LMFDB - Embedded newform 304.5.r.a.145.2

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 $ x^10 + 109x^8 + 4107x^6 + 61507x^4 + 300520x^2 + 108300
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$2.91518i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.5.r.a.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.18489 + 4.72555i) q^{3} +(-7.00036 - 12.1250i) q^{5} -19.8223 q^{7} +(4.16163 - 7.20815i) q^{9} +O(q^{10})$	\(q+(-8.18489 + 4.72555i) q^{3} +(-7.00036 - 12.1250i) q^{5} -19.8223 q^{7} +(4.16163 - 7.20815i) q^{9} +177.809 q^{11} +(83.2716 + 48.0769i) q^{13} +(114.594 + 66.1610i) q^{15} +(26.8637 + 46.5293i) q^{17} +(-161.512 + 322.854i) q^{19} +(162.243 - 93.6710i) q^{21} +(-372.053 + 644.415i) q^{23} +(214.490 - 371.508i) q^{25} -686.875i q^{27} +(-738.578 - 426.418i) q^{29} -317.572i q^{31} +(-1455.35 + 840.247i) q^{33} +(138.763 + 240.344i) q^{35} +1697.87i q^{37} -908.759 q^{39} +(1748.55 - 1009.53i) q^{41} +(-938.059 - 1624.77i) q^{43} -116.532 q^{45} +(665.166 - 1152.10i) q^{47} -2008.08 q^{49} +(-439.753 - 253.891i) q^{51} +(-2043.31 - 1179.71i) q^{53} +(-1244.73 - 2155.93i) q^{55} +(-203.701 - 3405.76i) q^{57} +(-2574.85 + 1486.59i) q^{59} +(-2099.98 + 3637.27i) q^{61} +(-82.4929 + 142.882i) q^{63} -1346.22i q^{65} +(-7668.40 - 4427.35i) q^{67} -7032.62i q^{69} +(6430.03 - 3712.38i) q^{71} +(-4260.31 - 7379.07i) q^{73} +4054.33i q^{75} -3524.58 q^{77} +(-3800.18 + 2194.04i) q^{79} +(3582.95 + 6205.86i) q^{81} -10166.0 q^{83} +(376.111 - 651.443i) q^{85} +8060.24 q^{87} +(-3232.45 - 1866.26i) q^{89} +(-1650.63 - 952.993i) q^{91} +(1500.70 + 2599.29i) q^{93} +(5045.24 - 301.760i) q^{95} +(845.233 - 487.996i) q^{97} +(739.977 - 1281.68i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 9 q^{3} + 8 q^{5} + 24 q^{7} - 58 q^{9}+O(q^{10}) $ 10 * q - 9 * q^3 + 8 * q^5 + 24 * q^7 - 58 * q^9	$ 10 q - 9 q^{3} + 8 q^{5} + 24 q^{7} - 58 q^{9} - 50 q^{11} - 624 q^{13} - 504 q^{15} - 292 q^{17} - 305 q^{19} + 1158 q^{21} - 98 q^{23} - 681 q^{25} + 2598 q^{29} - 3441 q^{33} - 694 q^{35} + 5552 q^{39} - 1407 q^{41} - 5424 q^{43} + 9572 q^{45} + 2416 q^{47} - 17826 q^{49} + 3342 q^{51} + 1122 q^{53} - 11424 q^{55} - 7906 q^{57} - 15387 q^{59} + 860 q^{61} - 5318 q^{63} - 14763 q^{67} + 27264 q^{71} + 1561 q^{73} - 18392 q^{77} - 24750 q^{79} + 14311 q^{81} - 6002 q^{83} - 14944 q^{85} + 31996 q^{87} - 22566 q^{89} - 8724 q^{91} + 12476 q^{93} + 7312 q^{95} + 46287 q^{97} + 2048 q^{99}+O(q^{100}) $ 10 * q - 9 * q^3 + 8 * q^5 + 24 * q^7 - 58 * q^9 - 50 * q^11 - 624 * q^13 - 504 * q^15 - 292 * q^17 - 305 * q^19 + 1158 * q^21 - 98 * q^23 - 681 * q^25 + 2598 * q^29 - 3441 * q^33 - 694 * q^35 + 5552 * q^39 - 1407 * q^41 - 5424 * q^43 + 9572 * q^45 + 2416 * q^47 - 17826 * q^49 + 3342 * q^51 + 1122 * q^53 - 11424 * q^55 - 7906 * q^57 - 15387 * q^59 + 860 * q^61 - 5318 * q^63 - 14763 * q^67 + 27264 * q^71 + 1561 * q^73 - 18392 * q^77 - 24750 * q^79 + 14311 * q^81 - 6002 * q^83 - 14944 * q^85 + 31996 * q^87 - 22566 * q^89 - 8724 * q^91 + 12476 * q^93 + 7312 * q^95 + 46287 * q^97 + 2048 * 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
$3$	−8.18489	+	4.72555i	−0.909432	+	0.525061i	−0.880248	−	0.474513i	$-0.842624\pi$
$3$	−8.18489	+	4.72555i	−0.909432	+	0.525061i	−0.0291839	+	0.999574i	$0.509291\pi$
$4$		0			0
$5$	−7.00036	−	12.1250i	−0.280014	−	0.484999i	0.691374	−	0.722497i	$-0.257006\pi$
$5$	−7.00036	−	12.1250i	−0.280014	−	0.484999i	−0.971388	+	0.237498i	$0.923673\pi$
$6$		0			0
$7$	−19.8223			−0.404536			−0.202268	−	0.979330i	$-0.564831\pi$
$7$	−19.8223			−0.404536			−0.202268	+	0.979330i	$0.564831\pi$
$8$		0			0
$9$	4.16163	−	7.20815i	0.0513781	−	0.0889896i
$10$		0			0
$11$	177.809			1.46950			0.734749	−	0.678339i	$-0.237300\pi$
$11$	177.809			1.46950			0.734749	+	0.678339i	$0.237300\pi$
$12$		0			0
$13$	83.2716	+	48.0769i	0.492732	+	0.284479i	0.725707	−	0.688004i	$-0.241513\pi$
$13$	83.2716	+	48.0769i	0.492732	+	0.284479i	−0.232975	+	0.972483i	$0.574846\pi$
$14$		0			0
$15$	114.594	+	66.1610i	0.509308	+	0.294049i
$16$		0			0
$17$	26.8637	+	46.5293i	0.0929539	+	0.161001i	0.908753	−	0.417335i	$-0.137036\pi$
$17$	26.8637	+	46.5293i	0.0929539	+	0.161001i	−0.815799	+	0.578336i	$0.803702\pi$
$18$		0			0
$19$	−161.512	+	322.854i	−0.447403	+	0.894333i
$19$	−161.512	+	322.854i	−0.447403	+	0.894333i
$20$		0			0
$21$	162.243	−	93.6710i	0.367898	−	0.212406i
$22$		0			0
$23$	−372.053	+	644.415i	−0.703314	+	1.21818i	0.263983	+	0.964527i	$0.414964\pi$
$23$	−372.053	+	644.415i	−0.703314	+	1.21818i	−0.967297	+	0.253648i	$0.918370\pi$
$24$		0			0
$25$	214.490	−	371.508i	0.343184	−	0.594412i
$26$		0			0
$27$		−	686.875i		−	0.942215i
$28$		0			0
$29$	−738.578	−	426.418i	−0.878213	−	0.507037i	−0.00814454	−	0.999967i	$-0.502593\pi$
$29$	−738.578	−	426.418i	−0.878213	−	0.507037i	−0.870069	+	0.492930i	$0.835926\pi$
$30$		0			0
$31$		−	317.572i		−	0.330460i	−0.986255	−	0.165230i	$-0.947163\pi$
$31$		−	317.572i		−	0.330460i	0.986255	−	0.165230i	$-0.0528367\pi$
$32$		0			0
$33$	−1455.35	+	840.247i	−1.33641	+	0.771577i
$34$		0			0
$35$	138.763	+	240.344i	0.113276	+	0.196199i
$36$		0			0
$37$			1697.87i			1.24022i	0.784514	+	0.620111i	$0.212913\pi$
$37$			1697.87i			1.24022i	−0.784514	+	0.620111i	$0.787087\pi$
$38$		0			0
$39$	−908.759			−0.597475
$40$		0			0
$41$	1748.55	−	1009.53i	1.04018	−	0.600551i	0.120299	−	0.992738i	$-0.461615\pi$
$41$	1748.55	−	1009.53i	1.04018	−	0.600551i	0.919885	+	0.392187i	$0.128281\pi$
$42$		0			0
$43$	−938.059	−	1624.77i	−0.507333	−	0.878727i	−0.999964	−	0.00848857i	$-0.997298\pi$
$43$	−938.059	−	1624.77i	−0.507333	−	0.878727i	0.492631	−	0.870238i	$-0.336035\pi$
$44$		0			0
$45$	−116.532			−0.0575464
$46$		0			0
$47$	665.166	−	1152.10i	0.301116	−	0.521549i	−0.675273	−	0.737568i	$-0.735974\pi$
$47$	665.166	−	1152.10i	0.301116	−	0.521549i	0.976389	+	0.216019i	$0.0693074\pi$
$48$		0			0
$49$	−2008.08			−0.836351
$50$		0			0
$51$	−439.753	−	253.891i	−0.169071	−	0.0976129i
$52$		0			0
$53$	−2043.31	−	1179.71i	−0.727417	−	0.419974i	0.0900597	−	0.995936i	$-0.471294\pi$
$53$	−2043.31	−	1179.71i	−0.727417	−	0.419974i	−0.817476	+	0.575962i	$0.804628\pi$
$54$		0			0
$55$	−1244.73	−	2155.93i	−0.411481	−	0.712705i
$56$		0			0
$57$	−203.701	−	3405.76i	−0.0626966	−	1.04825i
$58$		0			0
$59$	−2574.85	+	1486.59i	−0.739686	+	0.427058i	−0.821955	−	0.569552i	$-0.807117\pi$
$59$	−2574.85	+	1486.59i	−0.739686	+	0.427058i	0.0822690	+	0.996610i	$0.473783\pi$
$60$		0			0
$61$	−2099.98	+	3637.27i	−0.564358	+	0.977497i	0.432751	+	0.901514i	$0.357543\pi$
$61$	−2099.98	+	3637.27i	−0.564358	+	0.977497i	−0.997109	+	0.0759838i	$0.975790\pi$
$62$		0			0
$63$	−82.4929	+	142.882i	−0.0207843	+	0.0359995i
$64$		0			0
$65$		−	1346.22i		−	0.318632i
$66$		0			0
$67$	−7668.40	−	4427.35i	−1.70826	−	0.986266i	−0.936713	−	0.350099i	$-0.886148\pi$
$67$	−7668.40	−	4427.35i	−1.70826	−	0.986266i	−0.771551	−	0.636168i	$-0.780519\pi$
$68$		0			0
$69$		−	7032.62i		−	1.47713i
$70$		0			0
$71$	6430.03	−	3712.38i	1.27555	−	0.736437i	0.299520	−	0.954090i	$-0.403173\pi$
$71$	6430.03	−	3712.38i	1.27555	−	0.736437i	0.976026	+	0.217653i	$0.0698401\pi$
$72$		0			0
$73$	−4260.31	−	7379.07i	−0.799457	−	1.38470i	−0.919970	−	0.391989i	$-0.871787\pi$
$73$	−4260.31	−	7379.07i	−0.799457	−	1.38470i	0.120512	−	0.992712i	$-0.461546\pi$
$74$		0			0
$75$			4054.33i			0.720770i
$76$		0			0
$77$	−3524.58			−0.594465
$78$		0			0
$79$	−3800.18	+	2194.04i	−0.608906	+	0.351552i	−0.772537	−	0.634970i	$-0.781013\pi$
$79$	−3800.18	+	2194.04i	−0.608906	+	0.351552i	0.163631	+	0.986522i	$0.447679\pi$
$80$		0			0
$81$	3582.95	+	6205.86i	0.546099	+	0.945871i
$82$		0			0
$83$	−10166.0			−1.47568			−0.737840	−	0.674976i	$-0.764154\pi$
$83$	−10166.0			−1.47568			−0.737840	+	0.674976i	$0.764154\pi$
$84$		0			0
$85$	376.111	−	651.443i	0.0520568	−	0.0901651i
$86$		0			0
$87$	8060.24			1.06490
$88$		0			0
$89$	−3232.45	−	1866.26i	−0.408087	−	0.235609i	0.281881	−	0.959449i	$-0.409042\pi$
$89$	−3232.45	−	1866.26i	−0.408087	−	0.235609i	−0.689967	+	0.723841i	$0.742375\pi$
$90$		0			0
$91$	−1650.63	−	952.993i	−0.199328	−	0.115082i
$92$		0			0
$93$	1500.70	+	2599.29i	0.173512	+	0.300531i
$94$		0			0
$95$	5045.24	−	301.760i	0.559029	−	0.0334360i
$96$		0			0
$97$	845.233	−	487.996i	0.0898324	−	0.0518648i	−0.454411	−	0.890792i	$-0.650150\pi$
$97$	845.233	−	487.996i	0.0898324	−	0.0518648i	0.544243	+	0.838927i	$0.316817\pi$
$98$		0			0
$99$	739.977	−	1281.68i	0.0755001	−	0.130770i
$100$		0			0
$101$	−4591.76	+	7953.16i	−0.450128	+	0.779645i	−0.998394	−	0.0566592i	$-0.981955\pi$
$101$	−4591.76	+	7953.16i	−0.450128	+	0.779645i	0.548265	+	0.836305i	$0.315288\pi$
$102$		0			0
$103$			12570.5i			1.18489i	0.805611	+	0.592445i	$0.201837\pi$
$103$			12570.5i			1.18489i	−0.805611	+	0.592445i	$0.798163\pi$
$104$		0			0
$105$	−2271.52	−	1311.46i	−0.206033	−	0.118953i
$106$		0			0
$107$			5292.95i			0.462307i	0.972917	+	0.231153i	$0.0742499\pi$
$107$			5292.95i			0.462307i	−0.972917	+	0.231153i	$0.925750\pi$
$108$		0			0
$109$	470.631	−	271.719i	0.0396121	−	0.0228700i	−0.480063	−	0.877234i	$-0.659386\pi$
$109$	470.631	−	271.719i	0.0396121	−	0.0228700i	0.519675	+	0.854364i	$0.326053\pi$
$110$		0			0
$111$	−8023.35	−	13896.8i	−0.651193	−	1.12790i
$112$		0			0
$113$			6154.75i			0.482007i	0.970524	+	0.241003i	$0.0774765\pi$
$113$			6154.75i			0.482007i	−0.970524	+	0.241003i	$0.922523\pi$
$114$		0			0
$115$	10418.0			0.787752
$116$		0			0
$117$	693.092	−	400.157i	0.0506313	−	0.0292320i
$118$		0			0
$119$	−532.499	−	922.315i	−0.0376032	−	0.0651306i
$120$		0			0
$121$	16975.2			1.15943
$122$		0			0
$123$	−9541.12	+	16525.7i	−0.630651	+	1.09232i
$124$		0			0
$125$	−14756.5			−0.944414
$126$		0			0
$127$	−798.363	−	460.935i	−0.0494986	−	0.0285780i	0.475046	−	0.879961i	$-0.342431\pi$
$127$	−798.363	−	460.935i	−0.0494986	−	0.0285780i	−0.524545	+	0.851383i	$0.675765\pi$
$128$		0			0
$129$	15355.8	+	8865.69i	0.922771	+	0.532762i
$130$		0			0
$131$	−1380.77	−	2391.57i	−0.0804599	−	0.139361i	0.822988	−	0.568059i	$-0.192306\pi$
$131$	−1380.77	−	2391.57i	−0.0804599	−	0.139361i	−0.903448	+	0.428699i	$0.858972\pi$
$132$		0			0
$133$	3201.54	−	6399.70i	0.180990	−	0.361790i
$134$		0			0
$135$	−8328.34	+	4808.37i	−0.456973	+	0.263834i
$136$		0			0
$137$	1927.00	−	3337.67i	0.102669	−	0.177829i	−0.810114	−	0.586272i	$-0.800595\pi$
$137$	1927.00	−	3337.67i	0.102669	−	0.177829i	0.912784	+	0.408443i	$0.133928\pi$
$138$		0			0
$139$	18557.2	−	32142.1i	0.960469	−	1.66358i	0.239145	−	0.970984i	$-0.423133\pi$
$139$	18557.2	−	32142.1i	0.960469	−	1.66358i	0.721324	−	0.692598i	$-0.243534\pi$
$140$		0			0
$141$			12573.1i			0.632418i
$142$		0			0
$143$	14806.5	+	8548.53i	0.724069	+	0.418041i
$144$		0			0
$145$			11940.3i			0.567910i
$146$		0			0
$147$	16435.9	−	9489.27i	0.760604	−	0.439135i
$148$		0			0
$149$	−6237.55	−	10803.8i	−0.280958	−	0.486634i	0.690663	−	0.723177i	$-0.257319\pi$
$149$	−6237.55	−	10803.8i	−0.280958	−	0.486634i	−0.971621	+	0.236543i	$0.923986\pi$
$150$		0			0
$151$			477.784i			0.0209545i	0.999945	+	0.0104772i	$0.00333507\pi$
$151$			477.784i			0.0209545i	−0.999945	+	0.0104772i	$0.996665\pi$
$152$		0			0
$153$	447.187			0.0191032
$154$		0			0
$155$	−3850.56	+	2223.12i	−0.160273	+	0.0925336i
$156$		0			0
$157$	8199.07	+	14201.2i	0.332633	+	0.576137i	0.983027	−	0.183459i	$-0.0587296\pi$
$157$	8199.07	+	14201.2i	0.332633	+	0.576137i	−0.650394	+	0.759597i	$0.725396\pi$
$158$		0			0
$159$	22299.1			0.882048
$160$		0			0
$161$	7374.93	−	12773.8i	0.284516	−	0.492796i
$162$		0			0
$163$	−31690.4			−1.19276			−0.596379	−	0.802703i	$-0.703394\pi$
$163$	−31690.4			−1.19276			−0.596379	+	0.802703i	$0.703394\pi$
$164$		0			0
$165$	20375.9	+	11764.1i	0.748428	+	0.432105i
$166$		0			0
$167$	23949.0	+	13827.0i	0.858727	+	0.495786i	0.863586	−	0.504202i	$-0.168213\pi$
$167$	23949.0	+	13827.0i	0.858727	+	0.495786i	−0.00485911	+	0.999988i	$0.501547\pi$
$168$		0			0
$169$	−9657.72	−	16727.7i	−0.338144	−	0.585682i
$170$		0			0
$171$	1655.03	+	2507.81i	0.0565995	+	0.0857633i
$172$		0			0
$173$	−5352.32	+	3090.16i	−0.178834	+	0.103250i	−0.586745	−	0.809772i	$-0.699591\pi$
$173$	−5352.32	+	3090.16i	−0.178834	+	0.103250i	0.407911	+	0.913022i	$0.366257\pi$
$174$		0			0
$175$	−4251.68	+	7364.12i	−0.138830	+	0.240461i
$176$		0			0
$177$	14049.9	−	24335.1i	0.448463	−	0.776761i
$178$		0			0
$179$			37842.6i			1.18107i	0.807012	+	0.590535i	$0.201083\pi$
$179$			37842.6i			1.18107i	−0.807012	+	0.590535i	$0.798917\pi$
$180$		0			0
$181$	−25195.1	−	14546.4i	−0.769059	−	0.444016i	0.0634798	−	0.997983i	$-0.479780\pi$
$181$	−25195.1	−	14546.4i	−0.769059	−	0.444016i	−0.832539	+	0.553967i	$0.813114\pi$
$182$		0			0
$183$		−	39694.2i		−	1.18529i
$184$		0			0
$185$	20586.6	−	11885.7i	0.601507	−	0.347280i
$186$		0			0
$187$	4776.61	+	8273.34i	0.136596	+	0.236591i
$188$		0			0
$189$			13615.4i			0.381160i
$190$		0			0
$191$	−30917.5			−0.847497			−0.423748	−	0.905780i	$-0.639286\pi$
$191$	−30917.5			−0.847497			−0.423748	+	0.905780i	$0.639286\pi$
$192$		0			0
$193$	29762.5	−	17183.4i	0.799016	−	0.461312i	−0.0441110	−	0.999027i	$-0.514046\pi$
$193$	29762.5	−	17183.4i	0.799016	−	0.461312i	0.843127	+	0.537715i	$0.180712\pi$
$194$		0			0
$195$	6361.64	+	11018.7i	0.167301	+	0.289775i
$196$		0			0
$197$	−40466.2			−1.04270			−0.521351	−	0.853342i	$-0.674572\pi$
$197$	−40466.2			−1.04270			−0.521351	+	0.853342i	$0.674572\pi$
$198$		0			0
$199$	−3668.05	+	6353.25i	−0.0926253	+	0.160432i	−0.908615	−	0.417635i	$-0.862859\pi$
$199$	−3668.05	+	6353.25i	−0.0926253	+	0.160432i	0.815990	+	0.578066i	$0.196193\pi$
$200$		0			0
$201$	83686.6			2.07140
$202$		0			0
$203$	14640.3	+	8452.57i	0.355269	+	0.205115i
$204$		0			0
$205$	−24480.9	−	14134.1i	−0.582533	−	0.336325i
$206$		0			0
$207$	3096.69	+	5363.63i	0.0722699	+	0.125175i
$208$		0			0
$209$	−28718.4	+	57406.5i	−0.657458	+	1.31422i
$210$		0			0
$211$	46962.1	−	27113.6i	1.05483	−	0.609007i	0.130833	−	0.991404i	$-0.458235\pi$
$211$	46962.1	−	27113.6i	1.05483	−	0.609007i	0.923998	+	0.382398i	$0.124902\pi$
$212$		0			0
$213$	−35086.1	+	60770.8i	−0.773349	+	1.33948i
$214$		0			0
$215$	−13133.5	+	22747.9i	−0.284121	+	0.492112i
$216$		0			0
$217$			6295.00i			0.133683i
$218$		0			0
$219$	69740.3	+	40264.6i	1.45410	+	0.839528i
$220$		0			0
$221$			5166.09i			0.105774i
$222$		0			0
$223$	−5412.68	+	3125.01i	−0.108844	+	0.0628409i	−0.553434	−	0.832893i	$-0.686683\pi$
$223$	−5412.68	+	3125.01i	−0.108844	+	0.0628409i	0.444590	+	0.895734i	$0.353349\pi$
$224$		0			0
$225$	−1785.26	−	3092.15i	−0.0352643	−	0.0610796i
$226$		0			0
$227$			9794.98i			0.190087i	0.995473	+	0.0950434i	$0.0302990\pi$
$227$			9794.98i			0.190087i	−0.995473	+	0.0950434i	$0.969701\pi$
$228$		0			0
$229$	96224.9			1.83492			0.917458	−	0.397832i	$-0.130237\pi$
$229$	96224.9			1.83492			0.917458	+	0.397832i	$0.130237\pi$
$230$		0			0
$231$	28848.3	−	16655.6i	0.540626	−	0.312130i
$232$		0			0
$233$	−8410.60	−	14567.6i	−0.154923	−	0.268334i	0.778108	−	0.628130i	$-0.216180\pi$
$233$	−8410.60	−	14567.6i	−0.154923	−	0.268334i	−0.933031	+	0.359796i	$0.882846\pi$
$234$		0			0
$235$	−18625.6			−0.337268
$236$		0			0
$237$	20736.1	−	35915.9i	0.369173	−	0.639426i
$238$		0			0
$239$	−72495.2			−1.26915			−0.634576	−	0.772860i	$-0.718825\pi$
$239$	−72495.2			−1.26915			−0.634576	+	0.772860i	$0.718825\pi$
$240$		0			0
$241$	−9603.35	−	5544.50i	−0.165344	−	0.0954615i	0.415045	−	0.909801i	$-0.363766\pi$
$241$	−9603.35	−	5544.50i	−0.165344	−	0.0954615i	−0.580389	+	0.814340i	$0.697099\pi$
$242$		0			0
$243$	−10469.2	−	6044.41i	−0.177297	−	0.102363i
$244$		0			0
$245$	14057.3	+	24347.9i	0.234190	+	0.405629i
$246$		0			0
$247$	−28971.2	+	19119.6i	−0.474868	+	0.313389i
$248$		0			0
$249$	83207.2	−	48039.7i	1.34203	−	0.774822i
$250$		0			0
$251$	29276.9	−	50709.1i	0.464705	−	0.804893i	−0.534483	−	0.845179i	$-0.679494\pi$
$251$	29276.9	−	50709.1i	0.464705	−	0.804893i	0.999188	+	0.0402861i	$0.0128269\pi$
$252$		0			0
$253$	−66154.5	+	114583.i	−1.03352	+	1.79011i
$254$		0			0
$255$			7109.32i			0.109332i
$256$		0			0
$257$	−36320.5	−	20969.6i	−0.549902	−	0.317486i	0.199180	−	0.979963i	$-0.436172\pi$
$257$	−36320.5	−	20969.6i	−0.549902	−	0.317486i	−0.749083	+	0.662477i	$0.769505\pi$
$258$		0			0
$259$		−	33655.5i		−	0.501715i
$260$		0			0
$261$	−6147.37	+	3549.19i	−0.0902420	+	0.0521012i
$262$		0			0
$263$	−23379.5	−	40494.5i	−0.338006	−	0.585443i	0.646052	−	0.763294i	$-0.276419\pi$
$263$	−23379.5	−	40494.5i	−0.338006	−	0.585443i	−0.984058	+	0.177850i	$0.943086\pi$
$264$		0			0
$265$			33033.5i			0.470395i
$266$		0			0
$267$	35276.4			0.494836
$268$		0			0
$269$	−31807.3	+	18364.0i	−0.439565	+	0.253783i	−0.703413	−	0.710781i	$-0.748341\pi$
$269$	−31807.3	+	18364.0i	−0.439565	+	0.253783i	0.263848	+	0.964564i	$0.415008\pi$
$270$		0			0
$271$	39163.1	+	67832.5i	0.533259	+	0.923632i	0.999245	+	0.0388401i	$0.0123663\pi$
$271$	39163.1	+	67832.5i	0.533259	+	0.923632i	−0.465986	+	0.884792i	$0.654300\pi$
$272$		0			0
$273$	18013.7			0.241700
$274$		0			0
$275$	38138.3	−	66057.5i	0.504309	−	0.873488i
$276$		0			0
$277$	−106120.			−1.38305			−0.691524	−	0.722354i	$-0.743060\pi$
$277$	−106120.			−1.38305			−0.691524	+	0.722354i	$0.743060\pi$
$278$		0			0
$279$	−2289.11	−	1321.62i	−0.0294075	−	0.0169784i
$280$		0			0
$281$	22141.4	+	12783.4i	0.280410	+	0.161895i	0.633609	−	0.773654i	$-0.281573\pi$
$281$	22141.4	+	12783.4i	0.280410	+	0.161895i	−0.353199	+	0.935548i	$0.614906\pi$
$282$		0			0
$283$	−5959.93	−	10322.9i	−0.0744164	−	0.128893i	0.826416	−	0.563060i	$-0.190376\pi$
$283$	−5959.93	−	10322.9i	−0.0744164	−	0.128893i	−0.900832	+	0.434167i	$0.857043\pi$
$284$		0			0
$285$	−39868.8	+	26311.4i	−0.490844	+	0.323932i
$286$		0			0
$287$	−34660.2	+	20011.1i	−0.420792	+	0.242944i
$288$		0			0
$289$	40317.2	−	69831.4i	0.482719	−	0.836094i
$290$		0			0
$291$	−4612.09	+	7988.38i	−0.0544643	+	0.0943350i
$292$		0			0
$293$			78303.7i			0.912110i	0.889952	+	0.456055i	$0.150738\pi$
$293$			78303.7i			0.912110i	−0.889952	+	0.456055i	$0.849262\pi$
$294$		0			0
$295$	36049.7	+	20813.3i	0.414245	+	0.239165i
$296$		0			0
$297$		−	122133.i		−	1.38458i
$298$		0			0
$299$	−61962.9	+	35774.3i	−0.693090	+	0.400156i
$300$		0			0
$301$	18594.5	+	32206.5i	0.205234	+	0.355477i
$302$		0			0
$303$		−	86794.4i		−	0.945380i
$304$		0			0
$305$	58802.4			0.632114
$306$		0			0
$307$	−54731.0	+	31599.0i	−0.580707	+	0.335271i	−0.761414	−	0.648266i	$-0.775495\pi$
$307$	−54731.0	+	31599.0i	−0.580707	+	0.335271i	0.180708	+	0.983537i	$0.442161\pi$
$308$		0			0
$309$	−59402.5	−	102888.i	−0.622139	−	1.07758i
$310$		0			0
$311$	−93030.4			−0.961842			−0.480921	−	0.876764i	$-0.659698\pi$
$311$	−93030.4			−0.961842			−0.480921	+	0.876764i	$0.659698\pi$
$312$		0			0
$313$	63547.0	−	110067.i	0.648644	−	1.12348i	−0.334803	−	0.942288i	$-0.608670\pi$
$313$	63547.0	−	110067.i	0.648644	−	1.12348i	0.983447	−	0.181196i	$-0.0579968\pi$
$314$		0			0
$315$	2309.92			0.0232796
$316$		0			0
$317$	−162973.	−	94092.3i	−1.62180	−	0.936344i	−0.986440	−	0.164124i	$-0.947520\pi$
$317$	−162973.	−	94092.3i	−1.62180	−	0.936344i	−0.635356	−	0.772220i	$-0.719146\pi$
$318$		0			0
$319$	−131326.	−	75821.1i	−1.29053	−	0.745090i
$320$		0			0
$321$	−25012.1	−	43322.2i	−0.242739	−	0.420437i
$322$		0			0
$323$	−19361.0	+	1158.00i	−0.185576	+	0.0110995i
$324$		0			0
$325$	35721.9	−	20624.0i	0.338195	−	0.195257i
$326$		0			0
$327$	−2568.04	+	4447.98i	−0.0240163	+	0.0415975i
$328$		0			0
$329$	−13185.1	+	22837.3i	−0.121812	+	0.210985i
$330$		0			0
$331$			126301.i			1.15279i	0.817171	+	0.576396i	$0.195541\pi$
$331$			126301.i			1.15279i	−0.817171	+	0.576396i	$0.804459\pi$
$332$		0			0
$333$	12238.5	+	7065.89i	0.110367	+	0.0637204i
$334$		0			0
$335$			123972.i			1.10467i
$336$		0			0
$337$	−86740.5	+	50079.7i	−0.763769	+	0.440962i	−0.830647	−	0.556799i	$-0.812029\pi$
$337$	−86740.5	+	50079.7i	−0.763769	+	0.440962i	0.0668782	+	0.997761i	$0.478696\pi$
$338$		0			0
$339$	−29084.6	−	50375.9i	−0.253083	−	0.438353i
$340$		0			0
$341$		−	56467.3i		−	0.485611i
$342$		0			0
$343$	87397.9			0.742870
$344$		0			0
$345$	−85270.3	+	49230.8i	−0.716407	+	0.413618i
$346$		0			0
$347$	−52875.4	−	91582.9i	−0.439132	−	0.760598i	0.558491	−	0.829511i	$-0.311380\pi$
$347$	−52875.4	−	91582.9i	−0.439132	−	0.760598i	−0.997623	+	0.0689122i	$0.978047\pi$
$348$		0			0
$349$	−157850.			−1.29597			−0.647985	−	0.761653i	$-0.724388\pi$
$349$	−157850.			−1.29597			−0.647985	+	0.761653i	$0.724388\pi$
$350$		0			0
$351$	33022.8	−	57197.2i	0.268040	−	0.464259i
$352$		0			0
$353$	41636.7			0.334139			0.167069	−	0.985945i	$-0.446570\pi$
$353$	41636.7			0.334139			0.167069	+	0.985945i	$0.446570\pi$
$354$		0			0
$355$	−90025.0	−	51975.9i	−0.714342	−	0.412426i
$356$		0			0
$357$	8716.89	+	5032.70i	0.0683951	+	0.0394879i
$358$		0			0
$359$	−113309.	−	196258.i	−0.879179	−	1.52278i	−0.852244	−	0.523145i	$-0.824759\pi$
$359$	−113309.	−	196258.i	−0.879179	−	1.52278i	−0.0269346	−	0.999637i	$-0.508575\pi$
$360$		0			0
$361$	−78148.5	−	104290.i	−0.599661	−	0.800254i
$362$		0			0
$363$	−138940.	+	80217.0i	−1.05442	+	0.608770i
$364$		0			0
$365$	−59647.4	+	103312.i	−0.447719	+	0.775472i
$366$		0			0
$367$	53022.3	−	91837.3i	0.393664	−	0.681847i	−0.599265	−	0.800550i	$-0.704541\pi$
$367$	53022.3	−	91837.3i	0.393664	−	0.681847i	0.992930	+	0.118704i	$0.0378739\pi$
$368$		0			0
$369$		−	16805.1i		−	0.123421i
$370$		0			0
$371$	40503.1	+	23384.5i	0.294266	+	0.169895i
$372$		0			0
$373$		−	130059.i		−	0.934810i	−0.884043	−	0.467405i	$-0.845189\pi$
$373$		−	130059.i		−	0.934810i	0.884043	−	0.467405i	$-0.154811\pi$
$374$		0			0
$375$	120780.	−	69732.4i	0.858881	−	0.495875i
$376$		0			0
$377$	−41001.7	−	71017.1i	−0.288482	−	0.499666i
$378$		0			0
$379$		−	65649.6i		−	0.457040i	−0.973539	−	0.228520i	$-0.926611\pi$
$379$		−	65649.6i		−	0.457040i	0.973539	−	0.228520i	$-0.0733886\pi$
$380$		0			0
$381$	8712.68			0.0600208
$382$		0			0
$383$	76995.9	−	44453.6i	0.524892	−	0.303047i	−0.214042	−	0.976824i	$-0.568663\pi$
$383$	76995.9	−	44453.6i	0.524892	−	0.303047i	0.738934	+	0.673778i	$0.235330\pi$
$384$		0			0
$385$	24673.3	+	42735.5i	0.166459	+	0.288315i
$386$		0			0
$387$	−15615.4			−0.104263
$388$		0			0
$389$	−88063.1	+	152530.i	−0.581962	+	1.00799i	0.413285	+	0.910602i	$0.364381\pi$
$389$	−88063.1	+	152530.i	−0.581962	+	1.00799i	−0.995247	+	0.0973858i	$0.968952\pi$
$390$		0			0
$391$	−39978.9			−0.261503
$392$		0			0
$393$	22602.9	+	13049.8i	0.146346	+	0.0844927i
$394$		0			0
$395$	53205.2	+	30718.1i	0.341005	+	0.196879i
$396$		0			0
$397$	109805.	+	190188.i	0.696694	+	1.20671i	0.969606	+	0.244671i	$0.0786799\pi$
$397$	109805.	+	190188.i	0.696694	+	1.20671i	−0.272912	+	0.962039i	$0.587987\pi$
$398$		0			0
$399$	4037.82	+	67509.8i	0.0253630	+	0.424054i
$400$		0			0
$401$	192044.	−	110877.i	1.19429	−	0.689526i	0.235017	−	0.971991i	$-0.424485\pi$
$401$	192044.	−	110877.i	1.19429	−	0.689526i	0.959278	+	0.282465i	$0.0911521\pi$
$402$		0			0
$403$	15267.9	−	26444.8i	0.0940089	−	0.162828i
$404$		0			0
$405$	50163.9	−	86886.4i	0.305831	−	0.529715i
$406$		0			0
$407$			301896.i			1.82251i
$408$		0			0
$409$	250085.	+	144387.i	1.49500	+	0.863138i	0.999983	−	0.00574553i	$-0.00182887\pi$
$409$	250085.	+	144387.i	1.49500	+	0.863138i	0.495016	+	0.868884i	$0.335162\pi$
$410$		0			0
$411$			36424.6i			0.215631i
$412$		0			0
$413$	51039.3	−	29467.5i	0.299230	−	0.172760i
$414$		0			0
$415$	71165.3	+	123262.i	0.413211	+	0.715703i
$416$		0			0
$417$			350772.i			2.01722i
$418$		0			0
$419$	−180068.			−1.02567			−0.512835	−	0.858487i	$-0.671405\pi$
$419$	−180068.			−1.02567			−0.512835	+	0.858487i	$0.671405\pi$
$420$		0			0
$421$	199084.	−	114941.i	1.12324	−	0.648501i	0.181012	−	0.983481i	$-0.442063\pi$
$421$	199084.	−	114941.i	1.12324	−	0.648501i	0.942225	+	0.334980i	$0.108729\pi$
$422$		0			0
$423$	−5536.35	−	9589.24i	−0.0309416	−	0.0535924i
$424$		0			0
$425$	23048.0			0.127601
$426$		0			0
$427$	41626.3	−	72098.9i	0.228303	−	0.395433i
$428$		0			0
$429$	−161586.			−0.877989
$430$		0			0
$431$	87680.8	+	50622.5i	0.472008	+	0.272514i	0.717080	−	0.696991i	$-0.245478\pi$
$431$	87680.8	+	50622.5i	0.472008	+	0.272514i	−0.245072	+	0.969505i	$0.578811\pi$
$432$		0			0
$433$	−184631.	−	106597.i	−0.984756	−	0.568549i	−0.0810530	−	0.996710i	$-0.525828\pi$
$433$	−184631.	−	106597.i	−0.984756	−	0.568549i	−0.903703	+	0.428161i	$0.859162\pi$
$434$		0			0
$435$	−56424.5	−	97730.1i	−0.298187	−	0.516476i
$436$		0			0
$437$	−147961.	−	224200.i	−0.774789	−	1.17401i
$438$		0			0
$439$	292406.	−	168820.i	1.51725	−	0.875983i	0.517453	−	0.855711i	$-0.326880\pi$
$439$	292406.	−	168820.i	1.51725	−	0.875983i	0.999795	−	0.0202720i	$-0.00645323\pi$
$440$		0			0
$441$	−8356.88	+	14474.5i	−0.0429702	+	0.0744265i
$442$		0			0
$443$	−103171.	+	178698.i	−0.525717	+	0.910568i	0.473835	+	0.880614i	$0.342869\pi$
$443$	−103171.	+	178698.i	−0.525717	+	0.910568i	−0.999551	+	0.0299541i	$0.990464\pi$
$444$		0			0
$445$			52257.9i			0.263895i
$446$		0			0
$447$	102107.	+	58951.7i	0.511025	+	0.295040i
$448$		0			0
$449$			215003.i			1.06648i	0.845965	+	0.533239i	$0.179025\pi$
$449$			215003.i			1.06648i	−0.845965	+	0.533239i	$0.820975\pi$
$450$		0			0
$451$	310908.	−	179503.i	1.52855	−	0.882508i
$452$		0			0
$453$	−2257.79	−	3910.61i	−0.0110024	−	0.0190567i
$454$		0			0
$455$			26685.2i			0.128898i
$456$		0			0
$457$	70263.0			0.336430			0.168215	−	0.985750i	$-0.446200\pi$
$457$	70263.0			0.336430			0.168215	+	0.985750i	$0.446200\pi$
$458$		0			0
$459$	31959.8	−	18452.0i	0.151698	−	0.0875826i
$460$		0			0
$461$	184591.	+	319721.i	0.868579	+	1.50442i	0.863449	+	0.504436i	$0.168300\pi$
$461$	184591.	+	319721.i	0.868579	+	1.50442i	0.00512983	+	0.999987i	$0.498367\pi$
$462$		0			0
$463$	−113555.			−0.529719			−0.264860	−	0.964287i	$-0.585326\pi$
$463$	−113555.			−0.529719			−0.264860	+	0.964287i	$0.585326\pi$
$464$		0			0
$465$	21010.9	−	36392.0i	0.0971715	−	0.168306i
$466$		0			0
$467$	−97414.0			−0.446671			−0.223335	−	0.974742i	$-0.571695\pi$
$467$	−97414.0			−0.446671			−0.223335	+	0.974742i	$0.571695\pi$
$468$		0			0
$469$	152005.	+	87760.1i	0.691054	+	0.398980i
$470$		0			0
$471$	−134217.	−	77490.2i	−0.605015	−	0.349305i
$472$		0			0
$473$	−166796.	−	288899.i	−0.745526	−	1.29129i
$474$		0			0
$475$	85299.9	+	129252.i	0.378061	+	0.572862i
$476$		0			0
$477$	−17007.0	+	9819.01i	−0.0747466	+	0.0431550i
$478$		0			0
$479$	−121178.	+	209886.i	−0.528144	+	0.914772i	0.471318	+	0.881963i	$0.343778\pi$
$479$	−121178.	+	209886.i	−0.528144	+	0.914772i	−0.999462	+	0.0328084i	$0.989555\pi$
$480$		0			0
$481$	−81628.1	+	141384.i	−0.352817	+	0.611097i
$482$		0			0
$483$			139402.i			0.597552i
$484$		0			0
$485$	−11833.9	−	6832.28i	−0.0503087	−	0.0290457i
$486$		0			0
$487$			25446.0i			0.107290i	0.998560	+	0.0536452i	$0.0170840\pi$
$487$			25446.0i			0.107290i	−0.998560	+	0.0536452i	$0.982916\pi$
$488$		0			0
$489$	259382.	−	149754.i	1.08473	−	0.626270i
$490$		0			0
$491$	−90935.5	−	157505.i	−0.377199	−	0.653328i	0.613455	−	0.789730i	$-0.289779\pi$
$491$	−90935.5	−	157505.i	−0.377199	−	0.653328i	−0.990654	+	0.136402i	$0.956446\pi$
$492$		0			0
$493$		−	45820.6i		−	0.188524i
$494$		0			0
$495$	−20720.4			−0.0845644
$496$		0			0
$497$	−127458.	+	73587.7i	−0.516004	+	0.297915i
$498$		0			0
$499$	106046.	+	183677.i	0.425885	+	0.737655i	0.996503	−	0.0835609i	$-0.0266293\pi$
$499$	106046.	+	183677.i	0.425885	+	0.737655i	−0.570617	+	0.821216i	$0.693296\pi$
$500$		0			0
$501$	−261360.			−1.04127
$502$		0			0
$503$	−25084.6	+	43447.7i	−0.0991449	+	0.171724i	−0.911331	−	0.411674i	$-0.864944\pi$
$503$	−25084.6	+	43447.7i	−0.0991449	+	0.171724i	0.812186	+	0.583399i	$0.198277\pi$
$504$		0			0
$505$	128576.			0.504169
$506$		0			0
$507$	158095.	+	91276.1i	0.615038	+	0.355092i
$508$		0			0
$509$	176441.	+	101868.i	0.681026	+	0.393191i	0.800242	−	0.599678i	$-0.204705\pi$
$509$	176441.	+	101868.i	0.681026	+	0.393191i	−0.119215	+	0.992868i	$0.538038\pi$
$510$		0			0
$511$	84448.9	+	146270.i	0.323409	+	0.560161i
$512$		0			0
$513$	221760.	+	110939.i	0.842654	+	0.421550i
$514$		0			0
$515$	152417.	−	87997.9i	0.574670	−	0.331786i
$516$		0			0
$517$	118273.	−	204854.i	0.442490	−	0.766416i
$518$		0			0
$519$	29205.4	−	50585.3i	0.108425	−	0.187797i
$520$		0			0
$521$			289594.i			1.06688i	0.845839	+	0.533439i	$0.179101\pi$
$521$			289594.i			1.06688i	−0.845839	+	0.533439i	$0.820899\pi$
$522$		0			0
$523$	169469.	+	97843.1i	0.619566	+	0.357706i	0.776700	−	0.629871i	$-0.216892\pi$
$523$	169469.	+	97843.1i	0.619566	+	0.357706i	−0.157134	+	0.987577i	$0.550226\pi$
$524$		0			0
$525$		−	80366.0i		−	0.291577i
$526$		0			0
$527$	14776.4	−	8531.16i	0.0532044	−	0.0307176i
$528$		0			0
$529$	−136926.	−	237164.i	−0.489301	−	0.847494i
$530$		0			0
$531$			24746.5i			0.0877658i
$532$		0			0
$533$	194139.			0.683375
$534$		0			0
$535$	64176.9	−	37052.5i	0.224218	−	0.129452i
$536$		0			0
$537$	−178827.	−	309738.i	−0.620133	−	1.07410i
$538$		0			0
$539$	−357055.			−1.22902
$540$		0			0
$541$	129234.	−	223840.i	0.441553	−	0.764793i	−0.556252	−	0.831014i	$-0.687761\pi$
$541$	129234.	−	223840.i	0.441553	−	0.764793i	0.997805	+	0.0662210i	$0.0210942\pi$
$542$		0			0
$543$	274959.			0.932543
$544$		0			0
$545$	−6589.17	−	3804.26i	−0.0221839	−	0.0128079i
$546$		0			0
$547$	−76348.0	−	44079.5i	−0.255166	−	0.147320i	0.366961	−	0.930236i	$-0.380398\pi$
$547$	−76348.0	−	44079.5i	−0.255166	−	0.147320i	−0.622127	+	0.782916i	$0.713731\pi$
$548$		0			0
$549$	17478.7	+	30273.9i	0.0579914	+	0.100444i
$550$		0			0
$551$	256960.	−	169581.i	0.846375	−	0.558565i
$552$		0			0
$553$	75328.2	−	43490.7i	0.246324	−	0.142215i
$554$		0			0
$555$	−112333.	+	194566.i	−0.364686	+	0.631655i
$556$		0			0
$557$	−223661.	+	387392.i	−0.720908	+	1.24865i	0.239729	+	0.970840i	$0.422942\pi$
$557$	−223661.	+	387392.i	−0.720908	+	1.24865i	−0.960636	+	0.277809i	$0.910392\pi$
$558$		0			0
$559$		−	180396.i		−	0.577302i
$560$		0			0
$561$	−78192.1	−	45144.2i	−0.248449	−	0.143442i
$562$		0			0
$563$		−	341953.i		−	1.07882i	−0.842043	−	0.539410i	$-0.818647\pi$
$563$		−	341953.i		−	1.07882i	0.842043	−	0.539410i	$-0.181353\pi$
$564$		0			0
$565$	74626.1	−	43085.4i	0.233773	−	0.134969i
$566$		0			0
$567$	−71022.2	−	123014.i	−0.220916	−	0.382639i
$568$		0			0
$569$			58752.9i			0.181470i	0.995875	+	0.0907349i	$0.0289216\pi$
$569$			58752.9i			0.181470i	−0.995875	+	0.0907349i	$0.971078\pi$
$570$		0			0
$571$	184183.			0.564907			0.282453	−	0.959281i	$-0.408852\pi$
$571$	184183.			0.564907			0.282453	+	0.959281i	$0.408852\pi$
$572$		0			0
$573$	253057.	−	146102.i	0.770741	−	0.444988i
$574$		0			0
$575$	159603.	+	276441.i	0.482732	+	0.836117i
$576$		0			0
$577$	148555.			0.446207			0.223103	−	0.974795i	$-0.428381\pi$
$577$	148555.			0.446207			0.223103	+	0.974795i	$0.428381\pi$
$578$		0			0
$579$	−162402.	+	281289.i	−0.484434	+	0.839064i
$580$		0			0
$581$	201512.			0.596965
$582$		0			0
$583$	−363320.	−	209763.i	−1.06894	−	0.617152i
$584$		0			0
$585$	−9703.77	−	5602.48i	−0.0283550	−	0.0163707i
$586$		0			0
$587$	24400.0	+	42262.1i	0.0708132	+	0.122652i	0.899258	−	0.437419i	$-0.144107\pi$
$587$	24400.0	+	42262.1i	0.0708132	+	0.122652i	−0.828445	+	0.560071i	$0.810774\pi$
$588$		0			0
$589$	102530.	+	51291.9i	0.295541	+	0.147849i
$590$		0			0
$591$	331212.	−	191225.i	0.948267	−	0.547482i
$592$		0			0
$593$	−306822.	+	531431.i	−0.872524	+	1.51126i	−0.0131462	+	0.999914i	$0.504185\pi$
$593$	−306822.	+	531431.i	−0.872524	+	1.51126i	−0.859377	+	0.511342i	$0.829149\pi$
$594$		0			0
$595$	−7455.36	+	12913.1i	−0.0210589	+	0.0364750i
$596$		0			0
$597$		−	69334.3i		−	0.194536i
$598$		0			0
$599$	−339188.	−	195830.i	−0.945338	−	0.545791i	−0.0537086	−	0.998557i	$-0.517104\pi$
$599$	−339188.	−	195830.i	−0.945338	−	0.545791i	−0.891630	+	0.452765i	$0.850438\pi$
$600$		0			0
$601$		−	100418.i		−	0.278011i	−0.990292	−	0.139006i	$-0.955609\pi$
$601$		−	100418.i		−	0.278011i	0.990292	−	0.139006i	$-0.0443906\pi$
$602$		0			0
$603$	−63826.0	+	36850.0i	−0.175535	+	0.101345i
$604$		0			0
$605$	−118832.	−	205823.i	−0.324656	−	0.562321i
$606$		0			0
$607$			238074.i			0.646152i	0.946373	+	0.323076i	$0.104717\pi$
$607$			238074.i			0.646152i	−0.946373	+	0.323076i	$0.895283\pi$
$608$		0			0
$609$	−159772.			−0.430791
$610$		0			0
$611$	110779.	−	63958.3i	0.296739	−	0.171322i
$612$		0			0
$613$	−16165.6	−	27999.6i	−0.0430201	−	0.0745129i	0.843714	−	0.536794i	$-0.180365\pi$
$613$	−16165.6	−	27999.6i	−0.0430201	−	0.0745129i	−0.886734	+	0.462281i	$0.847031\pi$
$614$		0			0
$615$	267165.			0.706365
$616$		0			0
$617$	−47281.9	+	81894.6i	−0.124201	+	0.215122i	−0.921420	−	0.388567i	$-0.872970\pi$
$617$	−47281.9	+	81894.6i	−0.124201	+	0.215122i	0.797219	+	0.603690i	$0.206303\pi$
$618$		0			0
$619$	−351256.			−0.916731			−0.458366	−	0.888764i	$-0.651565\pi$
$619$	−351256.			−0.916731			−0.458366	+	0.888764i	$0.651565\pi$
$620$		0			0
$621$	442632.	+	255554.i	1.14778	+	0.662673i
$622$		0			0
$623$	64074.5	+	36993.4i	0.165086	+	0.0953122i
$624$		0			0
$625$	−30755.7	−	53270.5i	−0.0787347	−	0.136372i
$626$		0			0
$627$	−36220.0	−	605576.i	−0.0921326	−	1.54040i
$628$		0			0
$629$	−79000.4	+	45610.9i	−0.199677	+	0.115284i
$630$		0			0
$631$	40677.8	−	70456.0i	0.102164	−	0.176954i	−0.810412	−	0.585861i	$-0.800757\pi$
$631$	40677.8	−	70456.0i	0.102164	−	0.176954i	0.912576	+	0.408907i	$0.134090\pi$
$632$		0			0
$633$	−256253.	+	443844.i	−0.639531	+	1.10770i
$634$		0			0
$635$			12906.8i			0.0320090i
$636$		0			0
$637$	−167216.	−	96542.2i	−0.412096	−	0.237924i
$638$		0			0
$639$		−	61798.2i		−	0.151347i
$640$		0			0
$641$	212439.	−	122651.i	0.517032	−	0.298509i	−0.218688	−	0.975795i	$-0.570178\pi$
$641$	212439.	−	122651.i	0.517032	−	0.298509i	0.735719	+	0.677286i	$0.236844\pi$
$642$		0			0
$643$	44740.9	+	77493.5i	0.108214	+	0.187432i	0.915047	−	0.403348i	$-0.132154\pi$
$643$	44740.9	+	77493.5i	0.108214	+	0.187432i	−0.806833	+	0.590780i	$0.798820\pi$
$644$		0			0
$645$		−	248252.i		−	0.596724i
$646$		0			0
$647$	−75843.0			−0.181179			−0.0905893	−	0.995888i	$-0.528875\pi$
$647$	−75843.0			−0.181179			−0.0905893	+	0.995888i	$0.528875\pi$
$648$		0			0
$649$	−457832.	+	264329.i	−1.08697	+	0.627561i
$650$		0			0
$651$	−29747.3	−	51523.9i	−0.0701917	−	0.121576i
$652$		0			0
$653$	42943.0			0.100709			0.0503543	−	0.998731i	$-0.483965\pi$
$653$	42943.0			0.100709			0.0503543	+	0.998731i	$0.483965\pi$
$654$		0			0
$655$	−19331.8	+	33483.6i	−0.0450598	+	0.0780459i
$656$		0			0
$657$	−70919.3			−0.164299
$658$		0			0
$659$	692459.	+	399791.i	1.59450	+	0.920582i	0.992522	+	0.122066i	$0.0389521\pi$
$659$	692459.	+	399791.i	1.59450	+	0.920582i	0.601974	+	0.798516i	$0.294381\pi$
$660$		0			0
$661$	363517.	+	209877.i	0.831997	+	0.480354i	0.854536	−	0.519392i	$-0.173842\pi$
$661$	363517.	+	209877.i	0.831997	+	0.480354i	−0.0225389	+	0.999746i	$0.507175\pi$
$662$		0			0
$663$	−24412.6	−	42283.9i	−0.0555376	−	0.0961940i
$664$		0			0
$665$	−100008.	+	5981.56i	−0.226147	+	0.0135261i
$666$		0			0
$667$	549580.	−	317300.i	1.23532	−	0.713212i
$668$		0			0
$669$	29534.8	−	51155.8i	0.0659906	−	0.114299i
$670$		0			0
$671$	−373396.	+	646740.i	−0.829324	+	1.43643i
$672$		0			0
$673$			190516.i			0.420630i	0.977634	+	0.210315i	$0.0674490\pi$
$673$			190516.i			0.420630i	−0.977634	+	0.210315i	$0.932551\pi$
$674$		0			0
$675$	−255179.	−	147328.i	−0.560064	−	0.323353i
$676$		0			0
$677$			309546.i			0.675379i	0.941258	+	0.337690i	$0.109645\pi$
$677$			309546.i			0.675379i	−0.941258	+	0.337690i	$0.890355\pi$
$678$		0			0
$679$	−16754.4	+	9673.17i	−0.0363404	+	0.0209812i
$680$		0			0
$681$	−46286.7	−	80170.9i	−0.0998072	−	0.172871i
$682$		0			0
$683$			696373.i			1.49280i	0.665500	+	0.746398i	$0.268219\pi$
$683$			696373.i			1.49280i	−0.665500	+	0.746398i	$0.731781\pi$
$684$		0			0
$685$	−53958.8			−0.114996
$686$		0			0
$687$	−787590.	+	454715.i	−1.66873	+	0.963443i
$688$		0			0
$689$	−113433.	−	196472.i	−0.238947	−	0.413869i
$690$		0			0
$691$	138751.			0.290590			0.145295	−	0.989388i	$-0.453587\pi$
$691$	138751.			0.290590			0.145295	+	0.989388i	$0.453587\pi$
$692$		0			0
$693$	−14668.0	+	25405.7i	−0.0305425	+	0.0529012i
$694$		0			0
$695$	−519629.			−1.07578
$696$		0			0
$697$	93944.9	+	54239.1i	0.193378	+	0.111647i
$698$		0			0
$699$	137680.	+	79489.4i	0.281784	+	0.162688i
$700$		0			0
$701$	−323619.	−	560524.i	−0.658564	−	1.14067i	−0.980988	−	0.194070i	$-0.937831\pi$
$701$	−323619.	−	560524.i	−0.658564	−	1.14067i	0.322424	−	0.946595i	$-0.395502\pi$
$702$		0			0
$703$	−548163.	−	274226.i	−1.10917	−	0.554879i
$704$		0			0
$705$	152448.	−	88016.2i	0.306722	−	0.177086i
$706$		0			0
$707$	91019.0	−	157650.i	0.182093	−	0.315394i
$708$		0			0
$709$	303581.	−	525817.i	0.603923	−	1.04603i	−0.388297	−	0.921534i	$-0.626937\pi$
$709$	303581.	−	525817.i	0.603923	−	1.04603i	0.992221	−	0.124492i	$-0.0397300\pi$
$710$		0			0
$711$			36523.1i			0.0722484i
$712$		0			0
$713$	204648.	+	118154.i	0.402559	+	0.232417i
$714$		0			0
$715$		−	239371.i		−	0.468230i
$716$		0			0
$717$	593366.	−	342580.i	1.15421	−	0.666382i
$718$		0			0
$719$	20070.2	+	34762.5i	0.0388233	+	0.0672440i	0.884784	−	0.466001i	$-0.154306\pi$
$719$	20070.2	+	34762.5i	0.0388233	+	0.0672440i	−0.845961	+	0.533245i	$0.820972\pi$
$720$		0			0
$721$		−	249175.i		−	0.479330i
$722$		0			0
$723$	104803.			0.200492
$724$		0			0
$725$	−316835.	+	182925.i	−0.602778	+	0.348014i
$726$		0			0
$727$	−227686.	−	394364.i	−0.430792	−	0.746154i	0.566149	−	0.824303i	$-0.308433\pi$
$727$	−227686.	−	394364.i	−0.430792	−	0.746154i	−0.996942	+	0.0781484i	$0.975099\pi$
$728$		0			0
$729$	−466186.			−0.877211
$730$		0			0
$731$	50399.4	−	87294.4i	0.0943172	−	0.163362i
$732$		0			0
$733$	−727011.			−1.35311			−0.676555	−	0.736392i	$-0.736528\pi$
$733$	−727011.			−1.35311			−0.676555	+	0.736392i	$0.736528\pi$
$734$		0			0
$735$	−230114.	−	132857.i	−0.425960	−	0.245928i
$736$		0			0
$737$	−1.36351e6	−	787224.i	−2.51029	−	1.44932i
$738$		0			0
$739$	−38258.8	−	66266.2i	−0.0700555	−	0.121340i	0.828870	−	0.559441i	$-0.188984\pi$
$739$	−38258.8	−	66266.2i	−0.0700555	−	0.121340i	−0.898925	+	0.438102i	$0.855651\pi$
$740$		0			0
$741$	146776.	−	293397.i	0.267312	−	0.534341i
$742$		0			0
$743$	−496683.	+	286760.i	−0.899709	+	0.519447i	−0.877106	−	0.480297i	$-0.840529\pi$
$743$	−496683.	+	286760.i	−0.899709	+	0.519447i	−0.0226030	+	0.999745i	$0.507195\pi$
$744$		0			0
$745$	−87330.2	+	151260.i	−0.157345	+	0.272529i
$746$		0			0
$747$	−42306.9	+	73277.8i	−0.0758177	+	0.131320i
$748$		0			0
$749$		−	104918.i		−	0.187020i
$750$		0			0
$751$	885468.	+	511225.i	1.56998	+	0.906426i	0.996170	+	0.0874337i	$0.0278666\pi$
$751$	885468.	+	511225.i	1.56998	+	0.906426i	0.573805	+	0.818992i	$0.305467\pi$
$752$		0			0
$753$			553398.i			0.975995i
$754$		0			0
$755$	5793.11	−	3344.65i	0.0101629	−	0.00586756i
$756$		0			0
$757$	366529.	+	634847.i	0.639612	+	1.10784i	0.985518	+	0.169571i	$0.0542382\pi$
$757$	366529.	+	634847.i	0.639612	+	1.10784i	−0.345906	+	0.938269i	$0.612429\pi$
$758$		0			0
$759$		−	1.25047e6i		−	2.17064i
$760$		0			0
$761$	−250969.			−0.433362			−0.216681	−	0.976242i	$-0.569523\pi$
$761$	−250969.			−0.433362			−0.216681	+	0.976242i	$0.569523\pi$
$762$		0			0
$763$	−9328.97	+	5386.08i	−0.0160245	+	0.00925175i
$764$		0			0
$765$	−3130.47	−	5422.13i	−0.00534917	−	0.00926503i
$766$		0			0
$767$	−285882.			−0.485956
$768$		0			0
$769$	−79807.9	+	138231.i	−0.134956	+	0.233751i	−0.925581	−	0.378550i	$-0.876423\pi$
$769$	−79807.9	+	138231.i	−0.134956	+	0.233751i	0.790624	+	0.612301i	$0.209756\pi$
$770$		0			0
$771$	396372.			0.666799
$772$		0			0
$773$	−154342.	−	89109.5i	−0.258301	−	0.149130i	0.365258	−	0.930906i	$-0.380981\pi$
$773$	−154342.	−	89109.5i	−0.258301	−	0.149130i	−0.623559	+	0.781776i	$0.714314\pi$
$774$		0			0
$775$	−117981.	−	68116.1i	−0.196430	−	0.113409i
$776$		0			0
$777$	159041.	+	275467.i	0.263431	+	0.456276i
$778$		0			0
$779$	43517.0	+	727577.i	0.0717106	+	1.19896i
$780$		0			0
$781$	1.14332e6	−	660096.i	1.87441	−	1.08219i
$782$		0			0
$783$	−292896.	+	507310.i	−0.477738	+	0.827466i
$784$		0			0
$785$	114793.	−	198827.i	0.186284	−	0.322653i
$786$		0			0
$787$		−	445302.i		−	0.718961i	−0.933153	−	0.359481i	$-0.882954\pi$
$787$		−	445302.i		−	0.718961i	0.933153	−	0.359481i	$-0.117046\pi$
$788$		0			0
$789$	382718.	+	220962.i	0.614787	+	0.354947i
$790$		0			0
$791$		−	122001.i		−	0.194989i
$792$		0			0
$793$	−349737.	+	201921.i	−0.556155	+	0.321096i
$794$		0			0
$795$	−156101.	−	270375.i	−0.246986	−	0.427792i
$796$		0			0
$797$		−	1.00882e6i		−	1.58818i	−0.607802	−	0.794089i	$-0.707948\pi$
$797$		−	1.00882e6i		−	1.58818i	0.607802	−	0.794089i	$-0.292052\pi$
$798$		0			0
$799$	71475.2			0.111960
$800$		0			0
$801$	−26904.6	+	15533.3i	−0.0419335	+	0.0242103i
$802$		0			0
$803$	−757523.	−	1.31207e6i	−1.17480	−	2.03482i
$804$		0			0
$805$	−206509.			−0.318674
$806$		0			0
$807$	173560.	−	300614.i	0.266503	−	0.461596i
$808$		0			0
$809$	−720314.			−1.10059			−0.550294	−	0.834971i	$-0.685484\pi$
$809$	−720314.			−1.10059			−0.550294	+	0.834971i	$0.685484\pi$
$810$		0			0
$811$	−17483.1	−	10093.9i	−0.0265814	−	0.0153468i	0.486650	−	0.873597i	$-0.338219\pi$
$811$	−17483.1	−	10093.9i	−0.0265814	−	0.0153468i	−0.513232	+	0.858250i	$0.671552\pi$
$812$		0			0
$813$	−641091.	−	370134.i	−0.969926	−	0.559987i
$814$		0			0
$815$	221844.	+	384245.i	0.333989	+	0.578486i
$816$		0			0
$817$	676071.	−	40436.3i	1.01286	−	0.0605797i
$818$		0			0
$819$	−13738.6	+	7932.01i	−0.0204822	+	0.0118254i
$820$		0			0
$821$	−187608.	+	324946.i	−0.278333	+	0.482087i	−0.970971	−	0.239199i	$-0.923115\pi$
$821$	−187608.	+	324946.i	−0.278333	+	0.482087i	0.692638	+	0.721286i	$0.256449\pi$
$822$		0			0
$823$	−237091.	+	410654.i	−0.350039	+	0.606285i	−0.986256	−	0.165225i	$-0.947165\pi$
$823$	−237091.	+	410654.i	−0.350039	+	0.606285i	0.636217	+	0.771510i	$0.280498\pi$
$824$		0			0
$825$			720898.i			1.05917i
$826$		0			0
$827$	−152726.	−	88176.7i	−0.223307	−	0.128927i	0.384173	−	0.923261i	$-0.374487\pi$
$827$	−152726.	−	88176.7i	−0.223307	−	0.128927i	−0.607481	+	0.794334i	$0.707820\pi$
$828$		0			0
$829$		−	1.17657e6i		−	1.71202i	−0.516958	−	0.856011i	$-0.672936\pi$
$829$		−	1.17657e6i		−	1.71202i	0.516958	−	0.856011i	$-0.327064\pi$
$830$		0			0
$831$	868579.	−	501474.i	1.25779	−	0.726184i
$832$		0			0
$833$	−53944.4	−	93434.4i	−0.0777421	−	0.134653i
$834$		0			0
$835$		−	387175.i		−	0.555309i
$836$		0			0
$837$	−218132.			−0.311365
$838$		0			0
$839$	90561.0	−	52285.4i	0.128652	−	0.0742774i	−0.434293	−	0.900772i	$-0.643002\pi$
$839$	90561.0	−	52285.4i	0.128652	−	0.0742774i	0.562945	+	0.826494i	$0.309668\pi$
$840$		0			0
$841$	10024.0	+	17362.1i	0.0141726	+	0.0245477i
$842$		0			0
$843$	−241633.			−0.340018
$844$		0			0
$845$	−135215.	+	234199.i	−0.189370	+	0.327999i
$846$		0			0
$847$	−336486.			−0.469030
$848$		0			0
$849$	97562.8	+	56327.9i	0.135353	+	0.0781463i
$850$		0			0
$851$	−1.09413e6	−	631696.i	−1.51081	−	0.872266i
$852$		0			0
$853$	485750.	+	841343.i	0.667597	+	1.15631i	0.978574	+	0.205894i	$0.0660104\pi$
$853$	485750.	+	841343.i	0.667597	+	1.15631i	−0.310977	+	0.950417i	$0.600656\pi$
$854$		0			0
$855$	18821.3	−	37622.7i	0.0257464	−	0.0514657i
$856$		0			0
$857$	−700870.	+	404647.i	−0.954280	+	0.550954i	−0.894408	−	0.447252i	$-0.852403\pi$
$857$	−700870.	+	404647.i	−0.954280	+	0.550954i	−0.0598720	+	0.998206i	$0.519069\pi$
$858$		0			0
$859$	−345904.	+	599124.i	−0.468781	+	0.811952i	−0.999363	−	0.0356812i	$-0.988640\pi$
$859$	−345904.	+	599124.i	−0.468781	+	0.811952i	0.530582	+	0.847633i	$0.321973\pi$
$860$		0			0
$861$	189127.	−	327577.i	0.255121	−	0.441883i
$862$		0			0
$863$		−	239801.i		−	0.321980i	−0.986956	−	0.160990i	$-0.948531\pi$
$863$		−	239801.i		−	0.321980i	0.986956	−	0.160990i	$-0.0514687\pi$
$864$		0			0
$865$	74936.3	+	43264.5i	0.100152	+	0.0578228i
$866$		0			0
$867$			762083.i			1.01383i
$868$		0			0
$869$	−675708.	+	390120.i	−0.894787	+	0.516605i
$870$		0			0
$871$	−425707.	−	737346.i	−0.561144	−	0.971929i
$872$		0			0
$873$		−	8123.43i		−	0.0106589i
$874$		0			0
$875$	292507.			0.382049
$876$		0			0
$877$	129985.	−	75046.6i	0.169002	−	0.0975735i	−0.413113	−	0.910680i	$-0.635559\pi$
$877$	129985.	−	75046.6i	0.169002	−	0.0975735i	0.582115	+	0.813106i	$0.302225\pi$
$878$		0			0
$879$	−370028.	−	640907.i	−0.478913	−	0.829502i
$880$		0			0
$881$	472353.			0.608576			0.304288	−	0.952580i	$-0.401581\pi$
$881$	472353.			0.608576			0.304288	+	0.952580i	$0.401581\pi$
$882$		0			0
$883$	397034.	−	687684.i	0.509221	−	0.881997i	−0.490722	−	0.871316i	$-0.663267\pi$
$883$	397034.	−	687684.i	0.509221	−	0.881997i	0.999943	−	0.0106809i	$-0.00339991\pi$
$884$		0			0
$885$	−393417.			−0.502304
$886$		0			0
$887$	1.00255e6	+	578822.i	1.27426	+	0.735695i	0.975787	−	0.218722i	$-0.0701889\pi$
$887$	1.00255e6	+	578822.i	1.27426	+	0.735695i	0.298475	+	0.954418i	$0.403522\pi$
$888$		0			0
$889$	15825.3	+	9136.77i	0.0200240	+	0.0115608i
$890$		0			0
$891$	637083.	+	1.10346e6i	0.802492	+	1.38996i
$892$		0			0
$893$	264528.	+	400830.i	0.331718	+	0.502641i
$894$		0			0
$895$	458841.	−	264912.i	0.572817	−	0.330716i
$896$		0			0
$897$	338107.	−	585618.i	0.420212	−	0.727829i
$898$		0			0
$899$	−135419.	+	234552.i	−0.167556	+	0.290215i
$900$		0			0
$901$		−	126765.i		−	0.156153i
$902$		0			0
$903$	−304387.	−	175738.i	−0.373294	−	0.215521i
$904$		0			0
$905$			407321.i			0.497324i
$906$		0			0
$907$	−984582.	+	568449.i	−1.19684	+	0.690998i	−0.959850	−	0.280513i	$-0.909495\pi$
$907$	−984582.	+	568449.i	−1.19684	+	0.690998i	−0.236993	+	0.971511i	$0.576162\pi$
$908$		0			0
$909$	38218.4	+	66196.2i	0.0462535	+	0.0801135i
$910$		0			0
$911$			455546.i			0.548903i	0.961601	+	0.274452i	$0.0884963\pi$
$911$			455546.i			0.548903i	−0.961601	+	0.274452i	$0.911504\pi$
$912$		0			0
$913$	−1.80760e6			−2.16851
$914$		0			0
$915$	−481291.	+	277873.i	−0.574865	+	0.331898i
$916$		0			0
$917$	27370.0	+	47406.3i	0.0325489	+	0.0563764i
$918$		0			0
$919$	1.09770e6			1.29972			0.649862	−	0.760052i	$-0.274827\pi$
$919$	1.09770e6			1.29972			0.649862	+	0.760052i	$0.274827\pi$
$920$		0			0
$921$	298645.	−	517268.i	0.352076	−	0.609813i
$922$		0			0
$923$	713919.			0.838003
$924$		0			0
$925$	630770.	+	364175.i	0.737204	+	0.425625i
$926$		0			0
$927$	90610.0	+	52313.7i	0.105443	+	0.0608774i
$928$		0			0
$929$	857478.	+	1.48520e6i	0.993554	+	1.72089i	0.594947	+	0.803765i	$0.297173\pi$
$929$	857478.	+	1.48520e6i	0.993554	+	1.72089i	0.398607	+	0.917122i	$0.369494\pi$
$930$		0			0
$931$	324330.	−	648316.i	0.374186	−	0.747976i
$932$		0			0
$933$	761443.	−	439620.i	0.874731	−	0.505026i
$934$		0			0
$935$	66876.0	−	115833.i	0.0764975	−	0.132497i
$936$		0			0
$937$	57770.1	−	100061.i	0.0657997	−	0.113969i	−0.831249	−	0.555901i	$-0.812373\pi$
$937$	57770.1	−	100061.i	0.0657997	−	0.113969i	0.897048	+	0.441932i	$0.145707\pi$
$938$		0			0
$939$			1.20118e6i			1.36231i
$940$		0			0
$941$	1.16741e6	+	674004.i	1.31839	+	0.761173i	0.983470	−	0.181073i	$-0.0579571\pi$
$941$	1.16741e6	+	674004.i	1.31839	+	0.761173i	0.334921	+	0.942246i	$0.391290\pi$
$942$		0			0
$943$			1.50239e6i			1.68950i
$944$		0			0
$945$	165086.	−	95312.7i	0.184862	−	0.106730i
$946$		0			0
$947$	361524.	+	626178.i	0.403123	+	0.698229i	0.994101	−	0.108459i	$-0.0345915\pi$
$947$	361524.	+	626178.i	0.403123	+	0.698229i	−0.590978	+	0.806687i	$0.701258\pi$
$948$		0			0
$949$		−	819290.i		−	0.909715i
$950$		0			0
$951$	1.77855e6			1.96655
$952$		0			0
$953$	368933.	−	213004.i	0.406221	−	0.234532i	−0.282944	−	0.959136i	$-0.591311\pi$
$953$	368933.	−	213004.i	0.406221	−	0.234532i	0.689165	+	0.724605i	$0.257978\pi$
$954$		0			0
$955$	216434.	+	374874.i	0.237311	+	0.411035i
$956$		0			0
$957$	1.43319e6			1.56487
$958$		0			0
$959$	−38197.5	+	66160.1i	−0.0415334	+	0.0719380i
$960$		0			0
$961$	822669.			0.890796
$962$		0			0
$963$	38152.4	+	22027.3i	0.0411405	+	0.0237525i
$964$		0			0
$965$	−416697.	−	240580.i	−0.447472	−	0.258348i
$966$		0			0
$967$	156372.	+	270844.i	0.167226	+	0.289645i	0.937444	−	0.348137i	$-0.113186\pi$
$967$	156372.	+	270844.i	0.167226	+	0.289645i	−0.770217	+	0.637782i	$0.779852\pi$
$968$		0			0
$969$	152995.	−	100969.i	0.162941	−	0.107533i
$970$		0			0
$971$	−72576.9	+	41902.3i	−0.0769769	+	0.0444426i	−0.537994	−	0.842948i	$-0.680818\pi$
$971$	−72576.9	+	41902.3i	−0.0769769	+	0.0444426i	0.461018	+	0.887391i	$0.347485\pi$
$972$		0			0
$973$	−367846.	+	637128.i	−0.388544	+	0.672978i
$974$		0			0
$975$	−194920.	+	337611.i	−0.205044	+	0.355146i
$976$		0			0
$977$			439858.i			0.460812i	0.973095	+	0.230406i	$0.0740054\pi$
$977$			439858.i			0.460812i	−0.973095	+	0.230406i	$0.925995\pi$
$978$		0			0
$979$	−574761.	−	331838.i	−0.599683	−	0.346227i
$980$		0			0
$981$		−	4523.17i		−	0.00470008i
$982$		0			0
$983$	−720503.	+	415982.i	−0.745639	+	0.430495i	−0.824116	−	0.566421i	$-0.808328\pi$
$983$	−720503.	+	415982.i	−0.745639	+	0.430495i	0.0784772	+	0.996916i	$0.474994\pi$
$984$		0			0
$985$	283278.	+	490652.i	0.291971	+	0.505709i
$986$		0			0
$987$		−	249227.i		−	0.255836i
$988$		0			0
$989$	1.39603e6			1.42726
$990$		0			0
$991$	−298704.	+	172457.i	−0.304154	+	0.175603i	−0.644307	−	0.764767i	$-0.722854\pi$
$991$	−298704.	+	172457.i	−0.304154	+	0.175603i	0.340154	+	0.940370i	$0.389521\pi$
$992$		0			0
$993$	−596842.	−	1.03376e6i	−0.605286	−	1.04839i
$994$		0			0
$995$	102711.			0.103746
$996$		0			0
$997$	−740608.	+	1.28277e6i	−0.745071	+	1.29050i	0.205090	+	0.978743i	$0.434251\pi$
$997$	−740608.	+	1.28277e6i	−0.745071	+	1.29050i	−0.950161	+	0.311758i	$0.899082\pi$
$998$		0			0
$999$	1.16622e6			1.16856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.a.145.2		10
4.3	odd	2		19.5.d.a.12.4	yes	10
12.11	even	2		171.5.p.a.145.2		10
19.8	odd	6	inner	304.5.r.a.65.2		10
76.27	even	6		19.5.d.a.8.4	✓	10
228.179	odd	6		171.5.p.a.46.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.d.a.8.4	✓	10	76.27	even	6
19.5.d.a.12.4	yes	10	4.3	odd	2
171.5.p.a.46.2		10	228.179	odd	6
171.5.p.a.145.2		10	12.11	even	2
304.5.r.a.65.2		10	19.8	odd	6	inner
304.5.r.a.145.2		10	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-8.18489 + 4.72555i) q^{3} +(-7.00036 - 12.1250i) q^{5} -19.8223 q^{7} +(4.16163 - 7.20815i) q^{9} +O(q^{10})\)	\(q+(-8.18489 + 4.72555i) q^{3} +(-7.00036 - 12.1250i) q^{5} -19.8223 q^{7} +(4.16163 - 7.20815i) q^{9} +177.809 q^{11} +(83.2716 + 48.0769i) q^{13} +(114.594 + 66.1610i) q^{15} +(26.8637 + 46.5293i) q^{17} +(-161.512 + 322.854i) q^{19} +(162.243 - 93.6710i) q^{21} +(-372.053 + 644.415i) q^{23} +(214.490 - 371.508i) q^{25} -686.875i q^{27} +(-738.578 - 426.418i) q^{29} -317.572i q^{31} +(-1455.35 + 840.247i) q^{33} +(138.763 + 240.344i) q^{35} +1697.87i q^{37} -908.759 q^{39} +(1748.55 - 1009.53i) q^{41} +(-938.059 - 1624.77i) q^{43} -116.532 q^{45} +(665.166 - 1152.10i) q^{47} -2008.08 q^{49} +(-439.753 - 253.891i) q^{51} +(-2043.31 - 1179.71i) q^{53} +(-1244.73 - 2155.93i) q^{55} +(-203.701 - 3405.76i) q^{57} +(-2574.85 + 1486.59i) q^{59} +(-2099.98 + 3637.27i) q^{61} +(-82.4929 + 142.882i) q^{63} -1346.22i q^{65} +(-7668.40 - 4427.35i) q^{67} -7032.62i q^{69} +(6430.03 - 3712.38i) q^{71} +(-4260.31 - 7379.07i) q^{73} +4054.33i q^{75} -3524.58 q^{77} +(-3800.18 + 2194.04i) q^{79} +(3582.95 + 6205.86i) q^{81} -10166.0 q^{83} +(376.111 - 651.443i) q^{85} +8060.24 q^{87} +(-3232.45 - 1866.26i) q^{89} +(-1650.63 - 952.993i) q^{91} +(1500.70 + 2599.29i) q^{93} +(5045.24 - 301.760i) q^{95} +(845.233 - 487.996i) q^{97} +(739.977 - 1281.68i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 9 q^{3} + 8 q^{5} + 24 q^{7} - 58 q^{9}+O(q^{10}) \) 10 * q - 9 * q^3 + 8 * q^5 + 24 * q^7 - 58 * q^9	\( 10 q - 9 q^{3} + 8 q^{5} + 24 q^{7} - 58 q^{9} - 50 q^{11} - 624 q^{13} - 504 q^{15} - 292 q^{17} - 305 q^{19} + 1158 q^{21} - 98 q^{23} - 681 q^{25} + 2598 q^{29} - 3441 q^{33} - 694 q^{35} + 5552 q^{39} - 1407 q^{41} - 5424 q^{43} + 9572 q^{45} + 2416 q^{47} - 17826 q^{49} + 3342 q^{51} + 1122 q^{53} - 11424 q^{55} - 7906 q^{57} - 15387 q^{59} + 860 q^{61} - 5318 q^{63} - 14763 q^{67} + 27264 q^{71} + 1561 q^{73} - 18392 q^{77} - 24750 q^{79} + 14311 q^{81} - 6002 q^{83} - 14944 q^{85} + 31996 q^{87} - 22566 q^{89} - 8724 q^{91} + 12476 q^{93} + 7312 q^{95} + 46287 q^{97} + 2048 q^{99}+O(q^{100}) \) 10 * q - 9 * q^3 + 8 * q^5 + 24 * q^7 - 58 * q^9 - 50 * q^11 - 624 * q^13 - 504 * q^15 - 292 * q^17 - 305 * q^19 + 1158 * q^21 - 98 * q^23 - 681 * q^25 + 2598 * q^29 - 3441 * q^33 - 694 * q^35 + 5552 * q^39 - 1407 * q^41 - 5424 * q^43 + 9572 * q^45 + 2416 * q^47 - 17826 * q^49 + 3342 * q^51 + 1122 * q^53 - 11424 * q^55 - 7906 * q^57 - 15387 * q^59 + 860 * q^61 - 5318 * q^63 - 14763 * q^67 + 27264 * q^71 + 1561 * q^73 - 18392 * q^77 - 24750 * q^79 + 14311 * q^81 - 6002 * q^83 - 14944 * q^85 + 31996 * q^87 - 22566 * q^89 - 8724 * q^91 + 12476 * q^93 + 7312 * q^95 + 46287 * q^97 + 2048 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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