LMFDB - Embedded newform 304.4.i.e.273.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [304,4,Mod(49,304)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("304.49"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(304, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	304.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.9365806417$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 64x^{4} + 33x^{3} + 3984x^{2} - 945x + 225 $ x^6 - x^5 + 64x^4 + 33x^3 + 3984x^2 - 945x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			273.2
Root			$0.118706 + 0.205606i$ of defining polynomial
Character	$\chi$	$=$	304.273
Dual form			304.4.i.e.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.881294 + 1.52645i) q^{3} +(10.3546 + 17.9347i) q^{5} -8.76259 q^{7} +(11.9466 - 20.6922i) q^{9} +62.1780 q^{11} +(32.2611 - 55.8778i) q^{13} +(-18.2509 + 31.6115i) q^{15} +(23.2077 + 40.1970i) q^{17} +(-17.3798 + 80.9750i) q^{19} +(-7.72241 - 13.3756i) q^{21} +(-18.6424 + 32.2895i) q^{23} +(-151.936 + 263.161i) q^{25} +89.7038 q^{27} +(33.2119 - 57.5247i) q^{29} -112.370 q^{31} +(54.7971 + 94.9114i) q^{33} +(-90.7332 - 157.155i) q^{35} -189.018 q^{37} +113.726 q^{39} +(120.005 + 207.854i) q^{41} +(84.1370 + 145.730i) q^{43} +494.812 q^{45} +(93.9241 - 162.681i) q^{47} -266.217 q^{49} +(-40.9056 + 70.8506i) q^{51} +(56.5285 - 97.9102i) q^{53} +(643.830 + 1115.15i) q^{55} +(-138.921 + 44.8334i) q^{57} +(92.9940 + 161.070i) q^{59} +(-154.322 + 267.293i) q^{61} +(-104.684 + 181.317i) q^{63} +1336.20 q^{65} +(19.7279 - 34.1697i) q^{67} -65.7176 q^{69} +(-175.101 - 303.284i) q^{71} +(4.80280 + 8.31870i) q^{73} -535.601 q^{75} -544.840 q^{77} +(-588.269 - 1018.91i) q^{79} +(-243.504 - 421.761i) q^{81} +257.980 q^{83} +(-480.614 + 832.448i) q^{85} +117.078 q^{87} +(66.8743 - 115.830i) q^{89} +(-282.691 + 489.634i) q^{91} +(-99.0313 - 171.527i) q^{93} +(-1632.22 + 526.763i) q^{95} +(-598.387 - 1036.44i) q^{97} +(742.819 - 1286.60i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 5 q^{3} - q^{5} - 52 q^{7} - 54 q^{9} - 8 q^{11} + 129 q^{13} + 77 q^{15} - 51 q^{17} - 40 q^{19} - 170 q^{21} - 47 q^{23} - 338 q^{25} - 718 q^{27} - 125 q^{29} + 100 q^{31} + 274 q^{33} + 84 q^{35}+ \cdots + 3184 q^{99}+O(q^{100}) $ 6 * q + 5 * q^3 - q^5 - 52 * q^7 - 54 * q^9 - 8 * q^11 + 129 * q^13 + 77 * q^15 - 51 * q^17 - 40 * q^19 - 170 * q^21 - 47 * q^23 - 338 * q^25 - 718 * q^27 - 125 * q^29 + 100 * q^31 + 274 * q^33 + 84 * q^35 - 376 * q^37 + 1546 * q^39 + 475 * q^41 + 73 * q^43 + 3188 * q^45 + 241 * q^47 - 1354 * q^49 - 69 * q^51 + 29 * q^53 + 1838 * q^55 + 1755 * q^57 + 1065 * q^59 - 981 * q^61 + 872 * q^63 + 586 * q^65 - 877 * q^67 - 1526 * q^69 - 2135 * q^71 + 667 * q^73 - 4584 * q^75 - 492 * q^77 - 1671 * q^79 - 1287 * q^81 - 1176 * q^83 - 1929 * q^85 + 6430 * q^87 + 693 * q^89 - 1676 * q^91 - 3138 * q^93 - 4489 * q^95 - 985 * q^97 + 3184 * q^99

Character values

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

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.881294	+	1.52645i	0.169605	+	0.293765i	0.938281	−	0.345874i	$-0.112417\pi$
$3$	0.881294	+	1.52645i	0.169605	+	0.293765i	−0.768676	+	0.639638i	$0.779084\pi$
$4$		0			0
$5$	10.3546	+	17.9347i	0.926145	+	1.60413i	0.789709	+	0.613481i	$0.210231\pi$
$5$	10.3546	+	17.9347i	0.926145	+	1.60413i	0.136436	+	0.990649i	$0.456435\pi$
$6$		0			0
$7$	−8.76259			−0.473135			−0.236568	−	0.971615i	$-0.576022\pi$
$7$	−8.76259			−0.473135			−0.236568	+	0.971615i	$0.576022\pi$
$8$		0			0
$9$	11.9466	−	20.6922i	0.442468	−	0.766378i
$10$		0			0
$11$	62.1780			1.70431			0.852154	−	0.523291i	$-0.175296\pi$
$11$	62.1780			1.70431			0.852154	+	0.523291i	$0.175296\pi$
$12$		0			0
$13$	32.2611	−	55.8778i	0.688278	−	1.19213i	−0.284117	−	0.958790i	$-0.591700\pi$
$13$	32.2611	−	55.8778i	0.688278	−	1.19213i	0.972395	−	0.233343i	$-0.0749664\pi$
$14$		0			0
$15$	−18.2509	+	31.6115i	−0.314158	+	0.544137i
$16$		0			0
$17$	23.2077	+	40.1970i	0.331100	+	0.573482i	0.982728	−	0.185057i	$-0.0592469\pi$
$17$	23.2077	+	40.1970i	0.331100	+	0.573482i	−0.651628	+	0.758539i	$0.725914\pi$
$18$		0			0
$19$	−17.3798	+	80.9750i	−0.209852	+	0.977733i
$19$	−17.3798	+	80.9750i	−0.209852	+	0.977733i
$20$		0			0
$21$	−7.72241	−	13.3756i	−0.0802461	−	0.138990i
$22$		0			0
$23$	−18.6424	+	32.2895i	−0.169009	+	0.292732i	−0.938072	−	0.346441i	$-0.887390\pi$
$23$	−18.6424	+	32.2895i	−0.169009	+	0.292732i	0.769063	+	0.639173i	$0.220723\pi$
$24$		0			0
$25$	−151.936	+	263.161i	−1.21549	+	2.10529i
$26$		0			0
$27$	89.7038			0.639389
$28$		0			0
$29$	33.2119	−	57.5247i	0.212665	−	0.368347i	−0.739883	−	0.672736i	$-0.765119\pi$
$29$	33.2119	−	57.5247i	0.212665	−	0.368347i	0.952548	+	0.304389i	$0.0984523\pi$
$30$		0			0
$31$	−112.370			−0.651043			−0.325521	−	0.945535i	$-0.605540\pi$
$31$	−112.370			−0.651043			−0.325521	+	0.945535i	$0.605540\pi$
$32$		0			0
$33$	54.7971	+	94.9114i	0.289059	+	0.500665i
$34$		0			0
$35$	−90.7332	−	157.155i	−0.438192	−	0.758970i
$36$		0			0
$37$	−189.018			−0.839848			−0.419924	−	0.907559i	$-0.637943\pi$
$37$	−189.018			−0.839848			−0.419924	+	0.907559i	$0.637943\pi$
$38$		0			0
$39$	113.726			0.466942
$40$		0			0
$41$	120.005	+	207.854i	0.457112	+	0.791742i	0.998807	−	0.0488336i	$-0.0155504\pi$
$41$	120.005	+	207.854i	0.457112	+	0.791742i	−0.541695	+	0.840575i	$0.682217\pi$
$42$		0			0
$43$	84.1370	+	145.730i	0.298390	+	0.516827i	0.975768	−	0.218809i	$-0.0702170\pi$
$43$	84.1370	+	145.730i	0.298390	+	0.516827i	−0.677378	+	0.735635i	$0.736884\pi$
$44$		0			0
$45$	494.812			1.63916
$46$		0			0
$47$	93.9241	−	162.681i	0.291494	−	0.504883i	−0.682669	−	0.730728i	$-0.739181\pi$
$47$	93.9241	−	162.681i	0.291494	−	0.504883i	0.974163	+	0.225845i	$0.0725142\pi$
$48$		0			0
$49$	−266.217			−0.776143
$50$		0			0
$51$	−40.9056	+	70.8506i	−0.112312	+	0.194531i
$52$		0			0
$53$	56.5285	−	97.9102i	0.146505	−	0.253755i	−0.783428	−	0.621482i	$-0.786531\pi$
$53$	56.5285	−	97.9102i	0.146505	−	0.253755i	0.929934	+	0.367728i	$0.119864\pi$
$54$		0			0
$55$	643.830	+	1115.15i	1.57844	+	2.73393i
$56$		0			0
$57$	−138.921	+	44.8334i	−0.322815	+	0.104181i
$58$		0			0
$59$	92.9940	+	161.070i	0.205200	+	0.355417i	0.950196	−	0.311652i	$-0.100882\pi$
$59$	92.9940	+	161.070i	0.205200	+	0.355417i	−0.744997	+	0.667068i	$0.767549\pi$
$60$		0			0
$61$	−154.322	+	267.293i	−0.323916	+	0.561038i	−0.981292	−	0.192524i	$-0.938333\pi$
$61$	−154.322	+	267.293i	−0.323916	+	0.561038i	0.657377	+	0.753562i	$0.271666\pi$
$62$		0			0
$63$	−104.684	+	181.317i	−0.209347	+	0.362600i
$64$		0			0
$65$	1336.20			2.54978
$66$		0			0
$67$	19.7279	−	34.1697i	0.0359723	−	0.0623058i	−0.847479	−	0.530829i	$-0.821881\pi$
$67$	19.7279	−	34.1697i	0.0359723	−	0.0623058i	0.883451	+	0.468523i	$0.155214\pi$
$68$		0			0
$69$	−65.7176			−0.114659
$70$		0			0
$71$	−175.101	−	303.284i	−0.292686	−	0.506946i	0.681758	−	0.731578i	$-0.261216\pi$
$71$	−175.101	−	303.284i	−0.292686	−	0.506946i	−0.974444	+	0.224631i	$0.927882\pi$
$72$		0			0
$73$	4.80280	+	8.31870i	0.00770035	+	0.0133374i	0.869850	−	0.493316i	$-0.164216\pi$
$73$	4.80280	+	8.31870i	0.00770035	+	0.0133374i	−0.862150	+	0.506654i	$0.830882\pi$
$74$		0			0
$75$	−535.601			−0.824612
$76$		0			0
$77$	−544.840			−0.806368
$78$		0			0
$79$	−588.269	−	1018.91i	−0.837791	−	1.45110i	−0.891738	−	0.452552i	$-0.850514\pi$
$79$	−588.269	−	1018.91i	−0.837791	−	1.45110i	0.0539471	−	0.998544i	$-0.482820\pi$
$80$		0			0
$81$	−243.504	−	421.761i	−0.334025	−	0.578548i
$82$		0			0
$83$	257.980			0.341168			0.170584	−	0.985343i	$-0.445435\pi$
$83$	257.980			0.341168			0.170584	+	0.985343i	$0.445435\pi$
$84$		0			0
$85$	−480.614	+	832.448i	−0.613293	+	1.06226i
$86$		0			0
$87$	117.078			0.144276
$88$		0			0
$89$	66.8743	−	115.830i	0.0796479	−	0.137954i	−0.823450	−	0.567389i	$-0.807954\pi$
$89$	66.8743	−	115.830i	0.0796479	−	0.137954i	0.903098	+	0.429434i	$0.141287\pi$
$90$		0			0
$91$	−282.691	+	489.634i	−0.325649	+	0.564040i
$92$		0			0
$93$	−99.0313	−	171.527i	−0.110420	−	0.191253i
$94$		0			0
$95$	−1632.22	+	526.763i	−1.76276	+	0.568892i
$96$		0			0
$97$	−598.387	−	1036.44i	−0.626361	−	1.08489i	−0.988276	−	0.152678i	$-0.951210\pi$
$97$	−598.387	−	1036.44i	−0.626361	−	1.08489i	0.361915	−	0.932211i	$-0.382123\pi$
$98$		0			0
$99$	742.819	−	1286.60i	0.754102	−	1.30614i
$100$		0			0
$101$	−434.472	+	752.527i	−0.428035	+	0.741378i	−0.996698	−	0.0811919i	$-0.974127\pi$
$101$	−434.472	+	752.527i	−0.428035	+	0.741378i	0.568663	+	0.822570i	$0.307461\pi$
$102$		0			0
$103$	1491.56			1.42687			0.713437	−	0.700720i	$-0.247138\pi$
$103$	1491.56			1.42687			0.713437	+	0.700720i	$0.247138\pi$
$104$		0			0
$105$	159.925	−	276.999i	0.148639	−	0.257450i
$106$		0			0
$107$	1610.18			1.45478			0.727392	−	0.686222i	$-0.240732\pi$
$107$	1610.18			1.45478			0.727392	+	0.686222i	$0.240732\pi$
$108$		0			0
$109$	25.5111	+	44.1865i	0.0224176	+	0.0388284i	0.877017	−	0.480460i	$-0.159530\pi$
$109$	25.5111	+	44.1865i	0.0224176	+	0.0388284i	−0.854599	+	0.519289i	$0.826197\pi$
$110$		0			0
$111$	−166.580	−	288.526i	−0.142442	−	0.246717i
$112$		0			0
$113$	1789.55			1.48979			0.744895	−	0.667181i	$-0.232499\pi$
$113$	1789.55			1.48979			0.744895	+	0.667181i	$0.232499\pi$
$114$		0			0
$115$	−772.139			−0.626107
$116$		0			0
$117$	−770.823	−	1335.11i	−0.609082	−	1.05496i
$118$		0			0
$119$	−203.360	−	352.229i	−0.156655	−	0.271335i
$120$		0			0
$121$	2535.11			1.90466
$122$		0			0
$123$	−211.519	+	366.362i	−0.155057	+	0.268567i
$124$		0			0
$125$	−3704.31			−2.65059
$126$		0			0
$127$	138.888	−	240.560i	0.0970416	−	0.168081i	−0.813417	−	0.581681i	$-0.802395\pi$
$127$	138.888	−	240.560i	0.0970416	−	0.168081i	0.910459	+	0.413600i	$0.135729\pi$
$128$		0			0
$129$	−148.299	+	256.861i	−0.101217	+	0.175313i
$130$		0			0
$131$	−911.342	−	1578.49i	−0.607819	−	1.05277i	−0.991599	−	0.129349i	$-0.958711\pi$
$131$	−911.342	−	1578.49i	−0.607819	−	1.05277i	0.383780	−	0.923424i	$-0.374622\pi$
$132$		0			0
$133$	152.292	−	709.550i	0.0992886	−	0.462600i
$134$		0			0
$135$	928.849	+	1608.81i	0.592167	+	1.02566i
$136$		0			0
$137$	−330.481	+	572.411i	−0.206094	+	0.356966i	−0.950481	−	0.310783i	$-0.899409\pi$
$137$	−330.481	+	572.411i	−0.206094	+	0.356966i	0.744386	+	0.667749i	$0.232742\pi$
$138$		0			0
$139$	−622.975	+	1079.02i	−0.380144	+	0.658429i	−0.991083	−	0.133249i	$-0.957459\pi$
$139$	−622.975	+	1079.02i	−0.380144	+	0.658429i	0.610938	+	0.791678i	$0.290792\pi$
$140$		0			0
$141$	331.099			0.197756
$142$		0			0
$143$	2005.93	−	3474.37i	1.17304	−	2.03176i
$144$		0			0
$145$	1375.59			0.787835
$146$		0			0
$147$	−234.615	−	406.366i	−0.131638	−	0.228003i
$148$		0			0
$149$	−1136.01	−	1967.62i	−0.624599	−	1.08184i	−0.988618	−	0.150446i	$-0.951929\pi$
$149$	−1136.01	−	1967.62i	−0.624599	−	1.08184i	0.364019	−	0.931392i	$-0.381404\pi$
$150$		0			0
$151$	−3637.77			−1.96051			−0.980256	−	0.197734i	$-0.936642\pi$
$151$	−3637.77			−1.96051			−0.980256	+	0.197734i	$0.936642\pi$
$152$		0			0
$153$	1109.02			0.586005
$154$		0			0
$155$	−1163.55	−	2015.33i	−0.602960	−	1.04436i
$156$		0			0
$157$	225.885	+	391.244i	0.114825	+	0.198883i	0.917710	−	0.397251i	$-0.130036\pi$
$157$	225.885	+	391.244i	0.114825	+	0.198883i	−0.802885	+	0.596135i	$0.796702\pi$
$158$		0			0
$159$	199.273			0.0993922
$160$		0			0
$161$	163.355	−	282.940i	0.0799641	−	0.138502i
$162$		0			0
$163$	−215.631			−0.103617			−0.0518084	−	0.998657i	$-0.516498\pi$
$163$	−215.631			−0.103617			−0.0518084	+	0.998657i	$0.516498\pi$
$164$		0			0
$165$	−1134.81	+	1965.54i	−0.535421	+	0.927377i
$166$		0			0
$167$	−1660.74	+	2876.49i	−0.769533	+	1.33287i	0.168283	+	0.985739i	$0.446178\pi$
$167$	−1660.74	+	2876.49i	−0.769533	+	1.33287i	−0.937816	+	0.347132i	$0.887156\pi$
$168$		0			0
$169$	−983.055	−	1702.70i	−0.447453	−	0.775012i
$170$		0			0
$171$	1467.92	+	1327.00i	0.656460	+	0.593442i
$172$		0			0
$173$	−736.228	−	1275.19i	−0.323552	−	0.560408i	0.657667	−	0.753309i	$-0.271544\pi$
$173$	−736.228	−	1275.19i	−0.323552	−	0.560408i	−0.981218	+	0.192901i	$0.938210\pi$
$174$		0			0
$175$	1331.35	−	2305.97i	0.575091	−	0.996086i
$176$		0			0
$177$	−163.910	+	283.901i	−0.0696058	+	0.120561i
$178$		0			0
$179$	−3573.98			−1.49236			−0.746179	−	0.665745i	$-0.768114\pi$
$179$	−3573.98			−1.49236			−0.746179	+	0.665745i	$0.768114\pi$
$180$		0			0
$181$	1471.86	−	2549.34i	0.604436	−	1.04691i	−0.387705	−	0.921784i	$-0.626732\pi$
$181$	1471.86	−	2549.34i	0.604436	−	1.04691i	0.992140	−	0.125130i	$-0.0399347\pi$
$182$		0			0
$183$	−544.011			−0.219751
$184$		0			0
$185$	−1957.21	−	3389.98i	−0.777821	−	1.34722i
$186$		0			0
$187$	1443.01	+	2499.37i	0.564296	+	0.977390i
$188$		0			0
$189$	−786.038			−0.302518
$190$		0			0
$191$	700.359			0.265321			0.132660	−	0.991162i	$-0.457648\pi$
$191$	700.359			0.265321			0.132660	+	0.991162i	$0.457648\pi$
$192$		0			0
$193$	29.9508	+	51.8763i	0.0111705	+	0.0193478i	0.871557	−	0.490295i	$-0.163111\pi$
$193$	29.9508	+	51.8763i	0.0111705	+	0.0193478i	−0.860386	+	0.509643i	$0.829778\pi$
$194$		0			0
$195$	1177.59	+	2039.64i	0.432456	+	0.749035i
$196$		0			0
$197$	−374.382			−0.135399			−0.0676994	−	0.997706i	$-0.521566\pi$
$197$	−374.382			−0.135399			−0.0676994	+	0.997706i	$0.521566\pi$
$198$		0			0
$199$	2301.88	−	3986.98i	0.819981	−	1.42025i	−0.0857147	−	0.996320i	$-0.527317\pi$
$199$	2301.88	−	3986.98i	0.819981	−	1.42025i	0.905696	−	0.423929i	$-0.139349\pi$
$200$		0			0
$201$	69.5442			0.0244043
$202$		0			0
$203$	−291.022	+	504.065i	−0.100619	+	0.174278i
$204$		0			0
$205$	−2485.21	+	4304.51i	−0.846705	+	1.46654i
$206$		0			0
$207$	445.428	+	771.503i	0.149562	+	0.259049i
$208$		0			0
$209$	−1080.64	+	5034.86i	−0.357653	+	1.66636i
$210$		0			0
$211$	−1478.36	−	2560.60i	−0.482344	−	0.835444i	0.517451	−	0.855713i	$-0.326881\pi$
$211$	−1478.36	−	2560.60i	−0.482344	−	0.835444i	−0.999795	+	0.0202687i	$0.993548\pi$
$212$		0			0
$213$	308.631	−	534.564i	0.0992819	−	0.171961i
$214$		0			0
$215$	−1742.41	+	3017.95i	−0.552705	+	0.957313i
$216$		0			0
$217$	984.655			0.308031
$218$		0			0
$219$	−8.46536	+	14.6624i	−0.00261204	+	0.00452418i
$220$		0			0
$221$	2994.83			0.911555
$222$		0			0
$223$	265.320	+	459.548i	0.0796733	+	0.137998i	0.903109	−	0.429411i	$-0.141279\pi$
$223$	265.320	+	459.548i	0.0796733	+	0.137998i	−0.823436	+	0.567410i	$0.807946\pi$
$224$		0			0
$225$	3630.25	+	6287.78i	1.07563	+	1.86305i
$226$		0			0
$227$	3479.72			1.01743			0.508716	−	0.860934i	$-0.330120\pi$
$227$	3479.72			1.01743			0.508716	+	0.860934i	$0.330120\pi$
$228$		0			0
$229$	3566.48			1.02917			0.514584	−	0.857440i	$-0.327946\pi$
$229$	3566.48			1.02917			0.514584	+	0.857440i	$0.327946\pi$
$230$		0			0
$231$	−480.164	−	831.669i	−0.136764	−	0.236882i
$232$		0			0
$233$	2995.60	+	5188.53i	0.842267	+	1.45885i	0.887974	+	0.459894i	$0.152113\pi$
$233$	2995.60	+	5188.53i	0.842267	+	1.45885i	−0.0457068	+	0.998955i	$0.514554\pi$
$234$		0			0
$235$	3890.19			1.07986
$236$		0			0
$237$	1036.88	−	1795.92i	0.284187	−	0.492226i
$238$		0			0
$239$	606.478			0.164141			0.0820707	−	0.996627i	$-0.473847\pi$
$239$	606.478			0.164141			0.0820707	+	0.996627i	$0.473847\pi$
$240$		0			0
$241$	1722.58	−	2983.60i	0.460421	−	0.797472i	−0.538561	−	0.842586i	$-0.681032\pi$
$241$	1722.58	−	2983.60i	0.460421	−	0.797472i	0.998982	+	0.0451143i	$0.0143652\pi$
$242$		0			0
$243$	1640.20	−	2840.91i	0.432999	−	0.749977i
$244$		0			0
$245$	−2756.58	−	4774.53i	−0.718821	−	1.24503i
$246$		0			0
$247$	3964.01	+	3583.48i	1.02115	+	0.923124i
$248$		0			0
$249$	227.356	+	393.792i	0.0578638	+	0.100223i
$250$		0			0
$251$	902.687	−	1563.50i	0.227000	−	0.393176i	−0.729917	−	0.683535i	$-0.760441\pi$
$251$	902.687	−	1563.50i	0.227000	−	0.393176i	0.956918	+	0.290359i	$0.0937748\pi$
$252$		0			0
$253$	−1159.15	+	2007.70i	−0.288043	+	0.498905i
$254$		0			0
$255$	−1694.25			−0.416070
$256$		0			0
$257$	−1118.48	+	1937.27i	−0.271475	+	0.470208i	−0.969240	−	0.246119i	$-0.920845\pi$
$257$	−1118.48	+	1937.27i	−0.271475	+	0.470208i	0.697765	+	0.716327i	$0.254178\pi$
$258$		0			0
$259$	1656.29			0.397362
$260$		0			0
$261$	−793.541	−	1374.45i	−0.188195	−	0.325964i
$262$		0			0
$263$	416.129	+	720.757i	0.0975651	+	0.168988i	0.910676	−	0.413121i	$-0.135561\pi$
$263$	416.129	+	720.757i	0.0975651	+	0.168988i	−0.813111	+	0.582108i	$0.802228\pi$
$264$		0			0
$265$	2341.32			0.542741
$266$		0			0
$267$	235.743			0.0540347
$268$		0			0
$269$	1741.94	+	3017.13i	0.394826	+	0.683858i	0.993079	−	0.117449i	$-0.0374716\pi$
$269$	1741.94	+	3017.13i	0.394826	+	0.683858i	−0.598253	+	0.801307i	$0.704138\pi$
$270$		0			0
$271$	894.554	+	1549.41i	0.200518	+	0.347307i	0.948695	−	0.316192i	$-0.102404\pi$
$271$	894.554	+	1549.41i	0.200518	+	0.347307i	−0.748178	+	0.663498i	$0.769071\pi$
$272$		0			0
$273$	−996.533			−0.220927
$274$		0			0
$275$	−9447.09	+	16362.8i	−2.07157	+	3.58806i
$276$		0			0
$277$	−5548.66			−1.20356			−0.601781	−	0.798661i	$-0.705542\pi$
$277$	−5548.66			−1.20356			−0.601781	+	0.798661i	$0.705542\pi$
$278$		0			0
$279$	−1342.45	+	2325.19i	−0.288066	+	0.498944i
$280$		0			0
$281$	22.8948	−	39.6549i	0.00486046	−	0.00841856i	−0.863585	−	0.504203i	$-0.831786\pi$
$281$	22.8948	−	39.6549i	0.00486046	−	0.00841856i	0.868445	+	0.495785i	$0.165120\pi$
$282$		0			0
$283$	−3060.37	−	5300.72i	−0.642827	−	1.11341i	−0.984799	−	0.173699i	$-0.944428\pi$
$283$	−3060.37	−	5300.72i	−0.642827	−	1.11341i	0.341971	−	0.939710i	$-0.388905\pi$
$284$		0			0
$285$	−2242.54	−	2027.27i	−0.466094	−	0.421351i
$286$		0			0
$287$	−1051.55	−	1821.34i	−0.216276	−	0.374601i
$288$		0			0
$289$	1379.30	−	2389.02i	0.280746	−	0.486266i
$290$		0			0
$291$	1054.71	−	1826.81i	0.212468	−	0.368005i
$292$		0			0
$293$	−7395.39			−1.47455			−0.737276	−	0.675592i	$-0.763888\pi$
$293$	−7395.39			−1.47455			−0.737276	+	0.675592i	$0.763888\pi$
$294$		0			0
$295$	−1925.83	+	3335.64i	−0.380090	+	0.658334i
$296$		0			0
$297$	5577.61			1.08972
$298$		0			0
$299$	1202.85	+	2083.39i	0.232650	+	0.402962i
$300$		0			0
$301$	−737.258	−	1276.97i	−0.141179	−	0.244529i
$302$		0			0
$303$	−1531.59			−0.290388
$304$		0			0
$305$	−6391.76			−1.19997
$306$		0			0
$307$	−287.534	−	498.024i	−0.0534542	−	0.0925854i	0.838060	−	0.545578i	$-0.183690\pi$
$307$	−287.534	−	498.024i	−0.0534542	−	0.0925854i	−0.891514	+	0.452992i	$0.850356\pi$
$308$		0			0
$309$	1314.50	+	2276.79i	0.242005	+	0.419165i
$310$		0			0
$311$	36.6434			0.00668120			0.00334060	−	0.999994i	$-0.498937\pi$
$311$	36.6434			0.00668120			0.00334060	+	0.999994i	$0.498937\pi$
$312$		0			0
$313$	2441.86	−	4229.43i	0.440966	−	0.763775i	−0.556795	−	0.830650i	$-0.687969\pi$
$313$	2441.86	−	4229.43i	0.440966	−	0.763775i	0.997761	+	0.0668742i	$0.0213026\pi$
$314$		0			0
$315$	−4335.83			−0.775544
$316$		0			0
$317$	2933.65	−	5081.23i	0.519779	−	0.900284i	−0.479956	−	0.877292i	$-0.659348\pi$
$317$	2933.65	−	5081.23i	0.519779	−	0.900284i	0.999736	−	0.0229917i	$-0.00731913\pi$
$318$		0			0
$319$	2065.05	−	3576.77i	0.362447	−	0.627777i
$320$		0			0
$321$	1419.04	+	2457.85i	0.246739	+	0.427364i
$322$		0			0
$323$	−3658.29	+	1180.63i	−0.630195	+	0.203381i
$324$		0			0
$325$	9803.25	+	16979.7i	1.67319	+	2.89805i
$326$		0			0
$327$	−44.9655	+	77.8825i	−0.00760428	+	0.0131710i
$328$		0			0
$329$	−823.018	+	1425.51i	−0.137916	+	0.238878i
$330$		0			0
$331$	8866.06			1.47227			0.736137	−	0.676833i	$-0.236648\pi$
$331$	8866.06			1.47227			0.736137	+	0.676833i	$0.236648\pi$
$332$		0			0
$333$	−2258.13	+	3911.20i	−0.371606	+	0.643640i
$334$		0			0
$335$	817.098			0.133262
$336$		0			0
$337$	−1513.60	−	2621.63i	−0.244662	−	0.423767i	0.717375	−	0.696688i	$-0.245344\pi$
$337$	−1513.60	−	2621.63i	−0.244662	−	0.423767i	−0.962037	+	0.272921i	$0.912010\pi$
$338$		0			0
$339$	1577.12	+	2731.64i	0.252676	+	0.437648i
$340$		0			0
$341$	−6986.97			−1.10958
$342$		0			0
$343$	5338.32			0.840356
$344$		0			0
$345$	−680.481	−	1178.63i	−0.106191	−	0.183928i
$346$		0			0
$347$	−4437.88	−	7686.63i	−0.686564	−	1.18916i	−0.972942	−	0.231048i	$-0.925785\pi$
$347$	−4437.88	−	7686.63i	−0.686564	−	1.18916i	0.286378	−	0.958117i	$-0.407549\pi$
$348$		0			0
$349$	2808.70			0.430791			0.215395	−	0.976527i	$-0.430896\pi$
$349$	2808.70			0.430791			0.215395	+	0.976527i	$0.430896\pi$
$350$		0			0
$351$	2893.94	−	5012.46i	0.440078	−	0.762237i
$352$		0			0
$353$	11702.4			1.76446			0.882230	−	0.470819i	$-0.156041\pi$
$353$	11702.4			1.76446			0.882230	+	0.470819i	$0.156041\pi$
$354$		0			0
$355$	3626.21	−	6280.78i	0.542139	−	0.939012i
$356$		0			0
$357$	358.439	−	620.835i	0.0531390	−	0.0920394i
$358$		0			0
$359$	−843.014	−	1460.14i	−0.123935	−	0.214661i	0.797381	−	0.603476i	$-0.206218\pi$
$359$	−843.014	−	1460.14i	−0.123935	−	0.214661i	−0.921316	+	0.388815i	$0.872885\pi$
$360$		0			0
$361$	−6254.89	−	2814.66i	−0.911924	−	0.410359i
$362$		0			0
$363$	2234.17	+	3869.70i	0.323041	+	0.559523i
$364$		0			0
$365$	−99.4624	+	172.274i	−0.0142633	+	0.0247047i
$366$		0			0
$367$	−4218.01	+	7305.81i	−0.599941	+	1.03913i	0.392888	+	0.919586i	$0.371476\pi$
$367$	−4218.01	+	7305.81i	−0.599941	+	1.03913i	−0.992829	+	0.119542i	$0.961857\pi$
$368$		0			0
$369$	5734.62			0.809031
$370$		0			0
$371$	−495.336	+	857.947i	−0.0693169	+	0.120060i
$372$		0			0
$373$	−1743.67			−0.242048			−0.121024	−	0.992650i	$-0.538618\pi$
$373$	−1743.67			−0.242048			−0.121024	+	0.992650i	$0.538618\pi$
$374$		0			0
$375$	−3264.58	−	5654.42i	−0.449553	−	0.778648i
$376$		0			0
$377$	−2142.90	−	3711.62i	−0.292746	−	0.507050i
$378$		0			0
$379$	1591.45			0.215693			0.107846	−	0.994168i	$-0.465605\pi$
$379$	1591.45			0.215693			0.107846	+	0.994168i	$0.465605\pi$
$380$		0			0
$381$	489.603			0.0658350
$382$		0			0
$383$	4502.45	+	7798.48i	0.600691	+	1.04043i	0.992717	+	0.120473i	$0.0384410\pi$
$383$	4502.45	+	7798.48i	0.600691	+	1.04043i	−0.392026	+	0.919954i	$0.628226\pi$
$384$		0			0
$385$	−5641.61	−	9771.56i	−0.746814	−	1.29352i
$386$		0			0
$387$	4020.62			0.528113
$388$		0			0
$389$	−2034.97	+	3524.66i	−0.265236	+	0.459402i	−0.967625	−	0.252391i	$-0.918783\pi$
$389$	−2034.97	+	3524.66i	−0.265236	+	0.459402i	0.702389	+	0.711793i	$0.252117\pi$
$390$		0			0
$391$	−1730.59			−0.223835
$392$		0			0
$393$	1606.32	−	2782.23i	0.206178	−	0.357111i
$394$		0			0
$395$	12182.6	−	21100.9i	1.55183	−	2.68785i
$396$		0			0
$397$	−164.785	−	285.416i	−0.0208321	−	0.0360822i	0.855421	−	0.517933i	$-0.173298\pi$
$397$	−164.785	−	285.416i	−0.0208321	−	0.0360822i	−0.876253	+	0.481850i	$0.839965\pi$
$398$		0			0
$399$	1217.30	−	392.857i	0.152735	−	0.0492918i
$400$		0			0
$401$	−4093.53	−	7090.20i	−0.509778	−	0.882962i	−0.999936	−	0.0113281i	$-0.996394\pi$
$401$	−4093.53	−	7090.20i	−0.509778	−	0.882962i	0.490158	−	0.871634i	$-0.336939\pi$
$402$		0			0
$403$	−3625.19	+	6279.02i	−0.448098	+	0.776129i
$404$		0			0
$405$	5042.78	−	8734.35i	0.618710	−	1.07164i
$406$		0			0
$407$	−11752.8			−1.43136
$408$		0			0
$409$	−2499.25	+	4328.83i	−0.302152	+	0.523342i	−0.976623	−	0.214959i	$-0.931038\pi$
$409$	−2499.25	+	4328.83i	−0.302152	+	0.523342i	0.674472	+	0.738301i	$0.264372\pi$
$410$		0			0
$411$	−1165.00			−0.139819
$412$		0			0
$413$	−814.868	−	1411.39i	−0.0970873	−	0.168160i
$414$		0			0
$415$	2671.28	+	4626.80i	0.315971	+	0.547278i
$416$		0			0
$417$	−2196.10			−0.257898
$418$		0			0
$419$	−11941.1			−1.39227			−0.696134	−	0.717912i	$-0.745098\pi$
$419$	−11941.1			−1.39227			−0.696134	+	0.717912i	$0.745098\pi$
$420$		0			0
$421$	5991.40	+	10377.4i	0.693594	+	1.20134i	0.970653	+	0.240486i	$0.0773069\pi$
$421$	5991.40	+	10377.4i	0.693594	+	1.20134i	−0.277059	+	0.960853i	$0.589360\pi$
$422$		0			0
$423$	−2244.16	−	3886.99i	−0.257954	−	0.446790i
$424$		0			0
$425$	−14104.4			−1.60979
$426$		0			0
$427$	1352.26	−	2342.18i	0.153256	−	0.265447i
$428$		0			0
$429$	7071.26			0.795812
$430$		0			0
$431$	3541.49	−	6134.04i	0.395795	−	0.685537i	−0.597407	−	0.801938i	$-0.703802\pi$
$431$	3541.49	−	6134.04i	0.395795	−	0.685537i	0.993202	+	0.116401i	$0.0371358\pi$
$432$		0			0
$433$	3701.50	−	6411.19i	0.410815	−	0.711552i	−0.584164	−	0.811635i	$-0.698578\pi$
$433$	3701.50	−	6411.19i	0.410815	−	0.711552i	0.994979	+	0.100084i	$0.0319110\pi$
$434$		0			0
$435$	1212.29	+	2099.76i	0.133621	+	0.231438i
$436$		0			0
$437$	−2290.64	−	2070.75i	−0.250747	−	0.226676i
$438$		0			0
$439$	−3837.72	−	6647.12i	−0.417231	−	0.722665i	0.578429	−	0.815733i	$-0.303666\pi$
$439$	−3837.72	−	6647.12i	−0.417231	−	0.722665i	−0.995660	+	0.0930680i	$0.970333\pi$
$440$		0			0
$441$	−3180.40	+	5508.62i	−0.343419	+	0.594819i
$442$		0			0
$443$	−1341.94	+	2324.32i	−0.143923	+	0.249281i	−0.928970	−	0.370154i	$-0.879305\pi$
$443$	−1341.94	+	2324.32i	−0.143923	+	0.249281i	0.785048	+	0.619435i	$0.212638\pi$
$444$		0			0
$445$	2769.83			0.295062
$446$		0			0
$447$	2002.31	−	3468.10i	0.211870	−	0.366970i
$448$		0			0
$449$	−14097.6			−1.48175			−0.740874	−	0.671644i	$-0.765589\pi$
$449$	−14097.6			−1.48175			−0.740874	+	0.671644i	$0.765589\pi$
$450$		0			0
$451$	7461.67	+	12924.0i	0.779060	+	1.34937i
$452$		0			0
$453$	−3205.94	−	5552.85i	−0.332513	−	0.575929i
$454$		0			0
$455$	−11708.6			−1.20639
$456$		0			0
$457$	7040.20			0.720627			0.360314	−	0.932831i	$-0.382670\pi$
$457$	7040.20			0.720627			0.360314	+	0.932831i	$0.382670\pi$
$458$		0			0
$459$	2081.82	+	3605.82i	0.211702	+	0.366678i
$460$		0			0
$461$	−3676.54	−	6367.96i	−0.371440	−	0.643352i	0.618348	−	0.785905i	$-0.287802\pi$
$461$	−3676.54	−	6367.96i	−0.371440	−	0.643352i	−0.989787	+	0.142552i	$0.954469\pi$
$462$		0			0
$463$	−14054.7			−1.41075			−0.705377	−	0.708832i	$-0.749222\pi$
$463$	−14054.7			−1.41075			−0.705377	+	0.708832i	$0.749222\pi$
$464$		0			0
$465$	2050.86	−	3552.20i	0.204530	−	0.354256i
$466$		0			0
$467$	−5875.16			−0.582163			−0.291081	−	0.956698i	$-0.594015\pi$
$467$	−5875.16			−0.582163			−0.291081	+	0.956698i	$0.594015\pi$
$468$		0			0
$469$	−172.867	+	299.415i	−0.0170198	+	0.0294791i
$470$		0			0
$471$	−398.142	+	689.602i	−0.0389499	+	0.0674633i
$472$		0			0
$473$	5231.48	+	9061.18i	0.508549	+	0.880832i
$474$		0			0
$475$	−18668.8	−	16876.7i	−1.80334	−	1.63022i
$476$		0			0
$477$	−1350.65	−	2339.40i	−0.129648	−	0.224557i
$478$		0			0
$479$	−88.8904	+	153.963i	−0.00847914	+	0.0146863i	−0.870234	−	0.492639i	$-0.836032\pi$
$479$	−88.8904	+	153.963i	−0.00847914	+	0.0146863i	0.861755	+	0.507325i	$0.169366\pi$
$480$		0			0
$481$	−6097.92	+	10561.9i	−0.578049	+	1.00121i
$482$		0			0
$483$	575.856			0.0542492
$484$		0			0
$485$	12392.1	−	21463.8i	1.16020	−	2.00953i
$486$		0			0
$487$	−12319.9			−1.14634			−0.573172	−	0.819435i	$-0.694287\pi$
$487$	−12319.9			−1.14634			−0.573172	+	0.819435i	$0.694287\pi$
$488$		0			0
$489$	−190.034	−	329.149i	−0.0175739	−	0.0304389i
$490$		0			0
$491$	−4220.92	−	7310.84i	−0.387958	−	0.671963i	0.604217	−	0.796820i	$-0.293486\pi$
$491$	−4220.92	−	7310.84i	−0.387958	−	0.671963i	−0.992175	+	0.124857i	$0.960153\pi$
$492$		0			0
$493$	3083.09			0.281654
$494$		0			0
$495$	30766.4			2.79363
$496$		0			0
$497$	1534.34	+	2657.55i	0.138480	+	0.239854i
$498$		0			0
$499$	−3105.62	−	5379.09i	−0.278610	−	0.482567i	0.692429	−	0.721486i	$-0.256540\pi$
$499$	−3105.62	−	5379.09i	−0.278610	−	0.482567i	−0.971040	+	0.238918i	$0.923207\pi$
$500$		0			0
$501$	−5854.40			−0.522067
$502$		0			0
$503$	7836.70	−	13573.6i	0.694675	−	1.20321i	−0.275616	−	0.961268i	$-0.588882\pi$
$503$	7836.70	−	13573.6i	0.694675	−	1.20321i	0.970290	−	0.241944i	$-0.0777850\pi$
$504$		0			0
$505$	−17995.1			−1.58569
$506$		0			0
$507$	1732.72	−	3001.16i	0.151781	−	0.262892i
$508$		0			0
$509$	9897.72	−	17143.3i	0.861903	−	1.49286i	−0.00818701	−	0.999966i	$-0.502606\pi$
$509$	9897.72	−	17143.3i	0.861903	−	1.49286i	0.870090	−	0.492893i	$-0.164061\pi$
$510$		0			0
$511$	−42.0850	−	72.8933i	−0.00364331	−	0.00631039i
$512$		0			0
$513$	−1559.03	+	7263.76i	−0.134177	+	0.625152i
$514$		0			0
$515$	15444.5	+	26750.7i	1.32149	+	2.28889i
$516$		0			0
$517$	5840.02	−	10115.2i	0.496796	−	0.860476i
$518$		0			0
$519$	1297.67	−	2247.62i	0.109752	−	0.190096i
$520$		0			0
$521$	−21391.1			−1.79877			−0.899385	−	0.437157i	$-0.855986\pi$
$521$	−21391.1			−1.79877			−0.899385	+	0.437157i	$0.855986\pi$
$522$		0			0
$523$	1601.07	−	2773.13i	0.133862	−	0.231855i	−0.791300	−	0.611428i	$-0.790596\pi$
$523$	1601.07	−	2773.13i	0.133862	−	0.231855i	0.925162	+	0.379572i	$0.123929\pi$
$524$		0			0
$525$	4693.25			0.390153
$526$		0			0
$527$	−2607.86	−	4516.95i	−0.215560	−	0.373361i
$528$		0			0
$529$	5388.42	+	9333.02i	0.442872	+	0.767077i
$530$		0			0
$531$	4443.87			0.363178
$532$		0			0
$533$	15485.9			1.25848
$534$		0			0
$535$	16672.8	+	28878.1i	1.34734	+	2.33366i
$536$		0			0
$537$	−3149.73	−	5455.49i	−0.253111	−	0.438402i
$538$		0			0
$539$	−16552.9			−1.32279
$540$		0			0
$541$	3681.50	−	6376.55i	0.292569	−	0.506745i	−0.681847	−	0.731495i	$-0.738823\pi$
$541$	3681.50	−	6376.55i	0.292569	−	0.506745i	0.974417	+	0.224750i	$0.0721564\pi$
$542$		0			0
$543$	5188.58			0.410061
$544$		0			0
$545$	−528.315	+	915.068i	−0.0415239	+	0.0719215i
$546$		0			0
$547$	−6484.65	+	11231.7i	−0.506880	+	0.877942i	0.493088	+	0.869979i	$0.335868\pi$
$547$	−6484.65	+	11231.7i	−0.506880	+	0.877942i	−0.999968	+	0.00796294i	$0.997465\pi$
$548$		0			0
$549$	3687.25	+	6386.50i	0.286645	+	0.496483i
$550$		0			0
$551$	4080.84	+	3689.10i	0.315517	+	0.285228i
$552$		0			0
$553$	5154.76	+	8928.31i	0.396388	+	0.686565i
$554$		0			0
$555$	3449.75	−	5975.14i	0.263845	−	0.456992i
$556$		0			0
$557$	−9997.27	+	17315.8i	−0.760499	+	1.31722i	0.182095	+	0.983281i	$0.441712\pi$
$557$	−9997.27	+	17315.8i	−0.760499	+	1.31722i	−0.942594	+	0.333942i	$0.891621\pi$
$558$		0			0
$559$	10857.4			0.821502
$560$		0			0
$561$	−2543.43	+	4405.35i	−0.191415	+	0.331540i
$562$		0			0
$563$	15654.6			1.17187			0.585936	−	0.810358i	$-0.300727\pi$
$563$	15654.6			1.17187			0.585936	+	0.810358i	$0.300727\pi$
$564$		0			0
$565$	18530.1	+	32095.0i	1.37976	+	2.38982i
$566$		0			0
$567$	2133.72	+	3695.72i	0.158039	+	0.273731i
$568$		0			0
$569$	−6450.45			−0.475249			−0.237625	−	0.971357i	$-0.576369\pi$
$569$	−6450.45			−0.475249			−0.237625	+	0.971357i	$0.576369\pi$
$570$		0			0
$571$	−18704.6			−1.37086			−0.685431	−	0.728138i	$-0.740386\pi$
$571$	−18704.6			−1.37086			−0.685431	+	0.728138i	$0.740386\pi$
$572$		0			0
$573$	617.222	+	1069.06i	0.0449997	+	0.0779418i
$574$		0			0
$575$	−5664.90	−	9811.90i	−0.410857	−	0.711625i
$576$		0			0
$577$	−12394.4			−0.894257			−0.447128	−	0.894470i	$-0.647553\pi$
$577$	−12394.4			−0.894257			−0.447128	+	0.894470i	$0.647553\pi$
$578$		0			0
$579$	−52.7908	+	91.4364i	−0.00378914	+	0.00656298i
$580$		0			0
$581$	−2260.57			−0.161419
$582$		0			0
$583$	3514.83	−	6087.87i	0.249690	−	0.432476i
$584$		0			0
$585$	15963.2	−	27649.0i	1.12820	−	1.95409i
$586$		0			0
$587$	−3212.31	−	5563.88i	−0.225871	−	0.391220i	0.730710	−	0.682688i	$-0.239189\pi$
$587$	−3212.31	−	5563.88i	−0.225871	−	0.391220i	−0.956580	+	0.291469i	$0.905856\pi$
$588$		0			0
$589$	1952.97	−	9099.19i	0.136623	−	0.636546i
$590$		0			0
$591$	−329.940	−	571.473i	−0.0229643	−	0.0397754i
$592$		0			0
$593$	−9050.05	+	15675.2i	−0.626714	+	1.08550i	0.361493	+	0.932375i	$0.382267\pi$
$593$	−9050.05	+	15675.2i	−0.626714	+	1.08550i	−0.988207	+	0.153125i	$0.951066\pi$
$594$		0			0
$595$	4211.42	−	7294.40i	0.290171	−	0.502590i
$596$		0			0
$597$	8114.54			0.556291
$598$		0			0
$599$	−1423.60	+	2465.74i	−0.0971061	+	0.168193i	−0.910486	−	0.413541i	$-0.864292\pi$
$599$	−1423.60	+	2465.74i	−0.0971061	+	0.168193i	0.813380	+	0.581733i	$0.197625\pi$
$600$		0			0
$601$	6934.19			0.470635			0.235317	−	0.971919i	$-0.424387\pi$
$601$	6934.19			0.470635			0.235317	+	0.971919i	$0.424387\pi$
$602$		0			0
$603$	−471.364	−	816.426i	−0.0318332	−	0.0551367i
$604$		0			0
$605$	26250.1	+	45466.5i	1.76400	+	3.05533i
$606$		0			0
$607$	−9089.78			−0.607813			−0.303907	−	0.952702i	$-0.598291\pi$
$607$	−9089.78			−0.607813			−0.303907	+	0.952702i	$0.598291\pi$
$608$		0			0
$609$	−1025.90			−0.0682622
$610$		0			0
$611$	−6060.19	−	10496.6i	−0.401259	−	0.695000i
$612$		0			0
$613$	−12818.6	−	22202.5i	−0.844598	−	1.46289i	−0.885970	−	0.463743i	$-0.846506\pi$
$613$	−12818.6	−	22202.5i	−0.844598	−	1.46289i	0.0413712	−	0.999144i	$-0.486827\pi$
$614$		0			0
$615$	−8760.79			−0.574421
$616$		0			0
$617$	−10891.1	+	18863.9i	−0.710630	+	1.23085i	0.253991	+	0.967207i	$0.418257\pi$
$617$	−10891.1	+	18863.9i	−0.710630	+	1.23085i	−0.964621	+	0.263641i	$0.915077\pi$
$618$		0			0
$619$	23717.7			1.54006			0.770029	−	0.638008i	$-0.220242\pi$
$619$	23717.7			1.54006			0.770029	+	0.638008i	$0.220242\pi$
$620$		0			0
$621$	−1672.29	+	2896.50i	−0.108062	+	0.187170i
$622$		0			0
$623$	−585.992	+	1014.97i	−0.0376842	+	0.0652710i
$624$		0			0
$625$	−19364.7	−	33540.6i	−1.23934	−	2.14660i
$626$		0			0
$627$	−8637.81	+	2787.65i	−0.550177	+	0.177557i
$628$		0			0
$629$	−4386.68	−	7597.95i	−0.278074	−	0.481638i
$630$		0			0
$631$	−13101.6	+	22692.6i	−0.826571	+	1.43166i	0.0741409	+	0.997248i	$0.476379\pi$
$631$	−13101.6	+	22692.6i	−0.826571	+	1.43166i	−0.900712	+	0.434416i	$0.856955\pi$
$632$		0			0
$633$	2605.74	−	4513.28i	0.163616	−	0.283391i
$634$		0			0
$635$	5752.51			0.359498
$636$		0			0
$637$	−8588.45	+	14875.6i	−0.534202	+	0.925265i
$638$		0			0
$639$	−8367.48			−0.518016
$640$		0			0
$641$	−2092.66	−	3624.59i	−0.128947	−	0.223343i	0.794322	−	0.607497i	$-0.207826\pi$
$641$	−2092.66	−	3624.59i	−0.128947	−	0.223343i	−0.923269	+	0.384154i	$0.874493\pi$
$642$		0			0
$643$	16099.1	+	27884.5i	0.987383	+	1.71020i	0.630827	+	0.775924i	$0.282716\pi$
$643$	16099.1	+	27884.5i	0.987383	+	1.71020i	0.356556	+	0.934274i	$0.383951\pi$
$644$		0			0
$645$	−6142.31			−0.374966
$646$		0			0
$647$	−371.159			−0.0225530			−0.0112765	−	0.999936i	$-0.503589\pi$
$647$	−371.159			−0.0225530			−0.0112765	+	0.999936i	$0.503589\pi$
$648$		0			0
$649$	5782.19	+	10015.0i	0.349724	+	0.605739i
$650$		0			0
$651$	867.770	+	1503.02i	0.0522436	+	0.0904886i
$652$		0			0
$653$	1659.89			0.0994741			0.0497370	−	0.998762i	$-0.484162\pi$
$653$	1659.89			0.0994741			0.0497370	+	0.998762i	$0.484162\pi$
$654$		0			0
$655$	18873.2	−	32689.3i	1.12586	−	1.95004i
$656$		0			0
$657$	229.510			0.0136286
$658$		0			0
$659$	−12365.0	+	21416.8i	−0.730914	+	1.26598i	0.225578	+	0.974225i	$0.427573\pi$
$659$	−12365.0	+	21416.8i	−0.730914	+	1.26598i	−0.956493	+	0.291756i	$0.905760\pi$
$660$		0			0
$661$	4199.93	−	7274.48i	0.247138	−	0.428055i	−0.715593	−	0.698518i	$-0.753843\pi$
$661$	4199.93	−	7274.48i	0.247138	−	0.428055i	0.962731	+	0.270462i	$0.0871766\pi$
$662$		0			0
$663$	2639.32	+	4571.44i	0.154604	+	0.267783i
$664$		0			0
$665$	14302.5	−	4615.81i	0.834026	−	0.269163i
$666$		0			0
$667$	1238.30	+	2144.79i	0.0718846	+	0.124508i
$668$		0			0
$669$	−467.649	+	809.993i	−0.0270260	+	0.0468104i
$670$		0			0
$671$	−9595.41	+	16619.7i	−0.552052	+	0.956182i
$672$		0			0
$673$	27850.0			1.59516			0.797578	−	0.603216i	$-0.206114\pi$
$673$	27850.0			1.59516			0.797578	+	0.603216i	$0.206114\pi$
$674$		0			0
$675$	−13629.3	+	23606.6i	−0.777171	+	1.34610i
$676$		0			0
$677$	20343.1			1.15487			0.577437	−	0.816435i	$-0.304053\pi$
$677$	20343.1			1.15487			0.577437	+	0.816435i	$0.304053\pi$
$678$		0			0
$679$	5243.42	+	9081.86i	0.296353	+	0.513299i
$680$		0			0
$681$	3066.66	+	5311.60i	0.172562	+	0.298886i
$682$		0			0
$683$	26794.4			1.50111			0.750556	−	0.660807i	$-0.229786\pi$
$683$	26794.4			1.50111			0.750556	+	0.660807i	$0.229786\pi$
$684$		0			0
$685$	−13688.0			−0.763493
$686$		0			0
$687$	3143.11	+	5444.03i	0.174552	+	0.302333i
$688$		0			0
$689$	−3647.34	−	6317.38i	−0.201673	−	0.349308i
$690$		0			0
$691$	−29092.3			−1.60162			−0.800812	−	0.598916i	$-0.795598\pi$
$691$	−29092.3			−1.60162			−0.800812	+	0.598916i	$0.795598\pi$
$692$		0			0
$693$	−6509.02	+	11273.9i	−0.356792	+	0.617982i
$694$		0			0
$695$	−25802.7			−1.40827
$696$		0			0
$697$	−5570.08	+	9647.66i	−0.302700	+	0.524291i
$698$		0			0
$699$	−5280.00	+	9145.23i	−0.285705	+	0.494856i
$700$		0			0
$701$	−10761.5	−	18639.5i	−0.579824	−	1.00428i	−0.995499	−	0.0947713i	$-0.969788\pi$
$701$	−10761.5	−	18639.5i	−0.579824	−	1.00428i	0.415675	−	0.909513i	$-0.363545\pi$
$702$		0			0
$703$	3285.09	−	15305.7i	0.176244	−	0.821147i
$704$		0			0
$705$	3428.40	+	5938.17i	0.183150	+	0.317226i
$706$		0			0
$707$	3807.09	−	6594.08i	0.202518	−	0.350772i
$708$		0			0
$709$	−7482.91	+	12960.8i	−0.396370	+	0.686533i	−0.993275	−	0.115779i	$-0.963064\pi$
$709$	−7482.91	+	12960.8i	−0.396370	+	0.686533i	0.596905	+	0.802312i	$0.296397\pi$
$710$		0			0
$711$	−28111.4			−1.48278
$712$		0			0
$713$	2094.85	−	3628.39i	0.110032	−	0.190581i
$714$		0			0
$715$	83082.6			4.34561
$716$		0			0
$717$	534.485	+	925.756i	0.0278392	+	0.0482189i
$718$		0			0
$719$	3678.90	+	6372.03i	0.190820	+	0.330510i	0.945522	−	0.325557i	$-0.105552\pi$
$719$	3678.90	+	6372.03i	0.190820	+	0.330510i	−0.754702	+	0.656068i	$0.772219\pi$
$720$		0			0
$721$	−13069.9			−0.675104
$722$		0			0
$723$	6072.41			0.312359
$724$		0			0
$725$	10092.2	+	17480.1i	0.516984	+	0.895443i
$726$		0			0
$727$	14574.2	+	25243.2i	0.743503	+	1.28779i	0.950891	+	0.309527i	$0.100171\pi$
$727$	14574.2	+	25243.2i	0.743503	+	1.28779i	−0.207387	+	0.978259i	$0.566496\pi$
$728$		0			0
$729$	−7367.23			−0.374294
$730$		0			0
$731$	−3905.26	+	6764.11i	−0.197594	+	0.342243i
$732$		0			0
$733$	21514.5			1.08412			0.542059	−	0.840341i	$-0.317645\pi$
$733$	21514.5			1.08412			0.542059	+	0.840341i	$0.317645\pi$
$734$		0			0
$735$	4858.70	−	8415.52i	0.243831	−	0.422328i
$736$		0			0
$737$	1226.64	−	2124.60i	0.0613079	−	0.106188i
$738$		0			0
$739$	−11558.0	−	20019.0i	−0.575326	−	0.996495i	−0.996006	−	0.0892854i	$-0.971542\pi$
$739$	−11558.0	−	20019.0i	−0.575326	−	0.996495i	0.420680	−	0.907209i	$-0.361792\pi$
$740$		0			0
$741$	−1976.53	+	9208.95i	−0.0979889	+	0.456544i
$742$		0			0
$743$	7551.47	+	13079.5i	0.372862	+	0.645816i	0.990005	−	0.141035i	$-0.0450430\pi$
$743$	7551.47	+	13079.5i	0.372862	+	0.645816i	−0.617142	+	0.786852i	$0.711710\pi$
$744$		0			0
$745$	23525.8	−	40747.9i	1.15694	−	2.00388i
$746$		0			0
$747$	3081.99	−	5338.17i	0.150956	−	0.261464i
$748$		0			0
$749$	−14109.3			−0.688310
$750$		0			0
$751$	14297.9	−	24764.7i	0.694726	−	1.20330i	−0.275547	−	0.961288i	$-0.588859\pi$
$751$	14297.9	−	24764.7i	0.694726	−	1.20330i	0.970273	−	0.242013i	$-0.0778076\pi$
$752$		0			0
$753$	3182.13			0.154002
$754$		0			0
$755$	−37667.7	−	65242.3i	−1.81572	−	3.14492i
$756$		0			0
$757$	3822.82	+	6621.32i	0.183544	+	0.317908i	0.943085	−	0.332552i	$-0.107910\pi$
$757$	3822.82	+	6621.32i	0.183544	+	0.317908i	−0.759541	+	0.650460i	$0.774576\pi$
$758$		0			0
$759$	−4086.19			−0.195414
$760$		0			0
$761$	10724.9			0.510876			0.255438	−	0.966825i	$-0.417780\pi$
$761$	10724.9			0.510876			0.255438	+	0.966825i	$0.417780\pi$
$762$		0			0
$763$	−223.543	−	387.188i	−0.0106066	−	0.0183711i
$764$		0			0
$765$	11483.5	+	19889.9i	0.542726	+	0.940028i
$766$		0			0
$767$	12000.4			0.564938
$768$		0			0
$769$	1981.77	−	3432.52i	0.0929315	−	0.160962i	−0.815812	−	0.578317i	$-0.803710\pi$
$769$	1981.77	−	3432.52i	0.0929315	−	0.160962i	0.908743	+	0.417355i	$0.137043\pi$
$770$		0			0
$771$	−3942.85			−0.184174
$772$		0			0
$773$	2222.65	−	3849.74i	0.103419	−	0.179128i	−0.809672	−	0.586883i	$-0.800355\pi$
$773$	2222.65	−	3849.74i	0.103419	−	0.179128i	0.913091	+	0.407755i	$0.133688\pi$
$774$		0			0
$775$	17073.1	−	29571.5i	0.791335	−	1.37063i
$776$		0			0
$777$	1459.67	+	2528.23i	0.0673945	+	0.116731i
$778$		0			0
$779$	−18916.7	+	6104.92i	−0.870038	+	0.280785i
$780$		0			0
$781$	−10887.4	−	18857.6i	−0.498826	−	0.863992i
$782$		0			0
$783$	2979.23	−	5160.18i	0.135976	−	0.235517i
$784$		0			0
$785$	−4677.91	+	8102.37i	−0.212690	+	0.368390i
$786$		0			0
$787$	−3452.08			−0.156357			−0.0781787	−	0.996939i	$-0.524910\pi$
$787$	−3452.08			−0.156357			−0.0781787	+	0.996939i	$0.524910\pi$
$788$		0			0
$789$	−733.464	+	1270.40i	−0.0330951	+	0.0573223i
$790$		0			0
$791$	−15681.1			−0.704872
$792$		0			0
$793$	9957.16	+	17246.3i	0.445888	+	0.772301i
$794$		0			0
$795$	2063.39	+	3573.90i	0.0920516	+	0.159438i
$796$		0			0
$797$	−25298.0			−1.12434			−0.562171	−	0.827021i	$-0.690034\pi$
$797$	−25298.0			−1.12434			−0.562171	+	0.827021i	$0.690034\pi$
$798$		0			0
$799$	8719.06			0.386055
$800$		0			0
$801$	−1597.85	−	2767.55i	−0.0704833	−	0.122081i
$802$		0			0
$803$	298.629	+	517.240i	0.0131238	+	0.0227310i
$804$		0			0
$805$	6765.93			0.296233
$806$		0			0
$807$	−3070.33	+	5317.96i	−0.133929	+	0.231972i
$808$		0			0
$809$	−23140.8			−1.00567			−0.502834	−	0.864383i	$-0.667709\pi$
$809$	−23140.8			−1.00567			−0.502834	+	0.864383i	$0.667709\pi$
$810$		0			0
$811$	−5554.38	+	9620.46i	−0.240494	+	0.416548i	−0.960855	−	0.277051i	$-0.910643\pi$
$811$	−5554.38	+	9620.46i	−0.240494	+	0.416548i	0.720361	+	0.693599i	$0.243976\pi$
$812$		0			0
$813$	−1576.73	+	2730.97i	−0.0680176	+	0.117810i
$814$		0			0
$815$	−2232.78	−	3867.28i	−0.0959641	−	0.166215i
$816$		0			0
$817$	−13262.7	+	4280.24i	−0.567937	+	0.183289i
$818$		0			0
$819$	6754.41	+	11699.0i	0.288178	+	0.499140i
$820$		0			0
$821$	−6204.51	+	10746.5i	−0.263750	+	0.456829i	−0.967235	−	0.253881i	$-0.918293\pi$
$821$	−6204.51	+	10746.5i	−0.263750	+	0.456829i	0.703485	+	0.710710i	$0.251626\pi$
$822$		0			0
$823$	−9536.05	+	16516.9i	−0.403895	+	0.699567i	−0.994192	−	0.107619i	$-0.965677\pi$
$823$	−9536.05	+	16516.9i	−0.403895	+	0.699567i	0.590297	+	0.807186i	$0.299011\pi$
$824$		0			0
$825$	−33302.6			−1.40539
$826$		0			0
$827$	2143.56	−	3712.76i	0.0901317	−	0.156113i	−0.817435	−	0.576021i	$-0.804605\pi$
$827$	2143.56	−	3712.76i	0.0901317	−	0.156113i	0.907566	+	0.419909i	$0.137938\pi$
$828$		0			0
$829$	−22544.9			−0.944533			−0.472266	−	0.881456i	$-0.656564\pi$
$829$	−22544.9			−0.944533			−0.472266	+	0.881456i	$0.656564\pi$
$830$		0			0
$831$	−4890.00	−	8469.72i	−0.204130	−	0.353564i
$832$		0			0
$833$	−6178.29	−	10701.1i	−0.256981	−	0.445104i
$834$		0			0
$835$	−68785.3			−2.85080
$836$		0			0
$837$	−10080.1			−0.416270
$838$		0			0
$839$	19298.9	+	33426.7i	0.794127	+	1.37547i	0.923392	+	0.383858i	$0.125405\pi$
$839$	19298.9	+	33426.7i	0.794127	+	1.37547i	−0.129266	+	0.991610i	$0.541262\pi$
$840$		0			0
$841$	9988.44	+	17300.5i	0.409547	+	0.709356i
$842$		0			0
$843$	80.7081			0.00329743
$844$		0			0
$845$	20358.3	−	35261.6i	0.828813	−	1.43555i
$846$		0			0
$847$	−22214.1			−0.901164
$848$		0			0
$849$	5394.17	−	9342.98i	0.218054	−	0.377680i
$850$		0			0
$851$	3523.74	−	6103.30i	0.141942	−	0.245850i
$852$		0			0
$853$	−1804.94	−	3126.25i	−0.0724502	−	0.125488i	0.827524	−	0.561430i	$-0.189749\pi$
$853$	−1804.94	−	3126.25i	−0.0724502	−	0.125488i	−0.899975	+	0.435942i	$0.856415\pi$
$854$		0			0
$855$	−8599.72	+	40067.3i	−0.343982	+	1.60266i
$856$		0			0
$857$	1209.06	+	2094.15i	0.0481921	+	0.0834711i	0.889115	−	0.457683i	$-0.151321\pi$
$857$	1209.06	+	2094.15i	0.0481921	+	0.0834711i	−0.840923	+	0.541155i	$0.817987\pi$
$858$		0			0
$859$	17426.1	−	30183.0i	0.692168	−	1.19887i	−0.278958	−	0.960303i	$-0.589989\pi$
$859$	17426.1	−	30183.0i	0.692168	−	1.19887i	0.971126	−	0.238567i	$-0.0766777\pi$
$860$		0			0
$861$	1853.45	−	3210.28i	0.0733630	−	0.127068i
$862$		0			0
$863$	32080.0			1.26537			0.632685	−	0.774409i	$-0.281953\pi$
$863$	32080.0			1.26537			0.632685	+	0.774409i	$0.281953\pi$
$864$		0			0
$865$	15246.7	−	26408.1i	0.599311	−	1.03804i
$866$		0			0
$867$	4862.28			0.190463
$868$		0			0
$869$	−36577.4	−	63354.0i	−1.42785	−	2.47311i
$870$		0			0
$871$	−1272.89	−	2204.70i	−0.0495179	−	0.0857675i
$872$		0			0
$873$	−28594.9			−1.10858
$874$		0			0
$875$	32459.3			1.25409
$876$		0			0
$877$	−21507.3	−	37251.7i	−0.828107	−	1.43432i	−0.899521	−	0.436877i	$-0.856084\pi$
$877$	−21507.3	−	37251.7i	−0.828107	−	1.43432i	0.0714140	−	0.997447i	$-0.477249\pi$
$878$		0			0
$879$	−6517.51	−	11288.7i	−0.250091	−	0.433171i
$880$		0			0
$881$	20270.3			0.775170			0.387585	−	0.921834i	$-0.373309\pi$
$881$	20270.3			0.775170			0.387585	+	0.921834i	$0.373309\pi$
$882$		0			0
$883$	−9829.17	+	17024.6i	−0.374607	+	0.648838i	−0.990268	−	0.139173i	$-0.955556\pi$
$883$	−9829.17	+	17024.6i	−0.374607	+	0.648838i	0.615661	+	0.788011i	$0.288889\pi$
$884$		0			0
$885$	−6788.90			−0.257860
$886$		0			0
$887$	22422.7	−	38837.3i	0.848795	−	1.47016i	−0.0334891	−	0.999439i	$-0.510662\pi$
$887$	22422.7	−	38837.3i	0.848795	−	1.47016i	0.882284	−	0.470717i	$-0.156005\pi$
$888$		0			0
$889$	−1217.02	+	2107.93i	−0.0459138	+	0.0795251i
$890$		0			0
$891$	−15140.6	−	26224.3i	−0.569281	−	0.986023i
$892$		0			0
$893$	11540.7	+	10432.9i	0.432470	+	0.390955i
$894$		0			0
$895$	−37007.2	−	64098.4i	−1.38214	−	2.39394i
$896$		0			0
$897$	−2120.12	+	3672.16i	−0.0789173	+	0.136689i
$898$		0			0
$899$	−3732.03	+	6464.07i	−0.138454	+	0.239810i
$900$		0			0
$901$	5247.59			0.194032
$902$		0			0
$903$	1299.48	−	2250.77i	0.0478893	−	0.0829467i
$904$		0			0
$905$	60962.4			2.23918
$906$		0			0
$907$	3605.66	+	6245.18i	0.132000	+	0.228630i	0.924447	−	0.381310i	$-0.124527\pi$
$907$	3605.66	+	6245.18i	0.132000	+	0.228630i	−0.792448	+	0.609940i	$0.791194\pi$
$908$		0			0
$909$	10381.0	+	17980.3i	0.378784	+	0.656073i
$910$		0			0
$911$	−29098.8			−1.05827			−0.529136	−	0.848537i	$-0.677484\pi$
$911$	−29098.8			−1.05827			−0.529136	+	0.848537i	$0.677484\pi$
$912$		0			0
$913$	16040.7			0.581456
$914$		0			0
$915$	−5633.02	−	9756.68i	−0.203521	−	0.352509i
$916$		0			0
$917$	7985.71	+	13831.7i	0.287581	+	0.498104i
$918$		0			0
$919$	15321.9			0.549972			0.274986	−	0.961448i	$-0.411327\pi$
$919$	15321.9			0.549972			0.274986	+	0.961448i	$0.411327\pi$
$920$		0			0
$921$	506.804	−	877.811i	0.0181322	−	0.0314059i
$922$		0			0
$923$	−22595.8			−0.805796
$924$		0			0
$925$	28718.7	−	49742.2i	1.02083	−	1.76812i
$926$		0			0
$927$	17819.2	−	30863.7i	0.631346	−	1.09352i
$928$		0			0
$929$	10272.5	+	17792.4i	0.362787	+	0.628365i	0.988418	−	0.151754i	$-0.0484921\pi$
$929$	10272.5	+	17792.4i	0.362787	+	0.628365i	−0.625632	+	0.780118i	$0.715159\pi$
$930$		0			0
$931$	4626.80	−	21556.9i	0.162876	−	0.758861i
$932$		0			0
$933$	32.2936	+	55.9341i	0.00113317	+	0.00196270i
$934$		0			0
$935$	−29883.6	+	51760.0i	−1.04524	+	1.81041i
$936$		0			0
$937$	−23917.7	+	41426.6i	−0.833891	+	1.44434i	0.0610397	+	0.998135i	$0.480558\pi$
$937$	−23917.7	+	41426.6i	−0.833891	+	1.44434i	−0.894930	+	0.446206i	$0.852775\pi$
$938$		0			0
$939$	8608.00			0.299160
$940$		0			0
$941$	222.655	−	385.650i	0.00771344	−	0.0133601i	−0.862143	−	0.506665i	$-0.830878\pi$
$941$	222.655	−	385.650i	0.00771344	−	0.0133601i	0.869856	+	0.493305i	$0.164211\pi$
$942$		0			0
$943$	−8948.70			−0.309024
$944$		0			0
$945$	−8139.12	−	14097.4i	−0.280175	−	0.485278i
$946$		0			0
$947$	22023.0	+	38145.0i	0.755705	+	1.30892i	0.945023	+	0.327004i	$0.106039\pi$
$947$	22023.0	+	38145.0i	0.755705	+	1.30892i	−0.189318	+	0.981916i	$0.560628\pi$
$948$		0			0
$949$	619.775			0.0211999
$950$		0			0
$951$	10341.6			0.352629
$952$		0			0
$953$	−1758.66	−	3046.10i	−0.0597783	−	0.103539i	0.834588	−	0.550875i	$-0.185706\pi$
$953$	−1758.66	−	3046.10i	−0.0597783	−	0.103539i	−0.894366	+	0.447336i	$0.852373\pi$
$954$		0			0
$955$	7251.95	+	12560.7i	0.245725	+	0.425609i
$956$		0			0
$957$	7279.66			0.245891
$958$		0			0
$959$	2895.87	−	5015.80i	0.0975105	−	0.168893i
$960$		0			0
$961$	−17163.9			−0.576144
$962$		0			0
$963$	19236.2	−	33318.1i	0.643696	−	1.11491i
$964$		0			0
$965$	−620.257	+	1074.32i	−0.0206910	+	0.0358378i
$966$		0			0
$967$	−7621.77	−	13201.3i	−0.253464	−	0.439012i	0.711013	−	0.703179i	$-0.248237\pi$
$967$	−7621.77	−	13201.3i	−0.253464	−	0.439012i	−0.964477	+	0.264166i	$0.914903\pi$
$968$		0			0
$969$	−5026.20	−	4543.70i	−0.166630	−	0.150634i
$970$		0			0
$971$	1633.51	+	2829.33i	0.0539876	+	0.0935092i	0.891756	−	0.452516i	$-0.149474\pi$
$971$	1633.51	+	2829.33i	0.0539876	+	0.0935092i	−0.837769	+	0.546025i	$0.816140\pi$
$972$		0			0
$973$	5458.87	−	9455.05i	0.179860	−	0.311526i
$974$		0			0
$975$	−17279.1	+	29928.2i	−0.567562	+	0.983047i
$976$		0			0
$977$	40038.2			1.31109			0.655545	−	0.755156i	$-0.272439\pi$
$977$	40038.2			1.31109			0.655545	+	0.755156i	$0.272439\pi$
$978$		0			0
$979$	4158.11	−	7202.06i	0.135744	−	0.235116i
$980$		0			0
$981$	1219.09			0.0396763
$982$		0			0
$983$	11127.2	+	19272.9i	0.361040	+	0.625340i	0.988132	−	0.153605i	$-0.0490885\pi$
$983$	11127.2	+	19272.9i	0.361040	+	0.625340i	−0.627092	+	0.778945i	$0.715755\pi$
$984$		0			0
$985$	−3876.58	−	6714.43i	−0.125399	−	0.217197i
$986$		0			0
$987$	−2901.28			−0.0935652
$988$		0			0
$989$	−6274.06			−0.201722
$990$		0			0
$991$	7389.74	+	12799.4i	0.236875	+	0.410279i	0.959816	−	0.280630i	$-0.0905435\pi$
$991$	7389.74	+	12799.4i	0.236875	+	0.410279i	−0.722941	+	0.690910i	$0.757210\pi$
$992$		0			0
$993$	7813.60	+	13533.6i	0.249705	+	0.432502i
$994$		0			0
$995$	95340.5			3.03768
$996$		0			0
$997$	−14444.2	+	25018.1i	−0.458829	+	0.794716i	−0.998899	−	0.0469043i	$-0.985064\pi$
$997$	−14444.2	+	25018.1i	−0.458829	+	0.794716i	0.540070	+	0.841620i	$0.318398\pi$
$998$		0			0
$999$	−16955.6			−0.536990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.4.i.e.273.2		6
4.3	odd	2		38.4.c.c.7.2	✓	6
12.11	even	2		342.4.g.f.235.1		6
19.11	even	3	inner	304.4.i.e.49.2		6
76.7	odd	6		722.4.a.j.1.2		3
76.11	odd	6		38.4.c.c.11.2	yes	6
76.31	even	6		722.4.a.k.1.2		3
228.11	even	6		342.4.g.f.163.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.2	✓	6	4.3	odd	2
38.4.c.c.11.2	yes	6	76.11	odd	6
304.4.i.e.49.2		6	19.11	even	3	inner
304.4.i.e.273.2		6	1.1	even	1	trivial
342.4.g.f.163.1		6	228.11	even	6
342.4.g.f.235.1		6	12.11	even	2
722.4.a.j.1.2		3	76.7	odd	6
722.4.a.k.1.2		3	76.31	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.881294 + 1.52645i) q^{3} +(10.3546 + 17.9347i) q^{5} -8.76259 q^{7} +(11.9466 - 20.6922i) q^{9} +62.1780 q^{11} +(32.2611 - 55.8778i) q^{13} +(-18.2509 + 31.6115i) q^{15} +(23.2077 + 40.1970i) q^{17} +(-17.3798 + 80.9750i) q^{19} +(-7.72241 - 13.3756i) q^{21} +(-18.6424 + 32.2895i) q^{23} +(-151.936 + 263.161i) q^{25} +89.7038 q^{27} +(33.2119 - 57.5247i) q^{29} -112.370 q^{31} +(54.7971 + 94.9114i) q^{33} +(-90.7332 - 157.155i) q^{35} -189.018 q^{37} +113.726 q^{39} +(120.005 + 207.854i) q^{41} +(84.1370 + 145.730i) q^{43} +494.812 q^{45} +(93.9241 - 162.681i) q^{47} -266.217 q^{49} +(-40.9056 + 70.8506i) q^{51} +(56.5285 - 97.9102i) q^{53} +(643.830 + 1115.15i) q^{55} +(-138.921 + 44.8334i) q^{57} +(92.9940 + 161.070i) q^{59} +(-154.322 + 267.293i) q^{61} +(-104.684 + 181.317i) q^{63} +1336.20 q^{65} +(19.7279 - 34.1697i) q^{67} -65.7176 q^{69} +(-175.101 - 303.284i) q^{71} +(4.80280 + 8.31870i) q^{73} -535.601 q^{75} -544.840 q^{77} +(-588.269 - 1018.91i) q^{79} +(-243.504 - 421.761i) q^{81} +257.980 q^{83} +(-480.614 + 832.448i) q^{85} +117.078 q^{87} +(66.8743 - 115.830i) q^{89} +(-282.691 + 489.634i) q^{91} +(-99.0313 - 171.527i) q^{93} +(-1632.22 + 526.763i) q^{95} +(-598.387 - 1036.44i) q^{97} +(742.819 - 1286.60i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 5 q^{3} - q^{5} - 52 q^{7} - 54 q^{9} - 8 q^{11} + 129 q^{13} + 77 q^{15} - 51 q^{17} - 40 q^{19} - 170 q^{21} - 47 q^{23} - 338 q^{25} - 718 q^{27} - 125 q^{29} + 100 q^{31} + 274 q^{33} + 84 q^{35}+ \cdots + 3184 q^{99}+O(q^{100}) \) 6 * q + 5 * q^3 - q^5 - 52 * q^7 - 54 * q^9 - 8 * q^11 + 129 * q^13 + 77 * q^15 - 51 * q^17 - 40 * q^19 - 170 * q^21 - 47 * q^23 - 338 * q^25 - 718 * q^27 - 125 * q^29 + 100 * q^31 + 274 * q^33 + 84 * q^35 - 376 * q^37 + 1546 * q^39 + 475 * q^41 + 73 * q^43 + 3188 * q^45 + 241 * q^47 - 1354 * q^49 - 69 * q^51 + 29 * q^53 + 1838 * q^55 + 1755 * q^57 + 1065 * q^59 - 981 * q^61 + 872 * q^63 + 586 * q^65 - 877 * q^67 - 1526 * q^69 - 2135 * q^71 + 667 * q^73 - 4584 * q^75 - 492 * q^77 - 1671 * q^79 - 1287 * q^81 - 1176 * q^83 - 1929 * q^85 + 6430 * q^87 + 693 * q^89 - 1676 * q^91 - 3138 * q^93 - 4489 * q^95 - 985 * q^97 + 3184 * q^99

Introduction

L-functions

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