LMFDB - Embedded newform 304.5.r.a.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 $ x^10 + 109x^8 + 4107x^6 + 61507x^4 + 300520x^2 + 108300
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-4.58432i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.5.r.a.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.1306 + 5.84893i) q^{3} +(20.8352 + 36.0877i) q^{5} -24.1856 q^{7} +(27.9200 - 48.3589i) q^{9} +O(q^{10})$	\(q+(-10.1306 + 5.84893i) q^{3} +(20.8352 + 36.0877i) q^{5} -24.1856 q^{7} +(27.9200 - 48.3589i) q^{9} -62.4993 q^{11} +(-250.356 - 144.543i) q^{13} +(-422.149 - 243.728i) q^{15} +(-12.2538 - 21.2242i) q^{17} +(283.198 + 223.874i) q^{19} +(245.015 - 141.460i) q^{21} +(-302.902 + 524.641i) q^{23} +(-555.715 + 962.527i) q^{25} -294.318i q^{27} +(249.575 + 144.092i) q^{29} +418.074i q^{31} +(633.158 - 365.554i) q^{33} +(-503.912 - 872.801i) q^{35} -2023.50i q^{37} +3381.69 q^{39} +(-717.741 + 414.388i) q^{41} +(-632.930 - 1096.27i) q^{43} +2326.88 q^{45} +(421.122 - 729.404i) q^{47} -1816.06 q^{49} +(248.277 + 143.343i) q^{51} +(3144.31 + 1815.37i) q^{53} +(-1302.19 - 2255.46i) q^{55} +(-4178.41 - 611.581i) q^{57} +(4625.90 - 2670.77i) q^{59} +(1471.85 - 2549.32i) q^{61} +(-675.261 + 1169.59i) q^{63} -12046.3i q^{65} +(-4194.98 - 2421.97i) q^{67} -7086.61i q^{69} +(4788.02 - 2764.37i) q^{71} +(792.717 + 1373.03i) q^{73} -13001.4i q^{75} +1511.58 q^{77} +(-4627.33 + 2671.59i) q^{79} +(3982.97 + 6898.70i) q^{81} +740.501 q^{83} +(510.621 - 884.421i) q^{85} -3371.14 q^{87} +(4789.36 + 2765.14i) q^{89} +(6054.99 + 3495.85i) q^{91} +(-2445.28 - 4235.36i) q^{93} +(-2178.59 + 14884.5i) q^{95} +(2969.63 - 1714.52i) q^{97} +(-1744.98 + 3022.40i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 9 q^{3} + 8 q^{5} + 24 q^{7} - 58 q^{9}+O(q^{10}) $ 10 * q - 9 * q^3 + 8 * q^5 + 24 * q^7 - 58 * q^9	$ 10 q - 9 q^{3} + 8 q^{5} + 24 q^{7} - 58 q^{9} - 50 q^{11} - 624 q^{13} - 504 q^{15} - 292 q^{17} - 305 q^{19} + 1158 q^{21} - 98 q^{23} - 681 q^{25} + 2598 q^{29} - 3441 q^{33} - 694 q^{35} + 5552 q^{39} - 1407 q^{41} - 5424 q^{43} + 9572 q^{45} + 2416 q^{47} - 17826 q^{49} + 3342 q^{51} + 1122 q^{53} - 11424 q^{55} - 7906 q^{57} - 15387 q^{59} + 860 q^{61} - 5318 q^{63} - 14763 q^{67} + 27264 q^{71} + 1561 q^{73} - 18392 q^{77} - 24750 q^{79} + 14311 q^{81} - 6002 q^{83} - 14944 q^{85} + 31996 q^{87} - 22566 q^{89} - 8724 q^{91} + 12476 q^{93} + 7312 q^{95} + 46287 q^{97} + 2048 q^{99}+O(q^{100}) $ 10 * q - 9 * q^3 + 8 * q^5 + 24 * q^7 - 58 * q^9 - 50 * q^11 - 624 * q^13 - 504 * q^15 - 292 * q^17 - 305 * q^19 + 1158 * q^21 - 98 * q^23 - 681 * q^25 + 2598 * q^29 - 3441 * q^33 - 694 * q^35 + 5552 * q^39 - 1407 * q^41 - 5424 * q^43 + 9572 * q^45 + 2416 * q^47 - 17826 * q^49 + 3342 * q^51 + 1122 * q^53 - 11424 * q^55 - 7906 * q^57 - 15387 * q^59 + 860 * q^61 - 5318 * q^63 - 14763 * q^67 + 27264 * q^71 + 1561 * q^73 - 18392 * q^77 - 24750 * q^79 + 14311 * q^81 - 6002 * q^83 - 14944 * q^85 + 31996 * q^87 - 22566 * q^89 - 8724 * q^91 + 12476 * q^93 + 7312 * q^95 + 46287 * q^97 + 2048 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−10.1306	+	5.84893i	−1.12563	+	0.649881i	−0.942832	−	0.333270i	$-0.891848\pi$
$3$	−10.1306	+	5.84893i	−1.12563	+	0.649881i	−0.182796	+	0.983151i	$0.558515\pi$
$4$		0			0
$5$	20.8352	+	36.0877i	0.833410	+	1.44351i	0.895319	+	0.445426i	$0.146948\pi$
$5$	20.8352	+	36.0877i	0.833410	+	1.44351i	−0.0619087	+	0.998082i	$0.519719\pi$
$6$		0			0
$7$	−24.1856			−0.493583			−0.246791	−	0.969069i	$-0.579376\pi$
$7$	−24.1856			−0.493583			−0.246791	+	0.969069i	$0.579376\pi$
$8$		0			0
$9$	27.9200	−	48.3589i	0.344692	−	0.597023i
$10$		0			0
$11$	−62.4993			−0.516523			−0.258261	−	0.966075i	$-0.583150\pi$
$11$	−62.4993			−0.516523			−0.258261	+	0.966075i	$0.583150\pi$
$12$		0			0
$13$	−250.356	−	144.543i	−1.48139	−	0.855283i	−0.481617	−	0.876382i	$-0.659950\pi$
$13$	−250.356	−	144.543i	−1.48139	−	0.855283i	−0.999777	+	0.0210988i	$0.993284\pi$
$14$		0			0
$15$	−422.149	−	243.728i	−1.87622	−	1.08324i
$16$		0			0
$17$	−12.2538	−	21.2242i	−0.0424006	−	0.0734400i	0.844046	−	0.536270i	$-0.180167\pi$
$17$	−12.2538	−	21.2242i	−0.0424006	−	0.0734400i	−0.886447	+	0.462830i	$0.846834\pi$
$18$		0			0
$19$	283.198	+	223.874i	0.784483	+	0.620150i
$19$	283.198	+	223.874i	0.784483	+	0.620150i
$20$		0			0
$21$	245.015	−	141.460i	0.555590	−	0.320770i
$22$		0			0
$23$	−302.902	+	524.641i	−0.572593	+	0.991760i	0.423705	+	0.905800i	$0.360729\pi$
$23$	−302.902	+	524.641i	−0.572593	+	0.991760i	−0.996299	+	0.0859604i	$0.972604\pi$
$24$		0			0
$25$	−555.715	+	962.527i	−0.889144	+	1.54004i
$26$		0			0
$27$		−	294.318i		−	0.403728i
$28$		0			0
$29$	249.575	+	144.092i	0.296760	+	0.171334i	0.640986	−	0.767552i	$-0.278526\pi$
$29$	249.575	+	144.092i	0.296760	+	0.171334i	−0.344227	+	0.938887i	$0.611859\pi$
$30$		0			0
$31$			418.074i			0.435040i	0.976056	+	0.217520i	$0.0697968\pi$
$31$			418.074i			0.435040i	−0.976056	+	0.217520i	$0.930203\pi$
$32$		0			0
$33$	633.158	−	365.554i	0.581412	−	0.335679i
$34$		0			0
$35$	−503.912	−	872.801i	−0.411357	−	0.712491i
$36$		0			0
$37$		−	2023.50i		−	1.47809i	−0.673657	−	0.739044i	$-0.735278\pi$
$37$		−	2023.50i		−	1.47809i	0.673657	−	0.739044i	$-0.264722\pi$
$38$		0			0
$39$	3381.69			2.22333
$40$		0			0
$41$	−717.741	+	414.388i	−0.426973	+	0.246513i	−0.698056	−	0.716043i	$-0.745951\pi$
$41$	−717.741	+	414.388i	−0.426973	+	0.246513i	0.271083	+	0.962556i	$0.412618\pi$
$42$		0			0
$43$	−632.930	−	1096.27i	−0.342310	−	0.592898i	0.642552	−	0.766242i	$-0.277876\pi$
$43$	−632.930	−	1096.27i	−0.342310	−	0.592898i	−0.984861	+	0.173345i	$0.944542\pi$
$44$		0			0
$45$	2326.88			1.14908
$46$		0			0
$47$	421.122	−	729.404i	0.190639	−	0.330196i	−0.754823	−	0.655928i	$-0.772277\pi$
$47$	421.122	−	729.404i	0.190639	−	0.330196i	0.945462	+	0.325732i	$0.105611\pi$
$48$		0			0
$49$	−1816.06			−0.756376
$50$		0			0
$51$	248.277	+	143.343i	0.0954545	+	0.0551107i
$52$		0			0
$53$	3144.31	+	1815.37i	1.11937	+	0.646268i	0.941240	−	0.337739i	$-0.109662\pi$
$53$	3144.31	+	1815.37i	1.11937	+	0.646268i	0.178130	+	0.984007i	$0.442995\pi$
$54$		0			0
$55$	−1302.19	−	2255.46i	−0.430475	−	0.745605i
$56$		0			0
$57$	−4178.41	−	611.581i	−1.28606	−	0.188237i
$58$		0			0
$59$	4625.90	−	2670.77i	1.32890	−	0.767241i	0.343771	−	0.939053i	$-0.388296\pi$
$59$	4625.90	−	2670.77i	1.32890	−	0.767241i	0.985130	+	0.171812i	$0.0549622\pi$
$60$		0			0
$61$	1471.85	−	2549.32i	0.395552	−	0.685116i	−0.597620	−	0.801780i	$-0.703887\pi$
$61$	1471.85	−	2549.32i	0.395552	−	0.685116i	0.993171	+	0.116664i	$0.0372201\pi$
$62$		0			0
$63$	−675.261	+	1169.59i	−0.170134	+	0.294680i
$64$		0			0
$65$		−	12046.3i		−	2.85121i
$66$		0			0
$67$	−4194.98	−	2421.97i	−0.934501	−	0.539534i	−0.0462688	−	0.998929i	$-0.514733\pi$
$67$	−4194.98	−	2421.97i	−0.934501	−	0.539534i	−0.888232	+	0.459395i	$0.848066\pi$
$68$		0			0
$69$		−	7086.61i		−	1.48847i
$70$		0			0
$71$	4788.02	−	2764.37i	0.949816	−	0.548377i	0.0567923	−	0.998386i	$-0.481913\pi$
$71$	4788.02	−	2764.37i	0.949816	−	0.548377i	0.893024	+	0.450009i	$0.148579\pi$
$72$		0			0
$73$	792.717	+	1373.03i	0.148755	+	0.257652i	0.930768	−	0.365611i	$-0.119140\pi$
$73$	792.717	+	1373.03i	0.148755	+	0.257652i	−0.782012	+	0.623263i	$0.785807\pi$
$74$		0			0
$75$		−	13001.4i		−	2.31135i
$76$		0			0
$77$	1511.58			0.254947
$78$		0			0
$79$	−4627.33	+	2671.59i	−0.741440	+	0.428071i	−0.822593	−	0.568631i	$-0.807473\pi$
$79$	−4627.33	+	2671.59i	−0.741440	+	0.428071i	0.0811524	+	0.996702i	$0.474140\pi$
$80$		0			0
$81$	3982.97	+	6898.70i	0.607067	+	1.05147i
$82$		0			0
$83$	740.501			0.107490			0.0537452	−	0.998555i	$-0.482884\pi$
$83$	740.501			0.107490			0.0537452	+	0.998555i	$0.482884\pi$
$84$		0			0
$85$	510.621	−	884.421i	0.0706741	−	0.122411i
$86$		0			0
$87$	−3371.14			−0.445388
$88$		0			0
$89$	4789.36	+	2765.14i	0.604641	+	0.349089i	0.770865	−	0.636998i	$-0.219824\pi$
$89$	4789.36	+	2765.14i	0.604641	+	0.349089i	−0.166224	+	0.986088i	$0.553158\pi$
$90$		0			0
$91$	6054.99	+	3495.85i	0.731191	+	0.422153i
$92$		0			0
$93$	−2445.28	−	4235.36i	−0.282725	−	0.489693i
$94$		0			0
$95$	−2178.59	+	14884.5i	−0.241395	+	1.64925i
$96$		0			0
$97$	2969.63	−	1714.52i	0.315616	−	0.182221i	−0.333821	−	0.942637i	$-0.608338\pi$
$97$	2969.63	−	1714.52i	0.315616	−	0.182221i	0.649437	+	0.760415i	$0.275005\pi$
$98$		0			0
$99$	−1744.98	+	3022.40i	−0.178041	+	0.308376i
$100$		0			0
$101$	−702.204	+	1216.25i	−0.0688368	+	0.119229i	−0.898390	−	0.439200i	$-0.855262\pi$
$101$	−702.204	+	1216.25i	−0.0688368	+	0.119229i	0.829553	+	0.558428i	$0.188595\pi$
$102$		0			0
$103$		−	8424.53i		−	0.794093i	−0.917798	−	0.397047i	$-0.870035\pi$
$103$		−	8424.53i		−	0.794093i	0.917798	−	0.397047i	$-0.129965\pi$
$104$		0			0
$105$	10209.9	+	5894.70i	0.926069	+	0.534666i
$106$		0			0
$107$		−	8311.74i		−	0.725980i	−0.931793	−	0.362990i	$-0.881756\pi$
$107$		−	8311.74i		−	0.725980i	0.931793	−	0.362990i	$-0.118244\pi$
$108$		0			0
$109$	−8045.29	+	4644.95i	−0.677156	+	0.390956i	−0.798783	−	0.601620i	$-0.794522\pi$
$109$	−8045.29	+	4644.95i	−0.677156	+	0.390956i	0.121627	+	0.992576i	$0.461189\pi$
$110$		0			0
$111$	11835.3	+	20499.4i	0.960582	+	1.66378i
$112$		0			0
$113$			4056.19i			0.317659i	0.987306	+	0.158830i	$0.0507721\pi$
$113$			4056.19i			0.317659i	−0.987306	+	0.158830i	$0.949228\pi$
$114$		0			0
$115$	−25244.1			−1.90882
$116$		0			0
$117$	−13979.9	+	8071.28i	−1.02125	+	0.589618i
$118$		0			0
$119$	296.364	+	513.318i	0.0209282	+	0.0362487i
$120$		0			0
$121$	−10734.8			−0.733204
$122$		0			0
$123$	4847.45	−	8396.04i	0.320408	−	0.554963i
$124$		0			0
$125$	−20269.8			−1.29727
$126$		0			0
$127$	9729.41	+	5617.28i	0.603225	+	0.348272i	0.770309	−	0.637671i	$-0.220102\pi$
$127$	9729.41	+	5617.28i	0.603225	+	0.348272i	−0.167084	+	0.985943i	$0.553435\pi$
$128$		0			0
$129$	12824.0	+	7403.93i	0.770626	+	0.444921i
$130$		0			0
$131$	−3002.45	−	5200.40i	−0.174958	−	0.303036i	0.765189	−	0.643806i	$-0.222646\pi$
$131$	−3002.45	−	5200.40i	−0.174958	−	0.303036i	−0.940147	+	0.340770i	$0.889312\pi$
$132$		0			0
$133$	−6849.31	−	5414.52i	−0.387208	−	0.306095i
$134$		0			0
$135$	10621.3	−	6132.18i	0.582785	−	0.336471i
$136$		0			0
$137$	8783.25	−	15213.0i	0.467966	−	0.810540i	−0.531364	−	0.847144i	$-0.678320\pi$
$137$	8783.25	−	15213.0i	0.467966	−	0.810540i	0.999330	+	0.0366031i	$0.0116537\pi$
$138$		0			0
$139$	−5697.89	+	9869.03i	−0.294906	+	0.510793i	−0.974963	−	0.222367i	$-0.928622\pi$
$139$	−5697.89	+	9869.03i	−0.294906	+	0.510793i	0.680057	+	0.733160i	$0.261955\pi$
$140$		0			0
$141$			9852.45i			0.495571i
$142$		0			0
$143$	15647.0	+	9033.82i	0.765174	+	0.441773i
$144$		0			0
$145$			12008.8i			0.571167i
$146$		0			0
$147$	18397.9	−	10622.0i	0.851398	−	0.491555i
$148$		0			0
$149$	−8963.63	−	15525.5i	−0.403749	−	0.699314i	0.590426	−	0.807092i	$-0.298960\pi$
$149$	−8963.63	−	15525.5i	−0.403749	−	0.699314i	−0.994175	+	0.107778i	$0.965626\pi$
$150$		0			0
$151$		−	2550.85i		−	0.111874i	−0.998434	−	0.0559372i	$-0.982185\pi$
$151$		−	2550.85i		−	0.111874i	0.998434	−	0.0559372i	$-0.0178147\pi$
$152$		0			0
$153$	−1368.50			−0.0584605
$154$		0			0
$155$	−15087.3	+	8710.67i	−0.627984	+	0.362567i
$156$		0			0
$157$	−20083.8	−	34786.2i	−0.814793	−	1.41126i	−0.909476	−	0.415756i	$-0.863517\pi$
$157$	−20083.8	−	34786.2i	−0.814793	−	1.41126i	0.0946826	−	0.995508i	$-0.469816\pi$
$158$		0			0
$159$	−42471.9			−1.67999
$160$		0			0
$161$	7325.85	−	12688.7i	0.282622	−	0.489516i
$162$		0			0
$163$	−8363.32			−0.314777			−0.157389	−	0.987537i	$-0.550308\pi$
$163$	−8363.32			−0.314777			−0.157389	+	0.987537i	$0.550308\pi$
$164$		0			0
$165$	26384.0	+	15232.8i	0.969110	+	0.559516i
$166$		0			0
$167$	−25860.0	−	14930.3i	−0.927246	−	0.535346i	−0.0413065	−	0.999147i	$-0.513152\pi$
$167$	−25860.0	−	14930.3i	−0.927246	−	0.535346i	−0.885940	+	0.463801i	$0.846485\pi$
$168$		0			0
$169$	27504.8	+	47639.7i	0.963019	+	1.66800i
$170$		0			0
$171$	18733.2	−	7444.59i	0.640649	−	0.254594i
$172$		0			0
$173$	12746.0	−	7358.89i	0.425874	−	0.245878i	−0.271713	−	0.962378i	$-0.587590\pi$
$173$	12746.0	−	7358.89i	0.425874	−	0.245878i	0.697587	+	0.716500i	$0.254257\pi$
$174$		0			0
$175$	13440.3	−	23279.2i	0.438866	−	0.760139i
$176$		0			0
$177$	−31242.3	+	54113.2i	−0.997232	+	1.72726i
$178$		0			0
$179$			16538.4i			0.516163i	0.966123	+	0.258082i	$0.0830903\pi$
$179$			16538.4i			0.516163i	−0.966123	+	0.258082i	$0.916910\pi$
$180$		0			0
$181$	10274.9	+	5932.22i	0.313632	+	0.181076i	0.648551	−	0.761171i	$-0.275375\pi$
$181$	10274.9	+	5932.22i	0.313632	+	0.181076i	−0.334919	+	0.942247i	$0.608709\pi$
$182$		0			0
$183$			34435.0i			1.02825i
$184$		0			0
$185$	73023.6	−	42160.2i	2.13363	−	1.23185i
$186$		0			0
$187$	765.852	+	1326.49i	0.0219009	+	0.0379334i
$188$		0			0
$189$			7118.24i			0.199273i
$190$		0			0
$191$	−50556.6			−1.38583			−0.692917	−	0.721017i	$-0.743675\pi$
$191$	−50556.6			−1.38583			−0.692917	+	0.721017i	$0.743675\pi$
$192$		0			0
$193$	−41764.2	+	24112.6i	−1.12122	+	0.647335i	−0.941711	−	0.336422i	$-0.890783\pi$
$193$	−41764.2	+	24112.6i	−1.12122	+	0.647335i	−0.179506	+	0.983757i	$0.557450\pi$
$194$		0			0
$195$	70458.3	+	122037.i	1.85295	+	3.20940i
$196$		0			0
$197$	−39065.4			−1.00661			−0.503303	−	0.864110i	$-0.667882\pi$
$197$	−39065.4			−1.00661			−0.503303	+	0.864110i	$0.667882\pi$
$198$		0			0
$199$	12907.6	−	22356.6i	0.325941	−	0.564546i	−0.655761	−	0.754968i	$-0.727652\pi$
$199$	12907.6	−	22356.6i	0.325941	−	0.564546i	0.981702	+	0.190422i	$0.0609856\pi$
$200$		0			0
$201$	56663.8			1.40253
$202$		0			0
$203$	−6036.11	−	3484.95i	−0.146475	−	0.0845676i
$204$		0			0
$205$	−29908.6	−	17267.7i	−0.711686	−	0.410892i
$206$		0			0
$207$	16914.0	+	29296.0i	0.394736	+	0.683703i
$208$		0			0
$209$	−17699.7	−	13992.0i	−0.405204	−	0.320322i
$210$		0			0
$211$	−5877.77	+	3393.53i	−0.132023	+	0.0762232i	−0.564557	−	0.825394i	$-0.690953\pi$
$211$	−5877.77	+	3393.53i	−0.132023	+	0.0762232i	0.432534	+	0.901618i	$0.357619\pi$
$212$		0			0
$213$	−32337.2	+	56009.6i	−0.712759	+	1.23454i
$214$		0			0
$215$	26374.5	−	45682.0i	0.570568	−	0.988253i
$216$		0			0
$217$		−	10111.3i		−	0.214728i
$218$		0			0
$219$	−16061.5	−	9273.10i	−0.334886	−	0.193347i
$220$		0			0
$221$			7084.78i			0.145058i
$222$		0			0
$223$	−8103.55	+	4678.58i	−0.162954	+	0.0940816i	−0.579259	−	0.815143i	$-0.696658\pi$
$223$	−8103.55	+	4678.58i	−0.162954	+	0.0940816i	0.416305	+	0.909225i	$0.363325\pi$
$224$		0			0
$225$	31031.1	+	53747.5i	0.612961	+	1.06168i
$226$		0			0
$227$			32899.8i			0.638472i	0.947675	+	0.319236i	$0.103426\pi$
$227$			32899.8i			0.638472i	−0.947675	+	0.319236i	$0.896574\pi$
$228$		0			0
$229$	−34126.2			−0.650753			−0.325377	−	0.945584i	$-0.605491\pi$
$229$	−34126.2			−0.650753			−0.325377	+	0.945584i	$0.605491\pi$
$230$		0			0
$231$	−15313.3	+	8841.13i	−0.286975	+	0.165685i
$232$		0			0
$233$	45770.7	+	79277.2i	0.843094	+	1.46028i	0.887266	+	0.461258i	$0.152602\pi$
$233$	45770.7	+	79277.2i	0.843094	+	1.46028i	−0.0441722	+	0.999024i	$0.514065\pi$
$234$		0			0
$235$	35096.7			0.635522
$236$		0			0
$237$	31251.9	−	54129.9i	0.556391	−	0.963697i
$238$		0			0
$239$	4322.59			0.0756742			0.0378371	−	0.999284i	$-0.487953\pi$
$239$	4322.59			0.0756742			0.0378371	+	0.999284i	$0.487953\pi$
$240$		0			0
$241$	−38952.7	−	22489.4i	−0.670662	−	0.387207i	0.125665	−	0.992073i	$-0.459893\pi$
$241$	−38952.7	−	22489.4i	−0.670662	−	0.387207i	−0.796327	+	0.604866i	$0.793227\pi$
$242$		0			0
$243$	−60054.2	−	34672.3i	−1.01702	−	0.587179i
$244$		0			0
$245$	−37838.0	−	65537.4i	−0.630371	−	1.09183i
$246$		0			0
$247$	−38540.9	−	96982.5i	−0.631725	−	1.58964i
$248$		0			0
$249$	−7501.75	+	4331.14i	−0.120994	+	0.0698560i
$250$		0			0
$251$	−31250.4	+	54127.2i	−0.496030	+	0.859149i	−0.999990	−	0.00457824i	$-0.998543\pi$
$251$	−31250.4	+	54127.2i	−0.496030	+	0.859149i	0.503960	+	0.863727i	$0.331876\pi$
$252$		0			0
$253$	18931.1	−	32789.7i	0.295757	−	0.512267i
$254$		0			0
$255$			11946.3i			0.183719i
$256$		0			0
$257$	−64690.3	−	37349.0i	−0.979429	−	0.565474i	−0.0773313	−	0.997005i	$-0.524640\pi$
$257$	−64690.3	−	37349.0i	−0.979429	−	0.565474i	−0.902098	+	0.431532i	$0.857973\pi$
$258$		0			0
$259$			48939.5i			0.729559i
$260$		0			0
$261$	13936.3	−	8046.11i	0.204581	−	0.118115i
$262$		0			0
$263$	−12657.9	−	21924.1i	−0.182999	−	0.316964i	0.759901	−	0.650038i	$-0.225247\pi$
$263$	−12657.9	−	21924.1i	−0.182999	−	0.316964i	−0.942900	+	0.333075i	$0.891914\pi$
$264$		0			0
$265$			151295.i			2.15443i
$266$		0			0
$267$	−64692.4			−0.907467
$268$		0			0
$269$	−115616.	+	66751.1i	−1.59777	+	0.922474i	−0.605856	+	0.795574i	$0.707169\pi$
$269$	−115616.	+	66751.1i	−1.59777	+	0.922474i	−0.991916	+	0.126900i	$0.959497\pi$
$270$		0			0
$271$	−8684.87	−	15042.6i	−0.118256	−	0.204826i	0.800820	−	0.598905i	$-0.204397\pi$
$271$	−8684.87	−	15042.6i	−0.118256	−	0.204826i	−0.919077	+	0.394079i	$0.871064\pi$
$272$		0			0
$273$	−81788.0			−1.09740
$274$		0			0
$275$	34731.8	−	60157.2i	0.459263	−	0.795467i
$276$		0			0
$277$	151171.			1.97020			0.985098	−	0.171996i	$-0.0550217\pi$
$277$	151171.			1.97020			0.985098	+	0.171996i	$0.0550217\pi$
$278$		0			0
$279$	20217.6	+	11672.6i	0.259729	+	0.149955i
$280$		0			0
$281$	−71334.5	−	41185.0i	−0.903414	−	0.521586i	−0.0251079	−	0.999685i	$-0.507993\pi$
$281$	−71334.5	−	41185.0i	−0.903414	−	0.521586i	−0.878306	+	0.478098i	$0.841326\pi$
$282$		0			0
$283$	−38305.5	−	66347.1i	−0.478287	−	0.828417i	0.521403	−	0.853310i	$-0.325409\pi$
$283$	−38305.5	−	66347.1i	−0.478287	−	0.828417i	−0.999690	+	0.0248934i	$0.992075\pi$
$284$		0			0
$285$	−64987.6	−	163532.i	−0.800094	−	2.01332i
$286$		0			0
$287$	17359.0	−	10022.2i	0.210746	−	0.121674i
$288$		0			0
$289$	41460.2	−	71811.2i	0.496404	−	0.859798i
$290$		0			0
$291$	−20056.2	+	34738.4i	−0.236844	+	0.410226i
$292$		0			0
$293$		−	97102.9i		−	1.13109i	−0.824717	−	0.565545i	$-0.808666\pi$
$293$		−	97102.9i		−	1.13109i	0.824717	−	0.565545i	$-0.191334\pi$
$294$		0			0
$295$	192764.	+	111292.i	2.21504	+	1.27885i
$296$		0			0
$297$			18394.6i			0.208535i
$298$		0			0
$299$	151666.	−	87564.6i	1.69647	−	0.979459i
$300$		0			0
$301$	15307.8	+	26513.8i	0.168958	+	0.292644i
$302$		0			0
$303$		−	16428.6i		−	0.178943i
$304$		0			0
$305$	122665.			1.31863
$306$		0			0
$307$	32190.8	−	18585.4i	0.341550	−	0.197194i	−0.319407	−	0.947618i	$-0.603484\pi$
$307$	32190.8	−	18585.4i	0.341550	−	0.197194i	0.660957	+	0.750423i	$0.270150\pi$
$308$		0			0
$309$	49274.5	+	85346.0i	0.516066	+	0.893853i
$310$		0			0
$311$	−157167.			−1.62495			−0.812476	−	0.582994i	$-0.801881\pi$
$311$	−157167.			−1.62495			−0.812476	+	0.582994i	$0.801881\pi$
$312$		0			0
$313$	−6297.21	+	10907.1i	−0.0642776	+	0.111332i	−0.896373	−	0.443300i	$-0.853808\pi$
$313$	−6297.21	+	10907.1i	−0.0642776	+	0.111332i	0.832096	+	0.554632i	$0.187141\pi$
$314$		0			0
$315$	−56276.9			−0.567165
$316$		0			0
$317$	11437.7	+	6603.57i	0.113821	+	0.0657144i	0.555830	−	0.831296i	$-0.312401\pi$
$317$	11437.7	+	6603.57i	0.113821	+	0.0657144i	−0.442009	+	0.897011i	$0.645734\pi$
$318$		0			0
$319$	−15598.2	−	9005.65i	−0.153283	−	0.0884981i
$320$		0			0
$321$	48614.8	+	84203.3i	0.471801	+	0.817183i
$322$		0			0
$323$	1281.29	−	8753.95i	0.0122812	−	0.0839072i
$324$		0			0
$325$	278253.	−	160649.i	2.63434	−	1.52094i
$326$		0			0
$327$	54336.0	−	94112.7i	0.508150	−	0.880142i
$328$		0			0
$329$	−10185.1	+	17641.0i	−0.0940961	+	0.162979i
$330$		0			0
$331$			62057.0i			0.566415i	0.959059	+	0.283208i	$0.0913985\pi$
$331$			62057.0i			0.566415i	−0.959059	+	0.283208i	$0.908601\pi$
$332$		0			0
$333$	−97854.3	−	56496.2i	−0.882453	−	0.509485i
$334$		0			0
$335$		−	201849.i		−	1.79861i
$336$		0			0
$337$	128238.	−	74038.1i	1.12916	−	0.651922i	0.185438	−	0.982656i	$-0.440630\pi$
$337$	128238.	−	74038.1i	1.12916	−	0.651922i	0.943724	+	0.330734i	$0.107296\pi$
$338$		0			0
$339$	−23724.4	−	41091.9i	−0.206441	−	0.357566i
$340$		0			0
$341$		−	26129.3i		−	0.224708i
$342$		0			0
$343$	101992.			0.866917
$344$		0			0
$345$	255739.	−	147651.i	2.14862	−	1.24051i
$346$		0			0
$347$	12650.7	+	21911.7i	0.105064	+	0.181977i	0.913765	−	0.406244i	$-0.133162\pi$
$347$	12650.7	+	21911.7i	0.105064	+	0.181977i	−0.808700	+	0.588221i	$0.799828\pi$
$348$		0			0
$349$	−155086.			−1.27327			−0.636637	−	0.771164i	$-0.719675\pi$
$349$	−155086.			−1.27327			−0.636637	+	0.771164i	$0.719675\pi$
$350$		0			0
$351$	−42541.5	+	73684.1i	−0.345302	+	0.598080i
$352$		0			0
$353$	−119944.			−0.962561			−0.481280	−	0.876567i	$-0.659828\pi$
$353$	−119944.			−0.962561			−0.481280	+	0.876567i	$0.659828\pi$
$354$		0			0
$355$	199519.	+	115192.i	1.58317	+	0.914045i
$356$		0			0
$357$	−6004.73	−	3466.83i	−0.0471147	−	0.0272017i
$358$		0			0
$359$	−93344.7	−	161678.i	−0.724270	−	1.25447i	−0.959274	−	0.282478i	$-0.908843\pi$
$359$	−93344.7	−	161678.i	−0.724270	−	1.25447i	0.235004	−	0.971995i	$-0.424490\pi$
$360$		0			0
$361$	30081.7	+	126802.i	0.230828	+	0.972995i
$362$		0			0
$363$	108751.	−	62787.4i	0.825315	−	0.476496i
$364$		0			0
$365$	−33032.9	+	57214.7i	−0.247948	+	0.429459i
$366$		0			0
$367$	−113839.	+	197175.i	−0.845200	+	1.46393i	0.0402473	+	0.999190i	$0.487185\pi$
$367$	−113839.	+	197175.i	−0.845200	+	1.46393i	−0.885447	+	0.464740i	$0.846148\pi$
$368$		0			0
$369$			46278.9i			0.339884i
$370$		0			0
$371$	−76046.9	−	43905.7i	−0.552502	−	0.318987i
$372$		0			0
$373$		−	248937.i		−	1.78925i	−0.446814	−	0.894627i	$-0.647442\pi$
$373$		−	248937.i		−	1.78925i	0.446814	−	0.894627i	$-0.352558\pi$
$374$		0			0
$375$	205346.	−	118557.i	1.46024	−	0.843069i
$376$		0			0
$377$	−41655.0	−	72148.5i	−0.293079	−	0.507627i
$378$		0			0
$379$		−	236451.i		−	1.64612i	−0.567952	−	0.823061i	$-0.692264\pi$
$379$		−	236451.i		−	1.64612i	0.567952	−	0.823061i	$-0.307736\pi$
$380$		0			0
$381$	−131420.			−0.905342
$382$		0			0
$383$	−199085.	+	114942.i	−1.35719	+	0.783576i	−0.989245	−	0.146270i	$-0.953273\pi$
$383$	−199085.	+	114942.i	−1.35719	+	0.783576i	−0.367949	+	0.929846i	$0.619940\pi$
$384$		0			0
$385$	31494.1	+	54549.4i	0.212475	+	0.368018i
$386$		0			0
$387$	−70685.7			−0.471965
$388$		0			0
$389$	−12134.5	+	21017.5i	−0.0801904	+	0.138894i	−0.903332	−	0.428943i	$-0.858886\pi$
$389$	−12134.5	+	21017.5i	−0.0801904	+	0.138894i	0.823141	+	0.567837i	$0.192219\pi$
$390$		0			0
$391$	14846.8			0.0971132
$392$		0			0
$393$	60833.6	+	35122.3i	0.393875	+	0.227404i
$394$		0			0
$395$	−192823.	−	111326.i	−1.23585	−	0.713517i
$396$		0			0
$397$	−144488.	−	250260.i	−0.916748	−	1.58785i	−0.804322	−	0.594193i	$-0.797471\pi$
$397$	−144488.	−	250260.i	−0.916748	−	1.58785i	−0.112425	−	0.993660i	$-0.535862\pi$
$398$		0			0
$399$	101057.	+	14791.4i	0.634777	+	0.0929105i
$400$		0			0
$401$	8555.46	−	4939.50i	0.0532052	−	0.0307181i	−0.473161	−	0.880976i	$-0.656887\pi$
$401$	8555.46	−	4939.50i	0.0532052	−	0.0307181i	0.526367	+	0.850258i	$0.323554\pi$
$402$		0			0
$403$	60429.6	−	104667.i	0.372083	−	0.644466i
$404$		0			0
$405$	−165972.	+	287472.i	−1.01187	+	1.75261i
$406$		0			0
$407$			126467.i			0.763466i
$408$		0			0
$409$	154121.	+	88981.9i	0.921331	+	0.531931i	0.884060	−	0.467374i	$-0.154800\pi$
$409$	154121.	+	88981.9i	0.921331	+	0.531931i	0.0372718	+	0.999305i	$0.488133\pi$
$410$		0			0
$411$			205491.i			1.21649i
$412$		0			0
$413$	−111880.	+	64594.0i	−0.655923	+	0.378697i
$414$		0			0
$415$	15428.5	+	26723.0i	0.0895835	+	0.155163i
$416$		0			0
$417$		−	133306.i		−	0.766617i
$418$		0			0
$419$	−28240.8			−0.160860			−0.0804301	−	0.996760i	$-0.525629\pi$
$419$	−28240.8			−0.160860			−0.0804301	+	0.996760i	$0.525629\pi$
$420$		0			0
$421$	−54520.9	+	31477.6i	−0.307609	+	0.177598i	−0.645856	−	0.763459i	$-0.723499\pi$
$421$	−54520.9	+	31477.6i	−0.307609	+	0.177598i	0.338247	+	0.941057i	$0.390166\pi$
$422$		0			0
$423$	−23515.4	−	40729.9i	−0.131423	−	0.227632i
$424$		0			0
$425$	27238.4			0.150801
$426$		0			0
$427$	−35597.5	+	61656.6i	−0.195238	+	0.338161i
$428$		0			0
$429$	−211353.			−1.14840
$430$		0			0
$431$	144786.	+	83592.1i	0.779420	+	0.449998i	0.836225	−	0.548387i	$-0.184758\pi$
$431$	144786.	+	83592.1i	0.779420	+	0.449998i	−0.0568047	+	0.998385i	$0.518091\pi$
$432$		0			0
$433$	30557.5	+	17642.4i	0.162983	+	0.0940982i	0.579273	−	0.815134i	$-0.303337\pi$
$433$	30557.5	+	17642.4i	0.162983	+	0.0940982i	−0.416290	+	0.909232i	$0.636670\pi$
$434$		0			0
$435$	−70238.5	−	121657.i	−0.371190	−	0.642921i
$436$		0			0
$437$	−203235.	+	80765.7i	−1.06423	+	0.422926i
$438$		0			0
$439$	−163512.	+	94403.8i	−0.848440	+	0.489847i	−0.860124	−	0.510085i	$-0.829614\pi$
$439$	−163512.	+	94403.8i	−0.848440	+	0.489847i	0.0116842	+	0.999932i	$0.496281\pi$
$440$		0			0
$441$	−50704.4	+	87822.6i	−0.260716	+	0.451574i
$442$		0			0
$443$	101510.	−	175820.i	0.517249	−	0.895901i	−0.482551	−	0.875868i	$-0.660290\pi$
$443$	101510.	−	175820.i	0.517249	−	0.895901i	0.999799	−	0.0200330i	$-0.00637714\pi$
$444$		0			0
$445$			230449.i			1.16374i
$446$		0			0
$447$	181615.	+	104855.i	0.908942	+	0.524778i
$448$		0			0
$449$		−	182146.i		−	0.903497i	−0.892145	−	0.451748i	$-0.850801\pi$
$449$		−	182146.i		−	0.903497i	0.892145	−	0.451748i	$-0.149199\pi$
$450$		0			0
$451$	44858.3	−	25898.9i	0.220541	−	0.127329i
$452$		0			0
$453$	14919.7	+	25841.7i	0.0727051	+	0.125929i
$454$		0			0
$455$			291348.i			1.40731i
$456$		0			0
$457$	66790.2			0.319801			0.159901	−	0.987133i	$-0.448883\pi$
$457$	66790.2			0.319801			0.159901	+	0.987133i	$0.448883\pi$
$458$		0			0
$459$	−6246.65	+	3606.50i	−0.0296498	+	0.0171183i
$460$		0			0
$461$	34244.2	+	59312.7i	0.161133	+	0.279091i	0.935275	−	0.353921i	$-0.115152\pi$
$461$	34244.2	+	59312.7i	0.161133	+	0.279091i	−0.774142	+	0.633012i	$0.781818\pi$
$462$		0			0
$463$	−390746.			−1.82277			−0.911386	−	0.411552i	$-0.864987\pi$
$463$	−390746.			−1.82277			−0.911386	+	0.411552i	$0.864987\pi$
$464$		0			0
$465$	101896.	−	176489.i	0.471251	−	0.816230i
$466$		0			0
$467$	−72245.4			−0.331266			−0.165633	−	0.986187i	$-0.552967\pi$
$467$	−72245.4			−0.331266			−0.165633	+	0.986187i	$0.552967\pi$
$468$		0			0
$469$	101458.	+	58576.7i	0.461254	+	0.266305i
$470$		0			0
$471$	406925.	+	234938.i	1.83431	+	1.05904i
$472$		0			0
$473$	39557.7	+	68515.9i	0.176811	+	0.306245i
$474$		0			0
$475$	−372862.	+	148176.i	−1.65258	+	0.656735i
$476$		0			0
$477$	175578.	−	101370.i	0.771675	−	0.445527i
$478$		0			0
$479$	157819.	−	273351.i	0.687843	−	1.19138i	−0.284691	−	0.958619i	$-0.591891\pi$
$479$	157819.	−	273351.i	0.687843	−	1.19138i	0.972534	−	0.232760i	$-0.0747755\pi$
$480$		0			0
$481$	−292483.	+	506595.i	−1.26418	+	2.18963i
$482$		0			0
$483$			171394.i			0.734684i
$484$		0			0
$485$	123746.	+	71444.8i	0.526075	+	0.303730i
$486$		0			0
$487$			15586.3i			0.0657182i	0.999460	+	0.0328591i	$0.0104613\pi$
$487$			15586.3i			0.0657182i	−0.999460	+	0.0328591i	$0.989539\pi$
$488$		0			0
$489$	84725.8	−	48916.5i	0.354322	−	0.204568i
$490$		0			0
$491$	72237.5	+	125119.i	0.299640	+	0.518992i	0.976054	−	0.217530i	$-0.0698001\pi$
$491$	72237.5	+	125119.i	0.299640	+	0.518992i	−0.676414	+	0.736522i	$0.736467\pi$
$492$		0			0
$493$		−	7062.69i		−	0.0290587i
$494$		0			0
$495$	−145428.			−0.593525
$496$		0			0
$497$	−115801.	+	66857.7i	−0.468813	+	0.270669i
$498$		0			0
$499$	127001.	+	219972.i	0.510042	+	0.883419i	0.999932	+	0.0116348i	$0.00370355\pi$
$499$	127001.	+	219972.i	0.510042	+	0.883419i	−0.489890	+	0.871784i	$0.662963\pi$
$500$		0			0
$501$	349304.			1.39164
$502$		0			0
$503$	−166366.	+	288154.i	−0.657548	+	1.13891i	0.323700	+	0.946160i	$0.395073\pi$
$503$	−166366.	+	288154.i	−0.657548	+	1.13891i	−0.981248	+	0.192747i	$0.938260\pi$
$504$		0			0
$505$	−58522.4			−0.229477
$506$		0			0
$507$	−557282.	−	321747.i	−2.16800	−	1.25170i
$508$		0			0
$509$	189141.	+	109200.i	0.730044	+	0.421491i	0.818438	−	0.574594i	$-0.194840\pi$
$509$	189141.	+	109200.i	0.730044	+	0.421491i	−0.0883942	+	0.996086i	$0.528174\pi$
$510$		0			0
$511$	−19172.3	−	33207.4i	−0.0734231	−	0.127173i
$512$		0			0
$513$	65890.2	−	83350.4i	0.250372	−	0.316718i
$514$		0			0
$515$	304022.	−	175527.i	1.14628	−	0.661805i
$516$		0			0
$517$	−26319.8	+	45587.2i	−0.0984694	+	0.170554i
$518$		0			0
$519$	−86083.3	+	149101.i	−0.319584	+	0.553535i
$520$		0			0
$521$			199162.i			0.733722i	0.930276	+	0.366861i	$0.119568\pi$
$521$			199162.i			0.733722i	−0.930276	+	0.366861i	$0.880432\pi$
$522$		0			0
$523$	317690.	+	183419.i	1.16145	+	0.670564i	0.951651	−	0.307181i	$-0.0993856\pi$
$523$	317690.	+	183419.i	1.16145	+	0.670564i	0.209799	+	0.977744i	$0.432719\pi$
$524$		0			0
$525$			314445.i			1.14084i
$526$		0			0
$527$	8873.26	−	5122.98i	0.0319493	−	0.0184460i
$528$		0			0
$529$	−43578.5	−	75480.1i	−0.155726	−	0.269725i
$530$		0			0
$531$		−	298271.i		−	1.05785i
$532$		0			0
$533$	239587.			0.843353
$534$		0			0
$535$	299952.	−	173177.i	1.04796	−	0.605039i
$536$		0			0
$537$	−96731.9	−	167545.i	−0.335445	−	0.581007i
$538$		0			0
$539$	113502.			0.390685
$540$		0			0
$541$	20782.0	−	35995.5i	0.0710058	−	0.122986i	−0.828337	−	0.560231i	$-0.810712\pi$
$541$	20782.0	−	35995.5i	0.0710058	−	0.122986i	0.899342	+	0.437245i	$0.144046\pi$
$542$		0			0
$543$	−138789.			−0.470711
$544$		0			0
$545$	−335251.	−	193557.i	−1.12870	−	0.651653i
$546$		0			0
$547$	58247.7	+	33629.4i	0.194672	+	0.112394i	0.594168	−	0.804341i	$-0.297481\pi$
$547$	58247.7	+	33629.4i	0.194672	+	0.112394i	−0.399496	+	0.916735i	$0.630815\pi$
$548$		0			0
$549$	−82188.0	−	142354.i	−0.272687	−	0.472307i
$550$		0			0
$551$	38420.7	+	96680.0i	0.126550	+	0.318444i
$552$		0			0
$553$	111915.	−	64613.9i	0.365962	−	0.211288i
$554$		0			0
$555$	−493184.	+	854220.i	−1.60112	+	2.77322i
$556$		0			0
$557$	140576.	−	243485.i	0.453107	−	0.784805i	−0.545470	−	0.838131i	$-0.683649\pi$
$557$	140576.	−	243485.i	0.453107	−	0.784805i	0.998577	+	0.0533254i	$0.0169821\pi$
$558$		0			0
$559$			365942.i			1.17109i
$560$		0			0
$561$	−15517.1	−	8958.83i	−0.0493045	−	0.0284659i
$562$		0			0
$563$		−	559461.i		−	1.76503i	−0.470282	−	0.882516i	$-0.655848\pi$
$563$		−	559461.i		−	1.76503i	0.470282	−	0.882516i	$-0.344152\pi$
$564$		0			0
$565$	−146379.	+	84511.8i	−0.458544	+	0.264741i
$566$		0			0
$567$	−96330.3	−	166849.i	−0.299638	−	0.518988i
$568$		0			0
$569$		−	95700.7i		−	0.295590i	−0.989018	−	0.147795i	$-0.952782\pi$
$569$		−	95700.7i		−	0.295590i	0.989018	−	0.147795i	$-0.0472177\pi$
$570$		0			0
$571$	562671.			1.72577			0.862883	−	0.505403i	$-0.168656\pi$
$571$	562671.			1.72577			0.862883	+	0.505403i	$0.168656\pi$
$572$		0			0
$573$	512172.	−	295702.i	1.55993	−	0.900628i
$574$		0			0
$575$	−336654.	−	583102.i	−1.01824	−	1.76364i
$576$		0			0
$577$	−384557.			−1.15507			−0.577536	−	0.816365i	$-0.695986\pi$
$577$	−384557.			−1.15507			−0.577536	+	0.816365i	$0.695986\pi$
$578$		0			0
$579$	282066.	−	488552.i	0.841382	−	1.45732i
$580$		0			0
$581$	−17909.4			−0.0530554
$582$		0			0
$583$	−196517.	−	113459.i	−0.578180	−	0.333812i
$584$		0			0
$585$	−582548.	−	336334.i	−1.70224	−	0.982787i
$586$		0			0
$587$	176824.	+	306269.i	0.513176	+	0.888846i	0.999883	+	0.0152813i	$0.00486437\pi$
$587$	176824.	+	306269.i	0.513176	+	0.888846i	−0.486708	+	0.873565i	$0.661802\pi$
$588$		0			0
$589$	−93595.9	+	118398.i	−0.269790	+	0.341282i
$590$		0			0
$591$	395758.	−	228491.i	1.13306	−	0.654175i
$592$		0			0
$593$	−316633.	+	548424.i	−0.900423	+	1.55958i	−0.0734773	+	0.997297i	$0.523410\pi$
$593$	−316633.	+	548424.i	−0.900423	+	1.55958i	−0.826946	+	0.562282i	$0.809924\pi$
$594$		0			0
$595$	−12349.6	+	21390.2i	−0.0348835	+	0.0604201i
$596$		0			0
$597$			301982.i			0.847292i
$598$		0			0
$599$	−126946.	−	73292.3i	−0.353806	−	0.204270i	0.312554	−	0.949900i	$-0.398815\pi$
$599$	−126946.	−	73292.3i	−0.353806	−	0.204270i	−0.666360	+	0.745630i	$0.732149\pi$
$600$		0			0
$601$			565825.i			1.56651i	0.621701	+	0.783255i	$0.286442\pi$
$601$			565825.i			1.56651i	−0.621701	+	0.783255i	$0.713558\pi$
$602$		0			0
$603$	−234248.	+	135243.i	−0.644229	+	0.371946i
$604$		0			0
$605$	−223663.	−	387396.i	−0.611060	−	1.05839i
$606$		0			0
$607$			360850.i			0.979376i	0.871898	+	0.489688i	$0.162889\pi$
$607$			360850.i			0.979376i	−0.871898	+	0.489688i	$0.837111\pi$
$608$		0			0
$609$	81532.9			0.219836
$610$		0			0
$611$	−210860.	+	121740.i	−0.564823	+	0.326101i
$612$		0			0
$613$	19524.2	+	33816.9i	0.0519580	+	0.0899938i	0.890835	−	0.454328i	$-0.150120\pi$
$613$	19524.2	+	33816.9i	0.0519580	+	0.0899938i	−0.838877	+	0.544322i	$0.816787\pi$
$614$		0			0
$615$	403992.			1.06813
$616$		0			0
$617$	169457.	−	293507.i	0.445131	−	0.770990i	−0.552930	−	0.833228i	$-0.686490\pi$
$617$	169457.	−	293507.i	0.445131	−	0.770990i	0.998061	+	0.0622378i	$0.0198237\pi$
$618$		0			0
$619$	−308686.			−0.805631			−0.402815	−	0.915281i	$-0.631968\pi$
$619$	−308686.			−0.805631			−0.402815	+	0.915281i	$0.631968\pi$
$620$		0			0
$621$	154411.	+	89149.4i	0.400402	+	0.231172i
$622$		0			0
$623$	−115833.	−	66876.4i	−0.298440	−	0.172305i
$624$		0			0
$625$	−75003.9	−	129911.i	−0.192010	−	0.332571i
$626$		0			0
$627$	261147.	+	38223.4i	0.664279	+	0.0972286i
$628$		0			0
$629$	−42947.1	+	24795.5i	−0.108551	+	0.0626718i
$630$		0			0
$631$	−132924.	+	230231.i	−0.333845	+	0.578237i	−0.983262	−	0.182195i	$-0.941680\pi$
$631$	−132924.	+	230231.i	−0.333845	+	0.578237i	0.649417	+	0.760432i	$0.275013\pi$
$632$		0			0
$633$	39697.1	−	68757.4i	0.0990721	−	0.171598i
$634$		0			0
$635$			468150.i			1.16101i
$636$		0			0
$637$	454660.	+	262498.i	1.12049	+	0.646916i
$638$		0			0
$639$		−	308725.i		−	0.756083i
$640$		0			0
$641$	474195.	−	273776.i	1.15409	−	0.666316i	0.204211	−	0.978927i	$-0.434537\pi$
$641$	474195.	−	273776.i	1.15409	−	0.666316i	0.949881	+	0.312611i	$0.101204\pi$
$642$		0			0
$643$	−123976.	−	214732.i	−0.299857	−	0.519368i	0.676246	−	0.736676i	$-0.263606\pi$
$643$	−123976.	−	214732.i	−0.299857	−	0.519368i	−0.976103	+	0.217308i	$0.930272\pi$
$644$		0			0
$645$			617051.i			1.48321i
$646$		0			0
$647$	140129.			0.334749			0.167375	−	0.985893i	$-0.446471\pi$
$647$	140129.			0.334749			0.167375	+	0.985893i	$0.446471\pi$
$648$		0			0
$649$	−289116.	+	166921.i	−0.686408	+	0.396298i
$650$		0			0
$651$	59140.6	+	102434.i	0.139548	+	0.241704i
$652$		0			0
$653$	−457094.			−1.07196			−0.535980	−	0.844231i	$-0.680058\pi$
$653$	−457094.			−1.07196			−0.535980	+	0.844231i	$0.680058\pi$
$654$		0			0
$655$	125114.	−	216703.i	0.291623	−	0.505106i
$656$		0			0
$657$	88530.7			0.205099
$658$		0			0
$659$	−357061.	−	206149.i	−0.822188	−	0.474691i	0.0289821	−	0.999580i	$-0.490773\pi$
$659$	−357061.	−	206149.i	−0.822188	−	0.474691i	−0.851171	+	0.524889i	$0.824107\pi$
$660$		0			0
$661$	26307.5	+	15188.7i	0.0602111	+	0.0347629i	0.529803	−	0.848121i	$-0.322266\pi$
$661$	26307.5	+	15188.7i	0.0602111	+	0.0347629i	−0.469592	+	0.882883i	$0.655599\pi$
$662$		0			0
$663$	−41438.4	−	71773.4i	−0.0942705	−	0.163281i
$664$		0			0
$665$	52690.5	−	359989.i	0.119149	−	0.814040i
$666$		0			0
$667$	−151193.	+	87291.5i	−0.339845	+	0.196210i
$668$		0			0
$669$	54729.5	−	94794.2i	0.122284	−	0.211802i
$670$		0			0
$671$	−91989.4	+	159330.i	−0.204312	+	0.353878i
$672$		0			0
$673$			517440.i			1.14243i	0.820801	+	0.571215i	$0.193528\pi$
$673$			517440.i			1.14243i	−0.820801	+	0.571215i	$0.806472\pi$
$674$		0			0
$675$	283289.	+	163557.i	0.621759	+	0.358972i
$676$		0			0
$677$		−	391079.i		−	0.853272i	−0.904423	−	0.426636i	$-0.859699\pi$
$677$		−	391079.i		−	0.853272i	0.904423	−	0.426636i	$-0.140301\pi$
$678$		0			0
$679$	−71822.2	+	41466.6i	−0.155783	+	0.0899412i
$680$		0			0
$681$	−192429.	−	333297.i	−0.414931	−	0.718682i
$682$		0			0
$683$			416919.i			0.893739i	0.894599	+	0.446869i	$0.147461\pi$
$683$			416919.i			0.893739i	−0.894599	+	0.446869i	$0.852539\pi$
$684$		0			0
$685$	732005.			1.56003
$686$		0			0
$687$	345720.	−	199602.i	0.732506	−	0.422912i
$688$		0			0
$689$	−524797.	−	908975.i	−1.10548	−	1.91476i
$690$		0			0
$691$	430225.			0.901031			0.450516	−	0.892769i	$-0.351240\pi$
$691$	430225.			0.901031			0.450516	+	0.892769i	$0.351240\pi$
$692$		0			0
$693$	42203.3	−	73098.3i	0.0878780	−	0.152209i
$694$		0			0
$695$	−474868.			−0.983112
$696$		0			0
$697$	17590.1	+	10155.6i	0.0362078	+	0.0209046i
$698$		0			0
$699$	−927374.	−	535420.i	−1.89802	−	1.09582i
$700$		0			0
$701$	432212.	+	748612.i	0.879550	+	1.52342i	0.851836	+	0.523809i	$0.175489\pi$
$701$	432212.	+	748612.i	0.879550	+	1.52342i	0.0277137	+	0.999616i	$0.491177\pi$
$702$		0			0
$703$	453010.	−	573053.i	0.916636	−	1.15954i
$704$		0			0
$705$	−355552.	+	205278.i	−0.715361	+	0.413014i
$706$		0			0
$707$	16983.2	−	29415.8i	0.0339767	−	0.0588493i
$708$		0			0
$709$	162798.	−	281974.i	0.323859	−	0.560941i	−0.657422	−	0.753523i	$-0.728353\pi$
$709$	162798.	−	281974.i	0.323859	−	0.560941i	0.981281	+	0.192582i	$0.0616863\pi$
$710$		0			0
$711$			298363.i			0.590210i
$712$		0			0
$713$	−219339.	−	126635.i	−0.431456	−	0.249101i
$714$		0			0
$715$			752888.i			1.47271i
$716$		0			0
$717$	−43790.6	+	25282.5i	−0.0851810	+	0.0491793i
$718$		0			0
$719$	−263310.	−	456066.i	−0.509341	−	0.882205i	−0.999941	−	0.0108204i	$-0.996556\pi$
$719$	−263310.	−	456066.i	−0.509341	−	0.882205i	0.490600	−	0.871385i	$-0.336778\pi$
$720$		0			0
$721$			203752.i			0.391951i
$722$		0			0
$723$	526155.			1.00655
$724$		0			0
$725$	−277385.	+	160148.i	−0.527724	+	0.304682i
$726$		0			0
$727$	−345843.	−	599018.i	−0.654351	−	1.13337i	−0.982056	−	0.188589i	$-0.939609\pi$
$727$	−345843.	−	599018.i	−0.654351	−	1.13337i	0.327706	−	0.944780i	$-0.393725\pi$
$728$		0			0
$729$	165944.			0.312253
$730$		0			0
$731$	−15511.6	+	26866.8i	−0.0290283	+	0.0502784i
$732$		0			0
$733$	−248355.			−0.462238			−0.231119	−	0.972926i	$-0.574239\pi$
$733$	−248355.			−0.462238			−0.231119	+	0.972926i	$0.574239\pi$
$734$		0			0
$735$	766648.	+	442624.i	1.41913	+	0.819333i
$736$		0			0
$737$	262183.	+	151371.i	0.482691	+	0.278682i
$738$		0			0
$739$	363794.	+	630109.i	0.666141	+	1.15379i	0.978975	+	0.203982i	$0.0653885\pi$
$739$	363794.	+	630109.i	0.666141	+	1.15379i	−0.312833	+	0.949808i	$0.601278\pi$
$740$		0			0
$741$	957688.	+	757072.i	1.74417	+	1.37880i
$742$		0			0
$743$	602317.	−	347748.i	1.09106	−	0.629922i	0.157199	−	0.987567i	$-0.449753\pi$
$743$	602317.	−	347748.i	1.09106	−	0.629922i	0.933858	+	0.357645i	$0.116420\pi$
$744$		0			0
$745$	373519.	−	646954.i	0.672977	−	1.16563i
$746$		0			0
$747$	20674.8	−	35809.8i	0.0370510	−	0.0641742i
$748$		0			0
$749$			201024.i			0.358331i
$750$		0			0
$751$	−631954.	−	364859.i	−1.12048	−	0.646912i	−0.178960	−	0.983856i	$-0.557273\pi$
$751$	−631954.	−	364859.i	−1.12048	−	0.646912i	−0.941524	+	0.336945i	$0.890607\pi$
$752$		0			0
$753$		−	731125.i		−	1.28944i
$754$		0			0
$755$	92054.3	−	53147.5i	0.161492	−	0.0932372i
$756$		0			0
$757$	−141571.	−	245208.i	−0.247049	−	0.427901i	0.715657	−	0.698452i	$-0.246128\pi$
$757$	−141571.	−	245208.i	−0.247049	−	0.427901i	−0.962706	+	0.270551i	$0.912794\pi$
$758$		0			0
$759$			442908.i			0.768829i
$760$		0			0
$761$	−319277.			−0.551313			−0.275657	−	0.961256i	$-0.588895\pi$
$761$	−319277.			−0.551313			−0.275657	+	0.961256i	$0.588895\pi$
$762$		0			0
$763$	194580.	−	112341.i	0.334233	−	0.192969i
$764$		0			0
$765$	−28513.1	−	49386.1i	−0.0487216	−	0.0843882i
$766$		0			0
$767$	−1.54416e6			−2.62483
$768$		0			0
$769$	219721.	−	380569.i	0.371552	−	0.643547i	−0.618252	−	0.785980i	$-0.712159\pi$
$769$	219721.	−	380569.i	0.371552	−	0.643547i	0.989805	+	0.142432i	$0.0454924\pi$
$770$		0			0
$771$	873806.			1.46996
$772$		0			0
$773$	−785095.	−	453275.i	−1.31390	−	0.758583i	−0.331163	−	0.943573i	$-0.607441\pi$
$773$	−785095.	−	453275.i	−1.31390	−	0.758583i	−0.982740	+	0.184991i	$0.940774\pi$
$774$		0			0
$775$	−402407.	−	232330.i	−0.669980	−	0.386813i
$776$		0			0
$777$	−286244.	−	495789.i	−0.474127	−	0.821212i
$778$		0			0
$779$	−296034.	−	43329.6i	−0.487828	−	0.0714019i
$780$		0			0
$781$	−299248.	+	172771.i	−0.490602	+	0.283249i
$782$		0			0
$783$	42408.9	−	73454.3i	0.0691725	−	0.119810i
$784$		0			0
$785$	836904.	−	1.44956e6i	1.35811	−	2.35232i
$786$		0			0
$787$		−	461769.i		−	0.745548i	−0.927922	−	0.372774i	$-0.878407\pi$
$787$		−	461769.i		−	0.745548i	0.927922	−	0.372774i	$-0.121593\pi$
$788$		0			0
$789$	256465.	+	148070.i	0.411978	+	0.237855i
$790$		0			0
$791$		−	98101.3i		−	0.156791i
$792$		0			0
$793$	−736971.	+	425490.i	−1.17194	+	0.676617i
$794$		0			0
$795$	−884911.	−	1.53271e6i	−1.40012	−	2.42508i
$796$		0			0
$797$		−	936748.i		−	1.47471i	−0.675506	−	0.737354i	$-0.736075\pi$
$797$		−	936748.i		−	1.47471i	0.675506	−	0.737354i	$-0.263925\pi$
$798$		0			0
$799$	−20641.3			−0.0323328
$800$		0			0
$801$	267438.	−	154405.i	0.416829	−	0.240656i
$802$		0			0
$803$	−49544.2	−	85813.2i	−0.0768355	−	0.133083i
$804$		0			0
$805$	610544.			0.942160
$806$		0			0
$807$	780846.	−	1.35246e6i	1.19900	−	2.07672i
$808$		0			0
$809$	−55778.3			−0.0852252			−0.0426126	−	0.999092i	$-0.513568\pi$
$809$	−55778.3			−0.0852252			−0.0426126	+	0.999092i	$0.513568\pi$
$810$		0			0
$811$	562443.	+	324727.i	0.855140	+	0.493715i	0.862382	−	0.506259i	$-0.168972\pi$
$811$	562443.	+	324727.i	0.855140	+	0.493715i	−0.00724190	+	0.999974i	$0.502305\pi$
$812$		0			0
$813$	175967.	+	101594.i	0.266225	+	0.153705i
$814$		0			0
$815$	−174252.	−	301813.i	−0.262339	−	0.454384i
$816$		0			0
$817$	66181.1	−	452158.i	0.0991493	−	0.677402i
$818$		0			0
$819$	338111.	−	195208.i	0.504071	−	0.291025i
$820$		0			0
$821$	160712.	−	278361.i	0.238431	−	0.412974i	−0.721834	−	0.692067i	$-0.756700\pi$
$821$	160712.	−	278361.i	0.238431	−	0.412974i	0.960264	+	0.279093i	$0.0900337\pi$
$822$		0			0
$823$	239960.	−	415622.i	0.354273	−	0.613619i	−0.632720	−	0.774381i	$-0.718062\pi$
$823$	239960.	−	415622.i	0.354273	−	0.613619i	0.986993	+	0.160761i	$0.0513949\pi$
$824$		0			0
$825$			812575.i			1.19387i
$826$		0			0
$827$	−650685.	−	375673.i	−0.951393	−	0.549287i	−0.0578795	−	0.998324i	$-0.518434\pi$
$827$	−650685.	−	375673.i	−0.951393	−	0.549287i	−0.893513	+	0.449037i	$0.851767\pi$
$828$		0			0
$829$		−	96570.8i		−	0.140520i	−0.997529	−	0.0702598i	$-0.977617\pi$
$829$		−	96570.8i		−	0.140520i	0.997529	−	0.0702598i	$-0.0223828\pi$
$830$		0			0
$831$	−1.53146e6	+	884190.i	−2.21771	+	1.28039i
$832$		0			0
$833$	22253.6	+	38544.3i	0.0320708	+	0.0555482i
$834$		0			0
$835$		−	1.24430e6i		−	1.78465i
$836$		0			0
$837$	123047.			0.175638
$838$		0			0
$839$	1.05400e6	−	608525.i	1.49732	−	0.864479i	0.497326	−	0.867563i	$-0.334315\pi$
$839$	1.05400e6	−	608525.i	1.49732	−	0.864479i	0.999995	+	0.00308436i	$0.000981784\pi$
$840$		0			0
$841$	−312115.	−	540600.i	−0.441289	−	0.764335i
$842$		0			0
$843$	963553.			1.35588
$844$		0			0
$845$	−1.14614e6	+	1.98517e6i	−1.60518	+	2.78025i
$846$		0			0
$847$	259628.			0.361897
$848$		0			0
$849$	776119.	+	448093.i	1.07675	+	0.621659i
$850$		0			0
$851$	1.06161e6	+	612923.i	1.46591	+	0.846343i
$852$		0			0
$853$	−119586.	−	207129.i	−0.164355	−	0.284671i	0.772071	−	0.635536i	$-0.219221\pi$
$853$	−119586.	−	207129.i	−0.164355	−	0.284671i	−0.936426	+	0.350865i	$0.885888\pi$
$854$		0			0
$855$	658969.	+	520929.i	0.901432	+	0.712600i
$856$		0			0
$857$	1.00185e6	−	578418.i	1.36408	−	0.787553i	0.373918	−	0.927462i	$-0.378014\pi$
$857$	1.00185e6	−	578418.i	1.36408	−	0.787553i	0.990164	+	0.139908i	$0.0446808\pi$
$858$		0			0
$859$	−475365.	+	823357.i	−0.644230	+	1.11584i	0.340249	+	0.940336i	$0.389489\pi$
$859$	−475365.	+	823357.i	−0.644230	+	1.11584i	−0.984479	+	0.175504i	$0.943845\pi$
$860$		0			0
$861$	−117238.	+	203063.i	−0.158148	+	0.273920i
$862$		0			0
$863$			38746.3i			0.0520246i	0.999662	+	0.0260123i	$0.00828090\pi$
$863$			38746.3i			0.0520246i	−0.999662	+	0.0260123i	$0.991719\pi$
$864$		0			0
$865$	531131.	+	306649.i	0.709855	+	0.409835i
$866$		0			0
$867$			969991.i			1.29042i
$868$		0			0
$869$	289205.	−	166972.i	0.382971	−	0.221108i
$870$		0			0
$871$	700157.	+	1.21271e6i	0.922910	+	1.59853i
$872$		0			0
$873$		−	191478.i		−	0.251240i
$874$		0			0
$875$	490236.			0.640308
$876$		0			0
$877$	315242.	−	182005.i	0.409869	−	0.236638i	−0.280865	−	0.959747i	$-0.590621\pi$
$877$	315242.	−	182005.i	0.409869	−	0.236638i	0.690733	+	0.723110i	$0.257288\pi$
$878$		0			0
$879$	567949.	+	983716.i	0.735074	+	1.27319i
$880$		0			0
$881$	−243497.			−0.313720			−0.156860	−	0.987621i	$-0.550137\pi$
$881$	−243497.			−0.313720			−0.156860	+	0.987621i	$0.550137\pi$
$882$		0			0
$883$	−714345.	+	1.23728e6i	−0.916193	+	1.58689i	−0.111047	+	0.993815i	$0.535420\pi$
$883$	−714345.	+	1.23728e6i	−0.916193	+	1.58689i	−0.805146	+	0.593077i	$0.797913\pi$
$884$		0			0
$885$	−2.60376e6			−3.32441
$886$		0			0
$887$	963132.	+	556064.i	1.22416	+	0.706769i	0.965802	−	0.259280i	$-0.0834851\pi$
$887$	963132.	+	556064.i	1.22416	+	0.706769i	0.258358	+	0.966049i	$0.416818\pi$
$888$		0			0
$889$	−235311.	−	135857.i	−0.297741	−	0.171901i
$890$		0			0
$891$	−248933.	−	431164.i	−0.313564	−	0.543109i
$892$		0			0
$893$	282556.	−	112288.i	0.354324	−	0.140809i
$894$		0			0
$895$	−596832.	+	344581.i	−0.745086	+	0.430175i
$896$		0			0
$897$	−1.02432e6	+	1.77417e6i	−1.27306	+	2.20501i
$898$		0			0
$899$	−60241.1	+	104341.i	−0.0745373	+	0.129102i
$900$		0			0
$901$		−	88980.4i		−	0.109609i
$902$		0			0
$903$	−310155.	−	179068.i	−0.380368	−	0.219606i
$904$		0			0
$905$			494397.i			0.603641i
$906$		0			0
$907$	1.07643e6	−	621477.i	1.30849	−	0.755458i	0.326647	−	0.945146i	$-0.394081\pi$
$907$	1.07643e6	−	621477.i	1.30849	−	0.755458i	0.981844	+	0.189688i	$0.0607477\pi$
$908$		0			0
$909$	39211.1	+	67915.6i	0.0474549	+	0.0821944i
$910$		0			0
$911$		−	298558.i		−	0.359743i	−0.983690	−	0.179871i	$-0.942432\pi$
$911$		−	298558.i		−	0.359743i	0.983690	−	0.179871i	$-0.0575682\pi$
$912$		0			0
$913$	−46280.8			−0.0555212
$914$		0			0
$915$	−1.24268e6	+	717461.i	−1.48428	+	0.856951i
$916$		0			0
$917$	72616.0	+	125775.i	0.0863562	+	0.149573i
$918$		0			0
$919$	1.19613e6			1.41628			0.708138	−	0.706074i	$-0.249536\pi$
$919$	1.19613e6			1.41628			0.708138	+	0.706074i	$0.249536\pi$
$920$		0			0
$921$	−217409.	+	376564.i	−0.256306	+	0.443935i
$922$		0			0
$923$	−1.59828e6			−1.87607
$924$		0			0
$925$	1.94767e6	+	1.12449e6i	2.27632	+	1.31423i
$926$		0			0
$927$	−407401.	−	235213.i	−0.474092	−	0.273717i
$928$		0			0
$929$	234694.	+	406501.i	0.271938	+	0.471010i	0.969358	−	0.245652i	$-0.0790022\pi$
$929$	234694.	+	406501.i	0.271938	+	0.471010i	−0.697420	+	0.716662i	$0.745669\pi$
$930$		0			0
$931$	−514305.	−	406569.i	−0.593364	−	0.469067i
$932$		0			0
$933$	1.59220e6	−	919259.i	1.82909	−	1.05603i
$934$		0			0
$935$	−31913.4	+	55275.7i	−0.0365048	+	0.0632282i
$936$		0			0
$937$	−48982.6	+	84840.4i	−0.0557908	+	0.0966326i	−0.892572	−	0.450905i	$-0.851101\pi$
$937$	−48982.6	+	84840.4i	−0.0557908	+	0.0966326i	0.836781	+	0.547538i	$0.184435\pi$
$938$		0			0
$939$		−	147328.i		−	0.167091i
$940$		0			0
$941$	−253995.	−	146644.i	−0.286844	−	0.165609i	0.349674	−	0.936872i	$-0.386292\pi$
$941$	−253995.	−	146644.i	−0.286844	−	0.165609i	−0.636518	+	0.771262i	$0.719626\pi$
$942$		0			0
$943$		−	502075.i		−	0.564606i
$944$		0			0
$945$	−256881.	+	148310.i	−0.287653	+	0.166076i
$946$		0			0
$947$	−273771.	−	474186.i	−0.305273	−	0.528748i	0.672049	−	0.740506i	$-0.265414\pi$
$947$	−273771.	−	474186.i	−0.305273	−	0.528748i	−0.977322	+	0.211759i	$0.932081\pi$
$948$		0			0
$949$		−	458326.i		−	0.508912i
$950$		0			0
$951$	−154495.			−0.170826
$952$		0			0
$953$	−978151.	+	564736.i	−1.07701	+	0.621812i	−0.930088	−	0.367336i	$-0.880270\pi$
$953$	−978151.	+	564736.i	−1.07701	+	0.621812i	−0.146922	+	0.989148i	$0.546937\pi$
$954$		0			0
$955$	−1.05336e6	−	1.82447e6i	−1.15497	−	2.00046i
$956$		0			0
$957$	210694.			0.230053
$958$		0			0
$959$	−212428.	+	367936.i	−0.230980	+	0.400069i
$960$		0			0
$961$	748735.			0.810740
$962$		0			0
$963$	−401947.	−	232064.i	−0.433427	−	0.250239i
$964$		0			0
$965$	−1.74034e6	−	1.00478e6i	−1.86887	−	1.07899i
$966$		0			0
$967$	551522.	+	955264.i	0.589807	+	1.02158i	0.994257	+	0.107015i	$0.0341294\pi$
$967$	551522.	+	955264.i	0.589807	+	1.02158i	−0.404451	+	0.914560i	$0.632537\pi$
$968$		0			0
$969$	38221.0	+	96177.4i	0.0407056	+	0.102430i
$970$		0			0
$971$	−156634.	+	90432.6i	−0.166130	+	0.0959150i	−0.580760	−	0.814075i	$-0.697244\pi$
$971$	−156634.	+	90432.6i	−0.166130	+	0.0959150i	0.414630	+	0.909990i	$0.363911\pi$
$972$		0			0
$973$	137807.	−	238688.i	0.145561	−	0.252119i
$974$		0			0
$975$	−1.87925e6	+	3.25496e6i	−1.97686	+	3.42402i
$976$		0			0
$977$			962182.i			1.00802i	0.863698	+	0.504009i	$0.168142\pi$
$977$			962182.i			1.00802i	−0.863698	+	0.504009i	$0.831858\pi$
$978$		0			0
$979$	−299331.	−	172819.i	−0.312311	−	0.180313i
$980$		0			0
$981$			518748.i			0.539037i
$982$		0			0
$983$	−286561.	+	165446.i	−0.296558	+	0.171218i	−0.640896	−	0.767628i	$-0.721437\pi$
$983$	−286561.	+	165446.i	−0.296558	+	0.171218i	0.344338	+	0.938846i	$0.388104\pi$
$984$		0			0
$985$	−813937.	−	1.40978e6i	−0.838915	−	1.45304i
$986$		0			0
$987$		−	238287.i		−	0.244605i
$988$		0			0
$989$	766863.			0.784017
$990$		0			0
$991$	−1.08063e6	+	623905.i	−1.10035	+	0.635288i	−0.936313	−	0.351166i	$-0.885785\pi$
$991$	−1.08063e6	+	623905.i	−1.10035	+	0.635288i	−0.164038	+	0.986454i	$0.552452\pi$
$992$		0			0
$993$	−362967.	−	628678.i	−0.368103	−	0.637572i
$994$		0			0
$995$	1.07573e6			1.08657
$996$		0			0
$997$	−932962.	+	1.61594e6i	−0.938585	+	1.62568i	−0.170471	+	0.985363i	$0.554529\pi$
$997$	−932962.	+	1.61594e6i	−0.938585	+	1.62568i	−0.768114	+	0.640313i	$0.778804\pi$
$998$		0			0
$999$	−595553.			−0.596746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.a.145.1		10
4.3	odd	2		19.5.d.a.12.2	yes	10
12.11	even	2		171.5.p.a.145.4		10
19.8	odd	6	inner	304.5.r.a.65.1		10
76.27	even	6		19.5.d.a.8.2	✓	10
228.179	odd	6		171.5.p.a.46.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.d.a.8.2	✓	10	76.27	even	6
19.5.d.a.12.2	yes	10	4.3	odd	2
171.5.p.a.46.4		10	228.179	odd	6
171.5.p.a.145.4		10	12.11	even	2
304.5.r.a.65.1		10	19.8	odd	6	inner
304.5.r.a.145.1		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-10.1306 + 5.84893i) q^{3} +(20.8352 + 36.0877i) q^{5} -24.1856 q^{7} +(27.9200 - 48.3589i) q^{9} +O(q^{10})\)	\(q+(-10.1306 + 5.84893i) q^{3} +(20.8352 + 36.0877i) q^{5} -24.1856 q^{7} +(27.9200 - 48.3589i) q^{9} -62.4993 q^{11} +(-250.356 - 144.543i) q^{13} +(-422.149 - 243.728i) q^{15} +(-12.2538 - 21.2242i) q^{17} +(283.198 + 223.874i) q^{19} +(245.015 - 141.460i) q^{21} +(-302.902 + 524.641i) q^{23} +(-555.715 + 962.527i) q^{25} -294.318i q^{27} +(249.575 + 144.092i) q^{29} +418.074i q^{31} +(633.158 - 365.554i) q^{33} +(-503.912 - 872.801i) q^{35} -2023.50i q^{37} +3381.69 q^{39} +(-717.741 + 414.388i) q^{41} +(-632.930 - 1096.27i) q^{43} +2326.88 q^{45} +(421.122 - 729.404i) q^{47} -1816.06 q^{49} +(248.277 + 143.343i) q^{51} +(3144.31 + 1815.37i) q^{53} +(-1302.19 - 2255.46i) q^{55} +(-4178.41 - 611.581i) q^{57} +(4625.90 - 2670.77i) q^{59} +(1471.85 - 2549.32i) q^{61} +(-675.261 + 1169.59i) q^{63} -12046.3i q^{65} +(-4194.98 - 2421.97i) q^{67} -7086.61i q^{69} +(4788.02 - 2764.37i) q^{71} +(792.717 + 1373.03i) q^{73} -13001.4i q^{75} +1511.58 q^{77} +(-4627.33 + 2671.59i) q^{79} +(3982.97 + 6898.70i) q^{81} +740.501 q^{83} +(510.621 - 884.421i) q^{85} -3371.14 q^{87} +(4789.36 + 2765.14i) q^{89} +(6054.99 + 3495.85i) q^{91} +(-2445.28 - 4235.36i) q^{93} +(-2178.59 + 14884.5i) q^{95} +(2969.63 - 1714.52i) q^{97} +(-1744.98 + 3022.40i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 9 q^{3} + 8 q^{5} + 24 q^{7} - 58 q^{9}+O(q^{10}) \) 10 * q - 9 * q^3 + 8 * q^5 + 24 * q^7 - 58 * q^9	\( 10 q - 9 q^{3} + 8 q^{5} + 24 q^{7} - 58 q^{9} - 50 q^{11} - 624 q^{13} - 504 q^{15} - 292 q^{17} - 305 q^{19} + 1158 q^{21} - 98 q^{23} - 681 q^{25} + 2598 q^{29} - 3441 q^{33} - 694 q^{35} + 5552 q^{39} - 1407 q^{41} - 5424 q^{43} + 9572 q^{45} + 2416 q^{47} - 17826 q^{49} + 3342 q^{51} + 1122 q^{53} - 11424 q^{55} - 7906 q^{57} - 15387 q^{59} + 860 q^{61} - 5318 q^{63} - 14763 q^{67} + 27264 q^{71} + 1561 q^{73} - 18392 q^{77} - 24750 q^{79} + 14311 q^{81} - 6002 q^{83} - 14944 q^{85} + 31996 q^{87} - 22566 q^{89} - 8724 q^{91} + 12476 q^{93} + 7312 q^{95} + 46287 q^{97} + 2048 q^{99}+O(q^{100}) \) 10 * q - 9 * q^3 + 8 * q^5 + 24 * q^7 - 58 * q^9 - 50 * q^11 - 624 * q^13 - 504 * q^15 - 292 * q^17 - 305 * q^19 + 1158 * q^21 - 98 * q^23 - 681 * q^25 + 2598 * q^29 - 3441 * q^33 - 694 * q^35 + 5552 * q^39 - 1407 * q^41 - 5424 * q^43 + 9572 * q^45 + 2416 * q^47 - 17826 * q^49 + 3342 * q^51 + 1122 * q^53 - 11424 * q^55 - 7906 * q^57 - 15387 * q^59 + 860 * q^61 - 5318 * q^63 - 14763 * q^67 + 27264 * q^71 + 1561 * q^73 - 18392 * q^77 - 24750 * q^79 + 14311 * q^81 - 6002 * q^83 - 14944 * q^85 + 31996 * q^87 - 22566 * q^89 - 8724 * q^91 + 12476 * q^93 + 7312 * q^95 + 46287 * q^97 + 2048 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more