LMFDB - Embedded newform 304.5.r.c.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not 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:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 $ x^16 - 8x^15 + 1024x^14 - 7028x^13 + 404698x^12 - 2337188x^11 + 77836288x^10 - 367923764x^9 + 7565874847x^8 - 28081380444x^7 + 352870494000x^6 - 961846520868x^5 + 6856327325898x^4 - 12141615583188x^3 + 32749209391860x^2 - 26834137576128*x + 23840536514409
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$0.500000 + 6.55779i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.5.r.c.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.70447 + 2.13878i) q^{3} +(-17.7629 - 30.7663i) q^{5} -57.6374 q^{7} +(-31.3513 + 54.3020i) q^{9} +O(q^{10})$	\(q+(-3.70447 + 2.13878i) q^{3} +(-17.7629 - 30.7663i) q^{5} -57.6374 q^{7} +(-31.3513 + 54.3020i) q^{9} -144.450 q^{11} +(-165.547 - 95.5784i) q^{13} +(131.605 + 75.9819i) q^{15} +(273.834 + 474.294i) q^{17} +(208.119 - 294.971i) q^{19} +(213.516 - 123.274i) q^{21} +(-97.8608 + 169.500i) q^{23} +(-318.544 + 551.735i) q^{25} -614.695i q^{27} +(-16.6699 - 9.62437i) q^{29} -933.563i q^{31} +(535.110 - 308.946i) q^{33} +(1023.81 + 1773.29i) q^{35} -1973.80i q^{37} +817.683 q^{39} +(1409.98 - 814.052i) q^{41} +(1101.61 + 1908.04i) q^{43} +2227.56 q^{45} +(281.608 - 487.759i) q^{47} +921.075 q^{49} +(-2028.82 - 1171.34i) q^{51} +(-922.687 - 532.713i) q^{53} +(2565.85 + 4444.19i) q^{55} +(-140.093 + 1537.83i) q^{57} +(-1314.02 + 758.649i) q^{59} +(-2676.67 + 4636.13i) q^{61} +(1807.01 - 3129.83i) q^{63} +6791.02i q^{65} +(4365.12 + 2520.20i) q^{67} -837.209i q^{69} +(1231.70 - 711.125i) q^{71} +(2820.02 + 4884.42i) q^{73} -2725.18i q^{75} +8325.72 q^{77} +(-532.235 + 307.286i) q^{79} +(-1224.76 - 2121.34i) q^{81} +2748.68 q^{83} +(9728.19 - 16849.7i) q^{85} +82.3375 q^{87} +(4647.00 + 2682.95i) q^{89} +(9541.69 + 5508.90i) q^{91} +(1996.68 + 3458.36i) q^{93} +(-12772.0 - 1163.50i) q^{95} +(-8504.30 + 4909.96i) q^{97} +(4528.69 - 7843.92i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) $ 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9	$ 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9} + 84 q^{11} + 450 q^{13} + 390 q^{15} + 606 q^{17} + 306 q^{19} - 2160 q^{21} + 54 q^{23} - 434 q^{25} - 4914 q^{29} + 7890 q^{33} - 2328 q^{35} - 7620 q^{39} - 1692 q^{41} + 7402 q^{43} - 16720 q^{45} - 3198 q^{47} + 24816 q^{49} - 10710 q^{51} + 3870 q^{53} + 13588 q^{55} + 3702 q^{57} + 18288 q^{59} - 6522 q^{61} + 15676 q^{63} + 30168 q^{67} - 35874 q^{71} - 8080 q^{73} + 34560 q^{77} + 30738 q^{79} - 30920 q^{81} + 1476 q^{83} + 33626 q^{85} - 113100 q^{87} + 19782 q^{89} + 34260 q^{91} - 4272 q^{93} + 23706 q^{95} - 9936 q^{97} - 3848 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9 + 84 * q^11 + 450 * q^13 + 390 * q^15 + 606 * q^17 + 306 * q^19 - 2160 * q^21 + 54 * q^23 - 434 * q^25 - 4914 * q^29 + 7890 * q^33 - 2328 * q^35 - 7620 * q^39 - 1692 * q^41 + 7402 * q^43 - 16720 * q^45 - 3198 * q^47 + 24816 * q^49 - 10710 * q^51 + 3870 * q^53 + 13588 * q^55 + 3702 * q^57 + 18288 * q^59 - 6522 * q^61 + 15676 * q^63 + 30168 * q^67 - 35874 * q^71 - 8080 * q^73 + 34560 * q^77 + 30738 * q^79 - 30920 * q^81 + 1476 * q^83 + 33626 * q^85 - 113100 * q^87 + 19782 * q^89 + 34260 * q^91 - 4272 * q^93 + 23706 * q^95 - 9936 * q^97 - 3848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	−3.70447	+	2.13878i	−0.411608	+	0.237642i	−0.691480	−	0.722395i	$-0.743041\pi$
$3$	−3.70447	+	2.13878i	−0.411608	+	0.237642i	0.279873	+	0.960037i	$0.409708\pi$
$4$		0			0
$5$	−17.7629	−	30.7663i	−0.710518	−	1.23065i	−0.964663	−	0.263487i	$-0.915128\pi$
$5$	−17.7629	−	30.7663i	−0.710518	−	1.23065i	0.254145	−	0.967166i	$-0.418206\pi$
$6$		0			0
$7$	−57.6374			−1.17627			−0.588137	−	0.808761i	$-0.700139\pi$
$7$	−57.6374			−1.17627			−0.588137	+	0.808761i	$0.700139\pi$
$8$		0			0
$9$	−31.3513	+	54.3020i	−0.387053	+	0.670395i
$10$		0			0
$11$	−144.450			−1.19380			−0.596900	−	0.802316i	$-0.703601\pi$
$11$	−144.450			−1.19380			−0.596900	+	0.802316i	$0.703601\pi$
$12$		0			0
$13$	−165.547	−	95.5784i	−0.979566	−	0.565553i	−0.0774271	−	0.996998i	$-0.524670\pi$
$13$	−165.547	−	95.5784i	−0.979566	−	0.565553i	−0.902139	+	0.431445i	$0.858004\pi$
$14$		0			0
$15$	131.605	+	75.9819i	0.584909	+	0.337697i
$16$		0			0
$17$	273.834	+	474.294i	0.947522	+	1.64116i	0.750621	+	0.660733i	$0.229755\pi$
$17$	273.834	+	474.294i	0.947522	+	1.64116i	0.196902	+	0.980423i	$0.436912\pi$
$18$		0			0
$19$	208.119	−	294.971i	0.576506	−	0.817093i
$19$	208.119	−	294.971i	0.576506	−	0.817093i
$20$		0			0
$21$	213.516	−	123.274i	0.484163	−	0.279532i
$22$		0			0
$23$	−97.8608	+	169.500i	−0.184992	+	0.320416i	−0.943574	−	0.331162i	$-0.892559\pi$
$23$	−97.8608	+	169.500i	−0.184992	+	0.320416i	0.758582	+	0.651578i	$0.225893\pi$
$24$		0			0
$25$	−318.544	+	551.735i	−0.509671	+	0.882775i
$26$		0			0
$27$		−	614.695i		−	0.843203i
$28$		0			0
$29$	−16.6699	−	9.62437i	−0.0198215	−	0.0114440i	0.490057	−	0.871691i	$-0.336976\pi$
$29$	−16.6699	−	9.62437i	−0.0198215	−	0.0114440i	−0.509878	+	0.860247i	$0.670309\pi$
$30$		0			0
$31$		−	933.563i		−	0.971450i	−0.874112	−	0.485725i	$-0.838556\pi$
$31$		−	933.563i		−	0.971450i	0.874112	−	0.485725i	$-0.161444\pi$
$32$		0			0
$33$	535.110	−	308.946i	0.491377	−	0.283697i
$34$		0			0
$35$	1023.81	+	1773.29i	0.835764	+	1.44759i
$36$		0			0
$37$		−	1973.80i		−	1.44178i	−0.693049	−	0.720891i	$-0.743733\pi$
$37$		−	1973.80i		−	1.44178i	0.693049	−	0.720891i	$-0.256267\pi$
$38$		0			0
$39$	817.683			0.537596
$40$		0			0
$41$	1409.98	−	814.052i	0.838774	−	0.484267i	−0.0180730	−	0.999837i	$-0.505753\pi$
$41$	1409.98	−	814.052i	0.838774	−	0.484267i	0.856847	+	0.515570i	$0.172420\pi$
$42$		0			0
$43$	1101.61	+	1908.04i	0.595785	+	1.03193i	0.993436	+	0.114393i	$0.0364922\pi$
$43$	1101.61	+	1908.04i	0.595785	+	1.03193i	−0.397651	+	0.917537i	$0.630174\pi$
$44$		0			0
$45$	2227.56			1.10003
$46$		0			0
$47$	281.608	−	487.759i	0.127482	−	0.220805i	−0.795218	−	0.606323i	$-0.792644\pi$
$47$	281.608	−	487.759i	0.127482	−	0.220805i	0.922700	+	0.385518i	$0.125977\pi$
$48$		0			0
$49$	921.075			0.383622
$50$		0			0
$51$	−2028.82	−	1171.34i	−0.780015	−	0.450342i
$52$		0			0
$53$	−922.687	−	532.713i	−0.328475	−	0.189645i	0.326689	−	0.945132i	$-0.394067\pi$
$53$	−922.687	−	532.713i	−0.328475	−	0.189645i	−0.655164	+	0.755487i	$0.727400\pi$
$54$		0			0
$55$	2565.85	+	4444.19i	0.848216	+	1.46915i
$56$		0			0
$57$	−140.093	+	1537.83i	−0.0431188	+	0.473324i
$58$		0			0
$59$	−1314.02	+	758.649i	−0.377483	+	0.217940i	−0.676723	−	0.736238i	$-0.736600\pi$
$59$	−1314.02	+	758.649i	−0.377483	+	0.217940i	0.299240	+	0.954178i	$0.403267\pi$
$60$		0			0
$61$	−2676.67	+	4636.13i	−0.719341	+	1.24594i	0.241920	+	0.970296i	$0.422223\pi$
$61$	−2676.67	+	4636.13i	−0.719341	+	1.24594i	−0.961261	+	0.275639i	$0.911111\pi$
$62$		0			0
$63$	1807.01	−	3129.83i	0.455280	−	0.788569i
$64$		0			0
$65$			6791.02i			1.60734i
$66$		0			0
$67$	4365.12	+	2520.20i	0.972403	+	0.561417i	0.899968	−	0.435956i	$-0.143590\pi$
$67$	4365.12	+	2520.20i	0.972403	+	0.561417i	0.0724351	+	0.997373i	$0.476923\pi$
$68$		0			0
$69$		−	837.209i		−	0.175847i
$70$		0			0
$71$	1231.70	−	711.125i	0.244337	−	0.141068i	−0.372831	−	0.927899i	$-0.621613\pi$
$71$	1231.70	−	711.125i	0.244337	−	0.141068i	0.617169	+	0.786831i	$0.288280\pi$
$72$		0			0
$73$	2820.02	+	4884.42i	0.529184	+	0.916574i	0.999421	+	0.0340332i	$0.0108352\pi$
$73$	2820.02	+	4884.42i	0.529184	+	0.916574i	−0.470237	+	0.882540i	$0.655831\pi$
$74$		0			0
$75$		−	2725.18i		−	0.484476i
$76$		0			0
$77$	8325.72			1.40424
$78$		0			0
$79$	−532.235	+	307.286i	−0.0852804	+	0.0492367i	−0.542034	−	0.840357i	$-0.682346\pi$
$79$	−532.235	+	307.286i	−0.0852804	+	0.0492367i	0.456753	+	0.889593i	$0.349012\pi$
$80$		0			0
$81$	−1224.76	−	2121.34i	−0.186673	−	0.323326i
$82$		0			0
$83$	2748.68			0.398995			0.199498	−	0.979898i	$-0.436069\pi$
$83$	2748.68			0.398995			0.199498	+	0.979898i	$0.436069\pi$
$84$		0			0
$85$	9728.19	−	16849.7i	1.34646	−	2.33214i
$86$		0			0
$87$	82.3375			0.0108782
$88$		0			0
$89$	4647.00	+	2682.95i	0.586668	+	0.338713i	0.763779	−	0.645478i	$-0.223342\pi$
$89$	4647.00	+	2682.95i	0.586668	+	0.338713i	−0.177111	+	0.984191i	$0.556675\pi$
$90$		0			0
$91$	9541.69	+	5508.90i	1.15224	+	0.665245i
$92$		0			0
$93$	1996.68	+	3458.36i	0.230857	+	0.399856i
$94$		0			0
$95$	−12772.0	−	1163.50i	−1.41518	−	0.128919i
$96$		0			0
$97$	−8504.30	+	4909.96i	−0.903847	+	0.521836i	−0.878446	−	0.477841i	$-0.841419\pi$
$97$	−8504.30	+	4909.96i	−0.903847	+	0.521836i	−0.0254007	+	0.999677i	$0.508086\pi$
$98$		0			0
$99$	4528.69	−	7843.92i	0.462064	−	0.800318i
$100$		0			0
$101$	−3770.42	+	6530.55i	−0.369612	+	0.640187i	−0.989505	−	0.144499i	$-0.953843\pi$
$101$	−3770.42	+	6530.55i	−0.369612	+	0.640187i	0.619893	+	0.784687i	$0.287176\pi$
$102$		0			0
$103$			17918.4i			1.68899i	0.535567	+	0.844493i	$0.320098\pi$
$103$			17918.4i			1.68899i	−0.535567	+	0.844493i	$0.679902\pi$
$104$		0			0
$105$	−7585.35	−	4379.40i	−0.688013	−	0.397225i
$106$		0			0
$107$		−	18844.0i		−	1.64591i	−0.568110	−	0.822953i	$-0.692325\pi$
$107$		−	18844.0i		−	1.64591i	0.568110	−	0.822953i	$-0.307675\pi$
$108$		0			0
$109$	−2953.45	+	1705.17i	−0.248586	+	0.143521i	−0.619116	−	0.785299i	$-0.712509\pi$
$109$	−2953.45	+	1705.17i	−0.248586	+	0.143521i	0.370531	+	0.928820i	$0.379176\pi$
$110$		0			0
$111$	4221.51	+	7311.88i	0.342628	+	0.593448i
$112$		0			0
$113$		−	14671.8i		−	1.14902i	−0.818498	−	0.574509i	$-0.805193\pi$
$113$		−	14671.8i		−	1.14902i	0.818498	−	0.574509i	$-0.194807\pi$
$114$		0			0
$115$	6953.18			0.525760
$116$		0			0
$117$	10380.2	−	5993.01i	0.758288	−	0.437798i
$118$		0			0
$119$	−15783.1	−	27337.1i	−1.11455	−	1.93045i
$120$		0			0
$121$	6224.75			0.425159
$122$		0			0
$123$	−3482.15	+	6031.26i	−0.230164	+	0.398656i
$124$		0			0
$125$	429.447			0.0274846
$126$		0			0
$127$	4058.49	+	2343.17i	0.251627	+	0.145277i	0.620509	−	0.784199i	$-0.286926\pi$
$127$	4058.49	+	2343.17i	0.251627	+	0.145277i	−0.368882	+	0.929476i	$0.620259\pi$
$128$		0			0
$129$	−8161.73	−	4712.18i	−0.490459	−	0.283167i
$130$		0			0
$131$	5035.57	+	8721.86i	0.293431	+	0.508237i	0.974619	−	0.223872i	$-0.0718696\pi$
$131$	5035.57	+	8721.86i	0.293431	+	0.508237i	−0.681188	+	0.732109i	$0.738536\pi$
$132$		0			0
$133$	−11995.4	+	17001.4i	−0.678129	+	0.961126i
$134$		0			0
$135$	−18911.9	+	10918.8i	−1.03769	+	0.599111i
$136$		0			0
$137$	152.554	−	264.231i	0.00812798	−	0.0140781i	−0.861933	−	0.507023i	$-0.830746\pi$
$137$	152.554	−	264.231i	0.00812798	−	0.0140781i	0.870061	+	0.492944i	$0.164079\pi$
$138$		0			0
$139$	5384.92	−	9326.95i	0.278708	−	0.482737i	−0.692356	−	0.721556i	$-0.743427\pi$
$139$	5384.92	−	9326.95i	0.278708	−	0.482737i	0.971064	+	0.238820i	$0.0767605\pi$
$140$		0			0
$141$			2409.19i			0.121180i
$142$		0			0
$143$	23913.2	+	13806.3i	1.16941	+	0.675157i
$144$		0			0
$145$			683.828i			0.0325245i
$146$		0			0
$147$	−3412.09	+	1969.97i	−0.157902	+	0.0911645i
$148$		0			0
$149$	−6839.66	−	11846.6i	−0.308079	−	0.533608i	0.669863	−	0.742485i	$-0.266353\pi$
$149$	−6839.66	−	11846.6i	−0.308079	−	0.533608i	−0.977942	+	0.208876i	$0.933019\pi$
$150$		0			0
$151$			3932.97i			0.172491i	0.996274	+	0.0862455i	$0.0274870\pi$
$151$			3932.97i			0.172491i	−0.996274	+	0.0862455i	$0.972513\pi$
$152$		0			0
$153$	−34340.2			−1.46696
$154$		0			0
$155$	−28722.3	+	16582.8i	−1.19552	+	0.690232i
$156$		0			0
$157$	12478.1	+	21612.7i	0.506230	+	0.876817i	0.999974	+	0.00720913i	$0.00229476\pi$
$157$	12478.1	+	21612.7i	0.506230	+	0.876817i	−0.493744	+	0.869607i	$0.664372\pi$
$158$		0			0
$159$	4557.42			0.180270
$160$		0			0
$161$	5640.45	−	9769.54i	0.217601	−	0.376897i
$162$		0			0
$163$	−30994.7			−1.16657			−0.583287	−	0.812266i	$-0.698234\pi$
$163$	−30994.7			−1.16657			−0.583287	+	0.812266i	$0.698234\pi$
$164$		0			0
$165$	−19010.2	−	10975.6i	−0.698264	−	0.403143i
$166$		0			0
$167$	−40226.3	−	23224.7i	−1.44237	−	0.832753i	−0.444363	−	0.895847i	$-0.646570\pi$
$167$	−40226.3	−	23224.7i	−1.44237	−	0.832753i	−0.998008	+	0.0630935i	$0.979903\pi$
$168$		0			0
$169$	3989.97	+	6910.83i	0.139700	+	0.241967i
$170$		0			0
$171$	9492.71	+	20549.0i	0.324637	+	0.702745i
$172$		0			0
$173$	44065.9	−	25441.5i	1.47235	−	0.850061i	0.472832	−	0.881152i	$-0.343232\pi$
$173$	44065.9	−	25441.5i	1.47235	−	0.850061i	0.999517	+	0.0310913i	$0.00989826\pi$
$174$		0			0
$175$	18360.1	−	31800.6i	0.599513	−	1.03839i
$176$		0			0
$177$	3245.16	−	5620.78i	0.103583	−	0.179412i
$178$		0			0
$179$			43766.3i			1.36595i	0.730444	+	0.682973i	$0.239313\pi$
$179$			43766.3i			1.36595i	−0.730444	+	0.682973i	$0.760687\pi$
$180$		0			0
$181$	−35313.4	−	20388.2i	−1.07791	−	0.622332i	−0.147579	−	0.989050i	$-0.547148\pi$
$181$	−35313.4	−	20388.2i	−1.07791	−	0.622332i	−0.930332	+	0.366718i	$0.880481\pi$
$182$		0			0
$183$		−	22899.2i		−	0.683782i
$184$		0			0
$185$	−60726.5	+	35060.5i	−1.77433	+	1.02441i
$186$		0			0
$187$	−39555.3	−	68511.7i	−1.13115	−	1.95921i
$188$		0			0
$189$			35429.5i			0.991838i
$190$		0			0
$191$	49984.5			1.37015			0.685076	−	0.728472i	$-0.259769\pi$
$191$	49984.5			1.37015			0.685076	+	0.728472i	$0.259769\pi$
$192$		0			0
$193$	15307.8	−	8837.94i	0.410958	−	0.237267i	−0.280243	−	0.959929i	$-0.590415\pi$
$193$	15307.8	−	8837.94i	0.410958	−	0.237267i	0.691201	+	0.722662i	$0.257082\pi$
$194$		0			0
$195$	−14524.5	−	25157.1i	−0.381971	−	0.661594i
$196$		0			0
$197$	71077.4			1.83147			0.915734	−	0.401786i	$-0.131610\pi$
$197$	71077.4			1.83147			0.915734	+	0.401786i	$0.131610\pi$
$198$		0			0
$199$	−26220.6	+	45415.3i	−0.662119	+	1.14682i	0.317939	+	0.948111i	$0.397009\pi$
$199$	−26220.6	+	45415.3i	−0.662119	+	1.14682i	−0.980058	+	0.198712i	$0.936324\pi$
$200$		0			0
$201$	−21560.6			−0.533665
$202$		0			0
$203$	960.810	+	554.724i	0.0233155	+	0.0134612i
$204$		0			0
$205$	−50090.8	−	28919.9i	−1.19193	−	0.688160i
$206$		0			0
$207$	−6136.12	−	10628.1i	−0.143203	−	0.248036i
$208$		0			0
$209$	−30062.7	+	42608.5i	−0.688233	+	0.975446i
$210$		0			0
$211$	12929.6	−	7464.89i	0.290415	−	0.167671i	−0.347714	−	0.937601i	$-0.613042\pi$
$211$	12929.6	−	7464.89i	0.290415	−	0.167671i	0.638129	+	0.769929i	$0.279709\pi$
$212$		0			0
$213$	−3041.87	+	5268.68i	−0.0670474	+	0.116129i
$214$		0			0
$215$	39135.5	−	67784.7i	0.846631	−	1.46641i
$216$		0			0
$217$			53808.2i			1.14269i
$218$		0			0
$219$	−20893.4	−	12062.8i	−0.435632	−	0.251512i
$220$		0			0
$221$		−	104690.i		−	2.14350i
$222$		0			0
$223$	14187.1	−	8190.92i	0.285288	−	0.164711i	−0.350527	−	0.936553i	$-0.613997\pi$
$223$	14187.1	−	8190.92i	0.285288	−	0.164711i	0.635815	+	0.771841i	$0.280664\pi$
$224$		0			0
$225$	−19973.5	−	34595.2i	−0.394539	−	0.683361i
$226$		0			0
$227$			17808.1i			0.345594i	0.984957	+	0.172797i	$0.0552805\pi$
$227$			17808.1i			0.345594i	−0.984957	+	0.172797i	$0.944720\pi$
$228$		0			0
$229$	93393.3			1.78092			0.890461	−	0.455060i	$-0.150382\pi$
$229$	93393.3			1.78092			0.890461	+	0.455060i	$0.150382\pi$
$230$		0			0
$231$	−30842.4	+	17806.8i	−0.577994	+	0.333705i
$232$		0			0
$233$	18715.1	+	32415.5i	0.344731	+	0.597092i	0.985305	−	0.170804i	$-0.0546367\pi$
$233$	18715.1	+	32415.5i	0.344731	+	0.597092i	−0.640574	+	0.767897i	$0.721303\pi$
$234$		0			0
$235$	−20008.7			−0.362313
$236$		0			0
$237$	1314.43	−	2276.66i	0.0234014	−	0.0405324i
$238$		0			0
$239$	26610.8			0.465867			0.232934	−	0.972493i	$-0.425167\pi$
$239$	26610.8			0.465867			0.232934	+	0.972493i	$0.425167\pi$
$240$		0			0
$241$	−19387.5	−	11193.4i	−0.333801	−	0.192720i	0.323727	−	0.946151i	$-0.395064\pi$
$241$	−19387.5	−	11193.4i	−0.333801	−	0.192720i	−0.657527	+	0.753431i	$0.728398\pi$
$242$		0			0
$243$	52193.8	+	30134.1i	0.883907	+	0.510324i
$244$		0			0
$245$	−16361.0	−	28338.1i	−0.272570	−	0.472105i
$246$		0			0
$247$	−62646.2	+	28939.8i	−1.02683	+	0.474352i
$248$		0			0
$249$	−10182.4	+	5878.80i	−0.164229	+	0.0948179i
$250$		0			0
$251$	−20002.6	+	34645.6i	−0.317497	+	0.549921i	−0.979965	−	0.199169i	$-0.936176\pi$
$251$	−20002.6	+	34645.6i	−0.317497	+	0.549921i	0.662468	+	0.749090i	$0.269509\pi$
$252$		0			0
$253$	14136.0	−	24484.2i	0.220844	−	0.382512i
$254$		0			0
$255$			83225.7i			1.27990i
$256$		0			0
$257$	−92099.6	−	53173.7i	−1.39441	−	0.805065i	−0.400614	−	0.916247i	$-0.631203\pi$
$257$	−92099.6	−	53173.7i	−1.39441	−	0.805065i	−0.993800	+	0.111182i	$0.964536\pi$
$258$		0			0
$259$			113765.i			1.69593i
$260$		0			0
$261$	1045.24	−	603.472i	0.0153439	−	0.00885883i
$262$		0			0
$263$	−34717.4	−	60132.4i	−0.501922	−	0.869354i	−0.999998	−	0.00222053i	$-0.999293\pi$
$263$	−34717.4	−	60132.4i	−0.501922	−	0.869354i	0.498076	−	0.867134i	$-0.334040\pi$
$264$		0			0
$265$			37850.2i			0.538985i
$266$		0			0
$267$	−22952.9			−0.321970
$268$		0			0
$269$	48824.7	−	28188.9i	0.674738	−	0.389560i	−0.123132	−	0.992390i	$-0.539294\pi$
$269$	48824.7	−	28188.9i	0.674738	−	0.389560i	0.797869	+	0.602830i	$0.205960\pi$
$270$		0			0
$271$	20152.5	+	34905.2i	0.274405	+	0.475283i	0.969985	−	0.243166i	$-0.0781859\pi$
$271$	20152.5	+	34905.2i	0.274405	+	0.475283i	−0.695580	+	0.718448i	$0.744853\pi$
$272$		0			0
$273$	−47129.2			−0.632360
$274$		0			0
$275$	46013.6	−	79698.0i	0.608445	−	1.05386i
$276$		0			0
$277$	1727.77			0.0225178			0.0112589	−	0.999937i	$-0.496416\pi$
$277$	1727.77			0.0225178			0.0112589	+	0.999937i	$0.496416\pi$
$278$		0			0
$279$	50694.4	+	29268.4i	0.651255	+	0.376002i
$280$		0			0
$281$	71949.9	+	41540.3i	0.911208	+	0.526086i	0.880819	−	0.473452i	$-0.156992\pi$
$281$	71949.9	+	41540.3i	0.911208	+	0.526086i	0.0303881	+	0.999538i	$0.490326\pi$
$282$		0			0
$283$	−56498.8	−	97858.9i	−0.705451	−	1.22188i	−0.966529	−	0.256559i	$-0.917411\pi$
$283$	−56498.8	−	97858.9i	−0.705451	−	1.22188i	0.261078	−	0.965318i	$-0.415922\pi$
$284$		0			0
$285$	49801.8	−	23006.2i	0.613133	−	0.283241i
$286$		0			0
$287$	−81267.6	+	46919.9i	−0.986629	+	0.569630i
$288$		0			0
$289$	−108210.	+	187424.i	−1.29560	+	2.24404i
$290$		0			0
$291$	21002.6	−	36377.6i	0.248020	−	0.429584i
$292$		0			0
$293$			14942.5i			0.174056i	0.996206	+	0.0870280i	$0.0277370\pi$
$293$			14942.5i			0.174056i	−0.996206	+	0.0870280i	$0.972263\pi$
$294$		0			0
$295$	46681.7	+	26951.7i	0.536417	+	0.309700i
$296$		0			0
$297$			88792.6i			1.00662i
$298$		0			0
$299$	32401.1	−	18706.8i	0.362424	−	0.209246i
$300$		0			0
$301$	−63493.8	−	109974.i	−0.700806	−	1.21383i
$302$		0			0
$303$		−	32256.3i		−	0.351341i
$304$		0			0
$305$	190182.			2.04442
$306$		0			0
$307$	132089.	−	76261.9i	1.40149	−	0.809153i	0.406949	−	0.913451i	$-0.366593\pi$
$307$	132089.	−	76261.9i	1.40149	−	0.809153i	0.994546	+	0.104298i	$0.0332595\pi$
$308$		0			0
$309$	−38323.5	−	66378.3i	−0.401374	−	0.695199i
$310$		0			0
$311$	89623.6			0.926620			0.463310	−	0.886196i	$-0.346662\pi$
$311$	89623.6			0.926620			0.463310	+	0.886196i	$0.346662\pi$
$312$		0			0
$313$	9663.23	−	16737.2i	0.0986356	−	0.170842i	−0.812485	−	0.582983i	$-0.801886\pi$
$313$	9663.23	−	16737.2i	0.0986356	−	0.170842i	0.911120	+	0.412141i	$0.135219\pi$
$314$		0			0
$315$	−128391.			−1.29394
$316$		0			0
$317$	57395.2	+	33137.1i	0.571159	+	0.329759i	0.757612	−	0.652705i	$-0.226366\pi$
$317$	57395.2	+	33137.1i	0.571159	+	0.329759i	−0.186453	+	0.982464i	$0.559699\pi$
$318$		0			0
$319$	2407.96	+	1390.24i	0.0236629	+	0.0136618i
$320$		0			0
$321$	40303.0	+	69806.9i	0.391136	+	0.677467i
$322$		0			0
$323$	196893.	+	17936.5i	1.88723	+	0.171923i
$324$		0			0
$325$	105468.	−	60891.9i	0.998512	−	0.576491i
$326$		0			0
$327$	7293.97	−	12633.5i	0.0682132	−	0.118149i
$328$		0			0
$329$	−16231.2	+	28113.2i	−0.149954	+	0.259728i
$330$		0			0
$331$		−	927.898i		−	0.00846924i	−0.999991	−	0.00423462i	$-0.998652\pi$
$331$		−	927.898i		−	0.00846924i	0.999991	−	0.00423462i	$-0.00134793\pi$
$332$		0			0
$333$	107181.	+	61881.1i	0.966563	+	0.558046i
$334$		0			0
$335$		−	179065.i		−	1.59559i
$336$		0			0
$337$	87765.9	−	50671.7i	0.772798	−	0.446175i	−0.0610737	−	0.998133i	$-0.519452\pi$
$337$	87765.9	−	50671.7i	0.772798	−	0.446175i	0.833872	+	0.551958i	$0.186119\pi$
$338$		0			0
$339$	31379.7	+	54351.3i	0.273055	+	0.472944i
$340$		0			0
$341$			134853.i			1.15972i
$342$		0			0
$343$	85299.1			0.725030
$344$		0			0
$345$	−25757.8	+	14871.3i	−0.216407	+	0.124943i
$346$		0			0
$347$	77248.6	+	133799.i	0.641552	+	1.11120i	0.985086	+	0.172060i	$0.0550424\pi$
$347$	77248.6	+	133799.i	0.641552	+	1.11120i	−0.343535	+	0.939140i	$0.611624\pi$
$348$		0			0
$349$	−39100.9			−0.321023			−0.160511	−	0.987034i	$-0.551314\pi$
$349$	−39100.9			−0.321023			−0.160511	+	0.987034i	$0.551314\pi$
$350$		0			0
$351$	−58751.6	+	101761.i	−0.476876	+	0.825973i
$352$		0			0
$353$	35513.5			0.285000			0.142500	−	0.989795i	$-0.454486\pi$
$353$	35513.5			0.285000			0.142500	+	0.989795i	$0.454486\pi$
$354$		0			0
$355$	−43757.4	−	25263.3i	−0.347212	−	0.200463i
$356$		0			0
$357$	116936.	+	67513.0i	0.917511	+	0.529725i
$358$		0			0
$359$	47311.0	+	81945.1i	0.367091	+	0.635820i	0.989109	−	0.147183i	$-0.0470205\pi$
$359$	47311.0	+	81945.1i	0.367091	+	0.635820i	−0.622019	+	0.783003i	$0.713687\pi$
$360$		0			0
$361$	−43694.3	−	122778.i	−0.335282	−	0.942118i
$362$		0			0
$363$	−23059.4	+	13313.4i	−0.174999	+	0.101036i
$364$		0			0
$365$	100184.	−	173523.i	0.751989	−	1.30248i
$366$		0			0
$367$	−18897.2	+	32730.9i	−0.140302	+	0.243011i	−0.927610	−	0.373549i	$-0.878141\pi$
$367$	−18897.2	+	32730.9i	−0.140302	+	0.243011i	0.787308	+	0.616560i	$0.211474\pi$
$368$		0			0
$369$			102086.i			0.749747i
$370$		0			0
$371$	53181.3	+	30704.2i	0.386377	+	0.223075i
$372$		0			0
$373$			18426.9i			0.132445i	0.997805	+	0.0662225i	$0.0210947\pi$
$373$			18426.9i			0.132445i	−0.997805	+	0.0662225i	$0.978905\pi$
$374$		0			0
$375$	−1590.87	+	918.492i	−0.0113129	+	0.00653150i
$376$		0			0
$377$	1839.76	+	3186.56i	0.0129443	+	0.0224202i
$378$		0			0
$379$			53187.4i			0.370280i	0.982712	+	0.185140i	$0.0592739\pi$
$379$			53187.4i			0.370280i	−0.982712	+	0.185140i	$0.940726\pi$
$380$		0			0
$381$	−20046.0			−0.138095
$382$		0			0
$383$	125485.	−	72448.9i	0.855450	−	0.493894i	−0.00703582	−	0.999975i	$-0.502240\pi$
$383$	125485.	−	72448.9i	0.855450	−	0.493894i	0.862486	+	0.506081i	$0.168906\pi$
$384$		0			0
$385$	−147889.	−	256152.i	−0.997735	−	1.72813i
$386$		0			0
$387$	−138147.			−0.922401
$388$		0			0
$389$	−22790.0	+	39473.4i	−0.150607	+	0.260858i	−0.931451	−	0.363868i	$-0.881456\pi$
$389$	−22790.0	+	39473.4i	−0.150607	+	0.260858i	0.780844	+	0.624726i	$0.214789\pi$
$390$		0			0
$391$	−107190.			−0.701136
$392$		0			0
$393$	−37308.2	−	21539.9i	−0.241557	−	0.139463i
$394$		0			0
$395$	18908.1	+	10916.6i	0.121187	+	0.0699671i
$396$		0			0
$397$	89476.0	+	154977.i	0.567709	+	0.983301i	0.996792	+	0.0800358i	$0.0255035\pi$
$397$	89476.0	+	154977.i	0.567709	+	0.983301i	−0.429083	+	0.903265i	$0.641163\pi$
$398$		0			0
$399$	8074.59	−	88636.5i	0.0507195	−	0.556758i
$400$		0			0
$401$	−117639.	+	67918.8i	−0.731580	+	0.422378i	−0.819000	−	0.573794i	$-0.805471\pi$
$401$	−117639.	+	67918.8i	−0.731580	+	0.422378i	0.0874200	+	0.996172i	$0.472138\pi$
$402$		0			0
$403$	−89228.5	+	154548.i	−0.549406	+	0.951600i
$404$		0			0
$405$	−43510.6	+	75362.6i	−0.265268	+	0.459458i
$406$		0			0
$407$			285115.i			1.72120i
$408$		0			0
$409$	−49984.2	−	28858.4i	−0.298804	−	0.172514i	0.343102	−	0.939298i	$-0.388522\pi$
$409$	−49984.2	−	28858.4i	−0.298804	−	0.172514i	−0.641905	+	0.766784i	$0.721856\pi$
$410$		0			0
$411$			1305.12i			0.00772619i
$412$		0			0
$413$	75736.7	−	43726.6i	0.444024	−	0.256357i
$414$		0			0
$415$	−48824.6	−	84566.7i	−0.283493	−	0.491024i
$416$		0			0
$417$			46068.5i			0.264931i
$418$		0			0
$419$	−213159.			−1.21416			−0.607079	−	0.794642i	$-0.707659\pi$
$419$	−213159.			−1.21416			−0.607079	+	0.794642i	$0.707659\pi$
$420$		0			0
$421$	−77550.3	+	44773.7i	−0.437541	+	0.252615i	−0.702554	−	0.711630i	$-0.747957\pi$
$421$	−77550.3	+	44773.7i	−0.437541	+	0.252615i	0.265013	+	0.964245i	$0.414624\pi$
$422$		0			0
$423$	17657.5	+	30583.8i	0.0986846	+	0.170927i
$424$		0			0
$425$	−348913.			−1.93170
$426$		0			0
$427$	154276.	−	267214.i	0.846142	−	1.46556i
$428$		0			0
$429$	−118114.			−0.641782
$430$		0			0
$431$	−166815.	−	96311.0i	−0.898011	−	0.518467i	−0.0214568	−	0.999770i	$-0.506830\pi$
$431$	−166815.	−	96311.0i	−0.898011	−	0.518467i	−0.876554	+	0.481303i	$0.840164\pi$
$432$		0			0
$433$	198315.	+	114497.i	1.05774	+	0.610686i	0.924806	−	0.380439i	$-0.124227\pi$
$433$	198315.	+	114497.i	1.05774	+	0.610686i	0.132933	+	0.991125i	$0.457560\pi$
$434$		0			0
$435$	−1462.56	−	2533.22i	−0.00772919	−	0.0133873i
$436$		0			0
$437$	29630.8	+	64142.1i	0.155160	+	0.335877i
$438$		0			0
$439$	223947.	−	129296.i	1.16203	−	0.670897i	0.210238	−	0.977650i	$-0.432576\pi$
$439$	223947.	−	129296.i	1.16203	−	0.670897i	0.951789	+	0.306753i	$0.0992426\pi$
$440$		0			0
$441$	−28876.9	+	50016.2i	−0.148482	+	0.257178i
$442$		0			0
$443$	12720.2	−	22032.0i	0.0648166	−	0.112266i	−0.831796	−	0.555081i	$-0.812687\pi$
$443$	12720.2	−	22032.0i	0.0648166	−	0.112266i	0.896613	+	0.442816i	$0.146020\pi$
$444$		0			0
$445$		−	190628.i		−	0.962647i
$446$		0			0
$447$	50674.6	+	29257.0i	0.253615	+	0.146425i
$448$		0			0
$449$		−	286827.i		−	1.42275i	−0.702814	−	0.711374i	$-0.748073\pi$
$449$		−	286827.i		−	1.42275i	0.702814	−	0.711374i	$-0.251927\pi$
$450$		0			0
$451$	−203671.	+	117590.i	−1.00133	+	0.578118i
$452$		0			0
$453$	−8411.74	−	14569.6i	−0.0409911	−	0.0709986i
$454$		0			0
$455$		−	391417.i		−	1.89067i
$456$		0			0
$457$	189481.			0.907261			0.453631	−	0.891190i	$-0.350129\pi$
$457$	189481.			0.907261			0.453631	+	0.891190i	$0.350129\pi$
$458$		0			0
$459$	291546.	−	168324.i	1.38383	−	0.798954i
$460$		0			0
$461$	−9247.43	−	16017.0i	−0.0435130	−	0.0753668i	0.843449	−	0.537210i	$-0.180522\pi$
$461$	−9247.43	−	16017.0i	−0.0435130	−	0.0753668i	−0.886962	+	0.461843i	$0.847188\pi$
$462$		0			0
$463$	−36606.3			−0.170763			−0.0853815	−	0.996348i	$-0.527211\pi$
$463$	−36606.3			−0.170763			−0.0853815	+	0.996348i	$0.527211\pi$
$464$		0			0
$465$	70933.9	−	122861.i	0.328056	−	0.568210i
$466$		0			0
$467$	−209051.			−0.958558			−0.479279	−	0.877663i	$-0.659102\pi$
$467$	−209051.			−0.958558			−0.479279	+	0.877663i	$0.659102\pi$
$468$		0			0
$469$	−251594.	−	145258.i	−1.14381	−	0.660381i
$470$		0			0
$471$	−92449.2	−	53375.6i	−0.416736	−	0.240603i
$472$		0			0
$473$	−159127.	−	275616.i	−0.711248	−	1.23192i
$474$		0			0
$475$	96450.5	+	208787.i	0.427482	+	0.925374i
$476$		0			0
$477$	57854.8	−	33402.5i	0.254274	−	0.146805i
$478$		0			0
$479$	−142395.	+	246635.i	−0.620615	+	1.07494i	0.368756	+	0.929526i	$0.379784\pi$
$479$	−142395.	+	246635.i	−0.620615	+	1.07494i	−0.989371	+	0.145411i	$0.953550\pi$
$480$		0			0
$481$	−188653.	+	326756.i	−0.815404	+	1.41232i
$482$		0			0
$483$			48254.6i			0.206845i
$484$		0			0
$485$	302123.	+	174431.i	1.28440	+	0.741548i
$486$		0			0
$487$			318832.i			1.34432i	0.740404	+	0.672162i	$0.234634\pi$
$487$			318832.i			1.34432i	−0.740404	+	0.672162i	$0.765366\pi$
$488$		0			0
$489$	114819.	−	66290.8i	0.480171	−	0.277227i
$490$		0			0
$491$	37286.0	+	64581.2i	0.154662	+	0.267882i	0.932936	−	0.360043i	$-0.117238\pi$
$491$	37286.0	+	64581.2i	0.154662	+	0.267882i	−0.778274	+	0.627925i	$0.783905\pi$
$492$		0			0
$493$		−	10541.9i		−	0.0433736i
$494$		0			0
$495$	−321771.			−1.31322
$496$		0			0
$497$	−70992.3	+	40987.4i	−0.287408	+	0.165935i
$498$		0			0
$499$	−98295.9	−	170254.i	−0.394761	−	0.683746i	0.598310	−	0.801265i	$-0.295839\pi$
$499$	−98295.9	−	170254.i	−0.394761	−	0.683746i	−0.993071	+	0.117519i	$0.962506\pi$
$500$		0			0
$501$	198689.			0.791588
$502$		0			0
$503$	−26214.9	+	45405.5i	−0.103613	+	0.179462i	−0.913170	−	0.407578i	$-0.866374\pi$
$503$	−26214.9	+	45405.5i	−0.103613	+	0.179462i	0.809558	+	0.587040i	$0.199707\pi$
$504$		0			0
$505$	267895.			1.05046
$506$		0			0
$507$	−29561.4	−	17067.3i	−0.115003	−	0.0663971i
$508$		0			0
$509$	−179843.	−	103832.i	−0.694157	−	0.400772i	0.111011	−	0.993819i	$-0.464591\pi$
$509$	−179843.	−	103832.i	−0.694157	−	0.400772i	−0.805167	+	0.593048i	$0.797925\pi$
$510$		0			0
$511$	−162539.	−	281526.i	−0.622466	−	1.07814i
$512$		0			0
$513$	−181317.	−	127929.i	−0.688975	−	0.486112i
$514$		0			0
$515$	551285.	−	318284.i	2.07855	−	1.20005i
$516$		0			0
$517$	−40678.2	+	70456.8i	−0.152188	+	0.263598i
$518$		0			0
$519$	−108827.	+	188494.i	−0.404020	+	0.699783i
$520$		0			0
$521$			125122.i			0.460956i	0.973078	+	0.230478i	$0.0740290\pi$
$521$			125122.i			0.460956i	−0.973078	+	0.230478i	$0.925971\pi$
$522$		0			0
$523$	62316.2	+	35978.3i	0.227823	+	0.131534i	0.609567	−	0.792734i	$-0.291343\pi$
$523$	62316.2	+	35978.3i	0.227823	+	0.131534i	−0.381744	+	0.924268i	$0.624677\pi$
$524$		0			0
$525$			157072.i			0.569877i
$526$		0			0
$527$	442784.	−	255641.i	1.59430	−	0.920470i
$528$		0			0
$529$	120767.	+	209175.i	0.431556	+	0.747477i
$530$		0			0
$531$		−	95138.5i		−	0.337417i
$532$		0			0
$533$	−311223.			−1.09551
$534$		0			0
$535$	−579760.	+	334724.i	−2.02554	+	1.16944i
$536$		0			0
$537$	−93606.2	−	162131.i	−0.324606	−	0.562234i
$538$		0			0
$539$	−133049.			−0.457968
$540$		0			0
$541$	−171283.	+	296672.i	−0.585222	+	1.01363i	0.409626	+	0.912254i	$0.365659\pi$
$541$	−171283.	+	296672.i	−0.585222	+	1.01363i	−0.994848	+	0.101381i	$0.967674\pi$
$542$		0			0
$543$	174423.			0.591568
$544$		0			0
$545$	104924.	+	60577.8i	0.353249	+	0.203948i
$546$		0			0
$547$	−383525.	−	221428.i	−1.28180	−	0.740045i	−0.304619	−	0.952474i	$-0.598529\pi$
$547$	−383525.	−	221428.i	−1.28180	−	0.740045i	−0.977176	+	0.212429i	$0.931862\pi$
$548$		0			0
$549$	−167834.	−	290697.i	−0.556846	−	0.964485i
$550$		0			0
$551$	−6308.22	+	2914.12i	−0.0207780	+	0.00959851i
$552$		0			0
$553$	30676.7	−	17711.2i	0.100313	−	0.0579159i
$554$		0			0
$555$	149973.	−	259761.i	0.486886	−	0.843311i
$556$		0			0
$557$	27527.9	−	47679.7i	0.0887283	−	0.153682i	−0.818246	−	0.574869i	$-0.805053\pi$
$557$	27527.9	−	47679.7i	0.0887283	−	0.153682i	0.906974	+	0.421187i	$0.138386\pi$
$558$		0			0
$559$		−	421159.i		−	1.34779i
$560$		0			0
$561$	293062.	+	169200.i	0.931182	+	0.537618i
$562$		0			0
$563$			151431.i			0.477747i	0.971051	+	0.238873i	$0.0767781\pi$
$563$			151431.i			0.477747i	−0.971051	+	0.238873i	$0.923222\pi$
$564$		0			0
$565$	−451398.	+	260614.i	−1.41404	+	0.816398i
$566$		0			0
$567$	70592.0	+	122269.i	0.219578	+	0.380321i
$568$		0			0
$569$		−	234376.i		−	0.723917i	−0.932194	−	0.361958i	$-0.882108\pi$
$569$		−	234376.i		−	0.723917i	0.932194	−	0.361958i	$-0.117892\pi$
$570$		0			0
$571$	−41578.6			−0.127526			−0.0637628	−	0.997965i	$-0.520310\pi$
$571$	−41578.6			−0.127526			−0.0637628	+	0.997965i	$0.520310\pi$
$572$		0			0
$573$	−185166.	+	106906.i	−0.563965	+	0.325605i
$574$		0			0
$575$	−62346.0	−	107986.i	−0.188570	−	0.326613i
$576$		0			0
$577$	−71928.1			−0.216046			−0.108023	−	0.994148i	$-0.534452\pi$
$577$	−71928.1			−0.216046			−0.108023	+	0.994148i	$0.534452\pi$
$578$		0			0
$579$	−37804.8	+	65479.8i	−0.112769	+	0.195321i
$580$		0			0
$581$	−158427.			−0.469328
$582$		0			0
$583$	133282.	+	76950.4i	0.392134	+	0.226399i
$584$		0			0
$585$	−368766.	−	212907.i	−1.07755	−	0.622126i
$586$		0			0
$587$	−177751.	−	307875.i	−0.515866	−	0.893506i	−0.999830	−	0.0184185i	$-0.994137\pi$
$587$	−177751.	−	307875.i	−0.515866	−	0.893506i	0.483964	−	0.875088i	$-0.339196\pi$
$588$		0			0
$589$	−275374.	−	194292.i	−0.793765	−	0.560047i
$590$		0			0
$591$	−263304.	+	152019.i	−0.753846	+	0.435233i
$592$		0			0
$593$	141638.	−	245325.i	0.402784	−	0.697642i	−0.591277	−	0.806468i	$-0.701376\pi$
$593$	141638.	−	245325.i	0.402784	−	0.697642i	0.994061	+	0.108827i	$0.0347094\pi$
$594$		0			0
$595$	−560708.	+	971175.i	−1.58381	+	2.74324i
$596$		0			0
$597$		−	224320.i		−	0.629388i
$598$		0			0
$599$	48978.7	+	28277.9i	0.136507	+	0.0788121i	0.566698	−	0.823926i	$-0.308221\pi$
$599$	48978.7	+	28277.9i	0.136507	+	0.0788121i	−0.430191	+	0.902738i	$0.641554\pi$
$600$		0			0
$601$			680157.i			1.88304i	0.336954	+	0.941521i	$0.390603\pi$
$601$			680157.i			1.88304i	−0.336954	+	0.941521i	$0.609397\pi$
$602$		0			0
$603$	−273704.	+	158023.i	−0.752743	+	0.434596i
$604$		0			0
$605$	−110570.	−	191513.i	−0.302083	−	0.523223i
$606$		0			0
$607$			444821.i			1.20728i	0.797257	+	0.603640i	$0.206284\pi$
$607$			444821.i			1.20728i	−0.797257	+	0.603640i	$0.793716\pi$
$608$		0			0
$609$	−4745.72			−0.0127958
$610$		0			0
$611$	−93238.5	+	53831.3i	−0.249754	+	0.144196i
$612$		0			0
$613$	70542.1	+	122182.i	0.187727	+	0.325153i	0.944492	−	0.328534i	$-0.106555\pi$
$613$	70542.1	+	122182.i	0.187727	+	0.325153i	−0.756765	+	0.653687i	$0.773221\pi$
$614$		0			0
$615$	247413.			0.654142
$616$		0			0
$617$	129342.	−	224026.i	0.339757	−	0.588476i	−0.644630	−	0.764495i	$-0.722989\pi$
$617$	129342.	−	224026.i	0.339757	−	0.588476i	0.984387	+	0.176019i	$0.0563220\pi$
$618$		0			0
$619$	597838.			1.56028			0.780139	−	0.625606i	$-0.215148\pi$
$619$	597838.			1.56028			0.780139	+	0.625606i	$0.215148\pi$
$620$		0			0
$621$	104191.	+	60154.5i	0.270175	+	0.155986i
$622$		0			0
$623$	−267841.	−	154638.i	−0.690083	−	0.398420i
$624$		0			0
$625$	191462.	+	331622.i	0.490142	+	0.848951i
$626$		0			0
$627$	20236.4	−	222139.i	0.0514752	−	0.565054i
$628$		0			0
$629$	936162.	−	540493.i	2.36619	−	1.36612i
$630$		0			0
$631$	−74146.6	+	128426.i	−0.186223	+	0.322547i	−0.943988	−	0.329980i	$-0.892958\pi$
$631$	−74146.6	+	128426.i	−0.186223	+	0.322547i	0.757765	+	0.652527i	$0.226291\pi$
$632$		0			0
$633$	−31931.5	+	55306.9i	−0.0796914	+	0.138029i
$634$		0			0
$635$		−	166486.i		−	0.412887i
$636$		0			0
$637$	−152481.	−	88034.9i	−0.375783	−	0.216958i
$638$		0			0
$639$			89178.7i			0.218403i
$640$		0			0
$641$	387126.	−	223507.i	0.942185	−	0.543971i	0.0515404	−	0.998671i	$-0.483587\pi$
$641$	387126.	−	223507.i	0.942185	−	0.543971i	0.890645	+	0.454700i	$0.150254\pi$
$642$		0			0
$643$	205874.	+	356584.i	0.497942	+	0.862461i	0.999997	−	0.00237459i	$-0.000755857\pi$
$643$	205874.	+	356584.i	0.497942	+	0.862461i	−0.502055	+	0.864836i	$0.667423\pi$
$644$		0			0
$645$			334808.i			0.804780i
$646$		0			0
$647$	782873.			1.87018			0.935089	−	0.354413i	$-0.115319\pi$
$647$	782873.			1.87018			0.935089	+	0.354413i	$0.115319\pi$
$648$		0			0
$649$	189810.	−	109587.i	0.450639	−	0.260177i
$650$		0			0
$651$	−115084.	−	199331.i	−0.271551	−	0.470341i
$652$		0			0
$653$	111555.			0.261614			0.130807	−	0.991408i	$-0.458243\pi$
$653$	111555.			0.261614			0.130807	+	0.991408i	$0.458243\pi$
$654$		0			0
$655$	178893.	−	309852.i	0.416976	−	0.722223i
$656$		0			0
$657$	−353645.			−0.819289
$658$		0			0
$659$	531309.	+	306751.i	1.22342	+	0.706343i	0.965646	−	0.259861i	$-0.0836769\pi$
$659$	531309.	+	306751.i	1.22342	+	0.706343i	0.257776	+	0.966205i	$0.417010\pi$
$660$		0			0
$661$	−431091.	−	248890.i	−0.986656	−	0.569646i	−0.0823828	−	0.996601i	$-0.526253\pi$
$661$	−431091.	−	248890.i	−0.986656	−	0.569646i	−0.904273	+	0.426955i	$0.859586\pi$
$662$		0			0
$663$	223909.	+	387822.i	0.509384	+	0.882279i
$664$		0			0
$665$	736143.	+	67061.0i	1.66463	+	0.151645i
$666$		0			0
$667$	3262.66	−	1883.70i	0.00733364	−	0.00423408i
$668$		0			0
$669$	−35037.1	+	60686.0i	−0.0782845	+	0.135593i
$670$		0			0
$671$	386644.	−	669687.i	0.858750	−	1.48740i
$672$		0			0
$673$		−	233726.i		−	0.516032i	−0.966141	−	0.258016i	$-0.916931\pi$
$673$		−	233726.i		−	0.516032i	0.966141	−	0.258016i	$-0.0830687\pi$
$674$		0			0
$675$	339149.	+	195808.i	0.744359	+	0.429756i
$676$		0			0
$677$		−	634144.i		−	1.38360i	−0.722089	−	0.691800i	$-0.756818\pi$
$677$		−	634144.i		−	1.38360i	0.722089	−	0.691800i	$-0.243182\pi$
$678$		0			0
$679$	490166.	−	282997.i	1.06317	−	0.613823i
$680$		0			0
$681$	−38087.6	−	65969.6i	−0.0821275	−	0.142249i
$682$		0			0
$683$		−	438197.i		−	0.939350i	−0.882839	−	0.469675i	$-0.844371\pi$
$683$		−	438197.i		−	0.939350i	0.882839	−	0.469675i	$-0.155629\pi$
$684$		0			0
$685$	−10839.2			−0.0231003
$686$		0			0
$687$	−345972.	+	199747.i	−0.733041	+	0.423221i
$688$		0			0
$689$	101832.	+	176378.i	0.214509	+	0.371540i
$690$		0			0
$691$	−687997.			−1.44089			−0.720444	−	0.693513i	$-0.756062\pi$
$691$	−687997.			−1.44089			−0.720444	+	0.693513i	$0.756062\pi$
$692$		0			0
$693$	−261022.	+	452103.i	−0.543514	+	0.941393i
$694$		0			0
$695$	−382608.			−0.792108
$696$		0			0
$697$	772201.	+	445830.i	1.58951	+	0.917707i
$698$		0			0
$699$	−138659.	−	80054.9i	−0.283788	−	0.163845i
$700$		0			0
$701$	266610.	+	461781.i	0.542550	+	0.939724i	0.998757	+	0.0498501i	$0.0158744\pi$
$701$	266610.	+	461781.i	0.542550	+	0.939724i	−0.456207	+	0.889874i	$0.650792\pi$
$702$		0			0
$703$	−582213.	−	410784.i	−1.17807	−	0.831196i
$704$		0			0
$705$	74121.8	−	42794.2i	0.149131	−	0.0861007i
$706$		0			0
$707$	217317.	−	376404.i	0.434766	−	0.753036i
$708$		0			0
$709$	−439347.	+	760972.i	−0.874008	+	1.51383i	−0.0161930	+	0.999869i	$0.505155\pi$
$709$	−439347.	+	760972.i	−0.874008	+	1.51383i	−0.857815	+	0.513958i	$0.828179\pi$
$710$		0			0
$711$		−	38535.3i		−	0.0762288i
$712$		0			0
$713$	158239.	+	91359.3i	0.311268	+	0.179711i
$714$		0			0
$715$		−	980961.i		−	1.91884i
$716$		0			0
$717$	−98578.9	+	56914.6i	−0.191755	+	0.110710i
$718$		0			0
$719$	−107023.	−	185369.i	−0.207024	−	0.358575i	0.743752	−	0.668456i	$-0.233044\pi$
$719$	−107023.	−	185369.i	−0.207024	−	0.358575i	−0.950776	+	0.309880i	$0.899711\pi$
$720$		0			0
$721$		−	1.03277e6i		−	1.98671i
$722$		0			0
$723$	95760.4			0.183193
$724$		0			0
$725$	10620.2	−	6131.57i	0.0202049	−	0.0116653i
$726$		0			0
$727$	195439.	+	338510.i	0.369778	+	0.640475i	0.989531	−	0.144322i	$-0.0461003\pi$
$727$	195439.	+	338510.i	0.369778	+	0.640475i	−0.619752	+	0.784798i	$0.712767\pi$
$728$		0			0
$729$	−59389.6			−0.111752
$730$		0			0
$731$	−603314.	+	1.04497e6i	−1.12904	+	1.95555i
$732$		0			0
$733$	−437702.			−0.814648			−0.407324	−	0.913284i	$-0.633538\pi$
$733$	−437702.			−0.814648			−0.407324	+	0.913284i	$0.633538\pi$
$734$		0			0
$735$	121218.	+	69985.1i	0.224384	+	0.129548i
$736$		0			0
$737$	−630541.	−	364043.i	−1.16086	−	0.670220i
$738$		0			0
$739$	260845.	+	451796.i	0.477632	+	0.827282i	0.999671	−	0.0256391i	$-0.00816207\pi$
$739$	260845.	+	451796.i	0.477632	+	0.827282i	−0.522040	+	0.852921i	$0.674829\pi$
$740$		0			0
$741$	170175.	−	241193.i	0.309927	−	0.439266i
$742$		0			0
$743$	561882.	−	324403.i	1.01781	−	0.587634i	0.104343	−	0.994541i	$-0.466726\pi$
$743$	561882.	−	324403.i	1.01781	−	0.587634i	0.913470	+	0.406907i	$0.133393\pi$
$744$		0			0
$745$	−242985.	+	420862.i	−0.437791	+	0.758276i
$746$		0			0
$747$	−86174.5	+	149259.i	−0.154432	+	0.267484i
$748$		0			0
$749$			1.08612e6i			1.93604i
$750$		0			0
$751$	−297330.	−	171664.i	−0.527180	−	0.304367i	0.212687	−	0.977120i	$-0.431778\pi$
$751$	−297330.	−	171664.i	−0.527180	−	0.304367i	−0.739867	+	0.672753i	$0.765112\pi$
$752$		0			0
$753$		−	171125.i		−	0.301802i
$754$		0			0
$755$	121003.	−	69861.1i	0.212277	−	0.122558i
$756$		0			0
$757$	389018.	+	673798.i	0.678856	+	1.17581i	0.975326	+	0.220771i	$0.0708572\pi$
$757$	389018.	+	673798.i	0.678856	+	1.17581i	−0.296470	+	0.955042i	$0.595809\pi$
$758$		0			0
$759$			120935.i			0.209927i
$760$		0			0
$761$	−427214.			−0.737694			−0.368847	−	0.929490i	$-0.620247\pi$
$761$	−427214.			−0.737694			−0.368847	+	0.929490i	$0.620247\pi$
$762$		0			0
$763$	170229.	−	98281.8i	0.292405	−	0.168820i
$764$		0			0
$765$	609982.	+	1.05652e6i	1.04230	+	1.80532i
$766$		0			0
$767$	290042.			0.493026
$768$		0			0
$769$	399183.	−	691405.i	0.675024	−	1.16918i	−0.301438	−	0.953486i	$-0.597467\pi$
$769$	399183.	−	691405.i	0.675024	−	1.16918i	0.976462	−	0.215690i	$-0.0692002\pi$
$770$		0			0
$771$	454907.			0.765268
$772$		0			0
$773$	460472.	+	265854.i	0.770627	+	0.444922i	0.833098	−	0.553125i	$-0.186565\pi$
$773$	460472.	+	265854.i	0.770627	+	0.444922i	−0.0624714	+	0.998047i	$0.519898\pi$
$774$		0			0
$775$	515079.	+	297381.i	0.857572	+	0.495120i
$776$		0			0
$777$	−243317.	−	421438.i	−0.403024	−	0.698058i
$778$		0			0
$779$	53321.6	−	585322.i	0.0878674	−	0.964539i
$780$		0			0
$781$	−177919.	+	102722.i	−0.291690	+	0.168407i
$782$		0			0
$783$	−5916.05	+	10246.9i	−0.00964958	+	0.0167136i
$784$		0			0
$785$	443294.	−	767809.i	0.719371	−	1.24599i
$786$		0			0
$787$			929506.i			1.50073i	0.661024	+	0.750365i	$0.270122\pi$
$787$			929506.i			1.50073i	−0.661024	+	0.750365i	$0.729878\pi$
$788$		0			0
$789$	257219.	+	148506.i	0.413190	+	0.238555i
$790$		0			0
$791$			845646.i			1.35156i
$792$		0			0
$793$	886227.	−	511663.i	1.40928	−	0.813651i
$794$		0			0
$795$	−80953.1	−	140215.i	−0.128085	−	0.221850i
$796$		0			0
$797$		−	349224.i		−	0.549779i	−0.961476	−	0.274889i	$-0.911359\pi$
$797$		−	349224.i		−	0.549779i	0.961476	−	0.274889i	$-0.0886412\pi$
$798$		0			0
$799$	308455.			0.483169
$800$		0			0
$801$	−291379.	+	168228.i	−0.454143	+	0.262200i
$802$		0			0
$803$	−407352.	−	705554.i	−0.631740	−	1.09421i
$804$		0			0
$805$	−400764.			−0.618439
$806$		0			0
$807$	−120580.	+	208850.i	−0.185151	+	0.320692i
$808$		0			0
$809$	840086.			1.28359			0.641796	−	0.766876i	$-0.278190\pi$
$809$	840086.			1.28359			0.641796	+	0.766876i	$0.278190\pi$
$810$		0			0
$811$	982257.	+	567106.i	1.49342	+	0.862229i	0.999972	−	0.00754325i	$-0.00240111\pi$
$811$	982257.	+	567106.i	1.49342	+	0.862229i	0.493453	+	0.869772i	$0.335734\pi$
$812$		0			0
$813$	−149309.	−	86203.5i	−0.225894	−	0.130420i
$814$		0			0
$815$	550557.	+	953593.i	0.828872	+	1.43565i
$816$		0			0
$817$	792080.	+	72156.7i	1.18666	+	0.108102i
$818$		0			0
$819$	−598288.	+	345422.i	−0.891954	+	0.514970i
$820$		0			0
$821$	−416970.	+	722214.i	−0.618613	+	1.07147i	0.371126	+	0.928582i	$0.378972\pi$
$821$	−416970.	+	722214.i	−0.618613	+	1.07147i	−0.989739	+	0.142886i	$0.954362\pi$
$822$		0			0
$823$	−160435.	+	277881.i	−0.236864	+	0.410260i	−0.959813	−	0.280642i	$-0.909453\pi$
$823$	−160435.	+	277881.i	−0.236864	+	0.410260i	0.722949	+	0.690901i	$0.242786\pi$
$824$		0			0
$825$			393651.i			0.578368i
$826$		0			0
$827$	−454612.	−	262470.i	−0.664706	−	0.383768i	0.129361	−	0.991598i	$-0.458707\pi$
$827$	−454612.	−	262470.i	−0.664706	−	0.383768i	−0.794068	+	0.607829i	$0.792041\pi$
$828$		0			0
$829$			168815.i			0.245641i	0.992429	+	0.122821i	$0.0391940\pi$
$829$			168815.i			0.245641i	−0.992429	+	0.122821i	$0.960806\pi$
$830$		0			0
$831$	−6400.46	+	3695.31i	−0.00926850	+	0.00535117i
$832$		0			0
$833$	252222.	+	436861.i	0.363490	+	0.629583i
$834$		0			0
$835$			1.65015e6i			2.36674i
$836$		0			0
$837$	−573857.			−0.819130
$838$		0			0
$839$	−442064.	+	255226.i	−0.628002	+	0.362577i	−0.779978	−	0.625807i	$-0.784770\pi$
$839$	−442064.	+	255226.i	−0.628002	+	0.362577i	0.151976	+	0.988384i	$0.451436\pi$
$840$		0			0
$841$	−353455.	−	612202.i	−0.499738	−	0.865572i
$842$		0			0
$843$	−355381.			−0.500080
$844$		0			0
$845$	141747.	−	245513.i	0.198519	−	0.343844i
$846$		0			0
$847$	−358779.			−0.500104
$848$		0			0
$849$	418596.	+	241677.i	0.580738	+	0.335289i
$850$		0			0
$851$	334559.	+	193158.i	0.461969	+	0.266718i
$852$		0			0
$853$	−181309.	−	314036.i	−0.249184	−	0.431600i	0.714116	−	0.700028i	$-0.246829\pi$
$853$	−181309.	−	314036.i	−0.249184	−	0.431600i	−0.963300	+	0.268428i	$0.913496\pi$
$854$		0			0
$855$	463597.	−	657066.i	0.634174	−	0.898828i
$856$		0			0
$857$	230212.	−	132913.i	0.313449	−	0.180970i	−0.335020	−	0.942211i	$-0.608743\pi$
$857$	230212.	−	132913.i	0.313449	−	0.180970i	0.648469	+	0.761241i	$0.275410\pi$
$858$		0			0
$859$	134235.	−	232502.i	0.181920	−	0.315095i	−0.760614	−	0.649204i	$-0.775102\pi$
$859$	134235.	−	232502.i	0.181920	−	0.315095i	0.942534	+	0.334109i	$0.108435\pi$
$860$		0			0
$861$	200702.	−	347626.i	0.270736	−	0.468928i
$862$		0			0
$863$		−	832860.i		−	1.11828i	−0.829073	−	0.559140i	$-0.811131\pi$
$863$		−	832860.i		−	1.11828i	0.829073	−	0.559140i	$-0.188869\pi$
$864$		0			0
$865$	−1.56548e6	−	903831.i	−2.09226	−	1.20797i
$866$		0			0
$867$		−	925744.i		−	1.23155i
$868$		0			0
$869$	76881.3	−	44387.4i	0.101808	−	0.0587788i
$870$		0			0
$871$	−481754.	−	834422.i	−0.635022	−	1.09989i
$872$		0			0
$873$		−	615734.i		−	0.807913i
$874$		0			0
$875$	−24752.3			−0.0323295
$876$		0			0
$877$	−254777.	+	147095.i	−0.331254	+	0.191249i	−0.656398	−	0.754415i	$-0.727921\pi$
$877$	−254777.	+	147095.i	−0.331254	+	0.191249i	0.325144	+	0.945665i	$0.394587\pi$
$878$		0			0
$879$	−31958.7	−	55354.2i	−0.0413630	−	0.0716428i
$880$		0			0
$881$	269270.			0.346925			0.173462	−	0.984840i	$-0.444504\pi$
$881$	269270.			0.346925			0.173462	+	0.984840i	$0.444504\pi$
$882$		0			0
$883$	557021.	−	964788.i	0.714414	−	1.23740i	−0.248771	−	0.968562i	$-0.580027\pi$
$883$	557021.	−	964788.i	0.714414	−	1.23740i	0.963185	−	0.268839i	$-0.0866399\pi$
$884$		0			0
$885$	−230574.			−0.294391
$886$		0			0
$887$	−293723.	−	169581.i	−0.373329	−	0.215541i	0.301583	−	0.953440i	$-0.402485\pi$
$887$	−293723.	−	169581.i	−0.373329	−	0.215541i	−0.674912	+	0.737899i	$0.735818\pi$
$888$		0			0
$889$	−233921.	−	135054.i	−0.295982	−	0.170885i
$890$		0			0
$891$	176916.	+	306428.i	0.222850	+	0.385987i
$892$		0			0
$893$	−85266.8	−	184578.i	−0.106924	−	0.231460i
$894$		0			0
$895$	1.34653e6	−	777418.i	1.68100	−	0.970528i
$896$		0			0
$897$	−80019.1	+	138597.i	−0.0994509	+	0.172254i
$898$		0			0
$899$	−8984.96	+	15562.4i	−0.0111172	+	0.0192556i
$900$		0			0
$901$		−	583500.i		−	0.718772i
$902$		0			0
$903$	470421.	+	271598.i	0.576914	+	0.333082i
$904$		0			0
$905$			1.44862e6i			1.76871i
$906$		0			0
$907$	430360.	−	248469.i	0.523139	−	0.302035i	−0.215079	−	0.976597i	$-0.569001\pi$
$907$	430360.	−	248469.i	0.523139	−	0.302035i	0.738218	+	0.674562i	$0.235667\pi$
$908$		0			0
$909$	−236415.	−	409482.i	−0.286119	−	0.495573i
$910$		0			0
$911$		−	1.41006e6i		−	1.69903i	−0.527564	−	0.849515i	$-0.676895\pi$
$911$		−	1.41006e6i		−	1.69903i	0.527564	−	0.849515i	$-0.323105\pi$
$912$		0			0
$913$	−397046.			−0.476320
$914$		0			0
$915$	−704523.	+	406757.i	−0.841498	+	0.485839i
$916$		0			0
$917$	−290237.	−	502706.i	−0.345155	−	0.597826i
$918$		0			0
$919$	−376060.			−0.445273			−0.222637	−	0.974902i	$-0.571466\pi$
$919$	−376060.			−0.445273			−0.222637	+	0.974902i	$0.571466\pi$
$920$		0			0
$921$	−326214.	+	565020.i	−0.384577	+	0.666107i
$922$		0			0
$923$	−271873.			−0.319126
$924$		0			0
$925$	1.08901e6	+	628742.i	1.27277	+	0.734834i
$926$		0			0
$927$	−973008.	−	561766.i	−1.13229	−	0.653727i
$928$		0			0
$929$	485919.	+	841637.i	0.563032	+	0.975199i	0.997230	+	0.0743819i	$0.0236984\pi$
$929$	485919.	+	841637.i	0.563032	+	0.975199i	−0.434198	+	0.900817i	$0.642968\pi$
$930$		0			0
$931$	191693.	−	271690.i	0.221160	−	0.313455i
$932$		0			0
$933$	−332008.	+	191685.i	−0.381404	+	0.220204i
$934$		0			0
$935$	−1.40524e6	+	2.43394e6i	−1.60741	+	2.78411i
$936$		0			0
$937$	−301442.	+	522113.i	−0.343340	+	0.594683i	−0.985051	−	0.172264i	$-0.944892\pi$
$937$	−301442.	+	522113.i	−0.343340	+	0.594683i	0.641710	+	0.766947i	$0.278225\pi$
$938$		0			0
$939$			82669.9i			0.0937598i
$940$		0			0
$941$	−501844.	−	289740.i	−0.566747	−	0.327211i	0.189102	−	0.981957i	$-0.439442\pi$
$941$	−501844.	−	289740.i	−0.566747	−	0.327211i	−0.755849	+	0.654746i	$0.772776\pi$
$942$		0			0
$943$			318655.i			0.358342i
$944$		0			0
$945$	1.09003e6	−	629331.i	1.22061	−	0.704719i
$946$		0			0
$947$	−22184.3	−	38424.3i	−0.0247369	−	0.0428456i	0.853392	−	0.521270i	$-0.174541\pi$
$947$	−22184.3	−	38424.3i	−0.0247369	−	0.0428456i	−0.878129	+	0.478424i	$0.841208\pi$
$948$		0			0
$949$		−	1.07813e6i		−	1.19713i
$950$		0			0
$951$	−283491.			−0.313458
$952$		0			0
$953$	969638.	−	559821.i	1.06764	−	0.616401i	0.140102	−	0.990137i	$-0.455257\pi$
$953$	969638.	−	559821.i	1.06764	−	0.616401i	0.927535	+	0.373736i	$0.121923\pi$
$954$		0			0
$955$	−887872.	−	1.53784e6i	−0.973517	−	1.68618i
$956$		0			0
$957$	−11893.6			−0.0129865
$958$		0			0
$959$	−8792.83	+	15229.6i	−0.00956074	+	0.0165597i
$960$		0			0
$961$	51980.3			0.0562849
$962$		0			0
$963$	1.02327e6	+	590783.i	1.10341	+	0.637052i
$964$		0			0
$965$	−543822.	−	313976.i	−0.583986	−	0.337164i
$966$		0			0
$967$	123868.	+	214546.i	0.132467	+	0.229439i	0.924627	−	0.380874i	$-0.124377\pi$
$967$	123868.	+	214546.i	0.132467	+	0.229439i	−0.792160	+	0.610313i	$0.791044\pi$
$968$		0			0
$969$	−767745.	+	354664.i	−0.817654	+	0.377720i
$970$		0			0
$971$	−209743.	+	121095.i	−0.222459	+	0.128437i	−0.607088	−	0.794634i	$-0.707663\pi$
$971$	−209743.	+	121095.i	−0.222459	+	0.128437i	0.384629	+	0.923071i	$0.374329\pi$
$972$		0			0
$973$	−310373.	+	537582.i	−0.327837	+	0.567831i
$974$		0			0
$975$	−260468.	+	451144.i	−0.273997	+	0.474576i
$976$		0			0
$977$			1.57807e6i			1.65324i	0.562761	+	0.826620i	$0.309739\pi$
$977$			1.57807e6i			1.65324i	−0.562761	+	0.826620i	$0.690261\pi$
$978$		0			0
$979$	−671258.	−	387551.i	−0.700365	−	0.404356i
$980$		0			0
$981$		−	213837.i		−	0.222201i
$982$		0			0
$983$	−276804.	+	159813.i	−0.286461	+	0.165388i	−0.636345	−	0.771405i	$-0.719554\pi$
$983$	−276804.	+	159813.i	−0.286461	+	0.165388i	0.349884	+	0.936793i	$0.386221\pi$
$984$		0			0
$985$	−1.26254e6	−	2.18679e6i	−1.30129	−	2.25390i
$986$		0			0
$987$		−	138859.i		−	0.142541i
$988$		0			0
$989$	−431216.			−0.440862
$990$		0			0
$991$	−1.00216e6	+	578595.i	−1.02044	+	0.589152i	−0.914231	−	0.405192i	$-0.867205\pi$
$991$	−1.00216e6	+	578595.i	−1.02044	+	0.589152i	−0.106209	+	0.994344i	$0.533871\pi$
$992$		0			0
$993$	1984.57	+	3437.37i	0.00201264	+	0.00348600i
$994$		0			0
$995$	1.86302e6			1.88179
$996$		0			0
$997$	118329.	−	204951.i	0.119042	−	0.206186i	−0.800346	−	0.599538i	$-0.795351\pi$
$997$	118329.	−	204951.i	0.119042	−	0.206186i	0.919388	+	0.393351i	$0.128684\pi$
$998$		0			0
$999$	−1.21328e6			−1.21571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.c.145.3		16
4.3	odd	2		38.5.d.a.31.7	yes	16
12.11	even	2		342.5.m.c.145.4		16
19.8	odd	6	inner	304.5.r.c.65.3		16
76.27	even	6		38.5.d.a.27.7	✓	16
228.179	odd	6		342.5.m.c.217.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.7	✓	16	76.27	even	6
38.5.d.a.31.7	yes	16	4.3	odd	2
304.5.r.c.65.3		16	19.8	odd	6	inner
304.5.r.c.145.3		16	1.1	even	1	trivial
342.5.m.c.145.4		16	12.11	even	2
342.5.m.c.217.4		16	228.179	odd	6

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.70447 + 2.13878i) q^{3} +(-17.7629 - 30.7663i) q^{5} -57.6374 q^{7} +(-31.3513 + 54.3020i) q^{9} +O(q^{10})\)	\(q+(-3.70447 + 2.13878i) q^{3} +(-17.7629 - 30.7663i) q^{5} -57.6374 q^{7} +(-31.3513 + 54.3020i) q^{9} -144.450 q^{11} +(-165.547 - 95.5784i) q^{13} +(131.605 + 75.9819i) q^{15} +(273.834 + 474.294i) q^{17} +(208.119 - 294.971i) q^{19} +(213.516 - 123.274i) q^{21} +(-97.8608 + 169.500i) q^{23} +(-318.544 + 551.735i) q^{25} -614.695i q^{27} +(-16.6699 - 9.62437i) q^{29} -933.563i q^{31} +(535.110 - 308.946i) q^{33} +(1023.81 + 1773.29i) q^{35} -1973.80i q^{37} +817.683 q^{39} +(1409.98 - 814.052i) q^{41} +(1101.61 + 1908.04i) q^{43} +2227.56 q^{45} +(281.608 - 487.759i) q^{47} +921.075 q^{49} +(-2028.82 - 1171.34i) q^{51} +(-922.687 - 532.713i) q^{53} +(2565.85 + 4444.19i) q^{55} +(-140.093 + 1537.83i) q^{57} +(-1314.02 + 758.649i) q^{59} +(-2676.67 + 4636.13i) q^{61} +(1807.01 - 3129.83i) q^{63} +6791.02i q^{65} +(4365.12 + 2520.20i) q^{67} -837.209i q^{69} +(1231.70 - 711.125i) q^{71} +(2820.02 + 4884.42i) q^{73} -2725.18i q^{75} +8325.72 q^{77} +(-532.235 + 307.286i) q^{79} +(-1224.76 - 2121.34i) q^{81} +2748.68 q^{83} +(9728.19 - 16849.7i) q^{85} +82.3375 q^{87} +(4647.00 + 2682.95i) q^{89} +(9541.69 + 5508.90i) q^{91} +(1996.68 + 3458.36i) q^{93} +(-12772.0 - 1163.50i) q^{95} +(-8504.30 + 4909.96i) q^{97} +(4528.69 - 7843.92i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) \) 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9} + 84 q^{11} + 450 q^{13} + 390 q^{15} + 606 q^{17} + 306 q^{19} - 2160 q^{21} + 54 q^{23} - 434 q^{25} - 4914 q^{29} + 7890 q^{33} - 2328 q^{35} - 7620 q^{39} - 1692 q^{41} + 7402 q^{43} - 16720 q^{45} - 3198 q^{47} + 24816 q^{49} - 10710 q^{51} + 3870 q^{53} + 13588 q^{55} + 3702 q^{57} + 18288 q^{59} - 6522 q^{61} + 15676 q^{63} + 30168 q^{67} - 35874 q^{71} - 8080 q^{73} + 34560 q^{77} + 30738 q^{79} - 30920 q^{81} + 1476 q^{83} + 33626 q^{85} - 113100 q^{87} + 19782 q^{89} + 34260 q^{91} - 4272 q^{93} + 23706 q^{95} - 9936 q^{97} - 3848 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9 + 84 * q^11 + 450 * q^13 + 390 * q^15 + 606 * q^17 + 306 * q^19 - 2160 * q^21 + 54 * q^23 - 434 * q^25 - 4914 * q^29 + 7890 * q^33 - 2328 * q^35 - 7620 * q^39 - 1692 * q^41 + 7402 * q^43 - 16720 * q^45 - 3198 * q^47 + 24816 * q^49 - 10710 * q^51 + 3870 * q^53 + 13588 * q^55 + 3702 * q^57 + 18288 * q^59 - 6522 * q^61 + 15676 * q^63 + 30168 * q^67 - 35874 * q^71 - 8080 * q^73 + 34560 * q^77 + 30738 * q^79 - 30920 * q^81 + 1476 * q^83 + 33626 * q^85 - 113100 * q^87 + 19782 * q^89 + 34260 * q^91 - 4272 * q^93 + 23706 * q^95 - 9936 * q^97 - 3848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more