	−0.994039	−	0.109021i	$-0.965229\pi$
$461$	−34531.3	+	94873.8i	−0.162484	+	0.446421i	0.831556	+	0.555442i	$0.187451\pi$
$462$		0			0
$463$	−55945.6	−	46943.9i	−0.260978	−	0.218987i	0.502904	−	0.864342i	$-0.332265\pi$
$463$	−55945.6	−	46943.9i	−0.260978	−	0.218987i	−0.763882	+	0.645356i	$0.776709\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−212150.	+	122485.i	−0.972766	+	0.561627i	−0.900078	−	0.435728i	$-0.856491\pi$
$467$	−212150.	+	122485.i	−0.972766	+	0.561627i	−0.0726875	+	0.997355i	$0.523158\pi$
$468$		0			0
$469$	−2577.69	+	4464.68i	−0.0117188	+	0.0202976i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−38749.0	−	106462.i	−0.173196	−	0.475852i
$474$		0			0
$475$	19023.9	+	107890.i	0.0843164	+	0.478182i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−255407.	−	304382.i	−1.11317	−	1.32663i	−0.939783	−	0.341772i	$-0.888973\pi$
$479$	−255407.	−	304382.i	−1.11317	−	1.32663i	−0.173388	−	0.984854i	$-0.555471\pi$
$480$		0			0
$481$	−56279.4	+	319176.i	−0.243254	+	1.37956i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			290276.i			1.23404i
$486$		0			0
$487$	−384227.			−1.62006			−0.810029	−	0.586390i	$-0.800549\pi$
$487$	−384227.			−1.62006			−0.810029	+	0.586390i	$0.800549\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−44176.2	−	7789.46i	−0.183242	−	0.0323105i	0.0812739	−	0.996692i	$-0.474101\pi$
$491$	−44176.2	−	7789.46i	−0.183242	−	0.0323105i	−0.264516	+	0.964381i	$0.585212\pi$
$492$		0			0
$493$	−72899.1	+	61169.6i	−0.299936	+	0.251676i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1462.86	+	257.941i	−0.00592228	+	0.00104426i
$498$		0			0
$499$	193457.	−	70412.5i	0.776931	−	0.282780i	0.0770387	−	0.997028i	$-0.475453\pi$
$499$	193457.	−	70412.5i	0.776931	−	0.282780i	0.699892	+	0.714248i	$0.253231\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−251362.	−	145124.i	−0.993492	−	0.573593i	−0.0871759	−	0.996193i	$-0.527784\pi$
$503$	−251362.	−	145124.i	−0.993492	−	0.573593i	−0.906316	+	0.422600i	$0.861118\pi$
$504$		0			0
$505$	−119962.	−	207780.i	−0.470393	−	0.814745i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	88492.6	−	105461.i	0.341563	−	0.407060i	−0.567730	−	0.823215i	$-0.692178\pi$
$509$	88492.6	−	105461.i	0.341563	−	0.407060i	0.909294	+	0.416155i	$0.136623\pi$
$510$		0			0
$511$	−2532.14	−	921.622i	−0.00969718	−	0.00352948i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−172973.	+	475238.i	−0.652173	+	1.79183i
$516$		0			0
$517$	152477.	+	127944.i	0.570459	+	0.478672i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−405748.	+	234259.i	−1.49479	+	0.863019i	−0.999982	−	0.00598173i	$-0.998096\pi$
$521$	−405748.	+	234259.i	−1.49479	+	0.863019i	−0.494811	+	0.869001i	$0.664763\pi$
$522$		0			0
$523$	−99085.8	+	171622.i	−0.362250	+	0.627435i	−0.988331	−	0.152323i	$-0.951325\pi$
$523$	−99085.8	+	171622.i	−0.362250	+	0.627435i	0.626081	+	0.779758i	$0.284658\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−97130.0	−	266862.i	−0.349729	−	0.960873i
$528$		0			0
$529$	37476.2	+	212538.i	0.133919	+	0.759495i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−381381.	−	454512.i	−1.34247	−	1.59989i
$534$		0			0
$535$	92952.9	−	527162.i	0.324755	−	1.84177i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			156414.i			0.538392i
$540$		0			0
$541$	−178797.			−0.610894			−0.305447	−	0.952209i	$-0.598806\pi$
$541$	−178797.			−0.610894			−0.305447	+	0.952209i	$0.598806\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	567206.	+	100014.i	1.90962	+	0.336718i
$546$		0			0
$547$	−242815.	+	203746.i	−0.811524	+	0.680950i	−0.950971	−	0.309280i	$-0.899912\pi$
$547$	−242815.	+	203746.i	−0.811524	+	0.680950i	0.139447	+	0.990230i	$0.455468\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	90282.7	−	15919.3i	0.297373	−	0.0524348i
$552$		0			0
$553$	−2848.03	+	1036.60i	−0.00931311	+	0.00338970i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	237033.	+	136851.i	0.764008	+	0.441100i	0.830733	−	0.556671i	$-0.187922\pi$
$557$	237033.	+	136851.i	0.764008	+	0.441100i	−0.0667252	+	0.997771i	$0.521255\pi$
$558$		0			0
$559$	−186157.	−	322434.i	−0.595740	−	1.03185i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−317658.	+	378570.i	−1.00217	+	1.19434i	−0.0212842	+	0.999773i	$0.506775\pi$
$563$	−317658.	+	378570.i	−1.00217	+	1.19434i	−0.980889	+	0.194570i	$0.937669\pi$
$564$		0			0
$565$	−671164.	−	244284.i	−2.10248	−	0.765240i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−143217.	+	393485.i	−0.442353	+	1.21536i	0.495587	+	0.868558i	$0.334953\pi$
$569$	−143217.	+	393485.i	−0.442353	+	1.21536i	−0.937940	+	0.346797i	$0.887269\pi$
$570$		0			0
$571$	−345203.	−	289659.i	−1.05877	−	0.888414i	−0.0647820	−	0.997899i	$-0.520635\pi$
$571$	−345203.	−	289659.i	−1.05877	−	0.888414i	−0.993988	+	0.109486i	$0.965080\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	94732.1	−	54693.6i	0.286524	−	0.165425i
$576$		0			0
$577$	141127.	−	244440.i	0.423896	−	0.734209i	−0.572421	−	0.819960i	$-0.693996\pi$
$577$	141127.	−	244440.i	0.423896	−	0.734209i	0.996317	+	0.0857507i	$0.0273289\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	384.587	+	1056.65i	0.00113931	+	0.00313023i
$582$		0			0
$583$	−12134.5	−	68818.3i	−0.0357014	−	0.202473i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−139731.	−	166525.i	−0.405523	−	0.483284i	0.524172	−	0.851612i	$-0.324375\pi$
$587$	−139731.	−	166525.i	−0.405523	−	0.483284i	−0.929696	+	0.368328i	$0.879930\pi$
$588$		0			0
$589$	−47506.9	+	269425.i	−0.136939	+	0.776617i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			341168.i			0.970196i	0.874460	+	0.485098i	$0.161216\pi$
$593$			341168.i			0.970196i	−0.874460	+	0.485098i	$0.838784\pi$
$594$		0			0
$595$	6994.38			0.0197568
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−22301.2	−	3932.30i	−0.0621548	−	0.0109596i	0.142484	−	0.989797i	$-0.454491\pi$
$599$	−22301.2	−	3932.30i	−0.0621548	−	0.0109596i	−0.204639	+	0.978837i	$0.565602\pi$
$600$		0			0
$601$	16674.8	−	13991.8i	0.0461650	−	0.0387370i	−0.619413	−	0.785065i	$-0.712629\pi$
$601$	16674.8	−	13991.8i	0.0461650	−	0.0387370i	0.665578	+	0.746328i	$0.268185\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−332862.	+	58692.6i	−0.909398	+	0.160351i
$606$		0			0
$607$	237494.	−	86440.9i	0.644578	−	0.234607i	0.00101423	−	0.999999i	$-0.499677\pi$
$607$	237494.	−	86440.9i	0.644578	−	0.234607i	0.643564	+	0.765392i	$0.277455\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	566479.	+	327057.i	1.51740	+	0.876074i
$612$		0			0
$613$	−183595.	−	317996.i	−0.488586	−	0.846255i	0.511328	−	0.859386i	$-0.329154\pi$
$613$	−183595.	−	317996.i	−0.488586	−	0.846255i	−0.999914	+	0.0131305i	$0.995820\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	293338.	−	349587.i	0.770546	−	0.918301i	−0.227920	−	0.973680i	$-0.573192\pi$
$617$	293338.	−	349587.i	0.770546	−	0.918301i	0.998465	+	0.0553792i	$0.0176368\pi$
$618$		0			0
$619$	434664.	+	158205.i	1.13442	+	0.412894i	0.839894	−	0.542751i	$-0.182617\pi$
$619$	434664.	+	158205.i	1.13442	+	0.412894i	0.294523	+	0.955644i	$0.404839\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2851.56	+	7834.60i	−0.00734695	+	0.0201856i
$624$		0			0
$625$	−363049.	−	304635.i	−0.929406	−	0.779864i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	344789.	−	199064.i	0.871470	−	0.503143i
$630$		0			0
$631$	249675.	−	432451.i	0.627072	−	1.08612i	−0.361065	−	0.932541i	$-0.617587\pi$
$631$	249675.	−	432451.i	0.627072	−	1.08612i	0.988136	−	0.153579i	$-0.0490800\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	268924.	+	738862.i	0.666932	+	1.83238i
$636$		0			0
$637$	89258.2	+	506209.i	0.219973	+	1.24753i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−316769.	−	377510.i	−0.770951	−	0.918783i	0.227537	−	0.973770i	$-0.426933\pi$
$641$	−316769.	−	377510.i	−0.770951	−	0.918783i	−0.998487	+	0.0549865i	$0.982488\pi$
$642$		0			0
$643$	−28665.3	+	162569.i	−0.0693321	+	0.393202i	0.930318	+	0.366754i	$0.119531\pi$
$643$	−28665.3	+	162569.i	−0.0693321	+	0.393202i	−0.999650	+	0.0264481i	$0.991580\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	146391.i		−	0.349708i	−0.984594	−	0.174854i	$-0.944055\pi$
$647$		−	146391.i		−	0.349708i	0.984594	−	0.174854i	$-0.0559453\pi$
$648$		0			0
$649$	309272.			0.734261
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−208536.	−	36770.6i	−0.489052	−	0.0862331i	−0.0763160	−	0.997084i	$-0.524316\pi$
$653$	−208536.	−	36770.6i	−0.489052	−	0.0862331i	−0.412736	+	0.910851i	$0.635427\pi$
$654$		0			0
$655$	−324729.	+	272480.i	−0.756900	+	0.635114i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	277985.	−	49016.3i	0.640105	−	0.112868i	0.155830	−	0.987784i	$-0.450195\pi$
$659$	277985.	−	49016.3i	0.640105	−	0.112868i	0.484275	+	0.874916i	$0.339084\pi$
$660$		0			0
$661$	577616.	−	210235.i	1.32202	−	0.481174i	0.417912	−	0.908488i	$-0.362762\pi$
$661$	577616.	−	210235.i	1.32202	−	0.481174i	0.904104	+	0.427313i	$0.140540\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5835.32	−	3369.02i	−0.0131954	−	0.00761835i
$666$		0			0
$667$	−45767.8	−	79272.2i	−0.102875	−	0.178184i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	120817.	−	143984.i	0.268339	−	0.319794i
$672$		0			0
$673$	76252.3	+	27753.6i	0.168354	+	0.0612758i	0.424822	−	0.905277i	$-0.360337\pi$
$673$	76252.3	+	27753.6i	0.168354	+	0.0612758i	−0.256468	+	0.966553i	$0.582559\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	47923.1	−	131668.i	0.104560	−	0.287278i	−0.876369	−	0.481640i	$-0.840041\pi$
$677$	47923.1	−	131668.i	0.104560	−	0.287278i	0.980930	+	0.194362i	$0.0622637\pi$
$678$		0			0
$679$	−5591.94	−	4692.19i	−0.0121289	−	0.0101774i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−548738.	+	316814.i	−1.17632	+	0.679146i	−0.955159	−	0.296092i	$-0.904316\pi$
$683$	−548738.	+	316814.i	−1.17632	+	0.679146i	−0.221156	+	0.975238i	$0.570983\pi$
$684$		0			0
$685$	−78262.2	+	135554.i	−0.166790	+	0.288889i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−78542.8	−	215794.i	−0.165450	−	0.454571i
$690$		0			0
$691$	43963.9	+	249332.i	0.0920746	+	0.522181i	0.995605	+	0.0936562i	$0.0298554\pi$
$691$	43963.9	+	249332.i	0.0920746	+	0.522181i	−0.903530	+	0.428525i	$0.859033\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−737817.	−	879296.i	−1.52749	−	1.82039i
$696$		0			0
$697$	−126563.	+	717772.i	−0.260519	+	1.47748i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			461452.i			0.939055i	0.882918	+	0.469527i	$0.155576\pi$
$701$			461452.i			0.939055i	−0.882918	+	0.469527i	$0.844424\pi$
$702$		0			0
$703$	−383537.			−0.776063
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5941.86	+	1047.71i	0.0118873	+	0.00209605i
$708$		0			0
$709$	−120618.	+	101210.i	−0.239949	+	0.201341i	−0.754830	−	0.655921i	$-0.772281\pi$
$709$	−120618.	+	101210.i	−0.239949	+	0.201341i	0.514881	+	0.857262i	$0.327836\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	269014.	−	47434.5i	0.529171	−	0.0933072i
$714$		0			0
$715$	426382.	−	155190.i	0.834039	−	0.303565i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−800690.	−	462278.i	−1.54884	−	0.894223i	−0.998231	−	0.0594593i	$-0.981062\pi$
$719$	−800690.	−	462278.i	−1.54884	−	0.894223i	−0.550609	−	0.834764i	$-0.685604\pi$
$720$		0			0
$721$	−6359.06	−	11014.2i	−0.0122327	−	0.0211876i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	100526.	−	119802.i	0.191251	−	0.227924i
$726$		0			0
$727$	603792.	+	219762.i	1.14240	+	0.415800i	0.842780	−	0.538258i	$-0.180917\pi$
$727$	603792.	+	219762.i	1.14240	+	0.415800i	0.299621	+	0.954058i	$0.403140\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−156425.	+	429773.i	−0.292732	+	0.804275i
$732$		0			0
$733$	268719.	+	225482.i	0.500138	+	0.419666i	0.857643	−	0.514246i	$-0.171928\pi$
$733$	268719.	+	225482.i	0.500138	+	0.419666i	−0.357505	+	0.933911i	$0.616372\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	355793.	−	205417.i	0.655032	−	0.378183i
$738$		0			0
$739$	−373722.	+	647306.i	−0.684321	+	1.18528i	0.289328	+	0.957230i	$0.406568\pi$
$739$	−373722.	+	647306.i	−0.684321	+	1.18528i	−0.973650	+	0.228049i	$0.926765\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−181174.	−	497771.i	−0.328184	−	0.901678i	−0.988571	−	0.150753i	$-0.951830\pi$
$743$	−181174.	−	497771.i	−0.328184	−	0.901678i	0.660387	−	0.750925i	$-0.270392\pi$
$744$		0			0
$745$	57329.2	+	325130.i	0.103291	+	0.585794i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8652.81	+	10312.0i	0.0154239	+	0.0183815i
$750$		0			0
$751$	90981.7	−	515983.i	0.161315	−	0.914861i	−0.791468	−	0.611210i	$-0.790683\pi$
$751$	90981.7	−	515983.i	0.161315	−	0.914861i	0.952783	−	0.303651i	$-0.0982058\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	1.04982e6i		−	1.84171i
$756$		0			0
$757$	698556.			1.21902			0.609508	−	0.792780i	$-0.291367\pi$
$757$	698556.			1.21902			0.609508	+	0.792780i	$0.291367\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	628078.	+	110747.i	1.08454	+	0.191233i	0.687221	−	0.726449i	$-0.258831\pi$
$761$	628078.	+	110747.i	1.08454	+	0.191233i	0.397316	+	0.917682i	$0.369942\pi$
$762$		0			0
$763$	−11095.3	+	9310.09i	−0.0190586	+	0.0159921i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.00091e6	−	176487.i	1.70139	−	0.300000i
$768$		0			0
$769$	−188183.	+	68493.0i	−0.318220	+	0.115823i	−0.496192	−	0.868213i	$-0.665269\pi$
$769$	−188183.	+	68493.0i	−0.318220	+	0.115823i	0.177972	+	0.984036i	$0.443046\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	909650.	+	525187.i	1.52235	+	0.878931i	0.999651	+	0.0264151i	$0.00840916\pi$
$773$	909650.	+	525187.i	1.52235	+	0.878931i	0.522702	+	0.852516i	$0.324924\pi$
$774$		0			0
$775$	233354.	+	404181.i	0.388518	+	0.672934i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	451323.	−	537866.i	0.743725	−	0.886337i
$780$		0			0
$781$	111235.	+	40486.4i	0.182365	+	0.0663754i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−170099.	+	467343.i	−0.276034	+	0.758397i
$786$		0			0
$787$	564241.	+	473454.i	0.910993	+	0.764414i	0.972308	−	0.233705i	$-0.0750849\pi$
$787$	564241.	+	473454.i	0.910993	+	0.764414i	−0.0613147	+	0.998118i	$0.519529\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15555.0	−	8980.70i	0.0248609	−	0.0143535i
$792$		0			0
$793$	308840.	−	534926.i	0.491119	−	0.850643i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	51319.9	+	141000.i	0.0807922	+	0.221975i	0.973511	−	0.228639i	$-0.0734275\pi$
$797$	51319.9	+	141000.i	0.0807922	+	0.221975i	−0.892719	+	0.450614i	$0.851205\pi$
$798$		0			0
$799$	−139530.	−	791313.i	−0.218561	−	1.23952i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	138031.	+	164499.i	0.214065	+	0.255112i
$804$		0			0
$805$	−1168.27	+	6625.57i	−0.00180281	+	0.0102242i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			1.20492e6i			1.84103i	0.390704	+	0.920516i	$0.372232\pi$
$809$			1.20492e6i			1.84103i	−0.390704	+	0.920516i	$0.627768\pi$
$810$		0			0
$811$	−693796.			−1.05485			−0.527424	−	0.849602i	$-0.676842\pi$
$811$	−693796.			−1.05485			−0.527424	+	0.849602i	$0.676842\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−681795.	−	120219.i	−1.02645	−	0.180991i
$816$		0			0
$817$	337514.	−	283208.i	0.505648	−	0.424289i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.09007e6	−	192210.i	1.61722	−	0.285160i	0.709493	−	0.704713i	$-0.248924\pi$
$821$	1.09007e6	−	192210.i	1.61722	−	0.285160i	0.907731	+	0.419553i	$0.137813\pi$
$822$		0			0
$823$	228336.	−	83107.7i	0.337113	−	0.122699i	−0.167916	−	0.985801i	$-0.553704\pi$
$823$	228336.	−	83107.7i	0.337113	−	0.122699i	0.505029	+	0.863102i	$0.331482\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−314568.	−	181616.i	−0.459943	−	0.265548i	0.252077	−	0.967707i	$-0.418886\pi$
$827$	−314568.	−	181616.i	−0.459943	−	0.265548i	−0.712020	+	0.702159i	$0.752220\pi$
$828$		0			0
$829$	430732.	+	746051.i	0.626756	+	1.08557i	0.988198	+	0.153179i	$0.0489511\pi$
$829$	430732.	+	746051.i	0.626756	+	1.08557i	−0.361442	+	0.932394i	$0.617716\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	405872.	−	483699.i	0.584924	−	0.697085i
$834$		0			0
$835$	−487539.	−	177450.i	−0.699256	−	0.254508i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−96000.3	+	263759.i	−0.136379	+	0.374699i	−0.989017	−	0.147804i	$-0.952780\pi$
$839$	−96000.3	+	263759.i	−0.136379	+	0.374699i	0.852637	+	0.522503i	$0.175002\pi$
$840$		0			0
$841$	441557.	+	370511.i	0.624303	+	0.523852i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	487078.	−	281214.i	0.682158	−	0.393844i
$846$		0			0
$847$	4249.92	−	7361.07i	0.00592398	−	0.0102606i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	130978.	+	359858.i	0.180858	+	0.496903i
$852$		0			0
$853$	−151291.	−	858013.i	−0.207929	−	1.17922i	−0.892764	−	0.450524i	$-0.851237\pi$
$853$	−151291.	−	858013.i	−0.207929	−	1.17922i	0.684835	−	0.728698i	$-0.259874\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−53091.7	−	63272.3i	−0.0722879	−	0.0861493i	0.728689	−	0.684845i	$-0.240130\pi$
$857$	−53091.7	−	63272.3i	−0.0722879	−	0.0861493i	−0.800976	+	0.598696i	$0.795686\pi$
$858$		0			0
$859$	−8938.92	+	50695.1i	−0.0121143	+	0.0687036i	−0.990266	−	0.139191i	$-0.955550\pi$
$859$	−8938.92	+	50695.1i	−0.0121143	+	0.0687036i	0.978151	+	0.207894i	$0.0666610\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1.14484e6i		−	1.53717i	−0.639748	−	0.768585i	$-0.720961\pi$
$863$		−	1.14484e6i		−	1.53717i	0.639748	−	0.768585i	$-0.279039\pi$
$864$		0			0
$865$	890121.			1.18964
$866$		0			0
$867$		0			0
$868$		0			0
$869$	237858.	+	41940.8i	0.314976	+	0.0555388i
$870$		0			0
$871$	1.03424e6	−	867833.i	1.36328	−	1.14393i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5045.60	−	889.675i	0.00659017	−	0.00116203i
$876$		0			0
$877$	−789107.	+	287211.i	−1.02597	+	0.373424i	−0.799547	−	0.600604i	$-0.794927\pi$
$877$	−789107.	+	287211.i	−1.02597	+	0.373424i	−0.226428	+	0.974028i	$0.572705\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−32710.8	−	18885.6i	−0.0421443	−	0.0243320i	0.478780	−	0.877935i	$-0.341079\pi$
$881$	−32710.8	−	18885.6i	−0.0421443	−	0.0243320i	−0.520924	+	0.853603i	$0.674413\pi$
$882$		0			0
$883$	−66571.2	−	115305.i	−0.0853818	−	0.147886i	0.820172	−	0.572117i	$-0.193878\pi$
$883$	−66571.2	−	115305.i	−0.0853818	−	0.147886i	−0.905554	+	0.424231i	$0.860544\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−790801.	+	942440.i	−1.00512	+	1.19786i	−0.0249572	+	0.999689i	$0.507945\pi$
$887$	−790801.	+	942440.i	−1.00512	+	1.19786i	−0.980167	+	0.198172i	$0.936499\pi$
$888$		0			0
$889$	−18580.6	−	6762.80i	−0.0235102	−	0.00855703i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−264748.	+	727390.i	−0.331994	+	0.912146i
$894$		0			0
$895$	−573191.	−	480964.i	−0.715572	−	0.600436i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	338220.	−	195272.i	0.418485	−	0.241613i
$900$		0			0
$901$	−141048.	+	244303.i	−0.173748	+	0.300940i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−170150.	−	467484.i	−0.207747	−	0.570781i
$906$		0			0
$907$	69839.5	+	396079.i	0.0848959	+	0.481468i	0.997379	+	0.0723541i	$0.0230512\pi$
$907$	69839.5	+	396079.i	0.0848959	+	0.481468i	−0.912483	+	0.409114i	$0.865838\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	963484.	+	1.14824e6i	1.16094	+	1.38355i	0.909515	+	0.415670i	$0.136453\pi$
$911$	963484.	+	1.14824e6i	1.16094	+	1.38355i	0.251420	+	0.967878i	$0.419103\pi$
$912$		0			0
$913$	15560.4	−	88247.4i	0.0186672	−	0.105867i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	10660.2i		−	0.0126773i
$918$		0			0
$919$	−746216.			−0.883555			−0.441777	−	0.897125i	$-0.645652\pi$
$919$	−746216.			−0.883555			−0.441777	+	0.897125i	$0.645652\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	383099.	+	67550.6i	0.449684	+	0.0792914i
$924$		0			0
$925$	−501211.	+	420566.i	−0.585783	+	0.491531i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.66249e6	−	293142.i	1.92632	−	0.339661i	0.926947	−	0.375192i	$-0.122423\pi$
$929$	1.66249e6	−	293142.i	1.92632	−	0.339661i	0.999369	+	0.0355307i	$0.0113121\pi$
$930$		0			0
$931$	−571600.	+	208045.i	−0.659466	+	0.240026i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−482711.	−	278693.i	−0.552159	−	0.318789i
$936$		0			0
$937$	87619.8	+	151762.i	0.0997983	+	0.172856i	0.911601	−	0.411076i	$-0.134847\pi$
$937$	87619.8	+	151762.i	0.0997983	+	0.172856i	−0.811803	+	0.583932i	$0.801514\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−62199.3	+	74126.3i	−0.0702436	+	0.0837130i	−0.800022	−	0.599971i	$-0.795179\pi$
$941$	−62199.3	+	74126.3i	−0.0702436	+	0.0837130i	0.729778	+	0.683684i	$0.239623\pi$
$942$		0			0
$943$	−658784.	−	239778.i	−0.740832	−	0.269641i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	63774.2	−	175218.i	0.0711124	−	0.195380i	−0.899045	−	0.437857i	$-0.855738\pi$
$947$	63774.2	−	175218.i	0.0711124	−	0.195380i	0.970157	+	0.242477i	$0.0779599\pi$
$948$		0			0
$949$	540585.	+	453605.i	0.600249	+	0.503669i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.30855e6	+	755491.i	−1.44080	+	0.831847i	−0.997903	−	0.0647255i	$-0.979383\pi$
$953$	−1.30855e6	+	755491.i	−1.44080	+	0.831847i	−0.442898	+	0.896572i	$0.646049\pi$
$954$		0			0
$955$	−688565.	+	1.19263e6i	−0.754985	+	1.30767i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1346.27	−	3698.83i	−0.00146384	−	0.00402187i
$960$		0			0
$961$	42014.5	+	238276.i	0.0454938	+	0.258008i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.28149e6	−	1.52722e6i	−1.37613	−	1.64001i
$966$		0			0
$967$	268534.	−	1.52293e6i	0.287174	−	1.62865i	−0.410240	−	0.911978i	$-0.634555\pi$
$967$	268534.	−	1.52293e6i	0.287174	−	1.62865i	0.697414	−	0.716668i	$-0.254334\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	538093.i		−	0.570715i	−0.958421	−	0.285357i	$-0.907888\pi$
$971$		−	538093.i		−	0.570715i	0.958421	−	0.285357i	$-0.0921123\pi$
$972$		0			0
$973$	28865.4			0.0304897
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.07457e6	−	189476.i	−1.12576	−	0.198502i	−0.420392	−	0.907343i	$-0.638107\pi$
$977$	−1.07457e6	−	189476.i	−1.12576	−	0.198502i	−0.705369	+	0.708841i	$0.749218\pi$
$978$		0			0
$979$	508970.	−	427076.i	0.531039	−	0.445595i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.30228e6	+	229626.i	−1.34771	+	0.237637i	−0.800486	−	0.599351i	$-0.795425\pi$
$983$	−1.30228e6	+	229626.i	−1.34771	+	0.237637i	−0.547221	+	0.836988i	$0.684314\pi$
$984$		0			0
$985$	−1.74096e6	+	633658.i	−1.79439	+	0.653104i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−380984.	−	219961.i	−0.389506	−	0.224881i
$990$		0			0
$991$	292628.	+	506846.i	0.297967	+	0.516094i	0.975671	−	0.219241i	$-0.0703582\pi$
$991$	292628.	+	506846.i	0.297967	+	0.516094i	−0.677704	+	0.735335i	$0.737025\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.31700e6	+	1.56954e6i	−1.33027	+	1.58535i
$996$		0			0
$997$	450101.	+	163823.i	0.452814	+	0.164811i	0.558352	−	0.829604i	$-0.311434\pi$
$997$	450101.	+	163823.i	0.452814	+	0.164811i	−0.105537	+	0.994415i	$0.533656\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.k.a.17.10		72
3.2	odd	2		108.5.k.a.77.3	✓	72
27.7	even	9		108.5.k.a.101.3	yes	72
27.20	odd	18	inner	324.5.k.a.305.10		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.k.a.77.3	✓	72	3.2	odd	2
108.5.k.a.101.3	yes	72	27.7	even	9
324.5.k.a.17.10		72	1.1	even	1	trivial
324.5.k.a.305.10		72	27.20	odd	18	inner

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.k (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(32.0223 + 5.64639i) q^{5} +(-0.626400 + 0.525612i) q^{7} +O(q^{10})\)	\(q+(32.0223 + 5.64639i) q^{5} +(-0.626400 + 0.525612i) q^{7} +(64.1736 - 11.3155i) q^{11} +(201.230 - 73.2417i) q^{13} +(-227.814 - 131.529i) q^{17} +(126.708 + 219.465i) q^{19} +(162.645 - 193.833i) q^{23} +(406.237 + 147.858i) q^{25} +(123.728 - 339.941i) q^{29} +(826.999 + 693.935i) q^{31} +(-23.0266 + 13.2944i) q^{35} +(-756.733 + 1310.70i) q^{37} +(-947.625 - 2603.58i) q^{41} +(-301.907 - 1712.20i) q^{43} +(1963.42 + 2339.92i) q^{47} +(-416.813 + 2363.86i) q^{49} -1072.38i q^{53} +2118.88 q^{55} +(4673.98 + 824.148i) q^{59} +(2209.58 - 1854.06i) q^{61} +(6857.39 - 1209.14i) q^{65} +(5924.45 - 2156.32i) q^{67} +(1573.20 + 908.285i) q^{71} +(1647.68 + 2853.87i) q^{73} +(-34.2508 + 40.8185i) q^{77} +(3482.95 + 1267.69i) q^{79} +(470.324 - 1292.20i) q^{83} +(-6552.47 - 5498.18i) q^{85} +(8830.06 - 5098.04i) q^{89} +(-87.5538 + 151.648i) q^{91} +(2818.30 + 7743.22i) q^{95} +(1550.17 + 8791.48i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 9 q^{5}+O(q^{10}) \) 72 * q - 9 * q^5	\( 72 q - 9 q^{5} - 18 q^{11} + 1278 q^{23} + 441 q^{25} - 1854 q^{29} - 1665 q^{31} + 2673 q^{35} + 5472 q^{41} + 1260 q^{43} - 5103 q^{47} - 5904 q^{49} + 10944 q^{59} + 8352 q^{61} - 8757 q^{65} + 378 q^{67} + 19764 q^{71} + 6111 q^{73} + 5679 q^{77} - 5652 q^{79} + 20061 q^{83} + 26100 q^{85} - 15633 q^{89} - 6039 q^{91} - 48024 q^{95} - 37530 q^{97}+O(q^{100}) \) 72 * q - 9 * q^5 - 18 * q^11 + 1278 * q^23 + 441 * q^25 - 1854 * q^29 - 1665 * q^31 + 2673 * q^35 + 5472 * q^41 + 1260 * q^43 - 5103 * q^47 - 5904 * q^49 + 10944 * q^59 + 8352 * q^61 - 8757 * q^65 + 378 * q^67 + 19764 * q^71 + 6111 * q^73 + 5679 * q^77 - 5652 * q^79 + 20061 * q^83 + 26100 * q^85 - 15633 * q^89 - 6039 * q^91 - 48024 * q^95 - 37530 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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