LMFDB - Embedded newform 304.5.r.c.145.6

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			145.6
Root			$0.500000 - 6.86019i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.5.r.c.65.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.91584 - 4.57021i) q^{3} +(19.7357 + 34.1832i) q^{5} -91.5785 q^{7} +(1.27372 - 2.20614i) q^{9} +O(q^{10})$	\(q+(7.91584 - 4.57021i) q^{3} +(19.7357 + 34.1832i) q^{5} -91.5785 q^{7} +(1.27372 - 2.20614i) q^{9} +154.274 q^{11} +(-5.46159 - 3.15325i) q^{13} +(312.449 + 180.393i) q^{15} +(-35.4376 - 61.3797i) q^{17} +(-338.973 - 124.170i) q^{19} +(-724.921 + 418.533i) q^{21} +(-328.524 + 569.020i) q^{23} +(-466.494 + 807.991i) q^{25} +717.090i q^{27} +(-756.663 - 436.859i) q^{29} +1356.82i q^{31} +(1221.21 - 705.067i) q^{33} +(-1807.36 - 3130.45i) q^{35} +204.056i q^{37} -57.6441 q^{39} +(-1254.28 + 724.157i) q^{41} +(-694.511 - 1202.93i) q^{43} +100.551 q^{45} +(-396.636 + 686.994i) q^{47} +5985.63 q^{49} +(-561.037 - 323.915i) q^{51} +(-427.719 - 246.944i) q^{53} +(3044.71 + 5273.59i) q^{55} +(-3250.74 + 566.268i) q^{57} +(-414.766 + 239.465i) q^{59} +(-1244.82 + 2156.08i) q^{61} +(-116.645 + 202.035i) q^{63} -248.926i q^{65} +(3155.80 + 1822.00i) q^{67} +6005.69i q^{69} +(-408.962 + 236.114i) q^{71} +(656.228 + 1136.62i) q^{73} +8527.91i q^{75} -14128.2 q^{77} +(-6824.92 + 3940.37i) q^{79} +(3380.43 + 5855.07i) q^{81} +7247.57 q^{83} +(1398.77 - 2422.74i) q^{85} -7986.16 q^{87} +(-2753.52 - 1589.75i) q^{89} +(500.164 + 288.770i) q^{91} +(6200.94 + 10740.3i) q^{93} +(-2445.33 - 14037.8i) q^{95} +(4303.37 - 2484.55i) q^{97} +(196.502 - 340.351i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	7.91584	−	4.57021i	0.879538	−	0.507802i	0.00903204	−	0.999959i	$-0.497125\pi$
$3$	7.91584	−	4.57021i	0.879538	−	0.507802i	0.870506	+	0.492158i	$0.163792\pi$
$4$		0			0
$5$	19.7357	+	34.1832i	0.789427	+	1.36733i	0.926318	+	0.376742i	$0.122956\pi$
$5$	19.7357	+	34.1832i	0.789427	+	1.36733i	−0.136891	+	0.990586i	$0.543711\pi$
$6$		0			0
$7$	−91.5785			−1.86895			−0.934475	−	0.356029i	$-0.884130\pi$
$7$	−91.5785			−1.86895			−0.934475	+	0.356029i	$0.884130\pi$
$8$		0			0
$9$	1.27372	−	2.20614i	0.0157249	−	0.0272363i
$10$		0			0
$11$	154.274			1.27500			0.637498	−	0.770452i	$-0.279970\pi$
$11$	154.274			1.27500			0.637498	+	0.770452i	$0.279970\pi$
$12$		0			0
$13$	−5.46159	−	3.15325i	−0.0323171	−	0.0186583i	0.483754	−	0.875204i	$-0.339273\pi$
$13$	−5.46159	−	3.15325i	−0.0323171	−	0.0186583i	−0.516072	+	0.856545i	$0.672606\pi$
$14$		0			0
$15$	312.449	+	180.393i	1.38866	+	0.801745i
$16$		0			0
$17$	−35.4376	−	61.3797i	−0.122622	−	0.212387i	0.798179	−	0.602420i	$-0.205797\pi$
$17$	−35.4376	−	61.3797i	−0.122622	−	0.212387i	−0.920801	+	0.390033i	$0.872463\pi$
$18$		0			0
$19$	−338.973	−	124.170i	−0.938984	−	0.343962i
$19$	−338.973	−	124.170i	−0.938984	−	0.343962i
$20$		0			0
$21$	−724.921	+	418.533i	−1.64381	+	0.949056i
$22$		0			0
$23$	−328.524	+	569.020i	−0.621028	+	1.07565i	0.368267	+	0.929720i	$0.379951\pi$
$23$	−328.524	+	569.020i	−0.621028	+	1.07565i	−0.989295	+	0.145932i	$0.953382\pi$
$24$		0			0
$25$	−466.494	+	807.991i	−0.746390	+	1.29279i
$26$		0			0
$27$			717.090i			0.983663i
$28$		0			0
$29$	−756.663	−	436.859i	−0.899718	−	0.519452i	−0.0226091	−	0.999744i	$-0.507197\pi$
$29$	−756.663	−	436.859i	−0.899718	−	0.519452i	−0.877109	+	0.480292i	$0.840531\pi$
$30$		0			0
$31$			1356.82i			1.41188i	0.708272	+	0.705940i	$0.249475\pi$
$31$			1356.82i			1.41188i	−0.708272	+	0.705940i	$0.750525\pi$
$32$		0			0
$33$	1221.21	−	705.067i	1.12141	−	0.647445i
$34$		0			0
$35$	−1807.36	−	3130.45i	−1.47540	−	2.55547i
$36$		0			0
$37$			204.056i			0.149055i	0.997219	+	0.0745273i	$0.0237448\pi$
$37$			204.056i			0.149055i	−0.997219	+	0.0745273i	$0.976255\pi$
$38$		0			0
$39$	−57.6441			−0.0378988
$40$		0			0
$41$	−1254.28	+	724.157i	−0.746150	+	0.430790i	−0.824301	−	0.566152i	$-0.808432\pi$
$41$	−1254.28	+	724.157i	−0.746150	+	0.430790i	0.0781513	+	0.996942i	$0.475098\pi$
$42$		0			0
$43$	−694.511	−	1202.93i	−0.375614	−	0.650583i	0.614804	−	0.788680i	$-0.289235\pi$
$43$	−694.511	−	1202.93i	−0.375614	−	0.650583i	−0.990419	+	0.138096i	$0.955902\pi$
$44$		0			0
$45$	100.551			0.0496546
$46$		0			0
$47$	−396.636	+	686.994i	−0.179555	+	0.310998i	−0.941728	−	0.336375i	$-0.890799\pi$
$47$	−396.636	+	686.994i	−0.179555	+	0.310998i	0.762174	+	0.647373i	$0.224132\pi$
$48$		0			0
$49$	5985.63			2.49297
$50$		0			0
$51$	−561.037	−	323.915i	−0.215701	−	0.124535i
$52$		0			0
$53$	−427.719	−	246.944i	−0.152267	−	0.0879116i	0.421930	−	0.906628i	$-0.361353\pi$
$53$	−427.719	−	246.944i	−0.152267	−	0.0879116i	−0.574198	+	0.818717i	$0.694686\pi$
$54$		0			0
$55$	3044.71	+	5273.59i	1.00652	+	1.74334i
$56$		0			0
$57$	−3250.74	+	566.268i	−1.00054	+	0.174290i
$58$		0			0
$59$	−414.766	+	239.465i	−0.119151	+	0.0687920i	−0.558391	−	0.829578i	$-0.688581\pi$
$59$	−414.766	+	239.465i	−0.119151	+	0.0687920i	0.439240	+	0.898370i	$0.355248\pi$
$60$		0			0
$61$	−1244.82	+	2156.08i	−0.334538	+	0.579437i	−0.983396	−	0.181473i	$-0.941914\pi$
$61$	−1244.82	+	2156.08i	−0.334538	+	0.579437i	0.648858	+	0.760909i	$0.275247\pi$
$62$		0			0
$63$	−116.645	+	202.035i	−0.0293890	+	0.0509033i
$64$		0			0
$65$		−	248.926i		−	0.0589174i
$66$		0			0
$67$	3155.80	+	1822.00i	0.703008	+	0.405882i	0.808467	−	0.588542i	$-0.200298\pi$
$67$	3155.80	+	1822.00i	0.703008	+	0.405882i	−0.105459	+	0.994424i	$0.533631\pi$
$68$		0			0
$69$			6005.69i			1.26144i
$70$		0			0
$71$	−408.962	+	236.114i	−0.0811272	+	0.0468388i	−0.540015	−	0.841656i	$-0.681581\pi$
$71$	−408.962	+	236.114i	−0.0811272	+	0.0468388i	0.458888	+	0.888494i	$0.348248\pi$
$72$		0			0
$73$	656.228	+	1136.62i	0.123143	+	0.213290i	0.921005	−	0.389550i	$-0.127369\pi$
$73$	656.228	+	1136.62i	0.123143	+	0.213290i	−0.797863	+	0.602839i	$0.794036\pi$
$74$		0			0
$75$			8527.91i			1.51607i
$76$		0			0
$77$	−14128.2			−2.38290
$78$		0			0
$79$	−6824.92	+	3940.37i	−1.09356	+	0.631368i	−0.934523	−	0.355904i	$-0.884173\pi$
$79$	−6824.92	+	3940.37i	−1.09356	+	0.631368i	−0.159039	+	0.987272i	$0.550840\pi$
$80$		0			0
$81$	3380.43	+	5855.07i	0.515230	+	0.892405i
$82$		0			0
$83$	7247.57			1.05205			0.526025	−	0.850469i	$-0.323682\pi$
$83$	7247.57			1.05205			0.526025	+	0.850469i	$0.323682\pi$
$84$		0			0
$85$	1398.77	−	2422.74i	0.193601	−	0.335328i
$86$		0			0
$87$	−7986.16			−1.05511
$88$		0			0
$89$	−2753.52	−	1589.75i	−0.347623	−	0.200700i	0.316015	−	0.948754i	$-0.397655\pi$
$89$	−2753.52	−	1589.75i	−0.347623	−	0.200700i	−0.663638	+	0.748054i	$0.730988\pi$
$90$		0			0
$91$	500.164	+	288.770i	0.0603990	+	0.0348714i
$92$		0			0
$93$	6200.94	+	10740.3i	0.716955	+	1.24180i
$94$		0			0
$95$	−2445.33	−	14037.8i	−0.270950	−	1.55543i
$96$		0			0
$97$	4303.37	−	2484.55i	0.457367	−	0.264061i	−0.253569	−	0.967317i	$-0.581605\pi$
$97$	4303.37	−	2484.55i	0.457367	−	0.264061i	0.710936	+	0.703256i	$0.248271\pi$
$98$		0			0
$99$	196.502	−	340.351i	0.0200492	−	0.0347262i
$100$		0			0
$101$	3533.50	−	6120.21i	0.346388	−	0.599961i	−0.639217	−	0.769026i	$-0.720741\pi$
$101$	3533.50	−	6120.21i	0.346388	−	0.599961i	0.985605	+	0.169065i	$0.0540748\pi$
$102$		0			0
$103$			4182.70i			0.394260i	0.980377	+	0.197130i	$0.0631621\pi$
$103$			4182.70i			0.394260i	−0.980377	+	0.197130i	$0.936838\pi$
$104$		0			0
$105$	−28613.6	−	16520.1i	−2.59534	−	1.49842i
$106$		0			0
$107$		−	19195.8i		−	1.67664i	−0.545180	−	0.838319i	$-0.683539\pi$
$107$		−	19195.8i		−	1.67664i	0.545180	−	0.838319i	$-0.316461\pi$
$108$		0			0
$109$	8924.98	−	5152.84i	0.751198	−	0.433704i	−0.0749286	−	0.997189i	$-0.523873\pi$
$109$	8924.98	−	5152.84i	0.751198	−	0.433704i	0.826127	+	0.563485i	$0.190540\pi$
$110$		0			0
$111$	932.579	+	1615.27i	0.0756902	+	0.131099i
$112$		0			0
$113$			10459.9i			0.819167i	0.912273	+	0.409584i	$0.134326\pi$
$113$			10459.9i			0.819167i	−0.912273	+	0.409584i	$0.865674\pi$
$114$		0			0
$115$	−25934.5			−1.96102
$116$		0			0
$117$	−13.9130	+	8.03270i	−0.00101637	+	0.000586799i
$118$		0			0
$119$	3245.32	+	5621.07i	0.229173	+	0.396940i
$120$		0			0
$121$	9159.60			0.625613
$122$		0			0
$123$	−6619.11	+	11464.6i	−0.437511	+	0.757792i
$124$		0			0
$125$	−12156.7			−0.778028
$126$		0			0
$127$	26131.5	+	15087.0i	1.62016	+	0.935398i	0.986877	+	0.161475i	$0.0516252\pi$
$127$	26131.5	+	15087.0i	1.62016	+	0.935398i	0.633280	+	0.773923i	$0.281708\pi$
$128$		0			0
$129$	−10995.3	−	6348.13i	−0.660734	−	0.381475i
$130$		0			0
$131$	3772.02	+	6533.34i	0.219802	+	0.380708i	0.954747	−	0.297418i	$-0.0961255\pi$
$131$	3772.02	+	6533.34i	0.219802	+	0.380708i	−0.734945	+	0.678126i	$0.762792\pi$
$132$		0			0
$133$	31042.7	+	11371.3i	1.75491	+	0.642847i
$134$		0			0
$135$	−24512.4	+	14152.3i	−1.34499	+	0.776530i
$136$		0			0
$137$	−13701.7	+	23732.1i	−0.730019	+	1.26443i	0.226855	+	0.973929i	$0.427156\pi$
$137$	−13701.7	+	23732.1i	−0.730019	+	1.26443i	−0.956874	+	0.290502i	$0.906178\pi$
$138$		0			0
$139$	9868.94	−	17093.5i	0.510788	−	0.884711i	−0.489134	−	0.872209i	$-0.662687\pi$
$139$	9868.94	−	17093.5i	0.510788	−	0.884711i	0.999922	−	0.0125021i	$-0.00397965\pi$
$140$		0			0
$141$			7250.84i			0.364712i
$142$		0			0
$143$	−842.584	−	486.466i	−0.0412042	−	0.0237892i
$144$		0			0
$145$		−	34486.9i		−	1.64028i
$146$		0			0
$147$	47381.3	−	27355.6i	2.19266	−	1.26594i
$148$		0			0
$149$	3705.52	+	6418.15i	0.166908	+	0.289093i	0.937331	−	0.348440i	$-0.113288\pi$
$149$	3705.52	+	6418.15i	0.166908	+	0.289093i	−0.770423	+	0.637533i	$0.779955\pi$
$150$		0			0
$151$		−	8534.29i		−	0.374295i	−0.982332	−	0.187147i	$-0.940076\pi$
$151$		−	8534.29i		−	0.374295i	0.982332	−	0.187147i	$-0.0599242\pi$
$152$		0			0
$153$	−180.550			−0.00771284
$154$		0			0
$155$	−46380.3	+	26777.7i	−1.93050	+	1.11458i
$156$		0			0
$157$	14757.3	+	25560.4i	0.598699	+	1.03698i	0.993013	+	0.118001i	$0.0376487\pi$
$157$	14757.3	+	25560.4i	0.598699	+	1.03698i	−0.394315	+	0.918975i	$0.629018\pi$
$158$		0			0
$159$	−4514.34			−0.178567
$160$		0			0
$161$	30085.7	−	52110.0i	1.16067	−	2.01034i
$162$		0			0
$163$	27593.4			1.03856			0.519279	−	0.854605i	$-0.326201\pi$
$163$	27593.4			1.03856			0.519279	+	0.854605i	$0.326201\pi$
$164$		0			0
$165$	48202.9	+	27830.0i	1.77054	+	1.02222i
$166$		0			0
$167$	702.182	+	405.405i	0.0251777	+	0.0145364i	0.512536	−	0.858666i	$-0.328706\pi$
$167$	702.182	+	405.405i	0.0251777	+	0.0145364i	−0.487358	+	0.873202i	$0.662039\pi$
$168$		0			0
$169$	−14260.6	−	24700.1i	−0.499304	−	0.864819i
$170$		0			0
$171$	−705.693	+	589.665i	−0.0241337	+	0.0201657i
$172$		0			0
$173$	11940.9	−	6894.09i	0.398975	−	0.230348i	−0.287067	−	0.957911i	$-0.592680\pi$
$173$	11940.9	−	6894.09i	0.398975	−	0.230348i	0.686041	+	0.727562i	$0.259347\pi$
$174$		0			0
$175$	42720.8	−	73994.6i	1.39497	−	2.41615i
$176$		0			0
$177$	−2188.81	+	3791.13i	−0.0698654	+	0.121010i
$178$		0			0
$179$		−	49715.3i		−	1.55162i	−0.630969	−	0.775808i	$-0.717342\pi$
$179$		−	49715.3i		−	1.55162i	0.630969	−	0.775808i	$-0.282658\pi$
$180$		0			0
$181$	−21871.1	−	12627.3i	−0.667595	−	0.385436i	0.127570	−	0.991830i	$-0.459282\pi$
$181$	−21871.1	−	12627.3i	−0.667595	−	0.385436i	−0.795165	+	0.606394i	$0.792616\pi$
$182$		0			0
$183$			22756.3i			0.679516i
$184$		0			0
$185$	−6975.28	+	4027.18i	−0.203807	+	0.117668i
$186$		0			0
$187$	−5467.12	−	9469.33i	−0.156342	−	0.270792i
$188$		0			0
$189$		−	65670.1i		−	1.83842i
$190$		0			0
$191$	32047.2			0.878463			0.439232	−	0.898374i	$-0.355251\pi$
$191$	32047.2			0.878463			0.439232	+	0.898374i	$0.355251\pi$
$192$		0			0
$193$	−38641.8	+	22309.9i	−1.03739	+	0.598938i	−0.919093	−	0.394040i	$-0.871077\pi$
$193$	−38641.8	+	22309.9i	−1.03739	+	0.598938i	−0.118298	+	0.992978i	$0.537744\pi$
$194$		0			0
$195$	−1137.65	−	1970.46i	−0.0299184	−	0.0518201i
$196$		0			0
$197$	49921.4			1.28634			0.643168	−	0.765725i	$-0.277620\pi$
$197$	49921.4			1.28634			0.643168	+	0.765725i	$0.277620\pi$
$198$		0			0
$199$	14042.5	−	24322.3i	0.354599	−	0.614183i	−0.632451	−	0.774601i	$-0.717951\pi$
$199$	14042.5	−	24322.3i	0.354599	−	0.614183i	0.987049	+	0.160418i	$0.0512842\pi$
$200$		0			0
$201$	33307.8			0.824430
$202$		0			0
$203$	69294.0	+	40006.9i	1.68153	+	0.970830i
$204$		0			0
$205$	−49508.0	−	28583.5i	−1.17806	−	0.680154i
$206$		0			0
$207$	836.892	+	1449.54i	0.0195312	+	0.0338290i
$208$		0			0
$209$	−52294.9	−	19156.3i	−1.19720	−	0.438550i
$210$		0			0
$211$	−48943.0	+	28257.2i	−1.09932	+	0.634694i	−0.936043	−	0.351885i	$-0.885541\pi$
$211$	−48943.0	+	28257.2i	−1.09932	+	0.634694i	−0.163280	+	0.986580i	$0.552207\pi$
$212$		0			0
$213$	−2158.19	+	3738.09i	−0.0475696	+	0.0823930i
$214$		0			0
$215$	27413.3	−	47481.2i	0.593040	−	1.02718i
$216$		0			0
$217$		−	124255.i		−	2.63873i
$218$		0			0
$219$	10389.2	+	5998.21i	0.216618	+	0.125064i
$220$		0			0
$221$			446.975i			0.00915163i
$222$		0			0
$223$	2486.15	−	1435.38i	0.0499941	−	0.0288641i	−0.474795	−	0.880097i	$-0.657478\pi$
$223$	2486.15	−	1435.38i	0.0499941	−	0.0288641i	0.524789	+	0.851233i	$0.324144\pi$
$224$		0			0
$225$	1188.36	+	2058.30i	0.0234738	+	0.0406578i
$226$		0			0
$227$		−	65962.5i		−	1.28010i	−0.768331	−	0.640052i	$-0.778913\pi$
$227$		−	65962.5i		−	1.28010i	0.768331	−	0.640052i	$-0.221087\pi$
$228$		0			0
$229$	−29460.5			−0.561784			−0.280892	−	0.959739i	$-0.590630\pi$
$229$	−29460.5			−0.561784			−0.280892	+	0.959739i	$0.590630\pi$
$230$		0			0
$231$	−111837.	+	64569.0i	−2.09585	+	1.21004i
$232$		0			0
$233$	23522.7	+	40742.5i	0.433286	+	0.750474i	0.997154	−	0.0753912i	$-0.0240205\pi$
$233$	23522.7	+	40742.5i	0.433286	+	0.750474i	−0.563868	+	0.825865i	$0.690687\pi$
$234$		0			0
$235$	−31311.5			−0.566981
$236$		0			0
$237$	−36016.7	+	62382.7i	−0.641220	+	1.11062i
$238$		0			0
$239$	−50217.8			−0.879147			−0.439574	−	0.898207i	$-0.644870\pi$
$239$	−50217.8			−0.879147			−0.439574	+	0.898207i	$0.644870\pi$
$240$		0			0
$241$	60000.5	+	34641.3i	1.03305	+	0.596431i	0.917856	−	0.396913i	$-0.129918\pi$
$241$	60000.5	+	34641.3i	1.03305	+	0.596431i	0.115192	+	0.993343i	$0.463252\pi$
$242$		0			0
$243$	3215.37	+	1856.40i	0.0544527	+	0.0314383i
$244$		0			0
$245$	118130.	+	204608.i	1.96802	+	3.40871i
$246$		0			0
$247$	1459.79	+	1747.03i	0.0239275	+	0.0286357i
$248$		0			0
$249$	57370.6	−	33122.9i	0.925318	−	0.534232i
$250$		0			0
$251$	−47640.3	+	82515.4i	−0.756183	+	1.30975i	0.188601	+	0.982054i	$0.439605\pi$
$251$	−47640.3	+	82515.4i	−0.756183	+	1.30975i	−0.944784	+	0.327694i	$0.893729\pi$
$252$		0			0
$253$	−50682.8	+	87785.2i	−0.791808	+	1.37145i
$254$		0			0
$255$		−	25570.7i		−	0.393245i
$256$		0			0
$257$	−70302.9	−	40589.4i	−1.06440	−	0.614534i	−0.137757	−	0.990466i	$-0.543989\pi$
$257$	−70302.9	−	40589.4i	−1.06440	−	0.614534i	−0.926647	+	0.375932i	$0.877323\pi$
$258$		0			0
$259$		−	18687.1i		−	0.278576i
$260$		0			0
$261$	−1927.55	+	1112.87i	−0.0282959	+	0.0163367i
$262$		0			0
$263$	36206.1	+	62710.8i	0.523444	+	0.906632i	0.999628	+	0.0272860i	$0.00868647\pi$
$263$	36206.1	+	62710.8i	0.523444	+	0.906632i	−0.476184	+	0.879346i	$0.657980\pi$
$264$		0			0
$265$		−	19494.4i		−	0.277599i
$266$		0			0
$267$	−29061.9			−0.407664
$268$		0			0
$269$	1546.82	−	893.058i	0.0213765	−	0.0123417i	−0.489274	−	0.872130i	$-0.662738\pi$
$269$	1546.82	−	893.058i	0.0213765	−	0.0123417i	0.510650	+	0.859789i	$0.329405\pi$
$270$		0			0
$271$	−25581.7	−	44308.7i	−0.348329	−	0.603324i	0.637623	−	0.770348i	$-0.279918\pi$
$271$	−25581.7	−	44308.7i	−0.348329	−	0.603324i	−0.985953	+	0.167024i	$0.946584\pi$
$272$		0			0
$273$	5278.96			0.0708310
$274$		0			0
$275$	−71968.1	+	124652.i	−0.951644	+	1.64830i
$276$		0			0
$277$	−46030.2			−0.599906			−0.299953	−	0.953954i	$-0.596971\pi$
$277$	−46030.2			−0.599906			−0.299953	+	0.953954i	$0.596971\pi$
$278$		0			0
$279$	2993.33	+	1728.20i	0.0384544	+	0.0222017i
$280$		0			0
$281$	21812.2	+	12593.3i	0.276240	+	0.159487i	0.631720	−	0.775197i	$-0.282349\pi$
$281$	21812.2	+	12593.3i	0.276240	+	0.159487i	−0.355480	+	0.934684i	$0.615683\pi$
$282$		0			0
$283$	61381.5	+	106316.i	0.766417	+	1.32747i	0.939494	+	0.342564i	$0.111295\pi$
$283$	61381.5	+	106316.i	0.766417	+	1.32747i	−0.173078	+	0.984908i	$0.555371\pi$
$284$		0			0
$285$	−83512.4	−	99945.1i	−1.02816	−	1.23047i
$286$		0			0
$287$	114865.	−	66317.3i	1.39452	−	0.805124i
$288$		0			0
$289$	39248.9	−	67981.0i	0.469928	−	0.813939i
$290$		0			0
$291$	22709.8	−	39334.6i	0.268181	−	0.464503i
$292$		0			0
$293$		−	123220.i		−	1.43531i	−0.696397	−	0.717657i	$-0.745215\pi$
$293$		−	123220.i		−	1.43531i	0.696397	−	0.717657i	$-0.254785\pi$
$294$		0			0
$295$	−16371.4	−	9452.01i	−0.188122	−	0.108613i
$296$		0			0
$297$			110629.i			1.25417i
$298$		0			0
$299$	3588.52	−	2071.84i	0.0401396	−	0.0231746i
$300$		0			0
$301$	63602.3	+	110162.i	0.702004	+	1.21591i
$302$		0			0
$303$		−	64595.4i		−	0.703585i
$304$		0			0
$305$	−98269.1			−1.05637
$306$		0			0
$307$	58068.1	−	33525.7i	0.616114	−	0.355714i	−0.159240	−	0.987240i	$-0.550905\pi$
$307$	58068.1	−	33525.7i	0.616114	−	0.355714i	0.775355	+	0.631526i	$0.217571\pi$
$308$		0			0
$309$	19115.8	+	33109.6i	0.200206	+	0.346766i
$310$		0			0
$311$	101780.			1.05230			0.526152	−	0.850391i	$-0.323634\pi$
$311$	101780.			1.05230			0.526152	+	0.850391i	$0.323634\pi$
$312$		0			0
$313$	20271.4	−	35111.1i	0.206916	−	0.358389i	−0.743825	−	0.668374i	$-0.766991\pi$
$313$	20271.4	−	35111.1i	0.206916	−	0.358389i	0.950742	+	0.309985i	$0.100324\pi$
$314$		0			0
$315$	−9208.28			−0.0928020
$316$		0			0
$317$	−23876.6	−	13785.2i	−0.237604	−	0.137181i	0.376471	−	0.926428i	$-0.377137\pi$
$317$	−23876.6	−	13785.2i	−0.237604	−	0.137181i	−0.614075	+	0.789248i	$0.710471\pi$
$318$		0			0
$319$	−116734.	−	67396.2i	−1.14714	−	0.662299i
$320$		0			0
$321$	−87729.1	−	151951.i	−0.851400	−	1.47467i
$322$		0			0
$323$	4390.86	+	25206.4i	0.0420867	+	0.241605i
$324$		0			0
$325$	5095.60	−	2941.94i	0.0482423	−	0.0278527i
$326$		0			0
$327$	47099.2	−	81578.2i	0.440472	−	0.762919i
$328$		0			0
$329$	36323.3	−	62913.9i	0.335578	−	0.581239i
$330$		0			0
$331$			51678.7i			0.471689i	0.971791	+	0.235844i	$0.0757856\pi$
$331$			51678.7i			0.471689i	−0.971791	+	0.235844i	$0.924214\pi$
$332$		0			0
$333$	450.176	+	259.909i	0.00405970	+	0.00234387i
$334$		0			0
$335$			143834.i			1.28166i
$336$		0			0
$337$	−136060.	+	78554.5i	−1.19804	+	0.691689i	−0.960118	−	0.279595i	$-0.909800\pi$
$337$	−136060.	+	78554.5i	−1.19804	+	0.691689i	−0.237923	+	0.971284i	$0.576467\pi$
$338$		0			0
$339$	47804.2	+	82799.3i	0.415974	+	0.720489i
$340$		0			0
$341$			209322.i			1.80014i
$342$		0			0
$343$	−328275.			−2.79029
$344$		0			0
$345$	−205294.	+	118526.i	−1.72480	+	0.995811i
$346$		0			0
$347$	25867.2	+	44803.3i	0.214828	+	0.372092i	0.953219	−	0.302280i	$-0.0977477\pi$
$347$	25867.2	+	44803.3i	0.214828	+	0.372092i	−0.738392	+	0.674372i	$0.764414\pi$
$348$		0			0
$349$	−75431.6			−0.619302			−0.309651	−	0.950850i	$-0.600212\pi$
$349$	−75431.6			−0.619302			−0.309651	+	0.950850i	$0.600212\pi$
$350$		0			0
$351$	2261.17	−	3916.45i	0.0183535	−	0.0317891i
$352$		0			0
$353$	221690.			1.77909			0.889544	−	0.456850i	$-0.151023\pi$
$353$	221690.			1.77909			0.889544	+	0.456850i	$0.151023\pi$
$354$		0			0
$355$	−16142.3	−	9319.75i	−0.128088	−	0.0739516i
$356$		0			0
$357$	51379.0	+	29663.7i	0.403133	+	0.232749i
$358$		0			0
$359$	30200.4	+	52308.6i	0.234328	+	0.405868i	0.959077	−	0.283145i	$-0.0913778\pi$
$359$	30200.4	+	52308.6i	0.234328	+	0.405868i	−0.724749	+	0.689013i	$0.758044\pi$
$360$		0			0
$361$	99484.5	+	84180.7i	0.763381	+	0.645949i
$362$		0			0
$363$	72506.0	−	41861.3i	0.550251	−	0.317687i
$364$		0			0
$365$	−25902.2	+	44864.0i	−0.194425	+	0.336753i
$366$		0			0
$367$	−93007.4	+	161093.i	−0.690534	+	1.19604i	0.281129	+	0.959670i	$0.409291\pi$
$367$	−93007.4	+	161093.i	−0.690534	+	1.19604i	−0.971663	+	0.236370i	$0.924042\pi$
$368$		0			0
$369$			3689.49i			0.0270965i
$370$		0			0
$371$	39169.9	+	22614.7i	0.284580	+	0.164302i
$372$		0			0
$373$			36978.4i			0.265785i	0.991130	+	0.132893i	$0.0424266\pi$
$373$			36978.4i			0.265785i	−0.991130	+	0.132893i	$0.957573\pi$
$374$		0			0
$375$	−96230.4	+	55558.6i	−0.684305	+	0.395084i
$376$		0			0
$377$	2755.05	+	4771.89i	0.0193842	+	0.0335744i
$378$		0			0
$379$		−	202054.i		−	1.40666i	−0.710864	−	0.703330i	$-0.751696\pi$
$379$		−	202054.i		−	1.40666i	0.710864	−	0.703330i	$-0.248304\pi$
$380$		0			0
$381$	275804.			1.89999
$382$		0			0
$383$	54335.3	−	31370.5i	0.370412	−	0.213857i	−0.303227	−	0.952918i	$-0.598064\pi$
$383$	54335.3	−	31370.5i	0.370412	−	0.213857i	0.673638	+	0.739061i	$0.264731\pi$
$384$		0			0
$385$	−278830.	−	482948.i	−1.88113	−	3.25821i
$386$		0			0
$387$	−3538.44			−0.0236260
$388$		0			0
$389$	58638.1	−	101564.i	0.387508	−	0.671184i	−0.604606	−	0.796525i	$-0.706669\pi$
$389$	58638.1	−	101564.i	0.387508	−	0.671184i	0.992114	+	0.125341i	$0.0400026\pi$
$390$		0			0
$391$	46568.4			0.304605
$392$		0			0
$393$	59717.5	+	34477.9i	0.386649	+	0.223232i
$394$		0			0
$395$	−269389.	−	155532.i	−1.72657	−	0.996838i
$396$		0			0
$397$	154251.	+	267171.i	0.978695	+	1.69515i	0.667159	+	0.744915i	$0.267510\pi$
$397$	154251.	+	267171.i	0.978695	+	1.69515i	0.311536	+	0.950234i	$0.399156\pi$
$398$		0			0
$399$	297698.	−	51858.0i	1.86995	−	0.325739i
$400$		0			0
$401$	−246024.	+	142042.i	−1.52999	+	0.883339i	−0.530627	+	0.847606i	$0.678043\pi$
$401$	−246024.	+	142042.i	−1.52999	+	0.883339i	−0.999361	+	0.0357332i	$0.988623\pi$
$402$		0			0
$403$	4278.38	−	7410.38i	0.0263433	−	0.0456279i
$404$		0			0
$405$	−133430.	+	231108.i	−0.813474	+	1.40898i
$406$		0			0
$407$			31480.6i			0.190044i
$408$		0			0
$409$	104932.	+	60582.4i	0.627279	+	0.362159i	0.779697	−	0.626157i	$-0.215373\pi$
$409$	104932.	+	60582.4i	0.627279	+	0.362159i	−0.152419	+	0.988316i	$0.548706\pi$
$410$		0			0
$411$			250479.i			1.48282i
$412$		0			0
$413$	37983.6	−	21929.8i	0.222688	−	0.128569i
$414$		0			0
$415$	143036.	+	247745.i	0.830516	+	1.43850i
$416$		0			0
$417$		−	180413.i		−	1.03752i
$418$		0			0
$419$	−137920.			−0.785597			−0.392799	−	0.919624i	$-0.628493\pi$
$419$	−137920.			−0.785597			−0.392799	+	0.919624i	$0.628493\pi$
$420$		0			0
$421$	110340.	−	63704.5i	0.622539	−	0.359423i	−0.155318	−	0.987865i	$-0.549640\pi$
$421$	110340.	−	63704.5i	0.622539	−	0.359423i	0.777857	+	0.628441i	$0.216307\pi$
$422$		0			0
$423$	1010.40	+	1750.07i	0.00564695	+	0.00978081i
$424$		0			0
$425$	66125.7			0.366094
$426$		0			0
$427$	113998.	−	197451.i	0.625234	−	1.08294i
$428$		0			0
$429$	−8893.02			−0.0483208
$430$		0			0
$431$	123022.	+	71026.5i	0.662257	+	0.382354i	0.793136	−	0.609044i	$-0.208447\pi$
$431$	123022.	+	71026.5i	0.662257	+	0.382354i	−0.130879	+	0.991398i	$0.541780\pi$
$432$		0			0
$433$	−87079.8	−	50275.6i	−0.464453	−	0.268152i	0.249462	−	0.968385i	$-0.419746\pi$
$433$	−87079.8	−	50275.6i	−0.464453	−	0.268152i	−0.713915	+	0.700233i	$0.753080\pi$
$434$		0			0
$435$	−157612.	−	272993.i	−0.832936	−	1.44269i
$436$		0			0
$437$	182016.	−	152090.i	0.953118	−	0.796409i
$438$		0			0
$439$	−268003.	+	154731.i	−1.39062	+	0.802878i	−0.993384	−	0.114837i	$-0.963365\pi$
$439$	−268003.	+	154731.i	−1.39062	+	0.802878i	−0.397240	+	0.917715i	$0.630032\pi$
$440$		0			0
$441$	7623.99	−	13205.1i	0.0392017	−	0.0678994i
$442$		0			0
$443$	25678.9	−	44477.2i	0.130849	−	0.226637i	−0.793155	−	0.609020i	$-0.791563\pi$
$443$	25678.9	−	44477.2i	0.130849	−	0.226637i	0.924004	+	0.382383i	$0.124896\pi$
$444$		0			0
$445$		−	125499.i		−	0.633753i
$446$		0			0
$447$	58664.6	+	33870.0i	0.293604	+	0.169512i
$448$		0			0
$449$			220983.i			1.09614i	0.836433	+	0.548069i	$0.184637\pi$
$449$			220983.i			1.09614i	−0.836433	+	0.548069i	$0.815363\pi$
$450$		0			0
$451$	−193503.	+	111719.i	−0.951337	+	0.549255i
$452$		0			0
$453$	−39003.5	−	67556.1i	−0.190067	−	0.329206i
$454$		0			0
$455$			22796.3i			0.110114i
$456$		0			0
$457$	−43888.6			−0.210145			−0.105073	−	0.994465i	$-0.533507\pi$
$457$	−43888.6			−0.210145			−0.105073	+	0.994465i	$0.533507\pi$
$458$		0			0
$459$	44014.8	−	25412.0i	0.208917	−	0.120618i
$460$		0			0
$461$	−111284.	−	192750.i	−0.523640	−	0.906971i	−0.999621	−	0.0275157i	$-0.991240\pi$
$461$	−111284.	−	192750.i	−0.523640	−	0.906971i	0.475981	−	0.879455i	$-0.342093\pi$
$462$		0			0
$463$	−91798.8			−0.428228			−0.214114	−	0.976809i	$-0.568686\pi$
$463$	−91798.8			−0.428228			−0.214114	+	0.976809i	$0.568686\pi$
$464$		0			0
$465$	−244759.	+	423936.i	−1.13197	+	1.96062i
$466$		0			0
$467$	58856.8			0.269875			0.134938	−	0.990854i	$-0.456917\pi$
$467$	58856.8			0.269875			0.134938	+	0.990854i	$0.456917\pi$
$468$		0			0
$469$	−289004.	−	166856.i	−1.31389	−	0.758573i
$470$		0			0
$471$	233633.	+	134888.i	1.05316	+	0.608040i
$472$		0			0
$473$	−107145.	−	185581.i	−0.478907	−	0.829491i
$474$		0			0
$475$	258457.	−	215963.i	1.14552	−	0.957175i
$476$		0			0
$477$	−1089.59	+	629.073i	−0.00478878	+	0.00276480i
$478$		0			0
$479$	−210351.	+	364338.i	−0.916796	+	1.58794i	−0.112547	+	0.993646i	$0.535901\pi$
$479$	−210351.	+	364338.i	−0.916796	+	1.58794i	−0.804250	+	0.594292i	$0.797433\pi$
$480$		0			0
$481$	643.439	−	1114.47i	0.00278111	−	0.00481702i
$482$		0			0
$483$		−	549993.i		−	2.35756i
$484$		0			0
$485$	169860.	+	98068.5i	0.722116	+	0.416914i
$486$		0			0
$487$		−	439469.i		−	1.85298i	−0.376323	−	0.926488i	$-0.622812\pi$
$487$		−	439469.i		−	1.85298i	0.376323	−	0.926488i	$-0.377188\pi$
$488$		0			0
$489$	218425.	−	126108.i	0.913451	−	0.527381i
$490$		0			0
$491$	−129517.	−	224331.i	−0.537236	−	0.930519i	−0.999052	−	0.0435437i	$-0.986135\pi$
$491$	−129517.	−	224331.i	−0.537236	−	0.930519i	0.461816	−	0.886976i	$-0.347198\pi$
$492$		0			0
$493$			61925.0i			0.254784i
$494$		0			0
$495$	15512.4			0.0633094
$496$		0			0
$497$	37452.1	−	21623.0i	0.151623	−	0.0875393i
$498$		0			0
$499$	75250.9	+	130338.i	0.302211	+	0.523445i	0.976637	−	0.214898i	$-0.0689419\pi$
$499$	75250.9	+	130338.i	0.302211	+	0.523445i	−0.674425	+	0.738343i	$0.735609\pi$
$500$		0			0
$501$	7411.15			0.0295264
$502$		0			0
$503$	−64403.8	+	111551.i	−0.254551	+	0.440896i	−0.964774	−	0.263082i	$-0.915261\pi$
$503$	−64403.8	+	111551.i	−0.254551	+	0.440896i	0.710222	+	0.703978i	$0.248594\pi$
$504$		0			0
$505$	278944.			1.09379
$506$		0			0
$507$	−225770.	−	130348.i	−0.878313	−	0.507094i
$508$		0			0
$509$	181168.	+	104598.i	0.699273	+	0.403726i	0.807077	−	0.590447i	$-0.201048\pi$
$509$	181168.	+	104598.i	0.699273	+	0.403726i	−0.107804	+	0.994172i	$0.534382\pi$
$510$		0			0
$511$	−60096.4	−	104090.i	−0.230148	−	0.398628i
$512$		0			0
$513$	89041.2	−	243074.i	0.338342	−	0.923643i
$514$		0			0
$515$	−142978.	+	82548.4i	−0.539082	+	0.311239i
$516$		0			0
$517$	−61190.8	+	105986.i	−0.228931	+	0.396520i
$518$		0			0
$519$	63014.9	−	109145.i	0.233942	−	0.405200i
$520$		0			0
$521$			151066.i			0.556535i	0.960504	+	0.278268i	$0.0897602\pi$
$521$			151066.i			0.556535i	−0.960504	+	0.278268i	$0.910240\pi$
$522$		0			0
$523$	224920.	+	129857.i	0.822288	+	0.474748i	0.851205	−	0.524834i	$-0.175872\pi$
$523$	224920.	+	129857.i	0.822288	+	0.474748i	−0.0289168	+	0.999582i	$0.509206\pi$
$524$		0			0
$525$		−	780973.i		−	2.83346i
$526$		0			0
$527$	83281.0	−	48082.3i	0.299864	−	0.173127i
$528$		0			0
$529$	−75935.1	−	131523.i	−0.271351	−	0.469994i
$530$		0			0
$531$			1220.04i			0.00432699i
$532$		0			0
$533$	9133.80			0.0321512
$534$		0			0
$535$	656175.	−	378843.i	2.29251	−	1.32358i
$536$		0			0
$537$	−227210.	−	393539.i	−0.787913	−	1.36471i
$538$		0			0
$539$	923429.			3.17853
$540$		0			0
$541$	−258891.	+	448413.i	−0.884551	+	1.53209i	−0.0383234	+	0.999265i	$0.512202\pi$
$541$	−258891.	+	448413.i	−0.884551	+	1.53209i	−0.846227	+	0.532822i	$0.821132\pi$
$542$		0			0
$543$	−230837.			−0.782900
$544$		0			0
$545$	352281.	+	203390.i	1.18603	+	0.684756i
$546$		0			0
$547$	4516.32	+	2607.50i	0.0150942	+	0.00871463i	0.507528	−	0.861635i	$-0.330559\pi$
$547$	4516.32	+	2607.50i	0.0150942	+	0.00871463i	−0.492434	+	0.870350i	$0.663893\pi$
$548$		0			0
$549$	3171.09	+	5492.48i	0.0105211	+	0.0182232i
$550$		0			0
$551$	202243.	+	242039.i	0.666148	+	0.797226i
$552$		0			0
$553$	625016.	−	360853.i	2.04381	−	1.18000i
$554$		0			0
$555$	−36810.2	+	63757.1i	−0.119504	+	0.206987i
$556$		0			0
$557$	195505.	−	338624.i	0.630155	−	1.09146i	−0.357365	−	0.933965i	$-0.616325\pi$
$557$	195505.	−	338624.i	0.630155	−	1.09146i	0.987520	−	0.157495i	$-0.0503418\pi$
$558$		0			0
$559$			8759.87i			0.0280333i
$560$		0			0
$561$	−86553.7	−	49971.8i	−0.275017	−	0.158781i
$562$		0			0
$563$			599322.i			1.89079i	0.325924	+	0.945396i	$0.394325\pi$
$563$			599322.i			1.89079i	−0.325924	+	0.945396i	$0.605675\pi$
$564$		0			0
$565$	−357554.	+	206434.i	−1.12007	+	0.646673i
$566$		0			0
$567$	−309574.	−	536199.i	−0.962939	−	1.66786i
$568$		0			0
$569$			257309.i			0.794750i	0.917656	+	0.397375i	$0.130079\pi$
$569$			257309.i			0.794750i	−0.917656	+	0.397375i	$0.869921\pi$
$570$		0			0
$571$	624235.			1.91459			0.957296	−	0.289110i	$-0.0933592\pi$
$571$	624235.			1.91459			0.957296	+	0.289110i	$0.0933592\pi$
$572$		0			0
$573$	253681.	−	146463.i	0.772642	−	0.446085i
$574$		0			0
$575$	−306508.	−	530888.i	−0.927058	−	1.60571i
$576$		0			0
$577$	442248.			1.32835			0.664177	−	0.747575i	$-0.268782\pi$
$577$	442248.			1.32835			0.664177	+	0.747575i	$0.268782\pi$
$578$		0			0
$579$	−203922.	+	353203.i	−0.608284	+	1.05358i
$580$		0			0
$581$	−663722.			−1.96623
$582$		0			0
$583$	−65986.1	−	38097.1i	−0.194140	−	0.112087i
$584$		0			0
$585$	−549.167	−	317.061i	−0.00160469	−	0.000926471i
$586$		0			0
$587$	102866.	+	178169.i	0.298535	+	0.517078i	0.975801	−	0.218661i	$-0.0701687\pi$
$587$	102866.	+	178169.i	0.298535	+	0.517078i	−0.677266	+	0.735738i	$0.736835\pi$
$588$		0			0
$589$	168476.	−	459924.i	0.485633	−	1.32573i
$590$		0			0
$591$	395170.	−	228152.i	1.13138	−	0.653204i
$592$		0			0
$593$	−217809.	+	377256.i	−0.619392	+	1.07282i	0.370204	+	0.928950i	$0.379288\pi$
$593$	−217809.	+	377256.i	−0.619392	+	1.07282i	−0.989597	+	0.143869i	$0.954046\pi$
$594$		0			0
$595$	−128097.	+	221871.i	−0.361831	+	0.626710i
$596$		0			0
$597$		−	256708.i		−	0.720263i
$598$		0			0
$599$	−371458.	−	214461.i	−1.03528	−	0.597717i	−0.116785	−	0.993157i	$-0.537259\pi$
$599$	−371458.	−	214461.i	−1.03528	−	0.597717i	−0.918492	+	0.395440i	$0.870592\pi$
$600$		0			0
$601$			564476.i			1.56277i	0.624047	+	0.781387i	$0.285488\pi$
$601$			564476.i			1.56277i	−0.624047	+	0.781387i	$0.714512\pi$
$602$		0			0
$603$	8039.20	−	4641.44i	0.0221095	−	0.0127649i
$604$		0			0
$605$	180771.	+	313104.i	0.493876	+	0.855418i
$606$		0			0
$607$		−	34058.1i		−	0.0924365i	−0.998931	−	0.0462182i	$-0.985283\pi$
$607$		−	34058.1i		−	0.0924365i	0.998931	−	0.0462182i	$-0.0147170\pi$
$608$		0			0
$609$	731361.			1.97196
$610$		0			0
$611$	4332.53	−	2501.39i	0.0116054	−	0.00670036i
$612$		0			0
$613$	200437.	+	347166.i	0.533404	+	0.923882i	0.999239	+	0.0390107i	$0.0124207\pi$
$613$	200437.	+	347166.i	0.533404	+	0.923882i	−0.465835	+	0.884872i	$0.654246\pi$
$614$		0			0
$615$	−522530.			−1.38153
$616$		0			0
$617$	42818.9	−	74164.5i	0.112477	−	0.194817i	−0.804291	−	0.594235i	$-0.797455\pi$
$617$	42818.9	−	74164.5i	0.112477	−	0.194817i	0.916769	+	0.399419i	$0.130788\pi$
$618$		0			0
$619$	−289791.			−0.756316			−0.378158	−	0.925741i	$-0.623442\pi$
$619$	−289791.			−0.756316			−0.378158	+	0.925741i	$0.623442\pi$
$620$		0			0
$621$	−408038.	−	235581.i	−1.05808	−	0.610882i
$622$		0			0
$623$	252164.	+	145587.i	0.649690	+	0.375099i
$624$		0			0
$625$	51638.3	+	89440.1i	0.132194	+	0.228967i
$626$		0			0
$627$	−501506.	+	87360.6i	−1.27568	+	0.222219i
$628$		0			0
$629$	12524.9	−	7231.25i	0.0316572	−	0.0182773i
$630$		0			0
$631$	38693.7	−	67019.5i	0.0971811	−	0.168323i	−0.813336	−	0.581795i	$-0.802351\pi$
$631$	38693.7	−	67019.5i	0.0971811	−	0.168323i	0.910517	+	0.413472i	$0.135684\pi$
$632$		0			0
$633$	−258283.	+	447360.i	−0.644598	+	1.11648i
$634$		0			0
$635$			1.19101e6i			2.95371i
$636$		0			0
$637$	−32691.0	−	18874.2i	−0.0805657	−	0.0465146i
$638$		0			0
$639$			1202.97i			0.00294614i
$640$		0			0
$641$	−18429.5	+	10640.3i	−0.0448536	+	0.0258962i	−0.522259	−	0.852787i	$-0.674911\pi$
$641$	−18429.5	+	10640.3i	−0.0448536	+	0.0258962i	0.477406	+	0.878683i	$0.341577\pi$
$642$		0			0
$643$	49010.6	+	84888.8i	0.118541	+	0.205319i	0.919190	−	0.393815i	$-0.128845\pi$
$643$	49010.6	+	84888.8i	0.118541	+	0.205319i	−0.800649	+	0.599134i	$0.795512\pi$
$644$		0			0
$645$		−	501138.i		−	1.20459i
$646$		0			0
$647$	177251.			0.423429			0.211714	−	0.977332i	$-0.432095\pi$
$647$	177251.			0.423429			0.211714	+	0.977332i	$0.432095\pi$
$648$		0			0
$649$	−63987.7	+	36943.3i	−0.151917	+	0.0877095i
$650$		0			0
$651$	−567873.	−	983585.i	−1.33995	−	2.32086i
$652$		0			0
$653$	−273207.			−0.640716			−0.320358	−	0.947297i	$-0.603803\pi$
$653$	−273207.			−0.640716			−0.320358	+	0.947297i	$0.603803\pi$
$654$		0			0
$655$	−148887.	+	257880.i	−0.347035	+	0.601083i
$656$		0			0
$657$	3343.40			0.00774564
$658$		0			0
$659$	−259815.	−	150004.i	−0.598264	−	0.345408i	0.170094	−	0.985428i	$-0.445593\pi$
$659$	−259815.	−	150004.i	−0.598264	−	0.345408i	−0.768358	+	0.640020i	$0.778926\pi$
$660$		0			0
$661$	−256196.	−	147915.i	−0.586366	−	0.338539i	0.177293	−	0.984158i	$-0.443266\pi$
$661$	−256196.	−	147915.i	−0.586366	−	0.338539i	−0.763659	+	0.645619i	$0.776599\pi$
$662$		0			0
$663$	2042.77	+	3538.18i	0.00464721	+	0.00804921i
$664$		0			0
$665$	223940.	+	1.28556e6i	0.506393	+	2.90702i
$666$		0			0
$667$	497163.	−	287037.i	1.11750	−	0.645189i
$668$		0			0
$669$	13120.0	−	22724.5i	0.0293145	−	0.0507741i
$670$		0			0
$671$	−192043.	+	332629.i	−0.426534	+	0.738779i
$672$		0			0
$673$		−	83113.9i		−	0.183503i	−0.995782	−	0.0917516i	$-0.970753\pi$
$673$		−	83113.9i		−	0.183503i	0.995782	−	0.0917516i	$-0.0292466\pi$
$674$		0			0
$675$	−579402.	−	334518.i	−1.27166	−	0.734196i
$676$		0			0
$677$		−	23926.5i		−	0.0522037i	−0.999659	−	0.0261018i	$-0.991691\pi$
$677$		−	23926.5i		−	0.0522037i	0.999659	−	0.0261018i	$-0.00830941\pi$
$678$		0			0
$679$	−394096.	+	227531.i	−0.854796	+	0.493517i
$680$		0			0
$681$	−301463.	−	522149.i	−0.650039	−	1.12590i
$682$		0			0
$683$		−	438631.i		−	0.940281i	−0.882592	−	0.470140i	$-0.844203\pi$
$683$		−	438631.i		−	0.940281i	0.882592	−	0.470140i	$-0.155797\pi$
$684$		0			0
$685$	−1.08165e6			−2.30519
$686$		0			0
$687$	−233205.	+	134641.i	−0.494110	+	0.285275i
$688$		0			0
$689$	1557.35	+	2697.41i	0.00328056	+	0.00568210i
$690$		0			0
$691$	−137539.			−0.288050			−0.144025	−	0.989574i	$-0.546005\pi$
$691$	−137539.			−0.288050			−0.144025	+	0.989574i	$0.546005\pi$
$692$		0			0
$693$	−17995.4	+	31168.9i	−0.0374709	+	0.0649015i
$694$		0			0
$695$	779080.			1.61292
$696$		0			0
$697$	88897.2	+	51324.8i	0.182988	+	0.105648i
$698$		0			0
$699$	372404.	+	215007.i	0.762184	+	0.440047i
$700$		0			0
$701$	45346.4	+	78542.3i	0.0922798	+	0.159833i	0.908470	−	0.417950i	$-0.137251\pi$
$701$	45346.4	+	78542.3i	0.0922798	+	0.159833i	−0.816190	+	0.577783i	$0.803918\pi$
$702$		0			0
$703$	25337.7	−	69169.4i	0.0512691	−	0.139960i
$704$		0			0
$705$	−247857.	+	143100.i	−0.498681	+	0.287914i
$706$		0			0
$707$	−323593.	+	560479.i	−0.647381	+	1.12130i
$708$		0			0
$709$	389004.	−	673774.i	0.773858	−	1.34036i	−0.161576	−	0.986860i	$-0.551658\pi$
$709$	389004.	−	673774.i	0.773858	−	1.34036i	0.935434	−	0.353501i	$-0.115009\pi$
$710$		0			0
$711$			20075.7i			0.0397128i
$712$		0			0
$713$	−772055.	−	445746.i	−1.51869	−	0.876816i
$714$		0			0
$715$		−	38402.9i		−	0.0751195i
$716$		0			0
$717$	−397516.	+	229506.i	−0.773243	+	0.446432i
$718$		0			0
$719$	−235283.	−	407522.i	−0.455127	−	0.788304i	0.543568	−	0.839365i	$-0.317073\pi$
$719$	−235283.	−	407522.i	−0.455127	−	0.788304i	−0.998696	+	0.0510614i	$0.983740\pi$
$720$		0			0
$721$		−	383046.i		−	0.736851i
$722$		0			0
$723$	633272.			1.21147
$724$		0			0
$725$	705957.	−	407584.i	1.34308	−	0.775428i
$726$		0			0
$727$	−109552.	−	189750.i	−0.207278	−	0.359016i	0.743578	−	0.668649i	$-0.233127\pi$
$727$	−109552.	−	189750.i	−0.207278	−	0.359016i	−0.950856	+	0.309633i	$0.899794\pi$
$728$		0			0
$729$	−513693.			−0.966603
$730$		0			0
$731$	−49223.6	+	85257.8i	−0.0921168	+	0.159551i
$732$		0			0
$733$	−707123.			−1.31609			−0.658047	−	0.752977i	$-0.728617\pi$
$733$	−707123.			−1.31609			−0.658047	+	0.752977i	$0.728617\pi$
$734$		0			0
$735$	1.87020e6	+	1.07976e6i	3.46190	+	1.99873i
$736$		0			0
$737$	486860.	+	281089.i	0.896332	+	0.517498i
$738$		0			0
$739$	150067.	+	259924.i	0.274788	+	0.475946i	0.970082	−	0.242779i	$-0.0780591\pi$
$739$	150067.	+	259924.i	0.274788	+	0.475946i	−0.695294	+	0.718726i	$0.744726\pi$
$740$		0			0
$741$	19539.8	+	7157.69i	0.0355864	+	0.0130358i
$742$		0			0
$743$	−575271.	+	332133.i	−1.04206	+	0.601636i	−0.920417	−	0.390937i	$-0.872151\pi$
$743$	−575271.	+	332133.i	−1.04206	+	0.601636i	−0.121647	+	0.992573i	$0.538818\pi$
$744$		0			0
$745$	−146262.	+	253333.i	−0.263523	+	0.456435i
$746$		0			0
$747$	9231.35	−	15989.2i	0.0165434	−	0.0286540i
$748$		0			0
$749$			1.75793e6i			3.13355i
$750$		0			0
$751$	254570.	+	146976.i	0.451365	+	0.260596i	0.708406	−	0.705805i	$-0.249414\pi$
$751$	254570.	+	146976.i	0.451365	+	0.260596i	−0.257042	+	0.966400i	$0.582748\pi$
$752$		0			0
$753$			870906.i			1.53596i
$754$		0			0
$755$	291729.	−	168430.i	0.511783	−	0.295478i
$756$		0			0
$757$	−436923.	−	756773.i	−0.762453	−	1.32061i	−0.941583	−	0.336782i	$-0.890661\pi$
$757$	−436923.	−	756773.i	−0.762453	−	1.32061i	0.179129	−	0.983826i	$-0.442672\pi$
$758$		0			0
$759$			926525.i			1.60832i
$760$		0			0
$761$	676281.			1.16777			0.583886	−	0.811836i	$-0.301532\pi$
$761$	676281.			1.16777			0.583886	+	0.811836i	$0.301532\pi$
$762$		0			0
$763$	−817337.	+	471890.i	−1.40395	+	0.810572i
$764$		0			0
$765$	−3563.28	−	6171.77i	−0.00608873	−	0.0105460i
$766$		0			0
$767$	3020.37			0.00513417
$768$		0			0
$769$	295116.	−	511157.i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$769$	295116.	−	511157.i	0.499046	−	0.864373i	0.999999	+	0.00110121i	$0.000350527\pi$
$770$		0			0
$771$	−742009.			−1.24825
$772$		0			0
$773$	553601.	+	319622.i	0.926484	+	0.534906i	0.885698	−	0.464262i	$-0.153680\pi$
$773$	553601.	+	319622.i	0.926484	+	0.534906i	0.0407864	+	0.999168i	$0.487014\pi$
$774$		0			0
$775$	−1.09630e6	−	632946.i	−1.82526	−	1.05381i
$776$		0			0
$777$	−85404.2	−	147924.i	−0.141461	−	0.245018i
$778$		0			0
$779$	515085.	−	89726.0i	0.848798	−	0.147857i
$780$		0			0
$781$	−63092.4	+	36426.4i	−0.103437	+	0.0597192i
$782$		0			0
$783$	313267.	−	542595.i	0.510966	−	0.885019i
$784$		0			0
$785$	−582492.	+	1.00891e6i	−0.945258	+	1.63723i
$786$		0			0
$787$			129013.i			0.208297i	0.994562	+	0.104149i	$0.0332118\pi$
$787$			129013.i			0.208297i	−0.994562	+	0.104149i	$0.966788\pi$
$788$		0			0
$789$	573204.	+	330939.i	0.920778	+	0.531612i
$790$		0			0
$791$		−	957906.i		−	1.53098i
$792$		0			0
$793$	13597.3	−	7850.43i	0.0216226	−	0.0124838i
$794$		0			0
$795$	−89093.6	−	154315.i	−0.140965	−	0.244159i
$796$		0			0
$797$		−	540582.i		−	0.851030i	−0.904951	−	0.425515i	$-0.860093\pi$
$797$		−	540582.i		−	0.851030i	0.904951	−	0.425515i	$-0.139907\pi$
$798$		0			0
$799$	56223.3			0.0880690
$800$		0			0
$801$	−7014.42	+	4049.78i	−0.0109327	+	0.00631199i
$802$		0			0
$803$	101239.	+	175352.i	0.157007	+	0.271943i
$804$		0			0
$805$	2.37505e6			3.66506
$806$		0			0
$807$	8162.93	−	14138.6i	0.0125343	−	0.0217100i
$808$		0			0
$809$	−304565.			−0.465354			−0.232677	−	0.972554i	$-0.574749\pi$
$809$	−304565.			−0.465354			−0.232677	+	0.972554i	$0.574749\pi$
$810$		0			0
$811$	−773795.	−	446750.i	−1.17648	−	0.679240i	−0.221281	−	0.975210i	$-0.571024\pi$
$811$	−773795.	−	446750.i	−1.17648	−	0.679240i	−0.955197	+	0.295970i	$0.904357\pi$
$812$		0			0
$813$	−405001.	−	233827.i	−0.612738	−	0.353765i
$814$		0			0
$815$	544575.	+	943232.i	0.819866	+	1.42005i
$816$		0			0
$817$	86052.7	+	493998.i	0.128920	+	0.740084i
$818$		0			0
$819$	1274.14	−	735.623i	0.00189954	−	0.00109670i
$820$		0			0
$821$	−102914.	+	178253.i	−0.152683	+	0.264454i	−0.932213	−	0.361911i	$-0.882125\pi$
$821$	−102914.	+	178253.i	−0.152683	+	0.264454i	0.779530	+	0.626365i	$0.215458\pi$
$822$		0			0
$823$	−39049.5	+	67635.8i	−0.0576522	+	0.0998566i	−0.893411	−	0.449240i	$-0.851695\pi$
$823$	−39049.5	+	67635.8i	−0.0576522	+	0.0998566i	0.835759	+	0.549097i	$0.185028\pi$
$824$		0			0
$825$			1.31564e6i			1.93298i
$826$		0			0
$827$	691422.	+	399193.i	1.01096	+	0.583676i	0.911471	−	0.411364i	$-0.134947\pi$
$827$	691422.	+	399193.i	1.01096	+	0.583676i	0.0994844	+	0.995039i	$0.468281\pi$
$828$		0			0
$829$		−	643855.i		−	0.936870i	−0.883498	−	0.468435i	$-0.844818\pi$
$829$		−	643855.i		−	0.936870i	0.883498	−	0.468435i	$-0.155182\pi$
$830$		0			0
$831$	−364368.	+	210368.i	−0.527640	+	0.304633i
$832$		0			0
$833$	−212116.	−	367396.i	−0.305692	−	0.529474i
$834$		0			0
$835$			32003.7i			0.0459016i
$836$		0			0
$837$	−972959.			−1.38881
$838$		0			0
$839$	−551512.	+	318416.i	−0.783486	+	0.452346i	−0.837664	−	0.546186i	$-0.816079\pi$
$839$	−551512.	+	318416.i	−0.783486	+	0.452346i	0.0541786	+	0.998531i	$0.482746\pi$
$840$		0			0
$841$	28051.7	+	48586.9i	0.0396613	+	0.0686953i
$842$		0			0
$843$	230216.			0.323952
$844$		0			0
$845$	562886.	−	974947.i	0.788328	−	1.36542i
$846$		0			0
$847$	−838823.			−1.16924
$848$		0			0
$849$	971773.	+	561054.i	1.34819	+	0.778375i
$850$		0			0
$851$	−116112.	−	67037.2i	−0.160331	−	0.0925671i
$852$		0			0
$853$	18130.8	+	31403.5i	0.0249184	+	0.0431599i	0.878216	−	0.478265i	$-0.158734\pi$
$853$	18130.8	+	31403.5i	0.0249184	+	0.0431599i	−0.853297	+	0.521425i	$0.825401\pi$
$854$		0			0
$855$	−34084.0	−	12485.4i	−0.0466249	−	0.0170793i
$856$		0			0
$857$	−78544.1	+	45347.4i	−0.106943	+	0.0617435i	−0.552517	−	0.833501i	$-0.686333\pi$
$857$	−78544.1	+	45347.4i	−0.106943	+	0.0617435i	0.445575	+	0.895245i	$0.352999\pi$
$858$		0			0
$859$	−401667.	+	695707.i	−0.544351	+	0.942844i	0.454296	+	0.890851i	$0.349891\pi$
$859$	−401667.	+	695707.i	−0.544351	+	0.942844i	−0.998647	+	0.0519934i	$0.983443\pi$
$860$		0			0
$861$	606168.	−	1.04991e6i	0.817687	−	1.41627i
$862$		0			0
$863$		−	34074.8i		−	0.0457521i	−0.999738	−	0.0228761i	$-0.992718\pi$
$863$		−	34074.8i		−	0.0457521i	0.999738	−	0.0228761i	$-0.00728231\pi$
$864$		0			0
$865$	471324.	+	272119.i	0.629923	+	0.363686i
$866$		0			0
$867$		−	717503.i		−	0.954521i
$868$		0			0
$869$	−1.05291e6	+	607898.i	−1.39429	+	0.804992i
$870$		0			0
$871$	−11490.5	−	19902.1i	−0.0151461	−	0.0262339i
$872$		0			0
$873$		−	12658.5i		−	0.0166093i
$874$		0			0
$875$	1.11329e6			1.45409
$876$		0			0
$877$	−395994.	+	228627.i	−0.514860	+	0.297254i	−0.734829	−	0.678252i	$-0.762738\pi$
$877$	−395994.	+	228627.i	−0.514860	+	0.297254i	0.219969	+	0.975507i	$0.429404\pi$
$878$		0			0
$879$	−563143.	−	975393.i	−0.728855	−	1.26241i
$880$		0			0
$881$	−599177.			−0.771975			−0.385987	−	0.922504i	$-0.626139\pi$
$881$	−599177.			−0.771975			−0.385987	+	0.922504i	$0.626139\pi$
$882$		0			0
$883$	−5620.23	+	9734.53i	−0.00720830	+	0.0124851i	−0.869607	−	0.493744i	$-0.835628\pi$
$883$	−5620.23	+	9734.53i	−0.00720830	+	0.0124851i	0.862399	+	0.506230i	$0.168961\pi$
$884$		0			0
$885$	−172791.			−0.220614
$886$		0			0
$887$	−821694.	−	474406.i	−1.04439	−	0.602979i	−0.123317	−	0.992367i	$-0.539353\pi$
$887$	−821694.	−	474406.i	−1.04439	−	0.602979i	−0.921074	+	0.389388i	$0.872687\pi$
$888$		0			0
$889$	−2.39309e6	−	1.38165e6i	−3.02799	−	1.74821i
$890$		0			0
$891$	521513.	+	903288.i	0.656916	+	1.13781i
$892$		0			0
$893$	219753.	−	183622.i	0.275570	−	0.230262i
$894$		0			0
$895$	1.69943e6	−	981166.i	2.12157	−	1.22489i
$896$		0			0
$897$	18937.5	−	32800.6i	0.0235362	−	0.0407659i
$898$		0			0
$899$	592738.	−	1.02665e6i	0.733404	−	1.27029i
$900$		0			0
$901$			35004.4i			0.0431194i
$902$		0			0
$903$	1.00693e6	+	581352.i	1.23488	+	0.712958i
$904$		0			0
$905$		−	996831.i		−	1.21709i
$906$		0			0
$907$	925379.	−	534268.i	1.12488	−	0.649448i	0.182236	−	0.983255i	$-0.441667\pi$
$907$	925379.	−	534268.i	1.12488	−	0.649448i	0.942642	+	0.333807i	$0.108333\pi$
$908$		0			0
$909$	−9001.36	−	15590.8i	−0.0108938	−	0.0188687i
$910$		0			0
$911$			1.33286e6i			1.60601i	0.595972	+	0.803005i	$0.296767\pi$
$911$			1.33286e6i			1.60601i	−0.595972	+	0.803005i	$0.703233\pi$
$912$		0			0
$913$	1.11811e6			1.34136
$914$		0			0
$915$	−777883.	+	449111.i	−0.929120	+	0.536428i
$916$		0			0
$917$	−345436.	−	598313.i	−0.410799	−	0.711525i
$918$		0			0
$919$	−780374.			−0.923999			−0.462000	−	0.886880i	$-0.652868\pi$
$919$	−780374.			−0.923999			−0.462000	+	0.886880i	$0.652868\pi$
$920$		0			0
$921$	306439.	−	530768.i	0.361264	−	0.625727i
$922$		0			0
$923$	2978.11			0.00349573
$924$		0			0
$925$	−164875.	−	95190.8i	−0.192696	−	0.111253i
$926$		0			0
$927$	9227.63	+	5327.58i	0.0107382	+	0.00619969i
$928$		0			0
$929$	9446.97	+	16362.6i	0.0109461	+	0.0189593i	0.871447	−	0.490490i	$-0.163182\pi$
$929$	9446.97	+	16362.6i	0.0109461	+	0.0189593i	−0.860500	+	0.509450i	$0.829849\pi$
$930$		0			0
$931$	−2.02897e6	−	743237.i	−2.34086	−	0.857487i
$932$		0			0
$933$	805674.	−	465156.i	0.925541	−	0.534362i
$934$		0			0
$935$	215795.	−	373767.i	0.246841	−	0.427541i
$936$		0			0
$937$	234557.	−	406265.i	0.267159	−	0.462732i	−0.700968	−	0.713192i	$-0.747249\pi$
$937$	234557.	−	406265.i	0.267159	−	0.462732i	0.968127	+	0.250460i	$0.0805819\pi$
$938$		0			0
$939$		−	370578.i		−	0.420290i
$940$		0			0
$941$	1.12237e6	+	648002.i	1.26753	+	0.731808i	0.974520	−	0.224301i	$-0.0720100\pi$
$941$	1.12237e6	+	648002.i	1.26753	+	0.731808i	0.293009	+	0.956110i	$0.405343\pi$
$942$		0			0
$943$		−	951612.i		−	1.07013i
$944$		0			0
$945$	2.24481e6	−	1.29604e6i	2.51372	−	1.45130i
$946$		0			0
$947$	−327123.	−	566594.i	−0.364764	−	0.631789i	0.623975	−	0.781445i	$-0.285517\pi$
$947$	−327123.	−	566594.i	−0.364764	−	0.631789i	−0.988738	+	0.149656i	$0.952183\pi$
$948$		0			0
$949$		−	8277.01i		−	0.00919054i
$950$		0			0
$951$	−252004.			−0.278642
$952$		0			0
$953$	−190421.	+	109940.i	−0.209667	+	0.121051i	−0.601157	−	0.799131i	$-0.705293\pi$
$953$	−190421.	+	109940.i	−0.209667	+	0.121051i	0.391490	+	0.920182i	$0.371960\pi$
$954$		0			0
$955$	632474.	+	1.09548e6i	0.693483	+	1.20115i
$956$		0			0
$957$	−1.23206e6			−1.34527
$958$		0			0
$959$	1.25478e6	−	2.17335e6i	1.36437	−	2.36316i
$960$		0			0
$961$	−917429.			−0.993404
$962$		0			0
$963$	−42348.7	−	24450.1i	−0.0456655	−	0.0263650i
$964$		0			0
$965$	−1.52524e6	−	880600.i	−1.63789	−	0.945636i
$966$		0			0
$967$	109124.	+	189008.i	0.116699	+	0.202129i	0.918458	−	0.395519i	$-0.129435\pi$
$967$	109124.	+	189008.i	0.116699	+	0.202129i	−0.801759	+	0.597648i	$0.796102\pi$
$968$		0			0
$969$	149956.	+	179463.i	0.159704	+	0.191129i
$970$		0			0
$971$	643947.	−	371783.i	0.682986	−	0.394322i	−0.117993	−	0.993014i	$-0.537646\pi$
$971$	643947.	−	371783.i	0.682986	−	0.394322i	0.800979	+	0.598692i	$0.204313\pi$
$972$		0			0
$973$	−903783.	+	1.56540e6i	−0.954637	+	1.65348i
$974$		0			0
$975$	26890.6	−	46575.9i	0.0282873	−	0.0489951i
$976$		0			0
$977$			496951.i			0.520624i	0.965525	+	0.260312i	$0.0838254\pi$
$977$			496951.i			0.520624i	−0.965525	+	0.260312i	$0.916175\pi$
$978$		0			0
$979$	−424798.	−	245257.i	−0.443218	−	0.255892i
$980$		0			0
$981$		−	26253.0i		−	0.0272798i
$982$		0			0
$983$	−1.24870e6	+	720937.i	−1.29226	+	0.746088i	−0.979055	−	0.203597i	$-0.934737\pi$
$983$	−1.24870e6	+	720937.i	−1.29226	+	0.746088i	−0.313207	+	0.949685i	$0.601403\pi$
$984$		0			0
$985$	985233.	+	1.70647e6i	1.01547	+	1.75884i
$986$		0			0
$987$		−	664022.i		−	0.681629i
$988$		0			0
$989$	912653.			0.933068
$990$		0			0
$991$	139194.	−	80364.0i	0.141734	−	0.0818303i	−0.427456	−	0.904036i	$-0.640590\pi$
$991$	139194.	−	80364.0i	0.141734	−	0.0818303i	0.569190	+	0.822206i	$0.307257\pi$
$992$		0			0
$993$	236183.	+	409081.i	0.239524	+	0.414868i
$994$		0			0
$995$	1.10855e6			1.11972
$996$		0			0
$997$	93355.2	−	161696.i	0.0939178	−	0.162670i	−0.815239	−	0.579125i	$-0.803394\pi$
$997$	93355.2	−	161696.i	0.0939178	−	0.162670i	0.909156	+	0.416455i	$0.136728\pi$
$998$		0			0
$999$	−146326.			−0.146620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.c.145.6		16
4.3	odd	2		38.5.d.a.31.6	yes	16
12.11	even	2		342.5.m.c.145.1		16
19.8	odd	6	inner	304.5.r.c.65.6		16
76.27	even	6		38.5.d.a.27.6	✓	16
228.179	odd	6		342.5.m.c.217.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.6	✓	16	76.27	even	6
38.5.d.a.31.6	yes	16	4.3	odd	2
304.5.r.c.65.6		16	19.8	odd	6	inner
304.5.r.c.145.6		16	1.1	even	1	trivial
342.5.m.c.145.1		16	12.11	even	2
342.5.m.c.217.1		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)

\(f(q)\)	\(=\)	\(q+(7.91584 - 4.57021i) q^{3} +(19.7357 + 34.1832i) q^{5} -91.5785 q^{7} +(1.27372 - 2.20614i) q^{9} +O(q^{10})\)	\(q+(7.91584 - 4.57021i) q^{3} +(19.7357 + 34.1832i) q^{5} -91.5785 q^{7} +(1.27372 - 2.20614i) q^{9} +154.274 q^{11} +(-5.46159 - 3.15325i) q^{13} +(312.449 + 180.393i) q^{15} +(-35.4376 - 61.3797i) q^{17} +(-338.973 - 124.170i) q^{19} +(-724.921 + 418.533i) q^{21} +(-328.524 + 569.020i) q^{23} +(-466.494 + 807.991i) q^{25} +717.090i q^{27} +(-756.663 - 436.859i) q^{29} +1356.82i q^{31} +(1221.21 - 705.067i) q^{33} +(-1807.36 - 3130.45i) q^{35} +204.056i q^{37} -57.6441 q^{39} +(-1254.28 + 724.157i) q^{41} +(-694.511 - 1202.93i) q^{43} +100.551 q^{45} +(-396.636 + 686.994i) q^{47} +5985.63 q^{49} +(-561.037 - 323.915i) q^{51} +(-427.719 - 246.944i) q^{53} +(3044.71 + 5273.59i) q^{55} +(-3250.74 + 566.268i) q^{57} +(-414.766 + 239.465i) q^{59} +(-1244.82 + 2156.08i) q^{61} +(-116.645 + 202.035i) q^{63} -248.926i q^{65} +(3155.80 + 1822.00i) q^{67} +6005.69i q^{69} +(-408.962 + 236.114i) q^{71} +(656.228 + 1136.62i) q^{73} +8527.91i q^{75} -14128.2 q^{77} +(-6824.92 + 3940.37i) q^{79} +(3380.43 + 5855.07i) q^{81} +7247.57 q^{83} +(1398.77 - 2422.74i) q^{85} -7986.16 q^{87} +(-2753.52 - 1589.75i) q^{89} +(500.164 + 288.770i) q^{91} +(6200.94 + 10740.3i) q^{93} +(-2445.33 - 14037.8i) q^{95} +(4303.37 - 2484.55i) q^{97} +(196.502 - 340.351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) \) 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

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Database

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