LMFDB - Embedded newform 252.4.j.b.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(85,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.85");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.j (of order $3$, degree $2$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
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} - 7 x^{17} + 81 x^{16} - 470 x^{15} + 2687 x^{14} - 12243 x^{13} + 43732 x^{12} + \cdots + 5500612092612 $ x^18 - 7x^17 + 81x^16 - 470x^15 + 2687x^14 - 12243x^13 + 43732x^12 - 169303x^11 + 166449x^10 - 57172x^9 - 3758051x^8 + 73649097x^7 + 358194386x^6 + 3599409199x^5 + 26802380109x^4 + 114591208112x^3 + 655546044172x^2 + 1324018291596*x + 5500612092612
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			85.2
Root			$4.38317 - 3.94388i$ of defining polynomial
Character	$\chi$	$=$	252.85
Dual form			252.4.j.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.38317 - 3.94388i) q^{3} +(-8.26221 + 14.3106i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-4.10831 + 26.6856i) q^{9} +O(q^{10})$	\(q+(-3.38317 - 3.94388i) q^{3} +(-8.26221 + 14.3106i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-4.10831 + 26.6856i) q^{9} +(-5.18159 - 8.97478i) q^{11} +(10.5363 - 18.2493i) q^{13} +(84.3916 - 15.8300i) q^{15} -17.1034 q^{17} +121.074 q^{19} +(-12.0674 + 34.3129i) q^{21} +(-8.97878 + 15.5517i) q^{23} +(-74.0283 - 128.221i) q^{25} +(119.144 - 74.0793i) q^{27} +(-65.9200 - 114.177i) q^{29} +(155.855 - 269.950i) q^{31} +(-17.8652 + 50.7987i) q^{33} +115.671 q^{35} +109.965 q^{37} +(-107.619 + 20.1869i) q^{39} +(96.4372 - 167.034i) q^{41} +(-242.081 - 419.297i) q^{43} +(-347.943 - 279.274i) q^{45} +(117.243 + 203.070i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(57.8637 + 67.4537i) q^{51} +165.160 q^{53} +171.246 q^{55} +(-409.614 - 477.500i) q^{57} +(42.2968 - 73.2602i) q^{59} +(20.1098 + 34.8312i) q^{61} +(176.152 - 68.4943i) q^{63} +(174.106 + 301.560i) q^{65} +(-341.961 + 592.294i) q^{67} +(91.7108 - 17.2029i) q^{69} +1111.86 q^{71} +930.288 q^{73} +(-255.236 + 725.751i) q^{75} +(-36.2711 + 62.8234i) q^{77} +(-177.018 - 306.603i) q^{79} +(-695.244 - 219.266i) q^{81} +(729.335 + 1263.25i) q^{83} +(141.312 - 244.759i) q^{85} +(-227.281 + 646.260i) q^{87} +816.471 q^{89} -147.508 q^{91} +(-1591.93 + 298.611i) q^{93} +(-1000.34 + 1732.64i) q^{95} +(-190.952 - 330.739i) q^{97} +(260.785 - 101.403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) $ 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9	$ 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9} - 93 q^{11} - 18 q^{13} + 162 q^{15} - 54 q^{17} - 90 q^{19} - 49 q^{21} - 246 q^{23} - 315 q^{25} - 394 q^{27} - 318 q^{29} - 18 q^{31} + 33 q^{33} + 84 q^{35} - 72 q^{37} + 268 q^{39} - 57 q^{41} - 171 q^{43} - 318 q^{45} - 1056 q^{47} - 441 q^{49} + 705 q^{51} + 1512 q^{53} - 1800 q^{55} - 1271 q^{57} - 411 q^{59} - 198 q^{61} + 308 q^{63} - 1326 q^{65} - 441 q^{67} + 642 q^{69} + 3516 q^{71} + 54 q^{73} - 2497 q^{75} - 651 q^{77} + 72 q^{79} + 1163 q^{81} - 558 q^{83} - 1008 q^{85} + 2766 q^{87} + 2784 q^{89} + 252 q^{91} - 2618 q^{93} - 156 q^{95} + 909 q^{97} + 6318 q^{99}+O(q^{100}) $ 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9 - 93 * q^11 - 18 * q^13 + 162 * q^15 - 54 * q^17 - 90 * q^19 - 49 * q^21 - 246 * q^23 - 315 * q^25 - 394 * q^27 - 318 * q^29 - 18 * q^31 + 33 * q^33 + 84 * q^35 - 72 * q^37 + 268 * q^39 - 57 * q^41 - 171 * q^43 - 318 * q^45 - 1056 * q^47 - 441 * q^49 + 705 * q^51 + 1512 * q^53 - 1800 * q^55 - 1271 * q^57 - 411 * q^59 - 198 * q^61 + 308 * q^63 - 1326 * q^65 - 441 * q^67 + 642 * q^69 + 3516 * q^71 + 54 * q^73 - 2497 * q^75 - 651 * q^77 + 72 * q^79 + 1163 * q^81 - 558 * q^83 - 1008 * q^85 + 2766 * q^87 + 2784 * q^89 + 252 * q^91 - 2618 * q^93 - 156 * q^95 + 909 * q^97 + 6318 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.38317	−	3.94388i	−0.651092	−	0.758999i
$3$	−3.38317	−	3.94388i	−0.651092	−	0.758999i
$4$		0			0
$5$	−8.26221	+	14.3106i	−0.738995	+	1.27998i	0.213954	+	0.976844i	$0.431366\pi$
$5$	−8.26221	+	14.3106i	−0.738995	+	1.27998i	−0.952948	+	0.303133i	$0.901967\pi$
$6$		0			0
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$8$		0			0
$9$	−4.10831	+	26.6856i	−0.152160	+	0.988356i
$10$		0			0
$11$	−5.18159	−	8.97478i	−0.142028	−	0.246000i	0.786232	−	0.617931i	$-0.212029\pi$
$11$	−5.18159	−	8.97478i	−0.142028	−	0.246000i	−0.928260	+	0.371931i	$0.878696\pi$
$12$		0			0
$13$	10.5363	−	18.2493i	0.224787	−	0.389343i	−0.731468	−	0.681875i	$-0.761165\pi$
$13$	10.5363	−	18.2493i	0.224787	−	0.389343i	0.956256	+	0.292532i	$0.0944979\pi$
$14$		0			0
$15$	84.3916	−	15.8300i	1.45265	−	0.272485i
$16$		0			0
$17$	−17.1034			−0.244011			−0.122005	−	0.992529i	$-0.538933\pi$
$17$	−17.1034			−0.244011			−0.122005	+	0.992529i	$0.538933\pi$
$18$		0			0
$19$	121.074			1.46191			0.730954	−	0.682427i	$-0.239075\pi$
$19$	121.074			1.46191			0.730954	+	0.682427i	$0.239075\pi$
$20$		0			0
$21$	−12.0674	+	34.3129i	−0.125396	+	0.356557i
$22$		0			0
$23$	−8.97878	+	15.5517i	−0.0814003	+	0.140989i	−0.903852	−	0.427846i	$-0.859273\pi$
$23$	−8.97878	+	15.5517i	−0.0814003	+	0.140989i	0.822451	+	0.568835i	$0.192606\pi$
$24$		0			0
$25$	−74.0283	−	128.221i	−0.592227	−	1.02577i
$26$		0			0
$27$	119.144	−	74.0793i	0.849231	−	0.528021i
$28$		0			0
$29$	−65.9200	−	114.177i	−0.422105	−	0.731107i	0.574040	−	0.818827i	$-0.305375\pi$
$29$	−65.9200	−	114.177i	−0.422105	−	0.731107i	−0.996145	+	0.0877200i	$0.972042\pi$
$30$		0			0
$31$	155.855	−	269.950i	0.902983	−	1.56401i	0.0793800	−	0.996844i	$-0.474706\pi$
$31$	155.855	−	269.950i	0.902983	−	1.56401i	0.823603	−	0.567167i	$-0.191961\pi$
$32$		0			0
$33$	−17.8652	+	50.7987i	−0.0942404	+	0.267967i
$34$		0			0
$35$	115.671			0.558628
$36$		0			0
$37$	109.965			0.488596			0.244298	−	0.969700i	$-0.421442\pi$
$37$	109.965			0.488596			0.244298	+	0.969700i	$0.421442\pi$
$38$		0			0
$39$	−107.619	+	20.1869i	−0.441868	+	0.0828845i
$40$		0			0
$41$	96.4372	−	167.034i	0.367340	−	0.636252i	−0.621808	−	0.783169i	$-0.713602\pi$
$41$	96.4372	−	167.034i	0.367340	−	0.636252i	0.989149	+	0.146917i	$0.0469351\pi$
$42$		0			0
$43$	−242.081	−	419.297i	−0.858536	−	1.48703i	−0.873325	−	0.487138i	$-0.838041\pi$
$43$	−242.081	−	419.297i	−0.858536	−	1.48703i	0.0147887	−	0.999891i	$-0.495292\pi$
$44$		0			0
$45$	−347.943	−	279.274i	−1.15263	−	0.925151i
$46$		0			0
$47$	117.243	+	203.070i	0.363864	+	0.630231i	0.988593	−	0.150611i	$-0.0481240\pi$
$47$	117.243	+	203.070i	0.363864	+	0.630231i	−0.624729	+	0.780841i	$0.714791\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$		0			0
$51$	57.8637	+	67.4537i	0.158873	+	0.185204i
$52$		0			0
$53$	165.160			0.428047			0.214024	−	0.976828i	$-0.431343\pi$
$53$	165.160			0.428047			0.214024	+	0.976828i	$0.431343\pi$
$54$		0			0
$55$	171.246			0.419832
$56$		0			0
$57$	−409.614	−	477.500i	−0.951836	−	1.10959i
$58$		0			0
$59$	42.2968	−	73.2602i	0.0933317	−	0.161655i	−0.815579	−	0.578645i	$-0.803582\pi$
$59$	42.2968	−	73.2602i	0.0933317	−	0.161655i	0.908911	+	0.416990i	$0.136915\pi$
$60$		0			0
$61$	20.1098	+	34.8312i	0.0422097	+	0.0731094i	0.886358	−	0.463000i	$-0.153227\pi$
$61$	20.1098	+	34.8312i	0.0422097	+	0.0731094i	−0.844149	+	0.536109i	$0.819894\pi$
$62$		0			0
$63$	176.152	−	68.4943i	0.352271	−	0.136976i
$64$		0			0
$65$	174.106	+	301.560i	0.332233	+	0.575445i
$66$		0			0
$67$	−341.961	+	592.294i	−0.623540	+	1.08000i	0.365281	+	0.930897i	$0.380973\pi$
$67$	−341.961	+	592.294i	−0.623540	+	1.08000i	−0.988821	+	0.149106i	$0.952361\pi$
$68$		0			0
$69$	91.7108	−	17.2029i	0.160010	−	0.0300143i
$70$		0			0
$71$	1111.86			1.85850			0.929252	−	0.369446i	$-0.120452\pi$
$71$	1111.86			1.85850			0.929252	+	0.369446i	$0.120452\pi$
$72$		0			0
$73$	930.288			1.49153			0.745767	−	0.666207i	$-0.232083\pi$
$73$	930.288			1.49153			0.745767	+	0.666207i	$0.232083\pi$
$74$		0			0
$75$	−255.236	+	725.751i	−0.392962	+	1.11737i
$76$		0			0
$77$	−36.2711	+	62.8234i	−0.0536815	+	0.0929791i
$78$		0			0
$79$	−177.018	−	306.603i	−0.252102	−	0.436653i	0.712003	−	0.702177i	$-0.247788\pi$
$79$	−177.018	−	306.603i	−0.252102	−	0.436653i	−0.964104	+	0.265524i	$0.914455\pi$
$80$		0			0
$81$	−695.244	−	219.266i	−0.953695	−	0.300776i
$82$		0			0
$83$	729.335	+	1263.25i	0.964517	+	1.67059i	0.710907	+	0.703286i	$0.248285\pi$
$83$	729.335	+	1263.25i	0.964517	+	1.67059i	0.253610	+	0.967307i	$0.418382\pi$
$84$		0			0
$85$	141.312	−	244.759i	0.180323	−	0.312328i
$86$		0			0
$87$	−227.281	+	646.260i	−0.280081	+	0.796395i
$88$		0			0
$89$	816.471			0.972424			0.486212	−	0.873841i	$-0.338378\pi$
$89$	816.471			0.972424			0.486212	+	0.873841i	$0.338378\pi$
$90$		0			0
$91$	−147.508			−0.169923
$92$		0			0
$93$	−1591.93	+	298.611i	−1.77501	+	0.332952i
$94$		0			0
$95$	−1000.34	+	1732.64i	−1.08034	+	1.87121i
$96$		0			0
$97$	−190.952	−	330.739i	−0.199879	−	0.346200i	0.748610	−	0.663010i	$-0.230721\pi$
$97$	−190.952	−	330.739i	−0.199879	−	0.346200i	−0.948489	+	0.316810i	$0.897388\pi$
$98$		0			0
$99$	260.785	−	101.403i	0.264746	−	0.102943i
$100$		0			0
$101$	−851.077	−	1474.11i	−0.838468	−	1.45227i	−0.891175	−	0.453659i	$-0.850118\pi$
$101$	−851.077	−	1474.11i	−0.838468	−	1.45227i	0.0527071	−	0.998610i	$-0.483215\pi$
$102$		0			0
$103$	224.907	−	389.550i	0.215153	−	0.372655i	−0.738167	−	0.674618i	$-0.764308\pi$
$103$	224.907	−	389.550i	0.215153	−	0.372655i	0.953320	+	0.301963i	$0.0976418\pi$
$104$		0			0
$105$	−391.335	−	456.192i	−0.363718	−	0.423998i
$106$		0			0
$107$	−978.048			−0.883658			−0.441829	−	0.897099i	$-0.645670\pi$
$107$	−978.048			−0.883658			−0.441829	+	0.897099i	$0.645670\pi$
$108$		0			0
$109$	−1001.50			−0.880058			−0.440029	−	0.897984i	$-0.645032\pi$
$109$	−1001.50			−0.880058			−0.440029	+	0.897984i	$0.645032\pi$
$110$		0			0
$111$	−372.029	−	433.686i	−0.318121	−	0.370844i
$112$		0			0
$113$	−730.931	+	1266.01i	−0.608497	+	1.05395i	0.382991	+	0.923752i	$0.374894\pi$
$113$	−730.931	+	1266.01i	−0.608497	+	1.05395i	−0.991488	+	0.130196i	$0.958439\pi$
$114$		0			0
$115$	−148.369	−	256.983i	−0.120309	−	0.208381i
$116$		0			0
$117$	443.709	+	356.141i	0.350606	+	0.281412i
$118$		0			0
$119$	59.8619	+	103.684i	0.0461137	+	0.0798713i
$120$		0			0
$121$	611.802	−	1059.67i	0.459656	−	0.796148i
$122$		0			0
$123$	−985.025	+	184.769i	−0.722087	+	0.135447i
$124$		0			0
$125$	380.998			0.272620
$126$		0			0
$127$	704.533			0.492262			0.246131	−	0.969237i	$-0.420841\pi$
$127$	704.533			0.492262			0.246131	+	0.969237i	$0.420841\pi$
$128$		0			0
$129$	−834.654	+	2373.29i	−0.569668	+	1.61982i
$130$		0			0
$131$	−197.820	+	342.635i	−0.131936	+	0.228520i	−0.924423	−	0.381369i	$-0.875453\pi$
$131$	−197.820	+	342.635i	−0.131936	+	0.228520i	0.792487	+	0.609889i	$0.208786\pi$
$132$		0			0
$133$	−423.759	−	733.971i	−0.276275	−	0.478522i
$134$		0			0
$135$	75.7254	+	2317.08i	0.0482771	+	1.47720i
$136$		0			0
$137$	735.170	+	1273.35i	0.458466	+	0.794086i	0.998880	−	0.0473133i	$-0.0150659\pi$
$137$	735.170	+	1273.35i	0.458466	+	0.794086i	−0.540415	+	0.841399i	$0.681733\pi$
$138$		0			0
$139$	800.641	−	1386.75i	0.488558	−	0.846206i	−0.511356	−	0.859369i	$-0.670857\pi$
$139$	800.641	−	1386.75i	0.488558	−	0.846206i	0.999913	+	0.0131626i	$0.00418991\pi$
$140$		0			0
$141$	404.232	−	1149.41i	0.241436	−	0.686510i
$142$		0			0
$143$	−218.378			−0.127704
$144$		0			0
$145$	2178.58			1.24773
$146$		0			0
$147$	250.247	−	46.9407i	0.140408	−	0.0263375i
$148$		0			0
$149$	93.0610	−	161.186i	0.0511668	−	0.0886236i	−0.839308	−	0.543657i	$-0.817039\pi$
$149$	93.0610	−	161.186i	0.0511668	−	0.0886236i	0.890474	+	0.455033i	$0.150373\pi$
$150$		0			0
$151$	−861.422	−	1492.03i	−0.464248	−	0.804102i	0.534919	−	0.844903i	$-0.320342\pi$
$151$	−861.422	−	1492.03i	−0.464248	−	0.804102i	−0.999167	+	0.0408018i	$0.987009\pi$
$152$		0			0
$153$	70.2661	−	456.415i	0.0371286	−	0.241170i
$154$		0			0
$155$	2575.42	+	4460.76i	1.33460	+	2.31159i
$156$		0			0
$157$	977.042	−	1692.29i	0.496665	−	0.860249i	−0.503328	−	0.864096i	$-0.667891\pi$
$157$	977.042	−	1692.29i	0.496665	−	0.860249i	0.999993	+	0.00384662i	$0.00122442\pi$
$158$		0			0
$159$	−558.766	−	651.372i	−0.278698	−	0.324888i
$160$		0			0
$161$	125.703			0.0615328
$162$		0			0
$163$	−1750.03			−0.840937			−0.420469	−	0.907307i	$-0.638134\pi$
$163$	−1750.03			−0.840937			−0.420469	+	0.907307i	$0.638134\pi$
$164$		0			0
$165$	−579.353	−	675.371i	−0.273349	−	0.318652i
$166$		0			0
$167$	769.345	−	1332.55i	0.356489	−	0.617458i	−0.630882	−	0.775879i	$-0.717307\pi$
$167$	769.345	−	1332.55i	0.356489	−	0.617458i	0.987372	+	0.158421i	$0.0506402\pi$
$168$		0			0
$169$	876.474	+	1518.10i	0.398941	+	0.690987i
$170$		0			0
$171$	−497.409	+	3230.93i	−0.222443	+	1.44489i
$172$		0			0
$173$	−1149.33	−	1990.70i	−0.505099	−	0.874856i	−0.999983	−	0.00589734i	$-0.998123\pi$
$173$	−1149.33	−	1990.70i	−0.505099	−	0.874856i	0.494884	−	0.868959i	$-0.335211\pi$
$174$		0			0
$175$	−518.198	+	897.546i	−0.223841	+	0.387703i
$176$		0			0
$177$	−432.026	+	81.0384i	−0.183464	+	0.0344137i
$178$		0			0
$179$	1352.49			0.564747			0.282373	−	0.959305i	$-0.408878\pi$
$179$	1352.49			0.564747			0.282373	+	0.959305i	$0.408878\pi$
$180$		0			0
$181$	−3371.49			−1.38454			−0.692269	−	0.721640i	$-0.743389\pi$
$181$	−3371.49			−1.38454			−0.692269	+	0.721640i	$0.743389\pi$
$182$		0			0
$183$	69.3349	−	197.150i	0.0280076	−	0.0796381i
$184$		0			0
$185$	−908.550	+	1573.66i	−0.361070	+	0.625392i
$186$		0			0
$187$	88.6228	+	153.499i	0.0346564	+	0.0600266i
$188$		0			0
$189$	−866.085	−	462.994i	−0.333325	−	0.178190i
$190$		0			0
$191$	−2310.78	−	4002.38i	−0.875403	−	1.51624i	−0.856333	−	0.516424i	$-0.827263\pi$
$191$	−2310.78	−	4002.38i	−0.875403	−	1.51624i	−0.0190703	−	0.999818i	$-0.506071\pi$
$192$		0			0
$193$	69.7778	−	120.859i	0.0260244	−	0.0450756i	−0.852720	−	0.522368i	$-0.825049\pi$
$193$	69.7778	−	120.859i	0.0260244	−	0.0450756i	0.878744	+	0.477293i	$0.158382\pi$
$194$		0			0
$195$	600.286	−	1706.88i	0.220448	−	0.626832i
$196$		0			0
$197$	1600.47			0.578826			0.289413	−	0.957204i	$-0.406540\pi$
$197$	1600.47			0.578826			0.289413	+	0.957204i	$0.406540\pi$
$198$		0			0
$199$	4207.68			1.49887			0.749434	−	0.662079i	$-0.230326\pi$
$199$	4207.68			1.49887			0.749434	+	0.662079i	$0.230326\pi$
$200$		0			0
$201$	3492.84	−	655.179i	1.22570	−	0.229914i
$202$		0			0
$203$	−461.440	+	799.238i	−0.159541	+	0.276333i
$204$		0			0
$205$	1593.57	+	2760.14i	0.542925	+	0.940374i
$206$		0			0
$207$	−378.119	−	303.496i	−0.126962	−	0.101905i
$208$		0			0
$209$	−627.355	−	1086.61i	−0.207632	−	0.359629i
$210$		0			0
$211$	11.8198	−	20.4726i	0.00385645	−	0.00667957i	−0.864091	−	0.503336i	$-0.832106\pi$
$211$	11.8198	−	20.4726i	0.00385645	−	0.00667957i	0.867947	+	0.496656i	$0.165439\pi$
$212$		0			0
$213$	−3761.62	−	4385.05i	−1.21006	−	1.41060i
$214$		0			0
$215$	8000.51			2.53782
$216$		0			0
$217$	−2181.98			−0.682591
$218$		0			0
$219$	−3147.32	−	3668.94i	−0.971125	−	1.13207i
$220$		0			0
$221$	−180.206	+	312.126i	−0.0548505	+	0.0950039i
$222$		0			0
$223$	818.660	+	1417.96i	0.245836	+	0.425801i	0.962366	−	0.271755i	$-0.0876041\pi$
$223$	818.660	+	1417.96i	0.245836	+	0.425801i	−0.716530	+	0.697556i	$0.754271\pi$
$224$		0			0
$225$	3725.78	−	1448.72i	1.10394	−	0.429250i
$226$		0			0
$227$	−1163.93	−	2015.99i	−0.340322	−	0.589455i	0.644171	−	0.764882i	$-0.277203\pi$
$227$	−1163.93	−	2015.99i	−0.340322	−	0.589455i	−0.984492	+	0.175427i	$0.943869\pi$
$228$		0			0
$229$	1635.43	−	2832.66i	0.471932	−	0.817411i	−0.527552	−	0.849523i	$-0.676890\pi$
$229$	1635.43	−	2832.66i	0.471932	−	0.817411i	0.999484	+	0.0321119i	$0.0102233\pi$
$230$		0			0
$231$	370.479	−	69.4936i	0.105523	−	0.0197937i
$232$		0			0
$233$	−1015.02			−0.285390			−0.142695	−	0.989767i	$-0.545577\pi$
$233$	−1015.02			−0.285390			−0.142695	+	0.989767i	$0.545577\pi$
$234$		0			0
$235$	−3874.74			−1.07557
$236$		0			0
$237$	−610.325	+	1735.43i	−0.167278	+	0.475646i
$238$		0			0
$239$	500.317	−	866.575i	0.135409	−	0.234536i	−0.790344	−	0.612663i	$-0.790098\pi$
$239$	500.317	−	866.575i	0.135409	−	0.234536i	0.925754	+	0.378127i	$0.123432\pi$
$240$		0			0
$241$	112.667	+	195.145i	0.0301142	+	0.0521593i	0.880690	−	0.473694i	$-0.157080\pi$
$241$	112.667	+	195.145i	0.0301142	+	0.0521593i	−0.850576	+	0.525853i	$0.823746\pi$
$242$		0			0
$243$	1487.37	+	3483.77i	0.392654	+	0.919686i
$244$		0			0
$245$	−404.848	−	701.218i	−0.105571	−	0.182854i
$246$		0			0
$247$	1275.67	−	2209.52i	0.328618	−	0.569184i
$248$		0			0
$249$	2514.62	−	7150.18i	0.639990	−	1.81978i
$250$		0			0
$251$	6912.02			1.73818			0.869090	−	0.494654i	$-0.164705\pi$
$251$	6912.02			1.73818			0.869090	+	0.494654i	$0.164705\pi$
$252$		0			0
$253$	186.097			0.0462445
$254$		0			0
$255$	−1443.38	+	270.746i	−0.354463	+	0.0664894i
$256$		0			0
$257$	1566.09	−	2712.56i	0.380118	−	0.658384i	−0.610961	−	0.791661i	$-0.709217\pi$
$257$	1566.09	−	2712.56i	0.380118	−	0.658384i	0.991079	+	0.133277i	$0.0425501\pi$
$258$		0			0
$259$	−384.876	−	666.625i	−0.0923360	−	0.159931i
$260$		0			0
$261$	3317.70	−	1290.04i	0.786821	−	0.305945i
$262$		0			0
$263$	−3617.18	−	6265.14i	−0.848080	−	1.46892i	−0.882919	−	0.469524i	$-0.844425\pi$
$263$	−3617.18	−	6265.14i	−0.848080	−	1.46892i	0.0348397	−	0.999393i	$-0.488908\pi$
$264$		0			0
$265$	−1364.59	+	2363.54i	−0.316325	+	0.547891i
$266$		0			0
$267$	−2762.26	−	3220.06i	−0.633137	−	0.738069i
$268$		0			0
$269$	−7852.19			−1.77976			−0.889881	−	0.456192i	$-0.849213\pi$
$269$	−7852.19			−1.77976			−0.889881	+	0.456192i	$0.849213\pi$
$270$		0			0
$271$	5483.66			1.22918			0.614591	−	0.788846i	$-0.289321\pi$
$271$	5483.66			1.22918			0.614591	+	0.788846i	$0.289321\pi$
$272$		0			0
$273$	499.044	+	581.752i	0.110636	+	0.128972i
$274$		0			0
$275$	−767.169	+	1328.78i	−0.168225	+	0.291375i
$276$		0			0
$277$	248.515	+	430.440i	0.0539054	+	0.0933669i	0.891719	−	0.452590i	$-0.149500\pi$
$277$	248.515	+	430.440i	0.0539054	+	0.0933669i	−0.837814	+	0.545956i	$0.816166\pi$
$278$		0			0
$279$	6563.46	+	5268.13i	1.40840	+	1.13045i
$280$		0			0
$281$	−2568.88	−	4449.43i	−0.545361	−	0.944592i	−0.998584	−	0.0531954i	$-0.983059\pi$
$281$	−2568.88	−	4449.43i	−0.545361	−	0.944592i	0.453223	−	0.891397i	$-0.350274\pi$
$282$		0			0
$283$	−2786.88	+	4827.02i	−0.585381	+	1.01391i	0.409446	+	0.912334i	$0.365722\pi$
$283$	−2786.88	+	4827.02i	−0.585381	+	1.01391i	−0.994828	+	0.101576i	$0.967611\pi$
$284$		0			0
$285$	10217.6	−	1916.60i	2.12365	−	0.398349i
$286$		0			0
$287$	−1350.12			−0.277683
$288$		0			0
$289$	−4620.47			−0.940459
$290$		0			0
$291$	−658.369	+	1872.04i	−0.132626	+	0.377116i
$292$		0			0
$293$	−4416.26	+	7649.18i	−0.880548	+	1.52515i	−0.0298145	+	0.999555i	$0.509492\pi$
$293$	−4416.26	+	7649.18i	−0.880548	+	1.52515i	−0.850733	+	0.525598i	$0.823842\pi$
$294$		0			0
$295$	698.930	+	1210.58i	0.137943	+	0.238925i
$296$		0			0
$297$	−1282.20	−	685.441i	−0.250508	−	0.133917i
$298$		0			0
$299$	189.206	+	327.714i	0.0365955	+	0.0633852i
$300$		0			0
$301$	−1694.57	+	2935.08i	−0.324496	+	0.562044i
$302$		0			0
$303$	−2934.36	+	8343.70i	−0.556352	+	1.58196i
$304$		0			0
$305$	−664.605			−0.124771
$306$		0			0
$307$	−3696.79			−0.687253			−0.343627	−	0.939106i	$-0.611655\pi$
$307$	−3696.79			−0.687253			−0.343627	+	0.939106i	$0.611655\pi$
$308$		0			0
$309$	−2297.23	+	430.909i	−0.422929	+	0.0793320i
$310$		0			0
$311$	−1361.75	+	2358.62i	−0.248288	+	0.430048i	−0.963051	−	0.269319i	$-0.913201\pi$
$311$	−1361.75	+	2358.62i	−0.248288	+	0.430048i	0.714763	+	0.699367i	$0.246535\pi$
$312$		0			0
$313$	370.295	+	641.369i	0.0668699	+	0.115822i	0.897522	−	0.440970i	$-0.145365\pi$
$313$	370.295	+	641.369i	0.0668699	+	0.115822i	−0.830652	+	0.556792i	$0.812032\pi$
$314$		0			0
$315$	−475.212	+	3086.75i	−0.0850006	+	0.552123i
$316$		0			0
$317$	−939.326	−	1626.96i	−0.166428	−	0.288262i	0.770733	−	0.637158i	$-0.219890\pi$
$317$	−939.326	−	1626.96i	−0.166428	−	0.288262i	−0.937162	+	0.348896i	$0.886557\pi$
$318$		0			0
$319$	−683.141	+	1183.23i	−0.119901	+	0.207675i
$320$		0			0
$321$	3308.90	+	3857.30i	0.575342	+	0.670696i
$322$		0			0
$323$	−2070.77			−0.356721
$324$		0			0
$325$	−3119.93			−0.532500
$326$		0			0
$327$	3388.25	+	3949.79i	0.572998	+	0.667963i
$328$		0			0
$329$	820.699	−	1421.49i	0.137528	−	0.238205i
$330$		0			0
$331$	−838.381	−	1452.12i	−0.139219	−	0.241135i	0.787982	−	0.615698i	$-0.211126\pi$
$331$	−838.381	−	1452.12i	−0.139219	−	0.241135i	−0.927201	+	0.374563i	$0.877793\pi$
$332$		0			0
$333$	−451.769	+	2934.47i	−0.0743446	+	0.482907i
$334$		0			0
$335$	−5650.71	−	9787.31i	−0.921585	−	1.59623i
$336$		0			0
$337$	4383.62	−	7592.65i	0.708578	−	1.22729i	−0.256806	−	0.966463i	$-0.582670\pi$
$337$	4383.62	−	7592.65i	0.708578	−	1.22729i	0.965385	−	0.260831i	$-0.0839964\pi$
$338$		0			0
$339$	7465.85	−	1400.43i	1.19613	−	0.224368i
$340$		0			0
$341$	−3230.31			−0.512995
$342$		0			0
$343$	343.000			0.0539949
$344$		0			0
$345$	−511.551	+	1454.57i	−0.0798289	+	0.226989i
$346$		0			0
$347$	−3145.03	+	5447.35i	−0.486553	+	0.842735i	−0.999881	−	0.0154582i	$-0.995079\pi$
$347$	−3145.03	+	5447.35i	−0.486553	+	0.842735i	0.513327	+	0.858193i	$0.328413\pi$
$348$		0			0
$349$	5566.80	+	9641.98i	0.853822	+	1.47886i	0.877734	+	0.479149i	$0.159055\pi$
$349$	5566.80	+	9641.98i	0.853822	+	1.47886i	−0.0239118	+	0.999714i	$0.507612\pi$
$350$		0			0
$351$	−96.5677	−	2954.82i	−0.0146849	−	0.449335i
$352$		0			0
$353$	1031.09	+	1785.90i	0.155466	+	0.269274i	0.933228	−	0.359283i	$-0.116979\pi$
$353$	1031.09	+	1785.90i	0.155466	+	0.269274i	−0.777763	+	0.628558i	$0.783646\pi$
$354$		0			0
$355$	−9186.45	+	15911.4i	−1.37343	+	2.37884i
$356$		0			0
$357$	206.393	−	586.868i	0.0305980	−	0.0870038i
$358$		0			0
$359$	3465.52			0.509480			0.254740	−	0.967010i	$-0.418010\pi$
$359$	3465.52			0.509480			0.254740	+	0.967010i	$0.418010\pi$
$360$		0			0
$361$	7799.88			1.13717
$362$		0			0
$363$	−6249.05	+	1172.18i	−0.903554	+	0.169486i
$364$		0			0
$365$	−7686.24	+	13313.0i	−1.10224	+	1.90913i
$366$		0			0
$367$	−3850.64	−	6669.50i	−0.547688	−	0.948624i	−0.998432	−	0.0559706i	$-0.982175\pi$
$367$	−3850.64	−	6669.50i	−0.547688	−	0.948624i	0.450744	−	0.892653i	$-0.351159\pi$
$368$		0			0
$369$	4061.21	+	3259.71i	0.572949	+	0.459875i
$370$		0			0
$371$	−578.061	−	1001.23i	−0.0808934	−	0.140111i
$372$		0			0
$373$	−5016.90	+	8689.53i	−0.696422	+	1.20624i	0.273277	+	0.961935i	$0.411892\pi$
$373$	−5016.90	+	8689.53i	−0.696422	+	1.20624i	−0.969699	+	0.244303i	$0.921441\pi$
$374$		0			0
$375$	−1288.98	−	1502.61i	−0.177500	−	0.206918i
$376$		0			0
$377$	−2778.20			−0.379535
$378$		0			0
$379$	11087.4			1.50269			0.751346	−	0.659908i	$-0.229405\pi$
$379$	11087.4			1.50269			0.751346	+	0.659908i	$0.229405\pi$
$380$		0			0
$381$	−2383.56	−	2778.59i	−0.320507	−	0.373626i
$382$		0			0
$383$	5243.12	−	9081.35i	0.699507	−	1.21158i	−0.269131	−	0.963104i	$-0.586736\pi$
$383$	5243.12	−	9081.35i	0.699507	−	1.21158i	0.968638	−	0.248477i	$-0.0799302\pi$
$384$		0			0
$385$	−599.359	−	1038.12i	−0.0793407	−	0.137422i
$386$		0			0
$387$	12183.7	−	4737.49i	1.60035	−	0.622274i
$388$		0			0
$389$	−3728.66	−	6458.23i	−0.485991	−	0.841761i	0.513879	−	0.857863i	$-0.328208\pi$
$389$	−3728.66	−	6458.23i	−0.485991	−	0.841761i	−0.999870	+	0.0161012i	$0.994875\pi$
$390$		0			0
$391$	153.568	−	265.987i	0.0198625	−	0.0344029i
$392$		0			0
$393$	2020.57	−	379.013i	0.259349	−	0.0486480i
$394$		0			0
$395$	5850.23			0.745207
$396$		0			0
$397$	1954.58			0.247097			0.123549	−	0.992339i	$-0.460573\pi$
$397$	1954.58			0.247097			0.123549	+	0.992339i	$0.460573\pi$
$398$		0			0
$399$	−1461.04	+	4154.40i	−0.183318	+	0.521254i
$400$		0			0
$401$	−689.230	+	1193.78i	−0.0858317	+	0.148665i	−0.905745	−	0.423822i	$-0.860688\pi$
$401$	−689.230	+	1193.78i	−0.0858317	+	0.148665i	0.819914	+	0.572487i	$0.194021\pi$
$402$		0			0
$403$	−3284.27	−	5688.52i	−0.405958	−	0.703140i
$404$		0			0
$405$	8882.07	−	8137.71i	1.08976	−	0.998435i
$406$		0			0
$407$	−569.791	−	986.907i	−0.0693943	−	0.120194i
$408$		0			0
$409$	−6983.35	+	12095.5i	−0.844265	+	1.46231i	0.0419939	+	0.999118i	$0.486629\pi$
$409$	−6983.35	+	12095.5i	−0.844265	+	1.46231i	−0.886258	+	0.463191i	$0.846704\pi$
$410$		0			0
$411$	2534.73	−	7207.38i	0.304207	−	0.864997i
$412$		0			0
$413$	−592.155			−0.0705522
$414$		0			0
$415$	−24103.7			−2.85109
$416$		0			0
$417$	−8177.88	+	1533.99i	−0.960366	+	0.180143i
$418$		0			0
$419$	6252.43	−	10829.5i	0.729000	−	1.26267i	−0.228306	−	0.973589i	$-0.573319\pi$
$419$	6252.43	−	10829.5i	0.729000	−	1.26267i	0.957306	−	0.289076i	$-0.0933480\pi$
$420$		0			0
$421$	6529.95	+	11310.2i	0.755939	+	1.30932i	0.944906	+	0.327341i	$0.106153\pi$
$421$	6529.95	+	11310.2i	0.755939	+	1.30932i	−0.188968	+	0.981983i	$0.560514\pi$
$422$		0			0
$423$	−5900.72	+	2294.42i	−0.678258	+	0.263731i
$424$		0			0
$425$	1266.14	+	2193.01i	0.144510	+	0.250298i
$426$		0			0
$427$	140.768	−	243.818i	0.0159538	−	0.0276328i
$428$		0			0
$429$	738.811	+	861.257i	0.0831472	+	0.0969275i
$430$		0			0
$431$	−8780.65			−0.981320			−0.490660	−	0.871351i	$-0.663244\pi$
$431$	−8780.65			−0.981320			−0.490660	+	0.871351i	$0.663244\pi$
$432$		0			0
$433$	1384.64			0.153676			0.0768380	−	0.997044i	$-0.475518\pi$
$433$	1384.64			0.153676			0.0768380	+	0.997044i	$0.475518\pi$
$434$		0			0
$435$	−7370.51	−	8592.05i	−0.812388	−	0.947029i
$436$		0			0
$437$	−1087.10	+	1882.91i	−0.119000	+	0.206113i
$438$		0			0
$439$	−3470.52	−	6011.11i	−0.377309	−	0.653518i	0.613361	−	0.789803i	$-0.289817\pi$
$439$	−3470.52	−	6011.11i	−0.377309	−	0.653518i	−0.990670	+	0.136284i	$0.956484\pi$
$440$		0			0
$441$	−1031.76	−	828.135i	−0.111409	−	0.0894217i
$442$		0			0
$443$	−5462.27	−	9460.92i	−0.585824	−	1.01468i	−0.994772	−	0.102119i	$-0.967438\pi$
$443$	−5462.27	−	9460.92i	−0.585824	−	1.01468i	0.408948	−	0.912558i	$-0.365896\pi$
$444$		0			0
$445$	−6745.86	+	11684.2i	−0.718616	+	1.24468i
$446$		0			0
$447$	−950.541	+	178.300i	−0.100580	+	0.0188665i
$448$		0			0
$449$	4298.84			0.451837			0.225918	−	0.974146i	$-0.427462\pi$
$449$	4298.84			0.451837			0.225918	+	0.974146i	$0.427462\pi$
$450$		0			0
$451$	−1998.79			−0.208690
$452$		0			0
$453$	−2970.03	+	8445.12i	−0.308044	+	0.875908i
$454$		0			0
$455$	1218.74	−	2110.92i	0.125572	−	0.217498i
$456$		0			0
$457$	6285.76	+	10887.3i	0.643404	+	1.11441i	0.984668	+	0.174441i	$0.0558117\pi$
$457$	6285.76	+	10887.3i	0.643404	+	1.11441i	−0.341264	+	0.939968i	$0.610855\pi$
$458$		0			0
$459$	−2037.76	+	1267.01i	−0.207222	+	0.128843i
$460$		0			0
$461$	−3103.58	−	5375.56i	−0.313554	−	0.543091i	0.665575	−	0.746331i	$-0.268186\pi$
$461$	−3103.58	−	5375.56i	−0.313554	−	0.543091i	−0.979129	+	0.203240i	$0.934853\pi$
$462$		0			0
$463$	905.556	−	1568.47i	0.0908958	−	0.157436i	−0.816993	−	0.576648i	$-0.804360\pi$
$463$	905.556	−	1568.47i	0.0908958	−	0.157436i	0.907888	+	0.419212i	$0.137694\pi$
$464$		0			0
$465$	8879.60	−	25248.7i	0.885551	−	2.51802i
$466$		0			0
$467$	15682.4			1.55395			0.776974	−	0.629533i	$-0.216754\pi$
$467$	15682.4			1.55395			0.776974	+	0.629533i	$0.216754\pi$
$468$		0			0
$469$	4787.45			0.471352
$470$		0			0
$471$	−9979.66	+	1871.96i	−0.976303	+	0.183132i
$472$		0			0
$473$	−2508.73	+	4345.25i	−0.243872	+	0.422399i
$474$		0			0
$475$	−8962.89	−	15524.2i	−0.865781	−	1.49958i
$476$		0			0
$477$	−678.530	+	4407.40i	−0.0651316	+	0.423063i
$478$		0			0
$479$	7527.25	+	13037.6i	0.718014	+	1.24364i	0.961785	+	0.273805i	$0.0882822\pi$
$479$	7527.25	+	13037.6i	0.718014	+	1.24364i	−0.243771	+	0.969833i	$0.578385\pi$
$480$		0			0
$481$	1158.62	−	2006.78i	0.109830	−	0.190231i
$482$		0			0
$483$	−425.275	−	495.757i	−0.0400635	−	0.0467034i
$484$		0			0
$485$	6310.74			0.590837
$486$		0			0
$487$	16586.3			1.54332			0.771660	−	0.636035i	$-0.219427\pi$
$487$	16586.3			1.54332			0.771660	+	0.636035i	$0.219427\pi$
$488$		0			0
$489$	5920.64	+	6901.89i	0.547527	+	0.638271i
$490$		0			0
$491$	−4910.83	+	8505.80i	−0.451370	+	0.781795i	−0.998471	−	0.0552708i	$-0.982398\pi$
$491$	−4910.83	+	8505.80i	−0.451370	+	0.781795i	0.547102	+	0.837066i	$0.315731\pi$
$492$		0			0
$493$	1127.46	+	1952.81i	0.102998	+	0.178398i
$494$		0			0
$495$	−703.530	+	4569.79i	−0.0638815	+	0.414943i
$496$		0			0
$497$	−3891.52	−	6740.31i	−0.351224	−	0.608338i
$498$		0			0
$499$	9399.56	−	16280.5i	0.843251	−	1.46055i	−0.0438813	−	0.999037i	$-0.513972\pi$
$499$	9399.56	−	16280.5i	0.843251	−	1.46055i	0.887132	−	0.461516i	$-0.152694\pi$
$500$		0			0
$501$	−7858.22	+	1474.03i	−0.700757	+	0.131446i
$502$		0			0
$503$	6219.35			0.551307			0.275653	−	0.961257i	$-0.411106\pi$
$503$	6219.35			0.551307			0.275653	+	0.961257i	$0.411106\pi$
$504$		0			0
$505$	28127.1			2.47849
$506$		0			0
$507$	3021.93	−	8592.69i	0.264711	−	0.752692i
$508$		0			0
$509$	1780.91	−	3084.62i	0.155083	−	0.268612i	−0.778006	−	0.628257i	$-0.783769\pi$
$509$	1780.91	−	3084.62i	0.155083	−	0.268612i	0.933089	+	0.359645i	$0.117102\pi$
$510$		0			0
$511$	−3256.01	−	5639.57i	−0.281873	−	0.488219i
$512$		0			0
$513$	14425.2	−	8969.07i	1.24150	−	0.771918i
$514$		0			0
$515$	3716.45	+	6437.08i	0.317993	+	0.550780i
$516$		0			0
$517$	1215.01	−	2104.45i	0.103358	−	0.179021i
$518$		0			0
$519$	−3962.69	+	11267.7i	−0.335150	+	0.952981i
$520$		0			0
$521$	13766.1			1.15759			0.578794	−	0.815474i	$-0.303524\pi$
$521$	13766.1			1.15759			0.578794	+	0.815474i	$0.303524\pi$
$522$		0			0
$523$	−23232.3			−1.94241			−0.971204	−	0.238251i	$-0.923426\pi$
$523$	−23232.3			−1.94241			−0.971204	+	0.238251i	$0.923426\pi$
$524$		0			0
$525$	5292.96	−	992.841i	0.440007	−	0.0825355i
$526$		0			0
$527$	−2665.66	+	4617.05i	−0.220338	+	0.381636i
$528$		0			0
$529$	5922.26	+	10257.7i	0.486748	+	0.843072i
$530$		0			0
$531$	1781.22	+	1429.69i	0.145572	+	0.116842i
$532$		0			0
$533$	−2032.18	−	3519.83i	−0.165147	−	0.286043i
$534$		0			0
$535$	8080.84	−	13996.4i	0.653019	−	1.13106i
$536$		0			0
$537$	−4575.70	−	5334.04i	−0.367702	−	0.428642i
$538$		0			0
$539$	507.796			0.0405794
$540$		0			0
$541$	−11027.3			−0.876343			−0.438171	−	0.898891i	$-0.644374\pi$
$541$	−11027.3			−0.876343			−0.438171	+	0.898891i	$0.644374\pi$
$542$		0			0
$543$	11406.3	+	13296.8i	0.901460	+	1.05086i
$544$		0			0
$545$	8274.61	−	14332.0i	0.650358	−	1.12645i
$546$		0			0
$547$	1680.79	+	2911.22i	0.131381	+	0.227559i	0.924209	−	0.381887i	$-0.124725\pi$
$547$	1680.79	+	2911.22i	0.131381	+	0.227559i	−0.792828	+	0.609445i	$0.791392\pi$
$548$		0			0
$549$	−1012.11	+	393.544i	−0.0786807	+	0.0305939i
$550$		0			0
$551$	−7981.19	−	13823.8i	−0.617078	−	1.06881i
$552$		0			0
$553$	−1239.12	+	2146.22i	−0.0952855	+	0.165039i
$554$		0			0
$555$	9280.08	−	1740.74i	0.709761	−	0.133135i
$556$		0			0
$557$	−5114.38			−0.389054			−0.194527	−	0.980897i	$-0.562317\pi$
$557$	−5114.38			−0.389054			−0.194527	+	0.980897i	$0.562317\pi$
$558$		0			0
$559$	−10202.5			−0.771952
$560$		0			0
$561$	305.556	−	868.831i	0.0229957	−	0.0653870i
$562$		0			0
$563$	−10550.9	+	18274.7i	−0.789816	+	1.36800i	0.136263	+	0.990673i	$0.456491\pi$
$563$	−10550.9	+	18274.7i	−0.789816	+	1.36800i	−0.926079	+	0.377329i	$0.876843\pi$
$564$		0			0
$565$	−12078.2	−	20920.1i	−0.899353	−	1.55772i
$566$		0			0
$567$	1104.13	+	4982.12i	0.0817794	+	0.369011i
$568$		0			0
$569$	6545.80	+	11337.6i	0.482274	+	0.835323i	0.999793	−	0.0203485i	$-0.00647757\pi$
$569$	6545.80	+	11337.6i	0.482274	+	0.835323i	−0.517519	+	0.855672i	$0.673144\pi$
$570$		0			0
$571$	12158.4	−	21059.0i	0.891094	−	1.54342i	0.0525280	−	0.998619i	$-0.483272\pi$
$571$	12158.4	−	21059.0i	0.891094	−	1.54342i	0.838566	−	0.544800i	$-0.183395\pi$
$572$		0			0
$573$	−7967.15	+	22654.2i	−0.580859	+	1.65164i
$574$		0			0
$575$	2658.74			0.192830
$576$		0			0
$577$	23067.5			1.66432			0.832161	−	0.554534i	$-0.187103\pi$
$577$	23067.5			1.66432			0.832161	+	0.554534i	$0.187103\pi$
$578$		0			0
$579$	−712.722	+	133.691i	−0.0511567	+	0.00959584i
$580$		0			0
$581$	5105.34	−	8842.72i	0.364553	−	0.631425i
$582$		0			0
$583$	−855.793	−	1482.28i	−0.0607947	−	0.105300i
$584$		0			0
$585$	−8762.59	+	3407.22i	−0.619297	+	0.240805i
$586$		0			0
$587$	−2466.60	−	4272.27i	−0.173437	−	0.300401i	0.766182	−	0.642623i	$-0.222154\pi$
$587$	−2466.60	−	4272.27i	−0.173437	−	0.300401i	−0.939619	+	0.342222i	$0.888821\pi$
$588$		0			0
$589$	18870.0	−	32683.8i	1.32008	−	2.28644i
$590$		0			0
$591$	−5414.66	−	6312.05i	−0.376869	−	0.439328i
$592$		0			0
$593$	−26030.0			−1.80257			−0.901284	−	0.433228i	$-0.857374\pi$
$593$	−26030.0			−1.80257			−0.901284	+	0.433228i	$0.857374\pi$
$594$		0			0
$595$	−1978.37			−0.136311
$596$		0			0
$597$	−14235.3	−	16594.6i	−0.975900	−	1.13764i
$598$		0			0
$599$	4029.50	−	6979.29i	0.274859	−	0.476070i	−0.695240	−	0.718777i	$-0.744702\pi$
$599$	4029.50	−	6979.29i	0.274859	−	0.476070i	0.970100	+	0.242707i	$0.0780354\pi$
$600$		0			0
$601$	2089.84	+	3619.71i	0.141841	+	0.245675i	0.928190	−	0.372107i	$-0.121365\pi$
$601$	2089.84	+	3619.71i	0.141841	+	0.245675i	−0.786349	+	0.617782i	$0.788031\pi$
$602$		0			0
$603$	−14400.8	−	11558.8i	−0.972549	−	0.780612i
$604$		0			0
$605$	10109.7	+	17510.5i	0.679367	+	1.17670i
$606$		0			0
$607$	−8057.62	+	13956.2i	−0.538796	+	0.933221i	0.460174	+	0.887829i	$0.347787\pi$
$607$	−8057.62	+	13956.2i	−0.538796	+	0.933221i	−0.998969	+	0.0453924i	$0.985546\pi$
$608$		0			0
$609$	4713.23	−	884.095i	0.313612	−	0.0588265i
$610$		0			0
$611$	4941.20			0.327168
$612$		0			0
$613$	−10083.8			−0.664404			−0.332202	−	0.943208i	$-0.607792\pi$
$613$	−10083.8			−0.664404			−0.332202	+	0.943208i	$0.607792\pi$
$614$		0			0
$615$	5494.34	−	15622.9i	0.360249	−	1.02435i
$616$		0			0
$617$	−11953.6	+	20704.2i	−0.779956	+	1.35092i	0.152010	+	0.988379i	$0.451425\pi$
$617$	−11953.6	+	20704.2i	−0.779956	+	1.35092i	−0.931966	+	0.362545i	$0.881908\pi$
$618$		0			0
$619$	−6285.89	−	10887.5i	−0.408160	−	0.706954i	0.586523	−	0.809932i	$-0.300496\pi$
$619$	−6285.89	−	10887.5i	−0.408160	−	0.706954i	−0.994684	+	0.102978i	$0.967163\pi$
$620$		0			0
$621$	82.2930	+	2518.03i	0.00531772	+	0.162714i
$622$		0			0
$623$	−2857.65	−	4949.59i	−0.183771	−	0.318300i
$624$		0			0
$625$	6105.66	−	10575.3i	0.390762	−	0.676820i
$626$		0			0
$627$	−2163.01	+	6150.40i	−0.137771	+	0.391744i
$628$		0			0
$629$	−1880.77			−0.119223
$630$		0			0
$631$	−2626.09			−0.165678			−0.0828391	−	0.996563i	$-0.526399\pi$
$631$	−2626.09			−0.165678			−0.0828391	+	0.996563i	$0.526399\pi$
$632$		0			0
$633$	−120.730	+	22.6462i	−0.00758069	+	0.00142197i
$634$		0			0
$635$	−5821.00	+	10082.3i	−0.363779	+	0.630083i
$636$		0			0
$637$	516.277	+	894.218i	0.0321125	+	0.0556204i
$638$		0			0
$639$	−4567.88	+	29670.7i	−0.282789	+	1.83686i
$640$		0			0
$641$	7048.21	+	12207.9i	0.434302	+	0.752233i	0.997238	−	0.0742674i	$-0.0236618\pi$
$641$	7048.21	+	12207.9i	0.434302	+	0.752233i	−0.562937	+	0.826500i	$0.690328\pi$
$642$		0			0
$643$	9907.64	−	17160.5i	0.607651	−	1.05248i	−0.383976	−	0.923343i	$-0.625445\pi$
$643$	9907.64	−	17160.5i	0.607651	−	1.05248i	0.991627	−	0.129138i	$-0.0412212\pi$
$644$		0			0
$645$	−27067.1	−	31553.0i	−1.65235	−	1.92620i
$646$		0			0
$647$	−3815.35			−0.231834			−0.115917	−	0.993259i	$-0.536981\pi$
$647$	−3815.35			−0.231834			−0.115917	+	0.993259i	$0.536981\pi$
$648$		0			0
$649$	−876.658			−0.0530229
$650$		0			0
$651$	7382.00	+	8605.44i	0.444429	+	0.518086i
$652$		0			0
$653$	13894.5	−	24066.0i	0.832671	−	1.44223i	−0.0632420	−	0.997998i	$-0.520144\pi$
$653$	13894.5	−	24066.0i	0.832671	−	1.44223i	0.895913	−	0.444230i	$-0.146523\pi$
$654$		0			0
$655$	−3268.86	−	5661.84i	−0.195000	−	0.337750i
$656$		0			0
$657$	−3821.91	+	24825.3i	−0.226951	+	1.47417i
$658$		0			0
$659$	8601.80	+	14898.8i	0.508465	+	0.880687i	0.999952	+	0.00980242i	$0.00312026\pi$
$659$	8601.80	+	14898.8i	0.508465	+	0.880687i	−0.491487	+	0.870885i	$0.663546\pi$
$660$		0			0
$661$	−2408.46	+	4171.58i	−0.141722	+	0.245470i	−0.928145	−	0.372218i	$-0.878597\pi$
$661$	−2408.46	+	4171.58i	−0.141722	+	0.245470i	0.786423	+	0.617688i	$0.211931\pi$
$662$		0			0
$663$	1840.65	−	345.265i	0.107821	−	0.0202247i
$664$		0			0
$665$	14004.7			0.816662
$666$		0			0
$667$	2367.53			0.137438
$668$		0			0
$669$	2822.59	−	8025.89i	0.163121	−	0.463825i
$670$		0			0
$671$	208.401	−	360.962i	0.0119899	−	0.0207672i
$672$		0			0
$673$	3131.75	+	5424.35i	0.179376	+	0.310689i	0.941667	−	0.336546i	$-0.109259\pi$
$673$	3131.75	+	5424.35i	0.179376	+	0.310689i	−0.762291	+	0.647235i	$0.775925\pi$
$674$		0			0
$675$	−18318.5	−	9792.75i	−1.04456	−	0.558405i
$676$		0			0
$677$	−274.156	−	474.852i	−0.0155638	−	0.0269572i	0.858139	−	0.513418i	$-0.171621\pi$
$677$	−274.156	−	474.852i	−0.0155638	−	0.0269572i	−0.873702	+	0.486461i	$0.838288\pi$
$678$		0			0
$679$	−1336.66	+	2315.17i	−0.0755471	+	0.130851i
$680$		0			0
$681$	−4013.04	+	11410.9i	−0.225815	+	0.642093i
$682$		0			0
$683$	24764.5			1.38739			0.693695	−	0.720269i	$-0.255982\pi$
$683$	24764.5			1.38739			0.693695	+	0.720269i	$0.255982\pi$
$684$		0			0
$685$	−24296.5			−1.35521
$686$		0			0
$687$	−16704.6	+	3133.41i	−0.927686	+	0.174013i
$688$		0			0
$689$	1740.17	−	3014.07i	0.0962196	−	0.166657i
$690$		0			0
$691$	11873.3	+	20565.2i	0.653664	+	1.13218i	0.982227	+	0.187698i	$0.0601025\pi$
$691$	11873.3	+	20565.2i	0.653664	+	1.13218i	−0.328563	+	0.944482i	$0.606564\pi$
$692$		0			0
$693$	−1527.47	−	1226.02i	−0.0837283	−	0.0672041i
$694$		0			0
$695$	13230.1	+	22915.3i	0.722083	+	1.25068i
$696$		0			0
$697$	−1649.40	+	2856.85i	−0.0896350	+	0.155252i
$698$		0			0
$699$	3433.97	+	4003.10i	0.185815	+	0.216611i
$700$		0			0
$701$	−36609.4			−1.97249			−0.986247	−	0.165278i	$-0.947148\pi$
$701$	−36609.4			−1.97249			−0.986247	+	0.165278i	$0.947148\pi$
$702$		0			0
$703$	13313.8			0.714283
$704$		0			0
$705$	13108.9	+	15281.5i	0.700297	+	0.816360i
$706$		0			0
$707$	−5957.54	+	10318.8i	−0.316911	+	0.548906i
$708$		0			0
$709$	5501.06	+	9528.12i	0.291392	+	0.504705i	0.974139	−	0.225949i	$-0.0725483\pi$
$709$	5501.06	+	9528.12i	0.291392	+	0.504705i	−0.682747	+	0.730655i	$0.739215\pi$
$710$		0			0
$711$	8909.14	−	3464.20i	0.469928	−	0.182725i
$712$		0			0
$713$	2798.78	+	4847.64i	0.147006	+	0.254622i
$714$		0			0
$715$	1804.29	−	3125.12i	0.0943728	−	0.163459i
$716$		0			0
$717$	−5110.32	+	958.581i	−0.266176	+	0.0499287i
$718$		0			0
$719$	28743.4			1.49089			0.745443	−	0.666569i	$-0.232238\pi$
$719$	28743.4			1.49089			0.745443	+	0.666569i	$0.232238\pi$
$720$		0			0
$721$	−3148.69			−0.162640
$722$		0			0
$723$	388.456	−	1104.55i	0.0199818	−	0.0568172i
$724$		0			0
$725$	−9759.90	+	16904.6i	−0.499963	+	0.865962i
$726$		0			0
$727$	7109.10	+	12313.3i	0.362671	+	0.628165i	0.988400	−	0.151876i	$-0.0485315\pi$
$727$	7109.10	+	12313.3i	0.362671	+	0.628165i	−0.625728	+	0.780041i	$0.715198\pi$
$728$		0			0
$729$	8707.51	−	17652.2i	0.442388	−	0.896824i
$730$		0			0
$731$	4140.41	+	7171.41i	0.209492	+	0.362851i
$732$		0			0
$733$	−4098.10	+	7098.12i	−0.206503	+	0.357674i	−0.950611	−	0.310386i	$-0.899542\pi$
$733$	−4098.10	+	7098.12i	−0.206503	+	0.357674i	0.744107	+	0.668060i	$0.232875\pi$
$734$		0			0
$735$	−1395.85	+	3969.01i	−0.0700497	+	0.199183i
$736$		0			0
$737$	7087.60			0.354240
$738$		0			0
$739$	31225.0			1.55430			0.777152	−	0.629313i	$-0.216663\pi$
$739$	31225.0			1.55430			0.777152	+	0.629313i	$0.216663\pi$
$740$		0			0
$741$	−13029.9	+	2444.11i	−0.645971	+	0.121170i
$742$		0			0
$743$	−14438.2	+	25007.7i	−0.712901	+	1.23478i	0.250862	+	0.968023i	$0.419286\pi$
$743$	−14438.2	+	25007.7i	−0.712901	+	1.23478i	−0.963764	+	0.266758i	$0.914048\pi$
$744$		0			0
$745$	1537.78	+	2663.51i	0.0756240	+	0.130985i
$746$		0			0
$747$	−36706.8	+	14272.9i	−1.79790	+	0.699089i
$748$		0			0
$749$	3423.17	+	5929.10i	0.166996	+	0.289245i
$750$		0			0
$751$	−7447.78	+	12899.9i	−0.361882	+	0.626798i	−0.988271	−	0.152713i	$-0.951199\pi$
$751$	−7447.78	+	12899.9i	−0.361882	+	0.626798i	0.626388	+	0.779511i	$0.284532\pi$
$752$		0			0
$753$	−23384.6	−	27260.2i	−1.13171	−	1.31928i
$754$		0			0
$755$	28469.0			1.37231
$756$		0			0
$757$	−3486.75			−0.167409			−0.0837043	−	0.996491i	$-0.526675\pi$
$757$	−3486.75			−0.167409			−0.0837043	+	0.996491i	$0.526675\pi$
$758$		0			0
$759$	−629.600	−	733.945i	−0.0301094	−	0.0350995i
$760$		0			0
$761$	5224.64	−	9049.34i	0.248874	−	0.431062i	−0.714340	−	0.699799i	$-0.753273\pi$
$761$	5224.64	−	9049.34i	0.248874	−	0.431062i	0.963214	+	0.268737i	$0.0866062\pi$
$762$		0			0
$763$	3505.25	+	6071.27i	0.166315	+	0.288067i
$764$		0			0
$765$	5951.00	+	4776.54i	0.281253	+	0.225747i
$766$		0			0
$767$	−891.300	−	1543.78i	−0.0419596	−	0.0726761i
$768$		0			0
$769$	−19948.3	+	34551.5i	−0.935441	+	1.62023i	−0.161596	+	0.986857i	$0.551664\pi$
$769$	−19948.3	+	34551.5i	−0.935441	+	1.62023i	−0.773845	+	0.633375i	$0.781669\pi$
$770$		0			0
$771$	−15996.3	+	3000.56i	−0.747204	+	0.140159i
$772$		0			0
$773$	−28364.2			−1.31978			−0.659889	−	0.751363i	$-0.729397\pi$
$773$	−28364.2			−1.31978			−0.659889	+	0.751363i	$0.729397\pi$
$774$		0			0
$775$	−46150.9			−2.13908
$776$		0			0
$777$	−1326.98	+	3773.21i	−0.0612680	+	0.174212i
$778$		0			0
$779$	11676.0	−	20223.5i	0.537018	−	0.930142i
$780$		0			0
$781$	−5761.22	−	9978.72i	−0.263960	−	0.457192i
$782$		0			0
$783$	−16312.1	−	8720.16i	−0.744505	−	0.397999i
$784$		0			0
$785$	16145.1	+	27964.0i	0.734066	+	1.27144i
$786$		0			0
$787$	10735.5	−	18594.4i	0.486250	−	0.842210i	−0.513625	−	0.858015i	$-0.671698\pi$
$787$	10735.5	−	18594.4i	0.486250	−	0.842210i	0.999875	+	0.0158047i	$0.00503100\pi$
$788$		0			0
$789$	−12471.4	+	35461.8i	−0.562730	+	1.60009i
$790$		0			0
$791$	10233.0			0.459981
$792$		0			0
$793$	847.528			0.0379528
$794$		0			0
$795$	13938.1	−	2614.48i	0.621805	−	0.116637i
$796$		0			0
$797$	−10516.1	+	18214.4i	−0.467377	+	0.809520i	−0.999305	−	0.0372690i	$-0.988134\pi$
$797$	−10516.1	+	18214.4i	−0.467377	+	0.809520i	0.531929	+	0.846789i	$0.321467\pi$
$798$		0			0
$799$	−2005.25	−	3473.19i	−0.0887867	−	0.153783i
$800$		0			0
$801$	−3354.32	+	21788.0i	−0.147964	+	0.961101i
$802$		0			0
$803$	−4820.37	−	8349.12i	−0.211840	−	0.366917i
$804$		0			0
$805$	−1038.58	+	1798.88i	−0.0454724	+	0.0787605i
$806$		0			0
$807$	26565.3	+	30968.0i	1.15879	+	1.35084i
$808$		0			0
$809$	25486.1			1.10759			0.553797	−	0.832651i	$-0.313178\pi$
$809$	25486.1			1.10759			0.553797	+	0.832651i	$0.313178\pi$
$810$		0			0
$811$	−19211.8			−0.831833			−0.415916	−	0.909403i	$-0.636539\pi$
$811$	−19211.8			−0.831833			−0.415916	+	0.909403i	$0.636539\pi$
$812$		0			0
$813$	−18552.1	−	21626.9i	−0.800310	−	0.932948i
$814$		0			0
$815$	14459.1	−	25043.9i	0.621448	−	1.07638i
$816$		0			0
$817$	−29309.7	−	50765.9i	−1.25510	−	2.17390i
$818$		0			0
$819$	606.008	−	3936.33i	0.0258555	−	0.167945i
$820$		0			0
$821$	−6902.19	−	11954.9i	−0.293408	−	0.508198i	0.681205	−	0.732093i	$-0.261456\pi$
$821$	−6902.19	−	11954.9i	−0.293408	−	0.508198i	−0.974613	+	0.223895i	$0.928123\pi$
$822$		0			0
$823$	7784.97	−	13484.0i	0.329729	−	0.571108i	−0.652729	−	0.757592i	$-0.726376\pi$
$823$	7784.97	−	13484.0i	0.329729	−	0.571108i	0.982458	+	0.186484i	$0.0597093\pi$
$824$		0			0
$825$	7835.99	−	1469.86i	0.330684	−	0.0620288i
$826$		0			0
$827$	−5492.76			−0.230958			−0.115479	−	0.993310i	$-0.536840\pi$
$827$	−5492.76			−0.230958			−0.115479	+	0.993310i	$0.536840\pi$
$828$		0			0
$829$	18254.5			0.764785			0.382392	−	0.924000i	$-0.375100\pi$
$829$	18254.5			0.764785			0.382392	+	0.924000i	$0.375100\pi$
$830$		0			0
$831$	856.834	−	2436.36i	0.0357680	−	0.101705i
$832$		0			0
$833$	419.033	−	725.787i	0.0174293	−	0.0301885i
$834$		0			0
$835$	12713.0	+	22019.5i	0.526888	+	0.912596i
$836$		0			0
$837$	−1428.46	−	43708.5i	−0.0589901	−	1.80500i
$838$		0			0
$839$	−6187.38	−	10716.9i	−0.254603	−	0.440986i	0.710184	−	0.704016i	$-0.248612\pi$
$839$	−6187.38	−	10716.9i	−0.254603	−	0.440986i	−0.964788	+	0.263030i	$0.915278\pi$
$840$		0			0
$841$	3503.60	−	6068.41i	0.143655	−	0.248818i
$842$		0			0
$843$	−8857.03	+	25184.5i	−0.361865	+	1.02894i
$844$		0			0
$845$	−28966.5			−1.17926
$846$		0			0
$847$	−8565.23			−0.347467
$848$		0			0
$849$	28465.7	−	5339.52i	1.15069	−	0.215844i
$850$		0			0
$851$	−987.348	+	1710.14i	−0.0397718	+	0.0688869i
$852$		0			0
$853$	−14679.3	−	25425.3i	−0.589227	−	1.02057i	−0.994334	−	0.106302i	$-0.966099\pi$
$853$	−14679.3	−	25425.3i	−0.589227	−	1.02057i	0.405107	−	0.914269i	$-0.367234\pi$
$854$		0			0
$855$	−42126.8	−	33812.8i	−1.68503	−	1.35249i
$856$		0			0
$857$	4218.55	+	7306.74i	0.168148	+	0.291241i	0.937769	−	0.347260i	$-0.112888\pi$
$857$	4218.55	+	7306.74i	0.168148	+	0.291241i	−0.769621	+	0.638501i	$0.779555\pi$
$858$		0			0
$859$	−2603.51	+	4509.41i	−0.103412	+	0.179114i	−0.913088	−	0.407762i	$-0.866309\pi$
$859$	−2603.51	+	4509.41i	−0.103412	+	0.179114i	0.809677	+	0.586876i	$0.199643\pi$
$860$		0			0
$861$	4567.69	+	5324.71i	0.180797	+	0.210761i
$862$		0			0
$863$	−34840.1			−1.37424			−0.687121	−	0.726543i	$-0.741126\pi$
$863$	−34840.1			−1.37424			−0.687121	+	0.726543i	$0.741126\pi$
$864$		0			0
$865$	37984.1			1.49306
$866$		0			0
$867$	15631.9	+	18222.6i	0.612325	+	0.713807i
$868$		0			0
$869$	−1834.46	+	3177.39i	−0.0716110	+	0.124034i
$870$		0			0
$871$	7205.98	+	12481.1i	0.280328	+	0.485542i
$872$		0			0
$873$	9610.45	−	3736.89i	0.372582	−	0.144874i
$874$		0			0
$875$	−1333.49	−	2309.68i	−0.0515203	−	0.0892357i
$876$		0			0
$877$	10079.3	−	17457.9i	0.388090	−	0.672192i	−0.604103	−	0.796907i	$-0.706468\pi$
$877$	10079.3	−	17457.9i	0.388090	−	0.672192i	0.992193	+	0.124715i	$0.0398016\pi$
$878$		0			0
$879$	45108.4	−	8461.32i	1.73091	−	0.324679i
$880$		0			0
$881$	−42104.3			−1.61014			−0.805069	−	0.593182i	$-0.797872\pi$
$881$	−42104.3			−1.61014			−0.805069	+	0.593182i	$0.797872\pi$
$882$		0			0
$883$	25081.4			0.955896			0.477948	−	0.878388i	$-0.341381\pi$
$883$	25081.4			0.955896			0.477948	+	0.878388i	$0.341381\pi$
$884$		0			0
$885$	2409.79	−	6852.10i	0.0915301	−	0.260261i
$886$		0			0
$887$	18244.8	−	31601.0i	0.690645	−	1.19623i	−0.280982	−	0.959713i	$-0.590660\pi$
$887$	18244.8	−	31601.0i	0.690645	−	1.19623i	0.971627	−	0.236519i	$-0.0760065\pi$
$888$		0			0
$889$	−2465.87	−	4271.01i	−0.0930287	−	0.161130i
$890$		0			0
$891$	1634.61	+	7375.80i	0.0614606	+	0.277327i
$892$		0			0
$893$	14195.0	+	24586.5i	0.531936	+	0.921339i
$894$		0			0
$895$	−11174.5	+	19354.9i	−0.417345	+	0.722863i
$896$		0			0
$897$	652.348	−	1854.92i	0.0242823	−	0.0690455i
$898$		0			0
$899$	−41096.0			−1.52461
$900$		0			0
$901$	−2824.80			−0.104448
$902$		0			0
$903$	17308.6	−	3246.71i	0.637868	−	0.119650i
$904$		0			0
$905$	27856.0	−	48248.0i	1.02317	−	1.77217i
$906$		0			0
$907$	9619.00	+	16660.6i	0.352143	+	0.609929i	0.986625	−	0.163008i	$-0.0521198\pi$
$907$	9619.00	+	16660.6i	0.352143	+	0.609929i	−0.634482	+	0.772938i	$0.718786\pi$
$908$		0			0
$909$	42834.0	−	16655.4i	1.56294	−	0.607728i
$910$		0			0
$911$	16791.4	+	29083.5i	0.610674	+	1.05772i	0.991127	+	0.132918i	$0.0424346\pi$
$911$	16791.4	+	29083.5i	0.610674	+	1.05772i	−0.380453	+	0.924800i	$0.624232\pi$
$912$		0			0
$913$	7558.23	−	13091.2i	0.273977	−	0.474542i
$914$		0			0
$915$	2248.47	+	2621.12i	0.0812374	+	0.0947011i
$916$		0			0
$917$	2769.48			0.0997343
$918$		0			0
$919$	15279.6			0.548451			0.274225	−	0.961665i	$-0.411579\pi$
$919$	15279.6			0.548451			0.274225	+	0.961665i	$0.411579\pi$
$920$		0			0
$921$	12506.9	+	14579.7i	0.447465	+	0.521625i
$922$		0			0
$923$	11714.9	−	20290.8i	0.417768	−	0.723596i
$924$		0			0
$925$	−8140.49	−	14099.7i	−0.289360	−	0.501186i
$926$		0			0
$927$	9471.38	+	7602.16i	0.335578	+	0.269350i
$928$		0			0
$929$	−18721.0	−	32425.8i	−0.661160	−	1.14516i	−0.980311	−	0.197459i	$-0.936731\pi$
$929$	−18721.0	−	32425.8i	−0.661160	−	1.14516i	0.319151	−	0.947704i	$-0.396602\pi$
$930$		0			0
$931$	−2966.31	+	5137.80i	−0.104422	+	0.180864i
$932$		0			0
$933$	13909.1	−	2609.04i	0.488064	−	0.0915499i
$934$		0			0
$935$	−2928.88			−0.102443
$936$		0			0
$937$	−7666.49			−0.267293			−0.133646	−	0.991029i	$-0.542669\pi$
$937$	−7666.49			−0.267293			−0.133646	+	0.991029i	$0.542669\pi$
$938$		0			0
$939$	1276.71	−	3630.26i	0.0443705	−	0.126165i
$940$		0			0
$941$	3384.87	−	5862.77i	0.117262	−	0.203104i	−0.801420	−	0.598103i	$-0.795922\pi$
$941$	3384.87	−	5862.77i	0.117262	−	0.203104i	0.918682	+	0.394998i	$0.129255\pi$
$942$		0			0
$943$	1731.78	+	2999.53i	0.0598032	+	0.103582i
$944$		0			0
$945$	13781.5	−	8568.83i	0.474404	−	0.294967i
$946$		0			0
$947$	−1483.33	−	2569.21i	−0.0508995	−	0.0881605i	0.839453	−	0.543432i	$-0.182875\pi$
$947$	−1483.33	−	2569.21i	−0.0508995	−	0.0881605i	−0.890353	+	0.455272i	$0.849542\pi$
$948$		0			0
$949$	9801.76	−	16977.1i	0.335278	−	0.580718i
$950$		0			0
$951$	−3238.63	+	9208.87i	−0.110431	+	0.314004i
$952$		0			0
$953$	−9565.60			−0.325142			−0.162571	−	0.986697i	$-0.551979\pi$
$953$	−9565.60			−0.325142			−0.162571	+	0.986697i	$0.551979\pi$
$954$		0			0
$955$	76368.5			2.58767
$956$		0			0
$957$	6977.71	−	1308.86i	0.235692	−	0.0442106i
$958$		0			0
$959$	5146.19	−	8913.46i	0.173284	−	0.300136i
$960$		0			0
$961$	−33686.3	−	58346.4i	−1.13076	−	1.95853i
$962$		0			0
$963$	4018.13	−	26099.8i	0.134457	−	0.873369i
$964$		0			0
$965$	1153.04	+	1997.12i	0.0384638	+	0.0666213i
$966$		0			0
$967$	−12412.5	+	21499.1i	−0.412782	+	0.714960i	−0.995193	−	0.0979351i	$-0.968776\pi$
$967$	−12412.5	+	21499.1i	−0.412782	+	0.714960i	0.582411	+	0.812895i	$0.302110\pi$
$968$		0			0
$969$	7005.79	+	8166.88i	0.232258	+	0.270751i
$970$		0			0
$971$	−49543.4			−1.63741			−0.818704	−	0.574216i	$-0.805307\pi$
$971$	−49543.4			−1.63741			−0.818704	+	0.574216i	$0.805307\pi$
$972$		0			0
$973$	−11209.0			−0.369315
$974$		0			0
$975$	10555.3	+	12304.6i	0.346706	+	0.404167i
$976$		0			0
$977$	1836.86	−	3181.54i	0.0601498	−	0.104183i	−0.834382	−	0.551186i	$-0.814175\pi$
$977$	1836.86	−	3181.54i	0.0601498	−	0.104183i	0.894532	+	0.447003i	$0.147509\pi$
$978$		0			0
$979$	−4230.62	−	7327.64i	−0.138111	−	0.239216i
$980$		0			0
$981$	4114.48	−	26725.6i	0.133909	−	0.869811i
$982$		0			0
$983$	−8502.06	−	14726.0i	−0.275863	−	0.477809i	0.694489	−	0.719503i	$-0.255630\pi$
$983$	−8502.06	−	14726.0i	−0.275863	−	0.477809i	−0.970353	+	0.241694i	$0.922297\pi$
$984$		0			0
$985$	−13223.4	+	22903.6i	−0.427749	+	0.740883i
$986$		0			0
$987$	−8382.75	+	1572.42i	−0.270340	+	0.0507098i
$988$		0			0
$989$	8694.39			0.279540
$990$		0			0
$991$	−41838.3			−1.34111			−0.670554	−	0.741861i	$-0.733944\pi$
$991$	−41838.3			−1.34111			−0.670554	+	0.741861i	$0.733944\pi$
$992$		0			0
$993$	−2890.59	+	8219.24i	−0.0923767	+	0.262668i
$994$		0			0
$995$	−34764.8	+	60214.3i	−1.10766	+	1.91852i
$996$		0			0
$997$	22353.1	+	38716.7i	0.710059	+	1.22986i	0.964834	+	0.262858i	$0.0846652\pi$
$997$	22353.1	+	38716.7i	0.710059	+	1.22986i	−0.254775	+	0.967000i	$0.582001\pi$
$998$		0			0
$999$	13101.6	−	8146.10i	0.414931	−	0.257989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.j.b.85.2	✓	18
3.2	odd	2		756.4.j.b.253.8		18
9.2	odd	6		756.4.j.b.505.8		18
9.4	even	3		2268.4.a.i.1.8		9
9.5	odd	6		2268.4.a.h.1.2		9
9.7	even	3	inner	252.4.j.b.169.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.j.b.85.2	✓	18	1.1	even	1	trivial
252.4.j.b.169.2	yes	18	9.7	even	3	inner
756.4.j.b.253.8		18	3.2	odd	2
756.4.j.b.505.8		18	9.2	odd	6
2268.4.a.h.1.2		9	9.5	odd	6
2268.4.a.i.1.8		9	9.4	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.38317 - 3.94388i) q^{3} +(-8.26221 + 14.3106i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-4.10831 + 26.6856i) q^{9} +O(q^{10})\)	\(q+(-3.38317 - 3.94388i) q^{3} +(-8.26221 + 14.3106i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-4.10831 + 26.6856i) q^{9} +(-5.18159 - 8.97478i) q^{11} +(10.5363 - 18.2493i) q^{13} +(84.3916 - 15.8300i) q^{15} -17.1034 q^{17} +121.074 q^{19} +(-12.0674 + 34.3129i) q^{21} +(-8.97878 + 15.5517i) q^{23} +(-74.0283 - 128.221i) q^{25} +(119.144 - 74.0793i) q^{27} +(-65.9200 - 114.177i) q^{29} +(155.855 - 269.950i) q^{31} +(-17.8652 + 50.7987i) q^{33} +115.671 q^{35} +109.965 q^{37} +(-107.619 + 20.1869i) q^{39} +(96.4372 - 167.034i) q^{41} +(-242.081 - 419.297i) q^{43} +(-347.943 - 279.274i) q^{45} +(117.243 + 203.070i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(57.8637 + 67.4537i) q^{51} +165.160 q^{53} +171.246 q^{55} +(-409.614 - 477.500i) q^{57} +(42.2968 - 73.2602i) q^{59} +(20.1098 + 34.8312i) q^{61} +(176.152 - 68.4943i) q^{63} +(174.106 + 301.560i) q^{65} +(-341.961 + 592.294i) q^{67} +(91.7108 - 17.2029i) q^{69} +1111.86 q^{71} +930.288 q^{73} +(-255.236 + 725.751i) q^{75} +(-36.2711 + 62.8234i) q^{77} +(-177.018 - 306.603i) q^{79} +(-695.244 - 219.266i) q^{81} +(729.335 + 1263.25i) q^{83} +(141.312 - 244.759i) q^{85} +(-227.281 + 646.260i) q^{87} +816.471 q^{89} -147.508 q^{91} +(-1591.93 + 298.611i) q^{93} +(-1000.34 + 1732.64i) q^{95} +(-190.952 - 330.739i) q^{97} +(260.785 - 101.403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) \) 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9} - 93 q^{11} - 18 q^{13} + 162 q^{15} - 54 q^{17} - 90 q^{19} - 49 q^{21} - 246 q^{23} - 315 q^{25} - 394 q^{27} - 318 q^{29} - 18 q^{31} + 33 q^{33} + 84 q^{35} - 72 q^{37} + 268 q^{39} - 57 q^{41} - 171 q^{43} - 318 q^{45} - 1056 q^{47} - 441 q^{49} + 705 q^{51} + 1512 q^{53} - 1800 q^{55} - 1271 q^{57} - 411 q^{59} - 198 q^{61} + 308 q^{63} - 1326 q^{65} - 441 q^{67} + 642 q^{69} + 3516 q^{71} + 54 q^{73} - 2497 q^{75} - 651 q^{77} + 72 q^{79} + 1163 q^{81} - 558 q^{83} - 1008 q^{85} + 2766 q^{87} + 2784 q^{89} + 252 q^{91} - 2618 q^{93} - 156 q^{95} + 909 q^{97} + 6318 q^{99}+O(q^{100}) \) 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9 - 93 * q^11 - 18 * q^13 + 162 * q^15 - 54 * q^17 - 90 * q^19 - 49 * q^21 - 246 * q^23 - 315 * q^25 - 394 * q^27 - 318 * q^29 - 18 * q^31 + 33 * q^33 + 84 * q^35 - 72 * q^37 + 268 * q^39 - 57 * q^41 - 171 * q^43 - 318 * q^45 - 1056 * q^47 - 441 * q^49 + 705 * q^51 + 1512 * q^53 - 1800 * q^55 - 1271 * q^57 - 411 * q^59 - 198 * q^61 + 308 * q^63 - 1326 * q^65 - 441 * q^67 + 642 * q^69 + 3516 * q^71 + 54 * q^73 - 2497 * q^75 - 651 * q^77 + 72 * q^79 + 1163 * q^81 - 558 * q^83 - 1008 * q^85 + 2766 * q^87 + 2784 * q^89 + 252 * q^91 - 2618 * q^93 - 156 * q^95 + 909 * q^97 + 6318 * q^99

Introduction

L-functions

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Database

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