LMFDB - Embedded newform 76.3.j.a.13.2

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			13.2
Root			$0.656794i$ of defining polynomial
Character	$\chi$	$=$	76.13
Dual form			76.3.j.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.215056 - 0.590861i) q^{3} +(-1.30596 - 7.40644i) q^{5} +(3.03221 - 5.25195i) q^{7} +(6.59153 + 5.53095i) q^{9} +O(q^{10})$	\(q+(0.215056 - 0.590861i) q^{3} +(-1.30596 - 7.40644i) q^{5} +(3.03221 - 5.25195i) q^{7} +(6.59153 + 5.53095i) q^{9} +(4.46952 + 7.74143i) q^{11} +(-6.31563 - 17.3521i) q^{13} +(-4.65703 - 0.821160i) q^{15} +(-15.3773 + 12.9031i) q^{17} +(17.8300 + 6.56436i) q^{19} +(-2.45108 - 2.92108i) q^{21} +(-4.31353 + 24.4632i) q^{23} +(-29.6575 + 10.7945i) q^{25} +(9.58643 - 5.53473i) q^{27} +(-13.6106 + 16.2205i) q^{29} +(34.7238 + 20.0478i) q^{31} +(5.53530 - 0.976023i) q^{33} +(-42.8582 - 15.5991i) q^{35} -14.8707i q^{37} -11.6109 q^{39} +(19.0165 - 52.2475i) q^{41} +(6.72062 + 38.1145i) q^{43} +(32.3564 - 56.0430i) q^{45} +(1.10558 + 0.927693i) q^{47} +(6.11135 + 10.5852i) q^{49} +(4.31695 + 11.8607i) q^{51} +(23.5326 + 4.14943i) q^{53} +(51.4995 - 43.2132i) q^{55} +(7.71307 - 9.12335i) q^{57} +(-34.9963 - 41.7070i) q^{59} +(-0.501142 + 2.84212i) q^{61} +(49.0352 - 17.8474i) q^{63} +(-120.269 + 69.4374i) q^{65} +(71.6504 - 85.3896i) q^{67} +(13.5267 + 7.80966i) q^{69} +(-114.429 + 20.1770i) q^{71} +(-42.9373 - 15.6279i) q^{73} +19.8449i q^{75} +54.2101 q^{77} +(-5.39352 + 14.8186i) q^{79} +(12.2390 + 69.4107i) q^{81} +(-38.7171 + 67.0600i) q^{83} +(115.648 + 97.0402i) q^{85} +(6.65702 + 11.5303i) q^{87} +(49.3453 + 135.575i) q^{89} +(-110.282 - 19.4458i) q^{91} +(19.3130 - 16.2056i) q^{93} +(25.3334 - 140.630i) q^{95} +(-110.468 - 131.651i) q^{97} +(-13.3565 + 75.7486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	0.215056	−	0.590861i	0.0716853	−	0.196954i	−0.898676	−	0.438614i	$-0.855470\pi$
$3$	0.215056	−	0.590861i	0.0716853	−	0.196954i	0.970361	+	0.241660i	$0.0776919\pi$
$4$		0			0
$5$	−1.30596	−	7.40644i	−0.261191	−	1.48129i	−0.779666	−	0.626196i	$-0.784611\pi$
$5$	−1.30596	−	7.40644i	−0.261191	−	1.48129i	0.518475	−	0.855093i	$-0.326500\pi$
$6$		0			0
$7$	3.03221	−	5.25195i	0.433173	−	0.750278i	−0.563971	−	0.825795i	$-0.690727\pi$
$7$	3.03221	−	5.25195i	0.433173	−	0.750278i	0.997145	+	0.0755161i	$0.0240604\pi$
$8$		0			0
$9$	6.59153	+	5.53095i	0.732392	+	0.614550i
$10$		0			0
$11$	4.46952	+	7.74143i	0.406320	+	0.703766i	0.994474	−	0.104982i	$-0.0334786\pi$
$11$	4.46952	+	7.74143i	0.406320	+	0.703766i	−0.588154	+	0.808749i	$0.700145\pi$
$12$		0			0
$13$	−6.31563	−	17.3521i	−0.485818	−	1.33477i	−0.904435	−	0.426611i	$-0.859707\pi$
$13$	−6.31563	−	17.3521i	−0.485818	−	1.33477i	0.418617	−	0.908163i	$-0.362515\pi$
$14$		0			0
$15$	−4.65703	−	0.821160i	−0.310469	−	0.0547440i
$16$		0			0
$17$	−15.3773	+	12.9031i	−0.904547	+	0.759005i	−0.971074	−	0.238780i	$-0.923253\pi$
$17$	−15.3773	+	12.9031i	−0.904547	+	0.759005i	0.0665271	+	0.997785i	$0.478808\pi$
$18$		0			0
$19$	17.8300	+	6.56436i	0.938421	+	0.345493i
$19$	17.8300	+	6.56436i	0.938421	+	0.345493i
$20$		0			0
$21$	−2.45108	−	2.92108i	−0.116718	−	0.139099i
$22$		0			0
$23$	−4.31353	+	24.4632i	−0.187545	+	1.06362i	0.735097	+	0.677962i	$0.237136\pi$
$23$	−4.31353	+	24.4632i	−0.187545	+	1.06362i	−0.922642	+	0.385657i	$0.873975\pi$
$24$		0			0
$25$	−29.6575	+	10.7945i	−1.18630	+	0.431778i
$26$		0			0
$27$	9.58643	−	5.53473i	0.355053	−	0.204990i
$28$		0			0
$29$	−13.6106	+	16.2205i	−0.469332	+	0.559328i	−0.947836	−	0.318757i	$-0.896735\pi$
$29$	−13.6106	+	16.2205i	−0.469332	+	0.559328i	0.478504	+	0.878085i	$0.341179\pi$
$30$		0			0
$31$	34.7238	+	20.0478i	1.12012	+	0.646704i	0.941432	−	0.337202i	$-0.109480\pi$
$31$	34.7238	+	20.0478i	1.12012	+	0.646704i	0.178691	+	0.983905i	$0.442814\pi$
$32$		0			0
$33$	5.53530	−	0.976023i	0.167736	−	0.0295765i
$34$		0			0
$35$	−42.8582	−	15.5991i	−1.22452	−	0.445689i
$36$		0			0
$37$		−	14.8707i		−	0.401912i	−0.979600	−	0.200956i	$-0.935595\pi$
$37$		−	14.8707i		−	0.401912i	0.979600	−	0.200956i	$-0.0644048\pi$
$38$		0			0
$39$	−11.6109			−0.297714
$40$		0			0
$41$	19.0165	−	52.2475i	0.463818	−	1.27433i	−0.458775	−	0.888553i	$-0.651712\pi$
$41$	19.0165	−	52.2475i	0.463818	−	1.27433i	0.922592	−	0.385776i	$-0.126066\pi$
$42$		0			0
$43$	6.72062	+	38.1145i	0.156294	+	0.886385i	0.957594	+	0.288122i	$0.0930309\pi$
$43$	6.72062	+	38.1145i	0.156294	+	0.886385i	−0.801300	+	0.598263i	$0.795858\pi$
$44$		0			0
$45$	32.3564	−	56.0430i	0.719032	−	1.24540i
$46$		0			0
$47$	1.10558	+	0.927693i	0.0235230	+	0.0197382i	0.654473	−	0.756085i	$-0.272890\pi$
$47$	1.10558	+	0.927693i	0.0235230	+	0.0197382i	−0.630950	+	0.775823i	$0.717335\pi$
$48$		0			0
$49$	6.11135	+	10.5852i	0.124721	+	0.216024i
$50$		0			0
$51$	4.31695	+	11.8607i	0.0846461	+	0.232563i
$52$		0			0
$53$	23.5326	+	4.14943i	0.444011	+	0.0782911i	0.391184	−	0.920313i	$-0.372066\pi$
$53$	23.5326	+	4.14943i	0.444011	+	0.0782911i	0.0528270	+	0.998604i	$0.483177\pi$
$54$		0			0
$55$	51.4995	−	43.2132i	0.936354	−	0.785694i
$56$		0			0
$57$	7.71307	−	9.12335i	0.135317	−	0.160059i
$58$		0			0
$59$	−34.9963	−	41.7070i	−0.593158	−	0.706898i	0.383052	−	0.923727i	$-0.374873\pi$
$59$	−34.9963	−	41.7070i	−0.593158	−	0.706898i	−0.976210	+	0.216829i	$0.930429\pi$
$60$		0			0
$61$	−0.501142	+	2.84212i	−0.00821544	+	0.0465921i	−0.988640	−	0.150304i	$-0.951975\pi$
$61$	−0.501142	+	2.84212i	−0.00821544	+	0.0465921i	0.980424	+	0.196896i	$0.0630860\pi$
$62$		0			0
$63$	49.0352	−	17.8474i	0.778337	−	0.283291i
$64$		0			0
$65$	−120.269	+	69.4374i	−1.85029	+	1.06827i
$66$		0			0
$67$	71.6504	−	85.3896i	1.06941	−	1.27447i	0.109552	−	0.993981i	$-0.465058\pi$
$67$	71.6504	−	85.3896i	1.06941	−	1.27447i	0.959857	−	0.280490i	$-0.0904971\pi$
$68$		0			0
$69$	13.5267	+	7.80966i	0.196039	+	0.113183i
$70$		0			0
$71$	−114.429	+	20.1770i	−1.61168	+	0.284183i	−0.905659	−	0.424007i	$-0.860623\pi$
$71$	−114.429	+	20.1770i	−1.61168	+	0.284183i	−0.706022	+	0.708190i	$0.749512\pi$
$72$		0			0
$73$	−42.9373	−	15.6279i	−0.588182	−	0.214081i	0.0307476	−	0.999527i	$-0.490211\pi$
$73$	−42.9373	−	15.6279i	−0.588182	−	0.214081i	−0.618930	+	0.785446i	$0.712433\pi$
$74$		0			0
$75$			19.8449i			0.264599i
$76$		0			0
$77$	54.2101			0.704028
$78$		0			0
$79$	−5.39352	+	14.8186i	−0.0682725	+	0.187577i	−0.969137	−	0.246524i	$-0.920712\pi$
$79$	−5.39352	+	14.8186i	−0.0682725	+	0.187577i	0.900864	+	0.434101i	$0.142934\pi$
$80$		0			0
$81$	12.2390	+	69.4107i	0.151098	+	0.856922i
$82$		0			0
$83$	−38.7171	+	67.0600i	−0.466472	+	0.807952i	−0.999267	−	0.0382919i	$-0.987808\pi$
$83$	−38.7171	+	67.0600i	−0.466472	+	0.807952i	0.532795	+	0.846244i	$0.321142\pi$
$84$		0			0
$85$	115.648	+	97.0402i	1.36056	+	1.14165i
$86$		0			0
$87$	6.65702	+	11.5303i	0.0765175	+	0.132532i
$88$		0			0
$89$	49.3453	+	135.575i	0.554441	+	1.52331i	0.827584	+	0.561342i	$0.189715\pi$
$89$	49.3453	+	135.575i	0.554441	+	1.52331i	−0.273143	+	0.961973i	$0.588063\pi$
$90$		0			0
$91$	−110.282	−	19.4458i	−1.21190	−	0.213690i
$92$		0			0
$93$	19.3130	−	16.2056i	0.207667	−	0.174253i
$94$		0			0
$95$	25.3334	−	140.630i	0.266667	−	1.48031i
$96$		0			0
$97$	−110.468	−	131.651i	−1.13885	−	1.35722i	−0.924825	−	0.380394i	$-0.875789\pi$
$97$	−110.468	−	131.651i	−1.13885	−	1.35722i	−0.214020	−	0.976829i	$-0.568656\pi$
$98$		0			0
$99$	−13.3565	+	75.7486i	−0.134914	+	0.765137i
$100$		0			0
$101$	−31.0298	+	11.2939i	−0.307225	+	0.111821i	−0.491032	−	0.871142i	$-0.663380\pi$
$101$	−31.0298	+	11.2939i	−0.307225	+	0.111821i	0.183807	+	0.982962i	$0.441158\pi$
$102$		0			0
$103$	−162.740	+	93.9582i	−1.58000	+	0.912215i	−0.585146	+	0.810928i	$0.698963\pi$
$103$	−162.740	+	93.9582i	−1.58000	+	0.912215i	−0.994857	+	0.101287i	$0.967704\pi$
$104$		0			0
$105$	−18.4338	+	21.9686i	−0.175560	+	0.209224i
$106$		0			0
$107$	−55.5976	−	32.0993i	−0.519604	−	0.299994i	0.217169	−	0.976134i	$-0.430318\pi$
$107$	−55.5976	−	32.0993i	−0.519604	−	0.299994i	−0.736773	+	0.676141i	$0.763651\pi$
$108$		0			0
$109$	116.313	−	20.5091i	1.06709	−	0.188157i	0.387590	−	0.921832i	$-0.373308\pi$
$109$	116.313	−	20.5091i	1.06709	−	0.188157i	0.679501	+	0.733675i	$0.262196\pi$
$110$		0			0
$111$	−8.78654	−	3.19804i	−0.0791580	−	0.0288112i
$112$		0			0
$113$			49.2047i			0.435440i	0.976011	+	0.217720i	$0.0698619\pi$
$113$			49.2047i			0.435440i	−0.976011	+	0.217720i	$0.930138\pi$
$114$		0			0
$115$	186.819			1.62451
$116$		0			0
$117$	54.3437	−	149.308i	0.464476	−	1.27614i
$118$		0			0
$119$	21.1391	+	119.886i	0.177639	+	1.00744i
$120$		0			0
$121$	20.5468	−	35.5882i	0.169809	−	0.294117i
$122$		0			0
$123$	−26.7814	−	22.4722i	−0.217735	−	0.182701i
$124$		0			0
$125$	24.6713	+	42.7319i	0.197370	+	0.341855i
$126$		0			0
$127$	−46.1499	−	126.796i	−0.363385	−	0.998392i	−0.977824	−	0.209428i	$-0.932840\pi$
$127$	−46.1499	−	126.796i	−0.363385	−	0.998392i	0.614439	−	0.788964i	$-0.289382\pi$
$128$		0			0
$129$	23.9657	+	4.22580i	0.185781	+	0.0327581i
$130$		0			0
$131$	146.715	−	123.109i	1.11996	−	0.939761i	0.121361	−	0.992608i	$-0.461274\pi$
$131$	146.715	−	123.109i	1.11996	−	0.939761i	0.998603	+	0.0528470i	$0.0168295\pi$
$132$		0			0
$133$	88.5401	−	73.7377i	0.665715	−	0.554419i
$134$		0			0
$135$	−53.5121	−	63.7732i	−0.396386	−	0.472394i
$136$		0			0
$137$	−6.91656	+	39.2258i	−0.0504858	+	0.286319i	−0.999590	−	0.0286439i	$-0.990881\pi$
$137$	−6.91656	+	39.2258i	−0.0504858	+	0.286319i	0.949104	+	0.314963i	$0.101992\pi$
$138$		0			0
$139$	−185.193	+	67.4049i	−1.33233	+	0.484927i	−0.907388	−	0.420295i	$-0.861927\pi$
$139$	−185.193	+	67.4049i	−1.33233	+	0.484927i	−0.424939	+	0.905222i	$0.639704\pi$
$140$		0			0
$141$	0.785899	−	0.453739i	0.00557375	−	0.00321801i
$142$		0			0
$143$	106.102	−	126.447i	0.741971	−	0.884247i
$144$		0			0
$145$	137.911	+	79.6231i	0.951112	+	0.549125i
$146$		0			0
$147$	7.56865	−	1.33456i	0.0514874	−	0.00907862i
$148$		0			0
$149$	−204.136	−	74.2993i	−1.37004	−	0.498653i	−0.450895	−	0.892577i	$-0.648895\pi$
$149$	−204.136	−	74.2993i	−1.37004	−	0.498653i	−0.919143	+	0.393924i	$0.871117\pi$
$150$		0			0
$151$			30.3509i			0.201000i	0.994937	+	0.100500i	$0.0320442\pi$
$151$			30.3509i			0.201000i	−0.994937	+	0.100500i	$0.967956\pi$
$152$		0			0
$153$	−172.726			−1.12893
$154$		0			0
$155$	103.135	−	283.362i	0.665388	−	1.82814i
$156$		0			0
$157$	−9.72805	−	55.1705i	−0.0619621	−	0.351405i	−0.999988	−	0.00484024i	$-0.998459\pi$
$157$	−9.72805	−	55.1705i	−0.0619621	−	0.351405i	0.938026	−	0.346564i	$-0.112652\pi$
$158$		0			0
$159$	7.51255	−	13.0121i	0.0472487	−	0.0818372i
$160$		0			0
$161$	115.400	+	96.8322i	0.716771	+	0.601442i
$162$		0			0
$163$	103.169	+	178.693i	0.632936	+	1.09628i	0.986948	+	0.161037i	$0.0514838\pi$
$163$	103.169	+	178.693i	0.632936	+	1.09628i	−0.354012	+	0.935241i	$0.615183\pi$
$164$		0			0
$165$	−14.4577	−	39.7223i	−0.0876226	−	0.240741i
$166$		0			0
$167$	168.167	+	29.6524i	1.00699	+	0.177559i	0.652732	−	0.757589i	$-0.273623\pi$
$167$	168.167	+	29.6524i	1.00699	+	0.177559i	0.354257	+	0.935148i	$0.384734\pi$
$168$		0			0
$169$	−131.745	+	110.547i	−0.779557	+	0.654126i
$170$		0			0
$171$	81.2199	+	141.886i	0.474970	+	0.829743i
$172$		0			0
$173$	−15.6636	−	18.6671i	−0.0905410	−	0.107903i	0.718872	−	0.695143i	$-0.244659\pi$
$173$	−15.6636	−	18.6671i	−0.0905410	−	0.107903i	−0.809413	+	0.587240i	$0.800214\pi$
$174$		0			0
$175$	−33.2361	+	188.491i	−0.189920	+	1.07709i
$176$		0			0
$177$	−32.1692	+	11.7086i	−0.181747	+	0.0661504i
$178$		0			0
$179$	−147.021	+	84.8825i	−0.821346	+	0.474204i	−0.850880	−	0.525360i	$-0.823931\pi$
$179$	−147.021	+	84.8825i	−0.821346	+	0.474204i	0.0295346	+	0.999564i	$0.490597\pi$
$180$		0			0
$181$	−69.4091	+	82.7185i	−0.383476	+	0.457009i	−0.922908	−	0.385020i	$-0.874194\pi$
$181$	−69.4091	+	82.7185i	−0.383476	+	0.457009i	0.539432	+	0.842029i	$0.318639\pi$
$182$		0			0
$183$	1.57152	+	0.907318i	0.00858755	+	0.00495802i
$184$		0			0
$185$	−110.139	+	19.4205i	−0.595347	+	0.104976i
$186$		0			0
$187$	−168.617	−	61.3717i	−0.901697	−	0.328191i
$188$		0			0
$189$		−	67.1299i		−	0.355185i
$190$		0			0
$191$	−152.732			−0.799642			−0.399821	−	0.916593i	$-0.630928\pi$
$191$	−152.732			−0.799642			−0.399821	+	0.916593i	$0.630928\pi$
$192$		0			0
$193$	−7.21211	+	19.8151i	−0.0373685	+	0.102669i	−0.956974	−	0.290175i	$-0.906287\pi$
$193$	−7.21211	+	19.8151i	−0.0373685	+	0.102669i	0.919605	+	0.392844i	$0.128509\pi$
$194$		0			0
$195$	15.1633	+	85.9952i	0.0777604	+	0.441001i
$196$		0			0
$197$	174.804	−	302.769i	0.887329	−	1.53690i	0.0443078	−	0.999018i	$-0.485892\pi$
$197$	174.804	−	302.769i	0.887329	−	1.53690i	0.843021	−	0.537881i	$-0.180775\pi$
$198$		0			0
$199$	224.125	+	188.063i	1.12626	+	0.945041i	0.998903	−	0.0468167i	$-0.0149077\pi$
$199$	224.125	+	188.063i	1.12626	+	0.945041i	0.127352	+	0.991858i	$0.459352\pi$
$200$		0			0
$201$	−35.0445	−	60.6989i	−0.174351	−	0.301985i
$202$		0			0
$203$	43.9190	+	120.666i	0.216350	+	0.594416i
$204$		0			0
$205$	−411.803	−	72.6119i	−2.00879	−	0.354204i
$206$		0			0
$207$	−163.738	+	137.392i	−0.791004	+	0.663731i
$208$		0			0
$209$	28.8740	+	167.369i	0.138153	+	0.800810i
$210$		0			0
$211$	12.6261	+	15.0472i	0.0598394	+	0.0713138i	0.795134	−	0.606434i	$-0.207401\pi$
$211$	12.6261	+	15.0472i	0.0598394	+	0.0713138i	−0.735294	+	0.677748i	$0.762956\pi$
$212$		0			0
$213$	−12.6869	+	71.9510i	−0.0595629	+	0.337798i
$214$		0			0
$215$	273.516	−	99.5518i	1.27217	−	0.463032i
$216$		0			0
$217$	210.580	−	121.579i	0.970415	−	0.560270i
$218$		0			0
$219$	−18.4678	+	22.0091i	−0.0843280	+	0.100498i
$220$		0			0
$221$	321.012	+	185.337i	1.45254	+	0.838627i
$222$		0			0
$223$	−106.283	+	18.7405i	−0.476603	+	0.0840380i	−0.406789	−	0.913522i	$-0.633352\pi$
$223$	−106.283	+	18.7405i	−0.476603	+	0.0840380i	−0.0698139	+	0.997560i	$0.522241\pi$
$224$		0			0
$225$	−255.192	−	92.8824i	−1.13419	−	0.412811i
$226$		0			0
$227$			72.2905i			0.318460i	0.987241	+	0.159230i	$0.0509012\pi$
$227$			72.2905i			0.318460i	−0.987241	+	0.159230i	$0.949099\pi$
$228$		0			0
$229$	63.8810			0.278956			0.139478	−	0.990225i	$-0.455458\pi$
$229$	63.8810			0.278956			0.139478	+	0.990225i	$0.455458\pi$
$230$		0			0
$231$	11.6582	−	32.0306i	0.0504684	−	0.138661i
$232$		0			0
$233$	9.64695	+	54.7105i	0.0414032	+	0.234809i	0.998486	−	0.0550052i	$-0.0175175\pi$
$233$	9.64695	+	54.7105i	0.0414032	+	0.234809i	−0.957083	+	0.289814i	$0.906406\pi$
$234$		0			0
$235$	5.42707	−	9.39995i	0.0230939	−	0.0399998i
$236$		0			0
$237$	7.59581	+	6.37364i	0.0320498	+	0.0268930i
$238$		0			0
$239$	−23.3703	−	40.4785i	−0.0977835	−	0.169366i	0.812983	−	0.582287i	$-0.197842\pi$
$239$	−23.3703	−	40.4785i	−0.0977835	−	0.169366i	−0.910767	+	0.412921i	$0.864509\pi$
$240$		0			0
$241$	−156.442	−	429.821i	−0.649138	−	1.78349i	−0.620900	−	0.783890i	$-0.713233\pi$
$241$	−156.442	−	429.821i	−0.649138	−	1.78349i	−0.0282383	−	0.999601i	$-0.508990\pi$
$242$		0			0
$243$	141.756	+	24.9954i	0.583357	+	0.102862i
$244$		0			0
$245$	70.4173	−	59.0871i	0.287418	−	0.241172i
$246$		0			0
$247$	1.29737	−	350.845i	0.00525252	−	1.42043i
$248$		0			0
$249$	31.2968	+	37.2981i	0.125690	+	0.149792i
$250$		0			0
$251$	40.4570	−	229.443i	0.161183	−	0.914115i	−0.791730	−	0.610872i	$-0.790819\pi$
$251$	40.4570	−	229.443i	0.161183	−	0.914115i	0.952913	−	0.303244i	$-0.0980697\pi$
$252$		0			0
$253$	−208.660	+	75.9460i	−0.824742	+	0.300182i
$254$		0			0
$255$	82.2080	−	47.4628i	0.322384	−	0.186129i
$256$		0			0
$257$	134.459	−	160.241i	0.523185	−	0.623508i	−0.438146	−	0.898904i	$-0.644365\pi$
$257$	134.459	−	160.241i	0.523185	−	0.623508i	0.961331	+	0.275396i	$0.0888091\pi$
$258$		0			0
$259$	−78.1004	−	45.0913i	−0.301546	−	0.174098i
$260$		0			0
$261$	−179.430	+	31.6383i	−0.687471	+	0.121220i
$262$		0			0
$263$	407.312	+	148.249i	1.54872	+	0.563686i	0.968116	−	0.250503i	$-0.0805960\pi$
$263$	407.312	+	148.249i	1.54872	+	0.563686i	0.580599	+	0.814189i	$0.302818\pi$
$264$		0			0
$265$		−	179.712i		−	0.678157i
$266$		0			0
$267$	90.7180			0.339768
$268$		0			0
$269$	−45.8847	+	126.067i	−0.170575	+	0.468651i	−0.995295	−	0.0968902i	$-0.969110\pi$
$269$	−45.8847	+	126.067i	−0.170575	+	0.468651i	0.824720	+	0.565541i	$0.191333\pi$
$270$		0			0
$271$	−9.79532	−	55.5520i	−0.0361451	−	0.204989i	0.961387	−	0.275200i	$-0.0887440\pi$
$271$	−9.79532	−	55.5520i	−0.0361451	−	0.204989i	−0.997532	+	0.0702106i	$0.977633\pi$
$272$		0			0
$273$	−35.2066	+	60.9797i	−0.128962	+	0.223369i
$274$		0			0
$275$	−216.119	−	181.346i	−0.785889	−	0.659439i
$276$		0			0
$277$	75.3401	+	130.493i	0.271986	+	0.471094i	0.969370	−	0.245604i	$-0.0789862\pi$
$277$	75.3401	+	130.493i	0.271986	+	0.471094i	−0.697384	+	0.716697i	$0.745653\pi$
$278$		0			0
$279$	118.000	+	324.202i	0.422938	+	1.16201i
$280$		0			0
$281$	233.857	+	41.2352i	0.832230	+	0.146745i	0.573500	−	0.819205i	$-0.305585\pi$
$281$	233.857	+	41.2352i	0.832230	+	0.146745i	0.258729	+	0.965950i	$0.416696\pi$
$282$		0			0
$283$	307.886	−	258.347i	1.08794	−	0.912887i	0.0913804	−	0.995816i	$-0.470872\pi$
$283$	307.886	−	258.347i	1.08794	−	0.912887i	0.996555	+	0.0829295i	$0.0264276\pi$
$284$		0			0
$285$	−77.6445	−	45.2117i	−0.272437	−	0.158638i
$286$		0			0
$287$	−216.739	−	258.299i	−0.755188	−	0.899998i
$288$		0			0
$289$	19.7873	−	112.219i	0.0684682	−	0.388303i
$290$		0			0
$291$	−101.544	+	36.9590i	−0.348948	+	0.127007i
$292$		0			0
$293$	−136.838	+	79.0034i	−0.467024	+	0.269636i	−0.714993	−	0.699132i	$-0.753570\pi$
$293$	−136.838	+	79.0034i	−0.467024	+	0.269636i	0.247969	+	0.968768i	$0.420237\pi$
$294$		0			0
$295$	−263.197	+	313.666i	−0.892192	+	1.06327i
$296$		0			0
$297$	85.6935	+	49.4751i	0.288530	+	0.166583i
$298$		0			0
$299$	451.730	−	79.6522i	1.51080	−	0.266395i
$300$		0			0
$301$	220.554	+	80.2751i	0.732738	+	0.266695i
$302$		0			0
$303$			20.7631i			0.0685250i
$304$		0			0
$305$	21.7044			0.0711621
$306$		0			0
$307$	−176.325	+	484.450i	−0.574349	+	1.57801i	0.223209	+	0.974771i	$0.428347\pi$
$307$	−176.325	+	484.450i	−0.574349	+	1.57801i	−0.797559	+	0.603241i	$0.793876\pi$
$308$		0			0
$309$	20.5180	+	116.363i	0.0664012	+	0.376580i
$310$		0			0
$311$	−133.065	+	230.476i	−0.427863	+	0.741081i	−0.996683	−	0.0813813i	$-0.974067\pi$
$311$	−133.065	+	230.476i	−0.427863	+	0.741081i	0.568820	+	0.822462i	$0.307400\pi$
$312$		0			0
$313$	−143.393	−	120.321i	−0.458123	−	0.384411i	0.384317	−	0.923201i	$-0.374437\pi$
$313$	−143.393	−	120.321i	−0.458123	−	0.384411i	−0.842440	+	0.538790i	$0.818882\pi$
$314$		0			0
$315$	−196.223	−	339.869i	−0.622931	−	1.07895i
$316$		0			0
$317$	−49.3857	−	135.686i	−0.155791	−	0.428032i	0.837101	−	0.547048i	$-0.184248\pi$
$317$	−49.3857	−	135.686i	−0.155791	−	0.428032i	−0.992892	+	0.119016i	$0.962026\pi$
$318$		0			0
$319$	−186.403	−	32.8679i	−0.584335	−	0.103034i
$320$		0			0
$321$	−30.9228	+	25.9473i	−0.0963328	+	0.0808328i
$322$		0			0
$323$	−358.878	+	129.120i	−1.11108	+	0.399752i
$324$		0			0
$325$	374.612	+	446.445i	1.15265	+	1.37368i
$326$		0			0
$327$	12.8957	−	73.1354i	0.0394365	−	0.223656i
$328$		0			0
$329$	8.22456	−	2.99349i	0.0249987	−	0.00909877i
$330$		0			0
$331$	−365.183	+	210.839i	−1.10327	+	0.636975i	−0.937079	−	0.349118i	$-0.886481\pi$
$331$	−365.183	+	210.839i	−1.10327	+	0.636975i	−0.166194	+	0.986093i	$0.553148\pi$
$332$		0			0
$333$	82.2493	−	98.0209i	0.246995	−	0.294357i
$334$		0			0
$335$	−726.005	−	419.159i	−2.16718	−	1.25122i
$336$		0			0
$337$	66.7912	−	11.7771i	0.198193	−	0.0349468i	−0.0736701	−	0.997283i	$-0.523471\pi$
$337$	66.7912	−	11.7771i	0.198193	−	0.0349468i	0.271863	+	0.962336i	$0.412360\pi$
$338$		0			0
$339$	29.0731	+	10.5818i	0.0857615	+	0.0312146i
$340$		0			0
$341$			358.416i			1.05107i
$342$		0			0
$343$	371.281			1.08245
$344$		0			0
$345$	40.1765	−	110.384i	0.116454	−	0.319953i
$346$		0			0
$347$	−49.7258	−	282.009i	−0.143302	−	0.812705i	−0.968715	−	0.248176i	$-0.920169\pi$
$347$	−49.7258	−	282.009i	−0.143302	−	0.812705i	0.825413	−	0.564529i	$-0.190942\pi$
$348$		0			0
$349$	−236.860	+	410.253i	−0.678681	+	1.17551i	0.296698	+	0.954971i	$0.404115\pi$
$349$	−236.860	+	410.253i	−0.678681	+	1.17551i	−0.975378	+	0.220538i	$0.929219\pi$
$350$		0			0
$351$	−156.583	−	131.389i	−0.446106	−	0.374328i
$352$		0			0
$353$	106.688	+	184.789i	0.302233	+	0.523483i	0.976641	−	0.214876i	$-0.0689346\pi$
$353$	106.688	+	184.789i	0.302233	+	0.523483i	−0.674408	+	0.738358i	$0.735601\pi$
$354$		0			0
$355$	298.879	+	821.164i	0.841914	+	2.31314i
$356$		0			0
$357$	75.3818	+	13.2919i	0.211154	+	0.0372321i
$358$		0			0
$359$	−41.4292	+	34.7632i	−0.115402	+	0.0968334i	−0.698662	−	0.715452i	$-0.746221\pi$
$359$	−41.4292	+	34.7632i	−0.115402	+	0.0968334i	0.583261	+	0.812285i	$0.301777\pi$
$360$		0			0
$361$	274.818	+	234.085i	0.761270	+	0.648435i
$362$		0			0
$363$	−16.6089	−	19.7938i	−0.0457546	−	0.0545283i
$364$		0			0
$365$	−59.6729	+	338.422i	−0.163487	+	0.927183i
$366$		0			0
$367$	414.996	−	151.046i	1.13078	−	0.411570i	0.292204	−	0.956356i	$-0.405611\pi$
$367$	414.996	−	151.046i	1.13078	−	0.411570i	0.838575	+	0.544786i	$0.183389\pi$
$368$		0			0
$369$	414.326	−	239.211i	1.12284	−	0.648269i
$370$		0			0
$371$	93.1483	−	111.010i	0.251074	−	0.299218i
$372$		0			0
$373$	−463.827	−	267.791i	−1.24350	−	0.717937i	−0.273698	−	0.961816i	$-0.588247\pi$
$373$	−463.827	−	267.791i	−1.24350	−	0.717937i	−0.969806	+	0.243878i	$0.921580\pi$
$374$		0			0
$375$	30.5543	−	5.38754i	0.0814781	−	0.0143668i
$376$		0			0
$377$	367.419	+	133.730i	0.974586	+	0.354720i
$378$		0			0
$379$		−	638.979i		−	1.68596i	−0.537946	−	0.842980i	$-0.680799\pi$
$379$		−	638.979i		−	1.68596i	0.537946	−	0.842980i	$-0.319201\pi$
$380$		0			0
$381$	−84.8435			−0.222686
$382$		0			0
$383$	−52.7059	+	144.808i	−0.137613	+	0.378089i	−0.989287	−	0.145983i	$-0.953366\pi$
$383$	−52.7059	+	144.808i	−0.137613	+	0.378089i	0.851674	+	0.524072i	$0.175588\pi$
$384$		0			0
$385$	−70.7960	−	401.504i	−0.183886	−	1.04287i
$386$		0			0
$387$	−166.511	+	288.405i	−0.430260	+	0.745232i
$388$		0			0
$389$	−437.089	−	366.761i	−1.12362	−	0.942830i	−0.124839	−	0.992177i	$-0.539842\pi$
$389$	−437.089	−	366.761i	−1.12362	−	0.942830i	−0.998782	+	0.0493469i	$0.984286\pi$
$390$		0			0
$391$	−249.321	−	431.836i	−0.637649	−	1.10444i
$392$		0			0
$393$	−41.1882	−	113.164i	−0.104805	−	0.287948i
$394$		0			0
$395$	116.797	+	20.5944i	0.295688	+	0.0521377i
$396$		0			0
$397$	−389.565	+	326.883i	−0.981271	+	0.823384i	−0.984281	−	0.176611i	$-0.943486\pi$
$397$	−389.565	+	326.883i	−0.981271	+	0.823384i	0.00300971	+	0.999995i	$0.499042\pi$
$398$		0			0
$399$	−24.5277	−	68.1726i	−0.0614729	−	0.170859i
$400$		0			0
$401$	205.447	+	244.843i	0.512338	+	0.610580i	0.958751	−	0.284246i	$-0.0917434\pi$
$401$	205.447	+	244.843i	0.512338	+	0.610580i	−0.446413	+	0.894827i	$0.647299\pi$
$402$		0			0
$403$	128.568	−	729.144i	0.319027	−	1.80929i
$404$		0			0
$405$	498.103	−	181.294i	1.22988	−	0.447641i
$406$		0			0
$407$	115.121	−	66.4650i	0.282852	−	0.163305i
$408$		0			0
$409$	94.1956	−	112.258i	0.230307	−	0.274469i	−0.638498	−	0.769623i	$-0.720444\pi$
$409$	94.1956	−	112.258i	0.230307	−	0.274469i	0.868805	+	0.495154i	$0.164888\pi$
$410$		0			0
$411$	21.6895	+	12.5225i	0.0527726	+	0.0304683i
$412$		0			0
$413$	−325.159	+	57.3343i	−0.787310	+	0.138824i
$414$		0			0
$415$	547.239	+	199.179i	1.31865	+	0.479949i
$416$		0			0
$417$			123.919i			0.297169i
$418$		0			0
$419$	−271.782			−0.648644			−0.324322	−	0.945947i	$-0.605136\pi$
$419$	−271.782			−0.648644			−0.324322	+	0.945947i	$0.605136\pi$
$420$		0			0
$421$	−23.8085	+	65.4132i	−0.0565522	+	0.155376i	−0.964752	−	0.263161i	$-0.915235\pi$
$421$	−23.8085	+	65.4132i	−0.0565522	+	0.155376i	0.908200	+	0.418537i	$0.137457\pi$
$422$		0			0
$423$	2.15645	+	12.2298i	0.00509799	+	0.0289122i
$424$		0			0
$425$	316.771	−	548.663i	0.745343	−	1.29097i
$426$		0			0
$427$	13.4071	+	11.2499i	0.0313983	+	0.0263463i
$428$		0			0
$429$	−51.8950	−	89.8847i	−0.120967	−	0.209521i
$430$		0			0
$431$	−90.9398	−	249.855i	−0.210997	−	0.579710i	0.788373	−	0.615198i	$-0.210924\pi$
$431$	−90.9398	−	249.855i	−0.210997	−	0.579710i	−0.999370	+	0.0354877i	$0.988702\pi$
$432$		0			0
$433$	434.577	+	76.6277i	1.00364	+	0.176969i	0.651234	−	0.758877i	$-0.274252\pi$
$433$	434.577	+	76.6277i	1.00364	+	0.176969i	0.352408	+	0.935846i	$0.385363\pi$
$434$		0			0
$435$	76.7047	−	64.3629i	0.176333	−	0.147961i
$436$		0			0
$437$	−237.496	+	407.864i	−0.543468	+	0.933328i
$438$		0			0
$439$	−34.7798	−	41.4489i	−0.0792250	−	0.0944167i	0.724976	−	0.688774i	$-0.241851\pi$
$439$	−34.7798	−	41.4489i	−0.0792250	−	0.0944167i	−0.804201	+	0.594357i	$0.797406\pi$
$440$		0			0
$441$	−18.2629	+	103.574i	−0.0414125	+	0.234862i
$442$		0			0
$443$	−218.537	+	79.5408i	−0.493311	+	0.179550i	−0.576683	−	0.816968i	$-0.695653\pi$
$443$	−218.537	+	79.5408i	−0.493311	+	0.179550i	0.0833723	+	0.996518i	$0.473431\pi$
$444$		0			0
$445$	939.686	−	542.528i	2.11165	−	1.21916i
$446$		0			0
$447$	−87.8011	+	104.637i	−0.196423	+	0.234088i
$448$		0			0
$449$	343.201	+	198.147i	0.764368	+	0.441308i	0.830862	−	0.556479i	$-0.187848\pi$
$449$	343.201	+	198.147i	0.764368	+	0.441308i	−0.0664938	+	0.997787i	$0.521181\pi$
$450$		0			0
$451$	489.465	−	86.3059i	1.08529	−	0.191366i
$452$		0			0
$453$	17.9332	+	6.52714i	0.0395876	+	0.0144087i
$454$		0			0
$455$			842.196i			1.85098i
$456$		0			0
$457$	−660.306			−1.44487			−0.722435	−	0.691439i	$-0.756977\pi$
$457$	−660.306			−1.44487			−0.722435	+	0.691439i	$0.756977\pi$
$458$		0			0
$459$	−75.9983	+	208.804i	−0.165574	+	0.454910i
$460$		0			0
$461$	−120.280	−	682.139i	−0.260910	−	1.47969i	−0.780434	−	0.625238i	$-0.785002\pi$
$461$	−120.280	−	682.139i	−0.260910	−	1.47969i	0.519524	−	0.854456i	$-0.326109\pi$
$462$		0			0
$463$	−53.6664	+	92.9529i	−0.115910	+	0.200762i	−0.918143	−	0.396249i	$-0.870312\pi$
$463$	−53.6664	+	92.9529i	−0.115910	+	0.200762i	0.802233	+	0.597011i	$0.203645\pi$
$464$		0			0
$465$	−145.247	−	121.877i	−0.312360	−	0.262101i
$466$		0			0
$467$	−104.758	−	181.446i	−0.224320	−	0.388534i	0.731795	−	0.681525i	$-0.238683\pi$
$467$	−104.758	−	181.446i	−0.224320	−	0.388534i	−0.956115	+	0.292991i	$0.905350\pi$
$468$		0			0
$469$	−231.203	−	635.224i	−0.492969	−	1.35442i
$470$		0			0
$471$	−34.6902	−	6.11682i	−0.0736522	−	0.0129869i
$472$		0			0
$473$	−265.023	+	222.381i	−0.560303	+	0.470150i
$474$		0			0
$475$	−599.653	−	2.21742i	−1.26243	−	0.00466826i
$476$		0			0
$477$	132.165	+	157.509i	0.277076	+	0.330207i
$478$		0			0
$479$	58.0466	−	329.198i	0.121183	−	0.687262i	−0.862319	−	0.506365i	$-0.830989\pi$
$479$	58.0466	−	329.198i	0.121183	−	0.687262i	0.983502	−	0.180897i	$-0.0579000\pi$
$480$		0			0
$481$	−258.038	+	93.9181i	−0.536461	+	0.195256i
$482$		0			0
$483$	82.0318	−	47.3611i	0.169838	−	0.0980561i
$484$		0			0
$485$	−830.796	+	990.104i	−1.71298	+	2.04145i
$486$		0			0
$487$	282.361	+	163.021i	0.579797	+	0.334746i	0.761053	−	0.648690i	$-0.224683\pi$
$487$	282.361	+	163.021i	0.579797	+	0.334746i	−0.181256	+	0.983436i	$0.558016\pi$
$488$		0			0
$489$	127.770	−	22.5293i	0.261288	−	0.0460721i
$490$		0			0
$491$	−123.021	−	44.7760i	−0.250552	−	0.0911935i	0.213691	−	0.976901i	$-0.431451\pi$
$491$	−123.021	−	44.7760i	−0.250552	−	0.0911935i	−0.464243	+	0.885708i	$0.653674\pi$
$492$		0			0
$493$		−	425.047i		−	0.862164i
$494$		0			0
$495$	578.470			1.16863
$496$		0			0
$497$	−241.006	+	662.158i	−0.484921	+	1.33231i
$498$		0			0
$499$	89.2488	+	506.155i	0.178855	+	1.01434i	0.933599	+	0.358319i	$0.116650\pi$
$499$	89.2488	+	506.155i	0.178855	+	1.01434i	−0.754744	+	0.656020i	$0.772239\pi$
$500$		0			0
$501$	53.6857	−	92.9864i	0.107157	−	0.185602i
$502$		0			0
$503$	−101.395	−	85.0803i	−0.201580	−	0.169146i	0.536410	−	0.843958i	$-0.319780\pi$
$503$	−101.395	−	85.0803i	−0.201580	−	0.169146i	−0.737990	+	0.674812i	$0.764225\pi$
$504$		0			0
$505$	124.171	+	215.071i	0.245883	+	0.425883i
$506$		0			0
$507$	36.9855	+	101.617i	0.0729497	+	0.200428i
$508$		0			0
$509$	−87.0041	−	15.3412i	−0.170931	−	0.0301398i	0.0875273	−	0.996162i	$-0.472103\pi$
$509$	−87.0041	−	15.3412i	−0.170931	−	0.0301398i	−0.258459	+	0.966022i	$0.583215\pi$
$510$		0			0
$511$	−212.272	+	178.117i	−0.415405	+	0.348566i
$512$		0			0
$513$	207.258	−	35.7555i	0.404012	−	0.0696988i
$514$		0			0
$515$	908.427	+	1082.62i	1.76394	+	2.10218i
$516$		0			0
$517$	−2.24026	+	12.7051i	−0.00433318	+	0.0245747i
$518$		0			0
$519$	−14.3982	+	5.24053i	−0.0277423	+	0.0100974i
$520$		0			0
$521$	638.201	−	368.465i	1.22495	−	0.707227i	0.258984	−	0.965882i	$-0.416612\pi$
$521$	638.201	−	368.465i	1.22495	−	0.707227i	0.965970	+	0.258654i	$0.0832790\pi$
$522$		0			0
$523$	−59.1609	+	70.5052i	−0.113118	+	0.134809i	−0.819632	−	0.572890i	$-0.805822\pi$
$523$	−59.1609	+	70.5052i	−0.113118	+	0.134809i	0.706514	+	0.707699i	$0.250267\pi$
$524$		0			0
$525$	104.224	+	60.1740i	0.198523	+	0.114617i
$526$		0			0
$527$	−792.637	+	139.763i	−1.50405	+	0.265205i
$528$		0			0
$529$	−82.7460	−	30.1171i	−0.156420	−	0.0569321i
$530$		0			0
$531$		−	468.476i		−	0.882252i
$532$		0			0
$533$	−1026.70			−1.92627
$534$		0			0
$535$	−165.134	+	453.701i	−0.308661	+	0.848039i
$536$		0			0
$537$	18.5361	+	105.123i	0.0345179	+	0.195760i
$538$		0			0
$539$	−54.6296	+	94.6212i	−0.101354	+	0.175550i
$540$		0			0
$541$	151.780	+	127.358i	0.280554	+	0.235413i	0.772196	−	0.635385i	$-0.219159\pi$
$541$	151.780	+	127.358i	0.280554	+	0.235413i	−0.491642	+	0.870798i	$0.663603\pi$
$542$		0			0
$543$	33.9483	+	58.8002i	0.0625199	+	0.108288i
$544$		0			0
$545$	−303.799	−	834.681i	−0.557429	−	1.53152i
$546$		0			0
$547$	−174.568	−	30.7810i	−0.319137	−	0.0562725i	0.0117850	−	0.999931i	$-0.496249\pi$
$547$	−174.568	−	30.7810i	−0.319137	−	0.0562725i	−0.330922	+	0.943658i	$0.607360\pi$
$548$		0			0
$549$	−19.0229	+	15.9621i	−0.0346501	+	0.0290749i
$550$		0			0
$551$	−349.155	+	199.867i	−0.633675	+	0.362735i
$552$		0			0
$553$	61.4721	+	73.2596i	0.111161	+	0.132477i
$554$		0			0
$555$	−12.2113	+	69.2535i	−0.0220023	+	0.124781i
$556$		0			0
$557$	−473.669	+	172.401i	−0.850393	+	0.309518i	−0.730201	−	0.683233i	$-0.760573\pi$
$557$	−473.669	+	172.401i	−0.850393	+	0.309518i	−0.120192	+	0.992751i	$0.538351\pi$
$558$		0			0
$559$	618.921	−	357.334i	1.10719	−	0.639238i
$560$		0			0
$561$	−72.5243	+	86.4311i	−0.129277	+	0.154066i
$562$		0			0
$563$	187.639	+	108.334i	0.333285	+	0.192422i	0.657299	−	0.753630i	$-0.271699\pi$
$563$	187.639	+	108.334i	0.333285	+	0.192422i	−0.324014	+	0.946052i	$0.605032\pi$
$564$		0			0
$565$	364.432	−	64.2592i	0.645012	−	0.113733i
$566$		0			0
$567$	401.653	+	146.190i	0.708382	+	0.257830i
$568$		0			0
$569$		−	865.434i		−	1.52097i	−0.649353	−	0.760487i	$-0.724960\pi$
$569$		−	865.434i		−	1.52097i	0.649353	−	0.760487i	$-0.275040\pi$
$570$		0			0
$571$	−27.6175			−0.0483668			−0.0241834	−	0.999708i	$-0.507699\pi$
$571$	−27.6175			−0.0483668			−0.0241834	+	0.999708i	$0.507699\pi$
$572$		0			0
$573$	−32.8458	+	90.2432i	−0.0573226	+	0.157492i
$574$		0			0
$575$	−136.139	−	772.082i	−0.236763	−	1.34275i
$576$		0			0
$577$	−100.195	+	173.544i	−0.173649	+	0.300769i	−0.939693	−	0.342019i	$-0.888889\pi$
$577$	−100.195	+	173.544i	−0.173649	+	0.300769i	0.766044	+	0.642788i	$0.222222\pi$
$578$		0			0
$579$	10.1570	+	8.52271i	0.0175423	+	0.0147197i
$580$		0			0
$581$	234.797	+	406.681i	0.404126	+	0.699967i
$582$		0			0
$583$	73.0567	+	200.722i	0.125312	+	0.344291i
$584$		0			0
$585$	−1176.81	−	207.504i	−2.01164	−	0.354707i
$586$		0			0
$587$	172.908	−	145.087i	0.294563	−	0.247168i	−0.483514	−	0.875337i	$-0.660640\pi$
$587$	172.908	−	145.087i	0.294563	−	0.247168i	0.778077	+	0.628169i	$0.216195\pi$
$588$		0			0
$589$	487.525	+	585.392i	0.827717	+	0.993875i
$590$		0			0
$591$	−141.302	−	168.397i	−0.239089	−	0.284936i
$592$		0			0
$593$	174.512	−	989.709i	0.294287	−	1.66899i	−0.375797	−	0.926702i	$-0.622631\pi$
$593$	174.512	−	989.709i	0.294287	−	1.66899i	0.670084	−	0.742285i	$-0.266258\pi$
$594$		0			0
$595$	860.319	−	313.131i	1.44592	−	0.526270i
$596$		0			0
$597$	159.318	−	91.9826i	0.266865	−	0.154075i
$598$		0			0
$599$	699.578	−	833.725i	1.16791	−	1.39186i	0.263791	−	0.964580i	$-0.415027\pi$
$599$	699.578	−	833.725i	1.16791	−	1.39186i	0.904119	−	0.427281i	$-0.140529\pi$
$600$		0			0
$601$	−373.969	−	215.911i	−0.622245	−	0.359253i	0.155498	−	0.987836i	$-0.450302\pi$
$601$	−373.969	−	215.911i	−0.622245	−	0.359253i	−0.777743	+	0.628583i	$0.783635\pi$
$602$		0			0
$603$	944.572	−	166.553i	1.56645	−	0.276208i
$604$		0			0
$605$	−290.415	−	105.702i	−0.480025	−	0.174715i
$606$		0			0
$607$			693.123i			1.14188i	0.820991	+	0.570942i	$0.193422\pi$
$607$			693.123i			1.14188i	−0.820991	+	0.570942i	$0.806578\pi$
$608$		0			0
$609$	80.7421			0.132581
$610$		0			0
$611$	9.11494	−	25.0431i	0.0149181	−	0.0409870i
$612$		0			0
$613$	−14.2820	−	80.9973i	−0.0232986	−	0.132133i	0.970940	−	0.239323i	$-0.0769256\pi$
$613$	−14.2820	−	80.9973i	−0.0232986	−	0.132133i	−0.994238	+	0.107191i	$0.965814\pi$
$614$		0			0
$615$	−131.464	+	227.702i	−0.213763	+	0.370248i
$616$		0			0
$617$	541.872	+	454.684i	0.878236	+	0.736927i	0.965816	−	0.259230i	$-0.0834688\pi$
$617$	541.872	+	454.684i	0.878236	+	0.736927i	−0.0875797	+	0.996158i	$0.527913\pi$
$618$		0			0
$619$	−467.426	−	809.606i	−0.755131	−	1.30792i	−0.945309	−	0.326175i	$-0.894240\pi$
$619$	−467.426	−	809.606i	−0.755131	−	1.30792i	0.190178	−	0.981750i	$-0.439093\pi$
$620$		0			0
$621$	94.0461	+	258.389i	0.151443	+	0.416086i
$622$		0			0
$623$	861.659	+	151.934i	1.38308	+	0.243874i
$624$		0			0
$625$	−320.155	+	268.642i	−0.512248	+	0.429827i
$626$		0			0
$627$	105.101	+	18.9332i	0.167626	+	0.0301965i
$628$		0			0
$629$	191.878	+	228.672i	0.305053	+	0.363548i
$630$		0			0
$631$	−26.4137	+	149.800i	−0.0418601	+	0.237400i	−0.998558	−	0.0536820i	$-0.982904\pi$
$631$	−26.4137	+	149.800i	−0.0418601	+	0.237400i	0.956698	+	0.291082i	$0.0940154\pi$
$632$		0			0
$633$	11.6061	−	4.22429i	0.0183351	−	0.00667344i
$634$		0			0
$635$	−878.836	+	507.396i	−1.38399	+	0.799049i
$636$		0			0
$637$	145.077	−	172.897i	0.227751	−	0.271423i
$638$		0			0
$639$	−865.863	−	499.906i	−1.35503	−	0.782326i
$640$		0			0
$641$	175.672	−	30.9757i	0.274060	−	0.0483241i	−0.0349292	−	0.999390i	$-0.511121\pi$
$641$	175.672	−	30.9757i	0.274060	−	0.0483241i	0.308989	+	0.951066i	$0.400009\pi$
$642$		0			0
$643$	415.509	+	151.233i	0.646203	+	0.235199i	0.644269	−	0.764799i	$-0.277162\pi$
$643$	415.509	+	151.233i	0.646203	+	0.235199i	0.00193485	+	0.999998i	$0.499384\pi$
$644$		0			0
$645$		−	183.019i		−	0.283751i
$646$		0			0
$647$	340.919			0.526922			0.263461	−	0.964670i	$-0.415136\pi$
$647$	340.919			0.526922			0.263461	+	0.964670i	$0.415136\pi$
$648$		0			0
$649$	166.455	−	457.332i	0.256479	−	0.704671i
$650$		0			0
$651$	−26.5495	−	150.570i	−0.0407827	−	0.231290i
$652$		0			0
$653$	319.221	−	552.907i	0.488853	−	0.846719i	−0.511065	−	0.859542i	$-0.670749\pi$
$653$	319.221	−	552.907i	0.488853	−	0.846719i	0.999918	+	0.0128237i	$0.00408202\pi$
$654$		0			0
$655$	−1103.40	−	925.864i	−1.68458	−	1.41353i
$656$		0			0
$657$	−196.585	−	340.496i	−0.299217	−	0.518259i
$658$		0			0
$659$	101.557	+	279.024i	0.154107	+	0.423406i	0.992588	−	0.121525i	$-0.0387783\pi$
$659$	101.557	+	279.024i	0.154107	+	0.423406i	−0.838481	+	0.544930i	$0.816556\pi$
$660$		0			0
$661$	629.130	+	110.933i	0.951786	+	0.167825i	0.627920	−	0.778278i	$-0.283906\pi$
$661$	629.130	+	110.933i	0.951786	+	0.167825i	0.323865	+	0.946103i	$0.395017\pi$
$662$		0			0
$663$	178.544	−	149.816i	0.269297	−	0.225967i
$664$		0			0
$665$	−661.764	−	559.469i	−0.995133	−	0.841306i
$666$		0			0
$667$	−338.096	−	402.928i	−0.506891	−	0.604090i
$668$		0			0
$669$	−11.7837	+	66.8284i	−0.0176138	+	0.0998930i
$670$		0			0
$671$	−24.2419	+	8.82333i	−0.0361280	+	0.0131495i
$672$		0			0
$673$	−343.422	+	198.275i	−0.510286	+	0.294614i	−0.732951	−	0.680281i	$-0.761858\pi$
$673$	−343.422	+	198.275i	−0.510286	+	0.294614i	0.222665	+	0.974895i	$0.428524\pi$
$674$		0			0
$675$	−224.566	+	267.627i	−0.332690	+	0.396484i
$676$		0			0
$677$	589.512	+	340.355i	0.870771	+	0.502740i	0.867604	−	0.497255i	$-0.165659\pi$
$677$	589.512	+	340.355i	0.870771	+	0.502740i	0.00316684	+	0.999995i	$0.498992\pi$
$678$		0			0
$679$	−1026.38	+	180.979i	−1.51161	+	0.266538i
$680$		0			0
$681$	42.7136	+	15.5465i	0.0627219	+	0.0228289i
$682$		0			0
$683$			687.614i			1.00676i	0.864066	+	0.503378i	$0.167910\pi$
$683$			687.614i			1.00676i	−0.864066	+	0.503378i	$0.832090\pi$
$684$		0			0
$685$	299.556			0.437308
$686$		0			0
$687$	13.7380	−	37.7448i	0.0199971	−	0.0549414i
$688$		0			0
$689$	−76.6219	−	434.545i	−0.111207	−	0.630689i
$690$		0			0
$691$	−340.133	+	589.127i	−0.492233	+	0.852572i	−0.999960	−	0.00894577i	$-0.997152\pi$
$691$	−340.133	+	589.127i	−0.492233	+	0.852572i	0.507727	+	0.861518i	$0.330486\pi$
$692$		0			0
$693$	357.328	+	299.834i	0.515625	+	0.432660i
$694$		0			0
$695$	741.084	+	1283.60i	1.06631	+	1.84690i
$696$		0			0
$697$	381.731	+	1048.80i	0.547677	+	1.50473i
$698$		0			0
$699$	34.4010	+	6.06582i	0.0492145	+	0.00867785i
$700$		0			0
$701$	53.0747	−	44.5350i	0.0757129	−	0.0635306i	−0.604146	−	0.796874i	$-0.706486\pi$
$701$	53.0747	−	44.5350i	0.0757129	−	0.0635306i	0.679859	+	0.733343i	$0.262041\pi$
$702$		0			0
$703$	97.6169	−	265.145i	0.138858	−	0.377163i
$704$		0			0
$705$	−4.38694	−	5.22815i	−0.00622261	−	0.00741582i
$706$		0			0
$707$	−34.7738	+	197.212i	−0.0491851	+	0.278942i
$708$		0			0
$709$	527.372	−	191.948i	0.743826	−	0.270730i	0.0578204	−	0.998327i	$-0.481585\pi$
$709$	527.372	−	191.948i	0.743826	−	0.270730i	0.686005	+	0.727597i	$0.259363\pi$
$710$		0			0
$711$	−117.512	+	67.8459i	−0.165278	+	0.0954232i
$712$		0			0
$713$	−640.216	+	762.980i	−0.897919	+	1.07010i
$714$		0			0
$715$	−1075.09	−	620.703i	−1.50362	−	0.868116i
$716$		0			0
$717$	−28.9431	+	5.10344i	−0.0403669	+	0.00711777i
$718$		0			0
$719$	558.183	+	203.162i	0.776332	+	0.282562i	0.699642	−	0.714493i	$-0.253343\pi$
$719$	558.183	+	203.162i	0.776332	+	0.282562i	0.0766895	+	0.997055i	$0.475565\pi$
$720$		0			0
$721$			1139.61i			1.58059i
$722$		0			0
$723$	−287.608			−0.397799
$724$		0			0
$725$	228.566	−	627.980i	0.315264	−	0.866179i
$726$		0			0
$727$	172.775	+	979.857i	0.237655	+	1.34781i	0.836949	+	0.547280i	$0.184337\pi$
$727$	172.775	+	979.857i	0.237655	+	1.34781i	−0.599294	+	0.800529i	$0.704552\pi$
$728$		0			0
$729$	−271.912	+	470.966i	−0.372994	+	0.646044i
$730$		0			0
$731$	−595.140	−	499.382i	−0.814145	−	0.683149i
$732$		0			0
$733$	−639.935	−	1108.40i	−0.873035	−	1.51214i	−0.858841	−	0.512242i	$-0.828815\pi$
$733$	−639.935	−	1108.40i	−0.873035	−	1.51214i	−0.0141944	−	0.999899i	$-0.504518\pi$
$734$		0			0
$735$	−19.7686	−	54.3139i	−0.0268961	−	0.0738964i
$736$		0			0
$737$	981.280	+	173.026i	1.33145	+	0.234771i
$738$		0			0
$739$	288.561	−	242.131i	0.390475	−	0.327647i	−0.426323	−	0.904571i	$-0.640191\pi$
$739$	288.561	−	242.131i	0.390475	−	0.327647i	0.816798	+	0.576924i	$0.195747\pi$
$740$		0			0
$741$	−207.022	−	76.2179i	−0.279382	−	0.102858i
$742$		0			0
$743$	−410.971	−	489.776i	−0.553123	−	0.659187i	0.414953	−	0.909843i	$-0.363798\pi$
$743$	−410.971	−	489.776i	−0.553123	−	0.659187i	−0.968076	+	0.250656i	$0.919354\pi$
$744$		0			0
$745$	−283.701	+	1608.95i	−0.380807	+	2.15967i
$746$		0			0
$747$	−626.111	+	227.886i	−0.838168	+	0.305068i
$748$		0			0
$749$	−337.168	+	194.664i	−0.450157	+	0.259898i
$750$		0			0
$751$	823.889	−	981.873i	1.09706	−	1.30742i	0.149169	−	0.988812i	$-0.452340\pi$
$751$	823.889	−	981.873i	1.09706	−	1.30742i	0.947886	−	0.318608i	$-0.103216\pi$
$752$		0			0
$753$	−126.868	−	73.2475i	−0.168484	−	0.0972742i
$754$		0			0
$755$	224.792	−	39.6370i	0.297738	−	0.0524993i
$756$		0			0
$757$	−246.078	−	89.5649i	−0.325069	−	0.118316i	0.174330	−	0.984687i	$-0.444224\pi$
$757$	−246.078	−	89.5649i	−0.325069	−	0.118316i	−0.499400	+	0.866372i	$0.666446\pi$
$758$		0			0
$759$			139.622i			0.183955i
$760$		0			0
$761$	1028.82			1.35193			0.675966	−	0.736933i	$-0.263727\pi$
$761$	1028.82			1.35193			0.675966	+	0.736933i	$0.263727\pi$
$762$		0			0
$763$	244.973	−	673.058i	0.321065	−	0.882120i
$764$		0			0
$765$	225.573	+	1279.29i	0.294866	+	1.67227i
$766$		0			0
$767$	−502.678	+	870.664i	−0.655382	+	1.13515i
$768$		0			0
$769$	12.1673	+	10.2095i	0.0158222	+	0.0132764i	0.650664	−	0.759365i	$-0.274490\pi$
$769$	12.1673	+	10.2095i	0.0158222	+	0.0132764i	−0.634842	+	0.772642i	$0.718935\pi$
$770$		0			0
$771$	−65.7643	−	113.907i	−0.0852974	−	0.147739i
$772$		0			0
$773$	−136.685	−	375.540i	−0.176825	−	0.485822i	0.819341	−	0.573306i	$-0.194339\pi$
$773$	−136.685	−	375.540i	−0.176825	−	0.485822i	−0.996166	+	0.0874845i	$0.972117\pi$
$774$		0			0
$775$	−1246.23	−	219.744i	−1.60804	−	0.283540i
$776$		0			0
$777$	−43.4386	+	36.4493i	−0.0559055	+	0.0469103i
$778$		0			0
$779$	682.036	−	806.741i	0.875528	−	1.03561i
$780$		0			0
$781$	−667.643	−	795.666i	−0.854856	−	1.01878i
$782$		0			0
$783$	−40.7012	+	230.828i	−0.0519811	+	0.294800i
$784$		0			0
$785$	−395.913	+	144.101i	−0.504348	+	0.183568i
$786$		0			0
$787$	−344.910	+	199.134i	−0.438260	+	0.253029i	−0.702859	−	0.711329i	$-0.748094\pi$
$787$	−344.910	+	199.134i	−0.438260	+	0.253029i	0.264599	+	0.964358i	$0.414760\pi$
$788$		0			0
$789$	175.190	−	208.783i	0.222040	−	0.264617i
$790$		0			0
$791$	258.421	+	149.199i	0.326701	+	0.188621i
$792$		0			0
$793$	52.4816	−	9.25392i	0.0661810	−	0.0116695i
$794$		0			0
$795$	−106.185	−	38.6480i	−0.133565	−	0.0486138i
$796$		0			0
$797$		−	259.704i		−	0.325852i	−0.986638	−	0.162926i	$-0.947907\pi$
$797$		−	259.704i		−	0.325852i	0.986638	−	0.162926i	$-0.0520932\pi$
$798$		0			0
$799$	−28.9710			−0.0362590
$800$		0			0
$801$	−424.598	+	1166.57i	−0.530085	+	1.45640i
$802$		0			0
$803$	−70.9267	−	402.245i	−0.0883271	−	0.500928i
$804$		0			0
$805$	566.475	−	981.163i	0.703695	−	1.21884i
$806$		0			0
$807$	64.6203	+	54.2229i	0.0800748	+	0.0671907i
$808$		0			0
$809$	223.197	+	386.589i	0.275893	+	0.477861i	0.970360	−	0.241664i	$-0.0776931\pi$
$809$	223.197	+	386.589i	0.275893	+	0.477861i	−0.694467	+	0.719524i	$0.744360\pi$
$810$		0			0
$811$	358.279	+	984.364i	0.441774	+	1.21377i	0.938324	+	0.345757i	$0.112378\pi$
$811$	358.279	+	984.364i	0.441774	+	1.21377i	−0.496550	+	0.868008i	$0.665400\pi$
$812$		0			0
$813$	−34.9301	−	6.15911i	−0.0429644	−	0.00757579i
$814$		0			0
$815$	1188.75	−	997.478i	1.45859	−	1.22390i
$816$		0			0
$817$	−130.369	+	723.699i	−0.159570	+	0.885801i
$818$		0			0
$819$	−619.377	−	738.144i	−0.756260	−	0.901275i
$820$		0			0
$821$	255.736	−	1450.35i	0.311493	−	1.76656i	−0.279754	−	0.960072i	$-0.590253\pi$
$821$	255.736	−	1450.35i	0.311493	−	1.76656i	0.591246	−	0.806491i	$-0.298636\pi$
$822$		0			0
$823$	686.983	−	250.041i	0.834730	−	0.303817i	0.110931	−	0.993828i	$-0.464617\pi$
$823$	686.983	−	250.041i	0.834730	−	0.303817i	0.723799	+	0.690011i	$0.242394\pi$
$824$		0			0
$825$	−153.628	+	88.6971i	−0.186216	+	0.107512i
$826$		0			0
$827$	37.2850	−	44.4345i	0.0450846	−	0.0537298i	−0.743031	−	0.669257i	$-0.766612\pi$
$827$	37.2850	−	44.4345i	0.0450846	−	0.0537298i	0.788116	+	0.615527i	$0.211057\pi$
$828$		0			0
$829$	936.414	+	540.639i	1.12957	+	0.652158i	0.943827	−	0.330441i	$-0.107197\pi$
$829$	936.414	+	540.639i	1.12957	+	0.652158i	0.185743	+	0.982598i	$0.440531\pi$
$830$		0			0
$831$	93.3055	−	16.4523i	0.112281	−	0.0197982i
$832$		0			0
$833$	−230.557	−	83.9160i	−0.276780	−	0.100740i
$834$		0			0
$835$		−	1284.24i		−	1.53802i
$836$		0			0
$837$	443.837			0.530271
$838$		0			0
$839$	−5.00431	+	13.7492i	−0.00596461	+	0.0163876i	−0.942639	−	0.333813i	$-0.891664\pi$
$839$	−5.00431	+	13.7492i	−0.00596461	+	0.0163876i	0.936675	+	0.350201i	$0.113887\pi$
$840$		0			0
$841$	68.1822	+	386.680i	0.0810728	+	0.459787i
$842$		0			0
$843$	74.6565	−	129.309i	0.0885605	−	0.153391i
$844$		0			0
$845$	990.815	+	831.393i	1.17256	+	0.983897i
$846$		0			0
$847$	−124.605	−	215.822i	−0.147113	−	0.254807i
$848$		0			0
$849$	−86.4344	−	237.477i	−0.101807	−	0.279713i
$850$		0			0
$851$	363.786	+	64.1453i	0.427481	+	0.0753764i
$852$		0			0
$853$	−326.273	+	273.776i	−0.382501	+	0.320956i	−0.813683	−	0.581308i	$-0.802541\pi$
$853$	−326.273	+	273.776i	−0.382501	+	0.320956i	0.431182	+	0.902265i	$0.358097\pi$
$854$		0			0
$855$	944.802	−	786.847i	1.10503	−	0.920289i
$856$		0			0
$857$	172.163	+	205.176i	0.200891	+	0.239412i	0.857079	−	0.515185i	$-0.172277\pi$
$857$	172.163	+	205.176i	0.200891	+	0.239412i	−0.656188	+	0.754597i	$0.727832\pi$
$858$		0			0
$859$	−3.38084	+	19.1737i	−0.00393578	+	0.0223209i	−0.986712	−	0.162477i	$-0.948052\pi$
$859$	−3.38084	+	19.1737i	−0.00393578	+	0.0223209i	0.982777	+	0.184797i	$0.0591629\pi$
$860$		0			0
$861$	−199.230	+	72.5138i	−0.231394	+	0.0842204i
$862$		0			0
$863$	−933.120	+	538.737i	−1.08125	+	0.624261i	−0.931234	−	0.364422i	$-0.881267\pi$
$863$	−933.120	+	538.737i	−1.08125	+	0.624261i	−0.150018	+	0.988683i	$0.547933\pi$
$864$		0			0
$865$	−117.801	+	140.390i	−0.136186	+	0.162300i
$866$		0			0
$867$	−62.0507	−	35.8250i	−0.0715694	−	0.0413206i
$868$		0			0
$869$	−138.824	+	24.4783i	−0.159751	+	0.0281684i
$870$		0			0
$871$	−1934.20	−	703.992i	−2.22067	−	0.808257i
$872$		0			0
$873$		−	1478.77i		−	1.69390i
$874$		0			0
$875$	299.234			0.341982
$876$		0			0
$877$	458.351	−	1259.31i	0.522635	−	1.43593i	−0.344941	−	0.938624i	$-0.612101\pi$
$877$	458.351	−	1259.31i	0.522635	−	1.43593i	0.867576	−	0.497304i	$-0.165677\pi$
$878$		0			0
$879$	17.2522	+	97.8424i	0.0196271	+	0.111311i
$880$		0			0
$881$	768.865	−	1331.71i	0.872718	−	1.51159i	0.0135448	−	0.999908i	$-0.495688\pi$
$881$	768.865	−	1331.71i	0.872718	−	1.51159i	0.859174	−	0.511684i	$-0.170978\pi$
$882$		0			0
$883$	1133.53	+	951.148i	1.28373	+	1.07718i	0.992718	+	0.120458i	$0.0384363\pi$
$883$	1133.53	+	951.148i	1.28373	+	1.07718i	0.291012	+	0.956719i	$0.406008\pi$
$884$		0			0
$885$	128.731	+	222.968i	0.145458	+	0.251941i
$886$		0			0
$887$	−455.735	−	1252.12i	−0.513794	−	1.41164i	−0.877254	−	0.480027i	$-0.840627\pi$
$887$	−455.735	−	1252.12i	−0.513794	−	1.41164i	0.363460	−	0.931610i	$-0.381595\pi$
$888$		0			0
$889$	−805.861	−	142.095i	−0.906481	−	0.159837i
$890$		0			0
$891$	−482.636	+	404.979i	−0.541679	+	0.454522i
$892$		0			0
$893$	13.6228	+	23.7982i	0.0152551	+	0.0266497i
$894$		0			0
$895$	820.680	+	978.049i	0.916961	+	1.09279i
$896$		0			0
$897$	50.0838	−	284.039i	0.0558348	−	0.316655i
$898$		0			0
$899$	−797.799	+	290.375i	−0.887429	+	0.322998i
$900$		0			0
$901$	−415.407	+	239.836i	−0.461052	+	0.266188i
$902$		0			0
$903$	94.8628	−	113.053i	0.105053	−	0.125197i
$904$		0			0
$905$	703.295	+	406.048i	0.777122	+	0.448672i
$906$		0			0
$907$	−363.404	+	64.0779i	−0.400666	+	0.0706482i	−0.370350	−	0.928892i	$-0.620762\pi$
$907$	−363.404	+	64.0779i	−0.400666	+	0.0706482i	−0.0303155	+	0.999540i	$0.509651\pi$
$908$		0			0
$909$	−267.000	−	97.1799i	−0.293729	−	0.106909i
$910$		0			0
$911$			345.867i			0.379657i	0.981817	+	0.189828i	$0.0607931\pi$
$911$			345.867i			0.379657i	−0.981817	+	0.189828i	$0.939207\pi$
$912$		0			0
$913$	−692.188			−0.758146
$914$		0			0
$915$	4.66766	−	12.8243i	0.00510127	−	0.0140156i
$916$		0			0
$917$	−201.689	−	1143.83i	−0.219944	−	1.24736i
$918$		0			0
$919$	186.618	−	323.232i	0.203067	−	0.351722i	−0.746448	−	0.665443i	$-0.768243\pi$
$919$	186.618	−	323.232i	0.203067	−	0.351722i	0.949515	+	0.313722i	$0.101576\pi$
$920$		0			0
$921$	248.323	+	208.367i	0.269623	+	0.226240i
$922$		0			0
$923$	1072.81	+	1858.15i	1.16230	+	2.01317i
$924$		0			0
$925$	160.522	+	441.029i	0.173537	+	0.476789i
$926$		0			0
$927$	−1592.39	−	280.781i	−1.71778	−	0.302892i
$928$		0			0
$929$	440.859	−	369.925i	0.474552	−	0.398197i	−0.373900	−	0.927469i	$-0.621980\pi$
$929$	440.859	−	369.925i	0.474552	−	0.398197i	0.848452	+	0.529272i	$0.177535\pi$
$930$		0			0
$931$	39.4806	+	228.851i	0.0424066	+	0.245812i
$932$		0			0
$933$	107.563	+	128.188i	0.115287	+	0.137394i
$934$		0			0
$935$	−234.339	+	1329.00i	−0.250630	+	1.42139i
$936$		0			0
$937$	−459.523	+	167.253i	−0.490419	+	0.178498i	−0.575380	−	0.817886i	$-0.695146\pi$
$937$	−459.523	+	167.253i	−0.490419	+	0.178498i	0.0849605	+	0.996384i	$0.472924\pi$
$938$		0			0
$939$	−101.930	+	58.8494i	−0.108552	+	0.0626724i
$940$		0			0
$941$	897.696	−	1069.83i	0.953981	−	1.13691i	−0.0365101	−	0.999333i	$-0.511624\pi$
$941$	897.696	−	1069.83i	0.953981	−	1.13691i	0.990491	−	0.137577i	$-0.0439314\pi$
$942$		0			0
$943$	1196.11	+	690.577i	1.26841	+	0.732319i
$944$		0			0
$945$	−497.194	+	87.6687i	−0.526131	+	0.0927711i
$946$		0			0
$947$	618.662	+	225.175i	0.653286	+	0.237777i	0.647335	−	0.762205i	$-0.275883\pi$
$947$	618.662	+	225.175i	0.653286	+	0.237777i	0.00595130	+	0.999982i	$0.498106\pi$
$948$		0			0
$949$			843.750i			0.889094i
$950$		0			0
$951$	−90.7923			−0.0954704
$952$		0			0
$953$	94.4822	−	259.588i	0.0991418	−	0.272390i	−0.880200	−	0.474604i	$-0.842591\pi$
$953$	94.4822	−	259.588i	0.0991418	−	0.272390i	0.979341	+	0.202214i	$0.0648136\pi$
$954$		0			0
$955$	199.461	+	1131.20i	0.208859	+	1.18450i
$956$		0			0
$957$	−59.5074	+	103.070i	−0.0621812	+	0.107701i
$958$		0			0
$959$	185.039	+	155.266i	0.192950	+	0.161904i
$960$		0			0
$961$	323.329	+	560.023i	0.336451	+	0.582750i
$962$		0			0
$963$	−188.934	−	519.092i	−0.196193	−	0.539036i
$964$		0			0
$965$	156.178	+	27.5384i	0.161843	+	0.0285372i
$966$		0			0
$967$	333.973	−	280.237i	0.345370	−	0.289800i	−0.453557	−	0.891227i	$-0.649845\pi$
$967$	333.973	−	280.237i	0.345370	−	0.289800i	0.798928	+	0.601427i	$0.205401\pi$
$968$		0			0
$969$	−0.886798	+	239.815i	−0.000915168	+	0.247487i
$970$		0			0
$971$	−803.245	−	957.270i	−0.827235	−	0.985860i	−1.00000		0.000896801i	$-0.999715\pi$
$971$	−803.245	−	957.270i	−0.827235	−	0.985860i	0.172765	−	0.984963i	$-0.444730\pi$
$972$		0			0
$973$	−207.539	+	1177.01i	−0.213298	+	1.20967i
$974$		0			0
$975$	344.350	−	125.333i	0.353179	−	0.128547i
$976$		0			0
$977$	−1274.02	+	735.558i	−1.30402	+	0.752874i	−0.981090	−	0.193550i	$-0.938000\pi$
$977$	−1274.02	+	735.558i	−1.30402	+	0.752874i	−0.322926	+	0.946424i	$0.604667\pi$
$978$		0			0
$979$	−828.995	+	987.958i	−0.846777	+	1.00915i
$980$		0			0
$981$	880.115	+	508.135i	0.897162	+	0.517976i
$982$		0			0
$983$	−1422.51	+	250.827i	−1.44711	+	0.255165i	−0.841355	−	0.540483i	$-0.818242\pi$
$983$	−1422.51	+	250.827i	−1.44711	+	0.255165i	−0.605759	+	0.795648i	$0.707131\pi$
$984$		0			0
$985$	−2470.73	−	899.271i	−2.50835	−	0.912966i
$986$		0			0
$987$		−	5.50334i		−	0.00557582i
$988$		0			0
$989$	−961.395			−0.972088
$990$		0			0
$991$	39.4988	−	108.522i	0.0398576	−	0.109508i	−0.918167	−	0.396193i	$-0.870331\pi$
$991$	39.4988	−	108.522i	0.0398576	−	0.109508i	0.958025	+	0.286685i	$0.0925534\pi$
$992$		0			0
$993$	46.0416	+	261.115i	0.0463661	+	0.262955i
$994$		0			0
$995$	1100.18	−	1905.57i	1.10571	−	1.91515i
$996$		0			0
$997$	−411.248	−	345.078i	−0.412486	−	0.346116i	0.412810	−	0.910817i	$-0.364547\pi$
$997$	−411.248	−	345.078i	−0.412486	−	0.346116i	−0.825296	+	0.564701i	$0.808992\pi$
$998$		0			0
$999$	−82.3055	−	142.557i	−0.0823879	−	0.142700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.j.a.13.2	✓	18
4.3	odd	2		304.3.z.b.241.2		18
19.3	odd	18	inner	76.3.j.a.41.2	yes	18
19.4	even	9		1444.3.c.c.721.10		18
19.15	odd	18		1444.3.c.c.721.9		18
76.3	even	18		304.3.z.b.193.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.j.a.13.2	✓	18	1.1	even	1	trivial
76.3.j.a.41.2	yes	18	19.3	odd	18	inner
304.3.z.b.193.2		18	76.3	even	18
304.3.z.b.241.2		18	4.3	odd	2
1444.3.c.c.721.9		18	19.15	odd	18
1444.3.c.c.721.10		18	19.4	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)

\(f(q)\)	\(=\)	\(q+(0.215056 - 0.590861i) q^{3} +(-1.30596 - 7.40644i) q^{5} +(3.03221 - 5.25195i) q^{7} +(6.59153 + 5.53095i) q^{9} +O(q^{10})\)	\(q+(0.215056 - 0.590861i) q^{3} +(-1.30596 - 7.40644i) q^{5} +(3.03221 - 5.25195i) q^{7} +(6.59153 + 5.53095i) q^{9} +(4.46952 + 7.74143i) q^{11} +(-6.31563 - 17.3521i) q^{13} +(-4.65703 - 0.821160i) q^{15} +(-15.3773 + 12.9031i) q^{17} +(17.8300 + 6.56436i) q^{19} +(-2.45108 - 2.92108i) q^{21} +(-4.31353 + 24.4632i) q^{23} +(-29.6575 + 10.7945i) q^{25} +(9.58643 - 5.53473i) q^{27} +(-13.6106 + 16.2205i) q^{29} +(34.7238 + 20.0478i) q^{31} +(5.53530 - 0.976023i) q^{33} +(-42.8582 - 15.5991i) q^{35} -14.8707i q^{37} -11.6109 q^{39} +(19.0165 - 52.2475i) q^{41} +(6.72062 + 38.1145i) q^{43} +(32.3564 - 56.0430i) q^{45} +(1.10558 + 0.927693i) q^{47} +(6.11135 + 10.5852i) q^{49} +(4.31695 + 11.8607i) q^{51} +(23.5326 + 4.14943i) q^{53} +(51.4995 - 43.2132i) q^{55} +(7.71307 - 9.12335i) q^{57} +(-34.9963 - 41.7070i) q^{59} +(-0.501142 + 2.84212i) q^{61} +(49.0352 - 17.8474i) q^{63} +(-120.269 + 69.4374i) q^{65} +(71.6504 - 85.3896i) q^{67} +(13.5267 + 7.80966i) q^{69} +(-114.429 + 20.1770i) q^{71} +(-42.9373 - 15.6279i) q^{73} +19.8449i q^{75} +54.2101 q^{77} +(-5.39352 + 14.8186i) q^{79} +(12.2390 + 69.4107i) q^{81} +(-38.7171 + 67.0600i) q^{83} +(115.648 + 97.0402i) q^{85} +(6.65702 + 11.5303i) q^{87} +(49.3453 + 135.575i) q^{89} +(-110.282 - 19.4458i) q^{91} +(19.3130 - 16.2056i) q^{93} +(25.3334 - 140.630i) q^{95} +(-110.468 - 131.651i) q^{97} +(-13.3565 + 75.7486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) \) 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

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