LMFDB - Embedded newform 76.3.j.a.33.1

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			33.1
Root			$3.84460i$ of defining polynomial
Character	$\chi$	$=$	76.33
Dual form			76.3.j.a.53.1

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.45984	−	0.786390i	−1.48661	−	0.262130i	−0.629396	−	0.777085i	$-0.716698\pi$
$3$	−4.45984	−	0.786390i	−1.48661	−	0.262130i	−0.857217	+	0.514955i	$0.827809\pi$
$4$		0			0
$5$	5.56146	+	4.66662i	1.11229	+	0.933324i	0.998190	−	0.0601450i	$-0.0191563\pi$
$5$	5.56146	+	4.66662i	1.11229	+	0.933324i	0.114103	+	0.993469i	$0.463601\pi$
$6$		0			0
$7$	4.24641	+	7.35499i	0.606629	+	1.05071i	0.991792	+	0.127864i	$0.0408121\pi$
$7$	4.24641	+	7.35499i	0.606629	+	1.05071i	−0.385162	+	0.922849i	$0.625855\pi$
$8$		0			0
$9$	10.8145	+	3.93617i	1.20161	+	0.437352i
$10$		0			0
$11$	−4.58648	+	7.94401i	−0.416952	+	0.722183i	−0.995631	−	0.0933728i	$-0.970235\pi$
$11$	−4.58648	+	7.94401i	−0.416952	+	0.722183i	0.578679	+	0.815555i	$0.303568\pi$
$12$		0			0
$13$	8.90742	−	1.57062i	0.685186	−	0.120817i	0.179791	−	0.983705i	$-0.442458\pi$
$13$	8.90742	−	1.57062i	0.685186	−	0.120817i	0.505395	+	0.862888i	$0.331347\pi$
$14$		0			0
$15$	−21.1334	−	25.1859i	−1.40890	−	1.67906i
$16$		0			0
$17$	−6.76774	+	2.46325i	−0.398102	+	0.144897i	−0.533310	−	0.845920i	$-0.679052\pi$
$17$	−6.76774	+	2.46325i	−0.398102	+	0.144897i	0.135208	+	0.990817i	$0.456830\pi$
$18$		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	0.225628	−	0.974213i	$-0.427557\pi$
$23$	28.1571	−	23.6266i	1.22422	−	1.02724i	0.998593	−	0.0530300i	$-0.0168879\pi$
$24$		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	0.192286	+	0.981339i	$0.438410\pi$
$29$	−16.9884	+	46.6752i	−0.585806	+	1.60949i	−0.778092	+	0.628150i	$0.783813\pi$
$30$		0			0
$31$	30.9473	−	17.8675i	0.998301	−	0.576370i	0.0905562	−	0.995891i	$-0.471136\pi$
$31$	30.9473	−	17.8675i	0.998301	−	0.576370i	0.907745	+	0.419522i	$0.137802\pi$
$32$		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	$-0.686474\pi$
$37$		−	61.6609i		−	1.66651i	0.552888	−	0.833256i	$-0.313526\pi$
$38$		0			0
$39$	−40.9608			−1.05028
$40$		0			0
$41$	−21.8147	−	3.84652i	−0.532066	−	0.0938177i	−0.0988410	−	0.995103i	$-0.531514\pi$
$41$	−21.8147	−	3.84652i	−0.532066	−	0.0938177i	−0.433225	+	0.901286i	$0.642625\pi$
$42$		0			0
$43$	−50.2026	−	42.1250i	−1.16750	−	0.979651i	−0.167522	−	0.985868i	$-0.553577\pi$
$43$	−50.2026	−	42.1250i	−1.16750	−	0.979651i	−0.999981	+	0.00621716i	$0.998021\pi$
$44$		0			0
$45$	41.7760	+	72.3581i	0.928355	+	1.60796i
$46$		0			0
$47$	67.7251	+	24.6499i	1.44096	+	0.524466i	0.940051	−	0.341034i	$-0.110777\pi$
$47$	67.7251	+	24.6499i	1.44096	+	0.524466i	0.500908	+	0.865500i	$0.332999\pi$
$48$		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	0.812693	−	0.582692i	$-0.198000\pi$
$53$	5.17977	+	6.17301i	0.0977316	+	0.116472i	−0.714962	+	0.699163i	$0.753556\pi$
$54$		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	0.963197	−	0.268795i	$-0.0866255\pi$
$59$	3.10146	+	8.52118i	0.0525671	+	0.144427i	−0.910630	+	0.413222i	$0.864403\pi$
$60$		0			0
$61$	32.9022	−	27.6082i	0.539380	−	0.452594i	−0.331946	−	0.943298i	$-0.607705\pi$
$61$	32.9022	−	27.6082i	0.539380	−	0.452594i	0.871326	+	0.490705i	$0.163261\pi$
$62$		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	−0.916471	−	0.400101i	$-0.868975\pi$
$67$	2.86536	−	7.87251i	0.0427666	−	0.117500i	0.959238	+	0.282601i	$0.0911972\pi$
$68$		0			0
$69$	−144.156	+	83.2284i	−2.08921	+	1.20621i
$70$		0			0
$71$	5.02065	−	5.98338i	0.0707134	−	0.0842729i	−0.729528	−	0.683951i	$-0.760260\pi$
$71$	5.02065	−	5.98338i	0.0707134	−	0.0842729i	0.800241	+	0.599678i	$0.204705\pi$
$72$		0			0
$73$	17.9939	−	102.049i	0.246492	−	1.39793i	−0.570509	−	0.821291i	$-0.693254\pi$
$73$	17.9939	−	102.049i	0.246492	−	1.39793i	0.817002	−	0.576636i	$-0.195635\pi$
$74$		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	0.136044	−	0.990703i	$-0.456561\pi$
$79$	−5.92154	−	1.04413i	−0.0749563	−	0.0132168i	−0.211001	+	0.977486i	$0.567672\pi$
$80$		0			0
$81$	−39.9337	−	33.5084i	−0.493009	−	0.413684i
$82$		0			0
$83$	17.5461	+	30.3907i	0.211399	+	0.366153i	0.952152	−	0.305623i	$-0.0988648\pi$
$83$	17.5461	+	30.3907i	0.211399	+	0.366153i	−0.740754	+	0.671777i	$0.765532\pi$
$84$		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	0.153697	−	0.988118i	$-0.450882\pi$
$89$	56.6113	−	9.98210i	0.636082	−	0.112158i	0.482385	+	0.875960i	$0.339771\pi$
$90$		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	−0.972404	−	0.233305i	$-0.925046\pi$
$97$	−36.6141	−	100.596i	−0.377465	−	1.03708i	0.594939	−	0.803771i	$-0.297176\pi$
$98$		0			0
$99$	−80.8695	+	67.8576i	−0.816864	+	0.685430i
$100$		0			0
$101$	3.70196	+	20.9948i	0.0366530	+	0.207870i	0.997634	−	0.0687436i	$-0.0218990\pi$
$101$	3.70196	+	20.9948i	0.0366530	+	0.207870i	−0.960981	+	0.276613i	$0.910788\pi$
$102$		0			0
$103$	78.6526	+	45.4101i	0.763617	+	0.440875i	0.830593	−	0.556880i	$-0.188002\pi$
$103$	78.6526	+	45.4101i	0.763617	+	0.440875i	−0.0669756	+	0.997755i	$0.521335\pi$
$104$		0			0
$105$	95.5006	−	262.386i	0.909529	−	2.49891i
$106$		0			0
$107$	−44.0981	+	25.4601i	−0.412132	+	0.237945i	−0.691705	−	0.722180i	$-0.743140\pi$
$107$	−44.0981	+	25.4601i	−0.412132	+	0.237945i	0.279573	+	0.960124i	$0.409807\pi$
$108$		0			0
$109$	−88.5175	+	105.491i	−0.812087	+	0.967808i	−0.999896	−	0.0143979i	$-0.995417\pi$
$109$	−88.5175	+	105.491i	−0.812087	+	0.967808i	0.187809	+	0.982206i	$0.439861\pi$
$110$		0			0
$111$	−48.4895	+	274.998i	−0.436843	+	2.47746i
$112$		0			0
$113$			17.1143i			0.151454i	0.997129	+	0.0757271i	$0.0241278\pi$
$113$			17.1143i			0.151454i	−0.997129	+	0.0757271i	$0.975872\pi$
$114$		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	−0.0168409	−	0.999858i	$-0.505361\pi$
$127$	39.2818	−	6.92644i	0.309305	−	0.0545389i	0.326146	+	0.945319i	$0.394250\pi$
$128$		0			0
$129$	190.769	+	227.350i	1.47883	+	1.76240i
$130$		0			0
$131$	52.5919	−	19.1419i	0.401465	−	0.146121i	−0.133393	−	0.991063i	$-0.542587\pi$
$131$	52.5919	−	19.1419i	0.401465	−	0.146121i	0.534858	+	0.844942i	$0.320365\pi$
$132$		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	−0.873275	−	0.487228i	$-0.838008\pi$
$137$	−74.6775	+	62.6619i	−0.545091	+	0.457386i	0.328184	+	0.944614i	$0.393564\pi$
$138$		0			0
$139$	−5.83051	−	33.0664i	−0.0419461	−	0.237888i	0.956625	−	0.291321i	$-0.0940948\pi$
$139$	−5.83051	−	33.0664i	−0.0419461	−	0.237888i	−0.998571	+	0.0534329i	$0.982984\pi$
$140$		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	−0.820261	−	0.571990i	$-0.806172\pi$
$149$	21.7785	−	123.512i	0.146164	−	0.828939i	0.966425	−	0.256949i	$-0.0827173\pi$
$150$		0			0
$151$			40.1000i			0.265563i	0.991145	+	0.132781i	$0.0423908\pi$
$151$			40.1000i			0.265563i	−0.991145	+	0.132781i	$0.957609\pi$
$152$		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	0.984194	+	0.177093i	$0.0566693\pi$
$157$	208.732	+	175.147i	1.32950	+	1.11558i	0.345306	+	0.938490i	$0.387775\pi$
$158$		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	−0.716338	−	0.697753i	$-0.754183\pi$
$163$	40.1147	−	69.4807i	0.246103	−	0.426262i	0.962441	+	0.271491i	$0.0875166\pi$
$164$		0			0
$165$	297.005	−	52.3699i	1.80003	−	0.317394i
$166$		0			0
$167$	−41.3965	−	49.3344i	−0.247883	−	0.295416i	0.627727	−	0.778433i	$-0.283985\pi$
$167$	−41.3965	−	49.3344i	−0.247883	−	0.295416i	−0.875611	+	0.483017i	$0.839541\pi$
$168$		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	0.873225	+	0.487318i	$0.162025\pi$
$173$	89.5340	+	245.993i	0.517538	+	1.42192i	−0.355687	+	0.934605i	$0.615753\pi$
$174$		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	−0.272788	−	0.962074i	$-0.587946\pi$
$179$	−222.383	−	128.393i	−1.24236	−	0.717278i	−0.969575	+	0.244796i	$0.921279\pi$
$180$		0			0
$181$	62.3359	−	171.267i	0.344397	−	0.946224i	−0.639705	−	0.768621i	$-0.720943\pi$
$181$	62.3359	−	171.267i	0.344397	−	0.946224i	0.984102	−	0.177603i	$-0.0568344\pi$
$182$		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	−0.00931732	−	0.999957i	$-0.502966\pi$
$193$	−69.4951	−	12.2539i	−0.360078	−	0.0634915i	−0.350761	+	0.936465i	$0.614077\pi$
$194$		0			0
$195$	−227.802	−	191.148i	−1.16821	−	0.980248i
$196$		0			0
$197$	5.09230	+	8.82012i	0.0258492	+	0.0447722i	0.878661	−	0.477447i	$-0.158438\pi$
$197$	5.09230	+	8.82012i	0.0258492	+	0.0447722i	−0.852811	+	0.522219i	$0.825104\pi$
$198$		0			0
$199$	81.4237	+	29.6358i	0.409164	+	0.148924i	0.538398	−	0.842690i	$-0.319030\pi$
$199$	81.4237	+	29.6358i	0.409164	+	0.148924i	−0.129234	+	0.991614i	$0.541252\pi$
$200$		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	0.772321	−	0.635232i	$-0.219096\pi$
$211$	−48.0301	−	131.962i	−0.227631	−	0.625410i	−0.999952	+	0.00982217i	$0.996873\pi$
$212$		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	−0.924456	−	0.381289i	$-0.875480\pi$
$223$	−86.6197	+	103.229i	−0.388429	+	0.462912i	0.536027	+	0.844201i	$0.319925\pi$
$224$		0			0
$225$	−55.3713	+	314.026i	−0.246095	+	1.39567i
$226$		0			0
$227$		−	331.319i		−	1.45955i	−0.683685	−	0.729777i	$-0.739624\pi$
$227$		−	331.319i		−	1.45955i	0.683685	−	0.729777i	$-0.260376\pi$
$228$		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	0.785942	−	0.618300i	$-0.212179\pi$
$233$	73.0483	+	61.2948i	0.313512	+	0.263068i	−0.472430	+	0.881368i	$0.656623\pi$
$234$		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	−0.911863	−	0.410494i	$-0.865356\pi$
$239$	−24.0036	+	41.5754i	−0.100433	+	0.173956i	0.811430	+	0.584450i	$0.198690\pi$
$240$		0			0
$241$	4.76756	−	0.840650i	0.0197824	−	0.00348817i	−0.163748	−	0.986502i	$-0.552358\pi$
$241$	4.76756	−	0.840650i	0.0197824	−	0.00348817i	0.183531	+	0.983014i	$0.441247\pi$
$242$		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	−0.147449	−	0.989070i	$-0.547106\pi$
$251$	201.049	−	168.700i	0.800991	−	0.672111i	0.948439	+	0.316959i	$0.102662\pi$
$252$		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	−0.949170	−	0.314765i	$-0.898074\pi$
$257$	−5.07233	+	13.9361i	−0.0197367	+	0.0542262i	0.929433	+	0.368991i	$0.120297\pi$
$258$		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	−0.990491	−	0.137576i	$-0.956069\pi$
$263$	−3.33484	+	18.9128i	−0.0126800	+	0.0719119i	0.977811	+	0.209488i	$0.0671798\pi$
$264$		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	−0.176365	−	0.984325i	$-0.556434\pi$
$269$	−182.585	−	32.1946i	−0.678753	−	0.119683i	−0.502388	+	0.864642i	$0.667545\pi$
$270$		0			0
$271$	75.9591	+	63.7372i	0.280292	+	0.235193i	0.772085	−	0.635519i	$-0.219214\pi$
$271$	75.9591	+	63.7372i	0.280292	+	0.235193i	−0.491793	+	0.870712i	$0.663658\pi$
$272$		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	−0.365536	−	0.930797i	$-0.619114\pi$
$277$	172.661	−	299.058i	0.623326	−	1.07963i	0.988862	−	0.148836i	$-0.0475525\pi$
$278$		0			0
$279$	405.010	−	71.4142i	1.45165	−	0.255965i
$280$		0			0
$281$	−259.889	−	309.723i	−0.924871	−	1.10222i	−0.994510	−	0.104646i	$-0.966629\pi$
$281$	−259.889	−	309.723i	−0.924871	−	1.10222i	0.0696386	−	0.997572i	$-0.477815\pi$
$282$		0			0
$283$	−350.264	+	127.486i	−1.23768	+	0.450480i	−0.876222	−	0.481908i	$-0.839944\pi$
$283$	−350.264	+	127.486i	−1.23768	+	0.450480i	−0.361461	+	0.932387i	$0.617722\pi$
$284$		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	0.717469	−	0.696590i	$-0.245300\pi$
$293$	138.571	+	80.0042i	0.472939	+	0.273052i	−0.244530	+	0.969642i	$0.578634\pi$
$294$		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	−0.500178	−	0.865923i	$-0.666732\pi$
$307$	−388.771	−	68.5508i	−1.26635	−	0.223292i	−0.766176	+	0.642630i	$0.777843\pi$
$308$		0			0
$309$	−315.068	−	264.373i	−1.01964	−	0.855577i
$310$		0			0
$311$	33.8929	+	58.7042i	0.108980	+	0.188759i	0.915357	−	0.402642i	$-0.131908\pi$
$311$	33.8929	+	58.7042i	0.108980	+	0.188759i	−0.806377	+	0.591402i	$0.798575\pi$
$312$		0			0
$313$	−352.465	−	128.287i	−1.12609	−	0.409862i	−0.289217	−	0.957264i	$-0.593395\pi$
$313$	−352.465	−	128.287i	−1.12609	−	0.409862i	−0.836870	+	0.547402i	$0.815617\pi$
$314$		0			0
$315$	−354.796	+	614.524i	−1.12634	+	1.95087i
$316$		0			0
$317$	−187.794	+	33.1132i	−0.592411	+	0.104458i	−0.461813	−	0.886977i	$-0.652801\pi$
$317$	−187.794	+	33.1132i	−0.592411	+	0.104458i	−0.130598	+	0.991435i	$0.541690\pi$
$318$		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	0.345722	−	0.938337i	$-0.387634\pi$
$331$	−97.3276	−	56.1921i	−0.294041	−	0.169765i	−0.639763	+	0.768572i	$0.720967\pi$
$332$		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	−0.910416	−	0.413694i	$-0.864238\pi$
$337$	−116.236	+	138.525i	−0.344915	+	0.411054i	0.565501	+	0.824748i	$0.308683\pi$
$338$		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	0.944339	−	0.328973i	$-0.106703\pi$
$347$	272.168	+	228.376i	0.784347	+	0.658145i	−0.159992	+	0.987118i	$0.551147\pi$
$348$		0			0
$349$	−7.86775	−	13.6273i	−0.0225437	−	0.0390468i	0.854533	−	0.519396i	$-0.173843\pi$
$349$	−7.86775	−	13.6273i	−0.0225437	−	0.0390468i	−0.877077	+	0.480350i	$0.840510\pi$
$350$		0			0
$351$	−96.5566	−	35.1437i	−0.275090	−	0.100125i
$352$		0			0
$353$	79.2116	−	137.199i	0.224396	−	0.388665i	−0.731742	−	0.681581i	$-0.761293\pi$
$353$	79.2116	−	137.199i	0.224396	−	0.388665i	0.956138	+	0.292917i	$0.0946259\pi$
$354$		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	−0.976153	−	0.217085i	$-0.930345\pi$
$359$	−568.796	+	207.025i	−1.58439	+	0.576671i	−0.608237	+	0.793756i	$0.708123\pi$
$360$		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	−0.882176	−	0.470920i	$-0.843922\pi$
$367$	−78.6356	−	445.965i	−0.214266	−	1.21516i	0.667910	−	0.744242i	$-0.267189\pi$
$368$		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	0.543393	−	0.839479i	$-0.317139\pi$
$373$	575.203	−	332.094i	1.54210	−	0.890331i	0.998706	−	0.0508527i	$-0.0161939\pi$
$374$		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	$0.325251\pi$
$379$			646.614i			1.70610i	−0.521826	+	0.853052i	$0.674749\pi$
$380$		0			0
$381$	−180.637			−0.474114
$382$		0			0
$383$	194.765	+	34.3423i	0.508524	+	0.0896665i	0.422023	−	0.906585i	$-0.361320\pi$
$383$	194.765	+	34.3423i	0.508524	+	0.0896665i	0.0865013	+	0.996252i	$0.472431\pi$
$384$		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	0.154142	−	0.988049i	$-0.450739\pi$
$389$	−141.162	−	51.3788i	−0.362885	−	0.132079i	−0.517026	+	0.855970i	$0.672961\pi$
$390$		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	−0.934892	−	0.354933i	$-0.884504\pi$
$397$	−564.897	+	205.606i	−1.42291	+	0.517898i	−0.488022	+	0.872831i	$0.662281\pi$
$398$		0			0
$399$	374.893	+	627.265i	0.939580	+	1.57209i
$400$		0			0
$401$	251.842	+	691.930i	0.628035	+	1.72551i	0.686408	+	0.727216i	$0.259186\pi$
$401$	251.842	+	691.930i	0.628035	+	1.72551i	−0.0583738	+	0.998295i	$0.518592\pi$
$402$		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	0.133207	+	0.991088i	$0.457472\pi$
$409$	−247.811	+	680.855i	−0.605895	+	1.66468i	−0.739102	+	0.673594i	$0.764750\pi$
$410$		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	0.764012	−	0.645202i	$-0.223227\pi$
$421$	530.997	+	93.6291i	1.26128	+	0.222397i	0.497264	+	0.867599i	$0.334338\pi$
$422$		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	−0.927023	−	0.375004i	$-0.877642\pi$
$431$	−719.719	+	126.906i	−1.66988	+	0.294445i	−0.742858	+	0.669449i	$0.766530\pi$
$432$		0			0
$433$	106.091	+	126.435i	0.245015	+	0.291997i	0.874510	−	0.485007i	$-0.161183\pi$
$433$	106.091	+	126.435i	0.245015	+	0.291997i	−0.629496	+	0.777004i	$0.716738\pi$
$434$		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	0.814082	−	0.580750i	$-0.197241\pi$
$439$	−80.2667	−	220.531i	−0.182840	−	0.502349i	−0.996922	+	0.0784014i	$0.975018\pi$
$440$		0			0
$441$	−203.897	+	171.090i	−0.462352	+	0.387959i
$442$		0			0
$443$	12.6427	+	71.7002i	0.0285388	+	0.161851i	0.995747	−	0.0921352i	$-0.0293692\pi$
$443$	12.6427	+	71.7002i	0.0285388	+	0.161851i	−0.967208	+	0.253987i	$0.918258\pi$
$444$		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	−0.413702	−	0.910412i	$-0.635765\pi$
$449$	75.3812	−	43.5214i	0.167887	−	0.0969295i	0.581589	+	0.813483i	$0.302431\pi$
$450$		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	0.215552	−	0.976492i	$-0.430845\pi$
$461$	−326.699	−	274.133i	−0.708675	−	0.594649i	−0.924227	+	0.381844i	$0.875289\pi$
$462$		0			0
$463$	−78.9796	−	136.797i	−0.170582	−	0.295457i	0.768041	−	0.640400i	$-0.221232\pi$
$463$	−78.9796	−	136.797i	−0.170582	−	0.295457i	−0.938624	+	0.344943i	$0.887898\pi$
$464$		0			0
$465$	−1104.03	−	401.834i	−2.37426	−	0.864160i
$466$		0			0
$467$	−259.474	+	449.422i	−0.555618	+	0.962359i	0.442237	+	0.896898i	$0.354185\pi$
$467$	−259.474	+	449.422i	−0.555618	+	0.962359i	−0.997855	+	0.0654609i	$0.979148\pi$
$468$		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	−0.956101	−	0.293036i	$-0.905334\pi$
$479$	−399.267	+	335.025i	−0.833542	+	0.699425i	0.122559	+	0.992461i	$0.460890\pi$
$480$		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	−0.820776	−	0.571250i	$-0.806459\pi$
$487$	−358.650	+	207.067i	−0.736448	+	0.425188i	0.0843284	+	0.996438i	$0.473126\pi$
$488$		0			0
$489$	−233.544	+	278.327i	−0.477596	+	0.569176i
$490$		0			0
$491$	133.782	−	758.716i	0.272468	−	1.54525i	−0.474421	−	0.880298i	$-0.657343\pi$
$491$	133.782	−	758.716i	0.272468	−	1.54525i	0.746890	−	0.664948i	$-0.231546\pi$
$492$		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	0.917756	−	0.397145i	$-0.129999\pi$
$499$	342.319	+	287.240i	0.686011	+	0.575631i	−0.231745	+	0.972777i	$0.574444\pi$
$500$		0			0
$501$	145.826	+	252.578i	0.291069	+	0.504147i
$502$		0			0
$503$	48.2808	+	17.5728i	0.0959856	+	0.0349359i	0.389567	−	0.920998i	$-0.372625\pi$
$503$	48.2808	+	17.5728i	0.0959856	+	0.0349359i	−0.293581	+	0.955934i	$0.594847\pi$
$504$		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	0.980960	+	0.194212i	$0.0622148\pi$
$509$	509.956	+	607.742i	1.00188	+	1.19399i	0.0209192	+	0.999781i	$0.493341\pi$
$510$		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	0.988180	−	0.153296i	$-0.0489889\pi$
$521$	703.096	+	405.932i	1.34951	+	0.779141i	0.361332	+	0.932437i	$0.382322\pi$
$522$		0			0
$523$	−169.109	+	464.624i	−0.323345	+	0.888383i	0.666407	+	0.745588i	$0.267831\pi$
$523$	−169.109	+	464.624i	−0.323345	+	0.888383i	−0.989752	+	0.142795i	$0.954391\pi$
$524$		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	0.434657	−	0.900596i	$-0.356870\pi$
$541$	102.104	+	37.1628i	0.188732	+	0.0686928i	−0.245925	+	0.969289i	$0.579092\pi$
$542$		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	−0.986184	−	0.165652i	$-0.947027\pi$
$547$	−535.005	−	637.594i	−0.978070	−	1.16562i	0.00811388	−	0.999967i	$-0.497417\pi$
$548$		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	−0.999945	−	0.0105170i	$-0.996652\pi$
$557$	−35.5929	−	201.857i	−0.0639011	−	0.362401i	0.936044	−	0.351884i	$-0.114459\pi$
$558$		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	−0.196763	−	0.980451i	$-0.563043\pi$
$563$	311.875	−	180.061i	0.553951	−	0.319824i	0.750714	+	0.660627i	$0.229710\pi$
$564$		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	$-0.946201\pi$
$569$		−	191.423i		−	0.336420i	0.985751	−	0.168210i	$-0.0537987\pi$
$570$		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	−0.890195	−	0.455579i	$-0.849432\pi$
$577$	−484.473	−	839.131i	−0.839641	−	1.45430i	0.0505545	−	0.998721i	$-0.483901\pi$
$578$		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	−0.857247	−	0.514905i	$-0.827827\pi$
$587$	−694.399	+	252.741i	−1.18296	+	0.430563i	−0.325715	+	0.945468i	$0.605605\pi$
$588$		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	−0.194025	−	0.980997i	$-0.562154\pi$
$593$	437.857	−	367.406i	0.738376	−	0.619571i	0.932401	+	0.361426i	$0.117710\pi$
$594$		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	−0.778897	−	0.627152i	$-0.784220\pi$
$599$	132.318	−	363.541i	0.220898	−	0.606913i	0.999795	+	0.0202389i	$0.00644268\pi$
$600$		0			0
$601$	−687.476	+	396.915i	−1.14389	+	0.660423i	−0.947390	−	0.320081i	$-0.896290\pi$
$601$	−687.476	+	396.915i	−1.14389	+	0.660423i	−0.196497	+	0.980504i	$0.562957\pi$
$602$		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	$0.0811884\pi$
$607$			306.297i			0.504609i	−0.967648	+	0.252304i	$0.918812\pi$
$608$		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	0.0633198	−	0.997993i	$-0.479831\pi$
$613$	−556.921	−	467.312i	−0.908516	−	0.762336i	−0.971836	+	0.235658i	$0.924276\pi$
$614$		0			0
$615$	364.142	+	630.713i	0.592101	+	1.02555i
$616$		0			0
$617$	−860.598	−	313.232i	−1.39481	−	0.507670i	−0.468177	−	0.883635i	$-0.655089\pi$
$617$	−860.598	−	313.232i	−1.39481	−	0.507670i	−0.926634	+	0.375965i	$0.877311\pi$
$618$		0			0
$619$	288.193	−	499.166i	0.465579	−	0.806406i	−0.533649	−	0.845706i	$-0.679179\pi$
$619$	288.193	−	499.166i	0.465579	−	0.806406i	0.999227	+	0.0393000i	$0.0125128\pi$
$620$		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	−0.177892	−	0.984050i	$-0.556928\pi$
$631$	479.761	−	402.567i	0.760318	−	0.637982i	0.938210	+	0.346068i	$0.112483\pi$
$632$		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	−0.977785	−	0.209608i	$-0.932781\pi$
$641$	−385.607	+	459.549i	−0.601571	+	0.716924i	0.376214	+	0.926533i	$0.377226\pi$
$642$		0			0
$643$	−29.0611	+	164.813i	−0.0451961	+	0.256320i	−0.999031	−	0.0440117i	$-0.985986\pi$
$643$	−29.0611	+	164.813i	−0.0451961	+	0.256320i	0.953835	+	0.300331i	$0.0970972\pi$
$644$		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	−0.944542	−	0.328389i	$-0.893494\pi$
$653$	−494.102	−	855.810i	−0.756665	−	1.31058i	0.187878	−	0.982192i	$-0.439839\pi$
$654$		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	0.197492	−	0.980305i	$-0.436720\pi$
$659$	473.397	−	83.4727i	0.718357	−	0.126666i	0.520865	+	0.853639i	$0.325609\pi$
$660$		0			0
$661$	375.056	+	446.974i	0.567406	+	0.676208i	0.971096	−	0.238687i	$-0.0767171\pi$
$661$	375.056	+	446.974i	0.567406	+	0.676208i	−0.403690	+	0.914896i	$0.632273\pi$
$662$		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	0.778177	−	0.628045i	$-0.216145\pi$
$673$	419.523	+	242.212i	0.623363	+	0.359899i	−0.154814	+	0.987944i	$0.549478\pi$
$674$		0			0
$675$	107.656	−	295.784i	0.159491	−	0.438198i
$676$		0			0
$677$	131.246	−	75.7748i	0.193864	−	0.111927i	−0.399926	−	0.916547i	$-0.630964\pi$
$677$	131.246	−	75.7748i	0.193864	−	0.111927i	0.593790	+	0.804620i	$0.297631\pi$
$678$		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	$-0.826188\pi$
$683$		−	709.380i		−	1.03862i	0.854585	−	0.519312i	$-0.173812\pi$
$684$		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	0.885714	−	0.464232i	$-0.153669\pi$
$691$	28.2069	+	48.8559i	0.0408205	+	0.0707031i	−0.844893	+	0.534935i	$0.820336\pi$
$692$		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	−0.970299	−	0.241909i	$-0.922226\pi$
$701$	−1092.22	+	397.537i	−1.55809	+	0.567100i	−0.587796	+	0.809009i	$0.700004\pi$
$702$		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	−0.655190	−	0.755464i	$-0.727411\pi$
$709$	−211.209	−	1197.82i	−0.297897	−	1.68946i	0.357293	−	0.933992i	$-0.383700\pi$
$710$		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	−0.852736	−	0.522342i	$-0.825059\pi$
$719$	91.4748	−	518.779i	0.127225	−	0.721529i	0.979961	−	0.199188i	$-0.0638303\pi$
$720$		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	0.829684	−	0.558233i	$-0.188521\pi$
$727$	308.251	+	258.653i	0.424004	+	0.355782i	−0.405680	+	0.914015i	$0.632965\pi$
$728$		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	−0.983571	−	0.180521i	$-0.942222\pi$
$733$	−245.885	+	425.885i	−0.335450	+	0.581016i	0.648121	+	0.761537i	$0.275555\pi$
$734$		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	−0.299619	−	0.954059i	$-0.596860\pi$
$739$	62.1621	−	22.6252i	0.0841166	−	0.0306159i	0.383736	+	0.923443i	$0.374637\pi$
$740$		0			0
$741$	764.303	−	146.700i	1.03145	−	0.197976i
$742$		0			0
$743$	−136.920	−	376.186i	−0.184281	−	0.506307i	0.812810	−	0.582528i	$-0.197937\pi$
$743$	−136.920	−	376.186i	−0.184281	−	0.506307i	−0.997091	+	0.0762217i	$0.975714\pi$
$744$		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	−0.713377	−	0.700781i	$-0.752835\pi$
$751$	212.950	−	585.074i	0.283555	−	0.779060i	0.996931	−	0.0782796i	$-0.0249427\pi$
$752$		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	0.909827	+	0.414989i	$0.136214\pi$
$757$	−65.9084	+	373.785i	−0.0870653	+	0.493772i	−0.996892	+	0.0787829i	$0.974897\pi$
$758$		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	0.763586	−	0.645706i	$-0.223437\pi$
$769$	717.843	+	261.273i	0.933475	+	0.339757i	0.169889	+	0.985463i	$0.445659\pi$
$770$		0			0
$771$	33.5810	−	58.1641i	0.0435552	−	0.0754398i
$772$		0			0
$773$	−157.013	+	27.6857i	−0.203122	+	0.0358159i	−0.274283	−	0.961649i	$-0.588441\pi$
$773$	−157.013	+	27.6857i	−0.203122	+	0.0358159i	0.0711614	+	0.997465i	$0.477329\pi$
$774$		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	0.178308	−	0.983975i	$-0.442938\pi$
$787$	−460.148	−	265.666i	−0.584686	−	0.337568i	−0.762993	+	0.646406i	$0.776271\pi$
$788$		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	$-0.763027\pi$
$797$		−	1080.07i		−	1.35517i	0.735446	−	0.677583i	$-0.236973\pi$
$798$		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	−0.790870	−	0.611984i	$-0.790372\pi$
$809$	108.858	−	188.548i	0.134559	−	0.233063i	0.925429	+	0.378921i	$0.123705\pi$
$810$		0			0
$811$	−281.379	+	49.6147i	−0.346953	+	0.0611772i	−0.344409	−	0.938820i	$-0.611921\pi$
$811$	−281.379	+	49.6147i	−0.346953	+	0.0611772i	−0.00254373	+	0.999997i	$0.500810\pi$
$812$		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	−0.186925	−	0.982374i	$-0.559852\pi$
$821$	614.162	−	515.343i	0.748065	−	0.627701i	0.934990	+	0.354673i	$0.115408\pi$
$822$		0			0
$823$	173.536	+	984.174i	0.210858	+	1.19584i	0.887951	+	0.459939i	$0.152129\pi$
$823$	173.536	+	984.174i	0.210858	+	1.19584i	−0.677092	+	0.735898i	$0.736760\pi$
$824$		0			0
$825$	996.782	+	575.492i	1.20822	+	0.697566i
$826$		0			0
$827$	86.4404	−	237.493i	0.104523	−	0.287174i	−0.876396	−	0.481591i	$-0.840059\pi$
$827$	86.4404	−	237.493i	0.104523	−	0.287174i	0.980919	+	0.194417i	$0.0622814\pi$
$828$		0			0
$829$	66.6007	−	38.4520i	0.0803386	−	0.0463835i	−0.459293	−	0.888285i	$-0.651897\pi$
$829$	66.6007	−	38.4520i	0.0803386	−	0.0463835i	0.539631	+	0.841902i	$0.318564\pi$
$830$		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	0.526419	−	0.850225i	$-0.323534\pi$
$839$	612.719	+	108.039i	0.730297	+	0.128771i	0.203878	+	0.978996i	$0.434645\pi$
$840$		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	−0.760504	−	0.649333i	$-0.775048\pi$
$853$	−789.623	+	287.399i	−0.925701	+	0.336928i	−0.165197	+	0.986261i	$0.552826\pi$
$854$		0			0
$855$	−1038.66	−	1200.54i	−1.21481	−	1.40414i
$856$		0			0
$857$	−283.804	−	779.746i	−0.331160	−	0.909856i	−0.987811	−	0.155661i	$-0.950249\pi$
$857$	−283.804	−	779.746i	−0.331160	−	0.909856i	0.656650	−	0.754195i	$-0.271973\pi$
$858$		0			0
$859$	−222.494	+	186.695i	−0.259015	+	0.217339i	−0.763043	−	0.646348i	$-0.776295\pi$
$859$	−222.494	+	186.695i	−0.259015	+	0.217339i	0.504028	+	0.863688i	$0.331851\pi$
$860$		0			0
$861$	147.941	+	839.014i	0.171824	+	0.974464i
$862$		0			0
$863$	934.482	+	539.523i	1.08283	+	0.625172i	0.931658	−	0.363336i	$-0.118362\pi$
$863$	934.482	+	539.523i	1.08283	+	0.625172i	0.151171	+	0.988508i	$0.451696\pi$
$864$		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	0.441298	−	0.897361i	$-0.354518\pi$
$877$	481.531	+	84.9069i	0.549066	+	0.0968152i	0.107769	+	0.994176i	$0.465629\pi$
$878$		0			0
$879$	−555.091	−	465.777i	−0.631503	−	0.529894i
$880$		0			0
$881$	−184.835	−	320.143i	−0.209801	−	0.363386i	0.741851	−	0.670565i	$-0.233948\pi$
$881$	−184.835	−	320.143i	−0.209801	−	0.363386i	−0.951652	+	0.307179i	$0.900615\pi$
$882$		0			0
$883$	42.9539	+	15.6339i	0.0486454	+	0.0177055i	0.366228	−	0.930525i	$-0.380649\pi$
$883$	42.9539	+	15.6339i	0.0486454	+	0.0177055i	−0.317583	+	0.948231i	$0.602871\pi$
$884$		0			0
$885$	149.069	−	258.195i	0.168439	−	0.291745i
$886$		0			0
$887$	−831.091	+	146.544i	−0.936968	+	0.165213i	−0.621225	−	0.783632i	$-0.713365\pi$
$887$	−831.091	+	146.544i	−0.936968	+	0.165213i	−0.315743	+	0.948845i	$0.602254\pi$
$888$		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	0.399720	−	0.916637i	$-0.369107\pi$
$907$	1118.35	−	1332.80i	1.23302	−	1.46946i	0.833301	−	0.552820i	$-0.186448\pi$
$908$		0			0
$909$	−42.6043	+	241.621i	−0.0468694	+	0.265809i
$910$		0			0
$911$		−	105.673i		−	0.115997i	−0.998317	−	0.0579986i	$-0.981528\pi$
$911$		−	105.673i		−	0.115997i	0.998317	−	0.0579986i	$-0.0184719\pi$
$912$		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	0.975166	−	0.221473i	$-0.0710865\pi$
$919$	271.823	+	470.812i	0.295782	+	0.512309i	−0.679385	+	0.733782i	$0.737753\pi$
$920$		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	−0.658437	−	0.752636i	$-0.728782\pi$
$929$	−630.832	+	229.604i	−0.679044	+	0.247152i	−0.0206070	+	0.999788i	$0.506560\pi$
$930$		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	−0.929657	−	0.368427i	$-0.879897\pi$
$937$	−170.604	−	967.542i	−0.182075	−	1.03260i	0.747582	−	0.664169i	$-0.231215\pi$
$938$		0			0
$939$	1471.05	+	849.314i	1.56662	+	0.904487i
$940$		0			0
$941$	310.765	−	853.821i	0.330250	−	0.907355i	−0.657796	−	0.753196i	$-0.728511\pi$
$941$	310.765	−	853.821i	0.330250	−	0.907355i	0.988046	−	0.154159i	$-0.0492667\pi$
$942$		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	0.117873	+	0.993029i	$0.462392\pi$
$947$	−314.903	+	1785.91i	−0.332527	+	1.88586i	−0.450400	+	0.892827i	$0.648719\pi$
$948$		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	0.837391	−	0.546605i	$-0.184080\pi$
$953$	1369.78	+	241.528i	1.43733	+	0.253440i	0.599940	+	0.800045i	$0.295191\pi$
$954$		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	−0.712888	−	0.701278i	$-0.752613\pi$
$967$	−781.549	+	284.460i	−0.808220	+	0.294168i	−0.0953317	+	0.995446i	$0.530391\pi$
$968$		0			0
$969$	−579.058	+	220.717i	−0.597583	+	0.227779i
$970$		0			0
$971$	−508.037	−	1395.82i	−0.523210	−	1.43751i	−0.866928	−	0.498434i	$-0.833909\pi$
$971$	−508.037	−	1395.82i	−0.523210	−	1.43751i	0.343718	−	0.939073i	$-0.388314\pi$
$972$		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	0.194372	−	0.980928i	$-0.437733\pi$
$977$	−545.117	−	314.723i	−0.557950	−	0.322133i	−0.752322	+	0.658795i	$0.771066\pi$
$978$		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	−0.124185	−	0.992259i	$-0.539632\pi$
$983$	859.696	−	1024.55i	0.874564	−	1.04226i	0.998749	−	0.0500053i	$-0.0159238\pi$
$984$		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	0.663601	−	0.748087i	$-0.269027\pi$
$991$	1022.04	+	180.213i	1.03132	+	0.181850i	0.367720	+	0.929936i	$0.380138\pi$
$992$		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	0.188890	−	0.981998i	$-0.439511\pi$
$997$	−296.735	−	108.003i	−0.297628	−	0.108328i	−0.486518	+	0.873670i	$0.661733\pi$
$998$		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.33.1	✓	18
4.3	odd	2		304.3.z.b.33.3		18
19.2	odd	18		1444.3.c.c.721.17		18
19.15	odd	18	inner	76.3.j.a.53.1	yes	18
19.17	even	9		1444.3.c.c.721.2		18
76.15	even	18		304.3.z.b.129.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.j.a.33.1	✓	18	1.1	even	1	trivial
76.3.j.a.53.1	yes	18	19.15	odd	18	inner
304.3.z.b.33.3		18	4.3	odd	2
304.3.z.b.129.3		18	76.15	even	18
1444.3.c.c.721.2		18	19.17	even	9
1444.3.c.c.721.17		18	19.2	odd	18

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

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Representations

Groups

Database

Properties

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