LMFDB - Embedded newform 76.3.j.a.53.1

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			53.1
Root			$-3.84460i$ of defining polynomial
Character	$\chi$	$=$	76.53
Dual form			76.3.j.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.45984 + 0.786390i) q^{3} +(5.56146 - 4.66662i) q^{5} +(4.24641 - 7.35499i) q^{7} +(10.8145 - 3.93617i) q^{9} +O(q^{10})$	\(q+(-4.45984 + 0.786390i) q^{3} +(5.56146 - 4.66662i) q^{5} +(4.24641 - 7.35499i) q^{7} +(10.8145 - 3.93617i) q^{9} +(-4.58648 - 7.94401i) q^{11} +(8.90742 + 1.57062i) q^{13} +(-21.1334 + 25.1859i) q^{15} +(-6.76774 - 2.46325i) q^{17} +(-18.6594 - 3.58147i) q^{19} +(-13.1544 + 36.1414i) q^{21} +(28.1571 + 23.6266i) q^{23} +(4.81130 - 27.2863i) q^{25} +(-9.83845 + 5.68023i) q^{27} +(-16.9884 - 46.6752i) q^{29} +(30.9473 + 17.8675i) q^{31} +(26.7020 + 31.8222i) q^{33} +(-10.7067 - 60.7209i) q^{35} +61.6609i q^{37} -40.9608 q^{39} +(-21.8147 + 3.84652i) q^{41} +(-50.2026 + 42.1250i) q^{43} +(41.7760 - 72.3581i) q^{45} +(67.7251 - 24.6499i) q^{47} +(-11.5639 - 20.0293i) q^{49} +(32.1201 + 5.66364i) q^{51} +(5.17977 - 6.17301i) q^{53} +(-62.5792 - 22.7770i) q^{55} +(86.0344 + 1.29923i) q^{57} +(3.10146 - 8.52118i) q^{59} +(32.9022 + 27.6082i) q^{61} +(16.9724 - 96.2553i) q^{63} +(56.8677 - 32.8326i) q^{65} +(2.86536 + 7.87251i) q^{67} +(-144.156 - 83.2284i) q^{69} +(5.02065 + 5.98338i) q^{71} +(17.9939 + 102.049i) q^{73} +125.476i q^{75} -77.9041 q^{77} +(-5.92154 + 1.04413i) q^{79} +(-39.9337 + 33.5084i) q^{81} +(17.5461 - 30.3907i) q^{83} +(-49.1336 + 17.8832i) q^{85} +(112.470 + 194.804i) q^{87} +(56.6113 + 9.98210i) q^{89} +(49.3764 - 58.8445i) q^{91} +(-152.071 - 55.3493i) q^{93} +(-120.487 + 67.1581i) q^{95} +(-36.6141 + 100.596i) q^{97} +(-80.8695 - 67.8576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

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
$3$	−4.45984	+	0.786390i	−1.48661	+	0.262130i	−0.857217	−	0.514955i	$-0.827809\pi$
$3$	−4.45984	+	0.786390i	−1.48661	+	0.262130i	−0.629396	+	0.777085i	$0.716698\pi$
$4$		0			0
$5$	5.56146	−	4.66662i	1.11229	−	0.933324i	0.114103	−	0.993469i	$-0.463601\pi$
$5$	5.56146	−	4.66662i	1.11229	−	0.933324i	0.998190	+	0.0601450i	$0.0191563\pi$
$6$		0			0
$7$	4.24641	−	7.35499i	0.606629	−	1.05071i	−0.385162	−	0.922849i	$-0.625855\pi$
$7$	4.24641	−	7.35499i	0.606629	−	1.05071i	0.991792	−	0.127864i	$-0.0408121\pi$
$8$		0			0
$9$	10.8145	−	3.93617i	1.20161	−	0.437352i
$10$		0			0
$11$	−4.58648	−	7.94401i	−0.416952	−	0.722183i	0.578679	−	0.815555i	$-0.303568\pi$
$11$	−4.58648	−	7.94401i	−0.416952	−	0.722183i	−0.995631	+	0.0933728i	$0.970235\pi$
$12$		0			0
$13$	8.90742	+	1.57062i	0.685186	+	0.120817i	0.505395	−	0.862888i	$-0.331347\pi$
$13$	8.90742	+	1.57062i	0.685186	+	0.120817i	0.179791	+	0.983705i	$0.442458\pi$
$14$		0			0
$15$	−21.1334	+	25.1859i	−1.40890	+	1.67906i
$16$		0			0
$17$	−6.76774	−	2.46325i	−0.398102	−	0.144897i	0.135208	−	0.990817i	$-0.456830\pi$
$17$	−6.76774	−	2.46325i	−0.398102	−	0.144897i	−0.533310	+	0.845920i	$0.679052\pi$
$18$		0			0
$19$	−18.6594	−	3.58147i	−0.982073	−	0.188499i
$19$	−18.6594	−	3.58147i	−0.982073	−	0.188499i
$20$		0			0
$21$	−13.1544	+	36.1414i	−0.626400	+	1.72102i
$22$		0			0
$23$	28.1571	+	23.6266i	1.22422	+	1.02724i	0.998593	+	0.0530300i	$0.0168879\pi$
$23$	28.1571	+	23.6266i	1.22422	+	1.02724i	0.225628	+	0.974213i	$0.427557\pi$
$24$		0			0
$25$	4.81130	−	27.2863i	0.192452	−	1.09145i
$26$		0			0
$27$	−9.83845	+	5.68023i	−0.364387	+	0.210379i
$28$		0			0
$29$	−16.9884	−	46.6752i	−0.585806	−	1.60949i	−0.778092	−	0.628150i	$-0.783813\pi$
$29$	−16.9884	−	46.6752i	−0.585806	−	1.60949i	0.192286	−	0.981339i	$-0.438410\pi$
$30$		0			0
$31$	30.9473	+	17.8675i	0.998301	+	0.576370i	0.907745	−	0.419522i	$-0.137802\pi$
$31$	30.9473	+	17.8675i	0.998301	+	0.576370i	0.0905562	+	0.995891i	$0.471136\pi$
$32$		0			0
$33$	26.7020	+	31.8222i	0.809153	+	0.964311i
$34$		0			0
$35$	−10.7067	−	60.7209i	−0.305906	−	1.73488i
$36$		0			0
$37$			61.6609i			1.66651i	0.552888	+	0.833256i	$0.313526\pi$
$37$			61.6609i			1.66651i	−0.552888	+	0.833256i	$0.686474\pi$
$38$		0			0
$39$	−40.9608			−1.05028
$40$		0			0
$41$	−21.8147	+	3.84652i	−0.532066	+	0.0938177i	−0.433225	−	0.901286i	$-0.642625\pi$
$41$	−21.8147	+	3.84652i	−0.532066	+	0.0938177i	−0.0988410	+	0.995103i	$0.531514\pi$
$42$		0			0
$43$	−50.2026	+	42.1250i	−1.16750	+	0.979651i	−0.999981	−	0.00621716i	$-0.998021\pi$
$43$	−50.2026	+	42.1250i	−1.16750	+	0.979651i	−0.167522	+	0.985868i	$0.553577\pi$
$44$		0			0
$45$	41.7760	−	72.3581i	0.928355	−	1.60796i
$46$		0			0
$47$	67.7251	−	24.6499i	1.44096	−	0.524466i	0.500908	−	0.865500i	$-0.332999\pi$
$47$	67.7251	−	24.6499i	1.44096	−	0.524466i	0.940051	+	0.341034i	$0.110777\pi$
$48$		0			0
$49$	−11.5639	−	20.0293i	−0.235998	−	0.408761i
$50$		0			0
$51$	32.1201	+	5.66364i	0.629806	+	0.111052i
$52$		0			0
$53$	5.17977	−	6.17301i	0.0977316	−	0.116472i	−0.714962	−	0.699163i	$-0.753556\pi$
$53$	5.17977	−	6.17301i	0.0977316	−	0.116472i	0.812693	+	0.582692i	$0.198000\pi$
$54$		0			0
$55$	−62.5792	−	22.7770i	−1.13780	−	0.414127i
$56$		0			0
$57$	86.0344	+	1.29923i	1.50937	+	0.0227936i
$58$		0			0
$59$	3.10146	−	8.52118i	0.0525671	−	0.144427i	−0.910630	−	0.413222i	$-0.864403\pi$
$59$	3.10146	−	8.52118i	0.0525671	−	0.144427i	0.963197	+	0.268795i	$0.0866255\pi$
$60$		0			0
$61$	32.9022	+	27.6082i	0.539380	+	0.452594i	0.871326	−	0.490705i	$-0.163261\pi$
$61$	32.9022	+	27.6082i	0.539380	+	0.452594i	−0.331946	+	0.943298i	$0.607705\pi$
$62$		0			0
$63$	16.9724	−	96.2553i	0.269403	−	1.52786i
$64$		0			0
$65$	56.8677	−	32.8326i	0.874888	−	0.505117i
$66$		0			0
$67$	2.86536	+	7.87251i	0.0427666	+	0.117500i	0.959238	−	0.282601i	$-0.0911972\pi$
$67$	2.86536	+	7.87251i	0.0427666	+	0.117500i	−0.916471	+	0.400101i	$0.868975\pi$
$68$		0			0
$69$	−144.156	−	83.2284i	−2.08921	−	1.20621i
$70$		0			0
$71$	5.02065	+	5.98338i	0.0707134	+	0.0842729i	0.800241	−	0.599678i	$-0.204705\pi$
$71$	5.02065	+	5.98338i	0.0707134	+	0.0842729i	−0.729528	+	0.683951i	$0.760260\pi$
$72$		0			0
$73$	17.9939	+	102.049i	0.246492	+	1.39793i	0.817002	+	0.576636i	$0.195635\pi$
$73$	17.9939	+	102.049i	0.246492	+	1.39793i	−0.570509	+	0.821291i	$0.693254\pi$
$74$		0			0
$75$			125.476i			1.67301i
$76$		0			0
$77$	−77.9041			−1.01174
$78$		0			0
$79$	−5.92154	+	1.04413i	−0.0749563	+	0.0132168i	−0.211001	−	0.977486i	$-0.567672\pi$
$79$	−5.92154	+	1.04413i	−0.0749563	+	0.0132168i	0.136044	+	0.990703i	$0.456561\pi$
$80$		0			0
$81$	−39.9337	+	33.5084i	−0.493009	+	0.413684i
$82$		0			0
$83$	17.5461	−	30.3907i	0.211399	−	0.366153i	−0.740754	−	0.671777i	$-0.765532\pi$
$83$	17.5461	−	30.3907i	0.211399	−	0.366153i	0.952152	+	0.305623i	$0.0988648\pi$
$84$		0			0
$85$	−49.1336	+	17.8832i	−0.578042	+	0.210390i
$86$		0			0
$87$	112.470	+	194.804i	1.29276	+	2.23913i
$88$		0			0
$89$	56.6113	+	9.98210i	0.636082	+	0.112158i	0.482385	−	0.875960i	$-0.339771\pi$
$89$	56.6113	+	9.98210i	0.636082	+	0.112158i	0.153697	+	0.988118i	$0.450882\pi$
$90$		0			0
$91$	49.3764	−	58.8445i	0.542598	−	0.646643i
$92$		0			0
$93$	−152.071	−	55.3493i	−1.63517	−	0.595154i
$94$		0			0
$95$	−120.487	+	67.1581i	−1.26828	+	0.706927i
$96$		0			0
$97$	−36.6141	+	100.596i	−0.377465	+	1.03708i	0.594939	+	0.803771i	$0.297176\pi$
$97$	−36.6141	+	100.596i	−0.377465	+	1.03708i	−0.972404	+	0.233305i	$0.925046\pi$
$98$		0			0
$99$	−80.8695	−	67.8576i	−0.816864	−	0.685430i
$100$		0			0
$101$	3.70196	−	20.9948i	0.0366530	−	0.207870i	−0.960981	−	0.276613i	$-0.910788\pi$
$101$	3.70196	−	20.9948i	0.0366530	−	0.207870i	0.997634	+	0.0687436i	$0.0218990\pi$
$102$		0			0
$103$	78.6526	−	45.4101i	0.763617	−	0.440875i	−0.0669756	−	0.997755i	$-0.521335\pi$
$103$	78.6526	−	45.4101i	0.763617	−	0.440875i	0.830593	+	0.556880i	$0.188002\pi$
$104$		0			0
$105$	95.5006	+	262.386i	0.909529	+	2.49891i
$106$		0			0
$107$	−44.0981	−	25.4601i	−0.412132	−	0.237945i	0.279573	−	0.960124i	$-0.409807\pi$
$107$	−44.0981	−	25.4601i	−0.412132	−	0.237945i	−0.691705	+	0.722180i	$0.743140\pi$
$108$		0			0
$109$	−88.5175	−	105.491i	−0.812087	−	0.967808i	0.187809	−	0.982206i	$-0.439861\pi$
$109$	−88.5175	−	105.491i	−0.812087	−	0.967808i	−0.999896	+	0.0143979i	$0.995417\pi$
$110$		0			0
$111$	−48.4895	−	274.998i	−0.436843	−	2.47746i
$112$		0			0
$113$		−	17.1143i		−	0.151454i	−0.997129	−	0.0757271i	$-0.975872\pi$
$113$		−	17.1143i		−	0.151454i	0.997129	−	0.0757271i	$-0.0241278\pi$
$114$		0			0
$115$	266.851			2.32044
$116$		0			0
$117$	102.512	−	18.0756i	0.876169	−	0.154492i
$118$		0			0
$119$	−46.8558	+	39.3167i	−0.393746	+	0.330392i
$120$		0			0
$121$	18.4285	−	31.9191i	0.152301	−	0.263794i
$122$		0			0
$123$	94.2653	−	34.3098i	0.766385	−	0.278941i
$124$		0			0
$125$	−9.82707	−	17.0210i	−0.0786166	−	0.136168i
$126$		0			0
$127$	39.2818	+	6.92644i	0.309305	+	0.0545389i	0.326146	−	0.945319i	$-0.394250\pi$
$127$	39.2818	+	6.92644i	0.309305	+	0.0545389i	−0.0168409	+	0.999858i	$0.505361\pi$
$128$		0			0
$129$	190.769	−	227.350i	1.47883	−	1.76240i
$130$		0			0
$131$	52.5919	+	19.1419i	0.401465	+	0.146121i	0.534858	−	0.844942i	$-0.320365\pi$
$131$	52.5919	+	19.1419i	0.401465	+	0.146121i	−0.133393	+	0.991063i	$0.542587\pi$
$132$		0			0
$133$	−105.577	+	122.031i	−0.793813	+	0.917528i
$134$		0			0
$135$	−28.2087	+	77.5027i	−0.208953	+	0.574094i
$136$		0			0
$137$	−74.6775	−	62.6619i	−0.545091	−	0.457386i	0.328184	−	0.944614i	$-0.393564\pi$
$137$	−74.6775	−	62.6619i	−0.545091	−	0.457386i	−0.873275	+	0.487228i	$0.838008\pi$
$138$		0			0
$139$	−5.83051	+	33.0664i	−0.0419461	+	0.237888i	−0.998571	−	0.0534329i	$-0.982984\pi$
$139$	−5.83051	+	33.0664i	−0.0419461	+	0.237888i	0.956625	+	0.291321i	$0.0940948\pi$
$140$		0			0
$141$	−282.659	+	163.193i	−2.00467	+	1.15740i
$142$		0			0
$143$	−28.3766	−	77.9642i	−0.198438	−	0.545204i
$144$		0			0
$145$	−312.295	−	180.304i	−2.15376	−	1.24347i
$146$		0			0
$147$	67.3241	+	80.2337i	0.457987	+	0.545808i
$148$		0			0
$149$	21.7785	+	123.512i	0.146164	+	0.828939i	0.966425	+	0.256949i	$0.0827173\pi$
$149$	21.7785	+	123.512i	0.146164	+	0.828939i	−0.820261	+	0.571990i	$0.806172\pi$
$150$		0			0
$151$		−	40.1000i		−	0.265563i	−0.991145	−	0.132781i	$-0.957609\pi$
$151$		−	40.1000i		−	0.265563i	0.991145	−	0.132781i	$-0.0423908\pi$
$152$		0			0
$153$	−82.8857			−0.541736
$154$		0			0
$155$	255.493	−	45.0503i	1.64834	−	0.290647i
$156$		0			0
$157$	208.732	−	175.147i	1.32950	−	1.11558i	0.345306	−	0.938490i	$-0.387775\pi$
$157$	208.732	−	175.147i	1.32950	−	1.11558i	0.984194	−	0.177093i	$-0.0566693\pi$
$158$		0			0
$159$	−18.2466	+	31.6040i	−0.114758	+	0.198767i
$160$		0			0
$161$	293.340	−	106.767i	1.82199	−	0.663149i
$162$		0			0
$163$	40.1147	+	69.4807i	0.246103	+	0.426262i	0.962441	−	0.271491i	$-0.0875166\pi$
$163$	40.1147	+	69.4807i	0.246103	+	0.426262i	−0.716338	+	0.697753i	$0.754183\pi$
$164$		0			0
$165$	297.005	+	52.3699i	1.80003	+	0.317394i
$166$		0			0
$167$	−41.3965	+	49.3344i	−0.247883	+	0.295416i	−0.875611	−	0.483017i	$-0.839541\pi$
$167$	−41.3965	+	49.3344i	−0.247883	+	0.295416i	0.627727	+	0.778433i	$0.283985\pi$
$168$		0			0
$169$	−81.9328	−	29.8211i	−0.484810	−	0.176456i
$170$		0			0
$171$	−215.890	+	34.7145i	−1.26251	+	0.203009i
$172$		0			0
$173$	89.5340	−	245.993i	0.517538	−	1.42192i	−0.355687	−	0.934605i	$-0.615753\pi$
$173$	89.5340	−	245.993i	0.517538	−	1.42192i	0.873225	−	0.487318i	$-0.162025\pi$
$174$		0			0
$175$	−180.259	−	151.256i	−1.03005	−	0.864318i
$176$		0			0
$177$	−7.13103	+	40.4421i	−0.0402883	+	0.228486i
$178$		0			0
$179$	−222.383	+	128.393i	−1.24236	+	0.717278i	−0.969575	−	0.244796i	$-0.921279\pi$
$179$	−222.383	+	128.393i	−1.24236	+	0.717278i	−0.272788	+	0.962074i	$0.587946\pi$
$180$		0			0
$181$	62.3359	+	171.267i	0.344397	+	0.946224i	0.984102	+	0.177603i	$0.0568344\pi$
$181$	62.3359	+	171.267i	0.344397	+	0.946224i	−0.639705	+	0.768621i	$0.720943\pi$
$182$		0			0
$183$	−168.449	−	97.2542i	−0.920488	−	0.531444i
$184$		0			0
$185$	287.748	+	342.925i	1.55540	+	1.85365i
$186$		0			0
$187$	11.4719	+	65.0606i	0.0613473	+	0.347918i
$188$		0			0
$189$			96.4822i			0.510488i
$190$		0			0
$191$	−271.510			−1.42152			−0.710760	−	0.703434i	$-0.751649\pi$
$191$	−271.510			−1.42152			−0.710760	+	0.703434i	$0.751649\pi$
$192$		0			0
$193$	−69.4951	+	12.2539i	−0.360078	+	0.0634915i	−0.350761	−	0.936465i	$-0.614077\pi$
$193$	−69.4951	+	12.2539i	−0.360078	+	0.0634915i	−0.00931732	+	0.999957i	$0.502966\pi$
$194$		0			0
$195$	−227.802	+	191.148i	−1.16821	+	0.980248i
$196$		0			0
$197$	5.09230	−	8.82012i	0.0258492	−	0.0447722i	−0.852811	−	0.522219i	$-0.825104\pi$
$197$	5.09230	−	8.82012i	0.0258492	−	0.0447722i	0.878661	+	0.477447i	$0.158438\pi$
$198$		0			0
$199$	81.4237	−	29.6358i	0.409164	−	0.148924i	−0.129234	−	0.991614i	$-0.541252\pi$
$199$	81.4237	−	29.6358i	0.409164	−	0.148924i	0.538398	+	0.842690i	$0.319030\pi$
$200$		0			0
$201$	−18.9699	−	32.8568i	−0.0943777	−	0.163467i
$202$		0			0
$203$	−415.435	−	73.2524i	−2.04648	−	0.360849i
$204$		0			0
$205$	−103.371	+	123.193i	−0.504251	+	0.600943i
$206$		0			0
$207$	397.504	+	144.680i	1.92031	+	0.698935i
$208$		0			0
$209$	57.1296	+	164.657i	0.273347	+	0.787831i
$210$		0			0
$211$	−48.0301	+	131.962i	−0.227631	+	0.625410i	−0.999952	−	0.00982217i	$-0.996873\pi$
$211$	−48.0301	+	131.962i	−0.227631	+	0.625410i	0.772321	+	0.635232i	$0.219096\pi$
$212$		0			0
$213$	−27.0966	−	22.7367i	−0.127214	−	0.106745i
$214$		0			0
$215$	−82.6186	+	468.553i	−0.384272	+	2.17932i
$216$		0			0
$217$	262.830	−	151.745i	1.21120	−	0.699286i
$218$		0			0
$219$	−160.500	−	440.970i	−0.732877	−	2.01356i
$220$		0			0
$221$	−56.4142	−	32.5708i	−0.255268	−	0.147379i
$222$		0			0
$223$	−86.6197	−	103.229i	−0.388429	−	0.462912i	0.536027	−	0.844201i	$-0.319925\pi$
$223$	−86.6197	−	103.229i	−0.388429	−	0.462912i	−0.924456	+	0.381289i	$0.875480\pi$
$224$		0			0
$225$	−55.3713	−	314.026i	−0.246095	−	1.39567i
$226$		0			0
$227$			331.319i			1.45955i	0.683685	+	0.729777i	$0.260376\pi$
$227$			331.319i			1.45955i	−0.683685	+	0.729777i	$0.739624\pi$
$228$		0			0
$229$	123.297			0.538416			0.269208	−	0.963082i	$-0.413238\pi$
$229$	123.297			0.538416			0.269208	+	0.963082i	$0.413238\pi$
$230$		0			0
$231$	347.440	−	61.2631i	1.50407	−	0.265208i
$232$		0			0
$233$	73.0483	−	61.2948i	0.313512	−	0.263068i	−0.472430	−	0.881368i	$-0.656623\pi$
$233$	73.0483	−	61.2948i	0.313512	−	0.263068i	0.785942	+	0.618300i	$0.212179\pi$
$234$		0			0
$235$	261.619	−	453.137i	1.11327	−	1.92824i
$236$		0			0
$237$	25.5880	−	9.31329i	0.107966	−	0.0392966i
$238$		0			0
$239$	−24.0036	−	41.5754i	−0.100433	−	0.173956i	0.811430	−	0.584450i	$-0.198690\pi$
$239$	−24.0036	−	41.5754i	−0.100433	−	0.173956i	−0.911863	+	0.410494i	$0.865356\pi$
$240$		0			0
$241$	4.76756	+	0.840650i	0.0197824	+	0.00348817i	0.183531	−	0.983014i	$-0.441247\pi$
$241$	4.76756	+	0.840650i	0.0197824	+	0.00348817i	−0.163748	+	0.986502i	$0.552358\pi$
$242$		0			0
$243$	217.469	−	259.169i	0.894933	−	1.06654i
$244$		0			0
$245$	−157.781	−	57.4278i	−0.644006	−	0.234399i
$246$		0			0
$247$	−160.582	−	61.2085i	−0.650129	−	0.247808i
$248$		0			0
$249$	−54.3538	+	149.336i	−0.218288	+	0.599742i
$250$		0			0
$251$	201.049	+	168.700i	0.800991	+	0.672111i	0.948439	−	0.316959i	$-0.102662\pi$
$251$	201.049	+	168.700i	0.800991	+	0.672111i	−0.147449	+	0.989070i	$0.547106\pi$
$252$		0			0
$253$	58.5481	−	332.043i	0.231416	−	1.31242i
$254$		0			0
$255$	205.065	−	118.394i	0.804176	−	0.464291i
$256$		0			0
$257$	−5.07233	−	13.9361i	−0.0197367	−	0.0542262i	0.929433	−	0.368991i	$-0.120297\pi$
$257$	−5.07233	−	13.9361i	−0.0197367	−	0.0542262i	−0.949170	+	0.314765i	$0.898074\pi$
$258$		0			0
$259$	453.516	+	261.837i	1.75103	+	1.01095i
$260$		0			0
$261$	−367.442	−	437.901i	−1.40783	−	1.67778i
$262$		0			0
$263$	−3.33484	−	18.9128i	−0.0126800	−	0.0719119i	0.977811	−	0.209488i	$-0.0671798\pi$
$263$	−3.33484	−	18.9128i	−0.0126800	−	0.0719119i	−0.990491	+	0.137576i	$0.956069\pi$
$264$		0			0
$265$		−	58.5030i		−	0.220766i
$266$		0			0
$267$	−260.327			−0.975008
$268$		0			0
$269$	−182.585	+	32.1946i	−0.678753	+	0.119683i	−0.502388	−	0.864642i	$-0.667545\pi$
$269$	−182.585	+	32.1946i	−0.678753	+	0.119683i	−0.176365	+	0.984325i	$0.556434\pi$
$270$		0			0
$271$	75.9591	−	63.7372i	0.280292	−	0.235193i	−0.491793	−	0.870712i	$-0.663658\pi$
$271$	75.9591	−	63.7372i	0.280292	−	0.235193i	0.772085	+	0.635519i	$0.219214\pi$
$272$		0			0
$273$	−173.936	+	301.266i	−0.637128	+	1.10354i
$274$		0			0
$275$	−238.829	+	86.9267i	−0.868470	+	0.316097i
$276$		0			0
$277$	172.661	+	299.058i	0.623326	+	1.07963i	0.988862	+	0.148836i	$0.0475525\pi$
$277$	172.661	+	299.058i	0.623326	+	1.07963i	−0.365536	+	0.930797i	$0.619114\pi$
$278$		0			0
$279$	405.010	+	71.4142i	1.45165	+	0.255965i
$280$		0			0
$281$	−259.889	+	309.723i	−0.924871	+	1.10222i	0.0696386	+	0.997572i	$0.477815\pi$
$281$	−259.889	+	309.723i	−0.924871	+	1.10222i	−0.994510	+	0.104646i	$0.966629\pi$
$282$		0			0
$283$	−350.264	−	127.486i	−1.23768	−	0.450480i	−0.361461	−	0.932387i	$-0.617722\pi$
$283$	−350.264	−	127.486i	−1.23768	−	0.450480i	−0.876222	+	0.481908i	$0.839944\pi$
$284$		0			0
$285$	484.540	−	394.264i	1.70014	−	1.38338i
$286$		0			0
$287$	−64.3430	+	176.781i	−0.224192	+	0.615962i
$288$		0			0
$289$	−181.652	−	152.424i	−0.628554	−	0.527420i
$290$		0			0
$291$	84.1850	−	477.437i	0.289296	−	1.64068i
$292$		0			0
$293$	138.571	−	80.0042i	0.472939	−	0.273052i	−0.244530	−	0.969642i	$-0.578634\pi$
$293$	138.571	−	80.0042i	0.472939	−	0.273052i	0.717469	+	0.696590i	$0.245300\pi$
$294$		0			0
$295$	−22.5165	−	61.8635i	−0.0763271	−	0.209707i
$296$		0			0
$297$	90.2476	+	52.1045i	0.303864	+	0.175436i
$298$		0			0
$299$	213.699	+	254.676i	0.714711	+	0.851759i
$300$		0			0
$301$	96.6483	+	548.120i	0.321091	+	1.82100i
$302$		0			0
$303$			96.5448i			0.318630i
$304$		0			0
$305$	311.821			1.02236
$306$		0			0
$307$	−388.771	+	68.5508i	−1.26635	+	0.223292i	−0.766176	−	0.642630i	$-0.777843\pi$
$307$	−388.771	+	68.5508i	−1.26635	+	0.223292i	−0.500178	+	0.865923i	$0.666732\pi$
$308$		0			0
$309$	−315.068	+	264.373i	−1.01964	+	0.855577i
$310$		0			0
$311$	33.8929	−	58.7042i	0.108980	−	0.188759i	−0.806377	−	0.591402i	$-0.798575\pi$
$311$	33.8929	−	58.7042i	0.108980	−	0.188759i	0.915357	+	0.402642i	$0.131908\pi$
$312$		0			0
$313$	−352.465	+	128.287i	−1.12609	+	0.409862i	−0.836870	−	0.547402i	$-0.815617\pi$
$313$	−352.465	+	128.287i	−1.12609	+	0.409862i	−0.289217	+	0.957264i	$0.593395\pi$
$314$		0			0
$315$	−354.796	−	614.524i	−1.12634	−	1.95087i
$316$		0			0
$317$	−187.794	−	33.1132i	−0.592411	−	0.104458i	−0.130598	−	0.991435i	$-0.541690\pi$
$317$	−187.794	−	33.1132i	−0.592411	−	0.104458i	−0.461813	+	0.886977i	$0.652801\pi$
$318$		0			0
$319$	−292.871	+	349.030i	−0.918092	+	1.09414i
$320$		0			0
$321$	216.692	+	78.8695i	0.675053	+	0.245699i
$322$		0			0
$323$	117.460	+	70.2013i	0.363653	+	0.217342i
$324$		0			0
$325$	85.7126	−	235.493i	0.263731	−	0.724595i
$326$		0			0
$327$	477.731	+	400.864i	1.46095	+	1.22588i
$328$		0			0
$329$	106.288	−	602.791i	0.323065	−	1.83219i
$330$		0			0
$331$	−97.3276	+	56.1921i	−0.294041	+	0.169765i	−0.639763	−	0.768572i	$-0.720967\pi$
$331$	−97.3276	+	56.1921i	−0.294041	+	0.169765i	0.345722	+	0.938337i	$0.387634\pi$
$332$		0			0
$333$	242.708	+	666.834i	0.728852	+	2.00250i
$334$		0			0
$335$	52.6736	+	30.4111i	0.157235	+	0.0907795i
$336$		0			0
$337$	−116.236	−	138.525i	−0.344915	−	0.411054i	0.565501	−	0.824748i	$-0.308683\pi$
$337$	−116.236	−	138.525i	−0.344915	−	0.411054i	−0.910416	+	0.413694i	$0.864238\pi$
$338$		0			0
$339$	13.4585	+	76.3272i	0.0397007	+	0.225154i
$340$		0			0
$341$		−	327.795i		−	0.961275i
$342$		0			0
$343$	219.727			0.640604
$344$		0			0
$345$	−1190.11	+	209.849i	−3.44960	+	0.608258i
$346$		0			0
$347$	272.168	−	228.376i	0.784347	−	0.658145i	−0.159992	−	0.987118i	$-0.551147\pi$
$347$	272.168	−	228.376i	0.784347	−	0.658145i	0.944339	+	0.328973i	$0.106703\pi$
$348$		0			0
$349$	−7.86775	+	13.6273i	−0.0225437	+	0.0390468i	−0.877077	−	0.480350i	$-0.840510\pi$
$349$	−7.86775	+	13.6273i	−0.0225437	+	0.0390468i	0.854533	+	0.519396i	$0.173843\pi$
$350$		0			0
$351$	−96.5566	+	35.1437i	−0.275090	+	0.100125i
$352$		0			0
$353$	79.2116	+	137.199i	0.224396	+	0.388665i	0.956138	−	0.292917i	$-0.0946259\pi$
$353$	79.2116	+	137.199i	0.224396	+	0.388665i	−0.731742	+	0.681581i	$0.761293\pi$
$354$		0			0
$355$	55.8443	+	9.84686i	0.157308	+	0.0277376i
$356$		0			0
$357$	178.051	−	212.193i	0.498742	−	0.594378i
$358$		0			0
$359$	−568.796	−	207.025i	−1.58439	−	0.576671i	−0.608237	−	0.793756i	$-0.708123\pi$
$359$	−568.796	−	207.025i	−1.58439	−	0.576671i	−0.976153	+	0.217085i	$0.930345\pi$
$360$		0			0
$361$	335.346	+	133.656i	0.928937	+	0.370239i
$362$		0			0
$363$	−57.0872	+	156.846i	−0.157265	+	0.432082i
$364$		0			0
$365$	576.295	+	483.569i	1.57889	+	1.32485i
$366$		0			0
$367$	−78.6356	+	445.965i	−0.214266	+	1.21516i	0.667910	+	0.744242i	$0.267189\pi$
$367$	−78.6356	+	445.965i	−0.214266	+	1.21516i	−0.882176	+	0.470920i	$0.843922\pi$
$368$		0			0
$369$	−220.775	+	127.465i	−0.598307	+	0.345433i
$370$		0			0
$371$	−23.4070	−	64.3103i	−0.0630917	−	0.173343i
$372$		0			0
$373$	575.203	+	332.094i	1.54210	+	0.890331i	0.998706	+	0.0508527i	$0.0161939\pi$
$373$	575.203	+	332.094i	1.54210	+	0.890331i	0.543393	+	0.839479i	$0.317139\pi$
$374$		0			0
$375$	57.2123	+	68.1830i	0.152566	+	0.181821i
$376$		0			0
$377$	−78.0137	−	442.437i	−0.206933	−	1.17357i
$378$		0			0
$379$		−	646.614i		−	1.70610i	−0.521826	−	0.853052i	$-0.674749\pi$
$379$		−	646.614i		−	1.70610i	0.521826	−	0.853052i	$-0.325251\pi$
$380$		0			0
$381$	−180.637			−0.474114
$382$		0			0
$383$	194.765	−	34.3423i	0.508524	−	0.0896665i	0.0865013	−	0.996252i	$-0.472431\pi$
$383$	194.765	−	34.3423i	0.508524	−	0.0896665i	0.422023	+	0.906585i	$0.361320\pi$
$384$		0			0
$385$	−433.261	+	363.549i	−1.12535	+	0.944283i
$386$		0			0
$387$	−377.107	+	653.168i	−0.974436	+	1.68777i
$388$		0			0
$389$	−141.162	+	51.3788i	−0.362885	+	0.132079i	−0.517026	−	0.855970i	$-0.672961\pi$
$389$	−141.162	+	51.3788i	−0.362885	+	0.132079i	0.154142	+	0.988049i	$0.450739\pi$
$390$		0			0
$391$	−132.361	−	229.257i	−0.338520	−	0.586334i
$392$		0			0
$393$	−249.604	−	44.0120i	−0.635126	−	0.111990i
$394$		0			0
$395$	−28.0599	+	33.4405i	−0.0710377	+	0.0846594i
$396$		0			0
$397$	−564.897	−	205.606i	−1.42291	−	0.517898i	−0.488022	−	0.872831i	$-0.662281\pi$
$397$	−564.897	−	205.606i	−1.42291	−	0.517898i	−0.934892	+	0.354933i	$0.884504\pi$
$398$		0			0
$399$	374.893	−	627.265i	0.939580	−	1.57209i
$400$		0			0
$401$	251.842	−	691.930i	0.628035	−	1.72551i	−0.0583738	−	0.998295i	$-0.518592\pi$
$401$	251.842	−	691.930i	0.628035	−	1.72551i	0.686408	−	0.727216i	$-0.259186\pi$
$402$		0			0
$403$	247.598	+	207.759i	0.614387	+	0.515532i
$404$		0			0
$405$	−65.7190	+	372.711i	−0.162269	+	0.920275i
$406$		0			0
$407$	489.835	−	282.806i	1.20353	−	0.694856i
$408$		0			0
$409$	−247.811	−	680.855i	−0.605895	−	1.66468i	−0.739102	−	0.673594i	$-0.764750\pi$
$409$	−247.811	−	680.855i	−0.605895	−	1.66468i	0.133207	−	0.991088i	$-0.457472\pi$
$410$		0			0
$411$	382.326	+	220.736i	0.930234	+	0.537071i
$412$		0			0
$413$	−49.5032	−	58.9956i	−0.119862	−	0.142846i
$414$		0			0
$415$	−44.2400	−	250.898i	−0.106602	−	0.604573i
$416$		0			0
$417$		−	152.056i		−	0.364643i
$418$		0			0
$419$	100.633			0.240174			0.120087	−	0.992763i	$-0.461683\pi$
$419$	100.633			0.240174			0.120087	+	0.992763i	$0.461683\pi$
$420$		0			0
$421$	530.997	−	93.6291i	1.26128	−	0.222397i	0.497264	−	0.867599i	$-0.334338\pi$
$421$	530.997	−	93.6291i	1.26128	−	0.222397i	0.764012	+	0.645202i	$0.223227\pi$
$422$		0			0
$423$	635.389	−	533.154i	1.50210	−	1.26041i
$424$		0			0
$425$	−99.7746	+	172.815i	−0.234764	+	0.406623i
$426$		0			0
$427$	342.774	−	124.760i	0.802750	−	0.292177i
$428$		0			0
$429$	187.866	+	325.393i	0.437915	+	0.758491i
$430$		0			0
$431$	−719.719	−	126.906i	−1.66988	−	0.294445i	−0.742858	−	0.669449i	$-0.766530\pi$
$431$	−719.719	−	126.906i	−1.66988	−	0.294445i	−0.927023	+	0.375004i	$0.877642\pi$
$432$		0			0
$433$	106.091	−	126.435i	0.245015	−	0.291997i	−0.629496	−	0.777004i	$-0.716738\pi$
$433$	106.091	−	126.435i	0.245015	−	0.291997i	0.874510	+	0.485007i	$0.161183\pi$
$434$		0			0
$435$	1534.58	+	558.540i	3.52776	+	1.28400i
$436$		0			0
$437$	−440.776	−	541.702i	−1.00864	−	1.23959i
$438$		0			0
$439$	−80.2667	+	220.531i	−0.182840	+	0.502349i	−0.996922	−	0.0784014i	$-0.975018\pi$
$439$	−80.2667	+	220.531i	−0.182840	+	0.502349i	0.814082	+	0.580750i	$0.197241\pi$
$440$		0			0
$441$	−203.897	−	171.090i	−0.462352	−	0.387959i
$442$		0			0
$443$	12.6427	−	71.7002i	0.0285388	−	0.161851i	−0.967208	−	0.253987i	$-0.918258\pi$
$443$	12.6427	−	71.7002i	0.0285388	−	0.161851i	0.995747	+	0.0921352i	$0.0293692\pi$
$444$		0			0
$445$	361.424	−	208.668i	0.812189	−	0.468918i
$446$		0			0
$447$	−194.257	−	533.717i	−0.434580	−	1.19400i
$448$		0			0
$449$	75.3812	+	43.5214i	0.167887	+	0.0969295i	0.581589	−	0.813483i	$-0.302431\pi$
$449$	75.3812	+	43.5214i	0.167887	+	0.0969295i	−0.413702	+	0.910412i	$0.635765\pi$
$450$		0			0
$451$	130.610	+	155.654i	0.289600	+	0.345132i
$452$		0			0
$453$	31.5342	+	178.840i	0.0696120	+	0.394789i
$454$		0			0
$455$		−	557.682i		−	1.22568i
$456$		0			0
$457$	293.052			0.641251			0.320625	−	0.947206i	$-0.396107\pi$
$457$	293.052			0.641251			0.320625	+	0.947206i	$0.396107\pi$
$458$		0			0
$459$	80.5759	−	14.2077i	0.175547	−	0.0309536i
$460$		0			0
$461$	−326.699	+	274.133i	−0.708675	+	0.594649i	−0.924227	−	0.381844i	$-0.875289\pi$
$461$	−326.699	+	274.133i	−0.708675	+	0.594649i	0.215552	+	0.976492i	$0.430845\pi$
$462$		0			0
$463$	−78.9796	+	136.797i	−0.170582	+	0.295457i	−0.938624	−	0.344943i	$-0.887898\pi$
$463$	−78.9796	+	136.797i	−0.170582	+	0.295457i	0.768041	+	0.640400i	$0.221232\pi$
$464$		0			0
$465$	−1104.03	+	401.834i	−2.37426	+	0.864160i
$466$		0			0
$467$	−259.474	−	449.422i	−0.555618	−	0.962359i	−0.997855	−	0.0654609i	$-0.979148\pi$
$467$	−259.474	−	449.422i	−0.555618	−	0.962359i	0.442237	−	0.896898i	$-0.354185\pi$
$468$		0			0
$469$	70.0697	+	12.3552i	0.149402	+	0.0263437i
$470$		0			0
$471$	−793.176	+	945.270i	−1.68402	+	2.00694i
$472$		0			0
$473$	564.894	+	205.605i	1.19428	+	0.434682i
$474$		0			0
$475$	−187.501	+	491.914i	−0.394739	+	1.03561i
$476$		0			0
$477$	31.7188	−	87.1467i	0.0664964	−	0.182697i
$478$		0			0
$479$	−399.267	−	335.025i	−0.833542	−	0.699425i	0.122559	−	0.992461i	$-0.460890\pi$
$479$	−399.267	−	335.025i	−0.833542	−	0.699425i	−0.956101	+	0.293036i	$0.905334\pi$
$480$		0			0
$481$	−96.8458	+	549.240i	−0.201343	+	1.14187i
$482$		0			0
$483$	−1224.29	+	706.843i	−2.53476	+	1.46344i
$484$		0			0
$485$	265.817	+	730.327i	0.548077	+	1.50583i
$486$		0			0
$487$	−358.650	−	207.067i	−0.736448	−	0.425188i	0.0843284	−	0.996438i	$-0.473126\pi$
$487$	−358.650	−	207.067i	−0.736448	−	0.425188i	−0.820776	+	0.571250i	$0.806459\pi$
$488$		0			0
$489$	−233.544	−	278.327i	−0.477596	−	0.569176i
$490$		0			0
$491$	133.782	+	758.716i	0.272468	+	1.54525i	0.746890	+	0.664948i	$0.231546\pi$
$491$	133.782	+	758.716i	0.272468	+	1.54525i	−0.474421	+	0.880298i	$0.657343\pi$
$492$		0			0
$493$			357.732i			0.725623i
$494$		0			0
$495$	−766.418			−1.54832
$496$		0			0
$497$	65.3274	−	11.5190i	0.131443	−	0.0231770i
$498$		0			0
$499$	342.319	−	287.240i	0.686011	−	0.575631i	−0.231745	−	0.972777i	$-0.574444\pi$
$499$	342.319	−	287.240i	0.686011	−	0.575631i	0.917756	+	0.397145i	$0.129999\pi$
$500$		0			0
$501$	145.826	−	252.578i	0.291069	−	0.504147i
$502$		0			0
$503$	48.2808	−	17.5728i	0.0959856	−	0.0349359i	−0.293581	−	0.955934i	$-0.594847\pi$
$503$	48.2808	−	17.5728i	0.0959856	−	0.0349359i	0.389567	+	0.920998i	$0.372625\pi$
$504$		0			0
$505$	−77.3866	−	134.038i	−0.153241	−	0.265421i
$506$		0			0
$507$	388.858	+	68.5662i	0.766979	+	0.135239i
$508$		0			0
$509$	509.956	−	607.742i	1.00188	−	1.19399i	0.0209192	−	0.999781i	$-0.493341\pi$
$509$	509.956	−	607.742i	1.00188	−	1.19399i	0.980960	−	0.194212i	$-0.0622148\pi$
$510$		0			0
$511$	826.976	+	300.995i	1.61835	+	0.589031i
$512$		0			0
$513$	203.923	−	70.7535i	0.397511	−	0.137921i
$514$		0			0
$515$	225.512	−	619.588i	0.437887	−	1.20308i
$516$		0			0
$517$	−506.439	−	424.952i	−0.979572	−	0.821958i
$518$		0			0
$519$	−205.861	+	1167.50i	−0.396650	+	2.24951i
$520$		0			0
$521$	703.096	−	405.932i	1.34951	−	0.779141i	0.361332	−	0.932437i	$-0.382322\pi$
$521$	703.096	−	405.932i	1.34951	−	0.779141i	0.988180	+	0.153296i	$0.0489889\pi$
$522$		0			0
$523$	−169.109	−	464.624i	−0.323345	−	0.888383i	−0.989752	−	0.142795i	$-0.954391\pi$
$523$	−169.109	−	464.624i	−0.323345	−	0.888383i	0.666407	−	0.745588i	$-0.267831\pi$
$524$		0			0
$525$	922.874	+	532.822i	1.75786	+	1.01490i
$526$		0			0
$527$	−165.431	−	197.153i	−0.313912	−	0.374105i
$528$		0			0
$529$	142.745	+	809.549i	0.269840	+	1.53034i
$530$		0			0
$531$		−	104.360i		−	0.196536i
$532$		0			0
$533$	−200.354			−0.375899
$534$		0			0
$535$	−364.063	+	64.1940i	−0.680491	+	0.119989i
$536$		0			0
$537$	890.825	−	747.491i	1.65889	−	1.39198i
$538$		0			0
$539$	−106.075	+	183.728i	−0.196800	+	0.340868i
$540$		0			0
$541$	102.104	−	37.1628i	0.188732	−	0.0686928i	−0.245925	−	0.969289i	$-0.579092\pi$
$541$	102.104	−	37.1628i	0.188732	−	0.0686928i	0.434657	+	0.900596i	$0.356870\pi$
$542$		0			0
$543$	−412.690	−	714.801i	−0.760019	−	1.31639i
$544$		0			0
$545$	−984.573	−	173.607i	−1.80656	−	0.318545i
$546$		0			0
$547$	−535.005	+	637.594i	−0.978070	+	1.16562i	0.00811388	+	0.999967i	$0.497417\pi$
$547$	−535.005	+	637.594i	−0.978070	+	1.16562i	−0.986184	+	0.165652i	$0.947027\pi$
$548$		0			0
$549$	464.492	+	169.061i	0.846069	+	0.307944i
$550$		0			0
$551$	149.827	+	931.774i	0.271918	+	1.69106i
$552$		0			0
$553$	−17.4657	+	47.9867i	−0.0315836	+	0.0867752i
$554$		0			0
$555$	−1552.98	−	1303.11i	−2.79817	−	2.34794i
$556$		0			0
$557$	−35.5929	+	201.857i	−0.0639011	+	0.362401i	0.936044	+	0.351884i	$0.114459\pi$
$557$	−35.5929	+	201.857i	−0.0639011	+	0.362401i	−0.999945	+	0.0105170i	$0.996652\pi$
$558$		0			0
$559$	−513.338	+	296.376i	−0.918315	+	0.530189i
$560$		0			0
$561$	−102.326	−	281.139i	−0.182399	−	0.501138i
$562$		0			0
$563$	311.875	+	180.061i	0.553951	+	0.319824i	0.750714	−	0.660627i	$-0.229710\pi$
$563$	311.875	+	180.061i	0.553951	+	0.319824i	−0.196763	+	0.980451i	$0.563043\pi$
$564$		0			0
$565$	−79.8661	−	95.1807i	−0.141356	−	0.168461i
$566$		0			0
$567$	76.8790	+	436.002i	0.135589	+	0.768964i
$568$		0			0
$569$			191.423i			0.336420i	0.985751	+	0.168210i	$0.0537987\pi$
$569$			191.423i			0.336420i	−0.985751	+	0.168210i	$0.946201\pi$
$570$		0			0
$571$	411.860			0.721296			0.360648	−	0.932702i	$-0.382556\pi$
$571$	411.860			0.721296			0.360648	+	0.932702i	$0.382556\pi$
$572$		0			0
$573$	1210.89	−	213.513i	2.11325	−	0.372623i
$574$		0			0
$575$	780.154	−	654.627i	1.35679	−	1.13848i
$576$		0			0
$577$	−484.473	+	839.131i	−0.839641	+	1.45430i	0.0505545	+	0.998721i	$0.483901\pi$
$577$	−484.473	+	839.131i	−0.839641	+	1.45430i	−0.890195	+	0.455579i	$0.849432\pi$
$578$		0			0
$579$	300.301	−	109.300i	0.518654	−	0.188775i
$580$		0			0
$581$	−149.016	−	258.103i	−0.256481	−	0.444239i
$582$		0			0
$583$	−72.7954	−	12.8358i	−0.124863	−	0.0220168i
$584$		0			0
$585$	485.763	−	578.910i	0.830364	−	0.989590i
$586$		0			0
$587$	−694.399	−	252.741i	−1.18296	−	0.430563i	−0.325715	−	0.945468i	$-0.605605\pi$
$587$	−694.399	−	252.741i	−1.18296	−	0.430563i	−0.857247	+	0.514905i	$0.827827\pi$
$588$		0			0
$589$	−513.467	−	444.233i	−0.871761	−	0.754216i
$590$		0			0
$591$	−15.7748	+	43.3409i	−0.0266917	+	0.0733348i
$592$		0			0
$593$	437.857	+	367.406i	0.738376	+	0.619571i	0.932401	−	0.361426i	$-0.117710\pi$
$593$	437.857	+	367.406i	0.738376	+	0.619571i	−0.194025	+	0.980997i	$0.562154\pi$
$594$		0			0
$595$	−77.1106	+	437.316i	−0.129598	+	0.734985i
$596$		0			0
$597$	−339.831	+	196.202i	−0.569232	+	0.328646i
$598$		0			0
$599$	132.318	+	363.541i	0.220898	+	0.606913i	0.999795	−	0.0202389i	$-0.00644268\pi$
$599$	132.318	+	363.541i	0.220898	+	0.606913i	−0.778897	+	0.627152i	$0.784220\pi$
$600$		0			0
$601$	−687.476	−	396.915i	−1.14389	−	0.660423i	−0.196497	−	0.980504i	$-0.562957\pi$
$601$	−687.476	−	396.915i	−1.14389	−	0.660423i	−0.947390	+	0.320081i	$0.896290\pi$
$602$		0			0
$603$	61.9750	+	73.8590i	0.102778	+	0.122486i
$604$		0			0
$605$	−46.4649	−	263.515i	−0.0768014	−	0.435563i
$606$		0			0
$607$		−	306.297i		−	0.504609i	−0.967648	−	0.252304i	$-0.918812\pi$
$607$		−	306.297i		−	0.504609i	0.967648	−	0.252304i	$-0.0811884\pi$
$608$		0			0
$609$	1910.38			3.13691
$610$		0			0
$611$	641.971	−	113.197i	1.05069	−	0.185265i
$612$		0			0
$613$	−556.921	+	467.312i	−0.908516	+	0.762336i	−0.971836	−	0.235658i	$-0.924276\pi$
$613$	−556.921	+	467.312i	−0.908516	+	0.762336i	0.0633198	+	0.997993i	$0.479831\pi$
$614$		0			0
$615$	364.142	−	630.713i	0.592101	−	1.02555i
$616$		0			0
$617$	−860.598	+	313.232i	−1.39481	+	0.507670i	−0.926634	−	0.375965i	$-0.877311\pi$
$617$	−860.598	+	313.232i	−1.39481	+	0.507670i	−0.468177	+	0.883635i	$0.655089\pi$
$618$		0			0
$619$	288.193	+	499.166i	0.465579	+	0.806406i	0.999227	−	0.0393000i	$-0.0125128\pi$
$619$	288.193	+	499.166i	0.465579	+	0.806406i	−0.533649	+	0.845706i	$0.679179\pi$
$620$		0			0
$621$	−411.226	−	72.5103i	−0.662200	−	0.116764i
$622$		0			0
$623$	313.813	−	373.988i	0.503712	−	0.600301i
$624$		0			0
$625$	516.823	+	188.108i	0.826916	+	0.300973i
$626$		0			0
$627$	−384.273	−	689.417i	−0.612876	−	1.09955i
$628$		0			0
$629$	151.887	−	417.305i	0.241473	−	0.663442i
$630$		0			0
$631$	479.761	+	402.567i	0.760318	+	0.637982i	0.938210	−	0.346068i	$-0.112483\pi$
$631$	479.761	+	402.567i	0.760318	+	0.637982i	−0.177892	+	0.984050i	$0.556928\pi$
$632$		0			0
$633$	110.433	−	626.298i	0.174460	−	0.989412i
$634$		0			0
$635$	250.787	−	144.792i	0.394941	−	0.228019i
$636$		0			0
$637$	−71.5463	−	196.572i	−0.112318	−	0.308590i
$638$		0			0
$639$	77.8475	+	44.9453i	0.121827	+	0.0703369i
$640$		0			0
$641$	−385.607	−	459.549i	−0.601571	−	0.716924i	0.376214	−	0.926533i	$-0.377226\pi$
$641$	−385.607	−	459.549i	−0.601571	−	0.716924i	−0.977785	+	0.209608i	$0.932781\pi$
$642$		0			0
$643$	−29.0611	−	164.813i	−0.0451961	−	0.256320i	0.953835	−	0.300331i	$-0.0970972\pi$
$643$	−29.0611	−	164.813i	−0.0451961	−	0.256320i	−0.999031	+	0.0440117i	$0.985986\pi$
$644$		0			0
$645$		−	2154.64i		−	3.34053i
$646$		0			0
$647$	−686.345			−1.06081			−0.530405	−	0.847744i	$-0.677960\pi$
$647$	−686.345			−1.06081			−0.530405	+	0.847744i	$0.677960\pi$
$648$		0			0
$649$	−81.9171	+	14.4442i	−0.126220	+	0.0222561i
$650$		0			0
$651$	−1052.85	+	883.445i	−1.61728	+	1.35706i
$652$		0			0
$653$	−494.102	+	855.810i	−0.756665	+	1.31058i	0.187878	+	0.982192i	$0.439839\pi$
$653$	−494.102	+	855.810i	−0.756665	+	1.31058i	−0.944542	+	0.328389i	$0.893494\pi$
$654$		0			0
$655$	381.816	−	138.970i	0.582925	−	0.212167i
$656$		0			0
$657$	596.276	+	1032.78i	0.907574	+	1.57196i
$658$		0			0
$659$	473.397	+	83.4727i	0.718357	+	0.126666i	0.520865	−	0.853639i	$-0.325609\pi$
$659$	473.397	+	83.4727i	0.718357	+	0.126666i	0.197492	+	0.980305i	$0.436720\pi$
$660$		0			0
$661$	375.056	−	446.974i	0.567406	−	0.676208i	−0.403690	−	0.914896i	$-0.632273\pi$
$661$	375.056	−	446.974i	0.567406	−	0.676208i	0.971096	+	0.238687i	$0.0767171\pi$
$662$		0			0
$663$	277.212	+	100.897i	0.418117	+	0.152182i
$664$		0			0
$665$	−17.6891	+	1171.36i	−0.0266002	+	1.76144i
$666$		0			0
$667$	624.433	−	1715.61i	0.936181	−	2.57214i
$668$		0			0
$669$	467.488	+	392.269i	0.698787	+	0.586352i
$670$		0			0
$671$	68.4148	−	388.000i	0.101959	−	0.578241i
$672$		0			0
$673$	419.523	−	242.212i	0.623363	−	0.359899i	−0.154814	−	0.987944i	$-0.549478\pi$
$673$	419.523	−	242.212i	0.623363	−	0.359899i	0.778177	+	0.628045i	$0.216145\pi$
$674$		0			0
$675$	107.656	+	295.784i	0.159491	+	0.438198i
$676$		0			0
$677$	131.246	+	75.7748i	0.193864	+	0.111927i	0.593790	−	0.804620i	$-0.297631\pi$
$677$	131.246	+	75.7748i	0.193864	+	0.111927i	−0.399926	+	0.916547i	$0.630964\pi$
$678$		0			0
$679$	584.407	+	696.470i	0.860688	+	1.02573i
$680$		0			0
$681$	−260.546	−	1477.63i	−0.382593	−	2.16979i
$682$		0			0
$683$			709.380i			1.03862i	0.854585	+	0.519312i	$0.173812\pi$
$683$			709.380i			1.03862i	−0.854585	+	0.519312i	$0.826188\pi$
$684$		0			0
$685$	−707.735			−1.03319
$686$		0			0
$687$	−549.886	+	96.9597i	−0.800416	+	0.141135i
$688$		0			0
$689$	55.8338	−	46.8502i	0.0810360	−	0.0679973i
$690$		0			0
$691$	28.2069	−	48.8559i	0.0408205	−	0.0707031i	−0.844893	−	0.534935i	$-0.820336\pi$
$691$	28.2069	−	48.8559i	0.0408205	−	0.0707031i	0.885714	+	0.464232i	$0.153669\pi$
$692$		0			0
$693$	−842.497	+	306.644i	−1.21572	+	0.442487i
$694$		0			0
$695$	121.882	+	211.107i	0.175370	+	0.303750i
$696$		0			0
$697$	157.111	+	27.7030i	0.225411	+	0.0397460i
$698$		0			0
$699$	−277.582	+	330.810i	−0.397113	+	0.473261i
$700$		0			0
$701$	−1092.22	−	397.537i	−1.55809	−	0.567100i	−0.587796	−	0.809009i	$-0.700004\pi$
$701$	−1092.22	−	397.537i	−1.55809	−	0.567100i	−0.970299	+	0.241909i	$0.922226\pi$
$702$		0			0
$703$	220.837	−	1150.56i	0.314135	−	1.63664i
$704$		0			0
$705$	−810.435	+	2226.65i	−1.14955	+	3.15837i
$706$		0			0
$707$	−138.697	−	116.380i	−0.196176	−	0.164612i
$708$		0			0
$709$	−211.209	+	1197.82i	−0.297897	+	1.68946i	0.357293	+	0.933992i	$0.383700\pi$
$709$	−211.209	+	1197.82i	−0.297897	+	1.68946i	−0.655190	+	0.755464i	$0.727411\pi$
$710$		0			0
$711$	−59.9289	+	34.5999i	−0.0842881	+	0.0486638i
$712$		0			0
$713$	449.240	+	1234.28i	0.630070	+	1.73110i
$714$		0			0
$715$	−521.645	−	301.172i	−0.729573	−	0.421219i
$716$		0			0
$717$	139.747	+	166.544i	0.194905	+	0.232278i
$718$		0			0
$719$	91.4748	+	518.779i	0.127225	+	0.721529i	0.979961	+	0.199188i	$0.0638303\pi$
$719$	91.4748	+	518.779i	0.127225	+	0.721529i	−0.852736	+	0.522342i	$0.825059\pi$
$720$		0			0
$721$		−	771.319i		−	1.06979i
$722$		0			0
$723$	−21.9236			−0.0303232
$724$		0			0
$725$	−1355.33	+	238.981i	−1.86942	+	0.329629i
$726$		0			0
$727$	308.251	−	258.653i	0.424004	−	0.355782i	−0.405680	−	0.914015i	$-0.632965\pi$
$727$	308.251	−	258.653i	0.424004	−	0.355782i	0.829684	+	0.558233i	$0.188521\pi$
$728$		0			0
$729$	−531.483	+	920.556i	−0.729058	+	1.26277i
$730$		0			0
$731$	443.523	−	161.429i	0.606734	−	0.220833i
$732$		0			0
$733$	−245.885	−	425.885i	−0.335450	−	0.581016i	0.648121	−	0.761537i	$-0.275555\pi$
$733$	−245.885	−	425.885i	−0.335450	−	0.581016i	−0.983571	+	0.180521i	$0.942222\pi$
$734$		0			0
$735$	748.841	+	132.041i	1.01883	+	0.179647i
$736$		0			0
$737$	49.3974	−	58.8695i	0.0670250	−	0.0798772i
$738$		0			0
$739$	62.1621	+	22.6252i	0.0841166	+	0.0306159i	0.383736	−	0.923443i	$-0.374637\pi$
$739$	62.1621	+	22.6252i	0.0841166	+	0.0306159i	−0.299619	+	0.954059i	$0.596860\pi$
$740$		0			0
$741$	764.303	+	146.700i	1.03145	+	0.197976i
$742$		0			0
$743$	−136.920	+	376.186i	−0.184281	+	0.506307i	−0.997091	−	0.0762217i	$-0.975714\pi$
$743$	−136.920	+	376.186i	−0.184281	+	0.506307i	0.812810	+	0.582528i	$0.197937\pi$
$744$		0			0
$745$	697.504	+	585.275i	0.936246	+	0.785604i
$746$		0			0
$747$	70.1297	−	397.726i	0.0938818	−	0.532430i
$748$		0			0
$749$	−374.517	+	216.228i	−0.500023	+	0.288688i
$750$		0			0
$751$	212.950	+	585.074i	0.283555	+	0.779060i	0.996931	+	0.0782796i	$0.0249427\pi$
$751$	212.950	+	585.074i	0.283555	+	0.779060i	−0.713377	+	0.700781i	$0.752835\pi$
$752$		0			0
$753$	−1029.31	−	594.272i	−1.36694	−	0.789205i
$754$		0			0
$755$	−187.131	−	223.015i	−0.247856	−	0.295384i
$756$		0			0
$757$	−65.9084	−	373.785i	−0.0870653	−	0.493772i	−0.996892	−	0.0787829i	$-0.974897\pi$
$757$	−65.9084	−	373.785i	−0.0870653	−	0.493772i	0.909827	−	0.414989i	$-0.136214\pi$
$758$		0			0
$759$			1526.90i			2.01173i
$760$		0			0
$761$	545.257			0.716501			0.358251	−	0.933625i	$-0.383373\pi$
$761$	545.257			0.716501			0.358251	+	0.933625i	$0.383373\pi$
$762$		0			0
$763$	−1151.77	+	203.088i	−1.50952	+	0.266170i
$764$		0			0
$765$	−460.965	+	386.796i	−0.602569	+	0.505616i
$766$		0			0
$767$	41.0095	−	71.0305i	0.0534674	−	0.0926082i
$768$		0			0
$769$	717.843	−	261.273i	0.933475	−	0.339757i	0.169889	−	0.985463i	$-0.445659\pi$
$769$	717.843	−	261.273i	0.933475	−	0.339757i	0.763586	+	0.645706i	$0.223437\pi$
$770$		0			0
$771$	33.5810	+	58.1641i	0.0435552	+	0.0754398i
$772$		0			0
$773$	−157.013	−	27.6857i	−0.203122	−	0.0358159i	0.0711614	−	0.997465i	$-0.477329\pi$
$773$	−157.013	−	27.6857i	−0.203122	−	0.0358159i	−0.274283	+	0.961649i	$0.588441\pi$
$774$		0			0
$775$	636.433	−	758.472i	0.821204	−	0.978673i
$776$		0			0
$777$	−2228.51	−	811.112i	−2.86810	−	1.04390i
$778$		0			0
$779$	420.826	+	6.35503i	0.540213	+	0.00815793i
$780$		0			0
$781$	24.5049	−	67.3267i	0.0313763	−	0.0862058i
$782$		0			0
$783$	432.265	+	362.713i	0.552062	+	0.463235i
$784$		0			0
$785$	343.510	−	1948.14i	0.437592	−	2.48171i
$786$		0			0
$787$	−460.148	+	265.666i	−0.584686	+	0.337568i	−0.762993	−	0.646406i	$-0.776271\pi$
$787$	−460.148	+	265.666i	−0.584686	+	0.337568i	0.178308	+	0.983975i	$0.442938\pi$
$788$		0			0
$789$	29.7457	+	81.7257i	0.0377005	+	0.103581i
$790$		0			0
$791$	−125.876	−	72.6744i	−0.159135	−	0.0918766i
$792$		0			0
$793$	249.711	+	297.595i	0.314895	+	0.375277i
$794$		0			0
$795$	46.0062	+	260.914i	0.0578694	+	0.328194i
$796$		0			0
$797$			1080.07i			1.35517i	0.735446	+	0.677583i	$0.236973\pi$
$797$			1080.07i			1.35517i	−0.735446	+	0.677583i	$0.763027\pi$
$798$		0			0
$799$	−519.065			−0.649643
$800$		0			0
$801$	651.516	−	114.880i	0.813378	−	0.143420i
$802$		0			0
$803$	728.147	−	610.988i	0.906783	−	0.760881i
$804$		0			0
$805$	1133.16	−	1962.69i	1.40765	−	2.43812i
$806$		0			0
$807$	788.981	−	287.165i	0.977671	−	0.355843i
$808$		0			0
$809$	108.858	+	188.548i	0.134559	+	0.233063i	0.925429	−	0.378921i	$-0.123705\pi$
$809$	108.858	+	188.548i	0.134559	+	0.233063i	−0.790870	+	0.611984i	$0.790372\pi$
$810$		0			0
$811$	−281.379	−	49.6147i	−0.346953	−	0.0611772i	−0.00254373	−	0.999997i	$-0.500810\pi$
$811$	−281.379	−	49.6147i	−0.346953	−	0.0611772i	−0.344409	+	0.938820i	$0.611921\pi$
$812$		0			0
$813$	−288.643	+	343.991i	−0.355034	+	0.423114i
$814$		0			0
$815$	547.337	+	199.214i	0.671579	+	0.244435i
$816$		0			0
$817$	1087.62	−	606.228i	1.33124	−	0.742017i
$818$		0			0
$819$	302.361	−	830.729i	0.369183	−	1.01432i
$820$		0			0
$821$	614.162	+	515.343i	0.748065	+	0.627701i	0.934990	−	0.354673i	$-0.115408\pi$
$821$	614.162	+	515.343i	0.748065	+	0.627701i	−0.186925	+	0.982374i	$0.559852\pi$
$822$		0			0
$823$	173.536	−	984.174i	0.210858	−	1.19584i	−0.677092	−	0.735898i	$-0.736760\pi$
$823$	173.536	−	984.174i	0.210858	−	1.19584i	0.887951	−	0.459939i	$-0.152129\pi$
$824$		0			0
$825$	996.782	−	575.492i	1.20822	−	0.697566i
$826$		0			0
$827$	86.4404	+	237.493i	0.104523	+	0.287174i	0.980919	−	0.194417i	$-0.0622814\pi$
$827$	86.4404	+	237.493i	0.104523	+	0.287174i	−0.876396	+	0.481591i	$0.840059\pi$
$828$		0			0
$829$	66.6007	+	38.4520i	0.0803386	+	0.0463835i	0.539631	−	0.841902i	$-0.318564\pi$
$829$	66.6007	+	38.4520i	0.0803386	+	0.0463835i	−0.459293	+	0.888285i	$0.651897\pi$
$830$		0			0
$831$	−1005.22	−	1197.97i	−1.20965	−	1.44160i
$832$		0			0
$833$	28.9243	+	164.038i	0.0347231	+	0.196924i
$834$		0			0
$835$			467.553i			0.559944i
$836$		0			0
$837$	−405.965			−0.485024
$838$		0			0
$839$	612.719	−	108.039i	0.730297	−	0.128771i	0.203878	−	0.978996i	$-0.434645\pi$
$839$	612.719	−	108.039i	0.730297	−	0.128771i	0.526419	+	0.850225i	$0.323534\pi$
$840$		0			0
$841$	−1245.72	+	1045.29i	−1.48124	+	1.24291i
$842$		0			0
$843$	915.499	−	1585.69i	1.08600	−	1.88101i
$844$		0			0
$845$	−594.830	+	216.500i	−0.703941	+	0.256213i
$846$		0			0
$847$	−156.510	−	271.083i	−0.184781	−	0.320050i
$848$		0			0
$849$	1662.38	+	293.122i	1.95804	+	0.345255i
$850$		0			0
$851$	−1456.84	+	1736.19i	−1.71191	+	2.04018i
$852$		0			0
$853$	−789.623	−	287.399i	−0.925701	−	0.336928i	−0.165197	−	0.986261i	$-0.552826\pi$
$853$	−789.623	−	287.399i	−0.925701	−	0.336928i	−0.760504	+	0.649333i	$0.775048\pi$
$854$		0			0
$855$	−1038.66	+	1200.54i	−1.21481	+	1.40414i
$856$		0			0
$857$	−283.804	+	779.746i	−0.331160	+	0.909856i	0.656650	+	0.754195i	$0.271973\pi$
$857$	−283.804	+	779.746i	−0.331160	+	0.909856i	−0.987811	+	0.155661i	$0.950249\pi$
$858$		0			0
$859$	−222.494	−	186.695i	−0.259015	−	0.217339i	0.504028	−	0.863688i	$-0.331851\pi$
$859$	−222.494	−	186.695i	−0.259015	−	0.217339i	−0.763043	+	0.646348i	$0.776295\pi$
$860$		0			0
$861$	147.941	−	839.014i	0.171824	−	0.974464i
$862$		0			0
$863$	934.482	−	539.523i	1.08283	−	0.625172i	0.151171	−	0.988508i	$-0.451696\pi$
$863$	934.482	−	539.523i	1.08283	−	0.625172i	0.931658	+	0.363336i	$0.118362\pi$
$864$		0			0
$865$	−650.015	−	1785.90i	−0.751462	−	2.06462i
$866$		0			0
$867$	930.005	+	536.938i	1.07267	+	0.619306i
$868$		0			0
$869$	35.4536	+	42.2519i	0.0407981	+	0.0486213i
$870$		0			0
$871$	13.1582	+	74.6241i	0.0151071	+	0.0856764i
$872$		0			0
$873$			1232.02i			1.41125i
$874$		0			0
$875$	−166.919			−0.190765
$876$		0			0
$877$	481.531	−	84.9069i	0.549066	−	0.0968152i	0.107769	−	0.994176i	$-0.465629\pi$
$877$	481.531	−	84.9069i	0.549066	−	0.0968152i	0.441298	+	0.897361i	$0.354518\pi$
$878$		0			0
$879$	−555.091	+	465.777i	−0.631503	+	0.529894i
$880$		0			0
$881$	−184.835	+	320.143i	−0.209801	+	0.363386i	−0.951652	−	0.307179i	$-0.900615\pi$
$881$	−184.835	+	320.143i	−0.209801	+	0.363386i	0.741851	+	0.670565i	$0.233948\pi$
$882$		0			0
$883$	42.9539	−	15.6339i	0.0486454	−	0.0177055i	−0.317583	−	0.948231i	$-0.602871\pi$
$883$	42.9539	−	15.6339i	0.0486454	−	0.0177055i	0.366228	+	0.930525i	$0.380649\pi$
$884$		0			0
$885$	149.069	+	258.195i	0.168439	+	0.291745i
$886$		0			0
$887$	−831.091	−	146.544i	−0.936968	−	0.165213i	−0.315743	−	0.948845i	$-0.602254\pi$
$887$	−831.091	−	146.544i	−0.936968	−	0.165213i	−0.621225	+	0.783632i	$0.713365\pi$
$888$		0			0
$889$	217.750	−	259.505i	0.244939	−	0.291906i
$890$		0			0
$891$	449.346	+	163.549i	0.504317	+	0.183556i
$892$		0			0
$893$	−1351.99	+	217.397i	−1.51399	+	0.243446i
$894$		0			0
$895$	−637.613	+	1751.83i	−0.712417	+	1.95735i
$896$		0			0
$897$	−1153.34	−	967.764i	−1.28577	−	1.07889i
$898$		0			0
$899$	308.222	−	1748.01i	0.342849	−	1.94440i
$900$		0			0
$901$	−50.2610	+	29.0182i	−0.0557836	+	0.0322067i
$902$		0			0
$903$	−862.072	−	2368.52i	−0.954675	−	2.62295i
$904$		0			0
$905$	1145.91	+	661.594i	1.26620	+	0.731043i
$906$		0			0
$907$	1118.35	+	1332.80i	1.23302	+	1.46946i	0.833301	+	0.552820i	$0.186448\pi$
$907$	1118.35	+	1332.80i	1.23302	+	1.46946i	0.399720	+	0.916637i	$0.369107\pi$
$908$		0			0
$909$	−42.6043	−	241.621i	−0.0468694	−	0.265809i
$910$		0			0
$911$			105.673i			0.115997i	0.998317	+	0.0579986i	$0.0184719\pi$
$911$			105.673i			0.115997i	−0.998317	+	0.0579986i	$0.981528\pi$
$912$		0			0
$913$	−321.899			−0.352573
$914$		0			0
$915$	−1390.67	+	245.213i	−1.51986	+	0.267992i
$916$		0			0
$917$	364.115	−	305.529i	0.397072	−	0.333183i
$918$		0			0
$919$	271.823	−	470.812i	0.295782	−	0.512309i	−0.679385	−	0.733782i	$-0.737753\pi$
$919$	271.823	−	470.812i	0.295782	−	0.512309i	0.975166	+	0.221473i	$0.0710865\pi$
$920$		0			0
$921$	1679.95	−	611.451i	1.82405	−	0.663899i
$922$		0			0
$923$	35.3234	+	61.1820i	0.0382702	+	0.0662860i
$924$		0			0
$925$	1682.50	+	296.669i	1.81891	+	0.320724i
$926$		0			0
$927$	671.849	−	800.678i	0.724756	−	0.863731i
$928$		0			0
$929$	−630.832	−	229.604i	−0.679044	−	0.247152i	−0.0206070	−	0.999788i	$-0.506560\pi$
$929$	−630.832	−	229.604i	−0.679044	−	0.247152i	−0.658437	+	0.752636i	$0.728782\pi$
$930$		0			0
$931$	144.041	+	415.151i	0.154717	+	0.445919i
$932$		0			0
$933$	−104.992	+	288.464i	−0.112532	+	0.309179i
$934$		0			0
$935$	367.414	+	308.297i	0.392956	+	0.329729i
$936$		0			0
$937$	−170.604	+	967.542i	−0.182075	+	1.03260i	0.747582	+	0.664169i	$0.231215\pi$
$937$	−170.604	+	967.542i	−0.182075	+	1.03260i	−0.929657	+	0.368427i	$0.879897\pi$
$938$		0			0
$939$	1471.05	−	849.314i	1.56662	−	0.904487i
$940$		0			0
$941$	310.765	+	853.821i	0.330250	+	0.907355i	0.988046	+	0.154159i	$0.0492667\pi$
$941$	310.765	+	853.821i	0.330250	+	0.907355i	−0.657796	+	0.753196i	$0.728511\pi$
$942$		0			0
$943$	−705.119	−	407.101i	−0.747741	−	0.431708i
$944$		0			0
$945$	450.246	+	536.582i	0.476451	+	0.567812i
$946$		0			0
$947$	−314.903	−	1785.91i	−0.332527	−	1.88586i	−0.450400	−	0.892827i	$-0.648719\pi$
$947$	−314.903	−	1785.91i	−0.332527	−	1.88586i	0.117873	−	0.993029i	$-0.462392\pi$
$948$		0			0
$949$			937.251i			0.987620i
$950$		0			0
$951$	863.572			0.908068
$952$		0			0
$953$	1369.78	−	241.528i	1.43733	−	0.253440i	0.599940	−	0.800045i	$-0.295191\pi$
$953$	1369.78	−	241.528i	1.43733	−	0.253440i	0.837391	+	0.546605i	$0.184080\pi$
$954$		0			0
$955$	−1510.00	+	1267.04i	−1.58115	+	1.32674i
$956$		0			0
$957$	1031.68	−	1786.93i	1.07804	−	1.86722i
$958$		0			0
$959$	−777.988	+	283.165i	−0.811250	+	0.295271i
$960$		0			0
$961$	157.992	+	273.650i	0.164404	+	0.284756i
$962$		0			0
$963$	−577.116	−	101.761i	−0.599289	−	0.105671i
$964$		0			0
$965$	−329.310	+	392.456i	−0.341254	+	0.406691i
$966$		0			0
$967$	−781.549	−	284.460i	−0.808220	−	0.294168i	−0.0953317	−	0.995446i	$-0.530391\pi$
$967$	−781.549	−	284.460i	−0.808220	−	0.294168i	−0.712888	+	0.701278i	$0.752613\pi$
$968$		0			0
$969$	−579.058	−	220.717i	−0.597583	−	0.227779i
$970$		0			0
$971$	−508.037	+	1395.82i	−0.523210	+	1.43751i	0.343718	+	0.939073i	$0.388314\pi$
$971$	−508.037	+	1395.82i	−0.523210	+	1.43751i	−0.866928	+	0.498434i	$0.833909\pi$
$972$		0			0
$973$	218.445	+	183.297i	0.224506	+	0.188383i
$974$		0			0
$975$	−197.075	+	1117.67i	−0.202128	+	1.14632i
$976$		0			0
$977$	−545.117	+	314.723i	−0.557950	+	0.322133i	−0.752322	−	0.658795i	$-0.771066\pi$
$977$	−545.117	+	314.723i	−0.557950	+	0.322133i	0.194372	+	0.980928i	$0.437733\pi$
$978$		0			0
$979$	−180.348	−	495.503i	−0.184217	−	0.506132i
$980$		0			0
$981$	−1372.51	−	792.416i	−1.39909	−	0.807764i
$982$		0			0
$983$	859.696	+	1024.55i	0.874564	+	1.04226i	0.998749	+	0.0500053i	$0.0159238\pi$
$983$	859.696	+	1024.55i	0.874564	+	1.04226i	−0.124185	+	0.992259i	$0.539632\pi$
$984$		0			0
$985$	−12.8395	−	72.8166i	−0.0130351	−	0.0739255i
$986$		0			0
$987$			2771.93i			2.80844i
$988$		0			0
$989$	−2408.83			−2.43562
$990$		0			0
$991$	1022.04	−	180.213i	1.03132	−	0.181850i	0.367720	−	0.929936i	$-0.380138\pi$
$991$	1022.04	−	180.213i	1.03132	−	0.181850i	0.663601	+	0.748087i	$0.269027\pi$
$992$		0			0
$993$	389.877	−	327.145i	0.392625	−	0.329451i
$994$		0			0
$995$	314.536	−	544.792i	0.316116	−	0.547530i
$996$		0			0
$997$	−296.735	+	108.003i	−0.297628	+	0.108328i	−0.486518	−	0.873670i	$-0.661733\pi$
$997$	−296.735	+	108.003i	−0.297628	+	0.108328i	0.188890	+	0.981998i	$0.439511\pi$
$998$		0			0
$999$	−350.248	−	606.648i	−0.350599	−	0.607255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.j.a.53.1	yes	18
4.3	odd	2		304.3.z.b.129.3		18
19.9	even	9		1444.3.c.c.721.17		18
19.10	odd	18		1444.3.c.c.721.2		18
19.14	odd	18	inner	76.3.j.a.33.1	✓	18
76.71	even	18		304.3.z.b.33.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.j.a.33.1	✓	18	19.14	odd	18	inner
76.3.j.a.53.1	yes	18	1.1	even	1	trivial
304.3.z.b.33.3		18	76.71	even	18
304.3.z.b.129.3		18	4.3	odd	2
1444.3.c.c.721.2		18	19.10	odd	18
1444.3.c.c.721.17		18	19.9	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)

\(f(q)\)	\(=\)	\(q+(-4.45984 + 0.786390i) q^{3} +(5.56146 - 4.66662i) q^{5} +(4.24641 - 7.35499i) q^{7} +(10.8145 - 3.93617i) q^{9} +O(q^{10})\)	\(q+(-4.45984 + 0.786390i) q^{3} +(5.56146 - 4.66662i) q^{5} +(4.24641 - 7.35499i) q^{7} +(10.8145 - 3.93617i) q^{9} +(-4.58648 - 7.94401i) q^{11} +(8.90742 + 1.57062i) q^{13} +(-21.1334 + 25.1859i) q^{15} +(-6.76774 - 2.46325i) q^{17} +(-18.6594 - 3.58147i) q^{19} +(-13.1544 + 36.1414i) q^{21} +(28.1571 + 23.6266i) q^{23} +(4.81130 - 27.2863i) q^{25} +(-9.83845 + 5.68023i) q^{27} +(-16.9884 - 46.6752i) q^{29} +(30.9473 + 17.8675i) q^{31} +(26.7020 + 31.8222i) q^{33} +(-10.7067 - 60.7209i) q^{35} +61.6609i q^{37} -40.9608 q^{39} +(-21.8147 + 3.84652i) q^{41} +(-50.2026 + 42.1250i) q^{43} +(41.7760 - 72.3581i) q^{45} +(67.7251 - 24.6499i) q^{47} +(-11.5639 - 20.0293i) q^{49} +(32.1201 + 5.66364i) q^{51} +(5.17977 - 6.17301i) q^{53} +(-62.5792 - 22.7770i) q^{55} +(86.0344 + 1.29923i) q^{57} +(3.10146 - 8.52118i) q^{59} +(32.9022 + 27.6082i) q^{61} +(16.9724 - 96.2553i) q^{63} +(56.8677 - 32.8326i) q^{65} +(2.86536 + 7.87251i) q^{67} +(-144.156 - 83.2284i) q^{69} +(5.02065 + 5.98338i) q^{71} +(17.9939 + 102.049i) q^{73} +125.476i q^{75} -77.9041 q^{77} +(-5.92154 + 1.04413i) q^{79} +(-39.9337 + 33.5084i) q^{81} +(17.5461 - 30.3907i) q^{83} +(-49.1336 + 17.8832i) q^{85} +(112.470 + 194.804i) q^{87} +(56.6113 + 9.98210i) q^{89} +(49.3764 - 58.8445i) q^{91} +(-152.071 - 55.3493i) q^{93} +(-120.487 + 67.1581i) q^{95} +(-36.6141 + 100.596i) q^{97} +(-80.8695 - 67.8576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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