LMFDB - Embedded newform 76.3.j.a.33.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 93 x^{16} + 3429 x^{14} + 64261 x^{12} + 647217 x^{10} + 3386277 x^{8} + 8232133 x^{6} + \cdots + 69312 $ x^18 + 93x^16 + 3429x^14 + 64261x^12 + 647217x^10 + 3386277x^8 + 8232133x^6 + 8319228x^4 + 2467872x^2 + 69312
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			33.3
Root			$-4.09415i$ of defining polynomial
Character	$\chi$	$=$	76.33
Dual form			76.3.j.a.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.35830 + 0.592159i) q^{3} +(1.47441 + 1.23717i) q^{5} +(0.111774 + 0.193599i) q^{7} +(2.47031 + 0.899120i) q^{9} +O(q^{10})$	\(q+(3.35830 + 0.592159i) q^{3} +(1.47441 + 1.23717i) q^{5} +(0.111774 + 0.193599i) q^{7} +(2.47031 + 0.899120i) q^{9} +(0.796372 - 1.37936i) q^{11} +(0.784041 - 0.138248i) q^{13} +(4.21890 + 5.02789i) q^{15} +(6.30486 - 2.29478i) q^{17} +(-15.7574 - 10.6163i) q^{19} +(0.260730 + 0.716351i) q^{21} +(-24.2075 + 20.3125i) q^{23} +(-3.69793 - 20.9720i) q^{25} +(-18.8155 - 10.8632i) q^{27} +(4.58431 - 12.5953i) q^{29} +(-43.5383 + 25.1368i) q^{31} +(3.49126 - 4.16072i) q^{33} +(-0.0747145 + 0.423727i) q^{35} -6.71830i q^{37} +2.71491 q^{39} +(63.1648 + 11.1376i) q^{41} +(10.7499 + 9.02027i) q^{43} +(2.52988 + 4.38188i) q^{45} +(49.0942 + 17.8688i) q^{47} +(24.4750 - 42.3920i) q^{49} +(22.5325 - 3.97309i) q^{51} +(52.5656 + 62.6453i) q^{53} +(2.88068 - 1.04848i) q^{55} +(-46.6315 - 44.9836i) q^{57} +(2.86701 + 7.87704i) q^{59} +(-36.5415 + 30.6619i) q^{61} +(0.102049 + 0.578747i) q^{63} +(1.32703 + 0.766163i) q^{65} +(19.6178 - 53.8994i) q^{67} +(-93.3244 + 53.8809i) q^{69} +(19.1327 - 22.8015i) q^{71} +(-10.9883 + 62.3180i) q^{73} -72.6201i q^{75} +0.356055 q^{77} +(1.13111 + 0.199445i) q^{79} +(-74.8799 - 62.8317i) q^{81} +(39.0294 + 67.6008i) q^{83} +(12.1350 + 4.41677i) q^{85} +(22.8539 - 39.5841i) q^{87} +(50.7523 - 8.94900i) q^{89} +(0.114400 + 0.136337i) q^{91} +(-161.100 + 58.6355i) q^{93} +(-10.0986 - 35.1473i) q^{95} +(-45.2763 - 124.395i) q^{97} +(3.20750 - 2.69141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) $ 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9	$ 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9} - 15 q^{11} + 51 q^{13} + 21 q^{15} - 45 q^{17} + 30 q^{19} - 63 q^{21} + 48 q^{23} - 54 q^{25} - 198 q^{27} - 39 q^{29} - 108 q^{31} - 105 q^{33} + 51 q^{35} + 48 q^{39} + 54 q^{41} + 75 q^{43} + 288 q^{45} + 339 q^{47} - 24 q^{49} + 360 q^{51} + 69 q^{53} - 51 q^{55} + 510 q^{57} - 483 q^{59} - 36 q^{61} - 267 q^{63} - 585 q^{65} - 87 q^{67} - 351 q^{69} - 234 q^{71} - 132 q^{73} + 108 q^{77} + 363 q^{79} + 258 q^{81} + 279 q^{83} + 666 q^{85} + 600 q^{89} + 270 q^{91} - 456 q^{93} - 39 q^{95} - 801 q^{97} - 267 q^{99}+O(q^{100}) $ 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9 - 15 * q^11 + 51 * q^13 + 21 * q^15 - 45 * q^17 + 30 * q^19 - 63 * q^21 + 48 * q^23 - 54 * q^25 - 198 * q^27 - 39 * q^29 - 108 * q^31 - 105 * q^33 + 51 * q^35 + 48 * q^39 + 54 * q^41 + 75 * q^43 + 288 * q^45 + 339 * q^47 - 24 * q^49 + 360 * q^51 + 69 * q^53 - 51 * q^55 + 510 * q^57 - 483 * q^59 - 36 * q^61 - 267 * q^63 - 585 * q^65 - 87 * q^67 - 351 * q^69 - 234 * q^71 - 132 * q^73 + 108 * q^77 + 363 * q^79 + 258 * q^81 + 279 * q^83 + 666 * q^85 + 600 * q^89 + 270 * q^91 - 456 * q^93 - 39 * q^95 - 801 * q^97 - 267 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$

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
$3$	3.35830	+	0.592159i	1.11943	+	0.197386i	0.702592	−	0.711593i	$-0.252026\pi$
$3$	3.35830	+	0.592159i	1.11943	+	0.197386i	0.416842	+	0.908979i	$0.363137\pi$
$4$		0			0
$5$	1.47441	+	1.23717i	0.294881	+	0.247435i	0.778210	−	0.628004i	$-0.216128\pi$
$5$	1.47441	+	1.23717i	0.294881	+	0.247435i	−0.483329	+	0.875439i	$0.660572\pi$
$6$		0			0
$7$	0.111774	+	0.193599i	0.0159677	+	0.0276569i	0.873899	−	0.486108i	$-0.161584\pi$
$7$	0.111774	+	0.193599i	0.0159677	+	0.0276569i	−0.857931	+	0.513765i	$0.828250\pi$
$8$		0			0
$9$	2.47031	+	0.899120i	0.274479	+	0.0999023i
$10$		0			0
$11$	0.796372	−	1.37936i	0.0723974	−	0.125396i	−0.827554	−	0.561386i	$-0.810268\pi$
$11$	0.796372	−	1.37936i	0.0723974	−	0.125396i	0.899952	+	0.435990i	$0.143602\pi$
$12$		0			0
$13$	0.784041	−	0.138248i	0.0603109	−	0.0106344i	−0.143411	−	0.989663i	$-0.545807\pi$
$13$	0.784041	−	0.138248i	0.0603109	−	0.0106344i	0.203722	+	0.979029i	$0.434696\pi$
$14$		0			0
$15$	4.21890	+	5.02789i	0.281260	+	0.335193i
$16$		0			0
$17$	6.30486	−	2.29478i	0.370874	−	0.134987i	−0.149857	−	0.988708i	$-0.547881\pi$
$17$	6.30486	−	2.29478i	0.370874	−	0.134987i	0.520732	+	0.853720i	$0.325659\pi$
$18$		0			0
$19$	−15.7574	−	10.6163i	−0.829335	−	0.558752i
$19$	−15.7574	−	10.6163i	−0.829335	−	0.558752i
$20$		0			0
$21$	0.260730	+	0.716351i	0.0124157	+	0.0341119i
$22$		0			0
$23$	−24.2075	+	20.3125i	−1.05250	+	0.883153i	−0.993354	−	0.115097i	$-0.963282\pi$
$23$	−24.2075	+	20.3125i	−1.05250	+	0.883153i	−0.0591462	+	0.998249i	$0.518838\pi$
$24$		0			0
$25$	−3.69793	−	20.9720i	−0.147917	−	0.838880i
$26$		0			0
$27$	−18.8155	−	10.8632i	−0.696872	−	0.402339i
$28$		0			0
$29$	4.58431	−	12.5953i	0.158079	−	0.434320i	−0.835216	−	0.549922i	$-0.814657\pi$
$29$	4.58431	−	12.5953i	0.158079	−	0.434320i	0.993296	+	0.115602i	$0.0368797\pi$
$30$		0			0
$31$	−43.5383	+	25.1368i	−1.40446	+	0.810865i	−0.994846	−	0.101394i	$-0.967670\pi$
$31$	−43.5383	+	25.1368i	−1.40446	+	0.810865i	−0.409614	+	0.912259i	$0.634337\pi$
$32$		0			0
$33$	3.49126	−	4.16072i	0.105796	−	0.126082i
$34$		0			0
$35$	−0.0747145	+	0.423727i	−0.00213470	+	0.0121065i
$36$		0			0
$37$		−	6.71830i		−	0.181576i	−0.995870	−	0.0907878i	$-0.971061\pi$
$37$		−	6.71830i		−	0.181576i	0.995870	−	0.0907878i	$-0.0289385\pi$
$38$		0			0
$39$	2.71491			0.0696132
$40$		0			0
$41$	63.1648	+	11.1376i	1.54060	+	0.271650i	0.878493	−	0.477756i	$-0.158550\pi$
$41$	63.1648	+	11.1376i	1.54060	+	0.271650i	0.662111	+	0.749406i	$0.269661\pi$
$42$		0			0
$43$	10.7499	+	9.02027i	0.249999	+	0.209774i	0.759172	−	0.650890i	$-0.225604\pi$
$43$	10.7499	+	9.02027i	0.249999	+	0.209774i	−0.509173	+	0.860664i	$0.670049\pi$
$44$		0			0
$45$	2.52988	+	4.38188i	0.0562195	+	0.0973750i
$46$		0			0
$47$	49.0942	+	17.8688i	1.04456	+	0.380188i	0.806606	−	0.591089i	$-0.201302\pi$
$47$	49.0942	+	17.8688i	1.04456	+	0.380188i	0.237951	+	0.971277i	$0.423524\pi$
$48$		0			0
$49$	24.4750	−	42.3920i	0.499490	−	0.865142i
$50$		0			0
$51$	22.5325	−	3.97309i	0.441814	−	0.0779037i
$52$		0			0
$53$	52.5656	+	62.6453i	0.991804	+	1.18199i	0.983294	+	0.182022i	$0.0582643\pi$
$53$	52.5656	+	62.6453i	0.991804	+	1.18199i	0.00850957	+	0.999964i	$0.497291\pi$
$54$		0			0
$55$	2.88068	−	1.04848i	0.0523760	−	0.0190633i
$56$		0			0
$57$	−46.6315	−	44.9836i	−0.818096	−	0.789186i
$58$		0			0
$59$	2.86701	+	7.87704i	0.0485934	+	0.133509i	0.961615	−	0.274401i	$-0.0884797\pi$
$59$	2.86701	+	7.87704i	0.0485934	+	0.133509i	−0.913022	+	0.407911i	$0.866257\pi$
$60$		0			0
$61$	−36.5415	+	30.6619i	−0.599041	+	0.502655i	−0.891137	−	0.453734i	$-0.850092\pi$
$61$	−36.5415	+	30.6619i	−0.599041	+	0.502655i	0.292096	+	0.956389i	$0.405647\pi$
$62$		0			0
$63$	0.102049	+	0.578747i	0.00161982	+	0.00918647i
$64$		0			0
$65$	1.32703	+	0.766163i	0.0204159	+	0.0117871i
$66$		0			0
$67$	19.6178	−	53.8994i	0.292803	−	0.804469i	−0.702851	−	0.711337i	$-0.748090\pi$
$67$	19.6178	−	53.8994i	0.292803	−	0.804469i	0.995654	−	0.0931320i	$-0.0296878\pi$
$68$		0			0
$69$	−93.3244	+	53.8809i	−1.35253	+	0.780882i
$70$		0			0
$71$	19.1327	−	22.8015i	0.269475	−	0.321148i	−0.614289	−	0.789081i	$-0.710557\pi$
$71$	19.1327	−	22.8015i	0.269475	−	0.321148i	0.883764	+	0.467934i	$0.155001\pi$
$72$		0			0
$73$	−10.9883	+	62.3180i	−0.150525	+	0.853671i	0.812238	+	0.583326i	$0.198249\pi$
$73$	−10.9883	+	62.3180i	−0.150525	+	0.853671i	−0.962764	+	0.270345i	$0.912862\pi$
$74$		0			0
$75$		−	72.6201i		−	0.968268i
$76$		0			0
$77$	0.356055			0.00462409
$78$		0			0
$79$	1.13111	+	0.199445i	0.0143178	+	0.00252462i	0.180803	−	0.983519i	$-0.442131\pi$
$79$	1.13111	+	0.199445i	0.0143178	+	0.00252462i	−0.166485	+	0.986044i	$0.553242\pi$
$80$		0			0
$81$	−74.8799	−	62.8317i	−0.924444	−	0.775700i
$82$		0			0
$83$	39.0294	+	67.6008i	0.470233	+	0.814468i	0.999421	−	0.0340372i	$-0.0108365\pi$
$83$	39.0294	+	67.6008i	0.470233	+	0.814468i	−0.529187	+	0.848505i	$0.677503\pi$
$84$		0			0
$85$	12.1350	+	4.41677i	0.142764	+	0.0519620i
$86$		0			0
$87$	22.8539	−	39.5841i	0.262688	−	0.454990i
$88$		0			0
$89$	50.7523	−	8.94900i	0.570251	−	0.100551i	0.118914	−	0.992905i	$-0.462059\pi$
$89$	50.7523	−	8.94900i	0.570251	−	0.100551i	0.451336	+	0.892354i	$0.350947\pi$
$90$		0			0
$91$	0.114400	+	0.136337i	0.00125714	+	0.00149821i
$92$		0			0
$93$	−161.100	+	58.6355i	−1.73225	+	0.630489i
$94$		0			0
$95$	−10.0986	−	35.1473i	−0.106301	−	0.369972i
$96$		0			0
$97$	−45.2763	−	124.395i	−0.466766	−	1.28243i	−0.920309	−	0.391193i	$-0.872062\pi$
$97$	−45.2763	−	124.395i	−0.466766	−	1.28243i	0.453543	−	0.891234i	$-0.350160\pi$
$98$		0			0
$99$	3.20750	−	2.69141i	0.0323989	−	0.0271859i
$100$		0			0
$101$	21.3569	+	121.121i	0.211454	+	1.19922i	0.886955	+	0.461856i	$0.152816\pi$
$101$	21.3569	+	121.121i	0.211454	+	1.19922i	−0.675501	+	0.737359i	$0.736072\pi$
$102$		0			0
$103$	−29.5517	−	17.0617i	−0.286910	−	0.165647i	0.349638	−	0.936885i	$-0.386305\pi$
$103$	−29.5517	−	17.0617i	−0.286910	−	0.165647i	−0.636547	+	0.771238i	$0.719638\pi$
$104$		0			0
$105$	−0.501828	+	1.37876i	−0.00477931	+	0.0131311i
$106$		0			0
$107$	−104.839	+	60.5286i	−0.979800	+	0.565688i	−0.902210	−	0.431297i	$-0.858056\pi$
$107$	−104.839	+	60.5286i	−0.979800	+	0.565688i	−0.0775905	+	0.996985i	$0.524723\pi$
$108$		0			0
$109$	−19.1292	+	22.7973i	−0.175497	+	0.209149i	−0.846622	−	0.532195i	$-0.821367\pi$
$109$	−19.1292	+	22.7973i	−0.175497	+	0.209149i	0.671124	+	0.741345i	$0.265812\pi$
$110$		0			0
$111$	3.97830	−	22.5621i	0.0358406	−	0.203262i
$112$		0			0
$113$		−	131.353i		−	1.16242i	−0.813754	−	0.581209i	$-0.802580\pi$
$113$		−	131.353i		−	1.16242i	0.813754	−	0.581209i	$-0.197420\pi$
$114$		0			0
$115$	−60.8218			−0.528886
$116$		0			0
$117$	2.06113	+	0.363433i	0.0176165	+	0.00310626i
$118$		0			0
$119$	1.14899	+	0.964114i	0.00965535	+	0.00810180i
$120$		0			0
$121$	59.2316	+	102.592i	0.489517	+	0.847869i
$122$		0			0
$123$	205.531	+	74.8072i	1.67098	+	0.608189i
$124$		0			0
$125$	44.5525	−	77.1672i	0.356420	−	0.617338i
$126$		0			0
$127$	162.243	−	28.6078i	1.27750	−	0.225258i	0.506582	−	0.862192i	$-0.330909\pi$
$127$	162.243	−	28.6078i	1.27750	−	0.225258i	0.770919	+	0.636934i	$0.219797\pi$
$128$		0			0
$129$	30.7601	+	36.6585i	0.238451	+	0.284174i
$130$		0			0
$131$	−66.0009	+	24.0224i	−0.503824	+	0.183377i	−0.581413	−	0.813609i	$-0.697500\pi$
$131$	−66.0009	+	24.0224i	−0.503824	+	0.183377i	0.0775893	+	0.996985i	$0.475278\pi$
$132$		0			0
$133$	0.294032	−	4.23723i	0.00221077	−	0.0318589i
$134$		0			0
$135$	−14.3021	−	39.2948i	−0.105942	−	0.291073i
$136$		0			0
$137$	141.043	−	118.349i	1.02951	−	0.863860i	0.0387164	−	0.999250i	$-0.487673\pi$
$137$	141.043	−	118.349i	1.02951	−	0.863860i	0.990792	+	0.135390i	$0.0432287\pi$
$138$		0			0
$139$	36.1462	+	204.995i	0.260045	+	1.47479i	0.782784	+	0.622294i	$0.213799\pi$
$139$	36.1462	+	204.995i	0.260045	+	1.47479i	−0.522739	+	0.852493i	$0.675090\pi$
$140$		0			0
$141$	154.292	+	89.0805i	1.09427	+	0.631777i
$142$		0			0
$143$	0.433696	−	1.19157i	0.00303284	−	0.00833265i
$144$		0			0
$145$	22.3417	−	12.8990i	0.154081	−	0.0889585i
$146$		0			0
$147$	107.297	−	127.872i	0.729914	−	0.869877i
$148$		0			0
$149$	−44.2080	+	250.716i	−0.296698	+	1.68266i	0.363521	+	0.931586i	$0.381574\pi$
$149$	−44.2080	+	250.716i	−0.296698	+	1.68266i	−0.660220	+	0.751073i	$0.729537\pi$
$150$		0			0
$151$		−	235.963i		−	1.56267i	−0.624111	−	0.781336i	$-0.714539\pi$
$151$		−	235.963i		−	1.56267i	0.624111	−	0.781336i	$-0.285461\pi$
$152$		0			0
$153$	17.6383			0.115283
$154$		0			0
$155$	−95.2918	−	16.8025i	−0.614786	−	0.108403i
$156$		0			0
$157$	−155.187	−	130.217i	−0.988452	−	0.829410i	−0.00310895	−	0.999995i	$-0.500990\pi$
$157$	−155.187	−	130.217i	−0.988452	−	0.829410i	−0.985343	+	0.170586i	$0.945434\pi$
$158$		0			0
$159$	139.435	+	241.509i	0.876951	+	1.51892i
$160$		0			0
$161$	−6.63825	−	2.41612i	−0.0412314	−	0.0150070i
$162$		0			0
$163$	−46.5040	+	80.5474i	−0.285301	+	0.494156i	−0.972682	−	0.232141i	$-0.925427\pi$
$163$	−46.5040	+	80.5474i	−0.285301	+	0.494156i	0.687381	+	0.726297i	$0.258760\pi$
$164$		0			0
$165$	10.2951	−	1.81530i	0.0623943	−	0.0110018i
$166$		0			0
$167$	−119.165	−	142.015i	−0.713563	−	0.850392i	0.280425	−	0.959876i	$-0.409525\pi$
$167$	−119.165	−	142.015i	−0.713563	−	0.850392i	−0.993989	+	0.109484i	$0.965080\pi$
$168$		0			0
$169$	−158.212	+	57.5846i	−0.936168	+	0.340737i
$170$		0			0
$171$	−29.3803	−	40.3933i	−0.171815	−	0.236218i
$172$		0			0
$173$	−68.0593	−	186.991i	−0.393406	−	1.08088i	−0.965436	−	0.260642i	$-0.916066\pi$
$173$	−68.0593	−	186.991i	−0.393406	−	1.08088i	0.572029	−	0.820233i	$-0.306156\pi$
$174$		0			0
$175$	3.64682	−	3.06004i	0.0208389	−	0.0174860i
$176$		0			0
$177$	4.96382	+	28.1512i	0.0280442	+	0.159046i
$178$		0			0
$179$	−121.986	−	70.4285i	−0.681485	−	0.393455i	0.118929	−	0.992903i	$-0.462054\pi$
$179$	−121.986	−	70.4285i	−0.681485	−	0.393455i	−0.800414	+	0.599447i	$0.795387\pi$
$180$		0			0
$181$	−27.7089	+	76.1295i	−0.153088	+	0.420605i	−0.992401	−	0.123042i	$-0.960735\pi$
$181$	−27.7089	+	76.1295i	−0.153088	+	0.420605i	0.839314	+	0.543647i	$0.182957\pi$
$182$		0			0
$183$	−140.874	+	81.3337i	−0.769804	+	0.444447i
$184$		0			0
$185$	8.31171	−	9.90551i	0.0449282	−	0.0535433i
$186$		0			0
$187$	1.85569	−	10.5241i	0.00992348	−	0.0562789i
$188$		0			0
$189$		−	4.85688i		−	0.0256978i
$190$		0			0
$191$	−291.868			−1.52810			−0.764052	−	0.645155i	$-0.776793\pi$
$191$	−291.868			−1.52810			−0.764052	+	0.645155i	$0.776793\pi$
$192$		0			0
$193$	40.6139	+	7.16133i	0.210435	+	0.0371054i	0.277872	−	0.960618i	$-0.410371\pi$
$193$	40.6139	+	7.16133i	0.210435	+	0.0371054i	−0.0674368	+	0.997724i	$0.521482\pi$
$194$		0			0
$195$	4.00289	+	3.35882i	0.0205276	+	0.0172247i
$196$		0			0
$197$	−43.0652	−	74.5911i	−0.218605	−	0.378635i	0.735777	−	0.677224i	$-0.236817\pi$
$197$	−43.0652	−	74.5911i	−0.218605	−	0.378635i	−0.954382	+	0.298589i	$0.903484\pi$
$198$		0			0
$199$	190.071	+	69.1803i	0.955132	+	0.347640i	0.772124	−	0.635472i	$-0.219194\pi$
$199$	190.071	+	69.1803i	0.955132	+	0.347640i	0.183008	+	0.983111i	$0.441417\pi$
$200$		0			0
$201$	97.7995	−	169.394i	0.486565	−	0.842755i
$202$		0			0
$203$	2.95083	−	0.520312i	0.0145361	−	0.00256311i
$204$		0			0
$205$	79.3513	+	94.5672i	0.387080	+	0.461304i
$206$		0			0
$207$	−78.0635	+	28.4128i	−0.377118	+	0.137260i
$208$		0			0
$209$	−27.1924	+	13.2805i	−0.130107	+	0.0635431i
$210$		0			0
$211$	−25.3506	−	69.6503i	−0.120145	−	0.330096i	0.865012	−	0.501751i	$-0.167311\pi$
$211$	−25.3506	−	69.6503i	−0.120145	−	0.330096i	−0.985157	+	0.171655i	$0.945089\pi$
$212$		0			0
$213$	77.7556	−	65.2447i	0.365050	−	0.306313i
$214$		0			0
$215$	4.69014	+	26.5991i	0.0218146	+	0.123717i
$216$		0			0
$217$	−9.73291	−	5.61930i	−0.0448521	−	0.0258954i
$218$		0			0
$219$	−73.8043	+	202.776i	−0.337006	+	0.925917i
$220$		0			0
$221$	4.62602	−	2.67084i	0.0209322	−	0.0120852i
$222$		0			0
$223$	−0.983577	+	1.17218i	−0.00441066	+	0.00525642i	−0.768245	−	0.640156i	$-0.778870\pi$
$223$	−0.983577	+	1.17218i	−0.00441066	+	0.00525642i	0.763835	+	0.645412i	$0.223314\pi$
$224$		0			0
$225$	9.72131	−	55.1323i	0.0432058	−	0.245032i
$226$		0			0
$227$		−	172.467i		−	0.759767i	−0.925034	−	0.379883i	$-0.875964\pi$
$227$		−	172.467i		−	0.759767i	0.925034	−	0.379883i	$-0.124036\pi$
$228$		0			0
$229$	189.574			0.827832			0.413916	−	0.910315i	$-0.364161\pi$
$229$	189.574			0.827832			0.413916	+	0.910315i	$0.364161\pi$
$230$		0			0
$231$	1.19574	+	0.210841i	0.00517637	+	0.000912734i
$232$		0			0
$233$	−62.6380	−	52.5595i	−0.268832	−	0.225577i	0.498399	−	0.866948i	$-0.333922\pi$
$233$	−62.6380	−	52.5595i	−0.268832	−	0.225577i	−0.767231	+	0.641371i	$0.778366\pi$
$234$		0			0
$235$	50.2780	+	87.0840i	0.213949	+	0.370570i
$236$		0			0
$237$	3.68051	+	1.33959i	0.0155296	+	0.00565230i
$238$		0			0
$239$	−121.128	+	209.799i	−0.506810	+	0.877821i	0.493159	+	0.869939i	$0.335842\pi$
$239$	−121.128	+	209.799i	−0.506810	+	0.877821i	−0.999969	+	0.00788135i	$0.997491\pi$
$240$		0			0
$241$	167.567	−	29.5466i	0.695299	−	0.122600i	0.185181	−	0.982704i	$-0.440713\pi$
$241$	167.567	−	29.5466i	0.695299	−	0.122600i	0.510118	+	0.860104i	$0.329602\pi$
$242$		0			0
$243$	−88.5744	−	105.559i	−0.364504	−	0.434399i
$244$		0			0
$245$	88.5324	−	32.2232i	0.361357	−	0.131523i
$246$		0			0
$247$	−13.8221	−	6.14519i	−0.0559599	−	0.0248793i
$248$		0			0
$249$	91.0419	+	250.136i	0.365630	+	1.00456i
$250$		0			0
$251$	−154.546	+	129.680i	−0.615721	+	0.516652i	−0.896455	−	0.443134i	$-0.853867\pi$
$251$	−154.546	+	129.680i	−0.615721	+	0.516652i	0.280734	+	0.959786i	$0.409422\pi$
$252$		0			0
$253$	8.74002	+	49.5671i	0.0345455	+	0.195917i
$254$		0			0
$255$	38.1375	+	22.0187i	0.149559	+	0.0863478i
$256$		0			0
$257$	147.098	−	404.148i	0.572365	−	1.57256i	−0.228390	−	0.973570i	$-0.573346\pi$
$257$	147.098	−	404.148i	0.572365	−	1.57256i	0.800756	−	0.598991i	$-0.204432\pi$
$258$		0			0
$259$	1.30065	−	0.750932i	0.00502183	−	0.00289935i
$260$		0			0
$261$	22.6493	−	26.9924i	0.0867791	−	0.103419i
$262$		0			0
$263$	−0.0221657	+	0.125708i	−8.42801e−5	+	0.000477976i	−0.984850	−	0.173409i	$-0.944522\pi$
$263$	−0.0221657	+	0.125708i	−8.42801e−5	+	0.000477976i	0.984766	+	0.173887i	$0.0556328\pi$
$264$		0			0
$265$			157.397i			0.593953i
$266$		0			0
$267$	175.741			0.658206
$268$		0			0
$269$	145.098	+	25.5848i	0.539399	+	0.0951107i	0.436709	−	0.899603i	$-0.356144\pi$
$269$	145.098	+	25.5848i	0.539399	+	0.0951107i	0.102690	+	0.994713i	$0.467255\pi$
$270$		0			0
$271$	282.797	+	237.295i	1.04353	+	0.875627i	0.992399	−	0.123065i	$-0.0392724\pi$
$271$	282.797	+	237.295i	1.04353	+	0.875627i	0.0511326	+	0.998692i	$0.483717\pi$
$272$		0			0
$273$	0.303457	+	0.525603i	0.00111156	+	0.00192529i
$274$		0			0
$275$	−31.8728	−	11.6007i	−0.115901	−	0.0421845i
$276$		0			0
$277$	101.901	−	176.497i	0.367872	−	0.637173i	−0.621360	−	0.783525i	$-0.713420\pi$
$277$	101.901	−	176.497i	0.367872	−	0.637173i	0.989233	+	0.146352i	$0.0467531\pi$
$278$		0			0
$279$	−130.154	+	22.9497i	−0.466502	+	0.0822570i
$280$		0			0
$281$	245.804	+	292.938i	0.874747	+	1.04248i	0.998739	+	0.0502000i	$0.0159859\pi$
$281$	245.804	+	292.938i	0.874747	+	1.04248i	−0.123992	+	0.992283i	$0.539570\pi$
$282$		0			0
$283$	429.019	−	156.150i	1.51597	−	0.551767i	0.555830	−	0.831296i	$-0.312401\pi$
$283$	429.019	−	156.150i	1.51597	−	0.551767i	0.960137	+	0.279529i	$0.0901784\pi$
$284$		0			0
$285$	−13.1012	−	124.015i	−0.0459691	−	0.435142i
$286$		0			0
$287$	4.90395	+	13.4735i	0.0170870	+	0.0469460i
$288$		0			0
$289$	−186.902	+	156.829i	−0.646718	+	0.542661i
$290$		0			0
$291$	−78.3894	−	444.568i	−0.269379	−	1.52773i
$292$		0			0
$293$	22.2916	+	12.8701i	0.0760806	+	0.0439252i	0.537558	−	0.843227i	$-0.319347\pi$
$293$	22.2916	+	12.8701i	0.0760806	+	0.0439252i	−0.461477	+	0.887152i	$0.652680\pi$
$294$		0			0
$295$	−5.51814	+	15.1610i	−0.0187055	+	0.0513931i
$296$		0			0
$297$	−29.9683	+	17.3022i	−0.100904	+	0.0582567i
$298$		0			0
$299$	−16.1715	+	19.2725i	−0.0540854	+	0.0644565i
$300$		0			0
$301$	−0.544746	+	3.08941i	−0.00180979	+	0.0102638i
$302$		0			0
$303$			419.407i			1.38418i
$304$		0			0
$305$	−91.8112			−0.301020
$306$		0			0
$307$	156.302	+	27.5602i	0.509127	+	0.0897728i	0.422310	−	0.906452i	$-0.361219\pi$
$307$	156.302	+	27.5602i	0.509127	+	0.0897728i	0.0868168	+	0.996224i	$0.472331\pi$
$308$		0			0
$309$	−89.1403	−	74.7976i	−0.288480	−	0.242063i
$310$		0			0
$311$	−208.136	−	360.502i	−0.669246	−	1.15917i	−0.978115	−	0.208064i	$-0.933284\pi$
$311$	−208.136	−	360.502i	−0.669246	−	1.15917i	0.308869	−	0.951105i	$-0.400050\pi$
$312$		0			0
$313$	−450.837	−	164.091i	−1.44037	−	0.524253i	−0.500488	−	0.865743i	$-0.666846\pi$
$313$	−450.837	−	164.091i	−1.44037	−	0.524253i	−0.939885	+	0.341490i	$0.889068\pi$
$314$		0			0
$315$	−0.565550	+	0.979561i	−0.00179540	+	0.00310972i
$316$		0			0
$317$	−367.483	+	64.7972i	−1.15925	+	0.204407i	−0.720012	−	0.693962i	$-0.755864\pi$
$317$	−367.483	+	64.7972i	−1.15925	+	0.204407i	−0.439241	+	0.898369i	$0.644752\pi$
$318$		0			0
$319$	−13.7226	−	16.3539i	−0.0430174	−	0.0512662i
$320$		0			0
$321$	−387.923	+	141.192i	−1.20848	+	0.439851i
$322$		0			0
$323$	−123.710	−	30.7745i	−0.383003	−	0.0952771i
$324$		0			0
$325$	−5.79866	−	15.9317i	−0.0178420	−	0.0490206i
$326$		0			0
$327$	−77.7412	+	65.2326i	−0.237741	+	0.199488i
$328$		0			0
$329$	2.02808	+	11.5018i	0.00616439	+	0.0349600i
$330$		0			0
$331$	−273.287	−	157.783i	−0.825642	−	0.476685i	0.0267163	−	0.999643i	$-0.491495\pi$
$331$	−273.287	−	157.783i	−0.825642	−	0.476685i	−0.852358	+	0.522959i	$0.824828\pi$
$332$		0			0
$333$	6.04056	−	16.5963i	0.0181398	−	0.0498388i
$334$		0			0
$335$	95.6076	−	55.1991i	0.285396	−	0.164773i
$336$		0			0
$337$	−399.346	+	475.922i	−1.18500	+	1.41223i	−0.295473	+	0.955351i	$0.595477\pi$
$337$	−399.346	+	475.922i	−1.18500	+	1.41223i	−0.889529	+	0.456879i	$0.848967\pi$
$338$		0			0
$339$	77.7821	−	441.124i	0.229446	−	1.30125i
$340$		0			0
$341$			80.0731i			0.234818i
$342$		0			0
$343$	21.8966			0.0638384
$344$		0			0
$345$	−204.258	−	36.0162i	−0.592053	−	0.104395i
$346$		0			0
$347$	181.749	+	152.506i	0.523773	+	0.439498i	0.865945	−	0.500139i	$-0.166718\pi$
$347$	181.749	+	152.506i	0.523773	+	0.439498i	−0.342171	+	0.939638i	$0.611162\pi$
$348$		0			0
$349$	−284.458	−	492.695i	−0.815065	−	1.41173i	−0.909281	−	0.416183i	$-0.863368\pi$
$349$	−284.458	−	492.695i	−0.815065	−	1.41173i	0.0942157	−	0.995552i	$-0.469966\pi$
$350$		0			0
$351$	−16.2540	−	5.91596i	−0.0463076	−	0.0168546i
$352$		0			0
$353$	−14.4306	+	24.9946i	−0.0408799	+	0.0708061i	−0.885741	−	0.464179i	$-0.846349\pi$
$353$	−14.4306	+	24.9946i	−0.0408799	+	0.0708061i	0.844862	+	0.534985i	$0.179683\pi$
$354$		0			0
$355$	56.4188	−	9.94816i	0.158926	−	0.0280230i
$356$		0			0
$357$	3.28774	+	3.91817i	0.00920935	+	0.0109753i
$358$		0			0
$359$	460.079	−	167.455i	1.28156	−	0.466448i	0.390610	−	0.920556i	$-0.372264\pi$
$359$	460.079	−	167.455i	1.28156	−	0.466448i	0.890947	+	0.454108i	$0.150042\pi$
$360$		0			0
$361$	135.589	+	334.569i	0.375592	+	0.926785i
$362$		0			0
$363$	138.167	+	379.610i	0.380625	+	1.04576i
$364$		0			0
$365$	−93.2995	+	78.2875i	−0.255615	+	0.214486i
$366$		0			0
$367$	−90.2595	−	511.887i	−0.245939	−	1.39479i	−0.818302	−	0.574788i	$-0.805084\pi$
$367$	−90.2595	−	511.887i	−0.245939	−	1.39479i	0.572363	−	0.820000i	$-0.306027\pi$
$368$		0			0
$369$	146.023	+	84.3062i	0.395725	+	0.228472i
$370$		0			0
$371$	−6.25255	+	17.1787i	−0.0168532	+	0.0463039i
$372$		0			0
$373$	−86.4543	+	49.9144i	−0.231781	+	0.133819i	−0.611393	−	0.791327i	$-0.709391\pi$
$373$	−86.4543	+	49.9144i	−0.231781	+	0.133819i	0.379612	+	0.925146i	$0.376057\pi$
$374$		0			0
$375$	195.316	−	232.769i	0.520843	−	0.620717i
$376$		0			0
$377$	1.85302	−	10.5090i	0.00491517	−	0.0278753i
$378$		0			0
$379$			248.498i			0.655668i	0.944735	+	0.327834i	$0.106319\pi$
$379$			248.498i			0.655668i	−0.944735	+	0.327834i	$0.893681\pi$
$380$		0			0
$381$	561.800			1.47454
$382$		0			0
$383$	440.409	+	77.6560i	1.14989	+	0.202757i	0.715929	−	0.698173i	$-0.246003\pi$
$383$	440.409	+	77.6560i	1.14989	+	0.202757i	0.433964	+	0.900930i	$0.357114\pi$
$384$		0			0
$385$	0.524970	+	0.440502i	0.00136356	+	0.00114416i
$386$		0			0
$387$	18.4454	+	31.9484i	0.0476626	+	0.0825540i
$388$		0			0
$389$	−319.937	−	116.447i	−0.822460	−	0.299351i	−0.103699	−	0.994609i	$-0.533068\pi$
$389$	−319.937	−	116.447i	−0.822460	−	0.299351i	−0.718760	+	0.695258i	$0.755290\pi$
$390$		0			0
$391$	−106.012	+	183.619i	−0.271131	+	0.469613i
$392$		0			0
$393$	−235.876	+	41.5913i	−0.600194	+	0.105830i
$394$		0			0
$395$	1.42097	+	1.69344i	0.00359739	+	0.00428720i
$396$		0			0
$397$	488.833	−	177.921i	1.23132	−	0.448163i	0.357269	−	0.934002i	$-0.383708\pi$
$397$	488.833	−	177.921i	1.23132	−	0.448163i	0.874049	+	0.485839i	$0.161486\pi$
$398$		0			0
$399$	3.49656	−	14.0558i	0.00876332	−	0.0352275i
$400$		0			0
$401$	220.639	+	606.201i	0.550222	+	1.51172i	0.833408	+	0.552658i	$0.186386\pi$
$401$	220.639	+	606.201i	0.550222	+	1.51172i	−0.283186	+	0.959065i	$0.591391\pi$
$402$		0			0
$403$	−30.6607	+	25.7274i	−0.0760811	+	0.0638396i
$404$		0			0
$405$	−32.6697	−	185.279i	−0.0806659	−	0.457479i
$406$		0			0
$407$	−9.26693	−	5.35027i	−0.0227689	−	0.0131456i
$408$		0			0
$409$	147.128	−	404.230i	0.359726	−	0.988338i	−0.619399	−	0.785076i	$-0.712624\pi$
$409$	147.128	−	404.230i	0.359726	−	0.988338i	0.979125	−	0.203261i	$-0.0651541\pi$
$410$		0			0
$411$	543.746	−	313.932i	1.32298	−	0.763824i
$412$		0			0
$413$	−1.20453	+	1.43550i	−0.00291653	+	0.00347578i
$414$		0			0
$415$	−26.0889	+	147.957i	−0.0628647	+	0.356523i
$416$		0			0
$417$			709.841i			1.70226i
$418$		0			0
$419$	−211.180			−0.504008			−0.252004	−	0.967726i	$-0.581090\pi$
$419$	−211.180			−0.504008			−0.252004	+	0.967726i	$0.581090\pi$
$420$		0			0
$421$	−581.176	−	102.477i	−1.38047	−	0.243413i	−0.566374	−	0.824148i	$-0.691654\pi$
$421$	−581.176	−	102.477i	−1.38047	−	0.243413i	−0.814093	+	0.580735i	$0.802765\pi$
$422$		0			0
$423$	105.212	+	88.2832i	0.248728	+	0.208707i
$424$		0			0
$425$	−71.4411	−	123.740i	−0.168097	−	0.291152i
$426$		0			0
$427$	−10.0205	−	3.64716i	−0.0234672	−	0.00854137i
$428$		0			0
$429$	2.16208	−	3.74483i	0.00503982	−	0.00872922i
$430$		0			0
$431$	−160.724	+	28.3400i	−0.372910	+	0.0657541i	−0.356963	−	0.934119i	$-0.616188\pi$
$431$	−160.724	+	28.3400i	−0.372910	+	0.0657541i	−0.0159477	+	0.999873i	$0.505077\pi$
$432$		0			0
$433$	64.2513	+	76.5717i	0.148386	+	0.176840i	0.835118	−	0.550071i	$-0.185400\pi$
$433$	64.2513	+	76.5717i	0.148386	+	0.176840i	−0.686731	+	0.726911i	$0.740955\pi$
$434$		0			0
$435$	82.6684	−	30.0888i	0.190042	−	0.0691697i
$436$		0			0
$437$	597.090	−	63.0777i	1.36634	−	0.144343i
$438$		0			0
$439$	−153.049	−	420.498i	−0.348630	−	0.957854i	−0.982802	−	0.184662i	$-0.940881\pi$
$439$	−153.049	−	420.498i	−0.348630	−	0.957854i	0.634172	−	0.773192i	$-0.281341\pi$
$440$		0			0
$441$	98.5764	−	82.7154i	0.223529	−	0.187563i
$442$		0			0
$443$	47.3404	+	268.481i	0.106863	+	0.606052i	0.990460	+	0.137803i	$0.0440039\pi$
$443$	47.3404	+	268.481i	0.106863	+	0.606052i	−0.883596	+	0.468249i	$0.844885\pi$
$444$		0			0
$445$	85.9011	+	49.5950i	0.193036	+	0.111449i
$446$		0			0
$447$	−296.928	+	815.803i	−0.664268	+	1.82506i
$448$		0			0
$449$	507.150	−	292.803i	1.12951	−	0.652123i	0.185698	−	0.982607i	$-0.440545\pi$
$449$	507.150	−	292.803i	1.12951	−	0.652123i	0.943811	+	0.330484i	$0.107212\pi$
$450$		0			0
$451$	65.6654	−	78.2570i	0.145600	−	0.173519i
$452$		0			0
$453$	139.728	−	792.437i	0.308450	−	1.74931i
$454$		0			0
$455$			0.342549i			0.000752854i
$456$		0			0
$457$	−232.391			−0.508515			−0.254257	−	0.967137i	$-0.581831\pi$
$457$	−232.391			−0.508515			−0.254257	+	0.967137i	$0.581831\pi$
$458$		0			0
$459$	−143.558	−	25.3131i	−0.312762	−	0.0551484i
$460$		0			0
$461$	548.403	+	460.164i	1.18959	+	0.998187i	0.999866	+	0.0163505i	$0.00520475\pi$
$461$	548.403	+	460.164i	1.18959	+	0.998187i	0.189727	+	0.981837i	$0.439240\pi$
$462$		0			0
$463$	−4.13967	−	7.17012i	−0.00894097	−	0.0154862i	0.861520	−	0.507723i	$-0.169513\pi$
$463$	−4.13967	−	7.17012i	−0.00894097	−	0.0154862i	−0.870461	+	0.492237i	$0.836179\pi$
$464$		0			0
$465$	−310.069	−	112.856i	−0.666815	−	0.242701i
$466$		0			0
$467$	−297.265	+	514.878i	−0.636542	+	1.10252i	0.349644	+	0.936883i	$0.386303\pi$
$467$	−297.265	+	514.878i	−0.636542	+	1.10252i	−0.986186	+	0.165641i	$0.947031\pi$
$468$		0			0
$469$	12.6276	−	2.22659i	0.0269245	−	0.00474752i
$470$		0			0
$471$	−444.055	−	529.205i	−0.942793	−	1.12358i
$472$		0			0
$473$	21.0031	−	7.64451i	0.0444041	−	0.0161618i
$474$		0			0
$475$	−164.375	+	369.722i	−0.346053	+	0.778361i
$476$		0			0
$477$	73.5279	+	202.016i	0.154147	+	0.423514i
$478$		0			0
$479$	459.411	−	385.491i	0.959103	−	0.804783i	−0.0217035	−	0.999764i	$-0.506909\pi$
$479$	459.411	−	385.491i	0.959103	−	0.804783i	0.980807	+	0.194981i	$0.0624645\pi$
$480$		0			0
$481$	−0.928789	−	5.26743i	−0.00193095	−	0.0109510i
$482$		0			0
$483$	−20.8625	−	12.0450i	−0.0431936	−	0.0249378i
$484$		0			0
$485$	87.1433	−	239.424i	0.179677	−	0.493658i
$486$		0			0
$487$	435.692	−	251.547i	0.894644	−	0.516523i	0.0191856	−	0.999816i	$-0.493893\pi$
$487$	435.692	−	251.547i	0.894644	−	0.516523i	0.875459	+	0.483293i	$0.160559\pi$
$488$		0			0
$489$	−203.872	+	242.965i	−0.416915	+	0.496860i
$490$		0			0
$491$	−112.055	+	635.498i	−0.228219	+	1.29429i	0.628217	+	0.778038i	$0.283785\pi$
$491$	−112.055	+	635.498i	−0.228219	+	1.29429i	−0.856435	+	0.516254i	$0.827326\pi$
$492$		0			0
$493$		−	89.9314i		−	0.182417i
$494$		0			0
$495$	8.05889			0.0162806
$496$		0			0
$497$	6.55288	+	1.15545i	0.0131849	+	0.00232485i
$498$		0			0
$499$	−377.871	−	317.072i	−0.757257	−	0.635414i	0.180154	−	0.983638i	$-0.442340\pi$
$499$	−377.871	−	317.072i	−0.757257	−	0.635414i	−0.937411	+	0.348224i	$0.886785\pi$
$500$		0			0
$501$	−316.097	−	547.496i	−0.630932	−	1.09281i
$502$		0			0
$503$	−320.574	−	116.679i	−0.637323	−	0.231967i	0.00309227	−	0.999995i	$-0.499016\pi$
$503$	−320.574	−	116.679i	−0.637323	−	0.231967i	−0.640416	+	0.768028i	$0.721238\pi$
$504$		0			0
$505$	−118.359	+	205.003i	−0.234374	+	0.405947i
$506$		0			0
$507$	−565.425	+	99.6996i	−1.11524	+	0.196646i
$508$		0			0
$509$	−280.139	−	333.857i	−0.550371	−	0.655907i	0.417108	−	0.908857i	$-0.363044\pi$
$509$	−280.139	−	333.857i	−0.550371	−	0.655907i	−0.967479	+	0.252950i	$0.918599\pi$
$510$		0			0
$511$	−13.2929	+	4.83821i	−0.0260135	+	0.00946813i
$512$		0			0
$513$	181.157	+	370.926i	0.353132	+	0.723053i
$514$		0			0
$515$	−22.4630	−	61.7165i	−0.0436174	−	0.119838i
$516$		0			0
$517$	63.7447	−	53.4882i	0.123297	−	0.103459i
$518$		0			0
$519$	−117.835	−	668.276i	−0.227042	−	1.28762i
$520$		0			0
$521$	41.4944	+	23.9568i	0.0796437	+	0.0459823i	0.539293	−	0.842118i	$-0.318692\pi$
$521$	41.4944	+	23.9568i	0.0796437	+	0.0459823i	−0.459649	+	0.888101i	$0.652025\pi$
$522$		0			0
$523$	−309.214	+	849.559i	−0.591232	+	1.62440i	0.176990	+	0.984213i	$0.443364\pi$
$523$	−309.214	+	849.559i	−0.591232	+	1.62440i	−0.768222	+	0.640184i	$0.778858\pi$
$524$		0			0
$525$	14.0591	−	8.11705i	0.0267793	−	0.0154610i
$526$		0			0
$527$	−216.819	+	258.395i	−0.411421	+	0.490313i
$528$		0			0
$529$	81.5455	−	462.468i	0.154150	−	0.874230i
$530$		0			0
$531$			22.0365i			0.0415001i
$532$		0			0
$533$	51.0635			0.0958040
$534$		0			0
$535$	−229.459	−	40.4599i	−0.428896	−	0.0756259i
$536$		0			0
$537$	−367.960	−	308.755i	−0.685215	−	0.574963i
$538$		0			0
$539$	−38.9824	−	67.5195i	−0.0723236	−	0.125268i
$540$		0			0
$541$	−216.154	−	78.6736i	−0.399545	−	0.145423i	0.134429	−	0.990923i	$-0.457080\pi$
$541$	−216.154	−	78.6736i	−0.399545	−	0.145423i	−0.533974	+	0.845501i	$0.679302\pi$
$542$		0			0
$543$	−138.136	+	239.258i	−0.254393	+	0.440622i
$544$		0			0
$545$	−56.4084	+	9.94633i	−0.103502	+	0.0182501i
$546$		0			0
$547$	−446.030	−	531.558i	−0.815412	−	0.971770i	0.184527	−	0.982827i	$-0.440925\pi$
$547$	−446.030	−	531.558i	−0.815412	−	0.971770i	−0.999939	+	0.0110574i	$0.996480\pi$
$548$		0			0
$549$	−117.838	+	42.8894i	−0.214641	+	0.0781228i
$550$		0			0
$551$	−205.952	+	149.800i	−0.373778	+	0.271869i
$552$		0			0
$553$	0.0878166	+	0.241274i	0.000158800	+	0.000436300i
$554$		0			0
$555$	33.7789	−	28.3438i	0.0608628	−	0.0510700i
$556$		0			0
$557$	186.777	+	1059.26i	0.335326	+	1.90173i	0.423989	+	0.905667i	$0.360630\pi$
$557$	186.777	+	1059.26i	0.335326	+	1.90173i	−0.0886626	+	0.996062i	$0.528259\pi$
$558$		0			0
$559$	9.67543	+	5.58611i	0.0173085	+	0.00999305i
$560$		0			0
$561$	12.4639	−	34.2444i	0.0222174	−	0.0610417i
$562$		0			0
$563$	916.650	−	529.228i	1.62815	−	0.940014i	0.643508	−	0.765439i	$-0.277478\pi$
$563$	916.650	−	529.228i	1.62815	−	0.940014i	0.984644	−	0.174575i	$-0.0558551\pi$
$564$		0			0
$565$	162.507	−	193.668i	0.287623	−	0.342776i
$566$		0			0
$567$	3.79449	−	21.5196i	0.00669222	−	0.0379535i
$568$		0			0
$569$		−	13.0631i		−	0.0229579i	−0.999934	−	0.0114790i	$-0.996346\pi$
$569$		−	13.0631i		−	0.0229579i	0.999934	−	0.0114790i	$-0.00365395\pi$
$570$		0			0
$571$	41.1314			0.0720340			0.0360170	−	0.999351i	$-0.488533\pi$
$571$	41.1314			0.0720340			0.0360170	+	0.999351i	$0.488533\pi$
$572$		0			0
$573$	−980.181	−	172.832i	−1.71061	−	0.301627i
$574$		0			0
$575$	515.512	+	432.566i	0.896542	+	0.752288i
$576$		0			0
$577$	380.719	+	659.424i	0.659825	+	1.14285i	0.980661	+	0.195715i	$0.0627028\pi$
$577$	380.719	+	659.424i	0.659825	+	1.14285i	−0.320836	+	0.947135i	$0.603964\pi$
$578$		0			0
$579$	132.153	+	48.0999i	0.228244	+	0.0830740i
$580$		0			0
$581$	−8.72495	+	15.1121i	−0.0150171	+	0.0260104i
$582$		0			0
$583$	128.272	−	22.6178i	0.220020	−	0.0387955i
$584$		0			0
$585$	2.58931	+	3.08582i	0.00442618	+	0.00527491i
$586$		0			0
$587$	593.004	−	215.836i	1.01023	−	0.367693i	0.216708	−	0.976236i	$-0.430468\pi$
$587$	593.004	−	215.836i	1.01023	−	0.367693i	0.793521	+	0.608543i	$0.208246\pi$
$588$		0			0
$589$	952.908	+	66.1247i	1.61784	+	0.112266i
$590$		0			0
$591$	−100.456	−	276.001i	−0.169977	−	0.467007i
$592$		0			0
$593$	663.276	−	556.554i	1.11851	−	0.938540i	0.119981	−	0.992776i	$-0.461717\pi$
$593$	663.276	−	556.554i	1.11851	−	0.938540i	0.998528	+	0.0542360i	$0.0172723\pi$
$594$		0			0
$595$	0.501297	+	2.84299i	0.000842515	+	0.00477814i
$596$		0			0
$597$	597.351	+	344.881i	1.00059	+	0.577690i
$598$		0			0
$599$	−19.8028	+	54.4077i	−0.0330598	+	0.0908309i	−0.955124	−	0.296205i	$-0.904279\pi$
$599$	−19.8028	+	54.4077i	−0.0330598	+	0.0908309i	0.922065	+	0.387036i	$0.126501\pi$
$600$		0			0
$601$	410.973	−	237.276i	0.683816	−	0.394801i	−0.117475	−	0.993076i	$-0.537480\pi$
$601$	410.973	−	237.276i	0.683816	−	0.394801i	0.801291	+	0.598274i	$0.204147\pi$
$602$		0			0
$603$	96.9241	−	115.510i	0.160737	−	0.191558i
$604$		0			0
$605$	−39.5929	+	224.542i	−0.0654428	+	0.371144i
$606$		0			0
$607$			535.718i			0.882567i	0.897368	+	0.441284i	$0.145477\pi$
$607$			535.718i			0.882567i	−0.897368	+	0.441284i	$0.854523\pi$
$608$		0			0
$609$	10.2179			0.0167782
$610$		0			0
$611$	40.9622	+	7.22274i	0.0670412	+	0.0118212i
$612$		0			0
$613$	15.2410	+	12.7887i	0.0248630	+	0.0208625i	0.655134	−	0.755512i	$-0.272612\pi$
$613$	15.2410	+	12.7887i	0.0248630	+	0.0208625i	−0.630271	+	0.776375i	$0.717056\pi$
$614$		0			0
$615$	210.487	+	364.574i	0.342255	+	0.592803i
$616$		0			0
$617$	19.9187	+	7.24981i	0.0322831	+	0.0117501i	0.358111	−	0.933679i	$-0.383421\pi$
$617$	19.9187	+	7.24981i	0.0322831	+	0.0117501i	−0.325828	+	0.945429i	$0.605643\pi$
$618$		0			0
$619$	60.5976	−	104.958i	0.0978960	−	0.169561i	−0.812918	−	0.582379i	$-0.802122\pi$
$619$	60.5976	−	104.958i	0.0978960	−	0.169561i	0.910814	+	0.412818i	$0.135455\pi$
$620$		0			0
$621$	676.136	−	119.221i	1.08879	−	0.191982i
$622$		0			0
$623$	7.40531	+	8.82531i	0.0118865	+	0.0141658i
$624$		0			0
$625$	−339.123	+	123.431i	−0.542597	+	0.197489i
$626$		0			0
$627$	−99.1844	+	28.4977i	−0.158189	+	0.0454509i
$628$		0			0
$629$	−15.4170	−	42.3579i	−0.0245104	−	0.0673417i
$630$		0			0
$631$	5.27750	−	4.42835i	0.00836371	−	0.00701799i	−0.638596	−	0.769542i	$-0.720485\pi$
$631$	5.27750	−	4.42835i	0.00836371	−	0.00701799i	0.646960	+	0.762524i	$0.276040\pi$
$632$		0			0
$633$	−43.8910	−	248.918i	−0.0693381	−	0.393236i
$634$		0			0
$635$	274.604	+	158.543i	0.432448	+	0.249674i
$636$		0			0
$637$	13.3288	−	36.6207i	0.0209244	−	0.0574893i
$638$		0			0
$639$	67.7651	−	39.1242i	0.106049	−	0.0612272i
$640$		0			0
$641$	114.469	−	136.419i	0.178579	−	0.212822i	−0.669328	−	0.742967i	$-0.733418\pi$
$641$	114.469	−	136.419i	0.178579	−	0.212822i	0.847907	+	0.530145i	$0.177862\pi$
$642$		0			0
$643$	−23.5984	+	133.833i	−0.0367005	+	0.208139i	−0.997644	−	0.0686064i	$-0.978145\pi$
$643$	−23.5984	+	133.833i	−0.0367005	+	0.208139i	0.960943	+	0.276745i	$0.0892559\pi$
$644$		0			0
$645$			92.1052i			0.142799i
$646$		0			0
$647$	−487.032			−0.752755			−0.376377	−	0.926466i	$-0.622830\pi$
$647$	−487.032			−0.752755			−0.376377	+	0.926466i	$0.622830\pi$
$648$		0			0
$649$	13.1485	+	2.31843i	0.0202596	+	0.00357231i
$650$		0			0
$651$	−29.3585	−	24.6347i	−0.0450976	−	0.0378414i
$652$		0			0
$653$	−318.550	−	551.745i	−0.487825	−	0.844938i	0.512077	−	0.858940i	$-0.328876\pi$
$653$	−318.550	−	551.745i	−0.487825	−	0.844938i	−0.999902	+	0.0140017i	$0.995543\pi$
$654$		0			0
$655$	−127.032	−	46.2359i	−0.193942	−	0.0705891i
$656$		0			0
$657$	−83.1760	+	144.065i	−0.126600	+	0.219277i
$658$		0			0
$659$	−895.033	+	157.818i	−1.35817	+	0.239482i	−0.804845	−	0.593485i	$-0.797752\pi$
$659$	−895.033	+	157.818i	−1.35817	+	0.239482i	−0.553323	+	0.832967i	$0.686640\pi$
$660$		0			0
$661$	248.321	+	295.937i	0.375675	+	0.447712i	0.920444	−	0.390874i	$-0.127827\pi$
$661$	248.321	+	295.937i	0.375675	+	0.447712i	−0.544769	+	0.838586i	$0.683383\pi$
$662$		0			0
$663$	17.1171	−	6.23013i	0.0258177	−	0.00939688i
$664$		0			0
$665$	5.67571	−	5.88363i	0.00853491	−	0.00884756i
$666$		0			0
$667$	144.867	+	398.019i	0.217192	+	0.596730i
$668$		0			0
$669$	−3.99727	+	3.35410i	−0.00597499	+	0.00501361i
$670$		0			0
$671$	13.1931	+	74.8220i	0.0196619	+	0.111508i
$672$		0			0
$673$	−677.691	−	391.265i	−1.00697	−	0.581375i	−0.0966674	−	0.995317i	$-0.530818\pi$
$673$	−677.691	−	391.265i	−1.00697	−	0.581375i	−0.910303	+	0.413942i	$0.864152\pi$
$674$		0			0
$675$	−158.244	+	434.771i	−0.234435	+	0.644105i
$676$		0			0
$677$	−876.200	+	505.874i	−1.29424	+	0.747229i	−0.979403	−	0.201917i	$-0.935283\pi$
$677$	−876.200	+	505.874i	−1.29424	+	0.747229i	−0.314836	+	0.949146i	$0.601950\pi$
$678$		0			0
$679$	19.0221	−	22.6696i	0.0280148	−	0.0333868i
$680$		0			0
$681$	102.128	−	579.197i	0.149968	−	0.850509i
$682$		0			0
$683$		−	869.609i		−	1.27322i	−0.771186	−	0.636610i	$-0.780336\pi$
$683$		−	869.609i		−	1.27322i	0.771186	−	0.636610i	$-0.219664\pi$
$684$		0			0
$685$	354.373			0.517332
$686$		0			0
$687$	636.646	+	112.258i	0.926704	+	0.163403i
$688$		0			0
$689$	49.8742	+	41.8494i	0.0723863	+	0.0607393i
$690$		0			0
$691$	−325.984	−	564.622i	−0.471758	−	0.817108i	0.527720	−	0.849418i	$-0.323047\pi$
$691$	−325.984	−	564.622i	−0.471758	−	0.817108i	−0.999478	+	0.0323101i	$0.989714\pi$
$692$		0			0
$693$	0.879568	+	0.320137i	0.00126922	+	0.000461957i
$694$		0			0
$695$	−200.321	+	346.966i	−0.288231	+	0.499231i
$696$		0			0
$697$	423.803	−	74.7280i	0.608039	−	0.107214i
$698$		0			0
$699$	−179.234	−	213.602i	−0.256414	−	0.305583i
$700$		0			0
$701$	−991.288	+	360.799i	−1.41411	+	0.514692i	−0.932332	−	0.361603i	$-0.882230\pi$
$701$	−991.288	+	360.799i	−1.41411	+	0.514692i	−0.481774	+	0.876296i	$0.660007\pi$
$702$		0			0
$703$	−71.3234	+	105.863i	−0.101456	+	0.150587i
$704$		0			0
$705$	117.281	+	322.227i	0.166356	+	0.457059i
$706$		0			0
$707$	−21.0617	+	17.6728i	−0.0297902	+	0.0249969i
$708$		0			0
$709$	47.2525	+	267.982i	0.0666467	+	0.377972i	0.999828	+	0.0185654i	$0.00590988\pi$
$709$	47.2525	+	267.982i	0.0666467	+	0.377972i	−0.933181	+	0.359407i	$0.882979\pi$
$710$		0			0
$711$	2.61487	+	1.50970i	0.00367773	+	0.00212334i
$712$		0			0
$713$	543.361	−	1492.87i	0.762077	−	2.09379i
$714$		0			0
$715$	2.11362	−	1.22030i	0.00295612	−	0.00170671i
$716$		0			0
$717$	−531.018	+	632.842i	−0.740610	+	0.882625i
$718$		0			0
$719$	−41.3228	+	234.353i	−0.0574726	+	0.325943i	−0.999966	−	0.00828240i	$-0.997364\pi$
$719$	−41.3228	+	234.353i	−0.0574726	+	0.325943i	0.942493	+	0.334226i	$0.108475\pi$
$720$		0			0
$721$		−	7.62822i		−	0.0105801i
$722$		0			0
$723$	580.238			0.802542
$724$		0			0
$725$	−281.101	−	49.5656i	−0.387725	−	0.0683664i
$726$		0			0
$727$	−746.674	−	626.534i	−1.02706	−	0.861807i	−0.0365630	−	0.999331i	$-0.511641\pi$
$727$	−746.674	−	626.534i	−1.02706	−	0.861807i	−0.990498	+	0.137525i	$0.956085\pi$
$728$		0			0
$729$	204.918	+	354.928i	0.281094	+	0.486869i
$730$		0			0
$731$	88.4764	+	32.2028i	0.121035	+	0.0440531i
$732$		0			0
$733$	179.194	−	310.372i	0.244466	−	0.423427i	−0.717515	−	0.696543i	$-0.754721\pi$
$733$	179.194	−	310.372i	0.244466	−	0.423427i	0.961981	+	0.273115i	$0.0880540\pi$
$734$		0			0
$735$	316.400	−	55.7898i	0.430476	−	0.0759045i
$736$		0			0
$737$	−58.7235	−	69.9839i	−0.0796791	−	0.0949578i
$738$		0			0
$739$	565.439	−	205.803i	0.765140	−	0.278488i	0.0701779	−	0.997534i	$-0.477643\pi$
$739$	565.439	−	205.803i	0.765140	−	0.278488i	0.694962	+	0.719046i	$0.255421\pi$
$740$		0			0
$741$	−42.7799	−	28.8223i	−0.0577326	−	0.0388965i
$742$		0			0
$743$	−218.725	−	600.942i	−0.294381	−	0.808804i	−0.995413	−	0.0956744i	$-0.969499\pi$
$743$	−218.725	−	600.942i	−0.294381	−	0.808804i	0.701032	−	0.713130i	$-0.252723\pi$
$744$		0			0
$745$	−375.360	+	314.965i	−0.503839	+	0.422771i
$746$		0			0
$747$	35.6334	+	202.087i	0.0477021	+	0.270532i
$748$		0			0
$749$	−23.4365	−	13.5311i	−0.0312904	−	0.0180655i
$750$		0			0
$751$	−262.309	+	720.688i	−0.349280	+	0.959638i	0.633318	+	0.773892i	$0.281692\pi$
$751$	−262.309	+	720.688i	−0.349280	+	0.959638i	−0.982598	+	0.185746i	$0.940530\pi$
$752$		0			0
$753$	−595.804	+	343.987i	−0.791240	+	0.456822i
$754$		0			0
$755$	291.928	−	347.906i	0.386659	−	0.460803i
$756$		0			0
$757$	−47.3305	+	268.425i	−0.0625238	+	0.354590i	0.937455	+	0.348106i	$0.113175\pi$
$757$	−47.3305	+	268.425i	−0.0625238	+	0.354590i	−0.999979	+	0.00648404i	$0.997936\pi$
$758$		0			0
$759$			171.637i			0.226136i
$760$		0			0
$761$	−1210.51			−1.59068			−0.795341	−	0.606162i	$-0.792708\pi$
$761$	−1210.51			−1.59068			−0.795341	+	0.606162i	$0.792708\pi$
$762$		0			0
$763$	−6.55167	−	1.15524i	−0.00858672	−	0.00151407i
$764$		0			0
$765$	26.0060	+	21.8216i	0.0339947	+	0.0285250i
$766$		0			0
$767$	3.33684	+	5.77957i	0.00435050	+	0.00753529i
$768$		0			0
$769$	43.5369	+	15.8461i	0.0566150	+	0.0206062i	0.370172	−	0.928963i	$-0.379299\pi$
$769$	43.5369	+	15.8461i	0.0566150	+	0.0206062i	−0.313557	+	0.949569i	$0.601521\pi$
$770$		0			0
$771$	733.319	−	1270.15i	0.951128	−	1.64740i
$772$		0			0
$773$	−1363.49	+	240.421i	−1.76390	+	0.311023i	−0.959215	−	0.282678i	$-0.908777\pi$
$773$	−1363.49	+	240.421i	−1.76390	+	0.311023i	−0.804685	+	0.593701i	$0.797666\pi$
$774$		0			0
$775$	688.171	+	820.130i	0.887962	+	1.05823i
$776$		0			0
$777$	4.81266	−	1.75166i	0.00619390	−	0.00225439i
$778$		0			0
$779$	−877.069	−	846.075i	−1.12589	−	1.08610i
$780$		0			0
$781$	−16.2146	−	44.5493i	−0.0207614	−	0.0570414i
$782$		0			0
$783$	−223.081	+	187.187i	−0.284905	+	0.239064i
$784$		0			0
$785$	−67.7072	−	383.987i	−0.0862512	−	0.489155i
$786$		0			0
$787$	−313.616	−	181.066i	−0.398495	−	0.230071i	0.287339	−	0.957829i	$-0.407229\pi$
$787$	−313.616	−	181.066i	−0.398495	−	0.230071i	−0.685834	+	0.727758i	$0.740563\pi$
$788$		0			0
$789$	−0.148878	+	0.409039i	−0.000188692	+	0.000518427i
$790$		0			0
$791$	25.4298	−	14.6819i	0.0321489	−	0.0185612i
$792$		0			0
$793$	−24.4111	+	29.0920i	−0.0307832	+	0.0366860i
$794$		0			0
$795$	−93.2044	+	528.588i	−0.117238	+	0.664891i
$796$		0			0
$797$			433.899i			0.544415i	0.962239	+	0.272208i	$0.0877537\pi$
$797$			433.899i			0.544415i	−0.962239	+	0.272208i	$0.912246\pi$
$798$		0			0
$799$	350.537			0.438720
$800$		0			0
$801$	133.420	+	23.5256i	0.166567	+	0.0293703i
$802$		0			0
$803$	77.2079	+	64.7851i	0.0961493	+	0.0806788i
$804$		0			0
$805$	−6.79831	−	11.7750i	−0.00844511	−	0.0146274i
$806$		0			0
$807$	472.134	+	171.843i	0.585049	+	0.212940i
$808$		0			0
$809$	40.4183	−	70.0065i	0.0499608	−	0.0865346i	−0.839964	−	0.542643i	$-0.817424\pi$
$809$	40.4183	−	70.0065i	0.0499608	−	0.0865346i	0.889924	+	0.456108i	$0.150757\pi$
$810$		0			0
$811$	1188.41	−	209.549i	1.46536	−	0.258383i	0.616651	−	0.787237i	$-0.288489\pi$
$811$	1188.41	−	209.549i	1.46536	−	0.258383i	0.848713	+	0.528853i	$0.177378\pi$
$812$		0			0
$813$	809.202	+	964.369i	0.995328	+	1.18619i
$814$		0			0
$815$	−168.217	+	61.2260i	−0.206401	+	0.0751239i
$816$		0			0
$817$	−73.6289	−	256.260i	−0.0901211	−	0.313660i
$818$		0			0
$819$	0.160021	+	0.439654i	0.000195386	+	0.000536818i
$820$		0			0
$821$	−908.228	+	762.094i	−1.10625	+	0.928251i	−0.997829	−	0.0658545i	$-0.979023\pi$
$821$	−908.228	+	762.094i	−1.10625	+	0.928251i	−0.108417	+	0.994105i	$0.534578\pi$
$822$		0			0
$823$	−153.906	−	872.846i	−0.187007	−	1.06057i	−0.923350	−	0.383959i	$-0.874560\pi$
$823$	−153.906	−	872.846i	−0.187007	−	1.06057i	0.736344	−	0.676608i	$-0.236551\pi$
$824$		0			0
$825$	−100.169	−	57.8326i	−0.121417	−	0.0701001i
$826$		0			0
$827$	405.505	−	1114.12i	0.490333	−	1.34718i	−0.410043	−	0.912066i	$-0.634486\pi$
$827$	405.505	−	1114.12i	0.490333	−	1.34718i	0.900376	−	0.435113i	$-0.143292\pi$
$828$		0			0
$829$	−1199.56	+	692.566i	−1.44700	+	0.835423i	−0.998301	−	0.0582623i	$-0.981444\pi$
$829$	−1199.56	+	692.566i	−1.44700	+	0.835423i	−0.448694	+	0.893685i	$0.648111\pi$
$830$		0			0
$831$	446.727	−	532.389i	0.537578	−	0.640661i
$832$		0			0
$833$	57.0312	−	323.440i	0.0684649	−	0.388284i
$834$		0			0
$835$		−	356.817i		−	0.427325i
$836$		0			0
$837$	1092.26			1.30497
$838$		0			0
$839$	1556.62	+	274.474i	1.85532	+	0.327144i	0.985954	−	0.167018i	$-0.0534138\pi$
$839$	1556.62	+	274.474i	1.85532	+	0.327144i	0.869370	+	0.494162i	$0.164525\pi$
$840$		0			0
$841$	506.618	+	425.103i	0.602400	+	0.505473i
$842$		0			0
$843$	652.018	+	1129.33i	0.773450	+	1.33965i
$844$		0			0
$845$	−304.512	−	110.833i	−0.360369	−	0.131164i
$846$		0			0
$847$	−13.2411	+	22.9343i	−0.0156330	+	0.0270771i
$848$		0			0
$849$	1533.24	−	270.352i	1.80594	−	0.318435i
$850$		0			0
$851$	136.466	+	162.633i	0.160359	+	0.191109i
$852$		0			0
$853$	306.658	−	111.615i	0.359506	−	0.130849i	−0.155951	−	0.987765i	$-0.549844\pi$
$853$	306.658	−	111.615i	0.359506	−	0.130849i	0.515457	+	0.856915i	$0.327622\pi$
$854$		0			0
$855$	6.65507	−	95.9047i	0.00778371	−	0.112169i
$856$		0			0
$857$	143.551	+	394.404i	0.167504	+	0.460214i	0.994836	−	0.101500i	$-0.0323642\pi$
$857$	143.551	+	394.404i	0.167504	+	0.460214i	−0.827331	+	0.561714i	$0.810142\pi$
$858$		0			0
$859$	−344.202	+	288.820i	−0.400701	+	0.336228i	−0.820765	−	0.571267i	$-0.806452\pi$
$859$	−344.202	+	288.820i	−0.400701	+	0.336228i	0.420064	+	0.907495i	$0.362008\pi$
$860$		0			0
$861$	8.49050	+	48.1520i	0.00986121	+	0.0559257i
$862$		0			0
$863$	315.672	+	182.253i	0.365785	+	0.211186i	0.671615	−	0.740900i	$-0.265601\pi$
$863$	315.672	+	182.253i	0.365785	+	0.211186i	−0.305831	+	0.952086i	$0.598934\pi$
$864$		0			0
$865$	130.994	−	359.903i	0.151438	−	0.416072i
$866$		0			0
$867$	−720.540	+	416.004i	−0.831073	+	0.479820i
$868$		0			0
$869$	1.17589	−	1.40137i	0.00135315	−	0.00161262i
$870$		0			0
$871$	7.92969	−	44.9715i	0.00910412	−	0.0516320i
$872$		0			0
$873$		−	348.005i		−	0.398631i
$874$		0			0
$875$	19.9193			0.0227649
$876$		0			0
$877$	869.346	+	153.289i	0.991272	+	0.174788i	0.645689	−	0.763600i	$-0.276570\pi$
$877$	869.346	+	153.289i	0.991272	+	0.174788i	0.345583	+	0.938388i	$0.387681\pi$
$878$		0			0
$879$	67.2409	+	56.4218i	0.0764970	+	0.0641886i
$880$		0			0
$881$	−214.756	−	371.968i	−0.243764	−	0.422212i	0.718019	−	0.696023i	$-0.245049\pi$
$881$	−214.756	−	371.968i	−0.243764	−	0.422212i	−0.961783	+	0.273812i	$0.911716\pi$
$882$		0			0
$883$	1462.31	+	532.239i	1.65607	+	0.602762i	0.989739	−	0.142890i	$-0.0456395\pi$
$883$	1462.31	+	532.239i	1.65607	+	0.602762i	0.666336	+	0.745652i	$0.267862\pi$
$884$		0			0
$885$	−27.5093	+	47.6475i	−0.0310839	+	0.0538389i
$886$		0			0
$887$	−360.809	+	63.6204i	−0.406775	+	0.0717254i	−0.373292	−	0.927714i	$-0.621771\pi$
$887$	−360.809	+	63.6204i	−0.406775	+	0.0717254i	−0.0334829	+	0.999439i	$0.510660\pi$
$888$		0			0
$889$	23.6730	+	28.2123i	0.0266287	+	0.0317349i
$890$		0			0
$891$	−146.300	+	53.2487i	−0.164197	+	0.0597629i
$892$		0			0
$893$	−583.894	−	802.763i	−0.653857	−	0.898951i
$894$		0			0
$895$	−92.7243	−	254.758i	−0.103603	−	0.284646i
$896$		0			0
$897$	−65.7213	+	55.1467i	−0.0732679	+	0.0614791i
$898$		0			0
$899$	117.013	+	663.611i	0.130159	+	0.738166i
$900$		0			0
$901$	475.176	+	274.343i	0.527387	+	0.304487i
$902$		0			0
$903$	−3.65884	+	10.0526i	−0.00405188	+	0.0111324i
$904$		0			0
$905$	−135.040	+	77.9652i	−0.149215	+	0.0861494i
$906$		0			0
$907$	−373.241	+	444.812i	−0.411512	+	0.490421i	−0.931494	−	0.363756i	$-0.881494\pi$
$907$	−373.241	+	444.812i	−0.411512	+	0.490421i	0.519982	+	0.854177i	$0.325939\pi$
$908$		0			0
$909$	−56.1440	+	318.409i	−0.0617646	+	0.350285i
$910$		0			0
$911$		−	1512.78i		−	1.66057i	−0.557342	−	0.830283i	$-0.688179\pi$
$911$		−	1512.78i		−	1.66057i	0.557342	−	0.830283i	$-0.311821\pi$
$912$		0			0
$913$	124.328			0.136175
$914$		0			0
$915$	−308.330	−	54.3669i	−0.336972	−	0.0594173i
$916$		0			0
$917$	−12.0279	−	10.0926i	−0.0131166	−	0.0110061i
$918$		0			0
$919$	137.458	+	238.085i	0.149574	+	0.259069i	0.931070	−	0.364841i	$-0.118877\pi$
$919$	137.458	+	238.085i	0.149574	+	0.259069i	−0.781496	+	0.623910i	$0.785543\pi$
$920$		0			0
$921$	508.589	+	185.111i	0.552214	+	0.200989i
$922$		0			0
$923$	11.8486	−	20.5224i	0.0128370	−	0.0222344i
$924$		0			0
$925$	−140.896	+	24.8438i	−0.152320	+	0.0268582i
$926$		0			0
$927$	−57.6614	−	68.7182i	−0.0622022	−	0.0741297i
$928$		0			0
$929$	−459.791	+	167.350i	−0.494931	+	0.180140i	−0.577413	−	0.816453i	$-0.695938\pi$
$929$	−459.791	+	167.350i	−0.494931	+	0.180140i	0.0824819	+	0.996593i	$0.473715\pi$
$930$		0			0
$931$	−835.707	+	408.152i	−0.897644	+	0.438401i
$932$		0			0
$933$	−485.508	−	1333.92i	−0.520373	−	1.42971i
$934$		0			0
$935$	15.7563	−	13.2211i	0.0168516	−	0.0141402i
$936$		0			0
$937$	−42.5934	−	241.559i	−0.0454572	−	0.257801i	0.953607	−	0.301055i	$-0.0973387\pi$
$937$	−42.5934	−	241.559i	−0.0454572	−	0.257801i	−0.999064	+	0.0432539i	$0.986228\pi$
$938$		0			0
$939$	−1416.88	−	818.035i	−1.50892	−	0.871177i
$940$		0			0
$941$	−84.0372	+	230.890i	−0.0893063	+	0.245367i	−0.976303	−	0.216409i	$-0.930565\pi$
$941$	−84.0372	+	230.890i	−0.0893063	+	0.245367i	0.886996	+	0.461776i	$0.152788\pi$
$942$		0			0
$943$	−1755.30	+	1013.42i	−1.86139	+	1.07468i
$944$		0			0
$945$	6.00881	−	7.16102i	0.00635853	−	0.00757780i
$946$		0			0
$947$	−25.0588	+	142.116i	−0.0264613	+	0.150069i	−0.995176	−	0.0981087i	$-0.968721\pi$
$947$	−25.0588	+	142.116i	−0.0264613	+	0.150069i	0.968714	+	0.248178i	$0.0798318\pi$
$948$		0			0
$949$			50.3790i			0.0530864i
$950$		0			0
$951$	−1272.49			−1.33805
$952$		0			0
$953$	757.624	+	133.590i	0.794989	+	0.140178i	0.556369	−	0.830935i	$-0.312194\pi$
$953$	757.624	+	133.590i	0.794989	+	0.140178i	0.238619	+	0.971113i	$0.423305\pi$
$954$		0			0
$955$	−430.332	−	361.091i	−0.450609	−	0.378106i
$956$		0			0
$957$	−36.4004	−	63.0473i	−0.0380360	−	0.0658802i
$958$		0			0
$959$	38.6771	+	14.0773i	0.0403307	+	0.0146792i
$960$		0			0
$961$	783.220	−	1356.58i	0.815006	−	1.41163i
$962$		0			0
$963$	−313.407	+	55.2621i	−0.325448	+	0.0573853i
$964$		0			0
$965$	51.0217	+	60.8052i	0.0528722	+	0.0630106i
$966$		0			0
$967$	−652.700	+	237.564i	−0.674975	+	0.245671i	−0.656688	−	0.754162i	$-0.728043\pi$
$967$	−652.700	+	237.564i	−0.674975	+	0.245671i	−0.0182863	+	0.999833i	$0.505821\pi$
$968$		0			0
$969$	−397.232	−	176.606i	−0.409940	−	0.182256i
$970$		0			0
$971$	454.788	+	1249.52i	0.468370	+	1.28684i	0.919046	+	0.394149i	$0.128961\pi$
$971$	454.788	+	1249.52i	0.468370	+	1.28684i	−0.450676	+	0.892688i	$0.648817\pi$
$972$		0			0
$973$	−35.6466	+	29.9110i	−0.0366357	+	0.0307410i
$974$		0			0
$975$	−10.0396	−	56.9372i	−0.0102970	−	0.0583971i
$976$		0			0
$977$	−445.322	−	257.107i	−0.455806	−	0.263160i	0.254473	−	0.967080i	$-0.418098\pi$
$977$	−445.322	−	257.107i	−0.455806	−	0.263160i	−0.710279	+	0.703920i	$0.751431\pi$
$978$		0			0
$979$	28.0739	−	77.1323i	0.0286761	−	0.0787868i
$980$		0			0
$981$	−67.7526	+	39.1170i	−0.0690648	+	0.0398746i
$982$		0			0
$983$	100.455	−	119.717i	0.102192	−	0.121788i	−0.712524	−	0.701647i	$-0.752448\pi$
$983$	100.455	−	119.717i	0.102192	−	0.121788i	0.814716	+	0.579860i	$0.196893\pi$
$984$		0			0
$985$	28.7866	−	163.257i	0.0292250	−	0.165743i
$986$		0			0
$987$			39.8276i			0.0403522i
$988$		0			0
$989$	−443.454			−0.448386
$990$		0			0
$991$	−490.010	−	86.4019i	−0.494460	−	0.0871866i	−0.0791427	−	0.996863i	$-0.525218\pi$
$991$	−490.010	−	86.4019i	−0.494460	−	0.0871866i	−0.415317	+	0.909677i	$0.636329\pi$
$992$		0			0
$993$	−824.350	−	691.711i	−0.830161	−	0.696588i
$994$		0			0
$995$	194.654	+	337.151i	0.195633	+	0.338845i
$996$		0			0
$997$	1027.92	+	374.133i	1.03101	+	0.375259i	0.801467	−	0.598039i	$-0.204053\pi$
$997$	1027.92	+	374.133i	1.03101	+	0.375259i	0.229547	+	0.973297i	$0.426275\pi$
$998$		0			0
$999$	−72.9820	+	126.408i	−0.0730550	+	0.126535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.j.a.33.3	✓	18
4.3	odd	2		304.3.z.b.33.1		18
19.2	odd	18		1444.3.c.c.721.5		18
19.15	odd	18	inner	76.3.j.a.53.3	yes	18
19.17	even	9		1444.3.c.c.721.14		18
76.15	even	18		304.3.z.b.129.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.j.a.33.3	✓	18	1.1	even	1	trivial
76.3.j.a.53.3	yes	18	19.15	odd	18	inner
304.3.z.b.33.1		18	4.3	odd	2
304.3.z.b.129.1		18	76.15	even	18
1444.3.c.c.721.5		18	19.2	odd	18
1444.3.c.c.721.14		18	19.17	even	9

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(3.35830 + 0.592159i) q^{3} +(1.47441 + 1.23717i) q^{5} +(0.111774 + 0.193599i) q^{7} +(2.47031 + 0.899120i) q^{9} +O(q^{10})\)	\(q+(3.35830 + 0.592159i) q^{3} +(1.47441 + 1.23717i) q^{5} +(0.111774 + 0.193599i) q^{7} +(2.47031 + 0.899120i) q^{9} +(0.796372 - 1.37936i) q^{11} +(0.784041 - 0.138248i) q^{13} +(4.21890 + 5.02789i) q^{15} +(6.30486 - 2.29478i) q^{17} +(-15.7574 - 10.6163i) q^{19} +(0.260730 + 0.716351i) q^{21} +(-24.2075 + 20.3125i) q^{23} +(-3.69793 - 20.9720i) q^{25} +(-18.8155 - 10.8632i) q^{27} +(4.58431 - 12.5953i) q^{29} +(-43.5383 + 25.1368i) q^{31} +(3.49126 - 4.16072i) q^{33} +(-0.0747145 + 0.423727i) q^{35} -6.71830i q^{37} +2.71491 q^{39} +(63.1648 + 11.1376i) q^{41} +(10.7499 + 9.02027i) q^{43} +(2.52988 + 4.38188i) q^{45} +(49.0942 + 17.8688i) q^{47} +(24.4750 - 42.3920i) q^{49} +(22.5325 - 3.97309i) q^{51} +(52.5656 + 62.6453i) q^{53} +(2.88068 - 1.04848i) q^{55} +(-46.6315 - 44.9836i) q^{57} +(2.86701 + 7.87704i) q^{59} +(-36.5415 + 30.6619i) q^{61} +(0.102049 + 0.578747i) q^{63} +(1.32703 + 0.766163i) q^{65} +(19.6178 - 53.8994i) q^{67} +(-93.3244 + 53.8809i) q^{69} +(19.1327 - 22.8015i) q^{71} +(-10.9883 + 62.3180i) q^{73} -72.6201i q^{75} +0.356055 q^{77} +(1.13111 + 0.199445i) q^{79} +(-74.8799 - 62.8317i) q^{81} +(39.0294 + 67.6008i) q^{83} +(12.1350 + 4.41677i) q^{85} +(22.8539 - 39.5841i) q^{87} +(50.7523 - 8.94900i) q^{89} +(0.114400 + 0.136337i) q^{91} +(-161.100 + 58.6355i) q^{93} +(-10.0986 - 35.1473i) q^{95} +(-45.2763 - 124.395i) q^{97} +(3.20750 - 2.69141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) \) 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9} - 15 q^{11} + 51 q^{13} + 21 q^{15} - 45 q^{17} + 30 q^{19} - 63 q^{21} + 48 q^{23} - 54 q^{25} - 198 q^{27} - 39 q^{29} - 108 q^{31} - 105 q^{33} + 51 q^{35} + 48 q^{39} + 54 q^{41} + 75 q^{43} + 288 q^{45} + 339 q^{47} - 24 q^{49} + 360 q^{51} + 69 q^{53} - 51 q^{55} + 510 q^{57} - 483 q^{59} - 36 q^{61} - 267 q^{63} - 585 q^{65} - 87 q^{67} - 351 q^{69} - 234 q^{71} - 132 q^{73} + 108 q^{77} + 363 q^{79} + 258 q^{81} + 279 q^{83} + 666 q^{85} + 600 q^{89} + 270 q^{91} - 456 q^{93} - 39 q^{95} - 801 q^{97} - 267 q^{99}+O(q^{100}) \) 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9 - 15 * q^11 + 51 * q^13 + 21 * q^15 - 45 * q^17 + 30 * q^19 - 63 * q^21 + 48 * q^23 - 54 * q^25 - 198 * q^27 - 39 * q^29 - 108 * q^31 - 105 * q^33 + 51 * q^35 + 48 * q^39 + 54 * q^41 + 75 * q^43 + 288 * q^45 + 339 * q^47 - 24 * q^49 + 360 * q^51 + 69 * q^53 - 51 * q^55 + 510 * q^57 - 483 * q^59 - 36 * q^61 - 267 * q^63 - 585 * q^65 - 87 * q^67 - 351 * q^69 - 234 * q^71 - 132 * q^73 + 108 * q^77 + 363 * q^79 + 258 * q^81 + 279 * q^83 + 666 * q^85 + 600 * q^89 + 270 * q^91 - 456 * q^93 - 39 * q^95 - 801 * q^97 - 267 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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